Luminescence in Crystals D. CURIE Professor ill the Faculty of Sciences, Paris Translated by
G. F. J. GARLICK University of Hull
Professor of Physics,
LONDON: NEW YORK:
METHUEN & CO LTD JOHN WILEY
& SONS INC
LUMINESCENCE CRISTALLINE This
in 1960 by Dunod of Paris
translation,
©
1960 by Dunod
incorporating
was
first published
later revisions by the
and translator, first published in 1963
1963 by Methuen and Co Ltd Printed in Great Britain by Butler and Tanner Ltd Frame and Lon don
©
Catalogue No (Methuen) 2/2578/11
author
Contents
PREFA CE
I
2 3 4
page xi
INTR O D U CTI O N
Luminescence Fluorescence and phosphorescence Relation between life time and fluorescence efficiency Centres and traps in the different classes of phosphorescent solids CHA P T ER I
DIPOLE A N D QUADRUPOLE R ADIATION: TIES OF EMISSION AND ABSORPTION I. Dipole and Quadrupole Moments
1 3 5
PROBABILI-
Electrostatic potential due to a charge distribution 2 Potentials due to dipoles and quadrupoles 3 Developmen t of potential due to a multipole in spherical harmonics
1
10
II 11
12
14
Maxwell's equations Solution of Maxwell's equations by the retarded potential method 3 Systems in harmonic vibration 4 Potential distribution among successive multipole orders
21
1
21
1
II. Dipole and Quadrupole Radiation in Electromagnetism
2
The Hamiltonian of the particle The transition probability 3 Magnetic dipole and electric quadrupole radiation 4 Selection rules
ID. Probabilities of Radiative Absorption and Emission
2
V
14 14 15
16 17
22
25
25
vi
Contents
CHAPTER
II
SPECT RA AND THE CON ( EXAMPLE OF ALKALI HALIDES ) page 31
EMISSION AND ABSORPTION
FIGURATIONAL COORDINATE MODEL
THALLIUM
ACTIVATED
I. Structure of a 'Non-photoconducting' Luminescent
Solid: KCl(Tl)
2 3
Energy leve l s in
t he matrix lattice of KC! Energy levels of the fre e thallium ion L oca t i o n of t h e g rou n d state 1S0 of TJ+ in the energyband schem e of KC! II. Absorption and Emission Phenomena in KCl(Tl),
the
2 3
Configurational Coordinate Diagram
Introduction to the m odel The inte racti o n between T!+ and ClPositi o n of the absorption and emission band maxima HI. Calculation of Emission and Absorption Spectra from the Configurational Coordinate Model
I 2 3 4
Stat e ment of
the problem Ca l culati o n of energy distribution in the sp ectrum Calculation usin g a semi-classical app ro xi matio n Quantum-mechanical calcul at i o n fo r the case w h e re th e ion vibr a t ion s v, a nd 1'u are e qua l
32 32
33 35
36 36
37
41
44 44 45 47 53
CHAPTER Ill EXPERIMENTAL
DETERMINATI O N AN D
USE Of CON-
59 59
FIGURATIONAL COORDINATE DIAGRAMS
2 3
Tun gs ta tes , will e m ites , halophosphates, &c. Rel ation between F centre a bsorpti on bands and luminescence emission ascribed to F centres
the
The Smakula formula
CHAPTER
2
I. The 'Momentum' Selection Rule and its Consequences Conservation of m om en tum in optical transitions from band to band Discussion
68
IV
OPTICAL TRANSITIONS I N A PHOTOCONDUCTING
CRYSTAL
63
76 77 77
78
Contents
11. Luminescence Emission near to the Absorption Edge {'Edge Emission') page
S pectra for electron-positive hole recombination in
2 I
2 3
4 5
germanium Spectra of the Ewles-Kroger type
Ill. Absorption Spectra and Exciton Emission
The experimental evidence Theoretical aspects Model for the electron in orbit around a hole; hyd rogenlike spectra Deviations from the hydrogenlike formula Stark and Zeeman effects for the exciton CHAPTER
1 2 3
V
LUMINES CENCE CENTRES IN P HOS P HORESCENT SULP HIDES I. Constitution of Phosphorescent Sulphides Preparation Numerical values of the energy-band gap for phosphors of the ZnS type Observations on the nature of binding in ZnS 11. Luminescence Centres and Emission Spectra for ZnS and CdS
1
2 3 4
Copper as an activator Silver and gold as activators Rad iative recombination due to vacancies Manganese as an activator
Ill. Optical Transitions involving Localized Levels
Luminescence centres and electron traps in a photoconducting crystal phosphor 2 Various types of centres in photoconducting phosphors CHAPTER
VI
E LECTRON TR A PS, P H OSP H O RESCEN C E , THER MOLUMINESCENCE
vii
84 84 86 90 90 91
92 95 96
107 107 107 108 1I 1 113 114 119
120 121 125 125
127
142
I. Definition of Traps. Mean Life Times, Effective I
2
Cross-sections
Definitions Thermal activation of trapped electrons
142 142 143
Vlll
3
4
2
3
Contents
of Williams and Eyrin g page 146 escape probability and the effective capture cross-section of the trap 146 II. Decay of Luminescence 147 Monomolecular and bimolecular mechanisms 147 Kinetics of p h o s p h o rescen ce i n photoconducting
Therm o d yna mic expression Relation between t he
Investig at ion s of trap distri butions by analysis of
ex peri m en tal d ecay cu rve s Ill. The Method of Thermoluminescence Curves
2
Description of the method Simpl e theory of the thermolumincscence
3
Thermoluminescence curve measurements
4
150
phosphors
Randall a n d Wilkins
curve due
156 160
to
using two
different war mi ng rate s
Observations on thermoluminescence e qu a ti o n s IV. Data on Electron Traps in Various Phosphors 1 ZnS(Cu) p ho s pho rs 2 CdS phosph o r s 3 CaS(Bi) ph o spho rs 4 KCI(Tl) phosphors 5 Thermoluminescence of alkali halides with col ou r centres
160 161
163
163
165 165
170 171 171 173
CHAPTER V I I THERMAL AND OPTICAL ACT! VATION OF ELECTRONS: QUENCHING EFFECTS
TRAPPED
I. Traps, Thermal Activation and Optical Stimulation in the Configurational Coordinate Model D esc ripti o n of the escape from t ra p s 2 O p t i cal activation energies 3 Description of e ffec t s shown by the highly s timulable alkaline earth sul ph id es 4 S timulat i on and q uenching spectra of zinc a n d c a d m i um sulphides
190 190 190
192 195
198
IX
Contents
II. Non-radiative Capture by Impurity-states, Thermal and Optical Quenching of Luminescence
1 2
Non-radiative captu re by traps Thermal quenching of luminescence Ill. The Theory of Multiphonon Transitions CHA P TER V I I I ENERGY TRANSFER, SENSITIZATION CENTRATION QUENCHING
page 202
AND CON-
I. Resonance Transfer between Atoms with Overlapping
Electric Fields
202 203 208
220 221
11. Other types of energy transfer without charge displacement
1
2 1
2
Reabsorption of emitted light Transfer by electronic exchange between neighbouring atoms m. Energy Transfer by Hole Migration
Riehl's excitation mechanism The Schon- Klasens theory of energy transfer between two centres IV. Energy Transfer by Exciton Migration
224
224 225 226
226 227 229
C H A P T E R IX ELECTROL UMINESCENCE AND ELECTROPHOTOL UMINESCENCE I. 'Pure' or 'Intrinsic' Electroluminescence 1 Introduction: Historical. The electroluminescent cell 2 Discussion of the electroluminescence mechanism 11. Electroluminescence due to Charge Carrier Injection Electroluminescence in single crystals or thin films of zinc sulphide 2 Electroluminescence of cadmium sulphide 3 Electroluminescence of silicon carbide 4 Luminescence in electrolysis 5 Infra-red electrolu minescence in germanium 6 Other investigation s
2 37 237 237 248 256
258 259 259 26 I 262 265
X
Contents
2
1
3
4
5
Ill. Electrophotoluminescence page Pohl effect Permanent quenchin g of luminescence in Zn S ( Cu) by electric fields Permanent enhancement of l u m inescence by electric fi elds Photoelectroluminescence Application of electroluminescence in the development of The Gudden and
image amplifiers
CHAPTER
2 3
I. Cathodoluminescence
Introduction
274
288
295 298
301
Characteristics of the main crystalline scintilla tors of res p onse Size of the excitation channel, density of ionization and refilling of electron traps IV. Radiation Damage in Phosphorescent Solids Appendix I. Phosphors for monochrome and colour Linearity
television
Appendix II. Rel at io n between photometric
288
291
Historical
4
269
272
the excita-
tion process
3
267
288
The general laws of cathodoluminescence Penetration of fast electrons into matter and 11. X-ray Excitation of Phosphors Ill. Radioluminescence - Scintillations
2
265
X
C A T H O D OLUMI NES CEN C E , RA DIOLUMINES C E N C E , S C INTIL L A TIONS. EFFE CTS OF HIGH-ENE R GY R A DIATION ON PHOSPHORESCENT SOLIDS
1
265
units of
301
302
304 307 308
314
luminescence
319
GENERA L BIBLIOGRAPHY
325
SUBJECT INDEX
329
Preface This book contains the main topics developed by the author in his lectures given in the Faculty of Science of the University of Paris.
The treatment is mainly theoretical, though attention is given to the more important applications of luminescent processes, for instance, phosphors for fluorescent lamps, X-ray screens and television tubes. This English edition is for the main part a translation of a book entitled Luminescence Cristalline, published by Dunod. Many ad ditions have been incorporated, the most important being the extra chapters on electroluminescence and cathodoluminescence processes. Unfortunately the manuscript was written just before the advent of Lasers and so it has only been possible to include a few preliminary references on this item. However, a short discussion on the lumin escence of ruby is included . Professor G. F. J. Garlick has undertaken the translation and no one could be better qualified. My thanks are due to him for the trans lation and for many interesting discussions on the topics of the book. Professor Garlick, who acted as an impartial translator, is not responsible for my errors.
MARCH
D. CURIE
1962
xi
Introduction
Under the general term luminescence we include luminous em iss i o n not purely thermal in origin. Accord i ng to the mode of excitation we d istinguish : - photoluminescence pro duced by absorption of light (or usually ultra-violet radiation). -luminescence excited by accelerated partic l es (cathodolumines cence if electrons are used) or more generally by high energy radia tion- X-rays or y-rays as well as particles such as (f. and fJ particles, protons, fission fragments, &c. (radioluminescence). In effect, all these emissions are due to excitation by the secondary electrons produced. If the i ndivi dual emissions due to single particles are consid ered these are known as scintillations and are used in the detection of the s pecific particles or quanta. - electroluminescence produced by the application of an electric field. - the phenomeno n of triboluminescence, radiation being emitted by a substance subject to mechanical forces, e.g. grinding of sugar in a mortar; frictio n produces electrical charges and either d i scharges occur in the body of the material or s omething like electrolumines cence occurs. - chemiluminescence and bioluminescence in which emission accom panies a chemical reaction (oxidation of phosphorus in a humid atmosphere); or a bi o logi cal pr o cess (glo w worm: oxidatio n of luciferin). The foll o wi n g text is confined to lum i nescence in crys ta l s exclud in g the last group of phenomena above as well as luminescence in gases, vapours, and organic l iquids or solution s 1. Luminescence
which is
.
Fig. l shows a typical energy-level scheme used i n luminescence: the emitting system is raised by excitation from the ground state f to the excited state e; return to the ground state occurs with emission of 2. Fluorescence and phosphorescence
1
2
Luminescence in Crystals
light. The emission occurs at a time t a ft er excitation, t b ei n g the life time of t h e excited st ate and being of the ord e r of I o-s sec for atomic d ipole emission; it is of t he order of IO-.; sec in phosphorescent sulp h i d es of the ZnS(C u) typ e . In practice, the main concern is with visible emission, but for some years studies have been made of luminescence A bsorplian Emrssron in the ultra violet and in the infra red . Such an energy scheme applies equally well toX-rays and y-rays; hence we speak of X-ray or y-ray fluorescence. However, Fig. I some phenomena of radiation emission (e.g. brehmsstrahlung, Cerenkov r adiatio n ) cannot be described by a diagram of the type in Fig. 1. For fluorescence the system m us t remain in the excited state fo r a time t, large compared with the frequency of the emitted radiation 01avi !ov), and this is not so for suc h emissions. The question of their inclusion amongst lu minescen ce phenomena has been d i sc us se d , but it i s more usual to group them in another category with such phenomena as Rayleigh sca tte ring and the Raman effect. Fig. 1 is descriptive o ffluorescence, the return to the ground state occu rri ng by spontaneous emission. Fig. 2, which includes a meta stable level m (trap or t rapp ing state), represents the case for phos phorescence. The system on excitation to the state e c an make a transition to the state m, which being by definition metastable d oes not allow of further transition m __, f e Thus the system will not change from E 1 the s tate m unless it receives an energy E lifting it again to the excited state e. Emission Then phosphorescence occurs (if there Absorption is no re tur n to the state m, i.e. recap-
ture into the trap) usually identical in emission with fluorescence (although Fig. 2 the relative intensities of the various emission bands may be different), but d e lay ed in time by an a mo u n t r equal to the time spent i n the s tate m. If the energy E (us ual l y called the trap de pth) is provided by a thermal activation, then in gen eral :
�
=
sexp
(ii)
Introduction
3
where r � t, s is a constant, k is Boltzmann's constant, and T is the absolute temperature. Definition due t o J. and F.
Perrin
'The phenomenon is fluorescence if the emission takes place by one or more spontaneous transitions. 'If, on the contrary, the emission occurs with the intervention of a metastable state followed by return to the excited state due to addi tion of energy, then this is phosphorescence.' A luminescence emission with a life time of about 10-s sec is indis putably fluorescence. In contrast, an effect where emission persists for the order of a second, or a longer duration, after excitation ends is almost always phosphorescence. However, in the intermediate time range, say I0-1 to I0-5 sec, it is difficult to decide between a long fluorescence (forbidden transition) and a short phosphorescence (due to very shallow traps). A study of the variation of the luminescence decay with tempera ture enables the distinction to be made. The decay of fluorescence is little dependent on the temperature, but the duration of phosphores cence is strongly temperature-dependent (determined by a Boltzmann function). The emission during excitation is often defined as fluorescence, but this is wrong in the case of a phosphorescent solid since at least a part of the emission is phosphorescence. In the case of zinc sulphides it is not certain that all electrons spend a short time in shallow traps. The activation energy E for escape from the traps is usually pro vided by the thermal agitation of the environment ; hence the occur rence of the Boltzmann function. However, it can also be provided by absorption of an incident photon of sufficient energy, this being known as optical stimulation. A burst of light is obtained when a previously excited phosphorescent solid is irradiated by light of longer wavelength than that of the excitation (usually infra-red irradiation). Relation between life time� and fluorescence efficiency 1} (F. Perrin)
Under certain conditions the life time 7: for the fluorescence shows an appreciable dependence on temperature, the decrease in life time being accompanied by an associated fall in the fluorescence efficiency rJ (see Fig. 3).
3.
4
Luminescence in Crystals
The fluorescence of uranyl salts (002)2+ is due to a transition in the life time being of the order of I0-3 sec for the non-perturbed free ion. In these brilliantly t fluorescent salts, e.g. uranyl nitrate, the life time i � I0-3 sec is usually found to depend very little on temperature and the quantum yield of fluorescence is of the order of 100 per cent. In contrast in other salts such as RbU02(CH3C02)3, i is much smaller and I j, temperature-dependent. i At 4°K i � 1780 f.£Sec, at 293°K i � 57 ,asec and the efficiency is very small (Hall and Dieke). This effect is, however, never of I .. ; the same order as those observed in phos 0 T phorescence for the trapping life times. For Fig. 3 the traps giving the visible phosphorescence of zinc sulphide (ZnS-Cu) wi t h E = 0·65 eV and s � 109 sec-I, the trapping occurs for 3 min at ordinary temperatures and for 1,600 days at -l00°C and i � 10800 sec at 4°K, if it is sensible to extra polate a formula to such proportions. The explanation lies in a competition between radiative transitions with a probability Pr depending little on temperature and non-radia tive transitions ('de-excitation' of the material by thennal a gitatio n ) having a probablity Pnr increasing with temperature. The normal life time of the fluorescence will be 1/pr, but the ob served life time is given by the uranyl group,
i-:�1 I I
I
-�-
�
---·
__ ···--·
- -·
":t 1
=
Pr+Pnr
If there are no non-radiative transitions at zero temperature the life time is 1
-=pr 'i(O)
and so
Pr 'i('l') 1J(T) = - = -'i(ol
Pr+P,r In general, radiative and non-radiative transitions compete even at absolute zero, and so we have the characteristic fluorescence relation 'i(T) -
=
1)(T) -
Introduction
5
In phosphorescence the introduction of non-radiative transitions usually shortens the decay time, but a simple relation such as the above is not found. The phenomenon was first studied by Perrin i n organic fluorescent solutions and later by Kroger and Hoogenstraaten for willemite (Zn 2 Si04- Mn), &c.
The crystals of phosphorescent solids known as 'conventional' are not photoluminescent in the pure state : the luminescence is due to the addition of a luminogen or activator in the form of a trace im purity. For example, in phosphorescent sulphides, copper, man ganese, bismuth , &c. - ZnS(Cu), CaS(Bi) or ZnS: Cu, CaS: Bi, &c. In some cases crystal lattice defects provide localized levels, like those of impurities, which play the part of the activator. The exceptions, that is, crystals which sh ow photoluminescence in the pure state, are materials containing groups which function like foreign molecules in the matrix crystal from which they are separated by screening (J. T. Randall). For example, in uranyl salts such as (N03)2U02, nH20, the U02 2 + group responsible for luminescence behaves as a separate molecule surrounded by a shield due to the water molecules of hydration. The luminescence disappears on heat ing but reappears when water is reintroduced. Certain rare earth salts are luminescent (Eu, Gd, Sm, Tb, Dy), due to transitions of the in ternal 4f electrons. In these cases the crystalline state is not necessary for luminescence and it is observed when the ions are in solution or 4.
Centres and traps in the different classes of phosphorescent solids
Leaving aside these exceptions, we have introduced two kinds of states involved in luminescence : - luminescence centres which contain levels responsible for the luminescence emission spectrum. - electron traps responsible for the phosphorescence or persistence of emission after cessation of excitation. We follow Mott in distinguishing two main groups of l uminescent solids : in vitreo.
A. The cases where the emitting system is quasi-atomic (crystals often known as non-photoconductors). This does not mean that photo
conductivity cannot be excited by absorption of radiation of suitable
Luminescence
6
in
Crystals
wavelength, but that under the usual conditions of l u minesce nc e ex
�
7
lp
, ==3p0
ev
is
j4 '
13
{� Fig. 4
2 t
O
citation the photoconductivity is n egligible and it is not necessary to raise electrons i nto the co nduction band in orde r to pro-
duce luminescence.
The typical solid of this class is
a first ap pro ximatio n the TJ+ ion. and e of Fig. 2 are ap p licable to this ion (Fig. 4). The scheme used in this case is thus identical with that of Jablon ski for organic mole
being to
The
levels denoted by J, m
cules and dyes.
have the
The heavy atoms Hg, TJ+, Pb2+, Bi3+
belong to this class and are iso-electronic with Tl-1-, i.e. they
The homogeneous series of ions :
same set of electronic energy levels. Ga+Ge2+ . .
may also be added to this class (Tech.
B.
KCI(TI),
the system responsible for luminescence
. In+Sn21-
B. Louchtchik and e o -worke rs) .
Cd S (Ag) , &c. Exci t ati on
Photoconducting, phosphorescent crystals typical
of which
the valence band or from the luminescence centres i n to
are
the conduc also a semicond uctor) . There thus arises a marked photoconductivity s ho w in g strong correlation with t h e luminescence. Conduction band Between t h e valence and conduction bands we have to i nt r o ZnS(Cu), ZnS(Ag),
tion band of the crystal (wh ich is thus
raises electrons from
Trap Donor
duce and consider the recombina
tion centres, donor levels, a nd
electron traps. The distinction be tween luminescence centres and
traps is less easy than in the case
an
of quasi-atomic practice
systems,
b u t in
energy level can be
put in one or other of these classes.
Hole
Valence band Fig. 5
electrons and holes are charac an effective c ro ss-s ecti on a, fo r electron c ap ture and a1 for
(a) The recombination centres for terized by
Forbidden
Centre
Introduction
7
hole �apture, which if not of the same order of magnitude are at least both of the same importance. A centre is a luminescence centre if the probability of radiative emission Pr is much greater than that for non-radiative emission Pnr: i.e.
Pr � Pnr
which is the case for Cu centres in ZnS. A centre is a 'killer' centre if, on the contrary,
Pr �Pnr
which is the case for Fe, Ni and Co in ZnS. Their introduction in large quantities results in a 'poisoning' of the luminescence . (b) Elect ro n traps and electron donors show a large capture prob ability for conduction electrons, but transitions from them to the valence band are almost forbidden : i.e.
a. � at
i.e.
at � a.
If the l e ve l is normally empty (available for electron cap t u re) it con stitutes an electron trap, if normally occupied it is a donor level. (c) Hole traps and acceptor levels can be defined in the inverse sense to the cases of electron traps and donor levels :
If a level is normally unoccupied by holes it is a hole trap, and if it is empty of electrons and ready to capture a valence ban d electron it is an acceptor level. O F T H E P A P E R S QUO T ED IN T H E I NT R ODU C T I ONt
BIBLIOGRAPHY
PERRIN, F . (1929) Flu orescence des solutions. Induction molecu Iaire. Polarisation et duree d'emission. Photochimie.' Ann de Phys., 12, 169. These, Faculte des Sciences, Paris. Definition offluorescence and phosphorescence '
-r A general bibliography on books and comprehensive revi ews on lumin escence is g iven at the end of the book (page 325). We have not attemp ted to give an exhaustive list of references: this woul d be beyond the scope of this book. We have quoted some of the most important papers relative to each problem treated in the text; we hope that it will be suf ficient as a first step in es tabl ishing the relevant bibliography.
8
Luminescence in
Crystals
VAVILOV, S. I. (1934) 'U ber die Abklingungsgesetzc der umkehr baren Lumineszenzerscheinungen', Phys. Z. Sov.;jet Union, 5, 369.
Definition o( luminescent ph enom ena
E. I. ( 1 9 5 1 ) 'Theoretical questions on the luminescence of crystals', L State editions of technical and theoretical literature, Le ning rad . (1953) 'Ei nige Fragen zur Theorie der Lumineszen der Kristalle', L Ak ad e mi e - V e r l ag, Berlin.
See also
ADIROVITCH,
Life time and efficiency offluorescen ce D E LOR M E, R. a nd PERRIN, F . (1 929) 'Dun!es de fluorescence des sels d ' u ranyle solides et de leurs solutions', J. Phys. Rad., 10, 177. HALL , L. and DIEKE, G. H. (1957) 'Fluorescent life times of uranyl salts at different temperatures', J. Opt. Soc. Am., 47, 1092. KROG ER, F. A. and HOOGENSTRAATEN, W. (1948) 'The decay and quenching of fluorescence in willemite', Physica, 14, 425. PERRIN, F. ( 192 9 ) These Paris (loc. cit.), 1 2- 1 4, 101-3. RANDALL, J. T. (1 938) 'Luminescence of s olid s at low temperatures', Nature, 142, 1 13. RANDALL, J. T. ( 1 9 3 9) 'Some recent experiments in luminescence', Trans. Faraday Soc . , 35, 2.
Solids photoluminescent in t h e pure sta t e
'Photoconducting' and 'non-photoconducting' phosph ors MoTT, N. F. and GURNEY, R. W. (1948) 'Electronic
ionic crystals', 202-26. Clarendon Press, Oxford . Thallium as an activator : see Chapter II.
p r oce ss es
in
Other activators, isoelectronic with Tf+ LOUCHTCHIK, N . E. and L O U C H TCH IK , Tech. B. ( 1 960) 'Spectro
scopy of the luminescence centers and alkali halide crystals acti vated by ho mol o go u s series of ions', Optics and Spectr., 8, 441. PRENER, J. S., HANSON, R. E . and WILLIA M S, F. E. ( 1 953) 'Atomic mercury as a luminescent activator', J. Chem. Phys. , 21, 759.
Energy-level scheme of Jablonski J ABLONSKI, A. ( 1935) 'Ober der Mechanismus der Photolumineszenz von Farbstoffphosphoren', Z. fur Phys., 97, 38.
Introduction
9
Classification of the diferent localized levels in the forbidden gap, traps,
centres etc .... AIGRAIN, P., Lectures given at the Faculte des Sciences de Paris, ,
1956-7.
