Narrow Gap Semiconductors 2007: Proceedings of the 13th International Conference, 8-12 July, 2007, Guildford, UK (Springer Proceedings in Physics, 119)

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Narrow Gap Semiconductors 2007 Proceedings of the 13th International Conference, 8-12 July, 2007, Guildford, UK Editors: B.N. Murdin; S.K. Clowes

Volumes 69–94 are listed at the end of the book.

B.N. Murdin S.K. Clowes (Eds.)

Narrow Gap Semiconductors 2007 Proceedings of the 13th International Conference, 8–12 July, 2007, Guildford, UK

Prof. Ben Murdin Faculty of Engineering and Physical Sciences University of Surrey Guildford GU2 7XH UK Dr. Steve Clowes Faculty of Engineering and Physical Sciences University of Surrey Guildford GU2 7XH UK

Library of Congress Control Number: 2008924325 ISSN 0930-8989 ISBN-13 978-1-4020-8424-9 (HB) ISBN-13 978-1-4020-8425-6 (e-book)

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Preface The Thirteenth International Conference on Narrow Gap Semiconductors (NGS13) was held in Surrey, UK, on July 8-12, 2007. We brought together researchers from 15 countries to discuss recent advances and discoveries in the science and technology of narrow gap semiconductors, following the traditions of the previous twelve conferences in this series – Dallas, USA (1970), Nice, France (1973), Warsaw, Poland (1977), Linz, Austria (1981), Gaithersburg, USA (1989), Southampton, UK (1992), Santa Fe, USA (1995), Shanghai, China (1997), Berlin, Germany (1999), Kanazawa, Japan (2001), Buffalo, USA (2003) and Toulouse, France (2005). It was over 40 years ago, before we were born, that the first III-V semiconductors started to be crystallised in high quality, and the best materials available were the so called narrow gap materials. These materials were of fundamental interest at the time, and have continued to be so due to the strong effects of non-parabolicity and spin-orbit coupling, providing exciting tests of solid-state quantum mechanics. For applications they were overtaken in importance for microelectronics and optoelectronics by other wider gap materials, but they nevertheless became of great importance with the advent of mercury cadmium telluride mid-infrared detector applications. Recently narrow gap materials have had a resurgence in interest in a number of application areas. They can exhibit interesting spin-physics and have great potential for spintronic devices, thanks to strong coupling to the conduction band of the strongly spin-orbit split valence band. The growth of nanocrystals made from narrow gap materials has offered the possibility of cheaper nearinfrared devices, in competition with wide gap structures. Graphene has emerged as a zero-gap semiconductor with special properties and exciting physics and applications. Finally, now, the InSb transistor has exhibited record performance characteristics and forms one of the possible strands of the information technology roadmap. Although these applications have given new impetus, there remains a strong fundamental physics interest in narrow gap semiconductors, and effects such as zitterbewegung are especially strong in these materials. All of the above topics were represented at the Thirteenth Conference, and the subject is as vibrant as ever. It gives us great pleasure that some of the Fathers of this field were present at the Conference, and we are especially grateful to Professors Carl Pidgeon and Guenther Bauer, whose enormous enthusiasm made our job as Chairmen a great pleasure. The social events provided an excellent setting for informal discussions. The Welcome Reception took place at the Advanced Technology Institute on the

vi Preface campus of the University of Surrey. The Conference Excursion took the participants to the 16th century Hampton Court Palace; home to Cardinal Wolsey and King Henry VIII. The Conference Dinner was held at the award winning Denbies Wine Estate, the largest vineyard in England. We would like to thank all members of the program and advisory committees for their individual contributions for the organization of the conference and for setting up the scientific program, and we want to thank all participants for attending the conference and for their valuable scientific presentations. Our special thanks must go to Steven Clowes, whose responsibilities included setting up and maintaining the program for manuscript and abstract submissions and paper distributions to referees. We must also thank Julie Maplethorpe for her unwavering support as conference secretary, who assisted in the organisation of all aspect of the event and ensuring we were all well looked after during the conference week. Without Steven and Julie, putting together this Conference Proceedings in such a short period of time would have been impossible. Finally, we have the pleasure to announce that the next Conference, NGS14, will be held on 4-8 or 18-22 August 2009, at the Sendai International Center, Sendai, Japan, and will be chaired by Professor Junsaku Nitta and co-chaired by Professor Hiro Munekata.

Ben Murdin Conference Chair

Wolfgang Heiss Program Chair

Committees and Organisers Conference Chair B.N. Murdin (UK) Program Committee W. Heiss (Austria) – Chair F. Bechstedt (Germany) P.D. Buckle (UK) R. Magri (Italy) C. Sirtori (France) S.D. Ganichev (Germany)

International Advisory Committee G. Bauer (Austria) – Chair T. Ando (Japan) B.M. Arora (India) M. Helm (Germany) J. Leotin (France) B.D. McCombe (U.S.A.) N. Miura (Japan) H. Munekata (Japan) M. von Ortenburg (Germany) C.R. Pidgeon (UK) S.C. Shen (China) W. Zawadski (Poland)

Local Organising Committee B.N. Murdin – Chair S.J. Sweeney – Vice chair J. Maplethorpe – Secretary S.K. Clowes – Editor K.L. Litvinenko L. Nikzad

Conference Banquet – Denbies Wine Estate

viii Committees and Organisers Organising Institutions Advanced Technology Institute, University of Surrey (http://www.surrey.ac.uk/ati) Department of Physics, University of Surrey (http://www.surrey.ac.uk/physics) Institute of Semiconductor and Solid State Physics, University of Linz (http://www.hlphys.jku.at) Conference Website - http://www.ati.surrey.ac.uk/NGS13 Presentations - http://www.ati.surrey.ac.uk/NGS13/presentations

The Conference in Figures Attendance by country Country Number of participants

Algeria Austria Belgium

Country Number of participants

Norway Poland Russia Switzerland

1

10

1

1

3

4

Brazil

France Germany Isreal Japan Lithuania

1

2

5

6

U.K.

U.S.A.

TOTAL

25

7

76

8

1

Austria 13%

Algeria 1%

U.S.A. 9%

1

Belgium 1% Brazil 1% France 7%

U.K. 34% Germany 8%

Sw itzerland 3%

Russia 5%

Poland 4%

Norw ay 1%

Junior / senior distribution Junior 18%

Senior 82%

Lithuania 1%

Japan 11%

Isreal 1%

Contents Part I – Spin-Related Phenomena Gate Dependence of Spin-Splitting in an InSb/InAlSb Quantum Well W.R. Branford, A. M. Gilbertson, P. D. Buckle, L. Buckle, T. Ashley, F. Magnus, S.K. Clowes, J.J. Harris, and L. F. Cohen ………………………3 Photogalvanic Effects in HgTe Quantum Wells B. Wittmann, S. N. Danilov, Z. D. Kwon, N. N. Mikhailov, S. A. Dvoretsky, R. Ravash, W. Prettl, and S. D. Ganichev …………………..7 Magnetic and Structural Properties of Ferromagnetic GeMnTe Layers P. Dziawa, W. Knoff, V. Domukhovski, J. Domagala, R. Jakiela, E. Lusakowska, V. Osinniy, K. Swiatek, B. Taliashvili, and T. Story………..11 Control and probe of Carrier and Spin Relaxations in InSb Based Structures G. A. Khodaparast, R. N. Kini, K. Nontapot, M. Frazier, E. C. Wade, J. J. Heremans, S. J. Chung , N. Goel , M. B. Santos , T. Wojtowicz , X. Liu, and J. K. Furdyna …………………………………………………...15 Density and Well-Width Dependence of the Spin Relaxation in n-InSb/AlInSb Quantum Wells K. L. Litvinenko, B. N. Murdin, S. K. Clowes, L. Nikzad, J. Allam, C. R. Pidgeon, W. Branford, L. F. Cohen, T. Ashley, and L. Buckle ………. 19 Dependence of Layer Thickness on Magnetism and Electrical Conduction in Ferromagnetic (In,Mn)As/GaSb Heterostructures H. Nose, S. Sugahara, and H. Munekata ……………………………………23 Temperature Dependence of the Electron Lande g-Factor in InSb C.R. Pidgeon, K.L. Litvinenko, L. Nikzad, J. Allam, L.F. Cohen, T. Ashley, M. Emeny, and B.N. Murdin ……………………………………. 27 Anomalous Spin Splitting of Electrons in InSb type-II Quantum Dots in an InAs Matrix Ya.V. Terent’ev, O.G. Lyublinskaya, A.A. Toropov, B. Ya. Meltser, A.N. Semenov, and S.V. Ivanov …………………………………………….. 31

xii Contents Measurement of the Dresselhaus and Rashba Spin-Orbit Coupling Via Weak Anti-Localization in InSb Quantum Wells A.R. Dedigama, D. Jayathilaka, S.H. Gunawardana, S.Q. Murphy, M. Edirisooriya, N. Goel, T.D. Mishima, and M.B. Santos ………………... 35 Part II – Growth, Fabrication, Characterisation and Theory Picosecond Carrier Dynamics in Narrow-Gap Semiconductors Studied by Terahertz Radiation Pulses R. Adomaviþius, R. Šustaviþinjtơ, and A. Krotkus …………………………...41 Band Structure of InSbN and GaSbN A. Lindsay, A.D. Andreev, E. P. O’Reilly, and T. Ashley ………………….. 45 Growth and Characterisation of Dilute Antimonide Nitride Materials for Long Wavelength Applications S. D. Coomber, L. Buckle, P. H. Jefferson, D. Walker, T. D. Veal, C. F. McConville, T. Ashley …………………………………………………49 Electron Interband Breakdown in a Kane Semiconductor With a Degenerate Hole Distribution A. V. Dmitriev and A. B. Evlyukhin …………………………………………53 InMnAs Quantum Dots: a Raman Spectroscopy Analysis A. D. Rodrigues, J. C. Galzerani, E. Marega Jr., L. N. Coelho, R.. Magalhães-Paniago, and G. J. Salamo ..........................................................57 Conduction Band States in AlP/GaP Quantum Wells. M. Goiran, M..P. Semtsiv, S. Dressler, W. T. Masselink, J. Galibert, G. Fedorov, D. Smirnov, V. V. Rylkov,, and J. Léotin.....................................61 Growth of InAsSb Quantum Wells by Liquid Phase Epitaxy M. Yin, A. Krier, and R. Jones ………………………………………………65 Diode Lasers for Free Space Optical Communications Based on InAsSb/InAsSbP Grown by LPE M. Yin, A. Krier, P.J. Carrington, R. Jones, and S. E. Krier ..........................69 Epitaxial Growth and Characterization of PbGeEuTe Layers V. Osinniy, P. Dziawa, V. Domukhovski, K. Dybko, W. Knoff, T. Radzynski, A. Lusakowski, K. Swiatek, E. Lusakowska, B. Taliashvili, A. Boratynski, and T. Story ………………………………………………….73

Contents xiii

Monte Carlo Simulation of Electron Transport in PbTe V. Palankovski, M. Wagner, and W. Heiss ………………………………….77 L-Band-Related Interband Transition in InSb/GaSb Self-Assembled Quantum Dots S. I. Rybchenko, R. Gupta, I. E. Itskevich, and S. K. Haywood……………...81 Antimony Distribution in the InSb/InAs QD Heterostructures A.N. Semenov, O.G. Lyublinskaya, B. Ya. Meltser, V.A. Solov'ev, L.V. Delendik, and S.V. Ivanov ……………………………………………...85 Transport Properties of InAs0.1Sb 0.9 Thin Films Sandwiched by Al0.1In0.9Sb Layers Grown on GaAs(100) Substrates by Molecular Beam Epitaxy I. Shibasaki, H. Geka, and A. Okamoto ……………………………………..89 Modelling of Photon Absorption and Carrier Dynamics in HgCdTe Under mid-IR Laser Irradiation ……………………………………………. 93 A. S. Villanger, T. Brudevoll, and K. Stenersen Monte Carlo Study of Transport Properties of InN S. Vitanov and V. Palankovski ……………………………………………... 97 New Type of Combined Resonance in p-PbTe H. Yokoi, S. Takeyama, N. Miura, and G. Bauer.………………………….101 Part III - Carbon Nanotubes and Graphene Theory of Third-Order Optical Susceptibility of Single-Wall Carbon Nanotubes With Account of Coulomb Interaction D. Lobaskin and A. Andreev ……………………………………………….107 Unveiling the Magnetically Induced Field-Effect in Carbon Nanotubes Devices G. Fedorov, A. Tselev, D. Jimènez, S. Latil, N. G. Kalugin, P. Barbara, D. Smirnov, and S. Roche……………………………………..111 Transient Zitterbewegung of Electrons in Graphene and Carbon Nanotubes T. M. Rusin and W. Zawadzki ……………………………………………...115

xiv Contents Cross-Polarized Exciton Absorption in Semiconducting Carbon Nanotubes S. Uryu and T. Ando ………………………………………………………119 Part IV – Nanocrystals and Nanowires Self-Assembled InSb/InAs Quantum Dots for the Mid-Infrared Spectral Range 3-4 µm K. D. Moiseev, Ya. A. Parkhomenko, M. P. Mikhailova, S. S. Kizhaev, E. V. Ivanov, A. V. Ankudinov, A. N. Titkov, A. V. Boitsov, N. A. Bert, Yu. P. Yakovlev …………………………………………………………….125 InSb/InAs Nanostructures Grown by Molecular Beam Epitaxy Using Sb2 and As2 Fluxes V. A. Solov'ev, P. Carrington, Q. Zhuang, K. T. Lai, S. K. Haywood, S. V. Ivanov, and A. Krier …………………………………………………….129 Part V – Electronic Devices Performance Evaluation of Conventional Sb-based Multiquantum Well Lasers Operating Above 3µm at Room Temperature A. Kadri, K. Zitouni, Y. Rouillard, and P. Christol ………………………..135 Electroluminescence From Electrically Pumped GaSb-Based VCSELs O. Dier, C. Lauer, A. Bachmann, T. Lim, K. Kashani, and M.-C. Amann....139 Wavelength Tunable Resonant Cavity Enhanced Photodetectors Based on Lead-Salts Grown by MBE F. Felder, M. Arnold, C. Ebneter, M. Rahim, and H. Zogg..........................143 Farfield Measurements of Y-Coupled Quantum Cascade Lasers L. K. Hoffmann, C. A. Hurni, S. Schartner, M. Austerer, E. Mujagiü, M. Nobile, A.M. Andrews, W. Schrenk, G. Strasser, M. P. Semtsiv, and W. T. Masselink .....................................................................................147 Impact of Doping Density in Short-Wavelength InP-Based StrainCompensated Quantum-Cascade Lasers E. Mujagiü, M. Austerer, S. Schartner, M. Nobile, P. Klang, L. Hoffmann, W. Schrenk, I. Bayrakli, M. P. Semtsiv, W. T. Masselink, and G. Strasser .............................................................................................151

Contents xv Magnetic Field Effects in InSb/AlxIn1-xSb Quantum-Well LightEmitting Diodes B. I. Mirza, G. R. Nash, S. J. Smith, M. K. Haigh, L. Buckle, M. T. Emeny, and T. Ashley ………………………………………………..155 Electroluminescence from InSb-Based Mid-Infrared Quantum Well Lasers S. J. Smith, S. J. B. Przeslak, G. R. Nash, C. J. Storey, A. D. Andreev, A. Krier, M. Yin, S. D. Coomber, L. Buckle, M. T. Emeny, and T. Ashley……………………………………………………………….159 InAs Quantum Hot Electron Transistor T. Daoud, J. Devenson, A.N. Baranov, and R. Teissier ……………………163 Easy-to-Use Scalable Antennas for Coherent Detection of THz Radiation S. Winnerl, F. Peter, S. Nitsche, A. Dreyhaupt, O. Drachenko, H. Schneider, and M. Helm ..........................................................................167 Single Photon Detection in the Long Wave Infrared T. Ueda, Z. An, K. Hirakawa, and S. Komiyama…………………………...171 High-Performance Fabry-Perot and Distributed-Feedback Interband Cascade Lasers C. L. Canedy, W. W. Bewley, M. Kim, C. S. Kim, J. A. Nolde, D. C. Larrabee, J. R. Lindle, I. Vurgaftman, and J. R. Meyer …………….177 Mid-Infrared Lead-Salt VECSEL (Vertical External Cavity Surface Emitting Laser) for Spectroscopy M. Rahim, M. Arnold, F. Felder, I. Zasavitskiy, and H. Zogg……………..183 Optically Pumped GaSb-Based VECSELs N. Schulz, M. Rattunde, B. Rösener, C. Manz, K. Köhler, and J. Wagner…187 Part VI – Magneto-Transport and Magneto-Optics Cyclotron Resonance Photoconductivity of a Two-Dimensional Electron Gas in HgTe Quantum Wells Z. D. Kvon, S. N. Danilov, N. N. Mikhailov, S. A. Dvoretsky, W. Prettl, and S. D. Ganichev ………………………………………………………...195

xvi Contents Extrinsic Electrons and Carrier Accumulation in AlxIn1-xSb/InSb Quantum Wells: Well-Width Dependence A. Fujimoto, S. Ishida, T. Manago, H. Geka, A. Okamoto, and I. Shibasaki …………………………………………………………...199 Negative and Positive Magnetoresistance in Variable-Range Hopping Regime of Undoped AlxIn1-xSb/InSb Quantum Wells S. Ishida, T. Manago, K. Oto, A. Fujimoto, H. Geka, A. Okamoto, and I. Shibasaki …………………………………………………………... 203 Semimetal-Insulator Transition in Two-Dimensional System at the Type II Broken-Gap InAs/GaInAsSb Single Heterointerface K.D. Moiseev, M.P. Mikhailova, R.V. Parfeniev, J. Galibert, and J. Leotin ……………………………………………………………….209 Magnetoexcitons in Strained InSb Quantum Wells W. Gempel, X. Pan, T. Kasturiarachchi, G. D. Sanders, M. Edirisooriya, T. D. Mishima, R. E. Doezema, C. J. Stanton, and M. B. Santos……………………………………………………………213

Part I – Spin-Related Phenomena

Gate Dependence of Spin-Splitting in an InSb/InAlSb Quantum Well W.R.Branford1, A. M. Gilbertson1,2, P. D. Buckle2, L. Buckle2, T. Ashley2, F. Magnus1, S.K. Clowes1, J.J. Harris1 and L. F. Cohen1. 1

Blackett Laboratory, Imperial College London, Prince Consort Rd., London, SW7 2AZ, UK 2 QinetiQ, St. Andrews Road, Malvern, Worcestershire, WR14 3PS, UK

Abstract. A high mobility single subband occupancy InSb/InAlSb quantum well was grown by molecular beam epitaxy. The low-temperature, high-field magnetotransport properties are measured as a function of gate bias. Spin-resolved Shubnikov-de Haas oscillations are observed. A preliminary analysis of the Shubnikov-de Haas oscillations indicates a strong gate bias dependence of the Rashba spin-orbit term.

In materials with inversion asymmetry, spin-orbit coupling can split the conduction band into spin-resolved levels. In III-V heterostructures there are two potential sources of asymmetry, the bulk inversion asymmetry of the zinc-blende lattice and the structural inversion asymmetry associated with interfacial electric fields in the heterostructures. These are generally referred to as the Dresselhaus1 and Rashba2 terms respectively. The idea that the Rashba term is tunable by application of a gate voltage underpins numerous spintronic device proposals.3,4 The narrow-gap semiconductors (NGS) InSb and InAs offer many advantages for spintronic application over their wider gap counterparts GaAs and Si, including high electron mobility (µ) and large spin-orbit coupling. InSb has the lightest effective mass and largest g-factor (~ -51) of all the III-V semiconductors. These factors, combined with the now established high-speed transistor technology,5 make InSb QWs very appealing candidates for Datta-Das type spin-FET applications and spin filters. Experimentally the spin-splitting of the conduction band in NGS structures can be studied by measuring Shubnikov-de Haas (SdH) oscillations.6,7 The frequency of the oscillations is determined by the carrier density, and the resolution of the conduction band into spin-split subbands results in the superposition of SdH oscillations with characteristic frequencies determined by the relative spin-up and spin-down carrier densities. However, we note that other effects can result in a second series of oscillations, including second subband occupancy and magneto-intersubband scattering.8 Here we report on the growth of a high mobility InSb/InAlSb QW and low temperature magnetotransport measurements. We show a preliminary measurement of the Rashba term, determined by the method proposed by Engels et al.6

4 W.R. Branford et al.

Uxx (:/sq)

The QW was grown by molecular beam epitaxy on semi-insulating GaAs as shown in Fig. 1a. There is a 20nm Al0.1In0.9Sb spacer layer between the 30nm InSb QW and the Te į-doped donor sheet. A SiO2 gate oxide layer approximately 150nm thick was deposited on top of the well. Gated Hall Bar structures were prepared by standard lithographic techniques. From low-field Hall measurements at 2K the carrier concentration (n) was 3.1*1015 m-2 and µ was 40 m2/Vs. We calculate that the well has single subband occupancy and the +ve charge in the į-doped top sheet causes structural inversion asymmetry in the same sense as a +ve gate bias. 500 250 0 0.5

-1

1.0

-1

1.5

B (T ) Fig.1a Schematic of QW structure.

Fig.1b Expansion of ȡxx vs Inverse field in the intermediate field region.

The resistance (ȡxx) has three distinct regimes as a function of field. In lowfield (µB<1) there are no oscillations. In high-field the spin up and spin down Landau levels are narrow and fully resolved and ȡxx is not highly sensitive to spin-orbit effects in this regime. This leaves an intermediate field regime below 2T, which is shown vs inverse field in Fig. 1b, where the spin-up and spin-down level are partially resolved by the Zeeman energy. This regime is sensitive to spin-orbit effects, with increasing Rashba term enhancing the spin-resolution, whereas increased Dresselhaus reduces resolution.2 Following the method of Engels et al6 we determine a spin density difference (ǻn=nĻ-nĹ), as a function of gate bias and use equation 1 to convert to a Rashba term (Į), as shown in Fig. 2. This is done by taking the Fourier transform of ȡxx vs inverse field in the intermediate field region, and determining fundamental fields for each spin (BF=nh/e).

D

'n! 2 m*

S 2n  'n

(1)

The small number of oscillations in the intermediate regime means the spin-splitting is poorly resolved in the Fourier transform and the BF positions were measured from the (better resolved) 3rd harmonic, which is shown for +10V gate bias in the left inset to Fig 2. The total carrier concentration vs gate bias is shown in the right inset to Fig 2. The total change in sheet density over the studied region is 5%. From this we estimate that the bias across the well

Gate Dependence of Spin-Splitting in an InSb/InAlSb QW 5

14

-11

4x10

200 100 ParsPaper_nsdh

0 15 20 25 30 Frequency (T)

15

3x10

+10V

14

2x10

3.2

-10

-5

0

-11

3x10

3.1 3.0

D (eVm)

-2

'n (m )

4x10

300

n (10 m-2)

14

Fourier Transford (a.u.)

itself is only of the order of 10mV, with the majority of the voltage dropped across the gate oxide layer. The range of Rashba terms that we measure in Fig. 2 (2-4*10-11eVm) is similar to that measured in other III-V heterostructures.6,7 The Zeeman effect is particularly significant in InSb because g is so large and so this approach can only be an approximate guide because some of the ǻn we attribute to the Rashba is actually a Zeeman effect. However this term is unlikely to change significantly with gate bias (the effective g factor will change subtly for small change in the carrier density), whilst the measured Rashba doubles. This very large change for such small effective gate bias across the well reinforces the view that NGS, particularly InSb, are the material of choice for semiconductor spintronics. Increasing Rashba with positive bias is consistent with this QW structure; the opposite trend is observed with the į-doping below the well.9

-11

-10 -5 0 5 10 Gate Bias (V)

5

2x10

10

Gate Bias (V) Fig.2 Calculated spin density difference and Rashba parameter vs gate bias. Inset right: carrier density vs bias. Inset left: FFT at +10V showing splitting of 3rd Harmonic. Inset right: total n vs gate bias.

In summary, we have measured the 2K high-field magnetotransport of a high mobility single subband occupancy InSb QW that shows spin-resolved Shubnikov-de Haas oscillations. A preliminary analysis of the Shubnikov-de Haas oscillations indicates a strong dependence of the Rashba spin-orbit term on the gate bias. However, measurement of the spin orbit terms with this method is challenging in the presence of a large Zeeman splitting. 1

G. Dresselhaus, Phys. Rev. 100, 580 (1955). Y. A. Bychkov and E. I. Rashba, J. Phys. C 17, 6039 (1984). 3 S. Datta and B. Das, Applied Physics Letters 56, 665 (1990). 4 J. Schliemann, J. C. Egues, and D. Loss, Physical Review Letters 90, 146801 (2003). 5 T. Ashley et al, in 2004: 7th International Conference on Solid-State and Integrated Circuits Technology, Vols 1- 3, Proceedings (2004), p. 2253-2256. 6 G. Engels et al, Physical Review B 55, R1958 (1997). 7 J. Luo et al, Physical Review B 38, 10142 (1988). 8 A. C. H. Rowe et al, Physical Review B 6320, 201307 (2001). 9 J. Nitta et al, Physical Review Letters 78, 1335 (1997). 2

Photogalvanic Effects in HgTe Quantum Wells B. Wittmann1, S. N. Danilov1, Z. D. Kwon2, N. N. Mikhailov2, S. A. Dvoretsky2, R. Ravash1, W. Prettl1 and S. D. Ganichev1 1 2

Terahertz Center, University of Regensburg, Germany Institute of Semiconductor Physics, Novosibirsk, Russia

Abstract. We report on the observation of the terahertz radiation induced circular (CPGE) and linear (LPGE) photogalvanic effects in HgTe quantum wells. The current response is well described by the phenomenological theory of CPGE and LPGE.

1 Introduction HgTe quantum wells (QWs) structures, characterized by the inverted band structure and large spin splitting of subbands in the k-space, recently attracted growing attention as a potentially interesting material system for spintronics. Photogalvanic effects (PGE) in the terahertz range has proved to be a very efficient method to study nonequilibrium processes in semiconductor QWs yielding information on their point-group symmetry, details of the band spinsplitting, processes of momentum and energy relaxation etc. [1]. In this work we investigate photogalvanic effects in this novel material as a function of the radiation polarization, wavelength, and temperature. As a result the anisotropy of the structures under study has been observed and analyzed.

2 Experimental technique and results The experiments are carried out on Cd0.7Hg0.3Te/HgTe/Cd0.7Hg0.3Te QWs having two different widths: 16 nm and 21 nm. Structures are MBE grown on a GaAs substrate with the growth direction z || [013]. Samples with density of electrons Ns about 2˜1011 cm-2 and mobility at 4.2 K of about 5˜105 cm2/Vs are studied from 4.2 K to 300 K. Two pairs of contacts (along directions x and y) are centered in the middle of cleaved edges parallel to the intersection of the (013) plane and cleaved edge face {110}. For optical excitation we use pulsed molecular terahertz lasers [1] as well as a Q-switched CO2 laser. Linearly and circularly polarized radiation is applied in the wavelength range from 9.2 µm to 496 µm with a power of about several kW. To measure polarization dependences we applied O/4 plates for circular polarization, with variation of

8 B. Wittmann et al. helicity Pcirc according to Pcirc = sin 2M, where M is the angle between the initial plane of polarization and the optical axis of the O/4 plate, as well as O/2 plates for variation of the azimuth angle D of linearly polarized radiation. 3

2

(013)-grown HgTe QWs

(013)-grown HgTe QWs 1

2

jy (arb. units)

T = 297 K O = 90 Pm

jx (arb. units)

1

0

!Z

-1

jx

0

-1

-2

T = 297 K O = 148 Pm

-3

-2

Fit according to Eqs.(1,2)

Fit according to Eqs.(1,2) 0°

45°

90°

135°

180°

M

225°

270°

315°

360°

0°

45°

90°

135°

180°

225°

270°

315°

360°

M

Fig. 1. Helicity dependence of the photocurrent j in (013)-grown HgTe QW, measured in x-direction (a) and in y-direction (b).

With illumination of samples at normal incidence we observed in the inplane direction x a CPGE current signal proportional to the helicity jx = A˜Pcirc superimposed with a small polarization independent offset (Fig. 1a). Cooling down of the sample from 300 K to 4.2 K results in the sign inversion of the current measured at a fixed helicity. An electric current is also detected in the orthogonal y-direction (Fig. 1b). In this case, the observed current has a more complex dependence on the angle M well fitted by j = a sin 2M + b sin 4M + c cos 4M + d,

(1)

where a, b, c, and d are fitting parameters which can be determined by solving a system of four linear equations following from Eq. (1) for angles M = 0°, 22.5°, 45° and 135°, respectively. We have found that the ratio A/a between CPGE values detected in the x- and y-directions substantially changes under the variation of the radiation wavelength and temperature. For the longest wavelength used (496 µm) we observed that jx(M) follows to Eq. (1) with substantial contribution of all 4 terms. The three last terms in the right-hand side of the Eq. (1) we attribute to the LPGE [1]. This current can also be generated applying the linearly polarized radiation and has characteristic dependence on the azimuth angle D. We found that the current in x-direction in most cases can well be fitted by the sin 2D dependence with a polarization independent background. In contrast, the fit in the y-direction, can be obtained by using a more complex trigonometric function: j = ac sin 2D + bc sin 4D +dc. Experiments at oblique incidence show that the both CPGE and LPGE currents reach a maximal value at normal incidence.

Photogalvanic Effects in HgTe Quantum Wells 9 So far photogalvanic currents excited in zinc-blende structure based QWs by a normally incident radiation have been observed only in structures grown in [113] and asymmetrical [110] crystallographic directions which belong to the Cs symmetry group [1]. In experiments described here we use (013)grown QWs. These structures belong to the symmetry point group C1 which contains neither rotation axes nor mirror planes and consists of only one element, which is the identity operation. Phenomenologically, for the C1symmetry group, the PGE for the excitation along z || [013] for any orthogonal x and y is given by 2

 e e

 e e ,

jx / I

2 J xz Pcirc  F xxx e x  F xyy e y  F xxy e x e y  e y e x ,

jy / I

J yz Pcirc  F yxx ex  F yyy e y  F yxy

2

2

x y

(2)

y x

where e is the radiation polarization vector, I is the radiation intensity, Jxz, Jyz and six linearly independent components Fxxx, Fxyy, Fxxy = Fxyx , Fyxy = Fyyx, Fyxx, Fyyy are allowed components of the second-rank pseudo-tensor J describing the CPGE and the third rank tensor F related to the LPGE. For the elliptical polarization Pcirc = sin 2M, |ex| 2  |e y|2 (1  cos 4M) / 2 , exe y  ey e x sin 4M / 2 , and Eqs. (2) yield the polarization dependence given by Eq. (1) which well describe our data (see Fig. 1). The fact that the experimentally observed the ratio A/a varies with a change of the light frequency, sample temperature and radiation intensity is also in an agreement with Eqs. (2) which yields jx/jy = Jxz/Jyz. Indeed all above components of the tensors J and F are linearly independent and the ratio between them can change with varying of experimental conditions. The same is valid for LPGE.

3 Conclusion In summary, our experiments show that photogalvanic effects can be effectively generated in HgTe quantum wells with the strength, e.g. for CPGE current, of about an order of magnitude larger than that observed in GaAs, InAs and SiGe low dimensional structures. The low symmetry of investigated samples opens a rich field for investigation of microscopic properties of this novel and promising material.

References 1. Ganichev, S.D. and Prettl, W.: Intense Terahertz Excitation of Semiconductors, Oxford University Press, 2006

Magnetic and Structural Properties of Ferromagnetic GeMnTe Layers P. Dziawa, W. Knoff, V. Domukhovski, J. Domagala, R. Jakiela, E. Lusakowska, V. Osinniy, K. Swiatek, B. Taliashvili, and T. Story Institute of Physics, Polish Academy of Sciences Al. Lotników 32/46, 02-668 Warsaw, Poland

Abstract. Ferromagnetic Ge1-xMnxTe thin films with x”0.19 were deposited on (111) oriented BaF2 monocrystals using molecular beam epitaxy technique. X-ray diffraction carried out at high temperatures for samples with x”0.05 revealed ferroelectric transition from rock-salt to rhombohedral structure at T=625-675 K. The magnetic properties investigated with SQUID magnetometry and ferromagnetic resonance technique exhibit an easy magnetization direction normal to the plane in as grown samples. We attribute this finding to lattice strain due to mismatch of thermal expansion coefficients or to the crystalline stress related to inhomogeneous distribution of Mn ions in the sample volume. Thermal treatment changes the easy axis into in-plane direction which can be associated with distinct improvement of the structural properties.

1. Introduction GeTe is the only one from the family of IV-VI narrow gap semiconductors, which demonstrates ferroelectric transition observed as transformation (an inner displacement along a [111] direction) from paraelectric rock-salt to ferroelectric rhombohedral structure while the temperature is lowered [1]. Incorporation Mn into GeTe crystal matrix brings an additional mechanism – magnetic interaction via quasi-free carriers (Ruderman-Kittel-Kasuya-Yosida interaction) between spin of S=5/2 originating from Mn2+ ions (3d5 electron configuration) and makes this material ferromagnetic. Increase of Mn content in Ge1-xMnxTe brings about uptrend of ferromagnetic Curie temperature up to maximal TC=150 K for x=0.5 whereas temperature of ferroelectric transition shows opposite behaviour, i.e. decrease from around T=670 K for GeTe down to total decay about x=0.3 [2]. Such situation gives an opportunity to simultaneously control both transitions dependently on both Mn ions as well as the holes concentrations. The most interesting question is a role of coupling of these mechanisms, especially in the region located in between x=0.25 and 0.30 where the crossing of both ferroelectric and ferromagnetic transitions is expected to take place.

12 P. Dziawa et al.

Lattice parameter (Å)

6.16 (222) Bragg reflection Rhombohedral

6.14 6.12 6.10 6.08 6.06 6.04

GeMnTe 4.2 Mn (with GeTe buffer) 1.4 Mn

6.02 6.00 5.98

Rock-salt 300 350 400 450 500 550 600 650 700

T (K) Fig.1 Structural (ferroelectric) transition in GeMnTe layer (dots) and double transition in GeMnTe/GeTe heterostructure (squares)

2. Growth and characterization of layers. Thin films GeTe, GeMnTe and GeMnTe/GeTe heterostructures up to 1 µm thick were grown on (111) surface of cleaved BaF2 monocrystals using molecular beam epitaxy (MBE) technique. Concentration of Mn up to x=0.19 in Ge1-xMnxTe layers was determined by the energy dispersive X-ray fluorescence analysis (EDXRF). The reflection of high energy electron diffraction (RHEED) technique used during the growth process shows streaky patterns indicating layer-by-layer (Frank-van der Merve) mode of growth. However post-growth examination of structural properties performed by Xray diffraction (XRD) revealed stratification of some samples especially in GeMnTe. The secondary ion mass spectrometry (SIMS) confirms inhomogeneous distribution of Mn ions in such layers. In spite of this observation a relatively small full width at half maximum (FWHM) parameter of the X-ray rocking curves was found to be in the range 100-600 arcsec. To check ferroelectric properties of GeMnTe a high temperature (from 300 to 700 K) XRD measurements were performed. Clear structural transition was observed in GeMnTe (Fig. 1). More complicated phase diagram is presented for GeMnTe/GeTe where no clear single transition is observed. The standard four-probe Hall measurements at temperature 77 and 300 K in magnetic fields up to 1.3 T show anticipated p-type conductivity with high carrier concentration of the order of 1020 cm-3 in GeTe and 1021 cm-3 in

-4

2

M (10 emu/cm )

-4

2

M (10 emu/cm )

Magnetic and Structural Properties of GeMnTe Ferromagnetic 13

8 6 4 2 0 -2 -4 -6 6 4 2 0 -2 -4 -6 -8

GeMnTe//BaF2 10.6% Mn

as grown

out-of-plane in-plane

annealed

-1000

-500

0

500

1000

H (Oe)

Fig.2 Change of an easy magnetization axis from out-of-plane into in-plane direction after annealing.

GeMnTe. Magnetic properties investigations with SQUID magnetometry and ferromagnetic resonance (FMR) techniques carried out in the temperature range of 4.2-300 K shows ferromagnetic transition with TC up to 40 K for x=0.19. From magnetic hysteresis loops an easy axis of magnetization was found to be in unexpected out-of-plane direction for most GeMnTe samples (Fig. 2). Similar result was observed in FRM analysis of magnetic anisotropy pointing at possible influence of the crystal strain. To check this hypothesis the samples were annealed under various conditions (time, temperature, in vacuum or nitrogen atmosphere). These processes improve the structural properties (homogenization of the material as well) and moreover change the easy magnetization axis into in-plane direction was observed. Such influence of the thermal treatment confirms mentioned supposition of inhomogeneity of Mn ions in the sample volume and/or mismatch of the thermal expansion coefficients between layer and the substrate. 3. Conclusions The structural and magnetic properties of Ge1-xMnxTe layers grown on BaF2 (111) using MBE technique were studied. Structural (ferroelectric) transition in Ge1-xMnxTe with low Mn content was revealed in the range of temperatures T=625-675 K. Ferromagnetic transition was observed with maximal TC=40 K

14 P. Dziawa et al. in sample x=0.19 and holes concentration of the order 1021 cm-3. An easy magnetization axis in as grown samples was found to be out-of-plane which can be changed into in-plane direction by annealing process (reduce of crystal strain). Acknowledgements This work was supported by the research project 0992/T02/2007/32 of the Ministry of Science and Higher Education (Poland) granted for the period 2007-2010. References 1. Ciucivara A., Sahu B.R., Kleinman L., 'Density functional study of the effect of pressure on the ferroelectric GeTe', Phys. Rev. B., 73, 214105-1-6, 2006. 2. Fukuma Y., Asada H., Nishimura N., Koyanagi T., ‘Ferromagnetic properties of IV–VI diluted magnetic semiconductor Ge1-xMnxTe films prepared by radio frequency sputtering’, J. Appl. Phys., 93, 4034-9, 2003

Control and Probe of Carrier and Spin Relaxations in InSb Based Structures Giti A. Khodaparast1, R. N. Kini1, K. Nontapot1, M. Frazier1, E. C. Wade1, J. J. Heremans1, S. J. Chung 2, N. Goel 2, M. B. Santos 2, T. Wojtowicz 3, X. Liu4, J. K. Furdyna 4 1 Department of Physics, Virginia Tech., Blacksburg, VA, 24061, U.S.A. 2 Homer L. Dodge Department of Physics and Astronomy, University of Oklahoma, Norman, Oklahoma, 73019, U.S.A. 3 Institute of Physics, Polish Academy of Sciences, 02-668 Warsaw, Poland 4 Department of Physics, University of Notre Dame, Notre Dame, IN 46556, U.S.A

Abstract. Narrow gap semiconductors (NGS) offer several scientifically unique features important for the field of spintronics. In order to explore these features we are using standard pump-probe and magneto-optical Kerr effect (MOKE) spectroscopy at different excitation wavelengths, power densities, and temperatures. Our goal is measuring and controlling carrier/spin relaxation in a series of InSb-based quantum wells and films, and InMnSb ferromagnetic films. The dynamic effects observed in these structures demonstrate strong dependence on the photo-induced carrier density.

1. Introduction: Over the past several years there has been enormous progress in exploring and manipulating spin states toward developing spin based devices using semiconductors. Examples of some practical methods in developing spinbased devices include incorporating ferromagnetism in a semiconductor by introducing magnetic dopants such as Mn or taking advantage of spin precession controlled by an external electric field via spin-orbit (SO) coupling. NGS can play important roles in both approaches. They offer several unique electronic features such as a small effective electron/hole mass, a large g-factor, and large SO coupling effects. Here we report time-resolved studies of several InSb based ferromagnetic films, and InSb based heterostructures.

16

G. A. Khodaparast et al.

2. Samples: In this work, InMnSb samples were grown by low temperature molecular beam epitaxy (MBE) technique at Notre Dame and were 0.23 Pm thick on CdTe buffer layer (4.5 Pm thick) with GaAs substrate. The hole density and mobility are ~2x1020 cm-3 and ~100 cm2/Vs, respectively [1]. The InSb quantum wells (QW) were grown by MBE at the University of Oklahoma on GaAs (001) substrates. The AlxIn1-xSb (x=0.09 or x=0.15) barrier layers were G-doped with Si. The Si G-layers are located either on one side of the QW (asymmetric sample) or equidistant on both sides of the QW (symmetric sample), detailed growth conditions were described previously [3]. We studied five InSb QWs, three doped single QW and one undoped multiple QW (all 30 nm wide with x=9%) and one 11.5 nm wide with x=15%. In addition, an InSb 1.3 Pm thick film (Te doped with n=2.6x1016 cm-3, provided by J. J. Heremans) was studied and a carrier relaxation time of ~ 7 ps has been observed. 3. Experimental Techniques: We used two experimental schemes to probe carrier/spin dynamics, degenerate and two color pump/probe and MOKE. For a degenerate scheme, the source of the pump and probe beam was either a Ti-sapphire laser which generates near infrared (NIR) pulses with duration of ~ 100 fs, (a repetition rate of 80 MHz, and a maximum pulse energy of ~10 nJ) or a Ti:Sapphirebased chirped pulse amplifier (CPA) at 800 nm (with a pulse energy of ~ 1 mJ at repetition rate of 1 kHz) with the same pulse duration. We used an optical parametric amplifier (OPA) pumped by a CPA as the source of Mid Infrared (MIR) pulses in a two-color scheme. The details of experimental conditions are described in Ref. [2]. 4. Results: Figure 1 shows examples of carrier/spin relaxations in our InMnSb at two different laser fluences. The dynamical effects observed in these measurements demonstrated strong dependence on the photo-induced carrier density and can thus be controlled by the density of the photo-induced carriers. This observation can be explained by the Elliot-Yafet mechanism which is considered to be the dominant relaxation process in NGS [2]. In this model the spin relaxation is proportional to the momentum relaxation time, which itself depends on temperature, concentration, and mobility. In contrast, as we reported earlier [2] the observed temperature dependence of the dynamical effects is quite weak. This suggests that at low Mn concentrations (~ 2% in this case) the spin relaxation of photo-excited carriers might not be influenced by interactions with Mn ions. In addition, we measured carrier and spin lifetime in InSb based QWs with AlxIn1-xSb alloys as barrier materials (grown at the University of Oklahoma) at different excitation wavelengths,

Control and Probe of Carrier and Spin Relaxations in InSb Based 17

(a) 10 K

Fluence 2 20 PJ/cm

-10

-5

Pump/Probe 850 nm

0

5

10

15

MOKE (20 PV Per Div.)

