This content was uploaded by our users and we assume good faith they have the permission to share this book. If you own the copyright to this book and it is wrongfully on our website, we offer a simple DMCA procedure to remove your content from our site. Start by pressing the button below!
40
*
30
"
•
:
• •
.
.
1
1
1
1
20
40
60
80
:
• 1
100
T(K)
Fig. 3. Temperature dependence of the red exciton lifetime.
120
28 pump-probe experiments 6 . The dominant non radiative pathway involves two A9 states in series with respective lifetimes 450 fs and 2 ps. This situation is very reminiscent of that prevailing in polyenes 7 8 . Evidence for such A9 states has been found in two-photon absorption experiments on another PDA 9 . The high fluorescence yield and longer lifetime in the case of red chains indicate that these states are no more present in their optical gap. Thus the structural differences between both types of chains imply a much larger blue shift for Ag states than for the lBu exciton. 5. Discussion : hints for a possible structural difference between red and blue chains The blue and red chains are chemically identical so the differences can only be structural. The blue chain is known to be planar in bulk blue phase PDA crystals u 12. From structural studies, the bond lengths and chain repeat unit length in red PDA crystals are very similar to those of the blue chains 10. This disproves an earlier assumption that the red chains had butatrienic structure (See also paper by Katagiri et al. in these Proceedings). In the case of red chains, the simultaneous increase of fluorescence lifetime and decrease of fluorescence yield between 0 and 40 K must be accounted for. In our working hypothesis state(s) non radiant to the ground state, for symmetry reasons for instance, can be thermally populated from the exciton state. Such a situation naturally occurs if the red chain is assumed non planar, with successive repeat units tilted from the mean plane in alternative directions, implying a doubling of the unit cell in the chain direction. This doubling results in a splitting of the exciton level with a higher state of g symmetry. Preliminary calculations show that such a model accounts for the energy difference of 0.4 eV between the blue and red exciton states, and predicts a splitting of 1.5 meV (15-20 K) for the exciton doublet. Such a splitting accounts for the temperature dependence of the fluorescence lifetime and yield between 0 and 40 K reported above 13.The doubling also implies the splitting of vibrational levels. Possible evidence of such splitting is seen on the vibronic emission lineshapes which can be analyzed as two near-by lines. This simple model however does not explain the fact that As states present in the optical gap of blue chains lie at much higher energies for red chains. Explicit evaluation of electron correlation effects in non planar chains would be necessary. Acknowledgements This work is the result of the collective efforts of Drs J. Berrehar, J.-L. Fave, R. Lecuiller, M. Schott and S. Spagnoli in our laboratory. We gratefully acknowledge the collaboration with Drs S. Haacke and J.-D. Ganiere of EPFL Lausanne, Switzerland. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.
R. Lecuiller, J. Berrehar, C. Lapersonne-Meyer, M. Schott, Phys. Rev. Lett. 80, 4068 (1998). A. Horvath,G. Weiser, C. Lapersonne-Meyer, M. Schott, S. Spagnoli, Phys. Rev. B, 53 13507 (1996) S. Haacke, J. Berrehar, C. Lapersonne-Meyer, M. Schott, Chem. Phys. Lett, 308 363 (1999) R. Lecuiller, J. Berrehar, C. Lapersonne-Meyer, M. Schott, J.-D. Ganiere, Chem. Phys. Lett., 314 255 (1999) H. Fidder, J. Terpstra, D.A. Wiersma, J. Chem. Phys., 94 6895 (1991) B. Kraabel, M. Joffre, C. Lapersonne-Meyer, M. Schott, Phys. Rev. B, 58 15777 (1998) P.O. Anderson, S.M. Bachilo, R.-L. Chen, T. Gillbro, J. Phys. Chem., 99 16199 (1995) M. Mimuro, S. Akimoto, S. Takaichi, I. Yamazaki, J. Am. Chem. Soc, 119 1452 (1997) B. Lawrence, W.E. Torruellas, M. Cha, M.L. Sundheimer, G.I. Stegeman, J. Meth, S. Etemad, G. Baker Phys. Rev. Lett, 73 597 (1994) A. Kobayashi, H. Kobayashi, Y. Tokura, T. Kanatake, T. Koda, J. Chem. Phys., 87 4962 (1987) V. Enkelmann, Adv. Polym. Sci. 63 91 (1984) M. Schott, G. Wegner, in Non linear Optical Properties of Organic Molecules and Crystals ed. by D.S. Chemla, J. Zyss (Academic Press, Orlando, 1987) vol. II p. 1 R. Lecuiller et al., to be published
EXCITONS IN QUASI-ONE-DIMENSIONAL CRYSTALLINE PERYLENE DERIVATIVES: BAND STRUCTURE AND RELAXATION DYNAMICS M. HOFFMANN, T. HASCHE, K. SCHMIDT, T.W. CANZLER, V.M. AGRANOVICH, K. LEO Institut fur Angewandte Photophysik, TU Dresden, 01062 Dresden, Germany The exciton structure of crystalline MePTCDI (N-N'-dimethylperylene-3,4,9,10dicarboximide) is modeled by a one-dimensional Hamiltonian, which includes the interactions between Frenkel excitons with several vibronic levels and charge-transfer excitons. Using appropriate fitting parameters, which are verified by quantum chemical calculations, this model can explain the main features of the low temperature absorption spectrum. Polarized absorption spectra show different polarization ratios for the various peaks. This polarization behavior is explained by the varying contribution of the charge-transfer transition dipole, which has a direction different from the Frenkel transition dipole. Our model for the exciton band structure is supported by transient emission measurements. 1.
Introduction
Thin organic films with semiconducting properties have recently gained large interest due to promising device applications. Particularly attractive are organic molecules which form quasil d molecular crystals with strong orbital overlap between neighboring molecules. Here, the strong intermolecular interaction favors generation and transport of charge carriers. Despite the large interest in those materials, the nature of their lowest-energy excitations is not clear: models capable of describing significant aspects of the solid-state absorption spectra are just emerging ' , 2 . In this paper, we study the exciton states of crystalline MePTCDI. The crystal structure of MePTCDI and many related perylene derivatives is characterized by quasi-one-dimensional stacks 3 .The small distance between the molecular planes within the stacks results in a strong interaction of the 7r-electron systems. The interaction between the stacks is much weaker due to their larger separation. Therefore, we use a one-dimensional Hamiltonian to describe the excited states of the crystal. Within this model, we explain the main features of the low temperature polarized absorption spectra of MePTCDI (see Fig. la). The monomer absorption in the visible spectrum can be well described by an electronic transition with three vibronic levels. These levels become three mixed exciton bands if energy transfer between excited molecules is included in the crystal Hamiltonian. However, such a Frenkel exciton (FE) model cannot explain the four significant peaks of the crystal spectrum. To achieve that, we additionally consider one nearest neighbor charge-transfer (CT) state. A CT state can have a transition dipol moment with a direction different from the molecular transition dipole. Then, the direction of the total transition dipole for a mixed state depends on the relative contribution of F E and CT states. Considering this effect we can explain the experimentally observed polarization ratio, which varies for the different bands. Such a varying polarization ratio is a new phenomenon entirely due to the C T mixing.
29
30 2.
Model Hamiltonian
For the description of the excited states in a one-dimensional molecular crystal with one molecule per unit cell we use the following Hamiltonian: HF + HFF + Hc + nFC
n = nF = nFF =
Z'MZBLAnr
nc = nFC =
E K C H L A + I + BLC,.,-O+eJKBlA+i,-. 1 + iBLC B - 1 , +1 )+h.c.} nv
Here the operator B^, (Bnv) describes the creation (annihilation) of a neutral local excitation (Frenkel exciton) at lattice site n. Only one electronically excited local state is considered, the index v specifies the three excited vibrational levels. Then A p is the FE on-site energy and M^, the hopping integral for excitation transfer from level v at site n to level p, at site m. In addition to these Frenkel excitons we include nearest neighbor charge-transfer excitons. A localized CT exciton with the hole at lattice site n and the electron at lattice site n + a (a = — 1,-t-l) is created (annihilated) by the operator Cla (Cna). For simplicity, only the vibrational ground state is considered for the CT excitons with ACT as their on-site energy. Hopping of CT states will not be considered. The mixing between Frenkel and CT excitons is expressed in 7iFC. Here, the transformation of a CT state into any Frenkel state at the lattice site of either hole or electron is allowed. The relevant transfer integrals e£ (e£) can be visualized as transfer of an electron (hole) from the excited molecule n to its nearest neighbor. In the following, we outline the main steps described in detail in Ref. 2.Transforming all operators into momentum space representation results in a Hamiltonian that is already diagonal with respect to k, but still contains mixed terms of the three operators for the Frenkel excitons and the two operators for CT excitons. These are altogether five molecular configurations, which would yield five mixed exciton bands. We now consider only nearest neighbor FE transfer, keeping M as the electronic part of M^. In addition, we neglect coupling of CT excitons to the considered vibrations, the remaining electronic part of the transfer integral e£ (ejj) is ee (eh)Using symmetry adapted CT operators, one non-mixing CT state can be separated, which gives four mixed exciton bands. The remaining Hamiltonian can be diagonalized formally. With the knowledge of the excited states we are able to calculate for each band f) = 1...4 the total transition dipole moment P& for optical excitation into the k = 0 state. Each transition dipol can be written as a sum of a Frenkel and a CT transition dipole P& = PpE + PQT. They can be related to the molecular transition dipole ppE and the transition dipole of the even CT dimer state per by PpE = a,pE p F E and PQ T = a CT PCT- The specific contribution of the three molecular Frenkel exciton states (the even dimer CT state) to state k — 0 of band /3 is included in the prefactor a PE (a CT ). This composition, especially the CT parentage, varies for the different bands. In addition it follows from quantum chemical calculations that PCT has a large component within the moleculare plane. This component is not parallel but makes an angle of about 68° with p F E . Therefore, the direction of the total transition dipoles P& will vary from band to band. In summary, there are two main features of the model Hamiltonian: (i) if the FE-CT coupling is on the same order as the energetic separation between the CT and the Frenkel
31
excitons, the model predicts a strong mixing with four significantly absorbing bands, (ii) With a finite CT transition dipole, the polarization direction of the bands will vary due to the varying composition of the bands. 3.
Application to Polarized Absorption Spectra
We measured the absorbance spectra of highly oriented MePTCDI films for perpendicular incidence and two orthogonal polarization directions (s and p) at 5 K. The spectra are shown in Fig. la together with the peak positions from a peak fitting analysis using a four band model (Fig. lb). Remarkably, the peak positions are slightly different for both polarization directions. We interpret these peak shifts as Davydov splitting due to the two molecules in the MePTCDI unit cell. From the occurence of Davydov splitting follows that the excit? n states of the two non-equivalent stacks are coherently coupled. Also shown is the polarization ratio RP (ratio of the peak areas of the s and p polarized spectra). R$ varies for the different bands, which is an immediate consequence of a varying polarization direction within the Id stacks according to the Id model. a) Absorption
b) Polarization ratio
c) Band structure
d) Emission
transient (0..40ps)
V CT
•E^k) 0
i ' i 2 4 R
i 0.0
0.5 k/rc
1.0
L
Figure 1 a) Polarized absorption spectra of MePTCDI crystalline films at 5 K. The s-polarized spectrum is scaled for easier comparison, b) Comparison of experimental polarized absorption spectra (filled squares) with the exciton modell (open circles). Given are the polarization ratios at the transition energies, c) Scheme of the exciton band structure. The dispersion is drawn as a black line. The upper shaded stripe at the bands visualizes the Frenkel part of the oscillator strength |-PpE|2/PFE' t n e lower shaded stripe gives the CT part KCTP/PCT- °0 Transient emission spectrum at 5 K after a short pulse excitation at 2.77 eV. For weak coherent coupling between the two non-equivalent stacks the two Davydov components will have total transition dipoles oc (P&(A) ± Pff(B)). Then the absorption cross section and the polarization ratio for each band in the polarized spectra from Fig. 1 can be
32 expressed by the model parameters Ap,A CT , M,e+ = te + eh and the relative CT transition dipole pf?T = |PCT|/|PFEI- These five parameters we used to fit the experimental peak positions and intensities. We found the following values: A£ = 2.23 eV, A C T = 2.17 eV, M=0.10 eV, e+=0.10 eV and pg^=0.31. The model predictions for peak positions and polarization ratios according to these fitting parameters are shown in Fig. lb. The first three peaks are in good agreement with the experimental spectra. The relatively small polarization ratio of the second peak at 2.26 eV is well described. This peak is most strongly affected by the CT exciton. Since the transition dipole of the CT exciton is roughly perpendicular to the molecular transition dipole, the CT and Frenkel excitons influence the polarization ratio in the opposite way. The worse description of the fourth peak at 2.72 eV is due to limitations in our simple four-band model, where only one effective vibronic mode coupled to the electronic transition is considered. Quantum chemistry also provides the parameter \ee — eh| = 0.05 eV , which is not accessible from absorption experiments. With this parameter, the full momentum dependent band structure for the excitons can be calculated. The result is shown in Fig. lc. There the composition of the bands is also indicated by a schematic visualization of the fc-dependent values |^FEP/PME and
IPCTP/PCT-
Since the bottom of the proposed band structure lies at the edge of the Brillouin zone, luminescence is expected to appear as a weak, indirect transition from these k = n states. In Fig. Id, we show an experimental transient emission spectrum (time window 0 — 40 ps) after a short pulse excitation at 2.77eV. Interestingly, a small emission feature at 2.10eV, which has a short lifetime below the time resolution of ~ 10 ps, occurs around the energies of the lowest energy band. All lower emission peaks have a multi-exponential decay time on time scales in the order of 1 ns. These features coincide with the typical cw emission spectrum. The long-lived states might be identified with self-trapped excitons or emission from defects. Thus, we suggest that the main emission as observed in cw-luminescence spectra does not result directly from the bottom of the band structure but occurs only after further relaxation. In conclusion, we presented a simple model Hamiltonian which is capable of describing energetic positions, peak intensities and a varying polarization ratio for absorption spectra of quasi one-dimensional crystalline perylene derivatives. The exciton structure is essentially determined by a strong mixing of Frenkel and CT excitations. For the first time, a mechanism is considered that leads to polarization dependent spectra due to the varying contribution of a CT transition dipole. The model can be semi-quantitatively confirmed by a quantum chemical analysis of the irrfermolecular interactions. References [1] M.H. Hennessy et al, Chem. Phys. 245, 199 (1999). [2] M. Hoffmann et al., Chem. Phys. 258, 73 (2000). [3] E. Hadicke and F. Graser, Acta Cryst. C42, 189 (1986).
SPATIALLY D E P E N D E N T AMPLIFICATION OF A N E X C I T O N I C BOSE-EINSTEIN CONDENSATE IN CUsO EMERY FORTIN AND MATHIEU MASSE Department of Physics, University of Ottawa, Ottawa, KIN 6N5, Canada Experimental results are presented on the spatial dependence of amplification of a travelling Bose-Einstein condensate of excitons in C112O. The exciton condensate is created at T = 1.8 if by high intensity pulsed laser illumination (A = 532nm). Amplification of the moving condensate is triggered by the local, time-delayed injection of thermal excitons created by a lateral laser pulse tuned at the IS orthoexciton resonance (A = 609.48nm), perpendicular to the path of the condensate. The amplification factor depends on the trigger time of the lateral laser pulse and is related to the stimulated scattering into the condensate of non-condensed excitons present in the crystal volume. A spatial correlation is also observed between the amplification factor and the optical attenuation of the lateral laser radiation induced by the passing condensate. 1. I n t r o d u c t i o n Bose-Einstein condensation has recently been the subject of several experimental and theoretical studies 1 ' 2 . In addition to atomic condensates, excitons, in particular in C u 2 0 , are good candidates for experiments on Bose-Einstein condensation 3,4 ' 5 ; superfluidity was observed in a ballistic exciton packet propagating through the crystal at near sonic velocities (4.5 x 106 mm/sec)3. Using a CW laser tuned at the IS orthoexciton energy, stimulated scattering of particles into the condensate was observed 5 .The experimental results have raised debates among theoreticians 6 ' 7 ' 8 ' 9 ' 10 , and a recently proposed theory includes the effect of the coupling between excitons and phonons 6,11 . Up till now the role of non-condensed excitons has been largely ignored. In the present work a delayed resonant laser pulse is used instead of a CW laser in order to selectively excite different parts of the travelling condensate as well of its accompanying tail of non-condensed excitons. 2. E x p e r i m e n t The C u 2 0 sample is a high-quality natural single crystal ([100] oriented), kept at T = 1.8 K in superfluid helium. The excitons are created by an eight-nsec frequency-doubled YAG laser pulse (A = 532 n m ) , which is absorbed within a few fim of the crystal surface (3.5 x 3.6 m m ) . The exciton packet is detected at the end of its travel to the opposite face of illumination (1.94 m m travel) by means of the exciton-mediated photovoltaic effect3'12. Briefly, the detector consists of an ohmic Au electrode surrounding a C u / C u 2 0 Schottky barrier. When reaching the proximity of the Schottky barrier the excitons are field-ionized and give rise to an external current in the absence of an applied voltage. An additional weakly absorbed 1 3 resonant six-nsec laser pulse, tuned to the IS orthoexciton energy of 2.033 eV14, is incident on the middle of the crystal, perpendicularly to the direction of the travelling condensate. By varying the delay between the two pulses, the position of the injected IS thermal excitons relative to the moving condensate can be controlled. The resonant transmitted light is collected by an optical fibre in contact with the sample and connected to a fast detector situated outside the cryostat. The intensities of the laser pulses - thus the initial densities of excitons - are accurately controlled by a multi-prism variable attenuator and neutral density filters. 3. R e s u l t s Figure 1 shows the exciton packet resulting from the YAG illumination alone at an intensity of 11.6 MW/cm2 (A) and the amplified packet (B) in the presence of a lateral laser pulse at an intensity of 15 KW/cm2 synchronized to hit the initial packet as it passes through the middle of the crystal: this corresponds to a delay between the two pulses of 240 nsec. The large packet
33
34
0.50
Time (usee) Fig. 1. Excitonic signal detected when illuminating with only the YAG laser (A = 532 nm) (A) and when both the YAG laser and a delayed lateral laser pulse (A = 609.83 nm) are illuminating the sample (B). The intensity of the YAG is 11.6 MW/cm2 and that of the lateral laser pulse 15 KW/cm2. amplification is critically dependent on the wavelength of the lateral pulse and it has been verified that it vanishes within a narrow range of the order of the bandwidth of the laser. The attenuation of the lateral laser pulse, which also depends critically on wavelength, was studied as a function of its time of trigger or delay with respect to that of the YAG laser pulse: this trigger time can be related to the transit fraction of the packet across the crystal. The results displayed in figure 2 show a spatial correlation between the amplification factor (the amplification factor being defined here as the ratio of final to initial packet amplitude) and the normalized differential optical attenuation caused by the passing condensate. As expected, the normalized differential attenuation (defined (I - I') / I where I is the lateral light intensity transmitted in the absence of the packet and F is the intensity transmitted in the presence of the packet) is zero if the lateral laser pulse is synchronized to hit the crystal before the exciton packet is close enough to have an effect; the differential attenuation reaches a maximum at a transit fraction of 60-70 % or when the lateral laser pulse is synchronized with the passage of the packet and its thermal tail in front of the illumination spot. This implies that the packet either absorbs the thermal excitons in its path (thus liberating phase space for additional photon absorption) or that the laser light is simply absorbed or scattered by the condensate and its associated tail. Figure 2 gives information on how different parts of the travelling packet are affected by the IS excitons. An amplification is observed when the lateral pulse creates excitons in front of the packet (low trigger time) because the paraexcitons have a lifetime much longer15 than the transit time of the advancing condensate. A maximum in the amplification factor is observed at a transit fraction around 65-75 %: it occurs when the IS thermal excitons are created behind the moving packet. At longer trigger times, the amplification factor decreases and reaches one (i.e. no amplification) beyond one transit fraction, as the packet has then been detected at the electrodes. However an attenuation is still observed after one transit fraction, indicating the continued presence of primary excitons within the crystal. These results suggest a comet analogy to the packet: a core of condensed excitons surrounded by a coma, and a tail of
35 Trigger Time (nsec) rr r/ /v — i — > -
0.9
,}»*}. # j o o to
- 0.8 0.7
10
0.6
•l'.
g CO O
1.0
cb
0.5
I <
CO
c
a? c g .O
i5 H
0.4
CD CD
0.3
E
N tJ
0.2 0.1
' * / 0.00
i»« 0.25
•
" 0.50
o •
1 0.75
•
o
1—//-"1.00 2
0.0
Transit Fraction Fig. 2. Amplification factor (open circles) of the condensate and normalized differential attenuation of the lateral laser pulse (filled circles) as functions of the transit fraction of the packet (trigger time of the lateral laser pulse).
non-condensed excitons. Both the tail and the coma of non-condensed excitons are induced to scatter into, or as discussed below to form a condensate by the resonantly-created excitons. The tail is the predominant region where amplification occurs, thus implying that a large fraction of the excitons originally created by the YAG laser pulse are located there. Figure 3 shows the details of the exciton packet as the trigger time of the lateral laser pulse is varied. At low trigger time (i.e. when the lateral laser pulse is fired before the packet reaches the middle of the crystal), the resulting amplified packet is slightly faster than the original packet as shown by the dotted curve, which is a simple mathematical multiplication of the original exciton packet to match the amplitude of the amplified packet. The leading edge of the packet is amplified as it sweeps through the resonantly-created excitons; but the packet width remains unchanged. If the lateral pulse is synchronized with the arrival of the packet in the middle of the crystal (graph B), much the same occurs but now the width is slightly increased. At longer trigger times (graph C), the resulting condensate is again wider and a secondary feature appears on the trailing edge. Those features are even more evident in graph D; in addition the main amplified packet is now slower than the original one, indicating that slower tail excitons are scattered into an emerging new condensate. At even longer delay (graph E), the original packet is no longer amplified since it has been detected by the electrode; however a secondary packet appears clearly associated with the amplification of the tail of the primary condensate. This can be observed for very long trigger times (up to three transit fractions) as seen in graph F. Both primary and secondary features can be fitted to a soliton16. It can also be noted that the amplitude of the secondary packet is relatively smaller at the very long trigger time (graph F compared to graph E); this maybe related to a decrease in the attenuation of the lateral laser pulse at that delay (see figure 2). The above results have shown that the injection of a relatively modest amount of resonant
36 140
A
B
120 100
80
i
60
\
40 20 140
]s\
;,..,,,. ..,j/v'vS^.... D
C
:
120
\ ;\
100
>
80
'••
40
"to
c g> CO o "c o o X
:
60
20
n
,--i^r^>>.-,
\
. JiN^
LU
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Time (|isec) Fig. 3. Excitonic signal showing the exciton packet and the amplified packet for trigger time A: 145 nsec, B: 240 nsec, C: 395 nsec, D: 450 nsec, E: 700 nsec and F: 1500 nsec. The dotted curves represent the original exciton packet multiplied to match the amplitude of the amplified packets.
IS excitons can trigger large amplifications of a travelling exciton packet. The mechanism involved here is reminiscent of that occurring in a laser amplifier/oscillator chain. Experiments are underway to study the influence of different crystal orientations and the effect of different directions of lateral light polarization on the amplification of the travelling packet. The differential attenuation associated with the passing condensate and closely related to its amplification, has to be studied further in order to pinpoint its exact origin: in particular, studying the influence of the resonant lateral light intensity and direction of polarization as well as investigating the effects of a lateral pulse tuned near the band edge, could give useful information on the mechanisms involved. Acknowledgements We acknowledge the help of Andre Merizzi and Luc Charron in the experiments and support by the National Science and Engineering Research Council of Canada under grant number # T 0707-001-01.
37 References 1. A. Griffin, D. W. Snoke and S. Stringari, Bose-Einstein Condensation, Cambridge University Press, Cambridge, 1995. 2. S. A. Moskalenko and D. W. Snoke, Bose-Einstein Condensation of Excitons and Biexcitons: and Coherent Nonlinear Optics with Excitons, Cambridge University Press, Cambridge, 2000. 3. E. Benson, E. Fortin and A. Mysyrowicz, Phys. Status Solidi (b), 191, 345 (1995). 4. E. Benson, E. Fortin, B. Prade and A. Mysyrowicz, Europhys. Lett, 40, 311 (1997). 5. A. Mysyrowicz, E. Benson and E. Fortin, Phys. Rev. Lett, 77, 896 (1996). 6. I. Loutsenko and D. Roubtsov, Phys. Rev. Lett, 78, 3011 (1997). 7. G. A. Kopelevich, N. A. Gippius and S. G. Tikhodeev, Solid State Commun., 99-2, 93 (1996). 8. A. R. Vasconcellos, M. V. Mesquita and R. Luzzi, Europhys. Lett, 49, 637 (2000). 9. G. M. Kavoulakis and A. Mysyrowicz, Phys. Rev. B, 61-24, 16619 (2000). 10. D. B. I r a n Thoai and H. Haug, Solid State Commun., 115, 379 (2000). 11. D. Roubtsov and Y. Lepine, Phys. Rev. B, 6 1 , 5237 (2000). 12. E. Tselepis, E. Fortin and A. Mysyrowicz, Phys. Rev. Lett, 59, 2107 (1987). 13. P.W. Baumeister, Phys. Rev., 121-2, 359 (1961). 14. L. Hanke, D. Frohlich and H. Stolz, Solid State Commun., 112, 455 (1999). 15. A. Mysyrowicz, D. Hulin and A. Antonetti, Phys. Rev. Lett, 43, 1123 (1979). 16. E. Fortin, E. Benson and A. Mysyrowicz, Electrochemical Society Proceedings, Edited by R. T. Williams and W. M. Yen, 98-25, The Electrochemical Society, Pennington, 1998, 1-10.
ANOMALOUS SPECTRAL SHIFTS OF INDIRECT EXCITONS IN COUPLED GaAs QUANTUM WELLS D.W. SNOKE, V. NEGOITA, D. HACKWORTH Department of Physics and Astronomy, University of Pittsburgh, 3941 O'Hara St. Pittburgh, PA 15260, United States of America K. EBERL Max-Plank Institut fur Festkorperforschung, Heisenbergstr. 1 70506 Stuttgart, Germany We have studied the energy shifts of indirect excitons consisting of an electron in one quantum well and a hole in an adjacent quantum well. Several surprising effects occur: (1) a very strong blue shift with increasing intensity of resonant laser excitation, (2) a very strong red shift with weak magneticfield,and (3) very low-frequency (sub-Hz) fluctuations of the spectral position at high excitation density. We discuss the effect of screening by carriers excited in the substrate material. 1. Introduction The system of excitons in coupled quantum wells has extremely rich dynamics, and many surprises still arise. We have studied coupled quantum wells of GaAs with AlAs barriers, subject to an external electric field. This electric field has two main effects. First, as shown in Fig. 1, it splits the degeneracy of the two wells and makes the lowest exciton state, called the "indirect" exciton because it consists of an electron in one well and a hole in the adjacent well, have an energy which stronly depends on the electric field. This is known as the quantum-confined Stark effect (QCSE) and has been observed to give red shifts with DC electric field up to 70 m e V
. 1.2.3,4
Second, the electric field causes all of the indirect excitons to be polarized in the direction of the electric field. This causes the excitons to have a strong dipole-dipole interaction, which is expected to suppress the formation of electron-hole liquid. Both of these are advantageous for Bose condensation of excitons. The electric field shift has been used to create a macroscopic harmonic potential trap for the indirect excitons,4 which can be used to allow a true Bose condensation in two dimensions. The strong dipole-dipole interaction which prevents electron-hole liquid should cause the excitons to remain a gas at all temperatures, a necessary condition for Bose condensation. In our studies of the indirect excitons in these structures, we have found several novel effects, all of which involve the energy position of the indirect exciton line. These nonlinearities may have wide application in optical devices. 2. Experimental Results As shown in Fig. 1, we use a 60-40-60 coupled quantum well structure, with pure AlAs outer barriers. The quantum well structure is surrounded by pure GaAs buffer layers, grown on a heavily doped p-type GaAs substrate, with a heavily doped n-type GaAs capping layer. Similar but weaker effects are seen for 80-40-80 and 100-40-100 stuctures. Fig. 2 shows the first novel effect, which is a very strong blue shift of the indirect exciton line with excitation intensity.5 Almost the entire DC red shift due to the QCSE can be canceled out, roughly 25 meV at this applied electric field. Notably, the shift is much larger than the inhomogeneous line broadening, which means that this effect may have application in optical switching- the relative change in absorption at one wavelength is very large.
38
39
Fig. 1. The band structure of our samples, with externally applied field. Pure AlAs barriers with 200 A thickness surround a 60-40-60 A coupled quantum well structure with pure GaAs wells and a Al.3Ga.7As barrier. Under applied electric field, the indirect exciton consists of an electron in one well and a hole in the other well. This blue shift of the indirect exciton line occurs only for near-resonant excitation of the direct single-well transition; when the sample is excited with red light (ca. 630 nm), a red shift with increasing excitation is seen. The blue shift does not depend on the exact excitation wavelength, however. The same effect is seen for excitation from 750-765 nm. Fig. 3 shows another novel effect, which is a strong red shift with magnetic field. Shifts up to 60 m e V / T have been recorded, 6 depending on the applied voltage, the temperature, the well width, and the excitation density. Normally, in unbiased quantum wells, the exciton lines shift upward with increasing magnetic field,7,8,9 and at fields above 1 T, we also see a nearly-linear blue shift with increasing magnetic field.6 As seen in this figure, the red shift is larger at higher density. The shift with magnetic field is symmetric with the direction of B, and decreases for wider quantum wells. This effect is remarkable for how weak the magnetic fields are which cause it. This may have application in magnetic field detection.
100
r
1 .
.
.
.
A
30 J 10/
3
)
f\J :
.,,
,. }•
1.57 1.575
1.58 1.585 1.59 1.595 1.6 Photon Energy (eV) Fig. 2. The indirect exciton luminescence spectrum for several laser excitation intensities at A = 765 nm, at T = 2 K. The labels of the curves are the excitation power in mW. One mW of excitation power corresponds to approximately 109 ' of absorbed pair density in the quantum wells. Fig. 4 shows luminescence spectra at different magnetic fields for high excitation density, when a second line appears due to ionized excitons. The lower-energy line, corresponding to the indirect excitons, shifts downward strongly, while the upper line, corresponding to the indirect free-carrier transition, shifts upward slightly or remains at the same energy, depending on the
40 1.58 p-r
LU
1.57 -
8 c
8 w £
1.565 -
1 Z3
ca $
.
1.56 1.555 ' 0
0.05
0.1
0.15
0.2
0.25
' ' ' • • 0.3 0.35
B field (T)
Fig. 3. The indirect exciton luminescence peak energy as a function of magnetic field, for two excitation intensities at A = 632 nm, at T —2 K and applied field of 22.8 kV/cm. Open squares: 1.7 mW. Solid circles: 12 mW.
applied voltage. Finally, we have seen extremely low-frequency fluctuations of the spectral position of the indirect exciton line, with time scales on the order of seconds.10 These fluctuations occur only at high excitation density, but there is no sharp threshold of density. This effect is seen only weakly with red (630 nm) excitation. 3. Discussion A primary consideration in these experiments is the role of the photocurrent in the shift of the exciton line. When the laser excites the sample, about 1% of the light is absorbed in the quantum wells, and the rest is absorbed in the capping layer and the substrate. The large number of free carriers in the intrinsic GaAs layers can therefore contribute to screening. Fig. 5(a) shows the case when few photocarriers are excited (the coupled quantum well structure is represented by a single AlAs barrier.) Electrons and holes accumulate on opposite sides of the quantum well structure. This accumulation tends to increase the effective field within the coupled quantum well structure, as shown in Fig. 5(b). This leads to an overall red shift with increasing density, as seen in the case when we excite with a red laser (seen, e.g., in Fig. 3 at B = 0). If charge tunnels through or jumps over the barriers, this will tend to cancel out the effect of the screening. If there is a strong tunneling current through the barriers, it can completely cancel out the additional field due to the photoexcited charge. The tunneling current cannot reduce the field below the externally applied value, however. In the case of near-resonant excitation, the absorption length of the laser is about four times longer than with the red excitation.11 Fewer carriers are excited near the well structure for a comparable density of excitons in the well, which is 3000 A from the front surface, leading to less red shift due to the additional charge. We attribute the blue shift observed with increasing density, therefore, to many-body renormalization of the indirect exciton ground state. This renormalization can be thought of as arising from two effects: the repulsive interaction between the excitons, which leads to a mean-field blue shift, and screening out of the external electric field by the excitons themselves. These two effects, both of which arise from the Coulomb interaction of the carriers, are not ultimately separable, and a proper many-body theory must take both into account. The many-body interpretation of the blue shift is supported by the fact that the homoge-
41
1.595
« i
. b>
^r^
^^
^r^
,
^r^
-
•
1.59
'
0
k-
£ S umli
g K i
1 a.
o
1.585
o
1.58
1 1
B
•
1.575 -
1.57
1.565
•
•
•
°
0
o
o
•
•
•
•
' •
• • • • • • • • .•. •
0.1
1
•
0.2
B(T)
Fig. 4. a) The indirect recombination luminescence for various magnetic fields, for an exchange gas temperature of 4.4 K, with 12 mW excitation power at 632 nm, and applied electric field of 7.6 kV/cm. b) The peak luminescence energies of the two lines, for two values of the electric field, under the same conditions as in (a). Open symbols: E = 7.6 kV/cm. Filled symbols: 15.2 kV/cm. neous broadening of the indirect exciton line also increases linearly with density at very high density, 5 as expected for an imaginary self-energy due to two-body scattering. We have previously reported 5 that at early times after the laser pulse, the indirect exciton luminescence line sometimes shifts first to the red for a few nanoseconds, and then to the blue. We interpret this as a small red shift due to accumulation of charge at the barriers, as discussed above. It is also possible that the local temperature increases, leading to a red shift of the GaAs gap, but this is less likely. The substrate luminescence does not shift in energy, which imples that the overall lattice temperature does not change dramatically. The data of Fig. 4 support the interpretation that the red shift with magnetic field is due to an increase of the binding energy of the indirect exciton with magnetic field. This may also be a many-body effect, as indicated by the data of Fig. 3, which show that the shift is stronger for higher carrier densities. The fluctuations of the luminescence line position seen in our structures 10 could be due to an electronic phase transition, as suggested by Butov et al. 12,13 for a similar system. It could also be the case that the local density fluctuates, which would lead to changes in the many-body renormalization energy, or that the tunneling current fluctuates, which would lead to changes in the external electric field. In either case, the time scale of seconds, far longer than the exciton lifetime, is surprising. 4. C o n c l u s i o n s The coupled quantum well system with applied electric field seems hypersensitive to numerous parameters, namely excitation density, excitation wavelength, electric field, magnetic field, lattice temperature. The line position jumps dramatically under changes of all of these parameters, and is unstable to fluctuations at high density. The sensitivity may be due to both
42
a)
p:GaAs
p:GaAs
b)
+\ Vi
Vi
Fig. 5. (a) Overall band structure, (b) Effective band structure when there is significant excitation of the substrate and capping layer. tunneling current and many-body renormalization of the exciton gas. This hypersensitivity seems likely to have device applications. Acknowledgements Part of these experiments were performed at High Magnetic Field National Laboratory (HMFNL), which is supported by NSF Cooperative Agreement DMR-9527035. This work has been supported by the National Science Foundation under Grant No. DMR-97-22239 and by the Department of Energy under Grant No. DE-FG02-99ER45780. One of the authors (D.S.) also thanks the Research Corporation for financial support. References
9. 10.
11. 12. 13.
S.R. Andrews, CM. Murray, R.A. Davies, and T.M. Kerr, Phys. Rev. B37, 8198 (1988). A.M. Fox, D.A.B. Miller, G. Livescu, J.E. Cunningham, and W.Y. Yan, Phys. Rev. B44, 6231 (1991). Y. Kato, Y. Takahashi, S. Fukatsu, Y. Shiraki, and R. Ito, J. Appl. Phys. 75, 7476 (1994). V. Negoita, D.W. Snoke, and K. Eberl, Phys. Rev. B60, 2661 (1999). V. Negoita, D.W. Snoke, and K. Eberl, Phys. Rev. B 6 1 , 2779 (2000). V. Negoita, D.W. Snoke, and K. Eberl, Solid State Comm. 113, 437 (2000). K. Oettinger, Al. L. Efros, B. K. Meyer, C. Woelk and H. Brugger, Phys. Rev. B52, R5531, (1995). Q. X. Zhao, B. Monemar, P. O. Holtz, M Willander, B. O. Fimland, K. Johannensen, Phys. Rev. B50, 4476, (1994). L. V. Butov. A. Zrener, G. Abstreiter, A. V. Petinova and K. Eberl, Phys. Rev. B52, 12153, (1995). V. Negoita, D. Hackworth, D.W. Snoke, and K. Eberl, Optics Letters 25, 572 (2000). J. S. Blakemore, J. Appl. Phys. 53, R123 (1982). L.V. Butov, A. Zrenner, G. Abstreiter, G. Bohm, and G. Weimann, Phys. Rev. Lett. 73,304 (1994). L.V. Butov and A.I. Filin, Physical ReviewB58, 1980 (1998).
PHOTOLUMINESCENCE OF BIEXCITON IN ZnO EPITAXIAL THIN FILMS KENSUKE MIYAJIMA, AISHIYAMAMOTO, TAKENARI GOTO Dep. ofPhys., Grad. Sch. ofSci., Tohoku Univ., Aramaki, Aoba-ku, Sendai 980-8578 Japan HANG JU KO, TAKAFUMIYAO Inst, for Mat. Res., Tohoku Univ., Katahira 2-2-1, Aoba-ku, Sendai 980-8577 Japan We have measured excitation dependence of photoluminescence (PL) spectra, excitation spectra of PL (PLE) and temporal dependence of the PL intensity in ZnO epitaxial thin films. The ZnO films were grown on a sapphire substrate with a GaN buffer layer to reduce a lattice mismatch. We succeeded in observing a PL due to biexciton for the first time in ZnO epitaxial thin films.
Recently, wide band-gap semiconductors have been studied extensively. Because they are candidates for short-wavelength semiconductor laser diodes which have attracted many scientists for a great deal of commercial interest. Since ZnO is a wide band-gap semiconductor (3.37eV at room temperature) and has a large exciton binding energy (60meV), it is a hopeful material for short-wavelength exciton related optical devices. In 1997, ZnO epitaxial films on a sapphire substrate were grown successfully by a molecular beam epitaxy (MBE) method,1 and stimulated emission and optically pumped laser action were observed.2 This emission was reported to be due to exciton-exciton collision or electron-hole plasma. Although the existence of a biexciton state in ZnO bulk crystals has already been confirmed experimentally, there is no report on photoluminescence (PL) due to the biexciton in ZnO thin films until now to our knowledge. In this report, we study excitation intensity dependence of PL spectra, excitation spectra of PL (PLE) and temporal behavior of the PL, and discuss the biexciton state in ZnO epitaxial thin films. The ZnO thin films were fabricated on a sapphire substrate with a GaN buffer layer by a plasma assisted MBE method.4 The lattice mismatch between the ZnO and the GaN is about 2%, which is much less than that between the ZnO and the sapphire, 18%. Therefore, the crystallinity is thought to be improved by introducing the GaN buffer layer. The thicknesses of the GaN buffer layer and the ZnO film are 4(j,m and 2|xm, respectively. The surface of ZnO thin films is normal to the c-axis. We used a frequency-tripled output (355nm) of a Nd:YAG laser (pulse width 7ns, repetition rate 10Hz) for the measurement of excitation dependence of PL spectra. The sample was directly immersed in liquid nitrogen. The PL was analyzed by a monochromator with a charge-coupled device (CCD) detector. The spectral resolution was about 5meV. Excitation light ranges in intensity between 2.9W/cm2 and 4.7 kW/cm2. For the measurements of PLE and temporal dependence of the PL, we used a frequency
43
44 doubled pulse light of Ti:sapphire laser (pulse width ~2ps, repetition rate 76MHz) and excitation light ranges in energy between 3.357eV and 3.375eV. The sample was held in a N2-gas flow cryostat. The PL was analyzed by a subtractive doublemonochromator with a photomultiplier detector. The spectral resolution was about 0.05nm. Time-response of the PL intensity was measured by a streak camera. Figure 1 shows excitation intensity dependence of PL spectra at 77K. The PL spectrum at low excitation intensity obtained by using a cw He-Cd laser (325nm) is -i shown in Fig. 1 (A). A PL peak due to radiative recombination of free exciton is observed at 3.370eV which is denoted by X. PL peaks indicated by LOi (3.309eV) and L0 2 (3.235eV) are associated with oneand two-LO phonon-assisted recombination of the free exciton, respectively. We also notice two PL peaks, h (3.362eV) and L, (3.357eV) due to bound excitons.5 The '3.20 3.25 3.30 3.35 3.40 excitation intensity dependence of the PL spectrum is Photon Energy (eV) shown in Fig. 1 (B). When the excitation intensity is Fig. 1. (A) PL spectrum excited by a cw increased, a new PL peak, M, appears at the lower energy He-Cd laser. (B) PL spectra under the side of bound exciton lines. The spectral shape of the M excitation density of (a) 2.9W/cm2, (b) band is asymetric and has a tail to the lower energy side, as 15W/cm2, (c)150W/cm2, (d) 930W/cm2 clearly seen in the curve (c). The peak energy of the M and (e) 4.7kW/cm2. band slightly shifts to the lower energy side with 10° increasing excitation intensity. The origin of this M band will be discussed later. When the excitation intensity is increased furthermore, another emission band denoted by P appears at the lower energy side. This P band is assigned as the PL due to an exciton-exciton collision.2 When the exciton density becomes larger, a quantum number of the exciton generated by the collision changes from n=2 to n=o°, and as a result, the red shift of the P band is observed in the curves (d) and (e).
10' 10'
10 r J 10' LO i band Mband
10*
Pband
Figure 2 shows excitation intensity dependence of the PL intensities of M, P and LOi, which are indicated by IM, lp and ho, respectively. The PL intensity of ILo increases linearly with the excitation intensity (IEXC), whereas IM and lp increase superlinearly with the excitation intensity (*IEXCL5)- When the P band appears,
10
10
10
10
10
Excitation Intensity (W/cm ) Fig. 2. Excitation intensity dependence of the PL intensities of the M, P and LOj bands.
45
PL Intensity (a.u.)
the slope of IM becomes smaller. These experimental results strongly suggest that the M band originates from a biexciton state. As the excitation intensity increases, the kinetic energy of some of the excitons becomes higher than the biexciton binding energy, which would enhance the exciton-exciton collision. Generally spectral shape of the biexciton PL, 1(E), is expressed by an inverse Boltzmann distribution G-E 1(E) a JEX-Gm-Eexp(), (1) kT where Ex, Gm, k and T are energy of exciton state, bixciton binding energy, Boltzmann factor and biexciton effective temperature, respectively. The obtained spectral shape of the M band is fitted to Eq. (1). Since the higher energy side of the M band overlaps with the X band, the band shape is fitted in the lower energy side of the M band. As a result, Ex-Gm is obtained as 3.355eV. The energy of Ex is estimated to be 3.370eV from the spectral shape of the LOi band, E-Er L ILO(E)c(E-Ex-ELO)3,2exp((2) ), kT where Eio is LO phonon energy, 73meV. Thus, Gm is estimated to be 15meV, which is almost the same as that of the bulk crystal, 14.7meV.3 With increasing excitation intensity, the biexciton effective temperature is increased from 80K to 120K, which induces the red shift of the M band. The excitation intensity dependence of the M and P bands, IM, Ip^hxc15, is not the ideal dependence <*IEXC • It is supposed that there is a non-radiative process when the two excitons come across. In order to confirm that the M band is due to the biexciton state, we measured PLE. Figure 3 shows PL and PLE spectra of the M band. In the PLE spectrum high PL intensity is kept in the excitation energy higher than 3.370eV which is resonant to the free exciton energy and there is • PLE a shoulder at around 3.363eV. If the M band is • -PL due to the biexciton, giant oscillator strength of the two photon absorption is expected to < occur at 3.3625eV, which is almost the same energy as that of the shoulder. Consequently, Mb and the observed shoulder is thought to be due to ** exciton energy two photon absorption of the biexciton state. • / 1 Since one photon absorption band is broad, 3. 34 3.35 3.36 3.37 I'hoton Energy (eV) one- and two-photon absorptions may occur simultaneously in the energy region of two Fig. 3. PL (solid line) and PLE spectra (closed photon resonance. The absorption broadening circles) of M band. The dashed line shows guide to may result from local strain in the ZnO films. the eye of PLE spectrum. Thus, we can not see clear PLE peak but the shoulder. From this experimental result, it is confirmed that the M band is due to the biexciton state. Figure 4 shows temporal behaviors of the M and LOi PL intensities with the excitation
46 photon energy 3.371eV, which is resonant to the free exciton energy. The population dynamics of a biexciton and a single exciton is expressed by the following rate equations 6 — = -aM + /W", dt dN •• aM - 2/SiV" - yN . dt
(3) .(A) 1LO phonon side band
(4) experiment fitting
Here, M and N are the densities of the biexciton and exciton, respectively, a and y are decay rates of the biexciton and exciton, respectively, and /3 is a formation rate of the biexciton from the exciton. In general, the second term in the right hand side of Eq. (3) is $N2 and that of Eq. (4) is -2fiN2. As is shown in Fig. 2, however, the excitation dependence of PL of the biexciton shows IM^IEXC1'5-
Here, we adopt the 200 400 600 Decay Time (ps)
power dependence 1.5 according to the experimental results. In this analysis we assumed that a lifetime of LOi PL is the same as that of the X PL and a lifetime of biexcitons is long enough compared to the laser light pulse width. We fit experimental data by varing
800
Fig. 4. Temporal dependence of the PL intensities LO, (A) and M (B). The solid lines represent the fitting curves.
the three adjustable parameters a, /3 and y. The solid lines in Fig. 4 show the result of the fitting, which reproduce well the experimental data. From this fitting we obtained a"1 and y1 as 80ps and 260ps, respectively. We have studied excitation intensity dependence of PL spectra, two photon absorption and temporal dependence of the PL intensity of ZnO epitaxial thin films. In the excitation dependence of PL spectra, we newly observed an M band whose intensity increases superlinearly with the excitation intensity ("/ac 1 ' 5 ). The biexciton binding energy is estimated to be 15meV which is very close to that of the bulk crystal. From the above experimental results, we concluded that the M band is due to the biexciton state.
References 1.
Y. F. Chen, D. M. Bagnall, Z. Zhu, T. Sekiuchi, K. T. Park, K. Hiraga, T. Yao, S. Koyama, M. Y. Shen, T. Goto.X Cryst. Growth 181,165 (1997).
2.
D. M. Bagnall, Y. F. Chen, Z. Zhu, T. Yao, S. Koyama, M. Y. Shen, T. Goto, Appl. Phys. Lett. 70, 2230 (1997).
3.
J. M. Hvam, G. Blattner, M. Reuscher, C. Klingshirn, Phys. Stat. Sol. (b) 118,179 (1983).
4.
H. J. Ko, Y. F. Chen, T. Yao, K. Miyajima, A. Yamamoto, T. Goto, Appl. Phys. Lett. 77, 5371 (2000).
5.
D. C. Reynolds, C. W. Litton, T. C. Collins, Phys. Rev. 140, A1726 (1965).
6.
Y. Unuma, Y. Masumoto, S. Shionoya, J. Phys. Soc. Jpn. 51,1200 (1982).
INFRARED ABSORPTION B Y EXCITONS IN CUPROUS OXIDE
M. GOPPERT, R. BECKER, C. MAIER, M. JORGER, A. JOLK, C. KLINGSHIRN Institut fur Angewandte Physik, Universitdt Karlsruhe, Kaiserstr. 12, D-76128 Karlsruhe, Germany We report on the first observation of the Is to 2p exciton transition in a direct gap semiconductor. Cuprous oxide is well known for its excitonic features which provide a model case for the theory of Wannier excitons. In our pump-probe experiment we measured the infrared transmission of cuprous oxide with and without Ar + -laser illumination. The observed photo-induced absorption line in the differential transmission spectra at 126 meV is assigned to the excitonic transition from Is to 2p exciton levels i.e. to the analog of the Lyman series in atomic hydrogen. From the dependence of the integrated photo-induced absorption on the pump laser intensity we determine the lifetime of the paraexciton r p ss 0.3 ms. We also studied the influence of the pump laser on the phonon absorption band in the mid-infrared. Its observed shift to lower energies with increasing pump laser intensity can be explained by heating of the sample. 1. I n t r o d u c t i o n Cuprous oxide ( C u 2 0 ) is a semiconductor with a direct gap at the T point which crystallizes in a cubic lattice with two molecules per unit cell. Due to the inversion symmetry, its electronic states are of definite parity. Because the uppermost valence band and the lowest conduction band have the same parity, the transition between them is not dipole allowed. Since the exciton is composed of two fermions, the electron-hole exchange interaction results in the case of cuprous oxide in an energy splitting of 12 meV of the ground state n = 1 into a paraexciton (S = 0) and an orthoexciton (S = 1). The direct recombination of the paraexcitons is dipole and quadrupole forbidden. Snoke et al. 1 estimated from time-resolved luminescence measurements an intrinsic radiative lifetime of the paraexciton of at least 150 ^is. The radiative recombination rate of the orthoexcitons is about 500 times larger 1 . Due to the very large binding energy 2 of about 150 rr.eV, the ls-paraexcitons are very robust against thermal and impact ionization. In the usual spectroscopy the properties of the excitons are studied by measuring transitions between the vacuum state and the exciton states which means annihilation or creation of excitons. The ns excitons can be directly created by two-photon absorption 3 or by an indirect process under simultaneous absorption or emission of an LO phonon. The np exciton resonances can be studied via linear absorption spectroscopy 4 because of the negative parity of the p envelope. In case of high quality samples a beautiful hydrogenic series of absorption peaks up to the 12p exciton has been observed 6 . The spectroscopy of transitions between different exciton states is less common although it can give insight into the excitonic fine structure or can be used to check the applicability of the hydrogen model. Up to now such transitions have only been observed in bulk semiconductors with an indirect bandgap such as Si 6 and Ge 7 , where the lifetime of the excitonic ground state is long enough to generate a high exciton concentration via optical pumping resulting in an observable photo-induced absorption signal. Due to the large binding energy and the long lifetime of the exciton ground state the direct gap semiconductor cuprous oxide is also an excellent candidate for this kind of spectroscopy. 2. E x p e r i m e n t s The infrared transmission measurements have been performed with a Bruker 113v Fouriertransform spectrometer. In order to be able to observe the transitions from the exciton ground state to excited states, the ground state has to be populated. In our pump-probe experiment
47
48
a)
b) /2s
- j - j - ^ r 2 " + r3"+ r;+ r5~ 2p ortho Tj 2p para
T 6 Is ortho 120
130 140 150 energy(meV)
160
12meV
T 2 Is para
Fig. 1. a) Spectra of the optical density ad of sample 1 measured at 15 K with and without laser illumination. The intensity of the laser beam was 10 Wcm - . b) Level scheme of the n=l,2 exciton states including the dipole allowed transitions. we measured the transmission of CU2O at different temperatures with and without pump laser illumination. For excitation into the exciton continuum a continous wave Ar + -laser at 514.5 nm (KS 2.41 eV) was used as pump source. The investigated samples were cut and polished from naturally grown single crystals. The thicknesses of sample 1 and sample 2 discussed in this paper are 70 fim and 2.0 mm, respectively. 3. R e s u l t s a n d d i s c u s s i o n The mid-infrared absorption spectrum of sample 1 recorded with and without laser illumination is shown in Fig. la. The absorption band observed at 142 meV is of phononic nature. One sees from Fig. l a that the illumination results in a small red shift and a broadening of this phonon band which can be explained by a laser induced heating of the sample. This band was comprehensively discussed by Burlakov et al. 8 . In Fig. l b the energetic term scheme of the fine structure of the n = l , 2 states is shown including their symmetries. The relative positions of the exciton levels are known from one- and two-photon absorption spectra 3 . The still unknown energy splitting of the 2p states due to electron-hole exchange interaction is expected to be much smaller than in case of the Is states 9 . The vertical arrows show the dipole allowed transitions. Since the dipole operator has TJ-symmetry only the 2p-paraexciton level (Fif-symmetry) can be reached from the ls-paraexciton state (rj-symmetry) without spinflip. The Is orthoexciton can be optically excited into the remaining 2p states. The small photo-induced absorption line in the absorption spectrum at about 126 meV recorded during laser illumination is assigned to transitions from Is to 2p exciton states. This value is in very good agreement with the value shown in Fig. l b which has been determined from one- and two-photon absorption spectra. In a next step the photo-induced absorption has been studied as a function of the laser power. The sample temperature was kept constant at 100 K. Fig. 2a shows the differential transmission spectra (T w - Tw0)/Ty,0 of sample 2 where T w (T wo ) is the transmission measured with (without) laser illumination. Two distinct minima are observed. The minimum at 126 meV is as already
°)
b)
0.4
energy(meV)
energy(meV)
Fig. 2. a) The relative differential transmission spectra of sample 2 recorded in the range of the excitonic Lyman series for different pump intensities at 100 K. For clarity the spectra are vertically set off with respect to each other, b) Differential transmission spectra measured under the same excitation conditions at 10 K and 100 K. The spectra are again vertically shifted. mentioned assigned to ls-2p transitions. Since the sample temperature is comparable to the energy splitting of the Is state, not only transitions from the Is para state but also from the Is ortho state contribute to the absorption signal. Therefore the observed absorption structures are a superposition of the transitions shown in Fig. lb weighted by the occupation of the ground states and the respective oscillator strength. The minimum at about 158 meV which is little higher than the binding energy of the ground state is assigned to the photoionization of the Is paraexcitons. The small structures between the two main bands could be due to Is—>3p,4p transitions. The laser intensity has been varied between 0.7 and 10.0 Wcm -2 . The absorption strength for the ls-2p transitions increases linearly with increasing number of Is excitons created by the pump laser beam. Furthermore, the dependence of the photo-induced absorption on the temperature has been studied. Fig. 2b. shows the relative differential transmission spectra in the range of the ls-2p absorption for a pump intensity of 10.0 Wcm""2 measured at 10 and 100 K. The dependence of the shape of the absorption structure on the temperature can be explained by the different relative occupation of the para- and orthoexciton states. As already mentioned the observed ls-2p absorption structure is composed of transitions from the ortho- and paraexcitons the relative occupation of which depends on the temperature. At 10 K the relative occupation of the paraexcitons is higher than at 100 K. Therefore the relative absorption strength of nonspinflip transitions between para in comparison to ortho states should increase with decreasing temperature. Having in mind that the paraexciton transitions are at higher energies than the corresponding orthoexciton transitions, the high energy side of the absorption structure becomes stronger at lower temperatures in agreement with the findings in Fig. 2b. The oscillator strength of the ls-2p transition have been experimentally determined by fitting
50 the differential transmission spectra using the Lorentz oscillator model. The photo-generated exciton densities are in the range of 10 16 cm -3 and have been calculated from the oscillator strength within the limit of a hydrogen model. Prom the photo-generated exciton densities the lifetime of the paraexciton TP has been estimated to be about 0.3 ms. 4. Summary The excitonic Lyman series has been studied in cuprous oxide in dependence on the exciton density and the lattice temperature. The photo-generated exciton density was in the regime of about 10 16 cm -3 . Prom the absorption strength of the ls-2p absorption the lifetime of the paraexcitons of TP « 0.3 ms has been estimated. Acknowledgements We would like to thank the Deutsche Forschungsgemeinschaft for financial support and Prof. Dr. A. Mysyrowicz (Palaiseau) and Prof. Dr. G. M. Kavoulakis (NORDITA) for stimulating discussions. References
1. 2. 3. 4. 5. 6. 7. 8. 9.
D. W. Snoke et al., Phys. Rev. B45, 11693 (1992). E. Benson et al., phys. stat. sol. (b)191, 345 (1995). C. Uihlein et al., Phys. Rev. B23, 2731 (1981). A. Jolk et al., phys. stat. sol. (b)206, 841 (1998). H. Matsumoto et al., Solid State Communication 97, 125 (1996). D. Labrie et al., Phys. Rev. Lett. 61, 1882 (1988). T. Timusk, Phys. Rev. B13, 3511 (1976). V\ M. Burlakov et al., Physics Letters A254, 95 (1999). G. M. Kavoulakis et al., Phys. Rev. B55, 7593 (1997).
OPTICAL R E S P O N S E OF A CONFINED EXCITON IN A S P H E R E W I T H T H E E F F E C T S OF LT S P L I T T I N G A N D B A C K G R O U N D P O L A R I Z A T I O N : C O M P A R I S O N OF T W O D I F F E R E N T A P P R O A C H E S
KIKUO CHO, KIYOHIKO KAWANO, TETSUYA TSUJI, HIROSHI AJIKI Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama Toyonaka, 560-8531 Japan The optical response spectra of a weakly confined exciton in a. sphere, obtained via microscopic nonlocal response theory, have been compared with the macroscopic approach combined with Pekar type additional boundary condition (ABC). The results give a good agreement, with respect to the peak positions and their intensities, indicating that the non-escape boundary condition for the exciton wave function is equivalent to Pekar type ABC. It is also stressed that the microscopic approach is much suitable to discussing the details of the quantized excitons, such as the character of transverse (T), longitudinal (L) and LT-mixed modes, and the radiative shift and width of each level, and the details of the internal field. According to the standard optical response theory, the spectrum of scattering cross section due to excitons confined in a sphere can be obtained by solving the Maxwell equations with the polarization term describing the exciton resonance with the help of appropriate boundary conditions for the EM field amplitudes. The susceptibility contains spatial dispersion effect due to the exciton resonance, and correspondingly additional boundary condition (ABC) is required, as well as usual macroscopic ones, to uniquely determine the response field. This procedure was carried out by Ekimov et al. / I / and Ruppin / 2 / , where they assumed Pekar
type ABC. The solution of the Maxwell equation directly gives the amplitude of response field for a given incident light, and its frequency dependence leads to the spectrum of scattering cross section, which consists in general of many overlapping resonance lines with various line widths. In view of the fact that the result includes the effect of LT (longitudinal - transverse) splitting and the radiative correction (shift and width), it is difficult or impossible to assign each line to a size quantized exciton level, or to tell the L, T, and LT mixed character of the exciton levels. The assignment with respect to the L or T character is of essential importance in some of recent experiment / 3 / . In order to settle the above-mentioned difficulty, we have recently made a thorough theoretical study of the optical response of an exciton weakly confined in a sphere (with arbitrary radius R) by calculating firstly the exciton level scheme with the effects of size quantization, electron-hole (e-h) exchange interaction and the background polarization (bulk-like screening and image charge effect) / 4 / , and secondly the scattering cross section of an incident transverse field within the framework of nonlocal response theory which includes the radiative shift and width from the first principles / 5 , 6/. By this approach, we have [A] exciton level scheme with the effects of size quantization (SQ), LT splitting, and the image charge density due to background dielectric, and [B] the optical spectrum with many resonant lines of various strength and width. From [A] we understand how the exciton level scheme changes from the SQ dominated regime to the e-h exchange dominated one, as we increase R. Also it has become clear that most exciton levels are LT mixed mode except for a small number of pure L and T states. In the bulk limit, i.e., R —+ oo, the former tends to either (bulk) L or T levels, as expected. In addition to this, there arise a surface mode for each angular momentum quantum number, which is strongly affected by the image charge density induced by the exciton polarization.
51
52
R=500 (A) ' TEMode
Nonlocal T h e o r y ' — Macroscopic Theory •
i 1
ger
I*
H
' J
N^Lt.i
3.20
3.21
X50
•
\\\±
Energy (eV)
3.20
3.21 Energy (eV)
Fig.l. Calculated scattering cross sections for TE modes (upper) and TM modes (lower) for R = 500A. For a small value of R, the coupling strength of each level can be measured by oscillator strength, which is a valid concept in the long wavelength approximation (LWA). Our calculation shows that, except for the case of small sphere radius, the higher values of oscillator strength appear for the levels near the surface mode. Since the nonlocal scheme used for [B] does not depend on LWA, the comparison of the calculated oscillator strength with the peak intensity in [B] reveals the validity range of LWA. Denoting the wavelength of resonant light in vacuum as A, we observe the appearance of "forbidden" states in LWA already for R = 0 . 2 5 A / y ^ , where t\, is background dielectric constant. As we further increase R, this level becomes a dominant structure for R = 0.5\/y/ti. Thus our impression is that LWA tends to be broken rather earlier than one might expect. The radiative shift of each level shows a peculiar dependence on R. In most region of R, it has a monotonous increase in red shift, but near a particular value of R, the shift flips over to the higher energy side of the bulk L mode level and tends gradually to that level with the further increase of R. At the flip-over point, the corresponding radiative width takes maximum value, which indicates that a particular component of the EM field has a maximum amplitude, since radiative width is a most general indicator of the coupling strength / 7 / . For a given set of angular momentum quantum numbers, different exciton levels are specified by radial wave functions with different number of nodes in the sphere. The components of EM field are also specified by the number of nodes, which, for a given frequency, is determined by R. A rule of thumb is that the mode with (n — 1) nodes can be accommodated if 2R = n x 0.5A/' y/ei. This rule explains why such flip-over points appear regularly on R axis. A more detailed analysis would be required to obtain the exact values of R for flip-over points. In any case, the nonlocal framework gives the amplitudes of EM field components with various spatial structure, determined selfconsistently with the induced polarization, which also consists of components with various spatial structure.
53
3.20
3.21
3.22
Energy (eV)
R=800 (A)
Nonlocal Theory Macroscopic Theory
Fig.2. Calculated scattering cross sections for TE modes (upper) and TM modes (lower) for R = 800A. In the step [B], there exists the interference of the resonance scattering by excitons with the Mie scattering due to the sphere with constant ej. This feature becomes important for large values of R, where the frequency dependence, as well as the amplitude, of the Mie scattering becomes comparable to that of the exciton scattering. Due to this interference, there can arise a considerable change in the spectral form of the cross section for large R. ' The purpose of this work is to make a final check of the whole story, namely, whether the calculated spectra in the step [B] coincide with those from the macroscopic response theory / l , 2/. Since there are no available curves in / l , 2 / for this comparison, we have recalculated the spectra according to the formulation by Ruppin / 2 / , and put the results on the spectra in [B]. For the comparison, it is useful to classify the exciton states and EM field according to the angular momentum, because of the spherical symmetry. Denoting the angular momenta of exciton CM (center of mass) motion and that of transition dipoie moment of the electronic bands as £ and £' (\l'\ = 1), respectively, we define the total angular momentum as J = £ + £'. An incident light can be decomposed into components of various J, and each component can excite the excitons with the same value of J (and its projection). Thus, we make the comparison of spectra for a given J . Since \£'\ = 1, only limited number of states (£ = J + 1,J, J — 1) contribute to the spectrum for a given J in the nonlocal approach [B]. For small value of R, the spectrum is dominated by the component J = 1. Therefore we used only the exciton states with J = 1 in / 5 , 6 / . (As to the background polarization, however, higher J components were also taken into account.) For a CuCl sphere with R = 500A, the comparison with the macroscopic approach gives an almost perfect agreement as shown in Fig.l, except for the higher energy region, where the number of the radial basis function used in / 5 , 6 / is not enough. If we compare the spectra for an incident plane wave which contains various J components, we observe a few resonances missing in the spectra of / 5 , 6 / , although the general agreement is
54 very good. This tendency is more prominent for larger values of R. Fig.2 is an example of this situation. The difference is due to the contribution from the modes with higher values of J. For example, the resonant structure appearing only in the macroscopic calculation can be shown explicitly to arise from the J = 2 component. The exciton states with J > 2 are all optically forbidden in the LWA. Their emergence is the indication of the breakdown of the LWA. Thus, we may conclude that the two schemes are equivalent in calculating optical spectrum, if we take enough number of basis functions with respect to both J and the radial components. This means that the ABC assumed in / l , 2 / is consistent with the non-escape boundary condition for the center-of-mass (CM) wave function of exciton used for the nonlocal scheme. This is somehow expected, since the nonlocal scheme is a microscopic theory for deriving ABC from the first-principles, and since such a correspondence is known for a slab geometry / 8 / . In conclusion, we have shown that the two schemes, the macroscopic and microscopic ones, to calculate optical response agree quite well with one another. However, it should again be stressed that the microscopic nonlocal scheme is absolutely necessary in order to make detailed discussions about the L and T character and the amount of radiative shift and width of the exciton levels. Acknowledgements The authors are grateful to Prof. H. Ishihara for his useful discussions. This work was supported in part by the Grant-in-Aid for COE-Research (10CE2004) and Scientific Research on Priority Area (10207205) of the Ministry of Education, Science, Sports and Culture of Japan. References 1. 2. 3. 4. 5. 6. 7. 8.
A. I. Ekimov et al. : Sov. Phys. JETP 63, 1054 (1986) R. Ruppin: J. Phys. Chem. Solids 50, 877 (1989) A. V. Baranov et al.: Phys. Rev. B 55 (1997) 15675 H. Ajiki and K. Cho: Proc. EXCON'98, p.262 (1999) K. Cho, H. Ajiki, and T. Tsuji: Proc. QD2000 (phys. stat. sol. b) T. Tsuji: Master Thesis (Osaka Univ. 2000) T. Ikawaand K. Cho: J. Lumin. 87-89 (2000) 305 K. Cho and M. Kawata: J. Phys. Soc. Jpn. 54 (1985) 4431
SUB-5-fs R E A L - T I M E S P E C T R O S C O P Y of E X C I T O N I C S Y S T E M S TAKAYOSHI KOBAYASHI Department of Physics, Faculty of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo, 113-0033, Japan Pump-probe experiment was performed for spin-coated films of conjugated polymers (substituted polydiacetylene) and J-aggregates of a porphyrin derivative by using a sub-5fs visible laser. Real-time spectra were obtained for the systems and new dynamical processes have been observed, i.e. dynamic mode coupling, dynamic intensity borrowing. 1. Introduction Femtosecond pulses shorter than 10 fs have become easily available and enabled the study of real-time dynamics of various molecular systems. Especially, femtosecond wavepacket dynamics has been recently studied to realize the possibility of controlling molecular dynamics using tailored ultrashort pulse. Information about the dynamic coupling among vibrational modes in molecules in condensed phase is needed for the realization of such selective chemistry. Dynamic mode coupling is also important for the clarification of the mechanism of structural relaxation in the excited state of molecules. Recently sub-5-fs visible pulses have been generated in our group on the base of a novel optical parametric amplifier with a non-collinear configuration i.e. non-collinear optical parametric amplifier (NOPA) 1,a . The laser system generating such short pulses has enabled the real-time observation of the transmittance change associated with molecular vibrations. Realtime spectroscopy has been applied to conjugated polymers, J -aggregates of porphyrin, and dye molecules. Energy migration among the of C-C, C = C , and C = C stretching modes and other low frequency out-of-plane bending modes in polymers through mode coupling have been observed by using a sub-5fs visible laser 3 . Coupling with an out-of-plane bending mode in cresyl violet dye molecules is found to induce the phase and amplitude modulation of the breathing mode. Dynamic intensity borrowing has been observed for the first time using a Frenkel exciton system of J-aggregates of porphyrin. Dynamic Dushinsky effect was observed in cresyl violet doped in polyvinyl alcohol and in polymethylmethacrylate. 2. E x p e r i m e n t a l The pulse-front-matched NOPA generates transform-limited (TL) 4.7-fs, 5-mJ 1-kHz pulses centered at 650nm with a 250-nm bandwidth 1 , 2 . It has two sets of appropriately designed chirped mirrors for the compensation of group-velocity dispersion 1 ' 2 . One of the two sets is for pre-compensation to obtain efficient overlap of seed pulse and pump pulse in the BBO crystal for parametric amplification. The other set of chirped mirrors is for optimization of the amplified pulses. The broadband property of group-velocity matched NOPA is briefly mentioned. The problem of pulse-front tilting in the noncollinear interaction is fully utilized by using pulse-frontmatching (PFM) geometry that is essential to attain transform-limited (TL) pulse generation. The visible sub-5-fs pulse generation and tunable operation in a sub-10-fs regime are realized by the same NOPA system with and without the chirped mirrors, respectively. The NIR sub-10-fs pulse generation by angular dispersion compensation is also obtained. 3. P o l y d i a c e t y l e n e s Ultrafast dynamics of conjugated polymers such as polydiacetylenes (PDA) has been attracting many scientists because they are model systems of quasi-one dimensional semiconductors with a strong electron-phonon coupling. From our extensive studies 3,4,5,6 , the initial kinetics after
55
56 photo-excitation can be explained by a relaxation of a free exciton (FE) to a self-trapped exciton (STE) within 150fs. The recent achievement of sub-5-fs visible pulse generation based on a novel noncollinear optical parametric amplification (NOPA) 1,2 has enabled the real-time observation of the formation of a STE in a PDA for the first time. The stretching-mode vibration(C-C, 27 fs, C = C , 23 fs and C = C , 16 fs) coupled with the excitonic transition drives the coherent relaxation of the backbone structure from an acetylene (A)-like ( = C R - C = C - C R ' = ) n to a butatriene (B)like (-CR=C=C=CR'-)„ configuration.
Fig. 1. Coherent wavepacket motion in the transient differential transmittance. The probe photon energy is marked on the right with a 5-mm resolution. The real-time spectrum shown in Fig. 1 is given by the transient differential transmittance. It clearly shows a coherent molecular motion composed of several modes over the whole probe spectral range. From the complex features, it is also evident that more than two modes are contributing to the time-dependent transmittance change. In spite of the complexity, there are systematic features in the phases of the oscillations probed at various probe photon energies. For example, there are eight peaks at 23, 44, 90, 154, 180, 200, 260, and 308 fs among the eleven prominent peaks in the real time spectrum representing the trace of normalized transmittance change at 2.12 eV. The signal intensity is minimum at these delay times in the trace of 1.75 eV. This result of the coincidence indicates that there are constant phase relation among the
57 observed modes and that the coherence times of the relevant modes are substantially longer than 300fs. Previous papers 7 ' 8 reported that only the C = C stretching and ~700-cm _ 1 modes were observed and that they remained only for the initial 100 fs. This quick damping is explained by dephasing due to anharmonicity. The behavior observed in the present study probed around the exciton band has similarity to the previous results; but there is a striking difference, namely weak oscillations continue beyond 400-fs delay even after the population decay. The underlying signal due to the population change also decays quickly along with the oscillating component due to wave-packet motion. This fast decay is observed in the transients for probe photon energy Eproht. < ~ 2 . 0 eV. In the region B p r o b e > ~ 2 . 0 eV, on the other hand, the amplitude of the oscillations is maintained or even increases slightly in the initial positive signal range. The coherence is maintained as long as ~ 1 ps in the delay-time range of negative transmittance change due to photo-induced absorption. The integrated Fourier analysis of the real-time spectrum reveals two intense modes of C = C (~1455 c m - 1 ) and C = C (~2080 c m - 1 ) stretching, in addition to weaker modes around 220, 700, and 1220 c m - 1 , of which intensities are dependent on the probe wavelength. These modes are also observed in the static Raman spectrum. The A—>B isomerization and following thermalization of STE is visualized by a real-time frequency analysis using a spectrogram 9 .
Fig. 2. Left: Phases of the coherent wavepacket motion calculated from the sine- and cosine-Fourier transforms of the transient differential transmittance probed at various probe photon energies. Right: Potential curves of the excition state and the ground state to show the probe photon energy dependence of the vibrational phases. From the calculations the Fourier-sine and -cosine transform of the transmittance change, the wavelength dependence of the phases of molecular vibration was found to be same for three modes of C-C C = C , and C = C stretching as shown In Fig. 2. This indicates that these three modes are excited impulsively in a common phase. Energy migration among the three stretching modes and other low frequency mode presumably due to out-of-plane bending through mode coupling has been observed. This is the first observation of dynamic mode coupling. The spectrogram was calculated using various window functions and widths. Care must be taken for the mixing of the signal of Fourier power spectrum of neighboring modes between which frequency difference is smaller than the inverse of the width of window function used. Using broad enough width, modulation of frequencies and amplitudes of three high-frequency
58 modes of carbon-carbon stretching could are observed. Some of the modulations are correlated with the same low modulation frequency. 4. J - a g g r e g a t e s Time dependence of the absorbance change was observed also in porphyrin J-aggregates as is shown in Fig. 3. For the discussion of the molecular vibration, the oscillating components should be separated from the overall transient curves. The slowly varying decay component is subtracted from the transient signal. Fourier spectra clearly show a strong peak at 244 c m - 1 as shown in the figure. The Fourier amplitude is drastically reduced at 1.77 eV at which the sign of the phase is changed.
Fig. 3. Real-time spectra of porphyrin J-aggregate and the Fourier transform of the rapidly oscillating components in the spectra. The peak at 241 c m - 1 is observed in the stationary Raman spectrum. The Raman signal of this mode is drastically enhanced by a factor of more than 30 10 in the aggregation process. The phase of the oscillation is evaluated by the complex Fourier transformation. A 7r-phase jump is clearly observed around 1.77eV, which is slightly higher than the peak photon energy of the Q-band. At the probe photon energy of the phase jump, the signal changes from the
59 bleaching (positive signal) to the photo-induced absorption (negative signal) and the oscillation amplitude is small. Although the oscillation in the bleaching and photo-induced absorption is 7r-phase shifted, relative values show in-phase oscillations. Associated with the ruffling mode of the aggregates transmittance change is observed at various probe photon energies covered by the shortest visible pulse as broad as 150 THz. The phase of the molecular vibration is found nearly constant, if we take into account of the sign reversal of the signals between the bleaching region and photoinduced absorption region. Absorbance change is induced by either bleaching, induced emission, and/or induced absorption. The former two are clearly related with the stationary ground-state absorption. The induced absorption is also considered to be related to the ground-state absorption. This is because the induced absorption is due to the transition from the n = 1 exciton state to re = 2 exciton state. It is expected to resemble that of n = 0 to n = 1 exciton state except for blue-shift duet o Pauli exclusion principle. The constant phase is different from expected continuously varying phase change along the probe photon energy. This unexpected result can be explained in terms of dynamical intensity borrowing. The intensity of absorption associated with the transition of the ground state to the Q-band is borrowed from that of Soret band by the configuration-interaction mechanism. Since the mode appears 30 times more strongly than on a molecule dissolved in solution, it is concluded that the transition is strongly coupled to the Frenkel excitonic transition. The degree of the intensity borrowing is modified by vibrational motion of the ruffling mode by the exciton-phonon coupling. The coupling is not large enough to induce the potential minimum in the ground state from that of the ground state but large enough to large enough to modify the mount of the intensity borrowing. It was found that even a very small change in the vibrational amplitude could introduce the change in the transition probability. From the experimental transmittance change, the intensity of the vibronic coupling is estimated. 5. Conclusion The present results will offer a valuable information about the geometrical relaxation and encourage the theoretical investigations of the election-phonon and electron-electron interactions in non-degenerate conjugated polymers. The experimental technique of real-time spectroscopy with sub-5 fs pulses can reveals the dynamical processes in the excited states and intermediate states through the oscillating features appearing in the transmittance change. Acknowledgements The author is grateful to Dr. Shirakawa, and Messrs. Kanou and Saito for collaboration in experiment and analysis. He thanks Prof. Nakanishi and Mr. Matsuzawa for providing the polymer sample. He also thanks Profs. Toyozawa, Abe, and Okamoto for valuable discussion. This work was partly supported by Research for the Future of Japan Society for the Promotion of Science (JSPS-RFTF-97P-00101). References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
A. Shirakawa, I. Sakane, and T. Kobayashi, Opt. Lett. 23, 1292 (1998). A. Shirakawa, I. Sakane, M. Takasaka, and T. Kobayashi, Appl. Phys. Lett. 74, 2268 (1999). T. Kobayashi, A. Shirakawa, H. Matsuzawa, and H. Nakanishi, Chem. Phys. Lett. 321, 385 (2000). E.g., T. Kobayashi, M. Yoshizawa, U. Stamm, M. Taiji, and M. Hasegawa, J. Opt. Soc. Am. B. 7, 1558 (1990). M. Yoshizawa, Y. Hattori, and T. Kobayashi, Phys. Rev. B 123, 121 (1994). T. Kobayashi, M. Yasuda, S. Okada, H. Matsuda, H. Nakanishi, Chem. Phys. Lett. 267, 472 (1997). T. A. Pham, A. Daunois, J. C. Merle, J. Le Moigne, and J. Y. Bigot, Phys. Rev. Lett. 74, 904 (1995). J. Y. Bigot, T. A. Pham, and T. Barisien, Chem. Phys. Lett. 259, 469 (1996). M. J. J. Vrakking, D. M. Villeneuve, and A. Stolow, Phys. Rev. A 54, 37 (1996). D. L. Akins, H.-R. Ahu, and C. J. Guo, J. Phys. Chem. 98, 17159 (1995).
INTERBAND TWO-PHOTON TRANSITION IN MOTT INSULATOR AS A N E W M E C H A N I S M F O R U L T R A F A S T O P T I C A L N O N L I N E A R I T Y
M. Ashida Cooperative Excitation Project, Exploratory Research for Advanced Technology, Japan Science and Technology Corporation KSP D-842, Kawasaki 213-0012, Japan T. Ogasawara* N. Motoyama, H. Eisaki, S. Uchida, Y. Taguchi, Y. Tokura* and M. Kuwata-Gonokami* Department of Applied Physics, the University of Tokyo Hongo 7-3-1, Tokyo 113-8656, Japan H. Ghosh, A. Shuklat and S. Mazumdar Department of Physics and the Optical Sciences Center, University of Arizona Tucson, AZ 85721, USA
The dimensionality dependence of optical nonlinearity in cuprates was investigated by sub-picosecond pump-probe transmission measurements in the near-infrared region. It was found that cuprates with one-dimensional Cu-O networks show nonlinearity one order of magnitude larger than that of conventional band semiconductors and picosecond relaxation of the excited state. In contrast, a two-dimensional cuprate shows one order of magnitude smaller nonlinearity and slower decay of the excited state, as well as picosecond relaxation. The possibility for application of the present material to all-optical switching devices is also discussed. 1. Introduction Since the discovery of high-T c superconductivity, the anomalous behavior of conductivity and magnetic properties of the perovskite transition-metal oxides have attracted much interest 1,2 . Recently, we reported the on strong interband two-photon absorption and the picosecond recovery of optical transparency observed in a quasi-one-dimensional (ID) Mott insulator S r 2 C u 0 3 with single C u - 0 chains 3 ' 4 . The cluster calculation suggests that the enhancement of the nonlinearity is due to the strongly correlated nature of the electron system, specifically, strong on-site Coulomb repulsion U, as much as ~ 10 eV 4 , on Cu site. To clarify experimentally the origin of the nonlinearity and the dimensionality dependence of the optical properties in particular, we performed sub-picosecond pump-probe transmission measurements in low-dimensional cuprates with different C u - 0 networks. Since the family of cuprates includes many derivatives, it is convenient to elucidate the relationship between the crystal structure and electronic properties 1 . The specific materials were Sr 2 Cu03, SrCu02 and Sr 2 Cu0 2 Cl 2 . Sr 2 Cu03 is a typical ID Mott insulator with single C u - 0 chains along the 6-axis (lattice constant 6=3.91 A), shown in the inset of Fig. 1(a) 2,5 . S r C u 0 2 has a weakly coupled double C u - 0 chain structure, where the chain is along the c-axis (c=3.92 A), as shown in the inset of Fig. 1(b). Since the interchain coupling due to 90° Cu-O-Cu bonds is much weaker than the coupling along the 180° Cu-O-Cu bonds which form the chains, this material can be also considered as a ID Mott insulator in low-energy excitation phenomena, e.g. conductivity or magnetic properties 2,5 . In Sr 2 Cu0 2 Cl 2 , which is a 2D counterpart of these ID materials, the C u 0 2 layer perpendicular to the c-axis (a=6=3.98 'Also at Correlated Electron Research Center (CERC) and Joint Research Center for Atom Technology (JRCAT), Tsukuba 305-8562, Japan tAlso at Cooeperative Excitation Project
60
61
A) is the same as in the parent material, high-Tc superconductor La 2 Cu0 4 ; however, apical oxygen is substituted for the CI ion (inset of Fig. 1(c))6. Importantly, the lattice constants along the Cu-0 chain in these materials are almost the same, allowing us to investigate the effects of the Cu-0 network dimensionality on optical properties. A comparison of ID and 2D systems may allow us to elucidate the role of the spin-charge separation, which is a peculiar phenomenon of ID spin systems and was experimentally demonstrated for the first time with the present materials7, in strong ultrafast nonlinearity.
1.5
2.0
2.5
Photon energy (eV) Fig. 1. Linear absorption spectra at 290 K. (a): S r 2 C u 0 3 {E\\b), (b): SrCu0 2 (-E||c) and (c): Sr2Cu02Cl2 (EXc). Crystal structures are also shown in the insets.
Figure 1 shows the linear absorption spectra of these materials. All three materials show an absorption peak around 2 eV, which corresponds to the charge-transfer gap2,6. The materials are nearly transparent below 1.5 eV. In ID systems the allowed polarization of light is parallel to the direction of the axis of the Cu-0 chains (b in Sr 2 Cu0 3 , c in SrCu02). 2. Experimental results Single crystals of Sr 2 Cu0 3 and SrCu0 2 were grown by the traveling-solvent floating-zone method5, while Sr2Cu02Cl2 was grown by cooling the stoichiometric melt8. Thin flakes with thicknesses of 50 to 100 fun were cleaved out for transmission measurements. Two optical parametric generators (TOPAS, Quantronics) pumped by a KHz regenerative amplifier (CPA-2001, HOYA-Continuum) were used to change the pump and probe photon energies independently.
62 The laser system can generate pulses with a temporal width of 0.2 ps and photon energy from 0.3 to 1.5 eV. We measured the differential transmission AT/T, where T is the transmission in the absence of the pump pulse, as a function of the pump-probe delay. The pump and probe beams were linearly polarized along the C u - 0 chains. All measurements were performed at 290 K. Typical examples of the temporal behavior of the photo-induced absorption change, AaL = - l n ( l + AT/T), where L is a sample thickness, in S r C u 0 2 at 290K are shown in Fig. 2. As clearly seen in Fig. 2(b), the temporal profile of AaL in S r C u 0 2 consists of the instantaneous component, which is determined by the laser pulse duration, and the decaying component with a characteristic time of 1 ps. By comparing the temporal profiles at different pump photon energies we conclude that the relative magnitude of the decay component decreases with a decrease in the pump photon energy. The observed reduction of the decay component of the photo-induced absorption at lower pump photon energies indicates that this component is associated with real carrier relaxation. The temporal profile of photo-induced absorption in S r 2 C u 0 3 at 290K is similar to that in S r C u 0 2 . Note the similar behavior observed in S r 2 C u 0 3 at 10 K 4 . In contrast, Sr 2 Cu0 2 Cl 2 shows an additional decay component with a characteristic time of 30 ps, as shown in Fig. 2(d).
SrCu0 2 290K
(a)
— IP-
I < a> H
"5
60
E
1 Time (ps) Fig. 2. Temporal profiles of AaL at 290 K in SrCu0 2 for pump +probe energies of (a): 1.46 eV + 0.95 eV, (b): 1.31 eV + 0.95 eV and (c): 0.95 eV + 1.03 eV. The profiles are normalized at their maximum values for comparison of shape. The fitting curve (solid line), which consists of the Gaussian function with a width of 0.2 ps (dotted line), and the decay component, which is calculated by convolution of the Gaussian and the exponential function with a decay time of 1 ps (broken line), are also shown in Fig. 2(b). The inset (d) shows AaL at 290 K in Sr 2 Cu0 2 Cl 2 for 1.46 eV + 0.95 eV plotted on a logarithmic scale against an extended time scale. The solid line shows a fitting curve with two exponential functions with decay times of T = 1 ps and r=30 ps.
63
The observed instantaneous component in the pump-induced absorption is due to coherent optical nonlinearity, or more specifically, to the two- photon absorption (TPA) at the sum photon energy of the pump and the probe4. This is confirmed by the dependence of the TPA coefficient /? = Aa// p u m p , where / p u m p is pump laser intensity, on the sum of pump and probe photon energies presented in Fig. 3. The TPA spectrum of Sr 2 Cu0 3 at 290 K is similar to that obtained at 10K4 and shows maximum TPA ~ 150 cm/GW at 2.1 eV. In the case of SrCu0 2 and Sr2Cu02Cl2, the peak positions of the TPA nearly coincide with their corresponding linear absorption maxima (cf. Fig. 1), indicating that the overlapping of the TPA and linear absorption bands is an intrinsic property of cuprates. In Sr2Cu03 and SrCu0 2 , the P is on the order of 100 cm/GW, and the width of the TPA band is about 0.5 eV, while in Sr2Cu02Cl2, the TPA coefficient is one order of magnitude smaller and the TPA band is broader. In particular, the low energy tail of TPA Sr 2 Cu0 2 Cl 2 continues down to 1.0 eV of ^pump + Wprobe, while the TPA coefficient in ID materials falls below 0.1 cm/GW at 1.5 eV.
160
n • •
A : Sr2Cu03 • A : SrCuO A :Sr2Cu02CI2
[]
C-120 O ~E 80 o
ea.
40 0 -
1.0
1.5
co0
pump
2.0 +00 +co .u (eV) probe
Fig. 3. TPA coefficient P versus w p u m p + a; p r o b e at 290 K in the three materials. Empty squares and triangles correspond to w p u m p = 1.31 eV and 0.95 eV, respectively, in Sr2CuC>3. Gray-filled circles, squares and triangles: U)pump = 1.46, 1.31 and 0.95 eV in SrCu0 2 - Black-filled squares and triangles: uJpnmp = 1.31 and 0.95 eV in Sr 2 Cu0 2 CI 2 .
3. Discussion As mentioned in the previous section, cuprates with both single and double Cu-0 chains show the TPA coefficient of the order of 100 cm/GW, which is one order of magnitude larger than that of conventional band semiconductors9. In contrast to ID materials, the 2D cuprate shows one order of magnitude weaker nonlinearity. Cluster calculation with 12 sites in the case of the cuprate with single Cu-O chains using the two-band extended Hubbard model reveals that the TPA enhancement in cuprates is associated with the large on-site Coulomb repulsion energy C/QU ~ lOeV, which gives rise to near degeneracy between one- and two-photon allowed states and a large overlap between the relevant wave functions4. This large overlap causes a large transition dipole between the one- and two-photon allowed states and enhances the nonlinearity. The calculation for the double-chain system gives qualitatively the same results. Though the calculation for the 2D system is underway, the relatively stronger nonlinearity and sharper TPA band for ID in comparison with 2D cuprates is explained using simple arguments based on the sum rules for nonlinear susceptibilities10. The dimensionality dependence of the optical nonlinearity has also been theoretically discussed in terms of "spin-charge separation"11.
64 Picosecond relaxation of the optical excitation in these materials is due to the presence of the optically silent spinon (in ID) 2 , 1 2 or magnon (in 2D) 8,13 states, which are gapless and exist 1 eV below the charge- transfer gap. The antiferromagnetic exchange interaction between electrons in the neighbouring sites, J ~ 2000 - 3000 K for S r 2 C u 0 3 and S r C u 0 2 2 ' 12 and J ~ 1400 K for Sr 2 Cu0 2 Cl 2 13 , gives rise to wide spinon and magnon bands, respectively. The relaxation via these states, whose energies are much larger than the phonon energy in band conventional insulators, promotes the relaxation of the optical excitation in cuprates. The origin of the slower component (T = 30 ps) of AaL in Sr 2 Cu0 2 Cl 2 is not clear yet, although one may notice that non-doped 2D cuprates YBa 2 Cu30 6 and N d 2 C u 0 4 have also shown similar two-component relaxation with comparable decay constants 14 . As we have shown above, ID cuprates show ultrafast large optical nonlineaity at room temperature. These properties are suitable for application to all-optical switching (AOS), which is a key technology for next-generation terabit/s communication 15 . To implement the AOS device in practice, nonlinear optical materials with not only strong third-order nonlinearity but also ultrafast ground-state recovery are required. Since the accumulation of real carriers formed by linear absorption and/or TPA degrades the nonlinearity and lowers the modulation depth in AOS, picosecond ground-state recovery at room temperature in I D materials, which is much faster than the typical relaxation of excitons in conventional semiconductors (~ 1 ns), makes these materials promising candidates to be employed in AOS devices in some terabit/s operation 4 . 4. Conclusion The strong nonlinearity of cuprates is related to the large on-site Coulomb repulsion, while the ultrafast ground-state recovery originates from the existence of a wide spinon or magnon band below the optical gap. These properties are typical in Mott insulators but absent in conventional band semiconductors. Hence, the interband two-photon transition in Mott insulators is a new mechanism for ultrafast optoelectronics. Larger optical nonlinearity due to the concentration of density of states and the absence of a slower decay component in I D systems make ID Mott insulators fascinating candidates for nonlinear optical materials in AOS applications. Acknowledgements We thank Y. Svirko for helpful discussions. This work was supported by a grant-in-aid for COE Research from the Ministry of Education, Science, Sports and Culture of Japan. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.
C. N. R. Rao and B. Raveau, Transition Metal Oxideds (Wiley-VCH, New York, 1995) M. Imada, A. Fujimori and Y. Tokura, Rev. Mod. Phys. 70, 1039 (1998). T. Ogasawara, et a/., Technical digest QELS'99, 119 (1999). T. Ogasawara, et at, Phys. Rev. Lett. 85, 2204 (2000). N. Motoyama, H. Eisaki and S. Uchida, Phys. Rev. Lett. 76, 3212 (1996). Y. Tokura, et ai, Phys. Rev. B 4 1 , 11657 (1990). C. Kim, et ai, Phys. Rev. Lett. 77, 4054 (1996). J. D. Perkins, et al., Phys. Rev. Lett. 7 1 , 1621 (1993). E.W. Van Stryland, M.A. Woodall, H. Vanherzeele and M.J. Soileau, Opt. Lett. 10, 490 (1985). F. Bassani and S. Scandolo, Phys. Rev. B44, 8446 (1991). Y. Mizuno, K. Tsutsui, T. Tohyama and S. Maekawa, Phys. Rev. B62, R4769 (2000). H. Suzuura, H. Yasuhara, A. Furusaki, N. Nagaosa and Y. Tokura, Phys. Rev. Lett. 76, 2579 (1996). J. Lorenzana and G.A. Sawatzky, Phys. Rev. Lett. 74, 1867 (1995). K. Matsuda et ai, Phys. Rev. B50, 4097 (1994). G.I. Stegeman and A. Miller, in Physics of all-optical switching devices in photonics in switching, ed. J. E. Midwinter, (Academic Press, San Diego, CA, 1993), vol. 1, chap. 5.
Optical Spectroscopy of Individual Photosynthetic Pigment Protein Complexes J. Kohler', A. M. van Oijen2, M. Ketelaars3, C. Hofmann4, M. Matsushita2, T. J. Aartsma1 and J. Schmidt2 'Department of Physics, University of Bayreuth, Universitatsstr. 30, 95447 Bayreuth, Germany, 2
Centre for the Study of Excited States of Molecules, Huygens Laboratory, 'Department of
Biophysics, Leiden University, P.O. Box 9504, 2300 RA Leiden, The Netherlands 4
Photonics and Optoelectronics Group, Department of Physics and CeNS, University of
Munich, Amalienstr. 54, 80799 Munich, Germany
Photosynthesis is the process by which plants, algae and photosynthetic bacteria convert solar energy into a form that can be used to sustain the life process. The light reactions occur in closely coupled pigment systems. The energy is absorbed by a network of antenna pigment proteins and efficiently transferred to the photochemical reaction centre where a charge separation takes place providing the free energy for subsequent chemical reactions. The total conversion process, starting with the absorption of a photon and ending with a stable charge separated state occurs within less than 50 ps and has an overall quantum yield of more than 90%. The success of this natural process is based on both the highly efficient absorption of photons by the light-harvesting antenna system and the rapid and efficient transfer of excitation energy to the reaction centre. It is known that most photosynthetic purple bacteria contain two types of antenna complexes, light-harvesting complex 1 (LH1) and light harvesting complex 2 (LH2) which both have a ring-like structure [1,2]. (Some bacterial species like Rhodopseudomonas acidophila contain a third light-harvesting complex termed B800-820.) The reaction centre (RC) presumably forms the core of the LH1 complex, while LH2 complexes are arranged around the perimeter of the LH1 ring in a two-dimensional structure. However the full threedimensional structure of the whole photosynthetic unit is as yet unknown. The absorption of a photon (mainly) takes place in the LH2 pigments followed by a fast transfer of the excitation energy to the LH1 complex and subsequently to the reaction centre. It appears that the whole structure is highly optimized for capturing light energy and to funnel it to the reaction centre [3-7].
65
66 McDermott et al. [1] have elucidated the structure of the LH2 complex of the bacterium Rhodopseudomonas acidophila by X-ray crystallography in great detail. The lightabsorbing pigments of LH2 comprise 27 bacteriochlorophyll a (BChl a) and 9 carotenoid molecules which are held in place by a protein framework. The BChl a molecules are noncovalently bound to these proteins. The special feature of the LH2 complex is that these molecules are arranged in two concentric rings slightly displaced with respect to each other along the common axis perpendicular to the plane of the rings, fig. 1. One ring consists of a group of nine well-separated BChl a molecules (B800) with an absorption band around 800 nm. The other ring consists of eighteen closely interacting BChl a molecules (B850), in near van der Waals contact, absorbing at about 850 nm. Interestingly the LH2 complex is highly symmetric with a nine-fold symmetry axis which coincides with the cylindrical structure of the complex. The eighteen B850 molecules are oriented with the plane of the molecules parallel to the symmetry axis. In contrast, the B800 molecules have their plane aligned perpendicular to the symmetry axis (see fig. 1).
Fig.l: Arrangement of the BChl a molecules, yellow (B800), red (B850), in the LH2 complex of Rhodopseudomonas acidophila as determined by McDermott et al. [I]. Excitation of an isolated BChl a molecule by absorption of light involves a transition from the ground state to the first excited singlet state. The latter has an intrinsic lifetime of a few nanoseconds. Remarkably the assembly of BChl a molecules is able to transfer the excitation energy to the reaction centre in a time much shorter than this [8,9]. Energy transfer within the LH2 complex occurs from the B800 to the B850 molecules in less than 1 ps, while among the B850 molecules it is an order of magnitude faster. This has been observed as an ultrafast depolarization of the fluorescence on a 100 fs time scale [10-12]. The transfer of energy from LH2 to LH1 and subsequently to the reaction centre occurs in vivo on a time scale of 5 - 10 ps, i.e., very fast compared to the decay of an isolated LH2 which has a fluorescence lifetime of 1.1 ns. As yet there is no consensus about the details of the
67
mechanisms of the energy transfer process. The great difficulty to determine the various parameters that play a role in the description of the electronic structure of light-harvesting complexes and the process of energy transfer is the fact that the optical absorption lines are inhomogeneously broadened as a result of heterogeneity in the ensemble of absorbing pigments (see for instance fig.2 upper trace). In order to circumvent this problem we have applied single-molecule detection schemes to study the pigment protein complexes individually thereby avoiding ensemble averaging [13,14]. In fig.2, the fluorescence-excitation spectra of a single LH2 complex is compared with that of an ensemble of LH2 complexes. The two broad structureless bands at about 800 nm and 860 nm in the ensemble spectrum correspond to the absorptions of the B800 and B850 pigments respectively. 350-i
£50-
§00II)
fl50o i=ioo50o - l — . — , — . — i — . — i — . — , — . — i — . — i
780
800
820
840
860
880
900
Wavelength (nm)
Fig.2: Comparison of an absorption spectrum from an ensemble ofLH2 complexes (upper trace) and a fluorescence-excitation spectrum from an individual LH2 complex (lower trace). The vertical axis is valid for the lower spectrum, the ensemble spectrum is offset for clarity. When observing the complexes individually, the ensemble averaging in these bands is removed and remarkable new spectral features become visible. The striking differences between the two absorption bands can be rationalized by considering the intermolecular interaction strength J between neighbouring BChl a molecules in a ring and the spread in transition energies A. J is mainly determined by the intermolecular distance and the relative orientation of the molecular dipole moments. Variations in site energies, A, can often be attributed to structural variations in the environment of the BChl a molecules, leading to changes in the electrostatic interaction with the surrounding protein. If the ratio J/A is small it is expected that the excitations are mainly localized on individual BChl a molecules. If the
68 coupling strength J between the BChl a molecules is much larger than A the description should be in terms of delocalized excited-state wavefunctions with relatively short energy relaxation times. The analysis of our data yields that the first regime applies for the B800 pigments leading to excitations that are mainly localized on individual BChl a molecules [15]. In contrast the excitations of the B850 molecules have to be described as delocalized Frenkel excitons [16,17]. The presented model is in quantitative agreement with a theoretical study of the electronic excitations of such an aggregate [18].
Acknowledgement The authors thank J. Knoester (Groningen University, Groningen, the Netherlands) for sharing the results of his study with us prior to publication. We also thank D. de Wit for the preparation of the LH2 complexes and M. Hesselberth for assistance with the spincoating. This work is supported by the Stichting voor Fundamenteel Onderzoek der Materie (FOM) with financial aid from the Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO) and by the Volkswagen-Stiftung (Hannover).
References [I] G. McDermott, S.M. Prince, A.A. Freer, A.M. Hawthornthwaite-Lawless, M.Z. Papiz, R.J. Cogdell, and N.W. Isaacs, Nature 374(1995)517. [2] S. Karrasch, P.A. Bullough, and R. Ghosh, EMBO Journal 14 (1995) 631. [3] X. Hu, A. Damjanovic, T. Ritz, and K. Schulten, Proc. Natl. Acad. Sci. 95 (1998) 5935. [4] R.H. Austin, J.P. Brody, E.C. Cox, Th. Duke, and W. Volkmuth, Phys. Today 1997) 32. [5] V. Sundstrom, T. Pullerits, and R. van Grondelle, J. Phys. Chem. B 103 (1999) 2327. [6] V. Sundstrom and R. van Grondelle, in: R.E. Blankenship, M.T. Madigan, and C.E. Bauer (eds.), Anoxygenic Photosynthetic Bacteria (Kluwer Academic Publishers, Dordrecht, 1995) p. 350 [7] T. Pullerits and V. Sundstrom, Ace. Chem. Res. 29 (1996) 381. [8] V. Nagarajan and W.W. Parson, Biochemistry 36 (1997) 2300. [9] J.T.M. Kennis, A.M. Streltsov, T.J. Aartsma, T. Nozawa, and J. Amesz, J. Phys. Chem. 100 (1996) 2438. [10] J.T.M. Kennis, A.M. Streltsov, H. Permentier, T.J. Aartsma, and J. Amesz, J. Phys. Chem. B 101 (1997) 8369. [II] R. Monshouwer, I. Ortiz de Zarate, F. van Mourik, and R. van Grondelle, Chem. Phys. Lett. 246 (1995) 341. [12] H.-M. Wu, S. Savikhin, N.R.S. Reddy, R. Jankowiak, R.J. Cogdell, W.S. Struve, and G.J. Small,/ Phys. Chem. 100(1996)12022. [13] A.M. van Oijen, M. Ketelaars, J. Kohler, T.J. Aartsma, and J. Schmidt, Science 285 (1999) 400. [14] A.M. van Oijen, M. Ketelaars, J. Kohler, T.J. Aartsma, and J. Schmidt, Chem. Phys. 247 (1999) 53. [15] A.M. van Oijen, M. Ketelaars, J. Kohler, T.J. Aartsma, and J. Schmidt, Biophys. J. 78 (2000) 1570. [16] M. Ketelaars, A.M. van Oijen, M. Matsushita, J. Kohler, J. Schmidt, and T.J. Aartsma, submitted (2000). [17] M. Matsushita, M. Ketelaars, A.M. van Oijen, J. Kohler, T.J. Aartsma, and J. Schmidt, submitted (2000). [18]M.V. Mostovoy and J. Knoester,/ Phys. Chem. B, accepted (2000).
T H E O R Y OF E X C I T A T I O N - E N E R G Y T R A N S F E R P R O C E S S E S I N V O L V I N G O P T I C A L L Y F O R B I D D E N E X C I T O N STATES I N A N T E N N A S Y S T E M S OF P H O T O S Y N T H E S I S
KOICHIRO MUKAI * Electrotechnical Laboratory, 1-1-4 Umezono Tsukuba, Ibaraki, 305-8568, Japan SHUJI ABE Electrotechnical Laboratory, 1-1-4 Umezono Tsukuba, Ibaraki, 305-8568, Japan HITOSHI SUMI Institute of Materials Science, University of Tsukuba Tsukuba, Ibaraki, 305-8573, Japan The rate of excitation-energy transfer (EET) within the light-harvesting complex (LH) and from LH to the reaction center (RC) of photosynthetic purple bacteria is calculated, based on a formula for EET between molecular aggregates. We show that optically forbidden exciton states participate in EET processes through multipole EET interactions with the help of disorder. In the antenna systems of photosynthesis, high efficiency of energy transfer is implemented by these EET processes involving optically forbidden exciton states. 1. Introduction In the photosynthetic membrane of purple bacteria, the energy of light is captured by light harvesting complexes and transferred toward the special pair of bacteriochlorophylls (BChls) in the reaction center (RC) with extremely high efficiency. The photo-excitation of the higher band (B800) in the peripheral light harvesting complex 2 (LH2) is followed by rapid EET to the lower band (B850) in LH2 with time constants of 0.8 ps at room temperature and 1.3 ps at 77 K 1. The core light harvesting complex 1 (LHl) accepts the excitation energy from LH2 and transfers it to the RC. In Rhodobacter (Rb.) sphaeroides, these EET processes occur in ~ 5 ps and 30-40 ps, respectively 2 . The LH2 complex of Rhodopseudomonas (Rps.) acidophila is well known for its circular structure with 9-fold rotational symmetry 3 . In the protein matrix of LH2, BChls are packed to form two rings. One ring consists of loosely packed BChls, which correspond to B800. In another ring, B850, 18 BChls are closely packed with a distance of ~ 9 A between adjacent BChls. Although no 3D structural data of the LHl complex are available so far, several structural models are presented 4 ' 5,6 . According to these models, the LHl complex has a circular structure with closely packed BChls in it. It is believed that LHl encloses the RC. The detailed information of its structure, such as whether the LHl complex possesses rotational symmetry or not, is to be elucidated. The direct application of Forster's formula fails to explain these rapid EET processes between chromophore-protein complexes. In the formula, only the EET processes between optically allowed states are taken into account. In the LH2 complex, the luminescence spectrum of B800 has small overlap with the absorption of B850, from which small EET rate constant is derived according to Forster's formula. In molecular aggregates with rotational symmetry, such as LHl and LH2, the lowest exciton state is optically forbidden. But EET from this state plays important role in the primary processes in bacterial photosynthesis, as in the case of EET *E-mail: [email protected]
69
70 from LH1 to the RC. In the present work, we show that for EET between molecular aggregates with a small mutual distance, multipole interactions higher than the dipole-dipole interaction are of importance. Using the formula for E E T which takes into account these higher interaction terms, the EET rate from B800 to B850 in LH2 and the rate from LH1 to the RC are calculated for various temperatures. The obtained results agree well with the experimental data. 2. E E T within L H 2 and from LH1 t o t h e R C The EET rate between molecular aggregates is given by 7 ic = y / d £ T r < D > W A , D • IA(E) • WA)D • LD(E)
(1)
when the donor and the acceptor are, respectively, composed of Mr, and M A molecules. Here, W \ D is an M A X M D matrix whose i,j component represents the EET interaction between the ith electronic excited state in the acceptor (A) and the jth one in the donor (D). When the distance between the aggregates is not much larger than their physical sizes, as in the case of EET within LH2 and EET from LH1 t o the RC, the interaction between the donor and the acceptor is no longer approximated by the dipole-dipole interaction between their total transition dipoles. In this case, matrix elements of WA,D connecting optically forbidden states become significant due to higher-order interaction terms. LD(E) and IA(E) are an Mo- and an MA-dimensional square matrices spanned by electronic excited states in the donor and the acceptor, respectively. Matrix multiplication denoted by • can be performed on any basis set of excited states in the donor or the acceptor, including exciton states therein. EET processes between all the electronic states in the donor and the acceptor are summed up by taking a trace over electronic excited states in the donor (Tr' D '). IA(E) represents the density of exciton states (DOS) in the acceptor which is given by the imaginary part of the retarded Green's function for exciton 8 . For the k', k element, IA,k(E) = -\\mGm{E). LD(E)
is related to ID{E) defined similarly to IA{E), LD{E)
(2) as
= Be-0EID{E)
(3)
with (3 = (fcaT) -1 . B is a normalization constant. As mentioned in Section 1, in the B850 ring of LH2 and in the LH1 complex, BChls are closely packed. The small distances of BChls in these rings lead to large exciton transfer energy. Thus we start from excitonic picture in the calculation of the density of states (DOS) in the B850 ring and in the LHl complex. The following Hamiltonian is introduced, from which Green's function of exciton is obtained. H = He + .flph + #ex-ph
(4)
with He
=
Y,En(1lan+
E
Jmna\nan
#ph = £ ( * £ « ) i
(6)
n
tfex-ph = E [ ^ E 4 " » ( ^ + ^ ) ] i
(5)
n
(7)
71 He is the Hamiltonian for free excitons with the Qy-excitation energy En, which is regarded as independent of the site index n, being given by En = 12520 cm -1 . an and a* are annihilation and creation operators of an excitation at the nth site. The exciton transfer energy between the mth and nth BChls, Jmn, is given by the dipole-dipole interaction with a dielectric constant e = 1 and transition dipole moment \ftn\ = 7.1 Debye. Hph is the Hamiltonian for phonons arising from distortions of a protein matrix around each BChl. &£' is the annihilation operator of a phonon of the ith mode with energy Vi around the nth BChl. Phonon modes around a BChl are assumed to be independent of those around a different BChl, possessing the same continuous spectrum of 14. .ffex-ph describes interactions between an exciton and phonons around each BChl. Si is the coupling constant (called the Huang-Rhys factor) defined for each phonon mode and assumed to be independent of the site index n. Modulations of the exciton transfer energy coupling Jmn by phonons are neglected in the present paper. The exciton-phonon interaction iyex_ph is treated as a perturbation. Green's function for the full Hamiltonian is expressed in terms of the self energy S(E)
°W = E-H\s{Ey
W
S{E) is calculated numerically using the self-consistent second-order perturbation theory for exciton-phonon coupling. The distribution of phonon of energy f, and coupling constant Sj is derived from observed luminescence spectrum of a BChls in the antenna systems 9 . In the B800 ring of the LH2 complex, the distance of BChls is much larger than that in the B850: ~ 21 A between adjacent ones. The excitation in the B800 ring is regarded monomeric. L (E) in Eq.(l) reduces to the normalized luminescence spectrum LD(E) of a BChl monomer. In the absence of static disorder in the B850 ring and under the assumption of 18-fold rotational symmetry of the ring, self-energy takes diagonalized form and does not depend on the index of exciton states: angular momentum k. In this case, the EET rate from B800 to B850 is expressed as 8 K=ffdEj2W2kl£(E)L°(E).
(9)
LD(E) has the largest overlap with the fifth lowest peak (k = ±4) in the DOS of B850 which are optically forbidden. The obtained EET rates are dominantly ascribed to this overlap. Compared to this, the overlap of LP{E) with the peak of optically allowed states (k = ±1) is very small. In addition to exciton-phonon coupling, the effect of static disorder is taken into account as a perturbation and averaged Green's function is calculated to give a DOS of the B850 ring shown in Fig.l(A) 10. Static disorder broadens exciton DOS and increases the overlap of B800 with the DOS of B850, leading to larger EET rates: 1.2 ps at 4 K and 1.0 ps at 300 K. These values are in good agreement with the experiment in Rps. acidophila. In the temperature range from 77 K to room temperature, almost temperature independent EET with time constant of 30-40 ps takes place from the LHl complex to the RC of Rb.sphaeroides 2. As lowering temperature, population of excitation in LHl concentrates on the lowest exciton state. In the LHl complex with a perfect rotational symmetry, the lowest exciton state has no EET interaction with the special pair (SP) of the RC. This leads to the vanishing of EET at low temperatures, which contradicts to the observation. Disorder in the LHl complex breaks the rotational symmetry of the exciton wave function in the LHl ring and makes the EET from the lowest state of LHl to the RC possible. Thus for each single LHl complex, we take into account the effect of disorder and calculated exciton Green's function without the assumption of rotational symmetry. In this case, off-diagonal elements as well as diagonal ones of the self energy and Green's function are nonzero. In Fig.l(B), one of the calculated DOS for LHl is shown together with DOS of the SP of the RC. From the obtained DOS, the EET rate for each molecule is calculated by Eq.(l). Here IA(E) is the DOS of the RC, LD(E) is the DOS of LHl exciton weighted by Boltzman distribution.
72
(B)
CO
O D
11100
12000 13000 14000 11100 12000 13000 Energy (crrr1) Energy (cnrr1) Fig. 1. (A) Ensemble-averaged DOS of excitons in the B850 ring (solid line) and luminescence of B800 (broken line) at 300 K; (B) DOS of a single LH1 (solid line) and DOS of the SP of RC (broken line) at 300 K
14000
The EET rate is expressed as an ensemble average of the rate for each molecule. We obtained the rate of ~ 50 ps with weak temperature dependence in fair agreement with the experiments. 3. S u m m a r y We have shown that E E T from/to optically forbidden states are the origin of the fast EET observed in antenna system. There are two ways for forbidden states to participate in EET processes. One is the situation of small distance between donor and acceptor aggregates for which the EET interaction is not approximated by a dipole-dipole interaction. This is the situation in LH2. Another is utilization of disorder, which is the case of EET from LH1 to RC. We conclude that the role of circular structures of antenna complexes is to fix the chromophores at mutually close distances and produce exciton states in the ring. Through the exciton states, including optically forbidden ones, the energy of sunlight is transferred to RC with extremely high efficiency. References 1. Y. Z. Ma, R. J. Cogdell, T. Gillbro J. Phys. Chem. B 101,1087 (1997). 2. K.J. Visscher, H.Bergstrom, V. Sundstrom, C.N. Hunter, R. van Grondelle Photosynth. Res., 22 , 211 (1989). 3. G. McDermott, S. M. Prince, A. A. Freer, A. M. HawthornthwaiteLawless, M. Z. Papiz, R. J. Cogdell, N. W. lmacs,Nature 374, 517 (1995). 4. X. Hu, K. Schulten Biophys. J. 75, 683 (1998). 5. S. Karrash, P. A. Bullough, R. Ghosh, EMBO J. 14, 631 (1995). 6. C. Jungas, J.-L. Ranck, J.-L.Rigaud, P. Joliot, A. Vermeglio EMBO J. 18, 534 (1999). 7. H. Sumi, J. Phys. Chem. B, 103, 252 (1999). 8. K. Mukai, S. Abe, H. Sumi, J. Phys. Chem. B, 103, 6096 (1999). 9. T. Pullerits, F. van Mourik, R. Monshouwer, R. W. Visschers, R. van Grondelle, J. Lumin., 58, 168 (1994). 10. K. Mukai, S. Abe, H. Sumi, J. Lumin., 87-89, 818 (1999).
INTERACTING ELECTRONS IN PARABOLIC Q U A N T U M DOTS: E N E R G Y LEVELS, A D D I T I O N E N E R G I E S , A N D CHARGE DISTRIBUTIONS
MICHAEL SCHREIBER Institut fur Physik, Technische Universitdt Chemnitz, D-09107 Chemnitz, Germany JENS SIEWERT DMFCI, Universitd di Catania,I-95125 Catania, Italy THOMAS VOJTA Institut fur Physik, Technische Universitdt Chemnitz, D-09107 Chemnitz, Germany
We investigate the properties of interacting electrons in a parabolic confinement. To this end we numerically diagonalize the Hamiltonian using the Hartree-Fock based diagonalization method which is related to the configuration interaction approach. We study different types of interactions, Coulomb as well as short range. In addition to the ground state energy we calculate the spatial charge distribution and compare the results to those of the classical calculation. We find that a sufficiently strong screened Coulomb interaction produces energy level bunching for classical as well as for quantum-mechanical dots. Bunching in the quantum-mechanical system occurs due to an interplay of kinetic and interaction energy, moreover, it is observed well before reaching the limit of a Wigner crystal. It also turns out that the shell structure of classical and quantum mechanical spatial charge distributions is quite similar. 1. Introduction Nanostructured electronic systems like quantum wells, quantum wires, or quantum dots are one of the most active areas of research in todays condensed matter physics. On the one hand they are of fundamental interest, allowing the fabrication and investigation of artificial atoms, molecules and even solids with well-defined and highly adjustable properties. On the other hand, they are of immediate importance to applications, e.g. electronic devices. The problem of interacting electrons in a parabolic confinement potential is one of the paradigmatic examples in this field. It has attracted considerable attention recently, both from experiment and from theory. Experiments on parabolic quantum dots 1 have revealed peculiar properties of such systems, in particular the "bunching" of energy levels. This means that at certain gate voltages two or more electrons enter the dot simultaneously corresponding to a negative chemical potential. This is in contradiction to the picture of single-particle energy levels plus a homogeneous charging energy. To understand these properties, first a model of classical point charges in a parabolic potential was investigated. 2 It was found that the system displays a shell structure which is essentially independent of the type of interaction. However, the opposite is true for the addition energies: For Coulomb interaction the shell structure is nearly unimportant while a short-range interaction leads to fluctuations in the addition energies which can give rise to level bunching. The approximation of electrons by classical point charges becomes exact in the zero-density limit, but in the experiments 1 the density is rather high, and the system is likely to be in the Fermi liquid regime. Therefore a quantum-mechanical investigation is necessary. However, the interacting many-particle problem is not exactly solvable, and numerical calculations beyond the Hartree-Fock (HF) level are complicated since the dimension of the many-particle Hilbert
73
74 space grows exponentially with the number of particles. Recently, a multilevel blocking MonteCarlo method was used to investigate the crossover between the Fermi liquid and Wigner crystal regimes. 3 In this paper we investigate the problem of interacting electrons in a parabolic confinement using the Hartree-Fock based diagonalization (HFD) method 4 which is related to the quantum chemical configuration interaction approach. The paper is organized as follows: In section 2 we define the model Hamiltonian and describe our method, and the results are presented in section 3. 2. M o d e l and M e t h o d In the experiments the parabolic quantum dot is formed in the two-dimensional electron gas at a GaAs/AlGaAs interface. Thus, the confinement in lateral direction is very strong while the much weaker, approximately parabolic confinement in the layer is produced by a gate voltage. We model this situation by considering a system of electrons in two dimensions in a parabolic confinement interacting via a screened Coulomb potential (in the experiments screening is produced by the gate). The Hamiltonian reads
H = Y.jd2r^l{v)
ft2 d2
m
2
2
iMr)
2e-AT„|r-r'|
+
oE
/ d\d\'i,\(r)^,(r')e
\ _
Mr>g(r) •
(1)
The problem contains three length scales, the oscillator length scale, l0 = (h/muj)1/2, the Bornradius of the host, a 0 = h2e/me2, and the screening length, KQ1. Rescaling all lengths by Z0, and defining a = l0/a0, k0 = Kolo leads to Id2 h 2dr2 1 r ^ 3E/rfVrf2r>t(r)V)t((r0
H = Wd 2 rV4(r) +
1 ,' - r ^V(r) 2 n P -*o|r-r'| tMr')Vl(r).
(2)
A value of a = 0 corresponds to non-interacting electrons, experimentally realistic values of a are around 1...10. A numerically exact solution of this quantum many-particle system requires the diagonalization of a matrix whose dimension increases exponentially with the number of particles in the dot. This severely limits the possible particle numbers. In order to calculate the properties of this model we therefore use the HFD method. 4 The basic idea is to work in a truncated Hilbert space consisting of the HF ground state and the low-lying excited Slater states. For each disorder configuration three steps are performed: (i) find the HF solution of the problem, (ii) determine the B Slater states with the lowest energies, and (iii) calculate and diagonalize the Hamiltonian matrix in the subspace spanned by these states. The number B of basis states determines the quality of the approximation, reasonable values have to be found empirically. For the results reported here we have worked in a plane wave basis with up to 961 fc-points. This leads to accurate results for non-interacting electrons, the relative energy error is smaller than 10~ 9 for up to 20 electrons and smaller than 10~ 6 for up to 50 electrons. The truncated many-particle Hilbert space used in the HFD method consisted of up to B = 4000 Slater states. 3. R e s u l t s We have first carried out calculations for classical point charges (which corresponds to neglecting the gradient term in eq. (2)). Here the ground state is determined simply by minimizing the total energy with respect to the positions of the point charges in the dot. Figure 1(a) shows
75
••
0.8 Bunching: ji goes down with increasing N
1
»..-•
•• •• •
•
••
• |
•
• • •
t
screened Coulomb interaction 1 a=2, ko=10 J
(a) 5
•
• •
•
• . . • • • • . • . • • • . •
• .
• •
• •
• •
• • • • • •
•.v. • -
• • . • •. •
(b) 10 15 20 number N of electron entenng the dot
25
Fig. 1. (a) Addition spectrum for a system of classical point charges, (b) Real space configurations of the charges, the upper two configurations for 12 and 19 electrons are for unscreened interaction ( a — 4,fcrj= 0), the lower two are for a = 4 and kg = 1.
the resulting addition energies fj.^ — E^ — £jv-i and the corresponding configurations of the point charges in real space. While fi^ generally increases with N, it decreases for some N. If HM > (J-N+i two electrons will enter the dot simultaneously if the gate voltage reaches fiN, i.e. the system shows bunching. Figure 1(b) shows the sensitivity of the real space configurations to screening by comparing the charge configurations for screened and unscreened interactions. It is, clear that the kinetic energy term in the Hamiltonian which was neglected in the classical calculations will have a tendency to suppress the energy fluctuations connected with different real space configurations. As a first check we compare the radial charge densities of the classical and quantum-mechanical calculations in Figure 2. For the classical case the point charges are replaced by Gaussians whose width is half the minimum particle distance. The qualitative shell structures of the two systems are very similar. The kinetic energy leads to a slightly wider charge cloud in the quantum case.
unscreened, a=4, ko=0 —•— quantum --©--• classical screened, cc=4,1^=1 —*— quantum —*— classical
Fig. 2. Comparison of the classical and quantum-mechanical results for the radial charge densities for a quantum dot with 12 electrons, full spin-polarized case, 5 = 6 .
76
•# 8 HI
7
.•
11
tia
i Is
•
R
o m
s
I
4
_
•
•
.•
• ••
screened Coulomb interaction 1 o=2,ko=1 |
3 5
10 15 20 number N of electron entering the dot
Fig. 3. Addition energies for the quantum-mechanical case, Ot = 2, JCQ = 1, spin-polarized case, S=N/2.
In Figures 3 and 4 we present the addition energies and the radial charge distribution for quantum-mechanical electrons in the fully spin polarized case S = N/2, respectively. The parameters a = 2 and k0 = 1 are chosen to roughly correspond to the experiments1 while the number of electrons we simulate in the dot is almost one order of magnitude smaller. Figure 4 shows, that the charge distribution in the dot sometimes completely reorganizes when an electron is added. However, the fluctuations in the ground state energies caused by these reorganizations are not strong enough to lead to bunching as can be seen from Figure 3. The addition energies are rather dominated by the single-particle levels which possess the degeneracies due to rotational symmetry. However, if the interaction becomes larger, bunching can be observed already for the small electron numbers accessible in our simulation, as can be seen from Figure 5. For a direct comparison of our results with the experiment our calculations have to be
1.5
2 2.5 radius r
Fig. 4. Radial charge distribution for the quantum-mechanical case, a •• ko = 1, spin-polarized case, S=N/2.
77 v-+
9
LU
chemica potential
z LU II z
Bunchir
8
••
7
• 6
•
5 4
•
•. • screened Coulomb interaction 0=32,1*0=4
3 numbeT N of electron entering thVdot
Fig. 5. Addition energies for a quantum-mechanical dot with strong interactions, full spin-polarized case
extended to larger electron numbers. Furthermore, the spin degrees of freedom which have been suppressed in our calculations so far, probably play an important role. In particular, the spin structure will also change with increasing particle number. This leads to larger fluctuations in the ground state energy and enhances the possibility of bunching. Investigations along these lines are underway. Acknowledgements This work was supported in part by the German Research Foundation under Grant No. SFB393. References 1. 2. 3. 4.
N.B. Zhitenev, R.C. Ashoori, L.N. Pfeiffer, and K.W. West, Phys. Rev. Lett. 79, 2308 (1997) A.A. Koulakov and B.I. Shklovskii, Phys. Rev. B 57, 2352 (1998) R. Egger, W. Haeusler, C.H. Mak, H. Grabert, Phys. Rev. Lett. 82, 3320 (1999) T. Vojta, F. Epperlein and M. Schreiber, Phys. Rev. Lett. 81, 4212 (1998); Computer Phys. Commun. 121-122, 489 (1999).
R E T R I E V E D A N I S O T R O P Y OF O N E - D I M E N S I O N A L CRYSTAL PIPERIDINIUM TRIBLOMOPLUMBATE
JUNPEI AZUMA and KOICHIRO TANAKA Department of Physics, Kyoto University Kyoto 606-8502, Japan Polarization characteristics of luminescence in one-dimensional crystal piperidinium tribromoplumbate has been investigated to clarify the relaxed photo-excited states of this system. It has been observed that the emission band with non-exponential decay is almost depolarized at 10 K but becomes polarized drastically parallel to the chain as temperature is raised above 15 K. This indicates that anisotropy of the initial state of luminescence retrieved thermally. Electron spin resonance (ESR) technique has been applied to identify photo-induced defects. A hole center formed by several bromine ions has been observed. The initial state of this emission band is discussed from the retrieved anisotropy and the ESR measurements. 1. Introduction Piperidinium triblomoplumbate C5H 10 NH 2 PbBr3 (abbreviated as PLB hereafter) is well known to have a self-organized one-dimensional (ID) structure; [PbBre] octahedra connect to each other by sharing their faces to form ID [PbBr 3 ]^" chains. 1,2 The piperidine cations, which connect two adjacent chains, isolate them from each other. LCAO calculation in this system shows that the valence band mainly consists of the bromine 4p orbitals. 3 The conduction band is originated from the lead 6p orbital. The piperidine cation is transparent in the lowest transition energy of the [PbBrs]^ chain. This means that the electrons connected to the lowest transition are well confined within the chain. Figure 1(a) shows polarized absorption spectra at 15 K obtained by the Lorentz oscillator analysis from the polarized reflection spectra. The absorption spectra show strong anisotropy reflecting the anisotropy of the electronic structure. A strong absorption peak is observed at 3.87 eV. This peak is ascribed to the lowest exciton in [PbBr 3 ]^" chains. There is an absorption band around 4.5 eV, which corresponds to the band-to-band transition responsible to the lowest exciton. 4 Two luminescence bands are observed at 2.98 eV and 1.85 eV with large Stokes-shifts and broad bandwidths below 30 K under excitation into the intrinsic absorption region. These emission bands are denoted as V emission and R emission, respectively. Excitation spectra of two emission bands are shown in Fig.1(b). It can be seen that V emission is most stimulable in the exciton region and R emission becomes dominant to V emission in the band-to-band transition region. This means that the initial state of V emission is formed directly from free exciton whereas R emission from free electron-hole pair. The initial state of V emission (V state) is assigned to self-trapped exciton (STE) localized at the lead site distorting the [PbBre] octahedra. It should be noticed that R emission exhibits a non-exponential decay upon pulse excitation, which indicates that electrons and holes are randomly distributed and recombine each other via hopping motions. These electrons and holes are considered to be negative and positive small polarons, which should be separately localized at the lead and the bromine sites, respectively. These pair-annihilation of polarons are frequently observed in other ID systems. 5,6 As temperature is raised above 30 K, the intensity of V emission decreases and that of R emission alternatively increases with activation energy of 35 meV. Detailed experiments of the thermal stabilities revealed that the initial state of R emission (R state) is different type of STE from the V state, which has been probably ascribed to a charge-separated STE. 4 In this study, the polarization characteristics of the luminescence bands have been investigated in the wide temperature range. The polarization characteristics of an emission band
78
79
Photon Energy (eV) Figure 1: (a): Polarized absorption spectra of C 5 H 10 NH2PbBr3 at 15 K. (b): Excitation spectra of 2.98 eV and 1.85 eV emission bands (V emission and R emission, respectively). should be related to the symmetry of the relaxed excited state. We found that V emission and R emission are almost depolarized at 10 K. The anisotropy of R emission is retrieved when temperature is raised above 15 K. The initial state of R emission is discussed from the retrieved anisotropy and the ESR measurement of the photo-induced defects. 2. Experimental PLB complex is synthesized from piperidine hydrobromide and lead bromide in dimethylformamide. Columnar single crystals were grown in 2-3 weeks by evaporating the solvent slowly at room temperature. Typical sizes of crystals are 1.0x1.0x7.0 mm 3 . The X-ray diffraction measurement shows the chain axis (b-axis) is parallel to the major axis of the columnar crystal. Reflectivity and luminescence excitation measurements were performed at the beam line BL-lB in the synchrotron facility, UVSOR (Japan). Luminescence spectra were obtained by a single polychromator with a CCD detector cooled by liquid nitrogen. In the ESR measurement of the photo-induced defect, second harmonics of the regenerative amplified Ti:sapphire laser was injected into the ESR cavity to make in-situ defect formation at low temperature. The average power, pulse width and repetition rate of the second harmonics are 250 mW, 120 fs, and 1 KHz, respectively. Thermo-luminescence from the sample in the ESR cavity was guided in the optical fiber by the quartz rod for sample fixation in the capillary tube of ESR and monitored by the photo-multiplier. 3. Result and Discussion 3.1. Polarized
luminescence
Figure 2(a) shows polarized luminescence spectra at 10 K and 61 K. V emission and R emission are almost depolarized at 10 K in contrast with the anisotropy in the absorption spectra. It is
80 C5H10NH2PbBr3 Exc. = 4.19eV(E//b) T = 10K
"k
(b) Exc. = 4.19 eV(E//b) « 2.98 eV » 1.85 eV
ss o
1 °-4-
• E_Lb T = 61K E//b
8
'AV1 w 1.5
0.5-
2.0
»__
•a
•3 0.3OH O
••'/
i> 0.2-
/
*—
»»>- «
3.0
A
«-
Q o.i-
^. v^v 2.5
«-*—» A
^
0.03.5
10
15
20
25
30
35
40
45
Temperature (K)
Photon Energy (eV)
Figure 2: (a): Polarized luminescence spectra of C5H 10 NH 2 PbBr3 at 10 K and 61 K. (b): Temperature dependence of the degrees of polarization. (Solid lines are guides to eyes.) clear that V emission is slightly polarized and R emission is almost depolarized at 10 K. But the polarization of R emission comes to be retrieved at 61 K. The degrees of polarizations of the luminescence bands for the chain axis (b-axis), defined as P(u
(-TE||6 -
*)
{lE\\b + lELb)
(1)
are 0.14 for V emission and 0.03 for R emission band at 10 K. It should be noted that these degrees of polarization are independent of the polarization of excitation light. Figure 2(b) shows the temperature dependence of the degree of polarization. The degree of polarization for V emission is almost kept constant up to 30 K until V emission is quenched. On the contrary the degree of polarization for R emission gradually increases from about 15 K and becomes saturated at 0.35 around 30 K, while this band is completely depolarized at 10 K. This thermally retrieved anisotropy suggests that R state actually has an anisotropy. A thermal transfer model described below can explain this mysterious retrieved anisotropy: R state would have several equivalent configurations with different lifetimes, which transition dipoles are tilted against the ID chain. Below 15 K these configurations are randomly occupied to give rise to statistically depolarized luminescence. Above 15 K, polarized luminescence is selectively emitted from some specified configurations with shorter lifetimes by the thermal transfer. Such polarization nature is not observed for V emission. This indicates that the initial state of V emission is really an isotropic state. 3.2. Electron
spin resonance
of photo-induced
defect
It is important to investigate the defect structure in order to imagine the initial state of luminescence. ESR measurement has been performed to the photo-induced defect created by two-photon excitation at 4.2 K. Two signals of photo-induced defects are observed around 3100 Gauss and 4900 Gauss. The ESR spectrum around 3100 Gauss is shown in Fig.3(a). The signal around 3100 Gauss consists of a series of peaks over 12 which should be splitting by the hyperfine interaction. The lead atom with 22 % natural abundance has a nuclear spin of 1/2 and the bromine atom with 100 % natural abundance has a nuclear spin of 3/2. If the hyperfine interaction is originated from the lead nuclear spin, the intensity of the hyperfine structure out of the center of the spectrum becomes very weak because of the natural abundance of the lead isotope. Therefore, the hyperfine structures around 3100 Gauss is originated from the several
81
2600
2800
3000
3200
3400
3600
Magnetic Field (Gauss) Figure 3: (a): Photo-induced ESR spectra of C 5 HioNH2PbBr 3 at 25 K. Two spectra with different angles of applied magnetic field are shown in this figure. The definition of the angle <j> is depicted in Fig.(b). (b): Shematic model of the V* center configurations in one-dimensional chain. bromine ions. These hyperfine structures appear only at the several specified angles of the applied magnetic field and disappear at slightly different angles. This indicates that there are several equivalent configurations for the defect and the hyperfine structures of each configurations enhance each other by spectral overlapping at the specified angles. This defect center should be a hole-trapped center because almost all the bromine atomic 4p orbitals contributes to the valence band. 3 As temperature is raised above 70 K after the photo-induced defect formation, thermally stimulated luminescence (thermo-luminescence) appears at the same position of R emission. To investigate the relation between thermo-luminescence and the ESR signal of the bromine center, pulse-annealing technique was applied. The total integrated intensity of the thermoluminescnece and the integrated intensity of ESR signal around 3100 Gauss are shown in the Fig.4. It can be seen that luminescence is thermally stimulated around 80 K where the
S3
"to
8
a 0 20 40 60 80 100 Temperature of pulse annealing (K)
120
Figure 4: Total integrated intensity of thermo-luminescence obtained by the pulse annealing and the intensity of ESR signal around 3100 Gauss in C5rIioNH 2 PbBr 3 . The ESR signal have been measured at 4.2 K after each pulse-annealing. ESR signal decreases complimentarily. The signal of 4900 Gauss also decreases after the pulse-
82 annealing. This indicates that the trapped electrons of 4900 Gauss signal are thermally released and recombine with the bromine centers to emit R emission. V& center (BrJ" dimer) is the most probable candidate for the bromine hole-center with several equivalent configurations mentioned above: Two types of V* center can exist in the ID chain as shown by labels of I and II in Fig.3(b). One type of V* center exists between the two consecutive lead ions (type I). Other type is at the surrounding position of the ID chain (type II). Electrons should be trapped at the lead site because the conduction band is originated from the lead 6p orbital parallel to the chain. If it is assumed the recombination between the lead electron-center and bromine hole-centers, the transition probability of type I center should be smaller than that of type II center because the wave function of type I center is almost orthogonal to the chain. Direction of transition dipole for type I center is perpendicular to the chain and that of type II center is tilted to the chain. It is likely that the type I and type II centers are randomly occupied at 10 K and the recombination luminescence is statistically depolarized. Above 15 K, the transfer between these centers is thermally activated and the luminescence is emitted selectively from the type II center, which leads to the retrieved anisotropy of this one-dimensional system. 4. Conclusion Polarization characteristics of V emission and R emission have been investigated. V emission is a depolarized luminescence. It is strongly suggested that the V state should be one-center STE localized at the Pb site. R emission is also depolarized luminescence at 10 K. It is confirmed that the anisotropy of R emission is retrieved drastically above 15 K. This behavior can be explained by the thermal transfer between the several equivalent configurations with different lifetimes and tilted polarization against the chain. It is important that each configuration should be anisotropic. These results support that the R state should be a charge-separated STE. ESR measurement of the photo-induced defects shows that holes are trapped at the center which consists of several bromine ions. The most probable candidate of this center is a Vt center (Br^ dimer). Thermo-luminescence measurement suggests that the charge-separated STE consists of the bromine hole-center. If it is assumed that the charge-separated STE is a nearest neighbor pair of the V& center and an unknown lead electron-center, the retrieved anisotropy can be understood by the hopping motions between the type I and type II configurations of the Vt, center. Acknowledgements The authors are grateful to Prof. K. Kan'no for fruitful discussion. One of the authors (J.A.) was partly supported by a Grant-in-aid from the Venture Business Laboratory in Kyoto University (Japan). This work was supported by the Joint Studies Program(1997-1998) of UVSOR in the Institute for Molecular Science (Japan). References
1. 2. 3. 4. 5. 6.
G. V. Gridnova et a/., Doklady Akademii Nauk, 278, 414 (1984). A. B. Corradi et al, Inorg. Chim. Acta. 254, 137 (1997). J. Azuma, K. Tanaka, K. Kamada and K. Kan'no, (submitted to Phys. Rev. B). J. Azuma, K. Tanaka and K. Kan'no, (submitted to Phys. Rev. B). H. Ooi, M. Yamashita and T. Kobayashi, Solid State Commun. 86, 789 (1993). Hyo Soon Eom et al., Appl. Phys. Lett. 71, 563 (1997)
SPECTRAL EFFECTS OF MICROSCOPIC AND MESOSCOPIC DISORDER IN ORGANIC FILMS — MODEL CALCULATIONS PIOTR PETELENZ, MARCIN ANDRZEJAK, ANDRZEJ EILMES Faculty of Chemistry, Jagiellonian University, Ingardena 3, 30-060 Cracow, Poland E-mail: petelenz@chemia. uj. edu.pl Effects of microscopic orientational disorder on electro-absorption of charge-transfer (CT) states in the high-temperature phase of the C«> crystal are simulated on a cluster consisting of 108 molecules. The results suggest that this kind of disorder may be successfully modeled in terms of an effective crystal with full translational symmetry. Mesoscopic disorder is simulated for thin films of sexithiophene. The spectral broadening observed in absorption is attributed to the non-analyticity of the calculated dipole sums at k=0, resulting in their dependence on crystallte orientation with respect to incident radiation.
1. Introduction It is commonly observed and intuitively expected that the spectra of films are broader and less structured than those of single crystals; this is attributed to the disordered nature of film samples. In a molecular system, two limiting models of the disorder may be envisaged. One of the extremes is represented by a mesoscopically disordered set of microscopically ordered crystallites. On the other extreme, the disorder is microscopic: the arrangement of individual molecules is highly random, so that even the short-range order of the crystal is wiped out. In actual samples both kinds of disorder are expected to coexist. In order to be able to model this latter situation in the future, one has to be sure that at least the limiting cases are correctly described. This is the objective of the present paper. The situation is simple as long as the transition is intense and the disorder is microscopic; then it is immediately seen that the absorption bands must be inhomogeneously broadened. For two dipoles at a fixed distance the interaction energies of the end-on and side-on configurations differ by the factor of two; in effect, broadening of this magnitude may be introduced by orientational disorder alone. In reality, intermolecular distances may also vary, leading to a further variation of the energies. For intramolecular excitations endowed with large transition dipole moments, the resultant width may be substantial. There are two less obvious limiting cases. Firstly, for a weak transition (e.g. to a CT state) superficial scrutiny would generally suggest negligible broadening. Yet, in some contexts (electroabsorption, or EA, spectroscopy) even this minor broadening may be essential and require a reliable theoretical description. This situation is encountered in fullerene. Secondly, when the disorder is mesoscopic, it might seem that even for a strong transition the broadening should also be marginal, since the spectra should be dominated by the molecules located in the bulk of the crystallites, for all of which the local surroundings are the same. This expectation is in conflict with the observed spectra of sexithiophene thin films. The present paper deals with these two unusual cases. 2. CT States in Fullerene The main difference between the cases cases of mesoscopic and microscopic disorder consists in the fact that in the former case the wavevector is a reasonably good quantum number, whereas in the latter case it is not: there is no translational symmetry and the environment of each molecule is different. Paradoxically, these two extremes tend to meet in the room-temperature phase of the fullerene crystal. While the molecular centres form in this phase a very well defined (cubic) lattice with a period differing only marginally from that observed for the ordered low-temperature phase, the rotational disorder is practically complete, with only marginal correlation between the 83
84 orientations of neighbouring molecules. The complete lack of information regarding the orientation of individual molecules, combined with their symmetric shape, tempt one to view the molecules as spherical. In the spirit of the mean-field approximation, the disordered crystal is then represented by its hypothetical counterpart endowed with full translational symmetry, where the wavevector is again a good quantum number. Owing to the high symmetry of the fullerene molecule, this approximation barely affects the manifold of Frenkel states. However, the couplings in the CT manifold are governed by intermolecular overlap integrals which critically depend on the relative phase of the molecular wavefunctions and must be sensitive to the relative orientation of the interacting entities. In order to probe the possible deviations of the orientationally disordered C6o phase from the behaviour predicted for an effective ordered crystal, we studied the disorder effects on a model cubic cluster1 consisting of 108 molecules (with periodic boundary conditions). Conforming to the argument presented above, the disorder was assumed to be orientational, complete and purely offdiagonal, affecting exclusively the overlap-dependent charge transfer (CT) integrals. The orientations of the molecules were determined by a random draw, and the CT integrals were calculated numerically; other matrix elements, being orientation-independent, were assumed the same as for the ordered crystal. Subsequently, the model Hamiltonian (of Merrifield type) was constructed and diagonalized to yield the eigenstates. The procedure was performed at non-zero and at zero external electric field to generate the electro-absorption (EA) signal as the difference between the corresponding absorption spectra. The results were averaged over several random trials and over a random set of orientations with respect to the external electric field. We have focused on the (EA) spectra since the disorder in C6o affects primarily the exciton states of CT parentage, barely discernible in absorption spectroscopy, and since some time ago similar calculations performed within the model of effective crystal with complete translational symmetry2 very well reproduced the experimental EA spectrum.3 Our present results indicate that explicit inclusion of microscopic rotational disorder produces no dramatic changes. Qualitatively, the general shape and amplitude of the spectrum is similar. In the most prominent feature of the spectrum, namely the low-energy maximum followed by a double minimum in the 2.5-2.8 eV range (attributed to the nearest-neighbour HOMO-to-LUMO CT states, split by the off-diagonal interactions ), the second minimum becomes somewhat deeper. More interestingly, the energy separation between the two minima (previously underestimated) increases from 0.16 to about 0.20 eV, improving the agreement with experiment. This latter effect may probably be attributed to problems with defining the averaged values of the CT integrals for the effective ordered crystal. The EA spectrum depends primarily on the splittings of the eigenstates, governed by these integrals. The distribution of (random) relative orientations of the molecules gives rise to a distribution of the CT integrals. This distribution is centred at zero, so that the mean value is no measure of the actual splittings which are not sensitive to the sign of this matrix element. An effective value may be defined based e.g. on the width of the distribution or on its dispersion etc.; alternatively, some parameters characterizing the distribution of the absolute values of the integral may be used. Any choice is to some extent arbitrary, since there does not seem to exist a unique mapping of the disordered crystal properties onto the properties of the effective ordered crystal. This ambiguity is reflected in some latitude in the choice of the effective parameters and might justify their values larger from those used so far. If larger values of the CT integrals were adopted, a larger splitting between the low-energy minima would be easily obtainable within the ordered-crystal model. By and large, the description of the high-temperature fullerene phase in terms of an effective model endowed with full translational symmetry is remarkably successful. The effects of explicit inclusion of microscopic orientational disorder are somewhat trivial and may be effectively included by readjusting the transfer integrals and adopting larger widths for individual levels. This is probably a consequence of the high symmetry of the fullerene molecule and of the fullerene lattice, combined with the fact that the molecular symmetry axes do not coincide with the symmetry axes of
85 the site group. The actual level structure results from concerted shifts due to the interaction of the CT states deriving from the different degenerate HOMO (five) and LUMO (three) components and engaging different neighbours of the molecule in hand. Apparently, the sampling of a molecular orbital by the directions from a given molecule to its twelve nearest neighbours is dense enough to be statistically representative; the effect is strengthened by orbital degeneracy (15 components per CT state). Accordingly, even in the ordered crystal the CT integrals are effectively averaged, and the orientational disorder affects this situation only to a minor extent. This interpretation is supported by the temperature dependence of the fullerene EA spectra4 where no dramatic change is observed at the phase transition. Consequently, it is difficult to generalize the above conclusions for other cases. It might seem that for less symmetric systems the averaging would be less effective and the fluctuations should be spectrosocpically more discernible. On the other hand, for lower symmetry the smaller number of equivalent contributions would produce smaller net splittings between different CT eigenstates, and the response of individual levels to disorder would be hidden in the spectral width of the corresponding transitions. 3. Mesoscopic Disorder in Sexithiophene In classic cases (as polyacenes) the absorption spectra of thin films resemble those of the corresponding molecules in solution and, apart from poorer resolution, do not differ drastically from those of the corresponding single crystals. The recently studied crystal of sexithiophene5 (aT6) does not conform to this picture: the absorption spectra of the films used for EA experiments are essentially structureless and the entire low-energy absorption spectrum practically reduces to a single broad band; no vibronic structure is discernible. Abundant experimental evidence demonstrates that thin sexithiophene films are composed of well defined crystallites of the size ranging from tens of nanometers to micrometers. In effect, the disorder is mesoscopic rather that microscopic. This suggests a different mechanism of the observed broadening. In the crystal, the energies of exciton eigenstates are governed by Ar-dependent lattice sums representing the joint effect of the interaction between transition dipoles located at different molecules. At the centre of the Brillouin zone the part of the sums which is due to the macroscopic polarization of the crystal depends on the direction of the wavevector k, and so do the corresponding eigenenergies. In absorption spectroscopy, the wavevector of the probed eigenstates is the same as that of probing photons. It follows that the energies of observed absorption bands depend on the orientation of the crystal with respect to incident radiation. For the lowest exciton state of the sexithiophene crystal, exhibiting a large oscillator strength (/=0.67, corresponding to the transition dipole moment of 1.76 eA, cf. Ref. 6), the resulting energy shifts are likely to be substantial. We have tested the above hypothesis by evaluating the lattice sums by the Ewald method7'8 which allows one to split a lattice sum into the analytic part (the so-called Lorentz factor tensor) and the non-analytic direction-dependent part kkl^. Subsequently, we calculated the Frenkel eigenstates and the absorption spectra for different crystallite orientations, and weight-averaged the results to account for the disorder. The films of sexithiophene are polycrystalline, with a tendency of individual crystallites to have their long crystal axis set normal to the substrate,9"'4 although considerable deviations from this orientation are observed. There is no preference in the angular orientation around the normal to the surface. Hence, we simulated the disorder in the films by adopting a Gaussian type probability function of the angle 6 (in the spherical coordinates), characterized by the Gaussian width o=15°. Vibronic satellites were included in the limit of weak vibronic coupling, with the necessary input parameters estimated from the absorption spectrum of matrix-isolated sexithiophene. Fig. 1 shows the calculated absorption and electro-absorption (EA) spectra of the sexithiophene single crystal (for unpolarized light propagating perpendicular to the be plane) and the spectrum of a disordered sample, simulated as described above. The experimental spectra of a thin film" are also displayed.