Thermodynamics of luminescence phenomena KENNARD, H. E. (1 918) 'On the thermody n am i c s of fluorescence',
Phys. Rev., 11, 29. LANDAU, D. L. (1 946) 'On the thermodynamics of photolumines cence', Z. Phys. U. S.S.R., 10, 499, 503. VAVILOV, S . I. (1 948) 'Photoluminescence and thermodynamics', J. Phys. U.S.S.R., 10, 499. WEINSTEIN, A. ( 1 960) The rmo d ynam i c limitation on the co nversion of heat i nto l igh t' J. Opt. Soc. Amer , 50, 597. WEINSTEIN, A. ( 1 960) The r modyna mi cs of radiative emission pro cesses', Phys. Rev., 119, 499. WILLIAMS, F. E. (1 960) 'Irreversible thermodynamics of solid state lumi n e sce n ce', Spring Meeting, El ectrochemical Society, Chicago, '
,
.
'
May 1-5.
Angular distribution offluorescent brightness PRINGSHEIM, P. (1 949) 'Fluorescence and phosphorescence', 389, Inte rsci en ce Pub., New York.
CHAPT E R
I
Dipole and Quadrupole Radiation: Probabilities of Emission and Absorption
We
shall not give here the general theory for the ph en omena of
emission and absorption of radiation. The reader may refer to more
E.
H. S hortley The Theory of Atomic Spectra
specific writings for this, for example: U. Condon and G.
H ei tler The Quantum Theory of Radiation ,
(Cambridge University Press);
W.
,
(Oxford, C larend o n
Press).
We have made considerable use of the follow i n g :
F. Perrin, Emission
A.
de rayonnement par les atomes et les noyaux
(Cours du College de France, 1950-I-2); Berthelot,
Les champs multipolaires en electromagnetisme;
Only the elementary results fo r dipol e and quad rupol e radiations are necessary in considering luminescence. E ffective ly the e m is s io n p robabi lity for the various m ultipo l e orders falls by a factor� (a/A)2 unfortunately the last two have not been pu blished.
}. the
each time the ord er and
emitted radiation.
I changes
w avelength of the
by unity, a bei n g the source dimension
A)
For visible luminescence (}. � 5,000 factor
aj}.
is
from atoms (a �
thus 1/5000, and so quad r u po l e
feeble compa red
with
radiations
I A) the
are very
dipole radiat i ons and higher o rde r emissions
d ipole transition I 0-3 to 10-1 sec, and a qu adrupole transition an even longer life time.
are almost negligible.
An electric
-
dip ol e transition will have, for ex
ample, a life time of I0-8 to I0-7 s ec a magnetic ,
(In luminescent materials the interaction of the emitting atom with
the crystal lattice can usually cause
an appreciable redu cti on in these
In cont ra st for hard X-rays (A � I0-1 A and a� IQ-Io cm, the size of the inner shells of heavy atom) the same factor a/A can reach values.)
10
.
11
Dipole and quadrupole radiation
1/10; similarly for y-ray conditions multipole radiations are no longer n e gligible
I . D I P O L E AND Q UA D R U P O LE M O M ENT S
1. Electrostatic p otential due to a charge distribution An atom, molecule or luminescence centre is composed of one or more nuclei surrounded by a certain number of negatively charged electrons. These form an assembly of charges e; at points y;, z; . We no w find the potential due to this system at a poin t P(X, Y,Z) at a distanc e R from the orig i n of coordinates:
o;(x;,
)
the ch ar ge e;. Assuming R to be large compared with the distances of the charges from the origin, a Taylor series can be developed:
r1 being the distance from P to V= ��e;+
This indicates the total charge of the distribution dipole moment fJ. whi ch by defini t i o n has components
�e;, the vector
(=
fJ.x =
and the
...
�e;X;
•
•
•
tensor quadrupole moment
B<2>
Bxx
Bxv
Bxz
Bvx Bzx
Bv11
B11z
)
Bzz
a symmetric tensor of the second order (six separate components) Bzv
given by
I n genera l we have a series of polar moments 21 and each one charac terized by a tensor
and contributing to the total potential of the system the co n t racted product
denoting the tensor of the p arti al derivatives of order l of 1/ R calculated at the origin. The s imilari ty will be noted between the definition of dipole moment and that of the centre of gravity of a collection of masses grad0<1>
12
Luminescence i n Crystals
and also between the quadrupole moments and moments of inertia. By a suitable ch o ice of axes of reference it is p o ssibl e to diagonalize the tensor BC2l in the same way as the te ns or formed by the moments and products of i nertia. 2. Potentials due to dipoles and quadrupoles
A d ipol e formed by ch arge s A and B equal to +e and -e has a
mo m en t
!l. = eBA and gives rise to a potential which at large distances away, say ten times the length of the dipole, reduces to a term invo lvin g I IR2: cos 0 (n.!l.) _
n
being a uni t vector in
V1
-
11 --
th e direction
8 0
Fig.
I. I
A
_
R2
R.
:r
Electrostatic dipole
The p o ten ti al is zero along the axis for 8 = n/2, but not so the fiel d which is thus t ransv erse ; the field is radial about the axis of the d ip o le (0 = 0). A qu ad rupole is fo rmed by two e qual and opposed d ip o les dis placed from each other, say four charges ABCD of +e, --e, +e, -e arranged at the corners of a parallelogram. This gives rise to a p o t en ti al : V2 = 1 grad0<2>(1jR) .BC2l Using the two invariants attached to the tensor BC2l, we knowi its trace: B = Bxx+ B,"+ Bzz and the quadratic form: B(X,Y,Z) = BxxX2+ ... --i-2BvzYZ f ... ,
,
t In th e analogy between the tensor of the moments and products of inertia the invariant B corresponds to the moment of inertia with respect to the origin such t h at B(X, Y,Z) is the quadratic form appearing in the definition of the ellipsoid
of inertia.
Dipole and quadrupole radiation
13
We can then obtain explicitly the derivatives which occur in grad0C2>:
V2
=
� 3�(!kr2:)- J B
The anisotropy of a quadrupole is more complex than that of a
dipole and depend s on the type of quadrupole involved . .'ll
8
e
c 't
A:·e
0
8-//
"'
·
Fig. J.2
0
C
'. f: j
'
·•
21:.
A
'•
R
J
/
fJ
(�;
:('
Two types of quadrupoles
Consider first the case where the four charges
A, B, C, and Dare
arranged at the corners of a square. The only non-zero component
of the tensor
8<�> is
then
Vz
B,.v e(A 8)2, from which 3e(1 #)2 cos g �il! P
-
=
R3
The potential and the field are both zero along the axis
45°
Oz normal
to
the plane of the quadrupole. To diagonalize 8<2l it is sufficient here
to take the axes at
to the previous ones.
When the four charges
A, B, C, Dare aligned along the same axis The only non ze ro component is then
they form an axial quadrupole.
B:rx = 2e(A8)2•
V2
=
R3
2
cos 2
o-!) 2
0). In a 21 formed by charges
We see the appearance of the Legendre polynomial Plcos more general way, for an axial multiple of order
of alternate sign with equal distances between them, the number of charges a t each poi nt being equal to the successive coefficients in the
,
binomial ex p an sio n the potential is given by
Vz =
l!e(AB)1 Rl+
1
Pz(cos
{})
Luminescence in Crystals
14
3. Development of potential due to a multipole in spherical harmonics s am e order a rr anged along the ray vectors of th e poles . This
Any '21-pole' is eq u iva lent to the
us to
sum
of 21 axial multipoles of the
enables
expand the potential V1 of the 2 1-po le in the following form:
Vz =
We use for this
ll'-1
)
L of
a/" Yz"'(O,
t he
?n=-l
exp a nsi on
the
P1(cos
R
�m=l
m=l
=
.2:
o/)
Legendre polynomial
for the
Yt'(O, cj>) Yz"'(O', 4/)
where 0 and
I
nr = -r
the polar coordinates for the direction of the e,th ch a rge , a being the angle between these two directions. By i n tegr at ion over a volum e element dv of the charge system we obtain th e value of the coe fficie nt
am ! •
where
az
m_
4:n;
Qm
p(o) is the charge density. Qz"' is termed the multipole electric of order I, m. 21+ 1 coefficients are necessary to define the 21+ 1
1
'
moment
21 -poles in place of the 1-(l+ 1)(/-f-2) c oe fficien t s of the tensor B<1>. This is because the coefficients are not ind ependent , t he res ultant p oten ti al V h a v ing to satisfy Laplace's equation as well as its de riv a tives. In particular the moment
where
Q2o
Q
I.
=
about the axis ()
and defines the
rotation
=
v 156:n:. Q
J 02(3
cos2
0-!)p dv
q u adru pol e moment of = 0.
a
di stri buti on formed by
I I . D I P O L E A N D Q U A D RUP O L E R A D I A T I O N I N E L E C T R O MAG N E T I SM
Con sid e r an
elec t r om agne tic
Maxwell's
tion
equations
of density
p and a cu r ren t
field in vacuo due
to a
charge distribu
distribution of density j. This field is
Dipole and quadrupole radiation defi ned by the electric field
equation s
_!
curl E = div
E and
D = 4np
�C
div B
0
=
m agneti c field H related
by the
(law of ind u ction)
C
curl H =
the
15
theorem)
(Gauss's
+ 4nj (Ampere's theo rem) (i.e. no free magnetic poles)
The system of units is defi ned by
eo = flo =
1
vacuu m is
Unless otherwise indicated, magnetic quantities and also j are given
assumed : in
e.m.u
and electrostatic quantities in
D
E
=
B
and
e. s u . .
Since a
H
From these re l a t i on s o n e obtains the law of charge con servation :
d
The fields
E
and H can
and a vector pote n ti al E
lv 1 .
.
+ 1 ap
c at = o
be exp ress ed in te r m s of a scalar by the relations
A
I
oA
= - g rad
-c at
a nd H = curl
potential
A
When the poten t i a l s are c h o s en so that they s a tisfy t h e Lorentz
condition
and
A are solutions
Where 0 is the
of
o
=
d'Alembertian
D =
DA
4np
(}2
(}2
(}2
=
4nj
1 (}2
ox2 + iJy 2 + iJz2 - C2 o t2
2. Solution of Maxwell's equations by the retarded potential method Co n sid er a distribution of
occu p yin g a reg io n
sider the potential
moving charges p(x,y,z) and j(x,y,z) around the origin of coordinates. We now con
at P(X, Y, Z) at a
r from the charge (x,y,z).
d istan ce
R from the origin and
16
Luminescence in Crystals
When
P is ou ts i d e the ch a rge distribu t i o n we obta i n the
th e i n te g ra l ex ten d i n g
ch arge s .
The r e ta rd a tio n of velocity
<
r/c
p
-
-
r
fo l l o w i ng :
dx dy dz
J J J j(x,y,z,:. - r/c)d x dy d z
over the whole vol u m e o cc u pi e d by the
r e p re s e nts the time for electrom agnetic
to reach t h e po i n t P a ft e r
waves
emission by the cha rge at
p
Fig. l . 3 Poten tial produced by a moving charge
(x,y,z). These e xpres si o ns satisfy t h e equations for and A (involving the d'Aiembertian) as well as t h e Lorentz c on d i t io n resulting from t h e conservation of charge. 3.
If
Systems in harmonic vibration
r
is
the
vibrational
fr e q ue n cy then we can
write
i mpl yi n g of c our se the real parts of these expressions. We a l s o intro
duce the wav e l e n gth A. = cjv, the reduced wave number
Then we h ave
the
reduced wavelength j{ = A./2:n: and I
2m•
k = -- = -; J. c p
=
P o e i kcl ;
and charge conservation requires
that :
div kt- ikp0
j
=
=
0
j o e i kr t
Dipole and quadrupole radiation
17
U si ng these notations, the reta rded potential form ulae beco m e
=
=
A0 = 4.
o e ikrr
JJ J J. J J
,
Jo
A= e ikr
A o eikct
e - ikr · dv --
Potential distribution among successive multipole orders
The potential formu la
for <1> 0 d i ffers from that for the el ectrostat ic potential V for t h e charge d i stribution p 0 by the replacement of I /r by e - ikr f(r) r =
--
-
The exponential takes account of the different retardations between the different point charges of the system. Analogous to the d evelop ment of i n para. I . l , <1>0 can be given as follows :
V
o = f(R)
JJJ
Po dv -j-
6: ft
(grado<1) f(R) . B0<0)
the derivatives off(R) being taken at the origin . Each component of A 0 can be obtained in a s imi l ar way. Charge conservation during vibration requires that
We then obtain the results for successive multipole orders (1), taking together the (I+ l )th term of <1>0 and the /th term of A0•
Electric dipole radiation
We take the fi r st non-zero term of each series and obtain
grad 0/(R·) . (J. 0
<1> 0 A0
f(R)
JJJ
j 0 dv
(.1.0 is the vecto r d i po le m o m en t =
(.1.0 5 bei ng the
- gradpf(R) . (J.o
=
JJf
PoS d v
rad ial vector for a point charge (x,y,z) of the source.
18
Luminescence in Crystals
C hargc conservation gives :
so
that
the potentials
We now
I I I j0 dv
j( R)
=
i k!L o
finally d ep e nd only on the q u an t ity !Lo · and its d e rivative .f'(R)
introd uce .f(R)
=
f'(R) =
so t h a t we ca n n ow w ri t e
<}) o = - (D . (L0).f'(R) A 0 = ikELof( R) For small d i s t a n c e s , i.e. small compared with J.(k R � l ) but large c o m p ared with the size of the source, we can put .f(R) R: 1 /R : th us we obtain t h e electric field due to a stationary d ip o l e of moment !Lo and the magnetic field due to the curre nt j0• At l a rge distances (kR � 1 ) f'(R) red uces to - i f( R) , which gives terms in 1/R in the poten tia l s as well as in the fields, i.e. we have the ra d i atio n fiel d s . We find
k
H =
e2nio·t k 2 (n A !L o) -R e - iku
where n is t h e unit ve c t o r
e ikU
(n A !Lo)] -- e2nivt
in the direction R. These solutions are for divergent waves and this arises use of the retardation p o ten tial s . E
-k2[n
"
R
from the
We see that
(E and H hav e the s a m e magni tud e and are both t r an s v e r s e .) The ra d i a t i o n energy is equal to the flux of the Poynting vector : c S 4n(E " H)
a nd i nt eg ra t i n g over all space
=
where W i s the energy
W
1 6n·l y� 12 3 c 3 I tJ. o
radiated per second. The d ipo l e !Lo can be realized by assuming a p o i n t ch arge in har monic o sci l l a ti o n . Knowing the o sci l l a t o r energy and comparing this to W, we can d e d uc e the mean life time =
3m c 3
T = 8n2e2v2
For 1\
19
Dipole and quadrupole radiation
R:
6,000 A we obtain
r R:
1 ·6 x I0-8 sec
Anisotropy of the emission If the moment !J.o is real this corresponds to the case of a point charge axis Oz.
0 is the angle between the direction OP and this axis, the emission per unit solid a n g le is dependent on sin2 0 (t hi s is seen straight away oscillating along a direction which we take as the polar
0
If
fl- o
Un ear 05Cllla tor
Cwcutar oscillator
i.C
Fig. 1 . 4 Anisotropy of emission for in the expression for square of the field).
dipole oscillators
H, knowing that the radiant energy varies as the
The emission is zero along the dipole axis. However, the electro static field is a maximum (but radial for reasons of symmetry : there could not be a radiation field because
this must be transverse).
The angular d istribution of the radiation field is identical with that of the transverse component of the electrostatic field but differs from
In general !J. o = a + ib and i s complex. This corresponds to the case of the elliptical oscillator. In particular, if a = b the oscillator is cir that of the total electrostatic field.
cular and the anisotropy of the emission depends on 1 + cos2 e.
Case of a zero dipole
moment
The same approximation
as above the first
the potentials, i.e. we take
can be used in the derivation o f n on-zero term .
Consider first of all the scalar potential
o
=
-!(grad 0<2> f(R) . B0<2>)
20
Luminescence in Crystals
BCl.i being the tensor quad r up ole moment. Thus to describe Cl>0 it is any new quantities ; as in the electrostatic case it i s sufficient to replace 1 /R by f(R) e - ikRjR. However, it is necessary for the vector p ote nti al to introduce new pa ram eters related to the ch a rge distribution. If 5 is the radius vector of a p o i n t (x,y,z) of the source
not necessary to introduce
=
f'(R)
A0 =
We c an establish that
JJJ J JJ
xj0, d u yjoz d v
=
=
� ik Jik
J JJ J JJ
J J J (n . S)j0
p0xz
dv
'=
dv
iik 80
HJ J J
PoJ'Z d l'
.• .•.
(J}oz - zjo v) d r:
±ikBo uz + Mox We are thus led to introduce in addition to B0(2 l the magnetic dipole moment M0 M0
=
J
J J J (S
When only the magnetic mo men t
di pole wave
A
j0) du
is i nvolved we have a magn et i c
emi ss i o n for which
A0 f'(R)(M0 A n) Cl> 0 = 0 , Alth ough these potentials are very diferent from those o btained for the electric dipole radiation, the fields can be obtained by a simple perm utati o n of E and H (and of course repl ace me nt of !J.o by M0). The radiation energy is thus =
W
=
Mo
3c 3
j2
The magnetic d ipole moment is of the order of a Bo h r magneton
Mo � 4nm c eh
--
while
fl o � ea0,
where a0 is the Bohr
atom ic radius ft2 ao = 4.n Zmez
We can d ed uce that M0/!J.o is of the o rder of the fine structure constant
21
Dipole and quadrupole radiation
w h ich gives
a m uch smaller probability of magnetic dipole emission
than of electric dipole emission in the ratio 1 : 1 05 (and still 1 00 times weaker if the radiation comes from an intercombination transition). When M0 is zero bu t B0 <2> is not, we have the case of electric quadru pole e m i s si o n for which we h a ve already n oted t h e expression for
w h i le
Aox =
-f '(R)}ik(n . B0<2>),
From these form u l a e th e fields can be ded uced . We shaH not derive these b u t sim ply remark that at large distances they are agai n trans verse and s at i s fy the relation E = HAn
applying to a l l m u l t i p o l e orders . The emitted ra d i a t i o n has the va l u e
t h is
W =
�1�{2 I
Bvu
-
B,"
1 2 - !- 6
2I
Buz
1 2}
If a is the s o u rce dimension, the q uad r up o l e moment is of the order of ea2 whil e the e lec tri c dipole mo ment is R> ea, the coefficient is o n t h e other hand m u l t ip l i e d b y v 2 jc 2 and the emission p ro b ab il i t y is t h u s multipl ied by R> ( a/Jc) 2, which is of the o rder of 10 - 7 o r J Q - 8 • W e c a n a l so w r i t e W a s follows : 8 G 6
W= � 5c5 l
Q lz
J Q j 2 representing t h e expression J B,, - }B 1 2 + 1 Bv v - -}B 1 2 + 1 B•• - tB I 2 + 2(J Bxy J 2 + J B11z j 2+ j B,, \ 2)
or in the most condensed form
Q
=
B<2> -BI
B being the trace of the tensor B<2> and I the unit diagonal tensor. Reference may be made to J. Blatt a n d V. F. W ei ss kop f, Theoretical Nuclear Physics (Wiley, New York, 1 9 52), p. 586, for a study of the emission anisotropy for different multipole orders We only note here that the angul ar distribution of the radiation energy for the real axial quadrupole, osci l l a t i n g linearly along the OZ axis, depend s on cos2 e s i n 2 e.
Q tm·
I l l . P R O B A B I Ll T I E S O F R A D I ATIVE A B S O RPTI O N AND EMISSION
1 . The Hamiltonian of the particle (electron of mass m and charge - e, e b e i n g taken positive) in an electromagn etic field <1>, A is given in B
22
Luminescence in Crystals
non-relativistic
classical mechanics by I p z - e H _ 2m =
P = mv
p -i- �A c
P is t h e kinetic momentum, p t h e total momentum (that of particle and field ) . N eg l ect in g the terms i n (eA jc) Z, these e qu a ti o ns w h e re
gtve
H=
1
A 2mp2- e + mc(p . ) e
The term (eAjc)2 is a relativistic term and we H a mil to n i a n i s s e p a ra b le i n to I ., Hparticle = e
giving the el e ct r o n potential
In
and
motion
2nip - -
shall n e g l e c t
i n the field derived fro m
e
it. The
the electrostatic
- (p . A)
H; nter:ICtion
me
quantum mechanics p mu s t be rep l ace d by the operator p = �V !
where V is the operator g r a dien t . However, p and A are n o n - c o m
m utative and we have
V . A = A . V+ div A
is also convenient to choose a potential scale so that the scalar potential is zero for the radiation field (in contrast to previous condition imposed by using retarded potentials). We know that the physical results should be independent of the scale chosen for the potentials. The Lorentz condition implies that div A 0 and the difficulty of the non-commutative operators disappears. We then It
=
have Hinteraction ( radiat iou·elcctron)
2. The transition probability
e li = - -:(A · grad) me z
This interaction introduces simultaneous transitions between electron states and the photons of the radiation fiel d . The transition probability per unit time is ., ., P "' 't'�natHintemction\Fini tial d r
f
�-p(£)
Dipole and quadrupole radiation
where p(E) i s the density o f osci l l ator states aro u nd t h e ene rgy for the photons
p(E) dE =
c
E
23 =
hv
dv
(normalized to the volume V). The '¥ functions can be resolved into a 1p(r) function of the electron
coordinates multiplied by a product of the eigen functions of the oscillator for the photon field. The matrix elements for the latter are classical. We give here only the results of these calculations. When
the
vector potential
A is assumed constant at all points i n
the charge source, matrix elements appear o f the form
�f
1p1 * grad 1p dr
(a formula which when ?p;
of the centre of gravity).
=
f 1p1*r1p; d-r
m
= 1p1 red uces to p
=
mv for the movement
We also obtain the matrix elements for the electric dipole momen t :
We
!-'-it = erif,
r;1 =
f
1p1*r1p; dr
then have for the probability per second of emission :
N being
Pcmis•.