'R/R (10% per Div.)

MOKE (50µV Per Div.)

power densities, and temperatures. In addition to the degenerate scheme with pump/probe fixed at 800nm, in order to avoid the absorption by the barrier materials, we performed two-color measurements using MIR pulses ranging from 2-4.6 Pm (with the probe pulses fixed at 800 nm). In the measurements presented here, we observed spin life times in the range of 5-20 ps, depending on the pumping wavelengths and laser fluence. Examples of our measurements are shown in Fig. 2 for two InSb QWs with different well widths and Al concentrations. V Fluence

(b)

2

5 mJ/cm Pump 1.3 Pm Probe 800 nm -2

0

77 K 2

Time Delay (ps)

Time Delay (ps)

4

Fig. 1: a) MOKE and differential reflectivity of InMnSb at low laser fluence with pump/probe fixed at 850 nm. b) Two-color MOKE at high laser fluence is shown. Faster relaxations are observed in high fluence regime.

(a)

-4

0

4

8

12

Time Delay (ps)

MOKE (100 PV Per Div.)

InSb QW 30 nm Fluence 2 5 mJ/cm

MOKE (0.5 PV Per Div.)

'R/R (2% Per Div.)

Fig. 2: a) Differential reflectivity and b) MOKE of InSb QW (30 nm wide, x=9%) at RT. Relaxations of ~ 8 ps have been observed. The solid lines are Pump 2.6 Pm Pump 2 Pm (b) Pump 2 Pm exponential fits to the data. c) MOKE Probe 800 nmat 77 K and RT (the top Probe 800nm Probe 800nm measurements RTas a function of laser fluence ) for an2 11.5 nm trace) (ranging from 10 to 2 mJ/cm210 RT mJ/cm (at RT) 2 In Sb barrier. QW with x=15%. The pump wavelength is tuned to avoid the Al x (1-x) InSb QW 10 mJ/cm 30 nm Long Relaxation times are observed in this scheme. Fluence 2 5 mJ/cm

0

4

8

Time Delay (ps)

5 mJ/cm

2

(c) 2 mJ/cm

-5

0

5

10

Time Delay (ps)

15

2

20

References: 1) T. Wojtowicz, G. Cywinski, W. L. Lim, X. Liu, M. Dobrowolska, J. K. Furdyna, K. M. Yu, W. Walukiewicz, G. B. Kim, M. Cheon, X. Chen, S. M. Wang, and H. Luo, Appl. Phys. Lett. 82, 4310 (2003). 2) K. Nontapot K., R. N. Kini, A. Gifford, T. R. Merritt, G. A. Khodaparast, T. Wojtowicz ,X. Liu , J. K. Furdyna , Appl. Phys. Lett. 90, 143109 (2007). 3) T.D. Mishima, M. Edirisooriya, and M.B. Santos, Appl. Phys. Lett. 88, 191908 (2006).

18

G. A. Khodaparast et al.

Supported by: NSF-DMR-0507866, AFOSR Young Investigator Program, Advance-VT, Jeffress Trust Fund-J748, NSF-DMR-0618235, DMR-0520550, NSFDMR06-03752, and by the MNiSW (Poland) Network "New materials and sensors for optoelectronics, information technology, energetic applications and

medicine".

Density and Well-Width Dependence of the Spin Relaxation in n-InSb/AlInSb Quantum Wells K. L. Litvinenko1, B. N. Murdin1, S. K. Clowes1, L. Nikzad1, J. Allam1, C. R. Pidgeon2, W. Branford3, L. F. Cohen3, T. Ashley4 and L. Buckle4 1

Advanced Technology Institute, University of Surrey, Guildford GU2 7XH, UK 2 Department of Physics, Heriot-Watt University, Edinburgh EH14 4AS, UK 3 Blackett Laboratory, Imperial College, London, SW7 2BZ UK 4 QinetiQ Ltd, St.Andrews Rd, Malvern, UK

Abstract. We have used time resolved spectroscopy to measure the relaxation of spin polarisation in InSb/AlInSb quantum wells as a function of temperature and mobility. The results are consistent with the degenerate D'Yakonov-Perel (DP) mechanism over the temperature range from 77K to 300K. The spin-diffusion length in this regime is shown to rise with well width and band gap, but is independent of density, mobility and spin lifetime, the effects of which cancel out.

We have measured the spin relaxation rate in InSb/AlInSb quantum wells. We have investigated a set of InSb/AlInSb single QW samples grown by MBE on GaAs substrates. The mobility of all available QWs was measured by means of the Hall effect. The spin lifetimes were measured using the circularly polarised pump-probe absorption technique [1]. In n-type semiconductors two main spin relaxation processes have been found to be important in optical orientation experiments: the D'yakonov-Perel (DP) and the Elliott-Yafet (EY) mechanisms [1-3]. For quantum wells, only in the case of DP-dominated scattering will an electric field applied in the growth direction cause a modulation of the lifetime through the Rashba effect. This is an essential component for spintronic devices requiring modulation of the spin lifetime with an electric field. It is therefore important to establish the conditions in which spin polarisation lifetimes are both long and dominated by the DP process. The QW spin relaxation rates are [3]: 2 E 1 1 1 D 2 E1e C E k W p , EY C EY K 2 1  m * 2 12e E k (1) DP DP 2 2 ! Eg Wp Ws Eg Ws The k3 Dresselhaus term D, is [2] D=]m*, where ]=4K/—(3-K), K='/(Eg+'), m* is the electron effective mass ratio, Eg is the band gap and ' is the spin-orbit splitting energy of the valence band. The orbital momentum scattering time Wp is related to the mobility P (assuming the electron-electron

20 K. L. Litvinenko et al. scattering rate is low compared with inelastic scattering) by Wp = Pm*m0/e. CEY and CDP are dimensionless constants, Ek is the average electron kinetic energy, and E1e is the confinement energy above the bulk band edge for the lowest subband. Other symbols have their usual meaning.We assume parabolic bands and wells with infinite barriers, and define the quantities ES and PS (dimensions of energy & mobility) from ES E S P S2 2 UE k 1 1 2 U E P , (2) k e e P W sDP W sEY where U is the density of states. By comparison with Eqn 1 2 S 5! 4 ]2 1 e 2 C EY §¨ 3  K ·¸§ 1 · 2 2  , 1 L (3) ES C P ¨ ¸ DP S E g L4 4S 2 m0 C DP ¨© m * E g ¸¹© m * ¹ 16m02 where L is the well width. ES is a modified Rashba parameter, and Eqn 2 shows that when P = PS, WsEY = WsDP i.e. PS is the cross-over mobility from EY (dominates at low mobility) to DP (high mobility). ES and PS are constants for given material and well width, i.e. they have no explicit dependence on temperature, T, n, P or Ws. For CDP=16 and CEY=1 [3], and 77K InSb (Eg=0.24 eV, '=0.8 eV, m* = 0.013), Eqn 3 gives ES = 0.20meV and PS = 0.68m/Vs when L=20nm. For 300K (Eg=0.18 eV), ES = 0.30meV and PS = 0.77m/Vs. In the degenerate limit EkoEF/2= n/2U W sDP n o

e e 1 , W sEY n o P ES P E S P S2

(4)

In the non-degenerate limit EkokT W sDP n o

e n e n 1 , W sEY n o P 2 E S 2 UkT P E S P S 2 UkT

(5)

On a log-log graph of nWs vs P (Figure 1) the DP process gives lines of gradient -1, while EY gives gradient +1. In the degenerate limit the lines have intercepts dependent only on ES and PS. For n in units of 1011 cm-2, W in ps and P in m2/Vs, then the degenerate DP intercept, e/ES is in meV-1. Reducing the density into the non-degenerate regime (not shown) produces a family of lines with the same gradients but reducing intercept. Theory for the degenerate regime only is shown on Figure 1 using CDP=16 and CEY=1 from [3] i.e. no fitting parameters. The spin diffusion length is [4]: nW s P (6) l sd 2eU so constant lsd contours on Figure 1 are straight and parallel to the DP lines. In the degenerate DP regime lsd ĺ lsd0 = 11nm/—(m*ES) which has no explicit dependence on T, n, P or Ws, the effects of which have all cancelled. For InSb wells at 77K, lsd0 = 210, 490 & 860nm for L = 20, 30 & 40nm respectively. The experimental points seem to fit with the reciprocal relationship

Density and Well-Width Dependence of the Spin Relaxation

21

appropriate for degenerate DP, though the scaling of L4 at 300K seems smaller than predicted and at 77K seems larger. Going from 300K to 77K in the DP dominated regime the intercept increases due to the increase in Eg and consequent reduction in ES (we ignore the change in m*). The spin-diffusion lengths at 300K are smaller than expected, but much larger than expected at low-temperature for L=30nm. Reasons for departure from the theory could be effects of: non-parabolicity, finite barrier height, non-degeneracy (though the samples all have high density), dependence of m* and D on temperature, spin relaxation due to structural inversion asymmetry and dependence of D on well width. A treatment including both Rashba and Dresselhaus spin orbit coupling for realistic InSb/AlInSb QWs is currently in preparation[5]. This work was supported by UK-EPSRC (SPRINGS - EP/C511999). 10

77K

300K

9

-2

nWs (10 cm .ps)

1

11

1 2 9 7 4

1

3 1

experiment L=20nm 30nm theory L=20nm 30nm 40nm

10

1

3

10

2

mobility, P (m /Vs) Fig. 1. Experimentally determined spin relaxation time and concentration vs mobility, for a range of different InSb quantum wells of different widths and doping. The numbers next to the points are sample numbers. The densities were all above 2x1011cm-2 (for which EF~kT at 300K) and are degenerate. Theory for degenerate EY (low mobility) and DP (high mobility) from Eqns 3 & 4 is also shown.

References 1. K. L. Litvinenko et al., New J. Phys 8, 49 (2006). 2. P.H. Song and K.W. Kim, Phys. Rev. B66. 035207 (2002). 3. A. Tackeuchi et al., Appl. Phys. Lett.70, 1131 (1997); Physica B 272, 318 (1999); Jpn. J. Appl. Phys. 38, 4680 (1999) 4. A. Fert and H. Jaffres Phys. Rev. B. 64, 184420 (2001) 5. A. M. Gilbertson et al. In Preparation.

Dependence of Layer Thickness on Magnetism and Electrical Conduction in Ferromagnetic (In,Mn)As/GaSb Heterostructures H. Nose, S. Sugahara, and H. Munekata Imaging Science and Engineering Laboratory, Tokyo Institute of Technology, Yokohama 226-8502, Japan

Abstract. Relatively thick, ferromagnetic (In,Mn)As layers of up to around 150 nm with Curie temperature of Tc = 35 K were prepared successfully by molecular beam epitaxy. Dependencies of (In,Mn)As and GaSb layer thicknesses on electrical conduction in the (In,Mn)As/GaSb were studied experimentally to discuss the evidence of hole transfer from p-(In,Mn)As to adjacent GaSb.

1 Introduction III-V-based ferromagnetic semiconductors, such as (In,Mn)As1 and (Ga,Mn)As2, are characterized by hole-mediated ferromagnetism. Their ferromagnetic properties could be controlled by altering hole concentrations with an electric field3,4 and light illumination5,6. Up to now, experimental data available for (In,Mn)As have been obtained primarily from epilayers whose thicknesses were 20 nm or less, leaving this material less elucidated than (Ga,Mn)As. It has been believed that growing thick, ferromagnetic epilayers is difficult7,8, presumably because of the lack of a suitable template surface with good lattice match. If one can prepare bulk-like, ferromagnetic (In,Mn)As layers, it would expand opportunities of carrying out experiments that were not possible in the past. Likewise InAs/GaSb9, the band edge alignment of (In,Mn)As/GaSb is most likely the broken-gap type-II in which the valence band edge of GaSb lies above the conduction band edge of (In,Mn)As. In this situation, holes in (In,Mn)As is supposed to be transferred in part in GaSb at the vicinity of the (In,Mn)As/GaSb heterointerface. Yet, there has been no experimental work concerning hole transfer and its relation with hole-mediated ferromagnetism. In this paper, we report the growth of relatively thick, ferromagnetic (In,Mn)As layers of up to around 150 nm with Curie temperature of Tc = 35 K. This became possible by interrupting the growth at every 20nm to suppress radiative heating of a substrate from hot effusion cells. Dependencies of (In,Mn)As and GaSb layer thicknesses on electrical conduction in the (In,Mn)As/GaSb heterostructure samples have been studied to find experimental evidences for hole transfer from (In,Mn)As to GaSb across the heterointerface.

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H. Nose, S. Sugahara, and H. Munekata

2 Preparation of thick (In,Mn)As epilayers on GaSb surfaces A series of p-(In,Mn)As/GaSb heterostructures with different (In,Mn)As and GaSb layer thicknesses were grown on AlSb/GaAs(001) substrates by molecular beam epitaxy. We have followed the growth procedure by which (In,Mn)As with Curie temperature of 90 K was achieved10. A highly resistive, 300 nm AlSb buffer layer was first grown on a semi-insulating GaAs(001) substrate at a substrate temperature Ts = 560 qC. A GaSb layer was then grown on the AlSb layer at Ts = 460 qC. This was followed by the growth of a (In,Mn)As layer at Ts = 200 qC. Mn content x = [Mn] / ([In] + [Mn]) was fixed at 0.048. In/As flux ratio r were ranged between 1.8 and 2.511. Surface of a thin (In,Mn)As layer was relatively rough at the initial stage of the growth on a GaSb surfaces, but was smoothen as growth proceeded, as shown in insets of Fig.1 for 3 nm and 10 nm thick layers by spotty and streaky RHEED patterns, respectively. After the growth, samples were annealed in air atmosphere at 190 qC for 4 - 16 hours.

Fig 1. Curie temperature with various (In,Mn)As thickness. Insets show RHEED patterns at two different thicknesses.

We found that a growth interruption for every 20 nm thickness with interruption time of 5-10 min. evaded losing hole-mediated ferromagnetism in the layers. Suppression of an unintentional increase in Ts due to radiative heating from hot effusion cells is inferred to be responsible for this achievement. In Fig.1 is plotted the Curie temperature Tc as a function of (In,Mn)As layer thickness X. The thicknesses of GaSb layers were kept constant at 100 nm. Hole-mediated ferromagnetism was examined by measuring both magnetization and anomalous Hall effect. Tc of X = 10 and 20nm are 45-55 K with perpendicular magnetization. The observed perpendicular magnetic anisotropy is due to biaxial tensile strain caused by the lattice mismatch between (In,Mn)As and GaSb7,10,12,13. While Tc decreases for X = 50 and 150 nm samples, hole-mediated ferromagnetism is well preserved in these samples. Easy magnetization axis was changed from perpendicular to lateral direction, which can be understood qualitatively in terms

Dependence of Layer Thickness on Magnetism and Electrical 25 of the relaxation of the strain. The M-T curve (Hext = 20 Oe) obtained from the 150 nm sample indicates the presence of macroscopic MnAs. The magnetic contribution of MnAs is about 50% out of the entire magnetization of this sample. Nevertheless, the observation of hole-mediated ferromagnetism in such a thick sample was never report in past.

3 Evidence for hole transfer across the heterointerface The sheet conductance G [S] at 10 K as a function of (In,Mn)As thickness X is plotted in Fig. 2 for X nm-(In,Mn)As/100 nm-GaSb samples. The G value increases steeply with X up to around X = 20 nm, beyond which the magnitude of an increase moderates. The observed behaviour at X  20 nm suggests the occurrence of hole transfer from a low mobility region of the (In,Mn)As layer to a high mobility region in the GaSb side of a (In,Mn)As/GaSb heterointerface. An increase in conductance becomes gentle at X t 20 nm, suggesting the saturation of hole transfer at X a 20 nm. Assuming the hole mobility of Pp = 10 cm2/V˜s which is typical for the ferromagnetic p-(III,Mn)As9,14, we obtain p1 = 8.5 u 1019 cm-3 from the gentle-slope region (X t 20 nm). This p value is about 10 % of the entire Mn content. On the other hand, using Pp = 200-600 cm2/V˜s which is typical for MBE-grown p-GaSb15, we get p2 = 5 - 15 u 1018 cm-3 from the steep-slope region (X  20 nm). The p2 value corresponds to 0.6-2 % of the Mn contents. These analyses indicate that a small fraction of hole transfer can affect significantly the overall transport behaviour of the samples. Results of much detailed analysis will be discussed in a separate paper. In Fig,3, the sheet conductance G [S] at 10 K is plotted as a function of GaSb thickness Y for 20 nm-(In,Mn)As/Y nm-GaSb samples. The G value increases steeply with Y up to around Y = 20 nm, beyond which it hardly increases. The observed results are consistent with the established picture of modulation doping. The tendency of low hole concentration estimated by low-field Hall effect measurements7,12 is therefore inferred to be most likely due to finite contribution of parallel conduction at GaSb side of the (In,Mn)As/GaSb junction. In our case, p | 5 u 1019 cm-3 is obtained at RT with P0H = 0.38 T for a 20 nm-(In,Mn)As/300 nm-GaSb sample, which is substantially lower than that in the p-(In,Mn)As/AlSb system in which hole transfer seems negligible10. On the other hand, the presence of a hole channel may lead us to the opportunity of tuning hole-mediated ferromagnetism via a non-magnetic layer.

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Fig. 2. Dependence of sheet conductance on (In,Mn)As thickness X. Inset shows sample structure.

Fig. 3. Dependence of sheet conductance on GaSb thickness Y. Inset shows sample structure.

References 1. H. Munekata, H. Ohno, S. von Molnar, Armin Segmüller, L. L. Chang, and L. Esaki, Phys. Rev. Lett., 63, 1849 (1989). 2. H. Ohno, A. Shen, F. Matsukura, A. Oiwa, A. Endo, S. Katsumoto, Y. Iye, Appl. Phys. Lett., 69, 363 (1996). 3. H. Ohno, D. Chiba, F. Matsukura, T. Omiya, E. Abe, T. Dietl, Y. Ohno, and K. Ohtani, Nature (London), 408, 944 (2000). 4. D. Chiba, F. Matsukura, and H. Ohno, Appl. Phys. Lett., 89, 162505 (2006). 5. S. Koshihara, A. Oiwa, M. Hirasawa, S. Katsumoto, Y. Iye, C. Urano, H. Takagi and H. Munekata, Phys. Rev. Lett., 78, 4617 (1997). 6. A. Oiwa, Y. Mitsumori, R. Moriya, T. Slupinski, and H. Munekata, Phys. Rev. Lett., 88, 137202 (2002). 7. H. Munekata, A. Zaslavsky, P. Fumagalli, and R. J. Gambino, Appl. Phys. Lett., 63, 2929 (1993). 8. A. Shen, F.l Matsukura, Y. Sugawara, T. Kuroiwa, H. Ohno, A. Oiwa, A. Endo, S. Katsumoto, and Y. Iye, Appl. Surf. Sci., 113/114, 183 (1997). 9. L. L. Chang, J. Phys. Soc. Japan, 49A (Suppl.), 997 (1980). 10. T. Schallenberg and H. Munekata, Appl. Phys. Lett,. 89, 042507 (2006). 11. r =1 is defined as the minimum flux ratio to sustain an arsenic stabilized surface with (2u1) reconstruction during the growth of LT-InAs. 12. T. Slupinski, A. Oiwa, S. Yanagi and H. Munekata, J. Cryst. Growth, 237-239 1326 (2002). 13. X. Liu, W. L. Lim, Z. Ge, S. Shen, M. Dobrowolska, J. K. Furdyna, T. Wojtowicz, K. M. Yu and W. Walukiewicz , Appl. Phys. Lett., 86, 112512 (2005). 14. W. Limmer, M. Glunk, S. Mascheck, W. Schoch, A. K¸der, D. Klarer, K. Thonke, R. Sauer, and A. Waag, J. Supercond.: Incorp. Nov. Magne., 17, 417 (2004). 15. Pp value of our MBE-grown p-GaSb layer (undoped, 700 nm) is 600 cm2/V˜s with p = 1.9 u 1016 cm-3 at 10 K. For other cases see, e.g., C. Chang, R. Ludeke, L.L. Chang, and L. Esaki, Appl. Phys. Lett., 31, 759 (1977).

Temperature Dependence of the Electron Lande g-Factor in InSb C.R. Pidgeon1, K.L. Litvinenko2, L. Nikzad2, J. Allam2, L.F. Cohen3, T Ashley4, M Emeny4, and B.N. Murdin2 1

Department of Physics, Heriot-Watt University, Edinburgh EH14 4AS, UK Advanced Technology Institute, University of Surrey, Guildford GU2 7XH, UK 3 Blackett Laboratory, Imperial College, London SW7 2BZ, UK 4 QinetiQ Ltd, St Andrews Rd, Malvern WR14 3PS, UK 2

Abstract. We report Larmor precession in bulk InSb observed up to 300K in the time domain by means of the circularly polarized pump-probe technique. We show that provided we include only the dilational change of the energy gap with temperature, we obtain reasonable agreement between experiment and k.p theory for the high temperature g-factor in InSb.

We used a modified mid-infrared circularly polarized pump-probe transient absorption technique, which we have previously used for investigation of spin relaxation in narrow-gap semiconductors [1]. By inclusion of a small magnetic field in the Voigt geometry the optically oriented spins perform Larmor precession [1,2]. This allows us to obtain the g-factor even at elevated temperature. The InSb sample used for our study was undoped and 5 Pm thick, grown by MBE on a semi-insulating GaAs substrate. The mobility and carrier concentration measured by the Hall effect at 300K (77K) were 6.37 m2/Vs (3 m2/Vs) and 1.4×1015 cm-3 (2.8×1015 cm-3). Typical transients are shown in Fig.1. The measured polarization precesses coherently at angular frequency g*PBB/! while decaying with the spin lifetime, Ws. For InSb the electron effective mass is very much less than the heavy hole mass, so that it is a good approximation to assume that the bleaching of the probe absorption occurs when the dynamic Moss-Burstein shift of the conduction quasi-Fermi energy is also equal to the difference in the laser and bandgap energies. The precession period increases with quasiFermi energy reflecting the non-parabolicity. Increasing the energy also increases the spread of electron energies and therefore reduces the coherence time. The effective g-factor obtained from the transients is plotted in Fig 2 against quasi-Fermi energy. The experiment is insensitive to the sign of g*, and we assume that it is negative.

C. R. Pidgeon et al.

normalised optical polarisation (arb.units)

28

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12

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0

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0.00

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20

30

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50

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For negligible higher band interactions, the energy dependence of the gfactor for NGSs may be written analytically [3]: g * (E) 2

1

E P0 3

§ 1 1 · ¸ ¨ ¨' E E  E E¸ 0 0 ¹ © 0

(1)

In the case of InSb at low temperature where [4] E0(T=0) = -0.2352 eV, EP0 = 23.1 eV, '0 = -0.803, this leads to g*(E=0,T=0) = -51 which agrees well with experiment for low-temperature spin-resonance [5]. Following [6] we calculate the dilational change in the energy gap using InSb expansion coefficient measurements from [7]. An approximate parameterisation of the dilational change in E0 over the range 0 to 300K for InSb leads to a E0dil = 0.2352 +5.17x107T2 9.25x109T3+3.81x1011T4 5.12x1014T5 where T is in kelvin. Simple consideration of the momentum operator suggests that the interband momentum matrix element should also scale (inversely) with the lattice dilation, so its square, EP0, changes no more than 0.1% from 0 to 300K. The spin-orbit splitting '0 is temperature insensitive for the range from 5K to 300K for InSb [8]. As can be seen from Fig. 2, Eqn (1) is quite consistent with the experimental data without any fitting parameters. At the lowest energies the measured g-factor tends to a value of around 56 at 300K, corresponding to the dilational bandgap of -0.217 eV and not to a value of 73 corresponding to the optical bandgap of -0.174 eV. We note that incomplete bleaching, if occurring, would be especially apparent at high energy and high temperatures, and the experimental points would fall to the right of the line. There may be some evidence of this at 300K above 0.1eV. We would like to thank A Andreev and W Zawadzki for useful discussions. This work was supported by UK-EPSRC (SPRINGS - EP/C511999).

g factor

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Fig. 2. The g-factor (symbols) vs excess photon energy. The calculation of Eqn (1) is shown as a dashed (full optical bandgap) or solid line (dilational change only).

References 1. B.N.Murdin et al., Phys.Rev.B 72, 085346 (2005) 2. S. A. Crooker et al., Phys. Rev. B 56, 7574 (1997) 3. W Zawadzki, Phys. Lett. 4, 190 (1963) 4. H.J. Jimenez-Gonzalez, R.L. Aggarwal, G Favrot, Phys Rev. 49, 4571 (1994) 5. BD McCombe and RJ Wagner, Phys Rev B 4, 1285 (1971) 6. Stradling R A and Wood R A, J. Phys. C: Solid State Phys. 3 L94 (1970) 7. DF Gibbons, Phys Rev 112, 136, (1958) 8. M.Cardona, K.L.Shaklee, F.H.Pollak, Phys.Rev. 154, 696 (1967)

Anomalous Spin Splitting of Electrons in InSb Type-II Quantum Dots in an InAs Matrix Ya.V. Terent’ev, O.G. Lyublinskaya, A.A. Toropov, B. Ya. Meltser, A.N. Semenov and S.V. Ivanov Ioffe Physico-Technical Institute, St. Petersburg 194021, Russia

Abstract. Magnetooptical studies of InSb type-II quantum dots (QDs) grown by molecular beam epitaxy (MBE) in an InAs matrix have been done. Unusual behaviour of photoluminescence from QDs measured in Faraday geometry was observed in the samples with multiple sheets of QDs. In particular, the Ví polarized peak originating from optical transitions of electrons with s=+1/2 has higher energy than the V peak which corresponds to s=–1/2 that contradicts negative value of electronic g factor in InAs and InSb. We explain the effect in terms of competition of two channels of radiative recombination. They differ in initial electronic states that are attributed to electrons localized by InSb QDs and shallow donors in an InAs matrix.

Recent magnetooptical studies of InAs diode heterostructures grown by MBE have demonstrated their capability as an effective spin aligner [1]. This result together with considerable progress in the MBE growth of InSb nanoscale insertions in an InAs matrix [2] has inspired our present work devoted to magnetooptical studies of spin-related phenomena in this system. An active region of experimental structures consists of a bulk InAs layer centered with either a single sheet of InSb QDs (samples of type A) or 10 sheets separated by 100-Å-thick layers of InAs (samples of type B). Typical QDs density is as high as ~1012 cm-2. The InAs matrix has background electron concentration n0~5×1016 cm-3 at T=80 K. Note, that the holes in typeII InSb/InAs QDs are strongly localized, while the electrons located in the adjacent InAs are coupled to holes via Coulomb interaction. Circularly polarized PL spectra were measured in magnetic fields up to 4T in Faraday geometry at T=2K. Excitation power was about 1W/cm-2. Figure 1a presents a series of PL spectra of a type-A sample for different values of the magnetic field B. At zero field the spectrum is well fitted by a simple Gaussian function with maximum at 0.32 eV that is ~100 meV lower than the band gap of InAs. Observed field dependence of the PL peak energy (Fig. 2a) and weak or close to zero splitting of the line into V-polarized terms are inherent to the effect of magnetic freeze-out of electrons on shallow donors in n0-InAs [1]. So we attribute this PL peak to the recombination of heavy holes trapped at QDs and electrons localized by shallow donors in the InAs matrix. Additional small contribution into the PL contour emerging

32

Y. V. Terent’ev et al.

Single sheet of QDs Multiple sheets of QDs

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Fig. 1. Series of PL spectra for different values of magnetic field. (a) – samples with single sheet of QDs; (b) – samples with 10 coupled sheets of QDs.

on high energy slope at moderate magnetic fields, is a manifestation of the upper Landau level. A weak irregular line splitting occurring at the fields higher then 2T find its explanation in the context of the model suggested below. PL of type B structures (Fig. 1b) demonstrates strong splitting into circular polarized terms at the fields >2T. Surprisingly, the Ví peak has higher energy and amplitude than the V one. It is clearly seen from the spectrum recorded at B=0 (Fig. 1b) that there are two contributions into the PL band. The fit performed by superposition of two Gauss functions is presented in Figure 2b,c. At B<2T the peak I shifts at magnetic field likewise the PL line of type A samples, so we attribute it to the same recombination mechanism. As for the peak II, its energy decreases at the magnetic field and it moves toward the peak I. The contribution of the peak II in the PL band increases, whereas the other contribution decreases (Fig. 2c). At B~2T the peak II is in close proximity with the first one. After that critical point the PL behaviour changes cardinally and it experiences splitting into strongly polarized terms with the ı– upper band. To explain this effect we assume that the peak II originates from the recombination of electrons localized by the Coulomb potential around the QDs. At magnetic fields the peak II behaviour is controlled by the

Anomalous Spin Splitting of Electrons in InSb Type-II Quantum 33

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effect of magnetic localization, which causes the reduction of the PL peak energy. Eventually at B~2T energy levels of electrons in the QDs approach the high energy edge of the impurity band in InAs matrix and nonequilibrium electrons become shared among donors and the QDs. Thus the new effective channel of recombination opens involving electrons localized by the QDs. Strong relative growth of the ı– peak indicates dominant role of electrons with s=+1/2. In the samples with the single QDs sheet the effect is not so pronounced because total number of the QDs there is ten of times smaller. However weak irregular splitting of PL was observed in these structures as well, as was mentioned above. This work was supported by RFBR grants # 06-02-17279-ɚ and # 07-0201384-ɚ.

References 1. Terent’ev, Ya.V.et al.: 'InAs diode heterostructure as an effective electron spin aligner', Program of 28th Int. Conf. on the Phys. of Semicond., Vienna, 359, 2006 2. Ivanov, S. V. et al.: 'Molecular beam epitaxy of type II InSb/InAs nanostructures with InSb sub-monolayers', J. Cryst. Growth, 278, 72, 2005

Measurement of the Dresselhaus and Rashba Spin-Orbit Coupling Via Weak Anti-Localization in InSb Quantum Wells A.R. Dedigama, D. Jayathilaka, S.H. Gunawardana, S.Q. Murphy, M. Edirisooriya, N. Goel, T.D. Mishima and M.B. Santos Center for Semiconductor Physics in Nanostructures, University of Oklahoma, Norman, Oklahoma 73019, USA Abstract. Weak anti-localization has been observed in the magneto-resistance of both symmetrically and asymmetrically doped InSb/AlInSb quantum wells. We find that for both types of structures, the magnetic field corresponding to the conductance minimum is in good agreement with the dominant spin-orbit term, which is the cubic Dresselhaus and Rashba terms for symmetric and asymmetric samples, respectively.

1 Introduction InSb has the smallest electron effective mass (0.0139m0) and hence the largest room temperature mobility of all the III-V semiconductors, making InSb a promising material for high speed field-effect transistors and ballistic transport devices. Additionally significant spin-orbit (S-O) effects make InSb interesting for spintronic applications.1, Although the theoretical values for the Dresselhaus ( J 760eVÅ 3 ) and Rashba ( D 0 523eVÅ 2 ) coefficients are large2, there has been relatively little work on their measurement3. S-O effects in III-V heterostructures arise from two inversion asymmetries: bulk inversion asymmetry (BIA) and structural inversion asymmetry (SIA). BIA emerges from the zinc-blende nature of these materials leading to two Dresselhaus spin-splitting terms for a quantum well (QW) grown along the [001] direction, one linear and one cubic in the in-plane momentum4. SIA arises from the asymmetry of the QW structure, leading to the Rashba spin splitting term linear in the momentum. 4 The S-O interaction can be made manifest in a number of ways. In this paper we concentrate on weak anti-localization (WAL) in which the S-O terms invert the standard constructive interference of weak localization and instead yield an enhanced conductivity at zero field, which can be destroyed with the introduction of a perpendicular magnetic field.

36 A. R. Dedigama et al.

2 Experiment We studied a series of InSb QW structures grown on GaAs (001) substrates via molecular beam epitaxy with AlxIn1-xSb barriers (0.15<x<0.20) with electron densities varying from 2 to 5.3x1011cm-2 and with 4.2K mobilities from 30,000 to 192,000 cm2V-1s-1. Magneto-conductance was measured for each sample at 4.2K. Typical data are shown in Figure 1.

Fig. 1. Magneto-conductance in units of e2/! vs. perpendicular field for a symmetrically doped sample (ns=4.4x1011cm-2) at 4.2K.

Fig. 2. B(VMIN) (filled squares) compared to HD1, HD3 and HR (open squares, triangles and circles, respectively) for the symmetric (inset) and asymmetric QWs

There are two regimes for fitting WAL data each defined by the relative magnitudes of the magnetic length lB and the electron mean free path le: diffusive (lB>le) and ballistic (lBle, in these samples :SOW1a1 (where :SO is the magnitude of the spin precession vector) which exceeds the range of validity of the ILP model. Ignoring these limitations and fitting to the ILP theory results in extremely small S-O coefficients and unrealistic values of W3/W1, where W n1 ³ W (T )(1  cos nT )dT and W(T) is the probability of scattering by an angle T. For the ballistic samples, the large values of J and Do reduce the magnetic field range where the L-G model is valid. Fitting to the L-G model can only be satisfactorily performed with a prefactor 4 times larger than that predicted. 6 The inadequacies of these models motivated our use of an alternative empirical approach. Having observed that in previous published experiments7,

Measurement of the Dresselhaus and Rashba Spin-Orbit Coupling Via 37 the magnetic field at the minimum in the conductivity, B(VMIN), correlated well with the fitted values of the spin-orbit field, we have compared B(VMIN) in our samples with the theoretically expected values for the Rashba, linear Dresselhaus and cubic Dresselhaus fields:

HR 

D 02m 2 e! 3

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The inset to Figure 2 compares the empirically determined B(VMIN) with HD1 and HD38 for the three symmetric QWs (remotely doped on both sides). There is an excellent correlation between B(VMIN) and HD3, the dominant S-O term. The main panel of Fig. 2 shows the corresponding data for the five asymmetric QWs (remotely doped on one side), now including a comparison with HR. Once again there is good agreement between B(VMIN) and the dominant S-O term which is now HR, with the exception of two samples with nsa4x1011cm-2 which in contrast to all the other heterostructures included here, were grown 2° off the [001] direction on GaAs substrates. We speculate that the strain in these QWs may be anisotropically relieved resulting in additional S-O contributions that were not considered.9

3 Conclusions In conclusion, we report the first WAL studies in InSb/AlInSb QWs. Very good agreement is found between the magnetic field corresponding to conductivity minimum and the dominant S-O term, confirming the large values of the Dresselhaus and Rashba coefficients in InSb.

References 1. Zutic, Igor et al., Rev. Mod. Phys. 76, 323, 2004. 2. Winkler, R., Spin-Orbit Coupling Effects in Two-Dimensional Electron and Hole Systems, Springer, 2003. 3. Khodaparast, G.A. , et al., Phys. Rev. B 70, 155322, 2004; Chen, H., et al., Appl. Phys. Lett. 86, 032113, 2005. 4. Iordanskii, S.V., et al., JETP Lett. 60, 206, 1994. 5. Miller, J.B., et al., Phys. Rev. Lett. 90, 076807, 2003. 6. The L-G model for WAL is applicable only for fields B>Heff as defined in Ref. 5. 7. Knap, W. et al. Phys. Rev. B 53, 3912, 1996; Desrat, W. et al., Phys. Rev. B 74, 193317, 2006. 8. Since dislocation scattering is dominant in our samples, we expect W3/W1 ~1.

38 A. R. Dedigama et al. 9. Crooker, S.A. and Smith, D.L., Phys. Rev. Lett. 94, 236601, 2005; Chang, Shu-wei and Chuang, Shun-Lien, Phys. Rev. B 72, 115429, 2005.

Part II – Growth, Fabrication, Characterisation and Theory

Picosecond Carrier Dynamics in Narrow-Gap Semiconductors studied by Terahertz Radiation Pulses R. Adomaviþius, R. Šustaviþinjtơ and A. Krotkus Semiconductor Physics Institute, A. Goštauto 11, 01108, Vilnius, Lithuania

Abstract. In the present contribution, THz pulses were used for investigating carrier dynamics in the narrow-gap semiconductors. The measurement of the optically induced THz pulse absorption transients provided with important insights on the electron energy relaxation in the conduction band.In the second set of experiments THz generation from the surfaces of various semiconductors have been studied and compared. A substantial increase of the emitted THz power from CdHgTe surface was observed after lowering the sample temperature from 300K to 80K.

1 Introduction Sub-picosecond duration electrical pulses with the spectral content reaching to the frequencies of several terahertzes (THz pulses), which are generated and sampled by using femtosecond laser illuminated ultrafast semiconductor switches, are finding lately numerous applications in spectroscopy and characterization of various materials and devices [1]. Experimental techniques employing THz pulses are non-destructive, have enhanced temporal resolution, and excellent sensitivity. In the present contribution we will describe the use of two of these techniques for characterising the electron dynamics in various narrow-gap semiconductor materials. The first of such experiments is optical pump – THz probe measurement of the photoexcited electron dynamics that is normally used for studying carrier recombination in materials with picosecond and shorter lifetimes [2]. In narrow-gap semiconductors (NGS) investigated: InSb and CdHgTe, the carrier recombination was much slower, however, the measurement of the rising part of optically induced THz pulse absorption transients provided with important insights on the electron energy relaxation in the conduction band. In the second experiment – measurement of THz pulses emitted by semiconductor surface illuminated by femtosecond laser radiation – the observed effect gives extensive information on the physical processes that are taking place in the material. Numerous NGS have been investigated by this technique and physical mechanisms leading to the surface THz generation are

42 R. Adomaviþius, R. Šustaviþinjtơ, and A. Krotkus compared. It has been demonstrated that this effect can be used for determining intervalley separation in the conduction band in the material.

2 Experimental In the experiments, femtosecond Ti:sapphire laser (central wavelength of 800 nm, pulse duration of 150 fs, and repetition rate of 76 MHz) and photoconductor antennae manufactured from low-temperature MBE grown GaAs were used. In the optical pump – THz probe set-up, two parts of the laser beam were illuminating such antennae used as THz emitter and detector, whereas a third part arriving at the sample’s surface at different time delays creates non-equilibrium carriers. By investigating the THz emission, one of the optical beams was impinging at the surface of the semiconductor at 45o angle and the second was switching-on the antenna acting as THz pulse detector.

3 Results and discussion Fig. 1 shows rising parts of the optically induced THz absorption transients measured on bulk single crystalline InSb:Cr and epitaxial Cd0.2Hg0.8Te on CdTe samples at 80 K temperature. These transients are strikingly different: the duration of the rising parts for the latter material is more than 5 times longer than for the former. We explain this difference by the details of the conduction band structure of InSb and CdHgTe at high energies. For CdHgTe, the photoexcited electrons remain in a highly nonparabolic * valley all the time. After the excitation, their effective mass is very large and the mobility

1.0

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-4

-2

0

2

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8

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Fig. 1 THz transmission vs time delay at 80K for the Cd0.2Hg0.8Te and InSb samples

Picosecond Carrier Dynamics in Narrow-Gap Semiconductors 43 as well as the THz absorption low. Slow increase of THz absorption in this case is a consequence of the electron energy relaxation and the reduction of their effective mass. The comparison between the experiment and the rateequation model and Kane dispersion relation gives the value of the electron energy relaxation time equal to 1 ps. In the case of InSb, the electrons are excited by the Ti:sapphire laser quanta high above the position of the subsidiary L valleys [3] and contribute to the THz absorption only when they cool down and enter the main * valley at relatively low energy where the nonparabolicity is less significant than in the case of CdHgTe. One of the most important mechanisms leading to THz emission from the surfaces of NGS excited by femtosecond laser pulses are surface photovoltage transients caused by different electron and hole diffusion rates (the photoDember effect). This effect should be larger in the materials where excess energies of the electrons are higher, thus CdHgTe could be expected to be a better THz emitter than III-V NGS such as InAs or InSb. However this is not observed experimentally at room temperature because of an additional contribution of nonlinear optical mechanisms in III-V materials. After lowering the temperature to 80 K, THz pulse power emitted from CdHgTe increases by approximately two orders of magnitude, whereas in the case of InAs – the best THz emitter at room temperature - is only slightly enhanced. This fact demonstrates that the photo-Dember effect is the main cause of THz emission from CdHgTe. The efficiency of this effect is enhanced at low temperatures due to the reduction of the electron scattering rates and the increase in their mobility. An additional THz pulse echo is observed in CdHgTe at low temperatures following the main pulse after ~9 ps (a time corresponding to the electron cooling duration), but is not present in the case of InAs. This effect can be explained by the plasma oscillation that is developing after the electrons regain their high mobility after relaxing to the bottom of the conduction band.

References 1. Krotkus, A, Adomaviþius, R, Malevich, V.L.: 'Terahertz emission from semiconductor surfaces illuminated by femtosecond laser pulses', Proc. of SPIE Vol. 6257, 62570N 1-12, 2005 2. Beard, M. C, Turner, G. M., Schmuttenmaer, C. A. : 'Sub-picosecond carrier dynamics in low-temperature grown GaAs as measured by time-resolved THz spectroscopy' J. Appl. Phys., 90, 5915-5923, 2001 3. Adomaviþius, R, Molis, G, Krotkus, A, Sirutkaitis, V.: 'Spectral dependencies of terahertz emission fro InAs and InSb', App. Phys. Lett., 87, 261101 1-3, 2005

Band Structure of InSbN and GaSbN A. Lindsay1, A.D. Andreev2, E. P. O’Reilly1 and T. Ashley3 1

Tyndall National Institute, Lee Maltings, Cork, Ireland. Advanced Technology Institute, University of Surrey, Guildford, GU2 7XH, UK. 3 Qinetiq, St. Andrews Road, Malvern, Worcestershire, WR14 3PS, UK 2

Abstract. We use a tight-binding Hamiltonian to investigate the variation of energy gap with nitrogen (N) composition in InSbN and GaSbN, including the effect on the energy gap due to a random configuration of N atoms. We find that the assumed distribution of N atoms does not significantly affect the calculated energy gap in InSbN. By contrast, the electronic properties of GaSbN are strongly dependent on the assumed N distribution, with N-related defect levels strongly perturbing the lowest conduction band states and energy gap.