86 2.5e+05 S -
2e+05
S _o
1.5e+05
I
le+05
<
50000
^
40000
•u
8 5 & p "J
-20000
•o
-40000
|°
20000 0
16000
18000 20000 22000 24000 26000 28000 3C'<00
U Wavenumber, I/cm Fig.l. Experimental absorption (upper panel) and electro-absorption (lower panel)) spectra of the sexithiophene thin film" (solid line); simulated spectra of the T6 single crystal (dotted line) and of a disordered sample (broken line).
It is readily seen that the averaging over crystallite orientations does result in serious broadening of the absorption spectrum; it also gives rise to a long low-energy onset. The obtained diffuse, structureless shape roughly resembles that observed experimentally. Because of the inherent limitations of the applied model, it is pointless to compare the details of the theoretical spectrum with those of the experimental one. In fact, the experimentally observed low-energy peak is due to vibronic intensity transfer from the intense upper to the forbidden lower Davydov component, mediated by the out-of-phase combination of the intramolecular 1500 cm"' vibrations of the different molecules contained in the unit cell. This intensity borrowing, analogous to that described previously for the low-energy vibrations,16 is not included in the present simplistic model, focused on other effects. The asymmetric broad shoulder observed on the low-energy side of the film spectrum is probably due to the CT states, located just in that energy range.15'1 It is also worth noting that the orientational disorder practically affects only the position of the high-energy Davydov components, which is consistent with the fact that some structure is observed in the lowenergy region of the experimental spectrum. In our opinion, the results confirm the conjecture that the orientationally disordered texture of sexithiophene films allows one to rationalize the observed diffuse, structureless shape of the absorption spectrum. However, in smaller crystallites other broadening mechanisms are also expected to be operative. As the k=Q selection rule is only approximately satisfied, the exciton states from other parts of the Brillouin zone are expected to contribute to the spectrum, further smearing out its structure, as reported for instance for anthracene.1 Inclusion of disorder effects is of critical importance for correct reproduction of the EA spectra. As the EA spectrum is a differential signal, the trivial broadening of the absorption spectrum translates in electro-absorption into a major change of the intensity (amplitude). In this respect, the microscopic and mesoscopic disorder affect the spectrum in a similar way. For sexithiophene,
87 where the disorder-induced broadening is considerable, it reduces the amplitude of the EA signal by an order of magnitude, as shown in the left panel of Fig. 1. This explains why the Frenkel states barely contribute to the EA spectrum of aT6 in spite of their large absorption intensity, so that the EA spectrum is dominated by the CT states which, owing to their small transition dipole moment, are practically immune to the broadening mechanism discussed above. Acknowledgements This research was supported by Grant No 3T09A 125 15 from the Committe for Scientific Research (Poland). References 1. A.Eilmes and P.Petelenz, Chem. Phys. 237, 67 (1998). 2. B. Pac, P.Petelenz, A.Eilmes and R.W. Munn, J. Chem. Phys. 109, 7923 (1998). 3. B. Pac, P.Petelenz, M.SIawik and R.W.Munn, J. Chem. Phys. 109, 7932 (1998). 4. S.Kazaoui, N.Minami, Y.Tanabe, H.J.Byrne, A.Eilmes and P.Petelenz, Phys. Rev. B58, 7689 (1998). 5. M.Muccini, E.Lunedei, C.Taliani, D.Beljonne, J.Cornil and J.L.Bredas, J. Chem. Phys. 109, 10513 (1998). 6. D.Oelkrug, H.-J.Egelhaaf, J.Giershner and A.Tompert, Synth. Met. 76, 249 (1996). 7. M.Born and K.Huang, Dynamical Theory of Crystal Lattices (Oxford Univ. Press, 1954). 8. P.G.Cummings, D.A.Dunmur, R.W.Munn and R.J.Newham, Act. Cryst. -432, 847 (1976). 9. P.Ostoja, S.Guerri, S.Rossini, M.Servidori, C.Taliani and R.Zamboni, Synth. Met. 57, 4053 (1993). 10. G.Horowitz, B.Bachet, A.Yassar, P.Lang, F.Demanze, J.L.Fave and F.Gamier, Chem. Mater. 11, 2958 (1995). 11. D.Fichou, G.Horowitz, B.Xu and F.Garnier, Synth. Met. 48, 167 (1992). 12. F.Garnier, Chem. Phys. 227, 253 (1998). 13. C.Taliani and L.BIinov, Adv. Mater. 8, 353 (1996). 14. B.Servet, S.Ries, M.Trotel, P.Alnot, G.Horowitz and F.Garnier, Adv. Mater. 5, 541 (1993). 15. L.M.Blinov, S.P.Palto, G.Ruani, C.Taliani, A.A.Tevosov, S.G.Yudin and R.Zamboni, Chem. Phys. Lett. 232, 401 (1995). 16. M.Andrzejak and P.Petelenz, J. Chem. Phys. submitted. 17. M. Andrzejak and P.Petelenz, Theochem, in press. 18. A.H.Matsui, K.Mizuno, M.Takeshima, Y.Oeda and T.Goto, in Excitonic Processes in Condensed Matter, ed. M.Schreiber (Dresden University Press, Dresden, 1996), p. 247.
Transient grating induced by excitonic polaritons in thin film semiconductors K. Akiyama, N. Tomita, T. Nishimura, Y. Nomura and T. Isu Advanced Technology R&D Center, Mitsubishi Electric Corporation Amagasaki, Hyogo 661-8661, Japan Light propagation effects on nonlinear optical response of a size-controlled GaAs thin film at exciton resonance are investigated by transient grating using picosecond pulses (1.5 ps). The signals are enhanced at the exciton resonance and the temporal profiles strongly depend on the excitation pulse energies. The result indicates that the nonlinear response is induced by excitonic polaritons and its decay is determined by the round-trip of the polariton in the film.
1. Introduction Excitons play an important role in linear and nonlinear optical properties at resonant energy of band gap in semiconductors. The fast phase relaxation as well as the population decay of the exciton has been successfully measured by transient spectroscopy using ultrashort pulses1. On the other hands, importance of light propagation effects have been recognized by the recent progress of the experimental studies for thorough understanding of the ultrashort coherent dynamics of excitons. Propagating ultrashort pulses are severely distorted in a strong dispersive and absorptive sample due to polariton effects. Such distortion leads to significant changes to the coherent response as observed in linear 2 ' 3 and nonlinear 4 ' 5 response regime. The pulse propagation effects are mainly observed for considerably thick films ( > 1 um), where two polariton modes of upper and lower branch induce a pulse distortion due to different dispersion of group velocity ug. For such thick films, slow propagation of polaritons at the transverse energy cor cannot be well observed because of the short dephasing time Ti of the system. However, recent studies by authors have shown that the nano-scale Fabry-Perot interference of polariton at around o>r induces an strong enhancement of degenerate four-wave mixing (FWM) by controlling the film size of GaAs in the region less than the excitation light wavelength 6 ' 7 ' 8 . This means that the slow propagation effects due to polariton at o>r can lead a strong modulation of the coherent nonlinear response of excitons for thin film semiconductors. In this paper, we investigate propagation effects on coherent dynamics of thin film semiconductors in nonlinear response regime by transient grating (TG). The TG is a kind of the FWM using three excitation pulses and makes it possible to measure the coherent response as well as the incoherent one. High quality GaAs layers with 110 nm thickness are grown by molecular beam epitaxy and nonlinear optical response at exciton resonance is measured by the TG and analyzed in terms of polariton propagation. 2. Experimental , 3 pairs of high quality GaAs layers with thickness of 110 nm are separated by Alo.3Gao.7As barriers on a distributed Bragg reflectors (DBRs) composed of 24 pairs of n-doped GaAs (62 nm)/A!As (74 nm). The sample is grown on a (100) GaAs substrate by molecular beam epitaxy. The reflectance of the DBRs is approximately 99% at exciton resonance (1.5150 eV). In the TG measurement, we use picosecond pulses (1.5 88
89 ps) from a mode-locked Ti:sapphire laser with a relatively narrow bandwidth (0.7 meV) and change the center frequency of the pulses to measure the energy dependence of the temporal profiles. The two linearly polarized pump pulses simultaneously arrive at the sample and generate the grating of excitons. The parts of the probe pulses diffracted by the grating are detected as a function of the delay time between the two pump pulses and the probe pulse. The measurement is performed under a backward geometry and the sample is cooled at 5 K during the measurements. 3. Results The reflection spectrum of the sample exhibits several narrow dips at higher energy side of the exciton resonance (1.5150 eV) as shown in Fig. 1. The dips correspond to the quantized states of excitons due to | confinement of center of mass S motion along the growth direction. £ The exciton line width estimated by the spectrum is 0.09 meV, which is less than the LT splitting energy 0.133 meV. This small damping ensures that polariton picture is adequate when the light propagates in our sample. Also, the largest dip is observed at 1.5156 eV, indicating that absorption of the n = 2 quantized Energy (eV) state has a maximum value as a result Fig. 1 Reflection spectrum of GaAs layers with of nano-scale interference of thickness of 110 nm on DBRs. excitonic polariton. The result is consistent with the thickness dependence of absorption evaluated by the photoluminescence excitation spectra9. Figure 2-(a) shows the diffracted signal intensity obtained at the delay time T = 0. The signal is measured in low excitation regime, where the power dependence of the signal shows third-order nonlinear response. The signal intensity has maximum value at 1.5151 eV which is slightly lower than the resonant energy of the n = 2 quantized state. This result is explained by the large absorption of this state. Figure 2-(b) shows the temporal profiles of the diffracted signals for several excitation pulse energies around the exciton resonance. The temporal profiles show two decay processes for higher excitation energies than 1.5150 eV. The fast temporal response at around T= 0 is due to the coherent excitons while the slow decay process with a time constant of several picoseconds originates from the incoherent excitons. The signal intensity from the coherent excitons is an order of magnitude larger than that of the incoherent excitons, which means that the dynamics of nonlinear optical process is dominated by the coherent excitons. The single exponential decay is observed for lower excitation energies than 1.5142 eV, which is ascribed to the biexcitons. The contribution of biexciton to nonlinear optical response of a thin film GaAs is observed for the excitation density dependence ofFWM 10 . 1
'
•
•
1
'
'
^
I
^
'
'
I
'
' '
T
90 The rise and the decay time of the coherent signals strongly depend on the excitation pulse energy. For higher excitation pulse energies than 1.5150 eV, both the rise and the decay process are comparable to those of the excitation pulse. The A decay becomes slow down when the pulse energies are tuned to the exciton resonance. Furthermore when the 1.514 1.515 1.516 pulse is tuned to higher Energy (eV) Time (ps) energies, the coherent process becomes fast and Fig. 2 (a) Transient grating for different excitation pulse energies the incoherent process obtained at T = 0 and (b) corresponding temporal profiles. The cannot be observed. density of the pump pulses is 2.5 kW/cm2 The observed energy dependence of the coherent signals can be explained by a distortion of the excitation pulses due to strong polariton dispersion. The slow decay in the positive and negative delay region corresponds to slow propagation of the grating generated by the pump pulses and the probe pulse in the sample. The resonant polariton components constituting such pulses propagate with group velocity u g which is reduced even to 104 m/s for bulk GaAs. Figure 3 shows the dispersion of the polariton and the corresponding group velocity. The x>g of the upper polariton mode at the a>r is several times smaller than that of the lower polariton mode because damping effects induce a modulation of the dispersion curve of the upper branch. In the spectrum range for the TG experiment, the round trip time of the polariton pulses within the 3 pairs of GaAs layers changes 1.52
5
10
k vector (10s m"1)
15
ltf
10 5 HT Velocity (m/s)
Fig. 3 (a) Dispersion curves of excitonic polariton in GaAs and (b) corresponding group velocity. Solid and dashed lines represent lower and upper polaritons, respectively.
91 from several picoseconds to ten picosecons, which is slightly longer than the decay rates of the TG experiment. However, by taking into account of the strong absorption of the excitation pulses, the signals are mainly emitted from the top GaAs layer. This can reduce the response time and hence propagation of polariton can explain the experimental results. The reason why the contribution of the upper polariton dominates the coherent response can be interfering effects including dumping for thin films. These results reveal that dynamics processes of nonlinear optical process of the coherent excitons are dominated by the polariton propagation. 4. Conclusion We have investigated the propagation effects on nonlinear optical response of a thin film at exciton resonance by transient grating. The temporal profiles show dependence on the excitation pulse energies due to polariton dispersion. This result indicates that the grating is induced by excitonic polariton and the decay of the response is determined by the round-trip of the polariton in the film. Acknowledgment A part of this work was performed under the management of a technological re search association, the Femtosecond Technology Research Association (FESTA), which is supported by New Energy and Industrial Technology Development Organization (NEDO) References 1. J. Shah, Ulrtafast Spectroscopy of Semiconductors and Semiconductor Nanostructures (Springer-Verlag, Berlin, 1996) 2. D. Frohlich, A. Kulik, B. Uebbing, A. Mysyrowicz, V. Langer, H. Stolz, and W. von der Osten, Phys. Rev. Lett. 67, 2343 (1991) 3. S. Nusse, P. H. Bolivar, K. Kurz, F. Levy, A. Chevy, and O. Lang, Phys. Rev. BS5, 4620(1997) 4. K.-H. Pantke, P. Schilak, B. S. Razbirin, V. G. Lyssenko, and J. M. Hvam, Phys. Rev. Lett. 70, 327 (1993) 5. T. Rappen, G. Mohs, and M. Wegener, Phys. Rev. 47, 9658 (1993) 6. K. Akiyama, N. Tomita, Y. Nomura, and T. Isu, Appl. Phys. Lett. 75,475 (1999) 7. K. Akiyama, N. Tomita, Y. Nomura, and T. Isu, H. Ishihara, and K. Cho, Physica E 7, 661 (2000) 8. H. Ishihara and K. Cho, Phys. Rev. B53,15823 (1996). 9. K. Akiyama, N. Tomita, Y. Nomura, and T. Isu, J. Luminescence 87-89, 512 (2000) 10. K. Akiyama, N. Tomita, Y. Nomura, and T. Isu, Physica B 272, 505 (1999)
D E P E N D E N C E OF E X C I T O N F O R M A T I O N O N I T S CENTER-OF-MASS M O M E N T U M IN Q U A N T U M WELLS
I.-K. OH and JAI SINGH Faculty of Science, Information Technology and Education B-28 Northern Territory University, Darwin, NT 0909, Australia We present a comprehensive study of the process of exciton formation due to excitonphonon interaction. Using the exciton-phonon interaction arising from deformation potential, piezoelectric, and polar couplings, we have calculated the rate of formation of an exciton as a function of carrier densities, temperatures, and center-of-mass momentum (K||) in quantum wells. Our results show that excitons are dominantly formed at nonzero K||, which agrees very well with experiments. The formation of an exciton due to emission of longitudinal optical phonon is found to be more efficient at relatively small values of KM, and that due to acoustic phonon emission is more efficient at relatively large KM values for carrier temperature Te_A^50 K. 1. I n t r o d u c t i o n The process of exciton formation plays a very important role in understanding the dynamics of charge carriers and analyzing photoluminescence (PL) data in quantum wells (QWs). At low excitation intensities, both the processes of formation and relaxation of excitons are dominantly assisted by phonon emissions. From PL experiments, it has been reported that a photoexcited electron-hole pair with excitation energies larger than the band gap energy first forms an exciton with non-zero wave vector K||, corresponding to its center-of-mass motion (momentum=ftK||), it then relaxes non-radiatively down to K|| ~ 0. 1,2,3 Finally the exciton thus relaxed to K|| ~ 0 recombines radiatively by emitting a photon. It is known that acoustic (AC) phonons play a dominant role in the exciton relaxation. 4 However, a detailed study of processes involved in the exciton formation as a function of K|| are not very well understood. Experimentally, there are two different interpretations of PL data regarding the process of exciton formation. One is that the formation is mainly due to AC phonon emission 3 and the other longitudinal optical (LO) phonon emission 5 . As the deformation potential (DP) in a valence band and piezoelectric (PE) interactions are anisotropic in most III-V compound semiconductors, excitonphonon interaction is non-zero for both longitudinal acoustic (LA) and transverse acoustic (TA) phonons. 6 The polar (PO) coupling gives interaction only with LO phonons. Therefore, the present paper considers all three types of interactions, DP, PE, and PO, to study the process of exciton formation in QWs. Using the interaction operators 7 ' 8 related with the formation of excitons from free electron-hole pairs via LA, TA, and LO phonon emissions, we have calculated the rate of formation of an exciton as a function of carrier densities, temperatures, and centerof-mass momentum (K||) in GaAs QWs. It is found that excitons are dominantly formed at non-zero K||, which agrees very well with experiments. It is also found that the formation of an exciton due to emission of LO phonon is more efficient at relatively small values of K|| and that due to AC phonon emission is more efficient at relatively large K|| values for carrier temperature Te-h<,50 K. 2. R a t e of formation At low excitation densities, excitons are considered to be formed from free electron-hole pairs due to phonon emission or absorption in a A-mode (LA, TA, and LO) via DP, PE, and PO couplings. In this case, the interaction Hamiltonian involving such formation of excitons
92
93 can be written as 7 ' 8 H( = -fT
£
^[^qih^kll^Ki^WKii-qiii-k,,
VAOq||,,I,K||,k|| Xa<:,a«(K| r qn)+k„ + H+($\\i
9z, k||)SK|| & Aq4,a h (K||+q||)-k||a c , a ,(K||+q||)+k|| j
,
(1)
where A0 is the 2D area of QWs, q=(q||,
W/ + (Kn) = T -
1
£
|C J *F/ + (q|| )9 „k||)|V* lk ( Kn+<1|l )- klI
°q||,5».k|l
x / ^ ( K | | + q | | ) + k | | (fgn + l ) ( " , + l ) S (Ex - Ee.h + hu^x) h
,
(2)
ex
where f , f, f , and raq are the occupation numbers of hole, electron, exciton, and phonon, respectively. 7 ' 8 Here exciton energy Ex and electron-hole pair energy Et_h a r e , respectively, given by hx
~
2MJI
h
'
(
>
where E), is the exciton binding energy and (iT, = (1/mii + l / m j i i ) _ 1 reduced mass of the excited electron-hole pair. In order to calculate the rate of formation of excitons in Eq. (2), we assume that there are no excitons in the system in the initial state, i.e., / | ? = 0. The densities of the photogenerated electron and hole can be considered to be the same (n e = n/, = ne-fc) in an intrinsic QW. We also assume that electrons and holes are at the same temperature, i.e., T e = Th = Te-A- For the numerical calculations, we have considered [001] GaAs/Al 0 .3Gao.7As QWs with well width of LZ=8QA and lattice temperature of T=4.2 K. We have used a finite well model for the electron and hole wave functions in the QWs. 7 , 8 For the wave function of an exciton, we have used one parameter variational wave function. 7 3. R e s u l t s Figs. 1 (a) and (b) depict the dependence of the rate of exciton formation on center-of-mass wave vector K|| of exciton, charge carrier temperature Te-h, and density ne_fc. We have taken into account both TA and LA phonon due to DP and P E couplings for AC phonon processes and their details are given in Ref.[8]. As it can be seen from Figs. 1 (a) and (b), the rate of formation is very sensitive to K||, T e _t, and rje_/j. We find from Fig. 1 (a) that the rate of formation decreases for K|| <,2.24 x 108 m _ 1 whereas it increases for Ky >2.72 X 108 m - 1 with increasing T e _^ at the charge carrier density n e _/,=1.0xl0 1 0 c m - 2 . Fig. 1 (a) also illustrates that the maximum rate of formation occurs at a non-zero value of K|| in the range of 2.16— 2.24xl0 8 m - 1 which corresponds to a kinetic energy of center-of-mass motion about 20—22 meV. Fig. 1 (b) shows the rate of formation due to AC phonon emission as a function of Te^h and nc~h a t Ky = 2.16 x 108 m _ 1 and indicates that the rate of formation increases very fast
94
Fig. 1. The formation rate of an exciton due to AC phonon emission in GaAs QWs (Lz = 80A ) (a) as a function of center-of-mass wave vector K|| and charge carrier temperature Te-h at the charge carrier density of ne-.& = 1 x 10 10 c m - 2 and (b) as a function of charge carrier density n e _/, and temperature T e _ A at KM - 2.16 x 10 8 m " 1 .
(b) 10
12
10
10
10
_
S*
\ . V /\ NN
E*t
f
\\>V>.
VJ
L•
r *
1
8
hi 106
/•'•
fd> 10
4
. 0 1 2 3 4 K, [10 8 m-' ]
\ \
\
\
\
, \
0 1 2 3 4 K. [10 8 m"' ]
Fig. 2. The formation rate of an exciton in GaAs QWs as a function of the center-of-mass wave vector K|| for Lz = 80A , T = 4.2 K, (a) n e _ ft = 1 x 10 10 c m " 2 and (b) n e _;, = 5 x 10 10 c m - 2 . The solid, dotted, and dash-dotted curves correspond to the formation rate due to AC phonon emission at T e _h =: 20, 50, and 80 K, respectively. The dash-dot-dot-dot, dashed, and long-dashed curves correspond to the formation rates due to LO phonon emission at Te_/, = 20, 50, and 80 K, respectively in t h e low c a r r i e r t e m p e r a t u r e region T e _/,, w i t h i n c r e a s i n g p h o t o e x c i t e d c h a r g e c a r r i e r d e n s i t y ne-h in c o m p a r i s o n w i t h t h a t in t h e h i g h t e m p e r a t u r e region. S u c h a t e m p e r a t u r e d e p e n d e n c e of f o r m a t i o n r a t e d u e t o A C p h o n o n p r o c e s s is q u i t e different f r o m t h a t d u e t o L O p h o n o n p r o c e s s . In t h e case of L O p h o n o n p r o c e s s 7 , it is f o u n d t h a t t h e r a t e of f o r m a t i o n a t a n y v a l u e
95 of K|| always increases as Te-h increases. For comparison between AC and LO phonon processes, we have plotted in Figs. 2 (a) and (b) the calculated exciton formation rate as a function of K|| at carrier temperature T e _/,=20, 50, and 80 K for two different densities, i.e., ne_/, = 1 x 10'° c m - 2 and rae_j, = 5 x 10 10 c m - 2 , respectively. As it can be seen from Figs. 2 (a) and (b), the maximum rates occur at a non-zero K|| for both LO and AC phonon processes except for LO phonon process at Te_^ < 3 0 K where the maximum rate is at K||=0 (see Ref. [7] for LO phonon process in detail). In particular, we have found that excitons are formed mainly due to LO phonon interaction at relatively small values of Ky but at relatively large K|| the AC phonon interaction becomes dominant. For instance, LO phonon process dominates for K|| < 2 . 0 x l 0 8 m _ 1 and AC phonon process for K|| > 2 . 0 x l 0 8 m _ 1 at T e _/,=40 K and T=4.2 K. The maximum rate of formation due to LO phonon emission is at K|| ~ 0.74—0.82 x10 s m _ 1 (see Fig. 2) which corresponds to a much smaller kinetic energy of about 2—3 meV in comparison with 20—22 meV obtained for AC phonon process. This can be explained as follows: when the energy of photoexcited free electron-hole pairs is high enough, excitons formed at relatively small values of K|| are mainly due to LO phonon process whereas those at relatively large values of K|| are due to AC phonon process because the energy involved in the formation of exciton due to LO phonon emission is much larger than that due to AC phonon emission. In other words, as an excited electron-hole pair in a given state looses more energy in an LO phonon emission than that in an AC phonon emission, the exciton formed due to LO phonon emission has less kinetic energy than that formed due to AC phonon emission. We have also found from our calculations that LO phonon process is dominant over AC phonon process for Te-k>ZQ K (see Fig. 2). In conclusion, we have presented a comprehensive theory of formation processes of an exciton due AC and LO phonon emission via DP, PE, and PO couplings as a function of the center-ofmass wave vector Ky, charge carrier temperature Te-h, and charge carrier density rj e _/,. Our results in [001] GaAs/Alo.3Gao.7As QWs shows that the rate of formation of exciton is very sensitive to K||, Te-h, and n e _/,. We have also found from our calculations that the rate of formation due to LO phonon emission is dominant over that due to AC phonon emission at all K[| for T e _ft>50 K, but for T e _/,<50 K there is a crossover at an exciton wave vector K|j where the formation via AC phonon emission becomes dominant for K|| > Kjj. Acknowledgements This work was supported by an Australian Research Council Large Grant. References 1. J. Kusano, Y. Segawa, Y. Aoyagi, S. Namba, and H. Okamoto, Phys. Rev. B 40, 1685 (1989) 2. M. Gurioli, J. Shah, D. Y. Oberli, D. S. Chemla, J. E. Cunningham, and J. M. Kuo, Phys. Rev. B 58, 13403 (1998) 3. T. C. Damen, J. Shah, D. Y. Oberli, D. S. Chemla, J. E. Cunningham, and J. M. Kuo, Phys. Rev. B 42, 7434 (1990) 4. Z. L. Yuan, Z. Y. Xu, W. Ge, J. Z. Xu, and B. Z. Zheng, /. Appl. Phys. 79, 424 (1996) 5. P. W. M. Blom, P. J. van Hall, C. Smit, J. P. Cuypers, and J. H. Wolter, Phys. Rev. Lett. 71, 3878 (1993) 6. I.-K. Oh and J. Singh, J. Lumin. 85, 233 (2000) 7. I.-K. Oh, J. Singh, A. Thilagam, and A. S. Vengurlekar, Phys. Rev. B 62, 2045 (2000) and references therein. 8. I.-K. Oh and J. Singh, J. Lumin. (In press).
RELAXATION OF EXCITONS IN IONIC HALIDES: MOLECULAR DYNAMICS STUDY K. S. Song and Chun-Rong Fu Dept. ofPhysics, Univ. of Ottawa, Ottawa, Canada We report here the preliminary results of molecular dynamics simulation of exciton and holerelaxationin KBr and NaBr. The previously used semi-classical program has been modified to implement the solutions of Newton's equations with a time step of 0.50 femtosecond. Hole self-trapping process is studied at 80K. In both materials, there is a rapid bond-length oscillation. The oscillation, however, is damped faster in NaBr than in KBr. The relaxation of a Frenkel-type exciton (kwalized on a single site) is studied at 10 and 30K. It is found that the localization of the excited electron at an anion site drives the relaxation process, resulting in the formation of H and F centers simultaneously. There is a conspicuous absence of molecular bond oscillation which was observed in the Vt-center relaxation. In KBr, the FH-pair created is about 10 A apart (third neighbor). In NaBr, the separation is about 3 A. The maximum relaxation is achieved in about 1 -2 picosecond, depending on the temperature. These results are discussed in comparison with recent experimental works.
1. Introduction In a number of insulators the exciton-phonon coupling can be significant and as a result the exciton may be localized in the lattice spontaneously, leading to the formation of the self-trapped excitons (STE). Associated with a STE an energy package of a few electron volt is confined within a volume of the order of a unit cell. Such system can induce large scale atomic displacements leading to energetic atom desorption or permanent lattice defects. Of the many materials in which the STE is observed, the most extensively studied are the family of ionic halides '. Experiments have shown that F centers are created as early as 1 picosecond after excitation at very low temperature2. More recent ultra-fast spectroscopic studies have shown that the processes taking place even earlier are quite complex34. It is therefore clear that the dynamic aspects of exciton relaxation are important to understand. A series of calculations, of both semi-classicalS6 and ab initio types 7,8( has established the presence of strong trend toward the so-called off-center relaxation. In this work we present the preliminary results of molecular dynamics (MD) study of STE relaxation in NaBr and KBr. The main results are: starting from one-center hole state the Vk-center forms quite fast (within less than one picosecond), but undergoes a rapid oscillation which can last up to about 3 pico-second or more in KBr; no such fast bond oscillation is seen when an electron is localized at a nearby anion site; startingfroma onecenter exciton (such as a Frenkel type exciton), the off-center relaxation is found to be vigorous in KBr and reaches the maximum F-H separation (the third neighbor separation) in about 1-2 picosecond depending on temperature; a similar off-center relaxation is much weaker in NaBr; there is a slow oscillation of the H center after it has reached the maximum relaxation. 2. Method The cluster of atoms considered for MD is of finite size, in the range of between 120 to 150, and is embedded in an infinite static lattice. All atoms within the first five neighboring shells of a string of
96
97 halogen atoms are included in the MD study. The choice of the string of halogen atoms in fact restricts the kind of hole motion that can follow in the MD. For example, up to five halogen atoms along a (110) axis are taken in the study of the exciton relaxation. Such restriction is inevitable in our approximation in which the hole is treated by the CNDO code for a limited number of atoms while the excited electron is treated in the extended-ion approximation (or one-electron Hartree-Fock approximation) interacting with about 600 atoms. The polarization and the atom-atom interactions are treated classically. The details have been given earlier6. At the beginning of MD study, the cluster of atoms is equilibrated at the specified temperature in the ground state. This is achieved within about one thousand time steps (about 0.5 picosecond). After this, the exited species under consideration, such as a Frenkel-type exciton (described as a Br° plus an excited electron), is introduced. For each of the atoms in the MD cluster the forces are evaluated numerically from the calculated potential energies. Taking a time step of 0.48 femtosecond for the bromides the relaxation is left to run for about 6000 steps. As the relaxation proceeds part of the potential energy is converted to kinetic energy of the atoms. The thermodynamic temperature is calculated at each time steps and we can either reduce it by afixedfraction for all atoms (e.g. 10% every ten time steps), or keep the total energy constant. In general the temperature rises first and then gradually stabilizes. 3. Results A MD study of exciton relaxation presents some basic problem regarding the initial state to start the dynamics. Ideally, one should startfroma plane wave-like free exciton state and proceed to self-trapping of charge at a particular site accompanied by lattice relaxation and eventually ending at a stable (the recombined ground state) or a meta-stable state (Frenkel defect pair: an electronically excited state). This is not only a complex chain of processes, but also not a convenient one to consider as we are primarily interested in the transient triplet STE states as well as the F-H pairs. We have therefore adopted two idealized localized "initial" states in this study. One is a Frenkel-like exciton state in which the hole is represented by a Br° in a lattice under thermalfluctuation. The electron is relatively compact and bound to the hole. This process will show the competition between the electron localization and the Vk-center bond formation. It is considered that this may represent the experiment with fast band-to-band pulse at a very early stage4. The other case considered assumes a pre-existing Vk-center which attracts an electron nearby. This may describe the experiment of double excitation with pump/probe method3, or a later stage in the fast band-to-band pulse experiment 4. Beside the two cases, we have also studied the dynamics of hole selftrapping, as experiment has shown significant differences at 80K between NaBr and KBr4. 3.1 Relaxation of hole Relaxation of a single hole (a Br° atom) in NaBr and KBr lattice equilibrated at 80 K has been studied. The variation of the bond-length with time is shown in Fig. 1. The covalent molecule bond is formed very fast, within about 0.5 picosecond. This is accompanied with a rapid oscillation of the bond-length which persists in KBr beyond 3 ps. However, in NaBr the oscillation cools off within about 1 ps. The speed of damping is dependent to some degree on the kinetic energy dissipation rate used. There is less than about 1 eV of energy which is released when a Vk-center is formed. The total energy of the system has been kept
98
4.6 4.4 4.24.0
\ \
MD: Vk-center in KBr and NaBr(80K)
3.8 H c •o
c o
3.63.43.23.0 2.8 2.6-1 2.4 -I 0.0
0.5
1.0 time (ps)
1.5
2.0
constant in this study. It is interesting to compare the present work with a recent report which shows that at 80K the Vk -center stabilizes much faster in NaBr (within about 1 picosecond) than in KBr4. Our work is therefore in qualitative agreement with the experiment. The difference between NaBr and KBr can be understood by comparing the Vk -center stretching modefrequency(145 cm"1) with the Debye frequencies (129 cm"' and 160 cm"', respectively in KBr and NaBr). A localized mode with frequency outside the lattice mode spectrum may take longer time to dissipate its excess kinetic energy. When we present below the relaxation of a one-center exciton, we will see the striking effect of the excited electron in the bond formation of the Vk -center.
Fig. 1 Time evolution of the Vk-center bond length at 80K in NaBr (solid circle) and KBr (open circle).
3.2 Relaxation of Frenkel-type (one-center) exciton Our present objective is to compare the result of MD with the available low temperature femtosecond spectroscopic data of Ref. 4. The ground state lattice is first equilibrated at 1 OK. Then a Frenkel-type exciton is implanted as the initial state. To simulate the relaxation of a one-center exciton in KBr, we have started from a string of five Br atoms, with the first one represented by an excited Br atom. The electron is described by a gaussian (a= 0.025, in atomic unit) centered on Br°. The bond formation is realized in about 0.5 ps. However, no fast oscillation is seen as was the case for the Vk-center. This is one of the unexpected observations. On the other hand, the off-center relaxation begins while the bond is still forming. At about 2 picosecond, the system relaxes to reach the third neighbor F-H pair geometry. Fig. 2-a shows the result for KBr at 1 OK, obtained with a kinetic energy dissipation of 15% everyfivetime steps. A similar study conducted at 30K resulted in a faster relaxation (about 1.5 ps). In Fig.2-b is shown the result for NaBr at 10K. A string of four Br atoms is employed in this case as it was expected that the hole center would not diffuse beyond this number. There is an obvious difference with KBr in the range of diffusion of the hole center. The electron and hole centers are like in a primitive Frenkel pair. There is also some suggestion of difficulty toward the off-center relaxation early at about 0.25 ps. In both systems, the position of the hole center oscillates with a period of about 1 picosecond after reaching the maximum relaxation. It is estimated that the electron and hole centers separate with an apparent speed of about 1000 m/s. In the case of KBr the end product of relaxation is close to a stable Frenkel defect pair, probably safe from
99 annihilation via recombination. On the other hand, in NaBr the end product is either a very short lived Frenkel pair or a weakly off-center STE. Whether or not the triplet STE in NaBr is truly off-center or a metastable on-center is not clear, and requires further study.
-»—Br#1 - » — Br #2 -*— Br #3 -*— Br #4 -•—Br #5 -O— hole position
1614-
MD: STE in KBr (1 OK)
12-
12 <, 10 c o
1 8.
—•—Br#1 —*—Brtt - - » — Br #3 —•—Br #4 —O—hole position
mi
inn
i
»**
MD: STE in NaBr (1 OK)
^ iiiiiiiiiiimiiiiiniiiiiMii'ii'iimiiiw
8 «***4J*******J
V**~
6**"""*AA*
>
.*****
iin-Tiii
,„
uiiiiii
m
mi
4 2 0.0
0.5
1.0 1.5 time (ps)
2.0
2.5
°°
0-5
10
time
1-5 (P s )
2.0
2.5
Fig. 2.a Positions of thefiveBr atoms and the center of gravity of the hole distribution as functions of time in KBr at 1 OK (Frenkel exciton as the initial state). Fig. 2.b Positions of the four Br atoms and the centerof gravity of the hole distribution as functions of time in NaBr at 10K (Frenkel exciton as the initial state).
We now discuss the Vk-center bond formation with and without the accompaniment of excited electron. In the absence of an electron, the bond formation is simply due to covalent attraction, and the hole is equally distributed on the two Br atoms from the very earliest instants. As there is a modest amount of excess kinetic energy, the oscillation persists until it dissipates. In the presence of an excited electron the situation is quite different because of several factors: different symmetry of relaxation; much larger relaxation energy available; and a strong interaction between the hole and the electron. The process is a combination of electron localization, hole bond formation and the off-center axial relaxation along the (110) axis. As a result, the strong oscillation of the bond is suppressed. It is not surprising that the excited electron not only drives the off-center relaxation, but also has a strong influence on the bond formation of the hole center. We have briefly described the results of the MD studies. There are already some new observations which were not foreseen before this study. One is regarding the hole bond formation and its rapid oscillation: the difference between NaBr and KBr; and the absence of similar oscillation during the exciton relaxation. The
100 other is that the F-center, or a primitive form of it is created very early following the formation of a bound free exciton (Frenkel-type). This is clearly the consequence ofthe dynamic process induced by the localizing excited electron. A well-separated F-H pair can be formed in KBr within about 1 -2 ps following one-center exciton creation at low temperature. Molecular dynamics study of exciton relaxation is only at its beginning. The present work is relying on a semi-classical method and there are number of limitations. Even at this level of calculation, the computer time needed is quite considerable. There are needs to learn about various aspects such as the rate of energy dissipation for a finite cluster of atoms, especially in the case of an exciton. In view of the many difficulties associated with ab initio calculations of relaxed excited system, a molecular dynamics study based on an ab initio approach seems quite daunting for now. Still, this has to be undertaken eventually within some approximations acceptable both theoretically as well as computationally. In the meantime we can explore this new field based on more approximate approaches.
Acknowledgment The present work was partly supported by a grant from NSERC.
References 1 K. S. Song and R. T. Williams, Self-Trapped Excitons, Springer Sr. in Solid State Sciences 105, ed. M. Cardona (Springer Verlag, Berlin, sec. ed. 1996 ), chap. 5-6 2 R. T. Williams, H. Liu, G. P. Williams Jr.: Rev. Solid State Sci. 4,445 (1990) 3 T. Tokizaki, T. Makimura, H. Akiyama, A. Nakamura, K. Tanimura and N. Itoh, Phys. Rev. Lett. 67, 2701 (1991) 4 T. Sugiyama, H. Fujiwara, T. Suzuki and K. Tanimura, Phys. Rev. B 54,15109 (1996) 5 C. H. Leung, G. Brunet, K. S. Song, J. Phys. C18,4459 (1985) 6 Chun-Rong, Fu, L. F. Chen and K. S. Song, J. Phys.-Condens. Matter 11, 5517 (1999) 7 A. L. Shluger, N. Itoh, V. E. Puchin, E. N. Heifets, Phys. Rev. B44,1499 (1991) 8 K. S. Song, R. C. Baetzold, Phys. Rev. B46,1960 (1992)
ULTRAFAST CARRIER DYNAMICS IN ZnO EPITAXIAL THIN FILMS STUDIED BY OPTICAL KERR GATE LUMINESCENCE SPECTROSCOPY JUN TAKEDA, SUSUMU KURITA Department of Physics, Faculty of Engineering, Yokohama National University Hodogaya-ku, Yokohama 240-8501, Japan YEFAN CHEN, TAKAFUMI YAO Institute for Materials Research, Tohoku University, Aoba-ku, Sendai 980-8577, Japan Time-resolved luminescence spectra of ZnO epitaxial thin films have been measured by the optical Kerr gate luminescence spectroscopy under resonant excitation of the excitonic state. At moderate excitation density, a luminescence band (P band) which is attributed to an exciton-exciton collision process was observed. With increasing the excitation density, the P band disappears while a new luminescence band (EHP band) due to radiative recombination of electrons with holes in an electronhole plasma appears. The EHP band has a rise time of ~1 ps, and shifts to lower energy with time and then finally shifts to higher energy. The rise time of the EHP band shows a transition time from a high density excitonic state to an unbound electron-hole system due to the screening of Coulomb interaction. The red shift of the EHP band comes from the reduced band-gap effect, while the blue shift of the EHP band is mainly attributed to recovery of the renormalized band-gap, which occurs with decreasing the carrier density due to the radiative recombination of electrons with holes.
1. Introduction Optical properties of ZnO epitaxial thin film have been extensively studied because of their potentially superior properties as a material of short-wavelength optical devices. Recently, stimulated emission of luminescence and optically pumped laser action of ZnO epitaxial thin films were observed at room temperature1,2. The emission is thought to be originated from highly excited carriers — a high density excitonic state or an electron-hole plasma. In order to elucidate dynamics of such highly excited carriers, we measured time-resolved luminescence spectra of ZnO epitaxial thin films by the optical Kerr gate (OKG) method with a subpicosecond time resolution3,4. An advantage of this method is in its ability to directly observe time-resolved luminescence spectra in femtosecond time regime, which give important information of ultrafast carrier dynamics. 2. Experimental ZnO epitaxial thin films were fabricated on a sapphire (0001) substrate by a plasma enhanced MBE method as previously reported3,6. The thickness of samples is 233 nm. Time-resolved luminescence spectra of ZnO epitaxial thin films were measured at room temperature by the OKG luminescence spectroscopy3,4. The second harmonic (380 nm) and fundamental (760 nm) laser beams from a Ti: sapphire regenerative amplifier laser system with a repetition rate of 1 kHz were used as the excitation and gate pulses, respectively. The excitation energy (3.26 eV) lies at a lower 101
102 energy tail of the A-exciton of ZnO, and the optical density at this energy (~0.1) is small. Therefore the excitation pulse is expected to directly and homogeneously create a high density excitonic state in a sample. A quartz plate with a thickness of 0.5 mm was used as a Kerr medium. A detailed experimental setup of our OKG method is presented in Ref. 4. The time-resolved luminescence by the OKG method was detected by a monochromator with a CCD detector cooled by liquid N2. The overall time resolution of the experiment was 300 fs. 3. Results and Discussion Figure 1 shows time-integrated luminescence spectra at room temperature under different excitation densities. At moderate excitation density, a luminescence band (P band) is observed at 3.18 eV. With increasing the excitation density, the P band disappears while a new luminescence band (EHP band) appears around ~3.1 eV. The peak position of the EHP band shifts to lower energy and the half-width of the band becomes broader with increasing the excitation density. Judging from the energy position and spectral shape of these bands, the P band was attributed to an exciton-exciton collision process, while the EHP band was due to radiative recombination of electrons with holes in an electron-hole plasma7,8.
2.9
3.0
3.1
3.2
2.9
3.0
3.1
3.2
Photon Energy ( eV ) Fig. 1. Time-integrated luminescence spectra of a ZnO epitaxial thin film at room temperature under different excitation densities.
Figure 2 shows time-resolved luminescence spectra of a ZnO epitaxial thin film for different delay times at the excitation density of 12 mJ/cm2 (a) and 110 mJ/cm2 (b). The time-integrated luminescence spectrum is also depicted in the left-top of each figure. At the moderate excitation density, we only observed the P band. No spectral shift with time is observed. The rise and decay times of the P band are ~1 and ~2 ps, respectively. The rise time is thought to be the time in which the exciton-exciton collision process effectively takes place. In this experiment, the dense excitonic state was directly created under the resonant excitation, implying that the exciton-exciton collision process occurs immediately after the excitation. The reason for the observed slow rise time of 1 ps is unclear yet. On the other hand, the decay time represents the time in which one of
103 the two excitons scatters into higher excitonic state of n=°° while the other recombines radiatively.
0.67 ps
1.3 ps
2.0 ps
i^V s
0.33 ps
2.3 ps
**———^•-W
^f^0.67 ps
J
«
-
. 3.0 ps
4.7 ps
3.5 ps
7.3 ps
A******
-1—-f^^-T* . 0.83 ps
3.0
3.1
3.2
3.0
Photon Energy Fig. 2.
2.7 ps
3.1
3.2
2.9
(eV)
3.0
3.1
3.2
2.9
3.0
3.1
3.2
Photon Energy (eV)
Time-resolved luminescence spectra for different delay times at the excitation density of 12 mJ/cm2 (a) and
110 mJ/cm2 (b). The time-integrated luminescence spectrum is also depicted in a left-top of each figure.
At the high excitation density, the EHP band as well as the P band is observed as shown in Fig. 2(b). In such a high excitation density, the EHP state is stable but the excitonic state is unstable. Thus the P band should not be observed when the EHP band is observed. The observed P band is therefore thought to come from a low excitation portion of the sample. The time-resolved EHP luminescence shows the following prominent features. First, the EHP band has a rise time of ~1 ps. Next, the peak position of the EHP band shifts to lower energy, and then shifts to higher energy with time. Third, the decay time of the EHP band increases with increasing the detected luminescence photon energy. The red shift of the EHP band comes from the reduced band-gap effect, while the blue shift of the EHP band is mainly attributed to recovery of the renormalized band-gap. In order to evaluate the temporal evolution of the renormalized band-gap, we estimate the renormalized band-gap at a given delay time from the energy position in which the luminescence intensity of the EHP band is 0 as shown by downward arrows in Fig.2(b). Figure 3 shows the observed renormalized band-gap as a function of delay time. We fitted the temporal evolution of the renormalized band-gap EJt) by the following simple equation; Eg(t) =E0- £X{1 - exp(-f /T r )}exp(-r/ rd), where \ and xd are the rise and decay times, respectively. When the values are x, =0.9 ps and xd =1.8 ps, we obtained the best-fit curve as shown in Fig. 3. The rise time is thought to be a transition time from a high density excitonic state to an unbound electron-hole system due to the screening of Coulomb interaction. On the other hand, the decay time shows the recovery of the renormalized band-gap, which mainly occurs with decreasing the carrier density due to the
104 radiative recombination of electrons with holes. 3.05 _ 1
1
1
1
1
1
1 _
• 3.00
-
-1
CO
/•
1
2.95 - t&
9 on
a
1
1
0
1 2
1
1
3
4
1
1
1
5
6
7
Delay Time (ps) Fig. 3. Observed renormatized band-gap as a function of delay time.
In summary, we measured time-resolved luminescence spectra of ZnO epitaxial thin films by the optical Kerr gate luminescence spectroscopy under resonant excitation of the excitonic state. At high excitation density, EHP band due to radiative recombination of electrons with holes in an electron-hole plasma appears around ~3.1 eV. The EHP band has a rise time of ~1 ps, and shifts to lower energy with time and then finally shifts to higher energy. The rise time of the EHP band is a transition time from a high density excitonic state to an unbound electron-hole system due to the screening of Coulomb interaction. The red shift of the EHP band comes from the reduced bandgap effect, while the blue shift of the EHP band is mainly attributed to recovery of the renormalized band-gap, which occurs with decreasing the carrier density due to the radiative recombination of electrons with holes. This work was partly supported by grant-in-aid for Scientific Research (B) (No. 11440091) and by grant-in-aid on priority areas, "Photo-induced Phase Transition and Their Dynamics", from the Ministry of Education, Science, Sports and Culture of Japan. References 1. D. M. Bagnall, Y. F. Chen, Z. Zhu, T. Yao, M. Y. Chen and T. Goto, Appl. Phys. Lett. 73, 1038 (1998). 2. Z. K. Tang, G. K. L. Wong, P. Yu, M. Kawasaki, A. Ohtomo, H. Koinuma and Y. Segawa, Appl. Phys. Lett. 72,3270 (1998). 3. J. Takeda, K. Nakajima, S. Kurita, S. Tomimoto, S. Saito and T. Suemoto, J. Lumin. 87-89,927 (2000). 4. J. Takeda, K. Nakajima, S. Kurita, S. Tomimoto, S. Saito and T. Suemoto, Phy. Rev. B62, (2000) in press. 5. Y. F. Chen, D. M. Bagnall, H. J. Koh, K. T. Park, K. Hiraga, Z. Zhu and T. Yao, J. Appl. Phys. 84,3912(1998). 6. Y. F. Chen, D. M. Bagnall, Z. Zhu, T. Sekiuchi, K. T. Park, K. Hiraga, T. Yao, S. Koyama, M. Y. Shen and T. Goto, J. Cryst. Growth 181, 165 (1997). 7. P. Zu, Z. K. Tang, G. K. L. Wong, M. Kawasaki, A. Ohtomo, H. Koinuma and Y. Segawa, Solid State Commun. 103,459 (1997). 8. A. Yamamoto, T. Kido, T. Goto, Y. F. Chen, T. Yao and A. Kasuya, Appl. Phys. Lett. 75, 469 (1999).
Quasi-degenerate self-trapping and its application t o a n t h r a c e n e - P M D A : p h e n o m e n o n , optical absorption and luminescence time-resolved spectroscopy A.S. Mishchenko Correlated Electron Research Center, Tsukuba, 305-0046, Japan, and Russian Research Centre "Kurchatov Institute", 123182 Moscow, Russia N. Nagaosa Department of Applied Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113, Japan, and Correlated Electron Research Center, Tsukuba, 305-0046, Japan
The self-trapping by the nondiagonal particle-phonon interaction between two quasidegenerate energy levels of exitonic subsystem, is studied. We propose this is realized in charge transfer exciton, where the directions of the poralization give the quasi-degeneracy, as in quasi-one-dimensional compound A-PMDA. We present a quantitative theory for the optical properties (light absorption and time-resolved luminescence) of the resonating states, which gives a consistent resolution for the long-standing puzzles in A-PMDA. The charge transfer exciton in one-dimension attracts great interests recently due to its peculiar features, e.g., strong interaction with the phonons, magnons, and large nonlinearity in the optical responses. However the theoretical understanding of it is rather limited compared with that of Wannier and Frenkel excitons in 3D, because of its strong coupling nature. One of the most studied compounds in the past is Anthracene-PMDA (A-PMDA), which shows a sharp zero-phonon line and several vibronic structures in the optical properties 1>2'3'4. However there remain many puzzles (as described below) even in this prototypical compound. The most dramatic phenomenon which occurs at intermediate or strong coupling with the phonons is the self-trapping where the free (F) state of polaron with small lattice deformation coexists and resonates with the self-trapped (ST) one with strong lattice relaxation 5,e . However this self-trapping scenario was not supposed to work since the F-ST resonance is prohibited by Rashba-Toyozawa theorem 5 ' 6 in one-dimensional (ID) systems. However, when there are two quasi-degenerate quasiparticle states, i.e. the conditions of the theorem are violated, one can consider the quasi-degenerate self-trapping (QDST) mechanism, when the F-ST resonance is driven by nondiagonal interaction with phonons with respect to quasiparticle levels8. In this paper we study the optic properties of resonating QDST states, and resolve long-standing puzzle of the quasi-lD system A-PMDA 1'2'3-4. QDST existence. The quasi-lD compound A-PMDA consists of one-dimensional arrays of alternating donor (D) and acceptor (A) molecules 1'2. There are two possible configurations of CT exciton, i.e., A°D+A~ and A~D+A°, and the symmetric <j>8{r) and antisymmetric <j>a{r) linear combinations of these two constitute the nearly degenerate two branches of excitons. The minimal model to demonstrate the QDST possibility involves one optic phonon branch with frequency OJ, two quasiparticle branches with a gap A, and the quasiparticle-phonon coupling 2
2
# = * E E E E V^&AQWI - b-g)clk-qcj,k + h.c. Here c^k a n d bq are annihilation operators for the quasiparticle of branch j with momentum k and for the phonon with momentum q. If the quasiparticle is exciton, one can study the optical transition between the ground state G and the exciton-polaron states with zero momentum
105
(i)
106 Upper
\L-J lQF
'QU
T^ST
Fig. 1. Schematic configurational diagram. The dotted arrows correspond to nonradiative processes, and the dahsed arrows indicate the radiative (absorption/emission) transitions.
(see Fig. 1). To study the optical properties we consider the case when the coexistence occurs in the strong coupling limit, i.e. when MAX{7i20i 2 (g)}/w S> A and, therefore, the adiabatic approximation is justified 7 . In this case one can find for given lattice deformation Q = {Qi,..., QN] (N is the number of lattice modes) the adiabatic potential relieves £\{Q) (A is the index of lower I and upper u sheet) and express the eigenfunctions ij>\(r,Q) = a f {Q)
E{t1}
(2)
with the eigenvalues = q(Q') + E ^ = i ^ ? ( / n + 1/2). Spectrum of optical absorption. The optical properties of A-PMDA give the evidence of the strong exciton-phonon interaction 3 . The low energy part of the absorption spectrum consists of the zero phonon line (ZPL) and a broad band with the full width at half maximum (FWHM) of around 2 ' 4 500 c m - 1 . Therefore, the optical responce qualitatively reminds lineshape of Fcolor centers absorption spectra which correspond to transitions between displaced oscillators 9 10 ' . However, all attempts to interpret the optical properties of A-PMDA 1-2'3-4 encountered (i) absorption and emission spectra can not be apparent contradictions with the model described as one series of the equidistant lines 2 ; (ii) the value of Huang-Rhys parameter S, evaluated from the ratio of ZPL and total oscillator strength, is inconsistent with the intensity distribution of the broad band [E.g., the value 5 = 4 extracted from the oscillator strengths of ZPL leads to the estimate 2 FWHM=140cm- 1 .]. These long-standing puzzles can be interpreted (such treatment has never been attempted due to the Rashba-Toyozawa theorem) as response of the coexisting F and ST states. To calculate induced cross section oaba(E) at energy E of optical absorption which corresponds to transitions from the set IPQ(T,Q) = G{*)XG (Q) °^ XG (Q) ph°n<m states of ground electronic state 4»a(r) to the set of excited states in (2) one has to average over initial states {a} and sum over final states in (2). Using the standard approach, defining the electronic dipole matrix elements Mj = /dr((/> G (r))*r0j(r), and introducing an average optic phonon frequency
107 cjt one can take advantage of Huang-Rhys method
9
and obtain for zero temperature rabs, en
(3)
£ J (Q')
(4)
aabs(E)K J2 MtFr{E), t=F,ST
where
„-St
Ft^(E)
= -
DO Of
E
^
£
-
- PW., Tf)
(Here St = (2./V)_1
18400 18500 Energy (1/cm)
18600
Fig. 2. Comparison of light absorption experimental data (diamonds) with model curve (solid line) consisting of optic response of coexisting F (dashed line) and ST (dotted line) states with SF — 2.5, SST — 13.3, and = 0.82. The onsets are €F,ST(QF,ST)
MF/MST
and linewidthes are 1 F S T
: 29/72 cm"
1
(Vf
0
= 18322/18334 c m " 1
= 2.5 cm" 1 ).
Luninescence from QDST states. The main puzzle in luninescence spectra of A-PMDA is that although the pattern of satellites is symmetrically repeated in absorption and luminescence spectra, the intensity distribution of phonon sidebands is significantly different 6 . Also this puzzle can be resolved in terms of the adiabatic potential in Fig. 1. The experimental conditions of time-resolved luminescence spectroscopy are equivalent to the situation when at a moment t = 0 the system is excited to the upper sheet U of the adiabatic potential whereas F and ST wells are empty, and the population of wells P(t) obey the following rate equations, = -{wu-.sr
+
Psr(t)
Pv(t)
=
-(WST^F
+RsT)PsT{t)
PF(t)
=
-RfPf^
+
wu^F)Pu(t), +
wv^srPu(t},
Wu^FPui^+WsT^fPsTit),
108 where w's are the transiton probabilities between the wells, and R's are the ratiative rates. Here the "bottlenecks hierarchy" (BH) is expected, namely WU^ST 2> max{uj(y„,F,«; S T „ F }, due to Franck-Condon suppression of nonradiative processes U <-> F and ST <-> F. Skipping all the details of the analysis, we summarize here the main features of the luninescence spectra derived from the above equation u . (i) The relative weight of the time-integrated luninescence yields YST and YF from the selftrapped and free states Ysr/Yp > 1 provided the inequality RST > WST^F takes place. Therefore, due to specific BH of the relaxation processes it is possible that, e.g., the F state is distinctly observed in the light absorption spectra but is almost not seen in the spectra of non time-resolved luminescence. (ii) At the same time if criterion RF < RST is satisfied, at large times t > Rp1 the ratio of differential intensities Isr(t)/lF(t) -C 1 is opposite. (iii) Finally, the difference between absorption and luminescence spectra pattern arises in APMDA due to the BH which manifests itself in the mirror image of sidebands coming from ST and F series in absorption and luminescence spectra, which relative intensities are different in two types of experiment. Moreover, due to the BH both 13 cm""1 peak 4 and the whole broad structure 3,e have inverse relative spectral weights in luminescence and absorption spectrum. More evidences can be found in experiments on time-resolved luminescence because proper fit (Fig. 2) of the experimental curve 2 demands MFI-MT < 1 in (3), and, hence, criterion RF < RST is satisfied because radiative rates R are governed by electronic transition coefficients M. Conclusions. When there are more than one electronic levels of a particle within the energy range of the lattice relaxation energy, F and ST states can coexist and resonate even in ID. This conclusion is supported also by the recent quantum Monte Carlo study n . We have found several features which are unique for QDST states and can be checked in optical experiments. We have shown, that the QDST mechanism provides comprehensive description of the longstanding mystery of the optical properties of the quasi-lD compound A-PMDA. We are gratefull to M. Gonokami, B. V. Svistunov, Y. Tokura, and Y. Toyozawa for critical discussions. This work was supported by Priority Areas Grants and Grant-in-Aid for COE research from the Ministry of Eduction, Science, Culture and Sports of Japan, and RFBR Grant No 99-02-17288. ASM acknowledges the fellowship of the National Institute of Advanced Interdisciplinary Research (Tsukuba). References 1. 2. 3. 4.
D. A. D. D.
Haarer, M. R. Philpott and H. Morawitz, J. Chem. Phys. 6 3 , 5238 (1975). Brillante and M. R. Philpott, J. Chem. Phys. 7 2 , 4019 (1980). Haarer, Chem. Phys. Lett. 2 7 , 91 (1974). Haarer, J. Chem. Phys. 6 7 , 4076 (1977).
5. E. I. Rashba, Self-Trapping of Excitons, in Modern Problems in Condensed Matter Sciences, vol. 2, p.543, Ed. by V. M. Agranovich and A. A. Maradudin, Notrh Holland, Amsterdam (1982). 6. Excitonic Processes in Solids by M. Ueta, H. Kanzaki, K. Kobayashi, Y. Toyozawa and E. Hanamura, Springer-Verlag, Berlin (1986). 7. I. B. Bersuker, The Jahn- Teller Effect, New York, IFI/Plenum (1983). 8. K. A. Kikoin and A. S. Mishchenko, Sov. Phys. J E T P 7 7 , 828 (1993). 9. K. Huang and A. Rhys, Proc. Roy. Soc. (London) A 2 0 4 , 406 (1950). 10. R. C. O'Rourke, Phys. Rev. 9 1 , 265 (1953). 11. A. S. Mishchenko and N. Nagaosa, unpublished.
RELAXATION OF EXCITONS INTO CHARGE-SEPARATED PAIRS IN PbBr2 AND PbCl2 CRYSTALS MASANOBUIWANAGA Graduate School of Human and Environmental Studies, Kyoto University, Kyoto 606-8501, Japan
MASAYUKIWATANABE and TETSUSUKE HAYASHI Faculty of Integrated Human Studies, Kyoto University, Kyoto 606-8501, Japan We have studied the relaxed state of excitons in PbBr2 and PbCh crystals from the photoluminescence (PL) properties at low temperatures. The analysis of decay curves of intrinsic PL band reveals that excitons relax into charge-separated pairs of a self-trapped electron and a self-trapped hole in both crystals. The relaxation of excitons, found experimentally for the first time, is ascribed to the repulsive correlation via acoustic phonons between the electron and hole.
1. Introduction Lead halide crystals show various properties under UV or X-ray irradiation; photochemical decomposition at room temperature,' intense photoluminescence (PL) with large Stokes-shift,2 and self-trapping of electrons at low temperatures.3 All of these phenomena suggest that strong electronphonon interaction plays an important role in the relaxation dynamics of photo-excited electrons. In particular, PbBr2 and PbCl2 crystals belonging to the crystalline group D ^ have similar electronic band structures;4-6 the upper edge of the valence band is composed of hybrid orbits of nporbits of (halogen)- and 6s-orbits of Pb 2+ , and the conduction band is mainly composed of 6p-orbits of Pb 2+ . Moreover, PbBr2 and PbCl2 show similar PL properties at low temperatures;2 one PL band is mainly induced under excitation into the exciton band, and the other is mainly induced under bandto-band excitation. The origin of each PL band was attributed to the recombination of self-trapped excitons and electron-hole (e-h) pairs, respectively.2,7 That is, it was thought that two different relaxed states exist in PbBr2 and PbCl2, depending on the excitation energies. To clarify the intrinsic relaxed states of photoinduced carriers, it has been desired to examine the PL properties in both crystals. We have measured PL spectra, the one- and two-photon excitation spectra, and the decay curves of PL in PbBr2, and investigated the intrinsic relaxed state of excitons from the PL properties, so that it has been found that excitons relax into charge-separated pairs in the intrinsic relaxation process.8,9 Our recent investigation on the PL properties of PbCl2 also reveals that excitons decompose into charge-separated pairs just as in PbBr2. We present in this paper the PL properties in PbBr2 and PbCl2, clarify the intrinsic relaxed state of excitons, and discuss the physical origin of the exciton relaxation in both crystals from the comparison with the theoretical study by Sumi.10 2. Experimental Procedures The crystals of PbBr2 and PbCl2 were grown with the Bridgman technique from the powder of 99.999% purity. The powder of PbBr2 was previously purified under vacuum distillation. Both crystals were cleaved in ai-plane perpendicular to c-axis, for optical measurements. PL was induced by the light from an optical parametric amplifier (OPA) and detected by a CCD camera equipped with a grating monochromator. For obtaining two-photon excitation spectra, a sequence of PL spectra under two-photon excitation was measured with the CCD camera by scanning the energy of incident light from an optical parametric oscillator (OPO). The OPA and the OPO were pumped by the third harmonics from a Nd:YAG laser operating at 10 Hz or 30 Hz. Decay curves of PL induced by the pulsed 5-ns light from the OPA were measured with a photomultiplier (PM) equipped with a grating monochromator. The measurements of excitation spectra were performed with a Xe lamp equipped with a grating monochromator, and the PM. All the measurements were carried out below 10 K. The condition ensures that all the PL properties discussed here are independent of temperature. 109
110 3. Results Figures 1 (a) and 1 (b) show PL spectra (solid lines), the corresponding one-photon excitation spectra (dashed lines), and two-photon excitation spectra (dots) of PbBr2 and PbCh, respectively. The blue PL band peaked at 2.74 eV (B band) in Fig. l(al) is mainly induced under excitation into the exciton band.2 On the other hand, the blue-green PL band at 2.6 eV (BG band) in Fig. 1 (a2) is mainly induced under band-to-band excitation. Dots in Figs. I(a3) and l(a4) respectively denote two-photon excitation spectra for E || a and E || h configurations;" prominent peaks are located at 3.93 eV for both configurations and at 4.07 eV for E || a. Solid lines in Fig. I(a3) and l(a4) are the PL spectra induced under two-photon excitation at 3.95 eV (arrows). The PL spectra are composed of B band and BG band as shown later in Fig. 2. In Fig. 1(b), similar spectra of PbC^ are presented. The ultraviolet PL band at 3.77 eV (UV band) in Fig. l(bl) is mainly induced under excitation into the exciton band, and the blue-green PL band at 2.5 eV (BG band) in Fig. I(b2) is mainly induced under band-to-band excitation. Dots in Figs. I(b3) and l(b4) denote two-photon excitation spectra for E || a and E || b, respectively;b prominent peaks are located at 4.60 eV and 4.66 eV for E || a, and at 4.67 eV for E || b. Solid lines in Figs. I(b3) and l(b4) denote PL spectra under two-photon excitation at 4.66 eV (arrows). Time-resolved measurements revealed that the PL band at 2.6 eV in Figs. I(b3) and l(b4) are composed of 80% BG band and 20% PL band at 2.7 eV. We do not discuss the weak PL band at 2.7 eV, because of the extrinsic signs.1' (a) PbBr2
(b) PbCl, i i i | i ii
i | . i i i | i i i i | i i i i
(bl)
>C\ •
/
O"2'
_ yV E " a A../
\
3.5
ENERGY (eV)
4.0
2.5
3.0
(M) \ ;' EII b ; /
/ \
>> 3.0
rfJ^i
3.5
4.0
4.5
5.0
5.5
ENERGY (eV)
Fig. 1. PL and the excitation spectra of (a) PbBr2 and (b) PbCl2. (al) and (a2): B band and BG band (solid lines) excited at 3.81 eV and 4.43 eV (arrows), and the excitation spectra (dashed lines) observed at 2.95 eV and 2.38 eV, respectively. (a3) and (a4): PL spectra (solid lines) under two-photon excitation at 3.95 eV (arrows) for E || a and E || b, respectively, and the corresponding two-photon excitation spectra (dots), (bl) and (b2): UV band and BG band (solid lines) excited at 4.80 eV and 5.39 eV (arrows), and the excitation spectra (dashed lines) observed at 3.76 eV and 2.34 eV, respectively. (b3) and (b4): PL spectra (solid lines) under two-photon excitation at 4.66 eV (arrows) for E || a and E || b, respectively, and the corresponding two-photon excitation spectra (dots).
Figure 1 shows that PbBr2 and PbCi2 have similar luminescent properties; each crystal has a PL band mainly induced under excitation into the exciton band, and a PL band mainly induced by photons with higher energies than the energy of exciton absorption. Moreover, the electronic and optical properties are similar to each other under two-photon excitation: (i) Both of them have prominent peaks in the exciton absorption region, (ii) The PL spectrum under excitation into the exciton band is mainly composed of BG band in each crystal. According to excitation-power dependence of PL spectra, the intensity of each BG band, 7BG, was 7BG X I2 U- excitation-power of incident light), but the intensities of B band, 7B, in PbBr2 and of UV band, 7uv. in PbCl2 were 7B <* I13 and 7uv «I 0 6 , a Two-photon excitation spectra were obtained by dividing the integrated intensity of PL by the mean square intensity of incident light. b We integrated over the PL spectra from 2.2 eV to 3.2 eV, to obtain the two-photon excitation spectra in Figs. I(b3) and l(b4).
111 respectively. We have found for the first time that BG band in each crystal is induced even under excitation into the exciton band. From the prominent peaks and the edge of continuous rise in the two-photon excitation spectra, the exciton band corresponds to excitation energies over 3.8-4.1 eV in PbBr2 and 4.5-4.86 eV in PbCl2, and the band-gap energies of PbBr2 and PbCl2 are 4.1 eV and 4.86 eV, respectively.
TIME(s) Fig. 2. Decay curves of PL in PbBr2, represented with the log-log scale. Curve a (solid line): under band-to-band excitation at 4.35 eV, observed at 2.53 eV. Curve b (solid line): under two-photon excitation at 3.95 eV, observed at 2.64 eV. Dashed lines: calculated curves of BG band derived in Sec. 4. Dotted line: the difference between the curve b and the dashed line, in agreement widi the decay curve of B band.
Figure 2 shows decay curves of PL in PbBr2 under band-to-band excitation at 4.35 eV (curve a denoted by a solid line) and two-photon excitation at 3.95 eV into the exciton band (curve b denoted by a solid line). From the energies of observation, the curve a is almost the decay curve of BG band, and the curve b is composed of the curves of BG band and B band. Dashed lines in Fig. 2 are calculated curves of BG band, based on the recombination model described in Sec. 4, and a dotted line is the diference between the measured curve b and the calculated curve, in agreement with the decay curve of B band with the decay time of 3 /us. Thus, the decay curve b is resolved into those of BG band and B band. Similar analysis of decay curves for PbCl2 revealed that the measured curves are well described by the calculated curve derived from the same model applied to PbBr2. In both crystals, the intensities of BG band decay in proportion to t~l for sufficiently large t. 4. Discussion We first discuss the properties of the PL bands in PbBr2 and PbCh to clarify the intrinsic PL bands. The one- and two-photon excitation spectra in Figs. 1(a) and 1(b) indicate that B band in PbBr2 and UV band in PbCh are induced under excitation below and into the exciton band. Furthermore, the intensities of B band and UV band are not proportional to the number of excitons created under two-photon excitation, but show saturating tendencies. Thus, it is unlikely that B band in PbBr2 and UV band in PbCh are intrinsic PL bands. One of the plausible origins of the two bands is the recombination of localized excitons captured by dense lattice defect in the surface layer;12 one-photon excitation creates excitons only in the surface layer because of the large absorption coefficient.4'13 On the other hand, each BG band is induced under excitation into the whole fundamental absorption region including the exciton band, and moreover the intensity is proportional to the number of photoinduced excitons. These results indicate that each BG band is intrinsic PL band. To clarify the origin of BG bands, we derive the decay curve describing the measured curves in Fig. 2. In doped alkali halides, decay curves obeying t~l for sufficiently large t were observed and analyzed from the model containing tunneling of localized carriers.14'15 The model is as follows: First, either of a trapped electron and a trapped hole, which are photoinduced, tunnels toward the other.
112 Second, the pair forms a trapped exciton, and finally recombines with the decay time t. The above model can be applied to PbBr2 and PbCl2 by regarding trapped carriers as self-trapped carriers. We adopt here three assumptions modified from the earlier reports: 14 ' 15 (i) Recombination rate, p(R), of the pairs separated by a distance R is given by p(R) = ( 1 / t ) exp(—a(R - Ro)), where a is a constant and Ro the minimum distance of the pairs, (ii) The density of the pairs is enough low to discriminate a pair from the other, that is, NoR^/V
LATTICE-RELAXATION AND ENERGY-TRANSFER OF FRENKEL AND CHARGE-TRANSFER EXCITONS IN MOLECULAR CRYSTALS SUZUKI Masato Department of Physics, Graduate School of Science, Osaka City University, Sumiyosi-ku, Osaka, 558-8585, Japan We investigate the lattice-relaxation processes and the energy-transfer of excitons in crystalline C 60 , so as to clarify natures of the photoinduced polymerization process in this crystals. We calculate the adiabatic potential energies for Frenkel and charge-transfer (CT) excitons individually, relevant to the photoinduced dimerization processes occurring in a face centered cubic crystal of C 60 . The potential surfaces of the Frenkel excitons lead to the conclusion that structural defects are expected to exist at low temperatures even in the single crystal as an intrinsic property of this crystal. From the analysis of the potential surfaces of the CT excitons, it is confirmed that the CT exciton relaxes down to its self-trapped state, wherein the adjacent two molecules get close together. This implies that the CT between adjacent two molecules is one of mechanisms that triggers the photodimerization or the photopolymerization in crystalline C 60 .
1. Introduction As is well known, the Cgo crystal undergoes the structural phase transition from the fee to the simple cubic at the temperature Tc=260 K.1 Above Tc, the molecules rotate almost randomly around their lattice positions. The molecular rotation becomes restricted below Tc and it is finally frozen at 90 K. The polymerization has been reported to occur above Tc by the optical excitations with visible or UV light. 2 In this polymer phase, it was proposed that the adjacent molecules are coyalently linked by a four-membered ring joining the two molecular cages through the photochemical [2+2] cycloaddition reaction. Thus, the intermolecular bond changes from the van der Waals type to the covalent one as a consequence of the optical excitation. In order to see a role of the optical excitation in the polymerization process, let us briefly mention the nature of excitons and their lattice relaxations in molecular crystals such as Cgo- When we consider the interaction between excitons and phonons in molecular crystals, it is useful to classify the excitons into three types; free, Frenkel, and charge-transfer (CT) excitons, according to the distribution patterns of the electron-hole pair. The Frenkel exciton is basically an intramolecular excited state, and its motion is mainly restricted in one molecule, while only rarely it hops to other molecules through a weak intermolecular interaction. Therefore, the Frenkel exciton will strongly interact with the intramolecular vibrations rather than the intermolecular ones (lattice phonons). On the other hand, in the case of the CT exciton, an electron and a hole are divided into adjacent two molecules and they interact through the Coulombic force so as to make the intermolecular excitonic state. This means that the interaction between the CT exciton and the lattice phonons is strong compared with the case of Frenkel exciton, and this interaction brings about the large intermolecular lattice relaxations of the CT excitons. Therefore, the CT followed by the lattice relaxation will be the key mechanism of photodimerization. In the present paper, we investigate the adiabatic natures of the lattice relaxation and the energytransfer of the photogenerated excitions in the crystalline C^Q, SO as to clarify the mechanisms of the photoinduced polymerization in this crystal. 2. Model Hamiltonian and calculation methods In order to clarify the mechanism of the photodimerization processes in crystalline Cgo. w e investigate a many-it-electron system described by the following model Hamiltonian (=//), wherein the elastic energies between carbons are taken into account by effective potentials. H is given as (fi=l) H= //intra + Hj n t e r ,
(1)
//intra = 2 <=/, <*f/j,a aii.a + 2 (-Tuij a*li,a aij.a + H.c) + (7 2 n;,, a nufi + 2 Vny nu,a "lj,a' + 2 w«y. l.i.o l,i>j,a l.i l,i>j,o,d l,i>j « ) //inter = 2 (.-Tlfij ahi,a a.Vj,a + H.c) + 2 Vwij "li,a nrj.d1 + 2 a>ll'ij, t>l',i,j,a l>l',i,j,a,& l>l',i,j nii.o-ahi.oW.o-
113
(3) (4)
114 #intra denotes the Hamiltonian for the isolated molecules, and //inter is the intermolecular interaction. / indicates the fth C6o molecule and /' is its nearest neighbor ones, i or j represents the carbon in each C60 molecule, at;,- a (a;1>a) is the creation (annihilation) operator of a re-electron with spin a ( = a , P) at ith carbon site in Zth molecule. The first term in Eq.(2) means the site-diagonal part of the electronphonon interaction, and 6;,- is its interaction parameter. It is assumed to be inversely proportional to the distance {wwij) between lith carbon and other I'jth ones. Tmj or Tmj denote the resonance transfer integral of jt-electrons between carbon atoms. Its dependency on rwij is assumed to be an exponential function. U and V//,y (Vwij) denote the intrasite and intersite Coulombic repulsive energies, respectively. For Vwij, we use the Ohono potential. co//y and
115
FIG. 1. The adiabatic potential energy curves of the ground state and the lowest singlet and triplet excitons relevant to the dimerization process. The point of R?j=0 corresponds to the Franck-Condon state and Rtf=55 is the most stable dimerized structure in the crystal.
changes from the fee to the dimer. The energies of the fee and the dimerized structures are almost equal, and the energy barrier between them is about 2.5 eV. Moreover, these curves are quite uneven with several energy minimum points in the vicinity of Rtf=l, 14, 31, and so on. Therefore, these metastable structures are expected to exist as the structural defects with a relatively long lifetime at low temperatures even in the single crystal as an intrinsic property in such molecule crystals. From the potential curves of CT excitons, we can see that the CT exciton have a tendency to attract the adjacent two molecules immediately after the photoexcitation, and it will relax down to its self-trapped state, as appeared at Rff « 7. Because the two molecules close to each other as a result of the self-trapping, it is concluded that the CT between adjacent two molecules is one of the trigger mechanisms for the photoinduced dimerization. 4. Speculation for energy transfer in crystal with defects and dimer Let us briefly speculate how the dimerization is completed in the crystalline Ceo- The energy barrier between the fee and the dimer has been computed to be about 2.5 eV. So, it is difficult to dimerize through the relaxation of the relatively low-energy single exciton. Therefore, the multiphotons are needed to achieve the dimerization. That is, the dimerization will be completed when the energy of such metastable states as the defects exceeds the energy barrier by using the stepwise multi-photoexcitation, which will lead to the successive structural changes. Therefore, in this section, we investigate the behavior of the photogenerated excitons in the crystalline C^Q wherein the defects and/or the dimer have already been produced by the previous photoexcitations, so as to clarify how the defects or the dimer can cause nucleus of the successive structural changes that are induced by the subsequent photons. For this purpose, we consider the possible mechanisms of the energy-transfer of the excitons from bulk to defects or dimer which have already existed. In general, in such molecular crystals as Ceo, the exciton energy is considered to be transferred through the Fbrster mechanism or the exciton-transfer. However, the lowest singlet exciton in Cgo molecule is dipole forbidden to the ground state so that the Forster mechanism is less possibly the mechanism of energy-transfer even in the crystal. Contrary to this, the excitons possibly hop to the other molecules through the weak resonance transfer integral between molecules. Hence, we hereafter focus only on the exciton-transfer as the mechanism of the energy-transfer in this crystal. On the basis of the Fermi's golden rule, let us qualitatively compare the transition probabilities of exciton from the bulk to the defects or the dimer with the hopping probability of exciton in the single crystal, that is the bulk to bulk transition. In the previous section, we have calculated the local density of states (LDOS) of the Frenkel and the CT excitons created in the bulk, the three types of defects, and the dimer. They are appeared on the adiabatic potential energy curves of Fig.l at RN=Q, 7, 14, 31, and 55, respectively. We here calculate the overlap intensities of the LDOS between bulk and bulk (-/o), bulk and defects (ml\, I2, and 73), and bulk and dimer (-74) for the cases of the Frenkel and CT excitons. These overlaps approximately express the probabilities of the resonance transfer of the excitons between them.
116
°
1.5
2
2.5 3 Energy (eV)
3.5
4
1.5
2
2.5 3 3.5 Energy (eV)
4
FIG. 2. The overlapy intensities of the local density of states between bulk and bulk (•/()). bulk and defects (•/[, li, and 73), and bulk and dimer (3/4) for the cases of (a) Frenkel and (b) CT excitons. The overlap intensities of LDOS are shown in Figs.2(a) and (b) as a function of exciton energy ; (a) is the case of the Frenkel exciton and (b) is the CT exciton. From these figures we can see the qualitative properties of the exciton-transfer as follows. It can be seen from Fig.2(a) that the overlap intensities l\, I2, h, and I4 are higher than /rj in the energy regions below 2.5 eV and around 3.1 to 3.7 eV. Therefore, in these energy regions, it is quite possible for the Frenkel excitons to transfer from the bulk to the defects or the dimer through the resonance interaction. Contrary to this, as shown in Fig.2(b) I\, I2, h, and I4 has the intensities smaller than IQ, because the density of states of CT exciton in the defects and the dimer shift toward the low-energy side as compared with that of the CT exciton in the bulk crystal 6 . This means that the CT exciton in the bulk is less trapped resonantly in the defects or the dimer than the Frenkel exciton. 5. C o n c l u s i o n s The following conclusion is derived from the above results. As seen in the previous sections, the CT exction has a strong tendency to induce the local lattice distortion through the lattice relaxation of exciton, and then the defects or the dimer are newly created in the single crystal. On the other hand, the Frenkel exciton can not be expected to cause the lattice relaxation, and it has a strong tendency to transfer to the defects or the dimer which have been already existed in the crystal. As the results of these processes, it is concluded that the exciton energies gather at the defects or the dimer, and the collected excess energy can induce the novel lattice relaxations around them. If this process is repeatedly occurred with the help of the multi-photoexcitations, finally the macroscopic structural changes will be induced. This is one of the microscopic mechanisms of the successive structural changes and the photoinduced structural phase transition due to the stepwise multi-photoexcitation in the crystalline C^oReferences 1. P.A.Heinly, J.RFisher, A.R.McGhie, W.J.Romanow, A.M.Denenstein, J.P.McCauley,Jr., A.B.Smith.III and D.ECox, Phys.Rev.Lett. 66, 2911 (1991). 2. A.M.Rao, P.Z.Zhou, K.-A.Wang, G.T.Hager, J.M.Holden, Y.Wang, W.-T.Lee, X.X.Bi, P.C.Eklund, D.S.Cornett, MA.Duncan and I.J.Amster, Science 259, 955 (1993). 3. C.S.Yannoni, P.P.Bernier, D.S.Bethune, G.Meijer and J.R.Salem, J.Am.Chem.Soc. 113,3190 (1991). 4. J.Arbogast, A.Darmanya, C.Foote, Y.Rubin, F.Diederrich, M.Alvarez, S.Anz and R.Whetten, J.Phys.Chem. 95,11 (1991). 5. V.Capozzi, G.Casamassima, G.F.Lorusso, A.Minafra, R.Piccolo, T.Trovato and A.Valentini, Solid State Commun. 98,853(1996). 6. M.Suzuki, T.Iida and K.Nasu, Phys. Rev. B 61, 2188 (2000).
R A R E GAS PRECIPITATES IN METALS AS Q U A N T U M DOTS FOR T H E POLARITONS
IGOR GOLINEY and VOLODYMYR SUGAKOV Institute for Nuclear Research, Ukrainian Academy of Sciences, pr. Nauki J,l Kyiv, 03680, Ukraine
Energy spectra of the size quantization of excitons in Xe, Kr, Ar and Ne precipitates in Al and their manifestation in reflection spectra are calculated taking into account polariton effects (dipole-dipole exciton interactions), spatial dispersion and mixing of the electronic excitations of the inclusion with collective excitations of the surrounding metal (plasmons). It was shown that: 1) the proximity of energies of the exciton levels and the plasmons localized on the inclusion (surface plasmons) results in the gigantic shift (up to 1 eV) of the levels of coupled excitations, 2) the transfer of the oscillator strength from the plasmon level to the exciton levels leads to the amplification of optical transitions in bubbles by several orders of magnitude. Depending on the position of the surface polariton with respect to the surface plasmon the spectra either show additional broadenning due to the coupling with quantized exciton levels (Ar, Ne) or the polariton level is pushed out of the exciton band and manifests itself as a narrow dip in the reflection spectra. Keywords: Rare gas precipitates, surface plasmons, surface polaritons, size quantization 1. Introduction This paper presents results of the theoretical study of excitons in small crystallites of the rare gas atoms in metals. Rare gas atoms introduced into a metal matrix by ion implantation or created as a result of nuclear reactions have low solubility in the metal matrix and tend to collect into bubbles. The behavior of nanometer-size precipitates of noble gases in materials has been studied extensively because of problems associated with the development of fusion and fission reactors 1 . Pressure inside the bubbles reaches very high values, tens and hundreds kilobar. In these conditions rare gases crystallize at higher temperature. High temperature crystallization (precipitation) of rare gases in bubbles was discovered experimentally by electron and X-ray diffraction 2,3 ' 4 ' 5 . Crystallization of Xe in Al, Ar in Al, Kr in Cu, Ni and Au can be mentioned as the examples. Melting temperature of the rare gas precipitates can be very high. For instance, crystallized Kr in Ni exists up to the temperature of 825-875°K while at atmospheric pressure melting occurs at 115°K 2 . The paper presented here concentrates on the optical spectra of rare gas precipitates in metals. Small size of the precipitates leads to the quantization of the excitations. In fact considered system is an example of quantum dots that attract so much attention nowadays. Some aspects of the low dimensional quantization of small radius excitons in dielectric media were studied in the papers 8,9,10 . The present paper reports results of the calculations of the energy spectrum and the spectra of reflection of the electromagnetic waves by metals containing Xe, Kr, Ar, Ne precipitates. 2. Optical properties of a metal w i t h precipitates The determination of the optical properties of the precipitates is based on the solution of the problem of light scattering by a spherical inclusion in a metal matrix. Let us consider scattering of a plane electromagnetic wave E = E 0 e x p ( i k r — iurt) by a spherical inclusion. The system is
117
118 described by a set of Maxwell equations and Schrddinger equation for the exciton polarization. Equations for the polarization have the following form
^ ^ ^ T r "
h(cj-u0
+ irin/2)Pex
1
^
1
+ —APex
oj(ui + iTm)P2
(1)
^ * '
= - ^ E
(2)
u
= -^E2
(3)
Here index 1 refers to the medium inside the inclusion and index 2 refers to the metal, Pex is the exciton part of polarization of inclusion, o;0 is the frequency of the exciton band bottom of the material inside the inclusion, uip is the plasma frequency of the metal, £oo is the dielectric constant of the rare gas crystal accounting for the contribution into the polarization of all states except the exciton band under consideration, f3 = UILT^OSOO/'^, where U>LT is the transverse-longitudinal splitting for the exciton band, a = hu>0/M where M is the effective exciton mass, Tin is the damping constant of material of inclusion, Tm is the damping constant of metal. Fields and polarization should satisfy Maxwell equations and Maxwell boundary conditions and additional boundary conditions that will be chosen in the form of the zero exciton polarization at the boundary of the inclusion allowing exciton to reflect elastically from the interface 11 . Pex\r=R = 0. (4) Solutions of the sytem of Maxwell and polarization equations inside and outside the inclusion that satisfies the boundary conditions have been found by expanding fields into series of spherical harmonics. Knowing the coefficients of the expansion the cross section of the scattering can be determined. Since the size of crystallized precipitates are much smaller than the wavelength of the electromagnetic field the dipole term (/ = 1) of the transverse magnetic wave is dominant in the scattering. Polarizability of the dielectric sphere can be determined as a
{R)
3ic2
=
AqlJd/dR)
Qml
where h\
ln(flji(fcifl)) - Bk2{d/dR)
InjRj^R))
^2^2Aql{d/dR)\n{Rj1{klR))-Bkl{dldR)\n{Rh^\q2R)y
is a spherical Hankel function, q2 = A
= l ~ ^^fF2F{R), ( R ) > a2k( = 1
'
s/e2w/c,
B=1-^F(R)-^(1-F(R)), B=l-*F{R)-^( a2 aQ
(6)
2 - nR2(d/8R) HRjrjhRW/dR) ln(flj t (fe,fl)) 2-nR2(d/dR)ln{Rj1(k2R)){d/dR)\n(Rj1(k0R))' kl = — {w - wo - uLT + iTin/2),
(>
(8)
fci and k2 are the roots of the biquadratic equation fc4-
f - j T - ( w - u 0 + iT/2) + £ ° o ^ - ) k2 + ej^kl=
0.
(9)
Index j = 0 corresponds to the longitudinal wave while indeces j = 1,2 enumerate two types of the transverse exciton waves that would exist in the infinite crystal. otj, (j = 0,1,2) are defined as -
£
~ 4TT h2k]/2M
^LT + hu*,-hu>-
inTin/2
(10)
119
080-
^
^
f
I
Reflection
0.60-
Ar 0.40-
Transmission 0.20-
0.00 - j
^v^V
10 00
Exciton band bottom (eV)
^
i
•
1100
i
12 00
i
13 00
^
•
i
14 00
Frequency. eV
Figure 1: Dependence of the position of the levels of the surface polaritons and the surface plasmons for the spherical inclusion in Aluminum on the energy of the bottom of the exciton band of the material of inclusion. The dashed regions correspond to the exciton bands of the bulk material. The energies of the bottom of the exciton band for different rare gas crystals are shown along the x-axis.
Figure 2: Reflection and transmission spectra of Al with Ar precipitates. Reflection spectrum is calculated for the case of infinite metal matrix. Transmission is calculated for the film thickness of 50 nm.
Using the polarizability of the spheric inclusion given by Eq. (5) the dielectric constant and the reflection coefficient of the metal with a system of spheric precipitates have been calculated. Random distribution of the precipitates in the metal has been assumed for the calculations. Additionally, the spectra of the excitations localized on the precipitates were calculated in the limit of negligable effects of retardation and damping. 3 . C a l c u l a t i o n s and D i s c u s s i o n The spectra of excitatations and optical spectra were calculated for the precipitates of different rare gases in Aluminum. The calculations were performed for the values of excitonic parameters of the respective bulk rare gas crystals. The review of the studies of excitons in rare gas crystals can be found in the monograph 12 . The polarizability (5) contain singularity which correspond to positions of excitation levels in the system. In the case of the absence of both spatial dispersion M —> oo and effect of damping and retardation the singularities could be found from the reduced equation {I + l)e 2 + lei = 0,
(11)
where £i is the dielectric constant of the material of precipitate in the case of absence of spatial dispersion £i
:
1 + OJQ
— W2J
U2
Eq. (11) determines the position of the levels of the polariton excitations localized on the spherical inclusion (surface polariton) and surface plasmon. A unique feature of the considered system of rare gas precipitates in Aluminum is the fact that the frequencies of the surface plasmon and the surface polaritons are situated close to each other. This fact manifests itself in a number of remarkable effects in the energy spectrum and optical properties of the system. Fig. 1 schematically shows calculated from the equation (11) dependence of the position of the energy of the surface plasmons and polaritons on the value of
120
Ne o °' Z0 ~
s IT
0.10-
b
o.eo-
0.40-
lifi
V' -i—' 17.00
1B.0O
r~ 19.00
0. 20.00
Frequency, eV
Figure 3: Optical reflection spectra of Al with Ne precipitates.
-| 10.00
11.00
12.00
13.00
14.00
Frequency, eV
Figure 4: Optical reflection spectra of Al with Ar precipitates.
the frequency of the bottom of the exciton band u>o for the oscillations with / = 1 which interact strongly with light. Positions of the bottom of the exciton band for the real rare gas crystals are shown for reference. Strong resonant interaction between the excitation modes of the inclusion and the localized plasmons leads to the shift of the bands and to the essential change of their intensity. Frequency shift is proportional to i/utyJIr- Since for Aluminum hcup ~ 15 eV and for the rare gas crystals hwir ~ 0.1 eV, the shift of the of the energy levels may be up to 1 eV. Due to the finite value of the exciton band width the effects of the size quantization appear. The spectra of the excitations can be studied by optical transmission and reflection. Since the metal matrix is not transparent the experiments studying transmission spectra should be performed with very thin films. Fig. 2 shows for comparison transmission and reflection spectra of Al with Ar precipitates. Transmission increases in the regions of spectra in the vicinity to excitations. Excitations contribute both to the absorption and transmission. Effectively, light propagates through the metal tunneling from one inclusion to another. Figs. 3-6 show the results of the calculations of the reflection spectra of the ultra violet light from the Aluminum crystal containing precipitates of Ne, Ar, Xe, Kr. For the Aluminum matrix the decay constant was set r m = 0 . 1 eV, for the precipitate r i n = 0 . 0 1 eV in the case b and Vin = 0.1 eV in the case a. Calculations are performed for the inclusions with radius R — 2.5 nm for the bulk share of the precipitates in the metal S = 0.01 (S = 47riV.R3/3, where N is the concentration of inclusions). Dashed lines in the figures show the reflection spectra for the case when the spatial dispersion is not taken into account (Af —> oo). One can observe strong dependence of the intensity of the bands (depth of the dips) on the position of the values of the bottom of exciton band with respect to the localized plasmon frequency. This effect is due to the mixing of the exciton and plasmon states and the transfer of the oscillator strength from surface plasmons to excitons. Spectra of Al with Kr and Ar show the deepest dips (Fig. 4 and Fig. 5). Ne precipitates manifest themselves in the reflection spectra very weak (Fig. 3) since the exciton band is very far from the position of the surface plasmon level. The levels of the discrete spectrum are mixed with the level of the the surface polariton (for Ar) or surface plasmon (for Xe and Kr). Those of the discrete levels that are closest to the level of either surface polariton or surface plasmon manifest themselves most strongly. For Xe and Kr precipitates the level of the surface polariton is pushed out of the exciton band and its position depends weakly on the radius inclusion radius. Therefore this mechanism of broadening does not apply to the mentioned precipitates and the surface polariton spectral line should be narrow (see the lowest frequency band in Figs. 5 and 6).
121 1.20-
0.80-
0.40-
9.00
10.00
11.00
12.00
13.00
14.00
Frequency, eV
. nT |
0.00 - | ,.6.00
8.00
6.00
6.00
Xe
i
10.00
12.00
14.00
10.00
12.00
14.00
Frequency. eV
Figure 5: Optical reflection spectra of Al
Figure 6: Optical reflection spectra of Al
with Kr precipitates.
with Xe precipitates.
For the very small precipitates the spectrum of the excitations deforms and the lowest discrete level is the most prominent. 4. Conclusions Strong mixing of the precipitate excitations and localized plasmons results in the giant shift of the positions reflection and absorption spectrum bands, significant increase of the intensity of the excitations close to the frequency of the localized plasmons and strong redistribution of the position and the intensity of the levels of the quantized exciton spectrum of the precipitate. The considered system may have potential application for becoming novel and future devices working in ultraviolet and for the study of phase transitions in nanostructures14,15,16. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.
V.N.Chernikov, W.Kosternich and H.UUmaire. J. Nucl.Mater. 227, 157 (1996). J.H.Evans, D.J.Mazey. Jour.Phys.F. 15, LI (1985). W.Jager, R.Manzke, H.THnkaus et al., J. Nucl. Mater. 111/1X2, 674 (1982). D.I.Potter, C.J.Rossouw, J. Nucl.Mater. 161, 124 (1989). K.Mitsuishi, M.Kawasaki, M.Takeguchi, K.Furuya, Phys.Rev.Lett. 82(15), 3082 (1999). S.E.Donnelly, A.A.Lucas, J.P.Vigneron, Rad. Bff. 78 337 (1983). S.E.Donnely, J.C.Rife, J.M.Gilles and A.A.Lucas, J. Nucl. Mater. 93/94, 767 (1980). I.Yu.Goliney, V.I.Sugakov, Fizika Nizkikh Temperatur 11, 775 (1985). A.I. Ekimov, A.A.Onushchenko , M.E.Raikh, Al.L.Efros, Sov. Phys. JETP 63, 1054 (1986). I.Yu.Goliney, V.I.Sugakov, Ukr. Fiz. Zh. 33, 222 (1988). S.I.Pekar. Sov. Phys. JETP 6, 785 (1958). B.I.Verkiv and A.F.Prikhotko (Eds.) Kriokristaly (Kiev, Naukova Dumka, 1983, in Russian). A. von Felde, J. Fink et.al. Phys.Rev.Letts 53, 922 (1984). H.H.Andersen, E.Johnson Nucl.Instr.& Met. in physics research. Section B. Beam interaction with materials and atoms 106, 480 1995. 15. Q.Jiang, F.G.Shi, Materials Letters 37, 79 (1998). 16. M.Awaji, N.Ishikawa, K.Furuya, Nanostructures materials 8, 899 (1997).
ULTRAFAST ATOMIC DISPLACEMENT IN OPTICAL A N D SOFT X-RAY SPECTROSCOPIES
YOSUKE KAYANUMA College of Engineering, Osaka Prefecture University, 1-1 Gakuencho Sakai, Osaka 599-8531, Japan SATOSHI TANAKA College of Integrated Arts and Sciences, Osaka Prefecture University, 1-1 Gakuencho Sakai, Osaka 599-8531, Japan Recent advances in the spectroscopies of the second order processes both in the optical region and in the soft x-ray region are reviewed from a theoretical standpoint. A peculiar role of the breathing and oscillating spectral hole in the femtosecond pump-probe experiments is pointed out. The resonant x-ray emission spectrum in diamonds at the core-exciton excitation is analyzed by a simple model, and it is shown that a ultrafast off-center displacement occurs in the core-excited state. 1. Introduction It has been one of the major goals of the optical spectroscopies to detect time-resolved atomic movements in the excited states of materials. This is essentially a subject of optical device technology, but it is only recently that the atomic motion in the excited molecules was detected as a series of snap-shots of optical spectra. 1 This opened a possibility to unveil what is going on in the black boxes of chemical reactions, and even to control them by optical techniques. Thanks to the succeeding developments in the femtosecond pulse laser technique, the ultrafast relaxation processes in condensed matter are now being investigated extensively. 2 ' 3 Concurrently, a similar rapid development is now taking place for the spectroscopies in the soft x-ray region, thanks to the advent of new-generation synchrotron radiation facilities. As a tunable and intense light source, the synchrotron radiation has brought about highly enhanced spectral resolutions, not only to the x-ray photoelectron spectra but also to the second order spectra such as the resonant x-ray emission (RXES) and resonant Auger electron (RAES). It should be noted that all of these second order processes in the core excited states are essentially ultrafast phenomena because the lifetimes of the core excited states are very short, typically of the order of femtosecond, due to the Auger decay. One of the long-standing controversies in the core level spectroscopy is, therefore, whether any atomic displacement takes place during this short lifetime of the core-excited states. The poor resolutions of the spectra in this region have been hampering the settlement of this controversy. However, we can now say the answer is definitely "yes", at least for materials composed of light elements like B, C and N. The enhancement in spectral resolution has revealed that there exist long tails, a signature of energy relaxation, in RXES and RAES for various systems. 4 In this paper, we select two topics on recent spectroscopies in condensed matter, one from the optical region and the other from the soft x-ray region, and we discuss some new aspects of ultrafast phenomena from the theoretical viewpoint. 2. Breathing Wave Packets Ten years ago, one of the present authors 5 proposed that ultrafast relaxation of phonon wave packets in a strongly coupled two-level electron-phonon system could be observed through a subpicosecond pump-probe measurement of the induced transmission gains. Such a spectroscopy, the so-called pump-and-dump spectroscopy, has now begun to be used widely for condensed matter. In the pump-and-dump configuration, the gain of the transmission comes roughly from
122
123 two origins, one from the saturation of absorption, and the other from the induced emission. The temporal oscillations of the induced gain are usually assigned as due to the damping oscillation of the wave packet in the excited state adiabatic potential energy surface. However, it seems to be not well recognized that the phonon wave packet created by the sub-picosecond light pulses not only oscillates but also undergoes a breathing motion. Namely, its width also oscillates. 5 Furthermore, a hole wave packet of is created in the ground state, which also oscillates and breathes. 6
Fig. 1. Schemtic picture of the wave packet motion in the excited state and the ground state after a pulse excitation.
We would like to stress here that this oscillation and breathing of the hole wave packet plays an important role in the pump-and-dump processes for strongly coupled electron phonon systems in the degenerate case. In fact, it is a universal characteristic that the induced gains AT of transmission in the femtosecond pump-probe experiments have a long-lasting osillatory component, if the probe pulse is tuned near the excitation frequency. For example, Nisoli et al.3 observed in their experiment on F-centers in KI an oscillation of AT that lasts for more than 4ps. This should not be assigned to the oscillation of the excited wave packet, since the damping of the wave packet in the excited state is generally very fast in solids. Likewise, Dexheimer et al.7 have recently observed a long-lasting component of A T in their experiment on the halogen-bridged mixed-valence metal complex. This is in contrast to the experimental data by Tomimoto et al.8 for an analogous system: They confirmed clearly that the timeresolved spontaneous emission signal indicates that the wave packet in the excited state decays rapidly from the absorption region. Dexheimer et al. correctly interpreted that the lomg-lasting component should be due to the oscillation in the ground state, but the mechanism to induce the oscillation in the ground state has been left unclear. We have calculated the induced transmission gain A T as a function of the frequency LO\ for a pump pulse with time-profile Exit) and w2 for a probe pulse with E2{t) within the standard model 5 of a strongly coupled localized electron-phonon system. By the application of the pairing-off theorem, an approximate expression for A T is obtained as OO
/ -oo
TOO
E^fdrJ
J —oo
-
(
EfaydTjF^UuTi-Tj
+ Fh^UuTt-Ti)},
'
(1)
where Fa(u>x) is the absorption spectrum, F a (a) 1 ) = (V27r^ 2 /D)exp[—(a;] — e)2/2D2], with e the center of the absorption spectrum, \i the transition dipole moment, and Fe(aj2,t±>i\t) and Fh(uj2,^i',t) are the transient hot luminescence spectrum and the hot hole spectrum, respectively. The term Fe(u!2,wi;t) represents the gain by the induced emission from the wave packet in the excited state, and F/,(ui2,^i',t) represents the gain by the saturation of absorption due to the wave packet of spectral hole in the ground state. The motions of the wave packets in
124 the adiabatic potentials in the excited state and the ground state are schematically shown in Fig.l. Note that the central energies of the packets exhibits a damping oscillation around the respective equilibrium points. In addition, their width also oscillates with a frequency roughly twice of that of the representative phonon. In Fig.2, examples of the numerical calculation of A T by the exact formula are shown for (a) (wuu2) = (e,e), (b) (e - 5w,e - 5Q), (c) (e -5Q,e60a)), (d) (e - 5u>, e - 80w). Here, it is assumed that the spectral density of the phonon has a width 0.7u> around the central frequency a), Huang-Rhys factor is 40, and the laser pulses have a Gaussian width of 0.2a>_1. The oscillation in (a) is solely due to the breathing of the hole. The long lasting oscillation in (b) is assigned as due to the oscillation of the hole. In (c), the probe frequency is tuned at the midway of relaxation, so that A T shows a spike profile, indicating the passage of the wave packet. In (d), the probe frequency is tuned at the center of luminescence. The oscillatory increase of AT in this case reflects the passage and advent of the wave packet at the relaxed excited state. Since the pump-probe measurements detect the change both of the excited state and the ground state indiscriminately, it is of crucial importance to interpret properly the observed signals. (a)
h~ (b)
(c)
(d)
-5 0
5 10 15 20 25 30
Delay (1/m) Fig. 2. Calculated transmission gain for a strongly coupled electron-phonon system.
3. Resonant x-ray emission in diamond Next we consider the Is RXES of carbon (diamond). In Fig.3 (a) the x-ray absorption spectrum at the Is edge and the resonant emission spectrum for C measured by Ma al.9 are shown. The absorption spectrum has a peak structure corresponding to the core exciton. The RXES spectrum has been measured for the resonant excitation to this core exciton state. As can be seen from the figure, it has a long tail extending to the lower energy side from the exciton peak. Ma et al. assigned this structure as due to the lattice relaxation in the core exciton state. It should be noted that the electronic structure of the core exciton in C is almost identical with that of a neutral nitrogen donor in C. This is known as the N+1 equivalent-core approximation. It has been well established that the N donor in C forms a deep level with an accompanied off-center atomic displacement in the [1,1,1] direction. Some numerical calculations have revealed that the central C atom of the core exciton state in diamond in fact has
125
- 3 - 2 - 1 0 1 2 3 4 5 6 7 PHOTON ENERGY (cV) Fig. 3. (a) The observed x-ray absorption spectrum (X) and the x-ray emission spectrum (o), and (b) the calculated values for the corresponding spectra. an off-center instability, with relaxation energy of about l.leV. 10 Therefore, it will be quite natural to consider that the observed tail in the emission spectrum reflects this relaxation. In order to confirm this point, we have performed a calculation of the RXES of the coreexciton state in C for a simple model. 11 We consder a small cluster of Td symmetry consisting of five carbons with the core excited C being at the center. In accordance with the strong localization picture, the wave function of the core-exciton is assumed to be confined within this cluster. An excited core electron occupies the anti-bonding state composed of four sp3 hybridized orbitals beteewn the central and the ligand atoms. For simplicity, we take into account only the displacement (Qx,Qy,Qz) of the central atom, which belongs to the T2 irreducible representation in the Td group. It is assumed that the anti-bonding orbital has an energy gain for the elongation of the orbital which is a linear function of Q. The Hamiltonian of the core-exciton state is then given by
( He
e
"
aQx aQy
\ OtQz
aQx ep
-PQ. -PQy
aQy
-PQ> e
P
-PQ*
aQz \ -PQy + H0 -PQX
(2)
ePJ
where e, and ep are the energies of the 2s and the 2p states, respectively, a and /? are coupling constants, and H0 represents the unperturbed lattice Hamiltonian. The above is the most general Hamiltonian representing the Jahn-Teller effect and the quasi Jahn-Teller effect in the space of (a x + i 2 ) x ?2. In Fig.4, the adiabatic potential energy surfaces of the core-exciton state along the [1,1,1] direction is plotted for parameter values chosen consistent with ab initio calculations. The unit of displacement is the zero point fluctuation of the lattice vibration, and the unit of energy is the representative phonon energy (0.16eV). As shown in Fig.3, the lowest branch of the potential energy surfaces has an off-center instability due to the quasi Jahn-Teller effect. The x-ray absorption spectrum and the resonant emission spectrum have been calculated for this vibronic model with a full quantum treatment of the lattice vibration. Since the coupling constants are estimated to be fairly large, a large number of basis states of vibrational quanta (about 6500) must be taken into account. In actual calculations, the method of Fourier transform of the generating function has been adopted, which reduces the memory-size required
126
0 Displacement [111]
10 < fH~\
Fig. 4. Adiabatic potentials of the core-exciton state of C along the [1,1,1] direction. to a large extent and thus makes the calculation tractable. In Fig.3 (b), the calculated spectra for the x-ray absorption and the emission are plotted for a suitable choice of parameter values. The lifetime in the core excited state is assumed to be 50fs, which is roughly half of the lattice oscillation period. The features of the observed spectra, especially the long tail of x-ray emission, are reproduced well, but the observed intensity ratio of the tail part to the Rayleigh scattering region is too large as compared with the theoretical result. The reason of this discrepancy is yet to be clarified. 4. Concluding Remarks It should be noted that the characteristic line shape of the RXES in C is nothing but an analogue of the hot luminescence in the optical region. When time-resolved, this hot luminescence exhibits the temporal features shown in Fig.2. Similar structures of dynamical origin have been observed also in RAES for small molecules. 4 On the other hand, the driving force to induce such a strong atomic displacements should be considered case by case. For example, the origin of the strong lattice relaxation in the core-exciton state in C can be regarded as the tendency of localization of the electron by breaking the bond. The analysis of these spectra will be useful in clarifying the ultrafast processes both in the core excited states and the valence orbital excited states. References 1. T.S.Rose et a!., J. Chem. Phys. 91, 7415 (1989). 2. T . T o k i z a k i et al., Phys. Rev. Letters, 6 7 , 2701 (1991). 3 . M.Nisoli et at., Phys. Rev. Letters, 7 7 , 3463 (1996).
4. M.Simon et al., Phys. Rev. Letters, 79, 3857 (1997). 5. Y.Kayanuma Phys. Rev. B, 41, 3360 (1990). 6. The possibility of transient hole burning in the strong coupling system has also been pointed out by Hama et al. in the oral presentation at the Sectional Meeting of the Physical Society of Japan, (1990). 7. Dexheimer et al. Phys. Rev. Letters, 84, 4425 (2000). 8. S.Tomimoto et al., Phys. Rev. B 60, 7961 (1999). 9. Y . M a et al., Phys. Rev. Letters, 7 1 , 3725 (1993).
10. A.Mainwood and A.M.Stoneham, J. Phys. Condens. Matter, 6, 4917 (1994). 11. S.Tanaka and Y.Kayanuma, Solid State Gommun., 100, 77 (1996).
INNER-SHELL TRANSITIONS AND SECONDARY EXCITONS IN SOLID XE AND KR
S. VIELHAUER, E. GMINDER, M. KIRM, V. KISAND, E. NEGODIN, B. STEEG, and G. ZIMMERER //. Institutfur Experimentalphysik, Vniversitdt Hamburg Lumper Chaussee 149, D-22761 Hamburg, Germany Time-resolved photoluminescence of the exciton emission in rare gas solids has 'f een measured for excitation in the range of inner-shell transitions. The excitons are created both 'promptly' (within the experimental time resolution) and 'delayed' through electron-hole recombination. Excitation spectra at the 4d edge in Xe and the 3d edge in Kr are discussed. An outstanding feature of the time resolved spectra is the strong resonance that appears in a short time window above a threshold energy, which is the sum of the ionisation energy of the core level and the energy of the (valence) free exciton. 1. Introduction The dynamics of photo-carriers in rare gas solids (RGS), including secondary exciton (SE) creation, has been investigated in detail within the last years. Time-resolved luminescence spectroscopy turned out to be an excellent experimental method for these investigations 1 ' 2 ' 3 . Among the SEs, we have to distinguish between excitons originating from electron-hole recombination, and excitons originating from inelastic scattering of photo-carriers or from multi-particle excitations. The different SEs have different temporal behaviour. The recombination-type SEs are delayed with respect to the excitation event; the other SEs are prompt within the experimental time resolution. In the case of the heavier RGS Kr and Xe, the delay is of the order of a few nanoseconds, as there are no optical phonons in the atomic fee lattice of the RGS. Therefore, thermalization of photoelectrons due to electron-acoustic phonon scattering considerably slows down the recombination. In this way, in time-resolved experiments under pulsed primary excitation, one can discriminate between recombination-type SEs and other SEs. In our experiments, mostly the luminescence offree excitons was studied. Provided these excitons have been excited directly, we use the abbreviation FE, while secondary free excitons are abbreviated FSE. Recombination-type FSEs are obtained with hv > Eg {hv: photon energy of exciting light, Eg: band gap energy). Above an excitation threshold £,/, = Eg + Ea (E,/,: threshold energy, Ea: energy of the FE with main quantum number n = 1), all RGS show a significant change in the decay curves of the FE emission. The relative amount of 'prompt' FSE emission increases strongly compared with the delayed recombination-type FSE luminescence, thus indicating the onset of inelastic scattering and/or multi-particle excitation. Two models were proposed for the prompt SE creation. The model of the electronic polaron complex developed by Devreese et al. 4 concerns simultaneous excitation of a free electron-hole pair and an exciton. Whereas the free electron-hole pair contributes to the delayed FSE emission, the excitonic component of the multi-particle excitation leads to prompt FSE emission. The second model, the multiple parabolic branch model of Vasil'ev et al. 5 proposes scattering of an electron with sufficiently high kinetic energy as a source of SE creation. This process, which leads to a 'multiplication' of electronic excitations following primary excitation with, e. g., x-rays, is well established for ionic crystals 6 .
127
128 (0
i
•E 600
i
i
i
i
i
1 o •- 400 c 300
_ -
103.8 eV •
—
_ -
8 200 c
*E 100 -i
10 15 20 25 Decay time (ns)
i i
_ _
-S 400 .•^200 CO
i
KrFE "
3
101.7eV~
n
•*•
0
5
4<-^-J
1-—..
10
15 20 25 30 35 40 Decay time (ns) Fig. 1. Decay curves of the FE emission lines at 8.4 eV in solid Xe (left), and 10.2 eV in solid Kr (right). The lower decay curves are measured at energies below the resonances, the upper ones are taken in the maxima of the resonances.
In the experiment to be described, for the first time, the experimental methods to analyse SE creation have been applied to inner-shell excitations, in particular to Xe 4d and Kr 3d excitation. In the results we present, pronounced resonances are observed above the Xe Ad and Kr 3d ionization energies in time-resolved FE excitation spectra, indicating SE creation simultaneous with inner-shell ionization. 2. Experimental Setup The experiments were performed at the undulator beamline BW3 of HASYLAB at DESY, which is equipped with a Zeiss SX700 monochromator. Luminescence was analysed with a 40 cm SeyaNamioka monochromator (typical resolution interval AX = 10 A), and detected with an open microchannel plate detector. Without deconvolution techniques, a time resolution of « 400 ps was achieved. An essential basis of the experiment is the pulsed nature of synchrotron radiation (at HASYLAB: pulses with FWHM of 130 ps, interval between two pulses 192 ns). The samples were grown in situ from gas phase under near thermodynamic equilibrium conditions at T = 84 K (Kr) and 103.5 K (Xe) with an average growing rate of ss 2/jm/min. The thickness was ss 0.4 mm. The samples were cooled down at a rate of « 0.8 K/min to typically 10 K, the temperature at which the spectra were taken. During measurements, the pressure in the sample chamber was in the low 10~9 mbar range. Luminescence excitation spectra were measured with a resolution interval of AE RJ 80 meV. The photon energy scale was calibrated with the absorption measurements of Haensel et al.7 and the total electron yield spectra published by Kassuhlke8. The absolute accuracy of the scale is about 0.1 eV. Irradiation at a fresh spot of a sample with soft x-ray photons creates defects in RGS, leading to considerable changes of the FE intensity during the first 15-20 minutes, accompanied by changes in the decay curves. After this time, the total intensity of the FE emission decreases slowly under further irradiation (on a time scale of several hours), without further changes in the form of the decay curves. As a consequence, the excitation spectra with high spectral resolution presented in this paper, which were taken during two to three hours, suffer from this decrease. Test measurements with inverted scanning direction or large step size have shown that all structures are reproducible, although the relative heights of peaks may differ considerably. This effect is more pronounced for Kr than for Xe. 3. Results and Discussion In Fig. 1, decay curves of the FE luminescence of solid Kr (photon energy 10.2 eV) and solid Xe (photon energy 8.4 eV) are shown. The photon energies of excitation are given next to the curves. The lower value is below the resonance of prompt FSE creation (see below), the higher value is in the maximum of the resonance. The curves consist of a fast prompt part, and a slow cascade-type part.
129 420
1—'—i—'—I—'—i—'—I—'—r Xe: short time window (5t=0 ns, At=1.2 ns)
400 380 360 340 320 300 280
*
260 240
w
220 200 60
I. i I . I i I i L 65 70 75 80 85
90 95 100 105 110 115 120 125 130 Excitation energy (eV) Fig. 2. Time resolved excitation spectra of the FE of Xe (60 - 95 eV) and Kr (85 - 130 eV). Both spectra are 'quick' with a large step size in order to avoid the irradiation-induced intensity losses during measurement.
The fast part originates from prompt FSEs, the slow one from recombination-type FSEs. The decay characteristics of the fast part agrees with measurements of FE lines obtained with photon energies of excitation, Eex < h\ < Eg. An increase of the fast part relative to the slow one within the resonances by approximately a factor of two is observed. In the remaining figures, time-resolved excitation spectra of the FE luminescence are presented. For these spectra, the FE luminescence was measured as a function of photon energy of excitation within a 'time window' (length At), which is delayed with respect to the excitation pulse by 8r. With 8f = 0 and small values of At (1 to 2 ns), the contribution of prompt SEs (spike of the decay curves in Fig. 1) is separated to a great extent from the one of recombination-type SEs. In Fig. 2, 'quick' scans with a rather large step size are shown for Xe and Kr. In both cases, a decrease of intensity is observed at the low energy side, followed by an impressive resonance and a further increase (Xe) or maximum (Kr) at the high energy side. High resolution spectra are shown in Fig. 3 (Kr) and Fig. 4 (Xe). In addition to the excitation spectra of prompt FSEs, time-integrated excitation spectra of the respective FE lines and absorption curves are included. The scanning direction was towards higher photon energies. Compared with Fig. 2, the influence of the decrease of intensity as a consequence of defect formation is obvious. The signals within the short time windows were multiplied by the factors given in thefigures.The contribution of prompt FSEs amounts to 5 to 10 % of all FSEs. All excitation spectra yield a pronounced decrease and a sharp minimum at the energy of the first
Krypton Xenon
Coree xciton ener gies B A 91.61° 90.28 " 91.46 b 65.28 " 64.36 " 65.27 * 7
£
loniz ation ener gies F'
5/2
92.32 c 92.22 b 65.70 c 65.59 *
Reso lance thresholc energies Efh (calc.) £,A (exp.) 102.46 " 102.3 102.36 ' 74.06 " 74.0 73.95 '
93.58 c 93.42 * 67.71 c 67.54 b 8
Positio l of the resonanct ; maxima Ri 102.8
103.9
74.8
76.8
9
a) Values from Haensel et al. b) Values from Kassiihlke . c) Values from Resca et al. d) Calculated with ionization energies from Resca et al.9 e) Calculated with ionization energies from Kassiihlke8. Table 1. Experimental values of the core exciton energies and the ionization energies in solid Kr and Xe, calculated and experimental threshold energies of the resonances of prompt FSEs, and the measured positions of the two maxima in the resonances. All values are in eV.
130
Excitation energy (eV) Fig. 3. Time integrated (full line) and time-resolved (circles) excitation spectra of the FE luminescence of solid Kr in the region of the 3d transitions. For comparison, an absorption curve measured by Haensel et al.7 is included in the lower part of the figure.
allowed core exciton, marked 'B' in the spectra (note, the minimum of the conduction band is s-type, therefore, the first exciton, A, is dipole-forbidden7'9). The following structures are anticorrelated to the absorption curves. This anticorrelation (minima of luminescence intensity at the energetic positions of absorption maxima) indicates surface quenching. Below the energies of thefirstallowed core excitons B, the signals in the excitation spectra exclusively arise from primary valence excitations. The FEs observed originate from inelastic scattering of the primary photoelectrons. The decrease in intensity is ascribed to surface quenching due to the reduction of the penetration depth of the exciting radiation at the onset of (allowed) d excitations. It is less pronounced in samples with structural defects. Above the characteristic threshold energies marked with arrows, striking differences between the time-resolved and time-integrated spectra are observed. Whereas the time-integrated spectra are smooth (Xe) or only modulated in the same way as below threshold (Kr), the time-resolved spectra yield pronounced resonances, which are split into two components R\ and R2. All numerical values are given in Table 1. It turns out that the experimental threshold energies correspond within the experimental accuracy to the sum of ionization energy of the weaker bound d5/2 states E'5,2 and the energy of the n = 1 FE,
The energy differences between R\ and R2 in Xe (2.0 eV) and Kr (1.1 eV) are close to the spin-orbit splitting of the Ad levels (1.97 eV) in Xe and the 3d levels in Kr (1.22 eV)7, indicating a superposition of two resonances coupled to the spin-orbit split d levels. Similar to the case of valence excitations10, both models described in the introduction have to be considered for the explanation of the resonance. From point of view of energy conservation, above the characteristic threshold energy, both inelastic scattering and electronic polaron complex formation can contribute to the prompt FSEs observed. The theory by Devreese et al.4 explicitely predicts a resonance. Moreover, Kunz et al. applied the model also to core excitations11. At first sight, the resonances observed seem to rule out the scattering model of Vasil'ev et al. because the scattering probability of the photoelectrons does not produce a resonance above threshold, but approaches a constant value. Nevertheless, the scattering probability includes all scattered states. Taking into account the branching between excitons and free electron-hole pairs, the probability for
131
64
66
68
70
72
74
76
78
80
82
84
Excitation energy (eV) Fig. 4. Time-integrated (solid line) and time-resolved (circles) excitation spectra of the FE luminescence in solid Xe in the region of Ad transitions. For comparison, an absorption curve from Haensel et al.7 is included (lower part of the figure).
FE creation yields a maximum as well5. The resonances observed are much more pronounced than those predicted by the scattering model. Therefore, we conclude that the resonances at least include significant contributions of the electronic polaron complex. In both models, more than one prompt SE may be involved, provided the excitation energy is sufficiently high. Indeed, both spectra yield a second threshold near to E'5,2 + 2Eex, indicating an additional excitonic side band to the core ionization. The second thresholds (theoretical values) are indicated by arrows in Fig. 2. Although the question remains open to which extent we observe inelastic scattering or creation of electronic polaron complexes, the strength of the resonances observed (see also already published results on valence band excitations10) leads us to interprete the results as a resonant enhancement of electron scattering above the threshold by the electronic polaron complex. Acknowledgement The work was supported by the German Bundesministerium fur Bildung und Forschung (grant 05 ST8GU1 6) and by the Deutsche Forschungsgemeinschaft (grant DFG Zi 159). 1. B. Steeg, E. Gminder, M. Kirm, V. Kisand, S. Vielhauer, and G. Zimmerer, J. Electron Spectroscopy 101-103, 879 (1999). 2. V. Kisand, in Excitonic Processes in Condensed Matter, ed. R. T. Williams, and W. M. Yen, The Electrochem. Soc. Proc. Series PV 98-25, Pennington, NJ, 385 (1998). 3. I. Reimand, E. Gminder, M. Kirm, V. Kisand, B. Steeg, D. Varding, and G. Zimmerer, phys. stat. solidi (b) 214, 81 (1999). 4. J. T. Devreese, A. B. Kunz, and T. C. Collins, Solid State Comm. 11, 673 (1972). 5. A. N. Vasil'ev, Y. Fang, and V. V. Mikhailin, Phys. Rev. B 60, 5340 (1999). 6. A. Lushchik, E. Feldbach, R. Kink, Ch. Lushchik, M. Kirm, and I. Martinson, Phys. Rev. B S3, 5379 (1996). 7. R. Haensel, G. Keitel, and P. Schreiber, Phys. Rev. 188, 1375 (1969). 8. B. Kassiihlke, PhD thesis, Technische Universitat Munchen, Miinchen, 1998. 9. L. Resca, R. Resta, and S. Rodriguez, Phys. Rev. B 18, 702 (1978). 10. G. Zimmerer, in Excitonic Processes in Condensed Matter, ed. R. T. Williams, and W. M. Yen, 77ze Electrochem. Soc. Proc. Series PV 98-25, Pennington, NJ, 375 (1998). 11. A. B. Kunz, J. T. Devreese, and T. C. Collins, J. Phys. C: Solid Stale Phys. 5, 3259 (1972).
47t CONFOCAL MICROSCOPE FOR MULTIPHOTON OPTICAL SECTIONING OF GaN FILM LUMINESCENCE K. B. UCER, DIFEI LIANG, R. T. WILLIAMS Department of Physics, Wake Forest University Winston-Salem, NC 27109 USA H. MORKOC Department of Electrical Engineering, Virginia Commonwealth University PO Box 843072, Richmond, VA 23284 USA In the 4it confocal microscope developed by S. W. Hell et al, laser light coherently illuminates both sides of a thin sample through a pair of high-NA objectives, effectively producing a single standingwavefringeof 2-photonfluorescenceexcitation with weak side lobes. Developed initially for biological applications, the 4jt microscope of Hell et al demonstrated 75 nm axial resolution with 810 nm light. We have constructed a 4it confocal multiphoton microscope for 3d analysis of bandedge/excitonic photoluminescence in thin films. Excitation is with 130 fs pulsesfroma Ti:sapphire laser. Instrumental features and preliminary tests with rhodamine and GaN and InN films are reported.
Spatial resolution of photoluminescence response is a useful tool for characterizing inhomogeneous distributions of dopants, nonradiative recombination centers, and strain in optoelectronic materials. Cathodolummescence and scanning near-field optical microscopy (SNOM) achieve good lateral spatial resolution in the plane of the sample surface. For example, Rosner et al' imaged cathodoluminescence and compared it to an atomic force microscopy (AFM) map of surface pits believed to mark the ends of threading dislocations. A positive correlation of dark spots in luminescence with concentrations of the dislocation pits was found, and a model based on nonradiative recombination at dislocations with a minority carrier diffusion length of 0.25 \im was able to reproduce the cathodoluminescence image reasonably well. In a SNOM and AFM comparison of photoluminescence and pinholes in InGaN/GaN structures, Vertikov et al2 concluded that the pinholes had no clearly observable effect on the PL efficiency, at least partly due to the strong carrier localization in the InGaN alloy. Other cathodoluminescence studies by Ponce et al3 suggested correlation of band-to-band luminescence with the interior of crystallites in the epilayers, and the 560-nm yellow trap luminescence with the grain boundaries. To resolve luminescence and Raman spectra along the third axis, i.e. normal to the film plane, Siegle et al4 focused laser excitation on transverse cuts of thick (400 litn) films, showing that the yellow luminescence came preferentially from both the back and top interfaces of the GaN film. It would be useful to have a method which resolves luminescence along all 3 spatial axes, so that while imaging the x-y face of a film, one could also sample any chosen depth along the z axis. This concept of "optical sectioning" was developed in the context of confocal microscopy mainly for biological applications, where definition of the imaging plane (z) within about 700 nm is useful for many problems. Optical sectioning with conventional one-photon confocal fluorescence microscopy requires that the sample be reasonably transparent to the excitation light. This is not the case in band-edge/excitonic photoluminescence of pure
132
133 semiconductors, such as our present interest in GaN and InN. This problem was solved along with the biological one of cell viability when Webb et al developed multiphoton fluorescence microscopy, providing essentially the same 3-d resolution as confocal microscopy without attenuation or collateral damage by the excitation beam.5 Preliminary results of multiphoton fluorescence imaging in GaN were discussed in Ref. 6. The minimum sampled volume element in such an experiment with 800 nm light is about 200 nm in the x-y plane of the film surface and about 700 nm along the normal (z). While this method is able to provide some useful zresolution of, e.g., 3-p.m films, it is clearly desirable to improve the z-resolution if possible. A sampled volume with xyz dimensions 200 nm x 200 nm x 100 nm would be very useful for film characterization. The so-called 4rc confocal multiphoton fluorescence microscope developed by S. Hell and colleagues7 has achieved such resolution.8 Our implementation of the concept is illustrated in Figs. 1 and 2. A train of 130-fs pulses at 820 nm from a mode-locked Tirsapphire laser is divided by beamsplitter BS 1 into two arms which coherently illuminate the sample from
^^A>/—\
n SPECTROMETER
..
\ OBJ 1, SAMPLE
v Fig. 1. Schematic of 4xt confocal multiphoton fluorescence microscope as constructed in this work. opposite sides through the two objectives (OBJ). One of the arms contains a delay line to adjust for coincident arrival of the two oppositely-directed pulses at the sample. The position of one objective is piezoelectrically adjustable on 3 axes using New Focus picomotors.™ These are used to position the focal spot of one objective in coincidence with that of the other. The sample is positioned and scanned between the two objectives by an optically encoded Burleigh inchworm™ piezolectric stage with 4-nm adjustability and 100-nm encoding precision. When adjusted, two counter-propagating pulses overlap temporally in the focal volume. The sample is scanned relative to that fixed focal volume as luminescence is collected through one objective, picked off by a beamsplitter, monochromatized, and recorded.
1'34
Fig. 2. Photofp*aph of the 4m confocal multiphoton fluorescence microscope, corresponding to the layout diagrammed in Fig. 1. The standing wave pattern produced by the counterpropagating waves at the beam waist produces a two-photon excitation profile proportional to (cos kz)4, for which the FWHM of a single antinode peak is 0.182 X. If the depth of focus is larger than X, this concept is not veryuseful because multiple interference peaks repeat along the axis each X/2. However, the depth of field for beams converging through a numerical aperture NA and observed by a 2-photon process can be represented by the FWHM of the excitation profile: I2„ph oc {sin[kz sin2(a/2)]/[ kz sin2(a/2)]}4 where
a = arcsin(NA/n).
For the 1.3-NA objectives used in this experiment, the corresponding axial FWHM is about a wavelength, so the central interference fringe, of width slightly less than 0.182 Xf is isolated at • the beam waist with two excitation satellite fringes of about half the central peak height. The lateral resolution is about 0.36 A/NA, as in the 2-photon confocal microscope. The axial resolution is thus significantly better than the lateral. From the description above, it can be seen that the focal volume of a 4n confocal microscope is like a pancake aligned parallel to the sample surface. This can be advantageous in many thin-film studies. Finally, since the sample is piezoelectrically scanned through the fixed confocal spot of the lens pair, the point spread function is fixed and can be accurately determined. With point spread extraction, Hell et al achieved 75 nm axial resolution with 810 nm light.8
135 The usual objectives in our instrument are a pair of Zeiss Fluar lOOx, 1.3 NA (oil), each having a working distance of 170 (xm plus cover slip. The sample including substrate and cover slip must fit in the gap of approximately 640 |jm between the two objectives, and must have good optical quality at all interfaces. To meet this sample criterion, GaN epitaxial films were deposited by MBE at VCU on double-polished sapphire substrates 300 |xm thick. GaN thicknesses of 5.2, 2.85, and 0.125 um were prepared. The 0.125 |xm film is the main one we have used to test the instrument. In practice, it was found that the small clearance between the 300 um substrate and the Fluar lOOx objective was so small, that when the oil film was included, the thin substrate deformed under approach of the objective. A borrowed Zeiss C-apochromat 63x, 1.2 NA(water) objective having a larger working distance of 220 um eliminated this problem. We are also investigating polycrystalline InN films grown on glass cover slips at WFU by pulsed laser deposition from a liquid indium target in nitrogen ambient ionized by a synchronized electric discharge. As reported previously, PLD from liquid targets by excimer laser minimizes droplet production in the film. Spatial and temporal alignment of the system were achieved for longer 0.5-ps pulses and a rhodamine dye sample of several urn thickness, but that sample was not thin enough to test the axial resolution. Tests with thin GaN and InN samples are in progress. Our report at the moment is that this is a difficult instrument to align in all parameters. We have achieved spatial spot overlap and good 3-photon fluorescence count rates of about 3 x 1 0 s" exciting through both objectives. Acknowledgment: Research sponsored by NSF DMR-9732023. We thank Gang Xiong and Alexander Zherikhin for developing the InN film deposition. The Micromed facility of Wake Forest University is acknowledged for collaboration on 2n confocal microscopy and loan of the Zeiss C-apo objective. References 1. 2. 3. 4. 5. 6. 7. 8. 9.
S. J. Rosner, E. C. Carr, M. J. Ludowise, G. Girolami, and H. I. Erikson, Appl. Phys. Lett., 70,420(1997). A. Vertikov, M. Kuball, A. V. Nurmikko, Y. Chen, and S.-Y. Wang, Appl. Phys. Lett., 72, 2645 (1998). F. A. Ponce, D. P. Bour, W. Gotz, and P. J. Wright, Appl. Phys. Lett, 68, 57 (1996). H. Siegle, P. Thurian, L. Eckey, A. Hoffmann, C. Thomsen, B. K. Meyer, H. Amano, I. Akasaki, T. Detchprohm, and K. Hiramatsu, Appl. Phys. Lett., 68, 1265 (1996). W. Denk, J. H. Strickler, and W. W. Webb, Science 248, 73 (1990). K. B. Ucer, Y. C. Zhang, and R. T. Williams, Proceedings of the 3rd International Conference on Excitonic Processes in Condensed Matter, Boston, November 2-5 (1998), ed. by R. T. Williams and W. M. Yen (Electrochemical Society Proc. Vol. 98-25, 1999) p. 537. S. W. Hell and E. H. K. Stelzer, Optics Commun. 93, 277 (1992); S. Lindek, E. H. K. Stelzer, and S. W. Hell, Handbook of Biological Confocal Microscopy, ed. by J. P. Pawley (Plenum Press, New York, 1995), p. 417 S. W. Hell, M. Schrader, and H. T. M. van der Voort, J. Microsc, 187, 1 (1997). X. W. Sun, R. F. Xiao, and H. S. Kwok, SPIE Vol. 2888, 76 (1996).
CONTROL OF THE ENERGY TRANSFER WITH THE OPTICAL MICROCAVTTY M. HOPMEIER, W. GUSS, M. DEUSSEN Fachbereich Physikalische Chemie, Philipps-Universitat Marburg, Hans-Meerwein-Strafie, 35032 Marburg, Germany
E. O. GOBEL Physikalisch-Technische Bundesanstalt, Bundesallee 100, 38023 Braunschweig, Germany
R. F. MAHRT Max-Planck Institut fur Polymerforschung, Ackermannweg 10, 55128 Mainz, Germany We present the first experimental observation that dipole-dipole interaction can be strongly enhanced by placing the system in a microcavity. We have studied the excitation energy transfer in poly(phenyl-/?phenylene vinylene) (PPPV) doped with DCM molecules, placed within a Fabry-Perot resonator. As the spectral position of the cavity resonant mode is tuned across the DCM absorption profile, the transfer efficiency from PPPV to DCM changes dramatically as revealed by photoluminescence (PL) spectra. This behavior is clear evidence for the increase of the dipole-dipole interaction strength at the cavity resonances mediated by propagating modes emitted from the excited dipoles.
l.Introduction During recent years, there has been considerable interest in the optical and electronic properties of conjugated polymers and molecularly doped polymers due to their prospective applications in electronic and optoelectronic devices.1 At the same time, there has been much progress in the rapidly developing field of cavity quantum electrodynamics (QED). Within a resonant - or off-resonant - cavity, fundamental optical processes are modified in a characteristic way. Cavity effects on the photo- and electroluminescence of organic thin films have also been reported. "' Yet, it is expected that not only the radiative emission process will be modified by cavity effects but also the coupling between different states mediated by propagating electromagnetic modes. In fact, it has been predicted11'14 that dipol-dipol interaction can be modified in an optical cavity. We report here experimental evidence for the enhancement of dipoldipol interaction in a polymer microcavity. The active part of this cavity consisted out of PPPV doped with the laser dye DCM. It has been demonstrated15"17 that in this system energy transfer from PPPV to DCM occurs. Our data demonstrate that this energy transfer can be significantly enhanced in a resonant microcavity. 2.Results and Discussion The samples investigated consisted of a quarterwave stack of tantalum oxide and silicon dioxide (reflectivity -95% in the spectral range 2.25 eV - 2.7 eV, for transmission characteristics see Fig. 1) onto which a layer of polycarbonate (PC) doped with 19.7% PPPV and 0.21% DCM (by weight) was deposited by spin coating from chloroform solution. Film thicknesses were chosen to give fundamental cavity resonances between 2.25 eV and 2.61 eV. The cavity structures were completed by vacuum evaporation of an aluminum mirror on top of the polymer layer. The above PC:PPPV:DCM ratio was chosen on the basis of energy transfer studies without the cavity showing that the transfer efficiency in this system is such that the contributions of PPPV and DCM to the overall PL emission are comparable.15 This allows determination of their emission ratio with reasonable accuracy. The frequency-doubled output of a Ti:Sapphire laser running at 1.58 eV was used to excite the samples with 70fs pulses at a repetition rate of 82MHz. PL emission was dispersed with a 300 mm 1 grating and detected with a diode array. Sample excitation and PL detection were done through the dielectric mirror. In order to minimize direct excitation of DCM the excitation wavelength has been set to a spectral position at which the ratio between the extinction of the neat PPPV film (EppPV) and the extinction of the pure DCM solution (E D CM) gi y e a maximum. 136
137 For comparison, and in order to illustrate the following data analysis, the PL spectra of thin films of 19.7% PPPV and 5% DCM, respectively, in PC matrix on quartz substrates are shown in Fig. 1. The transmission characteristics of the dielectric mirror used in the cavity structures is also included. The PPPV emission shows a well developed vibronic progression, while there is no structure discernible in the DCM spectrum. In Fig. 2 we show three examples of microcavity PL spectra with fundamental resonances at 2.33 eV, 2.407 eV and 2.53 eV, respectively. The widths of 3
2.5 DCM absorption
400
Figl
500
energy (eV) 2 PPPV emission
DCM emission
600 wavelength (nm)
dielectric mirror
700
800
Regular PL spectra of thin films of PPPV(19.7%)/PC (solid line) and DCM(5%)/PC (dashed). The transmission characteristics of the dielectric mirror is also shown for comparison (dotted).
the cavity modes are about 8 nm (FWHM), close to the theoretical limit that can be calculated from the refractive index, the mirror reflectivities, and the cavity thickness.10,18 The PL at energies lower than 2.17 eV is essentially the free-space emission modulated by the transmission of the quarterwave stack. A first inspection shows that the intensity of this low energy part of the spectrum decreases as the cavity mode shifts to lower energies (Fig. 2).
3
2.5
energy (eV) 2
wavelength (nm)
Fig. 2 Room temperature PL spectra of two PPPV/DCM/PC microcavities of different thickness (different resonance wavelength). Excitation energy was 3.18eV (390 nm). The arrows mark the emission from the cavity resonant modes, the PL at X > 570 nm is essentially the free-space emission modulated by the transmission of the dielectric mirror (see Fig. I for comparison).
A comparison of the cavity spectra in Fig. 2 with the free-space emission of DCM and PPPV (Fig. 1) shows that the PL at the cavity resonances is almost exclusively due to PPPV, while the cavity emission at energies lower than 1.94 eV originates mainly from DCM. In order to analyze our
138 data we use the model of resonant energy transfer mediated by dipole-dipole interaction which is partitioned in two parts. One part of the overall dipole-dipole interaction is the so called ForsterDexter term1 '20, included in the total hamiltonian in the equation of motion for the density matrix of the given material system. This term which has been shown to afford a satisfactory description of both time-integrated15 and transient PL behavior16'17 of the PPPV/DCM system in non restricted geometries results in a longitudinal electromagnetic field and in the well known r"6 dependence of the energy transfer. Within this picture, the rate of resonant energy transfer, KDA, from donor D to acceptor A can be written as KDA = kD(Ro/R)6 where k D is the rate of excitation decay at the donor, containing both radiative and non-radiative processes in the absence of an acceptor, and R is the distance between donor and acceptor. The Forster radius, R0, which is characterized by equal probabilities for excitation decay at the donor and excitation transfer to the acceptor (kD = KDA), can be expressed in terms of experimentally accessible parameters as21 R* =
r$D
Q.
12&TTNA n0
where K2 accounts for the relative orientation of donor and acceptor transition dipoles (K2KJ0.6 for isotropic case), NA is Avogadro's number, and n0 is the refractive index of the PC matrix. <j>D denotes the fluorescence quantum efficiency of the donor, and Q is the spectral overlap between donor fluorescence and acceptor absorption given by21 Q = \eA(V)FD(v)—dv with the acceptor's molar absorption coefficient e A and the donor fluorescence F D , normalized according to \FD(v)dv = 1. However, a second term resulting from the retarded dipole-dipole field contributes to the energy transfer within a cavity. Following the Maxwell equation the emission of excited dipoles (induced polarization) results in a propagating transverse electromagnetic field which is sensitive to the boundary conditions given by the geometry of the resonator in which the radiation occurs. It is this propagating field which modifies the resonant energy transfer in the Fabry-Perot cavity discussed here.
2.6
0I
2.5
energy (eV) 2.4
2.3
1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 o.O 470 480 490 500 510 520 530 540 550 wavelength of resonance mode (nm)
Fig. 3 Emission ratio versus wavelength of the resonance mode. The absorption profile of DCM is included for comparision. The inset displays the emission ratio versus cavity resonance for an undoped PPPV/PC sample.
Fig.3 shows how the enhancement (T= Wlfree) of the emission from a DCM-doped sample depends on the wavelength of the cavity resonance. Ires and Ifree were determined by integrating the PL spectra from 1.55 eV to 2.15 eV for a microcavity sample and for a sample without photon confinement, respectively. Additionally, the absorption, eDCM (hv), of a DCM (5%)/PC film is displayed for comparision. Here, T is a direct measure for the resonant energy transfer from PPPV
139 to DCM. Fig.3 bears out a variation of the emission ratio T in the DCM doped sample (where Forster transfer takes place) of approximately one order of magnitude by tuning the cavity resonance across the DCM absorption profile. For a DCM free sample (neat PPPV/PC) no change of the emission ratio is observed as can be seen from the inset of Fig.3. This leads to the conclusion that the strength of the resonant dipole-dipole interaction could be enhanced (or suppressed) in restricted geometries of appropriate dimensions. Taking into account that restricted geometries indeed can give rise to a variation in the resonant dipole-dipole coupling strength, as claimed in the theoretical work by Agarwal et al.12 and Kobayashi et al.13,14 who treat the problem of resonant dipole-dipole interaction in a Fabry-Perot cavity by applying a fully quantum response function theory as well as a mode expansion calculation, respectively. We end up with the straightforeward conclusion that the enhancement of the emission ratio in our experiment is due to an enhanced resonant dipole-dipole interaction at the spectral positions of the cavity resonances. This enhancement results exclusively from propagating modes of the radiation field inside the cavity at spectral positions where the photonic density of modes is enhanced (resonant cavity modes). Besides the observed variation in the emission ratio r the enhanced dipole-dipole
Fig. 4 One set of photoluminescence transients detected at the cavity resonance (here, 485 nm) for a PPPV/DCM/PC (black squares) as well as for a neat PPPV/PC sample (dashed line). The inset shows the enhancement of the transfer rate for the DCM doped sample versus the cavity resonance.
interaction should manifest itself as an increase of the transfer rate from PPPV to DCM, additionally. Therefore, we performed time-resolved PL spectroscopy by means of streak-camera measurements with 6 ps time resolution. Fig 4 shows examplarily, the PL transients of the PPPV/DCM sample detected at the spectral position of the cavity resonance and at the same spectral positions for the sample without geometrical confinement (free space), for comparision. In the sample without a cavity the decay of the PPPV emission is determined by radiative recombination, trapping, energy relaxation and energy transfer to the DCM molecules. In the case of the microcavity the decay of the luminescence is faster. This shortening of the decay time is not observed in cavities with neat PPPV films because trapping and energy relaxation within the inhomogeneously broadened density of states (DOS) are the dominant processes.10 However, the aforementioned processes are present in the DCM doped samples, too. Furthermore, an additional contribution namely, the enhancement of the dipole-dipole interaction (enhanced transfer rate) at the cavity resonances contributes and results in an enhanced transfer rate manifested in the faster PL decay observed. The inset in Fig.4 displays the enhanced transfer rate for the cavity resonances when varied across the DCM absorption profile. Exactly, as for the emission ratio, a variation of approximately one order of magnitude is observed when the cavity resonance is tuned across the DCM absorption profile.
140 In conclusion, we have performed for the first time photoluminescence measurements on dyedoped conjugated polymer samples embedded in a Fabry-Perot resonator of suitable dimensions to study the cavity effect on resonant excitation energy transfer. Our experiments demonstrate that there is a pronounced dependence of the emission ratio, and thus the energy transfer efficiency, on the spectral overlap between PPPV cavity emission and DCM absorption. Usually, cavity effects on excited state properties are studied by probing photons emitted from the sample. Resonant energy transfer, however, is not due to the trivial process of photon emission by the donor and reabsorption by the accecptor, but induced by resonant dipole-dipole interaction. The correlation between energy transfer efficiency and the spectral overlap calculated from the real photon emission demonstrates that the coupling between donor and acceptor is strongly modified upon placing the system inside a cavity. In view of the rapidly growing field of polymer-lasers our findings could reveal a promising route towards electrically driven dye-doped polymer lasers. The authors would like to thank H.Bassler and P.Thomas for stimulating discussions, and A.Greiner for providing PPPV. Financial support of this work by the Stiftung Volkswagenwerk is gratefully acknowledged.