=
64n"v3
(N+ l) 3h c3 I fJ.it l 2
the mean number of photons in the energy hv (if N = 0 we
have spontaneous emission) and for the probability of absorption per second
Pal». _
64n"v3 N . 3h c 3 I !-'-it
I2
The luminous emission intensity per second from an atomic emitter (photon energy E
=
hv multiplied by the transition probability) is
64n4v4 I I(hv) = 3"CS IJ.if 1 2
The effective absorption cross-section is by definition
a(v)
=
Et!£ ���
No. of incident photons per cm 2 per sec
The numerator is Pats. and the denominator is the photon second
8 v2
n dv = cNc3
flux
per
24
Luminescence in Crystals
From which
a(v)
N
64;r-I J,3
[.Lit
I . c N Snv :i d ; c3
thus obtain the effective cross-section i ntegrated over an assembly matrix element [.L;r) in p ractice over all the possible n e i ghbouring energies t o hv fo r the abso rbed p h o t on s : =c
I
•
We
of 'physically identical' states (that is, with t h e same
One often c o n s i d e rs :
J J
8n31•
a(1·) cl J '
I
--3hc
[.Lit
8n3J'
a(E) dE = - - - I 3c
The absorption coefficient k(E)
[.Lit
I2
12
cm - 1 i s given by the product o f the e ffective cr o ss sect i o n a(E) and the concen tration o f absorbing a toms These classical fo rm ul a e are for atoms in vacuo. We shall see later -
.
crystalline m ed i u m of refractive index n . H o weve r the the study of e mi tted a n d absorbed rad i a
how they may be transformed fo r the case of absorbin g or emitting
atoms i n a
,
formulae above suffice for
tion as a function of the factor
sidering the
[ !L 1 2 ,
when
and we o nly need to introduce
absolute intensity of the radiation ( S m a k u l a formula) .
a coefficient w hich takes account of the refractive i ndex Compare the quantum
expression giving J(/w)
n
con
above and the pre
ceding formula from classical electrom agnetis m for the rad iated energy
(correspondence prin c iple) W
12
We see that the quantum formula differs fr o m the classical o n e in that =
!-L o
3 ca
we replace the dipole m o m e n t !-Lo by the matrix element of the dipole
do
have
of 2 in the matrix el e m e n t and of 4 i n the transition probability.
moment for the transitio n . I f we
this we
facto r 2 can be explai ned as fol lows :
The
to include a factor
tion between the i nt e ns ity at the harmonic of frequency v i n the fre The co rrespondence principle establishes in a general way a rela
quency spectrum and the rad iated energy in the quantum t h e ory d u e
to photons of en ergy h v . However, classically we d o n o t distinguish between v and - v, that i s , between photons emitted a n d ph oto ns absorbed . In applying t h e correspon dence principle to !-Lo
c �
e
spr
dr
Dipole and quadrupole radiation
t h e density p must b e replaced n o t b y tpt'lp; ; which gi v e s (.Lit
=
e
ftp1*np,
25
dr
but by the symmetrical expression 1J!f'IJ!; + 1fJ;1f!f> and we must take the real part R e (tp1*tp; + tp;*1f!t) 2 R e ( y•/ '1f•,) =
w h ich expl a i n s t h e correspondence
(.Lo -- 2(.Lit
3. Ma gnetic dipole and electric quadrupole radiation
The same correspondence occurs in the expressions for emission and absorption of magnetic dipole and electric quad rupole character. In the magnetic dipole case the luminous intensity emitted at fre quency v is
Jl(h 'jJ) - 64n4v4 � 1 Mif I •-
dE = 3c I Mi! ! 2
and the integrated absorption cross-section is
f a(E)
8:n:3v
In the case of electric quadrupole radiation (which is obtained when we introduce the first derivative of A (the first derivative of the re tardation c - l kr between different points of the c h a rge sou rce in t h e classical case) we obtai n
f
a(E) dE
=
4:n:5v 4
Sc3
I Q i! 1 2
Q
We refer back to the expression developed for at the end of paragraph II i n which each component Bxx , B x v . . . of the tensor B(2l can be replaced by the matrix element of the same quan tity for the transition i -- f 4. Selection rules
The selection rules are m ost easily appreciated by resolution of the dipole and quadrupole potentials, &c. , into spherical harmonics dependent on Q ';' (para. 1.3) with m = !, -l -!- 1 . . . !- 1 -!- 1, We can show that rad iation of multipole order /, m has a total angular
Luminescence in Crystals
26
momentum I for which the Oz component is m (m units of h/2n). Thus fo r the emitting atoms the angular momentum a n d for the D z component
J; = Jt + l
M; = M1 f - m
Since there is no multiple radiation for l 0 , all radiative tran sitions ]; 0 -+ 11 = 0 are forbidden in all multipole orders. For I 1 (dipole case) w e have =
=
6.1 = 0, ± 1 ,
!: M = 0, ± 1
givi ng an electr ic dipole wave if there is a change of parity fo r the w ave fu nct io n 1p (Lapo rte ' s rule) and a magnetic d i pole wave if the parity does not change (given the par i t i e s of the operators !J. a n d M). For I = 2 !:M = 0, ± 1 , ± 2 0.1 = 0, ± 1 , ± 2 ;
a n electric quad r u pol e wave i f there i s n o c h an ge i n parity. = ± 2, only quadrupole or higher o r d er radiation is allowed . For !:J 0 (0 �>- 0 excluded) or ± 1 , w e have an electric d ipol e wave if the parity changes and a mixture of electric quad rupo le and magnetic dipole waves if there is no change in parity. The m ag netic dipole radiation will usu ally predominate since its p rob ability is only I 0-5 times less than that for electric dipole radiation, while that for electric quadrupole radiation is about I0-8 times less. giving
For !:1
=
Forbiddenness of intercombination radiation. The operators !J., M and are symmetric al to the exchange of two electrons. If, for example, we consider a system of two electrons, the transition from a triplet state (spatial wave function antisymmetric with respect to the ex change) to a singlet state (spatial wave function symmetrical) is for bidden . The spin-orbit interaction partially lifts the for b id d e n ness . In an average atom, an intercombination transition will be 1 00 times weaker than an allowed transition of the same multipole order. In heavy atoms such as Hg, Tl+, &c. , this factor is reduced to about 1 0. B<2l
'Spin-flip' transitions. Chromium as an activator. In an allowed tran sition the electronic configuration changes by means of an electron transition from one 'orbit' to another. There are some transitions for which the configuration does not change, being the same in the ground and excited states . These states d i ffer only by the 'turning
Dipo le an d quadrupo le radiation over' o f o n e electron spin. I n luminescence the q uestion case of ruby (alu m in ium oxide containing
Cr203) :
27
arises in the
The emission spectra of chromium-activated phosphors are quite different from the spectra of other phosph ors, and to some extent
they can be co m p are d to the spectra of rare earth s . They consist of
m ay be resolved into a large n umber of narrow lines ; among them there is a characteristic intense doublet (Deutschbei n). In ruby, the position of this d ou blet is, at 20°C, at
a red fluorescence which
R1 : 6,942·3 A, (14,404 cm-1) R2 : 6,927·4 A, (14,435 cm-1)
These lines are sli ghtl y d i splace d when the temperature is varied , but 2 2
� 0·38
-1 I! '• r
G 912
G 7/ 2
} 4 F3 / 2
cm
Fig. 1.5 Energy-levels scheme for the emission spectrum of the main lines R1, R2 in ruby
the main effect is an exponential dependence of the relative inten sities :
I(R ,.) I( RJ
= ( - W) exp
kT
W � 29·2 cm- 1
Chromium i s incorporated a s Cr3 +. I n t h e fundamental level 4 F3;2,
the s pin s of the three outer 3d electrons are parallel ; in the excited 2G1;2 and 2Go;2 levels, one of the valence electrons is anti parallel to the other. In addition, when the
Cr3+ ion is incorporated into the crystal, the
,
fundamental level is s pli t into 2 tw ofold orbitally dege n erate states,
I and II,
3 single states (not shown on the Fig. !.5). The value of the splitting between I and II is accurately k nown from micro wave ab s orption measurements : it c o rres p on d s to a frequency of 1 1 ,593 Mc/s. It may be noted that this splitting is small compared with the and
28
Luminescence in Crystals
energy difference between states o f different J val ues : t h u s the de generacy of the levels of the free Cr3 + ion is raised by the crystal field, but the mixing of these levels is probably q u i te negligible fo r the mo st i mpo rta nt low energy levels, occurring in the red R-emission of ruby. A discussion, using as a starting-point the terms derived for t he free ion, as it was attempted by Deutschbein , Thosar and Pringsheim, is thus not too inaccurate.t A s p i n-fl ip transition is also assumed for the case of the activator manganese. Sometimes, this a ctivato r is embedded as M n 4+, wh ich is isoelectronic with Cr3 +, and an emission results which contains several lines, also situated in the red part of the sp e c t r u m . This is the case for mag n esiu m germanate, M g 2 G c 0 4 (M n ) , a n d magne s i um oxide, MgO(Mn), phosphors, but more often one has to deal with Mn2+ ions, with five outer 3d electrons : such is the case for ZnS(M n ), Zn2SiOiMn), &c . . . . We shall discuss these phosphors in Chapter V (page 1 22). Such transitions are naturally fo r b i d d e n for an electric d i po le approximation . They comprise v a r i o u s rad iations, some of elec t r ic quadrupole and others principally of m a gn e tic d ipole character. Their mean life time is rather l o n g (5 msec in r u b y) and very sensitive to cry s t al lattice interactions.
BI BLI OGRAPHY
References to some c o m p rehensive treatises o n the th e o ry of em issi o n absorption phenomena have already been gi ve n in t h e text.
and
On the anisotropy and polarization of luminescence in crystals F E OFIL OV , P . P . ( 1 9 5 6) 'Anisotropic optique des centres l u mi n oge n es dans Jes cristaux cubiques' , J. Phys. Rad., 1 7, 6 5 6 . F E OFI L OV, P . P . ( 1 9 60) The physical basis of polarized emission (Polarized luminescence of A toms, Molecules and Crystals), English t ranslation . Consultant B u re a u Books, New York. t The level scheme which is proposed here differs s l i g h t l y from the generally accepted scheme due to Suga n o and Tan a be ( 1 9 58). The fundamental level and t h e ex c i ted level i n v o lve d in the R-emission of ruby derive respectively from 4F and 2G sta tes ; the difference is in p a rt a matter of notation .
Dipole and quadrupo!e radiation
On
H . (1 929) 'Termaufspaltung in Kristallen',
the split t ing of terms in crys ta ls
1 33.
BETHE,
T . (1 960) Theorie Paris.
tique, D u n o d ,
K AH A N ,
29
Ann . der Phys. , 3 ,
des groupes e n physique classique et quan
0 . ( 1 932) 'Die D e u tu n g der linienhaften Emissions und Absorption sspektren der Ch romphosphore', Z. fir Phys. , 17, 489 ; Phys. Z. , 33 , 874 ; A nn. der Phys. , 14, 7 1 2, 729. GEUSI C , J . E . ( 1 956) 'Paramagnetic fine structure spectru m of Cr H· + in a single ruby crystal', Phys. Rev. , 102, 1 252. P R I N G S H E I M , P. (1 949) Fluorescence and Phosphorescen ce, 637-45 . Intersc. Pub . , New York. S uGANO , S. and T ANA B E , Y. (1 958) 'Absorption spectra of Cr++ + in A l 203', J. Phys. Soc. Japan, 13, 880. T A N A B E , Y . and S U G ANO , S. (1 954) 'On t h e a b s o rpt i o n spect ra of compl ex ions', J. Phys. Soc. Japan, 9, 769. T HO S A R , B. V. (1 938) 'On the fluorescent i o n s o f chromium i n corundum', Phi!. Mag. , 26, 380, 878. Structure and luminescence of ruby
D EUTS C H B E I N ,
( 1 956) 'Proposal for a maser', Phys . Rev . , 104, 324.
Some references on m icrowave and optical masers
B LOEMBERGEN, N .
new
type of solid state us
ing ruby
'Microwave modulation of light in paramagnetic cr y s t als
BLOEMBERGEN, N . , P ERSHAN, P. S. and W I L CO X , L. R . Rev. ,
120, 20 14.
teristics of a maser at 1 420
B i:i LGER , B . , R O B J N S O N , B . J . and U B B I N K , J .
( 1 960)
',
(1 960) Phys.
' S o m e charac
A . L. , B O N D , w . , (1 960) 'Coherence, narrowing, directionability and relaxation oscillations in the l i ght e m i s s i o n from ru b y , Phys. R e u . Letters, 5, 303. F O N E R , S . , M O M O L. R. and M A Y E R , A . (1959) ' M ultilevel pulsed field maser for generation of high frequencies', Phys. Rev. Letters, 3, 36. M A I M A N , T. H. (1 960) 'Optical and microwave optical experi m ents in ruby', Phys. R e v . Letters, 4 , 564. COLL I N S ,
R.
MHz' , Physica, 26, l .
J . , N ELS O N , D . F . , S CHA WL OW,
G A RRET, C . G . B . a n d K A I S E R , W . '
,
30 On
Luminescence in Crystals
/'.1n 1 ' as an activator
and V A N D E N B o o M G A R D , J. ( 1 9 50) 'The fluor of magnesi u m germanate activated by m a n ganese' , .!. Electrochem . Soc., 97, 3 7 7 . PATTEN , S . H . a n d W I L L I A M S , F . E . ( 1 949) ' Fluorescent M g 2GeO c M n ' , J. Opt. Soc. Am., 39, 702. PRENER, J . S . ( 1 953) 'Magnesiu m oxide ph osphor activated by M n + + + + ' , J. Chem. Phys., 21 , 1 6 1 . P R I N G S H E I M , P . ( 1 949) Fluorescence and Phosphorescence, 632. Intersc. P u b . New York. THORINGTON, L. ( 1 950) E m i s s i o n o f a n improved manganese activated m ag n esi u m germanate phosphor', J. Opt. Soc. Am., 40, 579.
KROGER ,
F. A.
escence
,
'
C H A PTER 1 1
Emission
the
and
Absorption
Spectra and
Configurational Coordinate Model
(Ex a m p le of Thallium Activa ted Alkali
Halides)
Luminescence spectra differ from atomic spectra in two basic aspects : (a) Bands (of the order of hund reds of angstroms wide) rather than lines are generally observed . Exceptions are the Ewles-Kroger lumin escence and exciton emission.
(b) The emitted radiation is displaced to longer wavelengths com pared to the absorbed radiation (Stokes's Law). More specifically, the band maxima for emission and absorption are displaced but it is possible to have an overlap of the long wavelength side of the absorp tion band and the short wavelength side of the emission band . The above phenomena are due to the interaction between the emission centre and the crystal lattice which can be treated by means
of the configurational coordinate model. This model is particularly appropriate for the case of a quasi-atomic emission system ; the inter· action can be represented i n a most satisfactory way by using a single configurational coordinate to give the distance between the lumin escent ion and its nearest neighbours in the surrounding lattice. As an example we take the case of thallium activated potassium chloride
F. Seitz F. E. Williams. The model can also be applied to cases where
KCl(Tl) which has been extensively studied, in particular by and by
the centres are less localized, in particular to luminescent semi conductors although the configurational coordinate can n ot be given such a specific interpretation as in the above case. 31
Lumin('sccncc in Cr_J •srals
1 . S T R U CT U R E O F A ' N O N - P H O T O C O N D U CT I N G '
In
L U M I N E S C E N T S O L I D : K CI(TI )
general, KCI(TI)
is p rep are d by i n c o rp ora ti o n
pa r t per
KCI. Two intense absorption b an d s of 1
due to we a ke r 1 0,000
TJ + i o n s are fo u nd at 1 ,960 and 2, 500 A respectively, wi th a b a n d at about 2, 1 00 A . Ex cita ti on is u s u al l y effected in the 2,500 A h a n d (merc u ry rad iation is at 2 , 5 3 7 A). A n i nte n s e ultra-violet emis s i o n occurs at 3 .050 A a n d a l s o a bl u e emission at 4,750 A to 4,900 A . to 1 part per 1 00 TIC!
in
L a t t iCI.� tJbsorpt. 1on
l
1 50 0
1800
Fig. I T . !
I . Energy levels in
'P,
2 0 0 0 2 2 0 0 2400 2 6 0 0 2 B O O A. I A )
.. ---�-- - -· -·-- ·-
-
_ _
_ _
_
Absorption spectra of KCI(Tl) (After Seit::) of KCl
The valence band (or filled ba n d ) is a s s u m e d to be d ue to
the Cl- i o n s . e m p ty) is a scri be d to l eve l s of the neutral K a to m s . The transitio n of an e l ectr o n from valence band to condu ction b a nd corre spo n d s to its mi gra t i on from the valence sh ell o f th e Cl - ion to the outer shell of a K + ion which thus becomes a
the matrix lattice
The co nd u c t i o n band (normally
p o s iti o ns of t h e bands relative t o th e zero of poten taken to i nfini ty ou t s id e th e crys tal) are d escribed by t h e v al u e s x a n d 'If' respectively (see Fig. I I . 2) : x is the electronic affi n i ty of the solid : it is the work obtained in taking an electron fro m i nfinity to th e bottom of the cond ucti on band o f the crystal . VJ is the separati on or extraction energy : it is the work done in re m ov i ng an electron fro m t h e top of the valence b an d to an i n fi nite d i s t a nce outside t h e crystal .
neutral ato m .
T h e energetic
t i al (electron
hv
1p --x
Emission and absorption spectra
33
i s the width o f the forbidden energy gap. a method o f ca lc u lat ing 1p and x by c o n si d eri n g the energy balance in a cycle w hich for 1p c on si sts of removing the C l - i o n from the crys ta l in o rd e r to rem ove its electron =
Mott and Gur ney h a ve d evel o pe d
K - - - r' j
__ _
i
-
--- - �
C L- -- -- -
I
7t:?rt') of p otwr tial
.
Fig. 11.2 Energy levels in KCI(T{). The filled band due to the K+ ions is situated below the valence band
a nd th e n p ut tin g it back into th e c ry s tal For x a K + ion is removed i n o rd e r to add an electron to it and th e n it is also put b a c k into the crystal. This ena b l es 1J! a n d x t o be determined fro m the electro n affinity of chlorine and the i on iza ti o n p o te n ti al of free K atoms which a re known from exp e ri m ent The res u l t is .
.
and
so
1f!
R:J
9 · 5 eV
hv
=
and
1p - x,
=
x R:J 0· 1
eV
9·4 eV
which c o rresp o n d s to a long wavelength absorption limit of 1 , 3 1 0 A . 2 . Energy levels o f the free thallium ion
The g roun d state of the Tl + i on is an 1S state (a central core outside which are two 6s electrons (6s 2 ). The first excited state is a P state (6s 6p). From Hund's r u l e we ass ume that the lowest state of t h e 6s 6p con fi gu ra t i on is a trip l et state 3P at a lower energetic position than the singlet 1P becau s e of the sign of the exchange integ ral (th e inverse is true fo r nuclear spectra using the model of M . Mayer) . The effect of spin-orbit inte racti on is to lift the dege n e racy of t h e triplet state, the state with the lowest J value b ei n g the least altered , i.e. the electron spin being a n ti para l l el to the orbital moment. The e n e rgy level scheme of Fig. U.3 is o b ta i n e d the energy val ues given -
there being fro m experiment.
,
34
Seitz a n d
Luminescence in Crystals
Williams associate the observed absorption bands for
Tl + ions in the crystal with the following transitions :
1S0 -- 1P1 (f ;: 1 ) 1 S0 -- 3P2 (very weak) (f ;: 0· 1 ) 1S0 -- 3P1 T h e transition 1S0 -- 3P1 being a singlet t o triplet state transition will be forbidden if the cou pling is purely of Russell-Saunders type : spin o rbital interaction is considered as a very weak perturbation. t 1 ,960 A 2, 100 A 2,500 A
eV
: 10
'P.I ·· - ····--- - -- - - -- -- - � 9 Jp
i
I
S1ngle electron s: a t fl s
Wi�h !!.tchange
Fig. I I . 3 Energy levels
�o 1
3
i 2
With spm orbitai coupling
_ __ __ _ _
1 1
j0
of the free Ti+ ion
Actually, in heavy atoms it is allowed t with an oscillator strength (f) less than that for the transition 1S0 -- 1 P1 which indicates partial jj coupling. The ratio of oscillator strengths will be about 30 for the free Tl+ ion : (the intercombination transition is relatively enhanced in the crystal). The mercury line at 2,537 A used for excitation in this band (1S0-- 3P1) is due to a transition between the same spectroscopic states 3P1 -- 1 S0 (Hg and Tl + have the same electronic structure).
t It wil be remembered t h a t in Russel i Saunders coupling or L . S coupling the orb ital moments I couple to give a resultant L and the spins s to give a resul tant S and only then is spin orbital coupling introduced to give J = L + S. This is o n l y valid for weak s p in - o rb i tal coupling : if the coupling is strong, then I and s for each electron are coupled (j = 1 -1- s) and the va r iou s j's are then added, this being known as jj coupling. t The trans i t ion life time is of the o r de r of J O ' sec and so the use of thall ium activated alkali halides as scintillators gives a shorter life time than that of photo conducting phosphors of the ZnS type ( J o • to w • sec).
35
Emission and absorption :,pectra
The transition 1S0 -+ 3P0 is forbidden for all o rd e rs (J 0 to 0) t h e 3P0 l evel constituting a typical electron trap. The transition 1S0 -+ 3P2 is also forbidden but only for a d i po l e approximation : the level 3P2 also forms an electron trap. These tran sitions cease to be forbidden when the Tl + ion is perturbed by a neighbouring Tl+ ion which occurs at higher concentrations. ='
J
3.
=
Location of the ground state 1S0 of TI + in the energy band scheme of KCI
F. E. Williams has calculated the io ni zat io n energy of Tl+ in the c ry s tal :
TI + -+ TI 2 + + conduction electron Outside the crystal this ionization : Tl+ -+ TP+ + free electron requires an energy I equ al to the second ionization potential of thallium, i.e. I = 20· 3 eV. However, i n sid e the crystal the re p l ace m e nt of TJ + by Tl 2 + y i e l d s the energy ae 2 /d and is 8 eV (a is the M ad e lu n g constant, d t h e inter atomic distance). This value is only a first app ro xi m atio n and must be modified to take account of the different polarizabilities of the lattice ions. We obtain the energy x i n taking an electron from i n fi ni ty into the conduction band. From this calculation the ground state for thallium is found to be ae 2
I-(1--x
1 2 eV
below the conduction band : polarization terms reduce this to 9 · 5 eV. The ground state of t h e Tl + ion is thus 0 · 1 eV below the top of the valence band . Since 2, 500 A corresponds to a quantum of about 5 eV, the 3P1 excited state in KCI(Tl) is situated at 9 · 5 - 5 4· 5 eV below the cond uction band. It is this which determines the q ua s i ato m i c nature of the emission transitions in t he phosphor. Excitation with 2, 500 A radiation can excite the Tl + centre without ionizing it : in addition, the energy of 4·5 eV cannot be provided by thermal ionization. However, at high intensities the 2, 500 A can ionize certain Tl + ions already excited by a first quantum : this is stepwise excitation of an electron from valence to conduction band . Besides, KCl can have other levels than those of the Tl + ions (due to F ce n t res pairs of T!+ ions, &c.), some of =
-
,
36
w h ich
Luminescence in Crystals
be i o n ized givi n g a very s m all p r o b a b i l ity of a weak p h o t o the ter m non-photocond ucting was placed in in ve rte d commas in th e t it le) . However, this photoconductivity is not necessary in the p rod u c t i o n of em i ss i o n ; in fact, it perturbs the lumin escence k i ne t i c s, t he freed e l ect r on s b ei n g able to recombine with can
c o nd uct i vity ( t h u s
e m ission centres for intense excitation and for high thall ium concen
recomb i n at i o n results in the same emission ban d s as fo r d i rect excitation of the activator ion ( T e ch . B. Louch tchik and e o -wo r k ers ) ; but the filling o f traps will be tration (Antonov-Romanovsky) . Suc h a
d i fferent . Traps n o t connected with the t ha l l iu m centres will now con tribute to t h e
p h o s ph o r e s ce n ce
decay . The same kind of
n o mena appear u nder X-ray or vacu u m u l t r a -v i o l e t
p h e
e xc ita ti o n .
I I . ABSO RPTION AND EMISSION PHEN O M ENA IN
KCI(TI), T H E C O N F I G U R A T I O N A L C O O R D I N A T E D I A G R A M (Mott a n d Seitz) 1 . Introduction to the model To acco unt fo r the d i fference
lengths :
as
1 S0 -+
111
emiSSion a n d absorption wave
3P1 (ab so rp t i o n)
3P1 -+ 1S0 (emission)
},
}.
=
2, 500
=
3,050
well as the w i dth o f the e mi ss i on a n d a b s orpti o n E at
(values
.
h alf height
at o rdin a ry
_
A A
band s :
0 · 3 eV for absorption 0 · 6 eV for emission
temperatures : the values are
re d u c ed by o ne-half
at 80°K) we must introduce the interaction between th e th all i u m ion
Tl + and the remainder of the c rystal . To a first a pp r o xi matio n we consider the Tl + ion substituted fo r a K + i o n , the six neighbouring Cl - i o n s vibrating about the Tl + ion. We c o n s i d er only the v i b r atio n al mode in whi ch the same d i s t an ce r between the CJ - and TJ + io ns occurs for all Cl- ions. The s ta t e o f t h e system fo rmed by t h e C I - i o n s i nte ra c ti n g with t h e Tl + i o n can be characterized by the d i s t a n ce r cal le d the configurational coordinate. To a sec on d degree o f approximation we must also in t r od u ce the interaction of the six CI - ions with the six n e a r e st K + ions of the lat tice situated o n the same r a d i u s vector at a distance r' from the CI- i o n s . T h i s l ea d s clea rly to a re-definition o f the c o n fi g u ra ti o n a l c o o rd i n ate .
Emission and absorption spectra
The
37
configu rational c u rve o r d i agram is that w h ich defi nes the
potential energy
U(r)
the coordinate
Two curves must be considered : that for the ground
state
r.
of the system Tl+ plus lattice as a function of
oztu (T l + in 1S0 state) and that for the excited state of the Tl +
ions (3P1). It is rarely possible to give such a precise physical meaning to the coordi nate
r
and moreover to be able to calculate the configura
F. E.
tional cu rves.
Williams was able to obtai n both fo r KCl(Tl)
3
4
5
6
7
eV
Fig. 1 I .4 Absorption and emission �pectra of KCI( Tl). Experimental results at room temperature
and this is why it was chosen as an example. G eneral l y, the
can do is
to
b es t
one
s h o w that a system o f configurational curves can b e
drawn to represent t h e experimental results . In several cases, h ow ever, these curves, o nce derived experimentally, can be used to pre dict new phenomena, e.g.
F centre luminescence. We shall examine
the latter later.
In the case of KCI(Tl) Williams uses the Hartree functions for er
and
K+
and calculates those for Tl+. The value of these functions
has since been criticized , in particular by Knox and Dexter, but nevertheless the results obtained are still i n good agreement with the facts. 2. The interaction between TI + and
Cl-
This includes - a Madelung electrostatic term - an exchange repulsion term
EM,
ER,
- a Van der Waals attraction term
Evw,
- a correctio n to the preceding term for the attraction between the
d ipoles induced on the Cl- ions by the perturbation of the lattice
resulting from introd uction of the thallium E1,
- for the excited s t ate a corre cti on Ec to the electrostatic e nergy
due to overlap of th e charge distributions arou nd the different ions.