1 Introduction and Model The electronic structure of dilute nitride alloys such as GaNAs has attracted considerable interest [1]. When a small fraction of As atoms are replaced by N in GaAs, the energy gap initially decreases rapidly, due to a band-anticrossing (BAC) interaction between the host matrix conduction band edge (CBE) and a series of N-related defect levels above the CBE [2]. InSb has the smallest energy gap of any III-V semiconductor, and it has been proposed that the addition of N to form InSbN could give a zero-gap semiconductor [3]. GaSbN is also being considered as a potential emitter for wavelengths beyond the 1.5 Pm telecomm range [4]. We use an sp3s* nearest-neighbour tight-binding (TB) Hamiltonian to present the first systematic investigation of the influence of N on the band structure of InSbN and GaSbN. The calculations are carried out on a series of 1728 atom In864NmSb864-m and Ga864NmSb864-m supercells over a range of m=332 (N concentration x = 0.35-3.70 %). For each concentration, we calculated the band structure for a series of structures containing a randomly generated distribution of N atoms, with different constraints on the N atoms in each calculation, varying from structures which contain isolated N atoms only (no N atom having another N atom as a second nearest neighbour), to more complicated N arrangements, which for the highest concentrations included clusters of up to four interlinked N atoms. The tight-binding model used follows closely the approach described in [5].

46 A. Lindsay et al.

Fig. 1. (a) Variation of energy gap with N composition x for a series of GaSb1-xNx (solid circles) and InSb1-xNx supercells (open circles). Solid line: BAC fit to InSb1-xNx energy gap. (b) Band structure of an exemplar In864N14Sb850 (x=1.62%) supercell along the (001) direction up to the Brillouin zone boundary. Dashed line: Fit to lowest conduction band dispersion using a 10-band k.p Hamiltonian.

2 Results and Discussion The open circles in Figure 1(a) show the calculated low temperature variation of energy gap with composition x for the different InSbN structures considered, while the solid circles show the variation of energy gap for the GaSbN structures. The energy gap has a generally smooth variation with x in InSb1-xNx, which can be well fitted using the two-level BAC model [2] (solid line), where we assume that the InSb CBE, Ec, and the N defect state energy, EN, vary with x as Ec = 0.230 – 2.53x eV and EN = 0.720 – 2.74x eV, while the interaction parameter VNc varies with x as Ex½, where E = 1.97 eV. We estimate a zero low temperature energy gap in InSb1-xNx for x >~2.7%. By contrast, the calculated energy gap of GaSb1-xNx depends strongly on the assumed N distribution in each supercell calculation, reflecting that N cluster states introduce a series of defect levels close to the CBE in this alloy. Fig. 1(b) shows as an example the band structure of an In864N14Sb850 (x=1.62%) supercell containing nine isolated N atoms, one N-N pair and one

Band Structure of InSbN and GaSbN 47 Cs-symmetry triplet. The defect states associated with the different N environments all lie well above the conduction band minimum, with the lowest N-related level 375 meV above the CBE. The dashed line shows the conduction band dispersion calculated using a 10-band k.p Hamiltonian and the BAC parameters introduced above. The fit in Fig. 1(b) confirms that the band dispersion close to the conduction band minimum in InSb1-xNx is well described using the BAC model. The BAC dispersion starts to deviate from the full calculation at ~100 meV above the CBE, due to an anti-crossing interaction with the triplet defect level, which has a concentration in Fig. 1(b) much higher than that expected for a random alloy at x = 1.62%. Further calculations show that the deviation is reduced for a defect distribution closer to that of a random alloy. We therefore conclude that the two-level BAC model is appropriate near the conduction band minimum in InSbN. By contrast, we need to take explicit account of the distribution of N-related defect levels when analysing the band dispersion in GaSb1-xNx.

3 Summary In summary, the band dispersion of InSb1-xNx near the conduction band minimum is well described using the BAC model. However, the optical properties of GaSb1-xNx depend strongly on the distribution of N atoms within the alloy, with N-related defect levels strongly perturbing the lowest conduction band states and energy gap. We conclude that the incorporation of N in an ideal InSbN alloy should allow a zero-gap III-V semiconductor for x >~2.7% at low temperature. By contrast, there will in general be strong inhomogeneous broadening and localisation effects due to N-related defect levels close to the conduction band minimum in GaSbN. This work was funded by the Electro-Magnetic Remote Sensing (EMRS) Defence Technology Centre (U.K.) and Science Foundation Ireland..

References 1. For a review, see “Physics and Applications of Dilute Nitride”, ed. I. A. Buyanova and W. M. Chen (Taylor & Francis, New York, 2004) 2. W. Shan, W. Walukiewicz, J.W. Ager III, E.E. Haller, J.F. Geisz, D.J. Friedman, J.M. Olson and S.R. Kurtz, Phys. Rev. Lett. 82, 1221 (1999) 3. T. Ashley, T.M. Burke, G.J. Pryce, A.R. Adams, A.D. Andreev, B.N. Murdin, and E.P. O’Reilly, Solid State Electron. 47, 387-394 (2003) 4. D.P. Xu, J.Y.T. Huang, J.H. Park, L.J. Mawst, T.F. Kuech, I. Vurgaftman and J.R. Meyer, Appl. Phys. Lett. 90, 171913 (2007) 5. E.P. O’Reilly, A. Lindsay, S. Tomiü and M. Kamal-Saadi, Semicond. Sci. Technol. 17, 870879 (2002)

Growth and Characterisation of Dilute Antimonide Nitride Materials for Long Wavelength Applications S D Coomber1, L Buckle1, P H Jefferson2, D Walker2, T D Veal2, C F McConville2, T Ashley1 1 2

QinetiQ Ltd., Malvern, Worcestershire, WR14 3PS, UK Dept. of Physics, University of Warwick, Coventry, CV4 7AL, UK

Abstract. The addition of a small percentage of nitrogen to GaSb or InSb is predicted to move their response wavelengths into the long wavelength IR range due to the influence of band-gap bowing. We report the growth of GaNxSb1-x and InNxSb1-x by MBE, using an r.f. plasma nitrogen source. We demonstrate high structural quality, as determined by XRD, and FTIR absorption measurements show a shift in the cut-off wavelength to over 3 Pm for GaNSb and over 11 Pm for InNSb, allowing for the effect of Moss-Burstein band filling.

1 Introduction The addition of small amounts of nitrogen to III-V semiconductors leads to a large degree of band-gap bowing, giving rise to band-gaps smaller than in the associated binary materials1. The band-gap reduction is due to the localised interaction between the host conduction band and the nitrogen resonant level and can be described by the band anti-crossing (BAC) model2. This model predicts that the addition of a small percentage (< 5%) of nitrogen to GaSb or InSb will move their response wavelengths into the long (8 to 14 µm) or even very long (>14 µm) wavelength IR ranges.

2 Growth and structural characterisation The material has been grown by MBE, using techniques described previously3. The active nitrogen was supplied by an r.f. plasma source. The variation in nitrogen composition of GaNxSb1-x obtained as a function of growth temperature for various values of plasma power is shown in Figure 2(a). It can be seen that by varying the growth temperature the nitrogen incorporation can be increased from virtually zero to 1.75%, as determined from XRD. The high crystalline quality is demonstrated by the rocking curves shown inset in Figure 2(a).

50 S. D. Coomber et al. The variation in nitrogen composition of InNxSb1-x as a function of growth temperature, Figure 2(b), indicates a very narrow (~5qC) temperature window in which good structural quality, nitrogen containing material can be grown. This narrow growth temperature window may be due to two competing mechanisms controlling nitrogen incorporation and further investigation is required. GaSb

GaN0.006Sb0.994

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Figure 2(a) GaNSb nitrogen composition vs. growth temperature, inset XRD rocking curves, (b) InNSb nitrogen composition vs. growth temperature, inset XRD rocking curve showing good structural quality at Tg = 330qC.

3 Electrical and optical characterisation Single field Hall measurements have been performed and show the GaNxSb1-x and InNxSb1-x material to have p-type and n-type carrier concentrations in the 1018 cm-3 range respectively. GaSb and InSb material grown under equivalent conditions have carrier concentrations in the 1015 cm-3 range, suggesting that some nitrogen is incorporating interstitially or on antisites and having a detrimental effect on the electrical properties of these materials. The room temperature FTIR absorption spectra of GaNxSb1-x and InNxSb1-x have been measured and compared with the spectra for GaSb and InSb respectively, see Figure 3. The GaSb absorption edge is seen to move to significantly lower energies upon nitrogen incorporation. The higher nitrogen content layer shows a band-gap of 380r20 meV, a reduction of approximately 340 meV compared with GaSb and corresponding to a cut-off wavelength of 3.3 Pm. The InNSb spectra show the absorption edge moving to higher energies compared to InSb. This is due to the significant Moss-Burstein shift that results from the high, n-type, carrier concentration. Theoretical modelling of the InNxSb1-x band structure4 indicates that for InNSb containing 0.68%

Growth and Characterisation of Dilute Antimonide Nitride Materials 51 nitrogen, the band-gap has been reduced by over 50 meV compared with InSb, corresponding to a cut-off wavelength of over 11 Pm.

(a) GaNSb (b) InNSb

Figure 3 Absorption spectra of (a) GaNxSb1-x, (b) InNxSb1-x

4 Conclusions We have shown that nitrogen can be incorporated into GaSb (up to 1.5%) and InSb (up to 0.7%) grown by MBE, by use of an r.f. nitrogen source. XRD measurements have shown both materials to have an excellent crystalline quality. Optical absorption measurements have demonstrated a band-gap reduction of more than 300 meV for GaNSb and over 50 meV for InNSb allowing for the competing effect of Moss-Burstein band filling. Hall effect measurements have shown both GaNSb and InNSb to have high, background carrier concentrations and in order to realise devices using these narrow bandgap materials the free carrier concentration must first be dramatically reduced.

References 1. 2. 3. 4.

M. Weyers, M. Sato and H. Ando, Jpn. J. Appl. Phys., 31, L853-L855 (1992) W. Shan, W. Walukiewicz et al, Phys. Rev. Lett., 82, 1221-1224 (1999) T. Ashley, L. Buckle, G. W. Smith, B. N. Murdin, P. H. Jefferson, L. F. J. Piper, T. D. Veal and C. F. McConville, Proc. SPIE, 6206, 62060L (2006) P. H. Jefferson, L. Buckle, D. Walker, T. D. Veal, S. Coomber, P. A. Thomas, T. Ashley, C. F. McConville, Phys. Stat. Sol (RRL), 3, 104-106 (2007)

Acknowledgements This work was partially funded by the UK MOD through the EMRS-DTC.

Electron Interband Breakdown in a Kane Semiconductor with a Degenerate Hole Distribution A. V. Dmitriev1 and A. B. Evlyukhin2 1

Department of Low Temperature Physics, Moscow State University, Russia

2

Department of Physics and Applied Mathematics, Vladimir State University, Russia

Abstract. This work is devoted to the theoretical study and computational modelling of hot electron transport and interband breakdown in a semiconductor with the Kane band dispersion law and highly degenerate hole distribution. This is an unusual system where the ionization threshold is electric field dependent because the ionization in it takes place from the hole Fermi level which itself changes during the breakdown process. We found that a specific mechanism of S-type negative differential conductivity formation may take place in this material under breakdown conditions. The predicted current instability is connected with the entirely Coulomb electron scattering by heavy holes.

1 Introduction Interband breakdown is one of the most important high electric field phenomena in semiconductors. This is especially true in narrow bandgap materials where breakdown fields are low and the interband carrier lifetime is mainly determined by Auger transitions [1]. In this work we study theoretically the high-field charge carrier transport and breakdown in degenerate p-type narrow gap semiconductor. As a typical example, we consider Hg0.8Cd0.2Te at low temperatures. The majority charge carriers in this alloy are holes, and they dominate the Ohmic transport. However, as a high electric field is applied, the role of electrons in charge transport increases because of their high mobility. Therefore the breakdown can be caused by the electron impact ionization of the states in the heavy hole valence band. Our approach is based on several assumptions. First, we suppose that electrons in the conduction band are scattered by charged impurities, heavy holes and polar optical (PO) phonons. Second, we take into account two channels of Auger recombination. The first one is the process when an electron in the conduction band recombines with a heavy hole, whereas the excess momentum and energy are taken by another heavy hole which simultaneously hops to the light hole band. The second channel is also an electron-heavy hole recombination, but the excess momentum and energy are taken by another electron in the conduction band. Further, we neglect heating of holes, for

54 A.V. Dmitriev and A.B. Evlyukhin heavy holes because of their heavy mass and low mobility, and for light ones due to their frequent transitions to the heavy hole band, which makes them effectively heavier than electrons. Hence we assume that the hole distribution remains degenerate in the full electric field range. We take into account the fact that the electron ionization threshold energy depends on the hole Fermi level position in the valence band and hence the carrier concentration [3], because only occupied electron states can be ionized, and they lie only below the hole Fermi level. And finally, we consider a stationary and space-homogeneous case.

2 Calculations and Results Because the hole distribution is known, we should calculate only the electron distribution function. Applying the method proposed in [2] and taking into account that the electrons in the conduction band may be scattered by POphonons, we divide the electron momentum space into two parts — passive and active. In the first one, electron energy is smaller than the PO-phonon energy. In the second one, the opposite is true. Most of the electrons in the conduction band remains in the passive region and can be described by the quasi-equilibrium Maxwell distribution with a field dependent effective temperature. This dependence can be found from the electron energy balance equation. The number of electrons in the passive region is determined from the particle balance equation. The use of quasiequilibrium distribution function is justified by the high post-breakdown electron concentration in the high field regime. To calculate the electron distribution function in the active region, we suppose that the average energy of the electrons in this region is much greater than the PO-phonon energy. This condition may be justified in the high electric field, the case we consider here. So we can use the diffusion approximation [4] to solve the Boltzmann equation for the ionizing electrons with high energy. This approach allows us to find the electron distribution function in the whole momentum space. The final system of equations that we use to investigate the electron transport and breakdown, includes the particle balance equation for the electrons in the conduction band, the neutrality condition for the nonequilibrium electron and hole concentrations, and the energy balance equation for the electrons in the passive region:

Ge + Gh = Rehl + Reeh ; p  p0 = n  n0 ; e 2 IJ m E 2 / me = (Te  T0 ) / IJ İ ,

Electron Interband Breakdown in a Kane Semiconductor 55 Ge and Gh are the impact ionization rates by electrons and light holes, respectively; Rehl and Reeh are Auger recombination rates; p, n and p0,n0 are total and equilibrium hole and electron concentrations, respectively; e is the electron charge; E is electric field; me is the effective electron mass; IJm and IJİ are the electron momentum and energy relaxation times; T0 is the lattice temperature. The electron momentum and energy relaxation times in the passive region is determined by the electron scattering by the degenerate heavy holes. The total impact electron ionization rate is calculated on the base of the electron distribution function and the electron impact ionization probability found in [3]. This set of equations is then solved numerically. We use the material parameters of Hg0.8Cd0.2Te taken from [5].

Fig. 1. (a): The calculated I-V curves for different hole Fermi levels; (b): Field dependence of the effective temperature of electrons Fig. 1(a) shows that the breakdown electric field increases with the increase of the hole Fermi energy. This is caused by the obvious increase of the electron ionization energy for a state on the hole Fermi level. One can see from Fig. 1(b) that the field dependence of the effective temperature can have S-type shape (left curve). As a result, a current instability may take place under the breakdown conditions. It originates from the entirely Coulomb electron scattering mechanisms in the passive region. In conclusion, our results show that a specific mechanism of S-type negative differential conductivity formation may take place in p-type Kane semiconductor under breakdown conditions.

References 1. Dmitriev, A.V., and Mocker, M.: Phys. Rep., 257, 85—163, 1995 2. Popov, V.L.: Fiz. Tverd. Tela, 25, 2127—2132, 1983 3. Dmitriev, A.V., and Evlyukhin, A.B.: Semicond. Sci. Technol., 12, 29—34, 1997

56 A.V. Dmitriev and A.B. Evlyukhin 4. Levinson, I.B.: Fiz.Tverd.Tela, 6, 2113—2120, 1964 5. Gelmont, B., Lund, B., Kim, K., Jensen, G., Shur, M., and Fjeldly, T.A.: J. Appl. Phys., 71, 4977—4982, 1992

InMnAs Quantum Dots: A Raman Spectroscopy Analysis A. D. Rodrigues1, J. C. Galzerani1, E. Marega Jr.2, L. N. Coelho3, R. Magalhães-Paniago3 and G. J. Salamo4 1

Departamento de Física, UFSCar, 13565-905 São Carlos, SP, Brazil IFSC, Universidade de São Paulo, 13560-970 São Carlos, SP, Brazil 3 LNLS, CP 6192, 13084-971 Campinas, SP, Brazil and Departamento de Física, UFMG, Belo Horizonte, MG, Brazil 4 University of Arkansas, Dept. Phys. Fayetteville, AR 72701 USA. 2

Abstract. In1-xMnxAs quantum dots grown on [100] GaAs substrates at different temperatures and with different Mn concentrations were studied. The substitutional Mn incorporation to the InAs lattice and the conditions for obtaining coherent and non-relaxed structures are here discussed from the comparison between Raman spectroscopy and X-rays analysis.

1 Introduction The semiconductor heterostructures based in the In1-xMnxAs alloys, associating the InAs semiconducting behavior to the magnetic properties of Mn1, are considered as potential candidates for the new generation of optoelectronic devices and components which operations are based in the spin. Raman spectroscopy is here used in order to verify the characteristics of the InMnAs quantum dots grown in different growth conditions.

2 Experimental The samples were grown using a RIBER 32P solid-source Molecular Beam Epitaxy apparatus. A 0.3Pm high temperature (HT) GaAs buffer layer was grown on semi-insulating (100) GaAs substrate at 580oC after oxide desorption. After the buffer layer deposition, the temperature was decreased to 300 oC under As4 flux. Two sets of samples were grown. In the first set the substrate temperature was decreased to 320oC under As4 flux and then one monolayer (ML) of InAs was deposited on HT-GaAs; after that, without any growth interruption, a 1.4 ML’s of InMnAs was deposited, with different Mn concentrations. In the second set the Mn concentration was fixed at 15% and the growth temperature changed. The Raman spectra were acquired at 10K, with a Jobin Yvon T64000 equipped with a CCD detector. The samples were

58 A. D. Rodrigues et al. excited by the 488nm line of a Ar+ laser in the configurations z(x’y’) z and z(y’y’) z , with x’, y’, z parallel to [110], [1 1 0] and [001] axis respectively. The X-rays patterns were acquired at the XRD2 beamline (Brazilian Synchrotron Light Source); this is equipped with a double bounce sagitally focused Si (111) monochromator and a standard fourcircle diffractometer.

3 Results and discussion In Fig. 1(a) we show the Raman spectra for the z(y’y’) z geometry, for the quantum dots grown at 320oC and for several Mn concentrations. Besides the longitudinal optical (LO) and transversal optical (TO) GaAs modes, and a feature observed around 230 cm-1 (attributed to As clusters), it is evident the appearance of the InAs LO mode at around 245 cm-1 for 0 % Mn. The disappearance in the z(x’y’) z spectra (where it is forbidden by the Raman selection rules) confirms its longitudinal character. b)

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Fig. 1. a) Raman spectra of the InMnAs QD’s with different Mn concentrations; b) Xray scans for samples grown at 320oC without Mn (solid) and with 15% of Mn (dash).

Paying attention to this particular phonon, it is evident that its intensity decreases as Mn is incorporated to the InAs dots. This probably happens because the InAs lattice is gradually loosing its fcc character (pure InAs) with the substitutional incorporation of Mn. Besides, the frequency of this mode is quite close to the one observed for bulk InAs, what drives us to conclude that it corresponds to incoherent dots. For comparison, we present in Fig. 1(b), radial X-rays scans along the [220] direction for two samples grown at 320oC. Both samples present a reasonable amount of scattered X-ray intensity between the InAs (6.05Å) and GaAs (5.65Å) bulk peak positions. This shows the existence of the lattice parameter gradient inside the dots. For low temperature quantum dots, a peak

InMnAs Quantum Dots: A Raman Spectroscopy Analysis 59 around 6.0Å is related to the presence of incoherent quantum dots. These are relaxed dots formed due to the low Indium diffusion coefficient at low temperatures. The small shift in the peak between the no Mn sample and the 15% Mn one, can be attributed to the Mn incorporation in the InAs lattice. a)

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Fig. 2. a) Raman spectra of the InMnAs QD’s with 15% of Mn for different growth temperatures; fittings were made for the hole frequency interval but they are here shown only for the InAs LO modes. b) X-Ray scans for the same samples.

In order to analyse the differences obtained for the growth realized at different temperatures, we show the Raman spectra for samples grown at 320oC, 420oC and 520oC, in Fig. 2(a). The thicknesses are 2.4 ML’s and the Mn concentration is 15%. It is quite evident the shift of the InAs LO mode towards the region of low frequencies, as the growth temperature increases; this fact is associated with a decrease in the InAs lattice parameter in the growth plane, taking to a distensive stress in the perpendicular direction. The above observation agrees with the one made from the X-rays diffraction – Fig 2(b) – for these samples. At high temperature, the Indium diffusion increases and the observed relaxation of the quantum dots diminishes. We then expect to obtain good homogeneity of the dots for these growth conditions. At high temperatures, the Mn cannot dilute anymore in the InAs lattice and probably part of the Mn forms MnAs clusters.

Acknowledgements The authors acknowledge FAPESP, CNPq and LNLS. The research performed at the Brazilian Synchrotron Light Source was partially supported by ABTLus.

60 A. D. Rodrigues et al.

References 1. Chen, Y. F., Lee, W. N., Huang, J. H., Chin, T. S., Huang, R. T., Chen, F. R., Kai, J. J., Aravind, K., Lin, I. N. and Ku, H. C., J. Vac. Sci. Technol. B 23(4), 1376, 2005

Conduction Band States in AlP/GaP Quantum Wells. M. Goiran1, M.P. Semtsiv2, S. Dressler2, W.T. Masselink2, J. Galibert1, G. Fedorov3, D. Smirnov3, V. V. Rylkov1,4 and J. Léotin1. 1

. LNCMP, 143 Avenue de Rangueil - 31400 Toulouse, France. . Department of Physics, Humboldt-Universität Berlin, Newtonstrasse 15, D12489 Berlin, Germany. 3 . NHMFL,1800 E. Paul Dirac Drive. Tallahassee, FL 32310-3706.USA 4 . Russian Research Center «Kurchatov Institute», 123182 Moscow, Russia. 2

Abstract. We report on the investigation of the conduction band (CB) of AlP by high magnetic field cyclotron resonance (CR) and transport in a two-dimensional electron gas (2DEG) confined in AlP/ GaP. We found that for QW width <4nm the ground state subband is a single Xz valley with cyclotron mass mzc/m0= 0.3r0.02, whereas, for wider QW, > 10nm thick, the ground state becomes twofold Xxy valleys with cyclotron mass mxyc/m0= 0.52r0.01. We conclude that the bulk AlP CB displays three ellipsoidal valleys having minima at the X point of the Brillouin zone (BZ) with transverse and longitudinal effective masses mt/m0 = 0.3r0.02 and ml/m0 = 0.9r0.02.

1 Introduction AlP is probably one of the last III-V compound for which the band parameters are still uncertain [1]. Only recently, high magnetic field spectroscopy of 2DEG confined in AlP/GaP quantum wells (QW) has enabled to assign the CB minima exactly to the X-point of the BZ, giving for bulk AlP a valley degeneracy of 3 [2]. As expected for such systems [3], the valley degeneracy is lifted into a single Xz-valley and twofold Xxy-valleys, due to on one hand the valley-anisotropy confinement splitting and on the other hand the biaxial strain splitting caused by the lattice mismatch between AlP and GaP. Depending on whether the strain is tensile or compressive, splittings are additive or subtractive, the later being the case for AlP on GaP. As a result, for wide AlP QWs the prevailing compressive strain gives rise to a ground state Xxy-valley as reported in ref [2]. In the present study, we measure a new set of narrower QWs that displays a Xz-valley ground state.

2 Sample and experiments The samples were grown by gas source MBE on n-type unintentionally doped (001) GaP substrates. The samples are either heterostructures, with a single

62 M. Goiran et al. AlP quantum well (SQW) where only the top GaP barrier is doped, or multiple AlP quantum wells (MQW). The sheet carrier density is in the range between 2 and 5.1012cm-2, and the mobility is several times 103 cm2/Vs. Cyclotron resonance and magneto-transport experiments down to 1.55K were performed under high pulsed magnetic field while static fields were used for the low temperature transport measurements down to 280mK.

3 Results and discussion CR experiments were performed at 4K on two different samples, one being a 15nm wide multi-QW with 50 periods already presented in a previous paper [2], and the other a 4nm wide single-QW. Figure 1 summarizes the CR data by plotting excitation energy in the range between 1 and 6 meV versus resonant magnetic field, for the narrow and wide QWs. 6 m*= (0.30r0.02)m0

Energy, meV

5 4 3 2

m*= (0.52 r0.01 m0

1 0

0

5

10

15

20

25

30

Magnetic field (T)

Fig. 1. Values of the resonant fields determined from CR at different excitation energies for the 15nm MQW structure (full circles) and the 4nm SQW (open circles).

The two straight lines indicate parabolic conduction bands for both Xz and Xxy valleys, the deduced cyclotron masses are mc1=0.30r0.02m0 and mc2=0.52r0.01m0, respectively. The iso-energy surfaces are then ellipsoids elongated along the ' line of the BZ with longitudinal and transverse effective masses: ml/m0 = 0.9r0.02 and mt/m0 = 0.3r0.02. Regarding valley degeneracy, a direct determination is derived for each QW from combination of longitudinal and Hall resistances data. Fig. 2a shows Rxx(B) and Rxy(B) for the 10nm wide QW at 1.55K while Fig.2b shows the same for the 3nm wide QW at 280 mK. The idea is to derive the filling factor assigned to each minimum of Rxx(B). This is obtained by measuring the Hall resistance at each minimum and finding the filling factor Q by the ratio v= RK /Rxy , RK being the Klitzing resistance. In Fig2a, standing for the wide QW having the Xxy-valley populated, the sequence of integer filling factors at consecutive resistance minima are marked by squares in terms of Rxy values. A remarkable feature of

Conduction Band States in AlP/GaP Quantum Wells 63 the found Q-series is its increment by 4 at low magnetic fields, high Landau quantum numbers, and then by one at low quantum numbers. 3

Rxx(:

T = 1,55K

3

3x10

1,5x10

QW, t= 3nm

3

T = 280mK

3

8,0x10

4

Rxy(:

3 4

Q 22 Q 18

14 10

3

5,0x10

3

2x10

4

Rxy(:

1,0x10

3

1,0x10

5 Q 8

6 7

3

4,0x10

6

Rxx(:

QW, t= 10nm

2

5,0x10 3

Q 5

1x10

12 10 Q 14

0,0

0 0

10

20

Magnetic Field (T)

30

40

0,0

0,0 0

2

4

6

8

10

12

14

16

18

20

Magnetic Field (T)

Fig. 2. Rxx(B)and Rxy(B) for SQW having 10nm (a) and 3nm well width (b).

A straightforward interpretation is that Landau levels are, at low magnetic fields, degenerate by spin (2) and valley (gv) and this degeneracy is entirely lifted at high magnetic fields. Consequently, the Landau degeneracy value, 2xgv equal to 4 gives gv=2 for the Xxy-valley. Accordingly, a valley degeneracy gv=1 is expected for the populated Xz-valley of the 3nm sample. This is precisely displayed by the data in Fig. 2b showing a sequence of filling factors incremented by 2 at low magnetic fields and by one at high magnetic field.

4 Conclusion Magneto-spectroscopy of 2DEG confined in AlP QWs demonstrates that the CB minima in bulk AlP are located at the X point of the BZ. The Xxy-Xz valley crossover is found to occur for a well width between 3 and 10nm.. An interesting issue of this study is to provide effective masses for the design of intersubband detection or emission devices falling in the Thz gap (5-10THz). This gap is accessible only in AlP/GaP and GaN III-V materials because of the higher energy value of their restrahlen band making them transparent in the THz gap.

References 1. I. Vurgaftman, J. R. Meyer, and L. R. Ram-Mohan, J. Appl. Phys. 89, 5815, 2001 2. M. P. Semtsiv, S. Dressler, and W. T. Masselink, V. V. Rylkov, J. Galibert, M. Goiran, and J. Léotin. Phys. Rev. B 74, 041303(R), 2006

3. H. W. van Kesteren and E. C. Cosman, P. Dawson, K. J. Moore, and C. T. Foxon Phys. Rev. B 39 (18) ,13426, 1989.

Growth of InAsSb Quantum Wells by Liquid Phase Epitaxy M.Yin, A. Krier, R. Jones Mid-Infrared Research Group, Lancaster University, Lancaster, UK

Abstract. We report on the liquid phase epitaxy (LPE) growth with the use of linear rapid slider boat technology for the production of quantum well (QW) structures based on InAsSb/InAsSbP. Typical characteristics of some of these prototype sources are presented and analyzed, including the results of SEM, X-ray diffraction, photoand electro- luminescence characteristics of prototype DH & QW devices. LPE growth of InAsSb QW has been successfully obtained experimentally. The QW structure has been confirmed by SEM and electroluminescence measurements at different temperatures.

Having achieved a lasing temperature of more than 200 K and high efficiency [i] for our optimized DH lasers suggests that it should be possible to further increase the laser operating temperature by using a strained type-I QW structure based on the same InAsSb/InAsSbP alloys. It is generally accepted that the characteristic insensitivity of QW laser to temperature is associated with a reduced threshold current density (compared to that for the same threshold modal gain requirement in DH lasers) and reduced Auger recombination in strained QW structures. However, owing to the nature of the alloy system which contains three group V elements there has been little investigation of QW lasers in this system and almost all reports to date have concerned LPE growth of bulk DH. There are some difficulties in the accurate experimental determination of InAsSbP composition and also with epi-layer growth due to uncertainties in the thermodynamic parameters. Consequently, different research groups have published different values of InAsSbP band gap for nominally the same alloy composition [ii, iii]. In LPE growth of InAs1-x-ySbxPy, the miscibility gap (y>0.45) makes it difficult to grow alloys with a wide band gap for effective confinement. Thus, there are trade-offs in designing structures that simultaneously achieve both sufficient carrier confinement and good quality epitaxial growth in practice. LPE is relatively easy to grow alloys containing three group V’s such as InAsSbP which are lattice matched to InAs substrates and which can produce type I structures with suitable confinement. In this work, we report on the growth of quantum well structures using a linear rapid slider boat technique.

66 M. Yin, A. Krier, and R. Jones Typical characteristics of some of these prototype sources are presented and analyzed, including the results of SEM, X-ray diffraction, and electroluminescence characteristics of prototype QW & DH structures. The InAsSb QW with InAsSbP barriers was successfully grown by LPE using the rapid slider growth technique which we developed in our laboratory. The slider speed is controlled by a linear driver so that the minimum contact time of the melts and substrate is about 1 msec. Epitaxy is carried out with the boat inside a high purity quartz reactor tube under flowing purified hydrogen gas from a Pd-diffusion unit. The epi-layers were grown on InAs (001) substrate at the temperatures of 572 ºC. The thickness of the InAsSb epi-layer was progressively reduced through growth of a series of samples. The thickness of each epi-layer and QW was measured using an FEI Sirion field– emission scanning electron microscope (FEG-SEM) on cross-sectioned samples which were stained using the A:B etch. The epi-layer compositions were determined from energy-dispersive X-ray analysis (EDX), double crystal x-ray diffraction (DXRD) and photoluminescence measurements When we grew thinner InAsSb epi-layers as required for the QW active region using the linear rapid slider boat technique, the solid Sb composition was observed to be different from that of the bulk material, even though the same liquid composition was used for growth of all the samples. From DXRD and EDX analysis we observed that the solid Sb (x) composition increased as the epi-layer became thinner as shown in Fig. 1(a), where a logarithmic relation between the epi-layer thickness and Sb composition is obtained. Sb composition remained constant for the thick epi-layer growth but is significantly increased as the grown epi-layer becomes thinner. Since Sb is the heavier element in the liquid phase we associate this behaviour with the higher segregation of Sb from the melt during the early stages of growth. (a)

0.06

X of InAs1-xSbx

(b)

6

0.05

InAsSbP

5

0.04 0.03

4 3

0.02 0.01

2 1

InAsSb

Sample No.

0.00 10

100

1000

Thickness of InAsSb (nm)

InAsSbP

Fig. 1. (a) The influence of InAsSb thickness on the solid Sb composition (x) in InAsSb/InAsSbP DH structure and (b) SEM profile of the InAsSb QW grown by LPE

Growth of InAsSb Quantum Wells by Liquid Phase Epitaxy 67 Fig. 1(b) shows that a thin InAsSb epi-layer was successfully grown between the InAsSbP epi-layers by LPE, where the InAsSb QW is sandwiched by two InAsSbP layers. The thickness of InAsSb QW was measured to be ~20nm. The Sb composition of 0.057 was obtained from DXRD measurement. A ridge strip laser was processed from the epitaxial wafers using conventional photolithography. 0.000024

(a)

30K

Intensity/arb.

0.000022

0.000020

60K 40K 0.000018

80K 100K

0.000016

120K

0.000014

2.6

2.8

3.0

3.2

3.4

3.6

3.8

Wavelength(Pm)

Band Energy (eV)

0.45

(b)

Peak1 Theoretical Peak2

0.42

0.39

0.36

0.33 0

40

80

120

160

Temperature (K)

Fig. 2. (a) The electroluminescence spectrum for an InAs0.943Sb0.057/InAs0.61Sb0.13P0.26 QW p-i-n structure at different temperatures; (b) Emission energies from two QW sub-bands compared with the corresponding theoretical bulk band gap at different temperatures.

The electroluminescence spectrum from the edge emission of the diode was measured at different temperatures in Fig. 2. For the InAs0.94Sb0.057 QW and InAs0.61Sb0.13P0.26 barriers two peaks appeared in the EL spectrum over the temperature range from 30 to 120 K as shown in Fig. 2(a). The energy of these two peaks is significantly higher than that calculated for the equivalent bulk alloy material as shown in Fig. 2(b) and much lower than that of the

68 M. Yin, A. Krier, and R. Jones InAs0.61Sb0.13P0.26 emission. The results are in excellent agreement with calculated eigenstate transition energies for a 24nm InAs0.943Sb0.057 / InAs0.61Sb0.13P0.26 QW. Further work is in progress to develop the cladding layers for the laser waveguide based on wider band gap InAsSbP alloys with higher P content and also to increase the Sb composition in InAsSb active region. We are grateful to H.M. Government Communications Centre for supporting this project.

References i. M. Yin, A. Krier, P.J. Carrington, R. Jones, S.E. Krier, The Thirteenth International Conference on Narrow Gap Semiconductors, Guildford, UK, 2007

ii. H. Mani, et al, Journal of Crystal Growth, 121, 463-472, 1992 iii. I. Vurgaftman, et al, Journal of Applied Physics, 89(11), 5852-5853, 2001.

Diode Lasers for Free Space Optical Communications Based on InAsSb/InAsSbP Grown by LPE M. Yin, A. Krier, P.J. Carrington, R. Jones, S.E. Krier Mid-Infrared Research Group, Lancaster University, Lancaster, UK

Abstract. InAsSb/InAsSbP double heterojunction lasers have been grown by liquid phase epitaxy in which free carrier absorption loss was investigated and minimized by the introduction of two undoped quaternary layers on either side of the active region. The diode lasers operate readily in pulsed mode at elevated temperatures and emit near 3.45 µm with a threshold current density as low as 118 A/cm2 at 85 K. Compared to the conventional 3-layer DH laser, reducing the optical loss increases the maximum lasing temperature by 95 K to ~210 K in the optimized 5-layer structure.

To access the technologically difficult mid-infrared (2-5 µm) spectral range several different device designs (e.g. QCL etc.) are being investigated. However, although promising, some of these devices rely on very complex structures comprising many ultra-thin layers and the fluctuation in composition, uncertainties in material quality and interface roughness, etc, are difficult to control in manufacture. The LPE method has some useful features. In particular, because it is a near equilibrium growth technique it can produce epitaxial layers of high crystalline perfection containing few point defects and impurities. LPE also has a relatively high growth rate (~ 1 µm/min) which is useful for the production of the cladding layers or broad waveguide regions in a high power diode laser. Using LPE growth also gives us the potential for high power output and cost effective manufacture, which is attractive for applications such as mid-infrared free space optical communications The crucial role of internal loss (Di) in limiting both the differential quantum efficiency (Kd) and maximum operating temperature has been realised [1], together with the importance of Auger recombination for wavelengths longer than 3 µm. The absorption loss for doped InAs related alloys at wavelengths near 3.4 µm can be more than 200 cm-1 [2]. In this work we demonstrate mid-infrared diode lasers with improved performance fabricated using a simpler approach based on LPE. We report specifically on a 5-layer double heterojunction (DH) laser with reduced optical loss emitting at 3.45 µm and operating up to 210 K. In the conventional DH laser structure, the InAs1-xSbx active region is sandwiched between two InAs1-x-ySbxPy cladding layers. Some of the optical mode overlaps with the highly doped cladding layers, which introduces optical

70 M. Yin et al. loss due to free carrier absorption. In our optimised structure, undoped InAs0.61Sb0.13P0.26 layers are inserted between the heavily doped InAs0.61Sb0.13P0.26 cladding layers on either side of the InAs0.96Sb0.04 active region in an attempt to reduce the optical mode overlap with the heavily doped layers. The undoped layers also block unwanted impurity diffusion into the laser active region and give improved carrier confinement. The thickness of the undoped InAs0.61Sb0.13P0.26 layers was selected to be (S1) 0 µm, (S2) 0.25 µm and (S3) 1.0 µm in the lasers which were subsequently fabricated. The fundamental transverse TE mode profile confinement factor (ī) was calculated as 35% for the conventional 3-layer DH laser structure. In this case there is 65% mode overlap with the highly doped cladding layers. In the 5layer DH structure the confinement factor is nearly the same (32%) in the active region. However, the transverse mode overlap with the highly doped cladding layers is considerably decreased to 20% as a result of the insertion of the undoped layers. The DH structures were grown onto (100) oriented p-type InAs substrates using a conventional sliding boat LPE technique [3]. The thickness of each epitaxial layer was measured using scanning electron microscopy on crosssections which were stained using the A:B etch. The epilayer compositions were determined using both energy-dispersive X-ray analysis (EDX) and double crystal x-ray diffraction (DXRD) measurements. Edge emitting ridge laser structures were fabricated from the epitaxial wafers using conventional photolithography. (a)

1.6

S1, 3-layer DH S3 simulation S3, 5-layer DH (thick) S2, 5-layer DH (thin)

1.2

(b)

Current (A)

0.075 0.050

P(mW)

0.100

0.025

S3, 5-layer (thick) S2, 5-layer (thin) S1, 3-layer DH

0.8 0.4

0.000 -0.2 0.0 0.2 0.4 -0.025 Voltage (V) -0.050

0.6 0.0

0

500

1000

1500

2000

2

J (A/cm )

Fig.1. (a) Current-voltage and (b) Light-current relationships for the three different samples at the temperature of 100 K, where “thin” represents 2u0.25 Pm inserted undoped epi-layers and “thick” represents 2u1 Pm inserted undoped epi-layers in the device. P is the output power from both facets.

Diode Lasers for Free Space Optical Communications 71 From the I-V curves in Fig. 1(a), the sample S3 (1.0 µm thick insertion layers) exhibits the least forward and reverse leakage current associated with improved confinement and reduced impurity inter-diffusion. The calculated IV curve is represented by the solid line and is in excellent agreement with the experimental data for S3. In Fig. 1(b), it is evident that introducing two thin layers (S2) reduces the threshold current density and increases the efficiency at the same operating temperature. But, the lowest threshold current density and the highest efficiency are obtained for the sample S3. (a)

1

0.1

1000

Kd

2

Jth (A/cm )

S1 3-layer DH S2 5-layer DH (thin) S3 5-layer DH (thick)

0.01 S1 3-layer DH S2 5-layer DH (thin) S3 5-layer DH (thick)

100

1E-3 40

80

120

Temperature (K)

160

200

40

80

120

160

200

Temperature (K)

Fig.2. (a) The dependence of threshold current density (Jth) on temperature (T) and (b) the dependence of external differential quantum efficiency on temperature for the samples S1, S2 and S3. As shown in Fig.2, the laser sample S3 has the lowest threshold current density (Jth=118 A/cm2 at 85 K), the highest differential quantum efficiency (Kd=76% at 85K), slowest efficiency degradation (~ 2.4 times from 85 to 155 K, compared to ~10 times from 75 to 150K in Ref.[4]) and almost constant characteristic temperature, T0 over a wide temperature range (T0=24 K from 85 to 185 K). The internal loss was obtained from measurements on lasers with different cavity lengths (at 100K). The loss in sample S1 is about 40~70 cm-1, which is much higher than that of sample S3, where Di=11.9 cm-1. Similar structures reported in the literature have a loss in the range of 30-130 cm-1 [5,6]. The laser emission wavelength was measured as 3.45 Pm at 170 K. The maximum temperature of laser operation in pulsed mode was found to be 210 ± 5 K. We are grateful to H.M. Government Communications Centre for supporting this project and also to EPSRC for providing a studentship for P. Carrington.