References [I] [2] [3] [4] [5] [6] [7] [8] [9] [10] [II] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21]
J.H.Burroughes, D.D.C.Bradley, A.R.Brown, R.N.Marks, K.MacKay, R.H.Friend, P.L.Burn, and A.B.Holmes, Nature 347, 539 (1990). S.Haroche and D.Kleppner, Physics Today 42, 24 (1989). H.Yokoyama, Science 256, 66 (1992). Y.Yamamoto and R.E.Slusher, Physics Today 46 , 66 (1993). S.Haroche and J.M.Raimond, Scientific American 268, 54 (1993). A.Dodabalapur, L.J.Rothberg, and T.M.Miller, Appl.Phys.Lett. 65, 2308 (1994). V.Cimrova and D.Neher, J.Appl.Phys. 79, 0000 (1996). A.Ochse, U.Lemmer, M.Deussen, J.Feldmann, A.Greiner, R.F.Mahrt, H.Bassler, and E.O.Gobel, Mol.Cryst.Liq.Cryst. 256, 335 (1994). U.Lemmer, R.Hennig, W.Guss, A.Ochse, J.Pommerehne, R.Sander, A.Greiner, R.F.Mahrt, H.Bassler, J.Feldmann, and E.O.Gobel, Appl.Phys.Lett. 66, 1301 (1995). W.Guss, H.Vestweber, M.Hopmeier, Y.H.Tak, J.Feldmann, and R.F.Mahrt, Synth.Met. 83, 257 (1996) G.S.Agarwal and S.D.Gupta, Phys.Rev.A 57, 667 (1998) T.Kobayashi, Q.Zheng, and T. Sekiguchi, Phys.Rev.A 52, 2835 (1995) T.Kobayashi, Q.Zheng, and T. Sekiguchi, Phys.Lett.A 199, 21 (1995) G.Kurizki and A.Z.Genack, Phys.Rev.Lett. 61, 2269 (1988) M.Deussen, Ph.D. thesis, Philipps-Universitat Marburg (1995). P.Haring Bolivar, G.Wegmann, R.Kersting, M.Deussen, U.Lemmer, R.F.Mahrt, H.Bassler, E.O.Gobel, and H.Kurz, Chem.Phys.Lett. 245, 534 (1995). U.Lemmer, A.Ochse, M.Deussen, R.F.Mahrt, E.O.Gobel, H.Bassler, P.Haring Bolivar, G.Wegmann, and H.Kurz, Synth.Met., 78, 289 (1996) E.F.Schubert, N.E.J.Hunt, M.Micovic, R.J.Malik, D.L.Sivco, A.Y.Cho, and G.J.Zydzik, Science 265, 943 (1994). TLForster, Ann.Phys. 6, 55 (1948). D.L.Dexter, J.ChemPhys. 21, 836 (1953). W.Klopffer, in Electronic Properties of Polymers, edited by J.Mort and G.Pfister (Wiley, New York, 1982).
SYMMETRY LOWERING IN THE PHOTOINDUCED PHASE IN SPIN-CROSSOVER COMPLEXES
TAKESHI TAYAGAKI, KOICHIRO TANAKA, NAOKI YONEMURA and MASANOBU SHIRAI Department of Physics, Kyoto University, Kyoto 606-8502,JAPAN KEN-ICHI KAN'NO Department of Material Science and Chemistry, Wakayama University, Wakayama 640-8510, JAPAN
We investigated the resonant Raman scattering of the spin-crossover complex, [Fe(2pic)3]Cl2EtOH, with varying the temperature and clarified for the first time that the photoinduced phase is completely different state from the thermally-induced phase. In the photoinduced phase we observed splits of Raman lines and a number of additional lines which are not observed in the high- and the low-temperature phase. These splits and appearances strongly indicate that a symmetry lowering should take place in the photoinduced phase. We imagined that the symmetry lowering is induced by the Jahn-Teller effect in the photo-excited state of the low-temperature phase. 1. Introduction Spin-crossover complexes have been studied extensively as attractive materials, whose magnetic and chromatic properties can be controlled with external stimuli such as heat, pressure, magnetic field, and so on. 1 The spin-crossover transition can also be induced by the light irradiation, which is called "light induced excited spin state trapping (LIESST)". 1 ' 2 In the typical spin-crossover complex [Fe(2-pic)3]Cl2EtOH(2-pic=2-picolylamine), besides the thermal spincrossover transition at about 120K,3 LIESST is also observed. 4 Recently, Ogawa et al. 5 reported that LIESST in [Fe(2-pic) 3 ]Cl 2 EtOH shows nonlinear characteristics such as threshold-like behavior, incubation period and phase separation. From these characteristics, this photoinduced phenomenon should involve some cooperative interaction, and is called as "photoinduced phase transition". 6 The photoinduced phase is implicitly attributed to the same state as the hightemperature phase in the thermal phase transition. In this work, we investigated the photoinduced phase transition in [Fe(2-pic) 3 ]Cl 2 EtOH by the resonant Raman scattering with varying the temperature to obtain detailed information on the local structure. 2. P h o t o i n d u c e d Spin-crossover Transition in [Fe(2-pic)3]Cl2EtOH In the spin-crossover complex [Fe(2-pic) 3 ]Cl2EtOH, the Fe 2 + ion is octahedrally surrounded by six nitrogen atoms in three 2-picolylamine molecules. The crystal structure of [Fe(2pic)3]Cl 2 EtOH is monoclinic P2i/c,Z=4. 7 Therefore there are four octahedra including Fe 2 + ion in the unit cell. The d 6 electrons of Fe 2 + ion in the cubic ligand field play an important role in the electronic structure. In the weak ligand field, the splitting between t 2g and e g orbitals is so small that the ground state takes a high-spin state S=2, while in the strong field, takes a low-spin state S=0. Figure 1 shows absorption spectra at several temperatures. At room temperature, [Fe(2pic) 3 ]Cl 2 EtOH has a paramagnetic phase (S=2) where the ground state is 5 T 2 (left part of the inset in Fig.l). One can see an absorption band at 1.6eV which is assigned to the transition from 5 T 2 to 5 E, corresponding to the t 2g —> eg transition in the one-electron approximation. Since the absorption band of the picolylamine molecule exists over 2.4eV, the sample looks
141
142
Fig. 1. Absorption spectra in the [Fe(2-pic)3JCi2EtOH single crystal measured at 300K, 200K, 150K and 70K. Absorption band at 1.6eV and 2.0eV correspond to the transition from t2g to e g in the paramagnetic (S=2) and the diamagnetic (S=0) phases, respectively. Insets show electron configurations of the ground states in these phases. yellow. With lowering temperature, a first-order phase transition takes place from the paramagnetic phase (S=2) to the diamagnetic phase (S=0) in two steps at critical temperatures of 122K and 114K.1 In the low-temperature phase the ground state is 'Ai (right part of the inset in Fig.l). The t 2g —> eg absorption band (*Ai —>x Ti ) shifts to 2.0eV in the low-temperature phase, leading to the red color of the sample.
1.5
2.0 Photon Energy (eV)
Fig. 2. Differential absorption (AO.D.) spectra in the [Fe(2-pic) 3 ]Cl 2 EtOH single crystal measured at 5K with several W-lamp irradiation times. Inset shows the temporal change of the optical density at 2.0eV, indicating the disappearance of the absorption band with an incubation period T;„c. Notice that the axis of ordinate represents -AO.D. Figure 2 shows the temporal change of the absorption spectrum obtained under W-lamp irradiation at 5K. One can see clearly gradual disappearance of the absorption band at 2.0eV ( x Ai —j-1 Ti transition in the low-temperature phase) by the light-irradiation, indicating that the low-temperature phase changes to the photoinduced phase. The inset in Fig.2 shows the decrease of the optical density at 2.0eV, which shows a nonlinear behavior with an incubation
143 period as already reported. 5 Simultaneously, a weak absorption band appears around 1.5eV under light irradiation, and its peak energy is close to the t2g —> eg transition energy in the high-temperature phase. Since the absorption spectrum in the photoinduced phase is quite similar to that in the high-temperature phase, the photoinduced phase has so far been believed to be the same state as the high-temperature phase. 3. Results and Discussions 3.1. Raman
Scattering
Measurements
in [Fe(2-pic)s]Cl2EtOH
Figure 3 shows the Raman spectra of [Fe(2-pic)3]Cl2EtOH powder sample measured by a cw-Nd:YVO laser (2.33eV) at (a)160K, (b)40K and (c)4.2K, which correspond to (a) the hightemperature phase, (b)the low-temperature phase and (c) the photoinduced phase, respectively. Raman spectra obtained with the single crystal sample have basically the same structures as the powder sample. We assigned Raman lines over 600cm - 1 indicated by p in Fig.3(a) to the picolylamine molecule by referring the Raman spectrum of the 2-picolylamine molecule on the assumption of the solvated shift. The line at 630 c m - 1 is probably a twisting or bending mode of the picolylamine molecule. The lines at 820 c m - 1 and 1020 cm" 1 are the pyridine-ring stretching modes of the picolylamine molecule. Lines below 600 c m - 1 are assigned to vibrations of the [FeNg]2"1" cluster or the inter-cluster modes within the unit cell. Raman spectra in Figs.3(a) and 3(b), corresponding to the high- and the low-temperature phases, have quite similar structures except the signal intensity of the peak A depicted in Fig.3(b). The peak A should be assigned to the total symmetrical vibration A l g of the [FeN 6 ] 2+ cluster. The difference in the intensity between two phases can be understood by the resonant enhancement of the Raman efficiency. The exciting light (2.33eV) is resonant to the t2g —> e g transition in the low-temperature phase, whereas be off-resonant in the high-temperature phase. This resonance effect is consistent with the assignment of the peak A.
1
'
(a) 160K x 3
'W-wJl^W-V v
.yJ
1
1
\,—-*•*«"
(b) 40K X 3 A
W
V
250
J
^J\
A/
B
A/WV\_AAJUA, ' ^"•~ -J y
-._>v—/ VA.W
c
1
JsA^JL^n.> (c) 4.2K
>
p
P
J J.
A^AJ^ L_i.
I
500 750 Raman Shift (cm")
^"-"
~—-•*>—-i
~*^
*^
WJ
1000
Fig. 3. Raman spectra of the [Fe(2-pic)3]Cl2EtOH powder sample measured at (a)160K, (b)40K and (c)4.2K. Light source is a cw-Nd:YVO laser, 2.33eV. The labels p show vibrations of the 2-picolylamine molecules. Labels A-D in (b) and (c) are described in the text.
Below 30K the photoinduced phase transition simultaneously takes place with irradiation of the NdrYVO laser by which Raman spectra are measured. In the photoinduced phase we
144 observed a number of additional lines below 750 c m - 1 which are not observed in the high- and the low-temperature phases as shown in Figs.3(a)-3(b). Since these lines disappear quickly when temperature is raised above 40K and never seen in the Raman spectrum measured with the laser light that cannot induce the phase transition (e.g. 1.5eV), such a photoinduced change in the Raman spectrum should be a reproducible and an intrinsic process. These spectral changes are classified into four cases:(l) line seen in Fig.3(b) splits into two lines like A, (2) line not seen in Fig.3(b) appears additionally like B, (3) line grows extensively in its intensity like C, (4) line seen in Fig.3(b) disappears like D. The intensities of additional Raman lines (B) increase linearly under light irradiation in the initial stage and gradually saturate, as shown in Fig.4 for the 570cm - 1 line. In Fig.4, the incubation period cannot be seen. This is because the intensity of the light would be strong enough to induce the phase transition without the incubation period.
/—s
en
-*-» •« c a
A u a w
>-> •£ 8 it
••
°te •*-»
a o
[Fe(2-pic)3]Cl2EtOH
W •
570cm'line 4.2K
'• 0
"" 25
""
50 75 100 125 150 Time (sec.)
Fig. 4. Increase of the 5 7 0 c m - 1 Raman intensity in [ F e ( 2 - p i c ) 3 ] C l 2 E t O H at 4.2K. The axis of abscissa represents the light irradiation time.
3.2. Structure
of the photoinduced
phase
Since the Raman spectrum generally reflects the structural property, splits and appearances of Raman lines strongly indicate that a symmetry lowering should take place in the photoinduced phase. It should be noted that the pyridine-ring stretching modes of the picolylamine molecule at 820 c m - 1 and 1020 c m - 1 merely change even in the photoinduced phase. This indicates that the photoinduced change does not include chemical reactions which transform picolylamine molecules to other structures. The frequency region where lines B(D) appear(disappear), should be related to vibrations of the [FeN 6 ] 2+ cluster or the inter-cluster modes in the unit cell. These results suggest that the symmetry lowering takes place in the [FeN 6 ] 2+ cluster and/or in the unit-cell configuration. The symmetrical expansion of the [FeNg]2"1" cluster has so far accounted for the photoinduced phase transition from diamagnetic to paramagnetic, which also contribute to the elastic interaction as a cooperative interaction. 8 However, this mechanism can not explain the symmetry lowering characteristics observed in the Raman spectrum. The Jahn-Teller distortion in the photo-excited state at the low temperature is an alternative candidate for the mechanism of the symmetry lowering and the origin of the long-range cooperative interaction. The first photo-excited state in the low-temperature phase, triply-degenerated 'T^, can couple to the Eg or T 2 g distortion in the [FeN 6 ] 2+ cluster to be stabilized into a symmetry-lowered structure (Jahn-Teller effect). Based on this mechanism, splits and appearances in the photoinduced phase can be understood as follows: (1) The symmetrical vibration of the [FeN 6 ] 2+ cluster, quadruply-degenerated mode in the case of the weak coupling between the clusters in the unit
145 cell, the line A, splits into two lines in the photoinduced phase. The cooperative Jahn-Teller coupling of the four [FeN 6 ] 2+ clusters in the unit cell induces the splitting of the symmetrical mode. (2) Other vibrations of the [FeN 6 ] 2+ cluster, such as E g or T 2 g modes (below 370 c m - 1 ) are also split into several lines by the Jahn-Teller distortion. (3) The lines B should originally be Raman-inactive modes and appear by the symmetry lowering which breaks the selection rule for the Raman scattering in the photoinduced phase. Possible candidates are IR-active modes of the picolylamine molecule coordinated to Fe 2 + ion. The spectral change of Raman scattering can be understood qualitatively on the assumption of the Jahn-Teller distortion in the photoinduced phase as mentioned above. The cooperative Jahn-Teller effect may contribute to the photoinduced phase transition as a long-range force. In order to confirm the Jahn-Teller effect in the photoinduced phase, the local structure should be clarified by ESR or EXAFS measurements. 4. Conclusion We observed that the Raman spectrum in the photoinduced phase has quite different structure from those in the high- and the low-temperature phase. The spectral change strongly indicates that the symmetry lowering takes place in the photoinduced phase transition process. This is the first observation of the difference between the photoinduced phase and the thermally-induced phase, which means that the photoinduced phase transition can realize a new material phase that cannot be realized in the thermal phase transition. Acknowledgements Authors thank to Prof. S. Koshihara and Mr. Y. Ogawa for kind instructions of the crystalgrowth method and to Prof. K. Nasu for a fruitful discussion. This work is partially supported by a Grant-in-Aid for Scientific Research on Priority Areas, "Photo-induced Phase Transition and Their Dynamics", from the Ministry of Education, Science, Sports and Culture of Japan. References
1. 2. 3. 4. 5. 6.
P. Giitlich, A. Hauser and H. Spiering, Angem. Chem. 33, 2024 (1994). A. Hauser, J. Chem. Phys. 94, 2741 (1991). M. Sorai, J. Ensling and P. Giitlich, Chem. Phys. 18, 199 (1976). S. Decurtins, P. Giitlich, K.M. Hasselbach, A. Hauser and H. Spiering, Inorg. Chem. 24, 2174 (1985). Y. Ogawa, S. Koshihara, K. Koshino, T. Ogawa, C. Urano, and H. Takagi, Phys. Rev. Lett. 84, 3181 (2000). K. Nasu (ed.), Relaxation of Excited States and Photo-induced Structural Phase Transitions (Springer-Verlag Berlin Heidelberg,1997). 7. M. Mikami, M. Konno and Y. Saito, Acta Cryst. B36, 275 (1980). 8. K. Koshino and T. Ogawa, J. Phys. Soc. Jpn. 68,2164 (1999).
T H E O R Y OF P H O T O I N D U C E D P H A S E T R A N S I T I O N I N T H E Q U A S I ONE-DIMENSIONAL CHARGE TRANSFER COMPOUND TTF-CA
P. HUAI AND K. NASU Institute of Materials Structure Science, The Graduate University for Advanced Studies 1-1 Oho, Tsukuba, Ibaraki 305-0801, Japan We theoretically study the photoinduced ionic—>neutral phase transition in the quasi-onedimensional molecular crystal TTF-CA. Our theoretical model includes strong intra-chain Coulomb interactions as well as very weak inter-chain interactions. Within the mean-field picture, we investigate the nonlinear lattice relaxation of a charge transfer exciton, and clarify the adiabatic path from its Franck-Condon state to a macroscopic neutral domain. It is found that the lowest state of such a single charge transfer e:.citon can not relax down to the neutral domain straightly, but a large excess energy is necessary so that it can overcome a high barrier. The aggregation of two identically shaped neutral domains is also discussed. 1. Introduction Quasi one-dimensional organic donor-acceptor crystals consist of donor(D) and acceptor(A) molecules stacked alternately along one of crystal axes (D+pArp • • •D+I'A~1'). In the ground state of this type of crystals, a fractional charge transfer (CT) from D to A usually occurs. According to the degree of this charge transfer ( = p), they fall into two classes, the quasi neutral (N) phases with p < 0.5, and the quasi ionic (I) ones with p > 0.5. Among these crystals, tetrathiafulvalene(TTF)-p-chloranil(CA) happens to be near the boundary between the N-phase and the I one, and hence, undergoes the N<->I phase transition by applying hydrostatic pressure or by changing the temperature. 1 The temperature induced N<-»I phase transition was discovered at T c (=84 K), and is accompanied by the lattice dimerization along the stacking direction in low temperature Iphase. 2 Recently, the photoinduced I—>N phase transition (PIPT) has been investigated by means of time-resolved spectroscopic techniques. 3 Keeping TTF-CA at the low enough temperature (< T c ), and shining strong laser onto it, we can generate a large neutral domain in the ionic phase, and this domain is composed of about 200 neutral pairs. A simple scenario for this phenomenon could be given as follows. A single photon makes a single neutral pair (D+A~D+A~ • • • D°A° • • • D+A~D+A~), and after that it proliferates through the crystal like a domino game, and finally make the neutral domain (D+A~D+A~- • • D 0 A 0 D 0 A 0 • • •D+A~D+A~). However, this simple scenario is proved wrong experimentally. A single photon can't create such a macroscopic neutral domain, if its energy is resonated to the CT exciton. 4 In the present work, we will investigate the nonlinear lattice relaxation of the CT exciton, to shed light on the mechanism of the photoinduced I—»N phase transition. 2. Theoretical Treatment In order to clarify P I P T from a unified theoretical point of view, we introduce an extended Peierls-Hubbard model which consists of strong intra-chain Coulomb interactions and very weak inter-chain interactions. 5 We consider a A^-site sample chain, whose odd(D) and even(A) sites are occupied by the cations(TTF 2 +) and the acceptors(CA) alternately. The distance ( s dj,i+i) between neighboring T T F and CA is given as di,i+i = rf0(l + 9(+i - 9 i ) ,
(1)
where, d0 is the average inter-molecular distance, and qi is the relative and dimensionless lattice distortion of I th site. This sample chain is also assumed to be surrounded by neighboring ones,
146
147 which are always kept in the ionic ground state, whatever various domain structures may occur in this sample chain. Thus our Hamiltonian(= H) reads, H = He + i/ph + Winter ,
(2)
with
~{ J2 vi(
+ Y, Vi(ft,9i+i)[2 - n m ] n , } ,
I,odd
J,even
a
I
Winter
=
z
I
4
2
{ * l f o ~ ( " l ) ' * ) ] + K2[q< - ( - 1 ) ' ? „ ] 4 + K3[q, - ( - l ) ' 9 o ] 6 } ,
£
(3)
; where i/ e , i/ p h and //inter denote the Hamiltonians of the electron part, the phonon part and the inter-chain one. Cl(T{Ci^) is the creation(annihilation) operator of an electron with spin
(4)
Here V0 is the constant part, and A (ft) is its first(second) order expanding coefficient with respect to qi. In the phonon part / / p n , the kinetic energy is neglected because of the adiabatic approximation, and a fourth order potential energy is introduced, as well as the ordinary second order one. The coefficients of these two potentials are denoted by S\ and 52, respectively. In the ground state, the lattice is assumed to be uniformly dimerized as, Qi = ( - l ) V o ,
(5)
where qo is the amplitude of Peierls distortion, and it is determined to minimize the ground state energy. As for the inter-chain coupling term HinteT, qi is the lattice distortion of the sample chain, while the (—l)'g0 corresponds to the uniform dimerization of the neighboring chains, which are assumed to be always in the ionic ground state and can never be excited. Within the unrestricted Hartree-Fock approximation, we decouple the four-fermion terms in the Hamiltonian and introduce a self-consistent iteration procedure to calculate the ground state and the first excited state. We also enhance our calculation by the first order perturbation theory to take the exciton effect into account. 5 3. N u m e r i c a l R e s u l t s Our way of thinking throughout the present paper is the phenomenological parameter theory. In order to reproduce main experimental and theoretical results existing already prior to our theory, 5 as a set, we have determined the following values of parameters: t = 0.17, A = 2.716, U = 1.528, V0 = 0.604, ft = 1.0, ft = 8.54, Si = 4.86, S2 = 3.4 x 10 3 , K1 = 0.6949, K2 = —1.415 x 10 3 , K3 = 9.699 x 105. All the values above are in the unit of eV, and this notation will be used throughout this paper, hereafter. The periodic boundary condition is imposed on the sample chain whose total number of sites is Nt = 100.
148 1.2 1.0
00
0.6 0.4 0.2
"~0
20
40
60
80
Domain Size /Q Fig. 1. The energy surface along a typical relaxation path, which is from the Franck-Condon state of a CT exciton to large N-domain. All the energies are referenced from the ionic ground states (lo = 0, Aq = 0).
By using the aforementioned set of parameters, the ground state of the I-phase is 0.002 eV (per site) below that of the N one. Thus the I-phase is the true ground state, and the lowest CT excitation is (D+A~)—>(D°A°). Furthermore the lattice of I-phase has about 3% dimerization (<jo = 0.029) along the stacking axis, while that of N-phase is not dimerized. To describe the nonlinear lattice relaxation of a CT exciton, we introduce the following lattice pattern qt 9, = ( - l ) ' g o ( l + A 9 [tanh(fl(|/| - lj)) - 1]} .
(6)
Here (-l)'<7o denotes the Peierls distortion in the ionic ground state, and this q0 has already been determined to minimize the ground state energy. The second term in the curly brackets {• • •} denotes the local lattice displacement and Aq is its amplitude. 8 corresponds to the spatial extension of this pattern and lo is the domain size. Fig. 1 shows the adiabatic energy surface along a typical relaxation path from the FranckCondon state of a CT exciton to the macroscopic N-domain. The horizontal axis means the number of the neutral sites created in the I-phase. The energy curve of the first excited state (Exi)has two local minima, at the region of small / 0 ( ~ 0) and also at the region of large l0(zs 40). The first one corresponds to the CT exciton, while the second one is the N-domain, which is a little above the CT exciton. Moreover, these two local minima are separated by a high barrier. This result leads us to a very important conclusion that the lowest state of a single CT exciton can not relax down to the N-domain straightly, but a large excess energy is necessary so that it can overcome this barrier, as schematically shown by the dash-dot excitation line. Now let us proceed to the interactions between the N-domains thus created. Via nonlinear interactions between them, the N-domains simultaneously excited in the same chain (D+A~D"A 0 D + A~ • • • D + A~D°A°D + A~) attract each other, move closer and finally merge into a more stable larger N-domain. Such a multi-N-domains aggregation can also be investigated within our mean-field picture. To simplify the problem, we consider only two identically shaped N-domains in the following lattice configuration, Q, = ( - l ) ' 9 o ( l + A g {tanh[0(||*| - ^ | - | ) ] - 1}) .
(7)
Here, q0, Aq, 6 and l0 have the same meanings as in Eq.(6), while d is the inter-domain distance. The total number of sites is doubled (Nt = 200) to simulate a situation in which N-domains are separated by fairly long distance.
149
^^^ >u
1.0
-
0.9
:
- i- ..-
/'"*7
":
08 0.7
611 C
0.6
ID 0.5 0.4 20
40
60
80
100
d Fig. 2. The energies of ground state {Eg) and first excited state (Ex\) Vs. inter-domain distance d. For each neutral domain, Zo = 30 and Aq = 0.5, 6 is optimized to minimize the total energy of system.
Fig. 2 demonstrates the adiabatic energies of the ground and the first-excited states for d ranged from 20 to 100. Both energy curves exhibit three different stages: 60 < d < 100, 30 < d < 60 and d < 30. We call them as attracting stage, overlapping stage and merging stage, respectively. The energy curves in the attracting stage are flat lines slightly leaning to the small d side. In this stage, the two N-domains are so far away that the attraction between them is very weak. When a critical distance d = 60 is reached, the N-domains enter the overlapping stage. The energy curves in this stage are steep slopes dropping about 0.3 eV within 40-sites distance. The attraction between the domains quickly increases with the growing of overlap region. The third stage is merging of the N-domains. A new larger N-domain is built on the base of the two smaller ones. Apparently, the energy curves are moderately inclined slopes due to shrinking of domain size. Thus, the reactions between N-domains are again quite nonlinear.
4. Conclusion We have theoretically studied the photoinduced I—>N phase transition in the quasi-onedimensional charge transfer compound TTF-CA. An extended Peierls-Hubbard model was investigated by using mean-field theory to clarify the nonlinear lattice relaxation of the CT exciton, which starts from its Franck-Condon state and terminates up to the large neutral domain formation in the ionic phase. We found the lowest state of a single CT exciton can not relax down to the neutral domain straightly, but a large excess energy is necessary so that it can overcome the barrier. A three-stage process was also presented to describe the aggregation of two identically shaped neutral domains. References 1. 2. 3. 4. 5.
J. B. Torrance, J. E. Vazquez, J. J. Mayerle and V. Y. Lee, Phys. Rev. B46, 253 (1981). Y. Tokura, T. Koda, T. Mitani and G. Saito, Solid State Commun. 43, 757 (1982). S. Koshihara, Y. Takahashi, H. Sakai, Y. Tokura and T. Luty, J. Phys. Chem. B103, 2592 (1999). T. Suzuki, T. Sakamaki, K. Tanimura, S. Koshihara and Y. Tokura, Phy. Rev. B60, 6191 (1999). P. Huai, H. Zheng and K. Nasu, J. Phys. Soc. Jpn. 69, 1788 (2000).
RADIATIVE EFFICIENCY OF LOCALIZED EXCITONS IN ZnCdS TERNARY ALLOYS HIDEKAZU KUMANO, SATOSHIMURASAWA, ADRIAN AVRAMESCU, AKIO UETA AND IKUO SUEMUNE RIES, Hokkaido University, kita-ku, Sapporo 060-0812, Japan
The effect of exciton localization is investigated in ZnCdS ternary alloys. Zn^Cd^S films with Cd composition x (x=0.21-0.79) were prepared and transient optical properties of photoexcited excitons during the energy relaxation as well as steady-state photoluminescence (PL) properties are examined as a function of crystalline quality of the grown films. The sample with x=0.56 that is closely lattice matched to the GaAs substrate was found to show the maximum integrated band-edge PL (BEPL) intensity.
The samples with larger lattice mismatch showed stronger quenching of tho BEPL intensity,
which is well correlated to the crystalline quality evaluated by X-ray rocking curve measurement. In order to study the contribution of exciton localization, time-resolved PL measurements were carried out. It is clearly revealed that the excitons fully relaxed to the localized states exhibit high luminescence efficiency, while the relaxation process of excitons toward the localization states is shown to be influenced by the crystalline quality of the films.
1. Introduction Recently, remarkable success of InGaN-based light emitting diodes (LEDs) and laser diodes (LDs) with high luminescence efficiency have been achieved.1 In the InGaN ternary alloy system, localization effect of photoexcited excitons induced by compositional disorder plays an crucial role in realizing the high luminescence efficiency.2"4 For the purpose of investigating the universality of the exciton localization effects on the high luminescence efficiency among semiconductor materials, we will focus on ZnCdS ternary alloys. The compositional elements of Zn and Cd are arranged to the nearest neighbors of Ga and In, respectively, in the periodic table so that the chemical and physical properties analogous to InGaN will be expected. Therefore, the ZnCdS system may be promising from the viewpoint of exciton localization to realize the high luminescence efficiency.5'7 The large oscillator strength due | m . to the exciton binding energy of ZnCdS larger than the | thermal energy of 25 meV at RT may contribute to the i improvement of the luminescence efficiency. Furthermore, i Zn^Cb^S will cover the wide spectrum range from 2.4 eV to 3.7 eV by controlling the Cd composition x and will be very attractive for the active layers of optoelectronic devices Cd composition x in Zn j. CdJ> operating from ultraviolet to green wavelength regions. Fig.l Cd composition dependence of of XRD rocking curve (solid circles) Up to now, ZnCdS has been studied and many papers FWHM and integrated BEPL intensity (solid have been published.8"13 However, most of them are squares). Both are severely dependent on the degree of lattice matching. focused on Zn^CoyS films with the Cd composition nearly 8 10 lattice-matched to GaAs ' and there have been few papers dealing with the Zn,.xCd,S films with the wide range of Cd compositions. In this paper, the bandedge emission mechanism of Zn^Cc^S with various Cd composition x was studied. It is focused to clarify how the band-edge luminescence efficiency of ZnCdS films is affected by these factors; x
150
151 (i) the crystalline quality determined by the lattice matching or mismatching to the GaAs substrates, (ii) the effects of exciton localization by the alloy potential fluctuation. The understanding of the emission mechanism and the clarification of the role of each process in the Zni^Cb^S alloys will not only promote the physics related but also will be effective for the design of high-efficiency optoelectronic devices in the wide spectral range. 2. Experimental 2»....C'W Zn^CdJS films with the six Cd composition x (*=0.21, 0.46, K T,-126.2(ps) 0.55, 0.56, 0.59, 0.79) were grown on GaAs (001) substrates by metalorganic molecular-beam epitaxy (MOMBE). The growth ''. * % t t -370.8 (ps) temperature was 370-400 °C, and the layer thickness was 560 run r for all the samples. The structural characterization was carried \ ^ i *S*w&ikv^ ' •\\-'~tyr: W ' out by X-ray diffraction (XRD) measurements. Cd compositions * Exprimental data fitting data were estimated according to the Vegard's law from diffraction time decoy of x, and Tj peaks taken from 6-20 measurements. Crystalline quality of the 0 500 1000 1500 2000 Time delay (ps) samples was evaluated by the full-width at half maximum Fig. 2 PL decay curve of (FWHM) of the X-ray rocking curve measurements. Zn0.44Cdo eeS. Two decay components Photoluminescence (PL) measurements were performed using the *i=i26ps and is.=37iPs were required 8K
2
to reproduce the experimental results.
325-nm line of a cw He-Cd laser operating at an excitation power density of 6.5W/cm2 at the temperature of 15K. Time-resolved photoluminescence (TRPL) measurements were performed at 8K using a frequency-doubled Ti: Sapphire laser as an excitation source. The pulse duration and the repetition frequency were 100 fs and 82 MHz, respectively, and the excitation energy density per pulse was 8K Fitted time domain approximately 85 nJ/cm2 at the wavelength of 400 nm. The -•-0-400ps t -,-% • » synchro-scan streak camera was used as a detector and the - • » - 4 0 0 - 1 0 0 0 ps spectral and temporal resolutions of the total system were 0.6 <•> nm and 20 ps, respectively. j
^ »
*i
3. Results and discussion ]
(h<^)
(1)
152 where I(t) is the luminescence intensity, x, and x2 are the shorter and longer lifetimes, respectively. The solid line is a fitting and x,=126 ps and x2=371 ps give the SK Z-MCW best fit to the experimental result. As is shown in this figure, t, 400 represents the lifetime in the time domain with the larger P L | E„ = 43 meV integrated intensity, while the lifetime x2 is obtained from thel 10M - T=307(ps) 6^=2.835 eV 300 time domain later than T,. In the fitting process, both theg .1 V 1, E _ shorter lifetime component Xi and the longer lifetime^ 200 component x2 appeared in all the samples. Their behavior as a | •" jf 100 function of Cd composition is summarized in Fig. 3. The short & lifetime T, (closed circles) strongly depends on the Cd 2.65 2.7 275 2.8 283 2.9 2.95 composition x, that is, the samples close to the lattice-matching Emission energy (eV) show relatively longer lifetimes and decrease with the Fig.4 Time-integrated PL spectrum increase of the lattice mismatch. On the contrary, the long (solid line) and energy-dispersed lifetimes (closed circles) of the sample lifetime x2 (closed squares) shows almost identical values in with Cd composition x=0.55. The dashed represents the fitted lifetime xr the range of 300-400 ps, which could be a manifestation of curve obtained by eq. (2). exciton localization effect, in which the nonradiative recombination process is effectively hindered by the potential barriers around the localized excitons. In order to discuss the localization effect in Zn^Cd^S system in more detail, photon energydispersed lifetimes of the sample with the Cd composition of ;t=0.55 were analyzed and plotted as closed circles in Fig.4 as well as the time-integrated PL spectrum. Shorter lifetime is obtained in the higher energy side and the lifetime becomes longer as the emission energy decreases. Below approximately 2.75 eV, the variation of the lifetime saturates and it shows constant lifetime about 300 ps. This energy dependence of the lifetime is explained by ! considering the exciton transfer processes to the lower energy levels as well as the exciton radiative recombination.8 We analyzed these measured lifetimes using the theoretical expression1415 and lifetime at the photon energy E is described as; r1(E)=T^\l
+
exd^—^
(2) Cd composition x in Zn ^Cd^ Fig.5 Radiative lifetime (solid squares) and localization depth (solid circles) as a function of Cd composition x. The radiative lifetime Xr is free from the influence of both crystalline quality and localization depth, which indicates the effective suppression of nonradiative loss due to the exciton localization effect in this material system.
where x (E) is the lifetime measured at the emission energy E, t r is the radiative lifetime of the localized excitons, E0 is the characteristic energy indicating localization depth and Eme indicates the mobility edge. The parameters giving the best fit to the experimental data in this sample are x r=307 ps, E„=43 meV, and EBe=2.835 eV, respectively. Figure 5 shows the Cd composition dependence of radiative lifetime (closed squares) and localization depth (closed circles) obtained by the fittings using the equation (2). It is noted that the radiative lifetime x, has ranged the value of 300-400 ps for the measured Cd compositions so that the radiative lifetime xr is independent of both the crystalline quality and localization depth. This is quite interesting result because it is quite similar behavior not only qualitatively but also quantitatively to the longer lifetime component x2 obtained by the energy integrated PL time decay
153 profile shown in Fig. 3. Therefore it is interpreted that the longer lifetime component x2 measured in the later time domain typically more than 400 ps after the excitation originates from the exciton radiative recombinations in the localized states. This shows that when the excitons are fully relaxed to the tailed states, nonradiative recombination processes are effectively suppressed and the lifetime will tend to be the one of the intrinsic radiative recombination of excitons at localized states. This shows that the exciton radiative recombination will dominate the recombination processes in the localized states regardless of the density of the dislocations and crystalline defects. On the other hand, the lifetime x, measured in the earlier time domain after excitation is severely restricted by the crystalline quality because the exciton under the relaxation process are delocalized and likely to be captured by the nonradiative recombination centers with higher possibility than the localized excitons which are spatially separated by the potential barriers caused by compositional disorder. 4. Conclusion We have grown the Zn^Co^S films with the wide range of Cd composition and evaluated their luminescence features focusing on the relation between the crystalline quality and localization. When the excitons are fully relaxed to the tailed states, then the nonradiative recombination processes are effectively suppressed and consequently, excitons in the localized states exhibit high luminescence efficiency. The excitons under the relaxation process, however, are exposed to the nonradiative recombination centers and the luminescence efficiency strongly suffers from their influence whose amplitude is determined by the crystalline quality. References 1. For a review, see S. Nakamura and G. Fasol, The Blue Laser Diode (Springer-Verlag, Berlin, 1997). 2. Y. Narukawa, Y. Kawakami, and Sg. Fujita, Phys. Rev. B 59, 10283 (1999). 3. K. Osamura, S. Naka, Y. Murakami, J. Appl. Phys. 46, 3432 (1975). 4. R. Singh, D. Doppalapudi, T. D. Moustakas, L. T. Romano, Appl. Phys. Lett. 70, 1089 (1997). 5. Y. Narukawa, Y. Kawakami, M. Funato, Sz. Fujita Sg. Fujita, and S.Nakamura, Appl. Phys. Lett. 70, 981 (1997). 6. Y. Narukawa, S. Saijyo, Y. Kawakami, M. Funato, Sz. Fujita Sg. Fujita, and S.Nakamura, J. Cryst. Growth 189/190, 593 (1998). 7. S. F. Chichibu, T. Sota, K. Wada, S. P. DenBaars, S. Nakamura, MRS Internet J Semicond. Res. 4S1, G2.7(1999). 8. Y. Kawakami, M. Funato, Sz. Fujita, Sg. Fujita, Y. Yamada, and Y.Masumoto, Phys. Rev B 50, 14655 (1994). 9. Y. Kawakami, M. Funato, Sz. Fujita, Sg. Fujita, Y. Yamada, T. Mishina, and Y.Masumoto, J. Cryst. Growth 159, 830 (1996). 10. Sz. Fujita, M. Funato, S.Hayashi, and Sg. Fujita, Jpn. J. Appl. Phys. 28, 898 (1989). U . S . Yamaga,
and A. Yoshikawa, J. Cryst. Growth 117, 353 (1992).
12. T. Yasuda, T. Yasui, and Y. Segawa, J. Cryst. Growth 159,447 (1996). 13. T. Taguchi, Y. Yamada, T. Ohno, J. T. Mullins, and Y. Masumoto, PhysicaB 191 136 (1993). 14. M. Oueslati, C. Benoit a la Guillaume, and M. Zouaghi, Phys. Rev. B 37, 3037 (1988). 15. C. Gourdon, and P. Lavallard, phys. stat. sol. (b) 153, 641 (1989).
Nanostructured Organic Thin Films: Electronic Energetics and Devices C. TALIANI1, F. BISCARTNI1, E. LUNEDEI1, P. MEI1, M.MUCCINI1, M.MURGIA1, M. SCHNEIDER1 and G. LANZANI2. x Istituto di Spettroscopia Molecolare, Consiglio Nazionale delle Ricerche, 40129 Bologna, Italy 2 INFM, Dipartimento di Fisica, Politecnico di Milano, 20133 Milano, Italy Abstract We report on the optoelectronic properties of vacuum sublimed organic thin films of the oligothienyls (T„) model systems. The Davydov splitting (DS) of the lowest exciton is about 0.3 eV and decreases with the conjugation length when going from T4 to T6. The lowest DS component is partially forbidden due to the crystal packing and the spectral activity occurs via Herzberg-Teller (HT) vibronic coupling. We show the real time dynamics of the HT coupling by coherent vibrational spectroscopy and the role of aggregates in the energy transfer processes within the films. 1. Introduction Organic thin films of conjugated systems constitute the basic building blocks of a new promising branch of optoelectronics and electronics which takes advantage of the semiconducting properties of conjugated organic materials. The areas of application span from segmented and active colour flat panel displays based on organic light emitting diodes (O-LED) ' to the so called plastic electronics 2 3. Thin films of rigid-rod conjugated systems (RRCS) grown by vacuum sublimation have shown a large degree of ordering 4 5 which depends on the self-alignment characteristics of RRCS. Oligomers of RRCS are particularly suitable for optoelectronics and electronics and constitute at the same time good model compounds for the understanding of the basic properties of these materials. Charge and energy transport are the basic processes in optoelectronic and electronic devices. These processes are governed by the meso-scale spatial dimensions. The control of morphology at this spatial definition is therefore necessary in order to take advantage of the properties. Obtaining highly ordered thin films is particularly feasible by means of molecular beam growth in high and ultra-high vacuum (UHV).The basic understanding of the electronic structure of the lowest electronic excited states is of particular interest in this context. Conjugated organic polymers, which have an intrinsic large inhomogeneous broadening due to a large distribution of conjugation length defects, have been masking most of the intrinsic electronic properties and at some stage it has been thought that the lowest electronic excitation is due to a band to band excitation. The observation of structured photoluminescence in O-LED based on polymers as well as molecules has been instrumental in perceiving that the lowest excited state is an exciton. Nevertheless the exciton band structure and in particular its bandwidth have not been elucidated until recently. Furthermore, for the understanding of the efficient energy transfer into the manifold of low lying defect states, it is of particular importance the thorough understanding of the nature of the exciton band and the sub-band defect states. We have chosen to work on well studied model compounds such as oligothienyls (Tn). It has been shown that the lowest electronic excited singlet state in T6 is 'B u , and is polarised along the long axis of the molecule 6 7. The vibrational properties have been recently assigned by a combined work on single crystal polarised IR and Raman spectroscopy and quantum chemical calculations 8. The size of the lowest electronic excitation in the solid has been shown by momentum transfer dependence electron energy-loss spectroscopy (EELS) to be confined within the molecular unit 9. In this paper we review some of the most recent work done at the ISM-CNR in Bologna in this area. We will show that the exciton bandwidth at k=0 is about 300 meV 10 n and the Davydov splitting (DS) decreases with the conjugation length u. The lowest DS is accidentally forbidden by crystal packing and therefore the lowest DS component is dark. Spectral activity is due to Herzberg-Teller (HT) vibronic coupling n . We will show the real time dynamics of the HT coupling by coherent vibrational spectroscopy. The role of aggregates in energy transfer is also elucidated 13.
154
155 2. Exciton band structure of T6 and conjugation chain length dependence of the DS Since the low temperature crystalline structures of T6 and T4 14 15 are monoclinic with Z=4, the 1'BU state (polarised along the long axis) splits in the crystal in four components, two of which are parity allowed and polarised in the b axis (au) and in the ac plane (bu) respectively u . Gebauer et.al. by studying the highly resolved thin film spectrum on highly oriented pyrolytic graphite, have assigned the Davydov splitting (DS) to 120 cm"1 16. Many authors on the other hand 17 18 19 20 have assumed, on the ground of the dipole-dipole excitonic model, that the splitting is in excess of 10000 cm"'. We have shown that the dipole-dipole method with spherical boundary surface is invalid since the intermolecular distance is comparable to the dipole length. We mention that a similar result is obtained by using the dipole planewise method. The proper approach is to calculate the resonance integrals on first principles. This has indeed been done by the Mons group n 21 and the DS is calculated to be 3600 cm"1. The be polarised single crystal absorption spectrum of T6 is shown in Fig. lb. bu
b
T6 single crystal
tensity
1..-
u
lib
U//c
.2 0.8Q. 0.40.2-
a
u
0,022500
25000
22500
Wavenumbers cm'
Fig. 1 a) Polarised single crystal absorption of T4 at 4.2K. b) Polarised single crystal absorption of T6 at 4.2K. In both cases the crystalline plane is be. The electronic origin is completely polarised in the b direction at 18350 cm"1. Its intensity is negligibly weak since the molecular long axis projection on the b direction is vanishing small. Nevertheless it is possible to observe it in a micron size thick crystal. The higher DS component polarised along the c direction is saturated. We assume that it is located at 20945 cm"1 from the residual a polarised absorption observed in the b direction as the result of a slight off-plane misalignment. The DS is therefore about 2600 cm"1 (320 meV). This indicates the lower limit for the exciton bandwith and it is in satisfactory agreement with the calculation. The T4 single crystal absorption spectrum is shown in Fig. la. It resembles the T6 spectrum but the DS is considerably larger (2900 cm"1). Ab-initio calculations predict this trend 21 n. We conclude that the effect of intermolecular interactions in Tn causes a DS splitting which reaches a maximum for short chains lower or equal to T4 and then diminishes to lower values in longer chains. This is due to the weaker interaction of the more spread wavefunctions (wf) in longer conjugated chains. In infinite chains, if the conjugation were infinite, the interaction would be zero. This is not the case in real systems because the electron-molecular vibration interaction causes the excited state wf to localise in finite region of the chain. This region is not much longer than twelve double bonds like in T6. We therefore conclude that in real interacting conjugated chains the DS is of the order of 3000 cm"1 (300 meV). 3. Nature of the lowest Davydov component Even if the a„ Davydov component is very weak, the vibronic bands built on it acquire considerable intensity when the energy approaches the intense bu component. This is a typical signature of vibronic coupling with higher electronic states. The closer the lending state, the higher the intensity
156 borrowing as the result of energy denominator effects as in perturbation theory. The intensity increases in the region of few hundred wavenumbers and then reaches a plateau. If the lending state were the upper Davydov component the intensity would increase to the bu intensity. The low energy region of the absorption and emission spectra is shown in Fig. 2.
Wavenumber [cm ]
Fig.2 Polarised photoluminescence (left side) and absorption (right ride) of T6 be single crystal plane at 4.2K. The origin of the emission is 18 cm"1 lower than the absorption as the result of trapping in a shallow X-trap. All the spectral weight derives from the activity of c polarised low energy bands O' and O" in absorption and A and C in emission. These bands are due to totally symmetric vibrations in emission and absorption and have been assigned by 22. Since these bands are c polarised the bands cannot have a Franck-Condon origin. Their activity is assigned to Hetzberg-Teller (HT) vibronic coupling with the higher excited state 21BU polarised along the median in plane axis. The lowest Davydov component is therefore not completely dark but has some spectral weight due to HT coupling. The most effective coupling is provided by the C=C TS vibration at 1450 cm"1 (1275 cm"1 in the excited state). 4. Energy transfer in thin films The morphology of vacuum evaporated thin films has been shown 23 to depend on three parameters: substrate temperature, rate of evaporation and film thickness. This has been rationalised in terms of a diffusionally controlled growth of RRCS 24. The careful control of the growth parameters in UHV gives us for the first time the possibility to explore the role of morphological disorder in energy transfer. The morphology of a series of thin films grown on an insulating substrate is shown in Fig. 3a. The growth proceeds from the coverage of a first layer of molecules lying parallel to the substrate to more developed islands in which the second monolayer (ML) is formed by molecules standing upright forming eventually a layer by layer terrace structure. Finally the islands coalesce giving rise to larger grains and associated grain boundary defects. At higher coverage a new process of recrystallisation sets in with the formation of lamellae at the expense of grains. This large variance of morphologies is reflected in a marked difference in photoluminescence (PL) spectra as it is shown in Fig. 3b. PL is predominantly excitonic in sub-ML coverage films with sharp bands very similar to those of the single crystals. The origin is quite weak and most of the intensity resides in the false origin progression and in particular in the 1460 cm"1 vibronic component. The origin of these components is HT. At higher coverage new broad bands with a characteristic C=C vibronic pattern appear with higher intensity masking in part the excitonic bands. The origin of the new broad bands is attributed to aggregate states that act as efficient trapping sites. We suggest that grain boundary defects are responsible of these states. The higher is the coverage, the higher is the intensity of the aggregate states until finally the excitonic bands are almost completely washed out. The reminiscence of the strong 1460 cm HT component is still discernible. We observe that energy transfer is strongly
167 influenced by morphological disorder in the mesoscale. This is particularly true since the lowest exciton is forbidden. Aggregate emission is the characteristics signature of thick films. Aggregates are not only efficient traps but have a higher probability of radiative emission 25 .
Fig.3 a) AFM images of T6 films with sub-monolayer (1 nm), islands (2 nm), layers (3 nm and 5 nm), layers/lamellae (25 nm) and lamellae (100 nm)topologicalstructure obtained for deposition temperature T=150°C andfilmthickness (Viz. amount of deposited material) increasing from 1 nm to 100 nm. b) Steady state photoluminescence spectra at T=4K of T6filmswhose morphology is dominated by selected molecular architectures. The relative spectral weight of aggregates and excitons for die different molecular architectures is reported in the inset. It is interesting to notice that this broad emission has been erroneously attributed in the past to excitonic emission in part for its vibronic pattern. We know now that this is not true. We suggest that aggregates are possibly the origin of PL and electroluminescence in RRCS thin films on insulating substrates since the relative arrangement of the chromophores is such to give rise to i) dark states and ii) PL trapping sites at grain boundary defects. 5. Real time vibronic coupling from coherent vibrational spectroscopy. The advent of high repetition rate femtosecond tunable laser sources has made possible to observe the dynamics of vibrational wave-packets formed upon vertical electronic excitations. By exciting T6 with a 10 fs laser pulse at the lowest DS component (at 540 and 510 nm) and probing at the same energy the photoinduced absorption (PA) due to the absorption from 1!BU to higher n*Ag states, the PA is modulated by an oscillatory response which is the signature of the vibrational wave-packet formed into the vibrational manifolds of the ground and the excited ^Bu states 26. The Fig.4 shows the oscillatory response for a pump and probe experiment at 540 nm. The time response may be converted into the energy response by Fourier transformation giving the energy of the vibrations involved in the coherent process. This is shown in the inset of Fig. 4. Five well resolved vibrational modes are observed. The lowest two modes are assigned to the HT modes responsible for the O' and O" false origins in absorption (vide supra). The lowest mode at 126 cm"1 shows a damping time of about 3 ps. This indicates the lower limit of the coherent dephasing time since loss of coherence
158 may be well caused by defects.This is the first time at our knowledge that HT real time dynamics has been observed. 1
1
'
1
AA i l i
'
i
'
.1.
500 Time Delay (fs)
Fig. 4 Differential transmission dynamics AT/T for the a-T 6 film at 540 nm probe wavelength. The inset shows the Fourier transform of the oscillatory component of the signal. Ackowledgements This w o r k w a s partially supported by t h e E.U. T M R N e t w o r k S E L O A and t h e C N R P . F . M S T A . References l R. H. Friend, R. W. Gymer, A. B. Holmes, et al, Nature 397,121 (1999). 2 A. R. Brown, A. Pomp, C. M. Hart, et at., Science 270,972 (1995). 3 A. Dodabalapur, H. E. Katz, L. Torsi, etal., Science 269,1560 (1995). 4 P. Ostoja, S. Guerri, S. Rossini, etal., Synth. Met. 54,447 (1993). 5 6 7 8 9
B. Servet, S. Ries, M. Trotel, etal., Adv. Mater. 5,461 (1993). R. Lazzaroni, A. J. Pal, S. Rossini, et at., Synth. Met. 42, 2359 (1991). H.-J. Egelhaaf, P. Bauerle, K. Rauer, etal., Synth. Met. 61,143 (1993). A. Degli Esposti, M. Fanti, C. Taliani, etal., J. Chem. Phys. 112, 5957 (2000). M. Knupfer, T. Pichler, M. S. Golden, et al, Phys. Rev. Lett. 83,1443 (1999).
10 11
M. Muccini, E. Lunedei, A. Bree, etal., J. Chem. Phys. 108, 7327 (1998). M. Muccini, E. Lunedei, C. Taliani, etal., J. Chem. Phys. 109, 10513 (1998).
12 13
M. Muccini, M. Schneider, C. Taliani, et al., Phys. Rev. B , in press (2000).
14
M. Muccini, M. Murgia, C. Taliani, et al., Adv. Mat., submitted (2000). G. Horowitz, B. Bachet, A. Yassar, et al., Chem. Mater. 7, 1337 (1995).
15 16
T. Siegrist, C. Kloc, R. A. Laudise, et al., Adv. Mater. 10, 379 (1998).
17 18
K. Hamano, T. Kurata, S. Kubota, etal., Jpn. J. Appl. Phys. 33,1031 (1994). A. Yassar, G. Horowitz, P. Valat, et al, J. Phys. Chem. 99, 9155 (1995).
19
H.-J. Egelhaaf and D. Oelkrug, SPIE Proceeding Series 2362, 398 (1995).
20 21
G. Lanzani, S. Frolov, M. Nisoli, etal, Synth. Met. 84, 517 (1997). J. Corral, D. A. dos Santos, and J. L. Bredas, J. Am. Chem. Soc 120, 1289 (1998).
22 23
A. Degli Esposti, O. Moze, C. Taliani, et al, J. Chem. Phys. 104, 9704 (1996). F. Biscarini, R. Zamboni, P. Samori, et at., Phys. Rev. B 52, 14868 (1995).
24 25 26
F. Biscarini,, edited by B. Ratner and V. V. Tsukruk (ACS Book, Washinghton D C , 1998). P. Mei, M. Murgia, C. Taliani, et al, J. Appl. Phys. (2000). G. L. G. Cerullo, M. Muccini, C. Taliani, and S. De Silvestri, Phys. Rev. Lett. 83,231 (1999).
W. Gebauer, M. Sokolowski, and E. Umbach, Chem. Phys. 227, 33 (1998).
EXCITONIC BANDS IN THE PHOTOCONDUCTIVITY SPECTRA OF SOME ORGANIC-INORGANIC HYBRID COMPOUNDS BASED ON METAL HALIDE UNITS G. C. PAPAVASSILIOU, G. A. MOUSDIS, I. B. KOUTSELAS Theoretical and Physical Chemistry Institute, National Hellenic Research Foundation, 48, Vassileos Constantinou Ave., Athens 116 35, Greece G. J. PAPAIOANNOU Department of Physics, Athens University, Zographou, Athens 157 71, Greece The photoconductivity (PC) spectra of the compounds CH3NH3PW3, [CHjNHjtfCHjC^CftNHjkPbA, [CftCsftiCfiyvIHakPbL), [H2NC(I)=NH2]3Pbl5 as well as the spectra of similar compounds based on C10H21SC(NH2)2, H3N(CH2)6NH3, C,4H9CH2SC(NH2)2, SnL,, PbCU,-* and PbBrxl4_x are described. The position, intensity and shape of the PC bands depend on the dimensionality (or size) of the inorganic network as well as on the nature of metal halide and the organic groups. Excitonic features are discussed. 1. Introduction During the last years, the optical absorption (OA) and photoluminescence (PL) spectra in a number of low-dimensional (LD) organic-inorganic hybrid compounds (systems) have been studied, extensively1"16. In particular, compounds based on metal halide units have the general formulas
PR(CH2)„NH3]xMyXz,
[R(CH2)„NH(CH3)2]xMyXz,
[R(CH2)nS(CH3)2]xMyXz,
[R(CH2)„SC(NH2)2]xMyXz, and [R(CH2)„SeC(NH2)2]xMyXz (where R=organic-group; M=Bi(IH), Pb(II), Sn(II), Cu(I), Ag(I), etc; X=I, Br, CI; n,x,y,z=0,1,2,3,... ). Their OA and PL spectra exhibit excitonic bands in the UV-visible spectral region. The position, intensity and shape of these bands depend on the dimensionality or the size of the inorganic network as well as on the nature of M, X, R and onium-groups. The bands in the spectra of plumbates occur at shorter wavelengths (270-750 nm) than those of stannates (350-800 nm). The bands of AgX- and CuX- based compounds occur in the region 220-450 nm, while the bands of Bil- based compounds in the region 350-550 nm. The bands of bromides occur at shorter wavelengths than those of the corresponding iodides and the bands of chlorides at shorter wavelengths than those of bromides. Roughly speaking, when R is an alkyl- or phenyl-group, the inorganic network of the system behaves as an artificial LD system, in which the organic part plays the role of barrier. When R is a chromophore (e.g., aryl-group), the intensity and shape of the PL bands indicate electronic interactions11,12. In some cases, the results agree with the theory (e.g., refs. 1-3, 12, 13). However, little is known about the photoconductivity (PC) spectra of this wide variety of compounds1,14"16. In this paper, the room temperature PC spectra of compounds CH3NH3PM3 (3D),
[CH3NH3][CH3C«H4CH2NH3]2Pb2l7 (q-2D),
[CHsCeHUCItzNHafcPbL, (2D), [H2NC(I)=NH2]3Pbl5 (ID) and the PC spectra of similar compounds based on Ci0H2iSC(NH2)2, H3N(CH2)6NH3, Ci4H9CH2SC(NH2)2, Snl4, PbClxL,.x and PbBrxl4-x are described. The peak positions of the corresponding OA and PL spectra (from thin 159
160 deposits) are given, for comparison. The PC bands exhibit excitonic features (e.g., PC bands follow the excitonic OA bands) as in the case of other 3D and LD systems17. 2. Experimental Compounds were prepared by methods reported in our previous papers3'8"11. Flat crystals were carefully attached with silver paint on two gold strips, separated by 1mm and held on a bakelite substrate. The PC spectra were recorded in the spectral range from ca 340 nm to ca 850 nm by same instrumentation described elsewhere11'. 3. Results and discussion Fig. 1 shows the PC spectra of CH3NH3PbI3 (3D),
[CH3NH3][CH3C6H4CH2NH3]2Pb2l7
(double layer: q-2D), [CH3C6H4CH2NH3]2PbL, (single layer: 2D), and [H2NC(i)=NH2]3PbI5 (ID). One can see that the position of the low frequency PC band is shifted to shorter wavelengths as the dimensionality (or the size) of the inorganic network is decreased. The PC peaks are red shifted, in comparison the excitonic OA peaks. The PL peaks occur almost in between the OA and PC peaks. The PC peaks are more intense in the 2D than in the ID systems. The PC spectrum of the q-2D system [CH3NH3][CH3C6Ff4CH2NH3]2Pb2l7 exhibits a broad band at ca 585 nm. The broadening may be due to the contamination from other species [CH3NH3]n.i[CH3C6H4CH2NH3]2Pbj3n+i (here n=l,3,4,5,...). Also, there is a weak sample to sample dependence in the spectra of CH3NH3Pbl3 (Fig. la, la'), maybe due to the different degree of oxidation at the surface. Fig. 2 shows the PC spectra of some 2D systems, i.e., [CHsCsHtCFbNHskSriLt (two crystals) [Ci0H2iSC(NH2)2]2Pbl4, and [CFfeCeHtCI^NHb^bB^
(two phases). The PC spectrum of
[CH3C6H4CH2NH3]2SnLi exhibits a band at ca 604 nm, of which the intensity and shape varies from crystal to crystal, due to aging effects. The PC spectra of aged crystals exhibit peaks at longer 1 1D
• 2D
1 q-2D
•
1
•
r3D
Fig.l. PC spectra of CH3NH3Pbl3 (a,a': two samples), [CHaNHaHCHsCeftCHjNiyj Pb2I7(b), [OfeCsFLtCHzNHakPbMc), and [H2NC(I)=NH2]3Pbl5 (d). Arrows indicate the peak positions of the PL spectra and vertical bars those of the OA spectra.
161 wavelengths (e.g., at 630 nm) maybe associated to bound excitons2'15'17. Aging effects are more pronounced in the spectra of Sn- based materials (see also ref. 15). The PC spectrum of [CioH2iSC(NH2)2]2Pbl4, as in the case of [H3N(CH2)6NH3]Pbl4 (2D), exhibits a peak at ca 501 nm, while that of [CH3C6H4CH2NH3]2PbI4 at 535 nm (Fig.l). This shift is attributed to the small differences in the crystal structure8"'9'1,9'1, rather than to the nature of the organic component. Compound [CH3C6FJ4CH2NH3]2PbBr4 is crystallized in two different phases. The PC spectrum of one of them (space group P2!/a )9c exhibits a peak at 409 nm. The peaks in the PC, OA and PL spectra of the other phase occur at shorter wavelengths (e.g. at 387 nm for the PC spectrum). These peaks occur close to those of [H3N(CH2)6NH3]PbBr4, indicating similar structures (i.e., P2i/c)8a. PC peaks occur close to the OA peaks, indicating very pure compounds17.
Fig. 2. As in Fig. 1, but for [CH3C6H4CH2NH3]2SnI4 (a, a'; two crystals), [CioH2iSC(NH2)2]2Pbl4 (b), and [CH3C6H4CH2NH3]2PbBr4 (c, c', two phases). The PC spectra of two series [CH3C6H4CH2NH3]2PbX4 and [H3N(CH2)6NH3]PbX4 as well as the OA and PL spectra, for comparison, were studied, systematically. All the compounds are 2D systems. Each series contains isostructural crystals, namely the first9b contains crystals of the space group P2i/a and the second8" crystals of the space group P2i/c. The separation between the PbXlayers is ca \lk for the first series9" and ca 12A for the second9". The low frequency peaks in the spectra of the compounds of the second series occur at shorter wavelengths than those of the corresponding compounds of the first series. Fig. 3 shows the peak position dependence on the composition (x) of these two series. One can see that there are almost linear dependencies. The PC peaks are red shifted, in comparison to the excitonic OA peaks. The peaks are blue shifted after replacement of I by Br or CI and replacement of Br by CI. In some cases, in which only the OA and/or the PL spectra were observed, it is expected a similar behavior for PC spectra. One can say that in organic-inorganic hybrids with a variety of organic molecules ( : containing
162
500
_450 E c
350 0
1
2
V A
3
4 0
1
2
V A
3
4
Fig. 3. Peak positions as function of x in the spectra of [CHsC&HtCHzNHakPbXt (a), [H3N(CH2)6NH3]PbX4 (b). Linear lines are guides to the eyes, only. alkyl, aryl - alkyl groups), metals (Pb, Sn) or halogens (I, Br, CI), the low frequency PC bands follow the excitonic OA (and PL) bands1"12'14"16. It seems that, in the absence of defects or impurities etc., the PC peaks should occur very close to the excitonic OA peaks. The results indicate excitonic contribution to the PC, as in the case of other semiconductor systems1,2'17'18. However, for a complete discussion about it, the single crystal OA spectra are required. Because, the single crystal OA peaks occur at longer wavelengths than those of thin deposits1"3. In other words, for very pure crystals coincidence of the (excitonic) PC bands with the excitonic OA bands is expected. The PC spectra of hybrid compounds with an organic chromophore (e.g. naphthyl, anthranyl groups) are weak. Fig. 4 shows the PC spectra of [Ci4H9CH2SC(NH2)2]2PbBr4. In this case, the position of the excitonic OA peak and the corresponding PC peak, arising from the PbBr4 network, is not clear. It seems to occur at < 400 nm*1, while the first singlet level of the C14H9CH2- group occurs at ca 425nm9d. The PC spectrum exhibits only a broad band arising from the organic component18, while the PL spectrum exhibits a band at ca 450 nm9d. Details on the PC spectra of the hybrid compounds with chromophores will be reported elsewhere. Acknowledgments One of the us (IBK) thanks the Greek State Scholarship Foundation for financial support.
163 T
•
1
•
r
> 3
-co
8 Q O
r: a.
J
300
350
400
450
i
1
500
i
L
550
600
X[nm] Fig. 4. PC spectrum of [Ci^C^SCXNtfeihkPbB^; vertical bars indicate the OA peak positions and the arrow indicates the PL peak position. References 1. (a) T. Ishihara, in "Optical Properties of LD Materials": T. Ogawa, Y. Kanemitsu (Eds), World Sci., Singapore, p.288 (1995); (b) X. Hong, T. Ishihara and A. V. Nurmikko, Sol. St. Commun. 84, 657 (1992). 2. G. C. Papavassiliou, Progr. Sol. State Chem. 25,125 (1997). 3. D. B. Mitzi, Progr. Inorg. Chem. 48, 1 (1999). 4. T. Kondo, S. Iwamoto, S. Hayase, K. Tanaka, J. Ishi, M. Mizuno, K. Ema, R. Ito, Sol. State Commun. 105, 503 (1998). 5. T. Hattori, T. Taira, M. Era, T. Tsutsui, S. Saito, Chem. Phys. Lett. 254, 103 (1996); T. Gebauer, G. Schmid, Z. Anorg. Allg. Chem. 625, 1124 (1999); K. Chondroudis, D. B. Mitzi, Chem. Mater. 11,3028(1999). 6. T. Fujita, Y. Sato, T. Kuitani, T. Ishihara, Phys. Rev. B57, 12482 (1998). 7. C. R. Kagan, D. B. Mitzi, C. D. Dimitrakopoulos, Science 286, 945 (1999). 8. (a) G. A. Mousdis, G. C. Papavassiliou, C. P. Raptopoulou, A. Terzis, J. Mater. Chem. 10, 515 (2000); (b) Ibid. 8, 2259 (1998); (c) Z. Naturforsch. 53b, 927 (1998). 9. (a) G. C. Papavassiliou, G. A. Mousdis, A. Terzis, C. P. Raptopoulou, Z. Naturforsch. 54b, 109 (1999); (b) G. C. Papavassiliou, G. A. Mousdis, C. P. Raptopoulou, A. Terzis, Ibid. 54b, 1405 (1999); (c) Ibid. 55b, 536 (2000); (d) G.C. Papavassiliou, unpublished work. 10. G. C. Papavassiliou, G. A. Mousdis, I. B. Koutselas, C. P. Raptopoulou, A. Terzis, M. G. Kanatzidis, E. A. Axtell III, Adv. Mater. Opt. Electron. 8, 263 (1998). 11. (a) G. C. Papavassiliou, G. A. Mousdis, I. B. Koutselas, Adv. Mater. Opt. Electron. 9, 265 (1999); (b) T. Goto et al, unpublished. 12. M. Braun, W. Tuffentsammer, H. Wachtel, H. C. Wolf, Chem. Phys. Lett. 303, 157 (1999); 307, 373 (1999); M. Era, K. Maeda, T. Tsutsui, Ibid 296, 417 (1998); D. B. Mitzi, K. Chondroudis, C. R. Kagan, Inorg. Chem. 38, 6246 (1999). 13. D. M. Basko, V. M. Agranovich, F. Bassani, G. C. Larocca, Phys. Stat. Sol. 178a, 69 (2000) and refs. therein. 14. G. C. Papavassiliou, I. B. Koutselas, Synth. Met. 71, 1713 (1995). 15. G. C. Papavassiliou, I. B. Koutselas, D. J. Lagouvardos, J. Kapoutsis, A. Terzis, G. J. Papaioannou, Mol. Cryst. Liq. Cryst. 253, 103 (1994). 16. I. B. Koutselas, D. B. Mitzi, G. C. Papavassiliou, G. J. Papaioannou, H. Krautscheid, Synth. Met. 86, 2171 (1997). 17. B. Lavigne, R.T. Cox, Phys. Rev. B 43, 12374 (1991) and refs. 45-48 cited therein. 18. H. Meir in "Organic Semiconductors": Monographs in Modern Chemistry, Verlag Chemie, Weinheim (1974) and refs. 135, 755, 769, 773, 774, 775, 807, 1723 cited therein.
NaV2Os: A N EXOTIC EXCITON SYSTEM MAXIM V. MOSTOVOY, DANIEL I. KHOMSKII, JASPER KNOESTER Materials Science Center, University of Groningen, Nijenborgh 4 9747 AG Groningen, The Netherlands We show that the phase transition which sodium vanadate undergoes at Tc = 34 K is driven by a charge ordering. The relevant effective Hamiltonian is of the Frenkel exciton type, with a very large bandwidth to molecular energy ratio. This causes strong nonHeitler-London effects and a temperature dependent gap that vanishes at Tc. In addition to the phase transition, the model qualitatively explains the observed absorption spectrum and the anomaly in the static dielectric constant. Within our model, the observed spin-gap opening at Tc results from exciton-spinon coupling. 1. I n t r o d u c t i o n Sodium vanadate (a'-NaV 2 0 5 ) has recently received considerable attention in the literature. At Tc = 34 K, this insulator undergoes a phase transition, in which a spin-gap opens and the size of the lattice unit cell doubles in the a and b directions and quadruples in the c direction. 1,2 As early X-ray experiments seemed to indicate that the V ladders (Fig. 1) have one leg with nonmagnetic V 5 + ions and one with V 4 + , 3 the phase transition was originally identified as a spin-Peierls transition occurring in the spin-1/2 chains formed by the V 4 + legs. Recent experiments, however, have cast serious doubts on this explanation. For instance, it was demonstrated that the strong suppression of Tc by magnetic field, which is characteristic for spin-Peierls materials, is absent. 4 In addition, an anomaly was found in the static dielectric function, which is hard to explain within the spin-Peierls scenario. 5,6 Other important observations come from X-ray and NMR, which demonstrate that above T c all V ions are equivalent ( V 4 5 + ) , whereas below Tc two types of V sites occur. 7 ' 8
V £¥¥ *
a
b
tit
_• • M Wte
*
*:
'4
# 11
/
w M \n^
a
~*T
u d
b
Fig. 1: Crystal structure of the V-O plane in NaV^Os- Oxygens are located at the corners of the plaquettes, while vanadium ions are located at their centers. The relevant dIy-orbitals of the V ions are drawn. The ladders formed by the vanadium ions are indicated by the dashed lines and are also depicted in more detail to the right, along with the lattice vectors a and b, and with the vectors fj and fa which are used in the text. Each ladder has two legs: an upper one (u) and a lower one (d). We have recently shown that the experimental observations are consistent with a model in which the charge degrees of freedom play the leading role and drive the phase transition, only to be followed by the spins. 9,10 The charge degrees of freedom are described by a model
164
165 of coupled two-level systems (isospin model). In the present paper, we will discuss the formal equivalence of this model to the familiar Frenkel exciton model used in molecular crystals. 11 ' 12 As we will also show, however, the distinct difference with molecular crystals is the strength of the effective excitation transfer interaction, which enables a phase transition. We will briefly discuss how the above experimental observations are consistent with our model. 2. M o d e l Our low-energy effective model for NaV 2 05 is motivated by the magnitudes of the electron hopping integrals indicated in Fig. 1 and the typical Coulomb interactions between electrons. Density functional calculations have shown that the electron hopping amplitude between the V ions on one rung of the vanadium ladders is given by tj_ = 0.38eV, while the hopping integral between neighboring rungs is given by <|| = 0.17eV. 13 The hopping integral txy between two neighboring ladders is of the order of O.OleV. Moreover, as the Coulomb repulsion of two electrons on the same V ion is ~ 3eV, we may for all practical purposes neglect double occupation. The above numbers suggest that we may consider the rungs of the V ladders as basic building blocks. Neglecting in first instance the hopping between the rungs, each rung, labeled by a position index n, has two one-electron states: | ± ) n = (\u)„ =F |rf) n )/\/2, where \u)n (|d) n ) is the state with the electron residing on the upper (lower) V ion of the rung (Fig. 1). The energies of these states are E± = ±t±. To describe the low-energy properties of the quarter-filled (undoped) ladders, we may neglect states with doubly occupied and empty rungs (charged states), as those would involve an energy increase of 2t±_ = 0.76 eV plus an additional amount due to the increase of the Coulomb energy (~ 0.5 eV). This total increase cannot be compensated by the gain in the kinetic energy 4i|| = 0.72eV of the charged excitations. Thus, the ground state is dominated by singlyoccupied V rungs, the charged excitations are thermodynamically irrelevant, and the system is insulating in accordance with experimental observations. In this picture, the basic building block (the rung) can be regarded as a two-level system, of which the excitation energy is 2t±. These two-level systems may be described by (iso)spin-l/2 operators (T^,T^,T^), where T£ = o\j2 and a'n the ith Pauli operator working one the nth two-level system. In terms of these operators, the Hamiltonian of a single rung reads: H„ = 2t± J2(T* + h = 2t± £ T+T-, n
z
(1)
n
with T^ = T* ± iT% the raising and lowering operators for the two-level system. The ground state of a single two-level system has expectation values (T*) = —1/2 and (Tn) = 0- Since the dipole operator for the n t h rung is easily shown to be given by fj,„ = elT* (with I the length of a rung), the equality (T*) = 0 means that the ground state of a single rung has no permanent dipole. This is obvious from the fact that in the ground state the probability of the electron to be on either one of the V ions of the rung is equal. This will change when we account for interactions between rungs (see below). We note that also (T^) = 0, due to the fact that the Hamiltonian is real. From the above form of the dipole operator / j n , one also finds that the transition between the ground state of a rung and its excited state is dipole allowed and may thus be observed in absorption spectra. The corresponding transition dipole matrix element is given by el/2. This dipole is oriented in the direction of the rungs (the crystal a axis). We now turn to the inclusion of inter-rung interactions. We will primarily focus on the effects of Coulomb interactions between electrons on different rungs; the effect of inter-rung hopping (i||) will be briefly discussed in Sec. 4. Accounting for the Coulomb interactions, we arrive at: H = 2tx £ ( r * + h + \ £ n
z
^ n,m
K m r * T * = 2t± £ T ^ T ; + i £ n
* n,m
I s - p ? + T~)(T^ ^
+ T~),
(2)
166 with Vnm = V(U„, U m ) + V(d„, dm) - V(un, dm) - V(dn, Um).
(3)
Here, e.g., V(un,dm) is the Coulomb interaction between an electron on the upper V ion of rung n and one on the lower ion of rung m , etc. In Eq. (2), we have introduced the second form of the Hamiltonian to stress the formal equivalence to the familiar Frenkel exciton Hamiltonian for crystals of "two-level" molecules (i.e., molecules with one strong optical transition). 11,12 The role of the molecular transition energy in such systems is taken by the quantity 2t± in our model. In the theory of molecular excitons, the operators T + and T~ are usually denoted B* and B, respectively, known as Pauli raising and lowering operators. The interactions between the molecules are then understood to be of dipolar origin. Obviously, the inter-rung interactions in Eq. (2) are also of dipolar origin, except that the matrix elements (Eq. (3)) go beyond the point dipole approximation. 3. P h a s e transition and charge ordering Having shown the formal similarity between the usual Frenkel exciton Hamiltonian and our lowenergy model for N a V 2 0 5 , we should stress that an important difference lies in the ratio of the interactions and the single-molecule (rung) frequency, jV/(2tj_), with jV the typical nearestneighbor interaction matrix element. For molecular crystals, this ratio usually is of the order of 0.01 — 0.1, while for NaV 2 Os this parameter is of the order of unity. The latter was obtained from simple estimates of the Coulomb interactions, which give a value of Vn^+^/4 = 0.62 eV and V n] n + f 2 /4 = —0.54 eV, where ^ (f2) is the vector between two neighboring rungs on the same (neighboring) ladder (Fig. 1). This difference is crucial for the behavior of the system. If the interactions are small, one may apply the Heitler-London approximation, as one usually does in the theory of molecular excitons. 11 ' 12 This amounts to neglecting the terms of the form T+T^ and T^T^ in the Hamiltonian; these terms mix basis states that differ by twice the molecular energy, which is much larger than the interaction matrix element. In this approximation, the total ground state is the state in which all molecules are in their respective ground states. Moreover, the excited states are then classified with respect to the number of excitation quanta shared by the molecules in the crystal. For instance, the lowest band of excited states (the one-exciton band) consists of Bloch waves of singly-excited states; they span a band of width ~ V around the single-molecule frequency. The next higher band of excited states are the two-excitons, sharing two molecular excitations, etc. Within the Heitler-London approximation, only one-excitons states (of zero momentum) are optically accessible from the ground state. Thus, if we could treat NaV 2 Os in the Heitler-London approximation, its ground state would have all rungs in their ground state. As we have seen, this state has no permanent dipoles ((Tx) = 0). However, since the Heitler-London approximation cannot be applied, the ground state contains an admixture of rung excitations. In other words, the rungs are in a superposition of the symmetric and anti-symmetric state, giving rise to permanent dipoles on the rungs ({Tx) ^ 0). Moreover, one should expect that below a critical temperature, the Coulomb interactions drive these individual dipoles into a macroscopically charge ordered state, where (Tx) = exp(iQ • x n ) M x , with Mx jt 0. Here, x n is the position vector of rung n. We believe that it is this type of ordering that takes place in NaV 2 05 at 34 K. The physics of this phase transition may also be understood in terms of the Bose-Einsteinlike condensation of excitons at the bottom of the effective exciton band that exists above the new ground state. We have calculated this band using the random-phase approximation (RPA). Above Tc, the bandwidth increases when lowering temperature. 1 0 As soon as the energy of the lower band edge vanishes, the excitons tend to condense. The wave vector Q of the order parameter equals the momentum at which the lower band edge occurs. Figure 2 shows the generic phase diagram, distinguishing between the regions of the (t±,T) plane where Mx = 0 (disorder) and Mx ^ 0 (order). Calculating this phase diagram within
167
DISORDERED
T Fig. 2: Phase diagram of the model described by Eq. (2) in the (J_L,T) plane.
the mean-field approximation, we find t]_ = |V(Q)|/4 for the zero-temperature critical hopping integral (quantum critical point), with V(Q) = £ n e x p ( - i Q - ( x n - x m ) ) V m n . In addition, this yields a critical temperature in the limit of vanishing t±_ of the order of t*L. The smallness of the observed critical temperature relative to the matrix elements Vn.n+fj/ 4 and V„,n+f2/4 quoted above, possibly results from the fact that the ratio of the hopping integral and the Coulomb interactions places the system close to the quantum critical point. 4. D i s c u s s i o n The type of phase transition described above agrees with several recent experimental observations. First, in agreement with recent X-ray and NMR data, our model yields a hightemperature phase where all V ions are equivalent, while in the low-temperature phase this no longer is the case. Two obvious candidates for the low-temperature charge ordered phase are depicted in Fig. 3, where each arrow indicates a rung along with the direction of its permanent dipole. The two states differ in the wave vector Q, which equals (ir/fi,0) for the zigzag phase in Fig. 3(a), 9,14 while Q = 0 for the chain-like phase in Fig. 3(b). Obviously, the former one corresponds to an antiferroelectric ordering and the latter to a ferroelectric ordering. As according to our estimates IV^n+fJ < IVn.n+fJ, the zigzag phase seems to be the preferred one. This is consistent with the observed doubling of the unit cell in the crystal's a and b directions, which indeed occurs in the zigzag phase, as one sees from Fig 3, but not in the chain-like phase. Finally, calculating the static dielectric susceptibility x within the RPA, we have shown that the zigzag ordering is also consistent with the observed anomaly in this quantity, while the ferroelectric ordering results in a singularity of x a t the critical temperature, which is not in agreement with experiment. 10 Next, we discuss the optical absorption spectrum. The observed room temperature spectrum has a clear peak at an energy of ~ 1 eV with a rather broad high-energy shoulder. 15 This peak can be associated with the dipole allowed excitation of an electron on a rung from state |—) to state | + ) , renormalized by the inter-rung interactions. In the Heitler-London approximation, this would be a one-exciton excitation of wave vector zero (optical selection). The break-down of the Heitler-London approximation also makes the excitation of three-exciton states (and even higher ones) allowed. Using the exact expressions for the three-exciton absorption derived for one-dimensional chains in Ref. 16, it may be shown that this gives rise to a high-energy shoulder on the absorption peak, 10 which may (partially) explain the shoulder observed in experiment. It should also be noted that the existence of a high-energy peak in the absorption spectrum is another experimental indication t h a t the system has no tendency to order in a ferroelectric way. Namely, following the arguments of Sec. 3, ferroelectric ordering occurs if the excitons of wave vector Q = 0 reside at the bottom of the effective exciton band, implying that also the main absorption peak should occur at small energies (optical selection rule).
168
t l t l t l I t I t I M U M M M t
t t t t tt t t t tt t t t t tt t t t tt
(a)
(b)
Fig. 3: The two types of charge ordering discussed in the text. Arrows indicate the rungs of the V ladders and the direction of the permanent dipoles.
In addition to the high-energy absorption peak, experimental spectra exhibit a low-energy continuum that spans all frequencies below this peak. 15 Within our model, this continuum can be attributed to the simultaneous optical excitation of a low-energy exciton and two spinons. 10 Such processes are possible because due to virtual hopping of electrons to neighboring rungs (ty), terms appears in the Hamiltonian that couple the charge degrees of freedom (the excitons) to the spin degrees of freedom. In particular, we find a term in which exciton transfer is coupled to spin-exchange. As the spin excitations have small energy, they hardly increase the energy required for this collective excitation, while they are able to carry appreciable momentum, making it possible to break the zero-momentum selection rule for the exciton. Finally, we note that the charge ordering affects the spin exchange constants. In particular, one easily shows that the zigzag ordering leads to an alternation of the spin exchange constants along the legs of the V ladders. This alternation immediately leads to the opening of a spin gap. Thus, the experimentally observed opening of the spin gap does not drive the phase transition, but merely is a consequence of the charge ordering. We note that a similar effect does not occur for the ferroelectric ordering. 5. Conclusion In conclusion, we have shown that the phase transition in NaV2C>5, as well as its optical absorption spectrum, and the anomaly in its static dielectric function may be explained from a strongly coupled Frenkel exciton model. Within this description, the phase transition amounts to an antiferroelectric charge ordering transition. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.
M. Isobe and Y. Ueda, J. Phys. Soc. Jpn. 65, 1178 (1996). Y. Fujii et al., J. Phys. Soc. Jpn. 66, 326 (1997). A. Carpy and J. Galy, Acta Crystallogr. B31, 1481 (1975). W. Schnelle, Yu. Grin, and R. Kremer, Phys. Rev. B59, 73 (1999). A.I. Smirnov et al., Phys. Rev. B59, 14546 (1999). M. Poirier et a/., Phys. Rev. B60, 7341 (1999). J. Liidecke et ai., Phys. Rev. Lett. 82, 3633 (1999). T. Ohama, H. Yasuoka, M. Isobe, and Y. Ueda, Phys. Rev. B59, 3299 (1999). M. Mostovoy and D. Khomskii, Solid State Commun. 113, 159 (2000). M. Mostovoy, D. Khomskii, and J. Knoester, to be published. A. S. Davydov, Theory of Molecular Excitons (Plenum, New York, 1971). V. M. Agranovich and M. D. Galanin, Electronic Excitation Energy Transfer in Condensed Matter, ed. V. M. Agranovich and A. A. Maradudin (North Holland, Amsterdam, 1982). H. Smolinski et al., Phys. Rev. Lett. 80, 5164 (1998). H. Seo and H. Fukuyama, J. Phys. Soc. Jpn. 67, 2602 (1998). A. Damascelli et al., Phys. Rev. Lett. 81, 918 (1998). L. D. Bakalis and J. Knoester, J. Chem. Phys. 106, 6964 (1997).
B A N D G A P RENORMALIZATION D U E TO HIGH-DENSITY CARRIERS I N ZnO E P I T A X I A L T H I N FILMS
AISHI YAMAMOTO, TAKEO KIDO, TAKENARI GOTO Department of Physics, Graduate School of Science, Tohoku University Aramaki, Aoba-ku, Sendai 980-8578, Japan YEFAN CHEN, TAKAFUMI YAO Institute for Materials Research, Tohoku University Katahira 2-1-1, Aoba-ku, Sendai 980-8577, Japan Renormalized bandgap energy due to high-density carriers in ZnO is calculated and compared with our experimental results. Two different reported treatments for the correlation energy are employed for the calculation, and we prove that Beni and Rice's model sufficiently explains the experimental data. Furthermore, we calculate optical gain spectrum, which reproduces well the experimental data. In 1997, stimulated emission and optically pumped laser action in ZnO epitaxial thin films have been reported at room temperature. 1 ' 2 These emissions have been assigned as due to an exciton-exciton collision or an electron-hole plasma (EHP). Recently, we have studied timeresolved absorption 3 and photoluminescence 4 (PL) spectra using a sub-picosecond pulse laser. In the differential absorption spectra, absorption saturation of excitons, absorption increase due to a bandgap renormalization and optical gain due to the EHP were observed. In these experiments, the carrier density is estimated to be n = 2.7 x 1019 cm~ 3 and the bandgap shift is estimated to be 350 meV from the gain spectra. As far as we know, there is no systematic study on the comparison between experiment and theory of bandgap energy shift in ZnO. In this paper, we calculate the renormalized bandgap energy and discuss the applicability of previously reported theoretical treatments by comparing with our experimental results. Furthermore, we calculate optical gain spectrum, which reproduces well the experimental data. Saito and Gobel 5 calculated ground state energy (Eo) and renormalized bandgap energy (Eg) for CdS crystal by using the kinetic energy (E^) of the electron and hole, exchange energy (Eex) between them, and correlation energy (Eco). The kinetic and exchange energies can be calculated in a standard manner as a function of r s , 6 ' 7 which is defined through n = 3/(47rr 3 a 3 x ), where aex is a exciton Bohr radius. For a system of ve conduction bands and v^ valence bands, they are described as,
where m<je and m^
^*
_ ~
2.2099/ p \~m r2 r s \ve mde
Eex
=
-^-[^/^(pJ
+
ji \ ~273 }hR' i/h' mdhJ +^ ^ p ^ E n ,
t1) (2)
are the electron and hole density-of-state masses, respectively, \x is the
reduced mass, and ER is the effective Rydberg energy. The function (f>(p) is given by
with p = m±/m//, where m±_ and m// are the transverse and longitudinal effective polaron masses, respectively, and 0 ( p ) is the step function. On the other hand, E^, depends on the theoretical treatments. We employed, here, two calculated results for the correlation energy, which were reported by Vashishta et al.7 and by
169
170 Beni and Rice. 8 Hereafter we will refer them as models (I) and (II), respectively. Vashishta et al.1 calculated Eco as a function of rs with a mass ratio of hole to electron m,h/me = 2, 4, 6, 10 in self-consistent approximation. While, Beni and Rice 8 calculated grand state energy E0 as a function of r 5 for ZnO using random-phase approximation with band anisotropy, degeneracy of valence band and coupling to optical phonons. Therefore, Beni and Rice's model is expected to be more realistic. Since Ek and Eex can be calculated analytically, we obtain the correlation energy using the relation £ „ = E0 — Ek — Eex.
100 0 >
-100
CD
~ -200
>-
(3
tr -300 ill
W -400 -500 -600 1(
Fig. 1. Calculated bandgap energy shift (solid lines) and correlation energy (dashed lines) of models (I) and (II) as a function of carrier density. Experimental results are plotted as the closed square, circles and triangles.
In our calculation we use the parameters, me = 0.24m 0 , m^// — 1.9mo, and m/,j_ = 0.6mo.8 Since the energy splitting between A and B valence bands in ZnO is small (8 meV) compared to the bandgap shift (350 meV), we calculated Ek and Eex taking account of the two valence bands. Namely, we assume the hole masses of A and B bands are the same and they are fourfold degenerate (including spin). Thus we obtain Ek = 1.942ER/r2 and Eex = 1.716ER/rs. We also calculate Ek and Eex without considering anisotropy and the degeneracy of the hole bands, and find that Ek and Eex do not strongly depend on them. As will be shown bellow, Eg strongly depends on the treatment of Eco. Figure 1 shows the calculated results of bandgap energy shift using the two models. Since the mass ratio mdh/mde is 3.78 for ZnO, we use the calculated table 7 of Eco for mdh/'mde = 4 in model (I). The dashed lines show the correlation energies of models (I) and (II). The closed square shows the experimental results obtained from pump-probe measurement. 3 Previously, our group 3 and Zu et al.2 reported PL spectra as a function of excitation density. We assume Eg to be lower edge energy of the EHP PL band and plot them with closed circles 3 and triangles. 2 As is shown in Fig. 1, model (II) reproduces the whole experimental data well, and hence the model (II) is found to be suitable. In model (I) the calculation of Vashishta et al. is simple compared to Beni and Rice's calculation, i.e. model (I) does not take account of the coupling to optical phonons nor band degeneracy. As was pointed out by Beni and Rice, 8 the electron-phonon interaction increases the stability of EHP phase. Therefore, the calculated bandgap energy of model (II) is more than 100 meV lower than that of model (I). The agreement between the calculation of model (II) and experiment strongly suggests that the coupling to optical phonons in polar semiconductors is crucial. From the above comparison between experimental data and theoretical calculations, it is proved that Beni and Rice's model is sufficiently applicable to explain the experimental results. Figure 2 shows optical gain spectrum at the delay time of 4 ps. 3 The gain spectrum is
171 generally described as 9
J
g(hu))
y/EJhu, -Eg-
E[fc(E) - /„ (hu> - Eg - E)]dE ,
(4)
where, hu> is a photon energy, and fc and /„ are fermi distribution functions of conduction and valence bands, respectively. The electron and hole Fermi levels are obtained from the values of carrier density n and carrier temperature T. For this calculation, we take account of the anisotropy (i.e. density-of-state hole mass is used) and degeneracy of the hole bands. The solid line in Fig. 2 represents the fitted curve, where T = 1500 K and Eg = 3.02 eV. The calculated curve reproduces well the experimental data. We also calculate gain spectra without considering the anisotropy and the degeneracy. Although the fitting parameter, T, strongly depends on both the anisotropy and degeneracy, the best-fitted spectral shape hardly depends on them.
„
1-5 ZnO
'E o
"o <
1.0 0.5 h
4ps
T=1500K, n=2.7x1019cm"3 -0.5 I— 2.9 Fig. 2. spectra.
3.0 3.1 3.2 PHOTON ENERGY (eV)
3.3
Observed (closed circles) and calculated (solid line) optical gain
In summary, renormalized bandgap energy due to high-density carriers in ZnO is calculated and compared with our experimental results. Two different reported treatments for the correlation energy were employed for the calculation, and it is proved that Beni and Rice's model 8 sufficiently explains the experimental data. Furthermore, we calculate optical gain spectrum, which reproduces well the experimental data. Acknowledgements This work was a collaboration with Laboratory for Developmental Research of Advanced Materials, Institute for Materials Research, Tohoku University. References 1. D. M. Bagnall, Y. F. Chen, Z. Zhu, T. Yao, S. Koyama, M. Y. Shen, and T. Goto, Appl. Phys. Lett. 70, 2230 (1997). 2. P. Zu, Z. K. Tang, G. K. L. Wong, M. Kawasaki, A. Ohtomo, H. Koinuma, and Y. Segawa, Solid State Commun. 103, 459 (1997). 3. A. Yamamoto, T. Kido, T. Goto, Y. F. Chen, and T. Yao, Appl. Phys. Lett. 75, 469 (1999). 4. A. Yamamoto, T. Kido, T. Goto, Y. F. Chen, T. Yao, and A. Kasuya, J. Crys. Growth 214/215, 308 (2000).
172 5. H. Saito and E. 0 . Gobel, Phys. Rev. B 31, 2360 (1985). 6. T. M. Rice, in Solid State Physics, ed. H. Ehrenreich, F. Seitz, and D. Turnbull (Academic, New York, 1977), Vol. 32, p. 1-86. 7. P. Vashishta, P. Bhattacharyya, and K. S. Singwi, Phys. Rev. B 10, 5108 (1974). 8. G. Beni and T. M. Rice, Phys. Rev. B 18, 768 (1978). 9. S. Tanaka, H. Kobayashi, H. Saito, and S. Shionoya, J. Phys. Soc. Jap. 49, 1051 (1980).
ULTRAFAST PHOTO-INDUCED ABSORPTION CHANGE IN I N O R G A N I C - O R G A N I C MULTIPLE Q U A N T U M WELL C O M P O U N D
MASAKAZU KAJITA Department of Physical Electronics, Hiroshima University, 1-4-1 Kagamiyama Higashi Hiroshima 739-8527, Japan MAKOTO SHIMIZU, ARUP NEOGI AND TERUYA ISHIHARA * Frontier Research System, RIKEN, 2-1 Hirosawa Wako 351-0198, Japan
We have performed pump-and-probe measurements to investigate ultrafast excitonic nonlinearity expected in an inorganic-organic compound (CeHsC^HjNHa^Pbl^ which has huge exciton binding energy (220 meV) and oscillator strength (0.5 per formula unit) by virture of the small dielectric constant in the barrier layer (the dielectric confinement or image charge effect). When the pump photon energy is set at the exciton level at 2.37 eV or above the band gap, the absorption decreases immediately after the pump due to the phase space filling effect and retrieves in a few ps. The retrieval time is ascribed to the ultrafast radiative lifetime of the exciton level. The second exciton absorption at 2.39 eV exhibits induced absorption when the pump is at the first exciton band, which may provide a hint to the origin of the band. 1. Introduction Inorganic-organic perovskite layer compounds, such as (C6H5C2H 4 NH 3 )2Pbl4, have a multiple quantum well crystal structure, where P b l layers are the wells. The exciton has huge exciton binding energy (220 meV) and oscillator strength (0.5 per formula unit) by virture of the small dielectric constant in the barrier layer. It is called the dielectric confinement or image charge effect.1'2 The photoluminescence lifetime is dominated by the radiative decay at low temperature, which is less than 5 ps for a thin film. 3 Such material may be utilized for optical switches with ultrafast response time. Because of its two-dimensional crystal structure, screening is hardly expected: the electron and the hole in an exciton can have Coulomb interaction through the barrier layer where no excitons can exist even at high density excitation. Instead, the phase space filling effect is the main origin of the nonlinearity. 4 2. E x p e r i m e n t a l A spin coated polystyrene film of (C6H5C2H4NH3)2Pbl4 on a quartz substrate was mounted in a cryostat. Subpicosecond white light continuum was generated in a water cell by 775nm output ( at the repetition rate of 1kHz ) from a regenerative amplifier seeded by a fiber laser. A part of the amplifier output was wavelength-converted by an optical parameteric amplifier, which is used as the pump beam. The pump beam power was kept below a few mW in order to avoid sample deterioration. The spot size was 1mm. Scattering from the pump beam was kept below 1% of the transmitted light. 3. R e s u l t s and Discussion Figure 1 shows transmission spectra of the sample at cryogenic temperatures. Note that prominent exciton absorption is observed even at room temperature. As the temperature decreases, the structure becomes somewhat narrower, and below 100 K the exciton *email: [email protected]
173
174
400
450
500
550
600
650
Wavelength [nm] Fig. 1. Transmission spectra of (CgH5C2H4NH3)2Pbl4 for several temperatures.
absorption band slightly splits into two: A band at 524 nm (2.366 eV) and B band at 518 nm ( 2.393 eV). Above the exciton absorption peaks, a kink-like feature is seen at 477nm (2.60 eV), which has been ascribed to the band edge. Althogh the shape is not clear for polycrystallme films, a step like structure is observed for cleaved single crystals. 1 Furthermore two-photon absorption to the 2p exciton has been recently observed just below this structure, which is characteristic to the two-dimensional exciton series. 5 Figure 2(a) shows transmission spectra at 10 K under the pump at the band gap (477 nm) with several delay times. Absorption in both A and B band decreases. The temporal evolution is plotted in Fig.2(b). The absorption bleaches instantaneously but retrieval takes a short but finite time. Since the absorption change lasts beyond the laser pulse width, we may conclude that the optical Stark effect is not responsible for the observed nonlinearity. 6 Figure 3(a) shows transmission spectra under the pump at the B band (518 nm). Note that a significant blue shift is observed for the B band while hardly observed for the A band. This demonstrate that the shift is due to the phase space filling effect. Because the B band exciton is directly generated by the pump, the phase space of the exciton state is selectively occupied, which causes the filling of the absorption band from the lower energy side. On the other hand the phase space of the A band is occupied after phonon or exciton-exciton scattering so that all phase spaces are occupied evenly. Fig.3(b) shows that the bleaching of the A band has some rise time, which is consistent with our interpretation. Figure 4(a) shows transmission spectra under the pump at the A band (524 nm). A remarkable blue shift and bleaching is observed for the A band. The bleaching observed at A band amounts to 1.6 for our experimental condition, and falls to the half maximum within 0.3ps. This nonlinearity may be utilized for some switching application. On the other hand the B band shows almost no shift but exhibits an induced absorption. Because the B band is observed even in the linear spectroscopy, stepwise transition to the
175
V
\ 477nm
° 80 " x •f 60 -
V"
/
\
1
V \> It* Nt5
delay time g —probe onlyM 0 4ps 9 -0 13ps B I Ops ••- 013ps 9 0 67ps 9 — 4ps a — 6 67ps § — 33.3ps 9
/^ & J 1 * •»
V, Vt % \ l \V v V \
\
0.6 -
\ fi •
a)
ro
20-r
i
%^/| ,
i
"
518
,....,..,.^/...,,T 520 522 524 i
!b)
I
477nm
* A
*
& 4
0.4
1
4
y&3i
I 40
4
-i
I
!
!
0.2
^ D ° ° °" f o
0.0 < i
p
t 1
Wavelength [nm]
0
0
i
i
2
3
•"•"i
t
4
5
Delay Time [ps]
Fig. 2. (a) Transmission spectra at 10 K under the pump at the band gap (477 nm) at several delay times, (b) Transmission as a function of delay time. Open triangles and circles are for A and B bands, respectively.
A
.
o
A
A
b) ;518nm
4
p o o
518
520
522
Wavelength [nm]
524
0
1
2
3
4
Delay Time [ps]
Fig. 3. (a) TVansmission spectra at 10 K under the pump at the B band (518 nm) at several delay times, (b) Transmission as a function of delay time. Open triangles and circles are for A and B bands, respectively.
5
176
50
-524nm
40 30
'^fyffr
delay time •J — probe only- ft —-0.4ps I !» -0.13ps , J rft Ops , i * ••• 0.13ps • "•ft ••• 0.67ps - | " * — 4p S , Jl — 33 3ps . jS \\ — 6.67ps f
r "\
\
20
J \ l ' $ -
a)
^§y
518
520
522
524
Wavelength [nm]
1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0
-&F
-\
-4
b)
a
-H
524nm
AAa 4
& &
» a 4
i
i
a
So((ibo6°6 ? 6 ° " 9 ° ° I °
?
° T
0
1
2
3
4
5
Delay Time [ps]
Fig. 4. (a) Transmission spectra at 10 K under the pump at the A band (524 nm) at several delay times, (b) Transmission as a function of delay time. Open triangles and circles are for A and B bands, respectively. two-exciton states is unlikely. If the B band was the phonon assisted replica of the A band, induced absorption would be possible. However the phonon energy in the well is much smaller than the energy separation (27 meV) due to the large mass of the ions consisting the wells. If the blue shift of the A-band was the optical Stark effect, the instantaneous part of the induced absorption would be explained. The long-lived tail, however, can not be attributed to the effect. Analysis of the induced absorption will clarify the origin of the B band. 4. Conclusion Ultrafast transmission change was observed in natural multiple quantum well compounds. Since this material can form a thin film of good quality, conbination with waveguides and/or grating structures will open up a new way toward novel photonic devices. 5 Acknowledgements This work has been partly supported by Core Research for Evolutional science and Technology (CREST) of JST (Japan Science and Technology Corporation). References 1. T. Ishihara, Optical Properties of Low-Dimensional Materials, ed. T. Ogawa and Y. Kanemitsu (World Scientific, Singapore, 1995). 2. S. Schmitt-Rink, D.S.Chemla and D.A.B.Miller, Advances in Physics 38, 89 (1989). 3. X. Hong, T. Ishihara and A. V. Nurmikko, Phys. Rev. B45, 6961 (1992). 4. H. Fujimoto and T. Ishihara, to be published. 5. T. Fujita, H. Nakashima and T. Ishihara, Phys. Stat. Solidi b221, (2000). 6. N. Peyghambarian, H.M.Gibbs, J.L.Jewell, A. Antonetti, A. Migus, D. Hulin and A. Mysyrowicz, Phys. Rev. Lett. 53, 2433 (1984).
F I N E S T R U C T U R E OF E X C I T O N I N A Q U A N T U M D O T : E F F E C T OF E L E C T R O N - H O L E N O N A N A L Y T I C E X C H A N G E I N T E R A C T I O N
H. AJIKI and K. CHO Graduate School of Engineering Science, Osaka University Toyonaka 560-8531, Japan The nonanalytic part of the electron-hole exchange interaction, is studied theoretically in the strong confinement regime. The nonanalytic part raises some energy levels dramatically, and changes the oscillator strength of each level significantly. 1. Introduction The electron-hole (e-h) exchange interaction of an exciton in a quantum dot (QD) has been attracted considerable attention in the strong confinement regime, where the effective Bohr radius of exciton is much larger than the confinement size. It is well known that the e-h exchange interaction provides fine structure of the exciton levels. In the strong confinement regime, the energy splitting is strongly enhanced with decreasing QD's radius a as a'3. Recently, Woggon et.al.1 observed energy splittings of CdSe QDs due to the e-h exchange interaction as a function of the radius. Although the size dependence exhibits a - 3 , its magnitude is larger than theoretical predictions 2 - 4 . They pointed out that the deviation comes from the long-range or nonanalytic part of the e-h exchange interaction. A theoretical calculation of the nonanalytic part, including the image potential effect due to the difference of the background dielectric constants, was performed by Goupalov and Ivchenko5 for the lowest size-quantized level. However, there exists still discrepancy between the experimental and calculated results. In this paper, we give comprehensive results for the effect of the nonanalytic part of the e-h exchange interaction in a CdSe spherical QD. The fine structures of exciton levels are calculated not only the lowest size-quantized level but the higher states. In the lowest sizequantized level, the effect of the nonanalytic part on the oscillator strength, is studied. We also take into account the higher levels to compare with the experimental data by Woggon et.al. more precisely, however, the calculated splitting energy is larger than the experimental result. 2. N o n a n a l y t i c Part We start from the Luttinger Hamiltonian with spherical approximation for hole states of CdSe. Because of the spherical confinement, the heavy-hole states couple with the light-hole states. The eigenfunctions of the hole states are characterized by the odd or even parity states (designated by / ) , the total angular momentum F of those for envelope functions RFtIn(rh)Yeim and Bloch functions u^ (/j. = ± 3 / 2 , ± 1 / 2 ) of valence band T 8 , its projection M, and radial quantum number n as follows:
*™/„fo.) = £
E
(fl„iB(rh)y,,m(rk)iiM,
(1)
with the Bloch functions
«M= x T u ^ l i ^ f ^ b ^ ) ,
(2)
where (ii^; m\m-i\l.\l.2\ JM) is the Clebsch-Gordan coefficient, \pu*l) are the p-orbital states (u = 1,±1) with spin 7 = | (J.). In the summation in eq.(l) lj takes {F — 3/2, F + 1/2} or {F — 1/2, F + 3/2} depending on its parity. The normalized envelope functions of the radial
177
178 component RFI,™ are obtained from the equations reduced from the Luttinger Hamiltonian 6 . To obtain the radial wave numbers, we assume that a QD is surrounded by an infinitely high potential barrier. Both radial envelope functions and the size-quantized wave numbers depend on the ratio f) = mjh/mhh of the light-hole (mih) and the heavy-hole (mhh) effective masses. The size-quantized energy of the hole states is characterized by the heavy-hole mass. Since the effective mass of the conduction band is much smaller than the heavy-hole mass, we restrict our discussions to the lowest conduction states * £ ( r . ) = .Ro(r.)l'oo(p.)|«Of>,
(3)
where RQ is proportional to the spherical Bessel function of order 0, and \sa) are the s-like Bloch function with spin a = | (j). Then the induced polarization by hole states ^!\MI-H a n < i electron states ^ca is given by
p«,™/„(r) = (-i)*V E E(^§; "»• ~M x ( l | ; -M
- m - a,a\l\;
§, -M
-
m
l4f; F> ~M)
(4)
m)Ra{r)RFtin{r)Y00(r)YtIm{r)e^M_rn^a,
where \x = |(s|er|p„)| and e„ (v = 0,±1) is the spherical unit vector. The general expression of the e-h exchange interaction (containing both analytic and nonanalytic parts) has the same form as the Coulomb interaction between induced polarization charge as follows: ^ , = / d r / d r ' [ - V . P « ( r ) ] * [ i ^ - ^ + Mm(r,r')][-V'.P,-(r')],
(5)
where £ represents a set of quantum numbers (ct,FMIn), and the eV\m is the image potential due to the background dielectric constants inside (ei) and outside (£2) of a QD, which is written as
^^-i^{Wifw^Pi{cose]'
(6)
with e = ej/ei and P/(cos 8) being the Legendre polynomials. Since the present model of Pj(r) contains only the long wavelength components, the expression (5) gives the contribution of the nonanalytic part of the e-h exchange interaction. 3. N u m e r i c a l Results Let us consider the nonanalytic part of the e-h exchange interaction for the exciton consisting of the hole with F = 3/2. Calculating eq.(5) we get the reduced Hamiltonian in terms of the electron Pauli spin-1/2 matrix a and the hole spin-F matrix F #oNdd =
(^)3ALTCodd(/?,n)(^-
(odd states),
(7)
#eNven =
(^f) 3 A L T Ceven(/3,")(| + ^ )
(even states),
(8)
where ae is the effective Bohr radius of the exciton, ALT is the energy splitting of the longitudinal and transverse modes in a bulk crystal. The size-independent factor £(/?, n) includes the integration of the envelope functions. The reduced Hamiltonian has the operator CTF which lifts the eightfold degeneracy of the exciton states with F = 3/2 as well as the analytic part. Namely, degenerated levels split into the fivefold degenerate forbidden states with total angular momentum 2 and the threefold degenerate allowed states with total angular momentum 1. The magnitude of the splitting energy is proportional to £(/?, n) which depends on the radial quantum number n and the effective-mass ratio j3.
179 Radius (A) 300 250 200
50 20
15
13 12
11
10
Without Nonanalytic Part F=3/2 Odd
> 0)
0.0
0.2
0.4
0.6
0.8
1.0
Effective-Mass Ratio ((3) Fig.l. Calculated ((/3,n) effective-mass ratio /?
as a function of the
2
4
a- 3 (10 4 A" 3 ) Fig.2. Calculated fine structure of the exciton states with F = 3/2 and n — 1.
Figure 1 shows ((/3,n) for exciton consisting of odd- or even-hole states with F = 3/2 calculated as a function of the effective-mass ratio 0. We choose the background dielectric constants €\ = 6.2 and (.i = 1.5 corresponding to the situation that a CdSe QD is embedded in glass matrix. The splitting energy of the odd states with F = 3/2 and n = 1, on which the oscillator strength concentrates, becomes larger than that of any other states in the almost all the region of fl. The £'s of the even states are almost independent of /}, and smaller than those of the odd states. One example without image potential are calculated for odd states with F = 3/2 and n = 1. It is found that the image potential raises the nonanalytic part of the e-h exchange interaction. If a QD has the asymmetry of the hexagonal lattice structure, the crystal field lifts the hole state degeneracy. Therefore the fine structure of the QD with hexagonal lattice becomes more complicated. Considering the analytic and nonanalytic parts of the e-h exchange interaction and the asymmetric crystal field, we get energy levels of odd states with F — 3/2 and n = 1 in Fig.2. We apply the quasi cubic model 7 to introduce the anisotropic effect. In the calculation, we use the parameter of a CdSe crystal, i.e., 0 = 0.28, a# — 56A, A L T = 0.9meV, and A S T = 0.26meV which is the energy of the analytic part. On the right side, we denote the projection of the total angular momentum of the electron and hole states for each level. The U and L on the right shoulder denote the upper and lower levels, respectively 4 . The optically allowed states (bright states) are ± 1 L - U and 0 U , and other levels are forbidden (dark states). The dotted lines show the energy levels obtained by ignoring the nonanalytic part, and exhibit the same results calculated by Efros et.al.4 The nonanalytic part changes the energy levels for the 0 U and ± l u states dramatically. The oscillator strengths per unit volume of the bright states are calculated in Fig. 3. The oscillator strengths become quite different if we ignore the nonanalytic part of the e-h exchange interaction. One exception is the states 0 U whose oscillator strength does not change whether we consider the nonanalytic part or not, and it is independent of the radius.
180 0.7
' " I " " ! " " ! " " ! " " ! 1 " Without ±1L ±-|U 0.6 - Nonanalytic Part 0U
15
20
25
30
35
40
45
30
Radius (A) Fig.3. Calculated oscillator strength of the odd exciton states with F = 3/2 and n = 1.
40
50
60
Radius (A) Fig.4. Calculated energy level. The origin of the energy is that of the lowest level.
4. S u m m a r y and Discussion We have studied the effect of the nonanalytic part of the e-h exchange interaction on the exciton states confined in a spherical QD in the strong confinement regime. Numerical calculations have been performed for a CdSe QD having odd states with F = 3/2 and n = 1. The nonanalytic part affects strongly on the energy levels and oscillator strengths. Although Woggon et.al. observed the energy splitting between ± 1 L and ± 2 states as a function of the radius experimentally, the results does not agree with our calculation. For instance, the energy splitting is about 7meV for a QD with a = 20A in their experiment, however, our result is 12.4meV. The discrepancy does not originate from the effect of the higher levels. In fact, the levels of ± 1 L and ± 2 are not almost affected by the higher levels as is shown in Fig.4, where the energy of each level is measured from the lowest level. One possibility to explain the experimental result is to consider the deviation of the QD's shape from sphere 4 . Acknowledgements This work was supported in part by the Grant-in-Aid for COE Research (10CE2004) and Scientific Research (10304022) and Scientific Research on Priority Area (1020725), of the Ministry of Education, Science, Sports and Culture of Japan. References 1. 2. 3. 4. 5. 6. 7.
U. Woggon et.al, Phys. Rev. B54, 1506 (1996). T. Takagahara, Phys. Rev. B47, 4569 (1993). R. Romestain et.al, Phys. Rev. B49, 1774 (1994). Al. L. Efros et.al, Phys. Rev. B54, 4843 (1996). S.V. Goupalov et.al, Fizika Tverdogo Teh 42, 1976 (2000). A. I. Ekimov et.al, JETP 61, 891 (1985). J.J. Hopfield, J. Phys. Chem. Solids 15, 97 (1960).
FORMATION OF SILICON NANOCRYSTALS AND INTERFACE ISLANDS IN SYNCHROTRON-RADIATION-IRRADIATED SKh FILMS ON Si(100) H. AKAZAWA NTT Telecommunications Energy Laboratories 3-1 Morinosato Wakamiya, Atsugi, Kanagawa 243-0198, Japan Nucleation of nanocrystalline Si (nc-Si) in SiCh films irradiated with vacuum ultraviolet and soft x-ray radiation has been investigated by using in-situ spectroscopic ellipsometry, cross-sectional transmission electron microscopy, reflectivity measurement, and reflection high-energy electron diffraction. The formation of nc-Si proceeds in the repetition of two steps: (i) conversion of SiCh to SiOx through the creation of Frenkel pairs and the subsequent desorption of O2, and (ii) separation of SiO* into Si and SiCh domains. The average diameter of nc-Si increases from 2 to 10 nm as the irradiation temperature increases from 470X3 to 610X3. Above 700X3, oxide domains are gone and solid-phase recrystallization produces Si islands terminated by the Si(100) substrate interface. At temperatures higher than 800X3, these islands collapse and an atomically flat Si(100) interface appears.
1. Introduction The optoelectronic properties of low-dimensional Si/SiCh systems and suboxides (SiOx) have long been studied, and there is growing interest on the formation of nanocrystalline Si (nc-Si) embedded in a SiCh matrix. Visible light emission due to the quantum confinement effect is the technologically important aspect of nc-Si. Methods previously used to form SiOx films include plasma-enhanced CVD from a S1H4-O2 gas mixture, 12 sputtering of a solid Si target in O2 ambient, 34 Si ion implantation into Si02 films,5 and laser ablation.6 The SiOx films prepared are then annealed at temperatures higher than lOOO'C to make them separate into nc-Si and Si02 domains. Such formation processes result in small nc-Si grains. This paper describes instead a low-temperature approach to producing nc-Si: simply irradiate Si02 films with synchrotron radiation with wavelengths ranging from those of vacuum ultraviolet radiation to those of soft x-rays. The advantage of using synchrotron radiation instead of laser light7'8 is that one-photon excitation causes significant structural change and that the irradiation temperature can be adjusted precisely to the desired level. This allows us to distinguish the electronic and thermal processes involved in nc-Si formation. This paper focuses on how the size of the nc-Si grains and the shape of the Si interfacial islands change by varying the irradiation temperature. 2. Experimental The experiments were carried out on the beamline 7 connected to the compact electron storage ring "Super-ALIS" at the NTT Atsugi Research and Development Center.9 The surface of a sample mounted in an ultrahigh vacuum chamber was irradiated with a white photon beam. The energies of the photons ranged from 10 to 1500 eV, with the maximum flux at 100 eV. Si02 films 40- or 130-nmthick were grown on Si(100) wafers, and in-situ spectroscopic ellipsometry (SE) was used to monitor dynamical processes during irradiation as well as to evaluate the composition of the resulting films.10 The ellipsometry measures the Fresnel reflection coefficient ratio p between light p-polarized and spolarized with respect to the solid surface, and the ellipsometric angles ip and A are defined by the equation p = tan ip exp(i A). The atomic image of nc-Si formed at low irradiation temperatures were observed by cross-sectional transmission electron microscopy (XTEM). The interface Si islands emerging at higher irradiation temperatures were investigated by reflection high-energy diffraction (RHEED) and reflectivity measurement. 3. Results The 1/1 - A plot in Fig. 1 shows changes in the optical response of Si02 films irradiated at 58CC and 730*0. Both trajectories start from the origin O and share the trace 0-»A. The extensive trace O - » A - > B - » C - » D - > E obtained at 730°C shows that the Si02 layer maintains its stoichiometry as its thickness decreases through decomposing into volatile SiO product molecules.11 The trajectory obtained at 580"C, however, was directed from point A upward at a significantly lower rate and terminated at point F. The substream (trace A -> F) corresponds to the composition changing from that of
181
182
E, irradiated p*» f\ at730°Ci
40
AE* \
20
0
20
25
30
il> ( d e g ) FIG. 1. il> - A trajectories resulting from irradiation of 130nm-thick SiCh at 580"C and 730"C. The trajectory at 730"C is folded at the mirror plane of 1!) =45 ° because of the sensitivity drop inherent for the phase-modulated detection.
^_
20
initial Si02\ I
•40
v
1.5
2
2.5
3
3.5
\
/
"
irradiated at58Q°Q. 4
4.5
Photon Energy (eV) FIG. 2. Imaginary part of the pseudodiectric functions of the initial 130-nm-thick SiOz (solid line), the SiOx produced by irradiation at 580"C (solid circles), and the Si interface produced by irradiation at 730°C (open circles).
S i d to that of SiOxas the film lost oxygen. Figure 2 shows the room-temperature pseudodielectric functions of the initial S1O2film,the resulting SiOx, and the Si interface respectively corresponding to the points O, F, and E in Fig. 1. The Ei and E2 critical point features of band-to-band transition indicate a Si crystalline interface. Linear regression analysis of the SiOx spectra was performed using reference dielectric functions calculated from a two-layer model, in which the base layer was represented by a mixture of polycrystalline Si (pSi) and SiCh and in which the surface roughness layer was represented by p-Si and voids. This analysis showed that the volume fraction of the SiCh domain was 72.5%. After irradiation at 610"C, nc-Si particles were typically found embedded in an amorphous matrix (Fig. 3). The particles are randomly oriented and not necessarily spherical with their longest dimensions between 10 and 20 nm. The nc-Si grains at the surface are relatively small but so closely spaced that they form a continuous crystalline overlayer. This can be explained by the irreversible removal of oxygen atoms by photon-stimulated desorption. The nc-Si grains near the interface are typically 10 nm in diameter and 20 nm long, and the relatively larger size of the grains nearer to the substrate is a result of the more extensive crystallization associated with the electronic excitation due to secondary electrons backscattered from the substrate. The undulated SiOx/Si(100) interface results from solidphase crystallization of precipitated Si in contact with the interface. When the irradiation temperature was decreased to 47013, smaller (2 nm in diameter) grains were observed. And very few grains were observed after irradiation at 3001C. In the latter case, the Sin04-n (n=0-4) local composition structures12 resulting from radiation-stimulated bond breaking are distributed statistically throughout the SiOx film since Si-Si bond units stay at the metastable position. At irradiation temperatures higher than 700°C, all oxides were lost and the interface was exposed. This is shown by the RHEED patterns in Fig. 4. After irradiation for 80 min at 730"C, a ring pattern superimposed on the initial halo background indicated the presence of a crystalline network of randomly oriented Si aggregates. Diffraction spots indicating electron transmission through three-dimensional (3D) islands were evident after 150 min, and after 240 min the rings diminished. This observation suggests that nc-Si merged into the islands. The evolution in the RHEED pattern at 79013 is also shown in Fig. 4. Ring diffraction patterns appeared at 70 min and at 80 min the overlayer was gone. The streaky (2 X 1) pattern confirms that 3D islands are readily collapsed and an atomically flat Si surface is obtained. The interfaceflatteningwas also evident in the reflectivity at 3.4 eV monitored during the irradia-
183 1
r ^ " (a) 56010'
'
\ •\
(c) 780°C
|
I
(d) 860°C
j
0.95
_
."tS 1™
09
3 X» «0
0.85 1
:>. *> -» t> 0.95 <17
<1U
tx
0.9
V |
0.85 0
20 40 60 80 100 0 20 40 60 80 100120
Time (rnin) FIG. 3. XTEM image of a SiOx film resulting from irradiation of a 130-nm-thick Si0 2 at 6 1 0 ^ .
FIG. 5. Time-course of the reflectivity at 3.4 eV during irradiation of 40-nm-tnick S i d .
tion of 40-nm-thick films. As Fig. 5 shows, the reflectivity initially decreased at all mediation temperatures. This is the result either of the surface roughness increasing as the thickness decreased by random desorption of SiO molecules or of the optical- inhomogenity due to the creation of nc-Si. At 730°C the reflectivity became stable after 40 min, but at 780^ a slow recovery was discernible. At 860*0 the reflectivity fell to 0.9 at 20 min and then increased to 0.95, where it remained. This recovery indicates that the atomicaliy flat Si(100) was restored when the Si islands collapsed. 4. Discussion The primary effect of irradiating the SiOi film is the formation of Frenkel pairs (an Ei' center and an interstitial oxygen atom). This can be expressed, using Devine's notation,13 as follows: 0 3 = s i - 0 ~ - S i = 03 + h i; -* 03 = Si -+Si = 03 + 0 + e\ (1) An Ei' center is converted to a Si-Si bond unit when it accepts an electron: Os == Si • +Si ss Os + e- -> Os = Si - Si = Os. m (2) The displaced oxygen atom attaches to a nonbonding oxygen hole (NBOH) center, converting it to a peroxyradicai which then decomposes thermally by releasing an O2 molecule: (a) initial
(c) 150 min
(e) 70 min
FIG. 4. RHEED observation of microscopic structures in the SiOx film and at the interface resulting from irradiation of 130-uin-thick. SiOi at 730"C {(a), (b), (c), (d)) or at 790"C ((c), (1)).
184 Os = Si - O + 0 -> 03 = Si - 0 - O -* O3 = Si • + O2. (3) The loss, through diffusion and desorption, of the released O2 molecules reduces the concentration of oxygen atoms in the film, leaving it with a Si-rich SiOx composition. At low irradiation temperatures, the Si-Si bond units produced by reaction (2) stay close to their original positions and thus are distributed uniformly throughout the SiOx network. The accumulation of Si-Si bonds increases the valence electron density, which enhances the efficient quenching of the excited state. When the volume of the Si domain reaches a critical value, further Frenkel pair formation is terminated (see trace A -> F in Fig. 1). When the system is thermally activated, the volume loss is significant.11 The network is decomposed at Ei' centers into SiO fragment molecules. Si-Si bond units migrate and aggregate, leading to the separation of SiOx into nc-Si and Si02 phases.12 Once Si02 forms, it can be transformed to SiOx in the radiation-stimulated process described above. This sequence of oxygen loss and phase-separation continues until a diffusion-limited equilibrium composition is established. The size of the nc-Si grains increases as the migration of Si-Si bond units is enhanced by increasing temperature. The formation of nc-Si at a temperature lower than that required for its formation in the thermal annealing of sputterdeposited or ion-implanted SiOx is due to electronically excited bond rearrangement and to larger number of vacancies after oxygen atoms are lost from the network. The higher the irradiation temperature, the longer the stoichiometric composition is maintained unless the interface is exposed. The volume fraction of Si domains is determined by the balance between the rate at which Si domains aggregate and the rate at which the Ei' centers decomposes to SiO molecules. Above 700^3 only Si crystalline islands are left, and even they collapse when the temperature is high enough. Smoothing then minimizes the total surface area. 5. Conclusion Irradiation of Si02 at temperatures lower than 300"C produces Si-Si bond units distributed uniformly throughout an amorphous matrix. Irradiation at temperatures between 470CC and 610^3 results in the formation of nc-Si grains, with their longer dimensions between 2 and 10 nm, embedded in a SiOx matrix. The higher the temperature, the greater the size of nc-Si grains. Above 70CC the oxide is gone and Si islands created by solid-phase crystallization are left at the interface. At higher temperatures the islands collapse and make the interface smoother. Acknowledgments I thank A. Shibayama for supporting this research program and gratefully acknowledge the assistance of S. Mizuno and F. Fukumuro in the XTEM observations. References 1. L.A. lSlesbit,Appl. Phys. Lett. 46, 38 (1985). 2. Y. Wakayama, T. Inokuma, and S. Hasegawa, J. Cryst. Growth 183, 124 (1998). 3. M. Yamamoto, R. Hayashi, K. Tsunetomo, K. Kohno, and Y. Osaka, Jpn. J. Appl. Phys. 30,136 (1991). 4. S. Hayashi, T. Nagareda, Y. Kanzawa, and K. Yamamoto, Jpn. J. Appl. Phys. 32, 3840 (1993). 5. ML. Brongersma, A. Polman, K.S. Min, E. Boer, T. Tambo, and H.A. Atwater, Appl. Phys. Lett. 72,2577(1998). 6. T. Makimura, Y. Kunii, N. Ono, and K. Murakami, Appl. Surf. Sci. 127-129, 388 (1998). 7. K. Kurosawa, W. Sasaki, Y Takigawa, M. Ohmukai, M. Katto, and M. Okuda, Appl. Surf. Sci. 70/71, 712 (1993). 8. J. Qiu, K. Miura, and K. Hirao, Jpn. J. Appl. Phys. 37,2263 (1998). 9. H. Akazawa and J. Takahashi, Rev. Sci. Instrum. 69, 265 (1998). 10. H. Akazawa, Phys. Rev. B59, 3184 (1999). 11. H. Akazawa, Phys. Rev. B52, 12386 (1995). 12. D.V. Tsu, B.N. Davidson, and G. Lucovsky, Phys. Rev. B40, 1795 (1989). 13. R.A.B. Devine, Nucl. Instrum. Methods B46, 244 (1990).
EXCITONIC PHOTOLUMINESCENCE IN PENTACENE SINGLE CRYSTAL T. AOKI-MATSUMOTO, K. FURUTA, T. YAMADA, H. MORIYA and K. MIZUNO Department of Physics, Konan Univ. Okamoto, Kobe 658-8501, Japan A. H. MATSUI Organo-Optic Research Laboratory, 6-2-1, Seiwa-dai, Kita-ku, Kobe 651-1121, Japan Department of Physics, Konan Univ. Okamoto, Kobe 658-8501, Japan
Photoluminescence of pentacene single crystals is studied in the temperature range of 7 K to 200 K under excitation with He-Ne laser light. Photoluminescence spectra consist of four broad bands, LI to L4. The highest energy band, LI, located close to the lowest exciton absorption band mainly appears for //A-polarization. The intensity of the second one, L2, with Stokes-shift of about 1500 cm'1, decreases as temperature rises above 30 K and disappears at 100 K. The bands, L3 and L4, which are located at lower energy, are observed at higher temperatures up to 200 K. Based on their energy positions, the band L2 is assigned to a shallow self-trapped exciton luminescence band, and the bands L3 and L4 to deep self-trapped exciton luminescence bands. By comparing this result with reported result on tetracene crystals, self-trapped excitons are considered to be more stable in pentacene.
1. Introduction The exciton bandwidth, 2B, and the exciton-phonon coupling parameter, g, are key parameters in describing Frenkel exciton behaviors. Frenkel excitons are observed. molecular size changes. with the molecular size.
The exciton bandwidths for a series of polyacenes are known to increase Concerning the magnitude of g, confirmative information has been
obtained for anthracene and tetracene. 0.95.
3
Aromatic molecular crystals are typical systems where
It is interesting to study how exciton behavior changes when
For anthracene, g is reported to be 0.85 2 and for tetracene
In benzene and naphthalene crystals, g is expected to be smaller than that for anthracene. 1
We can safely say that the magnitude of the exciton-phonon coupling constant increases in the order of the constituent molecule size, benzene and naphthalene, anthracene and tetracene. that stability of self-trapped excitons (STEs) increases with the molecular size. the value of g has not been determined.
This means
As for pentacene,
In this study, we have studied luminescence spectra of
pentacene crystals to obtain information on the stability of STE.
On comparing the result with
reported luminescence spectra in tetracene crystals, STEs in pentacene crystals are suggested to be more stable than those in tetracene crystals.
185
186
2. Experimentals Single crystal flakes of pentacene were grown by sublimation in argon atmosphere of a reduced pressure. Specimens with well-developed ab face of a typical size of 1mm X 1mm were obtained. For luminescence measurements, thin single-crystal flakes sandwiched between two quartz plates were mounted to a cold fin of a cryogenic refrigerator (IWATANI Plantech, Cryomini D510). A He-Ne laser or a dye laser was used for excitation light sources. Luminescence was detected in a backward-scattering geometry by using a single monochromator (ARC, SpectraPro-300i) and liquid nitrogen cooled CCD (Roper Scientific, LN/CCD400-EB). Luminescence spectra were corrected for instrumental factors.
3. Results Absorption and (a) A lib • 10 photoluminescence (PL) ABSORPTION I 7K spectra of a pentacene single crystal at 7 K are SA-T^-^ shown in Fig. 1 (a) and (b) L2 (b), respectively. The L3 LUMINESCENCE lowest exciton absorption 7K L4 7/bl L1 x5 band is observed for llbpolarization at around • (C) 14850 cm 1 . For ±bpolarization, the lowest absorption band appears 2 s 12000 14000 16000 18000 10000 at around 15900 cm"1. WAVENUMBER [cm"1] The energy splitting between these two bands Fig. 1 (a)Absorption, (b)PL and (c) PL polarization of a pentacene single of about 1000 cm"1 crystal at 7K. PL spectra were obtained under excitation with He-Ne laser roughly corresponds to light Davydov splitting. Photoluminescence spectra were measured under excitation with He-Ne laser light (15800 cm" ). Polarized spectra (thin curves) are shown for energy region above 13000 cm"1 where a polarizer is available. Non-polarized spectrum (thick curve) consists of four broad PL bands, LI to L4. The highest energy band, LI, as shown in enlarged scale, is observed at 14700 cm"1, which is close to the peak energy of the lowest exciton absorption band for //fi-polarization. This band is observed mainly for //6-polarization. The second one, L2, located at 13400 cm"1, is Stokes-shifted by 1450 cm"1 from the lowest absorption band, which is a dominant band at low temperatures. The rest two bands, L3 and L4, are observed at 12000 cm"1 and at 10900 cm"1, respectively. Figure 1(c) shows the degree of polarization; (I//b-I±b)/(I//b+I±b), where 7±j and Im, indicate PL
fl
J
•
187 intensities for J- b- and //ft-polarizations. It is about 0.7 for the band LI and 0.4 for the band L2. Similar PL spectra were observed for all the crystals measured, independent of the degrees of purification. For excitation with dye laser light in the energy range of the lowest //6-polarization exciton absorption band (14900 cm"1 ~ 14000 cm"1), the luminescence spectra observed were essentially the same as shown in Fig. 1 (b), except for LI band, for which the spectral shape was not found clearly because it is located too close to excitation light energy. Under excitation at 13500 cm"1, no luminescence was observed.
TEMPERATURE DEPENDENCE
Figure 2 shows temperature dependence of non-polarized PL WAVENUMBER [cm1] spectra under excitation with a 1 Fig. 2 Temperature dependence of non-polarized PL spectra under He-Ne laser light (15800 cm" ). excitation with He-Ne laser light Interference structure below The intensity of band LI is almost constant below 30 K and 1 12500cm" is due to the detection system. gradually decreases upon raising temperature. The intensity of band L2 decreases with temperature above 20 K and disappears at about 100 K. The intensities of the other two bands, L3 and L4, increase with temperature till 50 K. They decrease at higher temperatures but are still observable at 200 K. The relative intensity of bands L3 and L4 does not change greatly upon raising temperature. 10000
12000
14000
16000
4. Discussion Judging from the facts that bands LI to L4 were observed for all the samples measured, these PL bands are considered to be intrinsic. Since temperature dependence of luminescence bands are categorized into three groups, LI, L2 and the rest, there should be 3 kinds of PL initial states. Photoluminescence band LI is assigned to free exciton luminescence band judging from its energy that is close to the lowest absorption band energy and polarization character which is the same as the lowest exciton absorption band in this material. Lower energy bands L2 to L4 are assigned to
188 luminescence from STEs taking account of their Stokes-shift of about 1500 cm"1, and weak polarization observed for L2 compared to LI. The band L2 is thus attributed to shallow STEs because its Stokes-shift is small. The band L3 with larger Stokes-shift is assigned to deep STE luminescence band. The band L4 is possibly assigned to a phonon-replica of the band L3. In order to estimate the exciton-phonon interaction strength, in what follows we discuss photoluminescence properties in pentacene crystals together with those in tetracene crystals. It should be noted that a pentacene molecule is composed of 5 benzene rings, while tetracene is composed of 4 rings. In tetracene crystals, STE luminescence bands are observed4 as well as in pentacene crystals. The Stokes-shift of the highest energy STE luminescence band is around 1000 cm"1, which is smaller than that in pentacene (about 1500 cm"1). This suggests that self-trap depth in pentacene is deeper than in tetracene of 60 cm"1. The temperature dependence of the FE luminescence intensity substantiates this suggestion. In tetracene, the thermal activation of STEs to the free exciton band is prominent above 95 K, while in pentacene, thermal activation of STEs to the free exciton band was not appreciable in the whole temperature range measured. Since the existence of STEs in pentacene is evident, as we have discussed above, we can discuss exciton behavior in a series of polyacenes. The self-trapped exciton state in anthracene is a metastable state. In tetracene, STE is stable compared to free excitons, and it is even more in pentacene. Since, the exciton bandwidth increases with the molecular size as mentioned in the introduction section, the increase in the STE stability with the constituent molecule size indicates that lattice relaxation energy increases more than the bandwidth does as molecular size increases. This tendency in STE stability can be explained in terms of the increasing contribution of CT excitons in the lowest absorption band as the size of the constituent molecules, increases. As the size of the molecule become larger, the energy of CT exciton reduces and approaches to that of the lowest Frenkel exciton.5 For pentacene, the existence of CT exciton has been confirmed by electroabsorption in the second and the third lowest absorption band region.5 When CT exciton energy is close to the lowest Frenkel exciton state, mixing of CT character to the lowest Frenkel exciton transition may become appreciable, which is favorable to the lattice relaxation due to electrostatic force between separated electron and hole. References [1] A. H. Matsui, M. Takeshima, K. Mizuno and T. Aoki-Matsumoto: this proceedings [2] A. Matsui: J. Phys.Soc.Jpn. 21 (1996) 2212. [3] K. Mizuno, A. Matsui and G. J. Sloan: J. Phys. Soc. Jpn. 53 (1984) 2799. [4] H. Nishimura, T. Yamaoka, A. Matsui, K. Mizuno and G. J. Sloan: J. Phys. Soc. Jpn. 54 (1985) 1627. [5] N. Pope and C.E.Swenberg: "Electronic processes in organic crystals" Oxford Univ. Press, New York (1982)
HIGH DENSITY EXCITATION EFFECTS ON EXCITONS AND ELECTRON-HOLE PAIRS IN ALGa, ,As/AIAs QUANTUM WHtES K. BANDO, I. AKAI, and T. KARASAWA Department of Physics, Graduate School of Science, Osaka City University 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan
K. INOUE and H. NAKASHIMA The Institute of Scientific and Industrial Research, Osaka University 8-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan High density excitation effects on excitons in Al/Sa^^As/AlAs (x=0.2~0.5) quantum wires (QWRs) have been investigated. In these samples, the difference between the type-I (xiaO.3) and type-II (x£0.4) band structures was clearly observed in high density effects on the photoluminescence (PL) and its temporal response. In the type-I samples, the PL is characterized by a fast radiative decay process reflecting intra-wire transitions. The PL peak shows a small blueshift with increasing excitation density, and the shift becomes large to 20meV under the highest excitation limit. The large shift is ascribed to intrinsic high density excitation effects appearing beyond the weak localization of the excitons into structural fluctuations. On the other hand, in the type-II PL, a huge blueshift appears, being much larger than the localization energies of the excitons. This shift is also considered to be due to another intrinsic high-density effects brought about by the long-lived type-II excitons. Keywords: Quantum Wire; Type-II; High Density Excitation Effect; Blueshift
1. Introduction In recent years, semiconductor nanostructures such as quantum wells (QWs) and quantum wires (QWRs) have become essential for investigation of optical and electrical properties in semiconductor devices. Particularly, for the QW structures, good quality samples have easily been fabricated contributing much progress to not only application but also basic physics. In such low-dimensional semiconductor systems, excitons with large binding energies are realized, and conspicuous behavior of the stable excitons have been expected at high density. On the other hand, excitonic properties at highdensity in bulk systems have been extensively studied since various phenomena due to many-body effects appear. In the low-dimensional systems, distinguishable many-body effects from those in 3D-systems have been expected. For example, in GaAs QWs, the blueshift of 2D-exciton resonance results from the Pauli repulsion,1 which has not been observed in bulk 3D-systems. Subsequently, the high-density regime of excitons has been easily realized in type-II QWs for their long lifetime. In the QWR structures, the e-h droplet2 and the biexciton3 have also been reported. However reports concerning the many-body effects on excitons in the QWRs are less in comparison with in the QWs. In this work, we pay attention to the many-body effects on the PL of the excitons and e-h pairs in the type-I and -II Al^Ga^^As/AlAs QWR structures in the high density regime.
2. Experimental We have already demonstrated that the ALGa,,^s QWRs are naturally formed on vicinal GaAs(llO) surfaces using the molecular beam epitaxy4. Before growing the QWRs, a 5-period A ^ G a ^ A s (30nm)/GaAs(30nm) SL was grown on the vicinal GaAs(llO) substrate misoriented by 6° toward ( l l l ) A surface in order to form the well-aligned giant steps at the surface. Next, an AlAs(30nm)/ AlxGa1.xAs(10nm, x = 0.2-0.5)/AlAs (30nm) single quantum well (SQW) was grown on the SL. Since, the AlAs fraction x in the QWR becomes smaller than that in the terraces for the migration of Ga
189
190 atoms onto the giant steps, the QWRs were formed in the SQW at the giant step edges. The PL measurements were performed at 2K. A 488nm line of a Ar+ laser was used for cw excitation. For the time-resolved PL measurements, a 532nm line of a mode locked Nd:YAG laser with a pulse width of ~70ps was used, and a streak camera and a CCD system was used for detection.
3. Results and Discussion As reported previously, the indirect recombination (type-II) between the X-electrons in the AlAs barriers and the T-holes in the QWRs provides weak PL bands in the samples with x=50.4. On the other hand, intense PL due to the direct transition (type-I) in the QWRs were observed in those with smaller x 5 Figs. 1(a) and (b) show the PL spectra for various excitation densities in the samples with x=0.2 and 0.5, respectively. From the consideration of the band alignment in the QWRs, the origin of each PL band for the weak excitation can be assigned as follows. The PL band for x=0.2 corresponds to the type-I transition. On the other hand, for x=0.5, the PL spectra consist of three bands as marked by triangles in Fig. 1(b). The band at 1.76eV was also observed in the samples of x=0.3 and 0.4. Then, the 1.76eV band can be attributed to type-II transition between the X-electron in the AlAs barrier layer of the QWR and the T-hole in the GaAs layer at the last of the SLs. The second peak (centered triangle) in the three bands is considered to be due to the type-II transition between the X-electron in the AlAs barriers and the T-hole in the QWRs. The band at 1.88eV is considered to be due to the typeI transition as also seen in the type-I sample although the transition energy is not the lowest one in this sample (type-D). For x=0.2 in Fig. 1(a), the PL band shows blueshifts with increasing excitation density. The shift value is small in the range of the weak excitation density and reveals abrupt increase under the heavier excitation densities. The shift values are plotted (open circles) in Fig. 1(c) as a function of excitation density. For x=0.5 in Fig. 1(b), the centered component shows huge blueshifts even in the weak excitation-density range; the shift value attains to lOOmeV for the highest excitation. The shift values are also plotted in Fig. 1(c) (closed triangles). The other two bands at 1.76 and 1.88eV do not shift with the excitation density. As mentioned above, the PL band at 1.76eV is a type-II transition at the interface of GaAs layer (30nm) of SL and AlAs layer (30nm) of the QWR. The volume of the GaAs and AlAs layers providing the 1.76eV band are much larger than those of the QWRs. Then it is considered that the high density effects on the 1.76eV band is rather weak than in the case of the typeII excitons in QWRs. In the sample of x=03, changing manner of the blueshifts behaves in the same manner as x=0.2. On the other hand, in the sample of x£0.4, the blueshift of the PL band is quite different. These results are also drawn in Fig. 1(c). The shifts of the type-II for x=0.4 and 0.5 are much larger than those of the type-I. This difference is considered to come from the exciton densities or the e-h separating mechanisms between the type-I and -II structures. For x=0.3(closed circle), however,
(c) ° x=0.2 • x=0.3 a x=0.4 •*• x = 0 . 5 A
-A A A
A AAA A • A A
A
A AA
A
•
* o
.
A A
_
- Sa 7
, *,
^J
1.9 1.7 1.8 1.9 10"2 10"1 10° 101 102 103 104 Photon Energy (eV) Excitation Density (W/cm 2 ) Fig. 1. Excitation density dependence of PL spectra in (a) x=0.2 and (b) x=0.5 samples; the triangles in (b) show the peaks of three components, (c): Excitation dependence of the PL peak shifts from the peaks under weak excitation limits in the samples with x=0.2~ 0.5. 1.7
1.8
191 the shift becomes large abruptly for higher excitation densities (~103W/cm2). The abrupt change is considered to relate with a crossover from the type-I to -II transitions under the high density limit, since the energy difference between the T-electron in the QWR and the X-electron in the barrier is small forx=0.3. Figs. 2(a) and (b) show time-resolved PL spectra with a time width 130ps of the samples with x=0.2 and 0.5 under the high density excitation. The excitation densities in Figs. 2(a) and (b) are 35 and 560 nJ/cm2, respectively. For x=0.2 in Fig. 2(a), the peak energy of the PL observed at Ops locates at the higher energy side by ~20meV than that for the weak cw excitation drawn in Fig. 1(a). The intensity decreases rapidly and the peak energy shifts to the lower energy side with time. The peak energy of the PL band ceases to shift and coincides with that of the PL band for the relatively weak cw excitation after 300ps. The total (photon-energy integrated) PL intensity shows rapid decay in the range of subnanosecond, reflecting the type-I transition rate. The time evolution per 13 Ops of the peak position for x=0.2 is plotted as a function of the integrated PL intensity in Fig. 2(c) by closed rectangles 1.725 2
35(nJ/cm ) (a) i=0.2 A PS / \ ' ° 130-2K 1 \ A \ \ \ ' \ \ • \ \ '
/
' \\
260 390 640 1020 1530
560(nJ/cm2)
(b) *=0.5
f\
2K
" /
/ /
/
-Ops" / ~ \ ' 130 260
/ \ \ \V
390 \ \ -640" \ \ 1020 \\l530
-^^V \ \
1.720
(c)
x=0.2
I0=560(nJ/cm2) .....^..«.tr...ii...a......-t)-»..
u W2 1.715^ V4
o.
It/8
16
•3 1.710f V ^ 1.705 ° V32 O V128 ° ^ S. 1.700
• .