38
Luminescence in Crystals
We
thus have for the g ro und state :
o/tU
=
ER + Evw+ EM + Er
an d for the excited state : OU•
= E'R + E'vw+ E', - E'r+- Ec +- 6 · 5 eV
6· 5 e V b e i n g the difference in the el ect ronic e n e rgies of the two states t he free thallium ion. It is the correction Ec to the Madelung electrostatic energy due to overlap of the c h arge distributions of t h e Tl + and Cl - ions (overlap w h ich is m u c h l a rge r in t h e excited state) which is r esp o nsi ble for the greater part of the cha nge in the equilibrium position of the ions acco rding to the p a rt icu l a r electro nic state of t he thalliu m i o n and t h u s for the Stokes separation between the abso rption and e miss ion in
band s .
I n t h e p e r fe ct KCl lattice the distance o f t h e K + ion from its near est C l - ion neighbour i s r0 = 3 · 1 4 A in e q ui li b riu m . At this distance fro m the nucleus the n o rmal charge density of the 6s electron of Tl + is o n l y 0· 0 1 , while that of t h e 6p electron is about 0·05 according to Williams's calculations. The overlap of the chlorine and thallium ions is t h u s effectively more important when the latter is in the ex c i t e d P sta te than when it is in the ground state S. Ec added only to the excited state energy is actually the difference in the overlap coulomb energies of the two states. The electrostatic attraction between the Tl + a nd Cl- ions is the resultant of the mutual coulomb repulsion of the nuclei, of the sur rounding electrons and of the attraction of the surrounding electrons of one nucleus for the other nucleus. The correction Ec is the sum of several terms of opposite sign but finally it res ults from the diminu tion in the repulsion of the two electron cl ouds. We consider an e x ternal l ay er of the thallium ion . The part of t h e chlorine electron cloud it includes is not repulsed but is subject to a null effect. There fore the attracti o n between c hl o ri n e and thallium i o n s with partia l e l ec t r o n ic o verl ap is greater t ha n that fo r the net c h a rge e of each co n ce n t rated at the centre of each respective ion. A s a c o n s e q ue nce the distance r between the chlorine and thallium ions in equilibrium is about 0·3 A smaller in the excited state than in the ground state. After Ec the most important terms are ER the exchange repuls ion a n d E,.w the Van der Waals a t t r a ct i o n Ec v a r ie s m o re rapidly with r .
Emission and absorption spectra
39
than Evw but le ss rapidly than ER. It follows that the curve 0k'•(r) is less sharp than '1/"(r), corresponding to a smaller vibrational quan tum for the ions when the thallium is in the excited state. The calculation of the e n er gie s 0U"(r) and crt•(r) is first made for the second n eig hbour K+ ions held in their equilibriu m po s itio n s in the perfect KC! la tt i ce while the different displacements of the CI- ions occur (.6.r r -- r0) . The energies '1 are thus sensibly quad ratic fu nc tions of .6.r : 0?/•· Y(.6.r) ae· u (.6.r-.6.r0)2 + constant 6. r0 is the displacement of Cl- ion s from equilibrium positions in the perfect lattice when a K+ ion is replaced by a TJ + l uminescence centre. The same calculation is t hen made for the d i s pl ace ment .6.r' o f the s econ d ne ighbo u r K + i on s from their normal position i n the per fect KCl latti ce . The energies '1 can then be represented by quad ratic functions of .6.r and 6.r' w i th coefficients assigned to them by the method of least squares : '1f•. u(6. r, .6.r') = Ae· Y(.6.r -6.r0) 2 + B(.6.r' -.6.r0')2 + constant These six K + ions are displaced .6. r' from their equilibrium position .6.r0' by the introduction of the Tl+ ion into the lattice. The coeffi cients A are obviously different fro m the a's. It would be most to use the two coordinates .6.r and .6.r'. However, in order to have only one configurational coordinate, Williams now assumes that for each .6.r value the remainder of the lattice has the equilibrium value .6.r' = .6. r0'. The energies '1 are then only functions of .6.r : '1f•. u(.6. r ) A•· q(6.r -.6.r0) 2 + constant as show n in Fig. II.5. It is clear that such a si m p le approach is only justified if the influ ence of the displacements .6.r' of the second neighbours is small. The pe rturbation resulting from .6.r'�O is no more than a tenth of an electro n volt. If the correction due to second n e i ghbo u r s had been large , then account would have had to be taken of the third neigh bour effects, and so on. Each ti m e a new definition of the configura tional c oo rd i na te 6.r would have had to be made . We thus see that this model is particularly appropriate to calcula tio ns for very localized centres suc h as Tl+ in KCl. For extensive centres such as boron acceptors in silicont it is better to use a mod el =
t Corresponding to absorption bands
at
about 0·04 cV.
Luminescence in Crystals
40
developed by various authors (Huang and Rhys, Pekar, Meyer, &c.) i n which a direct treatment o f the i nteractio n between the centre an d phonons of the perfect crystal is made, w i t hout giving special significance to the coordinates of specific atoms in the crystal. The results obtained by these two approaches arc o ften very si milar. u ev; 6
5
4 2
u9
2
( 1s0)
ar
F i g . 1 1 . 5 Configurational coordinate diagram /or KCI(Tl)
(After Williams, 1951)
D.r is the displacement of the neighbouring Cl- ionsjimn their mean positions in the pe1ject KC/ lattice
For luminescence where the centres are quite localized, more or less as in KCl(Tl), the configurational coordinate model is generally preferable, but with Lax we believe it is not always necessary to attri bute to the oscillators with energies cp;u and Olf• the nature of vibrating ions. Sometimes as a first approximation it may be possible to intro d uce only one configurational coordinate r, which can be described by a complicated function of the coordin ates r, of several io ns in the crystal : r = f(ri> r 2 , r") •
•
•
However, even if r exists, it will not be a linear fu nctio n of the co ordinates r11• From a theoretical aspect (see page 52) the general situation is that a configurational coordinate scheme is a convenient representation of the abso rption and emission characteristics over not too large a temperature range, but for large ranges the parameters such as ionic mass and oscillator frequencies must be modified . Experimental accu racy h as not yet revealed such variations.
Emission and absorption spectra
41
In the diagram of Fig. 11.5 we obtain the mean frequencies of absorp tion and emission v0 by using the vertical transitions hv0 (Franck Condon principle) from the minimum of the curve Cf/Y(r) of the ground state for absorption and from the minimum of the excited state curve 0/t• for the emission. Thus for absorption 1 S0 � 3P1 ; hv0 = 5 · 48 eV calculated (Fig. T I . 5) compared wi th 5 · 0 eV i n experim ent (Fig. li.4) and for emission 3P1 � 1S0 ; /zy0 = 3·9 eV calculated and 4·06 eV experimenta l . The vibrational quantum of the ground state is hYu = 0·0 1 6 eV and that of the excited state h1'• = 0·0 1 eV. The mean number of vibra tional qu anta thermally emitted after absorption in order for the system to fall into the minimum o f Cf/• is Sa = 41 , whil e after lumin escence emission the number emitted t o return to the minimum of 0/t" is s. = 67. The calculation described above is that made initially by F. E. Williams ( 1 9 5 1 ) . Since this time , many improvements in the theory have been suggested by different workers, ch i efl y the re-normaliza tion of the wave function for the thallous ions in the excited p- state , when these ions are introduced into the crystal, and the modification of the spin - orbit coupling affecting the U (eV l separation between the 1P and 3P states. These corrections are extremely sensitive to crystalline interactions. Configura Tnplet state tional curves much more intricate than the curves of Fig. II.5 have thus been proposed , including a pronounced mixing of singlet and triplet states. However, it is worthy of note that the last paper by Johnson and Williams ( 1 960) comes back again towards the simplicity of the initial 0 - o t. - 0 2 0 • 0 2 6r ( $. ) model. The configuration cu rve for the Fig. II.6 New, simplifed ground state 1S0 remains u nchanged , configuration model for 180, but the 3P1 curve suffers slight changes, 3P1 and 1P1 states inKC/(Tl) and the agreement with experiment is (Johnson and Williams, 1960) better. 3. Position of the absorption and emission band maxima
Luminescence in Crystals
42
An o t h e r fu n d am e n t a l c al cu lat i o n , i . e . using also the wave fu nc
tions of
Tl + i o n s
as starti ng-point, has been m ade by Kristoffe l
grou nd state 1 S0 and emitting l evel 3P1 a r e con sidered , a n d in the s a m e w a y as i n J o h n s o n a n d W i l l i a m s ' s c a lc u l a t i o n s , but o n ly t h e total l y symmet ric vi brati o n s of the e r - i o n s are considered . However, t h e ch oice o f the wave fu nct i o n s for the p-state i s s l i g h t l y different and takes into acc o u n t their angular depe n den c e . This ca l c ul a ti o n leads to a smaller d isp l ac e m e n t o f th e ions than i n th e J o h n s o n and Williams th e o ry . The ag re e m e n t with e xp e ri m e n t is a li tt l e better t h a n in the W i l liam s calcu latio n of 1 9 5 1 but not so good as in the Johnson and W i ll i a m s model of 1 960. H owever, for ( 1 9 59). The s a m e
t h e s e three calculations this agreement is as good as it may reasonably
be h o p e d to be from theories u s i n g only one configu rational co o r d i n at e .
TABLE
II. 1
the numerical values of the ionic vibrational quanta hJ't and hve, and the displacemen ts of t h e ions r0, for the three theories described in the text above Comparison between
hve
hvt
Williams, 1 9 5 1 J ohnson and Williams, 1 960 Kristoffe1, 1 9 59
0·0 1 6 eV 0·0 1 6 eV 0·0 1 9 eV
ro
0 · 0 1 0 eV 0·0 1 2 eV 0 ·0 1 5 eV
0·30 0·26 0· 1 6
A
A A
Other absorption and em ission bands in KC/(Tl)
While the 2,500- A a b s or p ti o n band
is
d e sc ri bed as d u e to the
1 S0 -+ 3P1 intercombination t r a ns iti o n , the intense ab s orp t i o n band at 1 ,960
A i s connected with the
a l l o w e d 1S0 -+ 1P1 transition
34) . In a d d i t i o n to the 3 , 050 A - em i ss i o n (3P1 -+ 1S0),
i s observed
i n the region 4,750-4,900
(pa ge a blue emission
A.
In the initial Williams th eo r y , this blue emission was ascribed to the 1P1 -+ 1S0 t r a n s iti on . Thus the long-wave emission band was
associated wi t h t h e sho r t- w ave a bs orpti o n ban d . This huge Stokes
(r0 � 0·5 A) fun dam e n tal calculation had then been
shift might be explained by assuming a much larger change in the
equil i b rium configuration of the ions for the 1P1 state than for the 3P1 state, but no
m a d e on t h is p o i n t . The state of a ffa irs is now more satisfactory s i nce the recent dis covery, by Eby and Teegard en and by J o h n s o n a n d Will iams, of a
Emission and absorption spectra
43
new emission band centred at 2,470 A ; this band is excited by i rradia tion in the 1 ,960-A absorption band . Thus the postulated sch e m e i s n o w t h e fol l owing :
2, 500 A absorpt i o n 3 ,050 A e mi ssi o n 1 ,960 A absorption 2,470 A emission
I So -+ 3p1 -+ rso -+ l p l -+
3p1 ISO rpl
ISO
In con t ras t to the earlier model, the configu rati onal coord inate cu rves for the triplet and si n gle t emitting states are very similar. This 2,470-A em i ssio n was not previously observed , because it fal l s within the 2,500-A absorption band, and thus the emitted light is strongly reabsorbed . The visible blue emission remains for t he presen t unexplained. Johnson and Williams suggest that it originates also from isolated Tl + i on s , but in a different excited or vibrational state. Other emission bands appear at high thallium concentrations, arising from TJ + pairs and other imperfections, such as molecular complexes of the form Tl(Cln) (P. Pringsheim, Ewles and J os hi). K C ! and TIC! may be mix ed in all proportions. Sunit Chandra Sen has shown that in such mixtures two phases exist :
(a) KC! activated by a large amount of thallium, in which one recognizes the emission bands described by the above autho rs ; (b) TIC! contaminated by potassium. TIC! seems to be luminescent in the pure state, the luminescence being due to structural defects (Sokolov and T olstoi) . Potassium acts here as a que nche r of this luminescence. The 3,050-A luminescence emission from isolated TJ+ centres in KC! is not polarized, except at temperatures near that of liquid helium (Klick and Dale Compton). This polarization is obtained when the exciting radiation is itself polarized. Theoretically, the spatial degeneracy of the centre may be removed when it is placed in the crystal lattice (Jahn-Teller effect), but the energy difference be tween these sub-levels is surely extremely small. However, at liquid helium temperature a preferential orientation of the centre may ap pear. The observed polarization is for centres distorted along the (100) d irections . On the other hand, the blue emiss i on is n ot polarized, even at liq uid helium temperature.
44
Luminescence in Crystals
a s T l+- pai r s , p robably shows much m o re pronounced
The emission from centres whose structure is fundamentally asym metric, s u c h
polarization effects.
I.
I l l . C A L C U LATI O N O F T H E E M I S S I O N A ND A B S O RPT I O N SPECTRA F R O M T H E CONFI G U RATIONAL COORDINATE M O D E L Statement of the problem
We have
seen how we can ob ta i n from the configurational co ordin ate
curves using the F r an ck- C o n don p ri nciple. We now c o nside r the form and magnitude of these bands. model the positions of the maxima of the absorption and emission
For the osci llators
-1fu
and o/• we have equi-distant vi brational
which we den ote by the symbol m i n the ground state and n i n the excited s t a te . In KCl(fl) and with t h e p r ese n t atio n d u e to Wi llia m s these arise fro m vibrational l eve l s of the Cl - i ons (co u pled to the rest of the lattice) surrounding the Tl + activator ion . For the tran sition from the vibrational level n of the excited state to the l e v el m of the gr ou nd state there is an emission o f a l i n e of fr e q u e n cy ln•nm levels
·
for all possible values of n and m forms the emission band . The same ideas a pp l y to the absorption. In practice, the ban d s cannot be resolved into l ines since the li ne s . 1 ' n m a re broadened by other vibrational modes of the lattice which are not taken account of i n the d iag ra m h aving a single configura t iona l coordinate. However, in one sa mp l e of Zn2Si01(Mn), C. Vlam has found a re s o l u t i o n of the emission spectrum into 1 9 lines wh e n the tem pe ra tu re is lowered to l 5°K. There is a non-zero band width at absolute zero : t h e emission transition begins from n 0, but because of t h e zero poi n t energy o f vibration can be to variou s o f the m level s . The explanation of the residual large wid t h (one or m o r e tenth s o f an electron volt) of t h e se bands at abso lute zero is one of the s u cce s s e s o f this model . The idea of i n tr o d u c i n g the ze r o - p o i n t energy in c onsi d e ratio n of l u m i nescence character is ti c s was due to M. Sch o n . If the temperat u re is suffi ciently high, then the band width increases because the emission transition can occu r fro m l evel s with n � 0. Experiment i n d i cate s that the form of The assembly of these 'lines'
=
Enu:uion and absorption spectra
45
the absorption and e m i s s i o n bands, a(hv) an d J(/w) respectively, general s en s ibly gau ssia n W e first define t h e notation used : .
The parameters of a gaussian distribution : If l !hv)
0
__
I(hv)
I I I
I _L_L _
�
is in
is a ga u ss i an dis-
�
Fig. I J . 7 Tire Gaussian distribution rr
rr
tribution about a mean value hv0 , the normalized distribution i s given b y
I(h 1')
=
� ex p
aV2n
[- (hv l�'o)2]
J J(hv)d(lw)
wi th
hv
and
hl'o
=
T h e mean square d ev i a ti on is
=
2a
=
J
I
I(hv)/IJI(/(hv)
1:1(hv) JJ(hv-l�v0)2l(hv)�(�l0 =
=� a
The cu rve J(h1') is s ymme t r ic a l abo ut the mean energy and h as points of inflexion for hv = hv0 ±a. T h e width at half m ax i mu m is 2L where [2 2a2 log. 2
h v0
=
2. Calculation of energy distribution in the spectrum
This can be made as for diatomic molecules. We set out the expres
s
i o n fo r the l i gh t i n tensity for t h e d i pole case which is
f(hl'nm)
_ ·-
64n411nm 4
-� I P.nm I 2
a n d we assume that f/nm is proportional (Condon ap p roximation).
to t h e
overl ap i n tegral
Luminescence in Crystals
46
th e ions, then we separate the e l ec t ron ic wave function tf>(x) and the vibrational wave fu ncti on 'lfJ(r) a n d thus postulate If
of
x
are the electron coordinates,
The factor
Pnm =
f
r
th e configurational coordin ate
t/>.* (x)v•n*'(r - r0)extf>a(X)1p,.,/'(r) dx dr ,f l ea =
f f,*(x)ex
depends only on the electronic states e a n d
dx g,
and s o
we
h a ve
To simplify m atte rs we change the no tat io n by reference to para graph 11 above ; the origin of the configurational coordinate cu rve u
I
h V0
u9
Fig.
·
0
r
Calculation of e m iss ion spectra: v0 is the frequency at the band maximum; >'n m is one of the possible emission frequencies
II.8
corresponds to the minimum in ct/q an d
excited state m i n i m u m of crt• rel ative to ct/9 :
is the displacement of t he the g ro u n d state minimum
r0
Emission and a bsorption spectra
47
The functions 'lflm0(r) and 'lfl,/(r - r0) are thus the eigenfuncti ons of
t he harmonic oscillator V'm"(r)
Nm e xp
[ -1(�Hm(�J - n
where H111 is the Hermitian polynomial, Nm a normalization fa cto r and au is the classical a m plitude of the ze r o p oi t vibration : ==
•
--
v'
au - = -
h
h M(J)u
,
= --
=
J�
liw0 is the vibrational quantum of the i o n s in the ground state : analo gous notations are used for the excited state. M is the mass of those ions which are vibratin g i.e. the mass of the six Cl - ions in KCI(TI) to a first approximatio n To a second de gree of approximation W i lliams gives 1'a
hvu
Wu
=
=-=
.,
Mc1* = Mc1 + a 2MK a being a couplin g constant equal to 0·4 3 . M = 6Mc1*
where
The quantum number m reached after e m i ssion is high (and i n the same way the number n reached after absorption) ; we h ave seen that it is about 67 for KC l (Tl) Thus J 'lflm0(r) J 2 tends towards th e classical density d i strib uti on which possesses a very sharp maxim u m aroun d the classical ampl i tud e rm given by 3. Calculation using a semi-classical approximation
.
0/IU(rm)
=
tkurm2
=
(m +!)hvu
In contrast, the initial state of the transition must be treated quantum mech ani cal ly Case for low temperatures. A t low temperatures the emission wil l begin from th e state n = 0, the only one occupied i n thermal equi
librium : Now
'lflo
.
is a gauss i an function and thus so also is p,,
j 'lflo" ( r - ro) f 2 , 1
f lom
=
No 2 exp
[
., 1 - = co n s t exp
.
I
L
-
( -0.--. )2] rm - r0
48
Luminescence in Crystals
is the vibrational amplitude at t he zero-po int ene rgy :
a.
"
By
qiP(rm) · - 1'19(r0)
T h u s we obtain The
li
=
li
VkeM Mwe differentiation of qig(r) in the regi o n of r = Oe"
"
llom"
moment
while the
a,
of
m o m en t
the
=-'
----
=
=
--
- h(l'om 1'0)
co n s t .
e xp
=
r0 :
k0r0(rm ·- r0)
[ (h1'0 m-h110)2] f.:.
2 " " 'a ro"a, ·
emission band is given by the expression 2a,2 kaz,.oza.z =
aa of the a b s o rpti o n band 2a"2 k.2ro2auz
is
g ive n by
=
We can alter these formulae to indicate the mean number s. [ = 67 in KCJ(TI)] of thermal vibrational quanta emitted after the photon
h 1 •0 = qf 0 SJn•0 -l- kar02 Sehl'a and so a.2 s.(h1·a) 3/lw, for the e m i ssi o n ban d . I n a s i m i l a r way, if we i n trod uce S,. [ '"' 4 1 for KCI(Tl)] , the n umber =
=
u
Sa h ve l - - - - - - - I
of
thermal
and
so
Fig. I I . 9
-
- - - ----
r
Introduction of the parameters Se and S,_,
vibrational quanta emitted after absorption of a p ho t on
ln•0 1k,r0 2 "
Gu ..
= =
@'o+ Sah1'e Sa111'e
(h1•,) 3 = Sa-- hl'u
Emission
In
the case w here
the vibrational frequencit:s a,
aa
The
and absorption !!pectra a;
Sa = S,
a 2 = S(h vphonons)2
a nd
v0
=
S
v,
a rc
49
equal
wid ths of the a b s o rpt i o n and emission bands are t h u s the same. KCI(TI) 1'• a n d 1 'v are q u ite d iffere n t : we h ave a l read y
H owever, fo r
se e n that
and s o �
h1•0
3
=
(Johnson, Wil l iams, O'n
:=:
to
4
0·0 1 6 eV
near
and
hl'e = 0·0 1 0 eV
This rat i o
to absol u te zero, which
S t u d er) .
is
is so e x p e r i me n ta l l y
only about 2
at o rdinary
Casefor any temperatures. The fr ac t i o n of excited centres to be found in the vibrational state n if t h e r m a l eq u i l i b r i u m is attained b et w een
temperatures .
absorption
and
so I
and e m i s s i o n t
,nnm
fi n
1 2 wi l l
is
�'-'
exp ( - - n/11',/kT) •o
_'2: exp (-- nh11e/kT)
" " ()
be affected
l(hvnm)
by t h e factor Pn
Pn
i 1Pn"(rm r0) 1 2
and wc then have
The e m i s s i o n i n tensity at freq u ency v can b e gi ven as a d ou b l e sum m ati o n over n and m , remembering that En" - Emu hJI. T h i s means that
n
m
s h o w t h a t the
OC
distribution remains ga u s s i a n . We use the
Franck-Condon principle, that is, we assume that emission occurs the position of the i o n s t and this position co rreWe now
with o ut change in
t Evi dence for this rapid ' ther:nostating' of the excited centres by the crystal lattice is given by the fact that the l uminescence quantum yiel d for KCl(Tl) is independent of the wavelength of the exciting light, as long as i t falls i n t o the 1 S0 -+3P abs o rpt ion band of the TI+ ions (Louchtchik, Tech. , Louchtchik, N. E. 1 and Shvarts). Th is is t r u e even if the exciting radi a ti on is s i tuated on the long wave side of the absorption band, for wh ich (as a result of the overlap between emission and absorption bands) part of the emission results from an anti-Stokes p roces s . � Actually Franck and Condon did not give this p ri n cipl e in such a restricted form. It is the mo s t intense lines which are emitted without change in the position of the ions. We are limited to a consideration of the latter.
50
Luminescence in Crystals
sponds to the cl assical vibrational a mp l i t u e
d
We can then replace
r"'
as defined above.
by Furthermore, we c a n replace the s u mmation over t h e fi nal vibrational states (m) by an i ntegral :
l(h v)
cc
f [LP" /
tp,."(r,. - r0)
"
/2]o[Oll'(rm)-"71°(rm)-111J dr,.
makes use o f the Mehler formula for the Slater summations of the harmonic oscillator :
The s umm a t i on
'\
11 = 0
n2"n !
H,,z(x) e -x'
where We h a ve thus
'�p,.
and
l(hv)
=
IX =
1 . ) 1 1 2 exp sm h IX
hl'e/k T
1 tp,/(rm r0) 1 � =
ex p
f [ -1k.(rm exp
cc
r0) 2 .
tanh
[- x2 (�2)]
[
�
ta n h
(;�)J
X
t an h
o (Ul/•(rm)
(�)]
O/t11(rm) - hv)
d r,.
We now take a new variable x = Ol! •(r,.,.) -
integration and obtain
I(h v)
cc
h ave
ex p
f f(x)o(x - hv) finally { exp [
a n d since we
f [
I(hv)
- -}k. (r -- r0) 2 •
cc
f(hv)
dx
••
ta n h
;�·�J ��}., =h•
r being related to the emission fr e q u e ncy by t h e linear relation
-h(v--Y0) = kur0(r- r0)
The exponential factor gives an esse n tially gaussian form to J(hv). A t high temperatures l(hv)
cc
e xp
[
J ��
Emission and absorption spectra
51
which is a classical formula, the exponential being that of the Boltz mann distribution , and gives the probability that the emitting system will be in the configuration r allowing by means of the Franck Condon principle the emission of a photon hv. This classical approximation w a s used by Williams for KCl(Tl) to which it applies wel l at liquid air temperature (90°K) which is suffi cie nt l y large. For KCl(Tl) the quantum hv. i s very small (0·0 1 0 eV). In contrast for CaWOlPb) it reaches 0·05 eV and Vlam has found that the classical approximation is onl y valid at temperatures w ell a b o v e ro o m te m pe ra ture
.