72 M. Yin et al.

References: 1. Jantsch W., in Dynamical Properties of IV-VI Compounds, Vol. 99 of Springer Tracts in Modern Physics, Springer, Berlin, 1983. 2. Bussman-Holder A., ‘Interplay of polarizability and ionicity in IV-VI compounds’, Phys. Rev. B, 40, 11639-45, 1989. 3. Ravel B., Cockayne E., Newville M.,. Rabe K.M, ’Combined EXAFS and firstprinciples theory study of Pb1-xGexTe’, Phys.Rev. B, 60, 14632-42, 1999. 4. Katayama S., Murase K,’Role of local displacement of Ge ions on structural instability in Pb1-xGexTe’, Solid State Commun., 36, 707-711, 1980. 5. Bose D.N., Pal S., ‘A new semiconducting ferroelectric Ga1-xGexTe’, Materials Research Bulletin, Vol. 29, 111-118, 1994. 6. Akimov B.A., Albul A.V., Ivanchik I.I., Ryabova L.I., Slyn’ko E.I., Khokhlov D.R., ‘Influence of doping with gallium on the properties of Pb1-xGexTe solid solutions’, Semiconductors, 27, 194-196, 1993.

Epitaxial Growth and Characterization of PbGeEuTe Layers V. Osinniy, P. Dziawa, V. Domukhovski, K. Dybko, W. Knoff, T. Radzynski, A. Lusakowski, K. Swiatek, E. Lusakowska, B. Taliashvili, A. Boratynski, and T. Story Institute of Physics, Polish Academy of Sciences Al. Lotników 32/46, 02-668 Warsaw, Poland

Abstract. The structural and electrical properties of Pb1-yGeyTe and Pb1-x-yGeyEuxTe (0”y”0.4 and x”0.05) monocrystalline layers grown by molecular beam epitaxy technique on BaF2 (111) substrate were studied by X-ray diffraction, Hall effect, and electrical conductivity measurements. Based on the temperature dependence of the lattice parameter the structural (ferroelectric) transition temperature was found in the temperature range before 100 to 250 K in layers with varying Ge and Eu content. Electrical measurements indicates that incorporation of Eu ions in the PbGeTe crystal matrix decreases the electrical conductivity in p-type PbGeEuTe layers by 1-2 orders of magnitude.

1. Introduction Pb1-yGeyTe semiconductor mixed crystals exhibit a structural (ferroelectric) transition from rock salt (high temperature, paraelectric phase) to rhombohedral (low temperature, ferroelectric phase) crystal structure [1-4]. The ferroelectric Curie temperature increases with increasing Ge content up to about TC=700 K in GeTe [2]. Although GeTe-based semiconductor alloys form unique non-oxidic ferroelectric materials with simple crystal lattice and high Curie temperature, the application of PbGeTe semiconductors in ferroelectric devices is strongly limited, mainly by their high electrical conductivity. The narrow energy gap of PbGeTe and GeTe is also not well suited for room temperature ferroelectric applications. On the base of these semiconductors various attempts to fabricate new materials with better ferroelectric parameters were undertaken [5, 6]. It is expected that the incorporation of Eu ions into Pb1-yGeyTe crystal matrix will offer an efficient way of controlling transition temperature Tc as well as increasing the electrical resistivity and the energy gap of this material. In this work we discuss the epitaxial growth and characterization of Pb1-x-yGeyEuxTe layers on BaF2 (111) substrate and study the influence of Eu ions on the structural transition temperature and electrical properties of the layers.

74 V. Osinniy et al.

5

10

-3

Pb0.83Ge0.16Eu0.01Te (p300 K=6E16 cm ) -3

4

Pb0.71Ge0.25Eu0.04Te (p300 K=1.2E17 cm )

10

6,368

-3

Pb0.70Ge0.29Eu0.01Te (p300 K=5E17 cm ) 3

10

Pb0.88Ge0.12Te

Pb0.71Ge0.28Eu0.01Te 6,366

-3

(p300 K=7E17 cm )

Rocksalt cubic

6,362

PbGeEuTe

a0 (A)

U (: cm)

6,364 2

10

1

10

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TC

Rhombohedral

6,358 0

10

6,356

PbGeTe -1

10

6,354 140

50

100

150

200

250

300

T (K)

Fig.1. Temperature dependence of electrical resistivity of PbGeEuTe layers.

160

180

200

220

240

260

T (K)

Fig.2. Temperature dependence of lattice parameter of PbGeEuTe/BaF2 layer.

2. Growth and characterization of layers The monocrystalline (111)-oriented layers of Pb1-x-yGeyEuxTe (xd0.05 and yd0.4) were grown on BaF2 (111) substrates by molecular beam epitaxy technique with employing effusion cells for PbTe, GeTe, Eu and Te. The content of Ge and Eu in PbGeEuTe layers was determined from the energy dispersive X-ray fluorescence analysis (EDXRF). The structural properties of the layers were studied by standard X-ray diffraction technique (XRD). No evidence for the presence of second phase inclusions was found in PbGeTe and PbGeEuTe layers with Ge content up to 40 at.%. The Vegard law composition dependence of the lattice parameter a0(y) was found in PbGeTe and PbGeEuTe layers with Ge content y<0.1. For larger Ge content (0.1
Epitaxial Growth and Characterization of PbGeEuTe Layers 75 with higher Eu content showed very large increase of resistivity as compared to PbGeTe (up to 2 orders of magnitude). To determine the critical temperature of the structural transition in PbGeEuTe layers we carried out the XRD measurements of the lattice parameter a0 over the temperature range from 100 to 300 K. At the transition temperature from the rock salt to rhombohedral lattice, a clear change of slope of the a0(T) curve has been experimentally found (Fig. 2). Our experimental findings indicate that the incorporation of Eu into PbGeTe matrix lowers the temperature of structural (ferroelectric) transition in comparison with reference data for bulk crystals [2]. 3. Conclusions The structural and electrical properties of monocrystalline Pb1-x-yGeyEuxTe layers grown by MBE technique on BaF2 (111) substrates were experimentally investigated. The incorporation of Eu in the p-PbGeTe layers strongly reduces their electrical conductivity, therefore improving the ferroelectric applicational parameters of PbGeEuTe. The structural (ferroelectric) transition temperatures for PbGeEuTe layers, estimated from the temperature dependence of the lattice parameter, are lower than those observed in bulk crystals. Acknowledgements This work was supported by the research project 0992/T02/2007/32 of the Ministry of Science and Higher Education (Poland) granted for the period 2007-2010.

References 1. Jantsch W., in Dynamical Properties of IV-VI Compounds, Vol. 99 of Springer Tracts in Modern Physics, Springer, Berlin, 1983. 2. Bussman-Holder A., ‘Interplay of polarizability and ionicity in IV-VI compounds’, Phys. Rev. B, 40, 11639-45, 1989. 3. Ravel B., Cockayne E., Newville M.,. Rabe K.M, ’Combined EXAFS and firstprinciples theory study of Pb1-xGexTe’, Phys.Rev. B, 60, 14632-42, 1999. 4. Katayama S., Murase K,’Role of local displacement of Ge ions on structural instability in Pb1-xGexTe’, Solid State Commun., 36, 707-711, 1980. 5. Bose D.N., Pal S., ‘A new semiconducting ferroelectric Ga1-xGexTe’, Materials Research Bulletin, Vol. 29, 111-118, 1994. 6. Akimov B.A., Albul A.V., Ivanchik I.I., Ryabova L.I., Slyn’ko E.I., Khokhlov D.R., ‘Influence of doping with gallium on the properties of Pb1-xGexTe solid solutions’, Semiconductors, 27, 194-196, 1993.

Monte Carlo Simulation of Electron Transport in PbTe V. Palankovski1, M. Wagner1, and W. Heiss2 1 2

Advanced Materials and Device Analysis Group, IuE, TU Vienna, Austria Inst. for Semiconductor and Solid-State Physics, University Linz, Austria

Abstract. A Monte Carlo (MC) technique is employed to investigate stationary electron transport in lead telluride (PbTe). Results for electron mobility as a function of lattice temperature, free carrier concentration, and electric field are compared with experimental data and the few available other Monte Carlo simulation results.

1 Introduction and Monte Carlo Simulation Setup Material models which incorporate the basic characteristics of the underlying physics in a given semiconductor material are the core of device modeling. While for Silicon and III-V materials such models are well established, models for IV-VI materials are topic of ongoing research. The lead chalcogenides material system is of interest for optoelectronic [1] and electrothermal [2] applications. The Monte Carlo method is a powerful technique to establish a consistent link between theory and experiments. Our model includes the two lowest valleys of the conduction band (L and W). Several stochastic mechanisms such as acoustic phonon, polar optical phonon, inter-valley phonon, ionized impurity, and optical deformation potential scattering, are considered and their impact is assessed. The particular advantage of the Monte Carlo method is that it provides a transport formulation on microscopic level, limited only by the extent to which the underlying physics of the system is included. Since the PbTe material system is yet not so well explored, several important input parameters are still not that accurately known, especially at higher temperatures. We assess, in an iterative approach, the influence of the input parameters and their interdependencies in order to get a set of parameters which gives agreement with experimental data available for different physical conditions (doping, temperature, field, etc.). Such a calibrated set of models and model parameters delivers valuable data for low-field mobility, velocity saturation, energy relaxation times, etc. These calibrated models can serve as a basis for the development of models for the simulation of PbTe-based electron devices. Device simulation results can in turn be validated against electrical device measurements.

78 V. Palinkovski et al. M. Wagner, and W.Heiss

Fig. 1: Low-field electron mobility as a function of carrier concentration in PbTe: Comparison of the MC simulation results and experimental data.

Fig. 2: Illustration of the corresponding scattering rates in our MC simulation of electron mobility in PbTe as a function of carrier concentration at 300 K.

The following calibrated set of model parameters for MC simulation was obtained in this work: energy separation between the lowest conduction bands ǻWL = 0.15 + 0.04 T0 eV (T0 stands for the reduced temperature T/300 K); longitudinal and transverse effective electron masses in the L and W valleys mL,l = 0.25 + 0.11 T0 í 0.011 T02, mL,t = 0.024 + 0.0112 T0 í 0.0013 T02, mW,l = mW,t = 0.5; non-parabolicity factor Į = 3; acoustic deformation potential (ADP) 10 eV; mass density ȡ = 8.24 g/cm3; longitudinal and transverse sound velocities vsl = 3297 í 170 T0 í 37 T02 m/s, vst = 2016 í 121 T0 í 45 T02 m/s; optical and static dielectric constants İ’ = 428 í 40 T0 and İs = 39 í 6 T0; optic phonon energy ƫȦLO = 13.6 meV; inter-valley phonon energy ƫȦij = 10.5 meV; inter-valley coupling constant 1.6ɯ108 eV/cm; optical deformation potential (ODP) coupling constant 109 eV/cm;

2 Simulation Results and Discussion Results for electron mobility as a function of lattice temperature and free carrier concentration were obtained and validated against available measured data [3, 4, 5]. Electron drift velocity versus the electric field was compared with the few available other Monte Carlo simulation results [6] and experimental data (see [6, 7] and the references therein). Fig. 1 shows the low-field electron mobility in n-PbTe as a function of free carrier concentration at 77K (open symbols í experiment, dashed lines í simulation) and 300K (filled symbols í experiment, solid lines í simulation). The impact of the non-parabolicity factor of the L-valley is demonstrated.

Monte Carlo Simulation of Electron Transport 79

Fig. 3: Low-field electron mobility vs. lattice temperature for different carrier concentrations.

Fig. 4: Drift velocity vs. electric field in PbTe: Comparison to other Monte Carlo simulations at 77 K.

Fig. 2 illustrates the interplay of the different scattering mechanisms for MC simulation at 300K and Į = 3. As can be also seen from Fig. 3, a very good agreement between measurement and simulation is achieved for wide range of carrier concentrations and lattice temperatures. Note, that using the parameter set from previous MC simulation from [6] the mobility is overestimated at 300 K and underestimated at 77 K. Including ODP scattering and reduced ADP to 15 eV, as proposed in [8] is a step in the right direction. In addition, in our simulation setup we had to secure temperature-dependent sound velocities and set ADP to 10 eV to further decrease the influence of ADP scattering at 77 K; we use temperature-dependent dielectric constants in the polar optical scattering model; we suggest higher ODP coupling coefficient than in [8]. A non-parabolicity factor of Į = 3 gives better results than the inverse bandgap value. Fig.4 gives the electron drift velocity versus the electric field. The low field data points are in good agreement, at higher fields we suggest either higher electron masses in the W-band or higher inter-valley scattering, etc., rather than higher ADP scattering in the L-band.

Acknowledgment: The authors acknowledge support from Austrian Science Funds (FWF), Project START Y247-N13. References [1] Rowe, D.M., CRC Handbook of Thermoelectrics, CRC Press, 1995. [2] Heiss, W. et al., Appl.Phys.Lett. 78, 862-864, 2001. [3] Allgaier, R.S. and Scanlon, W.W., Phys.Rev. 111, 1029-1037, 1958. [4] Ravich, Y.I. et al., Phys.Status Solidi (b) 43, 453-469, 1971. [5] Ueta, A.Y. et al., Thin Solid Films 306, 320-325, 1997. [6] Krotkus, A. et al., Solid State Electronics 26, 605-609, 1983. [7] Chattopadhyay, D. and Purkait, N.N. J.Appl.Phys. 54, 6439-6442, 1983. [8] Zayachuk D.M., Semiconductors, vol. 31, 173-176, 1997.

L-Band-Related Interband Transition in InSb/GaSb Self-Assembled Quantum Dots S. I. Rybchenko, R. Gupta, I. E. Itskevich, and S. K. Haywood Department of Engineering, University of Hull, Hull, HU6 7RX, UK

Abstract. Effect of lattice-mismatch-induced strain on ī-, X- and L-conduction-band edges in III-V self-assembled quantum dots has been calculated. The misfit strain is shown to strongly affect the band edges, leading to a possibility of ī-L and ī-X crossover. The ī-L crossover is predicted for realistic self-assembled InSb/GaSb (001) dots, in which the lowest interband transition is from the L-valley state. Available experimental PL data were found to be in good agreement with the crossover phenomenon.

1 Introduction Self-assembled quantum dot (SAQD) structures are of great interest both for fundamental research and device applications. Their essential feature is large strain due to lattice mismatch, which is inherent to the Stranski-Krastanov growth method. So far, the effect of strain on electronic structure has been mostly studied for the lowest conduction band and the top valence band edges, which are the ground states in unstrained materials [1]. However, the strain-induced shift/splitting may be comparable or larger than the energy gap between conduction bands of different symmetry, and this has not been analysed specifically. In this case, the strain can result in a crossover of ī-, Lor X- valleys, creating a ground electron level of symmetry different to the unstrained bulk material. Such a crossover for the ground electron state would dramatically affect the optical properties of the SAQD system. Here, we present analysis of the effect of strain on ī, X and L conduction bands in compressively-strained SAQDs, and discuss a possibility of a crossover. For InSb/GaSb (001) SAQDs, comparison with recent photoluminescence (PL) data provides experimental evidence for the ī-L crossover.

2 Effect of Strain on Conduction Band Edges Hydrostatic and shear strain components affect the conduction band states in a different way. For III-V compounds, the ī-valley hydrostatic deformation

82 S.I. Rybchenko et al. potential is typically 10 and 3 times larger than those for X- and L-bands [2, 3] respectively; the ī-L/X gaps are typically ~ 0.2-0.3 eV. Comparison with typical hydrostatic deformation potential and misfit strain values (2-7%) shows that the hydrostatic strain alone can cause a ī-X crossover at a moderate strain, but the ī-L crossover would require extreme misfit values. This is consistent with experimental observation of the ī-X crossover in bulk III-V materials under high pressure: for example, in bulk GaAs the crossover is observed [4] at ~40 kbar, which corresponds to hydrostatic strain of ~ 4 %. Meanwhile, shear deformation potentials for L- and X-bands are much larger, typically 1.5-2 times than the hydrostatic potentials for the ī-band. For SAQDs, shear strain is comparable to the lattice misfit value. Therefore, the effect of shear strain on the band shifts should be dominant, and a crossover can be observed at a misfit strain of only a few percent, which is a typical range for real SAQDs.

3 Application to InSb/GaSb Quantum Dots We consider a spherical InSb quantum dot in a GaSb matrix. Numerical modelling was performed within the continuum elasticity approximation and standard deformation potential theory [for details see Ref. 5]. Expressions for the strain-induced shift of L/X-bands were taken from Ref. [3], and the material parameters were taken from Refs. [2] and [6]. Figure 1 presents the band profile for the ī-band and lowest L-band. One can see that the strain-induced splitting of the L-band causes a local downshift of the L-band edge much below the ī-valley. This creates L-‘pockets’ in the matrix at the hetero-interface, providing electron ground states of symmetry different to the bulk material. The energy gap between the valence band and the L-conduction band also is considerably smaller than the ī-point band gap. PL from compressively strained InSb/GaSb SADQs has been reported in the spectral range of 0.6-0.85 eV [7]. It was interpreted as ī-ī transitions from the SAQDs and the wetting layer, as well as emission from shallow intrinsic-defect states in bulk GaSb. More recently, additional peaks have [001]

(a)

(b) [110]

Energy (eV)

Fig. 1. Conduction band-edge profiles for a spherical dot: (a) L-band; (b) ī-band.

L-Band Related Interchange Transition in InSb/GaSb Self-Assembled 83 been observed between 0.25 and 0.55 eV [8] that cannot be interpreted as ī-ī transitions. Our estimates of quantisation energies for holes in the dot and electrons in the L-pockets lead to transition energies of 0.35 eV and 0.5 eV for electron ground and excited levels, respectively. These values are in good agreement with the peak energies observed in the experiment.

4 Reverse L-ī transition in InSb/Ga(1-x)AlxSb SAQDs To provide a basis for further experimental verification of the ī-L crossover in the InSb/GaSb SAQDs, we analysed the possibility of the reverse L-ī crossover which occurs with Al incorporation in the GaSb host matrix. Such alloying is particularly attractive because Al incorporation has minimal effect on the strain and hence on the conditions for dot formation. This is due to the similarity between both the lattice parameters and the elastic constants for GaSb and AlSb. Al alloying produces an uplift of both the īvalley and the whole L-pocket in the matrix, which is nearly linear with Al concentration, x. This creates a condition for electron localization within the ī-potential in the dot. The “L-ī crossover” for the ground electron state was estimated to occur at x § 0.65. The shift of the hole level was found to be small (d 50 meV). The optical transition energy at the “crossover” was estimated as ~1.07 eV. The PL signal is expected to be much stronger than for the InSb/GaSb SAQDs due to the ī-ī nature of the transition. The work is supported by the EU Commission, grant No. FP6 – 017383 DOMINO.

References 1 Theory of Semiconductor Quantum Dots: Band Structure, Optical Properties and Applications. Ed. A. Andreev, World Scientific Publishing, 2006.

2 Landolt-Börnstein Series Vol. 22, Semiconductors, Ed. O. Madelung, M. Schulz, Springer-Verlag, Berlin Heidelberg, 1987.

3 We refer to the hydrostatic (Ȅd +1/3Ȅu) and shear potentials (Ȅu) in notation of W. C. Herring and E. Vogt. Phys. Rev. 101, 944 (1956).

4 A. R. Goni, K. Syassen, M. Cardona, Phys. Rev. B 39, 12921 (1989). 5 S. I. Rybchenko, G. Yeap, R. Gupta, I. E. Itskevich, and S. K. Haywood, J. Appl. Phys. 102, 13706 (2007).

6 R. A. Noack, Phys. Stat. Sol. B 90, 615 (1978). 7 E. Alphandery et al., Appl. Phys. Lett. 74, 2041 (1999); Phys. Rev. B 65, 115322 (2002); A. F. Tsatsul’nikov et al., J. Electron Mater. 27, 414 (1998); Semicond. 33, 886 (1999). 8 V. Tasco, N. Deguffroy, A. N. Baranov, E. Tournié, B. Satpati, A. Trampert, M. S. Dunaevskii and A. Titkov, Appl. Phys. Lett. 89, 263118 (2006).

Antimony Distribution in the InSb/InAs QD Heterostructures A.N. Semenov1, O.G. Lyublinskaya1, B.Ya. Meltser1, V.A. Solov'ev1, L.V. Delendik2, and S.V. Ivanov1 1 2

Ioffe Physico-Technical Institute RAS Saint-Petersburg State Electro-Technical University "LETI"

Abstract. The influence of surface segregation of Sb atoms on Sb redistribution during the molecular beam epitaxy of InSb/InAs nanostructure was investigated. The segregation of Sb is responsible for the wetting layer in the InSb QD structures produced without intentional deposition of InSb, when the Stranski-Krastanow growth mode is impossible.

1 Introduction Due to the large (~ 7%) lattice mismatch between InSb and InAs, the selfassembled compressively-strained InSb-enriched QDs have been shown to form with a mean lateral size of InSb-enriched QDs of ~ 2.5 nm and a sheet density as high as ~ 1012 cm–2 [1]. These InSb/InAs QD structures demonstrate bright photoluminescence (PL) in the 3.9—4.4 µm spectral range at 300K [2]. Recently we have obtained low temperature lasing from InSb/InAs QD structures under the injection pumping at 3.08 µm [3]. Due to poor electronic confinement around InSb QDs this wavelength more probably corresponds to the recombination in the surrounding alloyed InAsSb wetting layer. Obviously, in case of the sub-monolayer InSb deposition on InAs there is no Strancki-Krastanov growth mode that implied formation of the wetting layer. Therefore the growth mechanism of the InAsSb wetting layer during growing the InSb/InAsSb QD structures is a crucial issue. Another problem is determination of a nominal thickness of InSb layers in the InSb/InAs nanostructures. The value of InSb thickness derived from x-ray diffraction (XRD) measurements by modeling experimental rocking curves of the multilayer InSb/InAs structures reflects an average amount of In-Sb bonds per period, which were assumed in our previous paper [2] to be concentrated mostly in the InSb QD sheet. It has been shown recently [4] that the real thickness of InSb-enriched islands is larger than 1 monolayer (ML) due to the segregation of Sb atoms into the InAs layer, that should result in a decrease of the maximum Sb content in the QD.

86 A.N. Semenov et al. In this paper we determine quantitatively Sb distribution in InSb/InAsSb heterostructures in a wide growth temperature range (350–510qC), taking into account the segregation phenomenon.

2 Results and discussion The samples were grown by molecular beam epitaxy (MBE) on InAs(001) substrates using a RIBER 32P setup equipped by conventional solid source effusion cells for group III elements and antimony, whereas As4 flux was supplied from a VAC-500 valved cracking cell. The growth details and structure design were published elsewhere [1, 4]. Observation of RHEED specular spot intensity during the growth of InSb/InAs nanostructures allow to determine the Sb segregation length — Ȧ [4]. Following to K. Muraki [5] the segregation ratio R can be deduced from the segregation length of Sb as follows

R

§ d· exp¨  ¸ , © Ȧ¹

(1)

where d is InAs monolayer thickness. In the frame of this model Sb content (y) in InAs1–ySby layers can be expressed as

yn

1  R R n 1 ,

(2) is antimony

where n is the number of the overgrown InAs monolayer, y0 concentration in the InSb QD layer (y0 equals unity). In the case of a sub-monolayer InSb nominal thickness, the antimony concentration in the InSb-rich islands decreases due to the incorporation of Sb atoms into the overgrown InAs layer. Obviously, the segregated Sb atoms will be replaced by As atoms, therefore the InSb-rich island will present an InAsSb alloy. The distribution of Sb in the InSb/InAs nanostructure is plotted in Fig. 1.The average antimony concentration in the nominally pure InAs layer is approximately the same (0.7%) for samples grown at different growth temperatures, but the Sb distribution depends strongly on growth temperature. The solid line in Fig. 1 corresponds to the Sb distribution taking into account the segregation phenomenon (at 350qC), while the dotted line corresponds to the assumption that all Sb atoms are inside the 1-ML-thick InSb QDs. Note that the segregation model does not take into account influence of elastic strain on the incorporation of segregated Sb atoms into the InAs layer. In our opinion, both strain and presence of an immiscibility gap in InAsSb alloy could lead to the non-homogeneous Sb incorporation in InAs and forming InSb-rich islands.

Antinomy Distribution in the InSb/InAs QD Heterostructures 87

Fig. 1. Sb distribution in InSb/InAs nanostructures for different growth temperatures: a — Tsub = 350ºC; b — Tsub = 420ºC; c — Tsub = 500ºC; d — Sb distribution in the assumption that all Sb atoms are inside the 1-ML-thick InSb QDs.

The work was partially supported by RFBR and Physical Science Department of RAS.

References 1. S.V. Ivanov, A.N. Semenov, V.A. Solov’ev, et al: 'Molecular beam epitaxy of type II InSb/InAs nanostructures with InSb sub-monolayers', J. Crystal Growth 278, 72–77, 2005. 2. V.A. Solov’ev, O.G. Lyublinskaya, B.Ya. Meltser, et al: 'Room-temperature 3.4– 3.9 Pm photoluminescence from InSb submonolayers grown by by molecular beam epitaxy in an InAs matrix', Appl. Phys. Lett., 86, 011109–011112, 2005. 3. V.A. Solov’ev, I.V. Sedova, O.G. Lyublinskaya, et al: 'Midinfrared injectionpumped laser based on a III–V/II–VI hybrid heterostructure with dubmonolayer InSb insets', Tech. Phys. Lett. 31, 235–237, 2005. 4. A.N. Semenov, O.G. Lyublinskaya, V.A. Solov’ev, et al: 'Surface segregation of Sb atoms during molecular-beam epitaxy of InSb quantum dots in an InAs(Sb) matrix', J. of Crystal Growth 301/302, 58–61, 2007 5. K. Muraki, S. Fukatsu, Y. Shiraki, R. Ito: 'Surface segregation of ln atoms during molecular beam epitaxy and its influence on the energy levels in InGaAs/GaAs quantum well', Appl. Phys. Lett., 61, 557–559, 1992.

Transport Properties of InAs0.1Sb 0.9 Thin Films Sandwiched by Al0.1In0.9Sb Layers Grown on GaAs(100) Substrates by Molecular Beam Epitaxy Ichiro Shibasaki1, Hirotaka Geka2 and Atsusi Okamoto2 1

Asahikasei Corporation, 2-1,Samejima, Fuji-city, Shizuoka, 416-8501, Japan, Ashikasei EMD Corporation, 2-1,Samejima, Fuji-city, Shizuoka, 416-8501, Japan,

2

Abstract. Electron mobilities of InSb, InSb/AlInSb and InAsSb/AlInSb grown on GaAs(100) were compared as a function of layer thickness and temperature. InAs0.1Sb0.9 thin active layers sandwiched by Al0.1In0.9Sb layers showed the smallest thickness dependence and very large electron mobility at less than 500nm thickness. Basic transport properties and Sn doping effects of the InAs0.1Sb0.9 were studied.

1. Introduction InSb single-crystal thin films having very large electron mobility may be good for fabricating Hall elements with high sensitivity. However, because of the large lattice mismatch of 14% between InSb and GaAs substrates, it is difficult to fabricate InSb thin films of less than 500-nm thickness on GaAs substrates with sufficiently high electron mobility, as shown in Fig, 1. Moreover, a thin InSb active layer is seriously damaged by PCVD deposition of a Si3N4 or SiO2 thin layer on InSb surface in the device fabrication process. This may result in a mobility reduction of 50% or more in an InSb active layer with a thickness of less than 500 nm [1, 2]. In this work, since InSb does not have a good lattice matched insulating layer, we studied the growth of InAsxSb1-x (0<x<1) thin films instead of InSb as a new active layer good for Hall elements. In our previous work, to fabricate high-electron-mobility InSb thin films, we sandwiched InSb thin film between Al0.1In0.9Sb layers with a sufficiently high sheet resistance, where the lattice mismatch between the InSb and Al0.1In0.9Sb is 0.5% [3]. As shown in Fig. 1, the electron mobility of the InSb thin films was much improved; however, they still exhibited large thickness dependence. In the present work, to fabricate high-electron-mobility thin films with high sheet resistance and temperature stability, we grew the layered structure of GaAs (6 nm)/ Al0.1In0.9Sb (50 nm)/ InAsxSb 1-x / Al0.1In0.9Sb (700 nm) on GaAs(100) substrates, as shown in Fig.2. The InAsxSb 1-x layer was capped with thin Al0.1In0.9Sb and thin GaAs layers for protection from damage in PCVD process. Hereafter, for simplicity, Al0.1In0.9Sb is denoted as AlInSb and InAs0.1Sb 0.9 is denoted as InAsSb.

90 I. Shibasaki et al.

InSb on GaAs

InSb sandwiched

InAsSb sandwiched

GaAs 6 nm Al0.1In0.9Sb 50 nm InAs0.1Sb 0.9 15500 nm Al0.1In0.9Sb 700 nm GaAs (100) substrate

2

Electron mobility(cm /Vs)

㻝㻜㻜㻜㻜㻜

㻝㻜㻜㻜㻜

㻝㻜㻜㻜 㻜㻚㻜㻝

㻜㻚㻝

㻝

㻝㻜

Thickness(µm)

Fig. 1: Comparison of electron mobility for InSb and InSb and InAs0.1Sb0.9 thin films sandwiched by Al0.1In0.9Sb layers with a GaAs top layer grown on GaAs(100) substrates.

Fig. 2: Cross section of InAsSb thin film sandwiched by Al0.1In0.9Sb layers with a GaAs top layer grown on GaAs (100) substrates by MBE

2. Growth of InAsSb single crystal thin films The structure shown in Fig. 2 was grown by molecular beam epitaxy (MBE). The growth temperature, or substrate temperature, was 713K for the GaAs buffer layer, Al0.1In0.9Sb (700 nm) insulating layer, InAsSb active layer and Al0.1In0.9Sb (50 nm) and GaAs(6 nm) cap layers. The growth rate was 1.0 µm/hr for every layer. Beam intensity from all effusion cells was kept constant during the MBE growth. First, InAsxSb1-x thin films with a fixed thickness of 150 nm, as shown in Fig. 2, were grown for various x values on GaAs substrates. The maximum electron mobility was observed at x=0.1, corresponding to the lattice-match composition with the buffer layer of Al0.1In0.9Sb. Next, the layered structure of GaAs (6 nm)/ Al0.1In0.9Sb (50 nm)/ InAs0.1Sb 0.9 (15-500 nm)/ Al0.1In0.9Sb (700 nm) was grown by MBE and transport properties were studied. In this structure, the thin GaAs insulating top layer formed as the protection layer has no essential electrical effect.

3. Experimental results and discussion As shown in Fig.1, the un-doped InAs0.1Sb0.9 single crystal thin films with thickness from 15 to 500 nm sandwiched by Al0.1In0.9Sb showed very large electron mobility. Also, the smallest thickness dependence was achieved for InAs0.1Sb0.9. This may be the lattice-matching effect between InAs0.1Sb 0.9 and Al0.1In0.9Sb. On the other hand, the InSb directly grown on GaAs substrates

Transport Properties of InAs0.1Sb0.9 Thin Films 91

35000

㻝㻡㼚㼙 㻞㻜㼚㼙 㻟㻜㼚㼙 㻡㻜㼚㼙 㻣㻜㼚㼙 㻝㻜㻜㼚㼙 㻞㻜㻜㼚㼙 㻟㻜㻜㼚㼙 㻡㻜㻜㼚㼙

30000 25000 20000 15000 10000 5000 0 0

200

400

600

Temperature (K)

Fig. 3: Temperature dependence of electron mobility of InAs0.1Sb0.9 thin films of various thickness sandwiched by Al0.1In0.9Sb layers.

2

40000

Electron mobility (cm /Vs)

2

Electron mobility (cm /Vs)

and that grown on AlInSb have large thickness dependence, as shown in Fig. 1. In a previous paper, we proposed a model of transport phenomena in InSb single crystal thin films grown by MBE [1, 2]. The model described the variation of electron mobility, resistivity, and electron density in the thickness direction of the thin films. This variation in the thickness direction was roughly approximated as three layers: a low-electron-mobility layer near the hetero-interface with the substrate surface, a middle layer of thin film with high electron mobility, and a surface layer with low electron mobility. These low-electron-mobility layers at the hetero-interface and the surface layer are caused by the effect of lattice mismatch with the substrate and air at the surface. Therefore, as shown in Fig.1, the InSb thin film sandwiched by Al0.1In0.9Sb layers having smaller lattice mismatch of 0.5% with InSb showed high electron mobility and small thickness dependence compared to the InSb thin films grown directly on GaAs substrates [3]. This is the effect of the smaller lattice mismatch. On the other hand, the InAs0.1Sb 0.9 active layer shows the highest electron mobility and the smallest thickness dependence. The thickness of both the low-electron-mobility layer at the hetero-interface and the one near the surface of the InAs0.1Sb 0.9 layer is reduced because of the exact lattice matching between InAs0.1Sb 0.9 and Al0.1In0.9Sb. For the reduction of the temperature dependence of electron mobility and sheet resistance, Sn doping of InAs0.1Sb 0.9 thin films was tried. As shown in Fig. 4, Sn doping of InAs0.1Sb0.9 reduces the temperature dependence of the electron mobility. A similar reduction effect was also observed for the sheet resistance of InAs0.1Sb0.9. 40000 35000 30000 25000 20000 15000 10000 5000 0

un-dope

Sn doped

0

100

200

300

400

500

600

Temperature (K)

Fig. 4: Temperature dependence of Sn-doped and un-doped 100-nmthin films thick-InAs0.1Sb0.9 sandwiched by Al0.1In0.9Sb layers.

92 I. Shibasaki et al.

4. Conclusion By using InAs0.1Sb0.9 active layers sandwiched by Al0.1In0.9Sb layers, we obtained InAs0.1Sb 0.9 thin films with an electron mobility and sheet resistance that are high enough for practical high-sensitivity Hall elements and magnetoresistance devices. Basic transport properties of the InAs0.1Sb0.9 were studied. The InAsSb showed the smallest thickness dependence, and it was found that Sn doping is effective for reducing of the temperature dependence of the electron mobility and sheet resistance.

References [1] A. Okamoto and I. Shibasaki, Transport properties of Sn-doped InSb thin films and applications to Hall element, J. of Crystal Growth, 251, 2003, p.560 [2] A. Okamoto, H. Geka, I. Shibasaki, and K. Yoshida, Transport properties of InSb and InAs thin films on GaAs substrates, J. of Crystal Growth, 278, 2005, p.604 [3] H. Gaka, A. Okamoto, S. Yamada, H. Goto, K. Yoshida, and I. Shibasaki, Properties of InSb single-crystal thin films sandwiched by Al0.1In0.9Sb layers with 0.5% lattice mismatch grown on GaAs, J. of Crystal Growth, 301-302, 2007, p. 152

Modelling of Photon Absorption and Carrier Dynamics in HgCdTe under mid-IR Laser Irradiation A. S. Villanger1, T. Brudevoll1 and K. Stenersen1 1

FFI (Norwegian Defence Research Establishment), P.O. Box 25, NO-2027 Kjeller, Norway

Abstract. We present results from a numerical study on carrier dynamics, heating, and melting damage threshold in a 10 µm thick layer of Hg0.72Cd0.28Te induced by 1 µs long laser pulses at photon energies close to the band gap. At the shortest wavelength of 3.8 µm the simulations indicate that surface melting will occur at fluence levels in the range of 2-3 J/cm2, while fluences of more than 10 J/cm2 will be required for melting at wavelengths beyond 5 µm.

1 Introduction Interaction of laser radiation with materials involves such diverse fields as laser spectroscopy, laser processing of materials, laser annealing, and studies of damage thresholds in optical materials. Early modelling of semiconductor lattice heating by lasers was carried out by Meyer et al. [1]. Materials considered were Ge, Si, InSb, and GaAs. This paper describes simulations of heating in bulk HgCdTe irradiated by mid-IR µs laser pulses at fluence levels up to a few J/cm2. Heating of the material is characterized by an interplay between a number of highly nonlinear physical processes. Theory and modelling include one- and two-photon absorption, inter-valence band absorption, absorption by free carriers, generation of hot carriers, carrier diffusion and recombination, refractory changes, band gap renormalization, and a first principles representation of the HgCdTe energy band structure [2]. Assuming cylindrical symmetry, the equations for carrier density, lattice temperature, carrier temperature, and radiation intensity are solved simultaneously in a 2-D geometry with the finite element method (FEM). A commercial FEM package (COMSOL£) was used for solving the equations.

2 Theory and Model Description In Hg1-xCdxTe materials with x < 0.5 the direct band gap increases with temperature. For a given laser wavelength this leads to termination of regular

94 A. S. Villanger, T. Brudevoll and K. Stenersen one-photon valence to conduction band absorption when the lattice is heated above a certain temperature. The strong one-photon absorption leads to rapid heating of the material up to this temperature, and further heating driven by the other weaker absorption processes is much slower. We have used the expressions for one-photon absorption given in [3], [4], which are based on a very extensive set of experimental data. An important feature of the model is the inclusion of carriers with an excess temperature relative to the lattice. Excess heating of the carriers is produced both by absorption and by subsequent recombination, especially Auger recombination. The high carrier temperatures lead to a strong dispersion of carriers both in the conduction and valence bands, and have a significant influence on the strengths of the interband absorption processes.

3 Results Simulations have been performed on a geometry consisting of a 10 µm thick platelet of Hg0.72Cd0.28Te in ideal thermal contact with a highly thermally conductive underlying substrate which is kept at a temperature of 77 K. Fig. 1 shows examples of the temporal evolution of; a) lattice temperature, b) carrier excess temperature, c) the one-photon absorption (OPA), and d) inter-valence absorption (IVA) coefficients at the surface, for four different laser wavelengths; 3.8, 4.2, 4.8, and 5.2 µm. Termination of regular OPA at high temperatures is evident, and further heating of the material is driven by much weaker IVA, free-carrier absorption, and remaining OPA in the Urbach tail (below band gap absorption). Twophoton absorption is very weak in this case, but will be more important at higher intensities typically produced by Q-switched lasers with pulse lengths in the ns regime. As can be seen from the figure, carrier temperatures are very high for a short period at the beginning of the pulse. This is due to the large OPA coefficient combined with non-radiative Auger recombination. At such high carrier temperatures there may be some migration of carriers to higher lying conduction band valleys, which has not yet been included in the model. Our band structure calculations show an energy separation of 1.2 eV between the central conduction band valley and the higher lying L valleys. This large energy barrier allows a high electron temperature in the central valley before migration of electrons to higher conduction band valleys takes place, so this effect should not be very important for the present case. Carrier densities (not shown) initially reach 6u1017-1.5˜1018 cm-3, decreasing to 3-8.5u1017 cm-3 towards the end of the pulse. The melting temperature of HgCdTe is 990 K, which indicates that a fluence of 2-3 J/cm2 is required to melt the surface of the material for the shortest laser wavelength, increasing to over 10 J/cm2 for the longest wavelengths.

Modelling of Photo Absorption and Carrier Dynamics in HgCdTe 95 1000

Lattice temperature (K)

Carrier excess temperature (K) 3.8 Pm 4.2 Pm 4.8 Pm 1000 5.2 Pm

10000

800 600 400

3.8 Pm 4.2 Pm 4.8 Pm 5.2 Pm 0,8 1,0

200 0 0,0

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a)

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b)

10 0,0

OPA coefficient (cm )

250

3.8 Pm 4.2 Pm 4.8 Pm 5.2 Pm

1000

0,4 0,6 Time (Ps)

0,8

1,0

-1

-1

10000

0,2

IVA coefficient (cm ) 3.8 Pm 4.2 Pm 4.8 Pm 5.2 Pm

200 150 100

100

50

c)

10 0,0

0,2

0,4 0,6 Time (Ps)

0,8

1,0

d)

0 0,0

0,2

0,4 0,6 Time (Ps)

0,8

1,0

Fig. 1. Simulated lattice temperature a), carrier excess temperature b), one-photon c) and inter-valence absorption coefficients d) (OPA, IVA) at the surface, for radiation intensity 2 MW/cm2 and laser wavelengths of 3.8, 4.2, 4.8, and 5.2 µm.

4 Conclusions The described model permits detailed studies of the relative importance of the different highly nonlinear processes occurring in HgCdTe under laser irradiation, and can be used for analysis of the heating process in the material in a variety of applications. The model can also be extended to studies of other semiconductor materials.

References 1. Meyer, J. R., Kruer, M. R., Bartoli, F. J., 'Optical heating in semiconductors: Laser damage in Ge, Si, InSb, and GaAs', J. App. Phys., 51 (10), 5513-5522, 1980 2. Blaha, P., Schwarz, K., Madsen, G. K. H., Kvasnicka, D., Luitz, J.: Wien2k User’s Guide, Vienna University of Technology, Vienna, 2001 3. Li, B., Gui, Y., Ye, H., Chu, J., Krishnamurthy, S.: 'Logarithmic approximation for the energy band in nonparabolic semiconductors', J. App. Phys., 83 (12), 76687671, 1998 4. Li, B., Chu, J. H., Chang, Y., Gui, Y. S., Tang, D. Y.: 'Optical absorption above the energy band gap in Hg 1-x CdxTe', Infrared Phys. Technol., 37, 525-531, 1996

Monte Carlo Study of Transport Properties of InN S. Vitanov and V. Palankovski Advanced Material and Device Analysis Group, IuE , TU Vienna

Abstract. We use a Monte Carlo (MC) approach to investigate the electron transport in Indium Nitride (InN). Simulations with two different setups (one with a bandgap of 1.89 eV and one with bandgap of 0.69 eV) and accounting for all relevant scattering mechanisms are conducted. Results for electron mobility as a function of free carrier concentration and electric field are compared to previous studies and discussed.

1 Introduction and Monte Carlo Setup In recent years InN has attracted much attention due to the considerable advancement in the growth of high quality crystals. Furthermore, several new works on the material properties proposed a bandgap between 0.65 and 0.9 eV [1, 2, 3], instead of about 2.0 eV [4] as believed before. In this work we use a Monte Carlo approach to investigate the electron transport, using the two band structures [5, 6] (see Table 1). Our calculations include the three lowest valleys of the conduction band (depending on the chosen band structure) and account for non-parabolicity of the main valley. Several stochastic mechanisms such as acoustic phonon, polar optical phonon, inter-valley phonon, coulomb, and piezoelectric scattering are considered and their impact is assessed. The parameters for the acoustic deformation potential (ADP), inter-valley scattering (ƫȦiv), polar-optical phonon scattering (ƫȦLO), dielectric constants and mass density are adopted from [7, 8]. An accurate piezoelectric scattering model, which accounts for nonparabolicity and wurtzite material structure is also employed [9]. This is especially important since nitrides exhibit the largest piezoelectric constants among the III-V semiconductors. Considering the wurtzite structure we adopt the corresponding elastic constants [10] and piezo coefficients [11].. For the proper modeling of piezoelectric effects a good estimation for the elastic constants (c11, c12, and c44), the resulting longitudinal and transverse elastic constants (cL and cT) and sound velocities (vsl and vst) is required. Those are summarized in Table 2. Table 3 summarizes the theoretical values of the piezo-coefficients e15, e31, and e33 available in the literature. In cases, where e15 is not available, e15=e31 is assumed. From them we calculate the corresponding e2L and e2T and the coupling coefficient KAV=0.24.