4 a
If/
1.695 1.75 1.80 1.75 1.80 1.85 1.90 1.95 10° If/4 W1 10^ 10"' \
1.70
(Io/16=35nJ/cm2). For the other excitation densities, obtained peak energy changes under various excitation densities are shown in Fig. 2(c), and nearly the same monotonous decay behavior of the PL intensity was obtained. In the initial stage just after pumping, the PL peaks appear at the same energy position independent of excitation density denoted by dotted line in Fig. 2(c). The peaks shift rapidly to red in a few hundred picoseconds by about 20meV as denoted by a downward arrow in Fig.2(c). On the other hand, such large shifts are not resolved in the later stage after ~300ps. It has been well known that some localization of excitons owing to potential fluctuation at interfaces of the heterostructures gives rise to finite redshifts of the PL at lower temperatures than 10K. Higher quality samples have smaller localization energies less than lOmeV. In our QWR structures, the localization energies are expected to be small because a homogeneous distribution of the cathode-luminescence5 in the QWR was observed along the wire reflecting the high quality of the samples. Thus, the temporal behavior of the PL peak seen in Fig.2(c) is understood as follows. The photo-created e-h pairs firstly relax immediately to the intermediate state observed at 1.719eV(dotted line in Fig. 2(c)). The rapid relaxation and the energy transfer from the intermediate state to the exciton state in the QWRs occurs during 300ps with the large energy shift. In the later stage after the rapid redshifts, clear energy shift was not observed until ~1.5ns. This fact implies that the exciton distribution attains to the quasithermal equilibrium in the later stage. Since the integrated PL intensity is proportional to the exciton density at that time, the PL peak energies in the quasi-thermal equilibrium change depending on excitation densities as guided by dashed curve in Fig. 2(c). The largest shift value on the dashed curve from the lowest one is about lOmeV Since this value is comparable to the typical localization energy, a part of the blueshift is considered to come from a site-filling effect on the weakly localized excitons. The shift value lOmeV
192 corresponds to that obtained for the cw-laser excitation in the weak range (open circles) in Fig. 1(c). Under the cw-laser excitation, the shift reveals an abrupt increase to more than 20meV at near the highest density. Then, the large-shift component beyond lOmeV is considered to be due to a manybody effect of delocalized excitons overflowing from the localized sites. The time-resolved spectra in x=0.5 for the excitation density 560nJ/cm2 in Fig. 2(b) consist mainly of two components: the higher lying PL band decaying in sub-nanosecond range and the lower PL band having a very long decay time. The peak energy position of the rapid decay component coincides with that of the weak PL peak at 1.88eV assigned to the type-I transition in Fig. 1(b). On the other hand, the PL peak at ~1.83eV having a long decay time of ~50ns corresponds to the second peak in the three bands resolved in Fig. 1(b) revealing the feature of the type-II transition. The PL peak of the type-II excitons under cw excitation shifts largely to higher energy side with increasing excitation density as seen in Fig. 1(b). The same large shift has been seen under the pulse excitation depending on the excitation density. The shift mechanisms can be considered to be the same under the cw and pulse excitation. The observed blueshift of the PL peak at ~1.83eV seen in Fig. 2(b) from the peak at ~1.79eV for the weak excitation limit can be also explained in similar way. The type-II excitons also attain to the quasi-thermal equilibrium within a few hundreds of picoseconds after pumping as can be seen in Fig. 2(b) because the low energy shifts are hardly observed within the observing duration. However, the largest shift values for the cw and the pulse excitation are lOOmeV and 50meV, respectively. These values are much larger than the weak localization energy due to the structural fluctuation. This fact implies that the main portion of the large blueshift in this sample comes from the intrinsic high density effects such as the repulsive interaction between excitons, the band filling effects, or the Stark effects caused by interfacial electric field induced by spatially separated electrons and holes owing to the unique band structures in type-II samples. In addition to these effects, a coexistence between type-I and type-II excitons should be taken into account for the heavier excitation because the PL peak shift to higher energy side beyond the energy position of type-I excitons denoted by vertical dotted line in Fig. 1(b) under the heavier excitation. In the samples of x=0.3 and 0.4, the same behavior was obtained as x=0.2 (type-I) and 0.5 (type-II), respectively. These temporal profiles are also classified in two categories by the transitions of type-I and -II. In summary, we performed the PL measurements of A L G a ^ s / A l A s QWRs. The PL peaks show the small blueshifts for x S o . 3 and the larger blueshifts for x=5 0.4 with increasing excitation density. In the temporal profiles, the feature of the type-I transition for x^k 0.3 and that of the type-II for xii0.4 appear as the decay time durations. From the dynamics of the blueshifts in the type-I samples, it was found that the rapid relaxation from the higher lying intermediate state to the lowest exciton states occurs and the peak shift due to intrinsic high density excitation effects appears overcoming the weak exciton localization. On the other hand, in the type-II samples, much larger blueshifts of the type-II excitons than the weak localization energy was resolved. The huge blueshifts of the type-II excitons is considered to come from the intrinsic high-density excitation effects. The work is supported by a Grant-in-Aid for Scientific Research on Priority Areas, "Photo-induced Phase Transition and Their Dynamics", and Grant-in-Aid for Scientific Research (C), 12640319, 2000 from the Ministry of Education, Science, Sports and Culture of Japan.
References 1. 2. 3. 4.
T. Amand, X.Marie, B.Baylac, B.Dareys, J.Barrau, MBrousseau, RPlanel, D.J.Dunstan, Phys. Lett. A193,105 (1994). H. Kalt, J. Lumin. 60&61, 262 (1994). T.Baars, W.Braun, M.Bayer, AForchel, Phys. Rev. BS8,1750 (1998). K.Inoue, KKimura, K.Maehashi, S.Hasegawa, HNakashima, Mlwane, O.Matsuda, K.Muraseet, J. Cryst. Growth 127, 1041 (1993). 5. H Nakashima, MTakeuchi, BCKimura, Mlwane, Hu Kun Huang, Klnoue, J.Christen, MGrundmann, D. Bimberg, Solid-Slate Eletronics 40, 319 (1996)
DISORDER-INDUCED RELAXATION OF FRENKEL EXCITONS IN MOLECULAR AGGREGATES M. BEDNARZ Institute of Theoretical Physics, Warsaw University, Hoza Street 69, 00-681 Warsaw, Poland. IP. LEMAISTRE Laboratoire des Milieux Desordonnes et Heterogenes, CNRS-UMR 7603, Universite P. etM. Curie, Tour 22, 4, Place Jussieu, ¥-75252 Paris Cedex 05, France. Abstract A model, based on the intraband scattering of excitons in one-dimensional J-aggregates is proposed to describe the lengthening of the experimentally observed radiative lifetime with temperature. According to this mechanism, the exciton-phonon scattering transfers the oscillator strength from the lowest k = 0 optically allowed state to the other states within the excitonic band. A Pauli master equation, in which the hopping rates are calculated, is used to describe the thermalization of the excitonic band. Assuming a fast relaxation mechanism, the temperature dependence of the exciton radiative lifetime is simulated for various chain lengths.
1. Introduction Exciton dynamics in disordered linear chains is currently investigated for various systems like polymers'1' or J-aggregates'2"4'. In this presentation, numerical diagonalization of one-dimensional Frenkel exciton Hamiltonian, including dynamic disorder, is carried out and used to analyze the temperature dependence the radiative lifetime of excitons in strongly coupled molecular Jaggregates'2"4'. At low temperature, the properties of such aggregates are attributed to the lowest (k « 0) excitonic state which carries most of the oscillator strength (superradiance effect) while at finite temperatures, the exciton-phonon interaction destroys this intermolecular cooperativity'3'. At higher temperature, a simple level of modeling the exciton-phonon interaction, without addressing the environment in detail, is proposed by dressing the exciton model with dynamic disorder. This coupling creates local dynamical fluctuations in the site energies which are characterized by their amplitude (A) and correlation time (r c ). A microscopic model of exciton-phonon coupling is introduced by assuming a Bose-Einstein distribution for the phonon occupation density. The phonon-assisted scattering from the lowest excited state to the higher levels redistributes the oscillator strength within the quasi-exciton band states and is described as an incoherent energy transfer process. Using a numerical simulation method the hopping rates are calculated and used in a master equation to describe the time dependence of the exciton populations after initial excitation. It is shown that the thermalization of excitons within the band strongly depends on rc, the correlation time of the stochastic fluctuations. In the case of fast thermalization (as compared to the radiative decay time), the temperature dependence of exciton radiative lifetime is simulated for various chain lengths. 2. Model Hamiltonian We model an aggregate by a linear chain of N identical two-level molecules. The molecular site excitations have energies Et and we consider long range dipole-dipole couplings Vtj among the sites. The electronic Hamiltonian of such an aggregate is written in the localized site representation as 193
194
where the electronic interaction is written in the simplest approach of the point dipole V^VJiJijIR^. In the delocalized exciton representation, the electronic Hamiltonian of Eq.(l) is given by
"o = I , £*|*)(* |,
(2)
(3)
in which \k) denote the N eigenstates with energies I\ and are linear combinations of the site wavefunctions The knowledge of the coefficients C*, allows to define the transition moments {fit) and the oscillator strengths (yk) associated to the various exciton eigenstates Yk=W\rai (5) with y0 being the oscillator strength of the isolated molecule. It is well-known that, for J-aggregates, the intermolecular interaction V0 is negative meaning that the lowest exciton state of the chain, at the bottom of the band, carries most of the oscillator strength. 3. Dynamic disorder The dynamic disorder is analyzed in the framework of the Anderson's theory of the stochastic resonance'61 .We consider the dynamic fluctuations of the molecular energies induced by the coupling to a thermal bath. The stochastic fluctuations of the site energies are taken into account by adding to the excitonic Hamiltonian of Eq. (1) a time dependent Hamiltonian Hx(t)
#,(/)=5>(')|'}(''l-
(6)
By choosing e, (t) to be a stochastic variable, we take into account, in a phenomenological way, the influence on the site energies of other degrees of freedom such as phonons which are not explicitely included in our model. The stochastic variables et (t) are assumed to have the following properties <*,(/)) = 0 (7) {el(t)eJW)) = SvA1e-1'' where { ) denotes the statistical ensemble averaging. A and A represent respectively the average amplitude and the inverse of the correlation time (t c ) of the energy fluctuations. We assume that the time dependence of Eq. (7) is simply given by an exponentially decaying function with a rate r c . Equation (7) also implies that the fluctuations on different sites are uncorrelated. For large values of A (short exciton-phonon correlation time), the energy fluctuations vary rapidly among the energy distribution of width 2A whereas for small values of A the model describes a static disorder of Anderson's type. On the basis set of the delocalized states \k), eigenstates of //„, the matrix elements of the stochastic perturbation Hx{t) are ek,(t) = (k\Hl{t)\l) = YJIC-Clsi(t). (8) It can be noticed that, for k=l, the energy fluctuations of the collective eigenstates are simply
%(0 = ZJ^|%(')-
(9)
For example, the energy fluctuations of the totally symmetric state are reduced by a factor of N relatively to those of the molecules. We consider now the intraband scattering among the exciton states as an incoherent energy transfer with the rates (fi£/°,) given by the Fourier transform of the autocorrelation function of the stochastic perturbation|7'
195
nut = Ft,A2
M
{hXf+ (ka,klf
(10)
where Ftl =^.Icf I |c/| is a factor directly related to the excitonic wavefunctions overlap. This shows that the relaxation will occur mainly among states localized on the same segment of the aggregate'8'. %a>kl is the lack of resonance between k and 1 states. The scattering among the exciton states occurs by phonon absorption or emission processes. In order to satisfy the Boltzmann equilibrium condition, we assume Ut,{a>u
0.8
Figure 1. Thermalization of the lowest exciton state population after initial excitation of the —-—. w_ excitonic band for two values of the correlation time: tc=5 ps (full lines) and rc=\ ps (dotted Ubj- - - ^ r r r r = » _ ^ —~Js£ lines) at various temperatures : T=100K (a), 200K (b), 300K (c). "".. (c)
i \ \
0.6 0.4 0.2
M \ \
^
^
^ » * ^
2 t(ns)
After initial excitation by a short light pulse, the exciton eigenmodes are populated according to their oscillator strength. The stochastic exciton-phonon coupling induces the intraband scattering among the chain eigenmodes at rates given by Eq. (11). This thermalization process over the exciton states strongly depends on the temperature through the fluctuation amplitude (A), the exciton-phonon correlation time (r„) and also on the energy difference,fi«„, related to the chain length, between the thermally populated lowest exciton states bearing oscillator strengths. These three parameters define, at a given temperature, a timescale which has to be compared to the exciton radiative decay. Two limiting cases can be considered: i) slow relaxation (longer or comparable to the k = 0 exciton radiative lifetime. In that case, both mechanisms (radiative decay and thermalization) are competing processes which must be described by using a master equation; ii) fast relaxation (as compared to the k = 0 exciton radiative lifetime). In that case, Boltzmann populations (Wk) are rapidly established. Setting A2 = kT (a Bose-Einstein distribution of phonons), we show in Fig. 1 the thermalization of the lowest exciton population of a chain of N=100 molecules for two values of the exciton-phonon correlation time, r c , featuring slow and fast relaxation.
196 In what follows, we will assume that the intraband relaxation is fast enough to describe the temperature dependence of the exciton radiative lifetime by
r=(l t ^r*r\
(12)
with yk being the oscillator strength of the exciton state. In Fig.2, we show this temperature dependence obtained for various chain lengths (from N=20 to N=100) as well as an effective, temperature dependent, number of coherently coupled molecules, that we define as Nc = T0 I T, and based on the relative exciton oscillator strengths.
50
100
150
T(°K)
200
250
300
50
100
150
200
250
300
T(°K)
Figure 2. Exciton radiative lifetime (left) and number of coherently coupled molecules (right) versus temperature for various chain lengths; N=20, 30, 40, 50, 100. 5. Conclusions In this short communication, we have presented a model to analyze the role of the intraband scattering on the temperature dependence of the exciton radiative lifetime in J-aggregates exhibiting strong intermolecular interactions. Although a considerable number of works were devoted to interpretation of the radiative lifetime lengthening with increasing temperature, the thermalization process within the excitonic band was not considered in the past. Using a numerical approach applied to a homogeneous linear chain of molecules, in the absence of static disorder, we have shown that this thermalization all over the excitonic band plays a significant role. A simple model of energy transfer, based on the stochastic resonance theory was proposed to study such a relaxation mechanism emphasizing the effect of the exciton-phonon correlation time associated to the fluctuations. Finally, when the thermalization of the excitonic band is fast, a better description of the temperature dependence of the radiative decay is provided by shorter chain lengths. References [1] M. Shimizu, S. Suto, T. Goto, A. Watanabe and M. Matsuda, Phys. Rev B58 (1998) 5032. [2] V.K. Kamalov, LA. Struganova and K. Yoshihara, J. Phys. Chem. 100 (1996) 8640. [3] E.O. Potma and D.A. Wiersma, J. Chem. Phys. 108 (1998) 4894. [4] I.G. Scheblykin, MM. Bataiev, M. Van der Auweraer and A.G. Vitukhnovsky, Chem. Phys. Letters, 316 (2000) 37. [5] F.C. Spano, J.R. Kuklinski and S. Mukamel, Phys. Rev. Letters 65 (1990) 211. [6] P.W. Anderson, J. Phys. Soc. Japan 9 (1954) 316. [7] J.P. Lemaistre, Chem. Phys. 246 (1999) 283. [8] V.A. Malyshev, J. of Lum. 55 (1993) 225.
GIANT TWO-PHOTON ABSORPTION INTO EXCITED STATES OF BIEXCITON I.DMITRUK, A.KASUYA Center for Interdisciplinary Research, Tohoku University, Sendai, Japan,
T.GOTO Tohoku University, Faculty of Science, Sendai, Japan
Z.YANCHUK Kyiv Taras Shevchenko University, Kyiv, Ukraine Excited states of excitonic molecule have been observed for the first time by direct method of giant two-photon absorption in monoclinic ZnP2 single crystal. Two excited states with binding energies 3.3 meVand 1.9zneFhave been observed in absorption spectra of intense picosecond laser pulses. First one corresponds to rotational excited state. Interpretation of the second one and details of nonlinear absorption spectra are discussed.
1. Introduction The problem of excited states of excitonic molecule was studied theoretically long time ago 12 , but only few experiments with evidence for observation of the excited states of biexciton were reported 3 , i.e. new features were found in excitation and hyper Raman cross-section spectra. This fact is understandable by taking account of typical small binding energies of excitonic molecules in most semiconductors and of expected great values for vibrational quantum and rotational constant. Only for semiconductors with the heaviest holes (i.e. with the smallest ratio o = m'Jm'h) we can expect possibility that vibrational and rotational states of biexciton will be bound. Several years ago excitonic molecule with high binding energy was found in monoclinic zinc diphosphide f5-ZnP2 crystal. It was observed as inverse hydrogen-like series symmetrical to exciton series in photoluminescence under high excitation 4 and it also appeared in hyper-Raman scattering spectra 5 . 2. Experiment Among many possible methods of excitonic molecule observation such as luminescence, hyper-Raman scattering, luminescence excitation and two-photon absorption, we chose giant two-photon absorption as the most direct and reliable one for search of excited states of excitonic molecule. And this method is expected to provide the best resolution which is necessary to look for weakly bound excited states. High quality |3-ZnP2 crystals had been grown from gas phase in specially designed twelve-zone tubular form furnaces at the temperature 960°C in sublimation zone and 197
198
940°C in growth zone. A Ti:sapphire picosecond 3950B Tsunami laser was used as a source of incident radiation. The beam was focused by an objective lens of a microscope on the crystal immersed in superfluid helium. High thermal conductivity of superfluid helium and less than 2 ps duration of the laser pulse prevented damage of the crystal surface. Estimated power density in focal point was about 30 MW/cm2. The picosecond laser provided us with good balance of spectral resolution and power density.
3.6 I
3.4 -
-/\
/^
c
0
X^=795.2 nm
3.2 3.0 -
2.8 -
^___
Q
^^%-
r
22-
,
2.0 I
L
0
•
X^797.1 nm -
2.6 2.4 -
.
-
M-^"^
1
i
1
1
10
15
„, MW/cm
20
25
30
2
Fig.l. Dependence of optical density of |3-ZnP2 crystal on incident intensity at two different wavelengths. To distinguish two-photon absorption into biexciton from strong exciton absorption and bound exciton absorption usually existing even in high quality crystals we performed measurements at different intensities of laser beam. Examples of dependences of optical density on incident intensity are presented in Fig.l. Increasing absorption at the wavelength 797.1 nm close to half-energy of biexciton is clearly seen. From such dependences we determined intensity range where nonlinearity is clear enough and absorption is not too strong to have good spectral resolution. To obtain resolution better than halfwidth of laser line which was about 0.6 nm in our experiments we measured spectra of the transmitted pulses at two different incident intensities (Fig.2). Dips corresponding to two-photon absorption are seen on the wings of the laser line. A number of such spectra at two different intensities have been measured all over the spectral area from exciton line to biexciton luminescence band. Then a spectrum at low intensity is divided by that at high intensity and the results are summarized in Fig.3. It should be noted that obtained in this way absorption bands do not correspond
199
directly to the energy spectrum of the states transitions to which cause absorption. For example, even in the case of narrow final energy state EM we will obtain a broad band formed by a pair of photons with the energies symmetrical relative to energy position EM/2, hcu, + t>a>2 = EM . It becomes narrower at the wing of laser line, because only one photon largely contributes to the two-photon absorption and the other photon density becomes very weak, and it becomes broader at the center of laser line and when twophoton absorption is stronger.
797.0
798.0
797.5
798.5
X, nm
Fig.2. Spectra of laser pulse transmitted through |3-ZnP2 crystal at low (1.0 MW/cm2, dashed line) and high (8.4 MW/cm2, solid line) incident intensity.
i
i
i
i
3.5 3.0
-
i
i
I
i
i
i
i
i
iv \ M
1"
"
i
M
1.5 1.0
i
M-J \A
2.5 2.0
i
M
1
\
j\j - /~^J
V/^MAPV-A^
0.5 1
795
.
1
796
,
1
797
.
1
.
798
1
799
.
1
800
.
1
801
,
1
802
X, nm
Fig.3. Nonlinear absorption in (3-ZnP2 crystal. T=2 K.
200 According to group-theory calculations two-photon absorption into biexciton is allowed both in Ejjc and EXc polarizations. But the latter one is much weaker because of forbidden exciton transition in this polarization. One-photon resonance with exciton state is one of enhancement factors leading to giant oscillator strength. Thus we could observe two-photon absorption at .Siconly in very thick samples (3 mm and more). But in this case the second excited state of the molecule is difficult to resolve because its energy is too close to B-exciton energy. That is why in this paper we present results for two-photon absorption at Ejjc in thin sample {d= 50 fj.m) (Fig.3). Three two-photon absorption lines at 797.06 nm, 796.67.am and 796.32 nm are well resolved. The most intense one marked M in Fig.3 agrees well with the symmetry point of inverse hydrogen-like series and excitonic series {797.3 nm)* and with half-energy of excitonic molecule {1.5551 eV, i.e. 797.1 nm) obtained from hyper-Raman cross-section spectra 5 . So it should be interpreted as two-photon absorption into excitonic molecule. Lines M' and M" are less intense and appear on the higher energy side of the line M. We interpret them as two-photon absorption into excited states of excitonic molecule lying 1.52 meV and 2.9 meV above ground state as stated in section 3. 3. Discussion From theoretical calculations 1 we can expect for biexciton in p-ZnP2 crystal the existence of one rotational and one vibrational excited states with binding energy 0.075£^ = 3.4 meV and 0.012£^ = 0.5 meV, respectively. The first is in good agreement with 3.3 meV experimentally obtained from the position of the 796.7 nm absorption line. The highest energy two-photon absorption line at 796.3 nm corresponding to the binding energy 1.9 meV can be attributed to the first vibrational excited state. Discrepancy in binding energy is understandable taking account of strong anisotropy of fS-ZnP2 which was not considered in ref.1. But according to zeroth order approximation and to results of more accurate estimations 2 an oscillator strength of such transition should be slightly less than that for the ground state. While observed intensity of the third line is several times lower. That is why it is more likely that the third line is associated with the second rotational excited state with the binding energy increased in anisotropic case. Two-photon transition into a rotational state with 1=2is allowed by selection rules, but probability of direct optical transition to such state perhaps must be much lower, as we see in experiment. References 1. I.A.Karp and S.A.Moskalenko, Sov. Phys. Semicond., 8, 183 (1974). 2. V.I.Vybornov, Sov. Phys. Solid State, 20, 423 (1978). 3. Y.Nozue, N.Miyahara, S.Takagi and M.Ueta, J. of Luminesc, 24/25, 429 (1981). 4. N.M.Belyi, I.S.Gorban', V.A.Gubanov, and I.N.Dmitruk, JETP Lett., 50, 85 (1989). 5. T.Goto and Y.Goto, J. of Luminescence 48&49, 103 (1991).
Optical absorption of confined e x c i t o n s in T l halide t h i n films
A.FUJII Shock Wave and Condensed Matter Research Center, Kumamoto University Kurokami, Kumamoto 860-8555, Japan T.ONO , W.YU and R.MAKI Graduate School of Science and Technology, Kumamoto University Kurokami, Kumamoto 860-8555, Japan
Optical absorption spectra of the direct exciton of T1C1 and TIBr micro-crystals are measured in evaporated thin films at 5.OK. The energy of the direct exciton bands shift to higher energy with decreasing micro-crystal size. The lower component of the doublet of the exciton in T1C1 decreases its intensity with decreasing micro-crystal size. The experimental results are discussed with the quantum-size effect on the exciton states and on the electron-hole exchange interaction in an exciton. 1. I n t r o d u c t i o n Quantum-size effects upon electronic states have been studied extensively in micro-crystals of various solid materials in these years. Micro-crystals were grown in glass, thin films, quantum wells, and by gas evaporation method. Quantum-size effects on excitons are observed experimentally as the energy shift of the absorption and luminescence peak. Kayanuma studied the quantum-size effects of the electron and the hole in a spherical well to the full extent both analytically and numerically. 1 ' The motional state of the lowest level was classified into three regimes: the regime of exciton confinement for R/a#* > 4, the regime of individual particle confinement for R/a^* < 2 and the intermediate regime for 2 < R / a s * < 4 , where the transition of the former two regime occurs continuously but rather abruptly. Here as* and R denote Bohr radius of the exciton in a bulk crystal and the radius of a spherical well, respectively. The optical absorption spectrum of the weakly confined exciton was shown to have side bands closely lying above the Is peak and the whole Rydberg series structure gradually changes into the series of well isolated peaks peculiar to the strong confinement as R/ajj* becomes small. The exciton states of thallium halides in bulk crystals have been fully studied both theoretically and experimentally. 2 ' The extrema of the valence and the conduction band in thallium halides are not at the T point but at the X point. As the result, the direct exciton has a unique and complex structure due to intervallay exchange and Coulomb interactions. The lowest exciton state in T1C1 and TIBr have the effective Bohr radii a^* of 3.7nm and 4.1nm, respectively. It is, therefore, expected for thallium halides to show the quantum-size effects of the exction from the regime of exciton confinement to the regime of individual particle confinement by controlling the micro-crystal size of several nm to some tens nm. In this paper, we report absorption spectra of the exciton in thin films of T1C1 and TIBr, which were prepared by vacuum evaporation method. We discuss quantum-size effects on the exciton in the micro-crystal of T1C1 and TIBr. 2 . E x p e r i m e n t a l procedure Powder of T1C1 or TIBr (Johnson Matthey, Puratoronic grade) was purified by the filtration and the distillation in vacuum, and by zone-refining in HC1 or HBr atmosphere as those described in the previous work. 3 ' The single crystals were grown in vacuum by Bridgeman technique.
201
202 Absorption coefficient of the exciton bands in thallium halide is the order of 106cm~1, so a thin 11m must be used in the transmission measurements. Bachrach and Brown developed a skillfull method4^ and Kurita modified it5^ for the preparation of thin films to reduce the strain- induced by cooling the specimen down to low temperature. A bole of a single crystal of thallium halide was cut into a platelet- and a hole was drilled at its center. It was polished to be flat and an organic thin film was placed over it. The organic film was made of methyl methacrylate polymer (PMMA). Micro-crystals were prepared by evaporation of purified TlCl or TIBr on the PMMA thin film in vacuum. The evaporated specimens were cooled down slowly to 5.0K over a period of 20 hours not to induce strain. All manipulations of the specimens, including the crystal growth and the vacuum evaporation, were carried out in a dark room under safety red light. The average size of the micro-crystals was estimated from the photograph of a transmission electron microscope (JEM-1210) operated at lOOkV. 3. Results and discussion Figure 1 shows a photograph of an evaporated thin film of TlCl taken by a transmission electron microscope (TEM). It is found that the images of the TlCl micro-crystals are round and some images have small protuberances like comfits. Those protuberances are also round. The shape of the micro-crystal of TlCl is, therefore, supposed to be spherical or hemispherical and so dose it in TIBr. We take an average diameter of the TEM images as the size of the micro-crystal in a thin film.
0 %
•
Pig. 1. Transmission electron micrograph of an evaporated thin film of TlCl.
The absorption spectra of evaporated thin films of TlCl and TIBr are shown in Fig.2. In the figures, E is the average radius of the micro-crystal in the film. In the spectra for thin films in Fig.2, two peaks labeled as 1A and IB are clearly seen, which are also observed in bulk crystals. These bands has been explained to be due to the direct excitons in TlCl and TIBr.2) On the higher energy side of IB band, a new shoulder named 1C is observed in TlCl but not in TIBr. This structure has never been reported before. It is seen in Fig. 2 that absorption bands 1A and IB shift to high energy with the micro-crystal size R decreased. In the specimen of TlCl that R is smaller than 17nm, the absorption bands 1A and IB are rather broad and shift in a great extent to high energy, because of strong size dependence of the energy of the absorption bands in the individual particle confinement regime, and of size distribution of the micro-crystals in a film.
203
1B
TICI
1.5
XI
R/nm
J
1A
f\
J
39
I r
1 •
0.9
X5
f\
28
X
/V "
X80 •JU
3.38
3.4
PHOTON ENERGY(eV)
3.42
3.01 3.02 PHOTON ENERGY(eVl
Fig. 2. Optical absorption spectra of the direct exciton of TICI (left) and TIBr (right) in evaporated thin films of different thickness measured at 5.OK. The uppermost curves are those of bulk crystals measured by K. Takahei. 6 '' 7 '
The direct exciton in thallium halide is formed by the transition associated with the X6+—X6~ direct gap. As the results, four states are constructed by the doubly degenerate conduction band X$~ and the doubly degenerate valence band Xg+. These four states of the exciton are lifted the degeneracy by the intervalley and intravalley interaction. The transitions to two of them are optically allowed and observed as 1A and IB, but the rest are forbidden for the optical dipole transition. The photon energies of these absorption bands of TICI and TIBr are plotted in Fig. 3 as the function of the micro-crystal size R. In Fig. 3, the solid line and the dotted line represent calculated results followed to the theoretical analysis by Kayanuma,1' where the following values are used. The effective mass ratio of a hole to an electron is equal to 1, and the effective Rydberg energy of 1A and IB excitons and the band gap energy are of the corresponding values for bulk crystals.2' The experimental points for the absorption bands 1A(0) and 1B(») in Fig. 3 are generally on the respective theoretical lines. Therefore the direct excitons of TICI and TIBr in the micro-crystals are thought to be suffered the quantum size effects from the regime of exciton confinement to the regime of individual particle confinement. In the weak confinement region with large micro-crystal size, the center-of-mass state of an exciton is lifted the degeneracy.1' The absorption band 1C in TICI might be due to the excited state of the center-of-mass motion of IB exciton. The excited states of the center-of-mass motion should split off from its ground states and the energy separation between the excited and ground states increases as the micro-crystal size is decreased. This is not the case for the 1C band, because the energy separation of IB and 1C bands is nearly constant as shown in Fig.2. The origin of 1C band is not clear yet. It is seen in Fig. 2 that the relative intensity of the absorption bands 1A to IB decreases with decreasing the micro-crystal size and disappears in the film where the micro-crystal size is less than about lOnm in TICI and 20nm in TIBr.
204 3.022
T1CI 3.44
•
• 1A
1
t 1B
1
5 3.43 •
TIBr
3.41
Eb
I
*v
Eb
3.016
3.014
\ 3.012 •
• y+- i-
3.4
1
3.018
• • Ea o
3.42
• tB - • Ea
A 10
1
• 1A
300
1
•4-
A A A • • V • v • •¥•
mo .
3.008 10
10
R/a,'
Fig. 3. Photon energy of the absorption bands 1A,1B and 1C as a function of the micro-crystal size R in T1C1 (left) and TIBr (right). The solid and dotted lines show theoretical results, The lowest exciton state in T1C1 has doublet structure which is brought about by the intravalley and intervalley exchange interaction. The experimental results on the intensity ratio of the absorption bands 1A and IB may suggest that the exchange interaction plays more important role in smaller micro-crystals. It is still open what is the confinement effect on these exchange interactions, and further experimental and theoretical investigations will be required. Acknowledgements The authors would like to thank to Prof. S. Kurita for fruitful discussion. Thanks are also due to Prof. A. Kumao and Prof. T. Matsusaka for their guidance of TEM measurements. This work was partly supported by a Grant-in-Aid for Science Research (09640402) from the Ministry of Education, Science, Sports and Culture of Japan. References 1. Y.Kayamuma, Phys. Rev. B38, 9797 (1988). 2. K.Kobayashi, in: Exciton Processes in Solids, ed. M.Ueta, H.Kanzaki, K.Kobayashi, Y.Toyozawa and E.Hanamura (Springer-Verlag, Berlin, 1986), Chap. 7, p. 370. 3. K.Kobayashi, T.Kawai and K.Kanada, J. Phys. Soc. Jpn. 23, 305 (1967). 4. R.Z.Bachrach and F.C.Brown, Phys. Rev. B l , 818 (1970). 5. S.Kurita and K.Kobayashi, J. Phys. Soc. Jpn. 30, 1645 (1971). 6. K.Takahei and K.Kobayashi: J. Phys. Soc. Jpn. 43, 891 (1977). 7. K.Takahei, Ph.D. Thesis, Univ. of Tokyo,1976.
ELECTRO-ABSORPTION SPECTROSCOPY AND SEMI-EMPIRICAL MOLECULAR ORBITAL CALCULATIONS OF POLAR RETINOID ANALOGUES fflDEKI HASHIMOTO*, KJNGO HATTORL TAKASHI YAM ADA Department of Materials Science and Chemical Engineering, Faculty of Engineering, Shizuoka University, 5-1 Johoku 3-Chome, Hamamatsu 432-8561, Japan
TAKAYOSHIKOBAYASHI Department of Physics, Graduate School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan Nonlinear polarizabilities of a series of polar retinoid analogues were determined experimentally by means of electro-absorption (Stark) spectroscopy. The dependence of the magnitude of nonlinear polarizabilities on polyene chain-lengths as well as on the strength of electron-accepting groups was systematically compared. Semi-empirical molecular orbital calculations using AMI Hamiltonian (MNDO-AM1 method) could quantitatively predict the second ((3) and the third (y) order nonlinear polarizabilities of the present set of molecules except for the y value of C20BDCInd. The real and imaginary parts of x(3)(-
1. Introduction The third-order nonlinear optical effects are attracting increasing attention because of thenpotential photonic applications such as all optical switching and optical computing. Therefore, materials with large third-order optical nonlinearlity are required in order to make these applications feasible.1"5 Interest in the organic nonlinear optical materials is increasing, because the group of organic materials has the following excellent characteristics: (1) It possesses larger (in some case much larger) nonlinearlity than that of inorganic one. (2) Nonlinearlity can be enhanced by the modification of substituent groups. (3) No expensive equipment is needed for the crystal growth. Marder et ol.6 reported that carotenoid (a photosynthetic pigment) compounds with an electron-accepting group attached to its polyene backbone, namely polar carotenoid analogues, shows the largest third-order nonlinearlity among the organic compounds ever studied. We also have tried to develop a novel class of third-order nonlinear optical organic molecules with retinoid (a visual chromophore whose polyene chain-length is equivalent to one-half of the carotenoid) as its structural motif.7'8 The molecular and crystal structures of a novel polar retinoid analogues, 2-(all-frans-retinylidene)-indan-l,3-dion (C20Ind) were reported previously by our group.7 We have also reported the nonlinear polarizabilities of C20hid and its monodicyanomethylene (C20MDCInd) and bisdicyanomethylene (C20DBChid) derivatives.8 The present paper reports the systematic comparison of the magnitude of the nonlinear polarizabilities for a series of polar retinoid analogues that have been determined experimentally by means of electro-absorption spectroscopy as well as theoretically by means of semi-empirical molecular orbital calculations. 2. Experimental Figure 1 shows chemical structures of sample molecules studied in this investigation. They are (a) 2-(all-/ran5-P-ionylideneethylidene)-indan-l,3-dione (C15Ind), (c) 2-(all-fr,a«i-P-ionylidenecrotonylidene)-indan-l,3-dione (C17Ind), (c) C20Ind, (d) l-dicyanomethylene-2-(all-/ra«s-retinylidene)-indan-3-one (C20MDCInd), (e) l,3-bisdicyanomethylene-2-(all-/raw-retinylidene)-indan (C20BDCInd). All these compounds were synthesized by means of Knaevenagel type condensation * E-mail address: [email protected]
205
206
of corresponding aldehydes and an indan-l,3-dione or its monodicyanomethylene as well as bisdicyanomethylene derivatives under the presence of catalytic amount of p-toluenesulfonic acid. C15 and C17 aldehydes were synthesized by means of Horner-Emons reaction starting from P-ionone. C20 aldehyde was synthesized by the hydrolysis of retinylacetate followed by oxidation with MnC>2. Structures of these molecules were identified by 300MHz 'H-NMR and mass spectra. Systematical comparison for the dependence of the magnitude of nonlinear polarizabilities on polyene chain-length as well as the strength of electron-accepting groups can be made by using this particular series of molecules. Nonlinear polarizabilities of these molecules doped in PMMA polymer films (5 wt% dopant concentration) were determined by means of electro-absorption spectroscopy, of which detailed description was given elsewhere.8 Gold electrodes with a gap of 100 um were deposited on a glass substrate, and the sample polymer film was spin-coated on top of the electrodes. External AC electric field with a Fig. 1. Chemical structures of polar frequency / (500 Hz) was applied to a sample, and the retinoid analogues. absorbance change induced by the field was detected at 2/ frequency using a dual-phase lock-in amplifier. By applying 500V between these electrodes in the configuration, the sample film is under the intense electric field as high as 50 kV/cm. Semi-empirical molecular orbital calculations using AMI Hamiltonian were performed by the use of MOPAC97 in order to compare frequency independent (static) nonlinear polarizabilities of the present set of sample molecules with those measured by electro-absorption spectroscopy. 3. Results and Discussion Based on the perturbation theory applied to a two-level model, the linear and nonlinear polarizabilities of a linear polyene molecule can be simply expressed by Eqs. (I).9
a„ =2^=-. pm = 6 ^ ^ , E
£ge
ge
7xxxx
»24^(AS-MI)
(1)
Zge
Here, Ege, Mge, and Aft are the transition energy, the transition moment, and the difference of static dipole moments between the ground and excited states. From Ege and Mge determined by optical absorption spectrum, and A// determined by electro-absorption spectrum, we can calculate the nonlinear polarizabilities. Application of intense external electric field induces the slight deviation of optical absorption spectrum of a molecule. This phenomenon is well known as Stark effect. The modulation spectrum shows quadratic dependence on the applied electric field and can be expressed as Eq. (2): l0 z Hf(4vVv) , C* vtf2(^(v)/v) (2), ' 15/; dv 30fr dvl where h is Planck's constant, x is m e experimental angle between an external electric field (Fext) and the electric polarization of light at the frequency, v, used to probe the effect, and F^ =/-F e n , where/is the local field correction (assumed to be a scalar). Therefore, the modulation spectrum AA(v,F,Z)=F^
A A(r), x y
B
207 can be well accounted for by the summation of original absorption spectrum and its first and second derivative waveforms. Coefficient Ax provides information on the transition moment polarizability and hyperpolarizability, and 5X, on the change in polarizability (A a) associated with an electronic transition. 11 Cz =^|A i u| 2 +(3cos 2 ^-l|3(p-A / u) 2 -|A / o| 2 |, where p is a unit vector along the transition moment, has x angular dependence. However, in the special case of magic-angle configuration (x = 54.7°), the terms having angular dependence disappear and the relation becomes very simple. Especially, Cx at the magic angle directly provides us with the A/i value. Table I. Nonlinear polarizabilities of polar retinoid analogues. y
0-5 0 2
:
C15Ind C17Ind C20Ind C20MDCInd C20BDCInd
P / 10"28 esu y / 10 " esu 1.96 ±0.02 0.09 ± 0.03 3.39 ± 0.04 0.90 ± 0.06 5.2 ±0.1 1.8 ±0.01 6.7 ±0.1 2.9 ± 0.2 6.3 ± 0.1 5.5 ± 0.2
As an example of Stark spectroscopy, Fig. 2 shows the results of C20hid. They are (a) absorption spectrum, (b) its first and (c) second derivative waveforms, and (d) the Stark spectrum. Circles are the experimental results and solid line shows the result of spectral simulation. As shown in Fig. 2(d), the observed electro-absorption spectrum is fit successfully. 15000 20000 25000 Photon energy / cm-1 Table I summarizes the nonlinear polarizabilities determined in this investigation. Fig. 2. (a) Optical absorption spectrum, its (b) first Based on the comparison of the magnitude of the and (c) second derivative waveforms, and (d) Stark spectrum of C20Ind in PMMA. Circles and solid second (P) and the third (y) order nonlinear line in (d), respectively, show the experimental polarizabilities, we can conclude as follows. (1) results and the spectral simulation using the Elongation of the polyene chain-length increases waveforms of (b) and (c). both the p and y values, and good linear relations were found between the powers of van der Waals lengths of CISInd, C17Ind and C20Ind molecules and the nonlinear polarizabilities. (2) Introduction of the electron-accepting group does increase the nonlinear polarizabilities. Especially, the effect is significant for y. (3) Introduction of dicyanomethylene group increases furthermore the nonlinear polarizabilities. It is interesting to note that monodicyanomethylene indan derivative (C20MDCInd) has the largest p. In contrast, bisdicyanomethylene indan derivative (C20BDCInd) has the largest y. Figure 3 compares the p and the y values calculated semi-empirically and those determined experimentally. Those two values have good linear relation, hence it is concluded that the semi-empirical molecular orbital calculations using AMI Hamiltonian can quantitatively predict the nonlinear polarizabilities of the present set of molecules except for the y value of C20BDCInd. As regard the theoretical calculation of C20BDCInd that showed the largest y value, the more sophisticated calculation taking the effect of configurational interaction into consideration is necessary in order to explain the magnitude of the observed y value.
208
C20BDCInd^
-
Fig. 3. Comparison of the (a) p and the (c) y values of polar retinoid analogues calculated theoretically and those determined experimentally.
/
Si
J e| / C17lnd
C15lnd
/
h#H C20lnd
/
" "
/
-\/ *
i
2
,
4 /S/1(T28esu(Exp.)
6
2 4 r/KT^esufExp.)
Finally, we calculated both the real and imaginary parts of %®\-(a; 0, 0, co) spectra and the results are shown in Fig. 4. We believe that this set of data will provide us with useful information in order to account the figure of merit 12 of the third-order nonlinear optical material. Acknowledgements This work is supported by Grant-in-aid (# 10740145 and 1240179) from Ministry of Education, Science, Sports and Culture in Japan, and by Research for the Future of Japan Society for the Promotion of Science (JSPS-RFTF-97P-00101). References Photon energy / eV
1. D.J. Williams, Nonlinear Optical Properties of Organic and Polymeric Materials, ACS Symposium Series 233 (American Chemical Society, 1985). 2. D.S. Chemla and J. Zyss, Nonlinear Optical Properties of Organic Molecules and Crystals (Academic Press, Orlando, 1987). T. Kobayashi, Nonlinear Optics of Organic and Semiconductors (Springer, Berlin, 1989). R.A. Hann and D. Bloor, Organic Material for Non-linear Optics II (The Royal Society of Chemistry, Cambridge, 1991). J. Zyss, Molecular Nonlinear Optics (Academic Press, Boston, 1994). S.R. Marder, W.E. Tomiellas, M. Blanchard-Desce, V. Ricci, GI. Stegman, S. Gilmour, J.L. Bredas, J.L. Greg, U. Bublitz and S.G Boxer, Science 276,1233 (1997). H. Hashimoto, K. Hattori, Y. Okada, T. Yoda and R. Matsushima, Jpn. J. Appl. Phys. 37,4609 (1998). H. Hashimoto, T. Nakashima, K. Hattori, T. Yamada, T. Mizoguchi, Y. Koyama and T. Kobayashi, Pure Appl. Chem. (2000) in press. F. Meyers, S.R. Marder, B.M. Pierce and J.L. Bredas, J. Am. Chem. Soc. 116,10703 (1994). R. Mamies and L. Stryer, Proc. Natl. Acad. Sci. USA 73, 2169 (1976). H. Murakami, R. Morita, M. Yamashita and H. Shigekawa, Jpn. J. Appl. Phys. 38 (1999) 4056. T. Kobayashi, Nonlinear Optics 1,91 (1991). Fig. 4. x (-
3. 4. 5. 6. 7. 8. 9. 10. 11. 12.
Preparation and excitonic properties of high quality organic-inorganic nanocomposite CdSe nanocrystals Kenichi Hashizume 1 , Hitoshi Suzuki 1 , Martin Vacha1-2* and Toshiro Tani 1 1
Department of Applied Physics, 2Venture Business Laboratory, Tokyo University of
Agriculture and Technology, 2-24-16 Naka-machi, Koganei, Tokyo 184-8588, Japan *On leave from Charles University Prague, Czech Republic TOPO (trioctyl phosphine oxide) capped-OdSe nanocrystals were prepared chemically by injecting organometallic reagents into a hot coordinating solvent over a range of optical absorption peaks of 482 ~580nm For United size range of nanocrystals, we have succeeded to synthesize high quality nanocrystals which show fiirly sharp excitonic spectral features, by controlling the particle size with the concentration of precursors. Overcoating of ZnS following the synthesis of CdSe nanocrystals have lead to a large enhancement of the fluorescence intensity (quantumefficiency).
1. Introduction In excitonic material physics, it is significant and fruitful to elucidate exciton natures from both quantum confinement effects and coherent derealization effects in low dimensional mesoscopic systems. One such issue is to study quasi one-dimensional Frenkel exciton systems in linear molecular aggregates represented by J-aggregate, which we are now intensively investigating by microscopic spectroscopy' 1 ). The other is to investigate Wannier exciton systems made from "large artificial molecules" i.e. semiconductor nanocrystals which interact weakly or basically isolated from their surroundings. In order to get further insight into these subjects, it is essential to prepare nanocrystals of high crystallinity and narrow size distribution. Among various types of quantum dot systems, organic molecule capped nanocrystals synthesized as colloids are flexible and interesting. They possess potential applications in various novel fields such as single dot manipulation, incorporation into suitable polymer thin films*2) and fluorescence probe in biological systems' 3 ), formation of higher order structures* 4 ' 5 ) and so on. Two types of approach have been reported so far to prepare nanocrystals with narrow size distribution. In the first case, just after the nucleation of nanoparticles, growth is interrupted by rapid cooling accompanied with the injection of precursors. Keeping at an appropriate temperature between 230~300°C nanocrystals grow slowly, yielding a wide range of sizes* 6 - 7 ). In the second case, precursors of low concentrations are injected at higher temperature, yielding particles of narrow size distribution in a relatively short growth time* 8 , 9 ' 1 0 ). In order to decrease the number of critical parameters in the process and to establish working hypothesis in crystal growth, we have tried to control nanoparticle sizes with changing the concentration of the precursors to be injected into the hot coordinate solvent. Overcoating of ZnS were carried out successively just after the synthesis. In this contribution, we present the preparation of nanocomposite CdSe nanocrystals in detail. Although our approach is fundamentally based on the work by Murray et ai' 6 ), significant modifications are introduced. Preliminary experiments on single nanoparticle spectroscopy of CdSe nanocrystals dispersed in thin polymer films using a low temperature laser scanning GRIN-SIL 209
210 optical microscope'11) were also carried out. 2. Experimental
211
spectrophotometer(JASCO V-570ST) and a fluorescence spectrophotometer (JASCO FP-6500ST) respectively. 3. Results and discussion Prepared CdSe nanocrystals dispersed in anhydrous butanol, which display intrinsic colors corresponding to the particle sizes, are optically transparent and any precipitates are not formed for a long time. Typical optical absorption and fluorescence spectra at room temperature of as prepared nanocrystals are shown in Fig.1. The overall features and the narrow spectral band widths indicate that the size distributions of the nanocrystals are fairly narrow. Size selective precipitation(SSP) is not only unnecessary but also ineffective for these samples. Comparing the narrowest band width 29.0nm (0.12eV) of Figl(a) with those of ref.(5), the size distribution proves to be below 5%. Broad maximum on the low energy side of the fluorescence spectra as shown in the Figl(a) was observed for samples with the absorption peak 482~489nm. These spectral anomalies are due to surface traps of the excitation, which can be eliminated by overcoating wider gap materials such as ZnS or ZnSe'9,12>. Aliquots transferred from the reaction flask just after the injection and several minutes later have revealed that the former contains very small particles which do not flocculate with the addition of excess methanol, while in the latter small particles have already dissipated at all. After a brief period of stability, crystal growth of nanoparticles proceeds again but rather very slowly. This phenomenon maybe caused by Ostwald ripening leads to the broadening of size distribution. These behaviors are consistent with the description of ref (9). Therefore, it is reasonable to control the size of nanocrystals with the concentration of precursors relative to the main solvent TOPO and to take out them during a stable period. A 6X: 430nm R.T.
-^& *
D
Abs Drban
o
J
400
A ~2.0nm
AA / V
•
1 \ (a) \ size:
_ra_
V
(b) ~2.7nm
500 600 700 Wavelength (nm)
Figure 1: Absorption and fluorescence spectra of TOPO capped high quality CdSe nanocrystals (as prepared). Particle size was estimated from the wavelength of the absorption peak by use of the data of ref(6).
400
500 600 700 Wavelength (nm)
Figure 2: Enhancement of the fluorescence intensity due to ZnS overcoating. Although the fluorescence intensity of no coated sample is normalized to the absorption peak, linearity between the two fluorescence spectra holds.
212 Fig.2 shows absorption and fluorescence spectra of no-coated and ZnS-overcoated CdSe nanocrystals respectively. Although the fluorescence intensity of no-coated sample is normalized to the absorption peak, linearity between the two fluorescence spectra holds. Absorption peak of overcoated sample exhibits slight blue shift and broadening Fluorescence intensity is enhanced remarkably by overcoating. <Single dot observation> Preliminary experiments on single nanoparticle spectroscopy of "bare" and ZnS overcoated CdSe nanocrystals dispersed in PMMA[poly(methyl-methacrylate)] thin films were carried out using laser scanning GRIN-SIL optical microscope with high N.A.C1'. In a fluorescence image, several bright area were observed which disappear by the irradiation of a strong laser beam. These area are supposed to be clusters of CdSe nanocrystals. In summary, we achieved relatively easy control of the crystal growth by limitting the amount of precursors injected into the hot coordinate solvent TOPO. By this method, we have prepared CdSe nanocrystals over a range of absorption peakes of 482~580nm, especially high quality nearly monodisperse ones around the absorption peaks of 524~537nm, as seen from the typical absorption and fluorescence. According to the narrow spectral bandwidth, size distribution of as prepared CdSe nanocrystals is estimated below 5%. In fluorescence imaging, several bright areas which are supposed to be the cluster of CdSe nanocrystals were observed. Acknowledgement This work was supported by grant-in-aid of ministry of education, culture and sports (No. 11490008), and also partly supported by Hitachi CRL, NSG and Nakatani Foundations. References (1) M. Vacha, S. Takei, K. Haesented in this conference. (2) S. A. Empedocles, D. J.Norris and M. G. Bawendi: Phys. Rev. Lett., 77 (1996) 3873. (3) W. C. W. Chan and S. Nie: Science, 281 (1998) 2016. (4) B. Murray, C. R. Kagan, and M. G. Bawendi: Science 270(1995) 1335 (5) X. Peng, E. Troy, A. Wilson and A. P. Alivisatos: Angew. Chem. Int. Ed. Engl. 36(1997) 45 (6) C. B. Murray, D. J. Norris and M. G. Bawendi: J. Am. Chem. Soc, 115 (1993) 8706. (7) M. Kuno, J. K. Lee, B. O. Dabbousi, F. V. Mikulec and M. G. Bawendi: J. Chem. Phys., 106 (1997) 9869. (8) J. E. Bowen Katari, V. L. Colvin and A. P. Alivisatos: J. Phys. Chem., 98(1994) 4109. (9) X. Peng, J. Wickham and A. P. Alivisatos: J. Am. Chem. Soc, 120 (1998) 5343. (10) M. A. Hines and P. G. Sionnest: J. Phys. Chem., 100 (1996) 468. (11) M. Vacha, H. Yokoyama, T. Tokizaki, M. Furuki and T. Tani: Rev. Sci. Instrum., 70 (1999) 2041. (12) M. Danek, K. F. Jensen, C.B. Murray and M. G. Bawendi: Chem. Mater., 8 (1996) 173.C. B. (13) B. O. Dabbousi, J. Rodriguez-Viejo, F. V. Mikulec, J. R. Heine, H. Mattoussi, R. Ober, K. F. Jensen and M. G. Bawendi: J. Phys. Chem.,B101(1997) 9463.
ENERGY RELAXATION AND TRANSFER IN TRIMER PAVEL HERMAN Department of Physics, University of Education, V.Nejedleho 573, 500 03 Hradec Krdlove, Czech Republic IVAN BARVIK Institute of Physics of Charles University, Faculty of Mathematics and Physics, Ke Karlovu 5, 121 16 Prague, Czech Republic
We consider the relaxation and transfer in a symmetric trimer coupled to a phonon bath. The energy transfer within the trimer occurs via resonance interactions and coupling between the trimer and the bath occurs via modulation of the monomer energies by phonons. We compare the model introduced by Capek with the Redfield model used commonly with secular approximation. We discuss two initial conditions: a) The highest eigenstate of the trimer is initially excited, and b) the initial excitation is local. We find that the occupation probabilities in the representation of eigenstates are the same in both models. But it is not so for off-diagonal density matrix elements. Only if the off-diagonal elements vanish initially (initial condition a), they vanish at arbitrary time in both models. If the initial excitation is local, off-diagonal elements differ essentially even in the long time limit. 1. Introduction In the previous paper we have investigated relaxation and transfer in symmetric dimer as an archetype for more general situations. 1 In this paper we continue our analysis of the exciton transfer and relaxation by focusing on the exciton dynamics in a trimer as the simplest generalization beyond the dimer. We shall be dealing with an exciton in symmetric cyclic trimer interacting with phonon baths. 1.1.
Hamiltonian
Hamiltonian of our system has the form H = H0 + Hr + Hint,
(1)
where Ho is the system (exciton) part, HT bath part and Hint linear and local exciton phonon coupling. Solution of the Schrodinger equation for the symmetric cyclic trimer with the Hamiltonian
(2) leads to eigenenergies £7 = 2 J, EJJ = Enl 1/^=^(1,1,1),
= — J and eigenstates
|//>r=-L(l,e2fi,e^),
|///>r=-L(l,e=r,e¥).
(3)
In the following we specify the dynamical equations for the exciton density matrix in several different microscopic models and we show that the Redfield model within the secular approximation, usually applied to the optical experiments, could destroy the time dependence of the physical quantities calculated by means of the exciton density matrix p.
213
214 2. D y n a m i c a l Equations for t h e E x c i t o n D e n s i t y M a t r i x 2.1. Local site
representation
Capek's dynamical equations for the exciton density matrix with time dependent coefficients i^nm,qp(t) read 2 -7lPnm(t) m
=J2iuJnm,qp(t)Pqp(t) PQ
iUnm,qp(t) = i£l„m,gp
+ iS^nm,qp(t)
, •
(4)
The first time independent part iQ is given by the coherent part of Liouville superoperator. We shall consider also the second part iSilnmiQP(t), which determines dissipative and relaxation processes, to be, after some initial time interval, time independent. 2 We suppose that each site r has its own independent bath but with the same properties. In this case we parametrize iSQ using three coefficients A, C and D 3
0 0 0 A A 0 A A 0
0 0 0 -A 0 -A -A 0 -A
0 \ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -C -D 0 -D -A -D -C -D 0 0 0 0 -D -C -D -A 0 0 0 0 -D -C -D 0 0 0 -D -c -D 0 -A 0 0 -A -D 0 -D -c) 0
Here we have represented the exciton density matrix as column vector with following ordering of elements (11,22,33,12,13,23,21,31,32). The temperature dependence of parameters A, C and D is entirely different. Parameter A is independent of temperature, whereas parameter C ~ [1 + 2nt(3J)] and parameter D « [1 + rjf,(3J)] (nb(fiuj) is Bose-Einstein distribution of phonons). The Haken-Strobl-Reineker model of Stochastic Liouville Equations (HSR-SLE), 4 which has been many times succesfully used in the exciton transfer problem but very often also out of range of its applicability, has in case of a weak linear local exciton-phonon interaction the dissipation part with only one nonzero parameter C = 270 (in Capek's notation). 2.2. Eigenstate
representation
Equations of motion written for the exciton density matrix in the local site representation are convenient in the exciton transfer problem. On the other hand, dealing with the exciton relaxation a formulation of the dynamical equations for the exciton density matrix in the eigenstate basis (here \I >, \II > and \III >) should be preferred. The oldest way to treat the exciton-bath interaction is perhaps the Redfield model. 5,6 Redfield himself suggested so called secular approximation 5 , 6 , r leading for our hamiltonian to independent time development of each off-diagonal exciton density matrix element in the eigenstate basis. 3. Results To compare different models of exciton transfer in the local site representation as well as in the eigenstate representation, we have to transform equations of Capek and HSR-SLE into eigenstate basis and Redfield equations back to the local site representation. Comparing, in the site local representation, the form of the Redfield's equations within the secular approximation with those of the Capek's and HSR-SLE models we can conclude:
215 (i) There are nonzero elements Tiijji =£ 0 for i ^ j in the Redfield model contrary to Capek's and HSR-SLE models. This means (in the HSR-SLE notation) 7^ ^ 0. But for the linear and local exciton-phonon coupling parameters 7^ should be equal zero.8,9 (ii) In the Redfield model there are nonzero elements Ti-ajj which open the second - incoherent - channel (in addition to the quasicoherent one) of exciton transfer. To display more thoroughly differences between three above mentioned models we compare analytical and numerical solutions of the corresponding dynamical equations of motion for the exciton density matrix (for analytical solution see 3) with two different initial conditions a) excitation into the eigenstate \I >: Pi,i(0) = 1 and pa,^(0) = 0 for a / 7 or /3 ^ I, b) excitation into the local state |1 >: pi,i(0) = 1 and pm,n(0) = 0 for m ^ 1 or n ^ 1. 3.1. Excitation
into the
eigenstate
The diagonal and off-diagonal parts of exciton density matrix (in eigenstate representation) develop in time independently in Capek's and Redfield models. Then in the case of eigenstate \I > initially excited (or more commonly in case of initially diagonal density matrix in eigenstate basis) the time development of the whole density matrix is the same as in Capek's model as in Redfield one. 3.2. Excitation
into the local state
The time development of the eigenstate occupation probabilities is again the same in the Capek's and in the Redfield models. But this is not the case of the off-diagonal exciton density matrix elements in the eigenstate basis. In the Redfield model within the secular approximation, contrary to the Capek's one, each off-diagonal matrix element develops in time independently. The difference in the time dependence of the off-diagonal exciton density matrix elements between Capek's and Redfield models persists till long times t —> 00 and leads to different asymptotic values of p//,///(t-»oo) (Fig-1-)After transformation to the site local basis these diferences show themselves in the diagonal density matrix elements (Fig.l.). 4. Conclusions We have followed time development of the exiton density matrix elements in the eigenstate and in the local site representations to check the best unified picture of the exciton relaxation and its transfer. We have displayed the most interesting results on Fig.l. Summarizing, we can conclude: (i) the eigenstate representation: Exciting trimer to its upper eigenstate, Redfield and Capek's equations describe properly the energy relaxation to the lower eigenstates. Long time asymptotics of the eigenstate occupation probabilities reveal a proper Boltzman distribution. In high temperature limit, the HSR-SLE model leads to slower equilibrization among the eigenstates. Exciting trimer to its local state, main difference between the Capek's and Redfield results is in the real parts of the off-diagonal density matrix elements pnjii- Also their long time asymptotic behaviors are entirely different at low temperatures - see Fig.l. (ii) site local representation: Exciting trimer to its upper eigenstate, the coherence between the local sites is lost more quickly in the high temperature limit, in Capek's model in comparison with the HSR-SLE results. Exciting trimer to its local state, main difference between the Capek's and Redfield results is in site occupation probabilities. Due to spurious incoherent channel, the exciton transfer from site 1 to sites 2 and 3 is quicker in the Redfield model. In high temperature limit, Capek's results follow closer to the HSR-SLE one. Difference between the Capek's and Redfield results for the non-diagonal elements of the exciton density matrix is more pronounced in low temperature limit.
216 The long time asymptotic behaviors of site occupation probabilities show entirely different dependence on the parameter 7 0 .
Fig. 1. Time dependences of the real parts of density matrix elements pi //, PlJII and PIIJH f°r 7o ~ 0-5 (left column) and the occupation probabilities Plli P22 a n d P33 (right column) in the case of initial excitation to the local state 11 > in a) low temperature limit, b) high temperature limit. Results of HSR-SLE model shown only in the high temperature limit. Acknowledgements This work was supported by contracts GACR 202/98/0499 and GA UK 345/1998. While preparing this work P.H. enjoyed a kind hospitality of Professor Michael Schreiber and University of Technology, Chemnitz. References 1. 2. 3. 4. 5. 6. 7. 8. 9.
V. Capek, I. Barvik, P. Herman, J. Chem. Phys. - submitted V. Capek, Physica A203, 520, 495 (1994). P. Herman, I. Barvik, J. Chem. Phys. - submitted P. Reineker in Exciton Dynamics in Molecular Crystals and Aggregates - Springer Tracts in modern Physics, Vol. 94., ed. G. Hohler, (Springer, Berlin - Heidelberg, 1982), p. 111. A. G. Redfield, IBM J. Res. Develop. 1, 19 (1957). A. G. Redfield, in Advances in Magnetic Resonance, Vol 1., ed. J. J. Waugh, (Academic Press, New York London, 1965), p. 1. V. May and 0. Kiihn, Charge and Energy Transfer Dynamics in Molecular Systems, (Wiley-WCH, Berlin, 2000). V. Capek, Z. Physik B60, 101 (1985). E. A. Silinsh, V. Capek, Organic Molecular Crystals. Interaction, Localization, and Transport Phenomena, (Amer. Institute of Physics, New York, 1994).
N O V E L A P P R O A C H T O F A N O R E S O N A N C E OF E X C I T O N S IN S E M I C O N D U C T O R Q U A N T U M WELLS
KEN-ICH HINO Institute of Materials Science, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573, Japan
A new approach to Fano resonance of excitons in quantum-confined systems is presented based on the 4 x 4 Luttinger Haniiltonian. This method, consisting of two stages, namely, the adiabatic expansion and the R-matrix propagation, allows to implement highresolution calculations of Fano profiles having natural spectral widths without any empirical broadening parameter which is indispensable in conventional methods. As a demonstration, this approach is applied to Fano resonance of an exciton in a wide quantum well, where hole-subband mixing is substantial and a complicated energy-structure is expected. Resulting spectral profiles show rich fine structures due to overlap with adjacent resonances and the hole-subband mixing. 1. Introduction Fano resonance (FR) of excitons in semiconductor heterostructure is generated by interference between a discrete state belonging to one subband-pair (termed as a channel) of an electron and a hole and energetically degenerate continua pertaining to other subbands. Pronounced asymmetric spectral profiles characteristic of F R have been observed in various quantum-confined systems. 1 This effect is accurately understood by solving "the multi-channel scattering (MCS) problem" of the excitons at each given energy E under an incoming scattering-wave (ISW) boundary condition imposed at an asymptotic exciton-radius p O J . There are a great number of theoretical works reported thus far. 2,3 However, excitonic spectra obtained in most studies 2 are approximated variationally by a set of "pseudo-continuum" states having discrete eigenvalues and being independent of E. Thus the correct boundary condition imposed on the MCS states is disregarded from the beginning. Furthermore, the resulting spectra are fairy crude due to necessity of incorporating an empirical broadening parameter. As a result, employment of such approximations hampers detailed and accurate analysis of FR. On the other hand, a couple of attempts 3 have been made thus far of solving the MCS problem under the proper boundary condition, for instance, by use of a Green function approach in a real space and a finite difference method in a momentum space. In these works, nevertheless, an interaction between a heavy hole (HH) and a light hole (LH) due to hole-subband (HS) mixing is neglected in spite that importance of this effect is already well-recognized in a bound state problem. 4 Moreover, ability of these methods seems quite limited for rather pushed numerical accuracy and for applicability to larger-scale calculations of such a complicated exciton system as is concerned here. Generally speaking, intensive computational efforts are necessary for solving the MCS problems mostly due to propagation of wavefunctions up to a large distance, pa„ and still larger-scale calculations are required where HS mixing is indispensable. Quite recently, the author has found conspicuous change in asymmetry of Fano profiles of excitons due to the HS mixing, by virtue of the adiabatic expansion combined with the R-matrix propagation technique, based on the 4 x 4 Luttinger Hamiltonian. 5 The first purpose of this article is to outline this novel approach, allowing high accuracy calculations having numerical stability, without needing any empirical broadening parameter. Details are shown in §2. The second is to demonstrate competence of it by implementing large-scale MCS calculations of excitons in a wide single quantum well of GaAs/Al e Gai_ I As, where the HS mixing is substantial and a complicated energy-structure is expected. The calculations are given in §3, followed by discussion. The atomic units are used
217
218 throughout unless otherwise stated, aside from employment of the Rydberg unit for energy. 2 . Theoretical Framework A set of exciton coordinates (p, Q) is defined as follows, p is a distance of an electron and a hole projected onto a layer-plane and Q consists of other three variables: the two are z-coordinates of the electron and hole and the other is an in-plane angular coordinate. A center-of-mass motion in the layer-plane is separated. The 4 x 4 Luttinger Hamiltonian is represented as
H(P, a) = «W(ii) ^
+ «W(n)i ( ^ - ^ ) + « w ( « ) ^ + « ( « «),
(i)
where explicit expressions of operators a'*' (fc = 1 ~ 3) and an adiabatic Hamiltonian H are given in Eqs. (2.3)-(2.6) of Ref. 6. The i/-th envelope function *P„(p, fJ) satisfying an effectivemass equation [E — H] "J>„ = 0 is expressed by the adiabatic expansion
* v (*n) = £*„(/>; n)/^(p).
(2)
Here $^ is the /i-th adiabatic channel-function with an adiabatic potential Up, given by \U,,(p) — H(p; fi)]$/i(/); fi) = 0 at a fixed p. {F^} (p., v = 1 ~ N) is a set of radial functions to be determined, where the number of channels incorporated in Eq. (2) is denoted as N. Let the whole p-space [0,pa>] be divided into NR sectors, namely, S„ = [p„,pn+i] (n = 1 ~ NR) with pi = 0 and PivH+i = pat- The above effective-mass equation is recast in 5„ into * „ = [HL - E}-1 L * „ ,
(3)
where Hi(p,fl) = H{p,Q) + L(p,SI). Here the Bloch operator L, defined by L(p,Sl) = -S(p-pn+1)C(pn+uCl) + S(p-pn)C(pn,Q) with £(p,fi) = a W ( n ) ^ + | ( V 2 ' ( f i ) + a<3>(fi)) , has been introduced in order to enforce hermiticity on Hz, in 5„, while H is no longer hermite there. A set of wavefunctions {tpk} with the associated eigenvalues {£/,} are provided by solving [£k — Hztyk = 0 in 5„ by use of the adiabatic expansion similar to Eq. (2) in combination of the discrete variable representation (DVR). 6 Putting the complete set {ipk} into the midst of the right-hand side of Eq. (3) yields F„„(p) = £ £ [G^(p, Pn+1)Fl(pn+1) - G^(p,p„)F^{pn)] , where a propagator has been defined as G,a,(p,p') = Jlk^k(p)(E — £k)~1J:ki,(p') with F^„(p) = ( $ ^ ( p ; n ) | £ * „ ( p , f t ) ) n and T^p) = (*„(p;ft) \i>h(p,Sl))n. Here, < • • • >n means an integration over SI. Introducing the R-matrix, defined by Rliv(p) = - 2 { F^(p) \Fd(p) | , into the above expression of F^p) provides 5 pn+iR(p„+i) = G ( p n + i , p n + i ) - G ( p n + i , p „ ) — - j — r — —
r-G(p„,p„+,)-
(4)
This formula gives a forward propagation of the R-matrix from the one edge-point p„ to the other one p„+i within Sn. Thus the R-matrix R(pNx+i) a t t h e asymptotic distance is obtained by iterative application of Eq. (4) from the origin pj up to pjv„+i. F(pa.) is represented by a linear combination of two independent matching functions £<*) as: F^pa.) = £${pa.) - EfLi £rf\p™) £{„(£). £$ correspond to incoming and outgoing solutions of [E — ha3] £ = 0, where ha, is a N x N asymptotic Hamiltonian derived from Eq. (1). A matrix S is evaluated by inserting this expression of F(pa,) into R(pat) obtained by Eq. (4). On the other hand, there are N„ independent solutions, {FJ~}} (a = 1 ~ N„), for the present MCS problem, where JV„ is the number of open channels at a given E(> Ui(oo)). The ISW boundary condition imposed on them reads Fj^(pa,) = £<j^}(pat) — Y,(=i ^ (pas) 5^~'(E) for open channels (p. = 1 ~ N0) and F^~}(pa.) = 0 for closed channels (p. = Na + 1 ~ N). S<~'
219 is a scattering matrix. F^(paa) is expressed as a linear combination of N solutions of F(pa3): F(~) = FC. A N x N„ matrix C and further i>H are represented in terms of matrix elements of S. Once F ( ~ ' (pa,) is obtained, the backward propagation from pa, to the origin generates F'~'(0) and thus associated oscillator strengths f(E) concerned here. The present method consists of two stages. One is the adiabatic expansion. This allows us to minimize the number of the adiabatic channel functions, since these are eigen functions of the adiabatic Hamiltonian H with appropriate physical meanings, as discussed in detail in Ref. 6. The other is the R-matrix propagation technique. Since a size of each sector S„ is chosen arbitrarily small, it is possible to provide the R-matrix basis set {if>k} large enough to satisfy the closure relation, and the associated eigen values {efc} extending to extremely high energies. This contributes to numerical stability as well as high accuracy. Furthermore, oscillator strengths for "all" given E,& are obtained at a stroke just by a single calculation of R in the whole /j-space, since the propagator G(p, p') at every E is represented by the common R-matrix basis set. This advantage fulfills a decisive role to reduce a great deal of calculation time. In addition, for evaluating radial functions of this R-matrix basis set, the D VR is utilized, which provides an optimal point-wise basis set based on the Gaussian quadrature. This recipe also serves to somewhat facilitate large-scale computations. 3 . D e m o n s t r a t i o n and D i s c u s s i o n Figure 1 shows calculated results of oscillator strengths 1(E) of a rf-exciton in a single quantum well of GaAs/Al0.3Gao.7As having a well width 500 A, with and without HS mixing. Here / has been denned as / divided by fh/Eg with fa and Eg an oscillator strength for an interband transition of GaAs and its band-gap, respectively. Because of such a wide well width, an energy
104 X E
(Ry)
Fig. 1. Calculated absorption spectra of excitons in a single quantum well GaAs/Alo.3Ga07As with a well width 500 A as a function of E(> Ui(oo)) of a difference of energies between an incident photon and a band gap of GaAs. A solid line and a dashed line show results with and without HS mixing, respectively. Labels of manifolds are as follows. A : [1,3]'', B : [2,2] K , a : [1,1]', 6' : [1,2]\ c : [1,2]', d' : [2,1]\ e' : [1,4]", / : [2,1]'.
220 structure of this system is quite complicated and the HS mixing is substantial. These calculations are done with setting N=50, NR=60 and p o ,=5000 a.u. and a 40-point DVR basis set is adopted. A sector size of S„ is 50 ~ 100 a.u. Here each manifold for a HH-exciton (a LH-exciton) is designated as [rae,nfl]'*'''. Optically active even-parity HH-excitons are denoted as capital letters, A and B, while LH-excitons, optically induced by at least a first-order HS mixing, are as small letters, a,c,--- and odd-parity HH-excitons, optically induced by at least a second-order HS mixing, are as primed small letters, b',d', • • •. Here A(ls) and some states belonging to a are bound states, not F R states. As is seen in this figure, absorption spectra including HS mixing are quite complicated, compared with those excluding it. Energy intervals of channels in the present wide quantum well are so small as to cause effective interference between F R states belonging to different manifolds, resulting in marked overlap resonance. Such an effect becomes striking when an additional complexity due to the HS mixing is involved. According to Fano's resonance-formula for a number of bounds states embedded in a single continuum, 7 it is easily indicated that overlap resonance gives rise to conspicuous change of each spectral position, width and peak height from those of a corresponding isolated profile. A profile of B(ls) differs considerably from its counterpart excluding the HS mixing, especially, in a resonance width. Moreover, profiles seen around 4.0 x 1 0 - 4 Ry, probably pertaining to Rydberg series of A, are entangled. It is speculated that these profiles result from interplay between even-parity HH exciton states of A and B and LH exciton states of c. The HS mixing would also contribute to overlap resonance of B(2s) with odd-parity HH exciton states of d'. Furthermore, due to this effect, an oscillator strength for A(2s) is enhanced a lot and optically inactive excitons states of a, V and c manifest themselves with strong intensity. To summarize, a novel method by virtue of the R-matrix propagation and the adiabatic expansion is presented for the MCS problem of excitons in a quantum well. This method allows to implement large-scale calculations with high accuracy and numerical stability, and provides a Fano profile having a natural spectral width because of requiring no additional broadening parameter, which is necessary in usual methods. This sophisticated approach is applied, as a demonstration of its competence, to F R of excitons in a wide quantum well, where an energy structure is complicated and HS mixing is significant. It is found that overlapping with adjacent resonance states enriches structure of Fano profiles in close combination with the HS mixing. Acknowledgements This research is financially supported by Grant-in-Aid for Scientific Research (C) from the Ministry of Education, Science, Sports and Culture of Japan. References 1. D. Y. Oberli, et al., Phys. Rev. B 49, 5757 (1994); P. E. Simmonds, et al., Phys. Rev. B 50, 11251 (1994); S. Bar-Ad, et al., Phys. Rev. Lett. 78, 1363 (1997); C. P. Holfeld, et al., Phys. Rev. Lett. 8 1 , 874 (1998). 2. S. Glutsch, et al., Phys. Rev. B 54, 11592 (1996); Glutsch and F. Bechstedt, Phys. Rev. B 57, 11887 (1998); R. Winkler, Phys. Rev. B 5 1 , 14395 (1995) and see also references cited therein. 3. M. Graf, P. Vogl and A. B. Dzyubenko, Phys. Rev. B 54, 17003 (1996); A. N. Forshaw and D. M. WhiMaker, Phys. Rev. B 54, 8794 (1996) and see also references of this group cited therein. 4. D. A. Broido and L. J. Sham, Phys. Rev. B 3 4 3917 (1986); U. Ekenberg and M. Altarelli, Phys. Rev. B 35 7585 (1987); B. Zhu and K. Huang, Phys. Rev. B 36 8102 (1987). 5. K. Hino, Phys. Rev. B (in press). 6. K. Hino, J. Phys. Soc. Jpn. 69, 836 (1998). 7. U. Fano, Phys. Rev. 124, 1866 (1961).
E X C I T O N S IN COLLOIDAL Cul PARTICLES D I S P E R S E D IN A KI CRYSTAL
T. HIRAI, K. EDAMATSU and T. ITOH Graduate School of Engineering Science, Osaka University, Toyonaka 560-8531, Japan Y. HARADA Applied Physics, Osaka Institute of Technology, Osaka 535-8585, Japan S. HASHIMOTO Faculty of Science, Osaka Women's University, Sakai 590-0035, Japan We have investigated the luminescence spectra of colloidal Cul particles dispersed in a KI crystal under low- and high-density excitations of the Cul particles at low temperatures. Under the low-density excitation, we have observed the luminescence of both confined and bulk-like exciton transitions in the Cul particles with zincblende and two kinds of hexagonal structures. In the bulk-like particles with the zincblende structure, the emission line of bound excitons with small binding energy of ~ 5 meV has been recognized. The biexciton luminescence has been observed under the high-density excitation. We discuss the origins of the various excitonic states observed in the Cul particles dispersed in the KI crystal.
1. I n t r o d u c t i o n A lot of studies have been conducted on the optical properties of colloidal cuprous halide particles dispersed in alkali halide crystals so far. These studies have mainly focused on the confined excitonic states in CuCl nano-particles dispersed in an NaCl crystal. In contrast, there have been few studies for other cuprous halide particles dispersed in alkali halide crystals. In the present work, colloidal Cul particles dispersed in a KI crystal have been studied. We have investigated the luminescence spectra of the colloidal Cul particles under low- and highdensity excitations at low temperatures. In Cul crystals with zincblende structure, it is known that the radiative recombination of the free excitons, whose binding energy is 62 meV, appears at 3.057 eV 1 . Furthermore, there coexist the exciton transitions attributed to the zincblende and two hexagonal structures: wurtzite and another hexagonal one 2,3 ' 4 . Under the low-density excitation of the Cul particles dispersed in the KI crystal, we have observed the luminescence which originates from both the confined and bulk-like excitons. As to the bulk-like excitons in the particles with the zincblende structure, the emission lines of the free exciton and only one bound exciton have been recognized. Under the high-density excitation, the biexciton luminescence has been observed. In this paper, we discuss the origins of the various excitonic states found in the colloidal Cul particles dispersed in the KI crystal. 2. E x p e r i m e n t a l A bulk crystal of KI doped with Cul by 1 mol% was grown by the Kyropoulous method. A piece of the crystal was annealed at 800 K for 6 hours in Ar atomosphere. For the low- and high-density excitations, a He-Cd laser (325 nm) and a N 2 laser (337 nm) were used as excitation sources, respectively. The photoluminescence was detected by photon counting photomultiplier or CCD, after passing through a grating monochromator (focal length 75 cm). For the time-resolved photoluminescence, the second harmonic light (370 nm) of a mode-locked ThSapphire laser was used as an excitation source. The photoluminescence was detected by a grating monochromator (focal length 32 cm) equipped with a photon couting streak camera. By analyzing the image of the streak camera, the decay profile of the photoluminescence was obtained.
221
222 —
:
1
—
1
—
1
1
1
1
—
•
—
1
—
1
-—
i — • — i — > — i — <
IIK
bulk-like exciton
- He-Cd laser (325nm) excitation -
2.6
2.7
2.8
J
< \
"
i
1/
/ y
2.9
.
/ i .-
I
/
-
/
DA pair transition
2.5
j. 1
? <
before annealing after annealing
/
r
A/
2 I ! »/W :
H,
k
'. IIL-1 k 3
3.1
3.2
3.3
3.4
3.5
Photon Energy (eV) Fig. 1. Emission spectra of colloidal Cul particles dispersed in a KI crystal before (solid line) and after (broken line) annealing under a He-Cd laser (325 nm) excitation at 11 K. The arrows indicate the transition energies of the excitons in zincblende (Z1]2), wurtzite (Wi,W2) and another hexagonal (Hj,!^) structured Cul bulk crystals.
3. Results and Discussion Figure 1 shows the emission spectra of the KI crystal dispersed with the Cul particles before (solid line) and after (broken line) annealing under the He-Cd laser excitation at 11 K. The arrows indicate the transition energies of the excitons in zincblende (Zi]2), wurtzite (Wi,W2) and another hexagonal (Hi,H2) structured Cul bulk crystals2'3. In both of the spectra, one can see the emission line of the bulk-like excitons in the Cul particles with the zincblende structure. As for the crystal before the annealing, the broad emission band around 2.95 eV is due to a donor-acceptor pair transition1'5. Moreover, it has been concluded that the emission band peaking around 3.1 eV is associated with the confined states of the Z [i2 excitons6. On the other hand, for the annealed crystal, the emissions ascribed to the bulk-like excitons and donor-acceptor pairs become weak. This fact suggests that, by the annealing, most of the particles become smaller and almost free from the impurities7'8. Consequently, the emissions at the higher energy side of the Z1|2 exciton line are attributable to the confined excitonic states. However, they seem to be strong at the higher energy side rather than the confined Z 1 2 exciton band. Additionally, the same is the case for the absorption bands. This is probably because the confined excitons of the two hexagonal structures (W and H excitons), which have larger in transition energy than those of the zincblende structure, become strongly mixed2,4. It implies that, by the annealing, the Cul particles are possible to transform into the .hexagonal structures. Fig. 2(a) exhibits the emission spectra focused on the bulk-like excitons in the crystal before the annealing at different temperatures (11 ~ 100 K) under the He-Cd laser excitation. At 11 K, another weak emission line appears as a shoulder on the higher energy side of the intense emission line peaking at 3.052 eV. Above 77 K, the emission line of the higher energy side becomes dominant over that of the lower energy side. The higher energy component shifts to lower energy side and becomes weaker with increasing temperature up to 300 K. Judging from the exciton binding energy of 62 meV in Cul crystals (zincblende), this emission line is attributed to a free exciton. On the other hand, the lower component disappears above 100 K. Accordingly, it is assigned to a bound exciton. The intense emission lines ascribed to bound
223
3.04
3.05
3.06
3.07
Photon Energy (eV)
Fig. 2. (a) Emission spectra of the crystal before the annealing at various temperatures (11 ~ 100 K) under the He-Cd laser excitation, (b) Decay profile of the bound exciton line at 11 K with use of the second hormonic light of a mode-locked Ti:Sapphire laser (370 nm). excitons with such small binding energy of ~ 5 meV, however, has never been reported in the bulk and thin Cul crystals so far1,5,9. Figure 2(b) illustrates the decay profile of the bound exciton line at 11 K. From the analysis of the profile, it is found that it contains short decay component of ~ 90 ps. Generally, the decay times of the excitons bound to impurities such as acceptors and donors in bulk crystals are about several hundred picoseconds. Compared with the impurity-bound excitons, this bound exciton has small binding energy (~ 5 meV), short decay time (below 100 ps) and long tail in the lower energy side of the spectrum. These features suggest that the bound excitons are quite similar to the "surface bound excitons" which have been proposed for ZnO bulk crystal exposed to air10. On the analogy of the surface bound excitons, it is possible that the excitons are shallowly bound near the interface between the Cul particles and the KI matrix. Figure 3(a) shows the emission spectra of the crystal before the annealing at different excitation powers with use of the N2 laser at 11 K in the vicinity of the Z1>2 exciton line. The excitation power of the N2 laser is about 100 kW/cm 2 at 100 %. Fig. 3(b) is the emission spectrum at the weak excitation power with use of the He-Cd laser at 11 K. Under the highdensity excitation, at least two new emission bands as indicated by the arrows appear more than 10 meV below the bound exciton line. Integrated intensity of the whole new bands grows super-linearly with increasing the excitation power. Since the new bands are located at the higher energy side of the emission bands due to an exciton-exciton or an exciton-electron scattering, they are considered to be assigned to the biexciton11,12. In fact, the energy position of the highest component corresponds to that of the M band ascribed to the biexciton in Cul thin films12. Next, the emission spectra of the crystal at different temperatures (11 ~ 100 K) under the N2 laser excitation at 100 % are shown in Fig. 3(c). As the temperature increases, the lower component of the new bands weakens drastically, while the higher component remains up to 100 K. It should be pointed out that the behavior of the lower component resembles that of the bound exciton line mentioned above. In addition, it is confirmed that the intensity of the lower component saturates as the excitation power increases, just similar to the case of the bound
224
2.95
3.00
3.05
Photon Energy (eV)
3.10
2.95
3.00
3.05
3.10
Photon Energy (eV)
Fig. 3. Emission spectra of the crystal before the annealing at various excitation powers with use of (a) a N2 laser (337 nm) and (b) the He-Cd laser at 11 K. (c) Emission spectra at different temperatures (11 ~ 100 K) under the N2 laser excitation. exciton line. Therefore it should be related to the bound excitons. In other words, it might be attributed to a bound biexciton.13 In summary, we have investigated the luminescence spectra of colloidal Cul particles dispersed in a KI crystal under high- and low-density excitations at low temperatures. Under the low-density excitation, the luminescence of the confined and bulk-like excitons in the Cul particles with two hexagonal as well as zincblende structures has been observed. It is possible that the annealing makes the Cul particles transform from zincblende into hexagonal structures. In the bulk-like Cul particles with the zincblende structure, the intense emission line of a bound exciton has been recognized at about 5 meV lower than the Zi,2 exciton line at 11 K. On the grounds that the bound exciton has character quite similar to the surface bound exciton, the exciton is likely to be shallowly bound near the interface between the Cul particles and the KI matrix. Under the high-density excitation, the new emission bands have been observed more than 10 meV below the bound exciton line. These emission bands are probably attributed to a free biexciton and a bound biexciton. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.
T. Goto, T. Takahashi and M. Ueta, J. Phys. Soc. Japan 24, 314 (1968). M. Cardona, Phys. Rev. 129, 69 (1963). A. Goldmann, phys. stat. sol. (b) 81, 9 (1977). A. Tanji, I. Akai, K. Kojima, T. Karasawa and T. Komatsu, J. Lumin. 87-89, 516 (2000). V.A. Nikitenko and S.G. Stoyukhin, Opt. Spectrosc. 54, 111 (1983). T. Itoh, Y. Iwabuchi and T. Kirihara, phys. stat. sol. (b) 146, 531 (1988). K.P. Johansson, G. McLendon and A.P. Marchetti, Chem. Phys. Lett. 179, 321 (1991). H. Kanzaki and Y. Tadakuma, Solid State Commun. 80, 33 (1991). D. Kim, M. Nakayama, O. Kojima, I. Tanaka, H. Ichida, T. Nakanishi and H. Nishimura, Phys. Rev. B 60, 13879 (1999). V.V. Travnikov, A. Freiberg and S.F. Savikhin, J. Lumin. 47, 107 (1990). C.I. Yu, T. Goto and M. Ueta, J. Phys. Soc. Japan 34, 693 (1973). I. Tanaka, M. Nakayama and H. Nishimura, Meet. Abs. Phys. Soc. Jpn. 54, Issue 2, Part 4 (1999), p.675. M. Nakayama, H. Ichida and H. Nishimura, J. Phys. :Condens. Matter 11, 7653 (1999).
TRTANSITION FROM BIEXCITONS TO ELECTRON-HOLE PLASMA IN PHOTOLUMINESCENCE PROPERTIES OF A G a A s / A l A s MULTIPLE-QUANTUM-WELL S T R U C T U R E
H. ICHIDA, K. TSUJI, K. MIZOGUCHI, H. NISHIMURA, and M. NAKAYAMA* Department of Applied Physics, Faculty of Engineering, Osaka City University Sugimoto 3-3-138, Sumiyoshi-ku, Osaka 558-8585, Japan We report photoluminescence (PL) properties under various excitation-power conditions in a GaAs (15.0 nm)/AlAs(15.0 nm) multiple-quantum-well structure. We have clearly observed the PL bands from the biexciton and electron-hole plasma, and estimated the biexciton binding energy and the band-gap renormalization in the electron-hole plasma. The spectral change of the PL bands as a function of the excitation power demonstrates the transition from the biexciton to the electron-hole plasma under intense excitation conditions. 1. Introduction In quantum wells (QWs) and superlattices, optical properties under intense excitation conditions have been extensively studied from the viewpoint of the formation of excitonic molecules (biexcitons) and electron-hole plasmas. For the biexciton, the enhancement of the binding energy due to quantum-confinement effects has been attracted much attention from the first photoluminescence (PL) 1 and theoretical 2 studies. Recently, quantum-beat experiments 3 ' 4 and quantum-Monte-Carlo calculations 5 have revealed the precise characteristics of the biexciton in GaAs QWs. The electron-hole plasma, which corresponds to a collective phase of ionized dense electrons and holes, also has been the subject of considerable investigations from the aspect of many-body effects6: the band-gap renormalization, phase-space filling, and optical gain. However, the transition from the biexciton to the electron-hole plasma in PL properties has not been clearly revealed, which is a key subject for high-density-excitation phenomena. In the present work, we have investigated the PL properties under various excitation-power conditions in a GaAs (15.0 nm)/AlAs (15.0 nm) multiple quantum well (MQW) from the viewpoint of the formation of the biexciton and electron-hole plasma. We discuss the characteristics of the biexciton and electron-hole plasma by analyzing the shape of the PL bands. 2. E x p e r i m e n t a l The sample is a GaAs (15.0 nm)/AlAs (15.0 nm) MQW with 20 periods grown on a (001) GaAs substrate by molecular-beam epitaxy. The excitation source for PL measurements was a frequency-doubled YAG laser with the pulse width of 800 ps and maximum pulse power of ~ 1 fij. The PL spectra were analyzed using a CCD multi-channel detection system attached to a 32-cm single monochromator with a resolution of 0.5 nm. The sample temperature was 5 K, which was controlled using a closed-cycle helium-gas cryostat. 3. R e s u l t s and discussion Figure 1 shows the excitation-power dependence of the PL spectra in the GaAs/AlAs MQW at 5 K. In the excitation-power region <400 n j / c m 2 , we observe the growth of a doublet PL structure having an energy spacing of ~ 2 meV. The higher-energy PL band labeled X is attributed to the free exciton PL. The lower-energy PL band labeled M exhibits the superlinear dependence for the excitation power. The M-PL band has a low-energy tail, which is a typical
'Correspondence author: M.Nakayama, [email protected]
225
226 -GaAs(15.0 nm)/AIAs (15.0 nm) MQW pulsed-YAG (SHG) excitation EHP
1.52
1.54
1.52
1.56
Photon Energy (eV)
Fig. 1. Excitation-power dependence of the PL spectra in the GaAs (15.0 nm)/AlAs(15.0 nm) MQW at 5K.
1.53 1.54 Photon Energy (eV)
1.55
Fig. 2. Results of the line-shape analysis (broken line) of the exciton (X) and biexciton (M) PL bands, where the open circles indicates the experimental spectra, and the inset indicates the dependence of the M-PL intensity on the X-PL intensity.
characteristics of the biexciton PL: so-called an inverse-Boltzmann-type distribution. Thus, we consider that the M-PL band results from the biexciton-emission process. In order to confirm the formation of the biexciton, we analyze the doublet line shape of the X- and M-PL bands as shown in Fig. 2. The line shape of the biexciton-PL band is given by the following equation7: exp[-(Ex IM{TU*>) OC
l+
- Eb -
hu>)/(kbTeff)
exp{-(Ex-Eb-hw)/rM]
(1)
where Ex is the exciton energy, Eb is the biexciton binding energy, Tejf is the effective temperature, and the denominator represents the two-dimensional (2D) like density of states with a broadening factor of TM- In the line-shape analysis of the exciton PL band, we use an ordinarily Boltzmann type distribution function. From the line-shape analysis of the exciton- and biexciton-PL bands, we obtain the biexciton-binding energy of 1.8±0.2 meV. The inset in the Fig. 2 shows the integral PL intensity of the biexciton as a function of that of the exciton. We clearly observe the superlinear relation of IM oc Ix7. The binding energy is consistent with the recent results of the exciton-biexciton quantum-beat experiment4 and quantum-Monte-Cairo calculation5. In the excitation-power region >10 ^J/cm 2 in Fig. 1, it is obvious that the new PL band labeled EHP remarkably grows with a threshold nature in the low-energy side of the biexcitonPL band labeled M. As the excitation power is increased, the peak energy of the EHP band shifts to the low-energy side. The energy shift is considered to be due to the band-gap renormahzation originating from many-body effects. If the new PL band originates from the liquid phase, its energy hardly depends on the excitation power because of the carrier-concentration conservation peculiar to the liquid phase6. From the above feature of the EHP band, we consider that the EHP band originates from the electron-hole plasma. We note that the electron-hole plasma and exciton system, which are classified to the gas phase, are not coexistent because of the phase diagram. However, they were simultaneously observed as shown in Fig. 1. This is considered to be due to the following fact in the present experiment. The intensity of the excitation-laser beam has a spatial inhomogeneity with the Gaussian-type beam, so that the formation of the electron-hole plasma is occurred around the center of the laser beam under
227 GaAs(15.0 nm) /AIAs(15.0nm)MQW 1 mJ/cm2 5K
1.52 1.54 Photon Energy (eV)
1.56
Fig. 3. Results of the line-shape analysis of the EHP band, where the open circle indicates the experimental spectrum, and the solid line depicts the total lineshape fit. the intense-excitation conditions. The excitons and biexcitons are formed in a different region of the electron-hole-plasma formation, which corresponds to the outskirts of the laser beam. From Fig. 1, it is evident that the electron-hole plasma is formed under the excitation condition two-order higher than that for the biexciton-PL intensity comparable to the exciton-PL one. Next, we discuss the line shape of the EHP band. The line shape of the electron-hole plasma is given by the following equation taking account of the energy and momentum conservation8:
W ( M oc fJdEedEhfe(Ee)De(Ee)fh(Eh)Dh(Eh)5(huj -Ee-
Eh)6(ke - kh)
(2)
where f(E) is the Fermi distribution function, D(E) is the density of states which is the 2D like form same as Eq. (1), and the subscripts e and h indicate the electron and hole, respectively. Using Eq. (2), we have analyzed the line shape of the EHP band with the following fitting parameters: a renormalized band-gap energy (E'), a carrier concentration (nc) giving a quasiFermi energy, and an effective temperature (T3^p). The effective masses of the electron and hole were obtained from ref. 9. Fig. 3 shows the results of the line-shape analysis of the PL spectrum at 1 mJ/cm 2 in Fig. 1. The line-shape analysis includes the electron-hole plasma (EHP), exciton (X), and biexciton (M) bands. Moreover, we assume another PL band labeled P. The total line-shape fit almost corresponds to the experimental spectrum. If we neglect the P band, the total line-shape fit is insufficient in the energy region between the M and EHP bands. From Fig. 3, the energy difference between the P- and X-PL band is about 6 meV. This energy difference consists with that between the n=l and 2 excitons, 7 meV 10. Therefore, we consider that the P band results from the exciton-exciton scattering, so-called P2 emission11. The details of the P band are beyond the scope of the present paper. The fitting parameters for the EHP band in Fig. 3 are £^=1.515 eV, n c =2xlO u cm"2, and Tfff=35 K. In Fig. 3, some mismatch remains on the high-energy side of the X-PL band and the low energy side of the EHP band in the line shape analysis. On the high-energy side of the X band, we have to take account of the contribution of the light-hole exciton. We consider that the tail on the low energy side of the EHP band results from the Landsberg-type broadening due to electron collision processes12. Finally, we discuss the band-gap renormalization in the electron-hole plasma. In Fig. 4, we depict the band-gap renormalization (AEg) as a function of the carrier concentration obtained from the line-shape analysis. From the theory of many-body effects, the relation between the band-gap renormalization and carrier density is given by AEg = —anlJ3 in a 2D system13. The
228
o E
J-10
•
Theptritical fit BGR estimated from the line-shape analysis
1
i
o
I -20
& ™ -30 0.5 1 1.5 2 Carrier concentration (xlO11 cm'2)
Fig. 4. Band-gap renormalization as a function of the carrier concentration estimated from the line-shape analysis. The solid line indicates the theoretical fit according to ref. 13. solid curve in Fig. 4 indicates the fitted result with a=4.8 meV. According to the ref. 13, a in the 15-nm GaAs QW is estimated to be ~3.5 meV. In the present work, the value of a is affected by ambiguity of the line-shape analysis of the PL band. In summary, we have clearly observed the formation of the biexciton and the electron-hole plasma as a function of the excitation power in the GaAs (15.0 nm)/AlAs (15.0 nm) MQW. The spectral change of the PL bands as a function of the excitation power demonstrates the transition from the biexciton to the electron-hole plasma under intense excitation conditions. It is found that the electron-hole plasma is formed under the excitation condition two-order higher than that for the biexciton-PL intensity comparable to the exciton-PL one. Prom the line-shape analysis of PL spectra, we have estimated the biexciton binding energy and the band-gap renormalization in the electron-hole plasma. Acknowledgements This work is supported in part by a Grant-in-Aid for Scientific Research on Priority Areas, "Photo-induced Phase Transition and Their Dynamics", from the Ministry of Education, Science, Sports and Culture of Japan. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.
R. C. Miller, D. A. Kleinman, A. C. Gossard, and O. Munteanu, Phys. Rev. B 25, 6545 (1982). D. A. Kleinman, Phys. Rev. B 28, 871 (1983). D. Birkedal, J. Singh, V. G. Lyssenko, J. Erland, and J. M. Hvam, Phys. Rev. Lett. 76, 672 (1996). S. Adachi, T. Miyashita, S. Takeyama, Y. Takagi, A. Tackeuchi, and M. Nakayama, Phys. Rev B 55, 1654 (1997). T. Tsuchiya and S. Katayama, Solid State electron. 42, 1523 (1998). For a review, see H. Kalt, optical Properties of III-V Semiconductors, Springer Series in Solid State Sciences 120 (Springer, Berlin, 1996) p.41, and references for electron-hole plasmas in QWs therein. R. Cingolani, Y. Chen, and K. Ploog, Phys. Rev. B 38, 13478 (1988). M. Capizzi, S. Modesti, A. Frova, J. L. Staehli, M. Guzzi, and R. A. Logan, Phys. Rev. B 29, 2028 (1984). S. Adachi, J. Appl. Phys. 58, R l (1985). L. C. Andreani and A. Pasquarello, Phys. Rev. B 42, 8928 (1990). C. Klingshirn and H. Haug, Phys. Rep. 70, 315 (1981). G. Trankle, E. Lach, A. Forchel, F. Scholz, C. Ell, H. Haug, G. Weimann, G. Griffiths, H. Kroemer, and S. Subbanna, Phys. Rev. B 36, 6712 (1987). S. Schmitt-Rink, D. S. Chemla, and D. A. B. Miller, Adv. Phys. 38, 89 (1989).
TIME-RESOLVED SPECTROSCOPY OF KI UNDER ONE-PHOTON EXCITATION BY AN ArF EXCIMER LASER NOBUKO ICHIMURA* Department of Physics, Graduate School of Science, Osaka University Toyonaka, Osaka, 560-0043, Japan HISAO KONDO Department of Physics, Faculty of Science, Ehime University Matsuyama, Ehime, 790-8577, Japan SATOSHI HASHIMOTO Department of Environmental Sciences, Faculty of Science, Osaka Women's University 2-1 Daisen-cho Sakai, Osaka, 590-0035, Japan We investigated the absorption spectra of KI under excitation by an ArF excimer laser at 11 K. The laser light excited the sample through a one-photon process. Stable F centers were formed with excitation at a power level above ~2 mj/cm2. From the time-resolved absorption spectrum, it is evident that the F centers are generated within 50 ns after the time of initiation of the laser pulse. The width of the F band at 50 ns was broader than that of the stationary F band at 11 K, suggesting the temperature increase of the crystal. We discuss the relaxation process in KI under dense electronic excitation.
1. Introduction Point defect generation in alkali halide crystals has been extensively studied.1 The temperature dependence of the yields of F center formation is qualitatively anticorrelated with that of self-trapped exciton (STE) luminescence in the case of some alkali halides including KI and Rbl.2 F center formation at low temperatures in alkali iodides scarcely occurs under conventional irradiation conditions, such as X-ray and electron beam irradiation, because of the very low formation yield, 10~ 4 ~10 -6 . 3 According to the results of studies on nanosecond electron-beam radiolysis and picosecond laser photolysis, at 20 ns after the time of initiation of the pulsed electron beam, the main products are the lowest triplet state STE below 95 K. 4-6 Between 95 K and 140 K, the lowest triplet state STE is mainly produced, and slight production of F centers occurs simultaneously. Above 140 K, both are still produced with a rapid formation time. At 200 K, the transient absorption of the lowest triplet STE is not observed but the F band is observed at 20 ns.5'6 However, it has been reported that coloration at low temperatures occurs under dense electronic excitation in the case of Rbl due to the interaction between free exeitons and STE.7 Experiments on dense electronic excitation have been performed using two- (or more-) photon excitation in most cases. The density of F centers formed with two-photon excitation was estimated to be ~10 16 cm - 3 . The aim of this work was to investigate the relaxation process in KI under dense electronic excitation by an ArF excimer laser whose wavelength falls in the band-to-band transition region at 11 K. The excitation density of the ArF excimer laser is three orders of magnitude larger than that of a pulsed electron beam. We found that the stationary F band was observed at a laser power level above ~2 mj/cm2 and that the maximum density of F centers was ~10 20 cm -3 . Moreover, we measured the time-resolved absorption spectra of F centers in KI at 11 K. F centers were generated within 50 ns after the time of initiation of the laser pulse and the transient absorption of the lowest triplet state STE was scarcely observed. The width of the F band just after the laser pulse became broad in comparison with that of the stable F band at 11 K. This result suggests an increase in the temperature of the crystal.
2. Experimental Procedures We examined two kinds of KI crystals. One was a usual bulk crystal having a free surface. An ultra-pure KI single crystal was obtained from the University of Utah. Another was a thin crystal grown from the melt in a narrow gap between two quartz plates prepared in our laboratory.8 Since the quartz plates prevented emission "e-mail: [email protected]
229
230 of atoms or products from the surface even under high-power laser irradiation, the absorption spectra of the F band could be measured with a good S/N ratio.9 The results obtained in experiments on the thin crystals are reported here. The thickness of the thin crystals was about 0.3 /xm. The sample was irradiated with an ArF excimer laser whose wavelength and pulse duration were 193 nm and 15 ns, respectively. The maximum laser power per pulse was ~40 mJ/cm2, and the minimum was ~0.1 mJ/cm2. As the wavelength of the laser corresponds to the band-to-band transition region, the sample was excited through a one-photon process. The depth of penetration of the laser beam was only 0.05 /jm, which is much smaller than the thickness of the thin crystals. Supposing the colored region to be 0.05 pm, the density of the F centers was determined. The sample was cooled to 11 K by means of a conduction type cryostat. A Xe flash lamp with a pulse duration of ~1 ^s was used as the light source to measure the absorption spectra. Optical signals were detected through a monochromator equipped with an intensified CCD. The time resolved spectrum at the delay time of 50 ns was observed after initiation of the laser pulse with a gate width of 100 ns, where 0 ns is the time of starting the laser pulse. The time resolution of the optical system, that is, the time required to observe a change in absorption, was about 7 ns.
3. Results Figure 1 shows the absorption spectra of F centers in a thin KI crystal at 11 K. The spectra were measured after ~1 minute of laser excitation at various power levels. The number of irradiation shots at each power level was 100. The density of F centers was saturated above 100 shots. Thus, the absorption spectra show a saturated absorption intensity for given laser power levels. The F band was not observed at low power levels. It began to appear above ~2 mJ/cm2. The saturated absorption intensity increases rapidly with increasing laser power. The density of F centers at 8.4 mJ/cm2 is 2.3xl020 cm - 3 which is up to 2.0 % of the density of the matrix ions. Under usual irradiation conditions, such as X-ray or electron beam irradiation, stable F centers are not generated at low temperatures.
20mJ/cm
(c) stable
1.3mJ/cm
jjfylUMW*****^^ 0.32mJ/cm2 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 Photon Energy (eV) Fig. 1. Absorption spectra of stable F band in the thin KI crystal at 11 K. Laser pulses of 100 shots were irradiated for each excitation power. The optical density of F bands shows the saturated absorption intensity.
1,5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 Photon Energy (eV) Fig.2. Absorption Spectra at 50 ns after the onset of the laser pulse (a) and at 1 (is (b). In addition, the stable F band at 11 K is shown in (c). These bands are normalized at their maximum intensities.
231 Time-resolved absorption spectra of F centers at low temperature are shown in Fig.2. The delay time from the time of initiation of the laser pulse was 50 ns for (a) and 1 /is for (b) at a laser power level of 20 mJ/cm 2 . In addition, the stable F band at 11 K is shown in (c). In Fig.2(a) there is a broad band peaking at 1.78 eV. The width of the broad band becomes narrow at 1 /is. After a long delay time, the width coincides with that of the F band at 11 K shown in Fig.2(c). Thus, the broad band in Fig.2(a) and (b) is deemed to be the F band. This result shows that stable F centers are formed within 50 ns after initiation of the laser pulse. From the fact that the width at 50 ns is broader than the width of the stable F band at 11 K, an increase in temperature of the crystal is suggested to occur immediately after laser excitation. The temperature can be estimated from the width of the F band. In a previous study, after initiation of a pulsed electron beam at 10 K an absorption band due to the lowest triplet state STE peaking at 1.69 eV was observed. 6 In Fig.2(a), an isolated absorption band was not observed at about 1.7 eV, although broadening of the F band was evident. The transient absorption of the lowest triplet STE did not appear at 50 ns under excitation at a power level of 20 mJ/cm 2 . To determine the laser power dependence of the temperature increase, the absorption spectra at 50 ns of a " colored KI" crystal were measured at various laser power levels at 11 K, and the results are shown in Fig.3. The thin KI crystal was colored at a power level of 9.1 mJ/cm 2 with 100 irradiation shots. As the density of the F centers in the colored KI crystal was already saturated, the integrated area of the F band scarcely increased under successive excitation by the laser pulse. The laser power was varied from 0.40 to 26 mJ/cm 2 . At 0.40 mJ/cm 2 the half width of the F band is 0.15 eV which is equal to that at 11 K. Above ~ 2 m J / c m 2 the width becomes broad and the peak position shifts to the low energy side with increasing laser power, as seen in the figure. At 26 mJ/cm 2 , the width of the F band is 0.31 eV from which the temperature is estimated to be 225 K. It was found that the temperature increase at 50 ns begins above ~2 mJ/cm 2 and it becomes large with increasing laser power. The broad F bands in Fig.3 become narrow with the lapse of time. Here r is denned as the time required until the width of the F band at 50 ns returns to that of the stable F band at 11 K. At 2.9 mJ/cm 2 , T isS fjs. r becomes large with increasing laser power, r is more than 100 /JS at an excitation power level of 26 mJ/cm 2 . Since r is much longer than the 15 ns pulse duration of the ArF excimer laser, the temperature during the pulse seems not to exceed the temperature just after initiation of the laser pulse.
| »
HalfWidlh
o
3
8
Density
3
•8
1.7 1.8 1.9 2.0 2.1 2.2 2 3 Photon Energy (eV) Fig.3. F bands measured at 50 ns after initiation of the laser pulse at various power levels in the colored KI crystal. Coloration was made by the excitation at power level of 9.1 mJ/cm2 with 100 irradiation shots.
10°
101
102
Laser Power (mJ/cm2)
Fig.4. The saturated F density (closed circles) and the half width of F band at 50 ns after the time of initiation of the laser pulse (open circles) are plotted as a function of laser power.
232 4. Discussion It is noted that the formation of stationary F centers at 11 K occurs under excitation by an ArF excimer laser at power levels above ~2 mj/cm2. The saturated density and the half width of the F band at 50 ns are shown in Fig.4 on the same abscissa of laser power. From the results shown in Fig.l and 3, we obtained this figure, where the density is shown as closed circles and the half width is shown as open circles. The finding that the width is more than 0.15 eV means that the temperature of the crystal is higher than U K , because the half width of the F band at 11 K is 0.15 eV. Thus, an increase in temperature occurs above ~2 mJ/cm2. It can be clearly seen that there are threshold power levels for both the generation of the stable F center and the increase in temperature. Moreover, these two threshold values are the same. Consequently, it is suggested that the interaction between electronic excitations which arises from dense electronic excitation by the ArF excimer laser above threshold power level is closely related to formation of the F center and to an increase in temperature of the crystal. The conversion yields from photon energy to F centers and to heat energy were determined in order to consider the mechanism of relaxation of the absorbed photon energy. From the experimental results on the density of F centers vs. the number of shots, the conversion yield of F centers was calculated to be 0.01 for the first shot at an excitation power level of 9.1 mj/cm2. At this power level, the temperature is estimated to be 160 K from the F band width. On the other hand, the yield of the heating is 0.51, which is roughly calculated from the increase in temperature from 11 K to 160 K and the specific heat of KI. The heating energy is 3.5 mJ/cm 2 . It is estimated that the absorbed photon energy in KI is 6.8 mJ/cm2, where the reflection loss and the absorption coefficient of KI are taken into consideration. Half of the absorbed photons are consumed in the lattice heating. Since the absorbed photon energy per unit volume is three orders of magnitude larger than the energy of the pulsed electron beam, the photon energy may transfer efficiently to the lattice heating channel. The yield of the residual excitation energy is 0.48, which includes that of the radiative decay channel. We preliminarily measured the time-resolved luminescence spectra of STE at 11 K. The it and a luminescences were observed under excitation at various power levels from 0.1 to 40 mJ/cm2. In the power dependence of the intensity and decay time of the ir luminescence, there were no discontinuous changes at ~2 mJ/cm2. The relative yield of the it luminescence continuously decreases with increasing laser power, and is almost complementary to the result shown in Fig.l. As shown in Fig.2, transient absorption due to the lowest triplet STE was scarcely observed at a laser power level of 20 mj/cm 2 . The temperature just after the laser pulse at this power level was estimated to be 200 K, whereas the ir luminescence is not usually observed above 120 K.10 Thus, it is expected that the n luminescence does not appear at an excitation power level of 20 mJ/cm2. However, the •K band was observed even at high laser power. The dense electronic excitations make it possible efficiently to relax to the radiative decay channel of the lowest triplet state STE. Further experimental studies are now in progress.
References 1. N. Itoh, Adv. Phys. 31, 491 (1982). 2. N. Itoh, T. Eshita and R. T. Williams, Phys. Rev. 34, 4230 (1986). 3. D. Pooley and W. A. Runciman, J. Phys. C: Solid St. Phys. 3, 1815 (1970). 4. R. T. Williams and M. N. Kabler, Phys. Rev. 9, 1897 (1974). 5. M. Hirai, Y. Suzuki, H. Hattori, T. Ehara and E. Kitamura, J. Phys. Soc. Jpn. 56, 2948 (1987). 6. T. Karasawa and M. Hirai, J. Phys. Soc. Jpn. 39, 999 (1975). 7. K. Tanimura and N. Itoh, Phys. Rev. Lett. 60, 2753 (1988). 8. S. Hashimoto and M. Itoh, J. Jpn. Appl. Phys. 27, 726 (1988). 9. N. Ichimura, H. Kondo, Y. Harada and S. Hashimoto, J. Lurmn. 87-89, 586 (2000). 10. M. Ikezawa and T. Kojima, J. Phys. Soc. Jpn. 27, 1551 (1969).
O R D E R FORMATION A N D ELEMENTARY EXCITATIONS IN TYPE-II QUANTUM-WELL EXCITON SYSTEM T. Iida and M. Tsubota Department of Physics, Osaka City Sumiyoshi-ku, Osaka 558-8585,
University Japan
The ordered state and the elementary excitations are theoretically studied in an interacting dilute quasi-two-dimensional Bose gas of excitons in a type-II quantum well. This system is advantageous for studying the macroscopic quantum phenomena because those excitons have a long lifetime of the order of 10 -6 s, and their transport mechanism can be directly studied in experiments by observing electric current since the excitons consist of spatially separated electron-hole pairs. Using the obtained dispersion relations of excitations, we examine the Landau criterion for exciton superflow and the temperature dependence of the off-diagonal long-range order which characterizes the quasi-Bose-Einstein condensation in two-dimensional systems. Keywords: exciton, quantum-well, Bose-Einstein condensation, superfluidity 1. Introduction The assembly of excitons is an important candidate system for the study of the connection between Bose-Einstein statistics and superfluidity. Recently, Fortin et.al. 1 investigated the exciton system in CU2O by measuring the time- and the space-resolved spectroscopies. They found the supersonic ballistic exciton propagation over a macroscopic distance. This ballistic propagation has been interpreted from the two different stand points. One interpretation is based on the Bose-Einstein condensation and the transition of exciton gas to a superfluid state. Another interpretation is based on the phonon wind model in which excitons are dragged in the crystal by a flow of nonequilibrium ballistic phonons. 2 So far, the conclusive experimental evidence verifying the transport mechanism of excitons has not yet been obtained. In the experiments done so far, the amplitudes of the macroscopic wavefunctions have been studied. However, in order to obtain an unambiguous evidence for the superfluidity of excitons, the information about the phase of the macroscopic wavefunction is essentially important. As an advantageous candidate for this purpose, in the previous work 3 , we have proposed an exciton system in a type-II quantum well(QW) irradiated by a weak laser light, in which the spatial dependence of the phase in the ordered state is determined by the sine-Gordon (SG) equation, and showed that a possibility of the direct observation of superfluid motion of excitons associated with the spatial structure of the phase. In this paper, on the basis of the results obtained in Ref.[3], we study the elementary excitations when the ground state is the ordered state determined by the SG equation. We examine the Landau criterion for the superflow of the excitons and discuss the temperature dependence of the off-diagonal long-rage order. To investigate such problems is very important not only in the field of exciton physics but also in wide field of physics, since the similar problems have arisen in such diverse physical situation as theory of low temperature physics, dislocation theory and field theory with broken symmetry. 4 In order estimates, we adopt the parameter values appropriate to the excitons in GaAs/AlAs type-II QW assuming the exciton density to be n0 ~ 10 11 c m - 2 . 3 2. Basic Equations Let us consider many-exciton system in a type-II QW which is irradiated by a weak laser light. We adopt a simple model system of type-II QW in which electrons and holes are confined separately within two adjacent layers with the same thickness L. The claddings of both layers are assumed to be formed by high-barrier materials. The 2 axis is taken along the growth direction.
233
234 The exciton-exciton interaction plays an essential role to obtain the stable condensed state of excitons. In Ref.[3], we have studied the exciton-exciton interaction, Wx, and found that Wx can be taken to be repulsive when L is smaller than a critical thickness Lc; Lc ~ 28A in GaAs/AlAs type-II QW. 3 After eliminating the time dependence of the interaction with the laser light by a proper unitary transformation, we find that our system is described by the Hamiltonian of the translational motion of excitons in the xy plane. We introduce the condensate wavefunction *P(f) where f is the position vector in the xy plane. The wavefunction satisfies the Gross-Pitaevskii equation with the source term due to the interaction with the weak laser light whose coupling constant is gi = \gi\ exp(ix). When the condition |<7L|/"O WX
v«,
J d
W
2 /
where 2(j>(f) = 6(r) + x and A = k y no/2M\gi\. We consider the small fluctuation of phase around that for the stable state,
2 A 2 ^dx22f i = sin2^oW
dx
= 0,
(2)
n=boundary
where £ = 8|fft| v /noA 2 . The second order term SF^ is the potential energy due to the fluctuation. In order to find spectra of the excitations, it is necessary to take into account the kinetic energy term. Then, the equation of motion for the ip field is easily obtained as follows:
(f/s 2 )¥W
d2
]P_
dx2
dy2
tp + 2V(x)
(3)
where 77 = £/A 2 and s is the first sound velocity in the exciton system. On the basis of the basic equations (2) and (3), we will study the ordered state and the elementary excitations of the condensed excitons. 3. Ordered State The ordered state at T = OK is determined by (2). We have studied this problem in Ref.[3]. In this report, we briefly summarize the results for completeness of our discussion. The SG equation has conserved quantity, Ej = \2(d4>o/dx)2 + (1/2) cos2 1/2 and (b) —1/2 < ET < 1/2. In the case (a), the solution is given by cos
, AT2 = ET + - , 0 < k2 < 1
(4)
235 where the function sn refers to the Jacobian elliptic function. Using (4), we have the supercurrent
..... , ,. . .. .- dn x ,k) , MkX k~X' which shows a spacial oscillation with the periodicity a(k) = 2\kK(k) supercurrent
(3)
J(x) =
and causes the net
(6) J=l['Ax)dx = ^ ! o , a Jo Ma where K(k) is the complete elliptic integral of the first kind. From the boundary condition (2), we have the relation J„ = Jc/k where Jc = 2e'hn0/MX. Furthermore, we see that the solution (4) is possible only when JCT > Jc from the upper limit of k (see (4)). The creation and destruction of excitons via the interaction with the weak laser light causes the effective interlayer current IT, which is calculated to be IT = {Ze'^lgd/h) sm(2
1
1
Jex/Jc
- (a)
1.1
^fT
1.3 1.4
0.5
a(k)
0
0.5
1
S -
.
iJ(d) ^(c)
P(B)
'
^r
^ S
(b) 1.2 -(c) (d)
1
-
•
1.5
'
Fig. 1. Vortex-lattice for JeK > /„.
Fig. 2. Dispersion relations of elementary excitations.
4. E l e m e n t a r y E x c i t a t i o n s Let us consider the elementary excitations when the ground state is the ordered state of the vortex-lattice when Jex > Jc. Substituting (4) into (3), we have the explicit expression of potential and see that it has the translational symmetry with the period of a in the x direction and is unifoum in the y direction. Then we may put
236 with V in Fig.3, where \
I
i
A /V A
(b) 0
i
0.8
i
a,
1
"
/ \ -
iT i ~
(c)T
_
i
i
i
i
i
0
5
10
15
20
x'(=x/kX) Fig. 3. Potential V/bi (a) and amplitudes \fclh? (b), Ivc/hl2 (c) at qr = j t , m « / 2 when Jtx/Jc = l l - ' i , *i a r e constants.
i
0.6
L-^"^
/S^ V
_
/S
-
0.4 0.2 -
1
i
0.9
v /s J_ — 1
1 1.1 J
_
s 1 1.2 /J
1 1.3
1.4
ex Fig. 4. Landau criterion. vr,: critical velosity. u,: superfiow velocity of the excitons. s: sound velocity in the exciton system.
It is necessary for the stable superfiow that the velocity vs is smaller than the Landau critical velocity v^. Using the calculated dispersion relations, we examine this criterion and find that the necessary condition is satisfied when Jex/Jc > 1 as shown in Fig.4. So far, we confine our discussion within the case of T = OK. To proceed to the case of finite temperatures, it is important to study the temperature dependence of the phase coherence, that is, the temperature dependence of the correlation function, which is the essential quantity to characterize the quasi-Bose-Einsten condensation in two dimensional systems. By using the explicit expressions of tp's, the correlation function is calculated as follows: < * ( r ) f f (0) >
oc < exp[-i(tp(r)
- y(0))] > « exp -A-
.kBT
-G)
(7)
where a = A(kBT/2n£), A is a quantity related to the amplitude \XqJ, which can be approximately regarded as a constant of the order of 0 ( 1 ) at low temperatures; £/kg is estimated to be ~ IK. Thus, in our system, the correlation function tends to zero as r -> 0, but only according to a power law, and more slowly at low temperatures. Such a power-law decay of the correlation function means that our system has the quasi-long-range order at finite temperatures. 7 In order to discuss the phase transition at finite temperatures, we have to take into account another mechanism. We have studied this problem by introducing the defect-mediated KosterlitzThouless mechanism and showed preliminary results in Ref. [8]. Further detailed study at finite temperatures will be presented in a future work. References 1. 2. 3. 4. 5. 6. 7.
E. Fortin, S. Fafard, and A. Mysyrowicz, Phys. Rev. Lett. 70, 3951 (1993). G. A. Kopelevich, S. G. Tikhodeev, and N. A. Gipps, Sov. Phys.-JETP 82, 1180 (1996). T. Iida and M. Tsubota, Phys. Rev. B60, 5802 (1999). K. Huang, Quantum Field Theory, (John Wiley & Sons, INC.,1998). E. T. Whittaker and G. N. Watson A Course of Modem Analysis (Cambridge Univ. Press, London, 1999). B. Sutherland, Phys. Rev.B8, 2514 (1973). L. D. Landau and E. M. Lifshitz, Statistical Physics 3rd ed. (Butterworth-Heinemann, Oxford, 1980), p. 436. 8. T. Iida and M. Tsubota, J. Lumin. 87-89, 241 (2000).
ENHANCED POWER-LAW SINGULARITY B Y L I G H T FIELD I N Q U A N T U M W I R E S
JUN-ICHIINOUE* Department of Basic Science, University of Tokyo and CREST(JST) 3-8-1 Komaba, Meguro, Tokyo 153-8902, Japan AKIRA SHIMIZU Department of Basic Science, University of Tokyo and CREST(JST) 3-8-1 Komaba, Meguro, Tokyo 153-8902, Japan
We discuss an interplay of light field and electron interactions in one-dimensional systems. After constructing the Hamiltonian that includes the effect of a pump beam, probe absorption is discussed using the linear response theory with the bosonization technique. This describes a nonlinear optical property of the system. We show that (1) the absorption spectrum of the probe beam follows a power-law and (2) the power depends on the intensity of the pump beam, where electron correlation plays important roles. The result can be applied to other response functions, e.g. for transport phenomena. 1. Introduction Recently, nonlinear optical responses are extensively studied for correlated electron systems 1 . Although many interesting phenomena are reported experimentally, theoretical treatment for them has difficulties. These come from almost inability to obtain eigenenergies and eignefunctions of excited states, which are indispensable for calculation of nonlinear response functions in the conventional perturbation theory 2 . We proposed in our previous paper a method to discuss nonlinear optical responses, pumpprobe spectroscopy, without using excited states eigenfunctions, where a one-dimensional two band system consisting of electrons and holes was discussed 3 . Although, this is not the model for correlated electron systems, we believe that it would be the first step for the study of them. In the present paper, we discuss an interplay of light field and electron interactions in onedimensional systems by applying the method. With the use of the bosonization method 4 , we discuss absorption spectrum of a probe beam with coherent pumping under the conditions that (i)the interactions are restricted to the ones at the Fermi points, (ii)the interaction strengths between electrons (ee), holes(ftft), and electron-hole (eh) are identical, (iii)the shift of the Fermi points due to coherent pumping is small, and (iv)the band reconstruction due to a pump beam does not occur. We obtain the explicit expression of the spectrum nonperturbatively and show that the spectrum follows a power-law, whose exponent is enhanced by a pump beam. This effect is out of a scope of the usual perturbation theory 2 . 2. P u m p Built-in Hamiltonian We consider a one-dimensional system with a conduction and a valence band separated by energy gap Eg, where electrons and holes are distributed in thermal equilibrium, respectively. When a coherent pump beam with frequency u)p is irradiated off-resonantly, the system is virtually excited. The system is described by the following Hamiltonian in a rotating frame 5 : ( k2
k2
\
'Present address: Center for Frontier Science, Chiba University, Inage, 1-33 Yayoi-cho, Chiba 263-8522, Japan.
237
238 + Y, \(ck,ad-k,-a + H.c.) + nint{{c\
c, A!*, d}),
(1)
k,a
where A = Eg — UJP and A is a coupling constant of the pump beam and the matter. The interactions, which are not explicitly presented here, are restricted in the forward scatterings between ee, hh, and eh near the Fermi points, respectively. It is because the interactions in one-dimensional systems are dominated by the contribution near the Fermi points. What we discuss is absorption spectroscopy of a probe beam from this system under coherent pumping. Our strategy is as follows3: we treat the system and the pump beam as a new "system", and obtain a linear response from this "system" by using the linear response theory. For the purpose, we eliminate the third term of the Hamiltonian (pump term) by successive Bogoliubov transformation and obtain the following Hamiltonian: Umg —>Hpb = J2 ( ^ 7 + A J 4 , A „ + £ ir^dlj^ k,a \Zme
I
k,a
Zm
+ Hint({c\ c, d\ d}).
(2)
h
The fact that the pump term is eliminated is shown by iterative relations between before and after the transformation. The features of the transformed Hamiltonian are (l)the effect of the pump beam is renormalized into the masses of an electron and a hole, and the band gap, and (2)the form of the interaction is unchanged. This Hamiltonian contains the effect of the pump beam, so it should be called "pump built-in Hamiltonian (PBH)". Applying the linear response theory to PBH, we can obtain the response function of a probe beam, which is a nonlinear response of the original system. 3. Absorption Spectrum In order to obtain the absorption spectrum, we calculate a current-current correlation function at T = 06. Correlation functions in one-dimensional systems are found to follow a power-law. Since the exponent of the power-law is one of the most important quantities, we discuss the behavior of the exponent of the absorption spectrum against the pump beam intensity. Defining the current operator as ^ = £ ( c M < U , - * + H.c.), (3) k,a
the absorption spectrum of a probe beam is represented as I{w)<x. I''dtet iut(P(t)P(Q)).
(4)
For calculation of the correlation function, we use the standard bosonization technique of one-dimensional systems4. In the bosonization, dispersion relations are linearized around the Fermi points to yield two branches, which are denoted by r(right branch) and /(left branch), respectively. Since in the present case, the interactions are restricted into forward scattering, the scattering amplitude is described by two constants, gi{= g" = g%h = gf1), which is for the scattering from two r(l) particles to r(l), and #2(= <7fe = 02A = 92*)> which is for the scattering from r particle and I particle to r and I respectively. In the bosonization, a single particle is described by two degrees of freedom: the one corresponds to charge density and the other does to spin density, both of which are completely decoupled and the obtained Hamiltonian is equivalent to the one of a harmonic oscillator. In the present case, there are two kinds of particles, an electron and a hole, and the two are coupled via Coulomb interaction. This is decoupled by "rotation", and the decoupled "electron(c)" and "hole(d)" have "charge"(j = 1) and "spin" (j = 2) degrees of freedom, respectively. Using the bosonization, I(UJ) is expressed in the form of I(u) ~ (jv(£Pi-P)+i 'pjjg exponent Vl&pump) IS
\{
— + (^)ygj - 2«^j
(5)
239
4g2/A=4g4/A = 0 . 1 /
0.04
/
0.03
/
T) 0.02
^
0.01
/
/
____^----^'^
No interaction
5
0
10
15
20
2
pump intensity (a.u.) Fig. 1. The exponent of the power-law of absorption spectrum as a function of pump beam intensity. Solid line is for interaction case, and dotted line for no interaction case.
with the following notations:
- tan
¥>i
CD eld
9i
- f c F9r
„cW
aeiy^ COS ifij
•
COS Ifij
— sin ipj
sin
COS ifij
•?±^
9i ~92 2n ' „c(d)» , 92 + 9i
c{d)*
1-K
V^f
- sin
sin
(6)
• vpgf
W9i
(7)
(8)
F9J
•vfrafl-
c(d)*
,Xd)*
•vfr], _
94-92
•W _ ,Ad> ._ 92 + gt 92 2TT '
92 + gi
0,
(9) (10) (11) (12)
where vCp '* is the Fermi velocity of an electron (a hole) including the effect of a pump beam. The exponent against the pump beam intensity is plotted in the Fig. 1. As shown in the figure, the exponent is enhanced by the pump beam. In comparison with the result without interactions {g2 =
240 arguments \J 1 ± U/Vp. Since, U and Vp depend on a pump beam, so does the exponent under irradiation of a pump beam. In the present model, U = U due to the equality of ee, hh, and eh interaction strengths. The "renormaUzation" of the Fermi velocity plays crucial roles for the enhancement. This renormaUzation originates from two effects: the one is the AC Stark effect7 and the other is interaction effects. The main contribution to the renormaUzation comes from the former effect. However, this does not mean that the interaction effects are not essential for the enhancement, because even if the Fermi velocity is quite renormalized, the exponent will not depend on a pump beam when U = 0. The one-dimensional system discussed here can be realized in a quantum wire made of semiconductors. The two bands are either the lowest conduction subband and the highest valence subband, or the second and the first subbands of the conduction bands. The latter case is more likely to realize coherent pumping. 5. Further Problems In the present model, the renormaUzation of only the Fermi velocity plays important roles among two renormalizable quantities. This fact is related to the assumption of identical interaction strengths. It is an interesting problem when the three interaction strengths are different from each other. Once PBH is constructed, one can calculate other types of correlation function, if advantages of bosonization are fully exploited. This means that we can discuss other physical quantities, such as the effect of a pump beam on transport properties. This is one of the most interesting problems along this study. 1. H. Kishida, M. Matsuzaki, H. Okamoto, T. Manabe, M. Yamashita, Y. Taguchi, and Y. Tokura, Nature 405, 929 (2000). 2. Y. R. Shen, The Principles of Nonlinear Optics (Wiley&Sons, New York, 1984). 3. J. Inoue and A. Shimizu, J. Phys. Soc. Jpn. 68, 2534 (1999). 4. R. Shanker, in Low-Dimensional Quantum Field Theories for Condensed Matter Physicists — Lecture Notes of ICTP Summer Course, eds. S. Lundqvist, G. Morandi and Y. Yu (World Scientific, Singapore, 1995). 5. T. Iida, Y. Hasegawa, H. Higashimura and M. Aihara, Phys. Rev. B 47, 9328 (1990). 6. G. D. Mahan, Many-Particle Physics (Plenum. New York, 1993). 7. S. Schmitt-Rink and D. S. Chemla, Phys. Rev. Lett. 24, 2752 (1986).
T H E T H I R D O R D E R N O N L I N E A R S U S C E P T I B I L I T Y OF I N T E R A C T I N G ONE-DIMENSHONAL FRENKEL EXCITONS
H. Ishihara and T.Amakata Department of Physical Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan An analytical expression of the third order nonlinear susceptibility x' 3 ' has been derived rigorously for a system of interacting Frenkel excitons in a one-dimensional chain of size TV with the periodic boundary conditions. It has been clarified that the magnitude of interacting potential between excitons strongly influences the size dependence of x' 3 ' in the long wavelength approximation, which is well explained in terms of the cancellation effect between the contributions from [ground state] - [one-exciton] transitions and those from [one-exciton] - [two-exciton state] transitions. 1. I n t r o d u c t i o n In the weak excitation limit, the excitonic nonlinearity in confined systems remarkably depends on the system size and shape, which is related to the spatial structure of coherently extended wavefunctions of excitons. Especially, there has been a great deal of interest in the explicit size enhancement of the third order nonlinear susceptibility x' 3 ' • This effect is explained with the mechanism of size linear enhancement of the oscillator strength 1 , 2 , which works in the size region where the long wavelength approximation (LWA) is valid. If the coherent length of excitons is much smaller than the wavelength of the resonant light, the enhancement is saturated at a certain size due to the various scattering mechanism in samples. For a system of non-interacting Frenkel excitons, where the Pauli exclusion effect alone is introduced as a source of nonlinearity, the enhancement and saturation of x ' 3 ' near [ground state] - [oneexciton] (0-1) transitions has been explained consistently in terms of the cancellation between the contributions of opposite signs, namely those from (0-1) transitions and those from [oneexciton] - [two-exciton] (1-2) transitions 3,4 . However, for the interacting excitons, this aspect has not been studied sufficiently though x' 3 ' for interacting Frenkel excitons has been discussed in some cases 5 - 7 , where the resonant poles for bound two-exciton states (biexcitons) appear. Thus, in this contribution, we derive rigorously the analytical expression of x^3' of interacting Frenkel excitons in a periodic one-dimensional chain with the size N to study how the excitonexciton interaction Hex-ex influences the size dependence of x ' • 2. T h e M o d e l and Calculation As a model system that allows us an exact treatment, we consider one-dimensional Frenkel excitons with periodic boundary condition. The Hamiltonian is
J=0
N
JV+1
N+l
Ho = Yl
£
o a l a J ~bYl(a]-\aj
+ a j a J - i ) - V X)a)a]ajaj
j=l
j=l
N
-6^2a)a)+iajaj+u
(!)
j=0
where a] and a.j are the creation and annihilation operators of an exciton on the j-th. site, So the excitation energy of each site, b the transfer energy. As for V in the third term, we take the limit of V —> oo after the calculation to introduce the Pauli principle being based on the hard-core boson approach that is justified rigorously in the recent work by G. Juzeliunas and J. Knoester 8 . The fourth term expresses the interaction between two excitons on adjacent sites. The polarization operator and exciton-radiation interaction are expressed with this Hamiltonian, respectively, as follows,
241
242 P,(t) H'(t)
= exp(iH0t){-
= exp{iH0t)Pj
exp{-iH0t),
£ E PnFn(s) exp(-iujst n
(2) + 7 i ) } exp(-M0t),
(3)
s
where 7 = 0 + the factor for adiabatic switching of the electron-radiation interaction and Fn(s) the amplitude of the electric field at site n with frequency UJS. In the above expression, P, = Maj + M*aj, M being the transition dipole moment per site. By means of the standard perturbation expansion method, we calculate the third order polarization in the form
Pf] = E E E E E E « P H ( ^ + « . + « • + ZmFi{p)Fm{q)Fn{s)xtH.»v^"s), l
m
n
p
q
(4)
s
where XjiLn ls the third order nonlinear susceptibility. The eigenfunctions and eigenenergies of one-exciton states are \k>=-^^exp(zkj)a}\0>
(5)
E1(k)=e0-2bcosk,
(6)
where | 0 > is the ground state, k the wavenumber. Since V and 8 do not affect the total wavenumber of the two-exciton states K, we expand the eigenfunctions of the two-exciton states of the system (1) as
\K,\>=j;cix)\K,k>,
(7)
/t
where | K, k > is the two-exciton state with the wavenumber of the relative motion k in the case of V = 0 and 6 = 0. T h e allowed values of K and k axe {A', k) = {2(n + m)/N, 2(n m)/N}, where n and m take {0, ± 1 , . . . , ±iV/2} for even N, and {0, ± 1 , . . . , ±(N-1)/2} for odd N. Since the matrix elements of the third and fourth terms in (1) between \ K,k\ > and \ K,k2 > is separable in terms of kt and ki, we can solve the eigenvalue problem performing the summation over k by an integral in the complex k plane, and obtain the condition that the eigenvalues E2(K, A) = 2e0 - 46cos K cos A
(8)
satisfies, where A is the wavenumber of the relative motion of the two-exciton states. In terms of the energy eigenvalues of one-excitor states (6) and two-exciton states (8) and the dipole matrix elements, \k>
=
M(l/NY'2exp{ikl)
K, A >
=
2M(1/Nf/2
<0|P,
(9)
E £ C f ' exp {-ik'l') exp{iK(l' * c
+ I)} cos k(l' - Z),(10)
we can write the explicit expression of x • m this stage, x includes k and A summations, which can be performed by the contour integral again. From the resultant terms, we pick up the most resonant terms (triply resonant terms) of the pump-probe process and simplify the expression using LWA. T h e final expression is _
(3) XLWA(U)
S(P, b,6)4b sin P
-
2M
+
2M
{ j E
,i(0)_a;_ir}2
•4 S(P,b, ,5)46 sin P {E1(0)-u>-2iT}2
7
r
1 2
r
_J_ T T2 l T
'
i-y - 2{E1{0) - OJ - iT} iT{E1(0)-u}-if}{E1(0)~oj-iT}
-iT + 2{E1{0) -
u-iT} 2
;r{£1(o)-u;-;r}
(11
where 1
''
6tan(A-p/2) + ^ { ( c o s f - l ) 2 / s m P + t a n ( i V P / 2 ) ( c o s P - 2 ) } >~ -b + 6{cosP + smPt<m{NP/2)}
[
'
243 P = cos _ 1 {(e 0 + 2b-co1
P = c o s " ^ + 26 - u -
iT)/4b}
(13)
2iT)/ib}.
(14)
In the above expression, we fix the pump energy at -Bi(O), and UJ and T (7) denote probe frequency and the phenomenologically introduced transverse (longitudinal) damping constant, respectively. It should be remarked that the resonant poles of the transitions between the lowest one-exciton state and the two-exciton states {| K = 0, A > } are included in (11) through S(P, t, S) and S(P, b, S) besides the resonant pole of (0-1) transition. 3. R e s u l t s (3) nas In the case of 6 = 0, the size dependence of XLWA already been discussed , which is shown in Fig. 1(a) where the spectra of Im[x£,vi/^] for the pump-probe process are indicated for the several values of TV. In all cases, we can see the positive and negative peaks. The negative
( a ) 6 = 0meV
g 0.0
60.0
y= •• I
•-•>•-
N=5 N=10 N=15 AT=10O0
(b)N=15
0.995
1.0 Probe Energy (eV)
1.005
Fig.l. (a) Size dependence of the spectrum of ImXLWA in the case of 8 = 0. The line for /V = 1000 is shifted to the lower energy side by 4 meV. (b) ^-dependence of the spectrum of ^mXLWA m t n e c a s e °f N = 15. The lines for 6 = 0 and 4.0 meV (6 = 6.0 and 8.0 meV) are shifted to the higher (lower) energy side by 2 meV. In both (a) and (b), ^ ( 0 ) = 1.0 eV, b = 5.0 meV and T = 7 = 0.4 meV. The unit of the scale of the vertical axes is 2M /T .
Fig.2. The size dependence of the negative peak height in IKIXLWA n e a r w = -^l(O) f°r several values of 5. The values of £j(0), b, T and 7 are the same as in Fig.l.
peak arises from the phase space filling due to the pump-induced population of excitons, which, at the same time, causes the [one-exciton] - [two-exciton] transitions. The latter transitions are the origin of the positive peak. When N is small, the negative peak height is enhanced linearly with the size N at UJ — -Ei(O) due to the enhancement of the oscillator strength. As N increases, the positive peaks come close to the negative peak, and the cancellation between them occurs. Because of this cancellation, the enhancement of the negative peak at ui = -Ei(O) is saturated around a certain size TV. (We express such a size by Ns.) Since the extent of cancellation depends on b and the damping constants, Ns is a function of these parameters.
244 Fig. 1(b) shows how the spectrum of XLWA m the size near Ns is affected by Hex-ex- There arise three kinds of cases; (A) a biexciton state is formed whose peak splits off from the band of unbound two-exciton states (See the curve for 8 = 8.0 meV), (B) a shallow biexciton state is formed and the separation between its peak and the negative peak is smaller than the widths of them (curve for 8 = 6.0 meV), and (C) the lowest two-exciton level is lower than that in the case of 8 = 0 though the biexciton state is not formed (curve for 8 = 4.0 meV). There are differences in the height of the negative peaks depending on 8. This is due to the change of the level scheme of the two-exciton states, which affects the extent of the cancellation. The size dependence of the negative peak height for the several values of 8 is shown in Fig. 2. It should be noted that Na strongly depends on 8. The further enhancement is induced in the case of (A) and (B), whereas N, is reduced in the case of (C). The finite 8 also affects the slope of the enhancement, namely, the increase rate in the case of (B) becomes smaller. 4. D i s c u s s i o n s The results of the previous section show that the existence of -ffex-ex brings about the change of the spectrum and the size dependence of XLWA near u> = £ i ( 0 ) . Namely, the nonlinearity near (0-1) transitions and (1-2) transitions are not independent but closely connected with each other even when the latter energy is far from the former one. This is naturally understood if we note the fact that .ffex-ex changes the level scheme of the two-exciton states, which varies the cancellation behavior near u> = £ i ( 0 ) . The remarkable effect is that the large 8 induces the further N linear enhancement of XLWA- Namely, in the case of (A), a biexciton state splits off from the band of unbound two-exciton states, and the part that escapes from the cancellation increases near u = -Ei(O), which makes the negative peak higher. On the other hand, in the case of (C), the cancellation begins to occur when N is smaller than Ns in the case of 8 = 0, which leads to the saturation at smaller size. The situation in the case of (B) is different from that in (C) because the positive peak due to the biexciton level does not move closer to the negative peak with the increase of N, because biexciton levels do not depend on N as long as N is not very small. This is why Ns is larger in this case in spite of the close position of the positive peak to the negative one. However, the overlap between those peaks arises from when N is very small, which reduces the rate of increase. In this way, the effect of Hex-ex on the size dependence of XLWA c a n be well understood in terms of the cancellation mechanism. Although the present model is very simple, it is expected that the effect of Hex-ex appears on the size dependence being based on the similar mechanism in any confined systems of spatially dispersive media. The study of how it appears depending on the dimensionality and the internal degrees of freedom of excitons is a future subject. Acknowledgments The authors are grateful to Prof. K. Cho for fruitful discussions and support. They also thank Dr. H. Ajiki for useful discussions. This work was supported by Grants-in-Aid for COE Research (10CE2004) of the Ministry of Education, Science, Sports and Culture of Japan. References 1. 2. 3. 4. 5. 6. 7. 8.
E. Hanamura, Solid State Commun. 62, 465 (1987). T. Takagahara, Phys. Rev. B39, 10206 (1989). F. C. Spano and S. Mukamel, Phys. Rev. A40, 5783 (1989), Phys. Rev. Lett. 66, 1197 (1991) H. Ishihara and K. Cho, Phys. Rev. B42, 1724 (1990), J. Nonlinear Opt. Phys. 1, 287 (1991) F. C. Spano and S. Mukamel, J. Chem. Phys. 95, 1400 (1991). O. Dubovsky and S. Mukamel, J. Chem. Phys. 95, 7828 (1991). Y. Manabe, T. Tokihiro and E. Hanamura, Phys. Rev. B48, 2773 (1993). G. Juzeliunas and J. Knoester, J. Chem. Phys. 112, 2325 (2000).
LOCAL DOMAIN VS. COLLECTIVE DOMAIN: P R E C U R S O R S TO P H O T O I N D U C E D STRUCTURAL PHASE TRANSITIONS IN COUPLED CHAINS W I T H ELECTRON-LATTICE I N T E R A C T I O N Institute
K. IWANO of Materials Structure Science, High Energy Accelerator Research 1-1 Oho, Tsukuba 305-0801, Japan
Organization,
An electron-lattice model is proposed as a prototype system simulating photoinduced structural phase transitions. In particular, a coupled-chain system consisting of four chains is studied by both analyses of adiabatic potential surfaces and dynamical simulations. Special emphases are placed on nonlinearity in domain creations with respect to excitation density, intrinsic dissipation, sensitivity to initial conditions, and domain merging. 1.
Introduction
The phenomena of photoinduced structural phase transitions (PSPTs) are attracting more and more attentions in resent years. In fact, the number of realizing systems is increasing steadily. For example, they are conjugate polymers, manganese and gold oxides, charge-transfer salts, and spin-crossover materials. 1 - 6 Thus we can now see a wide variety in those systems and so begin to think that these phenomena will be rather general if the system is cleverly chosen. While, the mechanism of the P S P T s is not clear yet. In this article, we try to understand it from a point of view, namely, an electron-lattice(el-l) interaction. Although we here neglect other interactions such as mutual Coulombic interactions between electrons, we think that the former is one of the essential factors in describing the PSPTs. In fact, we see well-defined changes in the lattice structures in the above examples. Therefore we place our base for argument in a simple el-1 model with coupled chains, and discuss various features of domain growth. 2.
M o d e l and M e t h o d We use the following type of el-1 model:
H = -Y.
to(ClQ,a
+ h.c.) + £ £ ( 1 - ( - 1 ) > +
He„ph
where Cla and Ci„ are creation and annihilation operators of an electron with a spin at the 1th site in a system of general dimension, and Qi is the 1th dimensionless lattice displacement with frequency ui. The first term expresses the nearest-neighbor hopping with transfer energy tQ. In the cases with two directions, the factor ( - 1 ) ' means (—1)'*(—l)'v, with I - (lx,ly). Although we do not have a special system in mind, it is necessary to fix the type of el-1 coupling for practical calculations. Here we assume a site-diagonal term as
245
246 He_ph = -S J2Qi ( r u - 1 ) .
(2)
i
With this model and a half-filled band of electrons, the ground state becomes a charge-density wave(CDW), which corresponds to a modulation of electron density induced by Peierls instability. Namely, the electron occupancies are like ..., 0, 2, 0, 2, ... along each direction. Without the second term in (1), another state like ..., 2, 0, 2, 0, ... is energetically equal. In the present case, however, we have lifted up the degeneracy by the same term to prepare unequal two ground states, that are, stable and metastable phases. Next, we mention the number of chains. Although the simplest case is a single-chain system, that case is not appropriate in describing the nonlinearity in the converted fraction with respect to excitation density, because only one photon will possibly drive the whole system into another phase.7 Therefore we set the same number to four in this study, in order to give modest nonlinearity. Moreover, the periodic boundary condition is used for the chain-perpendicular direction, while the open boundary condition for chain ends. As for the method for the simulations, we apply the same procedure as in Ref. 7, that is, a classical approximation for the lattice motion and time-dependent Schrodinger equations for the electrons. Lastly, the parameters are chosen in the following way. The el-1 coupling energy S is 1.3£o, which corresponds to an intermediate coupling case. While, the lattice frequency w is set to 0.005t0. This choice means that we are more concerned with adiabatic situations. The degree of non-degeneracy, i.e., A, is O.OOlio- This small value is selected to simulate almost degenerate two phases, for example, those in a hysteresis loop around thermal transitions. 3.