At T = 0 the hyperbolic term tanh
( ;�)
is eq u al to u ni ty and we
obtai n the expression first derived for low temperatures. Finally the band width L varies with temperature according to the relation
L.(T)
[
L.(o) tanh
A ty pical example of this variation is gi v e n in Fig. I I . l O. The theoretical curve has a point of inflexion and the width L(T) finally =
-
11 2
:: � Fig.
0
1 0 0 2 0 0 3 0 0 400 5 0 0
of luminescence emission band width (at lwl}: b and height) with temperature for a Ca WOlPb) phosphor
II. I 0
Variation
varies as vT (classical approximation). However, in the fi g ure this temperature re gi o n is not reached . For the width of the ab s o rption band lrv. is replaced by hva in the a b ove form u l ae : (After Vlam)
La( T)
==
La(O) [tan h
-l/2
The introduction of the factor 'tanh' may be understood in the fol l o wing manner : in the expression for the moment of the emission
52
Luminescence in Crystals
band, fo r i nsta nce, established above for the case of emission at O " K : 2a.2 = ku 2ro 2a. z
amplitude o f vibration o f the ions a t the zero-point energy a . must now be replaced by the mean square value a.(n) of all the ampli tudes in t h e d i fferen t vi brational s tates n. T h ese a m p l itu des a re d e fined by J.k.a.2 (0 -H)Izl'e the
Jk.a.(n) 2
This
sum mation
=
(n + J.)hv. a. � a, (n) = v"i:,p"a-;(n)2 =
( ) [ ;;�J The case \\'here the configurational is
straightfo rward a, n
=
a• .
and
tanh
space
leads to -112
is many-dimensional. I n the
c a s e , we have seen ( page 39) that several coordinates must be used i n order to describe the configuration of the ions interacting with the luminescence centre. W e shal l assume th at the p ote ntial energies have been put in t o the d i ag o na l form : general
qlu(r1, r2
ql•(r1, r2
•
•
•
)
)
=
U0u + 2: J.ku;(r; - r;0u) 2 i
U0• + 2: -!ke;(r; - r;0•) 2
T h i s is i n d e e d the case in Williams's calculation, with 2 coordinates, r 1 describing the position of t h e Cl - i o ns neighbouring the Tl + a c ti vator ion, and r2 describing the position of the next n e a res t ne i gh •
•
•
=
i
bours, i . e . K + ions. The
position of the maximum of the emission band is then given by
hvo
and the
=
qto• - Olfou - 2:-!-ku;(r;o• - r;ou) Z
corresponding m oment by la . o
2
ta rili (h;;•j2kT) l t is seen that, th e o r e t i ca l l y , this result cannot be o b tained by means of a one-dimensional c o n fi gu rat i o n d iagram , except w h e n all the fre quencies v,C are equal. However, for KCl(Tl) t h e difference between the results obtained in this way and the results obtained by Williams and eo-workers in el iminati n g the se c o n d c o n fi g u ra t i o n al coordinate r2 is almost i ns ignifica n t (about 0 · 1 5 e V in the position of the ba nd) . The general case, wh e re Ol/• and q1u are in a non-diagonal tensor fo rm , h as been treated by Kubo a n d Toyozawa, and by K. Maeda
(1 959).
=
Emission and absorption spectra 4 . Quantum-mechanical calculation for
tions u. and u, are equal
the
case
53
where the
ion vibra-
We put hve hvu = fwJ as t h e vibrational quantum for th e ions and the frequ e n cy of the e mi tte d photon. We c a n now gi ve a rigorous calculation o f the o v e r l a p i nt e gra l =
v
J(hvnm) =
f'f/ln*'(r-r0)'rp,/'(r) dr
o cc u r s in t h e matrix el em e n t /lnm (J. Ruamps).t We have seen t h a t t h i s as s ump tio n is not val id for KCI(TI) (hv. 0·0 1 eV ; hvu 0·0 1 6 eV), bu t it is al l righ t fo r F ce n t res i n the same KC! crystal where from Klick we have hv. R: hva R: 0·0 1 1 eV We have thus a si ngle pa ra m e ter S which is th e mean number o f th e rmal vibrational quanta emitted after the op tic al transition resu l t i n g in ab so r pt io n or emission of a photo n . S is given by w h ich
=
=
f n e m is s i o n the line iS Of about a frequency
1-kr0 2
and in ab s o rpti on
hv0
=
=
Sliw
U0- Siiw
Vo
given
by
The Stokes s h i ft between absorpti on and e mi ss ion is thus 2Sho> . U0 is a l w ay s the electron ic energy difference between the g r o u n d and ex cited states . Consider the emission, for e x a m pl e . An e m i ssion of fre q u ency Ynm occu rs by tra n s i ti o n from a vibrational s tate n to a vibra tional s ta te m, th e tra n s i ti o n b ei n g followed by e mi s s i o n of p m n vibrational quanta (mean value o f p S) : =
overlap integral J(hv,m) is given hvnm
The
ii ,/'( S)
=
=
a
U0 + (n + -})liw - (m + -})liw
=
An11(S); (p fu nction : -S. S! P] LnP(S) [n!etn +p) AnP (S)
J(hv,m,)
=
bei n g a n orm al Laguerre
by
U0 - pnw
formula d u e to Erdelyi =
m - n)
=
t In a recent p u b li cat i on (1 960), J. Ruamps has described an extension of t h i s metho d for the case hve =F hvg. The form o f the emision band /(h•) c a nno t be e x plic i tly derived, but the ex p ress i o n s of the first and second m ome n ts are given as developments in series. In ad d i t i on let us remark that the anharmonicity effects arc probably les im portant for t he case of luminescence centres i n a soli d than for the spectra of diatomic molecules. However preci se computations must take these effects into account. See the paper by Rebane and Sild, quoted i n the bibl iography .
,
c
,
54
Luminescence
w h ere
Ln P (S) level :
can be emitted by transition fro m
v
only depends on p.
1'
!(hv)
,
Crystals
=
However, the mean frequency any n
in
T hu s we h av e
n = oo
o:
[An11(S)F
1l = O p = const.
e -no:
e
ncx
"
(/. is , as pre v i o u s ly given by !iwjkT. This sum mation is ma d e by u s i n g the Myller-Lebedefr fo rm ula :
J(hv)
0:
e Pa./ 2e S coth (a./2)]
P
(
.
S
.
smh (a/2)
)
If n = 1 /(ea.- 1), the m e an number of vibrational quanta excited at temperature T, we can then w ri te
!(hv)
where
i.e.
lv(x) is
the
0:
e - S(•H llJP [2SVfz(n + I )]
Bessel fu nction with complex argument
lp[2Sv'n (n T 1)]
=
oo [svrz(n + I ) 281., L s !(s+p) ! J -
, ,� o
-
------
-
,
i-7'J11(ix),
-
This formula is due to Huang and Rh y s Pekar, Lax, Meye r, O'Rourke, &c. We have obtained it by using the co nfi gu ra ti o n al co ordinate model, but it is u s u ally derived by using the model where the interaction between centre and lattice is obtained by rep re s e nti ng the la tt e r by its as sembly of ph onons (c f. para . II.3) ; !iw is then the pho ton energy in the perfect lattice i nstead of the vibrational q ua nt u m for the ionic neighbours of t h e centre. Apart from this detail the formulae obtained are identical . According
to Klick the configu rational coo rdinate model is the ce n t res : we h av e seen that the common value of liw. and liwa wh ich gives the best i n terpretatio n of the observed spectra is 0·01 1 eV , which for the opti ca l branch of the perfect lattice vibrations of KC! (optical phonons) is 0·028 eV. We shall not give the calculati ons for the model of Huang and Rhys and Pek ar, but simply indicate that each term in the summation for JP appears as a c o n t ri bution to I(hv) from the transitions in which better one for F
Emission and absorption spectra
55
quantum a n d s+p ga i n a quantum a n d the total effected by a n emission of p ph o n o n s. We can verify that the mean value of p is i nd eed equal to S ; the mean value of p 2 is, according to Lax s oscillators lose a transition is
-
p2
such
S(2n + 1 )
that the moment a 2 a2
=
=
of I(kv)
f (hv-hl'o)2/(lrv)
=
S coth
2k T
has the value
d(hv)
=
[ (J;T)J -I
S(/iw)2 tanh
which agrees with the expressions obtained b y the semi-classical approach for this moment at absolute zero and for its v a ri at i o n with temperature. When x 2SVn(rz + 1) is large compared w i th unit (n or S l a rge) we have the asymptotic form =
lp(x) -+
e"'
e -P'/2:1:
V2nx I(hv) is thus a gaussian functio n centred on p S. Not only the m omen t a2 but the form of the emission band are identical to those obtai ned in the semi-classical approximation. This expression for I'P is al re ad y accurate t o 5 per cent i f x 4. =
=
BIBLIOG RAPHY
I. Structure of KCI(Tl) Energy levels in KC! HOWLAND , L . P . ( 1 958) 'Band structure and cohesive energy of KCl', Phys. Rev., 109, 1 927. MoTT, N. F. and GURNEY, R. W . ( 1 948) Electronic Processes in Ionic Crystals, 7 1 , 80. Clarendon Press, Oxford. (1 939) 'An i nte rp re t a tio n
Energy levels in
SEITZ, F .
Faraday
KCI(Tl)
Soc., 35, 79.
of c rys tal luminescence', Trall.S·.
11. Absorption and emission phenomena in KCI(Tl). Experimental V. V. (1 942) 'Th e mechanism of l u m in e s cence of phosphors', J. of Phys. U.S.S. R., 6, 1 20 ; 7, 1 53 . B UTLER, K . H . ( 1 9 59) ' Fl uo re s cence of thal l i u m -act i vated h a l ide phosph o rs', J. Electrochem. Soc. , 103, 508.
A NTONOV- ROMA NOVSKY,
Lumin escence in
56
EBY,
J.
( 1 9 59)
Crystals
E . a n d T E E G A R D E N , K . J . ( 1 9 59). Q u o t e d by (see below) .
EwLE s , J .
Knox, R. S.
a n d Jos H I , R . W . ( 1 960) 'The l u m i n e s ce nce o f thallium
activa ted potassium ch l o ri d e p h o s p h o r s ' , ?ro e . Ror. Soc . ,
358.
A
254,
HUTTEN, E . and P R I N G S H E I M , P. ( 1 948) 'A new method preparing st r o ngl y lumin esce n t t h a l l i u m a c tivated a l k a l i h a l i d es a n d some properti es of t h ese p h o s p h o r s ' , J. Chem. Phys. , 1 6, 24 1 . .T O H N S O N , P . D . and W t LL ! A M S , F . E. ( 1 9 54) ' E flect of p re s s u re o n the optical a b s o rp t i o n o f t h e activa t o r sys t e m i n K CI(T l ) ' , f'!Jys. H I RSH LOFF of
Rev. , 95,
69.
K u c K , C. C. a n d D A LE C O M P T O N , W. ( 1 958) ' P o l a rized l u m i nes cen t e m i ss i o n fro m KCI(Tl) a t low t e m p e ra t u res', J. Phys. Chem. Solids, 7, 1 70.
L O U C H T C H I K , N . E . and L O U C IH C H I K , T e c h .
scopy of the luminescence centres in by h om ologous series of ions' ,
B . ( 1 9 6 0) ' S p e c t r o
alkali halide crystals activated
Opt ics and Spectr., 8,
44 1 .
Lou cHTCHIK, Tech. B . , LIIDY A , G . G . , Y A E K , I . V . and T I I S LER ,
( 1 9 60) 'The mechanism of the recombination luminescence Optika i Spektr. , 9, 70 ; Optics and Sp ectr. , 9, 35. P A T T E R S O N , D. A. a n d K LI C K , C . C . ( 1 9 57) 'Emission a n d excita tion spectra of KCl(Tl) at low temperatures', Phys. Rev., 105, 40 1 . P R I N G S H E I M , P . (1 942) ' Fluorescence and phosph orescence o f thal lium-activated potassium halide phosphors', Rev. Mod. Phys., 1 4 , 1 32. S C H U L M A N , J. H . , CLAFFY, E . W . and P O TT E R , R. J. ( 1 957) 'Con E. S .
of a cti v at e d alkali halide crystals',
centrati o n dependence o f quantum efficiency of l u m i n esce n ce in KCl(Tl)', Phys. Re v . ,
108, 1 398. A. and T O L S T O I , N . A. ( 1 960) ' T h e luminescence o f thallous chloride', Optika i Spek tr. , 9, 42 1 ; Op tics and Spectr., 9 ,
S O KOLOV , V . 2 1 9.
CH A N D R A S E N , S . ( 1 959) 'Some aspects of the luminescence CaF2(Ce, Mn) and KCI + TI C I phosphors'. Thesis, I n d i a n
S UNIT
of
I n st i tute o f Tech n o l o gy, Kharagpu r .
Computation of the configurational coordinate diagram for KCI(TI) J O H N S O N , P . D . and WILLT A M S , F . E . ( 1 960) 'Simplified con figura t i o n a l coordin ate m o d el fo r KCI (Tl)', Phys. Re v . , 1 17, 964.
Emission and absorption spectra
57
K A M I M U R A , H . a n d S u G A N O , S . ( 1 959) 'Luminescence processes in the KCI(TI) phosp h o r i n
s p ace ' , J. Phys .
a multid i m e n s i o n al co n fi gu rati o n a l
So c . Japan , 14, 1 6 1 2.
i n te raction in alkali h a l i d e phospho rs ' , Phys . Rev . , 1 1 5, 1 095. KNOX, R. S. a n d D EX T E R , D. L . ( 1 956) ' So l i d State luminescence theory a n d oscillator strengths in KCI(Tl)', Phys. Rev. , 104, 1 24 5 . K R I STOFFE L , N . N . ( 1 9 59) 'A quantum m ec h a n i ca l calculation of the K N O X , R . S . ( 1 959) 'Co nfigurational
l uminescent centre in KCl(Tl)', Optika i Spektr. , 7, 78 ; Optics and Spectr. ,
7, 45.
W I L LI A M S , F . E . ( 1 9 5 1 ) 'An
cence', J.
ab s o l u t e th eo ry o f solid-state l u mines
Ch em . Phys. , 19, 457.
E. ( 1 9 5 3) 'Th eory o f the l u minesce n ce o f i m p u rity J. Phys. Chemistry, 57, 780. W I L L I A M S , F. E. and J O H N S O N , P . D. ( 1 9 59) ' Confi gurati o n a l co o rd in a te model fo r KC J (Tl ) incl uding spin-orbit i nteracti o n ' , Phys.
WILLIAMS, F.
activated ionic c ry s ta l s ' ,
Rev. , 1 13, 9 7 .
Computation of emission and absorption spe c tr a
in th e configurational
coordinate model (with par t icular reference to KCI(Tl)-type phos phors)
Tech . B . , LOUCHTCH I K , N. E . a n d S H V A RTS, K . K . 'Electronic-vibrational processes in the luminescence centres of ionic crystals', Op tika i Spek tr . , 9, 2 1 5 ; Op t ics and Sp e c tr . , 9,
LoucHT CH I K ,
( 1 960) 1 1 3.
WILLI A M S , F . E . ( 1 950) 'Calculation
of the absorptio n a n d emission spectra of the thallium-activated p o tassi u m chloride phospho r ' ,
Phys. Rev. , 80 , 3 0 6 .
W r LL I A M S , F . E . ( 1 9 5 1 ) 'Theo retical low temperature spectra o f the thallium-activated potassium chloride phosph or', Phys. Rev . , 82 , 28 1 .
W I LL I A M S ,
F . E . and HEB B , M . H . ( 1 9 5 1 ) 'Theoretical spectra o f solids', Phys. R ev . , 84, 1 1 8 1 .
lu m in es ce n t
Ill. Calculation of emission and absorption spectra (general papers)
A comprehensive review
D E XTER, D . L. ( 1 958) ' T h e o ry
of the o p ti c al properties of imperfec
t i o ns in n o n-m etal s ' , Solid State Physics, 6, 353. A cad e m i c Pre ss ,
New Y o rk .
Luminescence
58
in
Crystals
Other papers D . ( 1 958) 'Sur le calcul des s p ec t res d'emission dans le modele des cou rbes de con fi gu ration' , Comptes-Rendus A cad. Se. Paris, 246, 404. CuRIE, D . ( 1 9 59) ' Calcul des spectres d'emission par l'emploi de d iag r amm e s a p lusieurs coordonnees de configuration', Comp t es Rendus A cad. Se. Paris , 249, 1 884. CURIE, D. ( 1 9 60) 'Calcul des spectres d'emission da ns le modele des
C U RI E ,
de c onfigu ra tion : sur une interpretation p hy s i que simple resultats', Comptes-Rendus A cad. Se. Paris, 250, 834. H U A N G , K . and RHYS, A. ( 1 950) 'Theory of light absorp ti on and n on - radiati v e transitions in F- cen t res ' , Proc. Roy. Soc., A 204, 406. K R I V O G LA Z , M . A . ( 1 956) 'Comparison of the theory of the lumines cence of solid bodies with expe rimen t', Opt ika i Spektr., 1, 54. Kuso, B. and T O Y O Z A W A , Y. ( 1 9 55) 'A pplicatio n of the method of ge ne rat in g functions to radiat iv e and non radiative transitions of a t r ap p ed electron in a crys t al ', Frog. Theor. Phys. lap . , 13, 1 60. LAX, M. ( 1 9 52) 'The Franck-Condon p ri nci p le and its ap p l ication to c rys tal s' , J. Chem. Phys. , 20, 1 752. LAX, M . and B uRSTEIN, E. ( 1 9 55 ) ' B ro a de n i n g of i mpu ri ty levels in silicon', Phys. Rev., 100, 592. M A E D A , K . ( 1 9 59) 'One-dimensional configurational c o - o rdin ate curves for luminescence centers', J. Phys. Chem. Solids, 9, 335. M EYER, H. G . J . ( 1 955) 'Some aspects of e l ect r on - la tti ce interaction in p ola r crystals', Physica, 2 1 , 253. Thesis, A m sterd am , 1 9 5 5 . O ' RoUR K E , P . R . (1 953) 'Absorp tion of light by tra pp ed electrons' , courbes des
Phys. Rev., 91, 265. S . I. ( 1 9 54) Untersuchungen uber die Elektronen theorie der Kristalle, 1 29-1 54. Akademie-Verlag, Berlin. R E B A N E , K. and S I L O , 0. (1960) 'The calculation of the prob abilities of electronic vibrational transitions for a n an harmonic o s cil lato r' , Issledovania po luminesc., Tartou, 12, 3 . R u A M P S , J . ( 1 95 6 ) 'Sur le c al c u l des intensites dans les spectres de ban de s des molecules diatom i qu es (cas de l'oscillateur harmo nique)', Comptes-Rendus A cad. Se. Paris, 243, 2034. RUAMP S , J. (1 960) 'Calcul de la position et de la largeu r de l'enveloppe des bandes d'une transition electronique', J. Phys. Rad. , 21, 52S. VLAM, C . C. ( 1 953) 'The structure of t h e emission bands of l u m in
PEKAR,
escent solids'.
Thesis,
G ro n i n ge n .
C H A PTER 1 1 1
Experi mental Determination and Use of Configurational Coordinate Diagrams
1. Tungstates, willemites, halophosphates, &c.
A s d i sc u sse d in the
previo u s chapter, F. E. Wi l l i am s was able for the of the t ran s i tion 1S0 ++ 3P1 in KCl(Tl) to obtai n th e en e r gy v ersus c o nfi g urational coordinate curves for g round and e xcite d states and from them to o b ta i n ab so rp tion and e mi s s i on spectra which coul d be compared with e x pe ri me nt . This is a rath er excep tional case. However, it is possible to obtain fro m e xperime n ta l results a confi g urational coord i nat e diagra m and to confirm this with other results. Such diagrams have been used for the alkali halides, wille mites , tun gstates , h alophosphates (Fonda), calcium oxide (Janin and Crozet), all being cases of phosphors in which lumines cence is not very clos e l y associated with photoconductivity. They have also been a p pl i ed to doubly activated phosphors such as Ca3(P04MCe-Mn), &c., to e xpl a i n the process of sen s it iza tio n (B ot de n ). In the case of ph otoco n du c ti ng phosphors of the ZnS(Cu) type the use of configurational coo rd in at e di ag rams has been somewhat criticized , especi al ly by F. Seitz. They certainl y cannot be applied to the kinetic processes which occur after absorptions and before final emission. However, they can be applied to processes which are c on fi n ed to the emission ce ntres. Th e opti ca l and thermal activation of electrons from traps may also be described with a confi gurat i o n diagram (see Chapter VII), but, as a general rule in these p h osphors , not on th e same diagram as for the luminescence centres . We shall co ns i d er some examples bri efly : (A) Tungstates. These are s o m et i m es used in X-ray fluorescent screens. The configurational coordinate diagram was derived by V l am. The typical ex peri m ent al d ata are as follows : for a CaWOlPb) phospho r containing I per cent by weight of lead . case
59
60
Luminescence in Crystals TA B LE II I . l
Emission spectra of Ca W04(Pb)t
Temp.
20 90 288 410
°K
hv0 (e V) 2·68 (4,630 2·69 (4,620 2·73 (4,540 2 ·77 (4,480
A) A) A) A)
2Le
(e V) 0·71
0·725 0·82 0·87
We see that the width of the emission d oes n o t ch a nge s ign i fi ca n t l y with temperature ( l 1 5 i n creas e between 90°K and 1 40°C) . From the rel ation
L.(T)
=
L,(O)[tanh
ln·,j2kT] - 11 2
t h ere fo r e, we find a h igh value fo r the v i brati onal quantu m e nergy
in the excited state of
a n d in the grou nd state
ln ·c
0·050 eV
=
ln·u
=
0 · 1 0 eV
t he distance between the e q u i l i b rium position excited and ground states
r0
is esti mated t o be
r0
=
of the
ions m the
0 · 20 A
the atomic grou p responsible for the e m iss i o n is the t u n gstat e i o n W04 2 -. V l a m i d en ti fi e s t h e configu rational coord i n at e r with the d istance of t h e tungsten fro m the fou r s u rrounding oxygen
We as s u m e that ions .
(B) Wil!emite : Zn 2 Si04(Mn).
numb er Zn 2S i04(M n) have
a
by
Klick and Schulman .
large
Manganese functions
as an activator
of fluorescent solids. The emission spectra o f
in
been studied by Kroger, Szigeti a n d Nagy and by Vlam , &c. The configu rational co o r d i na t e d i agram was derived
TABLE Ill.2
Emission spectra of Zn2SiO�(Mn) T. °K
20 90
28S
The
410
h"o (e V) 2-40 2·39 (5,200
2 38
2·37
A)
(5.220 A)
b a n d width dou bles betwee n
about
2Le
(e V)
0· 1 1 0· 1 3 0· 1 9 0·23
I 80°C and 1 40"C and t h e
t T h e n o t a t i o n o f t he p rev i o u s chapter is used.
Configurational coordinate diagrams
vibrational quantum is m uch smaller than for
phors . Klick an d Schulman give
hv. hvg
r0
=
0·025 eV
=
0·04 eV
= 0·06
61
Ca W04(Pb) p h o s
A
The value of r0 is p a rti cularly small, and as a result the a p p r o x i ma r r0 t o obtain
tion made in differentiating U0(r) in the region of
=
a linear relation between the emission hv and r is not s atis fa ctory . The form of the emission s p ectral curve is cl e a rly different from
Fig. J I ! . I Low temperature (20°K) emission sp ectrum
Zn2Si04(Mn)
oJ
Continuous curve: observed spectrum (C. V!am) Cross points: computed spectrum (Klick and Schulman)
gau ss i a n (in the q u a n tu m t h e ory of II.4 this -co rre s p o n d s with the case where the p a rame te r S is small and the asym p totical app ro x i ma tion to t h e ga u ss i a n form of J"P can no l o n ge r be used). The observed spectrum is asymmetric, show i n g a 't a i l ' on the longer wavelength side e x ten d i n g i nto the red . Before the work of Klick and S chu l m a n , attempts were made to resolve the spectrum into a nu m b er of gaus sian com p one nts with out trying to attri b u te them to different wel l defined centres .