98 S. Vitanoc and V. Palankovski Table 1:Summary of material parameters of wurtzite InN for Monte Carlo simulation.

Table 2: Summary of elastic constants of InN and the resulting longitudinal and transverse elastic constants and sound velocities.

Table 3: Summary of piezo coefficients of inN for Monte Carlo simulation of piezo scattering.

Monte Carlo Study of Transport Properties of InN 99

Fig. 1: Low-field electron mobility as a function of carrier concentration in InN: Comparison of the MC simulation results and experimental data.

Fig. 2: Low-field electron mobility as a function of carrier concentration in InN: Comparison of the MC simulation results with different setups.

2 Simulation Results and Discussion Simulations with two different setups were conducted: one with a bandgap of 1.89 eV (effective mass 0.11m0 in the G1 valley [5]), and one with bandgap of 0.69 eV (effective mass of 0.04m0 [6]), as summarized in Table 1. Results for electron mobility as a function of lattice temperature, free carrier concentration, and electric field were obtained. For example, Fig. 1 shows the low-field electron mobility in hexagonal InN as a function of free carrier concentration. Results from other groups and various experiments are also included. Assessing the classical band structure model (Eg=1.89 eV), we achieve electron mobility reaching 4500 cm2/Vs, which is in a good agreement with the theoretical results of other groups using the same setup [7]. Considering the newly calculated band structure model (Eg=0.69 eV), maximum mobility of about 10000 cm2/Vs is achieved. The corresponding scattering rates are illustrated in Fig. 2. The increased mobility can be explained with the lower effective electron mass. Polyakov, et al. [8] calculated a theoretical limit as high as 14000 cm2/Vs, however their simulation does not account for piezoelectric scattering, which is the dominant mobility limitation factor at low concentrations (see Fig. 2). Fig. 3 shows the electron drift velocity versus the electric field at 1017 cm-3 carrier concentration. Our MC simulation results differ compared to simulation data from other groups either due to piezoscattering at lower fields or, at high fields, due to the choice of parameters for epsilon, ƫȦLO, and vs. Fig. 4 illustrates the interplay between different scatterng mechanisms with the acoustic and polar optical scattering being dominant at high electric fields.

100 S. Vitanoc and V. Palankovski

Fig. 3: Drift velocity versus electric field in wurtztite InN:Comparison of MC simulation results.

Fig. 4: Drift velocity versus electric field in wurztite InN: MC simulation results with different parameter setups.

Acknowledgment The authors acknowledge support from Austrian Science Fund (FWF), Project START Y247-N13.

References [1] Wu et al. Phys. Rev. B 66, 201403 (2002). [2] Davydov et al. Phys. Stat. Sol. B 230, R4-R6 (2002). [3] Matsuoka et al. Appl. Phys. Lett. 81, 1246-1248 (2002). [4] Tansley et al. J. Appl. Phys. 59, 3241-3244 (1986). [5] Lambrecht et al. 11 EMIS Datareview Series, 151 (1994). [6] Fritsch et al. Phys. Rev. B 69, 165204 (2004). [7] Chin et al. J. Appl. Phys 75, 7365-7372 (1994). [8] Polyakov et al. J. Appl. Phys. 99, 113705 (2006). [9] Vitanov et al., Lecture Notes in Comp. Science, 4310, Springer, 197-204 (2007). [10] Wright et al. J. Appl. Phys 82, 2833-2839 (1997). [11] Bernardini et al. Phys. Rev. B 56, 10024-10027 (1997). [12] Zoroddu et al. Phys. Rev. B 64, 045208 (2001). [13] Bellotti et al. J. Appl. Phys. 85, 916-923 (1999). [14] Polyakov et al. Appl. Phys. Lett. 88, 032101 (2006). [15] O’Leary et al. J. Appl. Phys 83, 826-829 (1998). [16] Sheleg et al. Neorg. Matt 15, 1598 (1979). [17] Kim et al. Phys. rev. B 53, 16310-16326 (1996). [18] Wang et al. Phys. Stat. Sol. B 240, 45-54 (2003).

New Type of Combined Resonance in p-PbTe H. Yokoi1, S. Takeyama2, N. Miura2 and G. Bauer3 1

Dept. of Materials Sci. and Eng., Kumamoto Univ., Kumamoto, Japan Inst. for Solid State Phys., Univ. of Tokyo, Chiba, Japan 3 Semicond. Phys. Div., Johannes Kepler Univ., Linz, Austria 2

Abstract. A new type of combined resonance, named ‘merged resonance’ is observed for p-PbTe at high magnetic fields in the Faraday configuration (B//¢111²). The resonance becomes allowed as a result of spin merging in heavy mass Landau levels 1D and 1E. Six band k·p models are employed to investigate the spin merging.

1 Introduction Combined resonance, or spin-flip cyclotron resonance was first reported for nInSb in 1967 by McCombe et al.1 This transition is attributed to intraband spin-orbit interaction terms in Hamiltonian. As these off-diagonal terms are much smaller than the diagonal terms, the oscillator strength of the combined resonance transitions is some orders of magnitude weaker than that of cyclotron resonance transitions and the resonance has been observed only in the Voigt configuration. We have reported a new type of combined resonance for p-PbTe in ultra-high magnetic field region, which is observed in the Faraday configuration as strongly as cyclotron resonance2. This resonance transition is related to contiguity of Landau levels with opposite spins, 1D and 1E, due to strong nonparabolicity. In this work, we have extended the magnetic field range to study the coupling between the two Landau levels more in detail and refined calculations.

2 Experimental Ultra-high magnetic fields were generated by the single-turn coil technique. The samples were thin films of p-type PbTe grown on the (111) surface of BaF2 by the hot wall technique or the molecular beam epitaxy method. Their characteristics were as follows; Sample #1: p=1.3u1018 cm3, PH=15870 cm2/Vs, thickness=3.48 Pm; Sample #2: p=2.9 u 1017 cm3, PH=29000 cm2/Vs, thickness=2.7 Pm. All the magneto-transmission measurements were performed in the Faraday configuration.

102 N. Yokoi et al.

Fig. 1. absorption and transmission spectra vs. magnetic fields of (a) Sample #1 and (b) Sample #2, respectively, at around 20 K for various infrared photon energies.

Figure 1 shows absorption and transmission spectra vs. magnetic fields of Sample #1 and Sample #2 at around 20 K for various photon energies between 73.4 meV (16.9 Pm) and 135 meV (9.2 Pm). At the lowest photon energy, two absorption peaks labeled L and H are observed. These peaks are assigned to cyclotron resonance transitions for light mass (L0EoL1E) and heavy mass (H0EoH1E), corresponding to the nonequivalent valleys located at the L point in the Faraday configuration B//¢111². The light mass cyclotron resonance was not observed in Sample #2 due to its lower hole density. With increasing photon energy, a new absorption peak labeled X emerged and became larger on the lower field side of the absorption peak for the heavy mass, and exceeded it in the intensity at the highest energy.

3 Discussion The emergence of the new absorption peak X can not be explained in the framework of the Dimmock model3, in which off-diagonal terms in the Hamiltonian3, which represent intraband spin-orbit interactions, are neglected. Including the interactions, numerical calculation according to the six band model shows that merging of the two spin states is enhanced as the levels 1E and 1D approach each other due to strong nonparabolicity. In this spinmerging region, each Landau level, which we name 1D’ or 1E’, has both spin components, and both transitions 0Eo1E’ and 0Eo1D’ become allowed. In

New Type of Combined Resonance in p-Pb Te 103

Fig. 2. The six band model calculation including the intraband spin-orbit interactions using the new k·p parameter set (see text). (a) Magnetic field dependence of transition energies together with the experimental data, which are indicated with closed circles for the peaks L and H, and with open circles for the peak X. (b) Intraband transition dipole moments vs. fields for transitions H0EoH1E and H0EoH1D.

this context, we should assign both the peaks X and H to another kind of combined resonance, which might be named ‘merged resonance’. In the numerical calculation, a new set of k·p parameters have been determined so as to reproduce the field dependence of the transitions X and H as follows4; 2Pt2/m0=7.55 eV, 2Pl2/m0=0.490 eV, m0/mt=8.77, m0/ml=2.11, m0/mt+=1.91, m0/ml+=1.22, gt= 3.08, gl= 14.1, gt+=6.08, gl+=13.2. The parameters have been adjusted without modifying the band-edge parameters determined by Pascher et al.5 One would recognize in the calculated results (Fig. 2) that the calculation explains not only the resonance fields of merged resonance transitions but also an onset field of the merged resonance and the exchange of their intensities around the spin merging region successfully. In this study, it has been confirmed that the new k·p parameter set also reproduce transition fields in the light mass cyclotron resonance reasonably. In conclusion, a new type of combined resonance, named ‘merged resonance’ is observed in p-PbTe in the high field region. Taking advantage of this resonance, a new set of k·p parameters in PbTe is determined.

References 1. McCombe, B.D. et al.:’Combined resonance and electron g values in InSb’, Phys. Rev. Lett., 18, 748-750, 1967 2. H. Yokoi, et al.: ‘Observation of a New Type of Combined Resonance in p-type PbTe under High Magnetic-Fields up to 150T’, in Proc. of 20th Int. Conf. on Phys. of Semicond., (World Scientific, Singapore, 1990), pp. 1779-1782 3. Dimmock, J.O.: J. Phys. Chem. Solids Suppl., 32, 319, 1971 4. Details of the calculation will be reported elsewhere. 5. Pascher H.: Appl. Phys. B, 34, 107-122, 1984

Part III – Carbon Nanotubes and Graphene

Theory of Third-Order Optical Susceptibility of SingleWall Carbon Nanotubes With Account of Coulomb Interaction D. Lobaskin and A. Andreev Advanced Technology Institute and Department of Physics, University of Surrey, Guildford, Surrey, GU1 2SW, United Kingdom

Abstract. We present a detailed evaluation of the third order nonlinear optical susceptibility of single wall carbon nanotubes in the presence of Coulomb interaction. It is demonstrated that both the inter- and intraband transitions should be included in calculations in order to obtain the correct results for frequencies below the bandgap. For the case when the Coulomb interaction is artificially "switched off", the obtained results are consistent with previous study of third-order susceptibility for the noninteracting electrons. We demonstrate that Coulomb interaction significantly modifies the non-linear optical properties of the nanotubes: the resonance peaks are shifted to higher energies and the amplitudes of the resonances are noticeably increased.

1 Introduction The optical properties of single-wall carbon nanotubes (SWNT) are now intensively studied due to their unique physical properties and attractive potential applications [1,2]. In particular, Genkin-Mednis [3] approach was used by Margulis and Sizikova [4] to study third-order optical susceptibility ignoring Coulomb effects. Unfortunately, Genkin-Mednis approach is derived in the non-interacting case. It is shown previously [5] that Coulomb interactions play a very important role in linear optical properties of the SWCN. For instance, it is the self-energy correction and the exciton bound state that are responsible for the so-called ratio problem when the ratio of the first and second fundamental optic frequencies is less than two. Ando [5] showed that the shape of the optical conductivity is changed dramatically due to transferring most of the spectral weight to the lowest exciton transitions. In this paper we develop a theory of third order optical susceptibility of SWNT taking account of Coulomb interaction (excitonic effects) in the framework kp theory. We calculate the third order optical susceptibility F(3) in the regime of intensity dependent index of refraction (IDIR): F(3)IDIR =F(3)( –Z; Z–Z, Z), which was measured in recent experiments [2]. Other authors [6] considered previously only third harmonic generation regime.

108 D. Lobaskin and A. Andreev

(a)

Coulomb interaction strength: D = 0.0 D = 0.1

2

1

Re[F

(3)

IDIR

(Z)], x10

-4

e.s.u.

3

0

-1 0.9

1.0

1.1

1.2

1.3

1.4

hZ(0

(b) Coulomb interaction strength: D = 0.0 D = 0.1

2

1

Im[F

(3)

IDIR

(Z)], x10

-4

e.s.u.

3

0

-1 0.9

1.0

1.1

1.2

1.3

1.4

hZ(0 Fig. 1. Real (a) and Imaginary (b) parts of non-linear susceptibility F(3) in the IDIR regime calculated for interacting case with Coulomb interaction strength parameter, D= (e2/NL)/(1.5E0), equal to zero, D =0 (non-interacting limit) and D =0.1; E0 is the SWNT bandgap in the limit of non-interacting electrons; N is the dielectric constant, L=2SR is circumference of the nanotube of radius R=0.55 nm.

Theory of Third-Order Optical Susceptibility of Single-Wall Carbon 109

2 Model and Results We use exciton states found from Ando model [5]. Electromagnetic field perturbation is written in the dipole approximation, then the third order response in the field is found in the usual way [7]. Electric current matrix elements are written in the exciton representation. Excitons are not true boson and commutation relations for exciton operators were carefully derived and used for calculations of the third-order susceptibility. The third-order susceptibility calculated using our theory agrees with previous work by Margulis and Sizikova [4] when the Coulomb interaction is switched off by setting the inverse dielectric constant to zero. Figure 1 shows the calculated F(3) in the IDIR regime for the nanotobe of 1.1 nm in diameter. In comparison with non-interacting case, the resonance peaks of third-order susceptibility shift to higher energies, being around the same energies as the peak of linear absorption. This reflects the fact that in SWNT the Coloumb-induced band gap renormalisation is larger than the exciton binding energy [5]. In addition to the shift, the peaks are strongly enhanced due to the Coulomb interaction.

3 Summary and Acknowledgements In summary, we have studied third-order optical susceptibility in the SWNT (3) in the IDIR regime and found strong Coulomb-induced enhancement of F in resonance. This work was funded by EPSRC, grant EP/C010531/1.

References 1. O'Connel, M. J., et al.: ‘BandGap Fluorescence from Individual Single-Walled Carbon Nanotubes’, Science, 297, 593-596, 2002 2. Maeda A., et.al.: 'Large Optical Nonlinearity of Semiconducting Single-Walled Carbon Nanotubes under Resonant Excitations' Physical Review Letters, 94, 047404, 1-4 ,2005 3. Genkin V.N., Mednis P.M.: ‘Tribution to the theory of nonlinear effects in crystals with account taken of partially filled bands’, Sov. Phys. JETP, 27, 609-615, 1968 4. Margulis Vl.A., Sizikova T.A.: ‘Theoretical study of third-order nonlinear optical response of semiconducting carbon nanotubes’, Physica B, 245, 173-189, 1998 5. Ando T.: 'Theory of Electronic States and Transport in Carbon Nanotubes' Journal of the Physical Society of Japan, 74, 777-817, 2005 6. Jiang J., Dong J., Xing D.Y.: ‘Size and helical symmetry effects on the nonlinear optical properties of chiral carbon nanotubes’, Phys. Rev. B, 59, 9838-9841, 1999 7. Boyd R.W.: Nonlinear optics, Second Edition, Academic Press, 2003

Unveiling the Magnetically Induced Field-Effect in Carbon Nanotubes Devices G. Fedorov1, A. Tselev2, D. Jimènez3, S. Latil4, N. G. Kalugin5, P. Barbara2, D. Smirnov1 and S. Roche6 1

National High Magnetic Field Laboratory, Tallahassee, FL, USA. Department of Physics, Georgetown University, Washington, DC, USA. 3 Departament d'Enginyeria Electrònica, ETSE, UAB, Barcelona, Spain. 4 Department of Physics, Facultes Universitaires Notre-Dame de la Paix, 61 Rue de Bruxelles, Belgium. 5 Department of Chemistry, New Mexico Tech, Socorro, NM, USA. 6 Commissariat à l'Energie Atomique, DSM/DRFMC/SPSMS/GT, Grenoble, France 2

Abstract. Three-terminal devices with conduction channels formed by quasi-metallic carbon nanotubes (CNT) are shown to operate as nanotube-based field-effect transistors under strong magnetic fields. This spectacular effect results from the Aharonov-Bohm phenomena at the origin of a band gap opening in metallic nanotubes. The off-state conductance of the devices varies exponentially with the magnetic flux intensity. We extract the quasi-metallic CNT chirality from the temperature-dependent magnetoconductance measurements.

The nature of the CNT electronic spectrum is strongly dependent on its chirality (n,m)1. A CNT with n – m  3i, where i is an integer, is semiconducting with an energy gap İg v 1/r (r is the radius of the CNT). Nanotubes with n = m are truly metallic2, while those with n – m = 3i, n  m are quasi-metallic with a small energy gap İg v 1/r2 arising from curvature effects. It has been predicted3 that the CNT bandstructure can be tuned between metal and semiconducting one by an axial magnetic field. In particular, an increasing magnetic flux through the cross-section of a nanotube leads to an opening of the gap at the Fermi energy in metallic CNTs. Here we report on magnetotransport measurements of a device made in the configuration of a standard CNT field-effect transistor (CNFET)4 with a quasi-metallic single-walled CNT (SWNT). Diameter of the CNT found with AFM was 1.5 r 0.5 nm.

112 G. Federov et al. First, we measured the DC conductance G=I/Vd as a function of the gate voltage G(Vg) at the small constant bias voltage Vd (~1 mV) and at temperatures from 1.5 K up to 290 K (Fig. 1a). Suppression of the conductance around Vg* | 1 V indicates a small gap (few meV) in the electronic spectrum5 that is characteristic for quasi-metallic CNTs3. Evolution of G(Vg) curves with axial magnetic field clearly shows a decrease of such a gap until B reaches ~6 T and increase with magnetic field above that point.

10

-4

10

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10

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10 10

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6T

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b) 10 G (S )

G (S)

a)

2

-5

290K

10

-6

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-7

10

-8

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123K *

V g =V g 4.2K 0

10

80K 22K 20

30

B (T)

Fig. 1. a) Evolution of the G(Vg) characteristics with increasing axial magnetic field. b) Off-state magnetoconductance curves G(B) measured at Vg = Vg* at different temperatures.

Remarkably, under high axial magnetic fields the device operates as a CNFET with the on/off conductance ratio exceeding 104 at 10 K and 20 T. An exponential decrease of the device off-state conductance is observed under high axial magnetic fields up to room temperature (see Fig1b.). At B > 10 T, we find G v exp(– DB/kBT) (kB is the Boltsman’s constant), consistently with predicted linear İg(B) dependence2. As has been shown6, the value of D depends on both the intrinsic CNT and device properties. The temperature dependence of D(T) provides information about the energy band profile of the CNT forming the conduction channel of our device. In order to interpret observed evolution of the G(Vg) characteristics with magnetic field we calculated6 the İg(B) dependence for quasi-metallic and metallic SWNTs of different chiralities taking into account the curvature effects. Within this approximation İg(B) is found to be well described by linear relation İg(B)= O|B – B0|, where the coefficient O depends only on the CNT radius. The hallmark of the curvature effects is a non-zero value of B0 for n  m that appears to be very sensitive to the n/m ratio. In order to probe the İg(B) dependence close to B0 we measured effective activation energies '(B) determined from the linear parts (T > 70 K) of the

Unveiling the Magnetically Induced Field-Effect in Carbon Nanotubes 113 conductance Arrhenius plots (Fig 2a). The pronounced minimum of the '(B) at B0 = 6 r 0.5 T alongside with diameter estimations allows associating the sample with a (19,10) CNT.

10

-5

10

-6

10

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10

-8

10

-9

10

15T 29T 0T

b) Energy(meV)

Gmin (S)

a)

40 20 0

-10

0

2

-1

100/T (K )

4

' (B) Experiment '(B) (19, 10) Hg(B) (19, 10)

60

0

10

20

30

B (T)

Fig. 2. a) Arrhenius plots measured at Vg = Vg* at different values of magnetic field. b) magnetic field dependence of the effective activation energy ǻ(B) compared to the band gap vs. magnetic field dependence calculated for a (19,10) CNT

We then compare the experimental '(B) with that calculated for a (19,10) CNT using the Landauer-Buttiker formula with band profile parameters extracted from the D(T) dependence6. The perfect match between the experimental results and calculations proves validity of our bandstructure calculations and confirms the assignment of chirality based on the B0 value.

References 1. Saito, R., Dresselhaus, G. & Dresselhaus, M. S. Physical Properties of Carbon Nanotubes (Imperial College Press, London, 1998). 2. Kane, C. L. & Mele, E. J. Size, shape, and low energy electronic structure of carbon nanotubes. Phys. Rev. Lett. 78, 1932-1935 (1997). 3. Ajiki, H. & Ando, T. Electronic states of carbon nanotubes. J. Phys. Soc. Jpn. 62, 1255-1266 (1993). 4. Tans, S. J., Verschueren, A. R. M. & Dekker, C. Room-temperature transistor based on a single carbon nanotube. Nature 393, 49-52 (1998). 5. Zhou, C. W., Kong, J. & Dai, H. J. Intrinsic electrical properties of individual single-walled carbon nanotubes with small band gaps. Phys. Rev. Lett. 84, 56045607 (2000). 6. Fedorov, G., et al. Magnetically Induced Field-effect in Carbon Nanotubes devices. Nano Letters 7(4), 960-964 (2007).

Transient Zitterbewegung of Electrons in Graphene and Carbon Nanotubes Tomasz M. Rusin1 and Wlodek Zawadzki2 1 2

PTK Centertel Sp. z o.o., Warsaw, Poland Institute of Physics, Polish Academy of Sciences, Warsaw, Poland

Abstract. Observable effects due to trembling motion (Zitterbewegung, ZB) of charge carriers in bilayer graphene, monolayer graphene and carbon nanotubes are calculated. It is shown that, when the charge carriers are prepared in the form of gaussian wave packets, the ZB has a transient character with the decay time of femtoseconds in graphene and picoseconds in nanotubes.

The trembling motion (Zitterbewegung, ZB) has become a subject of great theoretical interest as it has turned out that this phenomenon should occur in many situations in semiconductors [1-3]. Whenever one deals with two or more energy branches an interference of the corresponding upper and lower energy states results in the trembling motion even in the absence of external fields. Most of the ZB studies for semiconductors took as a starting point plane electron waves. Since the ZB is by its nature not a stationary state but a dynamical phenomenon, it is natural to study it with the use of wave packets. Below we describe for the first time the transient character of ZB in solids and look for observable effects related to this phenomenon. Two-dimensional Hamiltonian for bilayer graphene is well known [4]. The energy spectrum is E=±α2k2/2m, so there is no energy gap. The position operator in the Heisenberg picture is a 2x2 matrix. We obtain

xˆ11 (t )

xˆ 

ky ª § !k 2 t ·º ¨¨ * ¸¸» .  1 cos « k2 ¬ © m ¹¼

(1)

The third term represents the Zitterbewegung with the frequency αZ= α2k2/2m*, corresponding to the energy difference between the upper and lower energy branches for a given value of k. We calculate the ZB of a charge carrier represented by a two-dimensional gaussian wave packet. In order to have the ZB in the direction x one needs an initial momentum αk0y. In Fig.1 we show the main characteristics of ZB in bilayer graphene. It can be shown that the decay of the ZB is due to an increasing spatial separation of the subpackets corresponding to the positive and negative energy states.

116 T. Rusin and W. Zawadzki

Fig.1 Zitterbewegung of a charge carrier in bilayer graphene versus time, calculated for a gaussian wave packet width d=300A and k0y=3.5x108m-1: a) displacement, b) electric current, c) probability densities for upper and lower components of the wave function, d) packet dispersion 'R(t).The decay time is *Z-1=40fs.

Fig. 2 Oscillatory electric current caused by the ZB in monolayer graphene versus time, calculated for a gaussian wave packet with k0y=1.2x109m-1 and various packet widths d.

The Hamiltonian describing the band structure of monolayer graphene is given in Ref. [5]. The resulting energy dispersion is linear in momentum E=±uαk, where u§1x108cm/s. Thus there is no energy gap. The velocity vˆi =˜H/˜pi is calculated in the Heisenberg picture and the current

ˆj (t )

qvˆ(t ) is averaged over the wave packet. The results are shown in Fig.

Transient Zitterbewegung of Electrons in Graphene and Carbon 117 2. It is seen that the ZB frequency does not depend on d and is nearly equal to

αZZ=2uαk0y. On the other hand, the amplitude of ZB does depend on d. We deal with decay times of the order of femtoseconds.

Fig. 3 Zitterbewegung of two charge carriers in the ground subband of a single carbon nanotube of L=200A versus time, calculated for gaussian wave packets of two different widths d. After the ZB disappears a constant shift remains.

Finally, we consider monolayer graphene sheets rolled into single semiconducting carbon nanotubes (CNT). The band Hamiltonian in this case is similar to that of monolayer graphene except that, because of the periodic boundary conditions, the momentum px is quantized and takes discrete values [6]. The results for the displacement yˆ (t ) are shown in Fig. 3. The complete results of this work can be found in Ref. [7].

References 1. 2. 3. 4. 5. 6. 7.

Zawadzki, W.: ‘Zitterbewegung and its effects on electrons in semiconductors’ Phys. Rev. B 72, 085217, 2005 Zawadzki, W.: ‘One-dimensional semirelativity for electrons in carbon nanotubes’, Phys. Rev. B 74, 205439, 2006 Schliemann, J et al. ‘Zitterbewegung of electronic wave packets in III-V zincblende semiconductor quantum wells’, Phys. Rev. Lett. 94, 206801, 2005 McCann, E. and Fal'ko, V.I.: ’Landau-level degeneracy and Quantum Hall Effect in a graphite bilayer’, Phys. Rev. Lett. 96, 086805, 2006 Slonczewski, J.C. and Weiss. P.R.: ’Band structure of graphite’, Phys. Rev. 109, 272-280, 1958 Ajiki, H. and Ando, T.:’ Magnetic properties of carbon nanotubes’, J. Phys. Soc. Jpn. 62, 2470-2480, 1993 Rusin, T.M. and Zawadzki, W.: ‘Transient Zitterbewegung of charge carriers in graphene and carbon nanotubes’, cond-mat/0702425, 2007

Cross-Polarized Exciton Absorption in Semiconducting Carbon Nanotubes Seiji Uryu and Tsuneya Ando Department of Physics, Tokyo Institute of Technology 2-12-1 Ookayama, Meguro-ku. Tokyo 152-8551, Japan

Abstract. The Aharonov-Bohm effect on optical absorption of light polarized perpendicularly to the tube axis in semiconducting carbon nanotubes is studied. The excitation energy quadratically decreases with the flux around zero in contrast to the linear splitting for light polarized parallel to the axis.

The Aharonov-Bohm (AB) effect of carbon nanotubes was predicted to appear prominently in optical absorption spectra for light polarized parallel to the tube axis [1,2] and observed in experiments [3]. The exciton effect and electron-electron interaction are known to play a crucial role in optical absorption and emission [4]. Recent theoretical [5-7] and experimental [8,9] studies clarified exciton absorption peaks for light polarized perpendicularly to the tube axis in spite of a strong depolarization effect known to reduce the absorption intensity of the interband continuum [10,11]. In this paper we study the AB effect on exciton absorption of perpendicular light. We use an effective-mass approximation in the description of carbon nanotubes [1,12]. The depolarization effect is considered in a self-consistent field method [10,11]. We shall use a screened Hartree-Fock approximation to calculate interaction effect on the band structure and introduce an attractive interaction between a photo-excited electron and hole using the Coulomb interaction screened by a static dielectric function. Actual calculations can be performed by solving the equation of motion for an electron-hole pair. Details are described in Ref. 7. The strength of the Coulomb interaction in nanotubes is characterized by the ratio of the typical Coulomb energy e2/NL and the typical kinetic energy 2SJ/L, where L is the circumference length, N is the phenomenological dielectric constant describing screening by electrons in the V bands, core states, and the S bands away from the K and K' points and by the surrounding material, and Jis the band parameter. This parameter becomes

§ e 2 · § 2SJ · 1 0.35 ¨ ¸¨ ¨ NL ¸ © L ¸¹ | N © ¹

120 S. Uryu and T. Ando

Fig. 1. Magnetic-flux dependence of excitation energy. Solid and dashed lines denote that for (e2/NL)(2SJ/L)-1 = 0.1 and 0.2, respectively. A cutoff energy describing the width of S bands is chosen as a typical value Hc(2SJ/L)-1 = 10 corresponding to nanotubes with diameter of about 1.4 nm.

Since N is considered to be of the order of unity, for example, N = 2.4 in bulk graphite [13], the typical strength of the Coulomb interaction is of the order of 0.1 or 0.2. Figure 1 shows the magnetic-flux dependence of the lowest excitation energy where the flux I threading the nanotube is in units of the flux quantum I0=ch/e. The solid and dotted lines denote results for (e2/NL)(2SJ/L)-1 = 0.1 and 0.2, respectively. The excitation energies quadratically decrease with increase of the magnitude of the magnetic flux around zero, take minimum values at |II0| = 1/3, and increase for |II0| > 1/3. They are within a range between about 1.2 and 1.36 for the solid line and between about 1.26 and 1.52 for the dotted line in units of 2SJ/L. These changes are smaller than that for parallel light lying between about 0 and 2SJ/L [1,2]. The narrow variation of the excitation energy due to the magnetic flux is because the magnetic-flux dependence of the band gap is absent without interaction and the Coulomb interaction is small comparing to the typical kinetic energy. Since the magnetic flux reduces the band gap at the K or K' points around zero [1,2], the screening effect due to interband transitions is enhanced, leading to reduction of the interband separation. The quadratic

Cross-Polarized Electron Absorption in Semiconducting Carbon 121 dependence of the excitation energy arises due to the fact that linear terms cancel between the K and K’ points when they are summed in the dynamical conductivity describing the depolarization effect. Dips at |II0|=1/3 are caused because the band gap closes at the K or K' point, the reduced mass vanishes, and the screening effect becomes strong. This work was supported in part by a 21st Century COE Program at Tokyo Tech “Nometer-Scale Quantum Physics” and by Grant-in-Aid for Scientific Research from the Ministry of Education, Culture, Sports, Science and Technology, Japan.

References 1. Ajiki, H. and Ando, T.: `Electronic states of carbon nanotubes', J. Phys. Soc. Jpn., 62, 1255-1266, 1993 2. Ando, T.: `Excitons in carbon nanotubes revisited: Dependence on diameter, Aharonov-Bohm flux, and strain', J. Phys. Soc. Jpn., 73, 3351-3363, 2004 3. Zaric, S., Ostojic, G. N., Kono, J., Shaver, J., Moore, V. C., Strano, M. S., Hauge, R. H., Smalley, R. E., and Wei, X.: `Optical signatures of the Aharonov-Bohm phase in single-walled carbon nanotubes', Science, 304, 1129-1131, 2004 4. Ando, T.: ` Excitons in carbon nanotubes’, J. Phys. Soc. Jpn. 66, 1066-1073, 1997 5. Chang, E., Bussi, G., Ruini, A., and Molinari, E.: `Excitons in carbon nanotubes: An ab initio symmetry-based approach', Phys. Rev. Lett., 92, 196401-1-4, 2004 6. Zhao, H. and Mazumdar, S.: `Electron-electron interaction effects on the optical excitations of semiconducting single-walled carbon nanotubes', Phys. Rev. Lett., 93, 157402-1-4, 2004 7. Uryu, S. and Ando, T.: `Exciton absorption of perpendicularly polarized light in carbon nanotubes', Phys. Rev. B, 74, 155411-1-9, 2006 8. Miyauchi, Y., Oba, M., and Maruyama, S.: `Cross-polarized optical absorption of single-walled nanotubes probed by polarized photoluminescence excitation spectroscopy', Phys. Rev. B, 74, 205440-1-6, 2006 9. Lefebvre, J. and Finnie, P.: `Polarized photoluminescence excitation spectroscopy of single-walled carbon nanotubes', Phys. Rev. Lett., 98, 167406-1-4, 2007 10. Ajiki, H. and Ando, T.: `Aharonov-Bohm effect in carbon nanotubes', Physica B, 201, 349-352, 1994 11. Ajiki, H. and Ando, T.: `Carbon nanotubes: Optical absorption in AharonovBohm flux', Jpn. J. Appl. Phys. Suppl., 34-1, 107-109, 1995 12. Ando, T.: ` Theory of electronic states and transport in carbon nanotubes’, J. Phys. Soc. Jpn. 74, 777-817, 2005 13. Taft, E. A., and Philipp, H. R.: `Optical properties of graphite’, Phys. Rev. 138, A197 (1965).

Part IV – Nanocrystals and Nanowires

Self-Assembled InSb/InAs Quantum Dots for the MidInfrared Spectral Range 3-4 Pm K. D. Moiseev, Ya. A. Parkhomenko, M. P. Mikhailova, S. S. Kizhaev, E. V. Ivanov, A. V. Ankudinov, A. N. Titkov, A. V. Boitsov, N. A. Bert, Yu. P. Yakovlev A. F. Ioffe Physico-Technical Institute, RAS, 26 Politekhnicheskaya, St. Petersburg, 194021, Russia

Abstract. We report the results on structural and optical properties of the InSb quantum dots (QDs) grown on InAs(100) substrate by liquid-phase epitaxy (LPE). The uniform self-assembled QDs with high density (0.7-1.9×1010 cm-2) with dimensions of 3-5 nm in height and 11-13 nm in diameter were obtained in the temperature range T=420-445 0C. Characterization of the InSb QDs was performed using atomic force microscopy and transmission electron microscopy methods. InAs or InAsSbP epilayer lattice-matched with InAs substrate was used as capping layer to bury InSb/InAs QDs. Photoluminescence and electroluminescence from the buried InSb QDs were observed in the spectral range 3-4 Pm at T=77 K.

1 Introduction Self-assembled quantum dots (QD) have attended a great interest for both fundamental sciences and potential applications due to their unique properties as 0-dimensional nanoobjects in the 3D-matrix [1]. Most of investigations were focused to obtain InAs/GaAs QD lasers for the spectral range 1.1-1.3 Pm. To penetrate in the longwavelength region (O>2 Pm) it should to use the narrow-gap semiconductors: GaSb and InAs as substrate matrix, whereas InSb based solid solution as QD material [2]. However, the density of InSb/GaSb and InSb/InAs QDs grown by molecular beam epitaxy (MBE) and metal-organic vapor phase epitaxy (MOVPE) did not exceed 109 cm-2 [3,4]. -2 We here report the results on the growing of high-density (~ 1010 cm ) InSb QD arrays on InAs(100) substrates by LPE method.

2 Experimental results and discussion The growing of InSb QDs was carried out in a horizontal LPE system equipped with a standard slider graphite boat under H2 flow atmosphere from

126 K. D. Moiseev et al. indium-enriched melt [5]. Structural characterization of uncapped InSb/InAs QDs was made by atomic-force microscopy (AFM). Small uniform InSb QDs with area density n~1010 cm-2 are characterized by average height of 3 nm and average diameter of 13 nm. The density of the small QDs were found to increase from 0.7×1010 to 1.9×1010 cm-2 with growth temperature decreasing in the temperature range T=420-445 0C. The large QDs with dimensions of 12 nm in height and 30 nm in diameter appear simultaneously with the small ones to be at a much lower density (~5×108 cm-2).

Fig.1. Dark-field electron micrograph of cross-section sample performed in <220> direction. InAs/InAsSbP interface can be ascribed to the fine dark line. Dark contrast spots at the interface represent InSb QDs.

Capping of the InSb QDs by binary InAs or InAsSbP epilayer latticematched with InAs substrate was performed using MOVPE method. The 0.5 Pm-thick cap layer was grown at T=500 0C. Cross-section transmission electron microscopy (XTEM) was used to identify the buried InSb QDs after deposition of InAs0.85Sb0.05P0.1 layer (Fig.1). Two types of small QDs can be seen in the image: (i) pyramidal-like - with a characteristic size of 6-7 nm; (ii) lens shape-like - with a height of 6 nm and lateral size of 10-15 nm. No loop dislocations, stacking faults and extended defects associated with these inclusions were found at the interface. The ternary content (InAs0.2Sb0.8) of the large inclusions, which are relaxed and have a dome-like shape, was also established by TEM high-resolution image. Thus, TEM data are in good agreement with AFM results. Photoluminescence (PL) spectrum of the structure with InSb QDs embedded in p-InAs/n-InAsSbP heterojunction contained three pronounced emission bands in the spectral range 3-4 Pm under pump level of 12 Wcm-2 at 77 K (Fig.2). The emission band at 0.390 eV was found to be associated with donor-acceptor radiation transitions in p-InAs. We suppose that the highenergy emission band at 0.427 eV is from InAsSbP capping layer, whereas the low-energy one at 0.366 eV can be ascribed to radiative recombination involving transitions on localized states of the InSb QDs. These PL results are in a good correlation with electroluminescence (EL) data obtained at T=77 K where intense emission was observed for the structures with InSb QDs embedded in p-InAs/n-InAs heterojunction. EL spectra at low injection level

Self-Assembled IsNb/InAs Quantum Dots for the Mid-Infrared 127 (i<50 mA) exhibited the emission band at 0.345 eV that can be related with radiative transitions though localized states of the InSb QDs. InAs

InAs0.85Sb0.05P0.1

PL intensity (a.u.)

InSb QDs

0.35

0.36

0.37

0.38

0.39

0.40

0.41

0.42

0.43

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Fig.2. PL spectra from the capsulated InSb QDs (solid line) and InAs substrate (dot line) measured at T=77 K.

In conclusion, we have obtained InSb/InAs uniform QDs with high area density (~1010 cm-2) using the standard LPE method. It was shown that such quantum dots are prospective for the fabrication of emitters and detectors operating in mid-infrared spectral range 3-4 Pm.

3 Acknowledgements This work was in part supported by “New materials and structures” OFN-5 Program of RAS.

4 References 1. Ledentsov, N.N.; Ustinov, V.M.; Shchukin, V.Ⱥ.; Kop’ev, P.S.; Alferov, Zh.I.; Bimberg, D.: Semiconductors, 32, 385-404, 1998 2. Shusterman, S.; Paltiel, Y.; Sher, A.; Ezersky, V.; Rosenwaks, Y.: J. Cryst. Growth, 291, 363-369, 2006 3. Mock, P.; Booker, G. R.; Mason, N. J.; Nickolas, R. J.; Aphandery, E.; Topuria, T.; Browning, N. D.: Mater. Sci. Eng., B80, 112-115, 2001 4. Lyublinskaya, O.G.; Solov’ev, V.A.; Semenov, A.N.; Meltser, B.Ya.; Yerent’ev, Ya.V.; et al: J. Appl. Phys., 99, 093517, 2006

5.Moiseev, K.D.; Parkhomenko, Ya.A.; Mikhailova, M.P.; Ankudinov, A.V.; Titkov, A.N.; Yakovlev, Yu.P.: Phys. Tech. Lett., 33, 2007

InSb/InAs Nanostructures Grown by Molecular Beam Epitaxy Using Sb2 and As2 Fluxes V.A. Solov'ev1,2, P. Carrington1, Q. Zhuang1, K.T. Lai3, S.K. Haywood3, S.V. Ivanov2, and A. Krier1 1

Physics Department, Lancaster University, Lancaster LA1 4YB, UK Ioffe Physico-Technical Institute, Polytekhnicheskaya 26, St. Petersburg 194021, Russia 3 Electrical Engineering Department, University of Hull, Hull, HU6 7RX, UK 2

Abstract. We report the molecular beam epitaxial growth of InSb sub-monolayers inserted in an InAs matrix using Sb2 and As2 fluxes. The InSb/InAs nanostructures exhibit intense mid-infrared photoluminescence up to room temperature. The nominal thickness of the sub-monolayer insertions can be controlled by the growth temperature (TGr = 450-3200C) which gives rise to the variation of the emission wavelength within the 3.6-4.0µm range at room temperature. A comparative analysis of the optical properties of the structures grown using (Sb2,As2) and (Sb4,As4) is also presented.

1 Introduction InSb quantum dots (QDs) embedded in InAs or InAsSb matrices [1,2] have been found to be a promising active medium for mid-infrared optoelectronics devices. A uniform dense array (with a mean sheet density of about 1012 cm-2) of extremely small (mean lateral size ~2.5 nm) self-assembled InSb-enriched QDs has been produced within an InSb submonolayer inserted in InAs(Sb). In spite of the type II band line-up, these InSb submonolayer QD structures showed bright electro- and photoluminescence (PL) up to room temperature in the 3.4-4.5 Pm spectral range [3]. Moreover, stimulated emission at wavelengths of 3.08 Pm (60 K) and 3.86 Pm (77 K) was demonstrated with a threshold current density of 2-3 kA/cm2 under pulse injection pumping in the first hybrid p-AlGaAsSb/InAs(Sb)/n-A2B6 double heterostructure laser diodes containing multiple InSb/InAs(Sb) QD sheets in the active region and grown by molecular beam epitaxy (MBE) with the use of conventional Sb4 effusion cell [4]. Numerous long growth interruptions needed for changing the Sb4 flux during the growth are one of the reasons for the high threshold current density in these laser structures. This paper reports the MBE growth and optical properties of InSb/InAs nanostructures grown using Sb2 and As2 fluxes.

130 V. A. Solov’ev et al.

2 Experimental The samples were grown on n-InAs (001) substrates using a VG-V80H MBE system. Two valved cracker cells were used to provide the Sb2 and As2 fluxes. The samples contained ten InSb sub-monolayer QD sheets separated by 8 nmthick InAs barriers and capped with 100 nm-thick InAs layer. The InSb submonolayer sheets were formed by briefly exposing the InAs growth surface to an antimony flux, exploiting an As-Sb anion exchange reaction, in the same manner as described in ref. [3]. The temperature during dot formation was varied in the 320-450°C range. X-ray diffraction (XRD) and scanning electron microscopy (SEM) studies indicated that the structures were of high crystalline quality. High-order satellite peaks as well as numerous Pendellosung fringes on the XRD rocking curves were clearly observed.