Results
In Fig.l, we show potential curves related to the lowest n-electron excited states (n-Ex). Here it is assumed that a domain of the metastable phase is created in the background of the stable phase. The domain shape is of a kink-antikink type along the chain direction, while it is almost uniform perpendicular to the chain. As is easily seen in the figure, ra-Ex states (n < 2) never lead to substantial domain formation if they evolve from zero domain size, simply because of the energy-conservation rule. While, in the 4-Ex state, it seems that the formation of a large scale is possible and it actually is, as will be shown later. Lastly, the 3-Ex state is marginal in this sense.
Domain Size
Fig. 1. Adiabatic potential curves with different number of electron excitations.
We then proceed to the dynamical simulations to prove the above expectations. In Fig. 2, we show two snapshots that evolved from the 1- and 2-Ex states with a very small domain size. Note that the ordinate is the alternate component of the lattice. Thus the stable phase before light irradiation corresponds to a horizontal line around Qi(—1)' = 0.47. We easily see that they remain localized around the configurations corresponding to the minima in Fig. 1. In this sense, we call them local domains. On the other hand, we clearly observe appreciable
247 growth of domains in the 4-Ex state. Several examples are depicted in Fig. 3. Although we do not mention here the details of their nature, they have a structure of a domain sandwiched with two domain walls (DWs), and therefore we call them collective domains. As for the features of their dynamics, we notice the following several points. Firstly, we find both the formation and reduction. As for the latter, this represents many degrees of freedom in the system. In fact, the upper limits of the domain size, which are less than 30 in these cases, are much smaller than that expected from the excess energy, which means energy dissipation into irrelevant modes. Moreover, we have also estimated the energy distribution into the DW motions, using the almost linear part in Fig. 3 (the straight line). As a result, it is found that the kinetic energy of the two DWs is as little as 9% of the total kinetic energy and 4% of the total excess energy. This finding is consistent with the above result, namely, relatively small domain sizes achieved, and again shows that a kind of intrinsic dissipation is working due to many degrees of freedom. Lastly, we briefly discuss sensitivity to initial conditions. There appear three completely different trajectories, but they have started from very similar initial conditions. In fact, their total energies, which are specified beside each line, are almost the same except for less than 2% differences. A more detailed analysis shows that the deviations in the trajectories evolve exponentially at least in an early stage of time. Although we can not determine its mechanism at present, we temporally conjecture that such behaviors come from multiply-degenerate electronic states. In the rest of this section we discuss our 'road maps' to possible scenarios for PSPTs. The above examples are still not so appropriate for describing PSPTs themselves. One reason is that the domains disappear eventually except for rather few examples in which large domains are trapped to survive. The typical life times, which depend on the scale of unit, are less than 2ps if we set io=leV. Therefore we think that at least two conditions will be necessary to simulate PSPTs. Firstly, trapping of domains, more specifically, that of DWs, must work in a more effective way. This problem will be solved, for example, by using a larger strength of el-1 interaction, because it can give a larger Peierls potential between neighboring two sites.
V
H. *
3.72j-~ J ~ L J 1 -L
V
J .N 20 CO
oma
c
lpr-4 f.yr\ f *~
«
: •V.i
i\
'3.69
'/tSyXs r~r : ; "• i yi/^3.67 !
a 5
0
Ith Site
Fig. 2. Snapshots at t = 32/u;, starting from a 1-Ex state (dashed line) and a 2-Ex state (solid line).
10 20 30 40 50 60 70 80 90 100
to
Fig. 3. Trajectories from different initial conditions. The numbers are total energies in unit of to-
Next, we must have a mechanism for domain merging, because otherwise it will be rather difficult to transform the whole system into another phase. Fortunately this condition is already satisfied in the present model, as demonstrated in Fig. 4. Here we have started from two small domains with 4 electron excitations in each. What is essential is that two DWs attract with each other if their internal degrees of freedom, namely, the electronic states, are in the ground state.
248 1
0.6
0.2
O
0.6
1 n !t=0 ' t... ..-i-1 "'V/fiV;' t '•1/ Vli 1 Sjl—ill
0.4
0.4
^-
-0.2
V.
-0.6
l|WtJ3£.Ao
W
-0.4
(
20
40
60
SO
Ith site
0.2
_g 0
0
u0
-0.2 -0.4 -0.6 C
Ith site
0.6 0.4 0.2
O
[ t=64/J[
0 -0.2 -0.4 -06
Ith site
4.
Fig. 4. Snapshots ?.t different times.
Summary
We have demonstrated our results related to PSPTs on the el-1 systems that consist of four coupled chains. The obtained features are nonlinearity in the converted fraction with respect to excitation density, intrinsic dissipation originating from the many degrees of freedom, sensitivity to initial conditions, and domain merging. Also, we have argued how the model should be improved in order to realize PSPTs. Much stronger trapping is thought to be necessary for that purpose. Acknowledgment This work was supported by the Grant-in-Aid for Scientific Researches on Priority Areas, "Photo-induced Phase Transitions and Their Dynamics", from the Ministry of Education, Science, Sports and Culture of Japan. References [1] S. Koshihara, Y. Tokura, K. Takeda, and T. Koda, Phys. Rev. Lett. 68, 1148 (1992); Phys. Rev. B 52, 6265 (1995). [2] S. Koshihara, Y. Tokura, T. Mitani, G. Saito, and T. Koda, Phys. Rev. B 42, 6853 (1990); S. Koshihara, Y. Takahashi, H. Sakai, Y. Tokura, and T. Luty, J. Chem. Phys. 103, 2592 (1999). [3] T. Suzuki, T. Sakamaki, K. Tanimura, S. Koshihara, and Y. Tokura, Phys. Rev. B 60, 6191 (1999). [4] K. Kiryukhin, D. Casa, J. P. Hill, B. Keimer, A. Vigliante, Y. Tomioka, and Y. Tokura, Nature 386, 813 (1997). [5] X. J. Xiu, Y. Moritomo, M. Ichida, and A. Nakamura, Phys. Rev. 61, 20 (2000). [6] K. Miyano, T. Tanaka, Y. Tomioka, and Y. Tokura, Phys. Rev. Lett. 78, 4257 (1997). [7] K. Iwano, Phys. Rev. B 61, 279 (2000).
FIRST OBSERVATION OF D Y N A M I C INTENSITY B O R R O W I N G INDUCED B Y COHERENT MOLECULAR VIBRATIONS IN J-AGGREGATES REVEALED B Y SUB-5-FS SPECTROSCOPY
HIDEAKI KANOt TAKASHI SAITO, AKIKATSU UEKI, and TAKAYOSHI KOBAYASHI Department of Physics, University of Tokyo, Hongo 1-3-1, Bunkyo Tokyo 113-0033, JAPAN
Sub-5-fe spectroscopy of porphyrin J-aggregates reveals for the first time coherent molecular vibration coupled to the Prenkel exciton. The oscillations with the frequency of 244cm -1 are described by a plus-cosine function for bleaching and a minus-cosine function for induced absorption. The coherent oscillation is explained by a modulated transition dipole moment, which is due to the transfer of an oscillator strength from the intense B-band to the weak Q-band through the ruffling mode with 244cm -frequency. 1. I n t r o d u c t i o n Molecular J-aggregates have attracted much attention because of the large optical nonlinearity and ultrafast response. The excitonic transition of the J-aggregates is characterized by a sharp absorption band, called the J-band, of which transition energy is lower than that of monomers by the value of twice the dipole-dipole interaction. Among J-aggregates composed of various aromatic or macrocyclic compounds, tetraphenylporphine tetrasulfonic acid (TPPS) J-aggregates are of special interest since they are model substances for aggregates of the Ught-harvesting antenna chlorophyll with a storage ring configuration and of primary charge-separation systems in photosynthesis. Figure 1 shows the absorption spectrum of T P P S aggregates. A relatively weak band in the visible region and a strong peak in the near ultraviolet
Photon energy (ev)
Fig. 1. Linear absorption spectrum of porphyrin J-aggregates (solid line) and laser spectrum (dashed line) are observed, which are denoted as Q- and B-bands, respectively, composing a quasi-three-band Prenkel exciton system. The former and latter correspond to the lowest and second lowest singlet excited state (Si- and S 2 -state), respectively. Although several studies have been made of incoherent coupling of excitons and phonons, 1 no investigation of the coherent exciton-vibration coupling in J-aggregates have ever been performed in real-time domain because the excitons interact only weakly with vibrations and very high time-resolution is required for direct measurement of intramolecular vibrations. In the present study, we apply for the first time the "E-mail address: kanouOfemto.phys.s.u-tokyo.ac.jp
249
250 sub-5-fs real-time spectroscopy to study the coherent exciton-vibration coupling in the Prenkel exciton system. We observed for the first time the coherent molecular vibration coupled to the Prenkel exciton. 2. Experimental A unidirectionally oriented film of porphyrin J-aggregates was prepared using a vertical spin-coating technique developed by our group.2 The experimental setup of the sub-5fs timeresolved pump-probe system is described elsewhere. Here only the important parameters of the experimental system are described. The probe pulse intensity after the sample is spectrally dispersed by a 30cm monochoromator (Ritsu, MC-30) and measured with a Si photodiode. The spectral resolution of the whole system is about 3nm. All measurements are performed at room temperature. Both the polarization of the pump and probe are parallel to the aggregate axis. 3. Results and Discussion The time dependence of the transmittance change in porphyrin J-aggregates at 3 different probe photon energies is shown in Fig.2 (a). The predominant feature common to the traces is
Fig. 2. (a) Time-dependence of the transmittance change in porphyrin Jaggregates at 3 photon energies marked on the right, (b) Fourier-power spectra of real-time spectra. high-frequency oscillations in addition to the underlying slow-dynamics transient components. The oscillations persist for delay times longer than 2ps. To the best of our knowledge, this is the first observation of the coherent molecular vibration in J-aggregates. The slow-decaying component and the oscillating component correspond to the electronic and molecular vibration contributions, respectively. The positive signal observed over the whole range of delay times for •Eprobe < 1.77eV is attributed to bleaching between the Q-band and a ground state. At probe energies higher than 1.77eV, the signal becomes negative due to induced absorption (IA), which is due to the transition to higher excited exciton states. Next we shall focus on the oscillating components. Figure 2 (b) shows the Fourier-power spectra calculated from the oscillating components. The Fourier-power spectra clearly show an intense peak at 244 ± 8cm _1 , which corresponds to a 137fs oscillation period, in the whole spectral region of the Q-band. We performed resonant Raman experiment under resonant excitation of the B-band and also observed a peak at the same frequency. This peak is assigned to a ruffling mode and the Raman signal of this mode is drastically enhanced by a factor of more than 30.3 The phase of the oscillation can be evaluated by the complex Fourier transformation. Figure
251 3 shows the probe-photon energy dependence of the phase and amplitude of the 244cm 1ruffiing mode. The phase of the oscillations are constant in the whole spectral region of the
Photon a n a w (»V)
Fig. 3. Probe-photon energy dependence of the phase (a) and amplitude (b) of the oscillation in the transient signals. Q-band and the sign of the amplitude is reversed around 1.77eV. The constant phase is different from expected continuously varying phase change along the probe photon energy assuming the conventional wave packet motion. Around 1.77eV, the transient signal changes from the bleaching (positive signal) to the IA (negative signal) and the sign of the amplitude of the oscillation also changes. This behavior indicates that the bleaching and IA increase (or decrease) synchronously. This unexpected result can be explained in terms of dynamic intensity borrowing (DIB) which results in the modulated transition dipole moment of the Q- and B-transition in the TPPS molecules. The modulation frequency corresponds to the 244cm~1-ruming-mode vibration. The transition dipole moment which depends on the normal vibrational coordinate means that the Condon approximation is not valid in this model. The increase (or decrease) in the transition dipole moment is reflected by the increase (or decrease) in the signal intensity both of the bleaching and IA. Although the intensity of absorption associated with the transition of the ground state to the Q-band is originally forbidden because of the symmetry of the molecular structure, the transition becomes allowed because of an static intensity borrowing from that of B-band by the configuration-interaction mechanism.4 Therefore, the modulation of the Qtransition is explained by the additional intensity borrowing from the B-band, which we call DIB. The amount of the modulation of the transition dipole moment is evaluated as follows. The normalized modulation of the transition dipole moment of the molecule is expressed as 6^/n, in which /z represent the Q-transition dipole moment of a TPPS molecule, and 8/J, denotes the change of fi induced by the ruffling mode. It is noted that the intermolecular dipole-dipole interaction, J, is also modulated as 8 J because J is proportional to fi2. Since the transition energy from the ground state to the first excited state of the aggregate is originally red-shifted by 2 J in comparison with the one of the monomer, 8(2 J) gives rise to a peak shift of the J-band in the absorption spectrum. The amount of 8fi and 5(2 J) is estimated as follows. The induced absorption spectrum AA(UJ) is assumed to be modulated as AA'(u) by 8)i and 8(2J), which is given by AA'(w) = AA(u> - M*))(l + SA(t)).
(1)
SA{t) = <5Acos(nt) = <5(/i2)//i2cos(nt) 8ui(t) = <5a;cos(Qt) = <5(2J)cos(nt).
(2) (3)
where
252 Here 5A and 5w correspond to the amplitude modulation and spectral shift of the signal, respectively. The modulation frequency, fi, corresponds to 244cm-1. Equation (1) is approximately expressed as AA'(w) ~ =
AA(ui) + (5A • AA(u}) - 5u • dA^^)
cos(flt)
AAsiow(w) + AJ4osc(u;)cos(nt).
(4)
Since the experimentally obtained transmittance change is composed of the slow-dynamics component (AAsiow(u)) and the oscillating component (AA^UJ)), the former and the latter correspond to the first and second terms in Eq.(4), respectively. Assuming that AT/T is proportional to AJ4 in the weak signal approximation, the slow-dynamics and oscillating components are fitted by AA(ui) and by both of AA{UJ) and dAA(u)/cL>, respectively. As a result, we obtained 6fi/fi = (2.2 ± 0.5) x 1(T2 and <S(2J) = (-5.6 ± 2.6) x l(T 4 (eV). Next we will focus on the DIB. Based on the vibronic coupling theory, following calculation is performed to estimate the amount of the oscillator strength transfer from the B-band to the Q-band. The perturbed transition dipole moment between the Q-band and the ground state, // = fi + <5/i, is expressed as follows in the first order using vibronic coupling theory: n' = (j. + 5/J. = n +
g0
_^o
^B-
(5)
Here /uB) £B> ^Q> a n d ^vib denote the transition dipole moment between the ground state and the B-band, the transition energy from the ground state to the B- and Q-band without the perturbation by the ruffling mode, and the perturbation to the Hamiltonian, respectively. E# — EQ ~ 0.93eV, and /UB/M ~ 2.6 are estimated from the stationary absorption spectrum of the monomer and aggregate and the amount of <5/z//x has been estimated as 5/j,/fj, = 2.2%. Consequently, we obtained /i' = (i + 8 x 10~3/LtB4. Conclusions The coherent molecular vibration coupled to the Prenkel exciton is observed for the first time using sub-5-fs pulse. The oscillation originates from the molecular vibration and is assigned to the 244cm-1-ruffling mode. It is interpreted by the modulated transition dipole moment of the Q-band, which is due to the dynamical intensity borrowing (DIB) mechanism from the intense B-band to the weak Q-band through the ruffling mode. DIB is a new mechanism of ultrafast nonlinearity and is observed for the first time in the present study. References 1. 2. 3. 4.
S. De Boer and D. A. Wiersma, Chem. Phys. 131, 135 (1989). K. Misawa, H. Ono, K. Minoshima, and T. Kobayashi, Appl. Phys. Lett. 63, 577 (1993). D. L. Akins, S. Ozcelik, H. R. Zhu, and C. Guo, J. Phys. Chem. 100, 14390 (1996). M. Gouterman The Porphyrins, volume III PART A. (Academic Press, 1979).
A T H E O R E T I C A L S T U D Y OF B I S T A B I L I T Y OF P O L Y D I A C E T Y L E N E : TCDU(poly(5,7-dodecadiyne-l,12-diyl-bis-phenylurethane)
HIDEKI KATAGIRItYUKIHIRO SHIMOI and SHUJI ABE Electrotechnical Laboratory, Agency of Industrial Science and Technoloyy(AIST), 1-1-4 Umezono, Tmkuba, Ibaraki 305-8568, Japan We performed a first-principles calculation of typical polydiacetylene (PDA), TCDU (poly(5,7-dodecaxnyne-l,12-diyl-bis-phenylurethane)). Potential energy curves (PEC's) as a function of two bond lengths of the backbone chain are presented. The present PEC's show that TCDU has only an acetylene-type stable structure and a butatriene-type structure is unstable, consistent with our previous calculations with a geometry optimization procedure. This result is in contrast to the case of a hypothetical hydrogen-substituted PDA where a butatriene-type structure is obtained as a meta-stable structure. 1. Introduction Photoinduced structural changes in photochromic materials have attracted growing interest with a goal to develop techniques for material design of optical storage devices. A family of polydiacetylenes (PDA's), which can be obtained from crystals of diacetylene monomers by the solid state polymerization, is one of the typical thermo- and photochromic materials. 1 Most PDA's are classified into two distinct groups according to their absorption spectra: one shows a prominent absorption peak at about 2.2eV, and the other at about 1.9eV. The transition between the two phases has been observed by thermal activation and photoirradiation in several PDA's. It is likely that the photochromism is originated from a change of electronic structure accompanied by some structural change in the main chain. However, the detailed mechanism of the structural change is still open in spite of much works devoted to this problem. At early stage of studies, the structural change was assigned to a transformation between the enyene and butatriene forms of the main chain, but it is not confirmed that the butatriene form definitely exists. Later experiments indicated that the phenomenon is not so simple, suggesting that the electronic structural change is related with some conformational change of side groups. To validate the origin of the two forms, it is very important to clarify the detailed structure of the main chain as well as the interplay between the electronic structure in the main chain and the conformation of the side group. However, theoretical studies was limited with a simplified model with side groups substituted by hydrogen atoms so far. 2,3,4 Recently, we performed a geometry optimization of a typical thermochromic PDA, TCDU (poly(5,7-dodecadiyne-l,12-diyl-bis-phenylurethane) with side group i?=-(CH 2 ) 4 OCONHC 6 H5, and a hypothetical PDA (H-PDA), where side groups are substituted by hydrogen atoms using a first-principles method. 5 We found that two local minimum structures exist in H-PDA, namely, acetylene-type (enyene-type) and butatriene-type structures, whereas only an acetylene-type structure exists in TCDU. This suggests that butatriene-type structure is no more stable in TCDU, and sidegroups may have a significant influence on the stability of backbone structures. However, the geometrical optimization procedure has an ambiguity in the choice of initial trial for geometry and cannot exclude completely the possibility to miss a local meta-stable structure. To make our conclusion, it is necessary to study potential energy maps of PDA's. For this purpose we focus our attention on potential energy curves (PEC's) of TCDU in a region where it forms butatriene-like structures. 2. M e t h o d We used the first-principles method based on the generalized gradient approximation (GGA) in the density functional theory, 6,7 for which we adopt the version developed by Perdew and "Electronic mail: [email protected]
253
254
,&-Q2-C3—C4
/ ^ ^ \
R
\R1 /
/ R2 Ha
.
Fig. 1. Definition of bond lengths R\, R2, and R3. R represents the sidegroup of TCDU (iJ=-(CrI2)40CONHC6H5). a denotes the lattice constant along the backbone chain. Wang. 8 We employed the plane-wave pseudopotential technique with Vanderbilt's ultrasoft pseudopotentials. 9,10 The wavefunctions are expanded by plane waves with 30Ry cutoff energy. For the Brillouin zone (BZ) sampling, we used 4 special k points along the a-axis (the direction along the backbone chain). The lattice parameters are taken from the X-ray diffraction data obtained by Kobayashi et al (a = 4.887A, b = 39.169A, c = 6.167A and /3 = 106.19 0 ). 11 3. Potential energy curves of T C D U Figure 1 illustrates a schematic view of the bonding structure of TCDU. Since we impose inversion symmetry at the center of the bond C1-C4 (or C2-C3) as the observed structure, 11 C2 and C3, and C\ and C4 carbon atoms are equivalent, respectively. As illustrated, we denote three parameters of bond length in the backbone chain as R\, R2, and R3. We summarize the optimized parameters for acetylene-type and butatriene-type geometries obtained in the previous work first. The bond lengths R\, R2, and R3 of the acetylene-type structures were almost equivalent between TCDU and H-PDA, that is, 1.37-1.38A, 1.40-1.41A, and 1.23A, respectively. On the other hand, those for the butatriene-type structure, which was found in H-PDA case only, were 1.45A, 1.34A, and 1.26A. It is evident that R^ and R2 change dramatically between the acetylene-type and butatriene-type structures due to the different bond alternation structures. R3 also changes on going from acetylene-type to butatriene-type, although the difference of R3 between the two structures is smallest among the three bond lengths. The bond angle LC^C\C2 is almost a constant (~ 120°) in TCDU and the both types of H-PDA. Taking into account these results, R\ and R2 are chosen as configurational coordinates to study potential energies of TCDU in the present work. If we impose restrictions that 1) the lattice parameter a is fixed as a constant, 2) LC^C\C2 is fixed, and 2) C\, C2, C3, and C4 atoms are aligned on a line, R3 is dependent only on R\ and R2. Hence we fixed lCiC-iC2 at an angle so that R3 is automatically determined from R\ and R2. We note that the positions of sidegroups R are automatically adjusted with R\ and R2 so that the angle LC3C4R and the length of C4-R bond do not change. Detail of our treatment to determine geometry of the backbone and sidegroups as a function of R1 and R2 will be reported elsewhere. 12 In order to investigate the stability of the butatriene-type structure of TCDU, we present potential energies as a function of Ri at some chosen R2 values. Figure 2 shows PEC's at iJ 2 =1.32, 1.34, and 1.36A. (As mentioned before, the optimized R2 for the butatriene-type structure of H-PDA was 1.34A.) At i? 2 =1.32A, the PEC is repulsive in the displayed area. At
255
1.32
1.36
1.40
1.44
1.48
1.52
R,/A Fig. 2. Potential energy curves of TCDU as a function of R\ at R%= 1.32, 1.34, and 1.36A. We set the potential energy at (i?i,i?2)=(l-38A,1.4oA) zero (see Fig.3)).
Fig. 3. A potential energy curve between (i?i,ilj)=(1.50A,1.34A) and (1.38A,1.40A). (Only R2 is shown in the figure.)
256 J R 2 = 1 ' 3 4 and 1.36A, each PEC has a stationary point at 1.50 and 1.46A. As R2 increases from 1.32A to 1.36A, the potential energies decrease in most region of R2 displayed in Fig. 2, and the position of the stationary point moves to smaller values of Ry. We verified that there is only one stationary point along i?i at R2 > 1.36A. In order to show energy correlation between butatriene-type and acetylene-type structures, we show a potential energy curve along a line between two geometries, that is, (Ri = 1.50A,R 2 = 1.34A) and (Rt = 1.38A,R 2 = 1.40A) in Fig. 3. Since both Rx and R2 vary proportionally, the PEC is displayed as a function of R2 only. It is notable that the two stationary points at (J?j = l.50k,R2 = 1.34A) and (R-, = 1.46A,R 2 = 1.36A) shown in Fig. 2 are also included in Fig. 3. Although the potential energy curve is quite flat near the butatriene-type structure (between #2=1.34 and 1.36A), the potential energy decreases with increase of R2. The PEC becomes suddenly steep at R2 > 1.37A. Therefore, the stationary points in Fig. 2 do not correspond to a local minimum. In H-PDA case, we found that there is a potential barrier in the pathway from the butatriene-type to the acetylene-type structure, 12 but no barrier is found in TCDU. 4. Conclusion We show that the potential energy curve connecting two geometries, butatriene-type and acetylene-type geometries, does not have any barrier in TCDU case. It is fully consistent that no butatriene-type structure was found by geometry optimization in the previous study. 5 The present result demonstrates that sidegroups of PDA's have a significant effect on potential energy shape of backbone chain structure. Consequently, we suggest that it is very important taking into account effects of sidegroups for understanding the photochromism of PDA's. Acknowledgements The calculations were performed on Hitachi SR8000 at the Tsukuba Advanced Computer Center (TACC) of AIST. We used a software package which was developed in the Theory Group at the Joint Research Center for Atom Technology (JRCAT). References
1. Nonlinear Optical Properties of Organic Molecules and Crystals Vol.IS, eds. D.S. Chemla and J. Zyss (Academic Press, 1987). 2. A. Karpfen, J. Phys. C 13, 5673 (1980). 3. E.A. Perpete and B. Champagne, J. Mol. Struct.(THEOCHEM) 487, 39 (1999). 4. M. Turki, T. Barisien, J.-Y. Bigot, and C. Daniel, J. Chem. Phys. 112, 10526 (2000). 5. H. Katagiri, Y. Shimoi, and S. Abe, Nonlinear Optics in press. 6. P.C. Hohenberg and W. Kohn, Phys. Rev. B 136, B864 (1964). 7. W. Kohn and L.J. Sham, Phys. Rev. 140, A1133 (1965). 8. J. Perdew, in Electronic Structure of Solids '91, eds. P. Ziesche and H. Eschrig (Akademie Verlag, Berlin, 1991), p. 1. 9. D. Vanderbilt, Phys. Rev. B 41, 7892 (1990). 10. K. Lassonen, A. Pasquarello, R. Car, C. Lee, and D. Vanderbilt, Phys. Rev. B 47, 10142 (1993). 11. A. Kobayashi, H. Kobayashi, Y. Tokura, T. Kanetake, and T. Koda, J. Chem. Phys. 92, 7581 (1990). 12. H. Katagiri, Y. Shimoi, and S. Abe, in preparation.
PHOTOLUMINESCENCE AND DYNAMICS OF EXCITONS IN Alq3 SINGLE CRYSTALS Y. KAWASUMI, I. AKAI, and T. KARASAWA Department of Physics, Graduate School of Science, Osaka City University, Sumiyoshi-ku, Osaka, 558-8585, Japan The relaxation dynamics of photo-excited states in single crystals of Alq^, utilized as organic electroluminescent (EL) devices, have been investigated. The photoluminescence (PL) peak of Alqj changes depending on the exciting photon energy and the temperature. Nevertheless, a PL peak appears at the same energy position as the EL peak for excitations at energies above the transition edge and a new PL band has been resolved at energies below the EL peak for excitation at the lowest part of the absorption tail. However, for low temperatures and for excitation in the intermediate energy region of the absorption tail, a PL peak appears at the lower energy side. This PL peak shifts into the same energy as the EL peak with increasing temperature. This behavior is explained by a model which takes account of two luminescent states and one non-luminescent intermediate state. In the intermediate energy region, the temperature dependence of the PL for the excitation is also explained by a thermal activation process mediated by the non-luminescent state. The lifetimes of the three states obtained from the temporal profiles of the PL are understood consistently on the basis of this model. Keywords: rra-8-hydroxyquinolate aluminum (Alq3); photoluminescence; relaxation dynamics of exciton
1. Introduction Luminescent organic dyes have attracted much attention to the application of electroluminescent (EL) devices. Afr7's-8-hydroxyquinolatealuminum (Alq3) has played an important role in the development of organic EL devices, since it has excellent luminosity in the green wavelength region and fine electronic transport properties.1 Figure 1 shows the molecular structure of Alq3. The electronic structures of the ground state and the Franck-Condon states concerning optical absorption processes were studied using an ab initio calculation.2 The absorption peak at 3.17 eV observed in evaporated thin films3 was assigned to an optical transition from the highest occupied molecular orbitals (HOMO) to the second lowest unoccupied molecular orbitals (LUMO+1).2 However, EL and photoluminescence (PL) peaks appear at the low energy side with a Stokes shift. The ab initio calculation does not give sufficient information to account for the luminescent states. The electronic structure of the luminescent states and the dynamic relaxation processes from the FranckCondon states to the luminescent states have not been clarified. Therefore investigation of the intrinsic optical processes in Alq3 single crystals is required. In this paper, the behavior of the PL on the temperature and exciting photon energy were studied.
CO p
Fig. 1 Molecular structure of Alq,
257
258 2. Experimental Single crystals of Alq3 were prepared using a diffusion zone method4 with solvents of chloroform and ethanol having different solubilities for Alq3 of 50 g/1 and 2 g/1, respectively. A small vessel was filled with a saturated solution of Alq3 in chloroform solvent and was capped with parchment paper which was used as a semi permeable membrane. The vessel was submerged into the ethanol solution and was settled for months. Needle-shaped crystals with a light yellow color grew in the vessel. The largest crystal had a dimension of 1 X 1 X 10 mm3. An N2 laser (3.675 eV) and a dye laser (2.772 eV) pumped by the N2 laser and a cw-Ar+ laser (2.409, 2.539 eV) were used as exciting light sources for the PL spectra. Pulse lasers, having time duration -800 ps and photon energies of 3.675 and 2.405 eV, were used for the observation of time resolved PL. Both spectral and temporal profiles were measured using a streak camera system.
3. Results and discussion Figure 2(a) shows an absorption spectrum of a 510 u.m thick Alq3 single crystal at 50 K. The absorption edge appearing at around 2.75 eV is considered to come from the dominant absorption peak at 3.17 eV due to the HOMO-LUMO+1 transition mentioned previously. A weak and broad absorption band at 2.15 eV is also resolved. Its energy position almost coincides with the energy interval between the HOMO and LUMO orbitals evaluated using the ab initio calculation.2 From this fact, the weak absorption band is considered to be due to the optical transition between HOMO and LUMO orbitals.
Fig.2 Absorption spectrum and temperature dependence of PL spectra for excitation at several photon energies. Vertical arrows indicate the exciting light photon energy. Figure 2(b) shows the PL spectra pumped with a photon energy of 2.772 eV at 280 K(upper) and 2 K(lower). In both spectra, the PL peaks appear at 2.40 eV which coincides with that of the PL excited by the N2 laser line and with that of the EL band1. The PL spectra pumped at 2.409 eV shown in Fig.2(d) shows a PL peak at 2.22 eV. The peak energy position does not change with temperature. However, for excitation at intermediate energy positions, i.e. between 2.772 and
259 2.409 eV, an obvious temperature dependence appears on the PL spectra as exemplified in Fig.2(c) for the excitation at 2.539eV. With increasing temperature, the PL peak shifts to the higher energy side, from 2.22eV at 2 K to 2.35 eV at 280K.
Fig.3
Configuration coordinate model consisting of three excited states; P1~P3 and a ground state
In order to explain the above results, we introduce a configuration coordinate model consisting of three excited states and a ground state. For simplicity, we consider a ground state to be on a simple adiabatic potential. The excited states are constructed using two luminescent states, PI and P3, and one non-luminescent intermediate state, P2, from which the excited electrons can be activated thermally to PI, the adiabatic potentials having three different minima are considered as shown in Fig.3. For the excitation at 2.409 eV, only the P3 state is excited and the PL band peaked at 2.22 eV appears from the P3 state. The insensitivity of the PL band to changes in temperature can be understood by considering the potential barrier from P3 to P2 being higher than the thermal energy of 230 K. For the excitation at 2.772 eV, the highest lying PI state is excited and the energy relaxation from PI to P2 and P3 occurs. After the relaxation, a superposition of the PL bands from PI and P3 gives rise to the PL band of 2.40 eV. For the excitation of the intermediate energy region around 2.539 eV, the P2 state is excited selectively and will relax to the lower lying P3 state independently of temperature. However, the thermal activation from P2 to PI is allowed at higher temperatures if the potential barrier from P2 to PI is comparable to the thermal energy. This process will be suppressed at lower temperatures. The re-distribution from P2 to PI induced by the thermal energy gives rise to the higher energy shifts of the PL peak from 2.22 eV to 2.40 eV The temporal profiles of the PL pumped by a laser pulse of 800 ps at 10 K are plotted in Fig.4. For excitation at 2.405 eV, which is nearly the same energy as in the case shown in Fig.2(d), a decay time constant of 12 ± 2 ns, indicating the lifetime of P3, was obtained from a deconvolution analysis of the temporal response as denoted by the closed triangles. However, for excitation at 3.675 eV, the PL temporal profile at 2.40 eV includes two decay components, as plotted by closed circles in Fig.4. Two decay components, 17 ± 3 ns and 31 + 3 ns, were obtained from deconvolution of the profile; the fitted result for the slower component is indicated by the solid line in the figure. From the analyzed decay times and intensities, the time integrated PL intensity of the short decay component is stronger than that of the long decay component and accounts for 62 % in strength of the whole luminescence. The intensity ratio between the short and long decay components changes depending on the detecting photon energy in the PL band. The intensity of the short decay time constant decreases in the tail part of the lower energy side of the 2.40 eV PL band and only the long decay component remains at 2.22 eV, where the PL from the P3 state appears. This fact means that the long and short decay times originate from the PL from P3 and PI, respectively. However, the life time constant of the P3 state by
260
0
50
100 150 Time (ns)
200
Fig.4 Temporal profile of PL intensity; Closed triangles denote the temporal profile of the PL component nearly 2.22 eV for the excitation at 2.405 eV, Closed circles being the PL component nearly 2.40 eV for the excitation at 3.675 eV direct excitation has already been obtained as 12 ns as mentioned above. Then, the longer decay time, 31 ns, of the P3 state for the excitation of higher lying states is not the intrinsic decay time of P3 but the supply time constant from the P2 state. Thus the non-luminescent intermediate state P2 has the longest decay time constant, 31 ns, presumably because of a very small radiative transition probability in contrast with the PI and P3 states.
4. Summary We prepared single crystals of Alq3 and studied the dynamics of the relaxation process of the photo excited states. The PL spectra vary depending on the exciting energy. The PL blue shift was observed with increasing temperature under excitation around the tail part of the absorption edge. These phenomena are interpreted by the coexistence of three states; the two luminescent states PI and P3, and the non-luminescent intermediate state P2, which is able to activate thermally to PI. From the excitation energy dependence of the temporal profile of the PL, the short decay time constants of the luminescent states, PI and P3, and the long decay time constant of the nonluminescent state, P2, are estimated to be 17 ns, 12 ns and 31 ns, respectively.
Acknowledgement This research was partially supported by the Ministry of Education, Science, Sports and Culture of Japan, Grant-in-Aid for Scientific Research (C), 12640319, 2000.
References 1. C. W. Tang and S. A. VanSlyke, Appl. Phys. Lett. 51, 913 (1987). 2. A. Curioni, M. Boero and W. Andreoni, Chem. Phys. Lett. 294,263 (1998). 3. A. Schmidt, M. L. Anderson and N. R. Armstrong, J. Appl. Phys. 78, 5619 (1995). 4. A. R. Vaala, A. H. Madjid and M. T. Torrado, J. Crystal Growth 18, 39 (1973).
P H O T O - I R R A D I A T I O N E F F E C T S O N P R E P A R A T I O N OF COLLOIDAL Q U A N T U M D O T S A N D THEIR SURFACE MODIFICATION
D. KIMtN. TERATANI, K. MIZOGUCHI, H. NISHIMURA, and M. NAKAYAMA Department of Applied Physics, Faculty of Engineering, Osaka City University Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan We have investigated the possibility of size control of CdS and PbS quantum dots (QDs) with a narrow size distribution and the influence of the surface modification of the dots on their luminescence properties. The reduction of the size-distribution width of the CdS QDs grown in polyvinylpyrrolidone or polyvinyl alcohol solutions was succeeded by a sizeselective photoetching. We controlled the size of the CdS QDs with the narrow distribution by changing the initial condition of the sample preparation and the irradiation-light energy. The QDs of PbS were grown with the different disperse agents and growth temperature. The band-edge emission is strongly activated by the surface modification of the CdS QDs. 1. Introduction Semiconductor quantum dots (QDs) have been extensively investigated to understand the size dependence of their electronic states and interactions between elementary excitations in them. 1 In such studies, the preparation of the QDs with a narrow size distribution is essential. Furthermore, surface modification is important since surface morphology affects excitonic relaxation process. Matsumoto et al. reported that a size-selective photoetching makes it possible to prepare CdS QDs with a narrow size distribution. 2 It is based on the fact that many semiconductors are photoetched in aqueous solution if electros and holes are excited under band-gap excitation. However, in studies of the photoetching of the CdS QDs, only sodium hexametaphosphate (HMP) has been used as a disperse agent so far. 2 ' 3 ' 4 In the present work, we have investigated the possibility of size control of CdS and PbS QDs with a narrow size distribution and the influence of the surface modification of the dots on their luminescence properties. We succeeded narrowing the size distribution of the CdS QDs by a size-selective photoetching in polyvinylpyrrolidone (PVP) and polyvinyl alcohol (PVA) solutions: The size distribution was reduced to ~ 6 %. We controlled the size of the CdS QDs with the narrow size distribution by changing the initial condition of the sample preparation and the irradiation-light energy. For the PbS QDs prepared in PVA solutions, a sharp absorption peak is observed, indicating a narrow size distribution. Furthermore, we demonstrated that the band-edge emission in the CdS QDs is strongly activated by the surface modification. 2. E x p e r i m e n t a l The CdS (PbS) QDs were prepared by injecting Cd(C10 4 ) 2 (Pb(C10 4 ) 2 ) and Na 2 S into aqueous solutions containing PVP, PVA, or HMP. For the photoetching of the QDs, a 150-W Xe lamp was used as a light source. Monochromatic light was obtained by using interference niters: The full-width at half of the intensity maximum of the light was ~10 nm. We performed absorption measurements at room temperature during the photoetching process. The surface modification was performed by the addition of Cd(C104)2 after adjusting pH of the solution to alkaline region. 3 For luminescence measurements, a 325-nm line of a He-Cd laser was used as an excitation-light source. 3. Results and discussion
Correspondence author: D. Kim, [email protected]
261
262
CdS QDs RT Eg
\
,.--''
/<** •-"f PVP 3wt% / CdS 2 n n n D l / L ^ ^
4-*
/
Abs jtion ( arb
3
/ PVP 4wt% CdS lOmmol/L
/ P V P 4wt%
^
J CdS lOmmoW^-^''^ f P V P 4wt% CdS lOwmM^'—
8
.•
PVP5wt% CdS a h n m l / L ^ ^ * * - * * PVA5wt% CdS lOmmol/L
2.5 3.0 3.5 4.0 Photon Energy (eV) Fig. 1. Absorption spectra for CdS QDs in PVP solutions during a size-selective photoetching process. Down arrows indicate the energy positions of the irradiated monochromatic light. Open circles indicate results of the line-shape analysis.
2.5
3.0 3.5 4.0 Photon Energy (eV)
Fig. 2. Absorption spectra after a photoetching process for CdS QDs prepared with different concentrations of CdS and disperse agents (PVP and PVA). Broken line indicates absorption spectrum before the photoetching for comparison.
In order to study the photoetching effect on narrowing the size distribution, we measured absorption spectra during the photoetching process. Figure 1 shows absorption spectra for the CdS QDs grown in 5 wt% P V P solutions during the photoetching process. The absorption spectrum in the bottom was measured before the photoetching. The absorption structure corresponding to the lowest optical transition energy is observed in the higher energy side than the band gap energy of ~2.5 eV in a CdS bulk crystal, which indicates the formation of CdS QDs. According to the theory for the quantum size effect in QDs, 5 the average radius of the CdS QDs before the photoetching is estimated to be 2.0 nm. Down arrows in Fig. 1 indicate the energy positions of the irradiated monochromatic light. With the increase of the photon energy, the energy position of the absorption structure is shifted to the higher energy side and the width is decreased. After the photoetching process, the sharp absorption peak is observed. This result indicates that the average radius and the width of the size distribution of the QDs become smaller by a sequential irradiation of the monochromatic light. The mechanism of the size-distribution reduction is explained as follows. Among the QDs of different sizes, the QDs whose exciton energies are resonant with the irradiation-light energy are photoetched. Since the exciton energy of the QD increases with the decrease of the QD size, the QDs to be photoetched become smaller by increasing the irradiation-light energy. This process results in narrowing the size distribution. Such a photoetching treatment was applied only to CdS QDs in HMP solutions. 2 ' 3 ' 4 Our results demonstrate the success of narrowing the size distribution of the CdS QDs in PVP solutions. We also achieved narrowing the size distribution of the CdS QDs in PVA solutions. Open circles in Fig.l indicate results of the lines-shape analysis. From the energy of the absorption peak or the minimum point of the second-derivative spectrum, the average radius Ro is first determined. The line shape of the calculated absorption spectrum scarcely depends on the spectral width of each QD since the width of the size distribution
263
2.0 2.5 Photon Energy (eV) Fig. 3. Absorption spectra for PbS QDs grown at room temperature in HMP and PVP, and at 60, 80, and 90 °C in PVA solutions. note that a is the only fitting parameter. The estimated values of RQ and
264
CdS QDs R T
PL LAAbsorption
1 Bi
1
i ^
lW 7\7,
$
^
1.5 2.0 2.5 3.0 3.5 4.0 Photon Energy (eV)
Fig. 4. Absorption and luminescence spectra for the surface-modified CdS QDs in HMP solutions during a photoetching process. Down arrows indicate the energy positions of the irradiated light. Broken line in the bottom indicates a luminescence spectrum before the surface modification. activated by the surface modification: The intensity was increased 85 times by the modification. This demonstrates that the surface modification improves the luminescence properties of the QDs, which is similar to the results in ref. 3. We note that the photoetching effect was not combined with the surface modification in ref. 3. In Fig. 4, the luminescence-peak energy as well as the absorption energy is shifted to the higher energy side by increasing the irradiation-light energy. In summary, we have investigated the possibility of size control of CdS and PbS QDs and the influence of the surface modification on the luminescence properties of CdS QDs. We succeeded narrowing the size distribution of the CdS QDs by the size-selective photoetching in PVP and PVA aqueous solutions: We achieved the narrowest size distribution of 6 % in the average radius of 1.8 nm. We controlled the size of the CdS QDs with the narrow size distribution by changing the initial condition of the sample preparation and the irradiation-light energy. For the preparation of PbS QDs without the photoetching, we obtained QDs with a narrow size distribution at 80 °C in PVA solutions: The average radius of 1.3 nm and the size distribution of 2 %. We note that the exciton energy of the PbS QDs is around ~2.08 eV which is sifted far from the band gap energy of ~0.4 eV in a bulk crystal. Furthermore, we demonstrated that the surface modification of the photoetched CdS QDs enhances the band-edge emission. References 1. 2. 3. 4. 5.
For a review, J. Lumin., 70 (1996), edited by L. E. Brus, Al. L. Efros, and T. Itoh. H. Matsumoto, T. Sakata, H. Mori, and H. Yoneyama, J. Phys. Chem., 100, 13781 (1996). L. Spanhel, M. Haase, H. Weller, and A. Henglein, J. Am. Chem. Soc, 109, 5649 (1987). A. Dijken, D. Vanmaekelbergh, and A. Meijerink, Chem. Phys. Lett, 269, 494 (1997). L. E. Brus, J. Chem. Phys., 80, 4403 (1984).
T H E O R Y OF E X C I T A T I O N E N E R G Y T R A N S F E R I N T H E I N T E R M E D I A T E C O U P L I N G C A S E A N D ITS A P P L I C A T I O N TO THE PHOTOSYNTHETIC A N T E N N A SYSTEMS
AKIHIRO KIMURA*, TOSHIAKI KAKITANI and TAKAHISA YAMATO Department of Physics, Graduate School of Science, Nagoya University, Chikusa-ku Nagoya 464-8602, Japan We developed the theory of excitation energy transfer (EET) in the intermediate coupling case using the decoupling procedure. We succeeded in treating the theory analytically by assuming that the two-time correlation function is represented as an exponential function. We examined the validity of its approximation. We calculated the time dependent probability na(t) of the EET, in which the acceptor molecule is in the excited state by making alternative calculation of the cumulant expansion method. Applying this calculation by this method to the photosynthetic antenna systems and comparing its result with the analytical formula, we found that these results coincide well with each other in the due time region of the approximation. 1. Introduction Many theoreticians have constructed many theories of excitation energy transfer (EET) for a few decades to elucidate the EET mechanisms in physical, chemical and biological systems. Historically, as a pioneer of E E T theory, Forster 1 derived a formula of E E T rate from the donor to the acceptor molecules which is applicable in the weak coupling cases between the donor and the acceptor molecules. In this case, the excited state is localized by strong phonon fluctuations and is incoherently transferred from the donor to the acceptor molecules. On the other hand, exciton theory using Frenkel Hamiltonian is applicable in the strong coupling case 2 . In this case, the excited state seems to be oscillating between the donor and the acceptor molecules. Namely, it is delocalized around the whole molecular system. EET between these two limiting cases, however, can be seen in many systems. For example, in biological systems, especially photosynthetic antenna systems, a number of complex structures and interesting phenomena 3 have been reported. In the case of the light harvesting system II (LH2), for instance, the total reorganization energy A is 80 c m - 1 and the coupling strength of the homodimer of B850 C/gso in the LH2 is about 350 c m - 1 which is only about 4 times bigger than the total reorganization energy. Then, in order to deal with it, the parameters of phonon-exciton coupling and exciton coupling between molecules must be treated equally. However, it is a rather hard task to construct such theory analytically since one can not simply utilize a perturbation method. Previously, we have constructed the theory of EET in the intermediate coupling case 4 which is applicable for any coupling strength. In this theory, we made two types of the three state model of EET which we call type I and type II 4 . Especially, we have recently succeeded in treating the theory of type II EET analytically 5,6 . In the EET model of type II, we treat a heterodimer system, namely the donor and the acceptor molecules, where we represent the coupling strength between the donor and the acceptor molecules as U. In this model, we assumed that EET starts from the non-equilibrium excited state (Franck-Condon state) at the donor molecule by absorption of an ultrashort pulse photon. We derive the time-dependent probability na(t) in which the molecular system is in the excited state at the acceptor molecule by the EET from the donor molecule in non-equilibrium excited state to the acceptor molecule. We used two important approximations in order to derive na(t). One is that we utilized a decoupling procedure to factorize the integro-differential equation to derive na(t) by a two-time correlation function. And the other is that we represented the two-time correlation function as
*Chikusa-ku Nagoya 464-8602, Japan
265
266 an exponential function. Under these assumptions, we could analytically express na(t). Some formulas were derived from na(i) as follows: the rate of type II EET, the formulas of criteria among exciton, intermediate coupling and Forster mechanism, and the coherency in the dimer system. It is very important to know how much the analytical formulas obtained using by the above approximation are available. In order to do it, we compared the analytical formula na(t) with the results of the calculation of the correlation function approximated by the cumulant expansion method, where the parameter is used for the photosynthetic antenna systems. 2. Theoretical According to the theory of ref. 7, the time dependent probability na(t) can be represented as na(t) = 1 — \(Uj(t))d\2, where the renormalized propagator {Ui(t))d can be calculated by the following integro-differential equation d{Ul
}t))d = - jT
(i)
where we assumed that h = 1 holds hereafter. In order to derive the analytical formula of na(t), we assumed that the correlation function is represented as the exponential function.
(HVKtJVKOlm)),, = U2 exp[-(t - tih(ti)]
(2)
where 7(
+
7sinh(- v /5t) 2h\/a
(3)
where a = 7 2 / 4 — U2. On the other hand, we can numerically solve the eq. (1) if we choose the two-time correlation function ((m\Vj(t)Vj(ti)\m))d in the other form. This can be rewritten as follows: ((m|V / (t)V f (t 1 )|m)) d = U2(eiH-te-iH^t-t^eiH^)d{eiH^-tl'>e-iH^t-t^}d
(4)
where (e*Hmte~lHd(t~tl^e'Hmtl)d represents the fourier transformation of the time-resolved emission spectrum of the donor molecule, and ( e * ff ''( t ~ tl )e~ ,Ho(t "' l '),j represents the fourier transformation of the absorption spectrum of the acceptor molecule. The exciton-phonon interaction was taken into account only by means of the variation of the equilibrium positions of the nuclei in the harmonic approximation. We represent them as vd = Hm — Hd — Gm + hv and fa = Ha — Hd — Ga + hv, respectively. Then, by applying the second-order cumulant expansion method 8 , we obtain: {eiHmte~iHd(t-tl)eiHmtl)d
=
( 5 d (t))<St(t 1 )) exp{Kd(tut)}
(e"W'-e-^(^))d
=
{Sa(t
- *,))
(5) (6)
where l n ( £ ( 0 ) = i{vi)dt - f ds f
- (Vi)2}
(i = d,a)
(7)
Jo
Kd{t, 0 = f ds f dsMviWvfa))* - (vd)2d\ (8) Jo Jo Substituting eqs. (7) and (8) into eq. (5), we can rewrite it as a function of the difference H = t - £1 and the average T — (t + ti)/2 instead of t and tx. The variable /i implies the time
267 scale necessary for the donor molecule in the excited state transitions to the ground state. By assuming that this time scale is much shorter than the inverse of the average phonon frequency a), we can expand eq. (5) by the second order of p.. Similarly, we expand eq. (6) by the second order of the difference fj,. Hence, we obtain {{m\Vi(t)VI(t1)\m))d
(Dl + Dl)
= exp
(i-tl)2-H£„m((* + *l)/2)(t-tl
(9)
where D2m = wAmcoth(/fc>) Eam(r)
and
= Ga-Gm
D\ = Q\a coth(/fo)
+ \a + \
m
- 2A m (r)
(10) (11)
2
where /9 = 1 / ( & B T ) , A m (r) = A m exp(-(T/(2"r m )) ) and Am and Aa are the reorganization energy of the donor and the acceptor molecules, respectively 6 . Equations (4) and (9) imply that the emission spectrum of the donor and the absorption spectrum of the acceptor molecule is represented as the gaussian profile where the peak of the emission spectrum of the donor shifts in accordance with A m (r). 3. R e s u l t s In order to recognize the relation between the above two forms of the two-time correlation functions, we apply these formulas to the E E T in the BChl-BChl dimer in the LH2. Parameters was used as the same as ref. 7. The figure 1. shows the graph of the time dependent probability n„(£) of the EET in the case of U = 350, 60 and 20 cm'1. The solid lines indicate the results
1
A'\ 7/
0.8 0.6 0.4
'V '
'N
\
/ \J
350 cm-i
]
0.2 I
/
V
y
1
y
'/
IZ.
^\ / "0'"*--'"""-' ^^^^ ^^ yS\ 60 cm' 20 cm' 1
_3— 0.1
0.2
~~ 0.3
time (ps) Fig. 1. The time dependent probability na(t) of the EET in the B850 dimer. Calculating in the case of the coupling strength U = 350, 60 and 20 cm~ respectively.
by the analytical formula of eq. (3) using eq. (2). The dashed lines indicate the results by the cumulant expansion method. In the case of U = 350cm - 1 the result by the cumulant expansion method is oscillating stronger than the result of the analytical formula. However, before the time when na(t) becomes maxima for the first time, these results coincide well with each other. We found that the weaker the coupling strength becomes, the better two results coincide with each other. Consequently, these results imply that the approximation by an exponential function for the two-time correlation function reproduces the character of the EET very well for the intermediate and weak coupling cases.
268 Acknowledgments The authors wish to express their sincere thanks to Professor H. Sumi in Tsukuba University for invaluable advises. References 1. Th. Forster, Ann. Phys. 2, 55 (1948). 2. A. S. Davydov, Theory of Molecular Excitons (Plenum, New York, 1971). 3. H. van Amerongen, L. Valkunas and R. van Grondelle, Photosynthetic EXCITONS (World Scientific, Singapore, 2000). 4. T. Kakitani, A. Kimura and H. Sumi, J. Phys. Chem. B 108, 3720 (1999). 5. A. Kimura, T. Kakitani and T. Yamato, J. Lumin. 87-89, 815 (2000). 6. A. Kimura, T. Kakitani and T. Yamato, J. Phys. Chem. B in press. 7. V. Novoderezhkin, R. Monshouwer and R. van Grondelle, Biophys. J. 77, 666 (1999). 8. V. Hizhnyakov and I. Tehver, Phys. Stat. Sol. 21, 755 (1967).
THEORETICAL STUDY ON THE PHOTOINDUCED DYNAMICS IN A MULTISTABLE ELECTRONIC SYSTEM
KAZUKI KOSHINO *and TETSUO OGAWA t Department of Physics, Tohoku University Aoba-ku, Sendai 980-8578, JAPAN
We theoretically discuss the photoinduced dynamics in multistable electronic systems, employing the photoinduced neutral-ionic (NI) transition in charge-transfer (CT) complexes as an example. On the NI transition temperature, a conventional picture of excitation in this material (CT exciton) does not hold; instead, the boundary between the two phases (NI domain wall) should be regarded as a basic excitation. After photoinjection of a microscopic ionic domain into the N phase, it grows into a large ionic domain through the band motion of NI domain wall. The domain extends at a constant speed, randomly choosing spins of transferred electrons. 1. Introduction In recent years, many exotic materials are successively found where a macroscopic change is induced in the material by photoinjection of excitations. Such photoinduced cooperative phenomena are often called photoinduced phase transitions 1 . These phenomena have been found in quite various kinds of materials with multistability, which is realized around the critical temperature of first-order phase transition. In the observed examples of photoinduced phase transition, the multistability of the system as well as the interaction among the constituent elements is brought about by different physical mechanisms in each material, which prevents us to understand the phenomena from a unified viewpoint. The photoinduced neutral(N)-ionic(I) transition in charge-transfer (CT) complexes 2 is a typical example of such phenomena. The N-I transition in CT complexes is brought about by a delicate balance between the loss of the ionization energy and the gain in the Madelung energy at ionization. In other words, the multistability in this system originates in the electronic Coulomb interaction. From theoretical viewpoints, the mechanism of the photoinduced cooperative phenomena in such systems has not been clarified yet, in contrast to transparency in the electron-lattice systems through the model of noninteracting electrons 3 . The objective of this study is to investigate the photoinduced cooperative dynamics of electrons mediated by the electronic Coulomb interaction, discussing the N-I transition in CT complexes as an example. 2. Theoretical m o d e l The theoretical model describing the electrons in a quasi-one-dimensional CT complex (TTF-CA) is the following tight-binding Hamiltonian,
« = y B - 1 ) V + U £n, a n jfi + VJ2 Wi+i - T E(4CJ+L- + 4+i,^)>
W
where odd (even) sites represent the HOMO (LUMO) of a donor (accepter) molecule, Cja, c!-„ and Uja are the annihilation, creation and number operator for an electron with spin a(=a •Present Address: Frontier Research System, The Institute of Physical and Chemical Research (RTKEN), Hirosawa 2-1, Wako 351-0198, JAPAN; E-mail: [email protected] 'Present Address: Department of Physics, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, JAPAN
269
270 or P) at the j t h site, and q-j represents the charge of the j t h molecule, which is denned by qj = 2 — Y,o Kja [— Y.o nja] for odd [even] j . The total number of the electrons is equal to the number of the sites, which we hereafter denote by N. The meaning of the parameters are the following; A' is the energy difference between the donor and accepter orbitals, U is the on-site Coulomb repulsion, V represents the intersite Coulomb interaction between the nearestneighbor molecules, and T is the nearest-neighbor CT integral. The parameters A', U and V are of the order of leV, while the CT interaction T is much smaller than these parameters and is of the order of O.leV. Using the definition of the charge qj, we can rewrite the Hamiltonian Eq. (1) into the following form by neglecting a constant term, n
= ~o X ! ( - 1 ) ; ' r V + U £ njanji3 + V ] T njanj+1^
- T YKC]"CJ+^
+ 4+i,^).
(2)
where A = A' - 4V. In fact, the intersite Coulomb interaction (the third term) in Eq. (1) or (2) is the shortrange limit of Madelung energy. The opposite limit, i.e., the long-range limit, has already been discussed in Ref. 4, where it is clarified that the mean-field effect results in nonlinear response of the photoinduced dynamics to the density of photoinjected excitations. In this study, we focus on the short-range limit Hamiltonian Eq. (2), and discuss the local mechanism of self-proliferation of the excited domain. 3. Ground s t a t e s and e x c i t a t i o n s In order to grasp the basic features of this model, we first consider the case of T = 0, where classical treatment of the electrons is allowed. This is a reasonable approximation because T is much smaller than the other parameters. There are two candidates of (meta)stable states; the neutral (N) and ionic (I) phases. The electronic configurations in each phase are shown in Fig. 1. The energies of these states are given by EN = -JV(A - U)/2 and El = -NV. The NI transition point for T = 0 is defined by En = Ei, i.e., A — U = 2V, which is the mathematical expression of the competition between the ionization energy and the Madelung energy. Because we are interested in a situation where the N and I phases are energetically degenerate, we assume that E^ = E\ is satisfied in the following. (a)N phase
4HT4T D0A0D°A0D°A0
(b)I phase
4+±+4>
D+A_D+A-D+A-
Fig. 1. The electronic configuration in (a) N phase and (b) I phase. Next we consider three kinds of charge-transfer (CT) excitations from these phases; CT electron-hole pair, CT exciton, and n-CT string. These excited states are shown in Fig. 2, from N phase for example. We call a charge-transferred state to the nearest neighbor site (to a remote site) a CT exciton (a CT electron-hole pair), and n successive CT excitons a n-CT string, respectively. The excitation energy of these states are shown in Fig. 2, which is given by Eq. (1), taking into account that we are on the transition point and E^ = E\ is satisfied. It should be noted that, on the NI transition point, the excitation energy is proportional to the number of NI domain walls. In other words, the elementary excitation in this situation should be regarded as the NI domain walls 5 . Thus, n-CT strings (n = 1,2, • • •) are energetically degenerate. This
271 number of CT
number of DW
1
i
DVDV
1
2
V
0 D ° A " D * A " D + A" D*A°D°A
n
2
V
(a) CT eh pair
DWD*A°DV D'ADY
excitation energy 2V
(b) CT exciton D 0 A 0 D 0 A 0 D + A" (c) n-CT string (n=3)
Fig. 2. Electronic configurations of a CT electron-hole pair, a CT exciton and a n-CT string form the N phase. The excitation energies are calculated on the NI transition point (i?fj = E\) and T = 0. is contrary to the fact that we should regard CT excitons as elementary excitations apart from the NI transition point. 4. Q u a n t u m m o t i o n of N I D W s As discussed in the previous section, the states with a single n-CT string (n = 1,2, • • •, ^ — 1) or, in other words, with two NIDWs are degenerate in energy on the NI transition line for T = 0. However, this degeneracy is lifted for nonzero T due to the motion of the NIDWs, which we discuss in this section. We treat the case of small T satisfying T -C V, where the effect of other states with different energies {e.g., 0- or 4-NIDW states) is negligible, and discuss the band motion of NIDWs within the first-order perturbation in T. The coupling with the photon field occurs through the current operator J = i(p-eT) £j,„(cj„c.j+i,,,— Cj+1 pCja), where p and e are the polarization vector and the stacking axis. Therefore, a CT exciton state (1-CT state) with the total momentum k = 0 and with odd parity is created just after absorption of a photon with energy V. Prom the N phase, it is given by \a) = - ^
( +
| • • - D 0 A 0 D" H 7 A-"D 0 A 0 D 0 • • •) - | • • • D°A-'D- H 7 A 0 D 0 A°D 0 • • •) | • • • D 0 A°D 0 A°D +<7 A- <7 D 0 • • •) - | • • • D°A°D°A- a D- H 'A 0 D 0 • • •) + •••), (3)
where a represents the spin of the electron (hole). Because the total momentum k of the NIDWs and the parity of the wavefunction are conserved due to the translational and inversion symmetry of the Hamiltonian, the wavefunction evolves restrictedly in the Hubert space of 2NEDW states with k = 0 and odd parity, which is spanned by n-CT states \o\a?, • • • <J„) denned similarly to Eq. (3). The matrix element of the Hamiltonian (1) connecting these states is then given by
The initial state just after photoexcitation in the N phase is a 1-CT state |^>N(T = 0)) = |<j) (
272 to increase at a constant speed inversely proportional to N [see the dotted lines in Figs. 3(a) and (b)], which means that the time A T required for one CT is independent of the system size N. A T is estimated at about 0.220(h/T). (7/) later grows to a large value almost unity, which means that the N—>I phase conversion can be induced even by one photon excitation through the domino effect. We can also gain the information on the spin of the transferred electrons by Fig. 3. The figure tells us that ((T/ Q ) — (77^)) is kept at a constant value of (2/N) at the initial stage of the temporal evolution, which means that the spin of the transferred electron due to CT interaction T is selected almost randomly. Summarizing, after injection of a CT exciton into the N phase, the ionized region extends at a constant speed, randomly choosing spins of transferred electrons. ' P 0.8 O 0 0.6
/ /(b)N=20
(a) N=10
/
& 0.4
c
S~
"""1
-"'77 2
T (ia units of E/T)
3
)
1
2
3
T (in units of E/T)
Fig. 3. Temporal evolution of 77^'s from the N phase for (a) TV = 10 and (b) N — 20, with the initial condition that a CT exciton with spin ct is photoinjected at T = 0. We touch here the long time behavior of {77(7-)). Neglecting the spin degrees of freedom, the problem is equivalent to a particle hopping one-dimensionally among (N/2 — 1) sites, where the position of the particle corresponds to (T](T)). Thus, qualitatively speaking, (T)(T)} oscillates between (2/N) and (1 — 2/N) with the period of TV A T without damping. This is due to our treatment of this electronic system as a closed one; in reality, the motion of domain walls will be damped through relaxational effects, so this calculation is reliable only at the initial stage of temporal evolution. We have discussed in the above the initial dynamics of CT just after absorption of a photon. However, there is another important aspect for complete description of N—>I phase conversion; dimerization takes place due to spin-Peierls instability in the I phase. In the ionized region, there exists a fine energy structure of order (T2/V) governed by the spin Hamiltonian Tis = (T2/V) J]j s"j • Sj+i. As we have seen, the spins of transferred electrons are selected randomly, which means that the ionic region just after CT is in highly excited spin configuration. Such a state does not have instability against dimerization. As the relaxation of spin state proceeds, this instability becomes more crucial. Thus there is some interval between CT and dimerization, and during this interval the system is kept ionic without dimerization. In this section, we focused on the N—>I direction of transition. To investigate the I—>N direction, we have to start from a model with electron-lattice coupling, because the I phase cannot be described well by the Hamiltonian (1) due to spin-Peierls mechanism, while the description of the N phase has no qualitative problem. This problem will be discussed elsewhere. References 1. 2. 3. 4. 5.
K. Nasu (ed.): Relaxations of Excited States and Photo-Induced Structural Phase Transitions (Springer, 1997). S. Koshihara, Y. Takahashi, H. Sakai, Y. Tokura and T. Luty, J. Phys. Chem. B 103, (1999) 2592. A. J. Heeger, S. Kilveson, J. R. Shrieffer and W. -P. Su, Rev. Mod. Phys. 60, (1988) 781. K. Koshino and T. Ogawa, Phys. Rev. B 61, (2000) 12101. N. Nagaosa and J. Takimoto, J. Phys. Soc. Jpn 55, (1986) 2745.
Enhancement of Exciton and Biexciton Luminescence in CuCl QDs on Dielectric Multilayers H. Kurisu, J. Horie, K. Nagoya, S. Yamamoto and M. Matsuura Department of Material Science and Engineering, Yamaguchi University Ube, Yamaguchi, 755-8611 Japan We investigated photoluminescence properties of the exciton and the biexciton in CuCl quantum dots embedded in an Si0 2 matrix on (X /4)Ti0 2 /( X /4)Si0 2 dielectric multilayers of the distributed Bragg reflector. The intensities of the free exciton luminescence band and the biexciton luminescence bands are enhanced by factors 2 and 6 times in comparison with those in only CuCl quantum dots embedded in an Si0 2 matrix. The origin of this luminescence behavior is partly reflection effects of the luminescence and excitation laser lights but additional effects need to be considered. One possible candidate is the strong exciton-photon interaction due to the confinement effect of the photons in the active layer with CuCl quantum dots.
l.Introduction Enhanced and inhibited spontaneous emission in a microcavity has attracted much attention from both scientific and technological viewpoints since a microcavity allows the control of the spontaneous and stimulated emissions. Recently, microcavities such as planar cavities using the Fabry-Perot mirrors and the distributed Bragg reflectors (DBR's) have been extensively studied, and then enhanced and inhibited spontaneous emissions have been observed in GaAs quantum wells ' and organic dye systems3 for the active layer in microcavities. If the active layer with strong electron (exciton)-photon coupling is used, larger enhancement of the spontaneous emission is expected. CuCl crystal has strong exciton-photon coupling and then the large absorption intensity with very sharp band of the exciton appears. Until now we have investigated CuCl quantum dots (CuCl QDs) embedded in an Si0 2 matrix prepared by a sputtering method. The sharp exciton absorption bands of Z3 and Zii2 appear with the blue shift due to the quantum confinement effect and the free exciton and the biexciton luminescence bands appear with linear and super-linear dependencies with the increase in the excitation density.4 Thus CuCl QDs is suitable to investigate the enhanced and inhibited spontaneous emission in a microcavity. In this paper we present results of the photoluminescence spectra of CuCl QDs in SiC>2 on the dielectric multilayers of the DBR and only CuCl QDs samples and the large enhancement of photoluminescence in CuCl QDs on the DBR sample appears. 2.Sample Preparation CuCl quantum dots embedded in an Si0 2 glass matrix on dielectric multilayers were prepared using an rf-magnetron sputtering with an inductively-coupled-plasma, named ICP sputtering. This sputtering system has an rf-magnetron cathode and a coil antenna for generation of the inductively-coupled-plasma. In this system, plasma characteristics and ion bombardment during the film deposition can be controlled and then the microcrystals as well as deposition films are expected to have high qualities. For preparation of the distributed Bragg reflector, Ti0 2 and Si0 2 targets with 50mm 4> were used. The base pressure of the sputtering chamber was 6.4xl0"5Pa, and then process gas (Ar) was introduced at 5.3xl0_1Pa. Typical rf-powers for the magnetron sputtering cathode and for the ICP antenna were set to be 100 W and 50 W, respectively. For preparation of the CuCl quantum dots embedded in an Si0 2 matrix, CuCl powder of 50mg was set on the Si0 2 target and then a co-sputtering was carried out. The process gas (Ar:N2=l:l) was introduced at 2.6xlO"'Pa, nitrogen was added to prevent the deposition films from being colored. Typical rf-powers for the magnetron sputtering cathode and for the ICP antenna were set to be 50 W and 10 W, respectively. 273
274 Figure 1 shows the schematic illustrations of the prepared samples. The distributed Bragg reflector is composed of 8 pairs of Ti02 and SiC>2 layers whose optical thickness is A /4. Here the wavelength of A is 385nm which matches with the energy of Z3 exciton in CuCl quantum dots. CuCl quantum dots embedded in an SiC>2 glass matrix with thickness of about 3 A /4 is accumulated on the DBR, named CuCl QDs with DBR. We also prepared only the CuCl quantum dots embedded in a SiC"2 glass matrix, called CuCl QDs without DBR. Figure 2 shows the transmission and reflection spectra of ( A /4)Ti02/( A /4)Si0 2 distributed Bragg reflector. The transmittance of the DBR is below 0.1 from about 350nm (3.54eV) to 420nm (2.95eV) and the reflectivity is 70% at this wavelength region, i.e., optical stop band appears clearly. Here the exciton energy of CuCl quantum dots, about 385nm (3.22eV), locates within the stop band of the DBR. Noted that the transmittance of the DBR is below 0.1 around at 300nm because of the absorption of Ti02For the photoluminescence measurements, excitation laser beam was let in the samples at the angle of about 20 degrees for the normal axis in plane, and the photoluminescence light along the normal axis in plane of the samples was detected backward scattering configuration at 10K. The wavelength of the laser beam is 250nm (4.96eV) using a SHG light of an optical parametric oscillator (OPO) laser with pulse duration about 5nsec.
(3 A /4) CuClQDs in Sil
8pair
(a) CuCl QDs in SiO z (fo) CuCl QDs in S i 0 2 with DBR Figure 1. Schematic illustrations prepared samples CuCl QDs in Si0 2 without DBR (a) and with DBR (b).
300
400 500 Wavelength
600 (nm)
700
Figure2. Transmission (a) and Reflection (b) spectra of the ( X /4)Ti0 2 / ( A /4)SiQ2 dielectric multilayers.
3.Results and Discussions Figure 3 (a) and (b) show the photoluminescence spectra in CuCl QDs without and with DBR, respectively, under the same excitation density, 3 fi J/cm2, at 10K. In CuCl QDs without DBR the luminescence bands named X, MXi and MX2 appear clearly at 3.224, 3.189 and 3.178eV as seen in Fig 3 (a). Where X band is due to the recombination of the free exciton, MX2 originates from the free biexciton luminescence leaving the free exciton and MX] is attributed to the bound biexciton luminescence leaving the bound exciton.4,5 The blue shift value of X band from the energy of Z3 exciton in bulk CuCl crystal is obtained to be 19meV. Considering the blue shift originates from the quantum size effect for the translational mass motion of the excitons6, and then the mean particle radius of CuCl QDs is estimated to be 3.4nm. From the half width of X band, lOmeV, the size distribution is ±0.4nm. Thus, it is found that prepared CuCl QDs embedded in Si0 2 matrix are nano-particles with very small size distribution and high quality samples in optical properties because of the appearance of the free exciton and the biexciton luminescence bands. In CuCl QDs with DBR the luminescence bands X, MXi and MX2 appear at almost the same energies of those in CuCl QDs without DBR and the shapes of luminescence bands are similar to those in CuCl QDs without DBR. It is considered that the same CuCl QDs are prepared between two samples with and without DBR, i.e., the excitons and the biexcitons of two samples have the
275
same radiative and non-radiative decay processes. We compare the intensities of 1.5With DBR (b) luminescence bands between CuCl QDs with and without DBR. The intensities of the free luminescence and the biexciton luminescence bands in CuCl QDs with DBR increase in 0.5 comparison with those in CuCl QDs without DBR by factors about 2 and 6 times, where we • , i"7T—, compare the total intensities of the biexciton luminescence bands of MX, and MX2. In the X ffl, W/0 DBR (a) biexciton luminescence the large enhancement S 0.5 appears. Then the origin of the enhancement of MX, luminescence bands needs to be considered and MX, is discussed in the following. Here the sample V X2 dependence for the luminescence properties is negligible because prepared samples have the ! 1 , . . same particle size and similar luminescence 3.15 3.2 3.25 shape as mentioned before. Photon Energy (eV) We estimate the enhancement factors of Figure3. Luminescence spectra of CuCl QDs in Si0 2 the free exciton and the biexciton luminescence without DBR (a) and with DBR(b). bands due to the simple reflection effect of the photons by the DBR. The reflectivities of the luminescence lights and the excitation light are about 70% and 20%, respectively, because the wavelengths of the luminescence bands, 385-390nm, are within the stop band of the DBR, 350-450nm, and that of the laser light of 250nm is not within the stop band. In the first, we assume that the re-absorption process of the luminescence light of the free exciton does not occur, and then the enhancement factor of the free exciton luminescence is estimated to be 2.0 (=1.2x1.7) and that of the biexciton luminescence is to be 2.4 (=1.22xl.7). From the experimental results, enhancement factors are obtained to be 2and 6 for the exciton and the biexciton luminescence bands, respectively. Then it seems to that the origin of the enhancement of X band can be explained by the reflection effect of the photons by the DBR, but that of the biexciton luminescence bands is not attributed only to the reflection effect. Here we mention the re-absorption effect for the enhancement of the luminescence bands. The re-absorption process of X band exist, because the optical density of Z3 exciton in the prepared CuCl QDs without DBR is about O.D.=0.8. Then in the relaxation process of the Z3 exciton, not only the radiative but also the non-radiative decay process exists.2 In CuCl QDs with DBR the reflection lights of the free exciton luminescence decrease since the reflection lights are re-absorbed and the excitons partly relax through the non-radiative process. Then the enhancement factor for X band due to the reflection effect actually becomes to be less than 2. Thus the origin of the enhancement of X band may not be explained by only the reflection effect and then additional effects may be necessary to be considered. While in the biexciton luminescence of the sample with the DBR, the increase in the exciton density due to the re-absorption effect of reflection lights can be considered to be small because the free exciton luminescence lights decrease due to the non-radiative process. Finally we discuss effects of strong exciton-photon coupling for which the confinement effect of the luminescence light in the active layer on the DBR is a candidate. In our sample with the DBR, the luminescence light can be confined in the active layer, because the active layer of CuCl QDs in Si0 2 layer forms the optical wave guided layer. In this case the increase in the exciton-photon coupling is expected in the optical wave guided layer. For the free exciton luminescence it is - " I
1
.
.
i
a
I
.
,
i
i
1
i
i
i
The decay time of X band is obtained to be ~ 10 psec in CuCl QDs embedded in Si0 2 prepared by ICP sputtering method. This value is smaller than those in another CuCl QDs prepared by liquid phase synthesis. Then in our samples it is considered that the non-radiative decay is not negligible.
276 considered that the confinement effect of the luminescence photons may contribute to the enhancement of X band in the sample with the DBR because the enhancement factor due to the reflection effect is estimated to be less than 2 due to the re-absorption effect as described above. While in the biexciton luminescence, the intensities of MXi and MX 2 bands in the sample with the DBR are enhanced clearly. It is considered that the biexciton has the very large photon coupling and the smaller non-radiative process resulting in large enhancement of the biexciton luminescence. In summary, we observed the enhancement of the exciton and biexciton luminescence in CuCl QDs embedded in SiC>2 on (X /4)Ti0 2 /( A /4)Si0 2 dielectric multilayers in comparison with only CuCl QDs sample. This luminescence behavior originates from partly reflection effect of the luminescence and excitation laser lights. In addition the increase in the exciton-photon coupling needs to be considered. The confinement effect of the luminescence phoions in active layer is one of the candidates for the increase. Acknowledgements This work was partially supported by a Grant-in-Aid for Encouragement of Young Scientists from the Ministry of Education. Photoluminescence measurements were carried out using the laser system in Venture Business Laboratory, Yamaguchi University. References 1. Yokoyama, K. Nishi, T. Anan and H. Yamada, Appl. Phys. Lett., 57, 2814, (1990). 2. Yamauchi, Y. Arakawa and M. Nishioka, Appl. Phys. Lett., 58, 2339, (1991). 3. De Martini, G. Innoccenti, G. R. Jacobovitz and P. Mataloni, Phys. Rev. Lett., 59, 2995 (1987) 4. Kurisu, K. Nagoya, N. Nakayama, S. Yamamoto and M. Matsuura, J. of Lumin., 87-89, 390 (2000). 5. Yano, T. Goto, T. Itoh, A Kasuya, Phys. Rev., B 55, 1667, (1997). 6. Itoh, Y. Iwabuchi, M. Kataoka, Phys. Stat. Sol. (b), 145, 8585, (1988)
EXCITON DYNAMICS OF ORTHORHOMBIC PHASE Pbl2 EMBEDDED IN Pbl2- PbBr2 MIXED CRYSTALS J. TAKEDA, T. SAKAMOTO*, T. ARAI, S. KURITA Department of Physics, Faculty of Engineering, Yokohama National University 79-5 Hodogaya, Yokohama 240-8501, Japan Reflection, time-integrated and time-resolved luminescence spectra nave been measured in Pblj,,.^r^ (jr>0.5) mixed crystals in order to elucidate the excitonic properties and relaxation processes of orthorhombic phase Pbl2 embedded in the mixed crystals. The crystal structure of P h l g ^ B ^ above x=0.5 is orthorhombic and an observed new reflection peak (~2.5 x KJ* cm') above JC=0.5 is due to an excitonic state of orthorhombic phase Pbl2. On the excitation energy above 2.5 x 10" cm"1, a broad luminescence band with a large Stokes shift from the reflection peak was observed. This luminescence band is attributed to a self-trapped exciton state. The decay of the luminescence has two components. Based on an atomic excitation picture, the shorter decay component (£10 ns) is attributed to the allowed transition from 3/>i to 'S0. On the other hand, the longer decay component (~3 \JLS) might be due to the forbidden transition from 3 P 0 to 'S0.
1. Introduction Crystal structure of Pblj^jBrj, mixed crystals is hexagonal below JC=0.25 but orthorhombic above *=0.5, reflecting the different crystal structures of the constituent materials1. A low lying excitonic state of lead halides is known to have a cationic nature - the electronic transition is from 6s to 6p state of a lead ion23. The reflection spectra of the Pbl^.^Br^ mixed crystals show a reflection peak located at ~2.5xl04 cm"1 above JC=0.5. This peak was assigned to be due to an excitonic state of orthorhombic phase Pbl2 embedded in PbI2(,_x)Br2l mixed crystals1. In this paper, we present the excitonic properties and relaxation processes of the orthorhombic phase Pbl2. 2. Experimental Single crystals of Pbl^.^Br^ were grown by the Bridgman method as previously reported1,4. Concentration x was determined by radio-activation analysis and the crystal structure of mixed crystals were analyzed by X-ray diffraction method4. Reflection and time-integrated luminescence spectra were measured by the conventional method1. A third harmonic (355 nm) of a pulsed Nd:YAG laser with a repetition rate of 10 Hz and a pulse duration of 5 ns was used as excitation of samples for the measurement of time-resolved luminescence spectra. Luminescence from sample surface was passed through a single grating monochromator and detected by a boxcar averager or a digital sampling oscilloscope. The overall time resolution of the present experiments was 10 ns. 3. Results and discussion Figure 1 shows reflection and time-integrated luminescence spectra of Pbl^.^Br^ mixed crystal (JC=0.6). The reflection spectrum shows a strong reflection peak located at ~2.5 x 104 cm"1. 277
278 This peak appears only when the crystal structure of the mixed crystal is orthorhombic (x a0.5), and the peak intensity decreases with decreasing the concentration of the iodine1. The energy of the peak is slightly lower than the excitation energy of the Pb2* ion diluted in alkali iodidess. These results strongly suggest that the reflection peak is due to an excitonic state of orthorhombic phase Pbl2 embedded in the mixed crystals. For the excitation energies above 2.5 x 104 cm"1, an intense broad luminescence band S with a large Stokes shift from the reflection peak was observed. This band disappears under the excitation below 2.5 x 104 cm"1. This suggests that the S band originates from orthorhombic phase Pbl2 and is due to a self-trapped exciton (STE) state of orthorhombic phase Pbl 2 \ In pure Pbl2 (x=0) whose crystal structure is hexagonal, a free exciton state is stable because of a large exciton band width (-1.4X104 cm"1). On the other hand, the exciton band width of the orthorhombic phase Pbl2 is much smaller (~4xl0* cm"1) than that of the hexagonal phase Pbl^ implying that the STE state would become more stable in orthorhombic phase Pbl2. Thus we may observe the S band originated from the STE state.
112 -J
16 20 24 28 32 36 Photon Energy (kcrrr1)
Fig. 1. Reflection and time-integrated luminescence spectra of Pbl^^jBr^ mixed crystal (JC=0.6) at 4.2 K. Figure 2 shows time-resolved luminescence spectra of Pblul_JiTu mixed crystal (x=0.6) at 4.2 K for different delay times. Two luminescence bands S and F were clearly observed at "1.4x10* and -2.1x10" cm"1, respectively. The luminescence intensity of the F band decays single exponentially and the decay time is less than 10 ns which is within the time resolution of present experiments. Because the F band has only a very short decay component, the F band was not clearly seen in the time-integrated luminescence spectrum as shown in Fig. 1. The intensity of the F band is strong when the excitation energy is around ~2.1xl04 cm"1, whose value is much lower than the reflection peak of the orthorhombic phase Pbl2. This indicates that the F band does not originate from the orthorhombic phase Pbl2. The energy region around -2.1x10* cm'1 is very close to the lowest excitonic energy of the hexagonal phase Pbl2. The F band also resembles the free exciton luminescence band of hexagonal phase Pbl2 in shapes. We therefore assume that the origin of the F band is luminescence from hexagonal phase Pbl2 clusters dispersed in Pbl^.jjBr^ mixed crystal1,4.
279 1
1
1
1
i
i
i
i
x = 0.6
s
8 / c 8 S
i
J
100
10 ns
xl
J
\
i
4.2K
X
5
30 ns
g 'E
430 ns
3
1930 ns
- ^ H 12
14
i
16
i
18
i
i
20
i
i
22
i
24
1
Photon Energy (kcnr )
Fig. 2. Time-resolved luminescence spectra of Pbl-^.^T^ different delay times.
mixed crystal (.1=0.6) at 4.2 K for
On the other hand, the decay of the luminescence of the S band has two components. The shorter decay component has a decay time less than 10 ns, while the longer one has a decay time of 3.2 us. The lowest allowed excitonic state in orthorhombic lead halides is known to be originated from an electronic transition from lS0 to 3P1 in the Pb2* ion, based on an atomic excitation picture3,6. Since the selection rule ASK) is non-rigorous, the transition from '.S0 to 3 P, is optically allowed. The origin of the shorter decay component is therefore attributed to the transition from 3 P, to '5 0 . The longer decay component implies forbidden character of the transition. It is known that the optical transitions from 3 P 0 to \S„ and from 3 P 2 to 1S0 are forbidden by the strict selection rule of AJ =13. Recently, the energy splits between 3 P, and 3 P 2 and between 3 P, and 3 P 0 were estimated to be 0.5~1 and ~0.08 eV, respectively, for the Pb2* ion in various host crystals7. The energy of 3 P 2 state is much higher than that of 3 P, state, while the energy of 3 P 0 state is slightly lower than that of 3 P, state. Therefore we speculate that the transition from 3 P 0 to lS0 is most likely responsible for the observed longer decay component in the relaxed STE state. Figure 3 shows decay time of the slow decay component as a function of temperature. Closed circles indicate the experimental data. The decay time is almost constant below 50 K and decreases with rising temperature above 50 K. We fitted the experimental decay time by the following equation;
1+
TRw0exp(-ElkBT)
where T„, O^, E and kB are decay time at low temperature, frequency factor, thermal activation
280 energy and Boltzmann factor, respectively. When the values are rR =3.2 (is, co0=1.5xlOs 1/s and E =30 meV, we obtained the best-fit curve as shown in Fig. 3. The TR and E might represent a radiative lifetime and an activation energy from the self-trapped exciton state to the ground state or to deeper impurity levels, respectively.
„
100 50
Temperature ( K ) 20
42
5
Ia E F
I
1
05
Q
0.1 0
0.02
0.04 0.06 0.08 1/T ( 1 / K )
Fig. 3. Decay time of the slower decay component of the S band as a function of temperature. In summary, we measured reflection, time-integrated and time-resolved luminescence spectra in Pbl^i.^Br^ mixed crystal in order to elucidate the excitonic properties and relaxation processes of orthorhombic phase Pbl2. The crystal structure of Pblj^Br^ mixed crystals above ;t=0.5 is orthorhombic. The observed reflection peak located at ~2.5 x 104 cm"1 above JC=0.5 is due to an excitonic state of orthorhombic phase Pbl2 embedded in the mixed crystals. A broad luminescence band due to a self-trapped exciton state is observed with a large Stokes shift from the reflection peak, and the decay of the luminescence has two components. Based on an atomic excitation picture, the shorter decay component (<10 ns) is attributed to the transition from 3Pt to 'S0. On the other hand, the longer decay component (~3 us) might be due to the transition from 3PB to 1S0. References 1. J. Takeda, T. Tayu, S. Saito and S. Kurita, J. Phys. Soc. Jpn. 60,3874 (1991). 2. CH. Gahwillerand G. Harbeke, Phys. Rev. 185, 1141 (1969). 3. A. F. Malysheve and V. G. Plekhanov, Opt. Spectrosc. 34,302 (1973). 4. J. Takeda, S. Saito and S. Kurita, J. Lumin. 48-49,79 (1991). 5. S. Radhakrishna and K. P. Pande, Phys. Rev. B 7,424 (1973). 6. M. Fujita, H. Nakagawa, K. Fukui, H. Matsumoto, T. Miyanaga and M. Watanabe, J. Phys. Soc. Jpn. 60,4393(1991). 7. T. Hayashi, T. Ohta, M. Watanabe and S. Koshino, J. Phys. Soc. Jpn. 63,4629 (1994). t) present address: Environmental Science Center, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan.
E N E R G Y T R A N S F E R I N T H E P E R I D I N I N C H L O R O P H Y L L a P R O T E I N OF AMPHIDINIUM CARTERAE STUDIED BY POLARIZED ABSORPTION MEASUREMENTS
STEFANIA. S. LAMPOURA Department of Physics and Astronomy, Vrije Universiteit, De Boelelaan 1081, 1081 HV, Amsterdam, The Netherlands B.P. KRUEGER 1 ' 2 , I.H.M. VAN STOKKUM 1 , J.M. SALVERDA1, C.C. GRADINARU 1 , D. RUTKAUSKAS 1 , R.G. HILLER 3 , R. VAN GRONDELLE 1 1 Department of Physics and Astronomy, Vrije Universiteit, De Boelelaan 1081, 1081 HV, Amsterdam, The Netherlands 2 University of California, San Francisco, Pharmaceutical Chemistry, Box 0446, San Francisco, CA 94143 3 School of Biological Sciences Macquarie University, NSW 2109, Australia In this work we report the results of ultrafast transient absorption studies which examined energy transfer between carotenoids and chlorophylls in Peridinin-Chlorophyll-a-Protein (PCP) light harvesting complex from the dinoflagellate Amphidinium carterae. Global analysis of the isotropic decay reveals that the peridinin lifetime in PCP is 2.3±0.2 ps. This time constant is the peridinin-Chla energy transfer, which is essentially entirely mediated by coupling of the peridinin Si and Chla Qj, transitions. Based on this lifetime we estimated an energy transfer timescale of ~2.4 ps and a peridinin-Chla coupling of 46 c m - 1 . The magnitude of this coupling suggests a peridinin Si transition dipole moment of ~ 3 D. Global analysis of the depolarization measurements, shows, a small decrease in the depolarization from the initial 0.4 value to 0.36±0.03. This decrease occurs on the same timescale as the S2—>Si internal conversion, suggesting that either the Si transition dipole is oriented ~15° away from the S2 transition dipole, or, that a small amount of peridinin S2-peridinin S2 energy transfer occurs in competition with internal conversion, or some combination of the two. 1. I n t r o d u c t i o n The dinoflagellate Amphidinium carterae which is found in the sea plankton contains a water soluble Peridinin-Chlorophyll-a-Protein (PCP) that acts as an accessory light harvesting pigment-protein complex. The main light-absorbing pigment of P C P is peridinin, which enables the organism to absorb light in the 470-550 nm region where the Chl's a of the complex do not absorb. P C P is a unique light harvesting complex due to it's peculiar carotenoid-Chla stoichiometry of 4:1 as it has been recently revealed from the crystal structure by means of X-ray crystallography to a resolution of 2 A 1 . The crystal structure not only reveals the transition dipole moment orientation of the pigments, but also that all peridinins are in Van der Waals contact with the Chls and that the distance between the centers of the two Chl's in one monomer is 17.4 A. Therefore, P C P makes an excellent system to study the peridininperidinin and peridinin-Chla interactions. In this work we study the energy transfer timescale between peridinin-Chla and peridinin-peridinin by means of ultrafast transient absorption and depolarization measurements. 2. E x p e r i m e n t a l Transient absorption experiments were carried out with ~i ml of sample, prepared as previously reported 2 , which was flowed using a peristaltic pump and cooled in an ice-water bath. Transient
281
282 absorption spectra were collected with a high-throughput diode array spectrometer that is described elsewere3.- Samples were excited by ~ 100 n j of 500 nm and 520 nm and the pulse width was 50 fs. Excitation densities we used were of ~ 10 15 photons/pulse/cm 2 . The data were analyzed using a global fitting routine 4 . Species-associated difference spectra (SADS) were determined assuming an irreversible, sequential A—>B—>C model, in which the three species represent primarily the peridinin S2 population, peridinin S i / S C T populations, and Chro Q„ population respectively. The depolarization data were fitted by combining model isotropic and anisotropic decays for each species 5 . Initial fits assumed a fixed anisotropy for each species. Later fits, allowing a time-dependent anisotropy for each species, showed no improvement in fit quality. 3. R e s u l t s The energy level scheme of P C P and the SADS for excitation at 500 nm and at 520 nm are depicted in figure 1 and figure 2 correspondingly. s2
So Peridinin
Chla
Fig. 1. Energy level scheme of PCP No significant differences between excitation at 500 nm and at 520 nm were found. The average lifetimes of A, B and C species from the fittings of all the data sets are 0.10±0.05 ps for the A—>B step, 2.3±0.2 ps for the B—)-C step and > 1 ns for the lifetime of C, respectively. The A species shows strong bleaching in the region of So<—S2 absorption together with excited state absorption (ESA) at longer wavelengths. The large S2«— So bleaching in the 450-570 nm is expected, however the dip at 670 nm and the large positive features from 600-700 nm are not expected for the peridinin S 2 state. The possibility that a small amount of Chla was directly excited by the pump pulses was ruled out after comparing our results to similar experiments performed on LHC-II and CP29 3 which show no direct Chla excitation. The broad feature from 600-700 nm is indicative of absorption from an excited singlet state. However, there is no Sn<— S2 absorption in this region and Chla ESA, if present, would be of much lower intensity. We tentatively attribute the ESA feature to a charge-transfer state SCT, which has been recently identified 6 . We suggest that the S C T is rapidly populated from the S 2 state, and that on the timescale that Si becomes populated (~100 fs) 6,7 , an equilibrium is established between Si and SCT- Thus, S c r , decays with the same timescale as Si and should appear in both species A and B. In species B, the magnitude of the 670 nm bleach is roughly the same as that in the species A spectrum, indicating the absence of energy transfer from peridinin to Chla during the lifetime of the S 2 state. This is indicative of the absence of energy transfer from peridinin to Chla, during the depopulation of the S 2 state. The 2.3±0.2 ps lifetime that we observe is faster than the 3.1±0.4 ps observed previously 6 . In general, the global analysis utilized in the present work is more reliable than the twocolour analysis because global analysis measures the evolution of entire spectral bands instead of specific wavelengths within the band. Both, peridinin S I / S C T decay and Chla rise are fitted by a single 2.3 ps component, which, is indicative of no significant electronic energy transfer
283
470
470
520
570
620
570
520
570
620
670
W a v e l e n g t h (nm)
Fig. 2. Species associated difference spectra (SADS) from 500nm excitation (above) and from 520nm excitation (below). In the figure, species A, species B and species C are the lower, middle and upper traces, respectively, as shown in the blue region of each spectrum.
(EET) to Chla from the peridinin S2 state. And last, species C is expected to consist of all the long-lived entities and the decay of this species, > 1 ns, is consistent with the ~ 4 ns lifetime expected for the Chla Qy state 8 ' 9 . Modeling the depolarization data assuming a fixed anisotropy of each species yields r^sO.40, r B =0.36±0.03, and r c =0.04±0.04. The experimental and model traces for all polarizations at two wavelengths are depicted in figure 3.
TLme Ipsl
Time tpsJ
Fig. 3. Anisotropy data (solid) and model (dashed) traces for the 466 and 620nm wavelengths. For both plots, the parallel trace has the largest absolute magnitude and the perpendicular the least. The depolarization from the initial 0.40 to 0.36 for the peridinin S i / S c r species represents an angle of 15° between the S2 and Si transition dipoles or a small amount of peridinin S2peridinin S2 EET. Modeling with a more complicated model allowing the anisotropy of each species to be time-dependent does not improve the quality of the fits, suggesting that there is no peridinin EET. A more thorough explanation of the transient absorption and depolarization measurements is presented elsewere 5 . The peridinin Si lifetime of 2.3±0.2 ps, in combination with the >95% peridinin-Chla EET efficiency yields a peridinin SI/S C T—>Chla E E T timescale of 2.4 ps (2.1-2.6 ps). Combining this EET timescale with a spectral overlap of 1.65 x 10~ 4 cm
284 suggests a peridinin SI/SCT—>Chla coupling of 46 cm l (44-49 cm l) and as a rough estimate a peridinin S i / S c r transition dipole moment of ~ 3 D as explained thoroughly elsewhere 5 . 4. C o n c l u s i o n s Our results support previous findings that energy transfer from peridinin to Chi a at room temperature proceeds entirely through a low lying singlet state -Si or - S C T after internal" conversion from the peridinin S 2 state. We suggest that after internal conversion, peridinin concentration is in equilibrium between two low lying singlet states, Si and SCT- Which of these two states is the donor state in the energy transfer to Chi a is not yet clear. Global analysis of the isotropic decays reveals that the peridinin lifetime in P C P is 2.3±0.2 ps, a slightly faster timescale than was found previously. This lifetime, in combination with the >95% peridininChla E E T efficiency yields a peridinin Si/Scr—>Chla EET timescale of 2.4 ps, which in turn, suggests a peridinin S i / S c r - > C h l a coupling of 46 c m - 1 and leads to a rough estimate of the peridinin S I / S C T transition dipole moment of ~ 3 D. Depolarization measurements suggest that either the S„<— Si transition dipole is oriented ~15° away from the S2<— So transition dipole, nor there is a small amount of peridinin S2-peridinin S2 energy transfer or a combination of these two. Except for this small efffect, there is no evidence in our data suggesting peridinin-peridinin EET, therefore, we assume that each peridinin is independently coupled to the central Chla, quite unlike the highly cooperative situation found in purple bacteria LH1 and LH2. 5. A c k n o w l e d g e m e n t s The authors thank Herbert van Amerongen, Ana Damjanovic and Foske Kleima for enlightening discussions. This work was funded by the Netherlands Organization for Scientific Research (NWO) via the Board of Earth and Life Sciences (ALK) and also by the research institute for Condensed Matter Physics and Spectroscopy (COMPAS). References 1. E. Hofmann, P. Wrench, F.P. Sharpies, R.G. Hiller, W. Welte and K. Diederichs, Science 1996, 272, 1788. 2. F.P. Sharpies, P.M. Wrench, K. Ou and R.G. Hiller, Biochem. Biophys. Acta 1996, 1276, 117. 3. C.C. Gradinaru, I.H.M. van Stokkum, A.A. Pascal, R. van Grondelle and H. van Amerongen, Biophys. J, in press. 4. I.H.M. van Stokkum, T. Scherer, A.M. Brouwer and J.W. Verhoeven, J. Phys. Chem. 1994, 98, 852-866. 5. B.P. Krueger, S.S. Lampoura, I.H.M. van Stokkum, H.M. Salverda, C.C. Gradinaru, D. Rutkauskas, R.G. Hiller and R. van Grondelle, submitted to Biochemistry. 6. J.A. Bautista, R.G. Hiller, F.P. Sharpies, D. Gosztola, M.R. Wasielewski and H.A. Frank, J. Phys. Chem. A, 1999, 103, 2267-2273. 7. S. Akimoto, S. Takaichi, T. Ogata, Y. Nishimura, I. Yamazaki and M. Mimuro, Chem. Phys. Lett. 1996, 260, 147-152. 8. P. Koka and P.-S. Song, Biochem. Biophys. Acta 1977, 495, 220-231. 9. F.J. Kleima, E. Hofmann, B. Gobets, I.H.M. van Stokkum, R. van Grondelle, K. Diederichs and H. van Amerongen, Biophys. J., 2000, 78, 344-353.
EXCITON LOCALIZATION IN (Cd,Zn)0 EPILAYERS AND ( C d , Z n ) 0 / ( M g , Z n ) 0 MULTI-QUANTUM WELLS ON LATTICE-MATCHED SUBSTRATES T. MAKINO 1 , N. T. TUAN, C. H. CHIA 2 , and Y. SEGAWA Photodynamics Research Center, RIKEN (Institute of Physical and Chemical Research), Sendai 980-0845, Japan M. KAWASAKI, A. OHTOMO, and K. TAMURA Department of Innovative and Engineered Materials, Tokyo Institute of Technology, Yokohama 226-8502, Japan H. KOINUMA Materials and Structure Research Laboratory, Tokyo Institute of Technology, Yokohama 226-8503, and CREST, Japan Science and Technology Cooperation We report on optical properties of epitaxial (Cd,Zn)0 layers and multi-quantum wells grown by laser molecular-beam epitaxy on lattice-matched ScAlMgC>4 substrates. Exciton-phonon coupling strength in (Cd,Zn)0 layers estimated by temperature dependence of the excitonic energy was similar to that deduced in ZnO. Time-resolved photoluminescence studies were performed on the multi-quantum wells, which are almost perfectly lattice-matched (0.034%). Radiative recombination of excitons exhibits a spectral distribution of times. We found that the radiative lifetime increases linearly with temperature, showing a two-dimensional feature of excitons in quantum wells.
1
Introduction
Recently, wide-gap semiconductors such as ZnO or its ternary alloys attract considerable attention Mg Content 0.1 0.2 0.3 for the applications of laser diodes. We can at3.28 tain a ( C d , Z n ) 0 / ( M g , Z n ) 0 (CZM) multi-quantum well — 3.26: (MQW) having a perfect lattice-matching by choosing ++ ++ appropriate combinations of C d and M g concentrations. This is one of the advantages compared to (In,Ga)N/(Al,Ga)N MQWs. In the latter case, an internal electric field induced by lattice strain makes the 3.18 excitonic properties complicated. Figure 1 shows an oaxis lengths and room-temperature bandgaps in these al3.14 loys. 1 There have been few experimental studies on prop3.2 3.4 3.6 3.8 4.0 erties of this alloyed film.1 Here, we describe (1) temperaBand Gap (eV) ture (T) dependence of absorption spectra in a (Cd,Zn)0 epilayer and (2) temperature dependences of photolumi- Figure 1: Parametric plot of a-axis nescence (PL) decay time and the time-integrated PL length and room-temperature bandgap (TIPL) intensity in CZM MQWs. in Zni-xCdxO and Mg-cZni^O grown on sapphire substrates. Curves for (In,Ga)N and (Al,Ga)N are also shown.
2
Experimental
Epilayers of Cdo.01Zno.99O were grown on ScAlMgO^OOOl) substrates, the lattice constant of which matches that of ZnO with 0.08%, 2 by laser molecular-beam epitaxy. 3 KrF excimer laser was used. The film was grown at 400 °C. The film had c-axis orientation and a thickness of 50 nm. A ten-period MQW, [Cdo.004Zno.996O/Mgo.12Zno.8sOJ10, had a buffer layer (360-A-thick 'Electronic mail: tmaiino9postman.riken.go.jp Also at Department of Physics, Tohoku University, Sendai 980-8578, Japan
2
285
286 ZnO epilayer). The well width (Lw) was 22 A, and that of the barrier layer was 50 A. Mismatch of the lattice constants between (Cd, Z n ) 0 and (Mg,Zn)0 was 0.034%. Optical measurement were performed by conventional setups. Excitation source for time-resolved PL (TRPL) was the frequency doubled Tiisapphire laser. The excitation energy was 3.397 eV, resonant to the B-exciton in the ZnO buffer at 5 K.
3
Results and discussion
3.1
E x c i t o n - p h o n o n interaction in ( C d , Z n ) 0 epilayers Figure 2: (Left hand side) Temperature dependence of absorption spectra in a (Cd,Zn)0 epilayer grown on ScAlMgC>4. Temperatures are shown on right hand side. Spectra were normalized and vertically shifted for clarity.
CdZnO Jrv-x X+LO epilayer j
I J\
5K
'•'• • y ^
30K
1: *-» f
< •--~
Z^H
80K
"--..
140K
—
200K
*•«.„
/
•—!-•' 1
i
J
P ft Exciton ener
r^
- X-LO/ s""\
3.38 3.36 3.34 3.32
l_
3.1 3.2 3.3 3.4 3.5 3.6 Photon energy (eV)
0
loo 200 Temperature (K)
Figure 3: (Right hand side) T dependence of absorption energy in the epilayer. Circles correspond to the experimental data, while a solid curve shows the calculated results by Eq. (1)
In the exciton resonance region, three absorption bands, labeled as X-LO, X, and X+LO, could be observed at 5-80 K in (Cd,Zn)0 as shown in Fig. 2. These peaks were attributed to be due to longitudinal-optical (LO) phonon assisted exciton transition, free excitons (A- and B-excitons are overlapped), and exciton-LO phonon complex transitions, 4 respectively. The energy difference between the X and X + L O bands coincides with the LO phonon energy of 72 meV. We plotted the peak energies of the X-band of (Cd,Zn)0 (open circles) and ZnO (closed circles, weighted average of A- and B-excitons) against T in Fig. 3. A shift in the exciton energy as a function of T results from a band-gap shift. This derives from both thermal expansion and exciton-phonon interaction, both of which contributes similarly. The shift can be reproduced by Einstein approximation using the effective phonon energy Tujj, and the variation of exciton energy with T is given by E(T) = E{0) - A/[exp(to/fc B T) - 1],
(1)
where E(0) is an exciton energy at T = 0 K, and A is a proportional coefficient, which relates to the exciton-phonon coupling strength. Obtained A's in both the films were 66 meV. 3.2
R e c o m b i n a t i o n p r o c e s s e s in a ( C d , Z n ) 0 / ( M g , Z n ) 0 M Q W
Figure 4 shows T dependence of the TIPL spectra in the MQW. Absorption spectrum could not be measured due to the presence of the ZnO buffer layer. There was no resonant structure in reflection spectra at 5 K. The resonance energy of the free excitons in the wells at 5 K were determined to be 3.408 eV, the calculation method of which was described elsewhere.5"6 The Stokes shift between the P L peak and the exciton energy at 5 K was «170 meV. The PL band is assigned to recombination of excitons localized at energy minima induced by well width and depth fluctuations and by the concentration fluctuations. In the lower part of Fig. 4, the PL decay times as a function of monitored photon energy at 5 K are shown. The decay time is a monotonically decreasing function of the energy. This could be interpreted on the basis of localization of excitons. If the density of the tail state is
287 CckuZnousO/MgouZmuaO MQW
:
CdZnO/MgZnO MQW A TpL
/ /
E1000
#
/
:
& •a
500
3.10
3.15
3.20
3.25
racJ
° \,
/
w/ +
3.05
T
330
Photon Energy (eV)
i 50
sv
O Q|
100
If
«p
Temperature (K)
Figure 4: (Light hand side) T dependence of TIPL in a [Cdo.oo4Zno.g960 (22 A)/Mgo.i2Zno.880(50 A)] 10 MQW. Xs are shown on the right-hand side. PL decay times as a function of photon energy at 5 K. The dashed curve is the theoretical one fitted by Eq. (2). Figure 5: (Right hand side) Dependence of recombination lifetimes on T, TPL, Trad and rnl The solid trace is the straight line fit. approximated as exp(E/Eo), and if the effective recombination lifetime (TPL) does not change with emission energy, the observed decay times T(E) can be expressed by: 7 T(E)
=
Tph
exp((£-.Eme)/£o)'
(2)
where E0 shows the degree of the depth in the tail state and Eme is the energy of mobility edge. The best fit could be obtained using r P L =228.9 ps, EQ =7.74 meV, and Eme =3.258 eV. The depth of localization is estimated to be about 8 meV. The spectrally integrated PL intensity decreases with increasing T, and the PL intensity versus T nicely follows an exp(T/T 0 ) law with To ~ 36 K. Since the measured PL decay time is simply given by Tpl = r ^ 1 + T~^, we obtain the radiative lifetime TT1U± = TPL/T? by assuming that r\ equals 1 at T = 0 K. Figure 5 shows temperature dependence of the effective, radiative, and nonradiative recombination times (TPL, Tracj, and r n r ) . The decay time was shorter than the temporal resolution of our setup above 200 K. The T ra d values were almost constant at values of T below 25 K because of the localization of excitons, and the r ra d increases proportionally to T 1 between 40 and 80 K. Since the nonradiative lifetimes are almost identical to that of PL above T = 100 K, radiative lifetime in this range was not shown. It is likely that excitons are delocalized and become nearly free two-dimensional (2D) excitons above 40 K because the theoretical calculation 8 for the oscillator strength predicts the relation of Trad oc T 1 for 2D excitons. 8,9 Note, the exciton Bohr diameter of 36 A. Since the radiative lifetime of the free-exciton at the low-T limit is known to be related to the slope of the straight line in Fig. 5, 8 , 9 the free-exciton lifetime in the low-T limit was estimated to be « 0.5 ps. This model is valid under the condition that the thermalization time is shorter than radiative recombination times. This radiative lifetime is one or two orders of magnitude smaller than that for GaAs MQW (25 ps), 8 which means that the oscillator strength in the MQW is larger. This is reasonable if the longitudinal-transverse splitting energies in ZnO (A-exciton of 2.2 meV, B-exciton of 11.0 meV) and GaAs of 0.08 meV are considered. 10 ' 11
288
4
Summary
In summary, the exciton-phonon coupling strength was estimated in a (Cd,Zn)0 epilayer, which remained unchanged irrespective of Cd incorporation. Radiative and nonradiative recombination processes were assessed in almost perfectly lattice-matched CZM MQWs by means of TRPL spectroscopy. We have determined the variation of the radiative lifetime of QW excitons versus T to be linear, attributed principally to the excitons from which we deduce a radiative lifetime of 0.5 ps in the low-T limit.
Acknowledgements This work was partially supported by the Proposal Based Program of NEDO (Grant No. 99S12010) and by the Special Postdoctoral Research Program of RIKEN, Japan.
References 1. M. Kawasaki, A. Ohtomo, R. Shiroki, I. Ohkubo, H. Kimura, G. Isoya, T. Yasuda, Y. Segawa, and H. Koinuma, in Extended Abstracts of the 1998 International Conference on Solid State Devices and Materials (Business Ctr. Acad. Soc. Jpn., Hiroshima, Japan, 1998), p. 356. 2. A. Ohtomo, K. Tamura, K. Saikusa, T. Takahashi, T. Makino, Y. Segawa, H. Koinuma, and M. Kawasaki, Appl. Phys. Lett. 75, 2635 (1999). 3. Y. Matsumoto, M. Murakami, Z. W. Jin, A. Ohtomo, M. Lippmaa, M. Kawasaki, and H. Koinuma, Jpn. J. Appl. Phys., Part2 38, L603 (1999). 4. W. Y. Liang and A. D. Yoffe, Phys. Rev. Lett. 20, 59 (1968). 5. T. Makino, N. T. Tuan, H. D. Sun, C. H. Chia, Y. Segawa, M. Kawasaki, A. Ohtomo, K. Tamura, and H. Koinuma, Appl. Phys. Lett. 77, 975 (2000). 6. T. Makino, N. T. Tuan, Y. Segawa, C. H. Chia, M. Kawasaki, A. Ohtomo, K. Tamura, and H. Koinuma, Appl. Phys. Lett. 77, 1632 (2000). 7. C. Gourdon and P. Lavallard, Phys. Status Solidi (b) 153, 641 (1989). 8. L. Andreani, F. Tassone, and F. Bassani, Solid State Commun. 77, 641 (1991). 9. P. Lefebvre, J. Allegre, B. Gil, A. Kavokine, H. Mathieu, W. Kim, A. Salvador, A. Botchkarev, and H. Morkog, Phys. Rev. B 57, R9447 (1998). 10. K. Hummer, Phys. Status Solidi 56, 249 (1973). 11. R. G. Ulbrich 'and C. Weisbuch, in Light scattering in solids III, edited by M. Cardona and G. Gutherodt (Springer-Verlag, Berlin, 1982), Vol. 51.
PHOTOPHYSICAL OVERVIEW OF EXCITATION ENERGY TRANSFER IN ORGANIC MOLECULAR ASSEMBLIES A ROUTE TO STUDY BIO-MOLECULAR ARRAYS A. H. MATSUI Organo-Optic Research Laboratory, Kobe 6-2-1, Seiwa-dai, Kita-ku, Kobe 651-1121, Japan Department ofPhysics, Konan University Okamoto, Kobe 658, Japan M. TAKESHUvlA Organo-Optic Research Laboratory, Bandoujima, Kitagou, Katsuyama, Fukui 911, Japan K. MIZUNO and T. AOKI-MATSUMOTO Department ofPhysics, Konan University, Okamoto, Kobe 658, Japan Exeitonic processes in organic molecular crystals are discussed in terms of two parameters, the crystal size and the constituent molecule size. From the luminescence and absorption spectra of a series of aromatic molecular crystals we find a systematic change in exciton energy transport as functions of the size of crystal and its constituent molecule size. Characteristic features of bulk crystals and microcrystallites are as follows. (1) In bulk crystals exciton energy transport depends on the constituent molecule size. When molecules are small, the exciton energy transport occurs by free excitons, but when molecules are large free exciton transport disappears because excitons get self-trapped (2) In microcrystallrtes, exciton energy transport depends on the crystallite size. When the size is larger 1han a critical one, excitons travel as quantum mechanical waves but when the size is smaller than the critical one the exciton waves get confined within the crystallite. The results are independent of the chemical species of constituent molecules and thus applicable to novel molecular arrays such as biological molecular arrays.
1.
Exciton transport in bulk crystals We describe exeitonic energy transport processes in bulk crystals using a single parameter, the size of the constituent molecules. Let us examine the exciton bandwidths of several aromatic bulk crystals, since the exciton bandwidth is a key factor to describe exeitonic processes and exciton energy transport in molecular crystals. Figure 1 shows the exciton bandwidth of the lowest exciton bands for aromatic molecular crystals as a function of the number of benzene rings in the molecule: l,2,3,4,and 5 represent benzene, naphthalene, anthracene, tetracene, and pentacene crystals, respectively. Open circles show the exciton bandwidth. For tetracene and pentacene crystals the minimum estimates of the bandwidth are shown. They were inferred from the magnitudes of the Davydov splitting, because the bandwidth is theoretically larger than the observed Davydov splitting. The Davydov splitting is shown by solid circles. In the figure, the exciton bandwidth increases with the size of the constituent molecules. This result indicates that the exciton may move more freely with increasing the size of constituent molecules. However, the excitons in crystals with large constituent molecules are generally self-trapped. Let us consider these characteristicsfromthe viewpoint of the exciton-phonon interaction strength. We first discuss the exciton-phonon interaction as a function of the size of the constituent molecules, taking examples in the series of aromatic crystals, benzene, naphthalene, anthracene, tetracene and pentacene. In benzene and naphthalene crystals, no evidence of exciton self-trapping (excimer formation) has been observed, suggesting that the exciton-phonon interaction is weak as free exciton transport occurs. In anthracene, where molecules are larger than benzene and naphthalene, the excimer state is located in energy a little above the free exciton band bottom . In tetracene, the excimer state (the self-trapped exciton state) is located a little below the free exciton band bottom2, suggesting that the exciton-phonon interaction is stronger than in anthracene.
289
290
T c
Ito
1000
.9 800 ®
cf 600 Exciton Bandwidth O O • • Davydov Splitting
I *" |
200
0
1 2 3 4 5 Number of Benzene Rings
6
Fig. 1. The exciton bandwidths for benzene (1), naphthalene (2), anthracene (3), tetracene (4) and pentacene (5) crystals. Open circles show the exciton bandwidth and solid ones Davydov splitting. For pentacene crystals, any quantitative data are not available but we can infer the exciton-phonon interaction strengthfiomthe presence of the charge transfer exciton absorption close to the lowest exciton bands. The presence of the charge transfer exciton absorption bands is a clear evidence of the strong exciton phonon interaction, because charge transfer between adjacent molecules is a cause of the excimer formation. In pentacene, a clear proof of the presence of charge transfer exciton bands which are superposed on Ihe lowest Frenkel exciton absorption band has been reported , while in tetracene the presence of the charge transfer bands is less confirmative. From this feet we confirm that the exciton-phonon interaction in pentacene is stronger than in tetracene. In conclusion, the exciton-phonon interaction becomes stronger for a larger size of constituent molecules and Ihe excimer formation is more feasible in such crystals. This statement is substantiated by experimental facts reported for several molecular crystals, chrysene, azulene and colonene crystals, where composite molecules are large. Their absorption spectra reflect the presence of charge transfer excitons4. What we have mentioned above is that in majority of large-molecule crystals, excitons are self-trapped In other words, the lattice relaxation energy becomes larger with increasing the molecule size and exceeds the exciton band half-width at a critical size. However, the self-trap depth, the energy difference between the free exciton band bottom and the self-trapped state, is not always large for large-molecule crystals. This happens because both the exciton bandwidth and the lattice relaxation energy increase with the size of constituent molecules. As a result of a delicate competition of these two factors, the self-trap depth is shallow. What we have discussed for bulk crystals is summarized in Table 1.
Size of the constituent molecules small large
Exciton transport mode Free Self-trapped
Table 1. Exciton energy transport in bulk crystals. How does it occur?
291 2. Exciton transport in microcrystallites The results mentioned in the previous section are not applicable when the crystal size is very small. To see the exciton energy transport in small molecular assemblies, we have studied the exciton bandwidth as a function of crystallite size. Pyrene microcrystallites provide a typical example. In pyrene microcrystallites whose size is les than 60 angstroms, the self-trapped exciton does not exist5. Therefore, in pyrene microcrystallites exciton energy transport is achieved by free excitons. We will discuss below how excitons travel in microcrystallites. In pyrene microcrystaUites, the band width increases with increasing crystallite size but it abruptly reduces to nearly zero at a critical crystallite size6. From this characteristic experimental fact we found that the minimum size (length) which is required for an exciton to be specified with the wave vector k is about 5 dimeric lattices (ten molecules). Similarly, we found the minimum size in anthracene microcrystallites, where the crystal structure is monomelic, to be 10 lattices with some ambiguity. From these facts we suggested that in organic molecular crystals the cyclic boundary condition is applicable with molecule number below 9 or 10 arranged in chain. In crystallites larger than this critical size, excitons travel, but in smaller crystallites they do not The results are summarized in Table 2.
Size of the constituent molecules Smaller than the critical size Larger than or equal to the critical size
Exciton transport mode Standing wave (no transport) Traveling-wave with the wave vector A
Table 2. Exciton energy transport in microcrystallites.
3. Exciton transport in biological molecular assemblies Biological molecular assemblies provide good examples of testing our conclusions described in Sections 1 and 2. In biological molecular assemblies, the constituent molecules are large and often arranged in one dimension Applying the conclusion given in the second row of Table 1, one can expect the presence of self-trapped excitons in biological large assemblies where constituent molecules are also large. However, in small biological molecular assemblies, self-trapping of excitons does not occur as we have discussed Thus in existing biological molecular assemblies, excitons behave as standing waves in small assemblies (Table 2) but in large assembhes, excitons are self-trapped (Table 1). We will discuss below exciton energy transport in bacteria and DNA. (Bacteria) In bacteriochlorophyll-a B850 rings in purple bacteria, the constituent molecules are large and arranged on a circle with 9 dimeric units. This means that in a bacteriochlorophyll-a B850 ring, the cyclic boundary condition with 9 units is established and the ring can be considered to be equivalent to a bulk crystal. However, B850 ring touches LH1ringto which exciton energy is transferred efFectively. Thus in a bacteriochlorophyll B850 ring, the exciton is like in one dimensional molecular array with 9 dimer units and can be considered to be a microcrystallite. The exciton formed in a B850 ring travels along the ring 4 or 5 dimer units on the average before its energy is transferred to LH1 ring. The exciton in a B850ringis, therefore, quite similar to that in pyrene microcrystallites which is composed of 4 or 5 dimer units, the critical size for exciton traveling. We, therefore, anticipate that the size of a B850 ring is the critical value for the transfer of excitons. This anticipation is substantiated by a recent experiment performed at 1.5 K by van Oijen et al7 for the light harvesting antenna system in purple bacteria. They found delocalized excitons, which extend over the B850 molecular assembly.
292 (DNA) DNA provides another interesting example to discuss the applicability of our results. DNA is a polymer where constituent molecules are large. In DNA, double helix molecular chains are bridged by two kinds of base pairs, A+T and C+G, which are considered to be large molecules. Here A, T, C, and G stand for adenine, thymine, cytosine, and guanine, respectively. The base pairs are located 0.34nm apart from each other and arranged around a ten-fold screw axis. This separation 0.34nm is already the minimum distance that the two adjacent molecules can access in molecular crystals and little margin is left for distance reduction upon excimer formation. Applying the result suggested in the second row of Table 1, one can expect the presence of self-trapped excitons (excimers) in DNA. The excimer in DNA is considered to be located over two base pairs. However, upon excimer formation, the displacement of the two base pairs is never large since, as mentioned above, Uttle margin is left for distance reduction. Thus, upon excimer formation only small lattice deformation occurs. A small lattice deformation associated with exciton self-trapping is advantageous to transport exciton energy as self-trapped excitonic polaron (Davydov soliton). In the discussion given above we considered a straight DNA like a solenoid. In existing DNA, it is not a straight assembly over the whole DNA assembly but there are many bending points. Thus excitons may also be trapped at the bending points, which give deeper self-trapped excitons. We therefore expect to observe two kinds of self-trapped exciton luminescence bands. Two luminescence bands which would be assigned to the self-trapped exciton luminescence bands have been observed 8. Acknowledgments We are very much indebted to Prof. J. Singh for valuable comments on this paper. This work is partly supported by a Grant-in-aid for Scientific Research on Priority Area (B) on "Laser Chemistry of Single Nanometer Organic Particles"fromthe Ministry of Education, Sports and Culture of Japanese Government (10207206)
References 1. R. Horiguchi,N. Iwasaki, and Y. Maruyama, J. Phys. Chem. 91 (1987) 5135. 2. H. Nishimura, Y. Yamaoka, A. Matsui, k. Mizuno and G. J. Sloan, J. Phys. Soc. Japan 54 (1985)1627. 3. Electronic processes in organic crystals" by M Pope and C.E. Swenberg ( 1982) Oxford University Press, New York, p575. 4. J. Tanaka, Bulletin of the Chem. Soc. Japan 38 (1965) 86. 5. K. Mizuno and A. Matsui, Mol. Cryst. Liq. Cryst. 218 (1992) 49. 6. Y. Oeda, O. Nishi, Y Matsushima, K. Mizuno, A. H. Matsui, M. Takeshima and T. Goto, Material Science and Engineering A217/218 (1996) 181. 7. A. M. van Oijen, M. Ketelaas, J. Koehler, T. J. Aartsma and J. Schmidt, Science 285 (1999) 400. 8. Detail will be published elsewhere.
Growth of epitaxial ZnO thin film by oxidation of epitaxial ZnS thin film on S i ( l l l ) A.Miyake\ H.Kominami1, T.Aoki2, H.Tatsuoka1,3, H.Kuwabara1,3, Y.Nkanishi1'2 and Y.Hatanaka1,2 Graduate School of Electronic Science and Technology, Shizuoka University Research Institute ofElectronics, Shizuoka University Faculty ofEngineering, Shizuoka University 3-5-1 Johoku, Hamamatsu 432-8011, Japan The growth of epitaxial ZnO thin film on Si substrate by the oxidation of epitaxial ZnS film is a novel method and we are reporting this first time.
The merits of the use of Si substrate are to make
driving voltage in LED lower and less expensive than sapphire substrate. In this study, the epitaxial ZnO thin film could be successfully grown on the Si substrate. The epitaxial films showed a strong near ultraviolet emission peaked at around 3.32 eV at room temperature under 325 nm excitation.
1.Introduction ZnO is much expected for a material of ultraviolet emission at room temperature. It has a wide band gap (3.37eV) and a high exciton binding energy (60meV) much larger than the energy corresponding to room temperature which allow efficient UV emission from exciton[l]. For an efficient and stable ultraviolet emission from the exciton, epitaxial growth of ZnO is necessary. Hence, various studies are carried out on the preparation of ZnO thin films for the efficient UV laser emission in room temperature[2]. The methods of epitaxial growth of ZnO film are generally prepared by plasma-enhanced molecular beam epitaxy(MBE) and laser MBE on sapphire(OOOl) substrate[3,4]. In this paper, we tried to grow that ZnO thin films epitaxially on Si(lll) substrate by oxidation of epitaxial ZnS thin film on Si(lll). The reason in the selection of Si substrates are due to the wide use for electronic devices, low cost and conductive. Moreover ZnS can be easily grown epitaxially on Si substrate because the lattice mismatch is very small of about 0.3%[5].
293
294 2.Experimental procedure The Si(lll) substrate were cleaned in ethanol, acetone and then ethanol for 5, 10 and 5 minutes, respectivery. Then the surface oxidized layer was etched with H2S04:H2C>2 (=3:1) for 10 min, HF:H20 (=1:20) for about 1 min, HC1:HN03 (=3:1) for 10 min and then with HF:H20 (=1:20) for about 1 min and finally washed with distilled water. ZnS films were grown epitaxially with a thickness of about 100~300nm on the cleaned surface of Si(lll) substrate by electron beam evaporation employing ZnS pellets at a substrate temperature of 200°C. After the deposition, the films were annealed at 800°C for 1 ~ 15 hours in air or 0 2 . The thin-film structural properties were characterized by X-ray diffraction (XRD), reflection high-energy electron diffraction (RHEED) and Auger electron spectroscopy (AES). Luminescent properties were characterized at the excitation with 325nm of He-Cd laser at RT.
3.Results and discussion Figure 1 shows XRD curves of the ZnS
g 8 O
films deposited at a substrate temperature of 200 °C and annealed at 800 °C for various durations in air. The diffraction peaks at 28.5°
=> -S .•&
and 34.4° are corresponding to ZnS(lll) and
£
ZnS/Si(111)' Ts z „ s =200°c annealed at 800 C in airannealed time. 15h
A. 0-311 .
en c
as-depo
ZnO(0002) planes, respectively. It has been observed from the figure that ZnO with c-axis orientation is successfully grown by oxidation of ZnS. The full-width at half maximum (FWHM) of the (0002) diffraction peak is decreasing with
20
30
40
50
60
2 6 (deg.) Fig.l XRD curves of ZnS thin films as-deposition and annealed at 800°C for several hour in air.
increasing intensity with respect to annealing durations. Figure 2 show RHEED patterns of ZnS thin film deposited on the Si(lll) substrate. It is seen that the epitaxial ZnS film was grown with the orientation of (111),[ 1 T0]ZnS//( 111),[ 1 TO]Si. Figure 3 shows RHEED patterns of ZnO thin films after annealing of the epitaxial ZnS film at 800°C for 5 hours in O2. The film after annealing shows spot pattern of ZnO. It has the orientation of (0002),[1120]ZnO//(lll),[ll0]ZnS//(lll),[lT0]Si . From the above result it is observed that ZnO epitaxial thin film could be successfully obtained by oxidation of ZnS epitaxial film.
295
Fig.2
Beaffi/VillQjZnO RHEED patterns of ZnS thin film.
Beam//[ 211]ZnO
Beam//[1120]ZnO Beam//[1010]ZnO Fig.3 RHEED patterns of ZnO thin film after annealing of the epitaxial ZnS film at 800°C for 5 hours in O2. Figure 4 shows PL spectrum of ZnO thin film, which was obtained by oxidation of ZnS
He-Cd 325nm
RT
ZnS/Si(111) oxidation annealed at 80CfCfor5h
measured at room temperature under excitation with 325 nm of He-Cd laser. The films shows a typical exciton emission peak at about 3.3eV[2] and visible emission peak at around 2^2.7eV at room temperature[6]. The intensity of the exciton Energy(eV)
emission is increasing and visible emission is decreasing by annealing in O2 than in air. The peak
Fig.4
PL spectrum of ZnO thin film.
at 3.19eV probably due to the exciton-exciton "p" emission as observed earlier [7]. From their results it has been suggested that the improvement of the stoicMometry due to compensation of the oxygen vacancy by the annealing in O2 involves in the increasing of exciton emission intensity. Furthermore, the intensity of visible emission due to oxygen vacancy decreased.
296 In summary, we have successfully obtained epitaxial ZnO thin film by the oxidation of epitaxial ZnS film. The observation present of strong exciton emission shows the advantages of epitaxial growth of ZnO thin film. It is a very simple and convenient method on the preparation of epitaxial ZnO at low cost. Further studies are in progress viz., annealing condition, film thickness to obtain strong excitonic emission at UV region.
4.References [1] D.M.Bagnall, Y.F.Chen, Z.Zhu, T.Yao, M.Y.Shen and T.Goto, Appl. Phys.Lett. 73 (1998) 1038. [2] P.Zu, Z.K.Tang, G.K.L.Wong, M.Kawasaki, A.Ohtomo, H.Koinuma, Y.Segawa, Solid State Commun. 103(1997)459. [3] H.Koinuma, M.Kawasaki, M.Yoshimoto, Mater. Res. Soc. Proc. Symp. Proc. 397 (1996) 145 [4] D.M.Bagnall, Y.F.Chen, Z.Zhuad, T.Yao, Appl. Phys.Lett. 70 (1997) 2230. [5] Y.Nakanishi, G.Shionoya, J. Vac. Sci.Thecnol. A 5 (1987) 2092. [6] K.Vanheusden, W.L.Warren, C.H.Seagen, D.R.Tallant, J.A.Voigt, Appl.Phys.Lett.68(1996)403 [7] D.M.Bgnll, Y.F.Chen, Z.Zhu, T.Yao, M.Y.Shen and T.Goto, Appl.Phys.Lett.73(1998)1038
RAMAN SPECTRA OF TITANIUM DI-, TRI-, AND TETRA-CHLORIDES H. MIYAOKA, T. KUZE, H. SANO, H. MORI, G. MIZUTANI, N. OTSUKA, and M. TERANO School ofMaterials Science, Japan Advanced Institute of Science and Technology Tatsunokuchi, Ishikawa 923-1292, Japan We have obtained the Raman spectra of TiCl„ («=2, 3, and 4). Assignments of the observed Raman bands were made by a normal mode analysis. The force constants were determinedfromthe observed Raman bandfrequencies.We have found that the Ti-Cl stretching force constant increases as the oxidation number of the Ti species increases.
1. Introduction Titanium chlorides are important components of the Ziegler-Natta catalyst for the production of highly stereospecific polyolefins, but its catalytic mechanism has not yet been fully understood. For instance, though it is believed that catalytic activity depends on the oxidation state of the titanium atom at the active sites1, there have not been decisive experimental evidences supporting this hypothesis. In order to open a new channel in the study of the catalytic mechanism, we intend to perform the in-situ observation of its catalytic reactions by Raman scattering. For this purpose, we need experimental data of the vibrational modes of titanium chlorides with 2+, 3+, and 4+ oxidation states of the Ti atom, namely, TiCl„ («=2, 3, and 4). The Raman bands of molecular TiCl4 have already been observed, and they have been assigned to the normal modes of the molecular vibration of TiCl42,3. On the other hand, only few attempts at Raman observations of TiCl3 and TiCl2 have been made so far4,56, because Raman measurements of them are very difficult. TiCl3 and TiCl2 are unstable materials reacting readily with moisture and oxygen in air, and they decompose easily under laser light irradiation. Thus, distinct Raman bands of oc-TiCL, have been observed only in our previous study4, and Raman spectrum of TiCl2 has not been reported. In the present study, we have obtained Raman spectra of TiCl„ (n=2, 3, and 4), and have carried out a normal mode analysis to make assignments of the observed Raman bands. From the systematic vibrational analysis of TiCl„, it was found that the Ti-Cl stretching force constant increases as the oxidation number of the Ti species increases. 2. Experimental The sample of TiCl4 (99.4 % purity), TiCl3, and TiCl2 (99.98 % purity) used in this study were produced by Wako, Toho Titanium, and Aldrich, respectively. TiCl4 is a transparent liquid at room temperature, and its molecular symmetry belongs to the Td point group. oc-TiCl3 and TiCl2 are dark-colored crystalline powder and have a layer structure consisting of CI and Ti layers. The symmetries of oc-TiCl3 and TiCl2 crystals belong to the C3j and D\d space groups, respectively. All the samples were kept in Ar or N2 atmosphere throughout the experiment. In the case of ocTiCl3, fresh surfaces were prepared by crushing the samples before every Raman measurement4. In the Raman study, a highly sensitive Raman spectroscopy system was used4. The excitation light in the Raman measurement was the 488 nm and 514.5 nm lines of an argon-ion laser. The power and the power density of the laser beam were 5 mW and 160 mW/mm2 or less on the sample surface, respectively. The resolution of the monochromator was set at -20 cm"1 for (X-TiCl3, and
297
298 was set at ~5 cm"' for TiCl, and TiCl,. 3. Results and discussion The observed Raman spectra and Raman band frequencies of TiCl„ (n=2, 3, and 4) are shown in Fig. 1 and Table 1, respectively. Four clear Raman bands are seen in the spectrum of TiCl4. These bands correspond to four optical active vibrational modes of -TTia =AI(R)+E(R)+2F2(R,IR). The frequencies of TiCl4 observed in this study agree well with those reported in Refs. 2 and 3. Five clear bands are seen in the spectrum of a-TiCl34. The frequencies of these five bands are different from those reported in Ref. 5. We inferred that this difference is caused by some difference in the purity or the crystal structure due to the difference of the sample preparation4. The Raman spectrum of TiCl2 shown in Fig. 1 is the first data, so far as we know. Five clear bands are seen in the spectrum of TiCl2. We have found that the Raman band at 157 cm"1 grows when the intense laser light is shined onto the TiCl2 sample. Thus, it is likely that the band at 157 cm"1 is not an intrinsic normal mode of a TiCl2 crystal, but results from a heating effect of TiCl2 by laser light illumination. Therefore, we will not discuss the band at 157 cm"' any further in this paper, but will discuss the other four bands. According to the factor group analysis ( rra =AH(R)+E%{R)+ A2JIR)+Ej(IRy), there should be only two Raman active modes in the lattice vibrations of the TiCl2 crystal. However, four clear bands were observed in Fig. 1. This fact indicates that not only the two Raman active modes, Alg+Eg, but also the two infrared (IR) active modes, A2u+Eu, contribute to the observed Raman spectra. This change of the selection rule probably arises from an optical resonance effect78, because the excitation photon energy is close to an allowed electronic transition energy of crystalline TiCl2. We have calculated a normal mode analysis of molecular and lattice vibrations of TiCl„ by the GF method910. The fitting of the calculated frequencies to the observed ones was performed by means of an automatic algorithm minimizing the sum of the squares of the deviations, during variation of the force constants. In the case of the normal mode analysis of 6 TiCl4, four force constants (K, F, H, and K) are defined on the basis of the Urey-Bradley force field. K and F are the stretching force constants § of Ti-Cl and Cl-Cl, respectively. H is the bending force constant of Cl-Ti-Cl valence angle. K is the force constant called "intramolecular The force constants F and K are tension" related to the off-diagonal elements of the force matrix (F-matrix). The results of the normal 2 mode analysis of TiCl4 are shown in Table 1(a). (5 The calculated frequencies agree with the observed ones, and the assignments of the vibrational modes agree with those in Ref. 2. 400 800 The force constants obtained from the normal Stokes shift (cm") mode analysis are shown in Table 2(a). The normal mode analysis of a-TiCl3 has Fig. 1. Raman spectra of TiCl„ (n=2, 3, and 4). been described in detail elsewhere4. The
f
299 Table 1. The Raman band frequencies of TiCl„ (n=2, 3, and 4) in cm"1. (a) TiCl4
(b) oc-TiCl3
(c) TiCl2
Obs. 127
Calc. Assign. 127.0 E
Obs. 175
Calc. Assign. 191.8 A„
Obs. 157
Case I Calc. Assign.
Case II Calc. Assign.
144
144.0 F2
260
269.1
Ag
197
197.0
Eg
197.0
385
385.0 A,
385
370.3
Ag
260
260.0
E„
260.0
A lg
490
490.0 F2
467
462.7
Eg
316
316.0
A lg
316.0
Eu
175+467
330
330.0
A2u
330.0
A2u
624
Eg
interaction between Ti-Cl bonds was considered in the off-diagonal elements of the F-matrix4,5. The results are shown in Table 1(b). For later discussion, we show the values of two force constants (KT, and KJ) obtained from the normal mode analysis in Table 2(b). K, is the stretching force constant of Ti-Cl bond, and K3 is the stretching force constant of neighboring CI atoms in a CI plane. In the case of the normal mode analysis of TiCl2, four force constants (Ku K2, H„ and H2) are defined on the basis of the valence force field. Kx and K2 are the stretching force constants of TiCl and Cl-Cl, respectively. H^ and H2 are the bending force constants of Cl-Ti-Cl and Ti-Cl-Ti valence angles, respectively. The off-diagonal elements of the F-matrix were set to zero, because the calculated frequencies converged only when the interaction between Ti-Cl bonds was quite small. The normal mode analysis was carried out assuming that the observed bands at the lowest and the highest frequencies (197cm"1 and 330cm"1) are assigned to Eg and A2u modes, respectively. We believe that this assumption is reasonable, because the lattice vibrations of E g and A2u modes of most metal di-halide crystals belonging to D\d space group, e.g. VC12, MnBr2, FeBr2, and CoBr2, are observed at the lowest and the highest frequencies in the Raman and IR absorption spectra, respectively12. Two candidates of the assignments (Case I and Case II) are proposed in the normal mode analysis of TiCl2. The calculated frequencies in these two cases are shown in Table 1(c) and the force constants used in the calculation are shown in Table 2(c). In Case I, the bands at 316 and 260 cm"1 are assigned to A, g and Eu modes, respectively. In Case II, they are assigned to Eu and A lg modes, respectively. In order to determine which candidate is more reasonable, we have compared the force constants of TiCl2 in these two cases with those of a-TiCl 3 . The agreement of the value of ^(a-TiCL,) with that of A:2(TiCl2) in Case II is much better than that in Case I. ^T2(TiCl2) and A^3(a-TiCl3) are expected to have similar values, because the atomic distances i?(ClCl) j^cncij) and iJ(Cl-Cl) Kj(a _ Tia]) relevant to these force constants are similar to each other as shown in Table 2. Thus, we conclude that Case II is more appropriate than Case I. Let us now look at the relative magnitudes of the three Ti-Cl stretching force constants derived Table 2. The force constants and atomic distances (R) of TiCl„ (n=2, 3, and 4). (a) TiCl4
(b) a-TiClj R 2.19
K 241.5 F 17.0 H 20.5 K -1.2 KandFinN/m,Hand
Kt K,
R 126.5 2.46 3.2 3.53
Kin 10" 20 Nm,Rink.
(c) TiCl2 Case I Case II 40.2 62.4 Ki 13.8 3.7 K2 9.4 32.0 Hx 45.4 81.2 H2
R 2.53 3.59
300 from the observed band frequencies of TiCl„ (n=2, 3, and 4). They are AT,=62.4 N/m for TiCl2, £,=126.5 N/m for a-TiCl3, and £=241.5 N/m for TiCl4. We find that the Ti-Cl stretching force constant increases remarkably as the number of CI atoms bonded to the Ti atom increases, i.e. the oxidation number of Ti increases. Referring to the Ti-Cl bond lengths shown in Table 2, we also find out a relation that the Ti-Cl bond length decreases as the Ti-Cl stretching force constant increases. A similar relation between the bond length and the force constant is seen in the case of C-C bond of ethane, ethylene, and acetylene13. Thus, the result obtained in this study is reasonable. Finally, we comment on the catalytic activity of the Ziegler-Natta catalyst in relation to our results. Catalytic reactions, i.e. adsorption of monomer molecules and polymerization, proceed at Ti species for this catalyst14. The shape of an orbital function of the valence electron of the Ti atom affects the catalytic activity for the production of stereospecific polymers14. The shape of the electron orbital should also affect the force constant of the Ti-Cl bond remarkably. Thus, we suggest that the Ti-Cl stretching force constant can be a good indicator of the catalytic activity of the Ziegler-Natta catalyst. We believe that our results in this study on the force constants of Ti-Cl in TiCl„ (n=2, 3, and 4) provide important information for the investigation of this catalyst on the above line. 4. Conclusion We have obtained Raman spectra of TiCl„ («=2, 3, and 4). Assignments of the Raman bands were made by a normal mode analysis. We have found that the Ti-Cl stretching force constant varies remarkably depending on the oxidation state of Ti. References [I] P. C. Barbe, G. Cecchin, and L. Noristi, Adv. Polym. Sci. 81, 23 (1986). [2] R. J. H. Clark and P. D. Mitchell, J. Chem. Soc. Faraday Trans. H 71, 515 (1975). [3] I. I. Kondilenko, V. E. Pogorelov, V. L. Strizhevskii, and E. E. Shinkareva, Optika I Spektrosk. 26, 203 (1969). [4] H. Miyaoka, K. Hasebe, M. Sawada, H. Sano, H. Mori, G. Mizutani, S. Ushioda, N. Otsuka, and M. Terano, Vibrational Spectroscopy 17,183 (1998). [5] I. Kanesaka, M. Yonezawa, K. Kawai, T. Miyatake, and M. Kakugo, Spectrochim. Acta 42A, 1415 (1986). [6] G. V. Fraser, J. M. Chalmers, V. Charlton, M. E. A. Cudby, Solid State Commun. 21, 933 (1977). [7] D. A. Long, Raman Spectroscopy (McGraw-Hill, New York, 1977), pp. 180-188. [8] Y. Rong-wen, Z. Jian-sheng, X. Mei-jie, L. Zhi-rong, Y Bing-zhang, Chin. Phys. Lett. 13, 54 (1996). [9] T. Shimanouchi, M. Tsuboi, T. Miyazawa, J. Chem. Phys. 35,1597 (1961). [10]E. B. Wilson, J. C. Decius, P. C. Cross, Molecular Vibrations (Dover, New York, 1980). [II] T. Simanouchi, J. Chem. Phys. 17, 245 (1949). [12] G. Benedek and A. Frey, Phys. Rev. B21,2482 (1980). [13] G. C. Pimentel and R. D. Spratley, Chemical bonding clarified through quantum mechanics (Holden Day, 1969). [14] E. P. Moore Jr., Polypropylene Handbook: Polymerization, Characterization, Properties, Processing, Applications (Hanser Gardner Pubns, Cincinnati, 1996).