The emission transition is att r i b u ted to a s p i n reversal of o n e of the 3d shell electron s of the M n 2 + ion. The mode of vibration is a radial one for the four oxygen ions surrou nding the m a n ga n ese. (C) If we apply the configurational coordinate m odel to Z n S (Cu) p hos p h o rs the b a n d wid th i ncreases with temperature i n a n inter medi at e m a n ner re l at i ve to CaWOlPb) and Zn 2Si04(Mn) ph osph o rs
62
Luminescence in Crystals
vibrational q uantum b e i n g between 0·03 and 0 · 04 eV."! lt migh t be ass oc i a te d with vibrations of the s u l p h u r i o n s urro u di n g the copper i o ns . the
s
n
A m o n g phosphors used in fl uorescent lamps the h al o ho p h ate s have first l ace as they enable a wide ra n ge of colours to be achieved by variations in their compositions. From a theoretical aspect they demonstrate the effect of activator environ ment on emission spectrum. The formula of the halophosphates is
( D) Halophosphates.
p s
p
3Ca (PO ) Ca i
!
F 2 (Mn 2+ Sb3+) Cl2
They can be excited by 2,537-A radiation o r by cathode rays. An timony g iv e two emission bands as follows ( h e most i nt e n e one is
3 4 2•
s underscored)
a nd
t
s
gh t on the behaviour of this a ct i v a o r has rece n tly been thrown by F. E. Williams ( 1 960) . o cc u rs in the form Sb3+ (Butler and Jerome), which is i s o e l ect r on i c with In+ and so its scheme 4,870 A
Some theoretical l
i
3,960 A
t
It
of energy levels is very similar to Tl+, except for a smaller spin-orbit (near to the p u re chlorophosphate) where structural changes are ex p ecte d , the osi tio n of the antimony peak shows a negligible dependence o n t h e ratio CI 2/F2 since the nearest neighbours of t he Sb3+ in the l a ti ce are six 02- ions. How ever, the i n ten s i ty of the peak suffers a noticeable ha n ge with this ratio. The manganese is present in the divalent state Mn 2 +. Its emission spectrum is conveniently described by two gaussian bands, t which are progressively displaced as the chlorine is replaced by fluorine from 5,950 A and 6,550 A coupl i ng. Except at
compositions
p
t
to
and
c
vibrational quantum hv. for the main emission band of Mn2+ 5, 700 A
6,250 A
is about 0·03 5 eV (Vlam). Comparison with the value of 0·025 eV for The
willemite shows that the value depends on both the activator and i t s s ur roundin gs.
with the method of preparation of the specimen : see H. PAYEN GARANDERJE and D. CURJE, Comptes Rendus, 248 (1 959), p. 3 1 5 1 . t The quantum
� This
energy
and also
the band width
of the emission vary markedly
is really only an empi rical way of describing a
DE
single asymmetric
LA
band.
Configurational coordinate diagrams
63
The l i fe time of the tran sition giving e m i s s i o n from the S b H i o n s i s about I I 1 500 sec, whi l e that for t h e M n 2 1- emission i s about I /75 sec. The anti mony is necessary as a sensitizer for e xcitation of the man ganese emission (see Fonda, Brit. J. Applied Physics, suppl. 4, 1 955). As sole activator it gives a light-blue emission . With similar concen trations of antimony and manganese c� 2 per cent) daylight simula tion can be obtained . Increasing the manganese content gives warmer tones, but truly red phosphors are not obtained ; the efficiency of the 'warm white' lamps made using these phosphors can reach 60-70 lumens per watt (Vanmaker and Ouweltjes).
2.
Relation between F centre absorption bands and the luminescence emission ascribed to F centres
The colour centres of
F type form the most investigated lattice in the alkali halides. They are defined as halogen ion vacancies which have cap t u red an electron. For other types of defects or imper fections in these crystals reference may be made, for example, to C. Kittel (Introduction to Solid State Physics, J. Wiley (1956), pp. 49 1 -
d e fects
502). F centres can be prod u ced by a stoichiometric excess of the cations.
For example, a sodium or potassium chloride crystal can be heated in sodium or potassium vapour at a temperature of about l 00°C below the melting-point and then cooled quickly so that colloidal aggregation of the excess ions (or v a cancies) does not occur. The observed crystal colours due to the presence of F centres are as follows : Yellow NaCI M agenta KC! Blue KBr KI Blue-green
Since the whole crystal must be electrostatically neutral the excess of positive ions must be co m pensated by an eq uivalen t number of elec trons captured in the negative ion vacancies forming F centres. The coloration can be produced by electrolysis in an electric field of a few hundreds of volts per centimetre at a temperature of 10°C or so below the melting-point and also by bombard m ent with X-rays or high energy particles which remove electrons from lattice ions which are then captured in the negative ion vacancies ; at present such i rrad i a t i o n i s the method most o ft e n used to colour these -
64
Luminescence
in
Crystals
crystals. H o wever , it gi v e s rise to other k i n d s of cen tres, e.g.
centres, a n d
V
th e observed effects are m u ch m o re co m p l e x than th ose
p r o d u ced by add itive c ol o r at i o n
.
The F ce n t re ab s o rp tio n is assumed to be d u e to t he transition -
fro m the gro u n d s tate uu to an excited state u•, the gr o u nd state, being of
Is
c h a r acter and the excited state l i ke a 2p state
(a ll o wed
t ra n
sit i o n) . The work of Gudden and Pohl s h o w e d that such absorption
p r o d u ce s p h o toconduction a t t em pe r a t u re s above 90°K, but thi s Ccrh1uc : ; :. ,, b a .i d
d ec rease s rap i d l y at
lower temperaexplained by activati o n energy
tu res . T hi s behaviour is
a ssu mi n g that an ::;,; O· I eV i s necessary t o ra ise an elec tron fro m the e xci te d state uu into t h e
I P cV
co nduction band (Fig.
At 90°K
Is
III.2) .
t e m p e ra t u re s not much above
a
l u m i n e sc e nce emission is ob
I s transition. For F cen tre luminescence Fig. I I I . 2 Energy-level scheme has b ee n l o oked fo r, and it now s e e ms for F centres in KBr to have b e e n o bse rv e d d u ri n g recent yea rs ( B o t d e n , v a n Doorn and Haven), fi r s t o f all with a very low quantum efficiency I to 3 per cent, but m o re recently with an e ffi ci e n cy of 91 per cent. This is due to the fewer ' killer' cen t res in served for the 2p -a long ti m e this
-
,.
the crystals n ow u sed . Measu rements were made at 77°K, 20°K and
we re fou n d t o ch ang e very little in position with a considerable Stokes shift is ob se rved be and emission which makes it d i ffic u l t to be certai n
4°K, and the b a n d s
temperatu re . However,
t ween
ab s or ption
that i t i s F-centre e m iss i on
.
A blue-green emis si o n is observed fro m many al kali-halide cry s ta l s
w h e n excited b y ultra-violet light, b u t it can c ry s tal s
are
mostly contaminated with
be shown that ' p u re
oxygen ( M ae nh ou t and van
and L ewis) : these oxygen ions accompanied by are o fte n respo nsib le for t h i s visible emission . Klick has shown th a t a detectable green luminescence is produced i n NaCI b y i ncorp o r a ti o n o f 4 · 1 0 -6 of copper. In add i ti o n , i n coloured crystals, a visible and u l tra vi o le t em ission may occu r when electrons c o mi n g from F centres recombine with V-type ce n t r es or with the '
der Dorst ; H al peri n
anion v acan cie s
-
above
oxygen impurity centres : such an e missi o n is pro duced by th e F ban d , o r d u ri n g the gl ow-cu rve experiment when
i rrad i ati o n in
coordinate diagrams
65
t h e F cen t res are thermally emptied , b u t it i s n ot thought t o be
F c e n tre l u m i n escence
(Bonfiglioli, B ro vetto and Cortese ; H a l p eri n kind had been earlier d e
scribed by G. Perny. Pekar and K l ick have p re d ic ted t h e w a vel e n gth regi o n where the -
a n d K ristianpoller) . Phenomena of th i s
emission of F cen tres would be expected .
The co nfigurational c o ordi n at e curves can be d rawn w i t h o u t r e fe r
n atu re of the coord i n ate ; it is though t to be the d is t a n ce from the centre of the vacancy to each of th e six surrou nding K+ ions. Th e re are fou r parameters to b e determ i ned : th e coordi nates o/1 0 and r 0 of the m in i mum of the excited state curve, the m i n i m u m o f the curve fo r "1111 be i n g taken as the o ri g i n and also the coeffi c i e n ts k,. a nd k0 : "lu = Jkur 2 e nce to the
,
"1.
=
-!k.(r - r0)2+ o/10
c a n be repl aced by e xpre s s i o n s for hvc a n d hv11• As shown by Klick's ex pe ri m en t , a good fit i s obtai ned by assuming hv. � hv11•
The coefficients ke a n d ku
We take now
(i) the
p o si t i o n of th e F abso rpt i o n b a n d ; K l ick u s e d that fo r
extrapolation to absolute zero.
(ii) the relatio n givi n g the variation of the band wi d t h w i t h tem
[
p e ra t ure
L,.(T)
hvo
La(O) tanh
=
J
- J /2
2kT
Since this is for t he absorption, it gi ve s the vibrational quan t u m fo r
th e
ground state h1•"
hl'u
and from t h e band w i d th at
La(O)
aa
=
0 · 0 1 1 eV
0°K
l o g. 2,
aa
2
-
Sa
(hv.) a h Va
and finally t h e approximate n u m b e r of phonons Sa e mitted after the t ran s i t ion. Klick a s s u m e d for KBr the value Sa 22 as gi ve n by H u a n g and Rhys . These data for the absorptio n e n a b l e the co n fi gu ra t ional co o rd i n ate curve to be drawn (see Fig. I I I . 3) . From t h i s d i a gram the positi o n of the em i ss i o n ban d s can be deduced . All these bands are in the near infra-red r egi o n Klick used th is model bu t Pekar u s e d that wh e re t he crystal is considered in terms of i ts optica I phonons. However, thei r c o n cl usio ns are very s i m ilar =
.
.
Luminescence in Crystals
66
T A B L E I II . 3
Data on absorption and luminescence of F c ent r es in alkali ha!ides Absorption maximum 290°K
Crystal
0 56 I' 0 63 I' 0·46 ,,
KCI KBr NaCI
78°K
0·54 ,, 0 · 60 I' 0·45 I'
Emission maximum (78°K) cafe. obs.
1 · 1 I' (Meyer) 1 ·2 I' (Klick) 1 · 25 I' (Pekar)
1 ·00
1 ·32 I' 1 ·20 I' I"
The agreement between t h e o re t i ca l and experimental v a l u es seems is th at fro m F c e n t res . The vibra tional qu a n tu m hv. R:! hv. = 0·0 1 1 eVt U(eV) is c l e a rl y smaller than the optical 2p p h o n on energy liw 0·028 eV, but ! Is 2·0 � the K + ions around the vacancy have I l es s b i n d i n g energy than those i n the
to s h o w that the observed em i ss i o n
=
i 0 ·4 0 2 0
I 0·2
0 4 r (A )
perfect lattice. The sign of the shift r0 between the ground and excited equilibrium posi tions of the ions. The absorption and emission spectra d epe nd o n r0 but
not on its sign. We have seen that for Fig. III.3 Configurational co ordinate curves obtained by KCl(Tl) r0 appears to be negative, the Klick for F centres in KBr i nt er i o n i c d is t a n ce b ei n g smaller in the excited state. T he reverse seems to be true of F cen tres . The F-centre electro n has a stronger attraction for the K + or Na+ ions in the ground state when its presence in the vacancy is much more localized. This conclusion rests on some work by I. J aco bs , who showed that at high p ressu re s (several thousand atmospheres) the absorption band is moved to higher energies. The effect is a tt ri b ute d to a decrease in the size of t h e vacancy as the
pressure is raised.
luminescence. M-centre em i s s i on peak s h a ve the infra-red re gi o n . In c o n t ra st to F-centre emission, the luminescence from M centres is observed at room te m perature as well as at liquid-air temperature. The excited state of the M c e n t r e is situated deep below th e c o n d uc ti on b a n d . M-centre and R-cen tre
al s o b e e n re p o rt e d in
t These va"lues are for NaCI (N . B . d i fferent
or
KC! : almost identical values a re obt ained for KBr, b u t cation) /we "'' h1•y "" O· O I R eV ( K l ick and R ussel l), ·
Configurational coordinate diagrams
67
TABLE 111.4
Absorption and luminescence of M centres (van Doorn and Haven)
Absorption peak
KC! NaCI
0 · 8 1 1-' 0·71 1-'
(78°K)
Emission peak
1 ·06
1 ·03
(78° K)
1-'
1-'
The M-centre l u minescence may be excited either by an irradiati o n i n the
M absorptio n band itself or i n the F absorption ban d .
N o polarizati on h a s be e n found for the F-band emission , even
when excited by polarized light. This is in agreement with
the cubic
sym metry of F centres . On the other hand , polarization effects are observed for the M-centre emission. Let p be the d egree of polariza tion defi ned by
(111
Iu - h
P = Iu +I.t
intensity of t h e emitted l ight with polarization parallel t o the
polarizer , and
f.t i ntensity
of the emitted light with polarization per
pendicular to the polarizer.) For exciting radiation absorb e d in the
M band : p
p
=
2/3 fo r exciting light polarized along the tO l l ) direction
=
1 /3
for exciting light polarized al ong the (00 1 ) direction
(Lambe and Dale Compton). These results indicate that the
M
centre can be represented as a
d ipole oriented along the face diagonal. Two models h ave so far been suggested for these centres. Both are i n agreement with the above representation : (a) Seitz's m odel : an electron trapped at a site consisting of two negative-io n vacancies with an adj ac ent positive-ion vacancy ; (b) van Doorn and Raven's model, consisti n g of an associated pair of F centres . Experiments made by the above authors are i n progress which m ay decide between these models. t When the exciting light is abso rbed in the F
band and then re
emitted as M luminescence, the degree of polarization is smaller and of the opposite sign.
't The model of van Doom and Haven seems to be the correct one since no (sec OHKURA and.
electron spin resonance has been detected for M centres MURASE, J. Phys. Soc. Japan, 16, pp. 2076 7, Oct . 1 9 6 1 ) .
Luminescence in Crystals
68
due t o high-energy irradiati on over a lon g p rod u c ed i nto the crystal i n add ition to F a n d M ce ntres. They a l s o give an i n fra-red e m issi o n (between 1 · 2 fl a n d 1 · 5 y), but the res u l t s re p o r ted by d i ffe re n t a u t h ors are not in go o d agreement with each o t h e r When the coloration is
t i m e,
R
cen tres are
.
3. The Smakula fonnula is often used to determine the concentration of a given impuri ty by measu ri n g the a b s orp t ion i n tensity due to the i m p u rity or d e fect If we have N a bsorb i ng ato ms per cubic centi metre in vacuo the absorption section for the ph oto n s i n tegrated over as ass e m b l y of i d e n tical phy s i ca l states, i . e . with the same matrix ele ment, is given by 8;z:v:; a(E) d E = 3c \ f/it \ The Smakula formula .
"
I n ex pe ri m e n t s we m easure t he a b s orptio n coefficient
w hi c h
i s given by
J
k(E) dE
=
N
We introduce t h e o sci ll a tor strength .fit 8n 2mv
(2:-f
=
I for a hannonic
f.r
_
k(E)
\ flit 1 2
3h I r,, I 2
oscillator)
J
k(E) cm - 1
and obt ain
dE =
me
For atoms i n a medium of refractive i nd e x n , c m u s t be replaced by cjn . We must also introduce the ratio effective field Eetr to the applied field (due to the electromagnetic ra dia t i o n) : this ratio occurs as a s q u are d term since the dipole moment Jl is proportional to the field, but ,u 2 app e a rs i n the expression for th e absorp ti o n coefficient. We can thus wri te z f, t dE = Kmc E
Finally we
m
Jk(E)
u s t divide b y the d iel ec t ric co nstant K. We then return absorption : No. of t ra n s i t io n s per atom a = ·-----· ---- -- - -· ·-- -
to the defini tion of the effective cross-section for ·
. .·
·-- . ..
.
No . of incident photons per cm 2
The e l ectrom agn etic
energy density being K£2j4;z:, the number
of
Co nfigurational coordinate diagrams
69
p h ot ons in the field is K t im e s greater in a m e d i u m of d ielect ric co n stant K. A l l these correct ions are u ni m po rta nt a s fa r a s t h e s p e ct r a l d i s t ributi o n o f the radiati o n i s co ncerned , but t h e y affect i ts i n t e n s i t y . S i nce t h e a p p l ied field freq u ency i s l a rge we m a y assu m e
K = n2 I + 4na: w h ere et. is the electronic polarizability of the a to m s , a n d so Ecrr = I + _!et. = n2+2 3 E 3 and we obtain k (E) d E = N . ! =
I
Numerically
N(cm - •)
n
ne zh (n z t- 2) );, me
3
=
k(E) d E
where k is i n cm - 1 a n d E is in electron volts. T h i s is t h e S m a k u l a formula as generalized by Dexter. D e x te r observes t h a t t h e L o re n tz Lorenz expression used for the e ffe ct i v e field is val i d fo r a h i g h l y localized centre, but for an extensive ce n t r e the effective fi el d is close to the value E.t The numerical S mak u l a fo rmu l a applies to t h e c a s e of a line of natural width :
I
k(E)
y 2 j4
=
k(E) dE = !nkroaxY
N(cm-•l
=
)/<max(cm ')Y
I · 29 .
( e V)
However, if t h e band is of gaussian shape, a s i s m o r e often t h e case (Dex ter), then k(E ) = kmax e xp
the half-width bei ng y
I
[- (h� ;d�vo)]
= 2L = 211 V2 log, 2
k(E) dE = a V2nkmax
=
-tJ
n
I og. 2
km�xY
a n d we obtain the Smakula formula as co r re c te d by Dexter :
N(cm-•)
=
0·87
kmax(cm •JY (e V)
t K . R. Silbsee proposed the use of the Onsager formu la E,n/ E
2n 2 + 1
3n2
=
·
Th is is perhaps not much better than t h e Loren tz Lorenz fo r m u l a , b u t s h ows the deg ree of prec i s i o n wh ich can he o b t a ined i n the t heory.
70
In p r a cti ce it
Luminescence in Crystals
is necessary, in o rd er to use this formula, to know the b y using a specimen with a known im purity con centration. Under these conditions it is not of a n y interest to use a formula with an exact numerical co e ffici en t H owever, it is n o w becoming p o ss ib l e to c a l c ul ate oscillator strength s on a theoretical basis. For comparison with exp eri m ent the corrected formula must be u s e d . Experimental values obtained by use of the D e xte r formula are listed below : For the two absorption b a n d s at 1 ,960 and 2, 500 A in KCl(TI) : o s ci l l a t o r strength
.
fi .oGo
/1.o6o
::
h,5oo f2.5oo
I;
::
= 2 x 1 0-4 TI + N = 1 o-z Tl +
0· 1
for N
0·07
for
The oscillator strength d ec reas e s with increase i n TI + concentration while new bands appear in both ab s o rption and emission sp e ctra (P. Pringsheim and Joshi). For the F-centre absorption b a nds : ::
0· 3 ;
::
KC!, KBr, NaCl / :: 0 · 5 t o 0 · 6 K I and
Csl f :: 0·3
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Configurational coordinate diagrams
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LEVERE N Z , H . W . (1 950) An Introduction 232. Wi ley, New York.
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On colour centres in alkali halides B O E R , J . H . ( 1 9 3 7) ' O ber d i e Natu r d e r Farbzentren in A l kali halogenid-Kristallen', R e c . trau. de Chimie Pays-Bas, 5 6 , 301 . PoH L , R . W . ( 1 9 3 8) 'Zusam m en fa s s e n d e r Bericht i.i ber Elektronen leitu n g u n d p h o t oc h e mi s c h e V o rga ng e i n A l kal ihal ogenidkris talle n ' , Phys. Z. , 39, 3 6 . S E I T Z , F . ( 1 9 54) ' C o l o u r centres i n a l k a l i h a l i d e c rys tals', R e v . Mod. DE
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co l o n�s d a n s l e s h a l ogc n u re s
73 Configurational coordinate diagrams On co lo ur cen tres and their lumin esc ence in alkali ha/ides, jfuorite, quartz and o ther minerals
P R Z I B R A M , K . ( 1 9 5 6) Irradiation,
gamon Press, L o nd o n .
Colours
and
Luminescence. Per
I . S . ( 1 9 54) 'Effect of pressure o n F ce n t re a b s o rp ti o n i n a1 ka l i h a l i de s ' , Phys. Rev . , 93, 993 . KLI C K , C . C . ( 1 9 54) ' Search for F-centre luminescence', Phys. Rev . , F centres
Configurational coordinate diagram for
J A CO B S ,
-
-
94,
1 54 1 .
KLICK, C .
C . and R u s s ELL, G .
n a t e cu rves fo r 1 47 3 .
See also : M EY E R , H .
A . ( 1 9 5 6) 'Configu rati o n a l coordi F-centres in al kal i h a l i de c ryst a l s Phys. Reu . , 1 0 1 , '
',
J . G . ( 1 9 5 6) ' S o m e aspects of electron-l attice i n teract i o n
in polar crystals', 32. Thesis, Amsterdam . and luminescence o f F-cen t rcs i n t h e alkali halides', J. eks. Teor. Fiz. S. S.S. R . , 22, 64 1 . P E K A R , S . I . ( 1 9 54) Untersuch ungen ilber die Elek tronen theorie der Kristalle, 1 09-7 6 . Akademie-Verlag, Berl i n .
P E K A R , S . I . ( 1 9 5 2) A b so rpt i o n '
F-,
M-
and R-cen tre
luminescence
P. J . , VAN D O O R N , C. Z. and H A V E N , Y. ( 1 954) ' Lu m i n es ce n ce of F-centres in al kali-halide c rys t a l s' , Phi!. Res. Rep., 9,
BOTDEN, T.
469.
VAN D O O R N , C. Z . and H A Y E N , Y. ( 1 956) 'Absorption a n d l umines ce n ce of col our centres in KC! and NaCI', Phi/. Res. Rep 1 1 , 479. VAN D O ORN, C . Z . ( 1 9 5 8) 'Quantum efficiency of F ce ntre fl u o res ce n ce in KCI' , Phi/. Res. Rep . , 1 3, 296 . K L I C K , C . C . ( 1 9 60) 'Polarization of F a n d M centres', Meeting o n C o l o u r Centres a n d Crystal Lum i nescence, T u r i n , S e p t ember 8- l l , .,
-
1 960.
and D A L E C O M P TO N , W. ( 1 957) 'Lu minescen ce and metry properties of colour centres' , Phys. Rev . , 1 0 6 , 6 8 4 .
L A M D E , J.
sym
V A N D O O R N , C . Z. and H A V E N , Y . ( 1 9 5 5) 'Dich roism of the F an d M absorpti on bands', Phys. Rev., 1 00, 7 5 3 . V A N D O O R N , C . Z . ( 1 9 6 0) 'Th e r m a l eq u i l i b ri u m between F a n d M
S e e also :
Luminescence in
74
Crystals
centres in pot as s i um chloride', Meeti ng o n Colour Centres and Crystal Luminescence, Turin, September 8 - 1 1 , 1 960. F E O FI L O V , P. P. (1956) 'Anisotropic optique des centres l um in o genes dans les cristaux cubiques', J. Phys. Rad. , 17, 656.
L . , KLICK, C . C . an d R U S S E L , D . A . ( 1 955) 'Criterion for the occurrence of luminescence', Phys. Rev., 1 00, 603 . K o V A R S K Y , V. A . ( 1 958) 'The theory of radiationless transitions in
Estimates of the quantum yield for
F fluorescence
DEXTE R , D .
an F centre', Optika i Spektr., 5, 222. PERLI N , Y. E. (1 957) 'On the problem of quantum yie l d of F fl uores ce nce , Optika i Spektr., 3, 328. '
On the
general problem of luminescence in 'pure' or coloured alkali
P . and CORTESE, C . ( 1 959) 'F and V centres thermoluminescent rec o m bi nati o n , Phys. Rev., 1 14, 95 1 , 956. H A L P E R I N , A . and KRISTI ANPOLLE R , N . ( 1 958) 'Thermolumines cence spectra of X-ray colored KC! crystals', J. Opt. Soc. Am. , 48, 996. H ALPERIN, A . and LEW I S , N . ( 1 960) 'Symmetry of the green phos phorescence of heat pretreated coloured KCI crystals', Phys. Rev., 1 19, 5 10. M A E N H O U T , F . W. and VAN DER DORST (1 958) 'Luminescence of pure and silver-activated alkali-halides', Physica, 24, 996. PERNY, G. ( 1 954) 'Contribution a l'etude des centres F dans les h a l o ge n u re s alcalins ' J. Phys. Rad. , 15, 356. ha/ides
B O N F I G L I O L I , G . , BROVETTO,
'
,
SMAKUL A , A . (1 929) 'Ober Erregung und Entfarbung Iichtelektrisch leitender Alkali-halogenide', Z. fur Phys. , 59, 603. S M A K U L A , A. (1 930) 'Ober die Ve r farbu n g der Alkalihalogenid kristalle durch U.V. Licht', Z. fiir Phys. , 63, 762.