3 Results PL spectra from the samples grown at different temperatures are shown in Figure 1. Two peaks can be clearly identified, one at a wavelength ~3.0 µm from InAs and a much stronger peak between 3.2-3.7 µm (at 4K) from the InSb QDs. The InSb-related PL is observed up to room temperature for all the samples. The QD PL shifts towards longer wavelengths as the growth temperature decreases corresponding to an increase in the InSb nominal insertion thickness. It should be noted that as the growth temperature decreases the QD PL intensity drops dramatically, since at growth temperatures as low as 320°C the material quality is poor. To overcome this difficulty and extend the PL wavelength we have used multiple Sb exchanges to increase the quantity of InSb deposited. Using a double Sb exchange 0.040

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Fig. 1. PL spectra at 4K (a) and 300K (b) of the InSb/InAs structures grown at different temperatures using (Sb2, As2). The numbers in brackets correspond to the InSb nominal thickness estimated from XRD simulation.

InSb/InAs Nanostructures Grown By Molecular Beam Epitaxy 131

4.0 3.9

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Fig. 2. InSb QD PL wavelength vs growth temperature for the samples grown using (Sb2, As2) or (Sb4, As4).

technique we have increased the wavelength from 3.2 to 3.4 µm for a sample grown at high enough temperature (~450°C). In this sample, an initial layer of the QDs is formed by a single Sb exchange, then capped with 1ML of InAs followed by a second Sb exchange. Figure 2 shows how the QD PL peak wavelength depends on growth temperature for the structures grown using different sets of volatile species: (Sb2,As2) and (Sb4,As4). For the structures grown using (Sb2,As2) cracker cells the PL is shifted towards shorter wavelengths at the same growth temperature. So Sb exchange is harder under As2 flux since it is more aggressive than As4.

References 1. Lublinskaya O. G., Solov'ev V. A., Semenov A.N. et al., J. Appl. Phys., 99, 093517, 2006 2. Ivanov S.V., Semenov A.N., Lyublinskaya O.G. et al., Inst. Phys. Conf. Ser. No.187, Edited by J. Kono, and J. Leotin, Part II, p. 83-91, 2006 3. Solov'ev V.A., Lublinskaya O.G., Semenov A.N. et al., Appl. Phys. Lett., 86, 0111091, 2005 4. Sorokin S.V., Sedova I.V., Semenov A.N. et al., Proc. 14th Int. Symp. "Nanostructures: Physics and Technology", St. Petersburg, Russia, 115, 2006

Acknowledgements The authors are grateful to EPSRC for providing a visiting fellowship V. Solov’ev (grant EP/E028209/1) and for the award of a studentship for P. Carrington. We also wish to thank HMGCC for supporting some aspects of this work. V. Solov’ev acknowledges the support of the RFBR (project 07-02-01384a).

Part V – Electronic Devices

Performance Evaluation of Conventional Sb-based Multiquantum Well Lasers operating above 3µm at Room Temperature A. Kadri1, K. Zitouni1, Y. Rouillard2, P. Christol2 1

Laboratoire d’Etude des Matériaux, Optoélectronique & Polymères LEMOP Department of Physics, University of Oran (Es-Sénia), Oran 31100, Algeria 2 Institut d’Electronique du Sud (IES), UMR-CNRS 5214, Université de Montpellier 2, Montpellier cedex 05, France

Abstract. We present the results of a theoretical performance evaluation of conventional type I Sb-based Quinary Multiple Quantum Well Lasers operating in cw at O!3µm at Room Temperature. In this purpose, we use a k.P band structure model to calculate the optical properties of these new Quinary Sb-based heterostructures. Our calculations show that for optimized laser structures emitting near 3.3µm, modal gain value Gmodal =50cm-1 and threshold current densities Jth = 2-3 kA/cm2 are expected. Thanks to the valence band offset enhancement, hole lifetime are shown to increase by one order of magnitude in Quinary laser with respect to Quaternary counterpart. Our results show that this kind of Quinary Sb-based type I laser structures are quite convenient for cw RT Laser operation at O>3µm.

1 Introduction Type I conventional Sb-based Multiple Quantum Well Lasers (MQWL) operating in the 2-4 µm MIR range are of high importance in atmospheric pollution detection and monitoring systems (e.g. Trace Detection by Laser Absorption Spectroscopy). Type I Quaternary InGaAsSb/AlGaAsSb MQWL showed a rapid degradation of their performances at O t 3 µm, mainly due to a strongly reduced valence band offset ('Ev) as O increases resulting in an important hole escape from valence band (VB) quantum well (QW). In order to avoid this issue, an additional Quinary AlGaInAsSb layer was introduced as a new barrier between InGaAsSb QW and AlGaAsSb barrier [1]. Good quality MQW lasers were obtained with O up to 3.26µm and working temperatures up to 50°C in pulsed operation. However, threshold current densities Jth~4-7kA/cm² are still too high and Room Temperature (RT) continuous work (cw) remains to be reached. In this work, we report on a k.P theoretical optimization study of band structure and optical properties of Quinary InGaAsSb/AlGaInAsSb MQWL for RT-cw operation at O t 3 µm.

136 A. Kadri et al.

2 Theoretical Model The theoretical model used in this work was described earlier [2]. Here, we include specific features and band properties related to the additional quinary layer together with band mixing, non-parabolicity and strain effects. The parameters used in the calculations were taken from references 2 and 3.

3 Results and Discussion Our k.P band structure calculations were performed on various structures, and particularly, on an In0.55Ga0.45As0.26Sb0.74/In0.20Ga0.60Al0.20As0.19Sb0.81 MQWL with a QW width LZ=18nm, as it is the most suitable structure showing several interesting parameters: a work wavelength O§3.3µm, a strain 'a/a lower than the 2% limit, and mainly, a hole QW depth of order 'EV =95meV instead of the 25meV value found in the corresponding quaternary MQWL. As expected, the introduction of the Quinary AlGaInAsSb layer in the AlGaAsSb barrier is thus found to improve the hole confinement. Within such a valence band QW, our k.P energy dispersion E(k) calculations show that 3 valence sub-bands are confined in the following order: HH1, HH2, and LH1. At LZ =18nm, the first two levels HH1 and HH2 are found lying at around 10meV and 40meV, respectively, from the bottom of the QW at k=0, and are characterized by large and almost energy independent effective masses; while, the third level, LH1 is found shifted by about 40meV away from the nearer HH2 level. The use of a Quinary barrier is found to induce a systematic red shift of O. This effect is found to decrease with increasing LZ , but is still §5% at LZ=18nm. Although modest, this increase shifts O in the right direction. However, the more important result is in fact the strong quantum lifetime (WQ) enhancement which is found directly related to hole confinement increase. As can be seen in Fig.1, this increase is very huge at low temperatures, but is still around one order of magnitude at T=300K. The quantum hole lifetime WQ was calculated by using the following formula [4]: WQ = ((2SLw²m*/(kT))(1/2)exp( Eb/kT) Where: Eb is the energy difference between the top of the barrier and the first confined energy level in the QW ('Ec-e1 and 'Ev-hh1). In addition to a strong reduction of hole escape from valence band QW, this enhanced WQ is found to have several consequences, and mainly: - A steep increase of the optical gain, and particularly, the modal gain which actually shows a value Gmodal § 50 cm-1, and,

Performance Evaluation of Conventional Sb-Based Multiquantum 137 -

a significant decrease of threshold current densities for we find for our optimized structure Jth § 2-3 kA/cm²,

200

'V=0.07 eV 'V=0.04 eV 'C=0.3 eV

(Wquinary/ Wquaternary)

150

100

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50

0

Electron 100

150

200

250

300

350

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Temperature (°K)

Fig.1: Variation of hole quantum lifetime ratio WQuinary/WQuaternary versus temperature for different values of Quinary/Quaternary energy barrier differences 'V and 'C; where: 'V= ('EvQuinary-'EvQuaternary) and 'C = ('EcQuinary-'EcQuaternary).

4 Conclusion Our k.P theoretical optimization study of band structure and optical properties of Quinary Sb-based MQW Lasers shows that the introduction of a Quinary AlGaInAsSb layer in the AlGaAsSb barrier efficiently improves the hole confinement by increasing hole QW depth up to 95meV. This effect induces in turn a 5% red shift of the operation O of the laser and one order of magnitude enhancement of the hole quantum lifetime. The optimized structure emitting near 3.4µm is found to show quite satisfactory values for the modal gain Gmodal § 50cm-1 and for the threshold current density Jth§2-3kA/cm² suggesting that this kind of Sb-based type-I MQW lasers with quinternary AlGaInAsSb barriers is quite convenient for cw RT operation above 3µm.

138 A. Kadri et al.

References 1. M.Grau, C.Lin, O.Dier, C.Lauer, MC.Amann, RT operation of 3.26 µm GaSb-based type-I lasers with quinary AlGaInAsSb barriers, Appl. Phys. Lett 87, 241104 (2005) 2. K.Zitouni, A.Kadri, P.Christol, A.Joullié, Effects of strain and nonparabolicity on optical gain & threshold current in MIR InxGa1-xAsySb1-y/Al0.35Ga0.65As0.03Sb0.97 Quantum Well Lasers, in proc. of NGS12 (Toulouse, France, July 2005), edited by J.Kono and J. Leotin, pages 343-348 (2005). 3. Y. Wang, H. S. Djie, and B. S. Ooi, Interdiffusion in InGaAsSb/AlGaAsSb Quantum Wells, Journ, of Appl. Physics 98, 073508 (2005). 4. H. Schneider, KV. Klitzing, Thermo-ionic emission and Gaussian transport of holes in GaAs/AlxGa1-xAs multiple quantum well structure, Phys. Rev. B 38, 6110, (1988).

Electroluminescence From Electrically Pumped GaSbBased VCSELs O. Dier, C. Lauer, A. Bachmann, T. Lim, K. Kashani, and M.-C. Amann Walter Schottky Institut, Technische Universität München, Germany

Abstract. A structure for a GaSb-VCSEL device using a buried tunnel-junction (BTJ) and a hybrid dielectric/gold DBR mirror is investigated. The BTJ approach combines several advantages such as reduced intravalence-band absorption, low ohmic losses and an efficient thermal management of the laser diode, which are crucial for roomtemperature operation of the device. First results have shown resonant electroluminescence, but due to a misaligned cavity no laser operation was achieved.

1 Introduction GaSb-based diode lasers emitting in the 2.0 – 3.3 µm wavelength range have drawn lots of attention for trace-gas sensing applications, for which singlemode emission and fast tunability of about 5 nm is necessary. These requirements are met by GaAs- or InP-based VCSELs in the 0.65-2.3 µm range [1], but for emission in the longer wavelength regime novel materials have to be used. One possibility to realise single-mode surface emitting devices with long emission wavelengths are GaSb-based VCSELs, for which impressive results have already been obtained with optically pumped structures [2,3]. In this work, a device concept for an electrically pumped VCSEL on GaSb substrates is introduced. It utilises the buried tunnel-junction (BTJ) approach, which showed its superior capabilities already in longwavelength InP-based devices [1].

2 Device structure and fabrication The device structure of the GaSb-based BTJ-VCSEL is shown in Fig. 1. The growth of the laser is divided into two parts: in the first growth step etchstop layers for substrate removal, the epitaxial DBR consisting of 19 pairs of GaSb:Te and AlAsSb:Te, the active region and the tunnel-junction are deposited. The active region is formed by 5 compressively strained, 10 nm thick GaIn0.35AsSb quantum-wells separated by 8 nm Al0.2GaAsSb barrier material. As silicon acts as a donor in InAsSb and as an acceptor in GaSb, it

140 O. Dier et al. can be used as dopant on both sides of tunnel-junction, forming a lowresistive contact structure. After the first growth the tunnel-junction is dry-chemically etched and overgrown with n-doped GaSb in the second MBE growth-step.

Fig. 1. Schematic structure of GaSb-based VCSEL. The cavity is formed by an epitaxial and an hybrid dielectric/gold DBR. Key feature is the buried tunnel-junction, which provides current confinement as well as carrier-conversion for lower ohmic losses and reduced intravalence-band absorption.

The structured tunnel-junction provides current-confinement by a low resistive contact in the inner part of the device, whereas in the etched regions a reverse-biased pn-junction is formed, blocking the current flow in the perimeter. n-type GaSb below and above the active region serves as currentand heat-spreading layer, reducing ohmic losses and improving heat-sinking. To form the cavity of the VCSEL, a hybrid dielectric/gold-DBR consisting of 2.5 pairs of CaF2 and amorphous silicon is deposited by e-beam evaporation. Electroplated gold serves as an effective heat-sink as well as a substrate substitute prior to the removal process of the GaSb-substrate. The key feature of the buried tunnel-junction is not only current confinement, but also carrier-conversion, resulting in less p-type layers within the cavity. This effect improves not only the series conductivity of the device, but also reduces the optical losses due to intra-valence-band absorption.

3 Results The fully processed device exhibited electroluminescence at roomtemperature in cw-mode for a wide spectral range, including some resonant features within the stop-band, as can be seen in Fig. 2. The stop-band width is indicated by the dotted line resulting from transmission measurements of the

Electroluminescence From Electrically Pumped GaSb-Based 141 epitaxial structure prior to processing. The shift between stop-band oscillations in transmission and electroluminescence is due to different temperatures of measurement.

Fig. 2. Electroluminescence of VCSEL device. The straight line represents the spontaneous emission of the device. Resonant features can be identified within the stop-band (depicted by the dotted transmission spectrum) .

As the cavity resonance is mistuned of about 100 nm due to loss of layer thickness during processing, no lasing could be observed.

4 Conclusion We successfully fabricated buried tunnel-junction VCSELs on GaSbsubstrates. Due to a misalignment of the cavity mode no lasing, but only resonant electroluminescence below lasing threshold could be observed. Acknowledgements The authors like to acknowledge the funding of this work by the European Union via “NEMIS” and the German Federal Ministry of Education and Research via “NOSE”.

References 1. Ortsiefer, M. et al.: Electron. Lett. 42 640-641 (2006). 2. Schulz, N. et al.: phys. stat. sol. ( c ) 3 386-390 (2006). 3. Cerutti, L. et al.: Electron. Lett. 40 869-870 (2004).

Wavelength Tunable Resonant Cavity Enhanced Photodetectors Based on Lead-Salts Grown by MBE F. Felder, M. Arnold, C. Ebneter, M. Rahim and H Zogg ETH Zürich, Thin Film Physics Group, Technopark, CH-8005 Zürich, Switzerland, www.tfp.ethz.ch

Abstract. Tunable resonant cavity enhanced detectors (RCED) have been realised for the mid-infrared (IR). The bottom mirror as well as the photodiode inside the cavity are based on narrow gap IV-VI materials and grown by molecular beam epitaxy (MBE) on Silicon substrate. The length of the cavity and therefore the resonance wavelengths can be adjusted continuously by a movable top mirror. We present measurements of such an RCED with a tuning range from 4.6 µm to 5.1 µm.

1 Introduction Mid-IR Photodetectors tunable within a broad wavelength region allow interesting applications for multispectral detection and spectroscopy. By using the principle of a resonant cavity enhanced detector with an adjustable cavity length, this can be achieved in a very compact way. Incoming light is reflected multiple times within a Fabry-Perot cavity formed by two mirrors (Fig. 1). The active layer, a photosensitive diode, is placed within the cavity. Due to multiple passes of the photons, the thickness of the diode can be reduced, while quantum efficiency stays high [1]. Compared to a bulk layer, this results in a considerably lower noise due to charge recombination [2]. The spectral widths of the resonances are determined by the finesse of the cavity. Narrower line widths can be obtained by using mirrors with a higher reflectivity, thereby increasing the finesse of the cavity. The free spectral range and the resonance wavelengths of the standing wave correlate to the optical distance of the two mirrors. By moving the top mirror and therefore changing the cavity length, the wavelength the detector is sensitive for can be selected.

144 F. Felder et al.

Fig. 1: Schematics of the RCED.

2 Fabrication The bottom mirror as well as the buffer layer and the active region are grown on silicon substrate by MBE. Because of their favourable properties at wavelengths around 5 µm, the narrow gap IV-VI semiconductor PbTe is used. Alloying of PbTe with adequate materials, e.g. Sr (or Sn), causes a band gap shift to shorter (longer) wavelengths and the whole mid-IR region from < 3 to > 15 µm can be covered. The buffer layer (Pb1-xSrxTe) can therefore be grown transparent for part of the spectral band of the incoming light. Radiation with shorter wavelengths than the band gap is absorbed within the buffer layer before it reaches the photodiode and only a single resonance peak results [3]. The active region itself consists of two thin layers of p-type PbTe and n-type Pb1-xSrxTe:Bi, forming a p-n hetero-junction. The Bragg mirrors consist of alternating EuTe/Pb1-xSrxTe layers, each having the thickness of a quarter wavelength. Because of the ample contrast of the refractive indexes (nPbTe ~ 6, nEuTe ~ 2.3), merely few pairs of layers yield a Bragg mirror with the desired high reflectivity.

3 Experimental results The first tunable RCED for the mid-IR with a p-n photodiode based on leadsalt materials has been realised using a piezo actuated top-mirror. The presented measurements feature a cavity length of approximately 30 µm, whereof the air-gap between active region and top-mirror accounts for 10 µm. The total travel of the mirror itself is 3.3 µm. Spectra were obtained for multiple positions of the mirror, with a stepping of 0.13 µm (Fig. 2). This yields a tuning range from 4.6 um to 5.1 µm.

Wavelength Tunable Resonant Cavity Enhanced Photodetectors 145

Fig. 2: Spectral response at various cavity lengths. Each line represents a discrete measurement.

Fig. 3: Left: Position of the resonance peak at three different cavity lengths. Right: Comparison of experimental data and simulation.

Most spectra show two resonance peaks. This is due to the large cavity length caused by the high refractive index of the buffer layer, and the therefore small free spectral range between two peaks. As seen in Fig. 3, the line width of a resonance at peak quantum efficiency is 74 nm, which corresponds to a spectral resolution GO/O = 1.5%. The contrast of peak maximum to minimum is greater than 8:1. Furthermore, the experimental values are in very good agreement with the simulated spectral response.

146 F. Felder et al.

4 Conclusions We have fabricated tunable RCEDs with IV-VI (lead chalcogenide) narrow gap semiconductors on Si-substrates. The tuning range spans from 4.6 µm to 5.1 µm. Other wavelength ranges may be covered by replacing the active PbTe layer by Pb1-xSrxTe (Pb1-xSnxTe) to obtain shorter (longer) cut-off wavelengths in a range from < 3 to > 15 µm. If narrower line-widths are desired, this can easily be obtained by using Bragg mirrors with a higher reflectivity, thereby increasing the finesse of the cavity. The devices may be applied for micro-spectrometers to detect/monitor gases which have strong absorption lines in the mid-IR range.

References 1. M.S. Unlü and S. Strite, J. Appl. Phys. 78, 607 (1995). 2. F. Felder, M. Arnold, M. Rahim, C. Ebneter and H. Zogg, in preparation 3. M. Arnold, D. Zimin, H. Zogg, Appl. Phys. Lett. 87, 141103 (2005) 4. N. Quack, S. Blunier, J. Dual, M. Arnold, F. Felder, C. Ebneter, M. Rahim, H. Zogg, Sensors and Actuators: A Physical (2007), to be published.

Farfield Measurements of Y-Coupled Quantum Cascade Lasers L. K. Hoffmann1, C. A. Hurni1, S. Schartner1, M. Austerer1, E. Mujagiü1, M. Nobile1, A.M. Andrews1, W. Schrenk1, G. Strasser1 M. P. Semtsiv2, W. T. Masselink2 1 2

Center for Micro- and Nanostructures, Technical University Vienna, Austria Department of Physics, Humboldt University Berlin, Germany

Abstract. Y-coupled cavity quantum cascade lasers have been processed from GaAs/AlGaAs and InP/InGaAs/AlAs/AlInAs wafers. Farfields of these samples were investigated. A phase coherence between the two coupled ridges was observed which results in the farfield pattern of a double slit experiment. Coherent coupling gives perspectives for high power laser arrays.

1 Introduction Quantum cascade lasers (QCLs) have been intensively investigated since their first demonstration in 1994 by J. Faist et al. [1]. QCLs are now able to cover a broad spectrum from a few microns wavelength to the THZ regime. As midinfrared sensing applications require high power coherent light sources, coherently coupled QCL arrays are desirable.

10 Pm 60 µm

Fig. 1 SEM pictures of the InP based sample. Merging of two 10 Pm ridges into one single 10 Pm ridge (left). Double facet side of the sample (right).

148 L. K. Hoffmann et al. 2 Processing Two QCL structures were used for the experiments. The first one is a GaAs/AlGaAs active region structure with a double plasmon waveguide [2]. Its emission spectrum peaks at about 10.5 Pm at room temperature (RT). The second structure is a strain-compensated InGaAs/AlAs active region structure with an InP based waveguide [3] and an emission wavelength of about 4.3 Pm at RT. Y-coupled ridges were etched using reactive ion etching (RIE). Thereafter, a 300 nm thick SiNx insulating layer was deposited by plasma enhanced chemical vapor deposition (PECVD). Windows were opened on top of the ridges, followed by evaporated Ge/Au/Ni/Au (150/300/140/1500 nm) top contacts. 500 nm Ti/Au extended contact pads finished the top side processing. For the back side contact again Ge/Au/Ni/Au (150/300/140/1500 nm) was deposited. The samples were then installed into an N2 flow cryostat, where they were analyzed at 78 K. Figure 1 shows SEM pictures of the processed samples. The left picture illustrates the merging point, where the two 10 µm wide ridges meet and overlap to form a single 10 µm ridge. A cleaved facet of the adjacent coupled ridges is shown on the right hand side. All measurements were operated in pulsed mode with a pulse length of 100ns at 5kHz repetition rate.

3 Results An infrared MCT detector was mounted on a 2-dimensional driving stage for lateral farfield measurements. On the left Figure 3 shows a 2D farfield of a GaAs based laser, where a sharp interference pattern is observed in lateral direction. Due to a high level of coherence the data reveal angles of constructive and destructive interference between the two coherent sources. Experimental data were nicely fitted with theoretical values [4], where the propagation of the calculated nearfield was summed for each point of the far screen. The right hand side of Figure 2 shows the farfield of an InP based device. InP based samples show reduced coherence. As the wavelength is shorter, the interference pattern shows a qualitatively different behaviour. Fitting the results was possible by considering more degrees of freedom than for the GaAs based samples. For GaAs devices, only the fundamental lateral mode in the coupled ridges had to be considered. However, at least the fundamental and the first harmonic mode are present in the InP devices to yield the observed farfield profiles. Additionally, the intensity of each ridge was found out to be slightly different.

Farfield Measures of Y-Coupled Quantum Cascade Lasers 149

GaAs

Growth direction

InP

Lateral distance

Fig. 2: 2-dimensional farfield measurement at the double facet side of a GaAs sample (left) and 1-dimensional farfield data of an InP sample (right) with simulated profile (solid line).

4 Conclusion In conclusion, coherent Y-coupled QCLs have been demonstrated for InP/AlGaAs and InP/InGaAs/AlAs/AlInAs materials. Farfield measurements of the GaAs based devices show a sharp interference pattern, which can be theoretically derived. In the InP based coupled cavities, lateral modes of higher order are present in the waveguide, which results in a reduction of coherence observed in the farfields.

5 References 1. Faist, F.Capasso et al.: 'Quantum cascade laser', Science 264, 553-556, 1994 2. C. Pflügl et al.: 'High-temperature performance of GaAs-based bound-tocontinuum quantum-cascade laser', Appl. Phys. Lett. 83, 23, 2003 3. M. P. Semtsiv et al.: 'Circular-beam cross section quantum-cascade laser' (to be published) 4. L. K. Hoffmann, C. A. Hurni et al. : 'Coherence in Y-Coupled quantum cascade lasers' (to be published)

Impact of Doping Density in Short-Wavelength InP-Based Strain-Compensated Quantum-Cascade Lasers E. Mujagiü1, M. Austerer1, S. Schartner1, M. Nobile1, P. Klang1, L. Hoffmann1, W. Schrenk1, I. Bayrakli2, M. P. Semtsiv2, W. T. Masselink2, and G. Strasser1 1 2

Center for Micro- and Nanostructures, TU Wien, 1040 Vienna, Austria Department of Physics, Humboldt University Berlin, 12489 Berlin, Germany

Abstract. The authors present the effect of injector doping concentrations between 0.7 x 1016 cm-3 and 3.9 x 1017 cm-3 on the performance of short-wavelength InP-based quantum-cascades lasers (QCL) emitting around 3.8 µm. For the maximum operation current an almost linear dependence on the doping is obtained. However, the maximum emitted optical power, the highest wall-plug efficiency as well as the maximum operating temperature are found for a doping density of 1.7 x 1017 cm-3. Characterization of the lowest doped sample indicated an unstable operation of the QCLs.

1 Introduction Development of quantum-cascade lasers (QCLs) which emit in 3-5 µm spectral region is driven by several applications including chemical and medical uses as well as military countermeasures and free space communication. InP-based short-wavelength QCLs with a very large conduction band offset were demonstrated by several groups [1]. However, the improvement of the performance of such devices, especially towards continuous wave operation at room temperature, and the better understanding of the limitations of particular designs, requires further investigation of the influence of relevant physical parameters. The impact of the QCL active region doping variation on the laser performance has been studied both experimentally and theoretically by several authors [2]. In this work we investigate the effect of the active region doping variation between 7 × 1016 cm-3 and 3.9 × 1017 cm-3 on the performance of a short-wavelength (Ȝ~3.8 µm) InP-based strain-compensated QCL.

152 E. Mujagiü et al.

2 Fabrication and Experimental Results 1.8 1.6

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100 ns/5 kHz

0.8 0.6 0.4 0.2 0.0 60 80 100 120 140 160 180 200 220 240 260 280 300 320

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Fig. 1. Peak optical power as a function of heat sink temperatures for 12 µm wide and 2 mm long laser ridges. Solid lines denote connection lines of the discrete data.

The QCL structures, including a 30-period strain-compensated InGaAs/ InAlAs/AlAs active region, were grown by using gas-source molecular-beam epitaxy. The exact layer sequence and the material compositions are well described in [3]. The grown material was processed into 12 µm wide ridges via a reactive ion etching process. A silicon nitride layer, serving as electrical insulation, was deposited by plasma enhanced chemical layer deposition technology. Windows were opened along the ridges and extended contact pads were sputtered on top. A lift off process was used to electrically insulate the ridges from each other. The back contact was evaporated and annealed. Finally, the lasers were mounted epilayer up on a gold-plated copper heat sink. The characterization shows an almost linear dependence of the maximum operation current on the doping density. The highest peak optical power was measured for a doping density of 1.7 x 1017 cm-3 (Fig. 1). Also the wall-plug efficiency has a maximum value for this doping density and decreases for the highest doping concentration (Fig. 2). The roll-over of the maximum optical power and wall-plug efficiency can be dedicated to the thermal back-filling effect due to the far higher doping density. During the first measurement of the lowest doped sample, the laser current was increased and held constant at the roll-over point. Instead of a usually constant peak power a decrease in power was observed. Further measurements showed a reduced peak power. After heating up to room temperature and cooling down to 78 K, the QCLs were lasing again with the highest power at the first turn-on followed by a decrease in power. One explanation can be given by reducing the effective carrier density due to traps in the material. At low temperatures the energy of the electrons is too low

Impact of Doping Density in Short Wavelength in InP-Based Strain 153 4.0

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to escape out of the traps. This lower electron density leads to reduced inversion population and thus lower optical power. At higher temperatures electrons gain enough energy to escape out of the traps. However, this effect is only significant for low doping densities.

3 Conclusions In this work the influence of the active region doping density variation between 3 × 1016 cmí3 and 4 × 1017 cmí3 on the performance of shortwavelength InP-based QCLs is described. For the maximum operation current a monotonic increase was observed. The maximum optical power was obtained for a doping level of 1.7 x 1017 cm-3 and degraded significantly for the highest doping density. Low doped samples indicated an unstable laser operation due to the electron density reduction by traps in the semiconductor material.

References 1. J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, S. N. G. Chu and A. Y. Cho, “Short-wavelength (Ȝ§3.4 µm) quantum cascade laser based on strained compensated InGaAs/AlInAs “, App. Phys. Lett., 72, 680-682 (1997) 2. T. Aellen, M. Beck, N. Hoyler, M. Giovannini, J. Faist, and E. Gini, “Doping in quantum cascade lasers. I. InAlAs–InGaAs/InP midinfrared devices”, App. Phys. Lett., 100, 043101 (2006) and references therein 3. M. P. Semtsiv, M. Ziegler, S. Dressler and W. T. Masselink, “Above room temperature operation of short wavelength (Ȝ=3.8 µm) strain-compensated In0.73Ga0.27As-AlAs quantum cascade lasers”, App. Phys. Lett., 85, 1478-1480 (2004).

Magnetic Field Effects in InSb/AlxIn1-xSb Quantum-Well Light-Emitting Diodes 1

2

3

3

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B. I. Mirza , G. R. Nash , S. J. Smith , M. K. Haigh , L. Buckle , M. T. 3 3 Emeny and T. Ashley 1

Photonics Group, Department of Electrical and Electronic Engineering, University of Bristol, BS8 1UB,UK 2 QinetiQ, St. Andrews Road, Malvern, Worcestershire, WR14 3PS, UK and Photonics Group, Department of Electrical and Electronic Engineering, University of Bristol, BS8 1UB,UK 3 QinetiQ, St. Andrews Road, Malvern, Worcestershire, WR14 3PS, UK

Abstract The spectral properties of InSb/AlxIn1-xSb quantum-well light-emitting diodes have been investigated at T = 15K in a magnetic field of approximately 250mT, applied by mounting the diodes inside a toroidal permanent magnet. In all cases, the low energy side of the spectra is shifted towards higher energy with the field applied.

1 Introduction The InSb material system has many unique properties that make it suitable for use in novel electronic and optical devices where manipulation of the electron spin is an important requirement. For example, the high electron g-factor (-51) results in strong interaction of the conduction electrons with an applied magnetic field. Polarised light emission from InSb based devices, such as a surface acoustic wave (SAW) single photon source [1, 2], should therefore be feasible with relatively small magnetic fields. Previous work has confirmed that InSb quantum-well light-emitting diodes (QWLEDs) have sufficiently high internal quantum efficiencies to realise such a single photon source [3], and in this paper preliminary data showing the effects of a magnetic field on the optical properties of InSb QWLEDs is presented.

156 B. I. Mirza et al.

2 Device Structure and Experimental Details One InSb/AlxIn1-xSb QWLED structure (QW1), containing an undoped 40nm InSb well with a barrier composition of x=0.077, was investigated. See [4,5] for further details of device structure, growth, and doping. Peak injection currents of 20, 4, and 1mA were used, and all measurements were carried out at T = 15K. Full details of the experimental setup can be found in [3]. The device was mounted inside a toroidal magnet with the field perpendicular to the plane of the QW. The system is fully quantized: discrete energy levels in the QW will be further split into Zeeman and Landau levels with energy splitting calculated to be approximately 0.75 and 2 meV respectively for the 250mT field.

Fig. 1. Normalized emission spectra measured at T=15K with and without an applied magnetic field at peak injection currents of 20, 4, and 1mA.

Magnetic Field Effects in InSb/Alxn1–xSb Quantum-Well Light 157

3 Results Normalized emission spectra as a function of current at T=15K are shown in Figure 1. The strong absorption at Ȝ=4.2µm is due to CO2. Significant differences are present between the zero and non-zero field cases. In all cases, the low energy side of the spectra is shifted towards higher energy with the field applied. A possible explanation may be selective energy level occupation, depending on the electron spin. On increasing current, the peak emission shifts to higher energy, and there is an increase in the FWHM. These observations are consistent with increased high energy subband occupation at higher drive currents.

4 Conclusions and Further Work The results indicate that a magnetic field of just 250mT has a significant effect on the emission in this material, confirming the potential suitability for use in a SAW single photon source. Further work is underway to measure directly the degree of polarization at a given set of wavelengths, corresponding to individual magnetic energy levels as described above.

Acknowledgements QinetiQ acknowledges support for this work from the UK Department of Trade and Industry's Technology Programme. One of the authors (G.N.) acknowledges the support of The Royal Society through an Industrial Research Fellowship.

References 1. C. L. Foden, V. I. Talyanskii, G. J. Milburn, M. L. Leadbeater, and M. Pepper, Phys. Rev. A 62, 011803 (2000). 2. G. R. Nash, S. J. Smith, C. J. Bartlett, M. K. Haigh, N. T. Gordon, H. R. Hardaway, J. Edwards, L. Buckle, M. T. Emeny, and T. Ashley, "Towards a Mid-Infrared Single Photon Source", Inst. Phys. Conf. Ser. No 187, 437 (2006). 3. B. I. Mirza, G. R. Nash, S. J. Smith, M.K. Haigh, L. Buckle, M. T. Emeny, and T. Ashley, Appl. Phys. Lett. 89, 131110 (2006). 4. H. R. Hardaway, T. Ashley, L. Buckle, M. T. Emeny, G. Masterton, and G. Pryce, Proc. SPIE 5564, 105 (2004). 5. G. R. Nash, M.K. Haigh, H.R. Hardaway, L. Buckle, A. D. Andreev, N. T. Gordon, S. J. Smith, M. T. Emeny, and T. Ashley, Appl. Phys. Lett. 88, 051107 (2006).

Electroluminescence From InSb-Based Mid-Infrared Quantum Well Lasers S. J. Smith1, S. J. B. Przeslak2, G. R. Nash1,2, C. J. Storey1, A. D. Andreev3, A. Krier4, Min Yin4, S. D. Coomber1, L. Buckle1, M. T. Emeny1, T Ashley1 1

QinetiQ, St. Andrews Road, Malvern, Worcestershire WR14 3PS, UK Photonics Group, Department of Electrical and Electronic Engineering, University of Bristol, BS8 1UB, UK 3 Department of Physics, Advanced Technology Institute, University of Surrey, Guildford, GU2 7XH, UK 4 Department of Physics, Lancaster University, Lancaster, LA1 4YB, UK 2

Abstract. AlxGayIn1-x-ySb heterostructures suitable for laser applications have been grown on GaAs substrates. The structures have been analysed using X-ray diffraction and photoluminescence. Laser diodes have been fabricated by wet etching 20Pm wide bars and cleaving into either 1mm or 2mm lengths. The electroluminescence of these bars has been investigated over a range of temperatures.

1 Introduction Mid-infrared semiconductor lasers which can operate at or near room temperature would have a wide range of potential applications in healthcare, environmental monitoring, manufacturing, security and defence. For example, the favourable atmospheric transmission characteristics at these wavelengths, including low atmospheric scattering and absorption relative to shorter wavelengths, would make them attractive for secure free-space communications in a range of security and military applications, in particular for communication via low orbit satellites or UAVs and with greater up-time, especially addressing the “last-mile” issue. In healthcare, such lasers could, for example, be used for the surface ablation of corneas for the treatment of epithelial corneal dystrophies, whilst they could also be used for improved detection and control of hydrocarbon leakage for reduction of harmful environmental emissions and increased production efficiency in the petrochemical industry, through improved process control.

160 S. J. Smith et al.

Figure 1: A schematic of the layer structure designed by Andreev et al. The left hand block shows the gross structure and the right hand block shows the detail around the quantum wells

2 Layer Structure and Characterisation Andreev et al. proposed a structure based on a AlxGayIn1-x-ySb heterostructure which is shown in figure 1 [1]. It was suggested that the system would exhibit lower threshold current densities due to increased gain in the strained quantum wells this gives the potential for the development of a mid IR laser operating at room temperature. Wafers were grown based on this design by molecular beam epitaxy, at QinetiQ Malvern, onto semi-insulating (SI) GaAs substrates. The structure is shown in figure 1 and comprises compressively strained Ga0.158In0.742Sb wells within Al0.12Ga0.12In0.76Sb confining regions and Al0.25In0.85Sb cladding layers, in this case two quantum wells were grown. To investigate the properties of QWs grown by this method a test structure was grown with a large number of quantum wells and without the upper cladding, this allowed detailed analysis by X-ray diffraction (XRD) and photoluminescence. Measurement of the layer lattice parameters was made using triple crystal XRD using the 155 and 400 reflections. Measurement of the lattice parameters of the buffer and barrier layers showed them to be well matched with less than 0.2% strain in the barrier, the majority of this due to residual strain in the buffer layer. The quantum well is under 0.6% compressive biaxial strain. The sharpness of the super-lattice peaks in the rocking curve is consistent with a fully strained system and indicates a well-ordered layer structure.

Electroluminescence From InSb-Based Mid-Infrared Quantum Well 161

3 Preliminary Electroluminesence 20Pm wide bars were defined in the material by wet etching with metallic contacts to the top p-type region and lower n-type region. These bars were cleaved into 1mm long devices and mounted on copper heatsinks. Electroluminescence measurements were taken as a function of current and temperature with the device installed in a CTI-cryogenics closed cycle cryostat. The results are shown in figure 2.

Figure 2: The emissivity in arbitary units of the laser bar as a function of temperature and current density.

4 Conclusions The GayAlxIn1-x-ySb heterostructure suggested by Andreev et al. for high temperature laser operation has been grown by MBE on a GaAs substrate. XRD analysis showed that they were of high crystal quality. Laser diodes fabricated from the material show electroluminescence up to 250K. This work was supported by the DTI technology program.

References 1. Andreev A. D., O'Reilly E. P., Adams A. R., and Ashley T.: 'Theoretical performance and structure optimization of 3.5-4.5 Pm InGaSb/InGaAlSb multiple-quantum-well lasers', Appl. Phys. Lett., 78, 2640-2642, 2001

InAs Quantum Hot Electron Transistor T. Daoud, J. Devenson, A.N. Baranov and R. Teissier Institut d’Électronique du Sud Université Montpellier 2 / CNRS 34095 Montpellier, France

Abstract. We report in this paper the conception and first characterizations of a Quantum Hot Electron Transistor, an innovative transistor design based on the concept of hot electron transistor and made of InAs/AlSb heterostructures, that has the potential to operate at very high frequency.

1 Introduction Very high frequencies (500 GHz – 1 THz) electronic devices are required for high speed telecommunications or THz-wave generation/detection systems. Recently, a record frequency of Ft=710 GHz has been obtained with an InP-based HBT, using indium rich InGaAs material [1]. Here we propose to exploit the InAs high velocity electron in a unipolar device based on the concept of the hot electron transistor [2]. The Quantum Hot Electron Transistor (QHET) is a unipolar vertical transport device (Fig. 1), with a base layer consisting of an n-doped ~10nm thick InAs quantum well (QW). Emitter and collector junctions are graded InAs/AlSb short period superlattices that offer high design flexibility. The 2D confinement created in the base allows to enhance hot electron transport: majority electrons in the base are confined in the QW ground state by means of the collector barrier, while minority hot electrons transit from emitter to collector through coherent transport via a resonant QW excited state.

InAs/AlSb superlattice

E InAs

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Fig. 1. Schematic QHET conduction band profile. The dotted lines show the Fermi levels in each electrode. The hot electron resonant state is also presented.

164 T. Daoud et al. Its first advantage over InP-HBT is the low base sheet resistance accessible with moderate n-type doping levels (typically 1018 cm-3). Secondly, electron transport in the short (typically 100nm) InAs collector is non equilibrium and very fast. Because of the small electron effective mass in InAs (0.023m0 as compared to 0.045m0 in InP) and the high lateral valleys (Ƚ-L > 0.73 eV) high speed ballistic transport is expected with transit times much shorter than in InP-based devices. Hence, QHET have the capability of extending the high speed limit of electronic devices, towards the THz range.

2 Study of QHET design The studied InAs/AlSb heterostructures have been grown by molecular beam epitaxy on InAs substrate, using a solid source Riber Compact 21 reactor. The base sheet resistance has been measured using conventional Hall measurement setup in a Van der Pauw geometry. For a doping level of 1.5 1018 cm-3 we measured an electron mobility of 11 000 cm2/V/s and a base layer resistance of 325 ȍ/†. This value is remarkably low as compared to usual base sheet resistance of conventional InP-based NPN HBTs obtained for very high P-doping. To design the QHET structure, we studied separately the two junctions in test diodes. Adjustment of the collector barrier is a fundamental point for a QHET. It must let the passage of the hot electrons from the emitter and block the electrons confined in the base in the same time. We studied two base-collector junctions with different barrier height. The experiment results are consistent with thermoionic emission: the higher the barrier, the smaller the current density (Fig. 2a). A 450meV barrier height is needed to reduce the current density below 1kA/cm² for a bias up to 2V. Two single emitter-base junctions with different doping level of the InAs/AlSb superlattice were fabricated. A higher doping level allows a better injection for low voltage, however the lower doping level gives a better diode ideality coefficient (Fig. 2b). It must be noted that turn-on voltage of 100kA/cm² achieved for 0.4V is much lower than in conventional HBTs. 100

1,8 1,6

0.3eV barrier

1,4 1,2 1,0 0,8

0.45eV barrier

0,6 0,4 0,2

Current density (kA/cm²)

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Vbc(V)

10

17 -3 N = 1x10 cm 1

0.1 0.0

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a)

17 -3 N = 4x10 cm

b)

0.1

0.2

0.3

0.4

Vbe (V)

Fig. 2. Electrical characterization of test diodes : a) base-collector junctions; b) emitter-base junctions.

0.5

InAs Quantum Hot Electron Transistor 165

3 First transistor static characterizations A key process step is the accurate contacting of the thin base. A high precision layer-by-layer etching process has been developed for that purpose. AFM imaging of the surface before metal deposition demonstrated the good control of the base layer clearance, with RMS value of surface roughness of 1.5 nm. Micrometer scale devices have been realized in a double mesa geometry with emitter area of 10x10µm². The transistor is designed with a 0.45eV collector barrier, 1017cm-3 doping level for the emitter-base junction and 1018cm-3 doping level for the base. The device exhibits a transistor amplification with current gain of 5 (Fig 3). However static current gain is not constant : for low Vbe, dominant emitter current is injected directly into the lower states of the base QW, while for higher Vbe, the injection of hot electrons is more efficient and a higher static current gain is obtained. Ic

Ib 1

5 4 3

E

Current (mA)

10

0.1

2 1 0

0,2 0,4 0,6 0,8 1,0 1,2

Vbe (V)

0.01 0.0

0.3

0.6

0.9

Vbe (V)

1.2

1.5

1.8

Fig.3. Gummel plot of a QHET device for Vbc = 0V. Inset : static current gain.