INITIAL CONDITION SENSITIVITY IN LATTICE RELAXATION A N D DOMAIN FORMATION AFTER PHOTOEXCITATION
H. MIZOUCHI Institute of Materials Structure Science, 1-1 Oho Tsukuba, Ibaraki 305-0801, Japan We theoretically study the lattice relaxation dynamics of a photogenerated exciton resulting in the macroscopic domain. Especially, we concentrate on the "initial condition sensitivity" of the exciton proliferation. This characteristic is as follows. The generation efficiency of the domain depends sensitively on the way of the initial photoexcitation, even if the total photon energy is same. We consider the 1-dimensional many exciton-Einstein phonon system interacting with a reservoir. Within the Markov approximation, the time evolution of the density matrix is investigated full-quantummechanically. Here, we derive the iterative equation for the proliferation and numerically solve it, so that we can treat multi-exciton states in the large system. Depending on the way of the photoexcitation, the initial distance between photogenerated excitons is assumed to take various values. We have shown that the exciton proliferation successfully occurs only when the initial distance is not too short neither too long. This sensitivity to the initial distance is due to the nonlinear interaction between excitons. 1. Introduction As is well-known, when a visible light is shone onto an insulator, an electron is excited, and then, it induces a change of the lattice structure. For a long time, it has been believed that such an optical excitation causes an only microscopic structural change. However, in the recent years, many unconventional insulators are discovered. In such insulators, the microscopic change induced by a photoexcitation grows up to be a macroscopic domain with new electronic and lattice orders. These phenomena are called "photoinduced structural phase transition" (PSPT). 1 For example, the charge transfer type salt crystal TTF-CA 2 is one of such unconventional insulators. In TTF-CA, the macroscopic neutral phase domain appears after a photoexcitation from its ionic ground state. According to a recent experiment in TTF-CA 3 , the small differences at the stage of initial optical excitations enhance into the remarkable differences of the neutral phase generation efficiency, although the total excitation energy of photons is same. When a photon energy is about leV, which is just above the inter-molecular charge transfer(CT) excitation energy, the efficiency of the neutral phase generation is quite small, and there is a critical value of the total photon energy to obtain the finite efficiency. On the other hand, when a photon energy is equal to the intra-molecular excitation energy of T T F + ( ~ 2 e V ) , the efficiency is large, and the aforementioned critical value does not exist. Here, it should be noted that, as far as the same total photon energy is given, any photoexcited state initially has the same energy and the same lattice configuration, irrespective of the way of the photoexcitation. Therefore, the efficiency of the neutral phase generation is sensitive to the way of the photoexcitation. Especially, when the total photon energy is smaller than the aforementioned critical value, the occurrence or nonoccurrence of the P S P T sensitively depends on the way of the photoexcitation. This is called the "initial condition sensitivity". In the aforementioned two cases, the electronic states created just after the photoexcitations can be considered as follows. Just after leV excitation, the many CT excitons are created homogeneously in the crystal, and thus, they sit at long intervals among them. In the case of the intra-molecular excitation, an electron is excited sufficiently above the CT absorption edge, and hence, it can be immediately converted into several CT excitons, due to intrinsic nonlinearity of the Coulomb interaction. These several CT excitons are newly created close to each other around where the originally excited molecule was. Therefore, the two initial states are different with respect to the distance between the photogenerated CT excitons. The purpose of this paper
301
302 is to clarify theoretically the relaxation dynamics which start from the initial states with various spatial configurations of excitons. Here, during the relaxation processes, an exciton does not stay within a single adiabatic potential surface but transits diabatically between the different potential ones. Hence, we treat the lattice vibration quantummechanically. Furthermore, a reservoir is considered in order to treat relaxation channels microscopically, as shown in the next section. 2. M o d e l Hamiltonian We consider the 1-dimensional many exciton-Einstein phonon system interacting with a reservoir.4 H = HS + HR + HSR (1) where H$ denotes the Hamiltonian of the exciton-phonon system, which is our relevant system. This is written as
Hs = '£t(\l-l'\)BJBl, + J2W-l'\)BlBlBlBll i,v
i,v
+ £9(\l - I'DBjB^BJ, + Be) + a- £b\k i,f
i
WSI:B/B,(&I+t,)+$>eo n piB'Bi-m). l
«
m^n) \
n
m
(2) /
Here, Bi and bi are annihilation operators of an exciton and a phonon, respectively, at a site I. Y!i i' and Yfi'f denote the sums under the condition that / > I' and I ^ I', respectively. In eq.(2), the first and second terms represent one-body and two-body interactions of excitons, respectively. In the second term, we assume the on-site strong repulsion and the inter-site attraction. The third term represents the third order anharmonic coupling between excitons, and through this coupling, an exciton is created and annihilated by another exciton. Such nonlinear interaction results from the original Coulomb interaction among electrons constituting excitons. The fourth term of eq.(2) represents one-body interaction of phonons, and w is its frequency. The fifth term represents the on-site exciton-phonon couplings, and S is its dimensionless coupling constant. The last term represents the potential depending on the number of excitons n. This term was not taken into account in the previous paper 4 . It comes from the effect of the interchain interaction. The product with respect to m denotes the number projection operator onto n-exciton states. h(n) is taken so that the lowest energy of the n-exciton s t a t e ( s Eo(n)) decreases as n increases from 1 to n c , and after that it rapidly increases, when g(\l — l'\) is neglected. Here, n c is the critical number of exciton. In eq.(l), HR denotes the Hamiltonian of the reservoir which is composed of the even and odd bosonic modes and photons. HSR denotes the interactions between the system and the reservoir. Here, the even modes couple linearly with the phonons and dissipate them, while the odd modes (photons) couple linearly with excitons and non-radiatively (radiatively) create and annihilate them. Therefore, through the phonon-even mode, exciton-odd mode and excitonphoton interactions, we can take into account the relaxation channels such as vibrational (or phonon) relaxation, non-radiative and radiative transitions of excitons, respectively. The parameter values are taken as follows. In eq.(2), u = O.leV, S = 8, t(0)/aj = 9.5, t(l)/u> = - 1 . 0 , /(0) = +oo, / ( l ) / w = - 1 . 7 , g(l)/w = 0.2, g(2)/u = 0.1, g(3)/u = 0.067, g(4:)/uj = 0.05 and g(5)/ui = 0.04. Here, / ( 0 ) can be taken into account by neglecting the exciton states with more than two excitons at a site. The other t(\l — l'\), f(\l — l'\) and g(\l — l'\) are taken as 0. n c = 10 and h(n) is taken so that E0{0) = 0, E0(l) = £0(13) = 1.5a) and E0(10) = I.OICJ when 2(1) and g(\l — l'\) are neglected. In these parameter, the ground state of the system is the vaccum state with repect to both excitons and photons. The coupling
303 constants between an even mode and a phonon, and between an odd mode and an exciton, are both assumed to be 0.2w. The coupling constant between a photon and an exciton is determined so that the radiative decay time becomes 1 0 - 9 sec at the Franck-Condon state. Within the Markov approximation for the reservoir, we numerically solve the equation for the time evolution of the density matrix in the system. However, there is numerical difficulty in calculating it directly for the large system, because the quantummechanical treatment of lattice vibration leads to too large dimensional calculation. To overcome this difficulty, we derive the iterative equation for the exciton proliferation and numerically solve it. The basic idea is as follows. At first, we focus on an exciton with the excess vibronic energy. We call this exciton "mother exciton". The other excitons are assumed to be frozen ones localized at their sites with only the lowest vibronic energies. The mother exciton can proliferate by using her excess energy, and her daughter exciton is born. The frozen excitons can help the proliferation through the nonlinear interaction g(\l — l'\) in eq.(2). When the total number of excitons increases by 1 from the initial one, we consider the daughter grows up to be an adult. Then, the mother exciton and the daughter one are approximated as a frozen exciton and a new mother one, respectively. The new mother exciton has smaller excess energy than the original mother one, due to the dissipation. We iterate this procedure until the excess energy is exhausted. 3. R e s u l t s and Discussion In this section, our results are shown.
100
200
300
Time(2n/co)
500
1000
1500
2000
Time(2itto)
Fig. 1. The time evolutions of energy(a) and the total number of excitons(b). The initial state is the 2-exciton state. One of the two excitons is an exciton created by the Franck-Condon excitation from the ground state, and it is taken to be localized at a site. The other exciton is a frozen one. d,Q denote the distance between the two excitons in the initial state, and the unit of length is the lattice constant. The unit of time is the phonon period, 2ir/u). In Figs. 1(a) and (b), the time evolution behaviors of the energy and the total number of excitons are shown, respectively. Here, we prepare two excitons as the initial state. One of the two excitons is an exciton created by the Franck-Condon excitation from the ground state, and it is taken to be localized at a site. This is a mother exciton. The other exciton is a frozen one. do denotes the distance between the two excitons in the initial state, and the unit
304 of length is the lattice constant. The unit of time is the phonon period, 2-K/UJ. In Fig. 1(a), we show only the case of d0 = 3. Here, the energy of the ground state is equal to 0. When do = 3, the exciton proliferation successfully occurs, as shown later. As time goes by, the energy decreases rapidly. Then, the decrease is suppressed and the energy takes finite values for a long time. This means the system stays in the excited states for a long time. In Fig.l(b), the total number of excitons increases from 2 at quite early time, for each value of do- However, no net proliferation occurs when d0 = 1 and oo. The proliferation successfully occurs when d0 is in the moderate range(do = 3). The reason is as follows. When the initial distance is too long, the nonlinear cooperative effect among excitons, does not work. On the other hand, in too short distance case, the nonlinearity is too strong, and the nonlinear interaction g(\l — l'\) in eq.(2) leads to the exciton annihilation rather than the proliferation. In the moderate distance case, the nonlinearity works suitably for the exciton proliferation. From these results, we have shown our system is quite sensitive to the way of the photoexcitation, even if the total photon energy is same. Acknowledgements The author would like to thank Professor K. Nasu for useful discussions. This work was supported by a Grant-in-Aid for Scientific Research on Priority Area B, "Photoinduced Phase Transitions and Their Dynamics" (No.11215101) from the Ministry of Education, Science, Sports and Culture, Japan. References 1. K. Nasu, Relaxations of Excited States and Photo-induced Structural Phase Transitions (Springer-Verlag, Berlin, 1997). 2. S. Koshihara, Y. Takahashi, H. Sakai, Y. Tokura and T. Luty, J. Phys. Chem. B103, 2592 (1999). 3. T. Suzuki, T. Sakamaki, K. Tanimura, S. Koshihara and Y. Tokura, Phys. Rev. B60, 6191 (1999). 4. H. Mizouchi and K. Nasu, J. Phys. Soc. Jpn. 69, 1543 (2000).
OPTICAL SECOND HARMONIC SPECTROSCOPY OF THE ANATASE Ti0 2 (101) FACE G. MIZUTANI1.2, N. ISHIBASHP, and S. NAKAMURAi ' Japan Advanced Institute of Science & Technology, Ishikawa 923-1292, Japan 2 PRESTO, Japan Science and Technology Corporation, Saitama 332-0012, Japan T. SEKIYA, and S. KURITA Yokohama National University, Hodogaya, Yokohama 240-8501, Japan We have investigated electronic levels of the H20/anatase TiO2(l0l) interface by optical second harmonic spectroscopy. We see a sharp rise of SH intensity above the SH photon energy 2ftco~3.6eV.
According to our previous analysis, the SH
signal from this face originates mainly from the EfeCVTiOzdOl) interface.
The sum
frequency intensity also shows a rise at fia)i+fl(02~3.6eV. Thus the observed sharp rise of the SH intensity is due to a resonance of an interface band gap at 3.6eV. The energy of this interface band gap is larger than that of the bulk band gap, 3.2eV.
1.
Introduction Titanium dioxide (TiOz) is known as a photo-catalyst for water decomposition 1 . Its interface electronic levels should play an important role in catalytic reactions. Thus the information on them will give us a key to the understanding of the mechanism of the catalytic reaction at this interface. The information on the mechanism of the catalytic reaction will then lead to the development of the related techniques. The optical second harmonic (SH) spectroscopy can be applied to the investigation of interface electronic levels of catalysts in gases or liquids. For H-20lrutile TiChdlO) interface the SH intensity as a function of the SH photon energy h a s been obtained and its interface electronic levels are discussed 2 . It is shown t h a t the photo-catalytic activity of anatase Ti02 is several times higher than t h a t of rutile TiC>23. Thus the details on the interface electronic levels of anatase Ti02 will lead to the clarification of the origin of high catalytic activity of titanium dioxides. However, there has been no report on SH spectroscopy for anatase TiCh, although a SH observation at a fixed photon energy h a s been reported 4 . In this paper we have measured SH intensity patterns of the H20/anatase TiChdOl) interface as a function of the sample rotation angle ty around the surface normal at different incident photon energies. We have also obtained SH intensity spectra as a function of the incident photon energy at a fixed sample rotation angle <|>. The interface band gap has been found at ~3.6eV, at higher energy t h a n the energy of the bulk band gap. 305
306 2.
Experiment The sample preparation method 4 and the experimental set-up 5 have been described elsewhere. In short, a sample of anatase Ti02 with a (101) face was grown by a chemical vapor transport reaction method 6 ' 7 . After the growth, it was annealed at 8 0 0 t for 110 hours in oxygen atmosphere and was etched with 5 moW NaOH at 110°C for 2 hours. Analyzing this surface by XPS after etching, we have found t h a t a H2O layer is formed on its surface. Therefore, on the samples prepared in this way the EbO/anatase TiO2(l0l) interface is formed. This interface is present in the catalytic reaction of water decomposition by Ti02. In SHG experiments, the light source of the fundamental frequency was an optical parametric oscillator (OPO) driven by a frequency-tripled Q-switched Nd^YAG laser. The laser pulses were focused into a spot of 0.3 mm diameter on the sample surface at an incident angle of 45°. The incident laser power was ~0.2mJ per pulse on the sample surface. In sum frequency generation (SFG) experiments, a light beam from the OPO and a beam of wavelength 1064 n m from the Q-switched Nd^YAG laser were used. 3.
Results and discussion Figure 1 shows the SH intensity from the EfeO/anatase TiO2(l0l) interface as
Fig. 1. SH intensity patterns from the HbO/anatase TiO2(101) interface as a function of the sample rotation angle at different incident photon energies.
307 a function of the sample rotation angle ty around the surface normal at incident photon energies Aco=1.84, 1.91, 2.07, 2.33, and 2.38 eV. The SH intensity is plotted in the radial direction. <]) is defined as the angle between the incident plane and the [101] direction on the (101) surface. In Fig. 1 all the SH intensity patterns are asymmetric and their shapes depend strongly on the combinations of input and output polarizations. The SH intensity patterns also have a drastic change as a function of the incident photon energy. These facts indicate t h a t the relative magnitudes of different nonlinear susceptibility elements change as a function of the incident photon energy.
3
• I-I GO
CD
GO
3.0 3.5 4.0 4.5 Figure 2 shows the SH intensity of the S H p h o t o n e n e r g y (eV) H20/anatase TiO2(l0l) interface as a function of Fig.2 SH intensity from the H20/anatase TiO2(101) interface as a functhe SH photon energy. The polarization tion of the SH photon energy. configuration is Pin/Pout and Sin/Sout and the The polarization configurations are (a)Pin/Pout and (b)Sin/Sout incident plane is parallel to the [010] direction. with incident plane parallel to the The reason why the horizontal axis is the SH [010] direction. photon energy will be mentioned later. The SH intensity rose at 2fta)~3.6 eV and a resonant enhancement peak was found at 2ft<»~3.9eV. 3 •3This onset energy of SH intensity rise depends weakly on the polarization configuration or the direction of the incident plane. In the SH intensity spectra in Fig. 2(a) and (b), contributions from the nonlinear susceptibility are elements %{£23 and xliii dominant, 3.0 3.5 4.0 4.5 respectively, as was found by an analysis of SH P h o t o n e n e r g y Jtio^ha^ (eV) intensity patterns 4 . Here, the nonlinear Fig.3 SF intensity from the HaO/anatase TiOadOl) interface as a funcsusceptibility element %S is defined after tion of the SF photon energy. 89 Guyot-Sionnest et al ' and the suffixes 1, 2 and 3 The polarization conf- iguration is Pin/all out with incdent plane denote [Toi], [010] and [ToT] directions on the parallel to the [101] direction. (101) surface, respectively. In order to determine whether the sharp rise of SH intensity at 2ftoo~3.6eV is due to a one-photon or two-photon resonance, the reflected optical sum frequency (SF) intensity from the same interface was measured. The result is shown in Fig. 3. The incident beam was P-polarized and the SF light of all polarizations
.1
308 was collected (Pin/all out configuration). The incident plane was parallel to the [101] direction. The photon energy ha>i was fixed at 1.17 eV and the photon energy htaz was scanned from 2.25 to 2.64 eV. In Fig. 3 we see that the SF intensity increases when the sum of the photon energies hcoi+haa exceeds 3.6 eV. This energy is identical to twice the fundamental energy of the onset of the resonance in SHG in Fig. 2. Hence, the sharp rise of SH intensity observed in Fig. 2 is due to a two-photon resonance of an interface band gap. This is the reason why we have adopted S H photon energy as the horizontal axis in Fig. 2. The bulk band gap of anatase TLO2 is located at 3.2 eV10. Thus the band gap of H 2 O/TiO2(l0l) interface is located higher in energy t h a n t h a t of bulk anatase Ti02. 4.
Conclusion We have observed SH intensity from the H20/anatase TiO2(l0l) interface as a function of the sample rotation angle and the SH photon energy. The SH intensity patterns as a function of the sample rotation angle around the surface normal showed a drastic change as the incident photon energy is varied from fto>=1.84 to 2.38 eV. The SH intensities for fixed sample rotation angles and fixed polarization configurations have sharp rises above the photon energy 2A(B~3.6eV. The sum frequency intensity also shows a rise at 7icoi+/iCQ2~3.6 eV. Thus the observed sharp rises of the SH intensity are assigned to a two-photon resonance of an interface band gap at 3.6 eV. The energy of this interface band gap is larger t h a n t h a t of the bulk band gap, 3.2 eV. Reference 1. A. Fujishima and K. Honda, Nature 238 (1972) 37. 2. E. Kobayashi, T. Wakasugi, G. Mizutani, and S. Ushioda, Surf. Sci. 402-404 (1998) 537. 3. J. Augustynski, Electrochem. Acta 38 (1993) 43. 4. S. Nakamura, K. Matsuda, T. Wakasugi, E. Kobayashi, G. Mizutani, S. Ushioda, T. Sekiya, and S. Kurita, J. Lumin. 87-89 (2000) 862. 5. H. Tanaka, H. Wakimoto, T. Miyazaki, G, Mizutani, and S. Ushioda, Surf. Sci. 427-428 (1999) 147. 6. H. Berger, H. Tang, and F. Levy, J. Cryst. Growth 130 (1993) 108. 7. N. Hosaka, T. Sekiya, M. Fujisawa, C, Satoko, and S. Kurita, J. Electron Spectrosc. Relat. Phenom. 78 (1996) 75. 8. M. Takebayashi, G. Mizutani, and S. Ushioda, Opt. Commun. 133 (1997) 116. 9. P. Guyot-Sionnest, W. Chen, and Y. R. Shen, Phys. Rev. B33 (1986) 8254. 10.H. Tang, H. Berger, P. E. Schmid, F. Levy, and G. Burri, Solid State Commun. 87 (1993) 847.
SCINTILLATION MECHANISM OF Ce 3+ DOPED Gd 2 Si0 5 K. MORI, M. YOKOYA, H.NISHIMURA, and M. NAKAYAMA Department of Applied Physics, Faculty of Engineering, Osaka City University Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan
H. ISHIBASHI Advanced Technology Laboratory, Research & Development Center, Hitachi Chemical Co. Ltd Tsukuba 300-4247, Japan Measuring the spectra of absorption, luminescence and excitation, and the decay times of the luminescence, at various temperatures, we investigate the scintillation mechanism of Ce3+ doped Gd 2 Si0 5 (GSO:Ce). We conclude that the excitation energy created by gamma-ray irradiation relaxes to the core exciton states formed by the 4f-4f transitions of Gd3+, and that the core exciton migrates to collide with Ce3+, and transfers the energy to Ce3+ to emit the luminescence. We also conclude that the decay time of the Ce3+ luminescence in GSO:Ce (70 ns for the case of 0.5 mol% of Ce concentration) is decided by the diffusion time of the core exciton. A very small value for the diffusion coefficient of the core exciton is estimated to be 7 X 10"'cm2/s.
1. Introduction Cerium doped gadolinium oxyorthosilicate, Gd 2 Si05:Ce 3+ (GSO:Ce) has widely been investigated1"5 in a viewpoint of useful scintillator with a large photoelectron yield (20-25% of NaLTl), 2 ' 5 short decay time (50-70 ns) 3 ' 5 and high stopping power for 7 -ray. The 4f-5d transition of Ce 3+ is dipole allowed, so that the decay time of the Ce 3+ luminescence is expected to be short. In fact it is 22 ns in GSO(Ce:0.5mol%) when excited directly into the Ce 3+ absorption bands. 5 This is favorable for scintillators with fast timing characteristics. However, when excited into the interband transition region, the decay time is not 22 ns; the decay curve consists of two exponentially decaying components with the decay times of 56 and 600 ns.3 This discrepancy is the principal problem to be discussed in this study. There exist two types of excitons in GSO; core exciton and charge transfer exciton.6 The core exciton is formed by the 4f-4f transitions of Gd 3+ , which is shielded from the external field by the outer closed shells of 5s 2 and 5p 6 electrons. The charge transfer exciton, on the other hand, is known to exist much higher in energy than the core exciton, '6 so that the core exciton with small diffusion coefficient seems to play a dominant role in energy transfer in GSO:Ce scintillator. The energy transfer from the core exciton to Ce 3+ is the second problem to be discussed. 2. Results and discussion Fig. 1(a) and (b) show the absorption spectra of GSO and GSO:Ce (Ce:0.5mol%) measured at 10K. The sharp lines in the spectra have been assigned to the core excitons formed by the 4f-4f transitions of Gd 3+ . 6 The core exciton states consist of the transitions from the ground state S7/2 to the excited states, ^Pj, 6 Ij, 6 Dj and 6 Gj. Each spectrum of absorption due to the core excitons is composed of many sharp lines; 7 or 8 lines for the 6P7/2-exciton state, 6 lines for the ^5/2 state and 4 lines for the 6 P 3 / 2 state. The 6P7/2, 6Ps/2, and 6P3/2 states, on the other hand, are expected to split into 4, 3. and 2 sublevels under the Stark effect in the P2!/c non-cubic crystal field of GSO. The numbers of the lines observed are twice larger than the numbers expected. Mori et al.6 have interpreted the factor of 2 coming from two different crystallographic sites occupied by Gd3+ in GSO. 7 ' 8 This means that there exist two series of core excitons with very small energy difference (about 20 meV) in GSO. The sharp lines in Fig. 1(a) and (b) are independent of temperature, suggesting that the exciton-phonon interaction for the core excitons is very weak. This is reasonable because the 4f electrons of Gd 3+ are shielded from the external field by the 5s 2 and 5p6 electrons. The broad bands labeled Cel and Ce2 in Fig. 1(b) are due to Ce 3+ . For the 4f-5d transition of Ce3+, the exciton-phonon interaction is strong, because the 5 d electron is located outermost, so that the absorption spectra due to Ce 3+ are broad. Suzuki et al.5 have discussed that Ce 3+ is substituted
309
310
1 0.5 0 L
,,,,,-
6p
%
J
Ilk 6Dj
6
4.0 4.1 (eV) r 1
ca.r
•
<*, *>~
/ i
j
4.0 4.1(eVi 5.0 5.5 6.0 6.5
Photon Energy (eV) Fig.l. Absorption spectra of GSO and GSOCe (Ce:0.5mol%) at 10 K. The inset is the spectra expanded in the *¥, (J=7/2, 5/2, 3/2) exciton region.
J
Vif
Luminescence
-
\ \cel
Cel Exc=3.76eV Ce2Exc=3.38eV
J j
Ce2
A
Excitation Cel Dct=3.0eV Ce2 Det=2.2eV
-Cel
'\J\ —
Gd3+
~.J.J.
4.0 4.5
1
Cel
V>*Ce2 CeZI
2 3.0 3.5
1
Absorption
6
fCel
GSOCe T=10K
GJ Intensity (arb. units.)
3 2.5 L(«) T=10K 2 TGSO 1.5
..,
3 4 5 Photon Energy(eV)
,..,, 6
Fig.2. Spectra of absorption, luminescence and excitation of GSO:Ce (Ce:0.5mol%) at 10 K.
for Gd 3+ occupying two different crystallographic sites in GSO, so that two series of broad absorption bands, Cel and Ce2, appear from the Ce 3+ occupying two different crystallographic sites. Mori et al.6 have pointed out that the charge transfer excitons are located in energy at 6.1-6.3 eV. Suzuki et al.5 have also discussed the fundamental absorption of GSO to start at 6.2 eV, consistent with the suggestion by Mori et al.6 The spectra of absorption, luminescence, and excitation of GSO:Ce (Ce:0.5mol%) at 10K are shown in Fig. 2. Comparing the excitation spectrum with the absorption spectrum, we conclude that two luminescence bands labeled Cel and Ce2 are related to two absorption bands Cel and Ce2, respectively. The ground state of Ce 3+ is well known to consist of the 4f electron state split into two sublevels 2Fs/2 and 2 F 7 / 2 under spin-orbit interaction: The energy difference between the sublevels is about 0.25 eV. 910 The excited state, on the other hand, consists of the 5d electron state split into two sublevels 2 E g and 2 T 2g in the crystal field Oi,: The energy difference between the sublevels is about 1.25 eV.9-10 There appear two peaks in the excitation spectra for the Cel luminescence and for the Ce2 luminescence. The energy difference between two peaks is about 0.8 eV for both Cel luminescence and Ce2 luminescence. Although the energy difference is a little smaller than the calculated value (1.25 eV), we interpret the two peaks to arise from two transitions from the 2Fs/2 ground state to the 2 E g and 2 T 2 g excited states at the different crystallographic sites of Ce 3+ . On the other hand, the Cel luminescence spectrum shows a small energy splitting of about 0.2 eV. This splitting is probably caused by two transitions from the 2 T 2g excited state to the 2 F 5/2 and 2 F 7 / 2 ground states at the Cel site, though similar splitting is not observed in the Ce2 luminescence spectrum. Fig. 3(a) shows the luminescence spectra observed at 10 K under various excitation conditions. The Cel luminescence is excited in the Cel absorption bands, and the Ce2 luminescence is excited in the Ce2 absorption bands. When excited into the interband transition region by 6.52 eV photon or x-ray, both the Cel and Ce2 luminescence bands appear. These spectra are normalized at the peak intensity. Fig. 3 (b) shows the integrated intensities of Ce luminescence as a function of temperature. The results depend strongly on the excitation energy. The intensity decreases at high temperature when excited into the Cel and Ce2 absorption bands, whereas the intensity increases when excited
311 (a)T=10K GSO:Ce /
s~?*frK'\ / A \ \ v
* if r JF / J?
I
I
-• — -
TL\\ fc
v \
Cel Ce2 Xray 6.52eV
120 - GSO:Ce -g-100
2
2.5 3 Photon Energy (eV)
4 (b)GSO:Ce 3
-
-
* o + o
•
Cel Ce2 Xray 6.52eV
•
•
•
i
+
+
•
•
+
0
100
«
•
i
+
•
•
•
•
a
A O
a
x»# " • * • 7 xxx^xx^xx^xx
• x
.
x***
60
# x
x
•
•
DOD DDDODODDDaoaDDDa D a :AAAA6aAAaaAAfiAOAfi4*AAA ayg
20
*
150 200 250 Temperature (K)
-
A
ft
o
0
•
x * x * x x
>
-
D
Q 40
+
o ° ° a
I & o
i
°
c
1- o A £
•
3.5
80
6.52eV 4.5UV Cel Ce2
•
1 . . . .
50
c
1
100 150 200 Temperature (K)
*
250
300
300
Fig.3. (a) Luminescence spectra of CSO:Ce(Ce:0.5 mol%) excited by the Cel and Ce2 bands, 6.52 eV photon and x-ray at 10 K, (b) Integrated intensities of Ce luminescence as a function of temperature.
Fig.4. Decay times of Cel and Ce2 luminescence in GSCKCe(Ce:0.5mol%) excited by the Cel and Ce2 bands, and 4.51 and 6.52 eV photons as a function of temperature.
into the interband region. Especially the intensity increases strongly by x-ray excitation. This result suggests that the rate of energy transfer from free carriers created by 6.52 eV photon or x-ray to Ce + increases remarkably at high temperatures. The decay times of the Cel and Ce2 luminescence are shown in Fig. 4 as a function of temperature. The decay time of the Cel luminescence excited in the Cel absorption band is 25 ns, and that of the Ce2 luminescence excited in the Ce2 absorption band is 45 ns. The difference in the decay time for the emitting state of the Ce 3+ located at Cel and Ce2 sites might be explained by the difference in the optical transition energy, 2,8 and 2.5 eV respectively. When core excitons are formed by 4.51 eV photon belonging to the 8 S 7 /2- 6 IJ transition of Gd 3+ , the decay time of the Cel and Ce2 composite bands is 80 ns. This value is much longer than those of the Cel and Ce2 bands, which suggests that the time of 80 ns represents the diffusion time of core excitons. When free carriers are formed by 6.52 eV photon, the decay curve is not single exponential, but consists of two exponentially decaying components; the decay times for GSO:Ce (Ce:0.5mol%) are 90 and 600 ns at low temperatures. We obtained similar result under y -ray excitation. It has been reported that the decay times of Ce luminescence measured by y -ray excitation depends strongly on the concentration of Ce. 2 ' 3 These results must support above suggestion that the fast decaying component, 80 ns, represents the diffusion time of core excitons, since the diffusion time must depend on the concentration of Ce. On the other hand, the slow decaying component, 600 ns, seems to represent the delay time in forming the core excitons from free carriers trapped by crystal defects. We show the reciprocal values of the decay times for the fast decaying component in the Ce luminescence excited by y -ray in Fig. 5. Clearly the reciprocal values of the decay times depend linearly on the concentration of Ce. This result suggests that the decay time of the Ce luminescence is given by a diffusion rate of the core excitons, l/T=4-naND, where a is the collision radius of a core exciton and Ce 3+ , N the concentration of Ce and D the diffusion coefficient of the exciton. Assuming the ionic radius of Ce 3+ for a(l A ) , and fitting the linear relation to the data in Fig. 5, we estimate the diffusion coefficient D of the core excitons to be 7xl0" 7 cm 2 /s. This value is very small, and consistent with the dipole forbidden core exciton formed by 4f-4f transitions of Gd3+. Using a relation L2=D T, we estimate the diffusion length L of the core exciton in GSO:Ce (Ce:0.5mol%) to be 2.2 nm. This length is consistent with the average distance (2.2 nm) between Ce for the case of
312
Fig.5. Reciprocal values of decay times for the fast decaying component of the Cel luminescence in GSO:Ce excited by 7 -ray at room temperature.
F
»g-6- Relaxation diagram of the excitation eneigy created by 7 -ray excitation.
0.5 mol%. Our model as to the relaxation of excitation energy created by 7-ray excitation is shown schematically in Fig. 6. The energy of free carriers formed by 7 -ray excitation transfers to the 6Gj state of the core exciton, and then relaxes to the 6Pj lowest energy state. Since the luminescence band arising from the ''Pj - 8S7/2 transition of the core exciton overlaps well with the Cel and Ce2 absorption bands, the energy transfer from the core exciton to Ce3+ occurs easily to lead the Ce3+ luminescence. Finally we refer to the fact that the luminescence intensity observed by x-ray excitation increases remarkably at high temperatures (Fig. 3(b)). There might be two origins to be considered for the result: (1) A potential barrier may exist between the free carrier state and the 6Gj state of the core exciton, and (2) Trapping states for free carriers may exist near the conduction band. These situations must suppress the energy transfer from free carriers to core excitons at low temperatures. It is, however, still difficult to conclude which situation is probable. In conclusion, the excitation energy created in GSO:Ce by 7 -ray excitation transfers to Ce3+by diffusion of the core excitons formed by the 4f-4f transitions of Gd3+, and the decay time of the Ce3+ luminescence, depending on the concentration of Ce3+, is decided by the long diffusion time of the core excitons. A very small value of diffusion coefficient for the core excitons is estimated to be 7xl0"7cm2/s. References 1. K. Takagi, T. Fukazawa, Appl. Phys. Lett, 42, 43 (1983). 2. H. Ishibashi, K. Shimizu, K. Susa and S. Kubota, IEEE Trans. Nucl. Sci., 36, 170 (1989). 3. C. L. Melcher, J. S. Schweitzer, T. Utsu and S. Akiyama, IEEE Trans. Nucl. Sci., 37, 161 (1990). 4. H. Suzuki, T. A. Tombrello, C. L. Melcher and J. S. Schweizer, Nucl. Instr. andMeth., A320, 263 (1992). 5. H. Suzuki, T. A. Tombrello, C. L. Melcher, C. A. Peterson and J. S. Schweizer, Nucl. Instr. andMeth., A346, 510 (1994). 6. K. Mori, H, Nishimura, M. Nakayama and H. Ishibashi, J. Lunin., 87-89, 266 (2000). 7. Yu. I. Smolin, S. P. Tkachev, Soviet Phys. -Cryst, 14, 14 (1969). 8. T. Utsu and S. Akiyama, J. Cryst. Growth, 109, 385 (1991) 9. T. Hoshina, J. Phys. Soc. Jpn., 48,1261 (1980). 10. M. Sekita, Y Miyazawa, T. Akahane and T. Chiba, J. Appl. Phys. 66(1), 373 (1989).
S Y N T H E S I S A N D O P T I C A L P R O P E R T I E S OF W A T E R S O L U B L E ZnSe N A N O C R Y S T A L S
N. Murase Physics Department and CeNS, University of Munich Amalienstrasse 54, D-80799, Munich, Germany and Department of Optical Materials, Osaka National Research Institute Ikeda-city, Osaka-563-8577, Japan * M. Y. Gaot Physics Department and CeNS, University of Munich Amalienstrasse 54, D-80799, Munich, Germany N. Gaponik Physics Department and CeNS, University of Munich Amalienstrasse 54, D-80799, Munich, Germany and Physico-Chemical Research Institute, Belarusian State University, 220050 Minsk, Belarus T. Yazawa Department of Optical Materials, Osaka National Research Institute Ikeda-city, Osaka-563-8577, Japan J. Feldmann Physics Department and CeNS, University of Munich Amalienstrasse 54, D-80799, Munich, Germany
ZnSe nanocrystals are prepared in water by a wet chemistry method. By selecting an appropriate pH value and surface-capping agents, a whitish blue fluorescence peaking at 470 nm is observed under UV irradiation. The intensity of this fluorescence increases dramatically under reflux and saturates after ~40 hrs. The final mean size of the ZnSe nanocrystals measured by transmission electron microscopy is about 2 nm in diameter. The quantum efficiency of the fluorescence from the final solution is estimated to be ~ 1 % , although the preparation conditions have not yet been completely optimized. These properties are discussed in comparison with those of similarly prepared CdTe and differently prepared ZnSe nanocrystals. 1. Introduction Methods of attaining bright photoluminescence (PL) from semiconductor nanocrystals have attracted a lot of attention in the past decade. Carefully controlled colloidal preparations have realized high PL efficiency in the case of CdS, 1 CdSe, 2 and CdTe. 3 Measurement of PL from single particles of these nanocrystals becomes possible due to their high PL efficiency.4,5'6 Moreover, the PL color tunability by size, and robustness of the semiconductor nanocrystals *Parmanent address tCorresponding author
313
314 make them a new type of light-emitting materials. However, the stability, particle size, and optical properties of these nanocrystals depend strongly on the specific method of preparation. Here we report the preparation and optical properties of water soluble ZnSe nanocrystals. The water solubility is of importance for applications such as biological staining. In addition, the possibility of inclusion of such highly fluorescent nanocrystals in a transparent matrix by a sol-gel method will also provide a new way to fabricate highly fluorescent composite glasses. ZnSe has a direct bandgap of ~2.7 eV (460 nm) at room temperature. Therefore, it is more suitable for producing nanocrystals with a short wavelength emission than those of CdS, CdSe and CdTe. In this paper, ZnSe nanocrystals are prepared by a method derived from the established colloidal method for CdTe. 5 The properties of ZnSe have been discussed in comparison with those of CdTe and differently prepared ZnSe nanocrystals. 7 - 1 2 2. Experimental The preparation method is similar to a previously reported one for highly fluorescent CdTe nanocrystals with their PL ranging from green to red. 3 The details are described below. Ultra-pure water (Millipore, Milli-Q synthesis grade) was used in every case after degassing for more than 30 min with Ar. An aqueous solution of zinc perchlorate (0.013 mol/L, 60 mL) was mixed with thioglycerol (CH 2 (SH)CH(OH)CH 2 (OH)) which was used as a surfacecapping molecule. The pH of the solution was set to 11.4. Aqueous solution of NaHSe was prepared by introducing H2Se that was generated by the reaction between Al 2 Se 3 and H2SO4 in a NaOH solution. The molar ratio among Zn, Se, and thioglycerol was set to 1:0.47:2.4.13 The mixture was clear and colorless in the beginning and then changed to yellow upon a reflux. Fluorescence appeared in the course of the reflux and kept increasing in intensity until the colloidal solution had been refluxed for 43 hours. Absorption spectra by a Varian Cary 50 spectrometer, fluorescence and excitation spectra by Varian Cary Eclipse were measured by using a 1-cm cuvette at room temperature during the reflux. A TEM image of the final ZnSe nanocrystals was taken using a Hitachi H-9000 transmission electron microscope. 3. Results and Discussion Figure 1 shows the absorption spectra of the ZnSe colloid (13 times diluted) as a function of the refluxing time. The inset of the figure is an enlarged version of a specific region. At an early stage of the reflux, the onset of absorption was in the ultra-violet region. The colloidal solution at this stage was transparent and colorless. As the reflux proceeded, the onset of the absorption
Wavelength/nm
Fig. 1. Absorption spectra of the ZnSe recorded at different refluxing time. The inset is the enlarged version of the specific region to show the onset of the absorption.
315 as shown in the inset of the figure steadily moved to the visible range. Consequently, the color of the colloid became shallow yellow. During the same period of this absorption change, the fluorescence intensity increased dramatically until a saturation was reached after 43 hours, as shown in Fig. 2. It can be seen that the peak position of the PL emission remains unchanged at 470 nm even though the absorption spectrum is red-shifted during the reflux, whereas one shoulder at around 400 nm appears gradually. The final fluorescence looks whitish blue. The excitation spectrum observed at the PL peak position (470 nm) showed some structure that was not observed in other kinds of similar samples. The origin of this structure is under investigation. Figure 3 is a TEM image of the final colloid. Even though most of the particles are agglomerated during the specimen preparation, the structure of ~ 2 nm is observed. From this we estimate the particle diameter to be ~ 2 nm. The quantum efficiency of the fluorescence from the final solution is estimated to be 1.4% by a comparison with R6G (Lambda Physik laser dye).
350 400 450 500 550 600 650 700 Wavetength/nm
Fig. 2. Fluorescence spectra of the ZnSe measured at different refluxing time. The excitation wavelength is 320 nm. So far, several methods have been reported for the preparation of ZnSe nanocrystals. ZnSe ranging in diameter from 3 to 10 nm in glass was prepared by a sol-gel method. 7 The fluorescence of the nanocrystals was heavily red-shifted to 600 nm probably due to presence of Se-vacancies. ZnSe nanoparticles of 4 - 6 nm in diameter dispersed in glass have also been prepared using a melt-quenched method. 8 This paper describes a band-edge emission. A simple aqueous synthesis was also tried. 9 The ZnSe nanocrystals about 3 nm in diameter were prepared. Their emission spectra were broad and peaking at around 455 nm. Reverse micelle method was also used to prepare ZnSe of 3 - 4 nm in diameter. 10 In this case, a heavily blue-shifted fluorescence is observed at 355 nm. Another different wet chemistry method was adopted to produce 2 - 3 nm ZnSe. 1 The emission peak was observed at 450 nm. However, in all these cases, the efficiency and properties of the emission were not clarified. An organometallic synthesis route similar to the commonly called TOPO method 2 gave the most successful results. 12 ZnSe nanocrystals ranging from 4 - 6 nm in diameter were successfully synthesized. The band edge emission around 400 nm was observed with high quantum efficiency (20% - 50%). In the case of CdTe, a bright photoluminescence can be produced by the colloidal method presented here. 3 By prolonging the refluxing time, the bright band edge emission can be tuned from 540 nm to 650 nm. In view of these results, especially the results from similarly prepared CdTe, a peculiar thing in the present research is that there is no change in the fluorescence peak position when the absorption onset shifts to the red during reflux. The observed fluorescence peaking at 470 nm has not been reported to the best of our knowledge. As this fluorescence is red-shifted with respect to the absorption edge, the PL is related to trap states. The increase of PL intensity during reflux indicates that the fluorescent ZnSe nanocrystals are formed from non-fluorescent small clusters during the reflux and increase in concentration. This is supported by the change
316
Fig. 3. Transmission electron microscope image of the final ZnSe nanocrystals.
in absorption spectra which indicate that the reflux process leads to both the formation of the ZnSe nanoparticles and their growth in size. However, more experiments such as ESE spectroscopy, temperature dependent PL and transient PL spectroscopy of the nanocrystals are required to further understand the PL properties as has been done in the case of ZnS nanocrystals. 14 It is worth mentioning here that we also tried to prepare ZnSe nanocrystals by using another thio-compound, mercaptoacetic acid (CH 2 (SH)(COOH)). By the adoption of pH 10.0 and the molar ratio among Zn, Se, and merocaptoacetic acid of 1:0.47:5.0, the resultant colloidal solution was transparent and clear, however much weaker PL was obtained. A different PL behavior was also observed from the CdTe system when different surface-capping agents were employed. For example, thiolactic acid 'covered CdTe exhibits both excitonic and surface trap emissions. We believe that the PL from ZnSe can be further improved by choosing an appropriate surfacecapping molecule. The appearance of the PL shoulder at 400 nm has already given a hint of band edge emission. Effective surface passivation may also help to further improve the PL efficiency. Acknowledgements This work is supported by a BMBP (03N8604 9) project and a bilateral international joint research program by special coordination funds for promoting science and technology (Fiscal year 2000) from Science and Technology Agency of Japan. References 1. L. Spanhel, M. Haase, H. Weller, and A. Henglein, J. Am. Chem. Soc. 109, 5649 (1987). 2. B. O. Dabbousi, J. Eodriguez-Viejo, F. V. Mikulec, J. E. Heine, H. Mattoussi, E. Ober, K. F. Jensen, and M. G. Bawendi, J. Phys. Chem. B 101, 9463 (1997). 3. M. Gao, S. Kirstein, H. Mohwald, A. L. Eogach, A. Komowski, A. Eychmuller, and H. Weller, /. Phys. Chem. B 102, 8360 (1998). 4. J. Tittel, W. Goehde, F. Koberling, Th. Bascfae, A. Komowski, H. Weller, and A. Eychmueller, J. Phys. Chem. B 101, 3013 (1997). 5. M. Nirmel, B. O. Dabbousi, M. G. Bawendi, J. J. Macklin, J. K. Trautman, T. D. Harris, and L. E. Bras, Mature 383, 802 (1996). 6. N._ Murase, M. Y. Gao, T. Yazawa, and J. Feldmann, in preparation. 7. G.' Li, and M. Nogami, J. Appl. Phys. 75, 4276 (1994). 8. H. W. H. Lee, C. A. Smith, V. J. Jeppert, and S. H. Eisbud, , Mat. Res. Soc. Symp. Proc. 571, 259 (2000). 9. J. Zhu, Y. Koltypin, and A. Gedanken, Chem. Mater. 12, 73 (2000). 10. F. T. Quinlan, J. Kuther, W. Tremel, W. Knoll, S. Eisbud, and P. Stroeve, Langmuir 16, 4049 (2000). 11. N. Kumbhojkar, S. Mahamuni, V. Leppert, and S. H. Eisbud, Nanostruct. Mater. 10, 117 (1998). 12. M. A. Hines, and P. Guyot-Sionnest, J. Phys. Chem. B 102, 3655 (1998). 13. A. L. Eogach, L. Katsikas, A. Komowski, D. Su, A. Eychmueller, and H. Weller, Ber. Bunsen-Ges. Phys. Chem. 100, 1772 (1996). 14. N. Murase, E. Jagannathan, Y. Kanematsu, M. Watanabe, A. Kurita, K. Hirafca, T. Yazawa, and T. Kushida, J. Pys. Chem. B 103, 754 (1999).
STE L U M I N E S C E N C E F E O M T H E S U P E R S T R U C T U R E P H A S E Na 6 CdCl g IN NaCl:Cd 2 + CRYSTALS H. NAKAGAWA, S.KISfflGAMI Department of Electrical and Electronics Engineering, Fukui University, Buntyo3-9-l, FuM 910-8507, Japan Optical Absorption and luminescence studies have been conducted in NaCl crystals containing various amounts of CdCl2 in order to investigate the electronic excited states and their lattice relaxation processes in Suzuki superstructure lattice. X-ray diffraction measurements have been also made to confirm the presence of the Suzuki phase and to determine its detailed structure. Two broad absorption structures are observed in the energy region of 4.25-5.0 eV (LE) and of 5.0-6.0 eV (HE). With excitation in the LE region, three emission bands are produced at 2.64 (BG), 3.14 (V) and 3.56 (UV1) eV. They are attributed to the Cd2+ impurity-related centers. In case of excitation in the HE region, two prominent emission bands are observed at 2.76 (B) and 2.08 (Y) eV. Taking into consideration the experimental results of Xray diffraction, thermal treatment and Cd2+ concentration dependence, the B- and Y-emission are connected to the STE in Suzuki lattice of small and large sizes, respectively.
1. Introduction In a substitutional solid solution, random arrangement of different atoms in equivalent positions in the crystal structure rearranges into a structure in which the different atoms occupy the same set of positions in a regular way on suitable heat treatment. This regular structure is described as a superstructure. There can be found many examples in binary metal oxides and binary metal alloys. In the present work has been dealt with the superstructure of NaCl lattice composed of NaCl and CdCl2 where the Na+ ion positions in a unit cell of the original NaCl lattice are occupied regularly with Na+ ions* Cd2+ ions and chargecompensating vacancies. The superstructure phase having the composition of NagCdClg (or CdCl2:6NaCl) is generally referred to as the Suzuki lattice1, the structure of which involves the fee lattice with a lattice parameter approximately twice that of the host NaCl. The unit cell of the Suzuki lattice is presented in Fig.l. The Na+ ions at the corners of the original NaCl unit cell are replaced by Cd2+ ions and cation vacancies alternately whereas the face centered Na+ ions are retained. The anion sub-lattice is the same as that of NaCl although the CI" ions are displaced from their original positions. This system has been studied by several experimental techniques, namely, X-ray diffraction2, dielectric relaxation3, ionic theme-conductivity4, Raman scattering5 and electron microscopy6. The foreign cation ions (Cd2+) can exist in the crystal as single substitutional ions, impurityvacancy (I-V) dipoles, dipole aggregates or precipi• Cd2* #Na + ©eltates (Suzuki phase). The size of the Suzuki phase Fig. 1. Unit cell of the Suzuki supercrystal is of sub-microns typically and is changed or structure, Na^CdClg. The spacing along the dissolved by thermal treatment In the present work, (001) direction is expanded so as to show optical absorption and luminescence studies have the inner atomic arrangement. The lattice been conducted in NaCl crystals containing various .constant is approximately twice that of the amounts of CdCl2 in order to investigate the elecNaCl lattice. Note that Cd2+ ions and cation vacancies occupy alternatively the comer torate excited states and their lattice relaxation procpositions of the Na+ sub-lattice of the NaCl esses .in the Suzuki lattice. X-ray diffraction measstructure. urements have been also made to confirm the 317
318 presence of the Suzuki phase and to determine its detailed structure. 2. Experimental The sample crystals of NaCl:Cd 2+ were grown from melt by the Stockbarger method. Various amount of CdCL, from 0.1 up to 14.3 mol % was doped in the melt. Any check has not been done on the real concentrations of grown crystals and the values in the following are the doped ones. The real one might be much smaller than the doped one. The crystals are transparent below 1 mol% content of CdCl 2 and translucent or opaque above 1 mol% content. The crystals were easily cloven along the cubic face just like as NaCl crystals irrespective of the CdCL, content. Absorption and luminescence measurements were conducted by using conventional apparata. X-ray diffraction measurements were carried out for Fast dlf&actlon s ectra powder samples with use of a con^ P ,0 (xl/2) 220 NaCl pure ventional X-ray diffractometer (JRX30VA, NEC). .£ 222
420
400 3. Results and Discussion s o 400 Fast X-ray diffraction spectra •Si (xl/3) (200) ooo NaCI:Cd 14.3mol% 440 were measured for the powdered as grown I (220) crystals to confirm the presence of the jt 800 840 444 (400) (420) superstructure phase in the crystals. c (222) 333 11 200 The results are shown in Fig.2 with _L^ r 40 10 indices of crystal planes assigned to angle 26 each diffraction peak. The point Fig. 2. Fast X-ray diffraction patterns for NaCl and specific to the fee lattice is beautifully NaCl:Cd21 (14.3 mol% doped, as grown). These patterns are illustrated in the figure, that is, no well assigned to those of the fee lattice as indicated in the reflection can occur in the fee lattice figure with indices of crystal planes. Additional lines in for which the indices are partly even NaCl:Cd2+ are connected to the presence of the NajCdClg and partly odd. In the NaCl:Cd 2+ (14.3 superstructure phase in the mixed crystal. The indices in parentheses give the corresponding ones in the NaCl lattice. mol%, as grown) crystal appear many additional lines, which are never observed in NaCl. This diffraction Absorption spectra pattern is well explained by assuming NaCl:Cd"(0.1mol%) LNT that the crystal contains the Na 6 CdCl g super-structured micro-crystals. The lattice constant of Na 6 CdCl g is twice that of NaCl as shown in Fig.l, so that the indices of crystal planes are doubled as assigned in the figure. The additional lines, e.g. I l l , 200, 220, 311 and so on, 0.5 are specific to the superstructure and can 6.0 4.5 5.0 5.5 not occur in NaCl. The indices in the Photon Energy (eV) parentheses indicate the corresponding Fig. 2. Absorption spectrum observed at LNT for the NaCl:Cd2+ (0.1 mol% doped) crystal. The low energy ones of NaCl. In order to fit relative band is connected to the various Cd-impurity centers intensities of these lines to the calculated and the high energy one is related to the superstructure ones, we have to displace halogen ions micro-crystals. surrounding a Cd ion rather severely to 2+ lead to the D 2h local symmetry at the Cd site. When the NaCl:Cd 2+ crystals are quenched from 673 K to room temperature, all additional lines specific to Na 6 CdCl 8 disappear, which means that the Cd2+ ions and vacancies dissolve into the host NaCl lattice at high temperature and the superstructure phase are totally destroyed. In Fig.3 is shown an absorption spectrum observed at liquid nitrogen temperature for the NaCl:Cd2+ (0.1 mol% doped) crystal. The crystal is sufficiently transparent in this case of the low
319 Cd2+ concentration. Two broad absorption structures are observed in the energy region of 4.25-5.0 eV (LE) and 5.0-6.0 eV (HE). As described later in connection with the luminescence excitation spectra, the HE absorption structure is related to the superstructure of Na6CdClg while the LE one is attributed to the Cd2+ impurity-related centers such as substitutional Cd2+ ions, impurity-vacancy (IV) dipoles or small dipole aggregates. The observed absorption coefficient is very small not only because of low concentration but also owing to the fact that almost all light beam pass through pure NaCl region of the crystal because of very small cross sections of the superstructure micro-crystals. Figure 4 shows emission and excitation spectra obtained at 5 K for the NaCl:Cd2+ (14.3 mol% doped) crystal. Excitation energy for each emission spectrum are indicated in the figure, the region of which is in the low energy side of the fundamental absorption regions of NaCl and CdCl2. The spectral profile of the emission spectrum changes rather drastically depending on the excitation energy. Five emission bands, namely, BG (2.63 eV), V (3.14 eV), UV1 (3.56 eV), UV2 (3.85 eV) and UV3 (4.09 eV), are excited only in the restricted region of LE absorption band in Fig.3. The apparent strong luminescence distribution in the excitation spectra for B- and V-emission in the HE absorption region comes from severe overlapping with the Y- and B-emission bands at the observed emission energies (at 2.62 and 3.18 eV), respectively. The peak positions of the excitation bands are indicated in the excitation spectra where are expected absorption bands responsible for these emissions. These emissions are to be attributed to some impurity centers related to the presence of Cd2+ ions or cation vacancies. On the other hand, the Y (2.08 eV) and B (2.76 eV) emissions are excited in whole HE absorption region in Fig.3. The excitation band for B in the region below 5 eV is due to the spectral overlapping with the BG-emission band. The intensity raiio of Y to B changes with the Cd2' concentration. The B emission become much pronounced as decreasing the Cd2t content, and the Y emission is hardly observed in the 0.1 mol% crystal. The wide excitation region spread over 1 eV means that the absorption band responsible for the luminescence excitation may have a band nature, namely, an excitonic one or band-to-band transition. Thus, the B- and Y-emission are connected to the luminescence emitted in the Suzuki lattice of small and large sizes, respectively.
Fig. 4 Emission and excitation spectra obtained at 5K for the NaCl:Cd2* (14.3 mol% doped, as grown) crystal. Excitation energies are given on each emission spectrum and energies of emission observed are indicated on each excitation spectrum. The Y- and Bemissions are attributed to the N a ^ d O s superstructure. Other emissions are due to the Cd 2 'related impurity centers.
320 In Fig.5 is shown the effect of thermal quenching treatment on the Emission NaCLCd 14.3mol% 5K luminescence properties. The upper half one gives emission spectra for the NaCl:Cd2+ (14.3 mol% doped) crystal which is grown from melt by decreasing the temperature very slowly. Dominant Y- and shoulderlike B-emission band are clearly observed with excitation at 5.30 eV, while relatively small peak of the UV1-emission band appears under excitation at 4.77 eV. After the measurement of these spectra, the sample specimen was sealed in a 2.5 3.0 3.5 4.0 4.5 quartz ampoule, kept at 673 K for 5 Photon Energy (eV) hours in a furnace and quenched Fig. 5. The effect of thermal quenching treatment on emission down to room temperature by spectra for the NaCl:Cd2+ (14.3 mol% doped) crystal. The crystal using a water bath. The lower part was quenched down to RT after being kept at 673 K for 5 hours. Drastic changes occur on the Y-, B- and UV1-emission bands. of the figure represents emission spectra observed after quenching. The Y- and B-emission disappear almost completely instead of remarkable enhancement of the UV1-emission. It has been known from ionic thermo-conductivity measurements4 on NaCl:Cd2+ crystals that the concentration of impurity-vacancy dipoles is drastically increased by thermal quenching treatment. It was also confirmed in the present study that the X-ray diffraction pattern of the Na6CdClg superstructure disappears completely in the quenched crystals. Thus, we can conclude that the Y- and B-emission belongs to the Na6CdCl8 superstructure. This means that the excitation band for these emissions, which corresponds to the HE region absorption band in the absorption spectrum, should be related to the excitonic or band-to band transitions in the superstructure crystals. The UV1-emission is attributed to the impurity vacancy pair centers. Finally, it may be worthy to note that there should be some optimal annealing temperature to grow the Na6CdCl8 superstructure crystals of larger sizes and some technique to arrange them regularly in the host NaCl crystal. References 1. K. Suzuki, J. Phys. Soc. Jpn. 16,67 (1961). 2. D. Figueroa and E. Laredo, Solid State Commun. 11, 1209 (1972). 3. R. W. Dreyfus, Phys. Rev. 121,1'675 (1961). 4. R. Capelletti and E. de Benedetti, Phys. Rev. 165,981 (1968). 5. W. Spengler and R. Kaiser,phys. stat. sol. (b) 66,107 (1974). 6. A. L. Guerrero, E. P. Butler, P. L. Pratt and L. Hobbs, Philos. Mag. A 43 1359 (1981)
2LO RESONANT RELAXATION OF EXCITON POLARITON INTO LONGITUDINAL EXCITON STATE IN |3-ZnP2
K. NAKAMURA, S. UMEMOTO* and O. ARIMOTO Department ofPhysics, Okayama University, Okayama 700-8530, Japan Efficiency dip is observed at 2LO phonon energy above the U longitudinal exciton energy in excitation spectra for Is exciton luminescence band in P-ZnP 2 at 2K This dip comes from the 2LO resonant relaxation of exciton polariton into the longitudinal exciton state which plays a role of the killer of exciton polaritons in p-ZnP 2 Increase of nonradiative processes is checked by the photocalorimetric (PC) measurement. The PC response is not affected by the resonant 2LO process. Relaxation processes of exciton polaritons and energy dissipation are discussed.
1. Introduction P-ZnP2 shows a typical hydrogen-like exciton series, though the symmetry of the crystal structure is so low, C2h5. Absorption spectra have been studied extensively.1 In P-ZnP2, weak but distinct luminescence from higher exciton states n = 2, 3 and 4 is clearly observed for E//c under the interband excitation as shown in Fig. 1(a), in addition to strong Is exciton PHOTON ENERGY (eV) polariton luminescence with two components 1.585 1.590 1.595 1.600 1.605 CLI and CL2. Intensities of these luminescence bands are 1/1000 of the Is luminescence band.2 The luminescence from the 3s level is especially weak compared with that from the 2s. Relative intensities of these luminescence bands vary in a complex manner as an exciting energy is changed. The changes of intensities for the 2s and 3s luminescence bands are shown in Fig. 1(b) in a logarithmic scale. When excited above the 3s exciton resonance by the LO phonon energy 32.2 meV, intensities of the 2s and 3s bands decrease anti-resonantly contrary to the expectation of the resonance enhancement.2 As the exciting laser energy is lowered, the 3s luminescence changes only slightly. On the contrary, the 2s band becomes to increase rapidly, attains to the peak when the ILO Raman line comes just on the n = 2 resonance and then decreases gradually. 1.585 1.590 1.595 1.600 1.605 These behaviors are explained as follows: POS. 1LO RAMAN LINE (eV) The LO phonon of faoLo = 32.2 meV plays a substantial role in the relaxation processes of Fig. 1. (a) Luminescence from the higher exciton levels 2s, 3 s exciton polaritons in p-ZnP2.3 Energy and 4s. The ILO Raman line is indicated by the downward separation between the 3s resonance and the arrow, (b) Area intensities of 2s and 3 s exciton luminescence Is longitudinal exciton energy EL (or the bands against the energy position of the ILO Raman line. 'Present address: Fujitsu Chugoku Systems Ltd., Hiroshima 321
322 energy of the bottom of the upper polariton branch) is accidentally coincides with the LO phonon energy. Consequently polaritons relaxed into the 3s bottleneck are easily scattered away by the 1LO process, which explains the weakness of the 3s luminescence. When the laser energy is 32.2 meV above the 3s exciton level, the created exciton polariton relaxes into the longitudinal exciton state or the bottom of the upper polariton branch through the resonant 2LO phonon scattering process.2 Since the 2LO Raman line does not show resonance enhancement at EL,4 the exciton polariton seems to relax into the longitudinal exciton state, that is, the state works as the killer of the exciton polaritons in P-ZnP2. If it is the case, the process will reduce the efficiency of the Is exciton polariton luminescence and produce more heat, raising the temperature of the crystal. In this study, we observe detailed excitation spectra for the lower exciton polariton luminescence band at 2K by scanning the Ti: Sapphire laser around the energy EL + 2/jcoL0. We also measured the photocalorimetric (PC) spectra around there at 4.5K to detect the temperature rise of the crystal. 2. Experimental Starting materials of P-ZnP2 were metallic zinc (99.999%) and red phosphorus (99.9999%) both from Furuuchi Chemicals. Single crystals of black zinc diphosphide were grown from vapor phase as described in ref. 5. The size of the specimen used for the optical measurement was 6x2x1 mm (c xbxa). Surface obtained in an as-grown crystal is the 6c-face. Measurement at 2 K was performed by immersing the specimen directly into the superfluid helium. For luminescence and excitation measurements, a CW Ti:sapphire laser (Spectra Physics 3900S) pumped by an Ar ion laser (Spectra Physics 2017) was used as an exciting light source. The birefringent filter in the laser cavity was driven with a synchronous motor to change the excitation energy continuously for measuring excitation spectra.6 Using this device, we can obtain excitation spectra with a high resolution limited by the linewidth of the Ti:sapphire laser. Light from the sample was analyzed through a double monochromator (Spex 1401) and a cooled photomultiplier (Hamamatsu R943-02). Signals are detected with a lock-in amplifier. Technique of the PC spectroscopy is described in ref. 7. Absolute conversion efficiency of exciting light energy into heat is roughly estimated by using a test sample coated with black paint: The test sample is considered to work as a black body and the temperature rise in the test sample is taken as a standard value. Temperature rise of the crystal sample is normalized to the standard value obtained above. 3. Results and Discussion 3.1. Excitation spectra First we measured excitation spectra for the Is exciton polariton luminescence at 2K. Monitoring energy was varied within the luminescence bands CLi and CL2. Exciting laser energy was changed continuously by about 50 meV around the energy EL + 2AcoLO for each monitoring energy. Results are shown in Fig. 2. In Fig. 2(a), 1.? exciton polariton luminescence at 2K composed of two components CLi and CL2 is shown for reference. Excitation spectra were measured for luminescence components in the energy region indicated by a horizontal bar. Excitation spectra monitored at energy points A, B,... and J are shown in Fig. 2(b) where corresponding curves are indicated by letters A to J. Excitation efficiency of the Is exciton polariton luminescence rapidly decreases when the excitation energy increases across the energy gap Eg 1.603 eV due to the loss of spin memory of excitons. The average efficiency above Es is about one tenth of the efficiency below £g. Each curve has several peaks. These peaks change regularly their positions with the change of monitoring energies. These peaks are, therefore, due to passages of the Raman lines across the monitoring point. In P-ZnP2 optical phonons observed in the ordinary Raman spectrum distribute
323
from 9 meV up to about 60 meV. Several Raman lines have been confirmed near 60 meV. At about 1.63 eV, a rather broad dip is found for each curve, the energy position of which does not change with the change of the monitoring energy. This energy is about one LO phonon energy 32.2 meV above the n = 3 exciton resonance and hence corresponds to the energy EL + 2haL0. The exciton polaritons created at this energy contribute less to the 1* exciton polariton luminescence compared with those created at other energies. The interpretation in terms of the 2LO resonant relaxation processes is supported by these results. The longitudinal exciton state works as the killer of exciton polaritons. 3. 2. Photocalorimetric measurement The decrease of the luminescence efficiency at E\. + 2to L o is considered to act to produce more heat. To confirm this effect, we have measured the efficiency of generating heat, that is, the photocalorimetric spectrum around this energy. Contrary to our expectation, no sign of increase in heat generation is observed. The PC curve is almost flat in this energy region. This is explained as follows. First, the absolute conversion efficiency of light energy into heat is roughly estimated to be more than 60 percent at 1.63 eV. This estimation implies that most of the incident energy is converted into heat in P-ZnP2. Second, the reflectivity at 1.63 eV is about 30 percent. As described above, the average luminescence efficiency in the band-toband region is about one tenth of that in the low energy exciton region. Third, total intensity of the phonon sidebands of the Is exciton luminescence band is more than ten times as large as that of the main band.8 The luminescence efficiency of the 1* exciton is, therefore, far less than one percent at this energy. The change within this small value of luminescence efficiency observed in Fig. 2(b) is considered hardly to affect the PC efficiency.
1.559
PHOTON ENERGY (eV) 1.560 1.561 1.562
>H V)
I 1-
1.615
1.620 1.625 1.630 1.635 EXC. PHOTON ENERGY (eV)
3. 3. Relaxation processes Dispersion curves of singlet exciton polaritons in (3-ZnP2 are illustrated in Fig. 3. Employed exciton parameters, translational exciton mass and
Fig. 2. (a) The Is exciton polariton luminescence of P-ZnP2 composed of two components. Excitation spectra are measured for point A to J. (b) Excitation spectra of polariton luminescence at 2K. Letters A to J given at the right ends of the curves correspond to monitoring energy shown above.
324 background dielectric constant are 3me and 9.0, respectively.5 Direction of the wavevector is nearly along a-axis. Dispersion curve of the Is longitudinal exciton is also shown. It is assumed that every exciton branch has the same mass. In the figure, the 3s resonance energy level is indicated by the horizontal chained line. LO phonons with arbitrary wavevectors are also shown. In general, exciton polaritons created at light branch in the band-to-band region are scattered mainly by the LO phonons into somewhere in the exciton branches, for example, along the lines made by the intersection of dispersion energy surfaces Is, 2s etc. with a horizontal energy plane like the one shown in Fig. 3. Those scattered by the optical phonons with large wavevectors are transferred to the Is branch and decay as polariton luminescence shown in Fig. 2(a). 5 10 15 Polaritons scattered by the optical phonons with Wavenumber (10 6cm"1) small wavevectors fall on the higher exciton branches, Fig. 3. Dispersion curves of singlet exciton only a part of which relaxes through subsequent polaritons in P-ZnP2. Horizontal chained line acoustic phonon scatterings and decays as shows the constant energy plane of the 3 s luminescence from higher exciton states. The rest is exciton resonance. Laser is set at Eh + 2hs>la. further scattered into the Is branch and contributes to the polariton luminescence. When the laser energy is at EL + 2to LO , 163 eV, exciton polaritons otherwise falling into 3s or 2s exciton bottleneck relax directly into the \s longitudinal exciton state through the resonant 2LO scattering. This brings little population of polaritons on the 45, 3.s and 2s branches, resulting anti-resonant decrease of luminescence as shown in Fig. 1(b). Though the phenomenon of luminescence from the higher members of exciton is distinct and conspicuous, the order of the magnitude is minute. This means that most of the polaritons suffer scattering with the phonons with large wavevectors and are transferred to the Is branch, coming out of the crystal as ordinary luminescence. In P-ZnP2, electron-lattice coupling is very weak and even the allowed 2LO Raman line is hardly observable. Nevertheless, the scattering of exciton polaritons through two phonon process is confirmed, with the help of accidental energy condition, in the form of the resonant two LO Raman process. References 1. T. Goto, S. Taguchi, Y. Nagamune, S. Takeyama and N. Miura, J. Phys. Soc. Jpn. 58, 3822 (1989). 2. M. Sugisaki, M. Nishikawa, O. Arimoto, K. Nakamura, K. Tanaka and T. Suemoto, J. Phys. Soc. Jpn. 64, 3506 (1995). 3. O. Arimoto, M. Sugisaki, K. Nakamura, K. Tanaka and T.Suemoto, J. Phys. Soc. Jpn. 63, 4249 (1994). 4. M. Sugisaki, Thesis, Okayama University (1996). 5. O. Arimoto, M. Tachiki and K. Nakamura, J. Phys. Soc. Jpn. 60, 4351 (1991). 6. M. Sugisaki, O. Arimoto and K. Nakamura, /. Phys. Soc. Jpn 65, 23 (1996). 7. O. Arimoto, S. Umemoto and K Nakamura, J. Lumin. 87-89, 284 (2000). 8. K. Nakamura, Proc. Int. Conf. EXCOIT98, Electrochem. Soc. Proc. 98-25, 456 (1998).
STRUCTURES AND OPTICAL PROPERTIES OF HYDRAZONES DERIVED FROM BIOLOGICAL POLYENES TAKAYASU NAKASHIMA, TAKASHIYAMADA, HIDEKI HASHIMOTO* Department of Materials Science and Chemical Engineering, Faculty of Engineering, Shizuoka University, 5-1 Johoku 3-Chome, Hamamatsu 432-8561, Japan
TAKAYOSHIKOBAYASHI Department of Physics, Graduate School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan A set of hydrazone molecules was derived from a series of biological polyenes that have different polyene chain-lengths with common substituent group of 2,4-dinitrophenylhydrazine. Their structures were determined by high-resolution NMR spectroscopy as well as X-ray crystallography, and their optical properties were investigated by room and low temperature optical absorption spectroscopy. Among the derivatives so far synthesized, the one that has the shortest polyene chain (C13-DNPH) afforded single crystals without inversion symmetry, hence applicable for the second-order nonlinear optical devices. Molecular structures in the crystals were closely inspected in order to explain the cause to violate the inversion symmetry. Hydrazones derived in this study gave rise to two transition moments along the molecular axis. Comparison of the optical absorption spectra among the derivatives showed a unique phenomenon that could be attributed to the crossover of the excited state potential energy surfaces along the elongation of the polyene chain-lengths.
1. Introduction
^'TX,
Recent quantum chemical calculation suggested that polar carotenoid analogues with electron accepting groups attached to its polyene backbones have large nonlinear optical polarizabilities.1' Among them push-pull charge-transfer hydrazones attract special attention since they can afford single crystals without an inversion symmetry with more than 70% probability and hence can be applicable to the second-order nonlinear optical devices. ,3) In order to design materials with enough optical nonlinearlity, it is crucial to reveal the relation between the structures and optical properties of the materials. In this investigation, we have synthesized a series of push-pull hydrazones using biological polyenes as their structural motif, and have determined their molecular and crystal structures. Results of spectroscopic examinations are also presented.
(a) C13-DNPH
2. Experimental Figure 1 shows chemical structures of hydrazone
Fig. 1. Chemical structures of hydrazones derived from a series of biological polyenes
* Corresponding author, E-mail address: [email protected]
325
326 molecules synthesized in this study. They were obtained by simple condensation of biological polyenes and 2,4-dinitrophenylhydraine (DNPH) under the presence of catalytic amount of /7-toluenesulfonate. A series of biological polyenes was synthesized starting from the shorter polyene molecules by the use of Horner-Emons, Wittig and Aldol reactions. For simplicity, we hereafter call them by referring to their carbon numbers at the polyene parts as C13-, C15-, C17-, CI8-, C20, C22- and C25-DNPH. High-resolution NMR measurements were performed for all the set of hydrazones using JEOL AL-300 NMR spectrometer, and the chemical structures as illustrated in Fig. 1 were confirmed. X-ray crystallography was also performed for CI3-, CI5- and C20-DNPH that can be afforded in single crystals with enough crystal sizes. Optical absorption spectra of the hydrazones in benzene solutions at room temperature were recorded using Hitachi U3000 or Otsuka MCPD-1000 spectrophotometer. Low (cryogenic) temperature absorption spectra were recorded using a home-made set-up composed of a 150W Xe-arc lamp, a Nikon G250 monochrometer, an Oxford Optistat-DN temperature controlled liquid-nitrogen cryostat, a Si photodiode, and a NF LI-574A auto-phase lock-in amplifier. 3. Results and Discussion Table I summarizes the crystallographic data of C13-, C15- and C20-DNPH. Based on the results of X-ray crystallography, we have reported that the crystal of C13-DNPH belonged to monoclinic P2i space group and hence lacked the center of symmetry.2' However, the increased number of conjugated double bonds of C13-DNPH resulted in the production of the crystals that had a center of symmetry. The crystal of C15-DNPH belonged to triclinic PI space group and that of C20-DNPH to monoclinic P2i/c. In order to clarify the cause of this tendency, the structures of molecules (e.g. bond lengths, bond angles, and dihedral angles) in the crystals were investigated in detail to reveal the effect of intermolecular interaction in the crystals. It was shown that highly polarized and conjugated molecules existed in the crystal of C13-DNPH2) although the intermediate Table I. Crystal data of C13-DNPH, C15-DNPH and C20-DNPH C13-DNPH Empirical formula Molecular weight Crystal system Space group Lattice parameters
Volume Z value Density
C15-DNPH
C20-DNPH
372.42 monoclinic P2,(#4) a = 8.597(4) A b = 34.103(4) A c = 13.170(3) A
C21H26N404 398.46 triclinic Pl(#2) a = 7.838 (2) A b = 20.518 (2) A c = 7.077(1) A OF 94.72 (1)°
C26H32N404 464.56 monoclinic P2,/c(#14) a = 6.42 (2) A b =11.85 (2) A c = 33.29 (2) A
/?= 96.85(3)°
P= 110.71 (1)°
P= 92.7 (2)°
3833(1) A 3 8 1.290 g/cm3
y= 93.21 (1)" 1056.6 (3) A 3 2 1.252 g/cm3
2529 (8) A 3 4 1.220 g/cm3
C 19 H 2 4N 4 04
327
20000
30000
Wavenumber /cm"1 JOOO
25000
30000
Wavenumber / cm Fig. 2. (a) Optical absorption spectra of DNPH, 2-NPH and 4-NPH in benzene solutions recorded at room temperature, and (b) the results of ZINDO-CI molecular orbital calculations of DNPH.
Fig. 3. Optical absorption spectra of (a) C13-, (b) C15-, (c) C17-, (d) CI 8-, (e) C20-, (f) C22-, and (g) C25-DNPH in benzene solutions recorded at room temperature. Solid lines show the observed absorption spectra and dotted and broken lines shows the results of deconvolution. Thinner dotted-broken lines show the absorption spectra of original aldehydes and ketones.
structures of the polarization and conjugation were found in the crystals of C15-DNPH and C20-DNPH. In the crystal of C13-DNPH, these polarized and conjugated molecules lie in the neighboring positions of the crystal lattice. Therefore, it is concluded that the intermolecular interaction between the polarized and conjugated structures would stabilize the crystal structure without the inversion symmetry. Figure 2(a) shows the optical absorption spectra of DNPH, 2-nitrophenylhydrazine (2-NPH), and 4-nitrophenylhydrazine (4-NPH) in benzene solutions recorded at room temperature. Figure 2(b) shows the result of ZINDO-CI molecular orbital calculations of DNPH. As shown in Fig. 2(a), DNPH gives rise to two absorption bands, i.e. a high-energy (HE) band and a low-energy (LE) band. Based on the calculation, 2 ' we have assigned the origins of the HE and LE bands to HOMO —» LUMO + 1 and HOMO —> LUMO transitions, respectively. In the former transition electrons distributed at hydrazine part in HOMO moves to para-position NO2 orbital in LUMO + 1, while in the latter transition electrons moves to orAo-position N 0 2 orbital in LUMO. According to Fig. 2(a), both 2-NPH and 4-NPH give rise to single absorption bands, and the peak energy of 2-NPH lies at the lower energy side of 4-NPH. In addition, 2-NPH shows the smaller absorption cross-section
328 than that of 4-DNPH. Therefore, the above assignment of the HE and LE bands are thus verified experimentally. It is interesting to note that both the HE and LE bands of DNPH shift to the higher energy side of the peak energies of 4-NPH and 2-NPH, respectively. This might be due to the interaction between two transition-dipole moments, and further theoretical analysis is necessary to explain the cause of this trend. Figure 3 shows the optical absorption spectra of a set of hydrazone molecules as well as original aldehydes and ketones. Comparison of the absorption spectra between hydrazones and the corresponding polyene molecules suggests that the polyenes just act as a substituent mat modifies the hydrazones' electronic states responsible for the overall absorption, because the absorptions due to the original polyenes are observed at the higher energy side of the main absorption bands. All these hydrazones gave rise to two absorption bands (HE and LE bands) the origins of which could be attributed to the same transitions as already explained in the case of DNPH. In order to improve the spectral resolution to separate two absorption bands, we attempted to record the absorption spectra at cryogenic temperature but in vain. With the decrease of temperature, both the HE and LE bands shift to higher energy and the separation of these two bands decreased. In addition, aggregation was found to take place in the case of CI7- and C18-DNPH. This interesting phenomenon is beyond the scope of this study and will be discussed elsewhere. As shown in Fig. 3, according to the elongation of polyene chain-lengths, the HE band showed red shift while the LE band does not shift. In the case of C22- and C25-DNPH with longer chain-length than C20-DNPH, bands corresponding to the HE band in the shorter polyenes appeared at the lower energy side of the LE band. This can be attributed to the crossover of the excited state potential energy surfaces due to the characteristic electronic structures of the hydrazones that have two transition dipole moments in one-dimensional systems. Lti other word, we have succeeded to engineer the electronic states of hydrazones by changing the polyene chain-lengths. We believe that this type of "electronic state engineering" is going to be very important to synthesize novel nonlinear optical materials for the practical applications in near future. Acknowledgements This work is supported by Grant-in-aid (# 10740145 and 1240179) from Ministry of Education, Science, Sports and Culture in Japan, and by Research for the Future of Japan Society for the Promotion of Science (JSPS-RFTF-97P-00101). References 1. H. Hashimoto, K. Hattori, Y. Okada, T. Yoda and R. Matsushima, Jpn. J. Appl. Phys. 37,4609 (1998). 2. H. Hashimoto, T. Nakashima, K. Hattori, T. Yamada, T. Mizoguchi, Y. Koyama and T. Kobayashi, Pure Appl. Chem. (2000) in press. 3. S. Follonier, Ch. Bosshard, U. Meier, G Knopfle, C. Serbutoviez, F. Pan and P. Giinter, J. Opt. Soc. Am. B3, 593 (1997). 4. F. Pan, C. Bosshard, M.S. Wong, C. Sebutoviez, K. Scenk, V. Gramlich and P. Giinter, Chem. Mater. 9, 1328 (1998).
Photoluminescence of Two-Dimensional Electron S y s t e m in M o d u l a t i o n - D o p e d G a A s Quantum Well
H. Nakata, K. Fujii, M. Saitoh, and T. Oliyama Department of Physics, Graduate School of Science, Osaka University 1-16 Machikaneyama-cho,Toyonaka, Osaka 560-0043, Japan
We have carried out the photoluminescence measurements of two-dimensional electron system (2DES) in modulation-doped GaAs quantum well. It was found that the H band caused by radiative recombination between 2DES and holes shows a high energy tail below 4.2 K. We explain that the tail originates in the apparent breaking of the momentum conservation law , and that its reason is the electron scattering by neutral donors with the Bohr radius of ~10 nm. The distance between the adjacent donors, 80nm, is obtained from the coupling of the Landau levels in the different 2DES's. Excitonic effect is suggested by nonlinear dependence of the peak energy of the H band on magnetic fields and the lineshape analysis of the H band. 1. Introduction In general, radiative recombination processes of photoexcited carriers in semiconductors require the energy as well as the momentum conservation law. In indirect semiconductors where electrons and holes have considerably different crystal momenta, the phonons are always related to the recombination of carriers in the high-purity sample. Impurity-assisted radiative recombination is, on the other hand, allowed for the doped semiconductors. For example, an electron and a hole which have formed a donor-bound exciton complex are able to recombine each other to result in zero-phonon emission line 1 . In this process, the donor atom restricting an exciton is responsible for satisfying momentum conservation law. We propose that such an impurity-assisted mechanism plays an important role in the radiative recombination between a two-dimensional (2D) electron and a hole. Here the electrons with finite wave numbers need assistance to fulfil the momentum conservation law in the radiative process. We utilized modulation-doped GaAs quantum well to serve two-dimensional electron system(2DES),which has been a stage for fruitful results such as fractional quantum Hall effect 2 . Some optical investigations have been applied to 2DES and the photoluminescence (PL) peak denoted H band due to radiative recombination between a 2D electron and a hole was observed by Yuan et al. 3 . Zhao et al. studied Fermi edge singularity of the H band due to many body effect in DC biased GaAs/A^Gai-^As heterostructure 4 . Excitonic effects for excited subbands have been reported by Stepniewski et al. in magneto-luminescence spectra of the H band 5 . They have explained the transition related to the lowest subband as the interband transition with many-body effects. In this report, we investigate the origin of the H band by the lineshape fitting and the analysis of the PL peaks in a modulation-doped GaAs quantum well. We have carried out PL experiments for a modulation-doped GaAs quantum well. The distinct H band whose peak shifts to higher energy with increasing excitation intensity 6 . Magnetoluminescence reveals oscillatory behavior originating in the interband transitions with the same Landau quantum numbers. Two series of peaks are assigned to two different 2DES's. The coupling of Landau levels for electrons in different potential notches gives us the imformation on the interaction between two 2DES's. We have analyzed the lineshape of H band by assuming the breaking of the momentum conversation law. It is concluded that the scattering of electrons by neutral donors is responsible for momentum conservation . The nonlinear property of the peak energies in the magnetic fields leads us to conclude that the lowest Landau level is associated with some bound state. We speculate that excitonic effect is also important to
329
330 understand the transition between the lowest Landau levels. 2. Experimental Sample used in this study was a modulation-doped GaAs quantum well whose thickness was 30 nm. The Alo.3Gao.7As barriers were <5-doped with Si donors. The sample was excited by an Ar ion laser or the second harmonics of an LED-excited Y V 0 4 laser. The PL signal dispersed by a SPEX 1269 monochromator was detected by a cooled photomultiplier and accumulated by photon counting technique. 3. Results and discussion Fig.l shows PL spectra in magnetic fields. In zero magnetic field, a broad peak at 1.503 eV with a high energy tail and a sharp peak at 1.515 eV were observed. We assign the broad and sharp peaks to H band (HB) and free exciton (X), respectively. The peak position of the H band shifts to higher energy with increasing excitation energy. The peak energy of the free exciton is almost the same as that in bulk GaAs. Two features appear under the application of the magnetic field. One is the remarkable increase of X line and another is the appearance of the oscillatory structures on PL spectra. As mentioned above, the PL intensity of the H band oscillates in magnetic fields. This phenomenon is similar to Shubnikov-de Haas and the Fermi energy is estimated to be 21 meV from the period of the oscillation. If the peak at 1.503 eV appears at the edge of the lowest subband, the shoulder at 1.524 eV should be the Fermi edge. We plot the peak energies of the oscillatory PL against magnetic fields as shown in Fig.2. The solid lines are the results of calculation based on interband transitions between the Landau levels of the lowest subband of 2DES and heavy holes. The transition energy is given by E = (n+
1.50
1.51
1.52
1.53
-)Hu}a
1.54
(n + -)hwch
- E'0
Magnetic Field (T)
Photon Energy (eV)
Fig.l Phololuminescence spectra of modulationdoped GaAs/AlnjGa^As double heterostructure in magnetic fields. X, IHB and HB denote a free exciton, impurity assisted H band and H band, respectively.
Fig.2 Photoluminescence peak energies vs magnetic fields. Solid lines show the result of the calculation based on the interband recombination for 2D electron with a heavy hole. Coupling between two 2DES is included for Landau numbers of n=2 and n'=l.
331 where n is Landau quantum number of electrons or heavy holes, u>„ and uci, are cyclotron frequencies of a 2D electron and a heavy hole, respectively and E'G is the effective band gap including the subband energy and the valence band bending. Here we used electron mass of 0.07 m0 and heavy hole mass of 0.45 m 0 . The estimated transition energy due to the edge of the lowest subband is 1.503 eV at zero magnetic field. Most intriguing occurence in this fitting is the branch denoted n ' = l just above the n = 2 one. We speculate that it is caused by another 2DES formed at another interface in the sample. As shown in Fig.l, we observed a peak denoted HB' just below the free exciton peak in magnetic fields. We consider the peak is H band due t o another 2DES. The energy difference between two H bands is about A = 8 meV. Around 4.5 T, two Landau levels n = 2 and n ' = l approach each other and repel by anticrossing rule due to mutual interaction. The levels can be obtained by solving a secular equation #11 — E "21
H12
T=2K A1251
.
\\
HB
A J V
1.495
1.500 1.505 1.510
IHB
1.515 1.520 1.525
1.530
Photon Energy (eV)
Fig.3 Photoluminescence spectra at 2K. X, IHB and HB denote a free exciton, impurity-assisted H-band and H band respectively. A broken line indicates the calculated result including the breaking of the momentum conservation law, the level broadening and the raise of electron temperature.
= 0
H22 E ^ 2 2 —•"->
where _ff12 is interaction energy, Landau levels. The meaningful solution is E=l-
<
Hn=(n+^)'hu}c, and i?22=(n'+|)ftu'ce+ A E are energies of
(HXX + H22 + y/{Hu - H„)> + i\Hu\*
The fitting result is displayed in Fig.2. The estimated interaction energy is about 1.5 meV. If the energy is caused by Coulomb interaction between two electrons, it is possible to estimate that the distance between two interacting electrons is 80 nm. This value is larger than the well thickness of 30 nm. It means that only the pairs separate by 80 nm contribute to the magneto-oscillatory structures. Under low excitation intensity at 2.OK, we can see the clear PL peak at 1.503 eV as shown in Fig. 3. We have tried to fit the lineshape of the H band by calculation. At low temperatures, most of heavy holes have very small momenta. In order to satisfy the momentum conservation law, only 2D electrons populating near the edge of the lowest subband can recombine with holes. In this case the lineshape is shown according to the exponential function with low energy cutoff, which is, on the whole, different from the observed one. We assume that the breaking of the momentum conservation rule induces the high energy tail. The luminescence spectra as a function of the photon energy offiware described by e>BT
I{hu>) = A f IdEdE' ex
p
y{-Jiti ?)+i
{\ + ±arctan{fE))8{E-E'-%u)
(kc - khy + *?
where k e and k/, are the wave numbers of an electron and a hole, respectively. The characteristic
332 wavenumber K represents the breaking of the momentum conservation law. The energies E and E' are for electrons and holes, respectively. We obtained the electron temperature of S K, the characteristic energy e (= ^ - ) of 6 meV, Fermi energy EF of 22.5 meV. In addition, we take into account the broadening of the subband <5E of 0.8 meV estimated from the half-width of cyclotron resonance line. The function of arctanx is deduced from the integral of Lorentzian function. The reason is that the step function related to the density of states for 2DES is connected with the integral of the delta function which becomes Lorentzian function. The resultant lineshape barely explains experimental results. We additionally take into account the free exciton peak with Gausian profile and another peak with Gaussian profile near band edge. The half widhs are 1 and 3 meV, respectively. The above mentioned characteristic energy e= 6 meV is obtained from the inverse of the characteristic length 1/K of 14 nm. This value corresponds to the extent where the 2D electrons localize and is close to the Bohr radius 10 nm of a shallow donor in GaAs. We speculate that 2D electrons collide with neutral donors in the process of radiative recombination to satisfy the momentum conservation during radiative recombination. Such a process is common for radiative recombination of bound excitons. The PL peaks due to such a process are called zero phonon line for bound excitons. Another peak at 1.503 eV is not due to the impurity-assisted process but excitonic effects. The experimental result is not reproduced by a model of the radiative recombination between 2DES and holes. The estimated separation 80 nm between adjacent regions is the distance of two impurities, which corresponds to the concentration of 2 x l 0 1 5 c m - 3 . It is quite normal for the GaAs sample. The excitonic effect should be significant to interpret the peak. The estimated Bohr radius of the donor is larger than that in bulk GaAs. The existence of degenerate 2DES might distort the wavefunction of donor electron and expand the Bohr radius effectively. In fact a calculation on the reduction of donor binding energy has been reported for quantum well7. The behavior of the lowest energy peak in magnetic field does not show the feature of a free carrier. The peak position does not linearly depend on magnetic fields. The excitonic effect should be responsible for the nonlinearity. Concerning the excitonic feature, further investigation is nescessary in order to get the decisive conclusion.
4. C o n c l u s i o n s In summary, the high energy tail of the H band is caused by neutral impurity scattering to satisfy the momentum conservation law in a modulation-doped GaAs quantum well. We speculate that the excitonic effect of the H band should be considered in order to explain its low energy peak.
References 1. 2. 3. 4.
E. F. Gross, B. V. Novikov, and N. S. Sokov, Sov. Phys.-Solid State 14, 368(1972). D. C. Tsui, H. L. Stormer, and A. C. Gossard, Phys. Rev. Lett. 48, 1559 (1982). Y. R. Yuan, K. Mohammed, M. A. A. Pudensi, and J. L. Merz, Appl. Phys. Lett. 45, 739(1984). Q. X. Zhao, P. O. Holtz, B. Monemar, E. Sorman, W. N. Chen, C. Hallin, M. Sundaram, J. L. Mertz, and A. C. Gossard, Phys. Rev. B 46, 4352 (1992). 5. R. Stepniewski, M. Potemski, H. Buhmann, D. Toet, J. C. Maan, G. Martinez, W. Knap, A. Raymond, and B. Etienne, Phys. Rev. B 50, 11895 (1994). 6. K. Fujii, M. Saitoh, H. Nakata, and T. Ohyama, Physica B 272, 454(1999). 7. G. Bastard.rays. Rev. B 24, 4714 (1981).
SCANNING NEAR-FIELD OPTICAL MICROSPECTROSCOPY OF SINGLE PERYLENE MICROCRYSTALS JUN-ICHINIITSUMA, TORU FUJIMURA and TADASHIITOH Division of Material Physics, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan HITOSHIKASAI, SHUJI OKADA, HIDETOSHI OIKAWA and HACHIRO NAKANISHI Institute for Chemical Reaction, Tohoku University, Sendai, 980-8577, Japan Perylene microcrystals are known to show characteristic change in the exciton fluorescence spectra depending on the crystal size less than about 200nm. However, the origin of the size-dependence is not yet clear. In this work, we have studied on individual microcrystals by a scanning near-field optical microscope (SNOM). The samples were prepared by a modified technique based on reprecipitation method. As a result, we could successfully measure the topographic and fluorescence images of perylene microcrystals with the size of ~200nm by SNOM at room temperature. In the fluorescence spectra of the single microcrystals, free and self-trapped exciton bands were successfully observed but they did not show any critical difference from that of the bulk crystals. Some possibility of environmental difference is discussed.
1. Introduction Recently, it has been reported that perylene microcrystals which have the average size less than about 200nm and dispersed in water show different exciton fluorescence spectra from that of the bulk crystals'; for the microcrystals, fluorescence intensity from the free exciton (FE) state is comparable or even larger than the self-trapped exciton (STE) component and the FE peak wavelength is dependent on the microcrystal size. However, the size is much larger than the dimension where so-called quantum confinement effects occur. Series of researches have followed, nevertheless the origin of this phenomenon is not clear yet. Therefore some of the sample characteristics, such as the size distributions and the water suspension, might affect the fluorescence spectra. Scanning near-field optical microscope (SNOM) 2 is one of the scanning probe microscopes having the spatial resolution beyond the diffraction limit (about the dimension of the wavelength of light) by using the near-field light from a sharpened optical fiber tip end. This is a powerful tool for investigation of optical systems microscopic systems, such as fluorescent single molecules 3 . To investigate the above phenomena of perylene microcrystals, we have measured not only the topographic and fluorescence images but also the fluorescence spectra of the individual microcrystals using the SNOM. 2. Experimental Procedures Figure 1 shows a schematic diagram of the SNOM system used in the present experiment. An atomic force microscope (AFM) (Seiko Instruments Inc. SPA300) was modified for SNOM measurement and controlled by SPI3800 (SII). The optical fiber probe was a bent-type with low spring constant (Nanonics SuperSensor). The probe tip coated with Al/Cr and having an optical aperture of ~100nm was mounted on a bimorph and vibrated near the resonance frequency (~9.5kHz). The distance between the probe tip and the sample surface was kept constant by the optical feedback control used for AFM operation. The excitation light was a second harmonic light (A,=400nm) of Ti:Sapphire laser converted by a LBO crystal. The light intensity was modulated by an AO modulator at the resonant frequency and coupled to the fiber so that the near-field light from the probe tip radiates the sample only when the distance between the tip and the sample is the
333
334
A.=800nm
X=400nm
J N LBO I/, LJ_, A/2 plate
AFM/SNOM images Controller SPI3800
Lock-in amp Spectrum Cooled CCD Spectrometer
Fig. 1. Schematic diagram of SNOM
smallest in order to make the best optical resolution. Fluorescent light was collected by an oil immersion objective (Olympus Plan 100x/N.A.1.25) from the rear side of the sample and spectrally filtered to eliminate the excitation light and the feedback control light for the AFM operation. The light intensity was detected by a photomultiplier tube (Hamamatsu R1617) and then fed to a lock-in amplifier for the measurement of fluorescence SNOM images, or the signal was sent to a spectrometer followed by a liquid nitrogen cooled CCD camera (Acton SP-150 & Princeton Instruments LN/CCD-1340PB) through a bundle fiber for the measurement of fluorescence spectra. The microcrystals of perylene were prepared by reprecipitation method4; the acetone solution of perylene (~lmM) of 0.2ml was injected into stirred water of 15ml by a microsyringe. We first prepared the microcrystal samples for the SNOM measurement by taking a few drops of the microcrystal-dispersed water on a cover slip and drying them. The substrate was ultrasonically cleaned for 10 minutes in an acetone before the preparation and in water after the preparation. 3. Results and Discussions We found out that the sample prepared by the above simple method was not suitable for the SNOM measurement. Perylene microcrystals had coalesced together during the drying process and often removed from the substrate during the scanning, which made it impossible to take good topographic and fluorescence images of single perylene microcrystals. Then we have modified the preparation method as follows; the acetone solution of perylene was injected directly onto a substrate held in stirred water. As shown in the AFM image of Fig.2 where an ordinary silicon
Fig. 2. AFM image of perylene microcrystals on sapphire (0001).
Fig. 3. (a) AFM and (b) SNOM fluorescence (X-475-600nm) images of perylene microcrystals on a quartz cover slip.
335 nitride tip was used, square-shaped perylene microcrystals with the size raging from lOOnm to several microns and the thickness from 30nm to sub-microns had successfully prepared in a well dispersed form. We could also take reliable images of these samples by the SNOM measurement without severe damage to the samples. Figure 3 shows the false-color images of topography and fluorescence of the perylene 500 550 microcrystals observed by SNOM. The sizes 450 600 Wavelength [nm] of the crystals denoted as A, B and C in Fig.3 Fig. 4. Fluorescence spectra of three single perylene were estimated from topographic cross microcrystals shown in Fig.3. FE: free exciton; STE: sections to be 206, 247 and 253nm, self-trapped exciton. respectively. They were to be small enough to show the characteristic fluorescence spectra different from that of the bulk crystals if they were dispersed in water. The fluorescence spectra of the three individual microcrystals are shown in Fig.4. FE and STE bands were clearly observed at 480nm and 570nm, respectively. Judging from the spectral position and shape of these bands, the microcrystals should be a-type perylene5. However we could not find out any critical difference from the bulk crystals. We also obtained similar spectra for many microcrystals with different sizes. Therefore we consider that the environmental difference could affect the fluorescence spectrum since the sample was directly exposed to air. Some effects, which might be caused by water, would be more enhanced as the average size of microcrystals becomes smaller. The SNOM measurement of the samples dipped in water is now going on and the result will be published elsewhere. 4. Summary We have succeeded to measure the fluorescence spectra of the single perylene microcrystals with the sizes of ~200nm by SNOM. The spectral changes dependent on the size which were reported previously have not been observed in this work. The modified reprecipitation method could be an easier and more general method of preparing organic microcrystal samples for scanning near-field optical microscopy or other scanning probe microscopy, which may widen the applications using the reprecipitation method. Acknowledgements We are grateful to H. Muramatsu, N. Chiba and K. Homma of Seiko Instruments Inc. for their support in the SNOM instruments. This work was supported by the Grant-in-Aids for Priority Area(B) on Laser Chemistry of Single Nanometer Organic Particles and Scientific Research(B) from the Ministry of Education, Science, Sports and Culture of Japan. References 1. H. Kasai, H. Kamatani, S. Okada, H. Oikawa, H. Matsuda and H. Nakanishi, Jpn. J. Appl. Phys. 35, L221 (1996); H. Kasai, Y. Yoshikawa, T. Seko, S. Okada, H. Oikawa, H. Matsuda, A. Watanabe, O.lto, H. Toyotama and H. Nakanishi, Mol. Cryst. Liq. Cryst. 294, 173 (1997); T. Seko, K. Ogura, Y. Kawakami, H. Sugino, H. Toyotama and J. Tanaka, Chem. Phys. Lett. 29), 438-44 (1998) A. Lewis, M. Issacson, A. Harootnian and A. Muray, Ultramicroscopy 13, 227 (1984); D.W. Pohl, W. Denk and M. Lanz, Appl. Phys. Lett. 44,651 (1984); E. Bezig and J.K. Trautman, Science 257, 189 (1992) E. Bezig and R.J. Chichester, Science 262, 1422 (1993) H. Kasai, H. S. Nalwa, H. Oikawa, S. Okada, H. Matsuda, N. Minami, A. Kakuta, K. Ono, A. Mukoh and H. Nakanishi, Jpn. J. Appl. Phys. 31, LI 132 (1992) H. Nishimura, T. Yamaoka, K. Mizuno, M. Iemura and A. Matsui, J. Phys. Soc. Jpn. 53, 3999 (1984)
MULTISTABLE NATURES A N D PHOTO-INDUCED CHARGE-SEPARATION IN H O L E - D O P E D STATES OF S T R O N G L Y C O U P L E D E L E C T R O N - P H O N O N S Y S T E M S
NITTA Hitoshi, SUZUKI Masato, and IIDA Takeshi Department of Physics, Graduate School of Science, Osaka City University, Sumiyoshi-ku, Osaka, 558-8585, Japan We investigate the effects of hole doping in the charge-density wave (CDW) state that has the strong electron-phonon (e-p) coupling, using the two-dimensional molecular crystal model. In calculations, we use the mean-filed theory for the interelectronic interactions and the adiabatic approximation for phonons. On the basis of this theory, we calculate e-p states of doped ground states for various values of the doping concentration of holes. Prom the calculated results, it is found that a multistable nature appears in the doped e-p states just before the CDW-metal phase transition. In order to see the effects of the photoexcitation in the hole-doped states, we also investigate the exciton states taking into account the electron-hole correlation. Results calculated here indicate that the separation of electron and hole occurs in the photoexcited states as a consequence of the energy relaxation of excitons. Keywords: hole doping, multistability, charge separation 1. Introduction Since the discovery of the chemically doped high-T c superconducting oxides such as BaBi03, the problems related to the hole doping have been extensively studied in connection with the clarification of the conducting mechanism of these materials. 1 - 3 In general, in an insulator with a strong electron-phonon (e-p) interaction such as BaBiOa, a doped hole induces a local lattice distortion through the strong e-p coupling and is trapped in it. This state is called a polaron. Two polarons attract each other through the e-p interaction, and they usually make a bound state, namely, a bipolaron. Therefore, when many holes are doped, they are expected to condense through the attractive interaction induced by the e-p interaction. However, the detailed structures of the many-hole-doped states are remained unsolved. In this paper, therefore, we investigate the structural changes via hole doping in the strongly coupled e-p systems over the wide region of the doping concentration of holes ( s p ) . Moreover, we investigate the photogenerated excited states in the hole-doped e-p states, so as to clarify the effects of the photoexcitation on the structural changes occurring in these states. 2. M o d e l H a m i l t o n i a n In order to clarify the effects of the hole doping in the strongly coupled e-p systems, we use the following quasi-two-dimensional molecular crystal model ( = H) with ft=l, H
=
-T £ 1,1',IT
aL°!V + V Y, nian0 + ir I
Yl
n
i"ni'"'
*• 1,1',ay
+^EWI? + ^ ^ E ( ^ - o ) a ; i .
(!)
where nia=a\^aia. I denotes the square lattice point of the site, and /' is its nearest neighbor one. a\a{aia) is the creation (annihilation) operator of an electron in the Zth site with spin a (=a,/3). T is the resonance transfer integral of an electron between nearest neighbor sites. U and V are the intrasite and the intersite Coulombic repulsive energies, respectively. In the molecular crystal model, the vibrational modes around the site are approximated by a single phonon mode localized at this site. We use the adiabatic approximation for phonons. The
336
337 fourth term in H denotes the elastic energy of the lattice distortion, and u is its modulus. xi means the classical variable for the lattice distortion. S is the coupling constant of the e-p interaction. So as to obtain a convenient form of the Hamiltonian, we normalize all the energies by T and introduce the dimensionless coordinate for the lattice distortion (=Qi = \]%xi)Let us explain our method to calculate the ground and the excited states of the doped e-p states. In the ground state, we use the mean-field theory for the interelectronic interactions. Within this theory, H is reduced to the mean-field Hamiltonian (= HHF), in which nla and a\aaii„ are replaced by their expectation values for the ground state as {ni„) and (alaaiia). They are unknown parameters to be determined later self-consistently. Diagonalizing HUF, we can obtain the energy and the wavefunction of the ground state (= \g)). The self-consistency between (nj„), (aj^ajv), and Qi is included in our calculations by using ^Ssil = o. The nth singlet exciton (s|
K> = E E tf>Lv» + "Wis).
(2)
where a1 {axa) denotes the creation (annihilation) operator of the x*h single particle electronic state with spin a. The coefficient /£ is determined by diagonalizing the real Hamiltonian H on the basis of the one-electron excited states obtained from i?HFIn numerical calculations, we use the 20x20 square lattice with the periodic boundary condition. Such a size of cluster is large enough to describe the distribution patterns of holes until p is about 40%, where p is defined by the ratio of the number of the doped holes to that of the lattice sites (= N). Since we are interested in the case where the e-p interaction is relatively strong, the interaction parameters are set to be S/T=2, VjT—\ and V/T=0.1. At these parameters, we can obtain the charge-density wave (CDW) state with the energy gap of about 2.5T in the case of the half-filled ground state. In order to determine {/"^} of Eq. (2) in the region near the lowest excitation, we use the 800 wavefunctions of the lower-lying one-electron excited states as a basis set for the diagonalization of H. 3. Results and discussion 3.1. Adiabatic structures
of hole-doped
states
Let us see the stable structures of the doped e-p states. The charge-density profiles are depicted in Fig. 1 for various values of p; (a) p=10%, (b) and (c) 26%, (d) 40%. In these figures, the area of each circle is proportional to the charge-density at the corresponding site. We can see from Fig. 1(a) that when p=10% the doped holes construct a localized domain as a result of the attractive interaction among holes that is induced by the e-p interaction. In this domain, the phase of the CDW is inverted from the original CDW state, and the holes are distributed at around the boundary region between them. It can be seen from Fig. 1(b) that its region extends as increasing of p. In addition to these localized domain-structures, when we start the self-consistent calculations using some what different initial conditions with respect to the charge distributions, the another structures are obtained as metastable states. One example of the charge-density profiles of such structures is depicted in Fig. 1(c) at p=26%. In this state, the doped holes construct the longer periodic CDW state than the half-filled one through the (1 Indirection, and a few holes localize as a unit of the bipolaron or the domain on this longer periodic background CDW. The energy of this structure is almost the same as that of the lowest solution appeared in Fig. 1(b). Therefore, these structures are expected to coexist around this value of p at the finite temperatures, and it brings about a multistability of the doped e-p states. The CDW amplitude finally disappears as shown in Fig. 1(d), which corresponds to the metallic state.
338 (a) p = 10 %
(b) p = 26 %
(c) p = 26 %
<
Fig. 1. Charge-density profiles for various values of p. The area of circle at each site is proportional to the charge-density. S/T = 2, U/2 = 1 and V/T = 0.1. 3.2. Electron-hole calized states
separation
in photoexcited
states between localized and delo-
Next, let us see the characteristics of the photoexcited states in the hole-doped states, so as to clarify the effects of the photoexcitation on the structural changes occurring in the doped e-p states. As discussed above, the doped ground states are expressed by both the delocalized periodic CDW states and the localized domain-structures. Hence, it is expected that the excited states are characterized by the localized and the delocalized states. Therefore, in order to see the distribution patterns of the electrons and the holes in the excited states, we calculate the averaged values of the spatial distribution lengths of the electron (= A£) and the hole (= Aj[) in the wavefunction of the nth excited state as unocc.
K
= E
E
\l-l'Mnx\nla\VlxWnx\nVcr\^nx),
(3)
occ.
Aj =
EEl'-n<<Jl-^|<<>KJl-n t,l',(T
i V
Kx),
(4)
X
and K*>
=
\X,O)(XM
(5)
where |x, o) denotes the xth single particle electronic state with spin a. If the exciton is uniformly distributed over the whole region of the crystal, A* and A|J take -^ T,i,i' \l — l'\ (=Ao)In the cluster used here, A0 is about 7.6 times of the lattice constant. The calculated results of A* and Ajj of the lower-lying 800 excited states are depicted in Fig. 2 by dots on the {A£}-{A£} plane, where A^ and A(J are normalized by A0- In this figure, (a)-(d) correspond to the excited states of the doped e-p states discussed in Figs. l(a)-(d), respectively. In each diagram, the arrow indicates the lowest excited state. When the electron or the hole is distributed within local lattice distortions, A£ or A£ becomes smaller than AoIt can be seen from Fig. 2(a) that when p=10% the distribution lengths of the electrons and the holes of the excited states appear in the region of 0.3A0
339 in the excited states become to be distributed in the vicinity of A*~0.95A0 and Ajj~0.95A0. Especially, in the case of (c), since Aj~A0 and Aj~0.8A 0 , the electron in the lowest excited state is distributed over the whole region of the crystal, while the hole has a localized nature. Therefore, in the lowest excited state the electron and the hole are expected to be separated between the delocalized and the localized states, respectively. This means that the exciton created by the relatively high-energy photon relaxes down to the lowest-energy charge-separated state. As a consequence of the charge separation followed by the energy relaxation of exciton, the hole is transferred from the delocalized state to the domainlike localized one. Through this process, the number of holes increases in the localized state, and then the localized domains grow up. When p=40%, the distribution lengths of almost all the excited states are A* ~A 0 and A£~AO- This indicates that both the electrons and the holes are distributed uniformly without being trapped on any local lattice distortions.
1
^= J,
B
(a) p=10%
(b) p=26%
£2tttti& lowest . .."•. excited " V state .*-" • .
•^
.
(c) p=26%
,
(d) p=40%
,
lowest excited state
lowest excited state
lowest excited state
' S'.i-
uw y
4
u'„/V
Fig. 2. A* and AJJ of the lower-lying 800 excited states. \„ and Ajj are normalized by Ao- (a)-(d) correspond to the excited states of the e-p states discussed in Figs. l(a)-(d). The coordinate of each dot indicates A^ and An of the excited state. S/T = 2, U/T = 1 and V/T = 0.1. Finally, we summarize the effects of the photoexcitation on the hole-induced multistable structures as follows. When the exciton is photogenerated in the doped e-p states, the charge separation is induced during the energy relaxation of exciton. In the charge-separated state, the electron is delocalized and the hole is localized. Therefore, the high-energy delocalized hole is expected to relax down to the low-energy domainlike localized one. If this process repeatedly occurs by the successive photoexcitation, the holes are expected to gather at the localized domains, and then the domains grow up. As a result of this process, the localized domain-structures become dominant in the doped system, which decreases the multistability of the doped e-p states. Therefore, it is concluded that the photoexcitation reduces the structural fluctuation in the doped states. References 1. 2. 3. 4. 5.
W. P. Su and X. Y. Chen, Phys. Rev. B38, 8879 (1988). G. Levine, and W. P. Su, Phys. Rev. B42, 4143 (1990). Z. G. Yu, J. T. Gammel, and A. R. Bishop, Phys. Rev. B57, R3241 (1998). L. F. Mattheiss, E. M. Gyorgy, and D. W. Johnson Jr., Phys. Rev. B37, 3745 (1988). R. J. Cava, B. Batlogg, J. J. Krajewski, R. Farrow, L. W. Rupp Jr., A. E. White, K. Short, W. F. Peck, and T. Kometani, Nature 332, 814 (1988). 6. D. G. Hinks, B. Dabrowski, J. D. Jorgensen, A. W. Mitichell, D. R. Richards, S. Pei, and D. Shi, Nature 333, 836 (1988).
Optical responses o f one-dimensional e x c i t o n s y s t e m i n correlated random potentials
Kenichi Noba and Yosuke Kayanuma College of Engineering, Osaka Prefecture University, 1-1 Gakuen-cho, Sakai, Osaka 599-8531, JAPAN Kouichiro Nojima Flash Memory Division, Fujitsu, 4-1-4 Kamikodanaka, Nakahara-ku, Kawasaki 210-8588, JAPAN
Urbach tails at absorption edge and photon echo signals are theoretically investigated for one-dimensional exciton systems which have correlated random potentials. As two limits, these correlated random potentials include inhomogeneous distribution of energy levels and random distribution of site-energies for excitons. It is shown that spectral profile of the optical responses reflects the continuous change of the correlated potentials between the two limits. 1. Introduction Photon echo signals are observed due to the existence of inhomogeneous energy distribution caused by the fluctuation of local environment. On the other hand, the Urbach tail, which is the exponential tail at the absorption edge, is caused by random distribution of exciton siteenergies. 1,2 A question is how these two phenomena can coexist in one system. J-aggregates which consist of several molecules in solvent are usually considered as one-dimensional Frenkel exciton systems. In such systems, there exist both the inhomogeneous broadening of energy levels and the site-energy randomness; the former is the inhomogeneous energy distribution among each of aggregates, while the latter means the randomness of site-energies in one aggregate. Although both of them are attributed to the same local fluctuation, they can be characterized by the correlation length of randomness for exciton site-energies. Namely, long and short correlation length correspond to inhomogeneous broadening and site-randomness conditions, respectively. In order to analyze the effect of the correlation of random potentials on optical responses, we calculated the Urbach tails and photon echo signals of one-dimensional exciton systems by the model that bridges the two limit situations. The effect of correlated randomness has been studied from a different point of view. 3 ' 4 ' 5 The correlated random variables, which are generated numerically from Gaussian random variables, are adopted as the site-energies for an exciton which travels in one aggregate. By varying three parameters, correlation length of disorder, the width of Gaussian distribution and the number of molecules in one aggregate, we can understand how the characteristics of optical responses change from the inhomogeneous broadening limit to the site randomness limit. 2. Correlated random variables One-dimensional exciton systems in inhomogeneous environments can be described by a tight-binding model. The Hamiltonian is written by
ff = EAi|i>oi-*E(l*>0-| + b-)
(i)
where Aj is the site-energy at j'-th site, t is a transfer between nearest-neighbor sites, and N is
340
341 the number of sites in one aggregate. In the present study, t is assumed to be a constant, and Aj is a Gaussian random variable specified by the correlation function (AjAj) = D2 exp(—*ya\i—j\), where 7 is the inverse of the correlation length, a is the lattice constant and D is the width of distribution of random variables. Hereafter we adopt the units t = a = 1. The correlated random variables Aj are generated numerically as follows. We choose an ensemble of non-correlated random variables {<£,} which has a Gaussian distribution with the width D and transform them into correlated ones by a matrix C:
A2
= C
\AJV7
92
(2)
\QNJ
In order to obtain the matrix C, let us consider the matrix Atj
= D 2 e x p ( - 7 | i - j \ ) . By a qn
unitary transformation, this matrix A can be transformed into the diagonal matrix UAU positive definite diagonal elements Aj (j = 1 • • • N). We define a matrix B as 0
(V*~i
sfc
B
with
\ (3)
\Aw
V 0 Then we can obtain the matrix C as C =
UTB.
(4)
3. Optical responses The absorption spectra and the intensity of photon echo signals are numerically calculated for the Hamiltonian described above. In the calculation of absorption spectra from the ground state \g) and the photon echo signals, we assume a transition operator p, = -4= ^ - (\g) (J \ + \j){g\) which represents the coupling with a radiation field within the long wave-length approximation. Absorption spectra are obtained as the average of the transition probability \n„^ = |(n|^i|g)| 2 , where \n) is an eigenstate of the Hamiltonian, over a large number of configurations of random potentials. In the calculations presented here, the dissipation effects are ignored. 3 . 1 . Urbach
tail
Urbach tails, which are observed in many kinds of insulators, originate from the local fluctuation of the site-energies caused by thermal effects2 or by the static randomness. It is expected that the ideal condition for the appearance of the Urbach tail is that the system has a noncorrelated Gaussian randomness for exciton site-energies and a large size. In Fig.l, low energy tails of absorption spectra are shown for several correlation length. The direct transition is assumed in the calculation of absorption spectra. As can be seen from the figures, the long range correlation is unfavorable to the appearance of the Urbach tail. Although in the weak correlation limit(7 —» 00), the spectra have exponential tails, they become Gaussian curves in the limit of strong correlation^ —» 0). In the strong correlation limit, the site-energies are almost the same in one aggregate, so that the major components of absorption spectra are assigned as due to the transition to the lowest levels which have a Gaussian distribution of energies. The N dependence of the spectra are shown in Fig. 2 for a weak correlation case. The results show that Gaussian spectra appear at the absorption edge in small systems even if the
342
•)t=0.01 o D=0.05 . D=0.10 • D D=0.I5 • D=0.20
-^ J&&
' D=0.25
1
J y f
V
: v. •
°
,','fm-
;
/
aa
-•
7=1.0 o • o • <•
\
J&
D=0.05 D=0.10 D=0.15 D=0.20 D=0.25
••Sk
^7^^. ^S / *#?/° fi
W: ^ • : .
/
e- H
„ <,% «
d
>
J t ';• * ° » • • *> t. J •
°
-1.5
*s s s 8
s
-1.5
• • o • •
D.0.05 D=0.10 D=0.15 D=0.20 D=0.25
-
-1
-0.5
g
-0.5
J0$j7^%^ sfv " ° v^s
/Hi-
N
' t s • &. ' 1 '
. * » '
5
•
•1
•ytlO.O
-1.5
-1
Energy
-0.5
Energy
Fig. 1. Low energy tails of absorption spectra for 7 = 0 . 0 1 , 0 . 1 , 1 . 0 , 1 0 . 0 in 100-sites systems.
1
^§ r*
ll
-
3-sites ° • o • 0
005 D=0.10 D=0.15 D=0.20 D=0.25
iS Abso
^ ^ B I L ^?P/» ^ jffSl" l\ / ! / / / 0 X / g / o
J e
£ 0.1
*
D=
• •
15-sites •> D = 0 . 0 5
• r>=o.io
° D=0.15 • D=0.20 <• D=0.25
1 *
4
<*
A
m 17* K . v«. /^ ?1
r/ 1 r n ": / j
•••
—. »
/ • '
7: •'
*,]
"
'% r *>•
Energy
•
, ° Energy
Fig. 2. Low energy tails of absorption spectra for 3- and 15-sites systems when
7 = 10.0.
correlation of site-energies is weak. Also, it is shown that the critical size of the system which is required to form exponential absorption edge is roughly 15-sites for the weak correlation limit(7 = 10.0). Urbach tails appear due to the cooperation of the Gaussian randomness of site-energies and the giant oscillator strength due to the spatial extension of exciton wave functions. If the exciton is confined in a small aggregate, the absorption spectra just reflect the Gaussian distribution of energy-levels of all aggregates. 3.2. Photon
echo
Usually, photon echo signals are measured to determine the relaxation time causing homogeneous broadening in absorption spectra. In the present study, however, we focus our attention to the effect of correlation of random potentials on the intensity of photon echo signals in systems without dissipation. For simplicity, we consider the laser pulses used in photon echo measurement as 6 functions of time. In this case, the intensity of photon echo signals at time
343 -Y=0.01 -•y=0.1 00
— y = IO.O 5-site i
6 t>»
0.6
d
(0
c
d)
«n O
« ° Q. co CD
d
CM
^T^^^-^^
\ \ ^^^^ \ \ ^^^^ \ \ ^"\^^ i
\
V
"•-.
\ \N > .
' -...
-
d i -
0.4
D
0.6
"r~"""—"-'
Fig. 3. D dependence of photon echo intensity at the time 2 T for several 7's in 5- and 15-sites systems.
t is obtained as
W) = <££KlV 2 | 2 e- E - T+iE - (t - r) >
(5)
where n i , n 2 are indices of levels with energies Em, En2 in one aggregate, |/i„J 2 and \fin2\2 a r e the transition probability, and T is the time interval between the first and the second pulses. When the intensity of photon echo signal is observed at time t = 2T, where the intensity of the signal is around its maximum value, it shows a quantum beat as a function of T because of the interference effect between multi-levels in one aggregate. If T is large enough, the beat vanishes because the interference is smeared out by the randomness of energy levels. In Fig. 3, the intensity of photon echo signals after the beat disappeared are plotted as a function of D. The intensity is normalized as the sum of the transition probability is unity in one aggregate. As seen from the figures, when D is large, the intensity of echo signals is suppressed. Since the selection rule is violated by randomness, the number of levels which contribute to the optical transition increases. Eq. (5) shows that the increase of such levels results in the decrease of the intensity of echo signals. The 7 dependence shows that weak correlation leads to weak intensity of echo signals in small systems(5-sites in Fig.3). This is due to the same reason as that for the D dependence. The conditions for the appearance of Urbach tails and that of the photon echo are therefore contrary with respect to 7, but not completely exclusive. In larger systems(15-sites in Fig. 3), the situation changes a little. When D is large enough, 7 dependence shows the same tendency as that in small systems. However, when D is very small, the intensity for the case 7 = 10.0 is larger than those for 7 = 1.0 and 0.1. At present, the reason for this anomalous 7 dependence at small D is not clear. This may be related to the hidden structure of wave function 6,7 which appears in the small D region. Further investigation will be necessary from the viewpoint of the localization of wave functions of excitons in the system with weak random potentials. 1. 2. 3. 4. 5. 6. 7.
H. Sumi and Y. Toyozawa, J. Phys. Soc. Jpn 31 342 (1971). M. Schreiber and Y. Toyozawa, J. Phys. Soc. Jpn 51 1544 (1982). J. Knoester, J. Chem. Phys. 99 8466 (1993). J. R. Durrant, J. Knoester and D. A. Wiersma, Chem. Phys. Lett. 222 450 (1994). E. W. Knapp, Chem. Phys. 85 73 (1984). V. A. Malyshev, J. Lumin. 55 225 (1993). V. Malyshev and P. Moreno, Phys. Rev. B 51 14587 (1995).
High D e n s i t y Exciton D y n a m i c s of CuBr Nanocrystals E m b e d d e d in P M M A
M. Oda, M.Y. Shen, and T. Goto Department of Physics, Graduate School of Science, Tohoku University, Sendai 980-8578, Japan When CuBr nanocrystals (NCs) embedded in poly methyl methacrylate are strongly excited, there appears a new luminescence band at the low energy side of exciton luminescence peak. The luminescence band is associated with biexcitons in the CuBr NCs. As the excitation intensity increases, the biexciton luminescence band shows obvious broadening, while the exciton band does not. Interaction among more than three excitons may cause this broadening effect. Optical gain has also been found by pump-probe measurement around the biexciton luminescence band at 77K. The decay time of the optical gain 15ps coincides with that of the biexciton luminescence band, which means that the lifetime of the biexciton is 15ps. Photogenerated carriers in highly excited nanocrystals (NCs) are strongly interacted with each other. As a result of the interaction, large optical nonlinearity can be observed. 1 ' 2 Also, in the case of CuBr NCs, the optical nonlinearity has been studied extensively because of its fundamental interest and application background. 3 The dynamics of exciton and biexciton, however, has not been studied in details. 4 This results from poor quality of CuBr NCs. In present work, we have succeeded in growing high quality CuBr NCs in poly methyl methacrylate (PMMA) which have high luminescence efficiency and no appreciable luminescence due to impurity at 77K. The luminescence spectra at different excitation intensities, temporal behaviors of the luminescence intensity and time-resolved absorption spectra have been investigated in these samples. Dynamics of exciton-biexciton system is discussed. The CuBr NCs embedded in PMMA were prepared by the modification of Yao's technique. 5 The CuBr NCs were grown by heat treatment followed by the dry process of PMMA film containing CuBr molecules. In Yao's technique, the PMMA film is dried in a vacuum chamber at pressure of about 130 Pa before the heat treatment. In the present work, the PMMA film was dried in a nitrogen gas-flow chamber at pressure of about 1300 Pa for five days. The efficiency of the photoluminescence increases one order using this modification technique. The weight concentration of the CuBr NCs in PMMA was about 0.18 %, and the thickness of the PMMA film was about 0.2 mm. The excitation light for the measurement of the luminescence spectra at different excitation intensities had a pulse width of 6 ns, a repetition rate of 10 Hz, and a wavelength of 355 nm. On the other hand, the excitation light for the temporal measurement of the luminescence had a pulse width of 470 fs, a repetition rate of 1 kHz, and a wavelength of 307 nm. The time profile of the luminescence was measured with an up-conversion method. The excitation light for the time-resolved absorption spectra had a pulse width of 350 fs, a repetition rate of 1 kHz, and a wavelength of 395.6 nm. The difference in the optical density between with and without pump light was measured as a function of the delay time of the probe light. For all the measurements, the sample was immersed in liquid nitrogen. Figure 1 shows the luminescence spectra of CuBr NCs for different excitation intensities indicated on the right side of the spectra. An average radius of the NC is about 6.2 nm which is estimated from a photograph taken by a transmission electron microscope. The luminescence spectra consist of two intense bands named X and M. Only the higher energy band (X band) can be observed in very weak excitation intensity (not shown in the figure). The X band is associated with radiative annihilation of the Zi, 2 exciton. 6 The pump intensity I p dependence of X and M bands shows that the X and M luminescence intensities are proportional to I p 0 ' 93 andTp1-7, respectively (not shown in the figure), below 0.05 m J / c m 2 excitation intensity, which is almost the same as that in CuBr NCs embedded in glass matrix at low excitation. 4 By the analogy with the NCs in glass, the M band is assigned as radiative annihilation of the biexciton leaving an exciton. The biexciton binding energy of CuBr NCs with average radius 5.2 nm 344
345
Exc. Intensity (mJ/cm )
3 3.2 Photon Energy (eV)
3.4
Fig. 1. Excitation intensity dependence of photoluminescence spectra of CuBr NCs in PMMA. Inset: excitation intensity dependence of FWHM of the X (open squares) and the M (closed circles) bands.
embedded in glass is 24 meV4 that is estimated from the energy difference between the X and M band peaks. The energy difference between the two peaks in this work is 30 meV. This value is larger than 24 meV, which may be originated from the difference in dielectric constant of matrix, because the biexciton binding energy is affected by dielectric confinement effect.7 A full width at half maximum (FWHM) of the X band (open squares) and M band (closed circles) as a function of the excitation intensity is shown in an inset of Fig. 1. The broadening of the M band in the higher intensity excitation range above 0.4 mJ/cm 2 is obviously seen, while the broadening of the X band in the lower intensity excitation range below 0.4 mJ/cm 2 is hardly seen. Under the assumption that the exciton lifetime is 100 ps,6 and the absorption coefficient of nanocryatal materials is the same as that of the bulk crystal, about two excitons can be generated in each NCs, in average, in the excitation intensity of 0.5 mJ/cm 2 . When more than three electron-hole pairs are generated in one NC by the strong 355 nm light, more than three thermalized excitons may interact with each other, and emit a photon with energy which is different from the radiative energy of only one biexciton leaving an excicton. Probably, this makes the M band broader. On the other hand, if the exciton emits a photon finally by a cascade process,8 no broadening of the X band is expected.
3
a o c
8 D C
'E
3
20
40
Time (ps)
Fig. 2. The temporal behavior of the biexciton luminescence. The solid curve represents a fitting curve when the intensity decays exponentially with the time width t = 15 ps. Inset: the enlargement of the rise part.
346 Figure 2 shows the temporal behavior of the M band luminescence. The average radius of the NC and the excitation intensity on the sample surface are 6.2 nm and about 20 fjJ/cm2, respectively. In order to avoid the overlap with the X band, the M band luminescence was detected at the low energy side of M band peak. A solid line represents a fitting curve to experimental data on the assumption that the luminescence intensity decays single exponentilally. The adjusted value of the decay time is 15 ps. The rise part of the temporal behavior is enlarged on the inset of Fig 2. The solid line represents the laser light pulse. The rise time from the onset of the biexciton luminescence is evaluated to be about 3 ps. 2.9
2.95
3
3.05
0.5 Q
6 _l
I
I
j
l_
i
i
i
L_i
•
i
i
I
i
I_I
L-
1.5 -
o < 0.5 -0.5 ps
a 3
0
i
(c)
i
i
I
i
M
-J
S E
2.9
2.95
1 L_J
3
1
L.
3.05
Photon Energy (eV)
3
Fig. 3. (a) Broken and solid curves represent the absorption 0.5 ps before and 9.3 ps after the pump light pulse, respectively, (b) Absorption change at different delay times: -0.5 ps, 0.5 ps, and 9.3 ps. (c) Time integrated luminescence spectrum.
Figure 3(a) shows the absorption spectra around the Zi,2 exciton band before and after the pump light pulse. The average radius of the CuBr NCs and the excitation intensity on the sample surface are 6.9 nm and about 500 /jJ/cm2, respectively. The broken and solid lines represent the absorption spectra measured just before (-0.5 ps) and after (9.3 ps) the pump light pulse, respectively. We can see a broadening and a blue shift of the Zi,2 exciton absorption band due to the pump light pulse irradiation, and it may be attributed to exciton-exciton interactions in NCs by analogy with exciton dynamics in CuCl NCs1. The curves in Fig. 3(b) are the difference in the optical density (O.D.) between before and after the pump pulse at various delay times indicated on the left side of each curves. Figure 3(c) shows the time-integrated luminescence spectrum. Optical loss was observed around the M band just after the excitation, as seen in the spectrum at the delay time of 0.5 ps, and turns into the optical gain at the longer delay time 9.5 ps, which is associated with the dynamics of biexcitons in NCs. Figure 4 shows the temporal change of the optical gain calculated by the integration of the spectra from 2.9435 eV to 2.9561 eV. The broken line represents a single exponential decay curve with the time constant of 15 ps which is the same as the decay time of the M band. This agreement indicates that the optical gain is attributed to the transition from the biexciton to the exciton state. The rise part of the temporal change is enlarged in the inset of Fig.4. The
347 0.1 i - i — • — • — • — I — • — i — • _
I
'
'
'
I
LI • I • I • I • I 'J
Fig. 4. Temporal change of the optical gain. The values are calculated by integration with the integration range from 2.9435 eV to 2.9561 eV. The broken line represents a single exponential decay curve with the time constant of 15 ps. Inset: the enlargement of the rise part.
solid line represents the laser light pulse. Before the beginning of the optical gain, the optical loss appears as is obviously seen in the middle curve of Fig 3. (b). The loss may be attributed to the induced absorption from the exciton to the biexciton state. If the photogenerated electronhole pairs relax to the biexciton state through the exciton state after a few picoseconds, the number of NCs having biexcitons becomes larger than that of NCs having one exciton. As a result, the gain is observed a few pico seconds later after the pump light pulse. This time is comparable to the relaxation time of the photogenerated electron-hole pair to the biexciton evaluated from the rise time of M band luminescence intensity as seen in the inset of Fig. 2. In summery, high quality CuBr NCs were grown in PMMA, and it made the investigation of their exciton dynamics possible. The broadening of the M band occurs under the higher intensity excitation, while the broadening of the exciton luminescence band under the lower intensity excitation does not. This M band broadening may be caused by interaction among more than three excitons. The optical gain is seen in the low energy side of the Zi, 2 absorption band. The decay time of the optical gain coincides with that of the M band luminescence. The agreement suggests that gain is attributed to the transition from the biexciton to the exciton state. References 1. 2. 3. 4. 5. 6. 7. 8.
K. Edamausu, S. Iwai, T. Itoh, S. Yano, and T. Goto, Phys. Rev. B51, 11205 (1995). E. Hanamura, Phys. Rev. B37, 1273 (1987). Y. Li, M. Takata, and A. Nakamura, Phys. Rev. B57, 9193 (1998). U. Woggon, 0 . Wind, W. Langbein, O. Gogolin, and C. Klingshirn, J. Lumin. 59, 135 (1994). H. Yao and T. Hayashi, Chem. Phys. Lett. 197, 21 (1992). M. Oda, M. Y. Shen, M. Saito, and T. Goto, J. Lumin. 87-89, 469 (2000). T. Takagahara, Phys. Rev. B39, 10206 (1989). S. Yano, A. Yamamoto, T. Goto, and A. Kasuya, Phys. Rev. B57, 7203 (1998).
B O S O N I Z A T I O N OF T W O - F E R M I O N C O M P O S I T E S WITH A N ARBITRARY INTERNAL MOTION: APPLICATION TO CORRELATED Is EXCITON SYSTEMS
TETSUO OGAWA* Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan SATORU OKUMURA Department of Physics, Tohoku University, Aoba-ku, Sendai 980-8578, Japan We propose an exact bosonization scheme for two two-fermion composites with identical internal structures, that is, a mapping of the two-exciton (four-fermion) subspace to a twoboson subspace. We obtain analytical, exact expressions of the boson-boson interactions and the boson-photon ones taking into full account that the commutation relation of the composite bosons deviates from the ideal-boson commutation due to internal motions of the composite. We can distinguish the "composite-particle effects" from the Coulomb interactions among the fermions in the interactions. With this method, origins of optical nonlinearity in a system with two Is excitons are studied in terms of the mutual excitonic correlations and exciton-photon interactions. 1. Introduction Bosonization is one of effective techniques for describing low-energy excited states in condensed matters and nuclei. 1 Thus far, many bosonization schemes for composite particles neglect or approximate their internal structures to treat as a point (structureless) bosons. In this paper, we propose an exact bosonization procedure for two-fermion composites with identical internal motions taking into account the quasiboson natures of such composites. Our method is valid for arbitrary separation of two fermions. With this bosonization, the interactions between two composites are evaluated as a function of the center-of-mass distance in the case of infinite hole-mass even when the separation of the composites is small comparable to the a relative distance of two constituents. Our bosonization is suitable to correlated exciton systems. 2 Recently, origins of the optical nonlinearity of semiconductors near the Is exciton resonance are studied experimentally. 3 The exciton unharmonicity and the exciton-exciton coupling are thought to be of importance. Our bosonization is employed to represent such systems by two kinds of bosons: photons and elementary excitations (Is excitons) in the materials. An exciton, which is composed of a conduction electron and a valence hole, does not always obey the ordinary bosonic commutation relations. 4 Such a deviation from the ideal-boson commutation relations results from the "composite-particle effect." In this paper, we investigate how this effect and the fermion-fermion Coulomb interactions play respective roles in the boson-boson and boson-photon interactions. 2. Exact Bosonization for T w o I s Excitons We consider the III-V semiconductor quantum wells with two electrons in a conduction band and two holes in a valence band, whose z-components of the total angular momenta are /J, = ±^ and v = ± | , respectively. These particles are assumed to form two Is excitons. Photons have polarizations a = ± 1 . The Coulomb interaction between electrons, holes, or an electron and a hole is V(q) = 27re 2 /(L 2 |q|) in two dimensions, where q is the two-dimensional wevevector and L is the system size. In this paper, we confine ourselves to the case of heavy-hole limit for simplification. "Also at Department of Physics, Tohoku University, Aoba-ku, Sendai 980-8578, Japan
348
349 We shall define an Is exciton operator 6!I1/R, where R is position of the center-of-mass. Here we choose an electron-hole Is relative wavefunction <^>(r) = (2/wa2)1'2 exp( — |r|/a) with the effective Bohr radius a in two dimensions. Two Is exciton states, b^^-^b •R.\Q), do not form an orthogonal set because of [ S ^ R , hL^,R,] 4- 6£,5",S2(R — R'), where <5£, is the Kronecker's delta. Simultaneously, the inner product between these two-exciton states has a deviation from Kronecker's delta. Only when | R — R'| is much larger than a, an effective separation of two fermions, the excitons seem to become structureless resulting in the orthogonality recovered, [W.^R']^^^,52(R-R'). We find that orthogonalized two-exciton states can be constructed as l/^Ri./ij-i/j-Rj)
=
blil,iRbl.u.Ri\0)Fd{Ri-Rj) +(-s)^jR,^RjO}FI(Ri-RJ),
(1)
where |0) is the vacuum of the fermion subspace and s is the statistics factor: s = — 1 for two constituents of a composite boson are fermions (s = 1 for bosons), and / ( R ) ] " I / 2 + [i + / ( f t ) ] " 1 7 2 } ,
(2)
F , ( R ) = \ {[1 - / ( R ) ] ^ 2 - [1 + / ( R ) ] - 1 / 2 } .
(3)
F„(R) = \{[i-
Here / ( R ) = \ (|R|/a) [/f2(|R|/ffl)] and K2 is the second-order modified Bessel function. This function / describes the "composite-particle effect," which is an origin of nonorthogonahty of two-exciton states in a region of |R| < a; we find / ( R ) ~ 1 for |R| -C a and / ( R ) ~ | R | 3 e x p ( - 2 | R | / a ) f o r |R| » a. Using the above orthogonalized two-exciton states, we can map exactly the original fermion subspace consisting of two electrons and two holes to the ideal-boson space: |0) ^ |0), & L * H J ° > ^ ^ , U R J 0 ) ' a n d \tHViRi,ft}"]**-]) ^ &IHl,.K.Bl.l,.K.\0) with an ideal boson operator B / U , R and the vacuum of the ideal-boson subspace |0). 3. Interactions in a Bosonized F o r m The Hamiltonian describing the two Is excitons and photons is given in the bosonized form with the above mapping. The interaction part is composed of four terms: two interactions between ideal bosons called the boson-boson direct {Ij) and exchange (Ix) interactions, and two nonlinear interactions between ideal bosons and a photon called the boson-photon direct (Gd) and exchange (G x ) interactions. In the real-space representation, we can obtain the following exact expression of the bosonized interactions: +\
E
//d2Rd2R'/d(R-R05U^v
fj,i/fx'u'
- \ +
-s
£
//d2Rd2R'/x(R-R')BivR^R,B,VR-^R / / d 2 Rd 2 R' <5£+" Gd(R
£
£
jjd2Rd2R'Sp"
- R ' J B ^ R B J V R . ^ V R ' ^ R + h.c.
G X (R - R ' ^ V R ^ R - ^ V ' R ' ^ R
+
ft.c-i
where J d (R) =
F1(R)«(R)-F2(R)v(R),
(4)
350
Fig. 1. The strength of the boson-boson direct Id and exchange Ix interactions as a function of the center-of-mass separation | R | / a .
4 ( R ) = F 2 ( R ) u ( R ) - F!(R)^(R),
(5)
G„(R) = g [F„(R) - 1 - F x ( R ) < z ( R ) / V Z V ( 0 ) ]
(6)
GX(R)
Fd(R)q(R)/^^(0)],
(7)
^{[l-ZfRf+ll+ZfR)]-1},
(8)
F2(R) = ^ I l i - Z C R ^ - t i + ZCR)]-1}.
(9)
= g[Fx(R)
-
with the dipole coupling g and Fx(R) =
Here u(R) shows a power decay as a function of R (u(R) ~ |R|~ 5 ) resulting from tfte Coulomb interaction between two quadrupoles, which is a characteristic in two dimensions. On the other hand, both v(R) and q(R) = ^y/T^ip*(0)(\R\/a)2K2(\R\/a) exp(—|R|/a) exhibit an exponential decay as a function of R coming from the composite-particle effect. Derivation and exact expressions of these elements are given in literature. 5 Figure 1 shows the strength of the boson-boson direct Id and exchange Ix interactions as a function of the center-of-mass separation | R | / a . Two bosons with different (identical) "spin" configurations feel the interaction Id (Id + Ix). Both are monotonically decreasing functions of |R| and repulsive anywhere. Despite of these repulsions, we show that both the bound and unbound biexciton states are realized. 5 Figure 2 shows the strength of the boson-photon direct Gd and exchange Gx interactions as a function of | R | / a . Both are positive in a whole region of | R | / o , which means that the exciton-photon coupling is enhanced when another exciton exists at an origin. 4. Concluding Remarks Our bosonization theory of excitons sheds light on the question what the exciton-exciton and exciton-photon interactions in many exciton systems are. So-called "phase-space filling effects" should also be reexamined from a microscopic viewpoint. Extension of our bosonization scheme to more than two exciton systems or to coexistence with 2s and 2p excitons is an important future problem. Acknowledgements This work is partly supported by a Grant-in-Aid from the Ministry of Education, Science, Sports and Culture of Japan and by CREST and PRESTO of Japan Science and Technology Corporation (JST).
351 0.5 0.4
o 0.3
1 m
E 0.2 0.1 0 0
1
2
3 4 5 R/a Fig. 2. The strength of the boson-photon direct Gd and exchange Gx interactions as a function of the center-of-mass separation | R . | / a .
References 1. 2. 3. 4. 5.
T. Kishimoto and T. Tamura, Phys. Rev. C27, 341 (1983). E. Hanamura, J. Phys. Soc. Jpn. 37, 1545 (1974). M. Kuwata-Gonokami, et al., Phys. Rev. Lett. 79, 1341 (1997). S. Okumura and T. Ogawa, J. Lumin. 87-89, 238 (2000). S. Okumura and T. Ogawa, preprint.
TIME-RESOLVED PHOTOLUMINESCENCE OF EXCITONS IN Hgl 2 N. OHNO and X. M. WEN 1 Academic Frontier Promotion Center, Osaka Electro-Communication University, Neyagawa, Osaka 572-8530, Japan
The time-resolved photoluminescence (TRPL) of red Hgl2 single crystal has been measured to determine the carrier lifetimes and to reveal the energy relaxation of excitons. Sharp near-bandgap luminescence lines due to free and bound excitons are observed at 530 nm, and a broad luminescence band appears at 630 nm at low temperatures. TRPL experiments of the near-bandgap luminescence have revealed that the luminescence comprise fast (30 to 200 ps) and slow (100 to 400 ps) decay components, showing several relaxation processes in free and bound exciton annihilation. TRPL of the broad band at 630 nm has shown that the luminescence is ascribed to the radiative recombination of donor-acceptor (DA) pairs.
1. Introduction Mercuric iodide HgL; in the red tetragonal modification 1 with a space group An,15 is a direct bandgap semiconductor. Its color is red at room temperature and turns yellow at high temperatures because of the tetragonal-orthorhombic structural phase transition at 1 2 6 t . Red HgL; crystal is a high potential material to fabricate X-ray and nuclear radiation detectors and photocell because of relatively high atomic number of the constituent elements, large bandgap at room temperature and good photosensitivity. The first exciton transition of red tetragonal Hgl 2 occurs at 530.1 nm (2.339 eV) at 4.2 K.2 The photoluminescence (PL) of red HgL: has been studied extensively by several groups.3"8 It has been found that three primary luminescence bands are observed in PL spectra at low temperature. Several sharp lines appearing in the band-edge region have been ascribed to the annihilation of free and bound excitons. Exciton luminescence spectra were also examined above 100 K by Goto et el. They have shown a good agreement of the low-energy tail of the bandgap luminescence with the Urbach tail of the fundamental absorption. Merz et a/.' 011 studied sublimation and doping experiments on PL at low temperature, and discussed the origin of the luminescence bands due to the stoichiometry in the crystal. However, very little control over the crystal quality and impurity contamination has far been achieved. In the present study, the time-resolved photoluminescence (TRPL) of Hgl 2 single crystal has been investigated at temperature range of 10 to 100 K to determine the carrier lifetimes and to reveal the energy relaxation of excitons. Sharp near-bandgap luminescence lines due to free and bound excitons are observed at 530 nm, and a broad luminescence band appears at 630 nm at low temperatures. TRPL experiments of the near-bandgap luminescence have revealed that they comprise fast and slow decay components, showing several relaxation processes in free and bound exciton annihilation. TRPL of the broad band at 630 nm has shown clearly that the luminescence is ascribed to the radiative recombination of donor-acceptor (DA) pairs. The energy relaxation of excitons is discussed on the basis of the results of the TRPL experiments.
Permanent address: Department of Physics, Yunnan University, Kunming, Yunnan 650091, P.R. China
352
353 2. Experimental Technique Red Hgh single crystals were grown from the saturated acetone solution of Hgk at room temperature.2 It needed several days to grow the single crystals in several mm size. As grown surface of the crystals had a crystallographic plane perpendicular to the c-axis. The TRPL measurements were performed using a streak camera in conjunction with a 25-cm spectrometer employing a 300-lines/mm grating. A laser pulse line with 400 nm, which was the double frequency of a mode-locked A^C^Ti laser pumped by an LD laser, was used as the excitation source. The repetition rate of the laser pulses was 2 MHz or 18 kHz with a pulse width of 1.5 ps. The time resolution of the system was -30 ps. The excitation laser energy density was 3 uJ/cm2 per pulse. The sample was mounted to the cold finger of a helium-cycled cryostat, where the temperature could be changed from 10 to 300 K.
3. Results and Discussion Figure 1 shows the TRPL spectra near the bandgap region of red Hgl2 at different time delays from 0 to 900 ps at 10 K. The arrow indicates the reflection peak position of the first exciton band for EXc at 10 K. It is found that the bandgap luminescence almost disappears in time range of several hundreds ps. The structure at 531.0 nm, which is clearly seen at 0 ps and disappears at 300-ps delay, is just located at the peak position of the first exciton band. Therefore, this structure is definitely due to radiative annihilation of free exciton-polaritons. Srong peaks are observed at 532.2 and 533.2 nm, just below the bandgap energy. The bandgap luminescence has been ascribed to radiative recombination of bound excitons localized at some impurities or defects.3"5 As can be seen in the TRPL sectra, the bound-exciton luminescence decays slowly as compared with the free exciton-polariton luminescence. On the long-wavelength side of the bound-exciton lines, shoulderlike structures appear at 532.7, 534.2 and 535.4 nm, which are due to phonon replicas of the free exciton-polariton and bound exciton annihilation.3"5 We can also see a broad band centered at -540 nm, where apparent rise is observed after the pulse excitation. The rise time is found to depend on the spectral wavelength, reaching -100 ps on the long-wavelength side. The temperature dependence of TRPL has been also investigated, which indicates that the bandgap luminescence becomes weak in intensity and almost disappears within 100 ps when the sample was warmed above 50 K. The PL decay curves at various wavelengths near the bandgap region are found to exhibit an
Wavelength (nm) Fig. 1. TRPL spectra near the bandgap region of Hgl2 measured at 10 K.
354 500
Hgl 2 400 nm exc. 10 K
300
slow fast
200
530
535 540 Wavelength (nm)
545
Fig. 2. Dependences of decay times of slow ( • ) and fast ( O ) components on the luminescence wavelength near the bandgap of H g t at 10 K. The solid curve represents the time-integrated PL spectrum.
exponential decay. Except the bound-exciton luminescence region, the decay curves cannot be fitted with a single exponential function, but can be reproduced using two exponential functions. Figure 2 shows the dependences of the decay times of slow and fast components on the luminescence wavelength at 10 K. The solid curve represents the time-integrated PL spectrum. The fast decay component appears in free exciton-polariton and the phonon-replica region: their decay times are 30 -50 ps. In these regions, there also appear the slow decay components, but their intensities are weak compared with that of the fast component. On the other hand, the decays of bound-exciton luminescence are slower than that of the free exciton-polariton luminescence: the decay-time value of the fast component changes up to 220 ps at 532.2 nm, while the decay time of the slow component also increases but the intensity becomes negligibly small. The fitting result reveals obviously that free exciton-polaritons have a short decay time and bound excitons exhibit relatively long lifetimes. The annihilation of free exciton-polaritons is mainly due to non-radiative decay such as trapping into impurities or defects, forming bound excitons. Electron-hole pairs created by pulse 2.5 -i Hgl 2 400 nm exc. 10K
620
640
680
Wavelength (nm) Fig. 3. TRPL spectra of the 630-nm luminescence in Hgl 2 measured at 10 K.