3.
Smakula's formula
D EXTER, D . L . (1 956) 'Absorption of ligh t by atoms in solids', Phys.
Further developments Rev., 101, 48.
S I LBSEE, R. H . ( 1 956) 'F-band oscillator s t re ngt h determination in NaCI and KC!', Phys. Rev., 103, 1 675.
Configurational coordinate diagrams
75
R . S . and D E X T E R , D . L . (1956) 'Luminescence th e o ry and oscillator strengths i n KCI(Tl)', Phys. Rev . , 104, 1 245. RAUCH, C. J . and HEER, C . V . (1 957) 'Some F-band optical oscil lator strengths in add i t i ve l y coloured alkali-halides', Phys. Rev. , Oscillator strengths in alkali ha/ides
KNOX,
9 1 4.
F . E . , S E G A L L , B . and JOHNSON, P . D . (1957) 'Oscillator strengths for luminescent t ra nsiti o ns in KCI(Tl) and KCI(In)', Phys. Rev. , 108, 46. 105,
W I L L I A MS ,
CHA PTER
I V
Op tical Transitio ns in
a
Photoconducting Crys tal
Principal characteristics of photoconducting
luminescent
solids. Cop
per activated zinc sulphide, ZnS(Cu), has been the most extensively studied : ZnS(Ag) and ZnS(Au) bel o n g to the same group and CdS has been s u bs ti t u t e d for ZnS in part or c o mp le t el y All t h e se materials are k n o w n as 'conventional' c rys ta l phosphors. I n these c ry sta l s e x citation raises electrons i n to the conductio n ban d . The g re a t e r t h e concentration of electrons i n this band the greater the luminescence and the photoconductivity. A m a rked photo .
c o n d uct i v i t y occurs showing parallel behaviour to the e m i s s i o n both
t h e c o n ducti o n e l ec tr o n d e n s i ty is n o t the only factor which the two phenomena : photocond ucti o n also de p e n ds on the electron mobility and charge distributi o n , &c. , while lumines cence depends on the number of empty recombinati o n centres and the rad i ative transition probab i l i ty , &c. The c o m p a r at iv e study of t h e two effects does, however, give m o s t u seful information. Another ch aracteristic of c o nv e n t i o n a l sulphide p h o sp h o r s th e d u ring e x c i t a t i o n and decay. This pa ra l l el behaviour is q u ali tative si n c e
i n fl uences
,
luminescence e m i ss io n occu rs only when c o n d u c t i o n electrons re
combine with s p e c ifi c i m p u ri t i es o r d e fects k nown as l u m i n e s ce nce
centres. It is only when such n o rm a l a c t i v a t o r impurities are absent that other l u minescence effects a re o bserved and o nly for s pe c ial c o nd i t i o n s s u c h as very low t e m p e r a t u r e s e.g. t h e Ewles-Kroger ,
t yp e of emission
and e x c i t o n luminescence.
Radiative transitions with visible light emission
due to conduction
e l ect ro n s re c omb i ni n g with p o si ti ve holes i n th e valence band a re not c o m p l e te l y fo rb i d d e n H o we ve r t he y obey momentum conserva tion rules which make the transition probability so s m a l l that emis sion is u n observable. .
,
76
I.
1.
Optical transitions
77
T H E ' M O M E N T U M ' S E LE CT I O N R U L E A N D I T S C O N S EQ U E N C E S
Conservation o f momentum in optical transitions from band t o band
Consider th e o p ti cal transition of an el ect r on between two stationary states i n the crystal la tt ice described by Bloch functions : 'ljJk Yk exp (ik . r) fo r the initial sta t e and Y�.;· exp (ik' . r) V'k' fo r t h e fi n al state. k is the red uced wave v e c to r i.e. k 2n �(k) = fi Zk z mv =
=
,
li
=
2m
A. '
=
where �(k) is the kinetic energy of the electron. For approximati on to free electron conditions, Y k and '�'k' will modulate the exponen tial fac to r with the 'periodicity' of the lattice. The m at ri x element corresponding to absorption or emiss i o n o f a photon o f wave number q is
=
Hkk' A
a
2 e �A. grad)1fk J1f"·*me 1
i s a vector po te n tia l of the fo rm
A=
a
exp
d-r
( ± iq . r)
being a vec t o r orientated in the direction of polarization.
Hw c a n be writte n Hw
J exp
[i (k -k'±q) . r](vk'* Xvk) d -r
where (Yk XYk) rep res en ts a q u a n ti ty
*
=
which need not be explai n ed but has the periodicity of the c ry s ta l lattice. It follows t h a t
H�.:�.:·
=
L exp [i(k - k ' ± q) . Rm] n ..
X
J�
xp [i(k - k ' ± q) . (r - Rm)](Yk·* X1•k) d r
the is extended to the mth cell f vector fro m the a represents t All the integrals J d n a and w h e re t h e in te gr a l
m
Rm is a
m
origin to
are i e ti c l
lh,.·
=
of
point which
equal to A a n d so
AL exp [i(k -k' ± q) . Rm] /{,,.
lattice and hi s
cel l .
Luminescence
78
in
Crystals
On the averagct the sum is zero u nless the fo llo w i ng condition is fulfilled : k-k'±q K where K is a p ri n ci p a l vector of the reciprocal lattice exp (iK . Rm) = 1 This is a ge ne ral iz a ti o n for a cry sta l lattice of the law of con se r vat i o n of momentu m . For a bs o rp t i on we have + q a n d for e mi ss i o n -q. I n general, the ph ot o n wavelength is large c o m p a red with the wavelengths of electrons involved in such tr an s i ti ons (for 1 eV elec tron }. 1 ·22 x 1 0 -• cm) and s o for these conditions we have =
=
k-k'
=
K
which shows that there is conservation of the r ed uced wave vecto r in d irect , radiative band-to-band transitions (often calle d the momen tum s e l ec tio n ru l e) . In t h e energy band model su c h transitions are
t'ertical.
2. Discussion
We now consider excitation in the fundamental ab so rpti o n band
of
lattice, i.e. pr o d uc in g a conduction band electro n . T h e electron and h o l e so pro d uced must obey this selection rule and can i m m e d i
the
ately recombine. However, the electron will d i ffu s e towards the bot t o m of the co n d u c ti o n band and the hole to the t op of the valence band . The diffusion is due (a) to i n t eracti o n s between electrons and (b) to interaction of electrons and holes with the c ry s tal lattice. The second effect (b) is us u all y assumed to p re d om in ate . The mean free path of the 'slow' electrons in ZnS is a b o u t I 0-7 cm and the mean velocity a b o u t 1 0 7 c m /s e c . Ph o n o n di ffu s i on o r s catte ri ng of the electrons occu rs every I0-14 sec. Th erm al equ ili bri u m between the electron s a n d the lattice can be attained in I Q - 1 2 to I0 10 s ec , a time wh i ch is m u ch smaller than the life ti m e for radiative dipole t rans i ti o ns (lo-s s ec) . It is the rapidity of this diffusion which in s e m i conductors allows us to i n t rod uce the idea of 'qu a si-Fermi levels'. The effect (a) above only occurs if th e re is a large concentration of conduction e lec tr on s (IQ-H ejc.c) alre a dy . t This c a n be the case for -r We often say - a little too hastily that the matrix element is zero in order that the above conservation law is justified. Actually the summation included in the expression for Hu· is rarely zero. It oscillates about zero while remaining fi n ite. When we n ormalize by dividing by the crystal volume we obtain a quantity tending to zero for an infinitely large volume and then the conservation rule is j ust ified . :� Cf. J. Bok, Thesis, Paris, 1 959.
Optical transitions
i ntense u l t ra-violet e x citati o n s or e x cita t i o n by partic l e s . A d is tinct difference in temperature between the electrons and the crystal lat tice is therefore not impos s ible due to the continued arrival of ener getic electrons in the band. This pos sib il ity was considered in 1 938 by Birus and SchOn. Whatever t h e cause of electron diffusion, once it has o cc u r red the electron and po s itive hole do not show identity of momenta and so cannot recombine with photon emission. They can, however, re combine with simultaneous emission of a photon and a phonon , the latter carrying away the excess momentum but with small energy. This effect is well known for germanium, where it is assumed to be responsible for the infra-red emission at about 0·68 eV (). � 1 ·8 t,t) obtained for high carrier densities. An analogous process is not im possible in zinc sulphide. However, this recombination process has a long life time of ab o ut a second, and in sulphides with activat o rs i s masked b y r eco mbinati o n and emission of the luminescence centres, apart from non-radiative transitions in defects. Even in germanium it only appears for carrier concentrations of � 1 0 1 9jc.c due t o injec tion of a dense flux of electrons and holes. At lower concentrations recombinations occur in defects which are in general non-radiative (deathnium). We now return to the case of direct band-to-band transitions solely with p h oton emission, which is highly likely if after diffusion the electron and hole have t h e same reduced wave vector. This is so i f the conduction and valence bands have their minima and maxima respectively at a wave vector value k 0 (see Fig. IV. I).
79
=
<. (1<) I
.j
I I
Emission 1
0
.
Absorp/J(m; 1<
--
Fig. IV. l
(a) Band structure allowing direct vertical band-to-band transitions with light emission (photon emission only) (b) Band structure with such transitions forbidden
80
H owever, e ne rgy
Lum inescence in Crystals
band structures a rc more complex than that in Fig. IV.2 shows the schematic energy band diagrams (k) for ge r m a n i u m (H e r m an) and i n d i u m antimonide (Kane and Dressel h au s ) respectivel y .
Fig.
IV. l .
0 1 8 oV .\£ 0 0 1 5 cV
0
,,
k
0 /, ·.
111
Fig. I Y . 2
k 111
(a) Energy band structure for germanium (after Herman)
(h) Energy band structure for
indium antimonide
(after Kane and Dresselhaus)
In german i u m the co n d u ctio n band has a mi n i m u m at k = 0 but also eight equi v al e nt minima situated at the band extremities al o n g t h e ( I 1 1 ) d ir ec t i o n s (and thus only four differe n t minima are ob served) a n d lower by !:E :: 0· 1 6 eV than the first m i n im um . The va le n c e b a n d maximum is at k 0 but is complex. In indium anti monide the conduction b a nd has a minimum at k = 0 but the vall nce band i n add i ti o n to a maximum at k = 0 has eigh t equivalent m a x i m a a l o n g t h e ( I l l ) directions close to the o rigi n and higher than the first m a x i mum by !:lE :: 0·0 1 5 eV. In s uch systems there are no vertical, rad iative transitions (wi t h o u t =
a t l o w temperatu res . O nly t h e lowest conduction band mi n i m u m and the h i ghest valence b a n d m a x i m u m a re pop u l a te d with
p h o n o n s)
el ectro ns a n d holes respectively, and t he se do n o t
have the same wave at higher temperatures (such that the value k 0 become appreciable
v ec to rs (see Fig. IV. l 6) . However,
kT :: and
6.£) the populati ons at
t here
i s a probability
with tem perature thus :
=
of d i rec t rad iative t ransitions
which
grows
Optical transitions Value
i\ 1
TABLE I V . !
of the energy gap for some semi-conduct o rs at ddrerent temperatures 4 °K (e V) 0·74 1 ·14 0·23 3 77 3 ·8 3 2·55 2·92
German i u m Silicon lnSb ZnS blende ZnS wurtzi lc
CdS wurtz i t c S i C hex .
7rK (e V) 0·72 1·13 0·22 3 75 HI 2·52 2 91
291 °K (c V) 0 65 1 ·08 0· 1 8 J 6! 3 · 70 2·43 2 86
such as was ob t a i n e d from th e c y c l o t r o n res o n a n ce ' , magneto- resist
T n t h e case of z i n c a n d cad m i um s u l p h i d es we d o n o t
h a ve
evidence,
m ag ne to-o pti cal e xpe r i ment s which lead to the above schemes in the case of ge r m a n i u m a n d J n S b . However, t h e s t u d y of the o p ti cal a b s o r p t io n al l ows us t o m a k e s o m e reaso n a b l e ass u m p t i o n s . It seems t h a t both valence and co n d u c t i on ban ds possess e x trem a at the o r i g i n k 0 o r very close to i t , b u t probably not t h e mi n im u m minimorum' of the co n d u cti o n band o r t h e ' m a x i m u m m a x i m o ru m o f the valence ban d . Thus the l ong wavel ength l i m i t o f t h e fundamental abs o rpti o n band is prob a b l y d u e t o p h on o n - a s s i sted t r a n s i t i o ns as for G e an d 'l n S b The energy o f d i rect vert ical t ra n s i t i o n s i s higher b y a few te nt h s o f a n electron-vol t . The cond uction ba n d i s d u e t o s-states o f t h e Zn o r Cd i o n s , a n d t h e valence band t o s- and p-orbitals of th e sulphur i o n s , m o re or less h yb ri d i ze d acco rdi ng to t h e covalent c h a rac te r of the c o m p ou nd (si1 o rbitals in a pu re l y covalent Pauling model). A s m al l degree of ad mixture of Zn or Cd levels inside the valence b a n d is q u i t e p o s s i b l e but it may probably be n eglected in the s em i -q u a n ti tati ve considera tions at present possible. '
ance an d
=
'
'
,
,
,
For CdS m o re elaborate computatio n s have been made than fo r
ZnS. Accord ing to Balkan ski and d es Cl oizeau x the valence band h a s As a fi rst approx imati o n , t h e band is d ivided i n to th ree parts . T h e
t h e fol l owin g structure :
other two from p-states. The (p,) orbitals exten d i n g a l o n g t h e he xago n al axis are more strongly b o u n d than t h e (p:r.) a n d (p") orbi tals. Thi s a s su mp ti o n (Dress elh a u s) comes fro m the fact that t h e c/a rati o in the Cd S l a t t i c e is s o m ewhat smal ler t h a n i ts va l u e i n t h e i d e a l l owest sub-ban d d e rives mai n ly from s-states of t h e sul p h u r i o n s , a n d
the
82
hex agon al structure :
Luminescence
in
� (hexagonal compact) � (CdS)
Crystals
=
a
J�
1 ·623
=
1 ·633
For ZnS, this ratio is very near to the ideal value ; the s ep a rat ion be and (p.,, Pv) is probabl y smaller. The value
t ween (pz)
� (ZnS)
=
has been give n , but the difference from the ideal value is of the order the ex perim en ta l errors and thus not s ig n i fica n t To a second-order app ro xi m atio n , the spin-orbit coup l in g lifts the degeneracy of the upper valence band . The states for which th e spi n i s parallel to the o rbital momentum (TD symmetry) h av e a higher =
a
1 · 637
of
.
Con duction ban d
T
EIIZ
s
metry).
energy
1I 1
r7
£1 l
Valen ce b a n d Without sp1n With spin
r1
Fig. IV.3 Structure suggested/or the valence and conduction bands of CdS according to Balkan ski and des Cloizeaux
t h a n the s t at es for wh ich the sp i n is antiparallel er, sym
This structure of the valence band results in a structure in t h e long wave l imi t of the fundam e n tal absorpti o n spectrum. With p ol a ri zed light the absorp ti o n transition between the r9 l evel s and t h e conduc tion band is observed with light po la rized perpendicularly to the opti c axis, and the transition arising from the r, levels with light polarized
83
Optical transitions
parallel t o the o p t i c axis. The energy d iffe re nce between the two transitions is 0·0 1 6 eV in CdS (B alkan s ki and Waldron). The same s tructu re is ob s e rv ed in studies of the maximum of the photoconductivity excitation spectrum. Bube has shown t h at this A bsorption coe ffJ c ienc /cm 1) ' 10
10'
·· -
21,000
20, 000
1 9,000
Wa ve n umber (cm 1!
Fig. lV.4 Absorption spectrum of monocrystals mium sulphide (Ba/kanski and Waldron)
of cad
E is the electric field of the radiation and z the optic axis of the crystal (Measurements at room temperature)
maximum is divided into two components whose separation is eV in CdS and 0 ·0 1 5 eV in CdSe respectively. A n a bs o rpt i o n band has been observed in the i n fr a- r ed , at I 7 fl
0·0 1 7
(0·074 eV) i n CdS, and ascribed by Balkanski a nd eo-workers to t h e transition between the (p.) and (p,., p11) sub-bands. T h e s p a rt of the valence band is much lower, p o ssib l y 1 eV lower. It has been s uggested (G. Cu rie) that infra-red stimulation and quenching bands, which appear in all sulphides at 1·3 fl for ZnS and 1 ·4 ,u for CdS, be asc ri be d t o a transition in s i d e the valence ban d ,
Luminescence in Crystals
84
le ad in g fro m the s-s t at es to one of the p-s tates. T h e p o s s i b i l i ty o f s u c h d i fferent l e v e l s , which m ay be s e n s i ti v e t o t h e i n c o rpo r at ion of the a c tiv at o r , b u t this p o i n t i s not yet resolved . a tra nsi t i o n depend s o n t h e o cc u p a t i o n of these
J T . LU M I NESCENCE E M I S S I O N N E A R TO T H E A B S O RPTI ON ED G E ( ' E D G E E M I S S I O N ' )
1 . Spectra for electron-positive hole recombination i n germanium
Near a P-N j un c ti on i t is possible to obta i n cons iderable elect r o n and
hole concentrations ( R: 1019/c.c). R a d i a t iv e recombi natio n of th e
el ectro ns and h oles is observed . A s seen above, there must arise non vertical transiti ons i n the b a n d d i a gr a m except a t sufficiently elevated
temperatu res. The width o f the forbidden band b e i n g about 0·72 eV
at 77°K (see Fig. IV.2) , an e mi ss io n band is observed in the i n fra-red
r e g i o n at 1 · 8 fl .
At liqui d air t e m p e r a t u r e we find o n ly this p h o n o n - a ss i s t e d tran
experiments are carried out at ro o m t e m pe r a t u re or it is possible to detect in a d d i t i o n a pe a k at 0 · 8 1 eV ( 1 · 5 11) (Haynes) wh ich is ascribed to vertical t r an s i t i o n s w i th o u t p h o n o n c o o p e r a t i o n at k = 0. The energy of t h i s seco n d peak is equal to t h e s u m Egnp -", - 6.£, where Egap 0 · 65 eV at r o o m temperature and 1:1£ 0· I 6 eV ( see Fig. I V . 2) . Its i n te n sity i ncreases w i th te mp e ra tu re, the a cti v ati o n energy b e in g 6.£. Ho we ve r , this ra d i a t i o n i s s t r o n gly reabsorbed . a n d i s observed o n l y when ve ry th i n s pe c i m e n s a re used . Using the law of d etailed bal a n c i ng, S h o ck l e y a n d v a n Roosb roek o b t a i ned the recombination emiss i o n p robability . If p(1•) is the rad ia s i t i o n . When the
a b o ve
=
=
tion intensity for a bl ack body
p(v)
87lhv3 1 = � h•·/kl' - 1 e
T h e i n t ensi ty o f e m issio n per seco n d a n d pe r el ect ron h ol e pa i r i n t h e frequency b a n d
v
to v + dv i s
J(v) d v
= const.
k(1•)p(v)n2(v) d1·
wh ere k(1·) is the measured absorption c o e ffi c i e n t a n d t i ve i n d e x at frequency 1' . Th i s ca l c u l at i o n gives t h e l i fe
n(v) the refrac
time fo r the recombination emission . 0-75 s ec a t or d i n a ry temperatures. The o bs e rv e d life t i m e d u e to recombi nation via defects rarely ex ceeds 1 / 1 00 sec,
T h i s i s about
Optical transitions
85
s h o w i n g t h a t direct reco mbination i s a relatively rare event. This i s
w h y it
is o n l y observed i n cases of high carrier concentrations. J lvl \ I \ I I 90°K I
' "'
l
05
I I I I I \
_____
---
\
A
7
08
hv [ e V l
I lvl Corre cted for absorp tion
6 -
) .
" -
3
2
Wa velength (p. ) Fig. A B
IV .5
Emission spec trum due to band-to-band recom bination in germanium
Experiments by Aigrain and Benoit a la Guillaume Experiments by Haynes performed on a very thin sample (/ - 1 · 3 . 1 0-3 cm)
The form of t he emission spectrum is a l s o determined by the re absorption of the emitted radiation : if l is the d i m ens i o n of the emitter, the rad i a ted energy is gi ve n by
J(v)
oc
J: I(v)e-i:(v)z
dx
This in teg ra l depends on the geometry of the specimen. If the emis sion origi nates at a p o i n t t h en J(v) l(v)e - k<•>. If the re c o m b i n a t i o n =
D
Luminescence in Crystals
86
takes pl ace u nifo r ml y t h r o u gh o u t the s a m p l e th ickness l (e x p er i m ent s of Haynes and Newman), then Germanium /
J(l')
=
I(v)
1 - e- k(•·)Z
The maxi m u m co r re s po n d s a l e xa ct ly with the width of t h e forbidden band, s ince at l o nge r p type wave l e ngt h s it falls off ra p i d ly ac contact cording to Kirchhoff's l aw and since at shorter wavelengths than t ha t of Fig. IV.6 Weierstrass sph ere t h e absorption edge the p h o t o n s are made of germanium (P. Aigrain strongly reabsorbed. and C. Benoit a la Guil/aume) : injection is made at the Weier In s i l ico n the energy band gap strass point which m in im izes the is 1 ·08 eV and a recombination light losses emission is observed at 1 ·2 fl . Haynes found a str u c t u re in th i s emission consisting of fou r peaks d ue t o the radiative transition e m i s s i o n coupled with longitud i nal o r t ra ns v e r s e phonons of the acoustic and optical b r a n ch e s re spe ct i vel y . m os t
2. Spectra
of the
Ewles-Kroger type
These emission spectra are observed at low t e m p e r a t ures in ZnS, Cd S and ZnO containing n o deliberate i m p u r i ty a c t i v a t o rs (F ig . (na r row IV.7). The l uminescence s h ow s a characteristic fine which o cc u r s equidistant bands, better resolved at low near the fundamental absorption edge. The effect is most noticeable in CdS, which has an edge i n the visible region, a very brilliant gree n luminescence being seen. In an activated phosphor the Ewles-Kroger emission is sup pressed and that usually d ue to the activator occurs. The line spacing i n CdS is 296 cm-1• I n some cases a substructure occurs of feeble lines with t h e sam e se pa rati on as the main set, but compared with it, sh ift e d towards the hi gh energy side, by 200 cm 1 in CdS. This is the first known case of edge emission, but it seems certain that it is not due to b a n d - t o - b and t ransitions. The e m issi on always has a smaller photon energy than the band gap energy ( � 0· 1 5 eV as in Fig. IV. 7). It is thought that it is d u e to the recombination of a hole
87
Optical transitions
with an electron captured in a level of 0· 1 5 eV depth , a theory first proposed by Schon. This 'shallow' level is not very localized and has an associated vibra tional frequency near to but not exactly that of the phonons of the 1 0 0 :�>
(a)
Fig. IV.7 Ewles-Kroger spectra of a single crystal of cadmiu m sulphide (after Klick), (a) at 77° K (b) at 4° K
the emission, brok en absorption spectra)
( The full curves g ive
curves
the
perfect lattice. Kroger and M ey e r have taken the line spacing of t h e principal e m i s s i on lines to correspond to Con duc tion b a n d the frequency of the longitudinal optical \ p ho n ons and that of the substructure to Loca lised level correspond to the frequency v, of the transverse optical phonons. For the case of ZnS (blende), the best measurements of these frequencies vz and Vt are given by studies on infra-red absorp tion and Raman Spectra (Mme L. Couture, Va len c e b a n d M. C. Haas and J. P . Mathieu). For CdS Fig. IV.8 Ewfes-Kroger and ZnO we have the measurements on emission 'Reststrahlen' by R . J. Collins. I n every (After Schon) case, the interval !J.v between the main lines of the emission spectrum is slightly different from v�, but the d is crepancy seems real. t Hopfield (1 959) has shown that the heights of the different peaks
t Quite recently, Choyke, Hamilton and Patrick ( 1 960) have described edge em ission phenomena in SiC which seem to i n dicate electron-hole recombina tion occurring i n donor-acceptor pairs . The separation (0·03 eV) of the l ines is here quite different from the energy of the optical phonons (0 09 eV for transverse phonons and 0· 1 2 eV for longitudinal phonons) . For a description of other luminescence emission shown by SiC, see Chap ter IX, §II . 3 .
ss
Luminescence in Crystals TABLE IV.2
,; , . Vj
l't
Blendc
ZnS Wurtzitc
3 64
3 68
274
?
349
Hex.