4 Conclusions This work demonstrates that the concept of InAs QHET is valid and promising. To exploit its potential for very high frequency operation, we are developing smaller devices with junction area < 10µm² and a process of metamorphic growth on semiinsulating GaAs. This will also allow to obtain higher current density and higher current gain.

References 1. W. Hafez, W. Snodgrass, and M. Feng, ‘12.5 nm base pseudomorphic heterojunction bipolar transistors achieving Ft=710 GHz and Fmax=340 GHz’, Appl. Phys. Lett. 87, 252109, (2005) 2. A.F.J. Levi, T.H. Chiu, ‘Room temperature operation of hot electron transistors’, Appl. Phys. Lett. 51, 984, (1987)

Easy-to-Use Scalable Antennas for Coherent Detection of THz Radiation S. Winnerl, F. Peter, S. Nitsche, A. Dreyhaupt, O. Drachenko, H. Schneider, M. Helm Institute of Ion Beam Physics and Materials Research, Forschungszentrum Dresden-Rossendorf, P.O. Box 510119, D-01314 Dresden, Germany Abstract. We report on a large-area THz antenna which is based on N+ implanted GaAs as a photoconductive material. The antenna consists of an interdigitated electrode structure, where every other electrode gap is covered by a second metallization layer. The antenna concept avoids resonances and offers a high degree of freedom with respect to the focusing of both the THz and the gating beam.

1 Introduction Photoconductive (PC) antennas are used for emitters and detectors for singlecycle THz radiation as well as for photomixers, which generate continuous wave THz radiation. Especially detector antennas and photomixers require materials with short carrier lifetimes. Krotkus and Coutaz [1] recently reviewed trapping times in low-temperature grown (LT) GaAs and GaAs implanted with As+, Ga+, Si+ and O+ ions. Furthermore N+-implanted GaAs has been used for THz photomixers [2] and detectors [3]. The electrodes of THz antennas form either resonant dipoles or broadband structures like logarithmic spirals or bowties. Typical gaps of these antennas have areas of a few µm2. Here we present scalable antennas with areas of 1 mm2 based on N+implanted GaAs and semi-insulating (SI) GaAs substrates.

2 Experimental Our photoconductive antenna is an interdigitated electrode structure where every other spacing between the gold fingers (electrode width 5 µm, spacing 5 µm) is covered by a second metallization, which is electrically isolated from the first one. If the structure is exposed to a THz field while an optical gating pulse is applied, a photocurrent is flowing in the external circuit. In the

168 S. Winnerl et al. absence of the second metallization layer the photocurrent would vanish due to equal contributions of opposite polarity. The detection antenna has an active area of 1 mm2 and is placed at a distance of 23 mm from a THz emission antenna. The active area of the emission antenna [4] is 9 mm2 and its electrode structure is similar as for the detection antenna. While the emitter antenna is based on SI-GaAs, different materials are used for the detection antennas. One GaAs:N detector is processed on an as-implanted substrate (dual energy implant, 0.4 MeV, dose 1 u 1013 cm-2 and 0.9 MeV, dose 3 u 1013 cm-2). A second detector is based on a similarly implanted material, but subsequently annealed in N2 ambient at 500 °C for 10 min. For comparison, a third detector is processed on SI-GaAs. Laser pulses (wavelength 786 nm, repetition rate 78 MHz, duration 50 fs) are used to excite the THz emitter and to gate the detection antenna. The spot size (FWHM) and average power of the near infrared radiation are 300 µm and 350 mW on the emitter and 400 µm and 70 mW on the detector antenna, respectively. The photocurrent of the detection antenna is amplified by a lownoise current amplifier and measured via lock-in detection (integration time constant 100 ms), where the bias voltage at the emitter serves as a reference.

3 Results and Discussion The THz waveforms of the different detectors are shown in Fig. 1a. Clearly the SI-GaAs with a carrier life time of a few tens of ps yields much smaller signal amplitudes and temporally broadened signals as compared to the materials with short carrier life times. The broadened signal of the annealed GaAs:N sample with respect to the as-implanted sample indicates that the annealing process results in an increased carrier lifetime. Long carrier life times lead to an increase of the noise on the detector signal. The signal-tonoise ratios are 1900, 450 and 50 for the as-implanted GaAs:N, annealed GaAs:N and SI-GaAs detectors, respectively. The Fourier transforms of the photocurrents are plotted in Fig. 1b. The spectra extend up to about 3 THz except for the SI-GaAs detector, which shows strongly reduced signals for frequencies above 0.3 THz. The pronounced structures on the spectra are due to reflections on the semiconductor surfaces and absorption by water vapor. In conclusion we have demonstrated detection of unfocussed THz radiation with a high signal-to-noise ratio with the large-area detector. Furthermore the large area makes the detector easy-to-use and insensitive against beam pointing fluctuations. Comparing different materials we obtained best results for N+ implanted GaAs which was not annealed.

Easy-to-Use Scalable Antennas for Coherent Detection of THz 169

200

(b) photocurrent (arb. units)

photocurrent (pA)

(a) 100

0

-100

-200

4

10

3

10

10 -4 -2 0 2 4 6 time delay (ps)

8

2

0

1 2 3 4 frequency (THz)

5

Fig. 1. THz waveforms (a) and spectra (b) for the different detector antennas. The substrate materials are as-implanted GaAs:N (solid), annealed GaAs:N (dots) and SIGaAs (dashed).

We thank A. Kolitsch for valuable discussions concerning the ion implantation. Part of this work has been supported by EuroMagNET under EU contract RII3-CT-2004-506239.

References 1. Krotkus, A. and Coutaz J.-L., 'Non-stoichiometric semiconductor materials for terahertz optoelectronics applications', Semicond. Sci. Technol., 20, 142-150, 2005 2. Mikulics, M., Marso, M., Cámara Mayorga, I., Güsten, R., Stanþek, S., Kováþ, P., Wu, S., Li, X., Khafizov. M., Sobolewski, R., Michael, E.A., Schieder, R., Wolter, M., Buca, D., Förster, A., Kordoš, P., and Lüth, H., 'Photomixers fabricated on nitrogen-ion-implanted GaAs', Appl. Phys. Lett., 87, 041106, 2005 3. Mikulics, M., Marso, M., Mantl, S., Lüth, H., and Kordoš, P., GaAs 'Photodetectors prepared by high-energy and high-dose nitrogen implantation', App. Phys. Lett., 89, 091103, 2006 4. Dreyhaupt, A., Winnerl, S., Dekorsy, T., and Helm, M., 'High-intensity terahertz radiation from a microstructured large-area photoconductor', Appl. Phys. Lett., 86, 121114, 2005

Single Photon Detection in the Long Wave Infrared T. Ueda1, Z. An1 and K. Hirakawa2, S. Komiyama1 1

Department of Basic Science, University of Tokyo, Komaba 3-8-1, Meguroku, Tokyo 153-8902, Japan 2 Institute of Industrial Science, University of Tokyo, Komaba 4-6-1, Meguroku, Tokyo 153-8505, Japan

Abstract. We developed a novel single-photon detector in the long wave infrared (LWIR) spectral region. The detector is a charge-sensitive infrared phototransistor (CSIP) fabricated in a GaAs/AlGaAs double quantum well (QW) structure, in which a photo-generated hole (+e) in the floating gate (upper QW) modulates the capacitivelycoupled conductance of the underneath channel (lower QW). The high responsivity (R=4x106A/W) and specific detectivity (D*=1x1015cmHz1/2/W) are achieved. The dynamic range is extended beyond 107 (~aW to pW) by repeatedly resetting the accumulated holes in the upper QW. The simple structure is feasible for detector array fabrication.

1 Introduction Development of sensitive infrared (IR) photodetectors is one of intensive research subjects in resent years. The activities are motivated by the basic research interests as well as by the viewpoint of versatile applications: biology and medical sciences; security; information and communications technology; non-destructive evaluations. For certain applications, ultimately high sensitivity reaching the photon-counting level is indispensable. For instance, a passive high-resolution microscopy, catching IR photons spontaneously emitted by a living cell or a small number of biomolecules, may be realized only with such ultimately sensitive detectors. Photon-counters have been developed in submillimeter and far-infrared regions.1-3 These photon-counters exploit a novel scheme, in which a photon is converted to a long-lived charge that is sensitively probed by a singleelectron transistor (SET).1-3 The use of SETs, however, necessitates ultra low temperatures (<1K) for operation, which leads to a certain restriction to applications.4 Here we describe yet another type of charge-sensitive infrared phototransistors (CSIPs) utilizing a double quantum-well (DQW) strucutre, 5-8 which is of photon-level sensitivity in the long-wavelength infrared (LWIR) region (wavelength of 14.7µm). In the new scheme, an isolated charge is

172 T. Ueda et al. generated by incident radiation as in the preceding works.1-3 However, a scheme of field-effect transistor (FET) is exploited, instead of a SET, to detect the induced charge (Fig.1).5-8 This makes the device workable at temperatures equal to or above 4.2K (all the experiment in this paper were performed at 4.2K). The CSIPs are therefore not only extremely sensitive, but can be operated in practical conditions. In addition, the simple structure of CSIP is feasible for array fabrication.

2 Mechanism and Device Structure The basic structure of the CSIP is schematically shown in Fig.1. The upper plate A is an isolated conductive island, which is so designed that IR photons can be absorbed and kick excited electron out of this island. The photoelectrons, in turn, are led to the lower conducting channel, where they are absorbed. The isolated island is thereby positively charged up and, through capacitive coupling, it increases the conductance of the lower conducting channel. This device is thus viewed as a field-effect transistor (FET) with a photosensitive floating gate.

Fig.1 Schematic representation of Charge Sensitive Infrared Phototransistor. (b) (a)

(c)

Fig.2 (a) GaAs/AlGaAs double quantum well structure. (b) Schematic representation of energy diagram. (c) Top view (left panel) and cross-sectional view of the CSIP.

Single Photon Detection in the Long Wave Infrared 173 To realize the scheme, the device is fabricated in a Si į–doped AlGaAs/GaAs double quantum-well heterostructure (shown in Fig.2 (a)) grown by molecular beam epitaxy (MBE). The energy band profile is shown in Fig2 (b). The subband energy splitting in the 10nm-thick GaAs upper QW is E01=E1-E0~84meV (Ȝ~14.7µm). Under photo illumination (hȞ=E01), an excited electron (E1) tunnels out of the upper QW through a thin tunnel barrier layer and escapes to the lower QW. The top view design and its cross section of the CSIP are shown in Fig.2 (c). Mesa structure, Ohmic contacts, and metal gates are fabricated using standard lithographic technique. The two metal pads works as antennas which causes inter subband transition (ISBT, E0ĺE1) in the upper QW against normally incident IR radiation (Ȝ~14.7µm). 9 In negative bias condition for the surface gate, an electrically isolated island is formed in the upper QW.

3 Single-photon detection The signal of a small CSIP (Fig.3 (a)) for very weak radiation (~7aW) is given as time-dependent stepwise increment of the conductance as shown in Fig.3 (b). The step height of ǻG§0.05µS meets the value of 0.07µS, which is estimated from simple relation ǻG§(1/A)eµ(W/L) with the active area A=LW§1.5x0.8µm2 and the mobility of lower channel µ§1x104cm2/Vs. As expressed in the relation of ǻG, the step height depends on the size of the device and the mobility in conductive channel. We observed this clear stepwise signal because of its small size. In this device, one of the cross gate (CG2 in Fig.3 (a)) also serves as antenna. Under dark condition, the signal showed stepwise, slow decrease by hole-electron recombination (Fig.3 (c)). The results display extremely long lifetime of photo-generated holes (up to hours).

(a)

Fig.3 (a) Electron microscopic image of the small device. Cross gate 1 (CG1), cross gate 2 (CG2, also serving as antenna), two side gates (SG) are displayed, (b) Stepwise conductance increase seen under a weak radiation (~7aW). (c) Stepwise conductance decrease seen in the dark after illumination.

174 T. Ueda et al.

4 Photosaturation and Reset operation The single photon detection is achieved by converting a photon into a longlived charge. On the other hand, the accumulation of long-lived holes in the upper QW causes photosaturation. This is because of the distortion of band profile as shown in Fig.4. Under photosaturation, the photon-charge conversion becomes inefficient owing to lack of built-in field between the two QWs. A method to extend the dynamic range is the reset operation of the CSIP. When a short positive pulse (1µs-duration) is applied to an additional resetting gate (RG) in Fig 5 (a), the accumulated charge on the isolated QW island is released to the ground, and thereby resetting the device in the highly photosensitive state. Application of such a pulse at an appropriate period makes it possible to use the device with high responsivity at any levels of IR radiation intensity. Fig. 5 (b) shows the dependence on radiation intensity under reset operation. The signal of CSIP is given as average slope of the time trace. (b)

(a)

Fig.4 The conduction band profile for (a) small density (b) large density of holes in upper QW (a)

(c)

(b)

Fig.5 (a) Schematic representation of CSIP with resetting gate (RG). (b) A microscopic image of the device with a 16x4µm2-isolated island of upper QW. (c) Time traces of ǻG obtained with reset operation. Different traces correspond to different IR radiation intensities (lowest: dark; others: 100fW ~20pW)

Single Photon Detection in the Long Wave Infrared 175

5 Quantum efficiency, Reponsivity and Specific Detectivity The quantum efficiency, responsivity and specific detectivity are determined accurately in all-cryogenic spectrometer shown in Fig.6 (a). In order to operate the detector in a condition without background blackbody radiation (BBR), the spectrometer is shielded by SUS pipe and kept in liquid helium. The system includes 1kȍ resistor in vacuum camber, serving as BBR source by Joule heating, and a diffraction grating to produce weak monochromatic photon flux. From the curves in Fig.5 (b), we get the relationship between counting rate (counts/sec) versus photon flux ĭ (photons/sec) as shown in Fig.6 (b). Here, the counting rate is given by dividing the slope of linear part of each curve by unit step height (ǻG§ (1/A)eµ(W/L)). The quantum efficiency is clearly given as Ș=2%. The dynamic range is extended beyond 107 (~aW to pW) by reset operation. The responsivity is defined as the electrical output to the optical input, and calculated as R=Į/(hȞĭ)=ȘǻGVȜ/hc=4x106A/W, where Į is the current slope for the given photon flux (ĭ), V=10mV is source-drain voltage and hȞ=hc/Ȝ=84meV the photon energy (Ȝ=14.7µm). This value is by many orders of magnitude larger than the values, ~10A/W, of well known quantum well infrared photoconductors (QWIPs).10 The noise equivalent power (NEP) is defined as the incident power required to obtain a unity signal to noise ratio (SNR) in the presence of some known noise (dark count or background). For photon counter, NEP is expressed as NEP hQ 2 N K , where N is dark count.11 For N=0.5 counts/sec as worst case, we get NEP=7x10-19 W/Hz1/2. The specific detectivity is defined as D* A NEP . For the detector with active area 2 15 A=16x4µm , we get D*=1x10 cmHz1/2/W. These extremely high values of NEP and D* can be further improved by increasing Ș by optimizing the antenna design.

Fig.6

(a) Overview of the all-cryogenic spectrometer. (b) Counting rate vs.

incident photon flux.

176 T. Ueda et al.

6 Conclusion We described the basics and the high performance of CSIP. The simple structure is feasible for array fabrication, and excellent sensitivity is useful for versatile applications.

Acknowledgement This work is supported by Core Research for Evolutional Science and Technology (CREST) of the Japan Science and Technology Corporation (JST).

References 1. Komiyama, S., Astavief, O., Antonov, V., kutsuwa, T., and Hirai, H.: ‘A single photon detector in the far-infrared range’, Nature, 403, 405-407, 2000 2. Astavief, O., Komiyama, S., Kutsuwa, T., Antonov, V., Kawaguchi, Y., and Hirakawa, K.: 'Single-photon detector in the microwave range', App. Phys. Lett., 80, 4250-4252, 2002 3. Hashiba, H., Antonov, V., Kulik, L., Tzalenchuk, A., Kleindschmid, P., Giblin, S., and Komiyama, S.: ‘Isolated quantum dot in application to terahertz photon counting’, Phys. Rev. B 73, 081310(R), 2006 4. Kastner, M. A.: ‘The single electron transistor and artificial atoms’, Ann. Phys. 9, 885-894, 2000 5. An, Z., Chen, J.C., Ueda, T., Komiyama, S., and Hirakawa, K.: ‘Infrared phototoransistor using capasitively coupled two-dimensional electron gas layers’, App. Phys. Lett., 86, 172126, 2005 6. An, Z., Ueda, T., Chen, J.C., Komiyama, S., and Hirakawa, K.: ‘A sensitive double quantum well infrared phototransistor’, J. Appl. Phys., 100, 044509, 2006 7. An, Z., Ueda, T., Komiyama, S., and Hirakawa, K.: ‘Metastable excited states of a closed quantum dot with high sensitivity to infrared photons’, Phys. Rev. B 75, 085417, 2007 8. An, Z., Ueda, T., Komiyama, S., and Hirakawa, K.: ‘Reset Operation of Quantum Well Infrared Phototransitors’, IEEE T. Electron., July issue, 2007 (in print) 9. Beck, W. A., and Mirotznik, M. S.: ‘Microstrip antenna coupling for quantum-well infrared photodetectors’, Infrared Phys. Technol. 42, 189-198, 2001 10. Levine, B.F.: ‘Quantum-well infrared photodetectors’, J. Appl. Phys., 74, R1-R81, 1993 11. Richards, P.L.: ‘Bolometers for infrared and milimeter waves’, , J. Appl. Phys., 76, 1-24, 1994

High-Performance Fabry-Perot and DistributedFeedback Interband Cascade Lasers C. L. Canedy1, W. W. Bewley1, M. Kim1, C. S. Kim1, J. A. Nolde1, D. C. Larrabee1, J. R. Lindle1, I. Vurgaftman1, and J. R. Meyer1 1

Code 5613, Naval Research Laboratory, Washington, DC 20375

Abstract. We review recent NRL progress in the development of interband cascade lasers for the 3-4 Pm spectral range. The maximum cw operating temperature has reached 269 K, and the pulsed threshold current density at room temperature is as low as 790 A/cm2. The internal loss in a broad-area laser (O= 3.5-3.9 Pm) varies from 11 cm-1 at 78 K to 28 cm-1 at 275 K, and most of the increase in threshold with temperature (T0 | 40 K) is due to a shorter non-radiative lifetime. We also discuss a distributed-feedback laser that demonstrated stable single-mode operation at all temperatures between 78 and 160 K, with a side-mode suppression ratio t25 dB.

1 Introduction Currently, no practical high-temperature semiconductor lasers are available to cover most of the important 3-4 Pm spectral band, and the interband cascade laser (ICL) is a promising candidate for filling the intervening gap. Although the dissipated threshold power densities in pulsed mode at 300 K are now considerably lower than in the best quantum cascade lasers (QCLs) [1,2], the high-temperature cw performance is not yet as good owing to the relatively low value of the characteristic temperature T0 (d 45 K) [3]. Until recently the reasons for this value of T0 were not fully elucidated, and uncertainty about the relative contributions of the internal loss, internal differential efficiency, and carrier lifetime persisted. In this paper, we review recent progress in the development of Fabry-Perot and distributed-feedback (DFB) ICLs at NRL, and discuss a cavity-length study that allows us to identify the different contributions to the temperature dependence of the threshold current.

2 ICL Growth, Fabrication, and Characterization Three ten-stage ICLs were grown by molecular beam epitaxy on n-GaSb substrates. The laser designs included a separate confinement region and are described in detail elsewhere [2,3]. Samples T061026 and T070605 had

178 C. L. Canedy et al. nominally identical layer structures, whereas Sample T061025 had thicker InAs quantum wells and lacked an AlSb barrier between the second active InAs electron well and the GaSb hole injector. As a consequence of imperfect lattice matching, the top cladding of Sample T070605 was partially relaxed. The devices were processed into broad-area 150-Pm-wide and 2-mm-long ridges with uncoated facets. The temperature-dependent central emission wavelengths for the three devices are shown in Fig. 1. Unintentional variations during the growths (7 months apart) account for the 150-nm difference between the wavelengths of Samples T061026 and T070605.

Wavelength (Pm)

4.4 4.2 4.0

150 Pm x 2.0 mm Pulsed T061026 T061025

3.8 T070605

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100

150 200 250 Temperature (K)

300

350

Fig. 1. Central emission wavelength vs. temperature for the three ICL samples.

Pulsed threshold current densities (jth) vs. temperature for the three devices are shown in Fig. 2. At T = 78 K, record low values of 4.8-6.0 A/cm2 are observed. While all three thresholds increase rapidly with temperature (T0 = 38-45 K), the result jth(300K) = 790 A/cm2 for Sample T070605 is comparable to the best ambient-temperature thresholds for quantum cascade lasers at somewhat longer wavelengths.[4] The threshold voltage depends only weakly on temperature, e.g., varying from 4.1 V at 78 K to 3.9 V at 220 K in Sample T061026. For the 2-mm-long broad stripe of Sample T070605 (uncoated facets), the pulsed differential slope efficiency per facet decreased only gradually from 526 mW/A at 78 K to 146 mW/A at 300 K. A narrow (13 Pm wide u 4 mm long) ridge from Sample T061026 was electroplated with gold for efficient heat dissipation. When mounted epitaxialside-up with a high-reflectivity coating on one facet, the maximum cw operating temperature was 269 K. The maximum cw output powers were 130 mW at 78 K, 58 mW at 200 K, and 9 mW at 260 K.

High-Performance Fabry Perot and Distributed-Feedback Interband 179

10000 150 Pm x 2.0 mm T061025 (T0 = 38 K) T061026 (T0 = 41 K) T070605 (T0 = 45 K)

2

jth (A/cm )

1000

100

10

1 50

100

150 200 250 Temperature (K)

300

350

Fig. 2. Threshold current densities vs. temperature for the three ICLs. The measurements employed cw injection at the lowest temperatures, 1 Ps pulses at intermediate temperatures, and 100 ns pulses at the highest temperatures.

3 Gain and Loss in Broad-Area ICLs The main limitation on the maximum cw operating temperature appears to be a relatively low value of T0. In order to better understand its origins, we have performed a cavity-length study, in which the dependence of both the lasing threshold and external differential efficiency above threshold was measured for five different cavity lengths (1, 1.2, 1.5, 2, and 3 mm) as well as several different devices for each cavity length. Values of the internal efficiency and internal loss were extracted from the inverse differential efficiency, and the average gain per unit current density was deduced from the extrapolation of the threshold to infinite cavity length. The results from the two sets of measurements are shown in Figs. 3 and 4, respectively. The internal efficiency at low temperatures is 70-80% and drops somewhat at the highest T. The internal loss Di increases from 11 cm-1 at 78 K to 28 cm-1 at 275 K. These values for Di are comparable to the recent results of Hakki-Paoli measurements on narrow-ridge ICLs grown and fabricated at JPL [5]. On the other hand, the decrease in the average gain per unit current density shown in Fig. 4 is quite considerable, with a characteristic temperature of T1 = 39 K in the 78-275 K range. It is well known from optical gain calculations that the differential gain per unit carrier density decreases only by a factor of |4 between 78 and 300 K.

180 C. L. Canedy et al. Therefore, we conclude that the major reason for the relatively low T1 is a rapid reduction of the carrier lifetime with temperature. This is presumably due to the role played by Auger recombination, and the strong carrierdensity dependence of the Auger rate. The results for the average gain are again in good agreement with those from the recent Hakki-Paoli study (note that T1 was computed incorrectly in that work). 1.0

Ki

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Fig. 3. Temperature dependences of the internal efficiency and internal loss for broadarea devices fabricated from Sample T061026.

10

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T061026 1

0.1

0.01 50

100

150

200

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300

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Fig. 4. Temperature dependence of the average gain per unit current density for broad-area devices fabricated from Sample T061026.

High-Performance Fabry Perot and Distributed-Feedback Interband 181

4 Broadly-Tunable, Single-Mode Distributed-Feedback ICLs

Spectral Power (Arb. Units)

Single-mode operation can be obtained when strong optical confinement in the lateral direction as well as a DFB grating to select a single longitudinal mode are introduced to the ICL. While we previously demonstrated singlemode operation with a maximum cw output power of 41 mW [6], here we explore a different DFB design. Narrow ridges (10-Pm-wide) are formed by contact lithography and chemical etching down to the bottom cladding in an ICL with only five active stages. Next a first-order grating pattern is written using e-beam lithography, followed by e-beam deposition of germanium and subsequent lift-off. The waveguide is completed by depositing 300 nm of Si using e-beam evaporation and lift-off, to produce a 4-Pm-wide pole on top of the ridge. The Si pole confines the optical mode in a low-index-contrast geometry, whereas the etched ridge constricts the current flow. DFBs with four different grating periods (492, 496, 500, and 504 nm) were patterned, to assure overlap of the grating resonance with the gain peak. For devices with each grating period, Fig. 5 shows emission spectra at T = 120 K and I = 50 mA. Interestingly, single-mode operation is achieved for all four, even when the grating resonance is significantly detuned from the peak of the gain spectrum. In all cases the side-mode suppression ratio is at least 25 dB. 10

0

10

-1

10

-2

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-3

/ = 492 nm

3.36

3.38

496 nm

3.40

500 nm

3.42

504 nm

3.44

3.46

Wavelength (Pm) Fig. 5. Emission spectra from 5-stage DFB ICLs with four different grating periods. The operating temperature is 120 K, and the injection current is 50 mA.

Figure 6 illustrates the wavelength tuning with injection current for the device with 496 nm grating period at T = 78, 120, and 150 K. At 78 K the

182 C. L. Canedy et al. maximum tuning range is nearly 10 nm, whereas at a fixed current of 90 mA the wavelength tunes by 20 nm as the heat-sink temperature varies from 78 to 150 K. The net tuning range is > 26 nm when current and temperature are both varied, with single-mode operation being maintained under all conditions. 3.42

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3.39

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References 1. R. Q. Yang, C. J. Hill, and B. H. Yang, 'High-temperature and low-threshold midinfrared interband cascade lasers' Appl. Phys. Lett. 87, 151109-151111, 2005 2. Canedy C. L., Bewley W. W., Kim M., Kim C. S., Nolde J. A., Larrabee D. C., Lindle J. R., Vurgaftman I., and Meyer J. R.: 'High-temperature interband cascade lasers emitting at O =3.6-4.3 Pm', App. Phys. Lett., 90, 181120, 2007 3. Bewley W. W., Canedy C. L., Kim M., Kim C. S., Nolde J. A., Lindle J. R., Vurgaftman I., and Meyer J. R., 'Interband cascade laser operating to 269 K at O= 4.05 Pm', Electron. Lett., 43, 283-285, 2007 4. S. Slivken, A. Evans, W. Zhang, and M. Razeghi, “High-power continuousoperation intersubband laser for wavelengths greater than 10 Pm”, Appl. Phys. Lett., 90, 151115-151117, 2007 5. Soibel A., Mansour K., Qiu Y., Hill C. J., and Yang R. Q.: 'Optical gain, loss, and transparency current in high performance mid-infrared interband cascade lasers', J. Appl. Phys., 101, 093104, 2007 6. Kim C. S., Kim M., Bewley W. W., Canedy C. L., Lindle J. R., Vurgaftman I., and Meyer J. R.: 'High-power single-mode distributed-feedback interband cascade lasers for the midwave-infrared', IEEE Photon. Technol. Lett., 19, 158-160, 2007

Mid-Infrared Lead-Salt VECSEL (Vertical External Cavity Surface Emitting Laser) for Spectroscopy Mohamed Rahim1, Martin Arnold1, Ferdinand Felder1, Ivan Zasavitskiy2 and Hans Zogg1 1

ETH Zürich, Thin Film Physics Group, Technopark, CH-8005 Zürich, Switzerland, www.tfp.ethz.ch 2 P. N. Lebedev Physical Institute, Russian Academy of Sciences, 117924 Moscow, Russia

Abstract. We present the first mid-infrared VECSEL (Vertical External Cavity Surface Emitting Laser) for wavelengths above 3 µm. The structure is very simple: A 2 µm thick PbTe layer is embedded between two high reflectance mirrors and used as gain medium. It is optically pumped with a 1.5 µm wavelength laser. Emission is around 5 µm wavelength and output power up to > 40 mWp at 110K.

Narrow gap IV-VI semiconductors have a direct band gap, and using compositions like Pb1-xYxZ (Y= Sn, Eu or Sr, Z= Te or Se), wavelengths from 3 µm to 40 µm are covered [1]. For PbTe as employed in the present work, the emission wavelength increases from 3.9 µm at RT to 5.7 µm at 80K. VECSELs are known for their good beam quality, tunable wavelength and power scalability. They have been realized with GaAs or GaSb based III-V compounds up to wavelengths of about 2.3 µm [2]. With IV-VI materials like PbYSe or PbYTe, monolithic VCSELs (vertical cavity surface emitting lasers) have been described which are optically pumped and emit in the 4-7 µm range [3-5]. Here we describe the first VECSEL using a IV-VI material and exhibiting an output power > 40 mWp. Fig 1 shows a schematic cross section. The resonant cavity is formed between the bottom Bragg mirror and the top curved mirror. BaF2 is used as substrate, followed by an AR (antireflection coating), a 2 µm thick PbTe layer as gain medium, and a Bragg mirror consisting of 2 pairs of Pb0.97Eu0.07Te/BaF2 layers. Its reflectance is >99% due to the high index contrast between Pb0.93Eu0.07Te (n=4.7) and BaF2 (n=1.46). All these layers are grown by molecular beam epitaxy. The top mirror, again with reflectivity >99%, consists of 2 pairs SiO2/Si and a Cr intermediate layer. Cavity length is slightly shorter than the radius of curvature of the top mirror (25 mm) in order to get a stable resonator at suitable mode diameters. The exciting 1.5 µm laser beam is focused and adjusted to pump through the substrate and the AR-coating and to match the pumped area with the laser

184 M. Rahim et al. mode size (~200 µm diameter). Pulse width was 3 µs with duty cycle up to the % range.

Fig. 1: Schematic representation of the VECSEL.

As shown in Fig. 2, the emission spectrum of the VECSEL operating at 100 K is monomode for lower excitation power, while the second spectrum taken after increasing the pumping power is multimode. The shift to lower wavelength in the second spectrum is due to heating. Linewidths are <0.4 cm-1, limited by the resolution of the spectrometer. The light-in/light-out characteristics (Fig. 3) shows the typical lasing behaviour with a threshold pump power below 2 kWp/cm2. Maximum output power is > 40 mWp at an excitation of 13Wp (limited by the pump laser). This corresponds to a power efficiency of 0.3%.

Fig. 2: Spectra: One mode at lower (left), multimode at higher pumping power (right).

The laser is designed to operate at 80-130K and may be applied for high sensitivity spectroscopy. Here, the detector has to be LN2 cooled; detector and laser may therefore be placed in the same dewar. For operation at higher

Mid-Infrared Lead-Salt VECSEL for Spectroscopy 185 temperature, due to the considerable temperature dependence of the band gap of IV-VI materials, the design wavelength of the Bragg mirror and ARcoating have to be adapted to fit the emission wavelength at that temperature.

Fig. 3: Light-in / light-out characteristics at 90K.

According to the low Auger recombination of narrow gap IV-VI materials, even CW (continuous wave) operation up to room temperature is feasible, as shown theoretically [4]. Experimentally, above RT operation was demonstrated in pulsed mode. QW (quantum well) structures should allow lower thresholds. However, a comparison of different IV-VI VCSEls did not show a significant difference between bulk, QW or QD (quantum dot) IV-VI lasers [5]. The performance of all IV-VI lasers described up to date seems to be limited by defects (dominating Shockley-Read recombination). Compared to theory, the threshold power observed for optically pumped edge emitting IV-VI lasers were about 100 times higher then the fundamental Auger-limit [6]. The present VECSEL shows about 10 times lower threshold power compared to that work, due to improved material quality. However, further optimization will further decrease threshold powers and therefore increased operating temperature.

References: [1] "Lead Chalcogenides: Physics and Applications", D. Khokhlov ed., in "Optoelectronic Properties of Semiconductors and Superlattices", Vol. 18, M.O. Manasreh, Series editor, Taylor & Francis Books, Inc., New York and London, 2003. [2] N. Schulz, M. Rattunde, C. Manz, K. Kohler, C. Wild, J. Wagner, S.-S. Beyertt, U. Brauch, T. Kubler, A. Giesen, IEEE Photonics Technol. Lett. 18, 1070, 2006. [3] T. Schwarzl, G. Springholz, M. Böberl, E. Kaufmann, J. Roither, W. Heiss, J. Fürst, and H. Pascher, Appl. Phys. Lett. 86, 031102, 2005. [4] S. Khosravani and Z. Shi, Appl. Phys. Lett. 78, 139, 2001.

186 M. Rahim et al. [5] J. Fürst, H. Pascher, T. Schwarzl, M. Böberl, W. Heiss, G. Springholz, and G. Bauer, Appl. Phys. Lett. 81, 208, 2002. [6] K. Kellermann, D. Zimin, K. Alchalabi, P. Gasser, N.A. Pikhtin, H. Zogg, J. Appl. Phys. 94 7053, 2003.

Optically Pumped GaSb-Based VECSELs N. Schulz, M. Rattunde, B. Rösener, C. Manz, K. Köhler, and J. Wagner Fraunhofer-Institut für Angewandte Festkörperphysik Tullastrasse 72, 79108 Freiburg, Germany

Abstract. We report on the current status of high-output-power optically pumped vertical-external-cavity surface-emitting lasers (VECSELs) with emission wavelengths of around 2.3 µm. The (AlGaIn)(AsSb) materials system used and the requirements for the VECSEL structure design and growth are discussed. Furthermore, two distinctive optical pumping concepts, barrier pumping at pump wavelengths around 1 µm, and “in-well” pumping at 1.96 µm are compared. For the barrier pumped VECSEL a cw output power of 1.5 W has been achieved with 10 W of pump power and at a heat sink temperature of –15°C. The in-well pumped VECSEL reached 3.2 W of output power at -15°C for an absorbed pump power of only 13.5 W, at a significantly increased differential power efficiency compared to the barrier pumped VECSEL (25% instead of 16%).

1 Introduction Optically pumped vertical-external-cavity surface-emitting lasers (VECSELs) recently have emerged as a new category of semiconductor lasers. They are capable of high-output power emission in a circular, nearly diffraction-limited beam [1]. These two properties are in general not simultaneously achievable using high-power edge-emitting diode lasers or VCSELs, making the VECSEL attractive for numerous applications which require a compact laser source with a high brightness or a highly collimated output beam. The current research activities are mainly focused on GaInAsbased VECSELs that emit at around 1 µm (see e.g. [2]). There also exists a strong demand for high-brightness lasers emitting at wavelengths between 2 and 3 µm. Possible applications include laser surgery, materials processing and infrared countermeasures. Up to now, there have only been few reports on VECSELs that emit in this spectral range. These long-wavelength devices have so far exclusively been realized on the basis of the (AlGaIn)(AsSb) material system. In [3], a single-frequency tunable VECSEL emitting at 2.3 µm has been reported. In [4] and [5], the emphasis was laid on the optimization of (AlGaIn)(AsSb)-based VECSELs for high power operation. By means of an effective heat sinking via intra-cavity heat

188 N. Schulz et al. spreaders, a cw output power of 1 W has been achieved at a wavelength of 2.0 µm [4] and of 1.5 W at 2.3 µm [5]. Here, the epitaxial layer design of (AlGaIn)(AsSb)-based VECSELs is discussed and the current status of high-power devices with emission wavelengths of around 2.3 µm is reviewed. The optical “in-well” pumping concept is presented as a promising alternative to the commonly used barrier pumping concept, yielding a significantly improved power efficiency.

Fig. 1. Schematic of a typical VECSEL set-up.

A schematic drawing of a typical VECSEL set-up is shown in Fig. 1. The VECSEL resonator is formed by a distributed Bragg reflector (DBR) integrated into the epitaxial layer structure of the VECSEL chip and an external, dielectric mirror serving as output coupling mirror. A pump laser is focused on the surface of the chip. Dependent on the resonator alignment, a nearly diffraction-limited beam is emitted.

2 Design and Growth of the Epitaxial Layer Structures The present (AlGaIn)(AsSb)-based VECSEL layer structures were grown by solid-source molecular beam epitaxy (MBE) on 2-inch GaSb substrates. They are composed of the following three sections: A DBR which serves as one of the cavity mirrors, an active region on top of the DBR where the incident pump radiation is absorbed and optical gain is produced, and a window layer on top that prevents carrier recombination at the top surface of the structure. Using 21.5 layer pairs of GaSb and lattice matched AlAs0.08Sb0.92 in the DBR (total DBR thickness: 7 µm), a sufficiently high reflectivity of more than 99.5% has been achieved. In the active region compressively strained 10-nm thick Ga0.65In0.35As0.10Sb0.90 quantum wells (QWs) are embedded between lattice matched Al0.30Ga0.70As0.024Sb0.976 barrier layers. For barrier pumped

Optically Pumped GaSb Based VECSELs 189 VECSELs (cf. section 3), the barrier layers serve also as pump absorbing layers. Their cumulated thickness is set to absorb more than 90% of the pump radiation incident on the VECSEL structure. The QWs are positioned according to the resonant periodic gain (RPG) design, i.e. they are placed in the antinodes of the standing-wave-type optical intensity distribution formed within the VECSEL structure (Fig. 2). In total, 10 QWs distributed in pairs are used for the barrier pumped VECSEL.

Fig. 2. Energy positions of the valence- and conduction band edges (solid lines) and optical intensity of the lasing mode (dashed line) in the active region of the present barrier pumped VECSEL, plotted vs. the distance from the top surface.

Positioning the QWs according to this RPG design yields a high modal gain at the lasing wavelength and hence a low quantum-well carrier density at lasing threshold. For the long-wavelength VECSELs discussed here, a low QW threshold carrier density is instrumental for an efficient laser operation since parasitic losses due to free carrier absorption and Auger recombination both increase with carrier density. On top of the active region, an Al0.85Ga0.15As0.068Sb0.932 window layer is grown and the whole VECSEL structure is capped by a thin GaSb cap layer. For an efficient VECSEL operation, the whole layer stack has to be grown according to the design with high precision. Besides an overall high material quality to minimize defect assisted non-radiative recombination, three specific design parameters have to be met in particular. These are (i) the DBR central wavelength, which has to match (ii) the maximum of the QW gain spectrum at the operating temperature. Furthermore, the resonance wavelength of the subcavity (iii) formed within the VECSEL chip by the DBR and the chip-ambient interface, which is determined by the structure’s optical thickness, has to match the above two wavelengths.

190 N. Schulz et al.

3 Optical Pumping Concepts For optical pumping of the VECSEL structures, two conceptually different approaches can be employed: one is the generally used barrier pumping concept (Fig. 3a). There, short-wavelength (O | 1 µm) pump radiation is absorbed in the barrier layers yielding a high total pump absorption. On the other hand, the quantum deficit (i.e. the fractional energy difference between pump and emitted photons) amounts to more than 50% for VECSELs emitting at 2.3 µm [3-5] which severely limits the overall device efficiency.

Fig. 3. Band edge profiles (solid lines) and quantized energy levels (dotted lines) of a Ga0.65In0.35As0.10Sb0.90 quantum well (emission wavelength: 2.35 µm) embedded between Al0.30Ga0.70As0.02Sb0.98 barrier layers. (a) Relevant transitions for barrier pumping at a pump wavelength of 980 nm. (b) Relevant transitions for in-well pumping at 1.96 µm.

To reduce the quantum deficit, the so-called “in-well” pumping concept, which has up to now only been applied to shorter-wavelength GaInAs-based VECSELs [6], has been transferred and adapted to longer-wavelength GaSbbased VECSELs [7]. As can be seen from Fig. 3b, the quantum deficit can be drastically reduced when using pump wavelengths of 1.9 – 2.0 µm, resulting in a pump absorption exclusively in the active QWs. Hence, the device efficiency and resulting maximum output power are expected to be higher. However, due to the small QW thickness, the pump absorption per QW in a single pump passage is only around one percent. Thus, to enhance the total pump absorption, a microcavity has to be formed within the VECSEL structure also at the pump wavelength to allow a multiple-pass absorption of the pump light [7].

Optically Pumped GaSb Based VECSELs 191

4 High-Power VECSEL Operation at 2.X µm Both a barrier pumped and an in-well pumped VECSEL were set up using a linear resonator configuration, as shown in Fig. 1. The concave output coupling mirror had a radius of curvature of –50 mm and a transmission of 3.6%. For the present experiments, pump spot diameters between 100 µm and 300 µm were used. For an efficient heat removal from the active region, uncoated SiC intracavity heat spreaders (thickness: 300 µm) were liquid-capillary-bonded to the VECSEL chip surface.

Fig. 4. CW output power vs. absorbed pump power of a VECSEL (emission wavelength: 2.30 µm) barrier pumped by a Nd:YAG laser at 1064 nm, recorded at several heat sink temperatures.

Fig. 5. CW power transfer characteristics of an in-well pumped VECSEL, recorded at several heat sink temperatures. The inset shows a lasing spectrum (pump power of 10 W, heat sink temperature -15°C).

The VECSEL designed for barrier pumping was optically pumped by a Nd:YAG laser emitting at 1064 nm. The lasing wavelength of the VECSEL was 2.30 µm. At a heat sink temperature of –15°C, the maximum cw output power was 1.5 W, limited by the available pump power of 10 W (Fig. 4). At a heat sink temperature of 20°C, the VECSEL reached a maximum cw output power of 0.7 W at an absorbed pump power of 6 W, limited by the onset of thermal roll-over. The second VECSEL structure designed especially for inwell pumping at 1.96 µm and to lase at 2.35 µm, was pumped by a Thuliumdoped fiber laser. At a heat sink temperature of -15°C, the cw output power reached 3.2 W, and still more than 2 W were obtained at +15°C, in both cases without any sign of thermal rollover. This is a clear indication of a reduced thermal load on the VECSEL chip due to the reduced quantum deficit. This is confirmed when comparing the differential power efficiencies of the barrier

192 N. Schulz et al. pumped and the in-well pumped VECSEL, which amount to 16% and 25%, respectively, at heat sink temperatures of –15°C. This significant improvement in power efficiency achieved when employing the in-well pumping scheme clearly demonstrates the potential of this concept for the realization of group III-antimonide based high-power VECSELs also at longer wavelengths.