355 excitation do transfer non-radiatively from free exciton-polaritons to bound excitons within a short time. Therefore, the observed decay time of the free exciton-polariton does not indicate the radiative lifetime, but is related with the total trapping rate into bound-exciton states. Bound excitons will also be converted to free exciton-polaritons, but the probability is expected to be quite small at low temperature since their binding energies are estimated as 4-5 meV. The decay time of 220 ps in the bound-exciton luminescence is thus supposed to be the radiative lifetime of the excitons localized at impurities or defects. In the long wavelength region, a broad PL band was observed around 630 nm. In the timeintegrated PL spectrum, the central wavelength was found to be 630.9 nm and the bandwidth 35.5 nm at 10 K. Figure 3 shows the TRPL spectra of the 630-nm band measured at 10 K. The decay time of the luminescence band is in the order of us, much slower compared with that of the bandgap luminescence. It is clearly seen that the central wavelength moves toward the long-wavelength direction from 624 to 634 nm with developing time from 0 to 20 us. It can be also seen that the decay time of shorter-wavelength region is faster than that of longer-wavelength region. The temporal behaviors of the luminescence intensity at different wavelengths all reveal approximately straight lines in the bi-logarithmic coordinate in the region of t < 20 us investigated. In other word, we can depict the luminescence intensity of the 630-nm band by f" function in this time period. The value of n is larger in shorter-wavelength region, e.g. n = 0.88, 0.62 and 0.56 at 610 nm, 630 nm and 650 nm, respectively. The power-low behavior of the luminescence intensity on time is well known for the tunneling recombination between electrons and holes trapped in impurity centers, that is, donor-acceptor (DA) pairs. It is the first time to obtain the direct evidence of DA-pair luminescence for the 630-nm broad band origin. The temperature dependence of this band is found to indicate the blue shift of the central peak with increasing temperature, showing further evidence for the DA-pair luminescence. Further study is needed to reveal the correlation between the nuclear-detector performance and the degree of the structural perfection in this system. Acknowledgements The authors thank T. Sakai for his assistance in the TRPL experiments. One of the authors (X.M.W.) would like to acknowledge the financial support of Osaka Electro-Communication University Foundation for Promotion of International Exchange on Research and Education. This work was partially supported by the Academic Frontier Promotion Project of the Ministry of Education, Science, Sports and Culture of Japan. References R. W. G. Wyckoff, Crystal Structure, Vol.1, 2nd edition (John Wiley & Sons, New York, 1963). K. Kanzaki and I. Imai, J. Phys. Soc. Jpn. 32, 1003 (1972). B. V. Novikov and M. M. Pimonenko, Sov. Phys. Semicon. 4, 1785 (1971). T. Goto and Y. Nishina, Phys. Rev. B17, 4565 (1978) I. Kh. Akopyan, B. V. Bondarenko, B. A. Kazennov and B. V. Novikov, Sov. Phys. Solid State 29, 238(1987). [6] I. Kh. Akopyan, B. V. Bondarenko, O. N. Volkova, B. V. Novikov and T. A. Pavlova, Phys. Solid State 39, 58(1997) [7] X. J. Bao, T. E. Schlesinger, R. B. James, S. J. Harvey, A. Y. Cheng, V. Gerrish and C. Ortale, Nucl. Instr. and Meth. A317, 194 (1992). [8] B. V. Shul'gin, V. A. Pustovarov, S. I. Gorkunova and E. I. Zinin, Tech. Phys. Lett. 21, 661 (1995) [9] T. Goto, J. Takeda, T. Ishihara and M. Matsuoka, J. Luminesc. 38, 55 (1987). [10] Z. L. Wu, J. L. Merz, L. van den Berg and W. F. Schnepple, J. Luminesc. 24/25, 197 (1981). [II] J. L. Merz, Z. L. Wu, L. van den Berg and W. F. Schnepple, Nucl. Instr. and Meth. 213, 51 (1983). [I] [2] [3] [4] [5]
E N E R G Y - T R A N S F E R P R O C E S S I N R A R E - E A R T H - I O N D O P E D SrTiQ 3
SHINJI OKAMOTO Graduate School of Materials Science, Nara Institute of Science and Technology, Ikorna, Nara 630-0101, Japan SHOSAKU TANAKA Department of Electrical and Electronic Engineering, Faculty of Engineering, Tottori University, Koyama, Tottori 680-8552, Japan HAJIME YAMAMOTO Faculty of Engineering, Tokyo University of Technology, Hachioji, Tokyo 192-0982, Japan
Enhancement of emission intensity of rare-earth-ion doped SrTiOa by Al addition has been investigated. In the case of Pr 3 + and T b 3 + , addition of 23-mol% Al intensifies emission by more than 200 times. In contrast, the addition of 20 mol% Al intensifies emission at most by three times in the case of other rare-earth ions. The temperature dependence of PL spectra shows that the energy transfer from carriers to Pr 3 + or Tb 3 + ions is much more efficient than that to other rare-earth ions in SrTi03. It can be speculated that the energy transfer in SrTi03:Pr 3+ or Tb 3 + occurs from carriers to Pr 3 + or Tb 3 + ion via 4f-5d transitions, which are much higher in oscillator strength than 4f-4f transitions. 1. Introduction A new red phosphor for field emission displays, perovskite-type SrTi03:Pr 3 + was successfully developed 1. The red emission is due to the intra-4f transition in Pr 3 + from 'D2 to 3 H 4 states. It was found that this red emission is intensified by more than 200 times under low-energy electron or UV light excitation by addition of Al(OH) 3 to the starting materials 1,s . The Al addition results in a change in the crystal field of Pr 3 + ions and the improvement of the crystallinity, as observed from the progress of characteristic red emission lines at low temperature and highresolution transmission electron microscope images, respectively 2 . In contrast, similar emission enhancement is not observed for other rare-earth ions except for T b 3 + . One of the origins of the difference among the rare-earth ions is due to the energy-transfer process from photoexcited carriers in SrTiOs to the rare-earth ions. In this work, the energy-transfer process in rare-earth-ion doped SrTiOa has been investigated in conjunction with the emission process. 2. Experimental A stoichiometric mixture of SrC03, Ti02 and rare-earth oxides was further mixed with a varied amount of A1(0H) 3 and fired in air at 1300 t for 2 h. In SrTiOa, rare-earth ions.can substitute for Sr 2 + because the ionic radius of a rare-earth ion almost coincides with that of Sr 2 + , as confirmed in SrTi03:Eu 3 + 3 , and Al 3+ substitutes for T i 4 + 4 . The samples are in powder form of ~ 1 \i m in diameter. For measurements of photoluminescence (PL) spectra, a cw He-Cd laser (325-nm excitation wavelength) was used as an excitation source. PL signal was dispersed by using a 50-cm monochromator and detected by a photomultiplier. A sample was mounted on a cold finger of a closed-cycle He-gas cryostat.
356
357 3. R e s u l t s a n d discussion 3 . 1 . X-ray
diffraction
It was found that the X-ray diffraction (XRD) patterns are hardly changed by Al addition and are independent of rare-earth ions °. The XRD measurements reveal that the samples consist of a single phase of SrTiOs, and only a small amount of Al can be incorporated in SrTi03:Pr 3 + , as reported in Ref. 6. iMost of Al is precipitated as SrAl 2 0 4 S and/or AI2O3 7 on the phosphor surface. 3.2. PL
spectra
Figure 1 shows PL spectra of SrTi03:Tb 3 + samples doped with various molar ratios of Al under the 325-nm laser excitation at room temperature. SrTiC^Tb3"1" shows remarkable emission enhancement similar to SrTi0 3 :Pr 3 + 2. The PL intensity of intra-4f transitions of Pr 3 + and T b 3 + increases with an increase in Al content, and then saturates above 23-mol% Al in our samples. A sample doped with 23-mol% Al shows emission intensity about 200 times higher than Al-free samples. It can be speculated that the number of Al-associated Pr 3 + or T b 3 + centers increases with an increase in Al molar ratio 2 . Complexes formed as a result of charge compensation of Pr 3 + or T b 3 + at Sr 2+ site by Al 3 + substituting for Ti 4 + is the most probable origin of the Al-associated Pr 3 + or T b 3 + centers. In contrast, similar emission enhancement is not observed for most of other rare-earth ions (Ho 3 + , Er 3 + , Nd 3 + , Eu 3 + , Tm 3 + , Yb 3 + , Sm 3+ and D y 3 + ) .
I I a. 0 400
500 600""" WAVELENGTH (nm)
700
Fig. 1. PL spectra of SrTi0 3 :Tb 3+ (Tb 3+ : 2 mol%) with various molar ratios of Al under the 325-nm laser excitation at room temperature: (A) 23, (B) 5, and (C) 0 mol%. 3.3. Correlation
between
emission
enhancement 3+
and if-Sd
transition
energy
3+
One of the common features between Pr and T b is the low energy of their 4f-od transitions. The 4f-5d transitions of Pr 3 + and T b 3 + in an oxide are located at 32,000 cm""1 3 . The energies of the 4f-5d transitions strongly depend on a host material, but the relative energy position among the rare-earth ions is almost independent of the host. Thus, the 4f-5d transitions of Pr 3 + and T b 3 + are at nearly the same energy in SrTi0 3 . On the other hand, the 4f-5d transitions of the other rare-earth ions are higher in energy than those of Pr 3 + and T b 3 + . It should be noticed that the 4f-5d transitions have large oscillator strength. 3.4. Temperature
dependence
of PL
spectra
Figure 2 shows the temperature dependence of PL spectra of the 23-mol% Al-added SrTi0 3 : T b 3 + at low temperatures, where PL spectra have two components: the line emission from T b 3 +
358 ions and the broadband emission from self-trapped excitons in SrTi0 3 centered at 500 nm 9 ' 10 . When temperature is raised above 40 K, the emission from the self-trapped excitons decreases due to thermal decomposition of the self-trapped excitons into free carriers 9 , 1 °, while the emission from T b 3 + increases. Similar inverse relationship is also observed in case of Pr 3 + 2 .
3
to
L___' B
A
C
A.
H Z _l Q_
0
400
L___ \ .
500 600 WAVELENGTH (nm)
700
Fig. 2. PL spectra of SrTi0 3 :Tb 3+ (Tb3+: 2 mol%) with 23 mol% of Al under the 325-nm laser excitation at various temperatures: (A) 20, (B) 60, and (C) 100 K. The inverse relationship suggests the following PL process. At low temperature, a portion of photoexcited carriers contributes to the energy transfer to the rare-earth ions, and the rest of the carriers forms self-trapped excitons. When the temperature is raised above 40 K, a decreasing number of the carriers forms self-trapped excitons, while an increasing number of the carriers contributes to the energy transfer to T b 3 + or Pr 3 + . Thus, this inverse relationship indicates the energy transfer from the carriers to T b 3 + or Pr 3 + ions. In contrast, similar inverse-relationship is not observed in other rare-earth-ion doped SrTi0 3 . Figure 3 shows the temperature dependence of PL spectra of Al-free SrTi0 3 :Ho 3 + at low temperatures. When the temperature is raised, both the emissions from self-trapped excitons and Ho 3 + ions decrease at the same time. These observations imply that SrTi0 3 :Pr 3 + and T b 3 + have much more efficient energytransfer process through the carriers than other rare-earth-ion doped SrTi0 3 . One of the possible origin in such efficient energy-transfer process is 4f-5d transition because oscillator strength of the 4f-5d transition is 1 0 " 3 ~ 1 0 - 2 , and much higher than that of 4f-4f transitions. When added Al reduces point defects around Pr 3 + or T b 3 + due to charge compensation and SrO planar faults 6 , an increasing number of carriers contributes to the energy transfer to the rare-earth ions. Thus, the energy-transfer process through the 4f-5d transitions is expected to enhance luminescence much more than other energy-transfer processes. This probably results in the remarkable emission enhancement observed only in the case of Pr 3 + and T b 3 + . 4. C o n c l u s i o n We have studied the energy-transfer process of rare-earth-ion doped SrTi0 3 by Al addition. Only the emissions from SrTi0 3 :Pr 3 + and Tb 3 + are intensified by more than 200 times by Al addition. These ions have the 4f-5d transitions almost at the same energy. Temperature dependence of PL spectra shows that the energy transfer from carriers in SrTi0 3 to Pr 3 + or T b 3 + ions is much more efficient than that to the other rare-earth ions. Thus, it can be speculated that the energy transfer in SrTi0 3 :Pr 3 + or T b 3 + occurs from carriers to Pr 3 + or T b 3 + via the 4f-5d transitions.
359
400
500 600 WAVELENGTH (nm)
700
Fig. 3. PL spectra of Al-free SrTi0 3 :Ho 3 + (Ho 3 + : 1 mol%) under the 325-nm laser excitation at various temperatures: (A) 20, (B) 60, and (C) 100 K.
Acknowledgements This work is supported by the "Research for the Future" Program (No. JSPS-RFTF 96R12501) from the Japan Society for the Promotion of Science. One of the authors (H. Y.) is also indebted to Futaba Electronics Memorial Foundation. References 1. 2. 3. 4. 5. 6. 7.
8. 9. 10.
S. Itoh, H. Toki, K. Tamura, and F. Kataoka, Jpn. J. Appl. Phys. 38, 6387 (1999). S. Okamoto, H. Kobayashi, and H. Yamamoto, J. Appl. Phys. 86, 5594 (1999). N. J. Cockroft and J. C. Wright, Phys. Rev. B45, 9642 (1992). N. H. Chan, R. K. Sharma and D. M. Smyth, J. Electrochem. Soc. 128, 1762 (1981). S. Okamoto, H. Kobayashi, and H. Yamamoto, J. Electrochem. Soc. 147, 2389 (2000). S. Okamoto, S. Tanaka, and H. Yamamoto, Electrochem. Solid-State Lett. 3, 242 (2000); J. Lumin. 87-89, 577 (2000). K. Horikawa, M. Kottaisamy, H. Kominami, T. Aoki, N. Azuma, T. Nakamura, Y. Nakanishi and Y. Hatanaka, Extended Abstract (The 46th Spring Meeting); The Japan Society of Applied Physics and Related Societies, p.1402 (1999) (in Japanese). See, for example, Phosphor Handbook, ed. S. Shionoya and W. M. Yen (CRC Press, Boca Raton, USA, 1999), Chap. 3, Sec. 3, p. 184. T. Feng, Phys. Rev. B25, 627 (1982). R. Leonelli and J. L. Brebner, Phys. Rev. B33, 8649 (1986).
ANDERSON TRANSITION IN TWO-DIMENSIONAL DISORDERED LATTICES WITH LONG-RANGE COUPLING A. RODRIGUEZ 1 GISC, Departamento de Matemdtica Aplicada y Estadistica, Universidad Politecnica, Madrid, Spain V. A. MALYSHEV 2 , F. DOMINGUEZ-ADAME 3 and J.R LEMAISTRE 4 National Research Center, "Vavilov State Optical Institute", Saint-Petersburg, Russia GISC, Departamento Fisica de Materiales, Universidad Complutense, Madrid, Spain 4 Laboratoire des Milieux Desordonnes et Heterogenes, Universite P. et M. Curie, Paris, France 3
Abstract We provide arguments indicating that an Anderson transition may exist in two-dimensional disordered systems with long-range coupling. As a working example, a two-dimensional dipolar Frenkel exciton Hamiltonian is used in order to confirm the existence of a localization-delocalization transition. It is found that the states of one of the band tails, but not of the band center, undergo the continuous Anderson transition.
1
Model and motivations
The Anderson transition in disordered solids 1 , despite its forty-year history, still excites great interest among researchers. After the pioneering work by Abrahams et al. for twodimensional systems 2 , a number of papers raised the general belief that in those systems all eigenstates were exponentially localized 3 and that the localization-delocalization transition no longer exists in the thermodynamical limit. In this work we show that extended states may appear in two-dimensional systems with a long-range intersite coupling even for moderately large diagonal disorder. In three and one dimensions, this fact has been outlined in Refs 4,5 . To this end, we consider a Frenkel exciton Hamiltonian on a regular N — N x N lattice with diagonal disorder: « = £ 6 n | n ) ( n | + £ Jnm|n)(m|. (1) n
mn
Here, e n and |n) are the energy and the state vector of the n-th excited molecule, respectively; n = (nx,ny), —N/2 < nx,ny < N/2, with N even. The dipole-dipole inter-site interaction is taken in an isotropic form J n m = J / | n — m| 3 , where J > 0, implying that the transition dipole moments of all molecules are perpendicular to the latice plane and all of them have the same magnitude. We assume that the on-site energies e n are uncorrelated random variables distributed according to a Gaussian function of variance A 2 . In the Bloch-wave representation, assuming periodic boundary conditions, Hamiltonian (1) takes the form «
= £EK|K>
K K
,|K)
where K = {2ir/N){kx, ky) runs over the first Brillouin zone, {-N/2 is the unperturbed exciton eigenenergy
& = ^Ei^ n?tO
and {6H)KK'
(2)
KK'
< kx, ky < N/2).
Here EK
(3)
I"I
is the inter-mode coupling matrix (^)KK'=^Eene'(K-K')n.
360
(4)
361 It can be shown that in close proximity of the extreme points of the band K = 0 (top) and K = n s (7r,7r) (bottom) the exciton energy spectrum behaves linearly and parabolically, respectively 6 : j 9.03J-2TTJ|K|, K
~ \
-2.65J + 0 . 4 J | K - n | 2 ,
|K|<1,
|K-II|<1.
, . (>
Depending on the degree of disorder A / J and the lattice size, the operator SH may couple the extended excitonic states |K) to each other (thus resulting in their localization) or not. The magnitude of the exciton inter-mode coupling is given by a = x /(|(5W) K ,K'| 2 ) = | ,
(6)
which reflects the well-known exchange narrowing effect7. At the top of the band, the energy spacing between the unperturbed states with K = 0 and K ' = (2TT/JV,0) is SE = 4ir2J/N. When comparing SE and a the most remarkable fact is that both quantities decrease on increasing N in the same manner as N~l = A/" -1 / 2 . Now take A
2
Numerical results
To examine the character of the exciton eigenfunction (localized or extended) we have calculated the inverse participation ratio (IPR) of the exciton eigenstates, according to the standard definition IPR,, = £ n |\l/„n|4, where the sum runs over lattice sites and it is assumed that the eigenfunction \t„ n of the iHh eigenstate is normalized to unity. For a completely delocalized state IPR„ = 1/A/" = N~2 whereas for a state concentrated in one site IPR„ = 1, so the smaller the value of the IPR, the more delocalized the state is. In fact, the participation ratio IPR^ 1 is of the order of the number of sites over which the eigenfunction is spread. We have used Lanczos and Householder algorithms to calculate the IPR of the uppermost eigenstate and of the complete set of eigenstates respectively. The IPR of the uppermost exciton state as a function of the lateral size N is shown in Fig. 1. The plots comprise the result of 20 averages over disorder realizations and A / J = 1 in all cases. The IPR calculated within the NN approximation shows no scaling which is in perfect agreement with the well-known result stating that those exciton states are localized. On the contrary, the slope of the straight line obtained within the exact model is equal to —1.97 that almost matches the theoretical value —2. This scaling undoubtedly confirms the extended nature of the uppermost exciton state. Figure 2 presents the IPR of the uppermost state as a function of A / J for different system sizes. At first glance, it seems that this state undergoes an abrupt Anderson transition at the
362 10 • 10"'
•
10"2
• Nearest-neighbor • D i pole-di pole
Slope=-1.97
10"' 10
J
J
• • • •
eg
^ 100
10 10"
• 50x50 • 100x100 A 150x150
, . . • • ? A
*
2
3 A/J
Figure 1: Lateral size scaling of the I P R of the uppermost exciton eigenfunction.
Figure 2: IPR of the uppermost exciton eigenfunction as a function of A / J .
i
-
J Figure 3: IPR as a function of energy for M = 50 x 50 and different values of A / J . Note the different scale of the E/J axis indicating the widening of the bandwidth with increasing A / J .
A/J=1 - A/J=2 A/J=3 A/J=4
iiS'"''V--
Figure 4: Absorption line shape in arbitrary units for 50 x 50 systems and different values of the degree of disorder A / J . Results comprise 20 realizations of disorder for each value of A / J .
critical value of A / J approximately equal to 2 independently of the system size. Nevertheless, this is not really true. The uppermost states whose IPR are shown in Figure 2 arise from large fluctuations in the on-site energies en- Indeed, it is straightforward to verify that at N ~ 100 and A / J > 2, the probability of a large site-energy fluctuation giving an energy e n outside of the band of the ordered system is of the order of unity. In Fig. 3, after the "transition" has occurred ( A / J > 2), it can be seen the dramatic increase in the IPR of the uppermost state whereas the increase in the IPR of the states actually coming from the top of the band of the ordered system is no so abrupt. The width of the absorption spectrum a A can be proposed to indirectly measure the extension of the optically active exciton eigenstates (top band states in our case): oA ~ IPRtop^- 8 We calculated the absorption spectra of the system at different degrees of disorder A / J . The results are shown in Fig. 4. The absorption line width aA presents a clear tendency to smoothly widen on increasing A / J , in correspondence with the fact that the IPR of the top band states smoothly go up. The uppermost eigenstate, being the only one coupled to the light in an ordered system, is now mixed with the other eigenstates, spreading its oscillator strength over them. As a result, the absorption spectrum widens.
363
3
Conclusions
In summary, we have found that a continuous Anderson transition may exist in twodimensional systems with dipole-dipole intersite coupling in the vicinity of the band top. In our opinion, the failure of the one-parameter scaling theory for the conditions considered in the present paper originates from that this approach deals only with the size scaling of the energy spacing but pays no attention to the subsequent renormalization of the disorder (6). As it follows from our treatment, the latter effect may play a major role in localization phenomena, violating the one-parameter scaling and thus leading to the impossibility to match our numerical results by this theory.
References [1] P. W. Anderson, Phys. Rev. 109, 1492 (1958). [2] E. Abrahams, P. W. Anderson, D. C. Licciardello, and V. Ramakrishnan, Phys. Rev. Lett. 42, 673 (1979). [3] P. A. Lee and T. V. Ramakrishnan, Rev. Mod. Phys. 57, 287 (1985). [4] D. E. Logan and P. G. Wolynes, Phys. Rev. B 29, 6560 (1984). [5] A. Rodriguez, V. A. Malyshev and F. Domi'nguez-Adame, J. Phys. A: Math. Gen. 3 3 , L161 (2000). [6] P. L. Christiansen, Yu. B. Gaididei, M. Johansson, K. 0 . Rasmussen, V. K. Mezentsev, and J. Juul Rasmussen, Phys. Rev. B 57, 11303 (1998). [7] E. W. Knapp, Chem. Phys. 85, 73 (1984). [8] L. D. Bakalis and J. Knoester, J. Lumin. 87-89, 66 (2000).
S P A T I A L A N D M O M E N T U M D I F F U S I O N OF E N E R G E T I C H O L E S I N I n A s B Y T W O COLOR P U M P - P R O B E M E T H O D
SHINGO SAITO and TOHRU SUEMOTO Institute for Solid State Physics, University of Tokyo Kashiwanoha 5-1-5, Kashiwa, Chiba 277-8581, Japan
Time-resolved electronic Raman scattering of a direct-gap semiconductor, InAs was measured by pump-probe method. We used fundamental pulses and second harmonic pulses of mode-locked Ti:S laser as excitation sources, and fundamental pulses as the probe beam. The time-resolved Raman intensities corresponding to the transition from heavy hole band to light hole band showed different features depending on the excitation energy. In case of the fundamental beam excitation, Raman intensity decreased monotonously. On the contrary, Raman intensity under the second harmonic excitation showed a maximum at a few picosecond after excitation. From the analysis, the temperature of photo-excited hole changed from 5300K to 1300K in 2psec and from 1300K to RT within 4 psec under the second harmonics excitation. It has been shown that the time-resolved Raman scattering measurement is a useful tool to investigate dynamics of the energetic carriers. 1. Introduction The ultrafast carrier dynamics in semiconductors continues to be one of the most interesting and important subjects from a viewpoint of application and fundamental research. The thermalization and cooling processes of the photo-generated hot carriers are dominated by electron-electron, electron-hole and hole-hole collisions and also by carrier-phonon interactions. In electronic Raman scattering measurement, the Raman signal by hole and electron are observed separately in the energy axis. This is the advantage of Raman spectroscopy in investigating the carrier dynamics. Time-resolved electronic Raman measurement of Ge was reported 1,2 . The rise of the intensity was interpreted in term of the hole population defined by the hole temperature and the decay in term of the spatial diffusion. In those works, the evolution of inter-valence band Raman scattering (IVRS) was observed by one color time-resolved Raman scattering measurement. In our previous report, we developed the two-color pumpprobe measurement system 3 and interpreted the dynamics of photo-generated holes with high kinetic energy as a spatial diffusion in Ge. In order to study the behavior of the energetic carriers, we performed two-color time-resolved Raman scattering measurements in InAs and compared the result with that of one-color measurements. A broad Raman band of InAs appears around 2000cm - 1 under the 1.58eV excitation and is ascribed to the hole excitation from heavy hole to light hole band by comparing the Raman shift with a band calculation 4 . In this report, by comparing the results of pumping by fundamental beam (1.58eV) and its second harmonic, the cooling of photo-excited holes were discussed. 2. E x p e r i m e n t In one-color pump and probe measurements, the fundamental light (1.58eV) from a 70fs modelocked Ti:Sapphire laser is divided in two beams and they are used as pump and probe beams. Polarization of the beams are perpendicular each other. In order to remove the undesirable
364
365 spectrum components due to the fluorescence from the Ti:Sapphire laser rod, the probe beam is passed through a spectrum trimmer consisting of a grating and a slit. The time resolution and spectral resolution are about 70fs and 300cm-1, respectively. The pump beam and the probe beam is resonant to the band-to-band transition near the T point in InAs. Beam intensities of the pump and probe beams on the sample surface were 30mW and 30mW, respectively. The diameters of the pump and probe beams on the sample were about 35/im. The initial distribution of carriers in the sample has a disk-like shape, because the penetration depth5 of the pumping light is only 0.14/im. Prom power density and the penetration depth of the pumping beam, carrier density excited by the pumping pulse is estimated to be in the order of 10 18 cnr 3 . In the two-color pump and probe measurement, the probe beam is the same as the one-color pump-probe system, but the pump beam is its second harmonic light(3.16eV). The second harmonic pulses are elongated by the BBO crystal and the over-all time resolution and spectral resolution are about 250fs and 300cm-1, respectively. The pump beam excites carriers far from the T point. Intensities of the pump and probe beams were 25mW and 30mW, and spot sizes were about 150/zm and 100/rni, respectively. From the power density and the penetration depth5 (0.03/im) of the pumping beam, carrier density excited by the pumping pulse is estimated to be about 1018cm"3. We performed time-resolved Raman measurements on the inter-valence-band Raman scattering (IVRS) in InAs. The crystal had (001) plane as the face and scattering geometry was z(x, y)z'. All the measurements were performed at room temperature. 3. Results and Discussion In order to obtain the net effect of the pumping pulse, we measure three spectra under different excitation conditions: (a) probe pulse only, (b) pump pulse only, (c) both pump and probe pulses. A time-resolved spectrum(d) is obtained by calculating, (d) = (c) - [ (a) + (b) ]. We obtain Raman spectra at various time-delay by changing interval between the pump and the probe pulses. Figures 1 and 2 show the time evolution of Raman intensity and our model calculation from Ops to 30ps under the 1.58eV and 3.16eV excitation condition, respectively. Open circles show the peak heights (2000cm-1) of the time-resolved Raman spectra. The Raman intensity decreased monotonously under the 1.58 eV excitation, but it showed maximum a few picosecond after pumping under the 3.16 eV excitation. In the following model, we will consider the time evolution of the heavy hole population. We do not have to consider the life time of carriers because it is far longer than the time scale considered in this report. The intensity of electronic Raman scattering, /, is the products of the hole distribution in the real space, N, and that in the momentum space, F, I = N-F.
(1)
Firstly, we apply a 1-dimensional diffusion model to treat the spatial distribution of the holes. The diffusion of particles which are placed at the surface as a Gaussian distribution at time t=0 is well described by a Fokker-Planck equation. Then the spatial population N(z, t) is given by, N{z, t) = [2Dn(t + i,)]" 1 / 2 • exp[-—^—J\,
(2)
where D is the diffusion constant of the holes. The parameter t\ is introduced to describe the initial distribution of the holes: 2y/Dt[ corresponds to the thickness of the distribution at £=0. To evaluate the Raman intensity, we have to consider the penetration depth of the probe beam and the re-absorption of the scattered Raman signal light and to perform a weighted integration. The total number of the heavy holes probed by Raman scattering, N(t) is given
366 by, /*0O
N(t)=
Jo
exp(-2az)
•
N{z,t)dz,
(3)
where a is the absorption coefficient of InAs for probe beam wavelength. The factor 2 corresponds to the penetration depth and the re-absorption. Prom the thickness 5 of the initial distribution of carriers for 1.58eV and 3.16eV excitation, these distribution depth corresponds to *i=0.8ps and ti=0.004ps, respectively. Diffusion constant 6 of holes at RT, 15.7cm 2 s _ 1 is used in Eq. (2). The solid curves in Figs. 1 and 2 are the calculated results. To discuss the cooling of the carriers, we will divide the experimental data by the results of the diffusion model calculation (F = I/N). The triangles in Figs. 1 and 2 are the quotients and show the maxima in the region of one or two picoseconds. Under the assumption that the excess energy of carrier corresponds to the initial hole temperature, the initial hole temperature should be about 5300K in case of the 3.16 eV excitation and 3200K in the case of 1.58eV excitation. In the resonant electronic Raman scattering, the probe beam is resonant to the transition between the light hole band and conduction band at the wave vector k and the heavy hole is excited to the light hole band at the same k. From the band structure of InAs 4 , it is expected that the energy of the heavy hole probed by Raman scattering corresponds to a temperature of 1300K. The maxima of triangles correspond to the temperature of the holes passing this temperature. 2.2
1.8
% ;
1.6
_t
1.4
T
i3.
1.2 1.0
•
0.8
• —
nte
m
0.6 0.4 0.2
\
I
•
- ; " . ik
units
2.0
I
+*»
1
1
1
+
-
\ A
A
A
• —> -\
— -
-
-
+
I 1 1 t 1 10 15 20 25 30 Delay Time (psec) Fig.l: The time evolution of Raman intensity from Opsec to 30psec pumped at 1.58eV photon energy. Open circles show the peak heights (2000cm -1 ) of the time-resolved Raman spectra. Solid curve shows the results calculated by the diffusion model discussed in the text. Triangles show the results of the division of experimental results by the calculation. Broken line is the result from the hole cooling model. 0.0
0
I 5
I
I
1
•
1.4 1.2
-
AA
T" ^
1.6
1.58eV excitation Diffusion model Experimental data / — Diffusion model Hole cooling model
! " %
k
3.16 eV excitation Calculation A Experiment Data / ~ Diffusion model Hole cooling model
0.8
1 0.6 0.4 0.2 -
0.0 bh 0
_L 5
10 15 20 25 30 Delay Time (psec) Fig.2: The time evolution of Raman intensity from Opsec to 30psec pumped at 3.16eV photon energy. Lines and marks mean the same as in Fig. 1.
Broken lines are the results of the calculation by the carrier cooling model. The Boltzmann distribution, / ( e , T) and the density of state for the parabolic band are assumed for the
367 calculation. f(e,T) = exp(-e/kBT), P(e)
(4)
= V~e-
(5)
Furthermore, cooling of the hole temperature, T(t), is assumed to be, T(t) = (Ti - Tc) • exp(-t/r)
+ Tc,
(6)
where T; is the initial temperature, and r and Tc are fitting parameters. As a result, the time development of Raman intensity is expressed as, I(t) = f(e,T(t))-p(e)-N(t).
(7)
The fitting parameters, r and Tc are determined to be 0.8ps and 700K, respectively for 3.16eV excitation. For 1.58eV excitation, we used the same r and adjusted Tc as 600K. Tj is the initial temperature of hole. The broken lines in Figs. 1 and 2 are the results of these calculations. The agreement with the experimental data (triangles) is very good in the case of 3.16eV excitation, while the agreement is still qualitative in the case of 1.58eV excitation. For both cases, the Raman intensities keep rather high level at long delay times. This suggests the hole keeps higher temperature than RT. It might be caused by following reasons. Due to the low heat conductivity of InAs, the lattice temperature within the laser spot might be significantly higher than the room temperature. Another possibility is the existence of energetic carriers stored in the side valleys. The electrons can be excited to the L or X valleys on the lowest conduction band by the 3.16eV excitation and could be excited to L valley even by the 1.58eV excitation. The temperature of the hole system might be increased via electron-hole collisions and might be kept at higher level for longer time. In conclusion, from the time evolution of the Raman intensity under two different excitation photon energies in InAs, we successfully extracted the information of the cooling process in long time scale, separating the contribution from the spatial diffusion of the holes. It has been also shown that the two-color time-resolved Raman scattering measurement is a useful tool for investigating the dynamics of the energetic carriers. Acknowledgements This work was partially supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Science and Culture of Japan. References 1. 2. 3. 4. 5. 6.
K. Tanaka, H. Ohtake, H. Nansei, and T. Suemoto, Phys. Rev. B , 5 2 (1995) 10709. K. Tanaka, H. Ohtake, and T. Suemoto, Phys. Rev. B , 5 0 (1994) 10694. S. Saito and T. Suemoto, J. Lumin. 8 7 - 8 9 (2000) 920-923. J. R. Chelikowski and M. L. Cohen, Phys. Rev. B , 1 4 (1976) 556. D. E. Aspnes and A. A. Studna, Phys. Rev. B , 2 7 (1983) 985. O. G. Folberth, O. Madelung, and H. Weiss, Z. Naturforsch. 9 a , (1954) 954.
NONLOCAL ELECTRO-OPTIC EFFECT IN S E M I C O N D U C T O R T H I N FILMS
MASAMICHI SAKAI Department of Functional Materials Science, Saitama University, 255 Shimo-okubo Urawa, 338-8570, Japan
Electroreflectance(ER) spectra of GaAs thin film/Alo.sGaojAs-substrate systems are investigated theoretically by taking into account the nonlocal effect caused by the presence of a crystal surface. Calculations are carried out by following the previous work by DelSole but considering influence of film thickness and nonflat-band modulation of a static electric field. It is shown from thickness variation of ER spectra that the refractive indexes of the thin films are reduced by a factor of about 0.1 when the nonlocal effect is considered. 1. I n t r o d u c t i o n In an inhomogeneous system without translational symmetry an induced polarization P is given in principle by nonlocal regime; P at position r depends not only on a light field E{r) but also on the behavior of the light field in its near vicinity, i.e., E(r'). A typical example is a crystal surface because translational symmetry is not sustained near the surface. The surfaceinduced nonlocal effect was first studied by DelSole who demonstrated theoretically that for photon energies larger than the direct gap the refractive index in Ge is reduced by a factor of about 0.04 compared to that predicted under local regime. 1 Experimentally it is, however, not easy to detect the surface-induced nonlocal effect from usual reflectance measurement because the measurement must be carried out taking advantage of the presence of a sample surface and then cannot be compared to a result uninfluenced by the surface. Accordingly another way is desired for detecting the surface-induced nonlocal effect. In the present work GaAs thin films grown on semi-infinite substrates of Alj,Gai_,.As (x ~ 0.3) are considered as model systems for detecting the nonlocal effect. Following the previous work by DelSole 2 but considering influence of film thickness and nonflat-band modulation, electroreflectance(ER) spectra associated with the direct gap of GaAs are calculated under a nonlocal regime of optical response. 2 . Solving t h e M a x w e l l ' s E q u a t i o n s We consider a system given in Fig. 1. Let a plane electromagnetic wave polarized along x enter the film at normal incidence. Omitting the time factor throughout, one can write the light fields as £<°> = E
=
£ie*(*.z+iM*))
+ ri2 £ 1 e
,
'<- (l ' 2 - , -M*»,
(2)
i{k +,hi ))
E<® = E2e "
' ,
(3)
where ko, ki and ki are the unperturbed propagation constants of vacuum, the film and substrate, respectively. Quantities rj>\ and ifa are caused by the nonlocal effect due to the presence of a surface and/or an interface incorporated with a uniform electric field. Using Maxwell boundary conditions associated with the plane z = 0 and z = d, we obtained a formula for the amplitude reflection coefficient, roi(fc0 - kx - j>[(0)) + r;2(fc0 + fci 7-01
ffi(0))
(ko + kl+ 01(0)) + r*u(k0 - k, + # ( 0 ) ) '
368
(
'
369 where _ fci - k2 + tj)\(i) - j'ijd) uhd i(4,Uo)-4>[ (0))d * i + ' * j - # ( d ) + V4(<0 When obtaining Eq. (4) we assumed that ipi and 4>i are given approximately by >12_
(5)
V>i(
(6)
& ( d ) ~ & ( 0 ) + #(0)d.
(7)
Making use of a relation \rf^ | < 1 we obtain from Eq. (4) -2k0(l+r($)
rn(F) - r01(F - AF)
^x(o),
(fc0 + fei + rfffo - fci))(t|, - fci + r^(k0 + fcx)) where r
(0) _ «fci l - -« 2k-2e i 2 M 12 — " ~ ^
(9)
ki + fc2
Ai/>[(o) =-i— C 2 Jo
( dz S dz"(e1(z',z",u,F)-e1(z',z",w,F
(8)
-
AF))eik^+z"
(10)
Jo
vacuum medium 0
film medium 1
substrate medium 2
> Fig. 1. Schematic diagram for the propagation of an electromagnetic wave through a film-substrate system.
Quantity ei(z,z',u>,F) is a dielectric function influenced by the presence of a surface and a static electric field, F, and is calculated with the aids of the wave functions of the system. The wave functions in the film region are determined under the presence of an infinite surface potential and a unifonn electric field. Depending on a field direction either electrons and holes are confined to the surface triangle potential. Influence of film thickness is included as the number, N, of the confined states responsible for the fundamental transition close to Eg of the film region. The quantity N is then determined as the maximum value of integer, j , which satisfies the equation: E(j) < eFd, where E(j) stands for the j-th energy of confined states. In practice there still exist confined states higher than the iV-th state. The higher states are however expected to have less contribution to the transition near E9 of the film region. After some manipulation we obtain an expression of Aip[(o) in terms of Airy functions characteristic to electronic states under a static electric field. When calculating Atp't^o) we assumed a weak field-modulation, i.e., AF
370 effects separately. The detail of the expression of Ai^[(o) will be indicated in an elsewhere. Consequently we can calculate ER intensity AR/R by using
4? R
=
2Rc( r o i ( F ) ~ r o l ( F ~^ F ) )
(11)
ra,
It is noted that unless ^ and tpi are assumed by Eqs.(6) and (7) quantity r 0 i cannot be determined only from the Maxwell boundary conditions at z — 0 and z = d. To solve the present problem without the aids of Eqs.(6) and (7), an additional-boundary-condition(ABC)free formulation may be useful.3 However its application to the present problem is outside of the scope of this report, and will be discussed in a feature work. 3. Numerical Results and Discussion All the calculation in the present work are carried out for the heavy-hole transition associated with Eo gap of the film region. For the heavy-hole transition Aip[(o) should be asymmetric with respect to a sign of the electric field because there exist a large difference in effective mass between conduction and heavy-hole bands associated with Eo gap of GaAs. Thus calculation is performed for both directions of field. Shown in Fig. 2(a) are results of calculation for the electron confinement case, i.e., F > 0. Calculation in Fig. 2(a) are made with a GaAs thickness, d, of 150 nm, an electric field, F, of 8 kV/m and a 10% field-modulation, i.e., AFjF= 0.1. These parameters of d and F give rise to N=14 for electron confinement. For heavy-hole confinement, i.e., F < 0 calculations are made with the same parameters as those of the electron confinement case, and are shown in Fig. 2(b). There exist a significant difference in the WFM and ELM components between electron and hole confinement cases. It is apparently due to the difference in effective mass between the conduction electron and heavy hole. 5xl0"4|
1
1
.
1
,
1
,
1
5x10'"
a5
B5
<
<
-5x10"
1.42
1.44
1.46
Photon Energy (eV)
1.48
-5x10" " " 1.4
1.42
1.44
1.46
Photon Energy (eV)
1.48
Fig. 2. ER spectra calculated for a GaAs thin film-substrate system having a film thickness of 150 nm. Calculations are made for (a) the electronconfinement case and (b) the hole-confinement case using ER parameters, i.e., an electric filed of 8 kV/cm, 10 % field modulation and zero-broadening energy. Solid and dashed lines indicate ELM and WFM components, respectively
In order to investigate our calculation from the viewpoint of nature of optical response, a calculation is performed by reducing Eg by a factor of ten but remaining other ER parameters used in Fig. 2 unchanged. This long wavelength condition makes significant change both in WFM and ELM parts; the WFM becomes insensitive to photon energy, while the ELM shows ordinary Franz-Keldysh oscillations predicted from the local response theory. It is believed that the nonlocal effect is reduced if the wavelength of probe light is increased. Therefore a unusual ER shape shown in Fig. 2 is most likely to be caused by the nonlocal effect.
371 To investigate influence of film thickness on ER, calculations of ELM part are made with various film thickness in the range of 30-500 nm. As shown in Fig. 3 (a) normalized energy positions of ER extrema are strongly affected by film thickness. Owing to a Fabry-Perottype interference between the reflected lights from the film surface and the film/substrate interface,4 a similar variation of ER extrema positions are also found when the nonlocal effect is neglected: the calculation is shown in Fig. 3(b). However the periodicity and amplitude in thckness variation are enlarged respectively by a factor of 1.1 and 2.4 when the nonlocal effect is considered. To explain the difference in periodicity in a phenomenological way, a calculation has been carried out under local regime but modifying refractive index of the film region. When reducing the refractive index by factor of about 0.1 the periodicity shown in Fig. 3 (a) is accounted for by the local regime. A reduction in refractive index was also predicted in Ge, though the calculation for Ge was carried out for a semi-infinite sample having no electric field.1 Accordingly the reduction in refractive index is probably due to not influence of sample thickness as well as electric field but the presence of a surface. In fact, according to our calculation up to 30 kV/cm the reduction factor is found to be insensitive to field strength.
6-
(b)
© 5Ha 4 >. 4w 3i
s 2-
0-
^
\T\f^\ e N
-1100 200 300 400 500 600 0 100 200 300 400 500 600 Thickness (nm) Thickness (nm) Fig. 3. Energy positions of ER extrema calculated under (a) nonlocal regime and (b) local regime are plotted as a function of film thickness. Calculations are made for the electron-confinement case using the same ER parameters as Fig. 2. Quantity tiQ stands for electro-optic energy.
4. Conclusion Following the previous work by DelSole ER spectra have been calculated under influence of surface-induced nonlocal effect incorporated with influence of nonflat-band modulation and film thickness. It is shown that ER spectra under nonfalt-band modulation can be accounted for in terms of WFM and ELM parts. Since thickness variation of ER spectra show different characteristics both in periodicity and amplitude compared to those expected from the local regime, ER measurement for various thickness may be rather available for detecting the surfaceinduced nonlocal effect compared to a usual reflectivity measurement. References 1. 2. 3. 4.
R. DelSole, J. Phys. C: Solid State Phys. 8, 2971 (1975). R. DelSole, Solid State Commum. 19, 207 (1976). K. Cho, J. Phys. Soc. Jpn. 55, 4113 (1986). M. Nakayama, I. Tanaka, T. Doguchi, and H. Nishimura, Jpn. J. AppL Phys. 29, 1760 (1990).
Comprehensive study of Frohlich polaron A.S. Mishchenko Correlated Electron Research Center, Tsukuba, 305-0046, Japan, and Russian Research Centre "Kurchatov Institute", 123182 Moscow, Russia N.V. Prokof'ev* and B.V. Svistunov Russian Research Centre "Kurchatov Institute", 123182 Moscow, Russia A. Sakamoto Department of Applied Physics, The University of Tokyo, 7-3-1 Hongo, E,,.nkyo-ku, Tokyo 113, Japan
A study of the Frohlich polaron model is performed on the basis of diagrammatic quantum Monte Carlo technique which is enhanced by novel method of spectral analysis of the polaron Green function. We make available for the first time precise data for the effective mass, including the region of intermediate and strong couplings, and analyze the structure of the polaron cloud. A non-trivial structure of the spectral density is observed: at high enough couplings the spectral continuum features pronounced peaks that we attribute to unstable excited states of the polaron. Despite a lot of work addressed to the Frohlich polaron model 1 , where an electron with the momentum-dependent energy k 2 / 2 is coupled to the optical dispersionless phonons uja = 1 via the polarization interaction V(q) = j ( 2 v 2 a 7 r ) - 1 / 2 / | q |, the problem is still far from being completely solved. In the most interesting region of intermediate values of a almost all available treatments are of variational character, some of which are known to be in qualitative disagreement with the others 2l3,4 . Besides, certain approaches 5 ' 6 ' 7 . 8 A'° suggest that the polaron states at small and large a's are of considerably different nature. In this case the level-crossing occurs (often called a "self-trapping" (ST) transition 11 ) between the two stable polaronic states with qualitatively different nature and the polaron properties change drastically in a narrow interval of a. Recently, the diagrammatic quantum Monte Carlo (MC) method has been developed 12 which, starting from a conventional diagrammatic expansion for the polaron Matsubara Green function G(k, T), generates continuous random variables k and r with a distribution function coinciding exactly with G(k, r ) . In this study (see also' J ) we significantly enhance the scheme 12 by (i) introducing ./V-phonon Green functions (with 2N external phonon lines), which are simulated in one and the same MC process with the ordinary (0-phonon) Green function; (ii) developing a novel procedure of spectral analysis of the Green function. The TV-phonon Green functions allow us to consider the structure of the phonon cloud and facilitate obtaining polaron parameters at large a, where the polaron is essentially a many-phonon object. The Lehman spectral function gk(u), which can be obtained by solving equation G(k, r ) = J^° dujg^w) e~"T , has poles (sharp peaks) at frequencies corresponding to stable (metastable) particle-like states and can reveal the metastable excited state if any. In this study we developed a novel method 1 3 of solving this equation, which is exact in the statistical limit and does not suffer drawbacks of the existing methods. Although the comparison with the Feynman's variational energy demonstrates the accuracy of Feynman's approach (Fig. 1), the effective mass is poorly reproduced (see Fig. 2, where up to 50% deviation from exact result is observed in the region 6 < a < 10) by variational 'Present address: Department of Physics, University of Massachusetts, Amherst, MA 01003, USA
372
373
^n
^'"\
-o- Feynman
*\
\\
. QMC
\\ _KA
0
5
10
15
20
a
Fig. 1. Bottom of the polaron band EQ as a function of a. The error bars are much smaller than the point size.
treatments 2 , 1 0 . At small a's the perturbation formula m , = (1 — a / 6 )
1
works well up to
Fig. 2. Effective mass as a function of coupling parameter. Our MC data (circles interpolated by solid line) are compared with perturbation-theory and strong-coupling-theory results (dashed lines), Feynman's (squares), and Feranchuk et al. approaches (diamonds).
a ss 2 only, whereas the strong-coupling theory 14 m, = a 4 / 4 8 drastically overestimates the effective mass in the whole range of physically interesting a's. We note that our m»(a) curve is smooth for all values of a and do not demonstrate ST transisiton at a ~ 7.5 suggested by the variational technique in l 0 , which should lead to an especially rapid increase of m , just after a ~ 7.5. Besides, a two-peak structure of Z-factors distribution (Fig. 3), which occurs in ST phenomenon due to the resonance between the two stable polaronic states with qualitatively different nature, is not observed. The average number of phonons N as a function of a (Fig. 4) shows a smooth increase which does not suggest ST transition too. In the strong-coupling limit the existence of the metastable relaxed excited state, i.e. the state which re-adapts the lattice to the new electronic configuration and manifests itself as a sharp peak of the optical absorption spectrum and Lehman function, was predicted 1 5 , 1 6 1 7 . However, actual spectral density (Fig. 5) does not demonstrate metastable excited states because the width of the peaks is comparable with the excitation energy, i.e. with the distance from the polaron ground state. Moreover, according to the strong-coupling approaches 15 , the excitation energy of the relaxed excited state is proportional to a2, whereas peak positions in 9k=o(^) with respect to E0 do not change with a. We note that the metastable excited state with energy less than the optical phonon energy ui0 = 1, which is characteristic of the ST phenomenon 11 , does not exist since for all coupling strengths
374
0.25
0
1
2
3
4
5
N
0 1
2 3 4 5 6 7 8 N
Z" 0.15
0.04
a=6
/
0.03
0.1
0.02 0.05
/
0.01
t
/ 0
0
4
8
12
16N
A °"17
. V
30 40 50 60 70 80 N
Fig. 3. Partial contributions of AT-phonon states to the polaron ground state.
Fig. 4. The average number of phonons N in the polaron ground state as a function of a. Filled circles are the MC data, the dashed line is the perturbation theory result, and the solid line is the parabolic fit for the strong coupling limit.
375 *
0.70 - 0.60-
I
0.50-
£
0.400.300.200.10 0.00-0.00
§ »
4.00
8.00
12.00 16.00 Energy
20.00
24.00
0.40 - p f" 0.30-
& i
02
°:
yw
& 0.100.00-0.00
4.00
8.00
12.00 16.00 Energy
20.00
24.00
4.00
8.00
12.00 16.00 Energy
20.00
24.00
0.25 - £
020-
I
0.15-
S
0.050.00-0.00
I °"10~
Fig. 5. Evolution of spectral density with Ct in the cross-over region from intermediate to strong couplings. (The polaron ground state peak is shown only for a = 8.)
the ST transition does not take place for Prohlich polaron. While there is no stable excited state in the energy gap between the ground state energy and incoherent continuum, there are several many-phonon unstable states which probably reveal themselves in variational approaches and can be mistreated as quasi-stable states of the polaron. We are indebted to N. Nagaosa for inspiring discussions. This work was supported by the RFBR Grant 99-02-17288, by Priority Areas Grants and Grant-in-Aid for COE research from the Ministry of Education, Science, Culture and Sports of Japan, and by the NSF Grant DMR-0071767. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17.
H. Frohlich, H. Pelzer, and S. Zienau, Phil. Mag. 41, 221 (1950). R.P. Feynman, Statistical Mechanics, (Benjamin, Reading, 1972) T.D. Schultz, Phys. Rev. 116, 526 (1959). T.D. Lee, F.E. Low and D. Pines, Phys. Rev. 90, 297 (1953). E.P. Gross, Ann. Phys. 8, 78 (1959). D. Matz and B.C. Burkey, Phys. Rev. B 3, 3487 (1971). J.M. Luttinger and C.Y. Lu, Phys. Rev. B 21, 4251 (1980). R. Manka and M. Suffczynski, J. Phys. C 1 3 , 6369 (1980). Y. Lepine and D. Matz, Phys. Stat. Sol. (b) 96, 797 (1979). I.D. Feranchuk, S.I. Fisher, and L.I. Komarov, J. Phys. C 18, 5083 (1985). M. Ueta, H. Kanzaki, K. Kobayashi, Y. Toyozawa and E. Hanamura, Excitonic Processes in Solids (SpringerVerlag, Berlin, 1986). N.V. Prokof'ev and B.V. Svistunov, Phys. Rev. Lett. 81, 2514 (1998). A.S. Mishchenko, N.V. Prokof'ev, A. Sakamoto, and, B.V. Svistunov, cond-mat/9910025. L.D. Landau, S.I. Pekar, Zh. Eksp. Tear. Fiz. 1 8 , 419 (1948). E. Kartheuser, R. Edvard and J. Devreese, Phys. Rev. Lett. 22, 94 (1969). J. Devreese, J. De Sitter and M. Goovaerts, Solid State Comm. 9, 1383 (1971). J. Devreese, J. De Sitter and M. Goovaerts, Phys. Rev. B 5, 3367 (1972).
COHERENT TRANSIENTS OF PSEUDOISOCYANTNE J AGGREGATES: VIRTUAL EXCITONS IN THE INTERMEDIATE EXCITON-PHONON INTERACTION SYSTEM
F. SASAKI, T. KATO , and S. KOBAYASFfl Electrotechnical Laboratory, Tsukuba, Ibaraki 305-8568, Japan
Results of picosecond and nanosecond pump-probe experiments are reported in pseudoisocyanine J aggregates near the inverse Raman resonance. Reflecting the width of the pump-light spectrum, the inverse Raman term dominates the nonlinear absorption spectra in the nanosecond experiments. Wefindat least four Raman lines around 170 meV, that are not resolved in the picosecond experiments. The observed spectra agree well with the calculated spectra based on the third order nonlinear susceptibility with four Raman lines. 1. Introduction Nonlinear optical spectra of pseudoisocyanine (PIC) I aggregates show the mixed nature of the nonresonant virtual exciton contribution and of the resonant inverse Raman spectrum under the virtual excitation in the picosecond and femtosecond experiments. The
intermediate
exciton-phonon
coupling enables us the observation of both optical processes. The observed
results of transient T3
absorption spectroscopy including the pump light
8
<
detuning can be well explained by the third-order nonlinear optical processes. We report here detailed studies of both optical processes in PIC J aggregates. 2. Experiments Samples
were
PIC
J
aggregates
in
ethyleneglycol and water mixture with the 4.2 meV
i
/TV—:—^ad44y
line width at 77 K 2 In the picosecond experiments -0.02
ultrafast white-continuum pulses were used for probing. The pump pulses were generated from an
-0.01 0 0.01 PROBE DETUNING (eV)
0.02
optical parametric amplifier (OPA). We used a KDP
Fig. 1 Transient absorption spectra observed at 0 ps time
crystal with the 20mm thickness for SHG of the
delay. The excitation intensity is 350 MWcm"2. The lowest
OPA output. The spectral width and temporal
curve shows the absorption specttum. One Raman line is taken
duration of the pump pulses were 3.5 meV and lps,
into account in the calculated spectra, shown by dotted lines.
respectively.
In the
nanosecond
experiments,
* present address: Institute for Molecular Science, Okazaki
376
377 fluorescence of Rhodamine 6G dye solution was used as probe pulses. The pump pulses were generated from an OPA excited by the Q-switched YAG laser.
£• •
- >
®pu
The spectral width and temporal duration of the pump pulses were 11 neV and Ins, respectively.
<%
Figure 1 shows the transient absorption spectra observed in the picosecond experiments. Solid and
'• c
dotted lines show the experimental and calculated
m=l-4
> t
r^
a
mcY
©„
\. J
(a)
(b)
results, respectively. The schematic energy levels are shown in Fig. 2a. The details of calculation have been
Fig. 2 Schematic energy levels of PIC J aggregates, (a)
reported in ref. 1 and will be described in the next
The ground state, the one-phonon excited state in the
section. Vertical arrows shown in Fig. 1 indicate the
electronic ground state and the lowest exciton state,
energy difference, (J^fOfe-ffifcc where the induced
respectively, represented by c, m, and b.
absorption peak of the inverse Raman line should
one-phonon excited state m is extended to four states, m=l
(b) the
appear.4 Here,fflfc,(Opu, and G V denote the excitonic to 4. energy of PIC J aggregates, the pump photon energy and the vibrational energy of PIC molecules. The value of GW is determined as 173 meV in the picosecond experiments. There are three discrepancies between the observed spectra and the calculated spectra. The induced absorption peaks around the vertical arrows are rather broader than the width of the pump spectrum. The amplitude of the observed spectra is largely different from the calculated spectra only under the 2.005 eV excitation. The blue shift, namely the energy position of the saturation peak well coincides with the calculated spectrum under large detuning from the inverse Raman resonance, as shown under the 2.066 and 1.939 eV excitation. However, it does not coincide with the calculated one near the inverse Raman resonance. It means the inverse Raman contribution is efficient as is expected in the calculation. To examine the differences, we carried out the nanosecond experiments, where the width of the pump spectrum is narrower than the ps pump pulse by two orders of magnitude. The results are shown in Fig. 3. In Fig. 3 solid and dotted lines show the experimental and calculated results, respectively. When the excitation photon energy was tuned to 2.0122 eV, three induced absorption peaks are clearly observed at 11.3, 9.0 and 7.0 meV probe detuning, indicated by arrows. These peaks shift to the low energy side with the decrease of the pump photon energy. The magnitude of the signals becomes large at the inverse Raman resonance, as shown under the 2.0057, 2.0024 and 1.9992 eV excitation. We also found the inverse Raman resonance when the excitation photon energy was tuned to 2.0220 eV Therefore, we find at least four Raman lines around 170 meV. According to the finding, we need to modify the model with multi Raman lines, as shown in Fig. 2b. The details are described in the next section. 3. Analysis and Discussions The nonresonant contribution of virtual excitons to the third order nonlinear susceptibility, ^VE is expressed by3
378
He ^3
•[-{ copr-abc + 'Ybc 7b
copu-aobc-'Ybc
1 CQpr-G)pU + iyb
(Dpu-abc-iYbc
(Opr~o>bc + iYb
°>pu-(Obc + iYbc
}-
} ] CD-
Here, Ofa. denote the frequency of probe light, % the population decay rate of the excitonic transition, and other notations are the same with those in ref. 1. The inverse Raman term in the third order nonlinear susceptibility, tf3>iR is expressed by4
Hr,
$ ' »>pr) = - X m=\
He {a>pr-a>bc + iYbc>
"(2).
^pr-^pu-fOmc
+ 'Ymc
We extend here the vibrational level m to four levels, m=l to 4, as shown in Fig. 2b. In both the picosecond and nanosecond experiments, we confirmed that the magnitudes of signals were proportional to the excitation intensity. Therefore, the third order analysis is I I • | • • • • | • i • 11 • • • T j T ^ T ^ T ^ r * - ! ! • • • • ! > enough to describe the results. Each Lorentzian ay=l;9928eV function in eqs. (1) and (2) is independently replaced by corresponding thermal averaged one-particle V\/fiy=L9960eV. Green's function within the coherent potential approximation (CPA).1 There are four terms in eq. 1. The first and second terms show the level population (LP) terms. The third and fourth terms show the pump •a s polarization coupling (PPC) and the perturbed free < 5 polarization decay (FPD) terms, respectively. The dominant term in PIC J aggregates is found to be the FPD term and it shows the blue shifted NLO spectra under the virtual excitation. In the intermediate exciton-phonon coupling systems, both terms contribute to the NLO spectrum in the same order of >rxd=3$ magnitude.1 In the ps experiments, the blue shifted spectra have been observed when the pump photon -0.02 -0.01 0 0.01 0.02 energy has been tuned to 2.066 and 1.939 eV, which PROBE DETUNING (eV) are about 60 meV high and low energy detunig from the inverse Raman resonance, as shown in Fig. 1. It Fig. 3 Transient absorption spectra in the ns experiments. means the FPD term is dominant optical process The excitation intensity is 205 MWcm"2. The lowest curve under such a large detuning in ps experiments. The shows the absorption spectrum. Four Raman lines are taken square of the ratio of the vibrational transition dipole into account in the calculated spectra, shown by dotted lines. 1
379 moment (p^) to the excitonic transition moment (/ijc) was set to 2% in the calculation. On the other hand, there are much difference between the observed and calculated results near the inverse Raman resonance, as shown in Fig. 1. The blue shifted spectrum caused by the FPD term and the red shifted spectrum caused by the inverse Raman term are canceled out in the calculated spectrum under the 2.005 eV excitation. The observed results is much different from calculated spectrum under the 2.005 eV excitation. The reason is the existence of multi Raman lines. This is also the origin of the broad induced absorption observed around the arrows in Fig. 1. The calculated results taking into account four Raman lines are shown by dotted lines in Fig. 3. In the calculation shown in Fig. 3, we took into account only eq. (2). Actually, in the nanosecond experiments we did not observe the nonlinear spectrum under the 2.04 eV excitation with the excitation intensity of 205 MWcm"2. It means that the FPD term in eq. (1) is negligible in the nanosecond experiments. As shown in eq. (2), the magnitude of the signals is inversely proportional to y^. When we used the pump pulse with the broad spectrum, we overestimated the value of ^ as the width of the pump spectrum. As a result, the inverse Raman term is underestimated in the picosecond experiments. In the nanosecond experiments, the width of the pump spectrum is narrow enough to resolve the value of y„c. However, in our experimental condition we used broad probe spectrum, so that the spectral resolution is limited by the spectrometer. The resolution was about 1 meV, so that the estimated value of y^ was also the same order of magnitude with the resolution. The correct value of y„c is probably narrower than the spectral resolution in this case, but we can evaluate four Raman lines within this resolution. The calculated spectra are shown by dotted lines in Fig. 3. Four Raman resonance were set as 172,170, 168, and 151 meV in the calculation. The values of p^c and y^ were common in all lines, for simplicity.
In
CPA calculation, the half band width and its fluctuation correspond to %& and they were set to 0.7 meV. Differences are seen between the observed and calculated spectra, but overall features are well described by the model calculation. 4. Conclusions We have studied coherent transients in PIC J aggregates in which the intermediate exciton-phonon interaction systems. In the picosecond experiments, both the FPD term of virtual excitons and the inverse Raman term contribute to the nonlinear spectrum within the same order of magnitude. In the nanosecond experiments, the inverse Raman term is dominant in the nonlinear spectrum because of the narrow line width of the pump spectrum. We found at least four Raman lines at 172, 170, 168 and 151 meV. The observed spectra agree well with the calculated spectra based on the third order nonlinear susceptibility with four Raman lines. 1 .F. Sasaki, T. Kato and S. Kobayashi, J. Lumin. 87-89,892(2000). 2.S. Kobayashi and F. Sasaki, Nonlinear Opt 4,305( 1993). 3.R. W. Boyd and S. Mukamel, Phys. Rev. A29(1984)1973. 4.S. Saikan, N. Hashimoto, T. Kushida, and K. Namba, J. Chem. Phys. 82(1985)5409. 5.C. H. Brito Cruz, J. P. Gordon, P. C. Becker, R. L. Fork, C. V. Shank, IEEE J. Quantum Electron. 24(1988)261.
MIGRATION OF THE ELECTRONIC EXCITATION ENERGY IN LANGMUIR - BLODGETT FILMS OF XANTHENE DYES N.Kh.IBRAYEV, D.Zh.SATYBALDINA, A.M. ZHUNUSBEKOV Department of Physics, Karaganda State University, Karaganda, Kazakhstan The concentration and temperature dependencies of the photophysical properties of three new amphiphilic xanthene dyes in the Langmuir-Blodgett (LB) films have been studied. The mechanisms of excitation-energy relaxation were discussed in terms of the excitons migration among energetically disordered monomers and the energy trapping by molecular aggregates. The experimental results were analyzed in view of carried out molecular mechanics and MO calculations. Triplet states of eosin in the LB films were investigated. The observed nonexponential decay kinetics of delayed fluorescence (DF) and phosphorescence were analyzed in the framework of an annihilation model for both exchange and multipolar interactions.
1.Introduction Xanthene dyes are distinguished by a high quantum yield of fluorescence and high photostability. Owing to these characteristics, they are often used for widespread applications. The photophysical properties of these dyes are well investigated in fluid and solid solutions. In contrast, there are not so many works1"4 devoted to the examination of optical properties of xanthene dyes in the LB films. The triplet states of organic molecules in the LB films are almost not investigated. 5,6 In this contribution, we report investigations of energy migration processes in LB films of three new amphiphilic derivatives of xanthene dyes: Rhodamine 6G (dye I), Rhodamine B (dye II) and Eosin Y (dye III). From the analyses of the concentration and temperature dependencies of the spectra the excitation energy relaxation is discussed in relation to distribution of the chromophores and their aggregates in the LB multilayers. The experimental results were analyzed in view of carried out quantum chemical calculations. Moreover, the present work is devoted to the examination of the dye III delayed luminescence in the multilayer films, because the new aspects of the triplet states relaxation can appear in such structures. 2. Experimental The dyes I-III were obtained from the NIOPIK Russian State Scientific Center and used without further purification. Stearic and palmitic acids (Merck) were purified by repeated recrystallization from alcohol solution. The pure dye and mixed dye-fatty acid multilayer films were prepared. The dye concentration in the monolayers was varied from 0.99 to 100 mol%. The properties of monolayers at the air - water interface and their transfer conditions onto a quartz plate have been described elsewhere.7,8 Absorption and fluorescence were obtained with the spectral setup KSVU-23 over the temperature range 90-293 K. Spectral-kinetic characteristics of the samples were measured by using a single-photon counting system. Optimized geometry of dye molecules were obtained using a molecular mechanics method (a MM2 force field).'0 In MO calculations, a three-dimensionally extended Pariser-Parr-Pople (PPP) approximation" with Komarov's parametrization' 2 was used. In the CI calculations, singly excited configurations among the highest 7 occupied and the lowest 7 vacant orbitals were taken into account. The resonance integrals j5'cc of the C-C single bond was calculated by the following equation P'cc = Pcc-cos (p, where
380
381 mixing ratio. When the temperature decreases from 293 K to 90 K, the red shift of the spectra of fluorescence becomes more significant and the luminescence intensity increases. For the LB films with dye concentrations over 50 mol% the broadening of the fluorescence band is observed (see Fig.3). o, Table 1 .The substituents of the Dye R, R2 + I NHC,8H37 N HC I8 H 37 + N (C II N(C2H5)2 2H5)2 O III OH
dyesmolecules R, R R, H CH3 H H H C17H35 Br C10H7, Br
LogC, mol%
Fig. 1. Basic structure of the investigated xanthene dyes. The substituents are shown in Table 1. For dyes I and II, C10.T is anion
Fig.2. Concentration dependencies of (a) the peak wavelength of absorption (1-3), fluorescence spectra (46) and (b) degree of fluorescence polarization for the LB films of the dyes: (1,4)-I, (2,5,7)-II and (3,6)-III
The similar behavior, as a small concentration dependence of the absorption and a large one of the fluorescence in the multilayers of the investigated xanthene dyes, has been observed for the Rhodamine B in the LB monolayers.'"4 In these works the time-dependent red shift of the monomer fluorescence band is interpreted in terms of energy migration to energetically disordered monomer sites and energy trapping by molecular aggregates. Our results indicates also that excitons migration to energetically lower monomer sites is dominant pathways of the Si states deactivation of the monomers. The observed concentration-dependent of fluorescence polarization is similar to behavior found for Rhodamine 6G in porous silicate xerogel monoliths.13 The decrease of PF and the rise of PF around the some dye concentration were explained by reorientation of emission transition dipole moments due to energy transfer from excited to unexcited monomers and by fluorescence lifetime shortening, respectively.13 During the course of energy migration, the excitation energy can be trapped by dimers and(or) higher aggregates. The slight bathochromic shift of the absorption maximum and the concentration quenching of the fluorescence are probably due to the increase in the refractive index and the contribution of associates of the dye molecules with the concentration increasing. The distribution of the site energy originates from distribution of twist angle
382 The cooling of the films from 293 K to 90 K leads to the considerable increase of the luminescence intensity. The typical decay kinetics of the DF and phosphorescence for the LB films of the dye III are shown in Fig. 4a and 4b, respectively. The kinetics of the delayed luminescence decay depends Table 2. Variation of the transition energies ET, oscillator strengths / (by using PPP method) and ground -state energy AES0 (by using MM2 method) of the dye I molecule as a function of the twist angle
±_ 1.25 1.26 1.25 1.30 1.38 1.48 1.61 1.76 1.88 1.92
Er, eV 2.56 2.60 2.63 2.68 2.75 2.84 2.92 3.01 3.03 3.05
AE,„, eV 245.1 65.4 9.36 2.25 0.19 0.01 0.22 0.48 0.68 0.77
a
Fig.3. Fluorescence spectra of dye II in LB films at different temperatures.
on concentration of the luminophore. All the kinetic curves are characterized by nonexponential fast component at the initial part of decay and exponential decay in longer times (t > 0.5 ms). The fast component is well approximated by the power function (IDF~ f ")• The values of the extent of power function n and the values koF and kpn obtained from the exponential part of the kinetics are presented in Table 3.
Table 3. The calculated values of parameters of the DF and phosphorescence decay kinetics for the LB films with various concentration (C) of the dye III at T=90K
c, mol% 0.99 1.96 9.10 50.00
"DF 0.54 0.58 0.84 0.87
I~ f" 1 nPH 0.40 0.49 0.80 0.82
AxlO"3 kDp I 0.33 0.32 0.36 0.61
c'1 kpH 0.23 0.35 0.40 0.68
1,2
Fig.4. The decay kinetics of (a) the DF and (b) phosphorescence at T=90 K with the dye III concentration in the LB films: (1, 1') 0.99 mol%) and (2, 2') 50 mol%. On the insert the curves(3,4), calculated by model'6 and model", respectively, are shown. Our experimental results suggest that at T=90K the triplet-triplet annihilation gives the main contribution to the initial part, and the monomolecular channel (T\—> S\ -> So) of the triplet states relaxation can define a view of the decay kinetics curves of the dye III LB films on long-range times.The triplet-triplet annihilation (TTA) in solid solutions of the dyes such as eosin has been studies intensively, both theoretically and experimentally.16"19 The observed nonexponential DF decay kinetics of erythrosin is explained by a time dependence of the constant rate of TTA. • Kucherenko et al. 16 ' 17 have offered static model of TTA in terms of three-partial correlation in a system of T-centers. In contrast to this model for exchange interactions, the multipolar mechanism of DF was considered by Gulis et al. 18 ' 19 The opportunity of such mechanism existence is on the basis of high probability of the inter system crossing T„ ->• S„. The energy transfer from one triplet molecule to another leads to the population of the T„ states. This approach has provided an accurate theoretical description of experiments on the frozen solutions of erythrosin.
383 The obtained DF kinetics of the dye III in the LB films were analyzed according to above described models of TTA. From insert of Fig.4 it is seen that the initial part of the DF kinetics of eosin molecules in the LB films at low luminophore concentration was good described by Gulis's approach. At high dye concentration the decay kinetics is in a better agreement with theoretical curve obtained according to the model of TTA in terms of the exchange interactions. Such behavior of the experimental data can be explained if both mechanisms of TTA, with account to exchange and multipolar interactions, are supposed to take place in the LB films of the dye III. For low concentrations of the dye molecules in the monolayer, when the luminophore molecules are divided by many molecules of a fatty acid, it is difficult to expect a considerable amount of triplet pairs with distance between reagents necessary for an exchange interaction (R ~ 10 A). Therefore, a multipolar mechanism gives the main contribution to the observed DF kinetics. Represented on the insert of fig. 4 theoretical kinetics (the curve 4) was obtained according to model of Kucherenko et al.16,17 at the distance between reagents R = 4 A. This value, which it is enough for an exchange interaction, was estimated from calculations by using the MM2 method if the phenyl ring is supposed to be in a plane of the pyronine (see Fig.l). It is achieved at a most density packing of molecules in a monolayer with a high dye concentration. 4.Conclusion On the basis of the MM2 and the PPP methods the relationship between the mechanism of excitation energy relaxation and the distribution of the xanthene dyes molecules in the LB films was demonstrated. The obtained information shows that the main contribution in fluorescence is caused by monomer with various orientation of the phenyl ring relative to the xanthene plane. The increasing Stokes shift between maxima of the absorption and the fluorescence with increasing dye concentration can be explained by the migration of excitation energy between monomers and the energy trapping by molecular aggregates. It was found that an annihilation of the triplet molecules of eosin in the LB films occurs both on exchange and multipolar mechanisms of TTA. References [1]. M. Van der Auweraer, B. Verschuere, F.C. De Schryver, Langmuir.4 (1988) 583. [2]. N. Tamai N, T. Yamazaki, I. Yamazaki, Thin Solid Films. 179 (1989) 451. [3]. N. Tamai, T. Yamazaki, I. Yamazaki, Can. J.Phys. 68 (1990) 1013. [4]. P. Ballet, M. Van der Auweraer, F. C. De Schryver, H. Lemmetyinen, E. Vuorimaa, J.Phys. Chem. 100(1996)13701. [5]. T-H.Tran-Thi, S.Palacin, B.Uergeot, Chem. Phys. Lett. 157 (1989) 92. [6]. N.Kh.Ibrayev, V.A.Latonin, In Abstr. Of the ICL'99, Osaka, Japan, Aug. 23-27 (1999), p.277. [7], N.Kh.Ibraev, D.Zh.Satybaldina, V.I.Alekseeva, E.A.Lukjanetz, L.E.Marinina, and L.P.Savvina, Rus.J. of Phys.Chem.73 (1999) 2217. [8]. N.Kh.Ibraev, D.Zh.Satybaldina, N.K.Kupriyanov, V.I.Alekseeva, L.E.Marinina and L.P.Savvina, Optics and Spectr., 86 (1999) 438. [9]. N.Kh.Ibraev, V.A.Latonin, Phys.Solid State. 41/4 (1999) 664. [10]. U.Burkert, N.L.Allinger, Molecular mechanics, Amer. chem. society, Washington, D.C. 1982. [11]. V.I.Minkin, B.Ya.Simkin, R.M.Minyaev, Theory of Molecules Structure, Vysshaya Shkola, Moscow, 1979. [12]. V.M.Komarov, Ph.D.Thesis, Moscow state Univ., Moscow, 1978. [13]. F.Ammer, A.Penzkofer, P.Weidner, Chem.Phys. 192 (1995) 325. [14]. A.S.Davydov, Theory of Molecular Excitons, Nauka, Moscow,1968. [15]. E.G.McRae, M.Kasha, J.Chem.Phys., 28 (1958) 721. [16]. M.G. Kucherenko, M.P. Melnik, J. of Applied Spectr., 53 (1990) 380. [17]. M.G. Kucherenko, Nonlinear photoprocesses kinetics in condensed molecular systems, Orenburg State Univ., Orenburg, Russia, 1997 [18]. I.M.Guhs, E.A.Ermiiov, C.A. Saharuk, J. of Applied Spectr, 64 (1997) 342. [19]. E.A.Ermiiov, O.L.Markovskyi, I.M.Gulis, J. of Applied Spectr, 64 (1997) 629.
OPTICAL PROPERTIES OF ANATASE Ti0 2 UNDER THE HIGH PRESSURE TAKAO SEKTXA, SfflNSUKE OHTA, SUSUMU KURITA Department of Physics, Yokohama National University, 79-5 Tbkiwadai, Hodogaya, Yokohama 240-8501 JAPAN Optical absorption, luminescence and Raman spectra were measured for anatase TiOz under high pressures. The pressure dependence of Raman frequencies is determined. The absorption edge of anatase shifts to higher energy side with increasing pressure and the edge jumps abruptly to lower energy side on the phase transition. A broad luminescence band of anatase shifts also to higher energy side with increasing pressure. These experimental results reveal that the pressure-induced phase transition from anatase to high-pressure phase arises in the range of 4.04.6 GPa.
1. Introduction Transition-metal oxides have attracted much attention in recent years due to their various electrical and optical properties, which depend on crystal structures, the number of tf-electrons of the metal, oxygen defects and doped impurities. Titanium dioxide has worth for study of such properties because it occurs three crystalline modifications, rutile, anatase and brookite, and may be able to control the number of rf-electrons by doping. Rutile, the most stable phase, has been investigated extensively because its single crystal can be synthesized easily and be commercially available. On the other hand, anatase, low temperature phase, has been less studied than rutile for lack of synthetic single crystals large enough to measure physical properties. Recently, we came to synthesize anatase single crystals by chemical vapor transport method 1 2. Some investigations were carried out for anatase using the synthetic single crystals under atmospheric pressure: Polarized reflection spectra were measured in the energy range of 2-25 eV in order to estimate the electronic state of anatase 1, 3. Optical absorption measurement showed that the low energy tail of the absorption edge depends exponentially on the photon energy. Tang at el} were analyzed the temperature dependence of the tail using Urbach's rule and suggested that a exciton will be relaxed to self-trapped state. While, the high pressure, which can introduce the distortion into the crystal lattice, is one of the powerful techniques for studying exciton-lattice interaction. Self-trapped state has a close relation with lattice distortion. The aim of this study is to investigate optical properties of anatase under the high pressure. 2. Experimental The high pressure was obtained by a diamond anvil cell (DAC). We used a pair of synthetic type-IIa diamond anvils in order to transmit ultra-violet light. The synthetic anatase single crystal plate of about 100x100x30 |xm3 in size was introduced in the sample chamber of a preindented stainless-steel gasket with a 4:1 mixture of methanol and ethanol as pressure medium. The pressure was determined by the rubyfluorescence method 5 . Raman spectra were measured by the excitation of 514.5 nm line of an Ar+ laser. The measurement of absorption spectra near the absorption edge was carried out by double-beam method. A monochromatic light beam was separated into two beams. One of them passed through the DAC and the other was used as a reference. 384
385 A stainless-steel foil of 50 um thickness with a hole of 50 um<j> was employed as a mask in order to prevent the light beam from passing outside of the sample. Luminescence was measured by 0.46 m grating monochromator with a CCD detector. The sample was optically excited by third harmonic generation of Nd:YAG laser. The emission from the ruby was so strong that the pressure was determined by the frequency shifts of Raman bands. All measurement was carried out at room temperature. 3. Results and Discussion Pressure dependence of Raman spectra shown in Fig. 1(a) indicates that pressureinduced phase transition occurs at the pressure of 4.3-4.6 GPa 6 . The intensities of Raman spectra of the high-pressure (hp) phase are much smaller than that of anatase. The spectra of the hp phase have a strong resemblance to that of Ti0 2 -II 7 which has isostructure with a-Pb0 2 8 . The Raman frequencies of anatase under atmospheric pressure agree with those in previous studies 9, 10. Figure 1(b) shows pressure dependence of the Raman frequencies. The bands vlt v2+v3, v4 and v6, shift to higher frequencies with increase in the pressure at rates of 4.1, 3.0, 3.1 and 3.2 cm'VGPa, respectively, while the band v6 has negative pressure-dependence at a rate of -0.8 cm'VGPa. When a single crystal with (011) face was used for absorption measurement, its transparency was lost on the phase transition. A single crystal with (001) face, however, changed to the hp phase keeping its transparency. Figure 2(a) shows absorption spectra of the crystal with (001) face at several pressures. The shape of the edge of anatase is almost independent of the pressure as far as our measurement. The absorption band edge shifts to higher energy side with increasing pressure. The spectrum at 4.2 GPa shows an abrupt jump of the edge to lower energy side. This suggests that the i i A quenched A A J \ j N ^ _ t o 0. IGPa
1^
i
x, r
AAJ V^AA^^ 6.7GPa *Aj\^^-^
4.6GPa
lxl/4
„A^J^_A *-3GP« _J\^^_Ai£^Pa_
lxl/4
L h
_ ^ \ _ _A_ - A - 2.3GPa
lV6xl/4
Ji. V2£> A400
600
a2GPa 1.0
2.0
3.0
Raman Shift (cm ) Pressure (GPa) Fig. 1 (a) Raman spectra measured at several pressures, (b) Pressure dependence of Raman bands of anatase. The different symbol refers to different runs.
386
(a)
3.40
4.2GPa5.0GPa-
® a
200
" w*^;- • 'ZlS^^'"'''
.a
<
rrrrTT 3.0
1 1 1 1 1
• • •
•
h ill •yh tf
_J* 1 1 1 1 1
a
3.32
H
ntfO.OlGPa f— 3.0GPa 3.9GPa
3.1 3.2 3.3 Photon Energy (eV)
ooo o
• • • .
g A a & 3.28 o
A
* * * * *
J=
a
PL,
3.24
i i | i i i . |_
O
P° °
:
5.8GPa
-
i | i i i i | i i i i | i
^(b)
• ••
:
'
: -
2.0 3.0 4.0 5.0 Pressure (GPa) Fig. 2 (a) Absorption spectra under several pressures. The absorption coefficients of anatase and the hp phase are shown by the solid and broken lines, respectively, (b) Pressure dependence of photon energies correspond to absorption coefficients, a = 300 and 600 cm'1, which are represented by solid and open symbols, respectively. The symbols, circles, triangles and squares, indicate different experimental configurations, (011)&EXa, (011)&E//a, and (001) measurements, respectively. 0.0
1.0
absorption edge of the hp phase lies lower energy side than that of anatase and the jump is due to the p h a s e transition. The shifts are estimated by the photon energies which give absorption coefficients, a = 300 and 600 cm"1, as shown in Fig. 2(b). The absorption edge i s due to the electronic transition from the valence b a n d to conduction one, which are composed mainly of 0 ( 2 p ) and Ti(3d) orbitals, respectively 1 . The pressure dependence of the absorption coefficient, Fig. 2(b), clearly indicates that the p h a s e transition starts at 4.0 GPa. This is inconsistent with the result given by Raman spectra. In the pressure range of 4.0-4.6 GPa, the hp phase m u s t coexist with anatase. Absorption spectrum near the edge is determined by a p h a s e with lower energy gap even though its portion i s very small. On the other hand, R a m a n spectrum depends on the ratio of their volumes. This difference may causes the inconsistent values of the transition pressure.
6GPa 9GPa 2.8GPa 1.2GPa 0.40GPa 2.0 2.5 3.0 3.5 1.5 2.0 2.5 3.0 Photon Energy (eV) Photon Energy (eV) Fig. 3 (a) and (b) Luminescence spectra of anatase and the hp phase under several pressures, respectively. Their intensities are normalized by the maximum. The broken line is drawn for a guide for the eyes.
387 Figure 3 shows luminescence spectra of anatase and the hp phase at several pressures. In Fig. 3(a), a broad luminescence is observed at around 2.3-2.4 eV with a large Stokes shift from the absorption edge, which is similar to the case of atmospheric pressure at 77 K11. The band becomes slightly broad and the top of the band shows blue-shift with increasing pressure. Since an excitonic state of anatase will be relaxed to self-trapped state 4 , the blue-shift of the luminescence suggests the expansion of the energy separation between the two states and it has good correlation with the shift of the absorption edge. In the spectrum at 4.6 GPa, the luminescence of only anatase is observed because that of the hp phase is so weak even if the hp phase coexists. When the pressure reaches at 4.7 GPa, the intensity of the luminescence becomes very weak and so the luminescence from the diamond window is not negligible. The spectral feature changes largely, as shown in Fig. 3(b). New emission band observed at about 1.5 eV is intrinsic and the band shifts to higher energy side with the pressure. On the other hand, the broad band observed in the range of 2.0-3.0 eV which is difficult to separate from that of the diamond, seems to shift to lower energy side. The large difference in the luminescence spectra between anatase and the hp phase remains to investigate. 4. Conclusions The pressure-induced phase transition from anatase to the hp phase arises in the range of 4.0-4.6 GPa. Pressure dependence of Raman active bands of anatase is determined. The shape of the absorption edge of anatase is independent of the pressure. The edge shows a blue-shift with increasing pressure and sudden red-shift is observed on the phase transition. The luminescence spectrum of anatase is largely different from that of the hp phase. The broad emission band of anatase observed at around 2.3-2.4 eV shifts to higher energy side with increase in the pressure. The hp phase has a weak emission band at about 1.5 eV. Acknowledgement The authors wish to thank Prof. M. Kobayashi of Osaka University for providing experimental advice. This work was supported in part by Grant-in-Aid for Scientific Research (No. 10640302) of Ministry of Education, Science and Culture. References 1. N. Hosaka, T. Sekiya, C. Satoko, S. Kurita, J. Phys. Soc. Jpn. 66 (1997) 877. 2. T. Sekiya, K. Ichimura, M. Igarashi, S. Kurita, J. Phys. Chem. Solids 61 (2000) 1237. 3. N. Hosaka, T. Sekiya, M. Fujisawa, C. Satoko, S. Kurita, J. Elect. Spectrosc. Rel. Phenom.78 (1996) 75. 4. H. Tang, F. Levy, H. Berger, P. E. Schmid, Phys. Rev. B52 (1995) 7771. 5. H. K. Mao, P. M. BeU, J. W. Shaner, D. J. Steinberg, J. Appl. Phys. 49 (1978) 3276. 6. T. Sekiya, S. Ohta, S. Kurita, J. Phys. Chem. Solids, submitted. 7. M. Nicol, M. Y. Fong, J. Chem. Phys. 54 (1971) 3167. 8. P. Y. Simons, F. Dachille, Acta CrystaUogr. 23 (1967) 334. 9. I. R. Beattie, T. R. Glison, Proc. Royal Soc. A307 (1967) 407. 10. T. Ohsaka, F. Izumi, Y. Fujiki, J. Raman Spectrosc. 7 (1978) 321. 11. T. Sekiya, S. Kamei, S. Kurita, J. Lumin. 87-89 (2000) 1140.
SUCCESSIVE STRUCTURAL CHANGES AND THEIR DYNAMICS IN MULTI-STEPWISED POTENTIAL-CROSSING SYSTEMS VIA MULTI-PHOTOEXCITATIONS
Masato Shin'i and Masato Suzuki Department of Physics, Graduate School of Science, Osaka City University Sumiyoshi-ku, Osaka, 558-8585, Japan We investigate the dynamical nature in multi-stepwised potential-crossing systems which are proposed as an elementary process of the structural phase transition in the strongly coupled electron-phonon systems, in order to clarify the effects of multi-photoexcitations and lattice relaxations on the successive structural changes in this system. We calculate the time-developments of the density operator of this system both for the diabatic and adiabatic cases using an unified model Hamiltonian. It is concluded from calculated results that in the both cases the system develops from the lowest-energy potential state to the higher ones by the effects of the multi-photoexcitation together with the lattice relaxation. In the diabatic case, the photoexcitation is essential for the successive structural changes, because the structural change is not expected only by the weak electronic interaction between potentials. In the adiabatic case, on the other hand, the system changes from the lowest to the higher potential states going up through the adiabatic potential surface of the ground state with the help of the multi-photoexcitations. Keywords: photoinduced structural changes, dynamics, multi-stepwised potential-crossing systems 1. Introduction In recently years, the problems related with the photoinduced structural phase transition in low-dimensional systems have been studied very extensively, from both theoretical and experimental points of view. 1 - 5 In general, the lattice relaxation of a single exciton will terminate up to create the microscopic relaxed excited domain in real materials. So, it is difficult to proceed with the photoinduced phase transition only by a single photon. This means that multi-photons are needed to achieve macroscopic structural changes or phase transitions. We have already calculated the adiabatic potential energy surfaces relevant to the nonlinear lattice relaxation of excitons in quasi-one-dimensional charge density wave (CDW) system, using the one-dimensional extended Peierls-Hubbard model. 6 From the analysis of the obtained results, the relaxation process can be divided into three stages; nucleation, condensation, and growth ones. In the nucleation stage, the exciton created by a photon relaxes down to the microscopic relaxed excited state through the electron-phonon interaction, which is expected to be nucleus of the following stages. In the condensation stage, the microscopic relaxed excited states which have been already photogenerated in the different sites are condensed through the attractive interaction between them, and finally the size of the condensed domain increases nonlinearly. When the relaxed domain is excited again by the subsequent photons, the further lattice relaxation processes will occur in it. This process leads to the novel structural changes step by step in consequence of the successive photoexcitation followed by the lattice relaxation, which is nothing but the growth stage. In Fig. 1(a) we show the conceptual diagram of the nonlinear lattice relaxation of the excitons in each stage. 6 Especially, in the growth stage, according to the calculated adiabatic potential energy surfaces, it is confirmed that the potential energies of the ground and the lowest two-electron excited state show a diabatic crossing during the lattice relaxation as shown in Fig. 1(a). This means that the lowest two-electron excited state before the lattice relaxation directly connects with the relaxed ground state whose region is extended as compared with the original ground state. Therefore, a multi-stepwised potentialcrossing (MSPC) system, as seen in Fig. 1(b), is proposed as an elementary process which can lead to successive structural changes by the multi-photoexcitations. In present study, we investigate the dynamics in the successive structural changes calculating the time-development of the density operator of the MSPC system, so as to clarify the
388
389
Fig. 1. (a) Conceptual diagram of the nonlinear lattice relaxation processes of the exciton in each stage. Point 0 is the Franck-Condon state, (b) Potential energy of the MSPC systems composed of four harmonic potentials.
structural changes via multi-photoexcitations in this system. 2. M o d e l H a m i l t o n i a n a n d calculation m e t h o d s In order to clarify the dynamics in the MSPC systems induced by the multi-photoexcitations, we use the following model Hamiltonian ( = H) with hut = 1 H
=
H0 + V(t) + HR + VR,
(1)
Ho = E { ( ^ + ^ ) + e i } o t a + E ( - T v a J a r + H . c . ) , L
i
(2)
i>v
V(t) = E(t)(e-int + eint) £(«*,,/.+ *,,),
(3)
¥1'
VR =
YK*kbRkb}+Kc),
(4)
l,k
where HQ is the Hamiltonian of the system, a] denotes the creation operator of an electron which is in the /th potential, and £; is its energy. b\ means the creation operator of a phonon in the /th potential. Tip is the resonance transfer energy of an electron between /th electronic state and /'th one. /' means the nearest neighbor potential of /. V(t) is the time-dependent interaction between an electron and a photon, wherein the photon is approximated by the classical dipole electric field. E(t) is the amplitude of its electric field, fi a photon energy, and dif a dipole moment of an electron between /th electronic state and /'th one. HR is the Hamiltonian of the reservoir, and VR is an interaction term between system and reservoir. 6 ^ is the creation operator of a phonon of fcth mode in the reservoir, and «;*, is the coupling constant between reservoir and system. In this study, using the Master equation with the Markoff approximation, we calculate the time-development of the density operator of the system ( = \$?(t))(\l/(t)|). |\P(i)} is the total wave function which is expressed by the superposition of the vibronic states in each potential as ^ ( t ) } = £j, m C(,m(*)|')lxL)j where |/} means an electronic wave function of the /th potential, and \x'm) is a wave function of a phonon in the /th potential which satisfies an equation &J&(|xD = ^ I x D - Citm(t) is the time-dependent coefficient with respect to the vibronic state |/}|Xm)3. R e s u l t s and discussion In numerical calculations, as shown in Fig. 1(b) we use four harmonic potentials with 300-phonon levels on each potential as the MSPC systems. In this figure, the solid line and the dashed line denote the diabatic and adiabatic potential energy curves, respectively. The excitation light is assumed to be an ideal white pulse. TltV is set to be 0.5 for the diabatic case
390
0
1
2
3 4 Time /(2jt/w)
5
0
1
2 3 Time /(2JI/O>)
4
5
Fig. 2. The time-development of the occupation probabilities in each electronic state in the diabatic case of TitV = 0.5 as the function of time. The system is photoexcited by white pulse at the time (a) t = 0, and (b) t = 0, 1.5, 3.0, and 4.5.
and 5.0 for the adiabatic one. At first, we investigate the case where the coupling between the system and the reservoir can be neglected before discussing the effects of the damping. In the case of Ttp = 0.5, in Fig. 2(a) we show the time-development of the occupation probabilities in each electronic state, that is, the diagonal elements of the density operator. In this figure, the system is photoexcited from |l)|xo) t o |2) by the white pulse only at time t/(2n/uj) = 0 with 90% excitation ratio. In this case, because the interaction between potentials is very weak, the time-development of the main component of the excited state is restricted only within the diabatic potential |2), and the excited component in |2) slightly transfers to the other potentials through the weak Tip. As a result of this transition, the probability of the state |4) gradually increases as increasing the time, as shown in Fig. 2(a). Next, let us consider the effects of the multi-photoexcitation in this case. In Fig. 2(b) we show the timedevelopment of the occupation probabilities of each electronic state, where the system is excited four times at t/(2n/ui) — 0, 1.5, 3.0, and 4.5. From this figure we can see the effect of the multiphotoexcitation on the time-development of the probabilities as follows. When t/(2ir/u)) = 1.5, the excited wave packet which is photogenerated in |2) by the first pulse at t/(2ir/Lo) = 0 is propagating in the vicinity of point A of Fig. 1(b) through the diabatic potential curve. In this situation, the excited wave packet is deexcited from point A in |2) to B in |3), which is induced by the second pulse at t/(2n/uj) = 1.5. Because its deexcited wave packet has almost no kinetic energy, it stays in point B until the third photoexcitation at t/{2n/u) = 3.0. At i/(2-7r/aj) = 3.0, the wave packet in the vicinity of point B is excited again by the third photon both to the |2) and |4) states. Repeating the excitation and the deexcitation on the diabatic potential surfaces by the successive photoexcitation, the occupation probabilities in the system change from |1) to |4) through the effects of the multi-photoexcitation. It is concluded from these results that in the diabatic case the photons are needed to achieve the successive structural changes because the transition at the potential crossing region via Tip is not expected in this case. Hence, the multi-photon is indispensable for successive structural changes in this case. Let us see the adiabatic case of Tip = 5.0. In this case, Tip is so strong that the potential at the vicinity of the crossing points separate into the adiabatic ground and excited states. Therefore, the adiabatic picture is suitable to investigate the dynamical nature of this system. The adiabatic potential is shown by the dashed line in Fig. 1(b). In the case where the system is photoexcited only at t/(2n/w) = 0, the time-development of the occupation probabilities in each state are seen in Fig. 3(a). From this figure, we can see that the probabilities in |1) and |2) oscillate each other. This means that the excited wave packet which is photogenerated from |l)|Xo) to |2) at t/(2ir/u>) = 0 mainly moves on the adiabatic potential curves of the excited state that is originated from the diabatic potentials |1) and |2). During the oscillation, the small component has a chance to leak from the excited state to the ground one of the diabatic potential surface through the nonradiative transition, and the leaked component can propagate to the state |4) through the adiabatic potential of the ground state, as shown in Fig. 3(a). This is an essential nature of the structural changes in the adiabatic case. Next, let us consider the
391
Fig.3. The time-development of the occupation probabilities in each electronic state in the diabatic case of Tip = 5.0 as the function of time. The system is photoexcited by white pulse at the time (a) t = 0, and (b) t = 0, 1.0, 2.0, 3.0, and 4.0. multi-photoexcitation case. The time-development of the occupation probabilities in each state are shown in Fig. 3(b), where the system is excited by the white pulse at t/(2v/u}) = 0, 1.0, 2.0, 3.0, and 4.0. It can be seen from this figure that the oscillation on the adiabatic potential of the excited state composed of |1) and |2) is broken down by the second excitation at t/(2n/ui) = 1.0, because of the deexcitation from the excited state to the ground state which is induced by the second pulse. The deexcited component appeared on the ground state can propagate to the state |4) through the adiabatic potential surface of the ground state, which is essentially the same as the single excitation case. When the system is excited again by the third pulse at t/(2ir/u}) = 2.0, the wave packet on the adiabatic ground state is lifted up both to the state 12) and |3), and then the occupation probabilities become to oscillate between |2) and |3), as shown in Fig. 3(b). This mean that the excited component is restricted within the adiabatic potential curves of the excited state composed of |2) and |3). The process of photoexcitation and deexcitation occurring between the ground state and excited states of the adiabatic curves is repeated by the successive photoexcitation, and the probability in |4) increase step by step as seen in Fig. 3(b). That is, the deexcited components from the excited states can propagate and go up through the adiabatic potential of the ground state by using the excess energy supplied by the multi-photoexcitation. This is the dynamical picture of the successive structural changes induced by the multi-photoexcitation in the adiabatic case. From the above results, it is concluded that the occupation probability goes up from the lowest electric state to the higher ones by the effect of the multi-photoexcitation and lattice relaxation both in the diabatic and adiabatic cases. Thus, we have clarified the dynamical natures in the both cases from the unified theoretical point of view. Calculations for the effect of dumping on this system is in progress by using the equation (4) and the results will be considered in detail in the future sutudy. References 1. 2. 3. 4.
M. Suzuki and K. Nasu, Phys. Rev. B 4 5 , 1605 (1992). S. Koshihara, Y. Tokura, K. Takeda and T. Koda, Phys. Rev. Lett. 6 8 , 1148 (1992). Y. Tokura and S. Koshihara, Phys. Rev. Lett. 6 3 , 2405 (1989). A. M. Rao, P. Z. Zhou, K. -A. Wang, G. T. Hagger, J. M. Holden, Y. Wang, W. -T. See, X. X. Bi, P. C. Eklund, D. S. Cornett, M. A. Duncan, and I. J. Amster, Science 2 5 9 , 955 (1993). 5. M. Suzuki, T. Iida and K. Nasu, Phys. Rev. B 6 1 , 2188 (2000). 6. M. Shin'i and M. Suzuki, preparing for publication.
SPATIAL BEHAVIOR OF EXCITON-POLARITON MASSES IN A LAYERED CRYSTAL Bil 3 Y. SHIRASAKA, H. MINO, T. KAWAT, I. AKAI, and T. KARASAWA Department of Physics, Graduate School of Science, Osaka City University, Sumiyoshi-ku, Osaka 558-8585, Japan b Department of Environmental Science, Osaka Women's University, Daisen-cho, Sakai 590-0035, Japan Spatial behavior of the stacking fault excitons (SFE's) excited heavily in a two-dimensional space at a stacking fault interface in Bil3 has been studied. The SFE's whose center-of mass motion is confined at the interface show more efficient spatial expansion for higher excitation densities. In order to get phase information of the high-density SFE masses, the degenerate four-wave-mixing (DFWM) measurements with two laser beams including space-resolved regime were performed. It was found that the increase in the dephasing due to exciton-exciton collision is suppressed above a certain density. In a space-resolved regime, it turned out that the high-density exciton mass excited at one laser spot propagates coherently to the other laser-spot site and induces nonlinear polarization resulting in momentum-selective emission of the DFWM lights. These results suggest the possibility of a coherent collective motion of the SFE masses in a new condensate of the high-density exciton-polaritons. Keywords; Bil3; High-density exciton-polariton masses; Degenerate four-wave-mixing
1.
Introduction
High-density exciton creation brings about new phases from the exciton phase such as biexcitons, electron-hole plasma, and electron-hole liquid, which have been examined in detail by detecting spectral changes and nonlinear optical response. When the exciton has a large binding energy, high-density excitons themselves have attracted much attention as a weakly interacting boson system in which Bose-Einstein condensation (BEC) is expected to occur. Macroscopic quantum phenomena of the new condensate such as superfluidity are an evidence for the BEC. For the investigation of the macroscopic quantum phenomena in excitons at high density, observing the spatial behavior of the high-density exciton masses is decidedly valuable. Recent report of the ballistic transport of high-density excitons in Cu 2 0 with a critical values of the density and temperature suggests the exciton superfluidity.1 This result has also been explained as a phononwind driven exciton motion.2 In order to clarify whether the exciton mass motion is coherent or not, it is necessary to obtain phase information instead of that concerning the amplitude. Contrary to the case in Cu 2 0, the exciton systems with directly allowed transitions are coupled strongly with photons resulting in the formation of polariton states to be good quantum states. The spatial behavior of the exciton-polaritons at high density has not been examined sufficiently. This is a new theme in the photo-excited state physics. An exciton state localized at a stacking fault interface in a layered crystal Bil3, called the stacking fault exciton (SFE) state, has a large binding energy and is stable even at high density. It's center-of-motion is confined in the quasi-twodimensional stacking fault interface. Figures 1(a) and (b) show absorption and luminescence spectra in Bil 3 in the lower photon energy region below the bulk indirect exciton edge. A very sharp transition line series of the SFE denoted by Q, R, S, and T appears; resonant luminescence lines have zero Stokes-shifts. The quantum efficiency of the lowest T luminescence shows almost unity through efficient cascade relaxation via R, and S states.3 These features show that this system is suitable for investigation of dynamical processes of the excitons at high density. In a previous paper 4 , we reported that heavier excitation by a nanosecond laser light brings about an expansion of exciton masses observing peak shifts due to mutual interaction in the spaceand time-resolved pump-probe absorption and luminescence measurements. For the excitation of a picosecond light pulse, the space-resolved measurements provided the results that the excitons propagate with a group velocity ~ 6 x 10s cm/s of an exciton-polariton mode.5 For the excitation
392
393 (a)
P
lescence Intens
1 ii 1J E1.S
T
Bil 3
4.2 K
.-JLJ,IJAA?J_9° . . . . 1.99
2.00
Photon Energy (ev)
Fig. 1 (a) Absorption spectrum of Bil3 at 4.2 K; R, S, and T, are the stacking fault excitons (SFE's). Luminescence spectrum for band-to-band excitation; R, S, and T show resonant luminescence lines of the SFE's
(b)
of the intense picosecond laser pulse, the expansion of the luminescence patterns on the sample surface was also observed.6 The temporal profiles of the T luminescence at the points with various distances from the laser spot give not only the rapid propagation of the wave front with the group velocity but an increase in a parameter value characterizing the coherency of the exciton masses with increasing excitation density. Furthermore, nonlinear optical response of the degenerate fourwave-mixing (DFWM) measurements in a space-resolved regime shows that the propagating exciton masses at high density induces third order nonlinear polarization generating the four-wavemixing light.7 In this report, we present the results of the DFWM measurements in detail including spaceresolved detection of the DFWM signals with spatially isolated two laser beams having a picosecond time duration. The obtained results provide new information on the quantum process of the third order nonlinear optical response. 2.
Experimental
Good quality single crystals having flat and parallel surfaces were selected. The samples were immersed in a liquid helium bath and all optical measurements were performed at 2 K. For the measurements of the DFWM signals, a dye laser pumped by a mode-locked Nd:YAG laser was used as a light source; the time duration being 3 ps, the repetition rate being 4 MHz and the maximum peak power being 2.5 kW. The laser beam was divided horizontally into two by a beam splitter and the correlation time between the two pulses was controlled through optical delay paths. In the usual spatially-coincident regime, the DFWM light emitted in the momentum-conserving direction in the horizontal plane was detected. In order to improve the detecting sensitivity, the two exciting pair lens
Screen - Selfock Lens
Crystal
Fig. 2 Schematic illustration of (a) DFWM emission by spatially separated two-laser beam excitation in the vertical direction and (b) optical arrangement for the DFWM light detection
394 laser beams were modulated by a double light-chopper and the difference-frequency component was detected with a lock-in amplifier. In the space-resolved regime, each exciting light was focused independently on the sample surface to -50 urn in diameter by a finely adjustable pair-lens system by which focusing points can be located at desirable points.7 In order to avoid overlapping of the two laser beams in the depth direction of the crystal, the separation of the two laser spots was done in the vertical direction as shown in Fig. 2(a). As a result, the DFWM light emitted plane was slightly inclined because of the momentum conservation. The DFWM light from the sample surface were taken in through an aperture, enlarged with a camera lens and projected as a image on a screen with a pinhole. The spatially resolved light in the image was picked up through a SELFOC-lens-terminated glass fiber attached on the pinhole as shown in Fig. 2(b).
3.
Results and Discussion
The increase in the scattering rate due to mutual collision of the excitons at high density can be obtained from the decrease in the dephasing time. Figure 3(a) shows excitation-intensity dependence of the DFWM signals as a function of the correlation time between the two exciting laser pulses under the condition of usual spatially-coincident geometry. The exciting light wavelength was tuned to the resonant energy of T. The decay of the DFWM intensity becomes faster with increasing excitation intensity. The dephasing time T2 was estimated for each excitation intensity, by assuming the SFE system to be homogeneously broadened. The dephasing time is plotted in Fig. 3(b) as a function of excitation intensity. The value of T2 decreases with increasing excitation intensity, but the reduction rate becomes small for heavier excitation intensity. The total dephasing rate rT0TAL = 1 / T2 in this system can be written as -'TOTAL
=
•'RAD
+
'NONRAD
+
-'PHONONV-')
+
* EX-EX W
where 7 ^ and /^ONRAD lae the radiative and non-radiative decay rates, respectively, and rmotlm(T) is the scattering rate with phonons and rEX_EX(I) is the exciton-exciton scattering rate. The first two terms are negligibly small compared with the other terms.8 From the measurements of the temperature dependence of the dephasing time, it was found that dominant phonon scattering process is governed by acoustic phonons and the value of rPH!Jti0N(T = 2 K) was estimated to be 0.025 (psec"1).8 The rest component 7^X-EX(0 due to exciton-exciton scattering is simply
-10
-5
0 5 10 15 Delay Time (psec)
20
25
10* 105 106 107, Excitation Intensity ( W / c m )
Fig. 3. (a) Excitation-intensity dependence of the DFWM signals as a function of the correlation time between the two exciting laser pulses, (b) Dephasing time as a function of the excitation intensity, (c) Scattering rate due to excitonexciton collision vs the excitation intensity
395 considered to be in proportion to the exciton density. Figure 3(c) shows the obtained scattering rate rEX.EX VS m e excitation intensity by subtracting the other components from ,TTOTAL in eq. (1). The rEX.EX can be fit to a linear relation with respect to the excitation intensity in the weaker excitation region and bears off to the lower side from the linear relation at a threshold intensity; the threshold is defined at the crossing of the two straight lines in Fig. 3(c). The number of SFE's is considered to be proportional to the excitation intensity since the DFWM signal intensity is proportional precisely to the cube of incident light power as expected from the third order nonlinear optical response. These results imply that nevertheless the exciting light supplies proportionally the number of SFE's, the increase in the dephasing rate due to the exciton-exciton scattering comes to be suppressed under higher density, i.e., they suggest the occurrence of a coherent collective motion of the high-density exciton-polariton masses. In order to clarify such coherent collective motion, we examined the spatial correlation of the two exciton masses created at different points detecting the DFWM signals in the space-resolved regime. Of course, the maximum DFWM intensity was obtained when the two exciting laser spots were completely on top of each other, but the DFWM signals were detectable even when the two spots were separated with distance r between the spot peaks.7 A part of the signals comes merely from the overlapping of the tail region of the two laser spots. It was found that the other component than the overlapping grows evidently under more intense excitation.7 For the excitation of two laser beams with wave vectors kx andfc,,the DFWM light was emitted in the two opposite directions of 2fc,-*2 a™1 2fc,-&, as illustrated in Fig. 2(a). Figure 4 (a) shows the spatial distribution of the DFWM light intensity for the direction of 2kr fc, on the sample surface for a higher excitation density with correlation time 0. When the distance r increases from 0, one component appears just at the overlapping region and another at one of the exciting spots (left-hand-side spot: beam £,). The former is that induced by the overlapping laser light (overlapping component) and it's intensity obeys by the cubic law for the overlapping light intensity estimated from the observed exciting laser spot profiles drawn by the dotted curves in the figure. The latter is that coming from the induced polarization by one of the exciting laser light (beam £,) and by the propagating exciton mass from the other spot; this component is called the "propagating component". It should be noted that no component appears around the other exciting spot (right-hand-side spot: beamfc,)at the symmetric position with respect to the overlapping center. On the other hand, as shown in Fig. 4(b) for the direction of 2k2-kl, the two components of the DFWM
r = 150 urn •>*«!-•••' .
0 100 Distance r (urn)
-100
0 100 Distance r (urn)
^fcynante
200
Fig. 4 Spatial distribution of the DFWM light intensity (full curve) for (a) 2*,-^ and (b) 2*2-4, directions; the dotted curves indicate intensity distribution of the exciting laser spot on the sample surface
396 pattern show symmetric changes to Fig. 4(a) with respect to the overlapping center. In this case, the "propagating component" appears only at the spot of beam fc,. This "propagating component" grows remarkably for the excitation intensity above the threshold. The propagating exciton mass must be in a coherent collective motion which brings about the third order nonlinear polarization generating the DFWM light. The quantum processes of the space-resolved DFWM phenomena can be qualitatively understood as the propagation of the off-diagonal elements of the exciton state on the basis of the doubleFeynman diagrams (DFD) shown in Fig. 5. In these diagrams, only the exciton state is considered as a excited state and the excitonic molecule is not taken into account. On the DFD in (a), the propagators between the vertices mean the time evolution of each quantum state. The propagator |g><x| marked by asterisks between -kj and kx vertices are considered to involve the spatial propagation in the stacking fault interface. Then, the exciton components above and below the asterisks are at different positions. The "propagating component" of 2£,-A2 DFWM light is generated around at the k, spot by the interaction between kx light and the exciton state |g><x| propagating from the fc, spot. The 0 correlation time must give finite time passage for the "propagating component" resulting in the asymmetric DFWM patterns with respect to the overlapping center, i.e., the k-selective generation of the DFWM light. For 2^-fc, DFWM light the DFD in Fig. 5(b) explains also the quantum process in the same manner. In conclusion, the obtained results in this work show evidently the existence of a coherently propagating collective motion of the exciton-polariton masses and suggest the possibility of a new condensate of the high-density exciton-polaritons. This work is supported by a Grant-in-Aid for Scientific Research on Priority Areas, "Photoinduced Phase Transition and Their Dynamics", from the Ministry of Education, Science, Sports and Culture of Japan. Ig>
Is)
lg)
DFWM
\
|x)
/* lg)
lg>
(a)
|g)
h
s<x|
lg)
<x|
lg)
(gl
\
(gl
|x)
(g|
W
v/ <x|
^ lg> ••-
.
(g|
DFWM
(gl
|x>
^
Is) '
(gl
DFWM
lg> lg)
^
•* (x|
|g)
••
(g|
|g)
(gl
(b)
Fig. 5 Double-Feynman diagrams describing many terms in the four-wave-mixing processes concerned (a) for the DFWM light with the k-vector 24,-i; and (b) that with 2^-4,; the bra and ket g being the ground state, x being the exciton state
References 1. A. Mysyrowicz, E. Benson, and E. Fortin: Phys.Rev.Lett. 77, 896 (1996) 2. G. A. Kopelevich, N. A, Gippius, and S. G. Tikhodeev: Solid State Commun. 99,93 (1996) 3.1. Akai, T. Karasawa, Y. Kaifu, A. Nakamura, M. Shimura, and M.Hirai: J.Lumin.42,357 (1989) 4. H. Kondo, H. Mino, I. Akai, and T. Karasawa: Phys.Rev. B58, 13835 (1998) 5. T. Kawai, S. Shimanuki, T. Karasawa, I. Akai, T. Iida, and T. Komatsu: J.Lumin. 48&49, 721 (1991) 6. H. Mino, M. Yamamoto, T. Kawai, I. Akai, T. Krasawa: J. Lumin. 87-89, 278 (2000) 7. T. Karasawa, H. Mino, M. Yamamoto: J. Lumin. 87-89,174 (2000) 8. M. Ichida, T. Karasawa, and T. Komatsu: Phys.Rev. B47, 1474 (1993)
U L T R A F A S T L A T T I C E R E L A X A T I O N D Y N A M I C S OF E X C I T O N IN A QUAISI-1-D METAL-HALOGEN COMPLEX
ATSUSHI SUGITA, TAKASHI SAITO, and TAKAYOSHI KOBAYASHI Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-0033, Japan MASAHIRO YAMASHITA Department of Chemistry, Tokyo Metropolitan University, 1-1, Hachioji, Tokyo, 192-0397, Japan
A quasi-one-dimensional halogen-bridged mixed-valence metal complex is studied by timeresolved pump and probe spectroscopy with sub-5 fs time resolution. Two kinds of oscillatory signals are observed, which are attributed to the wave packet motions both in an electronic ground state and in a self-trapped exciton (STE) state. The onset of the wave packet motion is found to be delayed by about 50 fs, comparing with the ideal wave packet in the electronic excited state. The delay reflects the thermalization process in a free exciton (FE) state and a lattice relaxation process from FE to STE states. 1. Introduction One dimensional exciton system is attracting a lot of attention in the optical, electronic, and magnetic properties, because of a large exciton confinement effect1. The transfer of an electron or a hole is allowed between different atomic or molecular sites, and the wave function of the exciton is widely extended among different sites. The exciton radius is closely dependent on an electron-phonon interaction. In the case of the weak e-ph interaction, the exciton radius is infinitely large, and it is called as free exciton (FE) state. On the other hand, in the strong e-ph interaction regime, the FE state is not only one stable excited state. The exciton deforms the surrounding lattice, and it is trapped by the deformed potential. This trapped state is called as a self-trapped exciton (STE) state. In the STE state, the exciton is considered to be localized among a few sites. In the one dimensional exciton system, there is no potential barrier between the FE and STE states, and accordingly the ultrafast optical response is expected, as have been seen in 7r-conjugated polymers 2 . Quasi-one-dimensional halogen-bridged mixed-valence metal complex (HMMC) is grouped in these one-dimensional exciton system with the strong e-ph coupling. The strong e-ph coupling is proofed by the large Stokes shift of the fluorescence spectrum 3 . The higher order overtones are observed in the resonant Raman scattering spectrum, and it means that the phonon potential is approximated to be harmonic 4 . In these points, the material satisfies the ideal model of the one dimensional exciton system with the strong e-ph interaction. In the present work, the ultrafast optical response in HMMC is studied with the temporal resolution better than 5 fs. The discussion is focused on the dynamical process of the initial photo-excited state just after the photo-excitation. 2. Experimental Time-resolved reflectivity is measured by pump and probe spectroscopy. Both the pump and probe lights are optical pulses with sub-5fs pulse duration, which are generated by a pulse-front
397
398 matched non-collinearly phase-matched optical parametric amplifier 5 . The broad band spectrum extends from 1.65 to 2.25 eV. A sample is a single crystal of [Pt(en) 2 ][Pt(en) 2 I 2 ](C104) 4 (as later abbreviated as Pt-I). The polarizations of the pump and probe lights are both parallel to the b-axis of the single crystal along the MX-chain. All the experiments are done at room temperature (293 K). The peak energy of the exciton band of Pt-I is 1.38 eV, which means that the excitation photon induces a transition from the electronic ground state to higher levels in the exciton state. 3. R e s u l t s a n d Discussion 1
n -5 10
»
AAAA^^""!
5
0 (b)
10
0.15
w
15
-5
i
-
x
-
r
-
1000 2000 Delay Time (fs)
100 200 Wavenumber (cm")
3000
Figure 1: (a)Time-resolved reflectivity change at 2.00 eV(solid curve). The dashed curve is the contribution of the slowly varying component ((AR/R)siow) described by Eq. (1). (b) The oscillatory component ((AR/R)0SC). (c) The fourier spectrum of the oscillatory component ((AR/R)osc)
Fig. 1(a) shows the normalized time-resolved reflectivity (AR/R) at 2.00 eV. The signal consists of two contributions, that is, slowly varying signal (AR/R)slom and the oscillatory signal (AR/R)0SC. Among them, the slowly varying signal is reproduced with the following equation as
K)
b + (a + b) • exp -a•exp (1) V R J slow \ T\J ' \ T2) The decay and rise time constants are determined to be T\ = 1400 ± 100 fs, and r 2 = 130 ± 30 fs, respectively. The decay time T\ = 1400 fs is well correspondent with the time required for the thermalization process of the STE in Pt-Br 6 . Hence, the slowly varying signal is attributed to the optical response of the non-thermal STE. On the other hand, the oscillatory signal is expressed with the summation of the two differently damped sinusoidal functions as,
(—)
A
. e x p (_ A)
. c o s (™-eA)+B.
(
exp (-±)
-
)
•
• cos ( g
-
0B)
(2)
( " ) _ •
Fig. 1(c) is the frequency spectrum of (AR/R) which is converted from the fast fourier transformation (FFT); there are two peaks at 124 and 107 c m - 1 in the F F T spectrum, and they correspond to the two differently damped oscillations. In the resonant Raman scattering experiment, a symmetric stretching mode (I~ — P t 4 + — I - ) is observed at 123 c m - 1 , and the frequencies of the two peaks observed in the present study are close to that of this mode. These oscillatory signals are attributed to the wave packet motions related to the I - ion stretching mode.
399 Two damping time constants are evaluated to be TA = 1200 ± 100 fs and rB = 210 ± 50 fs by the least squares fitting, where the oscillatory periods TA = 270 fs and TB = 290 fs are fixed. Judging from the quantities of the damping time constants TA and r B , the damped oscillations A and B are attributed to the wave packet motions in the ground state and STE state, respectively. The time constants TA and TB are contributed by two factors, that is, the dephasing rates kA and kB of the wave packet themselves and the population relaxation rate of the STE rf 1 . They are related to be
kA+rl
\
•kB+T[\
1
(a)
£ 3
o
—
o
180 90
-
0
" -
o
-o o o
l
1 0
&
(3)
° o
o
-
• 11 • o o
*
5
•
0
• o
(b)
•
• 1
1.7
1.8
•
1
•
1.9 2 2.1 Photon Energy (eV)
• 2.2
Figure 2: (a)Probe photon energy of the depahsing rates kA (open circles) and kB (filled squares), (b) Probe photon energy of the phases 8A (open circles) and 8B (filled squares). In Fig.2, the four quantities kA, kB, 8A and 8B are plotted against the probe photon energy. As for the wave packet motion in the ground state, the phase 8A ~ —85°, and the dephasing rate kA ~ 2.0 x 10 _ 1 ps _ 1 is almost constant against the probe energy. The phase 9A is close to —90°, which indicates that the oscillation of the wave packet motion is sine-like. In the ground state, the formation of the wave packet is explained by the Inpulisve Stimulated Raman Scattering mechanism, and the oscillation of the phonon is sine-like. Our present result is consistent with this expectation. On the other hand, the line width of the I - — P t 4 + — I~ stretching mode is reported to be 10 c m - 1 , and it corresponds to the vibrational dephasing rate of 3 x 10 _1 ps" 1 4 This quantity is in good agreement with our present experimental result of kA ~ 2.0 x 10 - 1 ps 1 In the next, the wave packet motion in the STE state is discussed. As can be seen in Fig.2, the dephasing rate kB decreases as the probe energy becomes larger. The tendency reflects the vibrational relaxation process of the non-thermal STE, that is, the exciton dissipates the excess vibrational energy to the surrounding heat bath. The population decreases faster at higher vibrational levels than at lower levels in the STE potential. Therefore, the time-dependence at higher probe energy has a larger dephasing rate, and it reflects the transition from higher vibrational levels in the STE potential, and vice versa.
400 There is no significant probe energy dependence observed in the phase 6 B ~ 230°. The oscillation of the phonon is expected to be cosine-like for the wave packet motion in the excited state. Hence, the phase 6B is late for the ideal value of 180° by 50°. Two probable mechanisms are considered for the delay of the onset of the wave packet motion. Firstly, the delay is caused by the thermalization process in the FE band. In the present study, the center of the excitation probe energy of 2.0 eV is much larger than the peak energy of the exciton band at 1.38 eV. Secondly, the lattice relaxation process from FE to STE states is also probable reason. In the one-dimensional exciton system, the boundary between FE and STE states are barrierless, and they connect with each other continuously. Therefore, the coherence of the FE is expected to remain even after the lattice relaxation process to STE. Around the boundary between these two exciton states, the curvature of the phonon potential should be smaller than that in the harmonic potential, and it is expected to be almost flat (Fig.3). Hence, just after the lattice relaxation, the exciton is not accelerated by the force from the potential, and the motion of the wave packet is delayed.
I
coordinate
Figure 3: Model of the relaxation dynamics and potential of the exciton in Pt-I. The arrows 1 and 2 denote the thermalization process in FE band and the lattice relaxation from FE to STE states, respectively.
Acknowledgements This work is supported by Research for the Future (RFTF) of Japan Society for the Promotion of Science. References 1. 2. 3. 4. 5.
K.S. Song and R.T. Williams, Self-trapped Excitons (Springer-Verlag, Berlin Heidelberg New York, 1996). T. Kobayashi, Relaxations in Polymers, (World Scientific, Singapore, 1993). M. Tanaka et al., Chem. Phys. 96, 343 (1985). R.J.H. Clark et al., J. Chem. Soc. Dalton. 524 (1985). A. Shirakawa et al., Appl. Phys. Lett. 74, 2268 (1999).
6. H. Ooi, Solid State Commim.
8 6 , 729 (1993).
PHOTOINDUCED PHASE TRANSITION IN SINGLE CRYSTALS OF URETHANE-SUBSTITUTED POLYDIACETYLENES Hiroaki Tachibana 1 \ Noriko Hosaka 3 , Masayuki Osaki 1 , and Yoshinori Tokura 1,3 'Joint Research Center for Atom Technology (JRCAT), Tsukuba 305-8562, Japan National Institute of Materials and Chemical Research, Tsukuba 305-8565, Japan department of Applied Physics, University of Tokyo, Tokyo 113-8656, Japan
2
Thermochromic behaviors were investigated by measurements of reflectance spectra for urethane-substituted polydiacetylene crystal having side groups of R=(CH2)6OCONHC2H5 (PDA-6UEt). The PDA-6UEt crystal shows an irreversible thermochromic A-to-B (blue-to-red) phase transition: the absorption band at 1.88 eV due to the lowest exciton shifts to higher energy (2.15 eV) in the heating run, but the reflectance spectra remain in the B phase even when cooled down to room temperature. We have demonstrated that photoinduced phase transition (PIPT) is observed by utilizing the irreversible A-to-B phase transition. The conversion shows the presence of a threshold of the light intensity and depends on photon energy, suggesting that the PIPT is mediated by the photogenerated electron-hole pairs. 1. Introduction
Photoinduced phase transition (PIPT) has been attracting considerable attention because bistable electronic state may be utilized for realization of fast photoswitching of the electronic state. The PIPT has been found in various compounds from organic compounds such as charge transfer complex,1,2 spin transition complex,3 and nconjugated polymers4 6 to transition metal oxides.7 Among these compounds, one of the strategies to realize PIPT in 7t-conjugated polymers is to utilize a conformation coupling between the long alkyl chain of sidegroups and the polymer backbone and to produce the first-order transition system. Based on this strategy, the first reversible PIPT has been found between two spectroscopically distinct A CH3 (blue) and B (red) phase in the CH3 CH2 crystals of urethane-substituted CH3 \ CH2 N-Hpolydiacetylene having side CH 2 H 0=C, groups of R = N-H 0=C, o=c, (CH2)4OCONHC2H5 (PDA(CH2)6 O (CH2)6 I 4UEt).5 Recently, the PIPT c-c=c(CH 2 ) 6 „C-C=C-C^ from order to disorder phase of •c-cr polythiophene backbones has (CH2)6 (CH2)6 been also reported in thin films (CH 2 ) 6 Q of regioregular poly(36 eicosylthiophene) (PEIT-HT). c=0---H-N' C = 0 - - H - N , CH2 In this paper, we have —-H-N, CH2 CH 3 CH2 newly synthesized a urethaneCH3 CH3 substituted polydiacetylene having side groups of R = PDA-6UEt (CH2)6OCONHC2H5 (PDA-
Vo-
401
402
6UEt) with an inner alkyl chain length different from the PDA-4UEt. We have found that the PDA-6UEt crystal shows an irreversible thermochromic behavior from A to B phase. The PIPT was investigated by utilizing the irreversible A-to-B phase transition. 2. Experimentals A urethane-substituted diacetylene (DA-6UEt) was synthesized as described previously. The single crystal of DA-6UEt was grown in the ethylacetate solution. The polymerization was carried out in vacuum by ""Co y-radiation (60 Mrad). The degree of polymerization estimated from the weight loss after dissolving the y-irradiated crystal in chloroform was more than 99 %. A light pulse (about 5 ns in duration) from a (3-BaB204 optical parametric oscillator (OPO) pumped with the third harmonic of a Q-switched Nd:YAG laser was utilized as the light source for the single pulse shot. The change of the reflectance spectra was measured by the single-shot irradiation varying the photon density and the A • • itin • • photon energy. •ling s
3. Results and Discussion
•
( Figure 1 shows temperature dependence of reflectance spectra for the PDA-6UEt crystal. In the reflectance spectra at room temperature, the peak assigned to the lowest 'Bu exciton is observed at 1.88 eV together with its vibronic sidebands. As the temperature increases, the A-to-B phase transition occurs at 420 K, which is caused by conformational changes in inner alkyl chains from trans to gauche forms. However, the reflectance spectra remain in the B form even when cooled down to room temperature. The different thermochromic behaviors between the heating and cooling run were analyzed by measurements of the differential scanning calorimetry (DSC) thermogram.
300
350 400 Temperature / K
Energy / eV Figure 1. Temperature dependence of reflectance spectra for PDA-6UEI crystal. The inset represents the change of the reflectivity of the lowest exciton band at 1.88 eV.
403
The DSC thermogram shows T 1 1 1—! 1 1 r—T— an endothermic peak in the PDA-6UEt heating run at the 360 K corresponding temperature fore irradiation for the spectroscopic changes. ter irradiation The estimated enthalpy change (AH) is 1.56 kcal/mol. On the other hand, an exothermic peak is also observed at 401 K in the cooling run, though the spectroscopic changes do not occur at the corresponding temperature. However, the enthalpy change (AH = 0.80 kcal/mol) is nearly half of those in the heating run. The difference in the enthalpy is likely to affect the irreversible thermochromic phase transition from A to B phase. The inset of Figure 1 Energy / eV shows the change in the Figure 2. Change of reflectance spectra on photoexcitation reflectivity of the lowest of laser pulse with different light intensity for PDA-6UEt exciton peak at 1.88 eV as a crystal. function of temperature in heating and cooling runs. The irreversible thermochromic phase transition enables us to induce the A-to-B phase transition by other stimuli such as the photoexcitation as described below. The change of reflectance spectra by 2.58-eV single-shot irradiation was measured varying the light intensity, as shown in Figure 2. The sample temperature was kept at 360 K in the region of the irreversible A-to-B phase transition. When a laser pulse with the intensity higher than 23.8 mJcm2 was irradiated, the A-to-B phase transition occurs. The conversion to the B phase reaches 100 % on photoexcitation of laser pulse with 31.8 mJcm"2. This indicates that threshold exists in the A-to-B PIPT, which is a feature characteristic of the PIPT as reported in organic crystals1"3 and 7t-conjugated polymers4"6, compared with photochromic reaction in which the photoconversion increases proportional to the light intensity. A similar change of reflectance spectra is observed when laser pulse with constant intensity is irradiated varying the photon energy, as shown in Figure 3. The spectral changes is not almost discernible on photoexcitaion of laser pulse with photon energy corresponds to the lowest exciton band, which induces lattice change of the A phase. On the other hand, the A-to-B phase transition is induced on photoexcitation at higher energy has no the lowest exciton band in the reflectance spectra, which probably corresponds to the interband transition region. Similar photon energy dependence of the PIPT has been also reported in PDA-4UEt crystal45 and PEIT-HT thin film6. The A-to-
404
B PIPT is likely to be triggered not by the simple laser-heating process but by the photoexcited electron-hole pairs or their lattice-relaxed polarons, not the lowest singlet exciton.
4. Conclusion A PDA-6UEt crystal shows the irreversible thermochromic phase transition from A to B phase, which is caused by the difference in the enthalpy change in heating and cooling runs. The A-toB PIPT was observed at 2.0 3.0 360 K in the region of the E n e r g y / eV irreversible phase transition, which depends on light Figure 3. Change of reflectance spectra on photoexcitaion of laser pulse with different photon energy for PDA-6UEI intensity and photon energy, crystal. The arrow represents the position of the photon suggesting that energy. photogenerated electronhole pairs not the lowest singlet exciton are the driving process. Acknowledgments This work was supported by a Grant-In-Aid for Scientific Research from the Ministry of Education, Science and Culture, Japan and by the New Energy and Industrial Technology Development Organization (NEDO). References 1. 2. 3. 4. 5. 6. 7.
S. Koshihara, Y. Tokura, T. Mitani, G. Saito, T. Koda, Phys. Rev. B42,6853 (1990). S. Koshihra, Y. Tokura, Y. Iwasa, T. Koda, Phys. Rev. B44,431 (1991). P. Gutlich, A. Hauser, H. Spiering, Angew. Chem. Int. Ed. Engl., 33,2024 (1994). S. Koshihra, Y. Tokura, K. Takeda, T. Koda, Phys. Rev. Lett., 68, 1148 (1992). S. Koshihara, Y. Tokura, K. Takeda, T. Koda, Phys. Rev. B52,6265(1995). N. Hosaka, H. Tachibana, N. Shiga and Y. Tokura, Phys. Rev. Lett., 82, 1672 (1999). T Tanaka, K. Miyano, Y. Tomioka, Y. Tokura, Phys. Rev. Lett., 78,4257 (1997).
PHONON SCATTERING OF FRENKEL EXCITONS IN MOLECULAR MICROCRYSTALLITES EMBEDDED IN A MATRIX MASUMI TAKESHIMA Organo-Optic Research Laboratory, 48-21 Bandoujima, Kitagou, Fukui 911 -0056, Japan
Katsuyama,
Email: [email protected]. jp
K. MIZUNO Department
of Physics, Konan University, Okamoto, Kobe 658, Japan ATSUO H. MATSUI
Organo Optic Research Laboratory, Kobe 6-2-1, Seiwa-dai, Kita-ku, Kobe 651, Japan A matrix effect on the exciton'phonon coupling in microcrystallites embedded in a matrix is investigated theoretically. It is shown that a parameter a defined as the square of the ratio of the phonon bandwidth of a matrix material to that of a microcrystaUite material is a crucial one, affecting the exciton-phonon scattering. Phonons flow in the microcrystaUite or out of it for either ofa>l or<j
coupling in the microcrystaUite is influenced by phonons in the
matrix. The flowingin of phonons, which have energies higher than the maximum energy of phonons in the microcrystaUite material, is of special importance and results in the broadening of the lines constituting an optical absorption spectrum.
1. Introduction It is an experimental fact 1 that the spectral bandwidth of an excitation spectrum of luminescence changes with the microcrystaUite size. In small microcrystaUites broad band spectra are obtained, although each transition is supposed to give a sharp line. This is the case for microcrystaUites with sizes below the critical one for which the one-phonon scattering does not occur because level-level separations of an exciton are larger than the phonon energies. The energy conservation requirement is not satisfied. For the microcrystaUite size above the critical one, absorption lines are greatly broadened by the exciton-phonon scattering, which becomes possible because the energy conservation is satisfied in the scattering. The heights of the absorption lines are thereby strongly reduced, leaving the lowest energy line unchanged. Above the critical size, therefore, almost only a single line is observed 2 . Thus, as the microcrystaUite size increases the excitation spectral shape changes from a broad band to a sharp line at a critical size 1 . The critical size is smaUer when phonons with energies larger than the maximum
405
406 phonon energy in the microcrystallite flow in from the matrix. As a result of this flow-in due to the matrix effect, the energy conservation in the exciton-phonon scattering can be satisfied more easily than when the solvent effect is hypothetically neglected, reducing the critical size. Such flow-in of phonons occurs when a parameter a which is defined as the square of the ratio of the phonon bandwidth of a matrix to that of a microcrystallite is larger than unity, i.e. o >1. For a <1, phonons flow out of the microcrystallite, increasing the critical size. To find the matrix effect on the critical size, we discuss the relaxation time for phonon scattering of excitons in microcrystallites, considering the phonon energy band in the microcrystallite-matrix system. 2. Theoretical model Let us consider a microcrystallite, which is sandwiched by matrices in the z direction with infinite extent in the x and y directions as shown in Fig.l. We assume a one-dimensional model that excitons and phonons propagate only in the z direction.
• • • • • • • • • • o o o o o o o o o o o o » « » » » » » » » « » —• z I
Mofflo 2 No lattices A
I
Mian2 Ni lattices C
'
Moax? No lattices B
'
Fig. 1. One dimensional configuration of a microcrystallite (o) sandwiched by matrices (•). A microcrystallite of Ni lattices (o in the C zone) with the mass Mi and the force constant Mioi2 between the nearest lattices is sandwiched by the matrices of lattice numbers No (• in the A and B zones) with the mass Mo and the force constant Moan2 (except at the microcrystallite-matrix boundaries). «i/(2 K ) and at>/(2 K ) are vibration frequencies of the microcrystallite lattice and the matrix lattice, respectively. We assume (l) the microcrystallite and the matrix are both crystalline, (2) the mechanical force works only between the nearest lattices, and (3) the electronic excitation energy of the matrix is higher than that of the microcrystallite, so that excitons in the microcrystallite can not migrate into the matrix. We consider the deformation potential for the exciton-phonon interaction
H'=wY'
(
defining W&s the transfer matrix and 2D as the site shift energy. In Eq.(l) W and D' are respectively the derivatives of Wand Z>with respect to the lattice constant in the z direction, and Bn+ and Bn are the creation and annihilation operators of the exciton at the n th lattice. Based on the above model the transverse relaxation time 71 are estimated 2 by calculating the exciton-phonon scattering.
407
3. R e s u l t s and discussion Fig.2 shows the probability P\ for finding phonons with various energies Ein a. microcrystallite and Po for matrices, in two cases of a =5 and 0.2 under the fixed values ofp, Ni and No. Here we define a = coo2/a> l2 and p -MolMi. Then a is the square of the ratio of the phonon bandwidth of a matrix to that of a microcrystallite since the phonon bandwidth of a microcrystallite is proportional to to i and that in a matrix is proportional to coo. The case where a =1 is a special case where phonons neither flow in nor out of the matrix. For this case, taking Ni=No=6 we have P I = F 0 . 3 and .Fb==0.7, respectively, of energy. These are evidently explained by the simple relations Pi = Ni/(2No+Ni) and Po^2No/(2No+ Ni). (A <7>1) 1
K
a =5 p = 1 No=Ni=6
0.8
\ -'
E5 0.6 <£
0 °-4
(B CT<1)
1 1
>-
\T^\ J
m
1
n
11
'"PO'V 1
O.b
< m
1A J'
Q- 0.2
.—' . Po ' ,'
0.8 1
1
0 0.4, , rr a. 0.2 | \
•
Pi
is—srrn \ ,-' \: •.• * a =0.2
J0=1 No=Nl=6
fv.
•
1—i_i
10 20 30 40 ENERGY ( c m - i )
50
5 10 15 20 ENERGY ( cm"1 )
25
Fig.2. The probability Pi and .ft for finding phonons with various energies i?in a microcrystallite and matrices, respectively, for two cases (A) and (B) of a >1 and a <1, respectively under fixed values of p, Ni and No. Fig.2 (A) shows the case where the phonon bandwidth of the matrix material is larger than that of the microcrystallite material. At almost all energies we have Pi>0.3 and Po<0.7. This means that phonons flow in the microcrystallite. In contrast, Fig.2 (B) shows the case where the phonon bandwidth of the matrix material is smaller than that of the microcrystallite material. At almost all energies we have .Pi<0.3 and Po>0.7. This means that phonons flow out of the microcrystallite. Fig.3 shows the inverse transverse relaxation time T2'1 calculated as a function of the microcrystallite size JVi for various values of a at an energy state &=3. We see the threshold value Mc, which is the smallest Ni giving nonzero Til, decreases with increasing a . As is understood from the discussion in Ref.2, Nic decreases as a result of flowing in the microcrystallite of phonons. The phonons with higher energies flow in the microcrystallite easily for a larger a , enhancing the exciton-phonon coupling strength at higher energies in the microcrystallite. Fig.4 shows the threshold value Nic calculated as a function of a for energy states k=3 and A=5. A^0 decreases with increasing a though the dependency is not monotonous.
408 This reflects the situation that the probability for finding phonons in microcrystallites increases with increasing a . It is concluded therefore that the matrix effect is very important in discussing the phonon related physics such as the exciton-phonon scattering. ^ ~
16 14
8 12 M
o ^
a=
l^\
k=s
10 8 6
No=25
-
, /' ^
CT=5*
4
A*-^
/
* * , * * * I
t 1 <7=0.2 ___'__7__v.
£ 2 0
2
4
6
8
10
12
14
16
18
20
N1
Fig. 3. The inverse transverse relaxation time Tz_1 as a function of the microcrystallite size Ni for various values of a in the case of an energy state A=3 of a one •dimensional exciton.
Fig. 4. The threshold value Mc calculated as a function of a for two energy states A=3 and i=5 of a one-dimensional exciton. Acknowledgements We thank Dr. T. Aoki-Matsumoto for constant inspiration. This work is partly supported by a GranHn-Aid for Scientific Research on Priority Area (B) on 'Laser Chemistry of Single Nanometer Organic Particles' from the Ministry of Education, Sports and Culture of Japanese Government (10207206). References 1. A. H. Matsui, K. Mizuno, O. Nishi, Y. Matsushima, M. Shimizu, T. Goto and M. Takeshima, Chem. Phys. 194(1996) 167. 2. M. Takeshima and A. H. Matsui, J. Lumin. 82(1999) 195.
Control of temperature dependence of exciton energies in CuI-CuBr alloy thin films grown by vacuum deposition I. Tanaka, K. Sugimoto, D. Kim, H. Nishimura, and M. Nakayama Department of Applied Physics, Faculty of Engineering, Osaka City University Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan We report the temperature dependence of exciton energies in CuI-CuBr (CuIi»Brx) alloy thin films with the thickness of 50 nm grown on A1 2 0 3 substrates by vacuum deposition. From X-ray-diffraction measurements, we have confirmed that crystalline alloy thin films are preferentially oriented along the <111> crystal axis. The Zi,2-exciton energy exhibits a negative bowing as a function of the alloy composition, while the Z3-exciton energy changes smoothly. The novel finding in the present work is a drastic change of the temperature dependence of the exciton energies in the alloy thin films. The temperature dependence in the Cul film exhibits the negative shift with the increase of temperature, while that in the CuBr film shows the positive one. We have found that the temperature dependence of the CuIi.jBr^ thin film changes from the negative shift to the positive one around the alloy composition of x=0.1. We qualitatively discuss the above finding from the aspect of electron-phonon interactions.
1. Introduction In cuprous halide crystals, the temperature dependence of the exciton energy is classified into two types: One is the positive energy shift with the increase of temperature in CuCl and CuBr, and the other is the negative one in Cul. The positive temperature dependence of the exciton energy is unusual in semiconductors and insulators. Thus, CuI-CuBr (CuIi-jBr*) and CuIi^Cl* alloys are interesting from the viewpoint of the control of excitonic properties; however, only the alloy-composition dependence of the exciton energy in CuIi-JJr* was reported. 1 In the present work, we have focused on the temperature dependence of the exciton energies in CuIi.^Br, alloys. For preparing alloy samples, we used a vacuum deposition method because of the convenience and potential for growth of high-quality thin films.2 Thin films of CuIi.JBr* with x=0 to 1 were grown on (0001) AI2O3 substrates. The X-ray diffraction patterns indicate high crystal quality and preferentially oriented growth of the alloy thin films. The alloy composition was characterized from the diffraction angle. We demonstrate that the temperature dependence of the exciton energy in CuI^JBr* drastically changes with the alloy composition. The temperature dependence is qualitatively discussed from the viewpoint of electron-phonon interactions. 2. Experimental Alloy thin films of CuIi^Br, with the thickness of 50 nm were grown on the (0001) AI2O3 substrates at -150 °C using a vacuum deposition method in high vacuum (-1X10"6 Torr). The deposition source was a mixture of 99.9%-purity-powders of Cul and CuBr with a given molar ratio. The deposition rate, which was controlled monitoring a crystal oscillator, was about 0.1 nm/s. The X-ray-diffraction patterns of the films were measured by a diffractometer with a radiation source of Cu-Ka line. The measurements of absorption spectra were performed by a double-beam spectrophotometer with a spectral resolution of 0.2 nm. The sample temperature was controlled using a closed cycle helium-gas cryostat.
409
410 i
i
i
i
|
i
i
i
|
i
i
/ a \ CuIj.^Br^ thin films
26 28 20 (Degree)
a "i
rb. ur
24
"a
.
A
1
"t.0.58
i
&
0.60
,
tensi
(111)
y=o A 0.2 A 0.5 A 0.8 A
i
f
i
(b)_
0 0.56
i -
0.5 y
1
Figure 1 (a). 6-26 X-ray-diffraction patterns measured at room temperature for alloy thin films , where the value of y indicates the molar ratio of CuBr in the deposition source, (b) Lattice constant estimated from the (111) diffraction angle as a function of y. The solid line shows Vegard's law.
3. Results and discussion Figure 1 (a) shows the 6-26 X-ray-diffraction patterns of alloy thin films, where the value of y indicates the molar ratio of CuBr in the deposition source. The 26 angles of the diffraction peak for y=0 and y=l just agree with those of the (111) spacing of Cul and CuBr bulk crystals, respectively. All the diffraction peaks of the alloy thin films are located between those of y=0 and y=l. Thus, the diffraction patterns clearly indicate that the crystalline thin films are preferentially oriented along the <111> crystal axis. Figure 1 (b) shows the lattice constant (aalu>y) estimated from the (111) diffraction angle as a function of y. The solid line shows Vegard's law: the lattice constant of an alloy is determined by the linear interpolation between those of end materials. The lattice constant plotted in figure 1 (b) almost fit to the solid line. The precise alloy composition of CuIi-jcBr*: is characterized from Vegard's law. Hereafter, we use the alloy composition of CuIi^Br, estimated from Vegard's law. Figure 2 (a) shows absorption spectra of the alloy thin films at 10 K. The Zi,2 exciton corresponds to the degenerate heavy-hole and light-hole excitons at the T point, and the Z3 exciton to the split-off-hole exciton. For Cul (x=0) and CuBr (x=l), the differences between the observed exciton energies and those of bulk crystals are within 10 meV.3 The doublet structure of the Zi,2 exciton in the Cul film is due to the thermal-strain-induced splitting of the heavy-hole and light-hole exciton energies.4 Figure 2 (b) shows the alloy composition dependence of the Zi,2- and Z3- exciton energies. The Z3-exciton energy smoothly decreases with the increase of the alloy composition x. On the other hand, the Zi,2-exciton energy exhibits a negative bowing characteristic. The above results are consistent with those in the previous report.1 Figure 3 shows the temperature dependence of the Zi,2-exciton energies in the alloy thin films with various alloy compositions from x=0 to 1, where the energy in Cul (x=0) is the average value of the split exciton peaks. The exciton energy in Cul (x=0) shows a negative shift with the increase of temperature, while that in CuBr (x=l) shows a positive one. We note that the temperature dependence of the alloy thin film changes from the negative shift to the positive one around the alloy composition of JC=0.1. Moreover, the exciton energy hardly depends on temperature at *=0.1 and x=0.2. The above results, which are the novel findings in the present work, indicate that we can control the temperature dependence of exciton energies changing the
411
S
Q
o
2.5
3.0 3.5 Photon Energy (eV)
0 0.5 1 Alloy Composition x
Figure 2. (a) Absorption spectra of CuIi^Br* thin films at 10 K. (b) Alloy composition dependence of Zi,2- and Z3-exciton energies, where the solid lines are a guide for the eyes.
Cu] I A
3.05
Z[ 2 Exciton
x=0
"~*^~-^.
•
•
£• 3.00 CD
nei
Si
»
0.10 2.95 0.80
~ft20 2.90 W-» 0.42 0
0.64
100 200 Temperature (K)
300
Figure 3. Temperature dependence of the Zii2-exciton energy in CuIi_xBr, thin films with various alloy compositions from x=0 to 1, where the solid lines are a guide for the eyes. alloy composition. Next, we discuss the temperature dependence of the exciton energy following that of the band-gap energy (Eg) because the exciton binding energy hardly depends on temperature. The temperature dependence of Eg at constant pressure derives partly from the thermal expansion effect and partly from the renormalization of band energies by electron-phonon interactions: 5
dT
dV
dT)P
I dT
(1)
412 where the first and second terms on the right-hand side represent the thermal expansion effect and the electron-phonon interaction, respectively. The thermal expansion term corresponds to a product of the hydrostatic deformation potential and the thermal expansion coefficient. In both Cul and CuBr, the deformation potentials are negative6 and the thermal expansion coefficients are positive.7 Thus, the thermal expansion term gives a negative shift with the increase of temperature; therefore, this term never causes the inversion of the temperature dependence. There are two types of electron-phonon interactions, the Debye-Waller and self-energy terms.5 Khan explained theoretically that the Debye-Waller term is the main factor for the positive shift with the increase of temperature, which is unusual in semiconductors and insulators, in CuCl and CuBr.8 The positive shift due to the Debye-Waller term originates in the large degree of the hybridization of the Cu d-orbital and the halogen p-orbital: 75 % and 64 % in CuCl and CuBr, respectively.3 There is no report on the theoretical investigation of the Debye-Waller term in Cul so far. It is considered that the relatively small degree of the p-d hybridization in Cul (50 % 3) results in the negative shift, similar to ordinary semiconductors and insulators. We consider the following qualitative explanation for the change of the temperature dependence in CuIi^Br,. The mixing of Br enhances the degree of the p-d hybridization, which causes a change of the Debye-Waller term. This leads to the inversion of the temperature dependence around the alloy composition of x=0.1. 4. Summary We have investigated the temperature dependence of the exciton energies in CuIi.^Br, thin films with the thickness of 50 nm grown on the (0001) AI2O3 substrates by vacuum deposition. The Zi,2-exciton energy exhibits a negative bowing as a function of alloy composition x, while the Z3-exciton energy changes smoothly. We have found that the temperature dependence of the exciton energy in CuIi^Br* changes from the negative shift to the positive one around the alloy composition of *=0.1. This demonstrates the control of the temperature dependence by changing the alloy composition. We consider that the change of the temperature dependence of the exciton energy is caused by the variation of the Debye-Waller term depending on the degree of the hybridization of the Curf-orbitaland the halogen p-orbital.