5 Summary An overview has been presented of the current status of optically pumped (AlGaIn)(AsSb)-based VECSELs with emission wavelengths at around 2.3 µm. For an efficient operation of these devices, the complex epitaxial layer structure has to be carefully designed and grown to this design with high precision. The maximum cw output power of a barrier pumped VECSEL amounts to 1.5 W. The cw output power of an in-well pumped device exceeds 3 W, with the differential power efficiency being significantly higher for the in-well pumped than for the barrier pumped variant.

References 1. Kuznetsov, M., Hakimi, F., Spraque, R. and Mooradian, A.: ‘High-Power (>0.5CW) Diode-Pumped Vertical-External-Cavity Surface-Emitting Semiconductor Lasers with Circular TEM00 Beams’, IEEE Photon. Technol. Lett. 9, 1063-1065, 1997. 2. Lutgen, S., Albrecht, T., Brick, P, Reill, W., Luft, J. and Späth, W.: ‘8-W highefficiency continuous-wave semiconductor disk laser at 1000 nm’, Appl. Phys. Lett. 82, 3620-3622, 2003. 3. Ouvrard, A., Garnache, A., Cerutti, L., Genty, F and Romanini, D.: ‘SingleFrequency Tunable Sb-based VCSELs Emitting at 2.3 µm’, IEEE Photon. Technol. Lett., 17, 2020-2022, 2005. 4. Härkönen, A., Guina, M., Okhotnikov, O., Rößner, K., Hümmer, M., Lehnhardt, T., Müller, M., Forchel, A. and Fischer, M.: ‘1-W antimonide-based vertical external cavity surface emitting laser operating at 2-µm’, Opt. Express 14, 64796484, 2006. 5. Rattunde, M., Schulz, N., Ritzenthaler, C., Rösener, B., Manz, C., Köhler, K., Wörner, E. and Wagner, J.: ‘High brightness GaSb-based optically pumped semiconductor disk lasers at 2.3 µm’, Proc. SPIE 6479, 6479-40, 2007. 6. Beyertt, S., Zorn, M., Kübler, T., Wenzel, H., Weyers, M., Giesen, A., Tränkle, G., and Brauch, U.: ‘Optical In-Well Pumping of a Semiconductor Disk Laser With High Optical Efficiency’, IEEE J. Quantum. Electron. 41, 1439-1449, 2005. 7. Schulz, N., Rattunde, M. Manz, C., Köhler, K., Wild, C., Wagner et al.: ‘GaSbbased VECSELs emitting at around 2.35 µm employing different optical pumping concepts’, Proc. SPIE 6184, 61840S1-10, 2006.

Part VI – Magneto-Transport and Magneto-Optics

Cyclotron Resonance Photoconductivity of a TwoDimensional Electron Gas in HgTe Quantum Wells Z. D. Kvon1,2, S. N. Danilov1, N. N. Mikhailov2, S. A. Dvoretsky2, W. Prettl1 and S. D. Ganichev1 1 2

Terahertz Center, University of Regensburg, Regensburg, Germany. Institute of Semiconductor Physics, Novosibirsk, Russia.

Abstract. Far-infrared cyclotron resonance photoconductivity (CRP) is investigated in HgTe quantum wells (QWs) of various widths grown on (013) oriented GaAs substrates. From the resonance magnetic field strength effective masses and their dependence on the carrier concentration is obtained. Combining optical methods with transport measurements we found that the transport time substantially exceeds the cyclotron resonance lifetime as well as the quantum lifetime which is the shortest.

1 Introduction Owing to the advances of molecular beam epitaxy (MBE) technology of narrow gap semiconductors high mobility HgTe quantum wells have recently become available for a wide range of experimental investigations. The twodimensional electron gas in HgTe is characterized by a highly specific energy spectrum with an inverted band structure, low effective mass and large spin splitting at zero magnetic field [1-4]. So far the effective mass in such QW structures has been determined by measurement of the temperature dependence of the SdH amplitudes which uncertainty is about 30%-50% [1]. Here we report on the first experimental study of the cyclotron resonance photoconductivity of a 2DEG in HgTe QWs. CRP is the standard method of effective mass determination and gives an accuracy of about few percent.

2 Experimental results and discussion The experiments are carried out on Cd0.7Hg0.3Te/ HgTe/Cd0.7Hg0.3Te quantum wells having three different widths: 8 nm, 16 nm and 21 nm. Structures are grown on a GaAs substrate with surface orientation (013) by means of a modified MBE method [5]. Samples with sheet density of electrons Ns from 2˜1011 cm-2 to 9.6˜1011 cm-2 and mobility µ ranging from 105 cm2/Vs to 5˜105 cm2/Vs have been studied in the temperature range from 2 K to 40 K.

196 Z. D. Kvon et al. The samples are prepared as Hall bars with 50 µm width and 100 µm and 250 µm distances between opposite contacts. For optical excitation we use a molecular terahertz laser with methanol as an active gas optically pumped by a CO2 laser. We use radiation at wavelength 118.8 µm (corresponding to photon energy !Z = 10.4 meV) with power of about 30 mW. Photoconductivity 'Gph has been measured applying standard modulation techniques at constant bias current of a few µA. All samples are also characterized by magnetotransport measurements. The sharp cyclotron resonance peaks in the photoconductivity are detected at the magnetic field ranging from 2.3 T to 3 T depending on the QW width Lw as well as on the electron density Ns. Figure 1a shows the magnetic field dependence 'Gph(B) of the cyclotron resonance induced photoconductivity for all three QW widths. First we compare the photoconductivity of the sample having Lw = 16 nm and Ns = 3.4˜1011 cm-2 to the sample of 8 nm width and Ns = 9.6˜1011 cm-2. Both resonances can reasonably be approximated by a symmetric Lorentzian with half-width of about 0.15 T (| 0.5 meV). However, the sign of the photoconductivity signals is different: while the illumination of the 16 nm QWs results in positive RPC, the RPC of the 8 nm QW is negative. We emphasize that in Fig. 1a the photoconductive signal of the 8 nm QW is inverted. This fact demonstrates that the RPC in our experiments is caused by radiation heating of the electron gas which results in the change of sample resistance. Indeed, these two samples have opposite slopes of the resistance as a function of temperature (Fig. 1a). The difference in the signal magnitude can be attributed to the difference in slope magnitudes. Another difference of RPC in the two samples is the position of the resonance peak (see Fig. 1a). The half-widths *CRP of the resonances are almost the same: ' | 0.19 T (0.76 meV) for 16 nm QWs and ' | 0.15 T (0.52 meV) for 8 nm QWs. This is in spite of the fact that the mobility in the 16 nm QWs, being of 4˜105 cm2/Vs, is four times larger than that of the 8 nm QWs. Comparing *CRP with the collision broadening *c = !/Wtr obtained from mobility measurements, we find that it is always larger. Indeed for samples with the smaller mobility (8 nm QWs) the *c | 0.3 meV. The experimental observations show that the broadening of the CRP resonance in our samples cannot be due to collision. A possible other broadening mechanism is controlled by the quantum life time Wq which determines SdH amplitudes. The quantum lifetime is given by Wq = ! /2S kBTD where TD is the Dingle temperature. We obtain from SdH oscillations measured in the same samples the *q | (5 – 10) meV which is much larger than *CRP and larger than *c. In 2DEG heterostructures with dominating small angle scattering *q is usually larger than *c [6,7], but the here obtained hierarchy of relaxation times as Wtr >> WCR >> Wq is not typical. We note that most recently the analogous discrepancy between Wtr, Wq and WCR has been observed in a completely other

Cyclotron Resonance Photoconductivity of a Two-Dimensional 197 system: 2DEG in AlGaN/GaN heterostructures [8]. Thus our result shows that this interesting situation can be presented in various 2DEG heterostructures. It is probably due to a nontrivial structure of scattering which is a complicated mixture of long range and short range scattering potentials [9,10]. 12

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Fig. 1. a. Photoconductive response to 118.8 µm wavelength of radiation measured in cyclotron resonance geometry as a function of the magnetic field for three HgTe QWs of different Lw. Lines are Lorentz-fits with half-width 0.44 T, 0.19 T, and 0.15 T for QWs with 21 nm, 16 nm, and 8 nm width, respectively. The inset shows resistance as a function of temperature. b. Effective mass as a function of electron sheet density. Triangles and dots: cyclotron resonance effective mass. Squares: effective masses obtained from SdH measurements taken from [1]. The solid line is a guide for the eye.

Now we discuss the CRP results in the third, widest QW of 21 nm width. The main difference in comparison to the previous samples is the presence of shoulders on the high-magnetic field side of the resonance (see Fig. 1a). The structure at 2.7 T is displaced by about 0.3 T (1.3 meV) from the main peak. This value is too small for Zeeman spin splitting, which at these fields is about 5 meV. It might be due to zero magnetic field spin splitting caused by inversion asymmetry of the structure [2,4], but to make this conclusion further experiments on structures with different asymmetries are required. Finally, we obtained cyclotron resonance effective mass as a function of the density of 2D electrons and the width of QWs. In Fig. 1b we show the dependence of the cyclotron effective mass on the electron sheet density in comparison to the SdH effective mass taken from [1]. It is seen that the effective mass slightly increases from the value (0.0260 r 0.0005) m0 at Ns = 2.2˜1011 cm—2 to (0.0335 r 0.0005) m0 at Ns = 9.6˜1011 cm-2. The cyclotron resonance mass, obtained with an accuracy of a few percent, indicates significantly larger values of mn and much less nonparabolicity than shown by earlier studies and calculations which gave the value of mn < 0.02 m0 varying by factor of two in the range of electron densities of Fig. 1b.

198 Z. D. Kvon et al. In summary, cyclotron resonance induced photoconductivity in novel narrow-gap and low-dimensional structures based on HgTe is investigated and cyclotron effective masses are obtained and compared to previous SdH measurements. From cyclotron resonance line widths and magneto-transport measurements relaxation times have been obtained yielding an unusual sequence of times with respect of their magnitude which has only been observed in 2DEG.

Acknowledgement The financial support of the DFG, RFBR (02-05-16591), and programs of RAS "Quantum nanostructures" and "Quantum macrophysics" is gratefully acknowledged.

References 1. Pfeuffer-Jeschke, A., Goschenhofer, F., Cheng, S.J., Latussek, V., Gerschütz, J., Becker, C.R., Gerhardts, R.R., Landwehr, G.: ’Cyclotron masses of asymmetrically doped HgTe quantum wells ‘, Physica B, 256-258, 486-489, 1998 2. Zhang, X.C., Pfeuffer-Jeschke, A., Ortner, K., Hock, V., Buhmann, H., Becker, C.R., Landwehr, G.: ‘Rashba splitting in n-type modulation-doped HgTe quantum wells with an inverted band structure’, Phys. Rev. B 63, 245305 (1-8), 2001 3. Zhang, X.C., Ortner, K., Pfeuffer-Jeschke, Becker, C.R., Landwehr, G.: ‘Effective g factor of n-type HgTe/Hg1-xCdxTe single quantum wells’, Phys. Rev. B 69, 115340 (1-7), 2004 4. Gui, Y.S., Becker, C.R., Dai, N., Liu, J., Qiu, Z.J., Novik, E.G., Schäfer, M., Shu, X.Z., Chu, J.H., Buhmann, H., Molenkamp, L.W.: ‘Giant spin-orbit splitting in a HgTe quantum well’, Phys. Rev. B 70, 115328 (1-5), 2004 5. Varavin, V.S., Vasiliev, V.V., Dvoretsky, S.A., Mikhailov, N.N., Ovsyuk, V.N., Sidorov, Y.G., Suslyakov, A.O., Yakushev, M.V., Aseev, A.L.: ‘HgCdTe epilayers on GaAs: growth and devices’, Proceedings SPIE, 5136, 381-395, 2003 6. M. A. Paalanen, D. C. Tsui, and J. C. Hwang, Phys. Rev. Lett. 51, 2226 (1983). 7. S. Das Sarma and Frank Stern, Phys. Rev. B 32, 8442 (1985) 8. Syed, S., Manfra, M.J., Wang, Y.J., Molnar, R.J., H. L. Stormer, H.L.: ‘Electron scattering in AlGaN/GaN structures’, Appl. Phys. Lett. 84, 1507-1509, 2004 9. Olshanetsky, E.B., Renard, V., Kvon, Z.D., Portal, C., Woods, N.J., Zhang, J., Harris, J.J.: ‘Conductivity of a two-dimensional electron gas in a Si/SiGe heterostructure near the metalinsulator transition: Role of the short- and longrange scattering potential’, Phys. Rev. B 68, 085304 (1-7), 2003 10. Cho, Hyun-Ick, Gusev, G.M., Kvon, Z.D., Renard, V.T., Lee, Jung-Hee, Portal, J.C.: ‘Negative quasiclassical magnetoresistance in a high density twodimensional electron gas in a AlxGa1íxN/GaN heterostructure’, Phys. Rev. B 71, 245323 (1-7), 2005

Extrinsic Electrons and Carrier Accumulation in AlxIn1-xSb/InSb Quantum Wells: Well-Width Dependence A. Fujimoto1, S. Ishida2, T. Manago2, H. Geka3, A. Okamoto3, I. Shibasaki3 1

Nanomaterials Microdevices Research Center, Osaka Institute of Technology, Osaka 535-8585, Japan 2 Tokyo University of Science, Sanyo-Onoda, Yamaguchi 756-0884, Japan 3 Asahi Kasei Corporation, Samejima 2-1, Fuji, Shizuoka 416-8501, Japan

Abstract. Hall coefficient (RH) and magnetoresistance (MR) effects were studied at room temperature and 77 K for undoped quantum well (QW) structures of InSb sandwiched by Al0.1In0.9Sb alloy grown by molecular beam epitaxy on GaAs substrates. As the result of two-carrier analyses of RH, it was found that the sheet density of the extrinsic electrons at room temperature decreases with the increase of the well width above 100 nm. At 77 K the electrons extended in the QW show the negative longitudinal MR in magnetic fields parallel to the QW, which originates in specular boundary scattering in the classical orbits at the walls of barriers.

A quantum well (QW) structure of InSb with AlxIn1-xSb barriers has been considered to be an ideal system for electronic device applications such as magnetic sensors and high-speed transistors. In this QW structure, an AlxIn1-xSb barrier layer is often selectively G-doped in order to supply the carriers to the QW [1]. This is not due to absence of extrinsic carriers but due to the small mobility of existing extrinsic electrons accumulated at the heterointerface even when neither InSb nor the barrier region is intentionally doped. In the undoped InSb QW structures, two sources of extrinsic electrons are expected: deep donors in the barrier layers and shallow donors in InSb. The electrons falling into the QW from the deep donors will result in the band bending near the interface, producing the accumulation layer. Classical size effects of magnetoresistance (MR) in semiconductors arising from the boundary scattering in the quasi-ballistic regime have been studied in the QWs [2], the ion-beam exposed channels of two-dimensional electron systems [3] and the quantum dots [4]. In the case of specular boundary scattering (SBS), negative MR appears, which originates in the suppression of the backward scattering of electrons by impurities under a magnetic fields because of the cyclotron motion. SBS requires that the length scale of roughness at the boundary is much smaller than the Fermi wavelength OF. Our InSb QW satisfies this condition. In order to investigate the transport properties of the extrinsic electrons of InSb QWs, we have measured the Hall coefficient (RH) and MR. InSb QWs

200 A. Fujimoto et al. were sandwiched by Al0.1In0.9Sb alloys grown on GaAs(100) substrates by molecular beam epitaxy. The samples were capped by a 6 nm-thick GaAs layer [5]. The lattice mismatch between the QW and the barriers is 0.5 %. The Hall and MR measurements for the QWs with different well widths (Lw = 15 ~ 300 nm) were performed under the magnetic fields (B) up to 1.5 T at room temperature (RT) and 77 K. The sample parameters for various Lw at 77 K are given in Table 1. At RT the carrier concentration for our InSb QWs is larger than the intrinsic one (= 2.0 x 1016 cm-3) in bulk InSb indicating that there are extrinsic carriers. Moreover, the B-dependence of RH for Lw = 30 nm as shown in the inset in Fig.1(a) indicates the two-carrier conduction, while for Lw = 200 nm RH is almost independent of B at RT. As regards the two carriers, we assume that one is the electron with high mobility which is extended in the QW and the other is the accumulated one with low mobility at the hetero-interface. Although there is not much difference in the sheet resistance between InSb QWs and InSb films grown directly on GaAs, the electron mobility of InSb QWs in thin regions of less than 0.5 Pm was significantly higher compared with InSb films on GaAs substrates [5]. These results indicate that there is a low-mobility layer at the hetero-interface. Fig.1(a) show the Lw-dependence of the sheet density of the extended electrons (nw) and the accumulated ones (nac) estimated by the two-carrier analysis. It is found that nw at RT increases and nac decreases gradually as Lw increases. We obtained the sheet density of extrinsic electrons (nw(ex)) at RT estimated by subtracting the one of intrinsic electrons (ni) from nw as shown in the left hand of Fig.1(a). The decrease in nw(ex) at RT with the increase of Lw above 100 nm is quite anomalous. This is different from the increase behavior followed by the saturation of nw(ex) found in InAs QWs reported in our previous paper [2]. The difference between them is the depth of the QW. It is shallow for InSb QWs, whereas it is deep for InAs QWs. There is a possibility that more electrons in InSb QWs with increasing Lw return to deep donors and the band bending near the interface becomes smaller. Therefore, a crossover from two-carrier conduction to oneTable 1. Sample parameters for InSb QWs at 77 K, where Rs is the sheet resistance, Pw (Pac) the mobility of the extended (accumulated) electrons and L0 the mean free path. Lw (nm) 15 30 70 100 150 200 300

Rs (104ȍ) 14 13 2.9 2.4 2.1 0.69 0.58

nw nac Pw Pac (1011cm-2) (1011cm-2) (103cm2/Vs) (cm2/Vs) 1.9 1.0 0.23 5.0 2.2 0.99 0.22 2.3 3.1 1.8 0.70 1.2 1.3 0.56 2.0 1.5 1.3 0.18 2.1 20 1.4 0.90 6.3 1.0 1.0 0.31 11 3.5

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Fig. 1. (a) Left figure: Lw-dependence of the sheet density of the extended electrons (nw) at RT and 77 K. Broken line represents the sheet density of intrinsic electrons (ni) at RT. ź means the sheet density of extrinsic electrons (nw(ex)) estimated by subtracting ni from nw. Right figure: Lw-dependence of the sheet density of the accumulated electrons (nac) at RT and 77 K. Inset: Normalized RH by Lw for 30 nm and 200 nm at RT. (b) Longitudinal MR under in-plane magnetic fields at 77 K.

carrier one is considered to be observed as shown in the inset in Fig.1(a). The perpendicular MR for InSb QWs at 77 K is positive one proportional to B2 due to Lorentz force, whereas the longitudinal MR in the parallel fields always starts from the negative one as shown in Fig.1(b), reaching a minimum at the characteristic magnetic field (BS) followed by the classical positive MR with B2 dependence with increasing field. As the Lw is wider, the value of BS shifts to lower fields, arising from SBS in the quasi-ballistic regime at the walls of barriers [3]. Saturation of the negative MR associated with SBS occurs at B > BS = 2mevF /edeff , where vF is the electron Fermi velocity and deff the effective QW width. As for the QW with Lw • 100 nm, we derived deff from the cyclotron diameter at BS and found that deff is almost equal to Lw as shown in Table 1. These results show that the SBS and the high-mobility electrons extended in the QW play important roles for the negative MR. 1. Liu, W. K., Zhang, X., Ma, W., Winesett, J., Santos, M. B.: J. Vac. Sci. Technol. B, 14, 2339-2342, 1996. 2. Ishida, S., Fujimoto, A., Araki, M., Oto, K., Okamoto, A., Shibasaki, I.,: J. of Crystal Growth, 301-302, 199-202, 2007. 3. For a brief review, see Beenakker, C. W. J., and van Houten, H.: 'Quantum Transport in Semiconductor Nanostructures', Solid State Physics 44, edited by Ehrenreich, H., and Turnbull, D., Academic Press. 1991. 4. Romanov, F. G., Fokin, A.V., Maude, D.K., Portal J. C. ,: Appl. Phys. Lett., 69, 2897- 2899, 1996. 5. Geka, H., Okamoto, A., Yamada, S., Goto, H., Yoshida, K., and Shibasaki, I.: J. Crystal Growth, 301-302, 152-157, 2007.

Negative and Positive Magnetoresistance in VariableRange Hopping Regime of Undoped AlxIn1-xSb/InSb Quantum Wells S. Ishida1, T. Manago1, K. Oto2, A. Fujimoto3, H. Geka4, A. Okamoto4 and I. Shibasaki4 1

Tokyo University of Science, Yamaguchi, Sanyo-Onoda, Yamaguchi 7560884, Japan 2 Department of Physics, Faculty of Science, Chiba University, Inage, Chiba 263-8522, Japan 3 Applied Physics, Osaka Institute of Technology, 5-16-1,Asahi, Osaka 5358585, Japan 4 Asahi Kasei Corporation, Fuji, Shizuoka 416-8501, Japan Abstract. Low-temperature magnetoresistance (MR) in the variable-range hopping (VRH) regime of undoped AlxIn1-xSb/InSb quantum wells was studied. The low-T resistance shows that the two dimensional (2D) Mott VRH crossovers to EfrosShklovskii (ES) VRH due to the Coulomb interaction with lowering T. The anisotropic negative MR in weak magnetic fields was explained by the quantum interference in the VRH. The in-plane positive MR in higher fields found in ES VRH regime was attributed to the spin-Zeeman effect that suppresses the hops between singly occupied states in the presence of intra-state correlation. As for the orbital MR subtracted from perpendicular MR, in deeply insulating regime the negative MR saturates above a characteristic field followed by an exponential increase of the positive MR in agreement with the quantum interference and the subsequent shrinkage of wave functions with increasing field, while in barely insulating regime of the 2D metal-insulator (MI) transition a large negative MR inexplicable survives even in the extremely high magnetic-fields.

Quantum wells (QWs) of InSb confined byAlxIn1-xSb (x = 0.1) barriers have long received much attention for the study of magneto-quantum transport [1]. In such QWs, existing extrinsic electrons accumulated at the hetero-interface even in undoped samples exhibit extraordinarily small mobility, suggesting that the carriers fall into the strongly localized states of a band-tail. In the insulating regime of the two-dimensional (2D) metal-insulator (MI) transition investigated until now in Si-MOSFETs [2] and AlxGa1-xAs/GaAs HEMTs [3], the variable-range hopping (VRH) resistance of the form U = U0 exp(T0/T) p was found with a T-independent prefactor U0, where p = 1/3 in the Mott VRH [4] and p = 1/2 in the Efros-Shklovskii (ES) VRH [5] in the appearance of Coulomb gap around the Fermi level. In the VRH, the quantum interference among alternative scattering paths in hops [6, 7] yields a weak-

204 S. Ishida et al. field negative magnetoresistance (MR) due to the orbital origin, while the spin-Zeeman effect in the presence of intra-state correlation results in a positive MR in higher fields [8]. In the present work, we study the magnetotransport properties of undoped AlxIn1-xSb/InSb QWs (x = 0.1) in the 2D-VRH regime under the magnetic fields up to 12 T in both BA and B//-configurations down to 0.4 K. The QW structures consisting of AlxIn1-xSb buffer/barrier (700 nm), InSb (Lw) and AlxIn1-xSb barrier (50 nm) layers (x = 0.1) with a cap layer of GaAs 6nm thick were grown on GaAs(100) substrates by MBE. The lattice mismatch between the QW and the barriers is 0.5%. The well widths are Lw = 30 and 70nm with the sheet carrier density of ns = 3 and 5 u1011 cm-2, respectively. In the magnetic fields parallel to the 2D plane, we measured both cases of (B//I) and (BAI), confirming no anisotropy between these configurations. The low-temperature resistance of our samples appears to follow the form U = U0 exp(T0/T)p accompanied by the crossover from p = 1/3 in the Mott VRH to p = 1/2 in the ES VRH with lowering T, which is evidently shown in Fig. 1 where U in the unit of quantum resistance h/e2 (25.9 k:) is plotted versus T-1/3 in (a) and T-1/2 in (b). The prefactor appears to be U0 = UM ~ h/e2 in the Mott VRH, and U0 = UES ~ 2h/e2 in the ES VRH. The values of UM and U(S are about two times what are obtained on 2D electron systems (2DES) in Si-MOSFETs [2] and G-doped AlxGa1-xAs/GaAs hetero-structures [3]. The fits of U(T) in Fig. 1 (a) to the Mott VRH law yield [ from the Mott temperature T0 = TM = 13.8/ (SkBg[2) as well as Rh = RM = (1/3)[(T0/T), where

Fig. 1. Resistance plotted in the unit of h/e2 versus T-1/3 down to 1.4 K in (a) and T-1/2 in (b). Insets: 'U/U(0) depicted in low BA- and low T- regions for Lw = 30 and 70nm in (a) and (b), respectively.

Negative and Positive Magnetoresistance in Variable-Range Hopping 205 kB is the Boltzmann constant, g = m*/(Sƫ2) the 2D density of states, Rh the average hopping length and [ the localization length:[~ 290 nm and RM ~ 130 nm at 4.2 K for Lw = 70nm. Also, the fits of U in Fig. 1 (b) to the ES VRH law yield Rh = RES = (1/4)[(TES/T), RES ~ 53 (92) nm at 4.2 (1.4) K with[~ 69 nm for Lw = 30nm (for Lw = 70 nm, RES ~ 125 nm at 1.4 K). The inset of Fig. 1 (a) and (b) depicts 'U/U(0) = [U(BA) – U(0)]/U(0) in BAconfiguration for Lw = 70 and 30nm, respectively. The low-field negative MR growing with lowering T arises from the quantum interference due to orbital origin in the VRH. Theories [6, 7] predict that the BA-field suppresses destructive interference among the alternative scattering paths from initial to final state in a long-range hop leading to negative MR and its field dependence is determined by the flux ) = BAA penetrating an area A in which phase coherence is maintained. The area A is that of an ellipse of width (Rh[)1/2 and length Rh. As a result, the negative MR grows with B = BAproportionally to B2 in vanishing fields and linearly with B in moderatefield region, followed by the saturation around Bswhen ) = BsA = h/e corresponding to the flux quantum. This implies that for moderate magnetic fields –'U/U(0)  BA = Rh3/2(T, B)[ 1/2(B)B, and for vanishing fields –'U/U(0)  (BA)2 = Rh3(T, B)[ (B)B2. Since Rh = RES  T–1/2 in ES VRH, theory predicts that – 'U/U(0) = f1(T)B  T–3/4B in moderately weak fields and – 'U/U(0) = f2(T)B2  T–3/2B2 in extremely weak fields [10] assuming that Rh and [ are nearly independent of B, which was confirmed from fits to the detailed data of 'U/U(0) in ES VRH regime. Further, we also confirmed the relations f1(T)  T–1/2 and f2(T)  T–1 in Mott VRH regime, being consistent with Rh = RM  T–1/3 in this regime. In an ideal 2D system, there should be no negative MR in B-configuration [9]. Nevertheless, we observe it for B// [10] possibly because of a finite thickness of the accumulation layer and (or) a background concentration of shallow donors in the QW. Regarding the positive MR in higher fields, we can observe it in both BA and B// for the ES VRH regime. Especially, Uxx(B//) shows a large initial increase with B followed by saturation as shown in Fig. 2. Quite similar results were observed in the insulating G-doped AlxGa1-xAs/ GaAs heterostructures [11, 12] and also Si MOSFETs [13, 14]. Kurobe and Kamimura [8] proposed that the alignment of electron spins due to the spin-Zeeman effect in the presence of intra-state correlation suppresses the hops between singly occupied states via the Pauli exclusion principle.

206 S. Ishida et al.

Fig. 2. Uxx(B) and Uxx(BA) in high-field region: left-hand panel for Lw = 70nm in low Ts down to 0.4 K and right-hand panel for Lw = 30 nm at 1.7 and 4.2K. Insets:'Rorb(B)/R(0) subtracted from Uxx(BA) for Lw = 70nm in left-hand panel and 30 nm in right-hand panel. The arrows in the insets indicate Bs estimated.

This mechanism yields a linear positive MR that saturates in high B-field when the spins are fully aligned ignoring the energy dependence of [, being consistent with the behavior seen in Fig. 2. On the other hand, Uxx(BA) in Fig. 2 exhibits an apparently complicated feature. Then, the orbital effect was subtracted from Uxx(BA) = Vxx-1(BA) data for B > 1 T, simply assuming 'Rorb(B)/R2(0) = 'Vxxorb(B) = Vxx(BA) - Vxx(B). The results of orbital MR ratio 'Rorb(B)/R(0) obtained are depicted in the insets of Fig. 2. In the deeply insulating regime (Lw = 30 nm) the negative MR saturates above Bs followed by an exponential increase of the positive MR in agreement with the quantum interference in weak fields and the subsequent shrinkage of wave functions with increasing B [10], while in barely insulating regime of the 2D-MI transition (Lw = 70 nm) a large negative MR inexplicably survives above Bs even in extremely high B-fields.

Negative and Positive Magnetoresistance in Variable-Range Hopping 207 References 1. Kohdaparast G. A. et al.: Phys. Rev. B 70, 155322-1-6, 2004 2. Mason W., Kravchenko S. V., Bowker G. E. and Furneaux J. E.: Phys. Rev. B 52, 7857-7859, 1995 3. Kohndaker S. I. et al.: Phys. Rev. B 59, 4580-4583, 1999 4. Mott N. F.: J. Non-Cryst. Solids 1, 1-, 1968 5. Efros A. L. and Shklovskii B. I.: J. Phys. C 8, L49-, 1975 6. Nguyen V. L., Spivak B. Z. and Shklovskii B. I.: Sov. Phys.–JETP 62, 1021-1029, 1985 7. Sivan U.,Entin-Wohlman O. and Imry Y.: Phys. Rev.Lett. 60, 1566-1569, 1988 8. Kurobe A. and Kamimura H.: J. Phys. Soc. Jpn. 51, 1904-1913, 1982 9. Ishida S. et al.: phys. stat. sol. (b) 205, 161-165, 1998 10. Ye Q. Y., Shklovskii B. I., Zrenner A., Koch F. and Ploog K.: Phys. Rev. B 41, 8477-8484, 1990 11. Kohndaker S. I., Pepper M., Ritchie D. A. and Schlimak S. I.: phys. stat. sol. (b) 218, 181-183, 2000 12. Yoon J., Li C. C., Shahar D., Tsui D. C. and Shayegin M. Phys. Rev. Lett. 84, 4421-4244, 2000 13. Pudalov V. M., Brunthaler G., Prinz A. and Bauer G.: Phys. Rev. Lett. 88, 076401-1-4, 2002 14. Mertes K. M. et al.: Phys. Rev. B 60, R5093-R5096, 1999

Semimetal-Insulator Transition in Two-Dimensional System at the Type II Broken-Gap InAs/GaInAsSb Single Heterointerface K.D. Moiseev1, M.P. Mikhailova1, R.V. Parfeniev1, J. Galibert2, J. Leotin2 1

A.F. Ioffe Physico-Technical Institute, RAS, 26 Politekhnicheskaya, St. Petersburg, 194021, Russia 2 L.N.C.M.P. 143, avenue de Rangueil, Toulouse, 31432, France

Abstract. The magnetotransport properties of a two-dimensional (2D) electron-hole system localized on a single type II broken-gap heterointerface have been studied in a pulsed magnetic field up to 35 T. The step-like decrease of the driving current indicates a conductivity path through localized states of the 2D system. Up to ~20 T, Hall resistance (Rxy) is completely antisymmetric, while, at the onset of the insulating state, Rxy switches its behavior to become totally symmetric which does not depend on the polarity of the applied magnetic filed. The insulating behavior is ascribed to the formation of energy mini-gaps in the 2D system spectrum due to the intersubband mixing at the type II broken-gap heterointerface and anticrossing of Landau levels of electrons and holes.

1 Introduction We examine the quantum Hall effect and magnetotransport properties of a bipolar system of coupled electrons and holes and demonstrate that such a system shows qualitatively different behaviour to that observer for a single carrier system [1,2]. The coupled electron-hole system can introduce the new possibility the edge states of electrons and holes subsystems at the interface may interact breaking the normal quantum Hall conditions. Here we study the behaviour of conductivity through the localised states formed by interband mixing due to the electron and hole subbands interaction.

2 Experimental and results Lattice-matched single GaIn0.06As0.13Sb/InAs heterostructures with planar and abrupt heteroboundary were grown by liquid-phase epitaxy [3]. The pGaInAsSb epilayers were unintentionally doped with a residual hole concentration of ~5×1016 cm-3 at 77 K whereas the p-type InAs substrate was

210 K. D. Moiseev et al. deliberately compensated with Mn to a hole concentration of p~1017 cm-3 at T=300 K. The P-GaIn0.06As0.13Sb/p-InAs heterostructure demonstrated high value of the Hall mobility for electrons (PH= 6.0×104 cm2V-1s-1) in low magnetic fields (B=0.1 T) at the temperature range 1.4-80 K [4]. Type II broken-gap GaInAsSb/InAs heterojunction is the system with the ability to possess both 2D-electrons and holes in equilibrium through intrinsic charge transfer without doping or the application of an electrical field bias. Electrons and holes are spatially separated and localized in self-consistent quantum wells on both sides of the heterointerface. The samples studied contained the coupled 2D electron-hole gas consisted of the electron and hole layers differing from a strained InAs/GaSb sandwiched system reported elsewhere [1]. In such heterojunction there is 2D-electron channel at the heterointerface with two energy subbands with a sheet electron concentration ne=6.2×1011cm-2 interacting with holes localized at the interface with concentration ph~1012 cm-2. MK-746/2 T=1.8 K 4

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When the net carrier concentration (nnet = ne - ph) is small, a special condition can be achieved in quantizing magnetic fields assisted by nearly equal numbers of occupied electron and hole Landau levels, but this was not observed at B<20 T due to low mobility values, ZcWh << 1. We found out that the 2D electron-hole gas exhibits insulating behavior in high magnetic fields B>20 T in the ultra-quantum limit when the Fermi level located between the last electron and hole Landau levels or in the region of overlapping of electron states and interface hole states [5]. As shown in Figure 1a, in this insulating state at B>20 T the Hall effect disappears and Hall voltage becomes symmetric under magnetic field reversal in contrary to the case with 2D single-carrier conductivity observed on Si MOSFET’s [2].

Semimetal-Insulator Transition in Two-Dimensional System 211 Hall resistivity rises without a significant increase in the sample resistance (Rxx) in high magnetic fields (B>20 T) that indicates on hopping conductivity in the insulator state (Fig.1b). A contribution of the quantized hole system is observed as a weak plateau in Rxy(B) near 20 T and a local extremum in Rxx(B) near 23 T. The change of the sign of Rxx can be ascribed to the change in the flowing path of the driving current. Moving of the last Landau level up through Fermi level results in hopping conductivity across totally localized states that are due to a hybridization of interface edge states [5] with an account of the surface potential modulation.

3 Conclusion We have demonstrated that the coupled 2D electron-hole system can oscillate between conducting and insulating states as the magnetic filed increased. A qualitative explanation has been proposed based on the formation of an energy gap due to the anticrossing between electron and hole subbands at the type II broken-gap interface. The insulating states have been shown to have unusual behaviour when the Hall resistance becomes symmetric with respect to field reversal.

4 Acknowledgement This work was supported by the Presidium of RAS grant, the “Leading scientific School” 5596.2006.2 grant, RBRF 06-02-16470 grant and the grant of OFN RAS.

5 References 1. Nicholas, R.J., et al : `Metal-insulator oscillations in a two dimensional electronhole system`, Phys. Rev. Lett., 85, 2364-2367, 2000 2. Dolgopolov, V.T., et al : `Metal-insulator transition in Si inversion layers in the extreme quantum limit`, Phys. Rev. B, 46, 13303, 1992 3. Moiseev, K.D., et al: `Type II broken-gap InAs/GaIn0.17As0.22Sb heterostructures with abrupt planar heteroboundary` Semicond., 34, 1438-1442, 2000 4. Mikhailova, M.P., et al, `Interface-induced optical and transport phenomena in type II broken-gap single heterostructures` Semicond. Sci. Technol., 19, R109-R128, 2004 5. Averkiev, N.A., et al: `Peculiarities of energy band spectrum and quantum magnetotransport in type II heterojunctions`, Sol. State Phys., 46, 2083-2091, 2004

Magnetoexcitons in Strained InSb Quantum Wells W. Gempel1, X. Pan2, T. Kasturiarachchi1, G.D. Sanders2, M. Edirisooriya1, T.D. Mishima1, R.E. Doezema1, C.J. Stanton2 and M.B. Santos1 1 2

Homer L. Dodge Dept. of Physics & Astronomy, University of Oklahoma Department of Physics, University of Florida

Abstract. Magneto-optical measurements of InSb quantum wells show absorption features due to transitions between Landau levels of the conduction and valance subbands. The energies and intensities of the strongest features are well explained by a modified Pidgeon-Brown model that explicitly incorporates pseudomorphic strain.

1 Introduction The small effective mass of electrons in InSb has been recently exploited in nchannel field-effect transistors (FETs) with high switching speeds and low supply voltage [1]. For CMOS applications, p-channel FETs with high hole mobility will be required. Improvements are expected in spin devices with pchannels since the Rashba splitting in holes is estimated to be much larger than for electrons in the same semiconductor [2]. In order to characterize the dependence of the valance bands on strain and confinement, we performed experimental and theoretical studies of interband magneto-optical transitions in strained InSb quantum wells.

2 Experimental and Theoretical Methods The heterostructure was grown by molecular beam epitaxy on an [001] GaAs substrate [3]. The structure contains 40 strained InSb wells that are 15 nm thick and separated by Al0.10In0.90Sb barrier layers that are 50 nm thick. A 0.5 Pm-thick AlxIn1-xSb buffer layer with a graded Al composition was deposited between the multiple-quantum-well (MQW) layers and the substrate in order to reduce the density of dislocations that result from the ~14% lattice mismatch between the substrate and the MQW layers. A 3 Pm Al0.10In0.90Sb, which is almost completely relaxed, was grown just prior to the MQW layers. The InSb wells are compressively strained to the lattice constant of the Al0.10In0.90Sb layer. We used a Fourier Transform Infrared spectrometer to monitor the transmission through the MQW structure as a function of photon

214 W. Gempel et al.

Magnetic Field B (T)

frequency. In previous exciton studies without a magnetic field, we deduced the band offsets for InSb/AlxIn1-xSb [3] and the strain parameters for InSb [4]. In the current study, a perpendicular magnetic field of 0”B”7.5 T was applied during far infrared transmission measurements at a temperature of 4.2 K. Our theoretical model for MQW magnetoabsorption is based on the Pidgeon-Brown model that includes spin-up and spin-down conduction electrons, heavy holes, light holes and split-off holes for a total of eight bands in the bulk [5]. In addition to adding a pseudomorphic strain energy to the effective mass Hamiltonian, we include the full wavevector dependence of the electronic states in bulk materials. The quantum confinement potential arises due to variations in the band gap as a function of position in the structure. The effects of quantum confinement in the MQW are easily included by making the replacement kz = - i d/dz in the effective mass Hamiltonian of Ref. [5] and solving the resulting Schrödinger equation for the electronic energies and envelope wavefunctions. We approximate the derivative operator d/dz by a finite difference expression. This converts the differential equation into a matrix eigenvalue problem that can be numerically solved by standard matrix diagonalization routines. 8

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Fig. 1. (a) Experimental data set of normalized absorption spectra, each taken at a constant value of B between 0 and 7.4 T in increments of 0.1 T. (b) Calculated data set of normalized absorption spectra.

3 Experimental and Theoretical Results Figure 1a shows a set of experimental normalized spectra, -T(B)/T(0) versus photon energy E where T(B) is the transmitted intensity at an applied magnetic field B. The spectra strongly reflect the dispersion relations for holes in the valance band and electrons in the conduction band. The experimental data in Fig. 1a are well explained by our theoretical model. Figure 1b shows the results of the model calculation including the effects of

Magnetoexcitons in Strained InSb Quantum Wells 215 pseudomorphic strain. Bright (“allowed”) transitions are expected between CB and HH, or LH, Landau levels (LLs) with the same LL and subband indices. For example, the brightest transition is between lowest LLs (LL index 0) of the lowest CB and HH subbands (subband index 1), c10-h10. Spin-split bright features for the c11-h11 and c12-h12 transitions are also prominent. In addition to identifying the bright exciton transitions, we identify several dark (“forbidden”) transitions, including c10-h30 and c10-h20. . The inclusion of pseudomorphic strain in our theoretical model has a pronounced effect on the computed normalized absorption spectra. Figure 2 shows experimental data and model calculations with and without the inclusion of strain effects at two magnetic fields. By comparing the experimental and model spectra, one can see that good agreement is only obtained when strain is taken into account. 7.4 T

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0.28 0.30 0.32 0.34 0.36 0.38 0.40 0.42 0.44 Energy(eV)

Fig. 2. Experimental data and model calculations for absorption spectra at (a) 7.4 T and (b) 6.0 T. The zeros of absorption are shifted for clarity.

4 Conclusion Observed magneto-optical transitions across the band gap in InSb quantum wells are well explained by a modified Pidgeon-Brown model that explicitly includes pseudomorphic strain and confinement effects. This agreement demonstrates the potential usefulness of the model for designing p-type InSb quantum wells.

References 1. Chau, R, et al.: 2005 IEEE CSICS Technical Digest, 17-20, 2005. 2. Gvozdic, D.M. and Ekenberg, U.: Europhys. Lett., 73, 927-933, 2006. 3. Dai, N., et al.: Appl. Phys. Lett., 76, 3905-3907, 2000. 4. Kasturiarachchi, T., et al.: Appl. Phys. Lett., 88, 171901, 2006. 5. Sanders, G.D., et al.: Phys. Rev. B, 68, 165205, 2003.

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