References 1. M. Cardona, Phys. Rev. 129, 69 (1963). 2. M. Nakayama, A. Soumura, K. Hamasaki, H. Takeuchi, and H. Nishimura, Phys. Rev. B 55, 10099 (1997). 3. M. Ueta, H. Kanzaki, K. Kobayashi, Y. Toyozawa, and E. Hanamura, Excitonic Processes in Solids (Springer-Verlag, Berlin, 1986), p l l 6 . 4. D. Kim, M. Nakayama, O. Kojima, I. Tanaka, H. Ichida, T. Nakanishi, and H. Nishimura, Phys. Rev. B 60, 13879 (1999). 5. P. B. Allen and M. Cardona, Phys. Rev. B 27, 4760 (1983). 6. A. Blacha, S. Ves, and M. Cardona, Phys. Rev. B 27, 6346 (1983). 7. J. N. Plendl and L. C. Mansur, Appl. Opt. 11, 1194 (1972). 8. M. A. Khan, Philos. Mag. 42, 565 (1980).
B R I D G I N G - H A L O G E N D E P E N D E N C E OF U L T R A F A S T D Y N A M I C S OF E X C I T O N S I N Q U A S I - O N E - D I M E N S I O N A L P L A T I N U M C O M P L E X E S
SHINICHI TOMIMOTO, SHINGO SAITO, TOHRU SUEMOTO The Institute for Solid State Physics, The University of Tokyo, Kashiwa, Chiba 277-8581, Japan KOJI SAKATA, JUN TAKEDA, SUSUMU KURITA Faculty of Engineering, Yokohama National University, Yokohama 240-8501, Japan The femtosecond time-resolved luminescence of a quasi-one-dimensional halogen-bridged platinum complex [Pt(en)2][Pt(en)2l2](ClC>4)4 (abbreviated as Pt-I) is observed. The observed lifetime of the exciton luminescence is rather shorter than those of the other Vt-X (X = halogen ion) systems which have relatively wider band gaps. This result is considered to show that the nonradiative relaxation process becomes more efficient in the narrow-gap system Pt-I. 1. Introduction Quasi-one-dimensional halogen-bridged platinum complexes [Pt(en) 2 ][Pt(en) 2 X 2 ](C104)4 (en = ethylenediamine, X = CI, Br or I. Hereafter we abbreviate them as Pt-X.) are one of the prototypical material groups which have structurally and electronically one-dimensional(lD) nature. They consist of linear chains of alternating platinum and halogen ions. The complexes have self-trapped exciton(STE) luminescence bands from near- to mid-infrared region. By observing the femtosecond time-resolved luminescence, we have investigated the self-trapping of photogenerated excitons and their vibrational relaxation so far. 1,2 In the cases of X = CI and Br, the time-evolution of luminescence is well-explained by the immediate localization of excitons as a result of the absence of energy barrier between free and self-trapped states, which is characteristic of the ID electron-phonon systems, and the vibrational relaxation of the STEs. The relaxation dynamics of excitons is affected by various material parameters, such as the form of the dispersion curve of the exciton band and the frequency spectrum of lattice vibrations which are coupled to the electronic states. The halogen-bridged P t complexes provide a desirable series of samples for the study of the dependence of exciton dynamics on those material parameters because they can be changed easily by the preparation of materials which are chemically substituted, for example, in bridging-halogen ions X, ligand molecules and counter anions. We present the experimental results of femtosecond time-resolved luminescence measurements of the complex in which the bridging-halogen ion X = I (Pt-I). By increasing the halogen ion mass, the phonon frequency is lowered and the band gap, which is generated by the Peierls distortion of the halogen ion positions, is made smaller. By comparing the observed dynamics of luminescence with those in Pt-Cl and Pt-Br, we will discuss the dependence of the exciton relaxation dynamics on the width of the Peierls gap in the Pt complexes. 2. E x p e r i m e n t a l The schematic illustration of the experimental setup is shown in Fig. 1. The single-crystal samples of Pt-I at room temperature was excited by 1.6 eV optical pulses from a Ti:sapphire regenerative amplifier. The repetition rate of the light source was 100 kHz, and the average power of the excitation light was about 1 mW. The time-evolution of the luminescence was investigated by the frequency up-conversion technique. The luminescence of the sample was collected and focused onto the nonlinear optical crystal LiI0 3 (thickness 0.5 mm) by two off-
413
414 axis paraboloidal mirrors. In the crystal, the luminescence was mixed with the fundamental laser pulses. As the phase-matching type for sum frequency generation in the crystal was Type I, only the polarization component of luminescence which was parallel to the polarization of the gating laser light could be frequency-up-converted. We changed the observed polarization direction of luminescence by rotating the half-wave plate (B) between the paraboloidal mirrors, and analyzed the polarization of luminescence. The time resolution of the measurement system was about 170 fs. Double monochromator
X12 plate A
W2 plate B
c
t : horizontally polarized ® : vertically polarized Sample I
Figure 1: Experimental setup for the time-resolved luminescence measurements. The direction of the polarization component of luminescence and the excitation light polarization can be changed by rotating the A/2 plate B and A/2 plate A, respectively.
3. R e s u l t s a n d D i s c u s s i o n Figure 2 shows the time-evolution of luminescence in Pt-I at various photon energies. The excitation light is polarized along the chain axis of the crystal, and the polarization component of luminescence parallel to the chain axis is observed. The time-dependence is well expressed by two exponential decay components. The faster decay component, which has a lifetime of about 650 fs, was observed all over the detection photon energy range (from 0.6 to 1.4 eV). The time-evolution of luminescence at 0.95 eV observed for several different polarization directions is shown in Fig. 3. In this figure, the luminescence of the sample excited by the light polarized at the angle of 45 degrees relative to the chain axis of the sample is shown. The observed polarization angle dependence shows clearly the luminescence is strongly polarized along the chain of the crystal. The excitation polarization dependence of the luminescence at 0.95 eV is shown in Fig. 4. From similar temporal behavior, we consider the fast decay component observed over the wide emission energy range (from 0.6 to 1.4 eV) originates from the same excitation species. The excitation energy of 1.6 eV is in the high energy side of the charge-transfer(CT) exciton absorption band. 3 This absorption band is known to be strongly polarized along the chain axis. As shown in Fig. 4, the intensity of the fast decay component becomes strong under the excitation polarized along the chain axis. This shows the photogenerated C T excitons on the chain are the precursors for the emission state of the fast decay component. As the stationary luminescence of STE in Pt-I at low temperature has the peak at about 0.6 eV, 3 the observed emission energy range (from 0.6 to 1.4 eV) corresponds to the STE luminescence band and its tail in the high energy side. The observed strong polarization of luminescence along the chain (Fig. 3) suggests that the fast decay component of the lifetime of about 650 fs should be attributed to the CT excitons localized on the Pt-I chain, i.e. STEs. The emission energy dependence of the lifetime of the fast decay component is shown in
415
;A i A : JA
1.4 eV :
1.3 eV J
1.2 eV "
1.1 eV : Time (ps) 1.05 e v :
I A_ : A "": \ A.. 1.0 eV :
Figure 3: Time-evolution of luminescence of several different polarization directions at 0.95 eV. The angles show those the polarization directions and the chain axis of the sample make. The excitation light is polarized at the angle of 45 degrees relative to the chain axis.
0.8 eV .
nsity
•
/
/ /
a
0.7 eV :
1.0
0
2
4
6
'"'•''11,1'J 8 10
Time (ps) Figure 2: Time-evolution of luminescence of Pt-I at room temperature. The emission photon energy is indicated for each data. The dots are experimental data. The solid curves are fitting ones that assume two exponential decay components. They are obtained from the convolution with the system response function. The sample is excited by the light polarized along the chain axis. The polarization component of luminescence which is parallel to the chain axis is shown in this figure.
"c
0.6
Polarization - © - 0° - & - 90°
•8
Normals
-2
\
\ \
/ A~*V^ ^*~"~-~«_ 0.0 -*-*&< Time (ps)
Figure 4: Time-evolution of luminescence at 0.95 eV for two different excitation polarization directions. The excitation light is polarized at the indicated angles relative to the chain axis of the sample. The polarization component of luminescence parallel to the chain is observed.
Fig. 5. The lifetime becomes shorter at higher emission photon energies, and is about 400 fs at 1.4 eV. The photogenerated CT excitons are expected to localize quickly because of the ID nature of the crystal. They are in the excited vibrational states just after the localization. They dissipate the excess energy to the lattice and relax to the adiabatic potential minimum of STE. We consider the shorter lifetime of luminescence at higher emission photon energies indicates this vibrational relaxation of STEs on the potential energy surface. The lifetime of about 650 fs around the luminescence peak energy (0.6 eV) gives the lifetime of excitons themselves determined by nonradiative decay. In Table 1, the comparison of the lifetimes of excitons in some halogen-bridged platinum complexes at room temperature is shown. The lifetime in Pt-I is obtained in this study, and those in other complexes (Pt-Cl and Pt-Br) have been obtained in the previous works by the time-resolved luminescence measurements. 1 ' 2 The lifetime shows the clear systematic dependence on the bridging-halogen ion, and becomes shorter for heavier ions. This fact is in good agreement with the experimental data of the stationary luminescence intensity of halogen-
416 III".
up
700 fs)
o 600
o
0
oo 0
L
J
0)
is
:-
o
fc 600
400
o
i-
O J ..1
i l l .
0.8
Table 1: Lifetimes of self-trapped excitons in some halogen-bridged platinum complexes at room temperature determined by the observation of luminescence decay.
1.0 1.2 Photon energy (eV)
1.4
Figure 5: Lifetime of the fast decay component of luminescence of Pt-I. The values are obtained by the fitting to the experimental data shown in Fig. 2.
Sample Pt-Cl Pt-Br Pt-I
Lifetime 30 ps 5 ps 0.65 ps
bridged Pt complexes. 4 It may suggest that the energy barrier height for the nonradiative decay of STEs, which includes the relaxation of excitons to polaron or soliton pairs on the chain, becomes lower in the heavier halogen ion systems which have relatively narrower CT band-gaps. In Fig. 2, the slow decay component with a lifetime of about 5 ps is seen around 1 eV. At present, we tentatively attribute this slow decay component to the STE perturbed by lattice imperfections because the relative intensity of this component to the fast decay component depends on the samples and the location of excitation area on samples. 4. Conclusions The time-evolution of luminescence of a halogen-bridged P t complex, Pt-I is observed by the femtosecond time-resolved spectroscopy. The decay component of the lifetime of about 650 fs is observed. By the polarization and the excitation polarization dependence of luminescence, this component is attributed to the luminescence of CT excitons localized on the Pt-I chain. The observed lifetime of excitons is compared with those in other systems, Pt-Cl and Pt-Br. It shows the clear dependence on the bridging-halogen ion, and becomes shorter for heavier ions. Acknowledgements This work is supported by a Grant-in-Aid for Scientific Research on Priority Areas, "Photoinduced Phase Transition and Their Dynamics", from the Ministry of Education, Science, Sports and Culture of Japan. References 1. 2. 3. 4.
S. Tomimoto, H. Nansei, S. Saito, T. Suemoto, J. Takeda and S. Kurita, Phys. Rev. Lett. 81, 417 (1998). S. Tomimoto, S. Saito, T. Suemoto, K. Sakata, J. Takeda and S. Kurita, Phys. Rev. B60, 7961 (1999). Y. Wada, T. Mitani, M. Yamashita and T. Koda, J. Phys. Soc. Jpn 54, 3143 (1985). H. Okamoto, T. Mitani, K. Toriumi and M. Yamashita, Mater. Sci. Eng. B13, L9 (1992).
A Q U A N T U M M O N T E CARLO STUDY ON EXCITONIC COMPLEXES IN GaAs/AlGaAs Q U A N T U M WIRES
TAKUMA TSUCHIYA* Japan Advanced Institute of Science and Technology (JAIST) 1-1 Asahidai, Tatsunokuchi, Ishikawa 923-1292, Japan Binding energies of biexcitons and charged excitons in GaAs/Alo.3Gao.7As quantum wires were calculated by the diffusion Monte Carlo method. The binding energy for the negatively charged excitons is enhanced strongly, because of the mismatch of the electron and the hole wave functions. The resulting biexciton binding energy reproduces experimental results quite well. 1. I n t r o d u c t i o n Excitonic complexes, i.e. biexcitons (XX) and negatively (X~) and positively (X + ) charged excitons, in quantum confined structures are attracting much attention both theoretically and experimentally. It is well accepted that their binding energies are strongly enhanced compared with those in bulk semiconductors. However, it is difficult to calculate the binding energies exactly, and inexact theoretical results sometimes cause wrong interpretation of experimental ones. There are many studies on excitonic complexes in two-dimensional and zero-dimensional systems, but quasi-one-dimensional structures have not been studied actively. To our best knowledge, there are only two experimental studies on biexcitons in one-dimensional systems 1,2 and the charged excitons have not been observed. Observed biexcitonic binding energy is 2.0 to 2.9 meV for InGaAs/GaAs rectangular quantum wires of size ranging from 30 x 300 A 2 to 50 x 850 A 2 , and about 2 meV for T-shaped GaAs quantum wires of 66 x 240 A 2 . However, the result of a variational calculation 3 is four times larger than the experimental ones. Diffusion Monte Carlo method is quite suitable to investigate binding energies of excitonic complexes. This method gives us exact binding energies within a small statistical error and has been applied to excitonic complexes in quantum wells, quantum dots, and type-II superlattices. 4 - 7 In this paper, we apply this method to GaAs/Alo.3Ga 0 .7As rectangular quantum wires with cross section dx x dy and demonstrate a strong enhancement of binding energies. In particular, the binding energy for negatively charged excitons reaches about 20 times of that in the bulk. The resulting biexciton binding energies are much smaller than previous theoretical results and comparable with the experimental ones. 2. M e t h o d of Calculation The Schrodinger equation for the present problem in the framework of the effective mass approximation is written as d
i
y
;
m'
= g $ ( R , t ) = (T + y ) $ ( R , t ) ,
T=
_y y JLJL Z^
2^
» i(=x,y,z)
V{K)=
£ ^J_
*E-mail: [email protected]
417
2m* • d z 2 •'
(i)
(2){>
u
^'"n.i -*"n,«
+
yvrf(rn)t
(3)
418 Table 1. Parameters used in the present calculation and calculated binding energies in the bulk GaAs.
V™ni (meV) 0.067 m 0 0.35 m 0 180 m 0 : electron rest mass
ml
Vhconf (meV) 120
e 12
Bx (meV) 5.3
Bxx0.24
Bx+ 0.44
B 0.64
where n identifies particles, V£on!(zn) is the confinement potential, e the dielectric constant, qn the charge of particles, m*ni the effective mass along i(= x,y,z) direction, r n = (xn,yn,zn), R = ( r i , r 2 , . . . , r n , . . . ) , and rnni = \rn — r'n\. We have assumed that the dielectric constant and the effective masses are independent of materials. Substituting r for it, we obtain the Schrodinger equation in imaginary time: d$(R,r) = -.ff*(R,T) = dr
£
2m*,: dxl
(4)
-*(R,T)-V(R)*(R,T)
This equation can be solved by Monte Carlo method and we can obtain the exact ground state energy, E, within a statistical error. 8 Binding energies are defined by BXx = -(Exx - 2i?x), Bx+ = ~(Ex+ - (Ex + Eh)), Bx- = -(Ex- - (Ex + Ee)), and Bx = -(Ex - (Ee + Eh)) for XX, X+, X " , and an exciton (X), respectively. In these equations, 'e' and 'h' denote electrons and holes. In Table 1, we show the parameters used in the present calculation and the binding energies in the bulk. 3. Numerical R e s u l t s Figure 1 shows the calculated binding energies for excitons and excitonic complexes in square quantum wires, dx = dy = d. The binding energy for XX is much smaller than the previous calculation. 3 All the binding energies increase as d decreases for d > 50 A, but its slope changes around d = 500 A. For d < 50 A, the binding energies decrease. At the peak, Bx, Bx-, -Bx+ and Bxx reach 23, 4.3, 3.0, and 3.5 meV, which correspond to 4.3, 18, 7, and 5.5 times of those in the bulk, respectively. In spite that Bx- is quite small in the bulk, its enhancement is the strongest and the peak binding energy is the largest among excitonic complexes.
GaA / A l
» 1
••
t
'
•
•
•
X X (eq
Ga
„ . As
.(6»
quantum wires d -d -d
• •
•
X
O
X-
o xA •
. XX X- (eq .(6» •
o•
X* (eq .(6)) XX (eq .<6»
•
•. 10 •»
10 5
^
•
' • • - \
-£1 S^-S^fJLU
: (a) 500
20 I
x
1000 1500 2000 2500 3000 d (A)
100 d (A)
Fig. 1. Binding energies as a function of the side length d for excitons, negatively and positively charged excitons, and biexcitons in GaAsZAlo.3Gao.7As quantum wires with square cross section. The results of simple estimation, eq. (6), are also shown. In (b), the region d < 200 A is magnified.
419 0.22 d = d =d; 0.20 0.18
5
0.16
•
*
» A A A
A
XVX : xVx xx/x •
°
•
Fo°°
o ^0.14 0.12
•
A
•
o
• o
:
• o
A
A
•:
A
0
0.10 p,
A
GaAs/AI
0.08
11
1
A :
Ga
quantum
III
As . wires ;
0.06 0
200
400
600
800 1000 1200 1400
d (A)
Fig. 2. Ratio of binding energies for excitonic complexes to those of excitons in GaAs7Alo.3Gao.7As quantum wires with square cross section. The above result suggests that there are three mechanisms cause the change of the binding energies. This is demonstrated more clearly in Figure 2. In this figure, the ratios of binding energies of excitonic complexes to that of excitons are shown. For d > 500 A, region III, the ratios increase as d decreases, and for 500 A > d > 100 A, region II, they decrease or are independent of d. For d < 100 A, region I, B x - / i ? x increases, but Bx+/Bx and Bxx/Bx decrease. In the region III, where the dimension of quantum wires is much larger than the radii of excitons and excitonic complexes, their internal structure is not affected by the confinement and they behave like point particles. Then, their energies change due only to the quantum confinement. 9 If we assume that that particles are completely confined in quantum wires, the confinement energy is „ , , , ^ ft2T2 / 1 1 \
^x,dy)
= —{-
+
^,
(5)
where m*A is the effective mass of the particle A. According to the definition of binding energy, that for the bound state A + B of particles A and B is given by BA+B{dx,dv)
n n
\dl
dl)\m\
mR
m*,,n)
'
BA+B,
(6)
where BA+B is the binding energy in the bulk. This equation shows that quantum confinement causes enhancement of binding energy. Further, it is found that the increase is larger for lighter particles. Since effective mass is much smaller for electrons than for holes in GaAs, the enhancement is larger for X~ than X+ and XX. In Fig. 1, we have also shown the results of eq. (6). This equation reproduces the Monte Carlo results for d > 2200 A for X~, and to much smaller d for the others. This difference of the limits comes from the difference of radii. In the region II, the quantum confinement affects the internal structures. In this case, individual electrons and holes are confined, and the Coulomb potential is thought to be a perturbation. The binding energies increase as d decreases, because the Coulomb energy increases. This explanation is quite correct for excitons. For excitonic complexes, however, the Coulomb repulsive potential as well as attractive one increase with decreasing d and quantum confinement of individual particles prevents the correlation between particles. These are reflected in the decreasing ratios in Fig. 2. Because of the finite barrier height, the wave functions of electrons and holes are penetrate into the barrier. As a result, the confinement gets weaker in region I, and the binding energies decrease. Since the effective mass for electrons is much smaller than that for holes in GaAs,
420 the penetration depth is larger for electrons. This mismatch between the electron and the hole wavefunctions is most pronounced where the confinement is weak for electrons but still strong for holes, i.e. just below the peak position of the exciton binding energy. In such situation, the Coulomb repulsion is larger for a hole pair than for an electron pair. Therefore, Bx- is stronglyenhanced and Bx+ is reduced.
o '
0
GaAs/AI Ga As quantum wires ' • " ' '°;7 1 o
200
400
600
800
1000 1200
Fig. 3. Binding energies for excitons, negatively and positively charged excitons, and biexcitons in GaAs/Alo.3Gao.7-As rectangular quantum wires with
dx = 56A. In Fig. 3, we show the binding energies for rectangular wires with dx = 56 A. The overall features are similar to Fig. 1. Binding energies for XX are about 2 meV and do not depend on dy strongly. This is in accordance with experimental results,1 and in contrast with variational ones3 in which Bxx is strongly overestimated. 4. Summary We have calculated binding energies of excitonic complexes in GaAs/Al0.3Ga0.7As quantum wires, using the diffusion Monte Carlo method. It has been found that the binding energy of the negatively charged excitons is strongly enhanced. The result for biexcitons reproduces the experimental ones quite well. The origin of the enhancement of binding energies has been discussed. Acknowledgements This work is partially supported by the Grant-in-Aid for Scientific Research (C) of the Ministry of Education, Science, Sports, and Culture, Japan. References 1. 2. 3. 4. 5. 6. 7. 8. 9.
T. Baars, W. Braun, M. Bayer, and A. Forchel, Phys. Rev. B58, R1750 (1998). W. Langbein, H. Gislason, and J. M. Hvam, Phys. Rev. B60, 16667 (1999). F. L. Madarasz, F. Szmulowicz, and F. K. Hopkins, Phys. Rev. B52, 8964 (1995). J. L. Osborne, A. J. Shields, M. Pepper, F. M. Bolton, and D. A. Ritchie, Phys. Rev. B53, 13002 (1996). T. Tsuchiya, in Proc. 24th Int. Conf. Phys. Semicond., ed. D. Gershoni, (World Scientific, Singapore, 1999), CD-ROM. T. Tsuchiya, Physica B 7, 470 (2000). T. Tsuchiya, J. Lumin. 87-89, 509 (2000). See for example, B.L. Hammond, W.A. Lester, Jr., and P.J. Reynolds, Monte Carlo Methods in Ab Initio Quantum Chemistry, (World Scientific, Singapore, 1994). Al. L. Efros and A. L. Efros, Sov. Phys. Semicond. 16, 772 (1982).
T H E O R Y OF O P T I C A L R E S P O N S E S O F S P H E R I C A L Q U A N T U M D O T S U N D E R STATIC A N D D Y N A M I C A L E X T E R N A L FIELDS
TAKAYUKI UOZUMI and YOSUKE KAYANUMA College of Engineering, Osaka Prefecture University, Gakuen-cho 1-1, Sakai 599-8531, Japan The influence of an external electric charge on optical properties of a spherical quantum dot (QD) is theoretically investigated within the effective-mass approximation. The absorption spectrum of QD is strongly affected when the electric charge approaches close to the surface of QD : the lowest excited state shows a rapid red-shift and partially loses its oscillator strength. The magnitude of the red-shift and the reduction rate of the oscillator strength in such a case shows a characteristic change as a function of the dot-size : the former monotonously increases as the dot-size is reduced, while the latter reaches its maximum when the dot-size corresponds to that of the intermediate confinement regime. 1. Introduction Optical properties of semiconductor nanocrystals, or quantum dots (QD's), have been extensively studied in recent years 1 . The three dimensional confinement of elections and holes drastically changes the electronic structure in QD's from that of bulk crystals and leads to the concentration of the oscillator strength in essentially discrete energy levels of QD's, which makes QD's a promising candidate for electro-optic and nonlinear optical applications in the optical device technology. Recent advances in material growth and optical measurement techniques allow further investigations of optical properties of QD's. The excited states of CuCl QD's have been directly observed in the recent measurements of transient absorption spectra under the size-selective excitation of the lowest excitons 2,3 , for example. Moreover, the single dot spectroscopy 4,5 have realized the observation of optical properties of QD's without ambiguity of inhomogeneous broadening which comes from the fluctuation of the dot-size and the shape of QD's. In such studies, it has been found that the local environment around QD's strongly affects optical properties of QD's. Especially, the external electric field induced by electric charges trapped around QD's are considered to take a crucial part in such an interesting phenomenon as blinking of QD's 5 . Such a mechanism is also considered to be important in the persistent hole burning phenomenon in QD's. 6 In the present study, the influence of an external electric charge on the optical absorption spectra of QD's is theoretically investigated within the effective-mass approximation. Although our interests are in both static- and dynamical perturbation effect on optical properties of QD's, here, we focus our attention on the case of static external field induced by an electric charge trapped outside QD. 2. M o d e l and Calculation We consider an interacting electron-hole pair confined in a spherical quantum dot with a radius of R. In the present study, we assume the complete confinement of electron-hole pair in QD. When the electric field induced by the electric charge outside QD is absent, the eigenstates of the system can be completely classified in terms of a set of quantum numbers (L, M) of the angular momentum operators L 2 and Lz. In such a case it is convenient to employ the Hylleraas coordinate system and to expand the wave function of the electron-hole pair in the form as
421
(1)
422 where 6' is the angle between r e and rj,, and 6, tp, ip' are the set of Euler angles. The function (j>i describes the internal motion of the electron-hole pair, while D^MK describes the angular part of the wave function which is identical to the eingenfunction of the spherical top. Within the effective-mass approximation, the unperturbed Hamiltonian Ho of the electronhole pair is represented in the present coordinate system as r H0 = + f2
(L+-L-)-jjgi-cQtff{L+
+ L-)Lt.
,
(2)
where we adopt the effective Bohr radius aB = Kinh2/ne2 as the unit of length and the effective Rydberg energy ERy = h2/2iJ,a,g as the unit of energy (fCjn is the dielectric constant of QD and p is the reduced effective-mass). In Eq. (2) the coefficients ce and c/, are defined in terms of the effective mass ratio a = mh/me as ce = 1/(1 + a) and cj, = <j/(l +
(3)
Z
ex
where 0< (i = e, h) is the angle between r< and z axis, and Pi is the Legendre polynomial. The coefficient Ai in Eq. (3) is given by A = Al
4i+ 2 l + {l + l)(Kout/Kiny
()
where K^ is the dielectric constant of host material. The eigenstates of the total Hamiltonian Ho + V are described by linear combinations of the eigenstates of the unperturbed Hamiltonian Ho with various angular momentum L, because the spherical symmetry of the system is broken due to the applied electric field. In the present study the unperturbed eigenstates with angular momentum L = S,P,D and F are considered to describe the perturbed eigenstates. The parameters in the theoretical model are chosen as a = 3.0 and Kin/Kmt — 3.0 in the following calculation. 3. Results and Discussion In Fig. 1 (b)-(d), we show the ze3:-dependence of the absorption spectrum of QD with a radius of Aa*B, where the absorption spectrum of the unperturbed system is also shown in Fig. 1 (a). The vertical lines in each panels show the calculated oscillator strength fj of j-th. excited states per unit volume which are normalized by the oscillator strength / d of Is exciton in the bulk crystal per unit volume. The continuous spectra in the figure are obtained by convoluting the vertical lines with the Gaussian function with the half width 0.05 E*Ry at half maximum, and the dotted lines show difference spectra of the continuous spectrum of the unperturbed QD from that of the perturbed QD. It is found that the absorption spectrum of QD is strongly affected when the external electric charge is placed near the surface of QD. In such a case, the oscillator strength of excited states of the unperturbed system are distributed to a number of excited states of the perturbed system through the electric field induced by the external electric charge.
423 1.0 0.8 -$0.6 ^0.4
1|0.2 So.o
111111111111111111111111111111111
'
(a) unperturbed ' R=4 "
mi nil
I I I I I I I I I I I II I I I I I I I I I I I I I I I I I I I I I
(c)z = 5 \ '
ex
Tiiiliiii|iiii|iiii|iiii|iiii|iin
1 i I V i 11111 11111 11 11 • • • 1 i • • • I
q 1 I I t I I I 1 I I I I | I | I f I I I I I t I I I I I I | |
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 Excitation Energy [ER ] Excitation Energy [ER ]
Fig. 1. Caculated absorption spectra of unperturbed QD (a), and perturbed QD's (b)-(d). The perturbation in the latter is induced by an electron placed
A special attention should be paid to the lowest excited state of the unperturbed system, which shifts toward the low energy side and partially loses its oscillator strength when the external field is applied. The behavior of the lowest excited state is systematically shown in Fig. 2 (a)-(c) for QD's with various dot-size. Fig. 2(a) shows the magnitude of the red-shift of the lowest excited state as a function of z^. Each lines in the figure ends at the surface of QD (zex = R). It is clearly shown in the figure that the magnitude of the red-shift rapidly increases when z M approaches close to the surface of QD. It is also noted that the magnitude of the red-shift of the lowest excited state in QD with the external electric charge at the surface monotonously increases as the dot-size is reduced. Fig. 2(b) shows the zex dependence of the oscillator strength fi/fex of the lowest excited state per unit volume, while Fig. 2(c) shows that normalized by the oscillator strength / } of the lowest excited state per unit volume of the unperturbed QD. We find that fi/fex of QD's with various dot-size gradually decrease when zex approaches the surface of QD. The reduction rate of f\/fcx have an characteristic dependence on the dot-size and it is clearly shown in Fig. 2(c): the reduction rate of fi/fex of QD with the external charge at its surface has a maximum in the intermediate confinement regime, which is in contrast with the monotonous change of the red-shift in Fig. 2(a). Consider the case that the external charge is fixed on the surface of QD. In this case the dot-size dependence of the red-shift and the oscillator strength can b e qualitatively understood as follows. In the weak confinement regime (R > a*B), the electron-hole pair in QD behaves as an exciton with the neutral electric charge. Then, roughly speaking, the exciton does not feel the induced electric field so strongly, and both the energy of the lowest state and the oscillator strength are not strongly affected by the external electric charge. According to the second-order perturbation theory, we can derive the magnitude of the red-shift in a form as AE - \/{a + fiR) in the strong confinement regime (R < a*B), where a and /? are positive constants. The second term of the denominator originates from the correlation energy of the electron-hole pair and leads to a monotonous reduction of AE as R is increased. Such a tendency of A E would smoothly continue to t h e weak confinement regime. The oscillator strength in the strong confinement regime is hardly affected by external perturbation because the electron and hole are strongly confined in QD from the beginning.
424 ini|nu|ini|iitniiii|niniin|ini|inniju 0.6 -R=0.5 (a) Redshift 1
lll|IHI[IIH|IMI|IIM|HII|llll|llll[MH|ll
(b) Oscillator strength R=0.5
3 4 5 llll|llll|lllllllll|llll|lllllllll|llll|llll|llll (c) Normalized oscillator strength
?0.8 ° 0.6 iliniliiiiliiulniiliinliiiilinilinilnii
0.4 0
1
2
3
4
5
6
7
8
9
10
Fig. 2. The 2 ea: -dependence of the red-shift (a), the oscillator strength per unit volume (b), and the normalized oscillator strength (c) of QD's with various dot-size. However, in the intermediate confinement regime (2ag < R < 4a*B), the spatial distribution of the electron and hole can be relatively easily changed by the induced electric field, because the electron-hole pair have a room to polarize. Then, the spatial separation between the electron and the hole induced by the external filed leads to a strong reduction of the oscillator strength. References 1. See, for example, A. D. Yoffe, Adv. Phys. 42, 173 (1993); U. Waggon, Optical Properties of Semiconductor Quantum Dots, (Springer, Berlin, 1997), and references therein. 2. K. Yamanaka, K. Edamatsu and T. ltoh, J. Lumn. 76 & 77, 256 (1998). 3. T. Uozumi and Y. Kayanuma, K. Yamanaka, K. Edamatsu and T. Itoh, Phys. Rev. B59, 9826 (1999). 4. M. Nirmal, B. O. Dabbousi, M. G. Bawendi, J. J. Macklin, J. K. Trautman, T. D. Harris and L. E. Brus, Nature 383, 802 (1996). 5. M. Sugisaki, H.-W. Ren, S. V. Nair, J.-S. Lee, S. Sugou, T. Okuno and Y. Masumoto, J. Lumin. 87-89, 40, (2000). 6. Y. Masumoto, J. Lumin. 70, 386 (1996). 7. T. Uozumi and Y. Kayanuma, J. Lumin. 87-89, 375 (2000). 8. Y. Kayanuma. Solid State Commun. 59, 405 (1986). 9. Y. Kayanuma, Phys. Rev. B38, 9797 (1988).
LOCAL MORPHOLOGY AND SUB-WAVELENGTH REGION SPECTROSCOPY OF MOLECULAR J-AGGREGATES: ONSET OF EXCITON-POLARITON STATES IN INDIVIDUAL AGGREGATE FIBERS MARTIN VACHA'- 2 *, SHOJI TAKEI', KEN-ICHI HASHIZUME' AND TOSHIRO TANI 1 'Department of Applied Physics, 2Venture Business Laboratory, Tokyo University of Agriculture and Technology, 2-24-16 Naka-machi, Koganei, Tokyo 184-8588, Japan "On leave from Charles University Prague, Czech Republic We present results on reflection microscopy and local spectroscopy of J-aggregates of pseudoisocyanine dyes in a thin film polymer matrix. Local reflectance spectra reveal a wide distribution of optical properties within different locations of one sample. The spectral lineshapes and absolute reflectivities are suggested to originate from varying strength of exciton-photon interaction. Polarization dependence measurements of local reflectivities at different wavelengths provide orientations of the excitonic transition dipole moments with respect to the orientation of the aggregate fibers.
1. Introduction Molecular aggregates play role in many biological processes, such as photosynthesis, and have great potential in many technological applications as linear and non-linear optical materials. In particular, J-type aggregates of pseudoisocyanine dyes 1,2 have unique electronic properties that demonstrate themselves in optical spectroscopy. Absorption spectra are dominated by a strong narrow red-shifted band (J-band) that originates from Frenkel exciton 3 states of large coherent length. Most of the spectroscopic studies presented so far have been performed on bulk samples. Here, we report results on the local excitonic structure of "fibers" of J-aggregates self-assembled in a polymer matrix with sub-micrometer resolution. As a method to probe resonantly the excitonic transitions far field reflection microscopy and spectroscopy are employed. 2. Experimental J-aggregates of pseudoisocyanine bromide (PIC-Br) were prepared in thin films of polyvinyl sulfate) (PVS) potassium salt by spin-coating 4 . Briefly, 5-10 mM methanol solution of PIC-Br is added to hot stirring mixture of 5-10 mg/mL aqueous solution of PVS and immediately spin-coated at 3000 rpm on a 0.12-0.17 mm cover glass. Details can be found elsewhere 5 . Microscopic reflection images are obtained with a reflection microscope (Union Tokyo, lOOx oil immersion lens, numerical aperture 1.25, lateral resolution of 280 nm at the wavelength of 570 nm), and a CCD camera (Princeton Instruments PentaMAX, Kodak KAF-1400 chip). Light source is provided by a 150 W tungsten-halogen lamp attached to a 1.5 m monochromator (Jobin Yvon THR 1500, operated at a resolution of 9 cm"'). The output from the monochromator is coupled to a large-core (800 micron) optical fiber and introduced to the microscope. Typical light density at the sample is 1.2 mWcm" 2 at 570 nm. A sheet polarizer placed behind the collimator provides rotatable polarized light with an extinction ratio > 50:1 (measured behind the objective lens). To obtain local polarization reflectance dependence the polarizer is rotated in small increments (~5°) at a fixed wavelength and reflection image is taken at each step. To measure reflectance spectra, a series of microscopic images (~ 200) is consequently recorded while scanning the monochromator. Local reflectance spectra are reconstructed from the image series by plotting the light intensity at a
425
426 selected location (pixel) of each image as a function of wavelength. To obtain absolute reflectivity values and to correct the spectra for an apparatus response function, a reflectance spectrum of chromium layer is detected in the same experimental configuration after each measurement. All experiments are carried out at ambient conditions. 3. Results and discussion Room temperature absorption spectrum of the PIC-Br/PVS thin film is shown in Fig. 1. The spectrum has typical features of good quality PIC J-aggregate sample, i.e. strong J-band with a maximum at 573.4 nm and higher energy structures at 540 nm and 506 nm. The thickness of the polymer film itself is on the order of 20-40 nm, depending on the preparation conditions and location on the sample. A typical reflection image of the J-aggregates studied is shown in Fig. 2. The aggregates form bright fiber-like structures that can be up to tens of microns long and their morphology (length, density, J-band diameter, shape, etc.) depend strongly on the p r e p a r a t i o n conditions. There are clearly observable differences between the intensity of light reflected from different fibers or their parts. These differences are accompanied by differences in the lineshapes of corresponding 500 550 600 Wavelength (nm) reflectance spectra, as illustrated in Fig. 3. The spectra numbered 1 -4 in Fig. 3 were taken at Figure 1: Room temperature bulk absorption the locations 1-4 of Fig. 2. The spectrum 4 spectrum ofPIC-Br in a thin film of polyvinyl shows a narrow peak with the position and sulfate). linewidth close to those of the bulk absorption J-band. This kind of spectrum is typical for fibers of relatively low reflectivity of about 5 % and can be interpreted as exciton-like counterpart to the absorption or emission J-bands. It is relatively easy to obtain absorption spectra at individual locations by using Kramers-Kronig analysis for the reflectance phase shift6. When done on statistical ensembles of different locations the analysis can provide distributions of the local absorption linewidths and peak positions that reflect fluctuations of local optical properties of the aggregate fibers5. Figure 2: Microscopic of the PIC-Br/PVS
reflection
image
sample taken at 572
nm. The markers 1-4 indicate
locations
where reflectance spectra of Fig. 3 have been analyzed. marker
lines
orientations
Orientations correspond
of local transition
of the to
the
dipole
moments at 572 nm (full lines) and 540 nm (dashed lines).
427 In the spectra 3-1, the reflectivity increases and the main band b r o a d e n s . In our reflectivity experiments, we observed reflectivities of up scale: 0.05 to 20 % and bandwidth up to 55 nm. As suggested before5 these features indicate an onset of exciton-polariton behaviour that can be caused by increased exciton-photon coupling due to, e.g., increased density of -i—i—i—I—|—i—r T—|—i—i—r individual 1-dimensional J-aggregate 500 550 600 650 segments that assemble together to form the Wavelength [nm] aggregate fibers. The main band of the Figure 3: Reflectance spectra corresponding spectrum 1 shows further structure that has to locations 1-4 of Fig. 2. The dashed lines been suggested to result from the finite indicate the wavelengths for the polarization thickness of the fiber. As the thickness dependence measurements of Fig. 4. increases a virtual optical mode7 (possibly due to the interference between light reflected from the front and rear faces) starts evolving around the reflectance spectrum peak5. Apart from the main band, a shoulder with maximum at about 540 nm can be seen in the spectra 1-4. With increasing reflectivity of the main band the relative intensity of this band also increases. Results of the polarization dependence of the reflected light at the wavelegths of 572 and 540 nm at locations 1-4 are shown in Fig. 4. The data were corrected for the polarization response of the apparatus and fitted with a+bcos2(cyi-ff) . The fit provides angles of the exciton transition dipole moments at the two wavelengths with respect to horizontal axis of Fig. 2. The results are summarized in the Table and indicated by line markers (full for 572 nm, dashed for 540 nm) in Fig. 2. A few unexpected observations have been made. Apart from locations 2 and 3 where the
location 1
1111111111111111111'
150 200 250
location
location
2
3
1111111111111111111 1 'i i i i 111111111111111 1 'i 11111111111111111
150 200 250
150 200 250
150 200 250
Polarization angle [deg]
Figure 4: Reflectivity at locations 1-4 as a function of the polarization angle of the incident light at 572 nm (crosses) and 540 nm (circles). Full lines are fits to the relation described in text.
428 572 nm transitions are aligned well along the fiber direction as supposed, locations 4 and, especially, 1 show large deviations between the two directions. Further, the angle between the 572 and 540 nm transitions is not constant but varies between 51° for location 4 and 84° for location 3. These data confirm that the local composition of the aggregate fibers is complex and varies hugely between individual locations, and may have broad implications for the studies of the J-aggregate structure. For example, the results obtained at point 1 might indicate a transition from 1dimensional to 2-dimensional character. Further work on this subject is in progress. Table: Orientations of the transition dipole moments at 572 and 540 nm with respect to the horizontal axis in Fig. 2. location 1 2 3 4
0572 [deg] 236 262 179 272
#540 t de g] 162 153 275 143
Acknowledgment The research was partly supported by grant-in-aid no. 11490008 of the Ministry of Education, NSG Foundation, Iketani Foundation and Hitachi CRL. The experiments were carried out by undergraduate students M. Saeki and O. Isobe. References (1) E.E. Jelly, Nature 138 (1936)1009 (2) G. Scheibe, Angew. Chem. 50 (1937) 212 (3) A.S. Davydov, Theory of Molecular Excitons, Plenum Press, New York - London, 1971 (4) D.A. Higgins, J. Kerimo, D.A. Vanden Bout and P.F. Barbara, J. Am. Chem. Soc. 118 (1996) 4049 (5) M. Vacha, S. Takei, K. Hashizume, Y. Sakakibara and T. Tani, to appear in Chem. Phys. Lett. (6) F. Stern, Solid State Phys. 15 (1963) 299 (7) R. Fuchs, K.L. Kliewer and W.J. Pardee, Phys. Rev. 150 (1966) 589
LUMINESCENCE PROCESS IN ANATASE T i 0 2 STUDIED BY TIME-RESOLVED SPECTROSCOPY
M. WATANABE, T. HAYASHI Faculty of Integrated Human Studies, Kyoto University, Kyoto 606-8501, Japan
H. YAGASAKI, S. SASAKI Graduate School of Human and Environmental Studies, Kyoto University, Kyoto 606-8501, Japan We have studied time response of self-trapped exciton (STE) luminescence in anatasc phase of T1O2 as functions of excitation photon energy and temperature. The decay curves, which consist of two components obeying exponential and power-law decay, are found to depend significantly on the two parameters. The exponential component is stimulated efficiently under excitation near the absorption edge. This fact suggests that under such an excitation condition, photogenerated electron-hole pairs directly form STE's. It is found from temperature dependence of the decay curves that the exponential component is thermally unstable compared with the power-law one. It is inferred that the electron-hole pairs are thermally separated, and thus the direct formation of STE's is prevented.
1. Introduction Anatase phase of titanium dioxide, TiC>2, is a wide band-gap semiconductor and is widely applied in various fields such as photoelectrochemistry. Although extensive studies have been made for applications, its fundamental optical and electronic properties have not been fully understood. Under interband excitation, anatase TiC>2 exhibits a broad luminescence band with a large Stokes shift.1'2 The luminescence band is assigned to radiative recombination of self-trapped excitons (STE's). The STE is supposed to be localized on a Ti06 octahedron which is the unit structure of anatase Ti02. However, the detailed mechanism of the luminescence process has not been well clarified. We studied the luminescence process of STE's by time-resolved spectroscopy and found that the decay curves of the luminescence band consist of two components obeying exponential and power-law decay.3 We ascribed the exponential component to a direct formation process of STE's and the powerlaw one to an indirect formation process in which carriers trapped at lattice defects or impurities are involved. In the present work, in order to clarify the two decay processes in detail, we investigate time response of the luminescence as functions of excitation photon energy and temperature. 2. Experimental Single crystals of anatase TiC>2 were grown by chemical transport reactions 4 and were then annealed in oxygen at about 200 °C for a few days. The crystals thus obtained were transparent and colorless. They were kept in an immersion type cryostat at 2 K. A continuous flow helium cryostat was also used for the experiments at higher temperatures. For the measurements of luminescence decay curves, the samples were excited with either the third harmonics of a Q-switched Nd:YAG laser (10 Hz repetition rate, 5 ns pulse width) or a dye laser (6 Hz, 5 ns, 2.5 meV spectral width, BPBD-365 in p-dioxane as the active medium) pumped by a N2 laser. Light pulses from a Xe flush lamp passed through a monochromator (100 Hz, 0.8 jus, 30 meV) were also used to achieve the wide tuning range for excitation. Luminescence was detected through a monochromator equipped with a photomultiplier and the signal was analyzed by an oscilloscope. 3. Results A dotted curve in Fig.l shows the luminescence spectrum of anatase TiC>2 measured at 2 K. Excitation energy is 3.54 eV. It was confirmed that the spectral shape was the same irrespective of the excitation energy. The peak energy and FWHM of the luminescence band are 2.3 eV and 0.6 eV, 429
430 i
^^
i
i
i
10 .1=
i
i
i
i -
/
ly *
\
f
.ri 1-
/ ^0 — // * / >J— c/5 ~ / / 2 * 111 / — |Z 1 . . . .
2.0
Ti0 2 2K
1
2.5
-
nL
l^v
* •
.
i— i — i — i — [ — i — i — i — r - 1 — i — i — i — i — | — i — i — r - T
»
*•-*„
iK
1r VV Hi M A yK So Will QJo ^V*V*JW I P % ' ^ ^ » I J& TJQ lv IX , • i'''i..i..jJr i i —i—i
3.0 3.5 PHOTON ENERGY (eV)
i
i
i
i
4.0
i
i
— ~ W
T*/i 'V
i
j
4.5
Fig. 1. Luminescence (dotted line) and excitation (solid line) spectra of anatase TiC>2 measured at 2 K. Closed and open circles are time-resolved excitation spectra for the exponential and power-law components, respectively. respectively, in agreement with the previous results.1'2 Excitation spectrum of the luminescence observed at 2.3 eV is shown by the solid line in Fig.l. Its intensity rises at 3.2 eV corresponding to the absorption edge of anatase TiC>2,5 becomes maximum at 3.3 eV, and dien gradually decreases with increasing the excitation energy. These features are in agreement with the results in ref.l. Figure 2 shows the decay curves of the luminescence intensity at 2.3 eV measured with various excitation photon energies. The excitation energies are indicated in the figure. Each decay curve is normalized at the peak intensity and is offset by two decades for clarity. In all cases, excitation density is about 0.4 /J/cm2, which is two orders in magnitude smaller than the excitation density causing saturation of the luminescence intensity. Under excitation at the absorption edge, (a), the decay curve can be well described by a single exponential function with a time constant of 1.5±0.1 ps as shown by a dotted curve. As the excitation energy increases, a slow decay component gradually appears in addition to the exponential one. The slow decay component obeys a power law, i.e., l/tm. The value of m is nearly equal to 1. The time constant of the exponential component is 1.5 jus for excitation below 3.4 eV, (a) - (d). When the excitation energy exceeds 3.4 eV, the time constant increases with the excitation energy, that is, 1.7 ps for (e) and 1.8 fis for (f). As can be seen in Fig.2, the dependence of the luminescence efficiency on the excitation energy differs with each decay component. Then we investigated the luminescence efficiency of the two components as a function of excitation energy, i.e., time-resolved excitation spectra. The results are shown by open and closed circles in Fig.l. These spectra were obtained by reconstruction from a series of decay curves taken at various excitation energies. The decay curves were measured at 2.3 eV and the Xe flush lamp was used as a light source. The closed circles indicate the excitation spectrum for the exponential component obtained by integrating the decay signal intensity from 1 to 3 /JS after excitation. The open circles correspond to the integrated signal from 100 to 200 fis, and represent the spectrum for the power-law component. For clarity, the two spectra are plotted so that the sum of them coincides with the time-integrated excitation spectrum (solid curve). For excitation between 3.2 and 3.4 eV, the exponential component is mainly stimulated. The efficiency of the power-law component gradually increases with excitation energy, in agreement with the result of Fig.2. The two components have comparable intensity above 3.4 eV. Figure 3 shows decay curves measured at various temperatures. Excitation is made at 3.31 eV and the signal is detected at 2.3 eV. For clarity, each decay curve is normalized at the peak intensity and is offset by one decade. In order to show the behavior of the exponential component clearly, the abscissa is proportional to time. One can see that the time constant of the exponential component decreases
431 10
1 1 (f) 3.49eV
10
r
10
10 9
fio8 •O
7
PHOTON ENERGY (eV)
Iz 106 UJ
z 10 12.2K to z
10"
r\*~~«*«*<W*$*
I 6.4K
=> .,„2 -J 10
10 10° 10
10
10 10 TIME (s)
10
Fig. 2. Log-log plot of luminescence decay curves measured with various excitation photon energies. Dotted curves represent the exponential components.
4.5K
! Laser 5
10
TIME (us)
Fig. 3. Temperature dependence of luminescence decay curves. Excitation density is 3.2 /J/cm 2 . Inset shows excitation spectra for two different temperatures.
with raising temperature. We analyzed the decay time with a formula T = 1R/(1 +atxp(—Ei/kT)) and obtained the radiative decay time XR of 1.5±0.1 yus and the activation energy £ a of 4±1 meV. The integrated intensity of the exponential component also decreases with raising temperature and the decay curve is dominated by the power-law component. As for the integrated intensity of the power-law component, it increases with temperature and becomes maximum around 15 K and then decreases. Inset in Fig.3 shows temperature dependence of the excitation spectra. The intensity near the absorption edge diminishes with raising temperature. By referring to the time-resolved excitation spectra in Fig.l, it is apparent that the decrease is caused by the quenching of the exponential component. 4. Discussion As reported already in ref.3, measurements of time-resolved luminescence spectra revealed that both the exponential and power-law components have the same spectral shape. This fact indicates that the two components originate from a common initial state, i.e., the STE state. Then the origin of the two components should be ascribed to the existence of two different formation processes of STE's. The exponential decay component is interpreted to be due to usual monomolecular recombination of a STE, i.e., direct formation of a STE from a photogenerated electron-hole pair in a TiC>6 octahedral site and the subsequent radiative recombination. As for the power-law component, we ascribe its origin to indirect formation of a STE, in which one of the constituent carriers (electron or hole) of the STE comes from the free state to the STE state via extrinsic trapped states. In fact, the power-law component was saturated compared with the exponential one with increasing the excitation density, suggesting that this decay process is related to lattice defects or residual impurities in the crystal.3 Similar experimental results and interpretation were reported for STE luminescence of SrTiC>3 in which the STE is supposed to be also localized on a TiC>6 octahedron.6 From the experimental results shown in Figs.l and 2, we found that the exponential component is stimulated efficiently under excitation near the absorption edge. This fact is interpreted as follows.
432 Recent band calculation shows that the top of the valence band is dominantly from O pn orbitals and the bottom of the conduction band from Ti d^ orbitals. 7 Both states have nonbonding character and thus are quite localized. Then under excitation near the absorption edge, it is expected that an electron-hole pair is created and confined in the same TiC>6 octahedral site and readily form a STE with inducing lattice distortion of the octahedron. The STE thus formed recombines, giving rise to the exponential decay component. On the other hand, if the excitation energy lies well above the absorption edge, electrons and/or holes are created in delocalized states and can migrate to the neighboring sites. This situation favors the appearance of the power-law component, because photocarriers have a chance to be trapped at impurity or defect sites during the migration. When the excitation energy is below 3.4 eV, the time constant of the exponential component at low temperatures is 1.5 ±0.1 fis irrespective of the excitation energy. We conclude that it represents the intrinsic radiative decay time of the STE in anatase Ti02- On the other hand, when the excitation energy exceeds 3.4 eV, the time constant is found to increase with the excitation energy. As can be seen from the time-resolved excitation spectra in Fig. 1, the efficiency of the power-law component is comparable to that of the exponential component above 3.4 eV. Then, it is supposed that in addition to the direct formation of STE's, retarded formation of STE's due to the indirect formation process also contributes to the time response of the luminescence in the short time range, causing the apparent increase in the time constant. The temperature dependence of the decay curves in Fig.3 shows that, as the temperature increases, the time constant of the exponential component abruptly decreases with the activation energy £ a of 4 ± 1 meV. There are two possibilities for the thermal decrease in the decay time. The one is thermal dissociation of free excitons before the formation of STE's. Although the existence of the stable free exciton states in anatase TK>2 has not been reported so far, the value of £ a is comparable to the reported value of free exciton binding energy in rutile Ti02, 4 meV.8 The other possibility is thermal decomposition of STE's , i.e., either an electron or a hole in a STE is shallowly localized and is thermally released from the localized state. In any case, thermally released carriers can migrate to the neighboring sites and are expected to contribute to the power-law component. In fact, at low temperatures, the intensity of the power-law component increases with temperature, though the integrated intensity is not conserved.
References 1. H. Tang, H. Berger, P. E. Schmid, F. Levy, Solid State Commun. 92, 267 (1994). 2. N. Hosaka, T. Sekiya, S. Kurita, J. Lumin 72-74, 874 (1997). 3. M. Watanabe, S. Sasaki, T. Hayashi, J. Lumin 87-89, 1234 (2000). 4. H. Berger, H. Tang, F. Levy, J. Cryst. Growth 130, 108 (1993). 5. H. Tang, F. L6vy, H. Berger, P. E. Schmid, Phys. Rev. B52, 7771 (1995). 6. R. Leonelli, J. L. Brebner, Phys. Rev. B33, 8649 (1986). 7. R. Asahi, Y. Taga, W. Mannstadt, A. J. Freeman, Phys. Rev. B61,7459 (2000). 8. J. Pascual, J. Camassel, H. Mathieu, Phys. Rev. B18, 5606 (1978).
SPECTROSCOPIC PROPERTIES OF SELECTIVELY DEUTERIUM-SUBSTITUTED RETINAL HOMOLOGUES TAKAYUKIYAMAMOTO, MOTOYA ABE, TAKASHIYAMADA, HTDEKI HASHIMOTO* Department of Materials Science and Chemical Engineering, Faculty of Engineering, Shizuoka University, 5-1 Johoku 3-Chome, Hamamatsu 432-8561, Japan
TAKAYOSHIKOBAYASHI Department of Physics, Graduate School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan A set of retinal homologue molecules (C15 aldehyde, C17 aldehyde, C18 ketone, C20 aldehyde) in which H H o r 1SH atom of their olefinic parts was selectively substituted by a deuterium (11D or 15D) was synthesized. Their spectroscopic properties were investigated by means of optical absorption and FT-IR spectroscopies. Normal coordinate calculations were performed for all the set of molecules in order to establish the assignment of vibrational modes. Upon deuterium substitution of the 11H or 15H atom, apparent decrease of the oscillator-intensity of the absorption transition was observed in the case of shorter polyene molecules (CIS and C17aldehydes and CISketone), while the decrease of the oscillator strength was negligible in the case of C20 aldehyde. Vibrational analysis suggested that the selective deuterium substitution induced the shift of electron distribution from double-bond site to single-bond site resulting in the decrease and increase in the bond orders of the former and the latter, respectively.
1. Introduction Carotenoids play light-harvesting and photo-protective functions
in photosynthesis. A
mechanism of natural selection of the specific trans-cis isomers of carotenoids to perform these functions was clarified.1-2> Extensive efforts have been devoted to reveal this mechanism by investigating the excited state properties of carotenoid molecules and by correlating these with their functions.3,4* On the other hand, recent progress of X-ray crystallography of photosynthetic pigment-protein complexes makes it possible to visualize the exact structures of reaction center and light-harvesting complexes with atomic resolution. 5 ' 6 ' It is pointed out that the specific spatial arrangement of photosynthetic pigments in these complexes is also important to perform the physiological functions.
Therefore, in order to fully understand the functions of carotenoids in
photosynthesis, it is important to reveal the relation between their structures and functions not only in the aspect of molecular configuration but also inter-molecular interaction. Vibrational spectroscopy is a powerful
tool in probing the molecular structures together with the
inter-molecular interaction of carotenoids once the assignment of vibrational modes has been established. Isotope substitution is inevitable to do this since one can modify the frequencies of normal vibrations without inducing drastic change of molecular structures. In this study, we synthesized retinal homologues (C15, C17, and C20 aldehydes and C18 ketone) as well as their derivatives in which 11H or 15H atoms were selectively substituted by deuterium (D). Their optical absorption and infrared absorption were compared with those of the unsubstituted ones. Normal coordinate analysis was performed in order to establish the assignments of the vibrational modes. X-ray crystallography of deuterium-substituted retinals was also performed.
* Corresponding author, E-mail address: [email protected]
433
434
E
7° 2
"o
% O
o c o •2 o c
2
'•4-*
X d>
JO
Fig. 1. Chemical structures of selectively deuterium-substituted retinal homologues.
o 2
200
300
400
500
Wavelength / nm Fig. 2. Optical absorption spectra of retinal homologues with or without deuterium substitution. NA is an abbreviation of natural abundant and shows the original homologue without substitution.
2. Experimental Figure 1 shows chemical structures of deuterium-substituted retinal homologues so far synthesized in this study. They are (a) 11D-C15 aldehyde, (b) 11D-C17 aldehyde, (c) 11D-C18 ketone, (d) 11D-C20 aldehyde, and (e) 15D-C20 aldehyde (C20 aldehyde corresponds to retinal). These derivatives were synthesized by the elongation of isoprenoid backbone from the shorter polyene molecules by the use of Horner-Emons or Wittig reaction as well as Aldol condensation. By using appropriate bases that include deuterium such as L1AID4, we could selectively introduce the deuterium atoms into the desired positions. Optical absorption spectra of retinal homologues and their deuterium-substituted derivatives in n-hexane solutions were recorded using Hitachi U3000 spectrophotometer. IR spectra of these compounds in KBr disks were recorded using Shimadzu FT-IR 8200A infrared spectrophotometer. Normal coordinate analysis was performed for model polyenes that mimic the structures of retinal homologues 8 ' using the computer programs of GCCC, BGLZ, LSMB and LXZ developed by group of Prof. Takehiko Shimanouchi at the University of Tokyo. Urey-Bradley-Shimanouchi force field8' was adopted for the calculation purpose. X-ray crystallography of retinals was performed using
435
Fig. 3. FT-IR spectra and vibrational assignments of (a) C15 and (b) 11D-C15 aldehydes.
Fig. 4. Comparison of the bond-lengths of C20 aldehyde (NA) and its 11D and 15D substituted derivatives.
Rigaku AFC-7R diffractometer at room temperature. 3. Results and Discussion Figure 2 shows the absorption spectra of (a) C15 and 11D-C15 aldehydes, (b) C17 and 11D-C17 aldehydes, (c) C18 and 11D-C18 ketone and (d) C20, 11D-C20 and 15D-C20 aldehydes. As regard the shorter polyene molecules than C20 aldehyde, apparent decrease of the oscillator-strengths was observed upon selective deuterium substitution, although the absorption band shape shows complete agreement before and after the deuterium substitution. Only the slight decrease was observed in the case of C20 aldehyde (retinal). Because of the magnitude of ca. 10% decrease in intensity, the possibility to explain the cause of the present observation by the use of vibronic coupling theory, which is proved to be important to ascribe the electronic states of carotenoid molecules, can be ruled out. We tentatively attribute these phenomena to the distortion of electronic structures of the retinal homologues upon deuterium-substitution as exemplified by the vibrational and crystallographic analyses shown below. As an example of FT-IR measurements and the vibrational assignments of retinal homologues, Fig. 3 shows the result of C15 and 11D-C15aldehydes. Large shift to lower frequency in the 11D in-plain (HDi.p.) and 11D out-of-plain (11D0.P.) bending modes is observed upon selective deuterium substitution. In accordance with this frequency shift of the bending modes, the low frequency shift (lfs) of the neighboring C=0 stretching mode (C=0) and the high frequency shift (hfs) of the neighboring C10-C11 stretching mode (10-11) were observed. Quite similar observation was found in other retinal homologues, i.e., lfs of C11=C12 stretching and the hfs of C10-C11 stretching in 11D-C17and 11D-C20 aldehydes and 11D-C18 ketone, lfs of C=0 stretching and hfs of C14-C15 stretching of 15D-C20 aldehyde. This result suggests that the selective deuterium-substitution induces the shift of the electron distribution from double-bond site to
436 single-bond site resulting in the decrease and increase in the bond orders of the former and the latter, respectively. Among the derivatives so far examined only C20 aldehydes (C20, 11D-C20 and 15D-C20 aldehydes) afforded single crystals that were applicable to the crystallographic analysis. All the crystals belong to the same monoclinic Yl\ln
space group, hence we can directly compare the
molecular structures of C20 aldehydes with or without deuterium substitution. Figure 4 compares the bond-lengths of the olefmic part of C20, 11D-C20 and 15D-C20 aldehydes. The results completely support the above findings by means of vibrational spectroscopy. Elongation of the C=C or C = 0 bond and shrinkage of C-C bond adjacent to the C-H bond selectively substituted by deuterium are observed. This finding is a strong evidence that the distortion of the electronic structures takes place upon selective deuterium substitution. Based on the close inspection, we can also find the deviation of bond lengths induced by deuterium substitution at the other parts of the polyene backbone. This finding will provide us with useful information concerning the inter-molecular interactions in the crystal. However, this topic is beyond the scope of the present study and it would be discussed in detail elsewhere.
Acknowledgements This work is supported by Grant-in-aid (# 10740145 and 1240179) from Ministry of Education, Science, Sports and Culture in Japan, and by Research for the Future of Japan Society for the Promotion of Science (JSPS-RFTF-97P-00101). References 1. Y. Koyama, J. Photochem. Photobiol. B: Biol. 9,265 (1991). 2. H. Hashimoto, Butsturi 50, 555 (1995). 3. Y. Koyama and H. Hashimoto, in Carotenoids in Photosynthesis, ed. A. Young and G Britton (Chapman & Hall, London, 1993) p. 327. 4. Y. Koyama and R. Fujii, in The Photochemistry of Carotenoids, Advances in Photosynthesis Vol. 8, ed. H.A. Frank et al. (Kluwer, Dordrecht, 1999) p. 161. 5. J. Deisenhofer and H. Michel, Science 245, 1463 (1989). 6. G McDermott, S.M. Prince, A.A. Freer, A.M. Hawthomthwaite-Lawless, M.Z. Papiz, R.J. Cogdell and N.W. Isaacs, Nature 374, 517 (1995). 7. R.J. Cogdell and J. Gordon-Lindsay, Trends in Biotechnology, 16, 521 (1998). 8. Y. Mukai, M. Abe, Y. Katsuta, S. Tomozoe, M. Ito and Y. Koyama, J. Phys. Chem. 99,7160 (1995). 9. H. Nagae, M. Kuki, J.-P. Zhang, T. Sashima, Y. Mukai, and Y. Koyama, J. Phys. Chem. A104 (2000) 4155.
P h o t o i n d u c e d infrared absorption s p e c t r a of CuCl q u a n t u m d o t s in N a C l
K. Yamanaka*, K. Edamatsu and T. Itoh Division of Materials Physics, Graduate School of Engineering Science, Osaka University 1-3, Machikaneyama-cho, Toyonaka, Osaka 560-8531, Japan We have studied infrared transient absorption spectra of CuCl QDs grown inside a NaCl matrix under tunable UV laser excitation on resonance with the confined excitons. In addition to the transient excited-state absorption, there appears induced IR absorption with lifetime much longer than that of the confined exciton. The peak energy remains at ~ 0 . 3 eV regardless of the QD size. The optical density is proportional to the square root of the UV laser power. The decay of the induced absorption is logarithmic on time and is accelerated by the irradiation of light below the band gap. We assign this absorption to be originated from the electron-bound defect center called 1, center generated in the NaCl side of the interface and discuss it phenomenon in relation with photo-irradiation effects, such as photofatigue, blinking of the luminescence and hole burning. 1. I n t r o d u c t i o n Quantum size effects on confined excitons in semiconductor quantum dots (QDs) have been extensively studied through the measurement of absorption, luminescence or luminescence excitation spectra. 1 Recently, we have studied infrared transient absorption spectra of CuCl QDs grown inside a NaCl matrix under tunable UV laser excitation which is on resonance with the confined excitons. 2 During the ns lifetime of the IS exciton generated by pulsed UV laser irradiation, the transient absorption from the IS t o 2P exciton states appears at the mid-IR region of a few hundred meV. The transition energy increases with the decrease of the QD size, from 170 meV for the bulk crystal to 380 meV for the QD radius of 1.4 nm. Although the lowest exciton state of CuCl QDs is well classified into the weak confinement regime because of the very small exciton Bohr radius, this fact has indicated that the confinement is no more weak for the higher Rydberg exciton states of CuCl QDs. 3 Furthermore, on the course of this study, there appears another type of induced IR absorption with much longer lifetime. 4 The peak energy remains at ~ 0.3 eV regardless of the QD size. The optical density is proportional to the square root of the UV laser power. The decay of the induced absorption shows logarithmic dependence on time. The decay is accelerated by the irradiation of light below the band gap. In the present paper, we report the characteristic behaviors of this long-lifetime infrared transient absorption, assign it to be that of the electron-bound defect center called I e center previously observed in NaCl bulk crystals, 6 and discuss the phenomena in relation with the photo-irradiation effects, such as photofatigue, 6 blinking 7 of the luminescence and hole burning. 8 2. E x p e r i m e n t a l P r o c e d u r e s Samples are CuCl QDs (mean radius ~ 3 nm) embedded in a NaCl matrix prepared by transverse Bridgman method followed by successive annealing processes. The size distribution of the dots is ranging from 1.2 nm t o tens of nm in radius for different samples. For the infrared transient absorption measurement, a xenon flash lamp with a MgF2 window was used as a probe light with a pulse width of 8 fjs. As a UV pump light source for the sizeselective excitation, we used the second harmonic light of a Ti-sapphire laser (pulse width: 15 ns, repetition rate: 10 Hz) pumped by the second harmonic of a pulsed Nd:YAG laser. The 'Present address: Department of Electrical and Electronic Engineering, Yamaguchi University, Tokiwadai 2-16-1, Ube, Yamaguchi 755-8611, Japan
437
438
10 7 Fig. 2
WAVELENGTH (nm) 5 4 3
'HI^
it- £ Fig. 1
77K A?^.
o*>10nm
't.A*
§
0
0.2 TIME (us)
200 400 PHOTON ENERGY (meV)
600
Fig. 1. Temporal change of the induced IR absorption at different temperatures. The photon energies (wavelengths) of the excitation and the probe light is 3.224 eV (384.6 nm) and 0.33 eV (3.8 flm), respectively. Ay. fast component, A?: slow component, A3: baseline shift. Fig. 2. Transient absorption spectra of the three components (Ay. solid circles, A2'. open circles, A3: solid triangles) for different sizes of dots at 77 K. The excitation photon energies and the corresponding effective radii of the dots are (a) 3.217 eV, > 10 nm, and (b) 3.224 eV, 5.4 nm, respectively.
power level of the UV excitation laser, ~ 100 MW/cm2, ensures that more than one exciton are generated in each dots. Temporal change of the transient absorption is measured and accumulated 50 ~ 1,000 times by a digital storage oscilloscope to improve the S/N ratio. The decay which is longer than the pulse duration of the probe light was measured by setting a delay time for the probe pulse ignition up to 100 ms which is limited by the laser repetition rate of 10 Hz. Furthermore, for the measurement of the decay longer than 1 s, the measurement procedure was modified as follows. At first the sample was irradiated by the 10 Hz pump laser for 30 s without the probe light irradiation, and then by stopping the pump laser, the probe light irradiation started and the absorption was measured for the duration of 5 s. By controlling the delay time, we could measure the decay of the transient absorption up to 600 s. 3. Results and Discussions Figure 1 (a) - (c) show the time profiles of the transient absorption observed at 4.2 K, 77 K and room temperature, respectively. The photon energies (wavelengths) of the excitation and the probe light are 3.224 eV (384.6 nm) and 0.33 eV (3.8 /mi), respectively. The transient absorption is decomposed into three components denoted as A± ~ A3. At is the fast component with the decay time of the order of ns or less, A2 is the slow component with the decay time of a few hundreds ps and A3 is the baseline shift due to the slow components with the decay time much longer than 100 ms, the repetition time of the UV pump laser. The fast component At is directly related with the confined exciton in QDs as already reported in the previous papers.2'4 The most remarkable feature is that the baseline shift A3 increases much with the decrease in temperature. This fact indicates the distinguished temperature dependence of the decay time
439 Fig. 4
Fig. 3
10
10"'
10"' 10 TIME (ms)
10
10
5 10 5 10 EXCITATION INTENSITY /(a.u.)
Fig. 3. Plots of the transient absorption at 77 K versus the delay time in logarithmic scale up to 100 ms. The dotted line is a guide for eyes. Fig. 4. Excitation power dependence of each component ( A i : solid circles, A2: open circles, A3: solid triangles) of the transient absorption at 77 K.
of the slow components. Figure 2 (a)-(b) show transient absorption spectra of the three components {A\: solid circles, A2: open circles, A3: solid triangles) for different sizes of dots at 77 K. Here, the abscissa is the photon energy of the probe light. The excitation photon energies and the corresponding effective radii of the dots are (a) 3.217 eV, > 10 nm, and (b) 3.224 eV, 5.4 nm, respectively. The components A\ and A2 show different spectra. While the spectra of the fast component A\ show peak energy shift depending on the dot size, those of the slow component A2 are almost independent of the dot size. The spectral shapes of the components A2 and A3 are the same except for their relative intensities. These facts indicate that the slow components A2 and A3 attribute to the same origin which originates from localized nature, such as a defect center or a surface state of QDs. Figure 3 shows the plots of the transient absorption at 77 K versus time in logarithmic time scale up to 100 ms. The excitation and probe wavelengths are the same as in Figure 1. In the time range between 10 /J,S and 100 ms, the decay is approximately proportional to the logarithm of delay time. This logarithmic behavior of the slow component is similar to that of the hole burning phenomena in semiconductor Q D s 8 and organic glass materials. 9 The logarithmic decay has been explained by assuming the broad distribution of the relaxation rate from the trapping state to the ground state by analogy with the two-level-system (TLS). 10 In our measurement at 77 K, the decay time is estimated to be distributed from sub ms to of several seconds. At 4.2 K the induced absorption remained stably more than 10 minutes. Besides, the remaining absorption was eliminated by the irradiation of white light with photon energy below the bandgap within the irradiation time of several tens of seconds. Similar phenomena of CuCl QDs at very low temperature have been observed in the luminescence photofatigue 6 and the persistent hole-burning. 8 Excitation power dependence of each component of the transient absorption is shown in Figure 4. The condition of the measurement is the same as that of Figure 1. The intensity of the fast component A\ and the slow component A2 is almost proportional to the excitation power, that is, number of exciton generated in the sample. In contrast, the components A3 is proportional to the square root of the excitation laser power. Such temperature dependence and the bleaching phenomenon assure us that a carrier/exciton trapping is the conceivable origin of the induced absorption with very long decay time. The power dependence of As shown in Figure 4 can be explained if a kind of equilibrium condition is realized between the confined exciton and the trapped carrier dissociated from the confined
440 exciton, since the decay time of the induced absorption is much longer than the repetition interval of the excitation. This fact indicates that the observed long-lived transient absorption is caused by either the trapping center of an electron or a hole dissociated from the confined exciton. The square root dependence on the excitation power is also observed in the photofatigue phenomenon.6 Furthermore, we should emphasize that the spectral shape and the peak energy of the slow components A2 and A3 in Figure 2 are quite similar to those of the IR transient absorption caused by an electron-bound center called Ie center. This absorption band was observed in NaCl when nominally pure X-ray colored crystal was irradiated in the F band at low temperatures and it could be due to the trapping of an electron by the isolated cation impurity.5 Therefore, the slow components of the transient absorption observed in our samples may be caused by an electron dissociated from the confined exciton and trapped on the NaCl side of the interface between the QD and the NaCl matrix by the tunneling through the interface. In Figure 1 the component A3 comes less obvious at lower temperatures, while the intensity of the slow component A2 increases as the increase in temperature. At 300 K, we should take into account the blue shift and the width broadening of the exciton line which reduces the effective absorption of the UV excitation light. Accordingly, we suppose that the intensity of A2 at 300 K is substantially greater than that at 77 K. Therefore, it is concluded that the initial intensity of the long-lived induced absorption becomes larger at elevated temperatures, while the decay time becomes much shorter. The above behavior of the transient absorption is similar to those of the photofatigue effect6 and the blinking of luminescence,7 which also become remarkable at higher temperatures. Since the photofatigue and hole-burning are considered to be closely related to the interface states, the origin of the induced IR absorption with long lifetime is caused by the Ie-like centers located on the NaCl side of the interface between the QDs and the matrix. 4. Conclusion It is found that an electron dissociated from the confined exciton in CuCl QD is bound to the QD surface and forms the Ie-like defect center on the NaCl side of the interface, that causes the transient IR absorption. While the remaining hole in the QD or the trapped electron may give the confined Stark effect on the QD, resulting in the photofatigue, blinking or hole-burning effect on the successively photo-generated excitons inside the QD. Acknowledgements This work was supported by the Research for the Future from JSPS (JSPS-RFTF97P00202) and Grant-in-Aids for COE Research (10CE2004) and Scientific Research from the Ministry of Education, Science, Sports and Culture of Japan. References 1. S. V. Gaponenko, Optical Properties of Semiconductor Nanocrystls (Cambridge University Press, Cambridge, 1998). 2. K. Yamanaka, K. Edamatsu and T. Itoh, J. Lumin. 76&77, 256 (1998). 3. T. Uozumi, Y. Kayanuma, K. Yamanaka, K. Edamatsu and T. Itoh, Phys. Rev. B59, 9826 (1999). 4. K. Yamanaka, K. Edamatsu and T. Itoh, J. Lumin. 87-89, 312 (2000). 5. G. Jacobs, Phys. Stat. Sol. B129, 755 (1985). 6. T. Itoh, S. Yano, N. Katagiri, Y. Iwabuchi, C. Gourdon and A. Ekimov, J. Lumin. 60-61, 396 (1994). 7. M. Nirmal et al, Nature 383, 802 (1996). 8. Y. Masumoto, J. Lumin. 70, 386 (1996). 9. W. Kohler, J. Meiler and J. Friedrich, Phys. Rev. B35, 4031 (1987). 10. W. Breinl, J. PHedrich and D. Haarer, Chem. Phys. Lett. 106, 487 (1984).
SELF-TRAPPED EXCITONS IN ORTHORHOMBIC SnBr2 Y. YAMASAKI and N. OHNO Division of Electronics and Applied Physics, Graduate School ofEngineering, Osaka Electro-Communication University, Neyagawa 572-8530, Japan
Luminescence properties of SnBr2 have been studied to reveal the photo-excited exciton relaxation process. Two types of luminescence with large Stokes shifts are found at low temperatures; the 2.2-eV luminescence band produced under the photo-excitation in the first exciton region, and the 2.5-eV luminescence band stimulated by photons with energies above the bandgap. The timeresolved photoluminescence measurements have revealed that the 2.2-eV luminescence comprises fast (1.2 us) and slow (6.4 us) exponential decay components, whereas the 2.5-eV luminescence shows the time dependence of 7(0°='"°''. These results suggest that the former band is attributed to the radiative decay of self-trapped excitons, and the latter band would originate from tunneling recombination of holes with the STEL as in the case of lead halides.
1. Introduction Optical properties of lead halides have been studied extensively so far by several groups. Especially, luminescence studies of these materials have been carried out since they give complimentary information on the photolysis phenomena. Two types of luminescence bands have been observed in PbBr2 and PbCb at low temperatures. 1 ' 2 Under the excitation in the first exciton region, the B (UV) luminescence is observed, attributed to the radiative decay of self-trapped excitons at Pb + ion sites in PbBr2 (PoCk). The other is the BG luminescence stimulated by photons with energies above the bandgap, which originates from tunneling recombination of holes released from some trapping centers with electrons trapped at the Pb23+ self-trapped electron (STEL) centers. ' These exciton relaxation processes are quite different with those of excitons in well studied alkali halides. 5 Grthorhombic tin halides, SnBr2 and SnCL;, have the same crystal structure (space group Pmnb) and the similar electronic configurations as orthorhombic lead halides. It is interesting to know the electronic structures and exciton states in Sn halides. The investigation of the optical properties of SnBr 2 and SnCb would deepen our understanding the energy relaxation processes which would involve the STEL. However, only a few studies on optical properties of Sn halides have been reported so far.6"8 Reflection measurement of SnBr 2 has revealed a pronounced polarization dependence of the first exciton band at 3.4 eV. 9 ' 10 The polarization dependence has been well interpreted as a cationic interband transition in Sn 2+ (5s—>5p) under the crystal field with Cs symmetry. 10 The observed first exciton structures in SnBr2 are found to be considerably sharp as compared with those in orthorhombic Pb halides. 11 ' 12 The exciton binding energy has also been estimated as 32 meV. The logarithmic plot of the absorption spectra at the absorption edge has been found to give a straight line, that is, the absorption tail of SnBr 2 is described as the Urbach rule. 10 The obtained small value of the steepness parameter
441
442
bandgap. The time-resolved photoluminescence measurements have revealed that the 2.2-eV luminescence shows an exponential decay, whereas the 2.5-eV luminescence has the time dependence of 7(f)°cf_a9. These results suggest that the 2.2-eV band is attributed to the radiative decay of self-trapped excitons, and the 2.5-eV band would originate from tunneling recombination of trapped holes with the STEL as in the case of lead halides. 2. Experiment The granule SnBr2 powders of 99.9 % purity were first filtrated from their melt through quartz wool in vacuum. Single crystals were grown by the zone-melting method. The sample crystals were prepared by cleavage along the crystallographic aft-plane. Optical measurements were carried out using synchrotron radiation as a light source from the UVSOR facility in the Institute for Molecular Science, Okazaki. The samples were mounted on a copper block attached to a temperature-variable cryostat of liquid helium-flow type. The light beam passed through a 1-m Seya-Namioka type monochromator was incident on the sample surface. Luminescence emitted from the illuminated surface was collected by lenses, and analyzed through a Jovin-Yvon HR320 monochromator equipped with an R955 photomultiplier. 3. Results and Discussion Figure 1 shows the luminescence spectra of SnBr2. The measurement was made at 12 K and the polarization of excitation light was along the 6-axis of the crystal. The spectrum shown by solid curve was obtained under the excitation with 3.39-eV light whose energy falls in the first exciton region. Two luminescence bands are observed at 2.17 eV and 1.85 eV. The 2.17-eV band has a Gaussian lineshape and a large Stokes shift of 1.24 eV from the lowest exciton energy for Ellb polarization. When the excitation was made with higher-energy light than the bandgap energy, on the other hand, the luminescence spectrum changed drastically as shown by hatched curve in the figure, where the excitation energy was 6.20 eV. The spectrum consists of a broad band peaking at 2.52 eV, and the weak structures around 2.3 and 2.9 eV. The intensities of these luminescence bands become weak when the sample is warmed above 50 K, and almost disappear at 100 K.
3.39 eV 'E
SnBr2 12 K E//b
3
.d n V> 0.5 z UJ i-
z
^*^^H^. 2.0 2.5 3.0 PHOTON ENERGY (eV) Fig. 1. Luminescence spectra of SnBr2 excited with 3.39-eV light (solid curve) and 6.20-eV light (hatched curve) with Ellb polarization measured at 12 K.
443
In order to investigate the origin of these luminescence bands, the excitation spectra were examined at low temperature. Figure 2 show the excitation spectra for the 2.17-eV band (solid curve) and 2.52-eV band (hatched curve) measured at 12 K. Arrows indicate the first exciton energies for Ellb polarization.910 As clearly seen, the 2.17-eV band is efficiently produced under the photo-excitation in the first exciton region. On the other hand, the 2.52-eV luminescence is hardly excited under the exciton region, but stimulated by photons with energies higher than the bandgap. It is thus confirmed that under excitation in the lowest exciton band the 2.52-eV luminescence is not observed while the 2.17 eV luminescence appears strongly. Although not shown in the figure, the excitation spectrum for the 1.85-eV band exhibits a strong peak at 3.11 eV, suggesting this band is ascribed to some impurity in the crystal. There have been found two types of luminescence in PbBr2 at low temperatures.1. One is the B luminescence (2.75 eV) produced under the excitation in the first exciton region, attributed to the radiative decay of self-trapped excitons at Pb2+ ion sites in PbBr2. The other is the BG luminescence (2.62 eV) stimulated by photons with energies above the band gap, which originates from tunneling recombination of holes released from some trapping centers with electrons trapped at the Pb23+ STEL centers. The 2.17-eV band in SnBr2 is probably ascribed to self-trapped excitons similar to the B band in PbBr2 since the 2.17-eV band appears under the excitation of the first exciton region, that is, this band is originated from the radiative decay of self-trapped excitons at Sn2+ ion sites. On the other hand, it is probable that the origin of the 2.52-eV band is due to the similar relaxed excited states to the BG luminescence in PbBr2, namely the tunneling recombination of holes with electrons trapped at the Sn2 + STEL centers. The time-resolved photoluminescence has been also measured in order to investigate the temporal behavior of the luminescence bands. The excitation pulse sources are the second harmonic light of a mode-locked Ti:Sapphire laser (pulse duration 2 ps) and a N2 laser (pulse duration 3 ns). The decay curve of the 2.17-eV band under the 3.35-eV excitation from Ti:Sapphire laser is found to consist of two exponential decay components of 1.2 |xs and 6.4 (as. On the other hand, the 2.52-eV luminescence intensity under the 3.68-eV excitation from N2 laser is approximately proportional to f~09 in the region of r<100 us. These results support the above assignment of the luminescence bands observed in SnBr2, suggesting strongly that there are two channels in the relaxation process for the photo-excited carriers in SnBr2; the 2.17-eV band is attributed to the radiative decay of self-trapped excitons, and the 2.52-eV band would originate from tunneling recombination of holes with the STEL as in the case of lead halides.
. 1~
I
SnBr2 12 K E//b
1 a
I J
g
xcit
^
111
2.52 eV
>•
t 0.5
(/> Z UJ H Z
: nift
:
L2.17eV I W ,
3.0
,
"\
I
1
^
1 " i M M ' V * W v A . r t , i r l - i . i_ j - i
3.5 4.0 4.5 PHOTON ENERGY (eV)
5.0
Fig. 2. Excitation spectra for 2.17-eV (solid curve) and 2.52-eV band (hatched curve) of SnBr2 at 12 K.
444
Acknowledgement The authors are grateful to Prof. M. Kamada and M. Hasumoto for support under the Joint Study Program of the UVSOR facility of the Institute for Molecular Science.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]
M. Kitaura and H. Nakagawa, J. Electron Spectrosc. and Relat. Phenom. 79, 171 (1996). M. Kitaura and H. Nakagawa, J. Luminesc. 72-74, 883 (1997). S.V. Nistor, E. Groovaert and D. Schoemaker, Phys. Rev. B48, 9575 (1993). S.V. Nistor, E. Groovaert and D. Schoemaker, Rad. Effects Defects 136, 157 (1995). K. Kan'no, K. Tanaka and T. Hayashi, Rev. Solid State Science 4, 383 (1990). N.S. Pidsyrailo, A.S. Voloshinovskii, N.G. Stan'ko and Z.A. Khapko, Sov. Phys. Solid State 24, 708 (1982). A.S. Voloshinovskii, S.V. Myagkota, N.S. Pidsyrailo and Z. A. Khapko, Opt. Spectrosc. (USSR) 52,457 (1982). A.S. Voloshinovskii, Phys. Solid State 35, 1588 (1993). Y. Yamasaki and N. Ohno, UVSOR Activity Report 1999, 84 (2000). N. Ohno, Y. Yamasaki, H. Yoshida and M. Fujita, submitted to Phys. Status Solidi (b). J. Kanbe, H. Takezoe and R. Onaka, J. Phys. Soc. Jpn. 41, 942 (1976). M. Fujita, H. Nakagawa, K. Fukui, H. Matsumoto,T. Miyanaga and M. Watanabe, J. Phys. Soc. Jpn. 60,4393 (1991).
The Collective Excitations in High-Tc Superconductors I. Kanazawa Department of Physics, Tokyo Gakugei University, Koganei, Tokyo 184-8501, Japan It is proposed that the collective modes around the hole for k ~ (TT,0) in underdoped cuprates might correspond to massive gauge fields J4£, which are introduced by the gaugeinvariant carrieron (GIC) model. 1. Introduction One of the most intriguing recent developments in the understanding of the high Tc superconductors has been given by angle-resolved photo emission spectroscopy (ARPES) experiments. Despite the progress, the line shape of photoemission spectra remains poorly understood. In underdoped high Tc cuprates, it has been reported that there are two aspects to the normal state gap in the spectra near (TT,0). The first is the broad maximum in 100-200 meV range, which becomes more pronounced in the more underdoped samples, while the second is the shift of the leading edge. Shen and Schrieffer [1] have argued that the broad features in the spectra are due to a strong dressing of collective modes around the photohole for k ~ (n, 0). Also Laughlin [2] has suggested that these features in the spectra are related to the decay of the injected hole into a spinon-holon pair. Recently it has been demonstrated that the resonance peak in the dynamic structure factor and the peak, dip, and/or hump structure of the electronic spectral function near (0,7r) in underdoped high Tc cuprates can simultaneously be explained by a strong spin-fermion interaction [3, 4]. In this study, we argue that the collective modes around the hole for k ~ (ir,0) correspond to the massive gauge fields .AjJ introduced by the gauge-invariant carrieron (GIC) model [5-10], which is based on the gauge-invariant effective Lagrangian density in the quasi-two dimensional strongly-correlated electron system. 2. A model system It has been proposed that in quasi-(2 + l)-dimensional quantum antiferromagnet the doped carrier is regarded as a kind of quasi-particle "carrieron" which is composed of the doped hole (electron) and the cloud of SU(2) Yang Mills fields A^ around the hole (electron) [5, 6]. In order words, we can think a "carrieron" is a complex particle composed of the hedgehog-like (monopole-like) soliton and the hole trapped into the mobile soliton. Taking into account that the symmetry in the undoped (2 -I-1) dimensional quantum antiferromagnet is invariant under local SU(2) [11], we think that the perturbing gauge fields A^ introduced by the hole has a local SU(2) symmetry. Then it is assumed that SU(2) gauge fields J4° are spontaneously broken through the Anderson-Higgs mechanism in a way similar to the breaking of the antiferromagnetic symmetry around the hole. We set the symmetry breaking (0|$o|0) = (0,0, fi(kF)} of the Bose field <j>a in the Lagrangian density as follows,
+1>+(id0-g2TaAZ)4>
445
446 ~
(d„A; - d.Al +
+ 2 (d^a
gseatoA^Al)2
- g4£abcAl
" A 2 (<pa
(1)
After the symmetry breaking (0|$„|0) = (0,0,/u(fcF)), we can obtain the effectice Lagrangian density, Ceff, at small doping of holes [5-10]. The value, n(kr), of the symmetry breaking depends strongly on an angle of Fermi momentum, kT, on the Fermi surface. That is, the valve fj,(kF), is much correlated to the gap-energy of the high energy pseudogap. Thus, the value, /i(fcF), is higher around the hot spot.
A// = \ {diNi g^e^N*)2 + i>+(ido-g2TaA^)rl, 1
(d„A°-dliAl + g3£abcAlAl)2
+ \™\ [(Alf + (A2)2] + mY [A%4>* - Afah] + 94m, {
- ^ T ^ 3 ( W ~^q^"M'
(2)
where AT* is the spin parameter, if> is Fermi field of the hole, mi = fj, • gt, rni = 2\/2A • fi. The effective Lagrangian describes two massive vector field A^ and A2,, and one massless U(l) gauge field A 3 . The generation function Z[J] for Green functions is shown as follows,
Z[J] =
I'
VADBVNVCVCV^V^V^ *-'GF+FP + J • * ) .
£ D F + P P = Bad»A;
+ ^aBaBa
(3)
+ iCad"VllCa,
(4)
where Ba and C" are Nakanishi-Lautrup(NL) fields and Faddeev-Popov fictitious fields, respectively. J-*
=
Ja'iAl + JaBBa + JaN-Na + J^-Ca
+
fji> + vi>+ + j ; ^ a
+ J^Ca (5)
BRS-quartet [12, 13] in the present theoretical system are (^uBl,C1,C1), (0 2 ,-B 2 ,C 2 ,C' 2 ), and ( A | , B3,C3, C3). Where A\^ is the longitudinal component of A3,. Because masses of A^ and A 2 are formed through the Higgs mechanism by introducing the hole, the fields A1 amd A 2 exist around the hole within the length of ~ 1/mi = Rc. The quantized gauge fields A° are expressed in A% = (2
e*P (ipr) + o a + ( p ) e » exp (-ipr)]
d3p/^,
447 where a>" = Jp2 + mf, (a = 1,2) and u§ = V^> (fl = 3), a"+(p) and aa(p) are the creation and annihilation operators of the gauge particle A£ with momentum p, respectively, and e£(p) are the polarization vectors. The masses, mi, of the gauge fields A1^ and Aj; induced by the hole depend strongly on an angle of Fermi momentum of the hole on the Fermi surface. The value, mi, is higher in the case of the hole aroimd the hot spot. It is thought that the interaction between two holes for the Cooper pair formation is derived from the exchange of the fields Aa [5-7]. The present theory (GIC model) is based on the SU(2) formulation [5, 6]. This is similar to recent SU(2) spinon-holon model [16, 17]. The spinon-holon model stresses that the low energy pesudo-gap corresponds to the crossover to spinon singlet RVB phase. While, the GIC model has stressed that the low energy pesudo-gap is due to the superconductivity fluctuation [18]. Recent experiments [19] seem to support the latter. In the present theory, the interaction between the charge and magnon is mediated with the gauge fields. Thus the present theoretical formula is extended more than the charge -magnon model. In addition, the GIC model satisfies the gauge-invariance, the renormarization, and the unitarity conditions. Now we shall consider the broad feature of the ARPES near (7r,0) in underdoped highTc cuprates from the present theoretical view. As Shen and Schrieffer [1] discussed, the loss feature, caused by collective excitations, will have a broad energy distribution of the ARPES because of the momentum dependence of the collective mode spectrum as well as the recoil energy of the hole when a collective excitation is emitted. Thus, the creation of a photohole is more likely to produce collective excitation plus a hole in the quasipaiticle band. From eq. (3), we can obtain the Green functions of the massive gauge fields A1 and A^ in 't Hooft-Feymann gauge as follows, that is, the Fourier transform of (J4JJ4J)O=I,2 is Dn(k,u>) ~ ^-aZ+m^+n • The photohole spectral function is represented by .,
,
tf
'
Im D(p, e) Re Zip, e)f + [/"• £(p, e)Y'
e>X
[e-eh-
W
where the self-energy is given by
5 > ' ) = -j£r <
—1
Un r &, r
(2-K)H J
J-oo
J-oo
•(tanh|f + c o t h ^ ) .
^Dip-nMAipr^) LJ + £i-£
— l5
M
The recoil relaxation with collective excitations occurs in a higher energy region in comparison with the hole energy ek + Re Zip, e)Thus, in the case of e 3>~ Jmf + (2kp)2, the imaginary part of the self-energy is introduced approximately as follows,
/mX)(e) ~ V™? + (2M 2 , This means that, in a higher energy region, the recoil relaxation is dominantly due to emission and absorption of the massive gauge fields A^ and A^. As described before, it should be noted that the valve of the mass, mi, of the massive gauge fields A1 and A2 is higher around the hot spot. So the present theory predicts that the broad feature of ARPES line shape is much remarkable near the hot spot. This is consistent with experimental results [14, 15]. Also, as the doping increases, both gap-energies of the low and high energy pseudogaps decrease remarkably, and these prendo-gaps annihilate in the overdoped region. According to decrease of the gap-energy of the high energy pseudogap, the value fi(kF) of the symmetry breaking and the masses of the gauge fields Aj, and A"^ decrease as the doping increases, and the massive gauge fields almost annihilate in the overdoped region. Thus, the value of the
448 imaginary part of the self-energy decreases as the doping increases, and the broad feature in the ARPES spectrum annihilates in the overdoped region. Now we can estimate roughly the spectral width in the ARPES in underdoped Bi 2212 as follows. Because the Cooper pair formation is derived from the exchange of the massive gauge fields in the present theoretical formula, the size of the Cooper pair seems to be ~ l / m i . Then it can be evaluated that mi is about 20 ~ 30 meV. In addition, the contribution of momentum distribution is estimated approximately to be half (~150 meV) of bandwidth. Thus we can estimate roughly that the spectral width in the ARPES is 170 ~ 180 meV. This is the same order to the measured spectral width in the ARPES. 3. Conclusion We have argued the anomalously broad feature of ARPES in underdoped high Tc cuprates by the gauge-invariant effective Lagrangian density in the quasi-two dimensional stronglycorrelated electron system. It is proposed that the collective modes around the hole for k ~ (TT,0) correspond to the massive gauge fields A^ and A^. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19.
Z. X. Shen and J. R. Schrieffer, Phys. Rev. Lett. 79, 1771 (1997). R. B Laughlin, Phys. Rev. Lett. 79, 1726 (1997). A. Chubukov and D. Morr, Phys. Rev. Lett. 81, 4716 (1998). Ar. Abanov and A. Chububov, Phys. Rev. Lett. 83, 1652 (1999). L Kanazawa, The Physics and Chemistry of Oxide Superconductors, Springer, Berlin, 1992, P481. I. Kanazawa, Physica C185-189, 1703 (1991). I. Kanazawa, Synth. Met. 71, 1641 (1995). I. Kanazawa, Superlattice Microst. 21, 279 (1997). I. Kanazawa, Advances in Superconductivity XII, Springer, Berlin, 2000, P275. L Kanazawa, Physica B, 244-288, 409 (2000). I. Affleck, Z. Zou, T. Hsu, and P. W. Anderson, Phys. Rev. B38, 745 (1988). C. Becchi, A. Rouet and R. Stora, Comrn. Math. Phys. 42, 127 (1979). T. Kugo and I. Ojima, Prog, Theor. Phys. SuppL 66, 1 (1979). M. Randeria. et.al., Phys. Rev. Lett. 74, 4951 (1995). P. J. White, Phys. Rev. B54, R15669 (1996). X. G. Wen and P. A. Lee, Phys. Rev. Lett. 76, 503 (1996). P. A. Lee, N. Nagaosa, T. K. Ng, and X. G. Wen, Phys. Rev. B57, 6003 (1998). I. Kanazawa, Physica C 282-287, 1763 (1997). Z. X. Shen, Physics and Chemistry of Transition-Metal Chides, Springer. Berlin, 1999, P144.
ABSORPTION SPECTRA SIMULATION OF PERSISTENCE-TYPE CYANINE DYE AGGREGATES IN LB FILMS A.G. VITUKHNOVSKY, A.N. LOBANOV, A.V. PIMENOV P.N.Lebedev Physics Research Centre, P.N.Lebedev Physical Institute, RAS, Leninsky Pr, 53, Moscow 117924, Russia
Y. YONEZAWA, N. KOMETANI Department of Applied Chemistry, Faculty of Engineering, Osaka City University, Sugimoto 3-3-138, Sumiyoshi-ku, Osaka, 558-8585, Japan Simulation of the absorption spectra of the 2D persistence-type molecular aggregates consisting of the combination of oxacyanine dye (S9) and thiacyanine dye (SI 1) is being considered. These aggregates are modeled by square matrix structure in the extended dipole approximation. The simulation takes into account the vector properties of the transitional dipole moment, its orientation, diagonal disorder and the composition of the aggregate. Good fit with the experiment is obtained for dipole tilt angle 9= 40°, dipole moment |i=8.1 D and the disorder parameter of 450 cm"1 for various molar fractions of dyes.
1. Introduction The J-aggregate of cyanine dyes in thin films is regarded as a sort of matrix-supported molecular clusters1. In this context, the mixed J-aggregates consisting of two kinds of cyanine dyes are interesting as a model of mixed molecular clusters. If two kinds of dyes have the similar molecular structure, the molecules of one kind may be chaotically substituted by another in the lattice, resulting in the J-aggregate of amalgamation type (HA-aggregate) or persistence type (HP-aggregate). The HA aggregate exhibits a single J-band, while two J-bands persist in the HP-aggregate. Analytical models of the mixed crystals composed of two types of molecules are reviewed by Broude et al? They have employed coherent-potential-approximation (CPA) and average-amplitude-approximation (AAA) approaches. The major part of these works is devoted to the isotope-substituted molecules (benzene, naphthalene and so on). In the former study3, the simulation of the amalgamation-type aggregate is carried out by means of the exact numerical solution of the eigenvalue problem of the exciton Hamiltonian. The present work is devoted to the simulation of the persistence-type aggregate. 2. Experimental The chemical structures of N,N'-dioctadecyl-oxacyanine perchlorate (S9) and N,N'-dioctadecylthiacyanine perchlorate (SI 1) are shown in Figure 1. These were purchased from the Japanese Research Institute for Photosensitizing Dyes (Okayama) and used without further purification. The cationic surfactant monolayer was formed on the water surface by spreading the CHC13 solution of S9, SI 1 and hexadecane. Dye layers were deposited on the quartz plate by the horizontal deposition method and subjected to absorption measurements by UV260 spectrophotometer (Shimadzu).
ccrto <xno i
i
i
C18H37 C 18 H 3 7
i
C18H37 Ci8H37
CIO/
CICV
S9
S11 Fig. 1. Chemical structures of S9 and S11.
3. Model The molecular aggregate is simulated by the 2D 10x10 molecules cluster with square-matrix structure3. The transitional dipole of each molecule is within the plane of the film and tilted relative to
449
450 the horizontal at the angle 8 as shown in Figure 2. All the interactions within the ensemble are treated in the extended dipole approximation 4 . The cluster is built of either the same type of molecules (SI 1 or S9) or their mixture (SllxA'+S9x(l-X)). The exciton Hamiltonian is constructed according the method similar to Schreiber and Toyozawa 5 , but considering all the intermolecular interactions.
H=£(£r°+4.MH+S I X » ( 4
(i)
Here, all symbols are same as those used in the previous paper3. This Hamiltonian is diagonalized numerically taking into consideration that the energies of the individual molecules are subjected to the diagonal energetic disorder simulated by the Gaussian-distributed pseudo-random numbers upon 25000 realizations. Resulting absorption spectra A(E) are calculated treating the dipole moments of the excitonic transitions as vectors fiy for natural polarization of incident light3,6.
A(E) =
fiA(E~EJ)^.
(2)
Here, A(£ - E) = 1/R for \E - El < R/2, and A(£ - E) = 0 otherwise. R is the resolution of the spectrum.
y-
1.0
• • • • • / -
•
•
/
0.8-I
<
/
/
/
/
/
/
-- 0.6 C O
"E. o 0.4-| CO
Si
< 0.20.0-
20000
25000
30000
20000
25000
30000
Wavenumber / cm'1
Fig. 2. Simulation of the absorption spectra of the 2D aggregates of A: S9 and B: S11. Solid line - experiment, squares ( • ) - calculation. 4. Results and Discussion As first step the spectra of the one-component systems (S9 and SI 1) were simulated. For each aggregate the magnitude of the molecular transition dipole Cu=8.1 D), tilt angle (tfe40°) and the disorder s450 cm'were adjusted to obtain good agreement with the experimental spectra of these aggregates. The energies of the monomer transitions were taken from the experiment as 23310cm"1 for SI 1 and 26212cm"1 for S9. For both aggregates we assumed the square-matrix structure with grid size of i?=10 A and the charge separation in the dipole equals to the above-mentioned distance. The results of this simulation are presented in Figure 2. For the simulation of the HP-aggregate, the molar fraction X of the S9 was substituted by S11 at random positions. This substitutional disorder is averaged upon 25000 realizations. The result of the simulation of the absorption spectra for different X is shown in Figure 3. Note that experimental
451 spectra are somewhat obscured by the existence of unaggregated dye molecules along with the formation of the small disordered dimers in the film, which are beyond the scope of this work. The similarity between the experimental and the simulated spectra is quite good. The dependence of the positions of the absorption spectra peaks upon the parameter l-X, shown in the Figure 4, depicts good agreement between experiment and simulation. It is noticed that with the increase of the concentration of one of the kinds of molecules the peaks of the mixed aggregate are pushed out of the
Experiment
Simulation
0.85
0.15 30000
30000 20000 Wavenumber / cm 1
25000
Fig. 3. Simulated and experimental absorption spectra of mixed dye aggregates for different X.
V V 26000
V*VE 2500024000 2 23000
^ O JPAO^-'
22000 — I
0.0
'
1
0.2
'
1
•
1
1
—~
i—
0.4 0.6 0.8 Molecular fraction 1-X
1.0
Fig. 4. Peak positions of the absorption spectra: filled circles - experimental blue peak, open circles - experimental red peak, upward filled triangles - simulated red peak, downward open triangles - simulated blue peak.
452 interval between peaks of pure aggregates, in contrast with the behavior of the HA-aggregates (Thia(et) + Thia(ph)) in the former paper 3 . As the difference of monomer transition energies AE and average bandwidth T of the S9 J-aggregate and S l l J-aggregate are about 2900 cm"1 and 2400 cm"1, the ratio AE/T= 1.2 is far larger than AE/T= 0.11 for the Thia(et) + Thia(ph) combination. This indicates that the value of AE/2Tis an important factor whether a given combination of dyes forms the HA- or HP-aggregate. In the Figure 5, the simulated density of states (DOS) 6 p(E) for the HP-aggregate is shown for different X.
0.9
c o o o
. 20000
.
25000 Wavenumber / cm"
.
. 0.1 30000
Fig. 5. Simulated density of states (DOS) function for different concentration X. As seen from Figure 3, the peaks of the spectrum gradually are broadened and shifted into the blue region upon the increase of the substituent molecule concentration. This is caused by the fact that upon the increase of the substitution concentration the localization length of the exciton is decreased from 10 to 2. This fact also influents the DOS in a way of changing the shape of the corresponding band shape. 5. Acknowledgments The work was partly supported by RFBR grants 99-02-17326, 00-15-96707, 00-02-16607 and NATO SfP97-1940 grant 6. References 1. Y. Yonezawa, T. MiyamaandH. Ishizawa,./ ImagingSci. Tech. 39,331 (1995). 2. V. L Broude, E. I. Rashba and E. F. Sheka, Spectroscopy of Molecular Excttons (Energoizdat, Moscow, 1981). 3. A. G. Vitukhnovsky, A. N. Lobanov, A. Pimenov, Y. Yonezawa, N. Kometani, K. Asami and J. Yano, J. Luimin. 8789,260 (2000). 4. V. Czikkely, H. D. Forsterling, H. Kuhn, Chem. Phys. Lett. 6,207 (1970). 5. M. Schreiber and Y. Toyozawa, J. Phys. Soc. Jpn. 51,1528 (1982). 6. H. Fidder, J. Knoester, D. A. Wiersma, J. Chem. Phys. 95,7880 (1991).
PROPAGATION PROPERTIES OF HIGH-DENSITY EXCITON POLARITONS T. J. Inagaki and M. Aihara Graduate School of Materials Science, Nara Institute of Science and Technology, 8916-5 Takayama-cho, Ikoma, Nara 630-0101 Japan We investigate the time evolution of the exciton wave packet by an interacting exciton polariton model. The analysis is based on the equation-of-motion for the expectation value of exciton polariton operator with respect to the macroscopic quantum state. We find that the nonlinear interaction between exciton polariton leads to the extraordinary fast propagation of high-density exciton polaritons. This result helps the proper understanding of the experiments on the unusually fast propagation of exciton polaritons in strongly excited B1I3. 1. I n t r o d u c t i o n T h e nature of high-density electron-hole (e-h) systems induced by an intense optical field has received considerable attention because of the attractive possibility of the Bose-Einstein condensation (BEC) and superfluidity of excitons 1 . Recent developments in the experimental techniques make it possible the simultaneous measurements of the spectroscopic and transport properties. In particular, the fast and coherent propagations of high-density excitons were observed in CU2O2 and Bilj}. These phenomena arise from the macroscopic quantum coherence of condensed exciton systems, because the fast exciton transport is more pronounced with increasing the exciton density. However, current understanding of these results still remain tentative and unclear because of the complicated situation, such as the polariton effect, the spatial inhomogeneity of exciton density, the finite life-time of excitons, the phonon effect and so forth; the decisive verification of the excitonic BEC and superfluidity have not yet been performed. The purpose of this work is to theoretically investigate the anomalous transport phenomenon of two-dimensional excitons with large oscillator strength, taking into account the excitonexciton interaction and the polariton effect. The equation-of-motion for expectation value of the exciton polariton operator with respect to the macroscopic quantum state is derived by the decoupling approximation assuming that the macroscopic quantum coherence is maintained. The numerical solution shows the significant deviation from the simple ballistic (or diffusive) polariton propagation. This result indicates that the exciton-exciton interaction considerably enhances the fast coherent propagation of exciton polaritons in the high-density state. 2. M o d e l H a m i l t o n i a n We consider the two-dimensional interacting exciton system in which the contact excitonexciton interaction is assumed. This assumption is justified because we pay our attention to the system in which the mean interparticle distance is much larger than the exciton Bohr radius. In the present analysis, we regard excitons as pure Bosons, and neglect the state-filling effect and the band-gap renormalization. The model Hamiltonian is written in terms of the annihilation operators of photons (bq) and excitons (Bq) as follows,
H = Jl{egBqBq + uqbqbq}-iY,9q{Bqbq + Bqbq} + ±Y: B{+qB^qBpBk, 1
1
fc,p,<j
453
(1)
454 where eq and ojq are the energies of free excitons and photons, respectively; A is the coupling constant of the exciton-exciton interaction, and gq is the strength of the exciton-photon interaction. The effect of the exciton polaritons is taken into account by using the polariton operators which are defined by the linear combinations of the exciton and photon operators: Bk = ukak
- ivk(5k,
bk = uk/3k - ivkak.
(2)
Here ak and /3k are the annihilation operators for lower- and upper-branch polaritons, respectively, and the Bogoliubov parameters uk and vk satisfies u\ + vk = 1. The model Hamiltonian can be rewritten in terms of the polariton operators by substituting Eq. (2) into Eq. (1). We choose the Bogoliubov parameters as to diagonalize the bilinear part of Eq. (1), and find u2 _ ! [ 1 Uk
H
4
1/
Sfc-^fc e w
\ 2
s2 + ( *- *) /'
v2
^ 1 f1 2
"
sk~tjk
1
yltfu +
1
^-uu?)
The model Hamiltonian is written as follows,
(uk+qak+q + ivk+q0l+q)(up^qal,__q
+o S
+ TOp_,/?£_,)(upap - ivp/3p)(ukak
- ivk/3k), (4)
fe,P,9
where the free polariton energies for lower- and upper-branches are given by
4 T ) = \ {(^ + wfc) =F ^9l + {ek-^k)2)
•
(5)
3. Equations of M o t i o n for E x p e c t a t i o n Value of Polariton Operators The equations of motion for the expectation value for polariton operators are easily obtained by the Heisenberg equation-of-motion. We consider the case where the excitons are in the macroscopic quantum state which is generated by the coherent incident light and is maintained by the exciton condensation effect. Under this circumstance, it is allowed to approximate the expectation value of the product of the polariton operators into the product of the expectation values of each components. We write the expectation value of the polariton operators as i>k = (ofc) a n d (pk = ( A ) , and their equations-of-motion are written as, i ^ K - V x - ^^{uk+p-KUKUkUplpl+p-Kl/Jklpp
dt
~
2iUk+p-KUKUkVp1pl+p_Klpk
k,p
-Uk+p-KUKVkVplpl+p_K
-I&KUK
ivk+p~KUKUkUp
- ivk+p-KUKVkvP4>k+p^K
,
{vk+p-KVKVkVp(f>k+p-K
-i^Yl k,p
-Vk+p-nVKUkUp^l+^xipkipp +2uk+p-KvKukVpilJk+p_K'ipk(t>p
-
iuk+p-KvKvkvpipl+p_K(j)k(j)p
+ iuk+p-KVKUkUpipl+p_Kipkipp}
(6)
455
4. Numerical Calculations In the numerical calculation, we use the units of the single-particle energy of exciton with k = 0 and the speed of light in a background material being unity. For simplicity, we consider the one-dimensional propagation problem in two dimensional materials. As an initial condition, we prepare the exciton wave packet at the origin which has the form ^eK(x,t = 0) = v/p7v/¥exp[-(a;/(T)2/2], where p is the mean exciton density, and a = 5.0 is the width of the initial wave packet. We calculate the expectation value of the upper- and lower-branch polariton operators at t — 0 by the relation Eq. (2). We numerically solve the equation of motion (6) by Adams method and then calculate the exciton amplitude by the inverse relation of Eq. (2). In the present analysis, we choose the exciton-photon coupling strength as gk = 0.1. 1 0.8
s 3
\ I -I
t=o
I
0.6
r
0.4
.
—
t = 11 - t = 22 - - t = 33 — -
Figure 1: The time evolution of the exciton wave packet in the high exciton density, p = 10. The coupling constant of excitonexciton interaction is A = 0.01.
X=0.01
0.2 - T~"\
I
\
0 0
40
20
60
80
100
We show, in Figs. 1 and 2, the time evolution of the exciton wave packet in the highand low-density exciton systems; the coupling constant of the exciton-exciton interaction is A = 0.01. Figure 3 depicts the time evolution of the exciton wave packet in the absence of the exciton-exciton interaction, i.e., free exciton polariton model. We find that the expansion velocity of the exciton wave packet significantly increases as the exciton density grows. 1 t=o t = 11
0.8 \ \
• ^
3
2
0.4
t = 22 - - - t = 33 t = 44 - - -
\\ \\
0.6
— - - •
A
X=0.01
V
0.2 ,N s
'
^\
0
5
10 15 20 25 30 35 40 45 50 x
Figure 2: The time evolution of the exciton wave packet in the low exciton density, p = y/n. The coupling constant of excitonexciton interaction is A = 0.01.
456 This phenomenon arises from the nonlinear polariton interaction generates the wide polariton distribution in the momentum space, and therefore the polariton effects is more pronounced. Namely, the simple nonlinear Schrodinger equation cannot describe the unusually fast exciton propagation, and the combination of the nonlinear exciton interaction and the polariton effect plays the essential role in understanding the transport phenomena for the high-density excitons with large oscillator strength. In summary, we have analyzed propagation property of the high-density exciton polariton by an interacting polariton model, and find that nonlinear many-body interaction between polaritons leads to the extraordinary fast expansion of coherent excitons. This may provides us with the proper interpretation of noticeable experiments on the transport phenomena in high-density exciton systems.
o X
Figure 3: The time evolution of the exciton wave packet in the absence of the exciton-exciton interaction, A = 0.
X
9?
0
5
10 15 20 25 30 35 40 45 50 x
Acknowledgement This work is partially supported by a Grant-in-Aid for Scientific Research on priority areas, "Photo-induced Phase Transitions and Their Dynamics" from Ministry of Education, Science, Culture and Sports of Japan. References 1. S. A. Moskalenko and D. W. Snoke, Bose-Einstein Condensation of Excitons and Biexcitons (Cambridge University Press, Cambridge, 2000). 2. E. Fortin, S. Farad and A. Mysyrowicz, Phys. Rev. Lett. 70, 3951 (1993), A. Mysyrowicz, E. Benson and E. Fortin, Phys. Rev. Lett. 77, 896 (1996). 3. H. Kondo, H. Mino, I. Akai and T. Karasawa, Phys. Rev. B 58, 13835 (1998).
EXCITON DYNAMICS AND LATTICE RELAXATION IN OLIGOSILANES S. SUTO, H. SUZUKI, R. ONO, M. SHIMIZU, and T. GOTO Department of physics. Graduate School of Science, Tohoku University, Sendai 980-8578, Japan
A. WATANABE, and M. MATSUDA Institute for Chemical Reaction Science, Tohoku University, Sendai 980-8577, Japan
We have measured the absorption, photoluminescence, photoluminescence excitation spectra and the time response of luminescence intensity of the permethyl-hexasilane (Sij(CH3)i4) glass and permethyldodecasilane (Sii2(CH3)26) in 3-methylpentane solution. The Sig(CH3)i4 oligomer shows a strong lattice relaxation in the photo-excited state and we have determined the parameters in configuration coordinate of Sig(CH3)]4 oligomer. The luminescence is attributed to the self-trapped exciton state. The Sii2(CH3)26 oligomer has several conformers at room temperature and only one conformer at 77 K. The Sij2(CH3)26 shows a weak lattice relaxation at room temperature and form free excitons at 77 K.
1. Introduction Recent progress in understanding the photo-excited states in a 0-conjugated polymer of polysilanes have led to a next question about the exciton-phonon coupling in silicon polymers.1-2 The excitons have two extreme cases: one is the free excitons and the other is the self-trapped excitons due to the strong exciton-phonon coupling. Several experimental3'4 and theoretical4-5 studies are carried out for the permethyl-oligosilanes, i.e. Sin(CH3)2n+2- The oligomers have a transconformation and the conformation does not change with silicon chain length. This nature enable us to investigate the dependence on the chain length for excitonic nature. Raymond and Michl reported that the self-trapped excitons are formed below n=6 and free excitons exist above n=7 judging from the measurements of absorption and luminescence spectra: large Stokes shifts are observed below n=6 and Stokes shifts are not observed above n=7. In spite of these studies, the nature of excitons are still not clear. In this report, we have measured the absorption, luminescence, luminescence excitation spectra and the time response of the luminescence intensity to investigate the excitonic nature of permethyl-oligosilanes (SinMe2n+2 )> in particular, the permethyl-hexasilane (SieMen) and the permethyl-dodecasilane (Si]2Me26). 2. Experiment The permethyl-hexasilane (SigMei4) and the permethyl-dodecasilane (Sii2Me26) were synthesized by the Wultz coupling method. Since the Si6Mei4 oligomer is liquid at room temperature, we dropped it on the quarts glass plate and made the SigMe^ glass film to cool down to 2 K. The Sii2Me26 is solid at room temperature and used 3-methylpentane as solvent. For the absorption measurements, we used a deuterium lamp, a single monochromator, and a silicon diode array as a detector. The resolution was 3.6 meV. For the measurements of 457
458 luminescence excitation spectra, a combination of a Xenon-arc lamp and a home-made single monochromator of 1.2 m in focal length was used. The resolution was 11.9 meV. For the measurements of luminescence spectra and the time response, the excitation source was the frequency doubled output of Rhodamine B and 6G dye lasers pumped by the doubled out put of a cw mode-locked Nd:YAG laser. The luminescence was detected by a photomultiplier or a synchroscan streak camera. The time resolution was 32 ps and the repetition was 77 MHz. 3. Results and discussion 3.1. Permethyl-hexasilane (Si^Me^) Figure 1 shows the absorption and luminescence spectra of Si^Me^ glass at 2 K. The absorption peak due to the a - a * transition is observed at 4.70 eV and the luminescence peak is at 3.60 eV. The luminescence is observed with the excitation energy of 4.66 eV. The large Stokes shift of 1.1 eV is observed. As shown in Fig.l, the Gaussian line shape fits well with the luminescence peak. Moreover, the decay time of luminescence intensity has a single component of 1120ps. These results indicate the strong lattice relaxation occures in Si6Mei4 glass. To conform the lattice relaxation and to determine the parameters of configuration coordinate of SigMeu oligomer, we have measured the temperature dependence of luminescence intensity, width and the decay time. We consider the configuration coordinate in this system as shown in Fig. 2. Once the photo-excitation occurs and free excitons are formed at process A, then strong lattice relaxation takes place. The excitons returns to the ground state with radiative decay
PHOTON ENERGY (eV) Fig. 1. Absorption and luminescence spectra of S i 6 M e i 4 oligomer at 22 K. The excitation energy is 4.66 eV. The dashed line indicates the Gaussian line shape.
Fig. 2. Configuration coordinate of S i g M e ^ oligomer. A indicates the absorption, B luminescence, C tunneling and D thermally activated processes. Eg is the height of potential barrier.
459
o
(B), tunneling (C), and thermally activated decay (D) processes. The difference in energy between A and B gives a Stokes shift and the thermal barrier EB is present in this model. The decay time of luminescence T_1 is sum of the radiative decay (x r ) _1 , the tunneling (Tt)_1, and thermally activated decay (tth) -1 rates. If we consider that (xth)_1 is only temperature dependent, the temperature dependence of the luminescence decay time is written as E, -T1 = T(0tfr + vexp (1) k,T where v is the frequency factor. The temperature dependence of luminescence intensity I is E.\ / ^ / ( O / Q - ' + Aexpj (2) k.Tj Here, A is a fitting parameter. l i Figure 3 display the temperature ' 1 ' ' dependence of luminescence — -8- - 10J 10° r 08-- 8 - —5" intensity and decay time. The : : * dashed line indicates the result of >• 2 0 least square fit using the eq(l). SlO 1 rot z H w Following parameters are obtained: • -- P L INTENSITY - :'• H Z E B = 600 + 44 cm-1, v =2.6 x 1012 W m l o - -DECAY TIME _ 10' -\l 1 s- , and T(0K) = 1096 ps. The a io barrier height obtained by eq(2) is 626 + 6 cm-1. These results shows that the configuration coordinate explains the t e m p e r a t u r e dependence of luminescence intensity and decay time quite well.
10"
i
0.05 1/T (K"1)
I
0.1
10u
Fig. 3. Temperature dependence of luminescence intensity and decay time of Si6Me]4 oligomer. The dashed line is obtained with least square fitting using eq.(l).
Moreover, the temperature dependence of FWHM of luminescence band H is in good agreement with the following equation between 3 and 150 K: H = Ht cothf — Vk,T
(3)
12 _1
where v=2.5 x 10 s and Hn=0.525 eV. The frequency factor is almost the same as that obtained from eq(l). With these results, we conclude that the luminescence is attributed to the recombination of self-trapped exciton state of SigMe^ oligomer. 3.2. Permethyl-dodecasilane (Sii2Me2f) Figure 4 shows the absorption, luminescence, and luminescence excitation spectra of Si]2Me26 in 3-methylpentane solution. These spectra are measured at room temperature in (a) and 77 K in (b). At room temperature, the absorption peak of the a-a* transition is observed at 4.28 eV and the width is very broad. In contrast, the widths of luminescence and excitation bands are narrower than the absorption band. The FWHM of luminescence band is 200 meV. The peak energies of luminescence an excitation spectra are 3.85 and 4.08 eV, respectively. The peak energy of luminescence band does not depend on the excitation energy. The difference between the excitation
460 and the luminescence excitation spectra in (a) indicates that the Sii2Me26 molecules have different conformations at room temperature. The different conformers make broad absorption band due to the distribution of transition energy of the fj-o* band. The luminescence band is almost a mirror image of the excitation band and the intensity of luminescence band is too weak to measure the time response in the picosecond region. The quantum efficiency is very low. Considering these results, the difference in energy between luminescence and excitation bands could be attributed to the lattice relaxation with a small Stokes shift of 0.23 meV. In contrast, the Stokes shift disappears at 77K. The absorption, luminescence and excitation bands are observed around 4.05 eV and the FWHM's of these bands are approximately 200 meV. The decay time of the luminescence band is 400 + 20 ps with the excitation energy of 4.07 eV and does not depend on the observed energy. These results clearly show that the Sii2Me26 oligomer take only one conformation and the exciton does not localize in contrast to the Si6Mei4 oligomer.
(a) Luminescence
Excitation
R.T. Absorption.
PHOTON ENERGY (eV)
Fig. 4. Absorption , luminescence, and excitation spectra of Sii2Me26 oligomer at room temperature in (a) and 77 K in (b).
The peak energy and the FWHM of absorption band are the same as those of the luminescence band at 4.08 eV. Moreover, the lattice relaxation occurs at 300 K and does not occur at 77K. We consider that these effect is due to the viscosity of 3-metyhlpentane solution. The oligomer backbones are able to take several conformers are present in a low viscous solution at room temperature while the oligomer form only one stable conformation in a high viscous solution at 77K. 4. Conclusion We have measured the absorption, photoluminescence, photoluminescence excitation spectra and the time response of luminescence intensity of Sig(CH3)i4 glass and Sii2(CH3)26 in 3methylpentane solution. The self trapped excitons are observed in Si6(CH3)i4 oligomer and we have determined the configuration coordinate, i.e. EB = 600 ± 44 cm 1 , v =2.6 x 1012 s_1, and x(0K) = 1096 ps. The Sij2(CH3)26 shows a weak lattice relaxation at room temperature and form free excitons at 77 K. References 1. T. Hasegawa el ai, Phys. Rev. B54, 11365 (1996). 2. M. Shimizu etal.,Phys. Rev. BS8, 5032 (1998). 3. H. Kishida el ai, J. Phys. Soc. Jpn. 65, 1578 (1996) . 4. M. K. Raymond and J. Michl, Int. J. Quantum Chem. 672, 361 (1999) and references therein. 5. Z. Liu et ai, J. Chem. Phys. 105, 8237 (1996).
SPIN ALIGNMENT BETWEEN THE TRIPLET EXCITED STATE OF PHENYLANTHRACENE AND THE DANGLING VERDAZYL RADICAL AS STUDDZD BY TEVIE-RESOLVED ELECTRON SPIN RESONANCE Y O S H I O TEKI, 1 - 2 M A S A A K I N A K A T S U J I 3 , Y O Z O MIURA 3 PRESTO Department
JST,1
Department
of Material
Science,
Graduate
of Applied Chemistry, Faculty of Engineering,3
Sugimoto, Sumiyoshi-ku, Corresponding
Osaka 558-8585,
School
of Science,2
Osaka City University,
and
3-3-J38
Japan
Author: Yoshio Teki;
E-mail: teki(S)sci.osaka-cu.ac.jp
The photo-excited quartet (S = 3/2) high spin state of a radical-excited triplet pair of a novel compound, phenylanthracene-verdazyl radical, was detected by time-resolved electron spin resonance (TRESR) technique. The TRESR spectrum was well analyzed by the ordinary spin Hamiltonian with the Zeeman and fine-structure terms. The g value,fine-structuresplitting, and relative population of the Ms sublevels have been determined to be g = 2.0043, D = 0.0230 cm1, E = 0.0 cm"' and P,a = P.,r= 0.5 and Pm = P.m. = 0.0, respectively, by the spectral simulation. The direct observation of the excited quartet state shows that the photo-induced intramolecular spin alignment is realized between the excited triplet state (S=1) of the phenylanthracene moiety and the doublet spin (S =1/2) of the dangling verdazyl radical.
1. Introduction The studies on the spin ahgnment between the metastable excited triplet state and the stable radicals will give very important knowledge on the novel spin ahgnment, and this leads to a new strategy for the photo-induced magnetic spin systems. However, there are only few examples of the direct observation of excited high-spin states arising from the radical-triplet pair in the solid phase [1-5]. We have recently reported the first observation of the photo-excited quartet (S = 3/2) and quintet (S = 2) states on the purely organic nconjugated spin systems [5]. In these systems, a stable iminonitroxide radical phenylanthracene has been used for the unpaired spin origin. moiety The study of the photo-induced spin (Triplet Excited State; ahgnment between the photo-excited S=l) triplet state and the unpaired spins of other kind of radicals is interasting and worthy of exploration. verdazyl radical
In this paper, we report another (S=l/2) example for the excited quartet state arising from the radical-triplet pair of the purely organic 7t-conjugated spin system. The target molecule is 9-[4-(l,5-Dimethyl-6-oxo-3verdazyl)phenyl]anthracene (1) in which verdazyl radical is linked to the phenylanthracene moiety through the m-conjugation.
461
462 2. Experimental 1 was synthesized from 9-bromoanthracene using a series of literature methods. The details of the synthetic procedures will be published elsewhere. The photo-excited state was examined by time-resolved electron spin resonance (TRESR) technique. TRESR method is a very powerful technique to detect short-lived paramagnetic excited states by electron spin resonance. A conventional X-band ESR spectrometer (JEOL TE300) was used in measurements of TRESR spectra without field modulation. Excitation of 1 was carried out at 355 nm light using YAG laser (Continuum Surelite 11-10). The typical laser power used in the experiments was c.a. 5 - 1 0 mj. Temperature was controlled using an Oxford ESR 910 cold He gas flow system. 2MTHF glass matrix was used for the TRESR experiments. The measurements were carried out at 30 K 3. Results and Discussion 3.1 TRESR Spectra and Excited Spin States of 1 TRESR spectrum with well resolved fine structure splitting has been observed in 2M-THF rigid glass matrix as shown in Figure 1(a). The observed TRESR spectrum has been unambiguously analyzed to be a excited quartet (S = 3/2) state by spectral simulation shown in Figure 1(b). The spectral simulation was carried out by the eigenfield/exactdiagonalization hybrid method [6], taking electron spin polarization (ESP) into account. The effective-exchange interaction between the triplet state of the phenylanthracene moiety and the dangling radicals is undoubtedly much larger than the Zeeman and finestructure interactions in the present nconjugated systems. We can therefore use the ordinary spin Hamiltonian of the pure spin state (negligible 250 300 350 400 quantum mixing of the different spin Magnetic Field / mT states) for the analysis which is given by Fig. 1 Typical TRESR spectra of 1 at 30 K in 2MTHF rigid glass H^ = fffig.S+&D.S matrix, (a) The observed spectrum of I a at 1.0 ms after laser 2 excitation, (b) The simulation of the excited quartet spectrum =&B.g.s+ij[sz -s(,&i)m using the spin Hamiltonian parameters described in text.Here, 2 2 X, Y, and Z are the signals corresponding to the canonical ori+ J ^^ --S f ), (1) entation of the fine-structure tensor. where ^rand Z>are the electron ^tensor
463 and fine-structure tensor, respectively. The g value, fine-structure splitting, and relative population of the Ms sublevels have been determined to be g- 2.0043, D- 0.0230 cm'1, E= 0.0 cm 'and P^ = P^ 0.5 and Pm^ ^ = 0 . 0 , respectively. In the present system the triplet state of the phenylanthracene moiety couples ' n t h the doublet state of the dangling stable radical by the spin-exchange interaction. In such a exchange-coupled system the wave function of the whole molecule I W9, M)> is approximately given by the direct product of the wave functions of the two isolated moieties, I 7{&, m£> and I m&, mj>, as I !P(S Ms)> = 2 a ^ & S mx mB M) I H&,md> | ^,m^>, for & =1 and #=1/2 (2) where C(5* 9* 9, mA m^ M) is the Clebsch-Gordan coefficient. Here, one quartet and one doublet spin states are comprised of the radical-triplet pair. The g and D values for the quartet state (Q) are given by the following relationship [7]; iKQ) = (2/3)£
(3)
and Z*Q) = (l/3) J 0ro + (l/3)J0(RT). (4) From Eq. 3, the Rvalue for the excited quartet state of 1 was estimated to be g(Q) = 2.004 using the g values of the radical (g(R) - 2.005) and excited rot* triplet state of free anthracene (g(T) = 2.003). The fine-structure parameter D of the excited quartet state was also estimated to be ZJ(Q) = 0.0256 cm' from Eq. 4 using £XJ) = 0.0710 cm'1 of the excited triplet state of free anthracene22 and ZJ(RT) = 0.0057 cm 1 calculated by the point dipole approximation. In this estimation, we used the D value of anthracene itself instead of the value of the phenylanthracene, since D value of the T[ state of phenylanthracene was unknown. The experimentally determined gaxiA l v a l u e s for the excited quartet states of 1 (g(Q) = 2.0043 and .D(Q) = 0.0230 cm' 1 ) are in excellent agreement with the calculations. The relative population of the Ms sublevels can be interpreted by assuming the selective intersystem crossing to Ms = ±1/2 spin sublevels, which is generated by spin-orbit coupling between the excited doublet states and the eigenfunctions of the excited quartet state in zero magnetic field. The direct observation of the excited quartet state shows that the photoinduced intramolecular spin alignment is realized between the excited triplet state (9=1) of the phenylanthracene moiety and the doublet spin (5=1/2) of the dangling verdazyl radical. References [1] (a) C. Corvaja, M. Maggini, M. Prato.G. Scorrano, M. Venzin, M. J. Am. Chem. Soc. 117, 8857 (1995). (b) N. Mizouchi, Y. Ohba, S. Yamauchi, J. Chem. Phys.101, 5966. (1997) [2] (a) K Ishii, J. Fujiwara, Y. Ohba, S.Yamauchi, S. J. Am. Chem. Soc. 118, 13079 (1996). (b) K. Ishii, J. Fujisawa, A. Adachi, S. Yamauchi, N. Kobayashi, N. J. Am. Chem. Soc. 120, 3152 (1998). [3] P. Ceroni, F. Conti, C. Corvaja, M. Maggini, F. Paolucci, S. Roma, G. Scorrano, A. Tbffoletti, J. Phys. Chem. A, 104, 156 (2000). [4] (a) N. Mizouchi, Y. Ohba, S. Yamauchi, J. Phys. Chem. 103, 7749 (1999). (b) Conti, F; Corvaja, C; Tbffoletti, A.; Mizouchi, N.; Ohba, Y; Yamauchi, S.; Maggini, M.; J. Phys. Chem. 104, 104, 4962 (2000). [5] Y. Tfeki, S. Miyamoto, K. Iimura, M. Nakatsuji, andY Miura, J.Am. Chem. Soc, 122, 984 (2000). [6] Y. Tfeki, I. Fujita, T. Takui, K Kinoshita, K. Itoh, K J.Am. Chem. Soc. 116, 116, 11499 (1994). [7] A. Bencini, D. Gatteschi, D. EPR ofExchange Coupled Systems; Springer-Verlag: Berlin, 1990.
PHONON BROADENING OF EMISSION SPECTRA FOR STE AND AUGER-FREE LUMINESCENCE V.N.MAKHOV Lebedev Physical Institute, Leninsky Prospect 53, 117924 Moscow, Russia V.N.KOLOBANOV Physics Department, Moscow State University, 117234 Moscow, Russia M.KIRM, S.VIELHAUER, G.ZIMMERER //. Institutfiir Experimentalphysik der Universitat Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany The temperature dependencies of the bandwidths for self-trapped exciton emission spectra in several alkali halide crystals with high temperature of thermal quenching for self-trapped exciton emission (NaBr, KI, Csl) have been studied and compared with a typical temperature behavior of Augerfree luminescence spectra. It was shown that different phonon modes are responsible for broadening of emission band for different types of self-trapped excitons as well as for different bands in the spectrum of Auger-free luminescence. The features found indicate that the lattice structure of emitting state for Augerfree luminescence has most probably the on-center character.
1. Introduction Though discovered more than 15 years ago1,2, the Auger-free luminescence (AFL), alternatively known as crossluminescence or as core-valence radiative transitions, is not well enough described by any of the existing models for luminescence centers. The simple "energy band" model of AFL which considers this kind of intrinsic luminescence as a result of radiative recombination of valence electrons with the holes in the uppermost core band, cannot explain many features of AFL. In particular, the electronic and lattice structures of initial and final states of AFL transitions are not yet definitely revealed. However, in all cases the AFL transition is treated as a transition from the localized (self-trapped) state of the core hole because complete lattice relaxation should take place in the vicinity of the core hole (the typical time for such a process is - 10 42 s) during its radiative lifetime (x ~ lfj9 s). Due to this fact, it is reasonable to suggest that some properties of AFL can be similar to those of another type of intrinsic luminescence of localized excitations in ionic crystals, namely of self-trapped exciton (STE) luminescence. In the present work, the temperature dependencies of the bandwidths for STE emission spectra in several alkali halide crystals with high temperature of thermal quenching for STE emission (NaBr, KI, Csl) have been studied and compared with a typical temperature behavior of AFL spectra. 2. Experimental The measurements were carried out at the SUPERLUMI station 3 of HASYLAB under the excitation by VUV synchrotron radiation from the DORIS storage ring at DESY (Hamburg). The spectra were detected with a 0.5 m Czerny-Turner type secondary monochromator (with an instrumental resolution of about 1 nm) equipped with a fast UV-sensitive photomultiplier. In some cases the technique of time-resolved spectroscopy was used for the selection of fast (singlet STE) and slow (triplet STE) components of luminescence. The width of the time gate for the measurements of time-resolved spectra was varied in the range between 10 and 200 ns. 3. Results and discussion As it was shown before the temperature behavior of the bandwidths for both AFL4 "9 and STE emission spectra10,11 is rather well described in the framework of the model of phonon broadening in the limit of strong electron-lattice coupling: W(T) = W0x [coth(ha/2kBT)]m, where W(T) and W0 464
465 are the spectral widths of the emission band at temperatures T and T = 0, respectively, m is the phonon frequency, fcs is Boltzmann constant. However, different phonon modes are responsible for emission band broadening for different types of STE as well as for different bands in the spectrum of AFL. Moreover, in the case of AFL the bandwidth of some bands is almost independent of temperature (see Table 1 and Fig.l as an example). Table 1: Parameters of AFL in RbF, CsF, CsCl, CsBr and BaF2 crystals7"9: E AFL is the energy of the AFL emission band at T = 0, AFL band type I has ..strong" temperature dependence, AFL band type II has „weak" temperature dependence, W0 is the full width at half maximum of the AFL emission band at T = 0, hoto is the phonon cutoff energy of the crystal, hajn is the value of phonon energy corresponding to the best fit of experimental data to above mentioned formula.
Crystal
EAFL, eV
AFL Type
W0,eV
RbF CsF
5.25
I I I II I II I I I
0.40 0.27
3.1 5.1 4.5 6.0 5.8 5.6 6.4 7.0
CsCl CsCl CsBr CsBr BaF 2 BaF 2 BaF 2
haio, meV 35.5 24*>
0.20 0.39
20.4
0.23
13 13 43 43 43
0.16 0.46 0.37 0.22
20.4
hcOfiu meV
39 24 12 110 9
38 38 18
*' Debye frequency.
>
Temperature, K Fig.l: Temperature dependence of the bandwidths for AFL in CsCl. Dots are experimental values. Lines are the best fits of data to the formula in the text. Excitation energy was 15 eV.
The results of measurements performed for CsBr crystal 8 have shown a close similarity of temperature broadening for the triplet STE (type II) emission band (3.5 eV) and for the 6.0 eV AFL band, as well as a very weak temperature dependence (in the range 10-100 K) for the bandwidths of singlet STE (type I) emission (4.6 eV) and 5.8 eV AFL band. However, such a similarity cannot be regarded as well established fact because of low accuracy of fitting procedure (to the sum of Gaussians) for STE emission spectrum of CsBr at higher temperatures (T > 60 K) when thermal quenching decreases strongly the intensity of STE
luminescence in CsBr. The results we obtained for several crystals with higher temperature stability of STE emission (NaBr, KI, Csl) have shown (see Figs. 2-4 and Table 2) that the temperature broadening for type I STE (on-center configuration) is described usually by coupling with phonons corresponding to the stretching mode of X2" molecular ion vibrations (X is a halogen atom) or to the vibration modes of the lattice itself, whereas for type II STE (off-center configuration) the coupling with "soft" phonon
466 modes corresponding to the translational motion of X2" is responsible for temperature ! 0.8 " hv = l l e V u' \ broadening (very strong / \ : j ' \ •* 1 temperature dependence; see also STE 0.6 / S\ t *• ' " ' 1 •'\ Ref. [11]). type II ' f \ In the case of AFL bands A STE j 1 0.4 whith comparatively strong •\ type I ^ '\ »> temperature broadening (denoted •,/ 1 • T=120K^",' as Type I) the best fit of the 80 KI 0.2 *" /' 10 K experimental bandwidths was V* obtained for values of co which 0.0 are close to characteristic 2.0 2.5 3.0 3.5 4.0 5.0 frequencies of the host lattice Photon energy, eV vibrations. This feature indicates probably that the lattice structure Fig.2: Temperature dependence of STE luminescence spectrum for of the emitting state for AFL has KI crystal. Excitation energy was 11 eV. Spectra are the on-center character. For the normalized with respect to their maxima. AFL bands with very weak temperature broadening (denoted 1 1.0 as Type II) the model of the local Csl NaBr i /• ' l optical center gives unreasonable 0.8 - hv = 11 eV " '7 •' m energy of phonons involved into * / • * j *i-T=180K electron-phonon coupling. It is \1 i*f / i / • 0.6 well known that the initial state x, 1c * ' 1 — 80 K for different bands in the spectrum \ V LU 0.4 -_T=120 K*,' of AFL is the same. So, in the •'L-10K jf > -a M0 K\ \"\i case of AFL the very weak •l\ A temperature dependence of the 0.2 bandwidth can indicate that the *\ K/J final state has approximately the ^ 0.0 same lattice relaxation as the 4.5 4.0 3.5 5.0 5.5 initial state. However the model Photon energy, eV proposed cannot describe reasonably well the observed Fig.3: Temperature dependence of STE luminescence spectrum for temperature behavior of the 'Type Csl and NaBr crystals. Excitation energy was 11 eV. Spectra II" AFL bands, and so the nature are normalized with respect to their maxima. of AFL, i.e. the localized or delocalized character of electronic states involved, remains unclear. 1.0
1
\
1
KI
'
1
1
3
IV
,/so
J-
Table 2: Parameters of STE luminescence in NaBr, Csl and KI crystals: ESTE is the energy of the luminescence band peak at T = 0, STE type I has the on-center configuration, STE type II has the offcenter configuration, W„ is the full width at half maximum of the STE luminescence band at T = 0, hcou, is the phonon cutoff energy of the crystal, tiaj,, is the value of phonon energy corresponding to the best fit of experimental data to above mentioned formula. ESTE, eV
STE Type
Wo,eV
ft COLO, meV
NaBr
4.5
I
0.46
26.2
Csl KI
3.6 4.1
II
0.33
11.8
hcOfu, meV 19.7 6.2
I
0.32
17.8
15.2
KI
3.3
II
0.37
17.8
5.4
Crystal
467 4. Conclusions The studies of the temperature dependencies of the bandwidths for STE and AFL emission spectra have shown that different phonon modes are responsible for the broadening of emission bands originating from different types of STE as well as for different bands in the AFL spectra. Thermal broadening for STE type I (on-center configuration) is described by coupling with phonons corresponding to the stretching mode of X2~ molecular ion vibrations or to the vibration modes of the lattice itself, whereas for type II STE (off-center configuration) the coupling with "soft" phonon modes corresponding to the translation motion of X2~ is responsible for thermal broadening hv v = 11 eV my^ 0,8 h " ex ' ' "" m^ H 0 f the emission band. For the ex bands in the AFL spectra which Kl Type \\S show comparatively strong thermal > Csl ^ ^ J , broadening, the temperature 0,6 dependence of the bandwidth is —^^""NaBr well described by coupling with phonons, the frequencies of which 0,4 are very close to characteristic " r - * ^ frequencies of the host lattice vibration. This feature can indicate 0,2 that the lattice structure of emitting 50 100 150 200 state for AFL has the on-center Temperature, K character. For the AFL bands with very weak thermal broadening the Fig.4: Temperature dependence of the bandwidths for STE model of the local optical center luminescence in NaBr (4.5 eV), Csl (3.6 eV) and Kl (4.1 eV, cannot give a reasonable Type I and 3.3 eV, Type II). Dots are experimental values. explanation of the observed Lines are the best fits of data to the formula in the text. Excitation energy was 11 eV. temperature behavior of the bandwidths. •
!
i
—
r
\ a| '
Acknowledgments The support of Graduiertenkolleg „Fields and localized atoms - Atoms and localized fields: Spectroscopy of localized atomic systems" is gratefully acknowledged. References 1
Yu.M. Aleksandrov, V.N. Makhov, P.A. Rodnyi, T.I. Syrejshchikova and M.N. Yakimenko, Sov.Phys.- Solid State 26, 1734 (1984). J.A. Valbis, Z.A. Rachko and J.L. Jansons, Sov. Phys. - JETF Letters 42,172 (1985). G. Zimmerer, Nucl. Instr. and Meth. A 308,178 (1991). V.N. Makhov, I.A. Kamenskikh, M.A. Terekhin, I.H. Munro, C. Mythen and D.A. Shaw, Proc. Int. Conf. SCINT'95 "Inorganic scintillators and their applications", Delft, The Netherlands, Delft University Press, 1996, p.208. 5. V.N. Makhov, M.A. Terekhin, I.H. Munro, C. Mythen and D.A. Shaw, Proc. 2-nd Int. Conf. on Excitonic Processes in Condensed Matter, Kurort Gohrisch, Germany, Dresden University Press, 1996, p. 187. 6. V.N. Makhov, I. Kuusmann, J. Becker, M. Runne and G. Zimmerer, HASYLAB Annual Report 1996, Part I, p.269. 7. V.N. Makhov, M.A. Terekhin, I.H. Munro, C. Mythen and D.A. Shaw, J.Lumin. 72-74, 114 (1997). 8. V.N. Makhov, V.N. Kolobanov, J. Becker, M. Kirm and G. Zimmerer, HASYLAB Annual Report 1998, Part I, p.249. 9. V.N. Makhov, I. Kuusmann, J. Becker, M. Runne and G. Zimmerer, J. Electron Spectroscopy and Related Phenomena 101-103, 817 (1999). 10. M. Ikezawa and T. Kpjima, J. Phys. Soc. Japan 27,1551 (1969). 11. S. Suzuki, K. Tanimura, N. Itoh and K.S. Song, J. Phys.: Condens. Matter 1,6993 (1989).