CdS Wurf::ifc
Zn O
305 24 1
591 414
550
296
cm 1 cm 1 cm - 1
P o i s s o n d i s tribu t i o n . T h e fi rs t em is i s a s cr i b e d to el ectron-hole recombination l ea d i n g to the emission o f one p h o t o n a n d n o p h o n o n , t h e seco nd l i ne /1 to a pho t o n a cc om pa n i e d by o n e p h o n o n , the (n + l ) th line In t o the simultaneous emission of the photon a n d n p h o n o n s . The r e s p e ct i ve i n tensities are a re
conve n i e n t l y descri bed by a
s i o n line /0
where
N is
Nn In = /0n .1
the m e a n n u mber o f e m i t ted p h o t o n s .
t a i n ed wi t h N
=
0·87.
I n CdS a
fi t is ob
TABLE I V . 3
Number
of phonons
n = O 1 2 3 4
Re/alive peak
height
1 ·00
0· 87 0·38 0· 1 1 0· 03
Polarization of t h e edge emission. The emission is mainly polarized wi th E.lz (E the electric field of the ra d i a ti o n , z the op ti ca l axis o f t h e CdS c ry s t a l ) . At 7 7 ° K (Dutton, Hopfield a n d Collins)
li = h
6·3
I n ZnO the polari za ti o n i s almost total .
These results are in a g reement with the st ructure of the abso rption
l i mit as d escri bed in Fi g . IV.4 i f we admit that the s h a l l ow level re spons i bl e for the ed ge emission po s s e s s es the same symmetry as the c o n d u ction b a n d . If 6.£ (0 ·0 1 6 eV in C d S) is the s epara t ion between the r9 and r, l evel s in the valence band , the polarization ra t io is
h
7;1
- exp -
(6.kT£)
I n Cd S the app r o x i m a te theoretical va l u e i s
7.
Other e x peri m e n t s a r e necessary i n o rder to identify t h i s shallow
l evel . F. E. Williams has su gge s t e d that it be c o nsi d e r e d as a level o f an electron t ra pped in the field o f an electric d i p o l e constituted by
Optical transitions
tw o a ss o c iat e d
89
va c a n ci e s ac ti n g like s u bsti t u ti o n a l c h a r g e s of o p p o
site sign s . Some p r o o f of t h i s h y p oth esi s h a s b een g i v e n b y L .
P a t r i ck fo r
th e case o f
SiC. I ndeed, i t s e e m s m o s t
probable t h a t t h e
e d g e emission m u s t b e ascribed to p h y s ic a l d e fects i n t h e l attice (vaca ncies o r i n tersti tial a t o m s ) rath e r t h a n to c h e m ical i m p u ri t i e s . Th i s i d ea is su p p o rt ed by the fact that s o m a n y peo p l e h ave m ad e
experi m e n t s o n t h e i n c orp o r at i o n of
chemical i m purities
i n zinc
or
c a d m i u m s u l p h i d es that, i f one of these i mp u ri t i e s h ad b e e n r e s p o n s i b l e fo r the Ewles-Kroger spectru m , s o m e o n e wo u l d ce rta i n l y h a v e
X (page
fou n d it. The ex p eriments of K u l p and K el l e y, d escribed i n C h a p
ter
309) indicate quite d efinitely t h e occurrence o f v a c a n c i e s
or interstitial s . E dge emission appears on bombard ment by acc e l e r
a ted electrons, wh e n the energy of these electro n s is h i gh e r t h a n t h e th reshold for S-v ac a n cy p r od u c tio n . As a general rule, the emission that o cc ur s at t h e b a n d ed ge s ee m s
to b e d epe n den t o n th e su rface conditi on o f t h e crystal ( D . C .
Reynold s) . I t is des t ro y ed b y s c rap i ng the su rface ( b u t i t i s r es t o re d
by etching). This re s u lt does n o t prove that the edge e m i s s i o n o cc u rs
at the surface, but more pro b ably that s c r ap i n g produces d e fe c t s acting like 'killer' ce n t r e s .
We notice al so in Fig. IV.7 the appearan ce at 4 ° K of a s p e ct ru m
i n the blue re g i on which also "shows structure . This spect r u m (n o n h yd rogenlike) has been obse
�ed b y various w o rker s ( K roger, K li c k ,
A r kh an gu el s kai a and Feo:fi lov, Furlong and Rav il i o u s ) . I t i s fo u n d
a t t h e fu nd a m e n tal a bs o rpt i o n edge b u t d i ffe rs
which had been i n q ues t i o n . It a ri ses from
i mpu ri t i e s .
fro m e x c i to n spectra superficially abso rbed
The Ewles-Kroger s p e ct rum is u s ua l l y obtained by ph oto-ex cita
ti o n . H owever, i t
w a s obtained b y R. W. S mi th by i nj ec t i o n o f e l e c
t r o n s and h oles into unactivated cad m i u m sulp h i de u s i n g i n d i u m
electrodes. I n t h e Ew les - Kr o g er spectrum observed o n l y a t l o w t e m pe r at u r e s a
s eco nd emission band was superimposed nearer
to
t h e absorption edge which appeared t o b e d u e t o d ir e c t electro n-hole recombination : this band persisted at room temperatu re and above (see Fig. IX. l 5) . I n a remarkable ex p e r i m e n t , t h e excitati on o f t h e Ewles-Kroger spectrum has been produced by in fr a- r ed excitation (Halste d , Apple
and Prener, 1 959). Th i s result is a m a r k ed violati o n of rule. I t
is ex p l a i n e d
b y a two-stage
e xc i t a t i o n p rocess .
the Stokes
Luminescence in Crystals
90
A CdS sam p l e con t ai n i n g coppe r is used .
The concentratio n of a n d the edge emission is n o t suppressed ; how ever, the copper levels play a fu n d a m e n tal part in the excitation procopper is r a t h er low
Conduction band
Electron 1 st . I. R. photon
Edge
e m i S S I On
Valence band
Fig. I V . 9 Two stage excitation of the edge emission (Halsted, Apple
and Prener)
cess. The fi rst i n fr a red p ho to n
ionizes the Cu-level into the cond uc one raises an electron of the v a l e nce band i nto the copper level. Then this level i s filled a ga i n while a free electro n -
t i o n band ; the s ec o nd
,
hole p air has been prod uced. Their recombination produces the
green emission (and a ls o , of cou rse, the i nfra-red emission
associated
with copper).
I l l . A B S O RPTI O N S PECTRA AND EXCITON EMISSION
1.
The experimental evidence
In recent years Gross, Nikitine and their eo-workers have found in C u 20 , CdS, Hgl2, Agl, Pbl2, &c. , series o f a b s o rp t i o n
lines a ppea rin g near the ab s orpt i o n e d ge and which can be rep rese nte d by a hydro genlike formula. The lines can be i n terp re t e d as the o p t i c al spect ra associated with the creati o n of e x c i ton s Since 1 956 h om o l o gou s line series have been fo und in emission fro m the same materials. They were first observed i n CdS but w it h l aye r s p rep ared in a special way. These crystals, deposited by sublimation at rel a t i vely low tempera t u res (700°C), are assumed to contain few defects . They show a ve ry weak Ewles - K roger l u m i n e s cen c e i n the green reg i o n , but the exten.
91
sion into the blue appears t o b e absent and i s replaced by a series of quasi-hydrogenlike lines (E. and M. Grillot, Pesteil and Zmerli). Lines of the same kind were observed for Hgl 2 , Pbl 2 , Agl and CdS by Arkhanguelskaia and Feofilov, Nikitine, Perny, Reiss and Sies kind. They obtained a detailed spectrum for Agl and numerous l i nes i n the other cases i nvestigated . Whether i n absorption or emission these spectra are observed at low temperatures ; at higher temperatures the lines broaden and merge into the absorption tail. Thin layers are needed for the ex p e r i ments (one to a few tens of microns, depending on the l i ne i n t e n s i ties) and they must be free from defects. Optical transitions
From a theoretical point of view the exciton was first thought of as a neutral excitation wave capable of movement through a crystal (Frenkel, 1 930) : in recent years this idea has received new interest, correlated with studies of exciton transfer (see later). Then in 1 9 3 8 Wannier established the quasi-hydrogenlike character of the levels prod uced while M ott, Slater and Shockley described the exciton as an electron in orbit around a hole bound to it by the coulombic attraction. In the excitation-wave model the formation of an exciton in KC! corresponds to the movement of an electron from a Cl - ion to one of the neighbouring K + ions while excitation of an electron from the valence band (Cl -) to the conduction band K (see Fig. Il.2) corre sponds to a complete freeing of the electron in the body of the crystal. The calculation of the energy cycle analogous to those made to find the forbidden energy gap enabled von Hippel, J. de Boer et alia to find the energy for exciton formation . Thus the width of the fo r bidden band in KC! is 9-42 eV, giving an optical absorption edge at 1 ,3 1 0 A, wh i le exciton formation requires o nl y 7 · 6 eV, giving a first absorption peak at 1 ,620 A . We thus obtain the first exciton state. In a similar way for CdS the first exciton state corresponds to the transit of an electron from a sulphur ion (i) to one of the neighbour ing cadmium ions (M) (M. Balkanski and P. Andre). However, the wave function obtained from that of the matrix crystal by replacing that for the sulphur ion by the Hartree function for this ion contain ing a positive hole and replacing that of the cad mium ion M by the Hartree function for this ion with an excess electro n , say rf>(i, M), 2. Theoretical aspects
92
Luminescence in Crystals
4>(i, M)
is not an eigen fu ncti o n of t h e crystal . For th e eige n function a wave
packet
It
of
t he
fu nct i ons must be taken :
1p (fo r c r ys t al co n tai n i n g exciton)
"J.Ai.Mf(i, M ) i,.l[
is p o s s i b l e t o take A c o effici e n ts of the fo rm A
ex
exp
(ik . R)
R l oca t e s the exc i to n and k pl ays the pa rt o f a propagati o n Near to the limit k0 w e can obtai n the energy C(k)
k'
where
=
=
t'(k0) +
li22 �k'2-j- . . .
k - k0, this co rrespond i ng to the m o tion of M.
vector.
a n exciton
with effective mass
This m od e l is p referable for calculating th e ground state
an d
t r a nsition s i n v o lving this s t ate and m o re ge ne r all y for the case where
the el ectron 'orbit' around the hole is of s m al l
th e
alkali halides
radius. This is so for con
because of their re lat ivel y small die lec tric
s tants (Slater and Shockley, T.
Muto
and
Okuno).
3. Model for the electron in orbit around a hole ; hydrogenlike spectra In contrast to the above the mod el fo r an electron orbiting
about
a
hole, called the 'quasi-positro n i um' model , gives a d i rect e x pl an a t i o n
of
the h y d r o gen l i k e spectra fo r the excited state.
Let
m.
and
mh
be the effective masses for c o n d u cti o n electrons and
h oles i n the valence band respectively, the bands being is o tr o pic and
for non-d egen erate conditions. The Wannier equa t i on
is then
H
=
Ji 2
2m.
- -b.,-
1i 2
2mh
-
for the exciton
e2
b.h - -Kr
K being the d i e l ectric co nstant of the materi al . Let r, be the electron co-ord i n a t e ,
rh
t ha t o f the hole and
R
R that of the centre of gravity :
m.r. + mhrh
The eq u a t i o n has solutions of the form
7p(R, r)
=
exp
(i kR)tp(r)
corresponding to a motion of the centre of gravity with wave vec tor k. It is easily shown that 1p(r) is a solution of the h y d rogen l i ke
Optical transitions
eq u a ti o n
fi 2
E
=
fi 2
2
e -f(,!P(r)
=
93
M = m. + mh
k 2 + I! ;
2M
M is the effective m a s s of the m oving exci t o n a n d ,a the red uced mass The e n e rg i es I!
R'
l
f-l
=
_!_+__!_
m. mh form a h yd r ogenlike s eri e s : lfn
=
R'
n2
'
R'
- - ·
bei n g a p s e u d o- R yd berg
=
R J!:. -
K2 · m
constan t ; R i s the Ryd berg c o n s t a n t fo r
h yd ro gen (1 3 · 5 eV) and m the free electron
separation in the orbit nS of the exciton i s
mas s . The e l ectro n - h o l e
is the Bohr r a d i u s 0· 5 3 A). For a given I! there is a corresp o ndi ng energy band, the total energy of the exciton being I! plus the translational energy !z2k2/2M. In general, we can only expect to obtain weak absorption tails, only the limits o(which form a series. However, in contrast we get a series of hyd rogenlike lines when m., m and K are isotropic and for vertical transitions at k = 0, or more generally for a k value which is the same for a m a x i m u m or minimum for the valence and conductio n bands respectively. This requires a c o rre sp o n d e n c e as shown in Fig. IV. l a. For such a band structure we have in either absorption o r e missio n t h e l i nes (a0
=
hvn
=
hvoo
R'
2 n
hYoo corresponding to the forbidden band-gap energy ( F i g . I V . l O) . W e can very likely observe the l i n e spectra for more complex band structures such as those pr o p o sed for CdS in which the extrem a of t h e bands lie at k 0, but th e minimum k 0 o f the conducti o n band i s not the lowest minimum. After absorption a t k 0 a nd formation of a free electron hole pair, the electron and the h o l e wi l l d i ffuse away from each other and will not normal l y recombine by a vertical ra di a ti ve transition. In contrast, after an a b s o rp t i o n at kJ 0 giving a bound electron h o l e pair, t h e el e c tr o n a n d h o l e w i l l =
=
=
=
94
problem
Luminescence
d i ffuse together and the Th e
in
Crystals
p oss i bi l i ty o f radiative recombinati o n e x is ts .
of de t e rm i n i ng the band structures which wil t give rise
to exciton line spectra and those which will n o t is s t ill far fro m clarification.
When the valence band is divided into several sub-bands, a simil a r n umber of exciton line series m ust appear ; each series limit coincides
1
Conduction band
n=3
t I
Valence band
Fig. J V . l 0
Energy
le vels
Continuous spectrum L in e spectrum
of exciton spectra
with the transition leading t o the i o n ization of the co r r e s p on d in g
N ik i tin e and eo-workers) : o n e is s i t u a te d in the yel low pa rt
sub-level . Two
m ai n
hydrogenlike s e ri es have been o b s e rv ed i n Cu20
o f the a b so rpt i o n spect r u m and i s observed with relatively thick
(G ross,
s peci m en s
( 10 to 1 00 p) ; the second series is i n the green and is ob
served with t hi n ne r speci mens ( '"'-' stronger in this
re gi o n .
'
�t) because th e abso rpti o n is
abso rp t i o n
(B alkan ski
s e ri e s
t he valence band
expe c t three exciton line
Since for CdS the upper part of
(p-band) is
and des Cloizeaux) . In emission, t h es e t h ree
d i vid ed into three sub-levels, we
series in
mig h t perhaps be observed at a s u ffici e n t ly high temperature, p o l ari zatio n ratio . At 4°K, t he holes are concentrated in the up per T9 level (Fig. IV. 3) and the e mi s s i o n is c o m p le te l y p olariz e d (El.z) . This has b e e n effe cti v e l y shown i n experiments (E. and M . Grillot, Gross a n d Razb i rine ; Thomas, H o pfi el d and Power) . Elliott has shown t h at theo ry c a n d is ti n g ui s h t w o kinds of exciton e a ch of them with a different
l i ne s pe ct r a :
95
Optical transitions
I. Spectra o f t h e first kind i n wh ich transitions fo r k
We observe thus the spectral series for
n
= I, 2
.
.
.
=
0 occur.
The osci l lator
strengths are proportional to the squares of the a m pl itudes of t h e hydrogenlike wave functions
Is, 2s,
&c. , a n d
I
a re
fn oc � na0 n
They are weaker than the lines for isolated atoms in the rat i o (a0' ja0) 3, t h e i r i n tensity decreases rapidly w i t h tor
I /n3
and very few lines are observed .
2. Spectra o f the
n
because of the fac
second kind in which the transition at k
forbidden b u t vertical transitions at a constant
1 n2 - l
k
val ue
and leading to p-states are allowed. We obtain i n th i s ca s e
fn
ex
=
near to
0 is
zero
3n ao'5n5
These li nes are weaker than the lines for isolated ato m s
in
the ratio
(a0' Ia0)", but the line intensity falls less rapidly than that for spectra of the first kind and more lines are observed . In all cases the l ine fo r n =
I
is absent since there is no p-state for
n
=
I.
These ded uctions are ma rked ly in agreement with experimen t
(Nikitine e t
al.).
Thus C u i shows absorption s pe ct ra
of
the fi rs t
kind, Cu 2 0 those of t h e second kindt a n d t h e oscil lator strengths show the expected theoretical ratios. The same d i fference occurs for
emission spectra. When the transition is not vertical and involves a sim ultane o u s
germanium), line spectra absorption curve. been fo u n d that are thought to
emission o r absorption of a ph onon (as i n
are not observed, but s uccessive k nees occur i n the At the p resent time, those knees have
be due to the formatio n of the ground state of the exciton (Macfar Iane et
al.).
4. Deviations from the hydrogenlike formula
To begin with, the treatment of the exciton in the Wannier equation (called the 'effective mass approximation') makes the crystal a con
1
tinuous medium of dielectric constant K: this is not valid except fo r
2 m ay
large orbital radii . Also the state state
n =
n
=
and to a lesser degree the
be normally perturbed.
Kittel and Mitchell h ave used the Wannier equation with a non isotropic effective m ass : Barriol, Nikitine and Sieski n d have studied
t T h e line
for
n
=
1 i s observed b u t is
very weak.
96
Luminescence in Crystals
t h e a n i s o tr o py of the d ielec t ri c constan t : in cease to
be h yd ro ge nl ike .
b o t h ca ses the s pect ra
In an ionic c rys tal d efined by i t s two dielectric c on s tan ts Kstntic
a nd K0 (at high frequencies) i t is necessary for
a l o ca lized level t o
i n troduce a n 'effective d iel ec tr ic constant' . However, in the case o f
established in the crystal and it is s u ffi c i en t t o use K0 in the above
t h e ex ci to n , in a bs orpt i o n i oni c p o l arizat i o n has no time to become c a l cu l a ti o n s .
Fo r e m i s s i o n t h e pr o b lem is m o re complex . I f the electron a n d h ol e are very mobile the polariza ti o n t h ey p r o d u ce wi l l be self-destructive a n d we have a non-polarizing exciton (Dyk m a n and P e ka r) and again K0 is u sed i n the calcu lati o n s . In an i o n ic crys tal o nly a non-polarizing exci t o n ca n give a hyd rogenlike emiss i o n spectrum c o r re sp o nding to the absorption s p ec tru m . The observation o f such agreement between a b s o rp ti o n spectra of CdS obta i n e d by G r oss and emi ss io n s pect ra obtained by G ri l l o t i s a strong argu m e n t fo r att ri bu ti n g them to excito n s si nce it d o es not occur for a hydro genlike impurity (electron in o r b it about a fixed p osi tive charge in the l a tti ce , the effective d i
electric constant d epe ndi ng on the p a r t icul a r l e v el co n sid ere d ) .
Tf the e l ec t r o n and hole are not very m ob i le t h e y p o la rize the sur rou n d i n g l attice : each o f t h em can be treated as a p o laro n , i.e. su r rounded by an as sem bly of phonons. In the s i m p lest case we can t a k e acco u n t o n l y of t he mean val u e o f such p o l a riz a ti o n (p o l a riz i ng e x c i t o n of D y k m a n and Pekar) , but in general the el ectro n-hole int e r action will be modified by their res p ec t ive su rr ou n d i n gs of phonons.
F o r this c a se we m a y refer to the work o f Haken a n d o f Meyer. M eyer cal ls s u ch a c o m p l e x e x ci t o n
5. Stark
an ' ex c i t a r o n'.
and Zeeman effects for the exciton
i n Cu20 by G ro ss et al. and in CdS by E. a n d M. G r i l l o t in collaboration with
Th ese t w o effects h ave been st u d ie d more recen tly
G ro s s . The Stark effect i s observed i n relatively weak el e ct r i c field s becau se of the large size of the ex c i t o n o r b i t . For the h y d r o gen atom
the Stark effect fo r a field F is
t:.E
=
- �-neFa0'
(all
fo r levels of p ri n cip a l quantum n u mber
fi rst Bohr
o rbi t , approximately
fo r hydroge n .
For Cu20 a n d
n =
5 the
n va l ues )
n. a0 ' i s
K0 t i m e s greater
t h e rad i u s of the
for the ex ci t o n
e ffect i s observed fo r fi e l d s o f
than
5 kV /cm .
Optical transitions
97
Furthermore, w e find the p he n o m e no n of ionization of t h e e x c ito n the sh i fti n g of th e levels n 6, 5, 4, &c., into the ioniza tion c o ntinue s as the field increases. The ab s o rp ti o n limit is shifted and affects successively each of the ter m s in the series. For Cu20 and for F = 25 kV/cm o n ly the levels n = I an d n = 2 su rvi v e . Such an e ffect for a hyd ro ge n atom requires 600,000 to 700,00 V/cm . The Zeeman effect for the line n = I (ye ll o w series of C u 20) s h o ws a normal t ripl et s tru ctu re . Us i n g the q uasi-positronium m o d e l , the separation of neighbouring lines is /:£ = m11 - m. �H p ro d u ced by
=
m.m"
We find
/: £ =
--
4nc
eh
4nmc
H
i f m" eo, while if m11 = m., t h e l i near Zeem an effect is ze r o . T h i s i s we l l k n own for p o si t r o n i um : the Larmor p r o cess i o n w efl/2mc produces an e n h a nce me n t of the electron velocity and a d i m i nution of the p o si t r o n velocity so that the energy of the system i s u n a l tered to a first approximation. P o sitro n i u m only shows the quad ratic Zeeman e ffe c t . A splitting of terms with n > I h a s been observed , b u t the d i ffer e n t components have not b e e n res o l v ed . The emission l i nes of CdS a ls o show a Zeeman effect. S o m e t i m es , e . g . that a t 4,870 A, t h ey give t h e normal t riplet. However, t h e n a n d a c om p on e n t s are inverted. This s u gge st s a ma g n et i c d i po le n ature for the emission (E. Gri llo t) (see Fig. IV. l l ). =
=
()
Normal trip/et Jt.
(J'
4 8 70 �
Jt.
line from ()
Cd 5
J1.
Fig. IV . l l Normal Zeeman triplet and the inverted triplet obtained by Grillot and Gross for CdS
reference to t h e li nes, a displacement of th e cen tre of the li n e s occ urs o n appli cati o n of a field H which i s q uad ra ti c in H. It is explained as a change i n m a g n e ti c energy d u e With
of
fu rt h e r
gra vi ty
Luminescence in
98
Crystals
t o the d iamagnetism o f the exciton. The effect fo r the n'th level is !:,£
__£_n
Go
' 2Hz
Th is effect, which only occurs for atoms with higher membe r s of the series, is observed for n 3 (H 25 to 30,000 oersted). The radius n 2a0' is of the order of 200 A for n 5 in the yellow series of c u pro u s =
_
- 8mc2
4
=
oxide. I n conclusio n , experimental evidence re v e a l s the existence of quasi a tomic systems in certai n crystals w h i c h show hydrogenlike absorp tion and emission spectra gi v en to a first a pproxima t i o n by the q uasi positronium level system of excitons. The large orbital radii indi cated by t h e Stark and Zeeman effects and the a greeme n t between the experimental and theoretical oscillator s t re n gt h s str o ngly sup port this model , a lt h o u gh the t h e o r ie s are often over-simpl ified and althou gh numerous points still need to be clarified. The identification of the system responsible for these o p t ica l transi tions with t h e Frenkel exciton rests on the evide n ce of its m o bility and its role in energy transfer, wh i c h re q u i res other experiments wh i ch we shal l refer to later (e x pe ri m e n ts of Broser and of B a l kanski on CdS). Light emission due to e xcito n recombination would s e em to be more li kely once the e xci t o n has been i mmob i l ized in the n e i g h b o u rhood of a l at t i ce defect. =
B I B LI O G R A P H Y
M . ( 1 938) ' D ber die Form der Emissions banden von Krystallphosphoren, un s be s o n d ere deren Temperatu r
1 . 1 . The 'momentum' selection rule and its consequences
B I RU S , K . a n d S c H 6 N ,
abhangigkeit', Verhandl. der deutsche Physikal. Gesellschaft, 19, 8 3 . F . a n d R o M P E , R . ( 1 9_AOJ ' O ber En e rgie u m w and lu ng in
M 6 G LI C H ,
Krystallphosphoren', Physikal. Z. , SEITZ, F. 2.
41,
2 36.
( 1 940) Modern Theory of Solids. McG raw-Hill Co., New
York.
H E R M A N , F. ( 1 955) 'The electronic e n e rgy band structure of s i l ic o n and germanium', Proc. I. R.E. , 43, 1 703. M A C FARLANE, G . G . and R O B ERTS , V . (1 955) 'Infra-red ab s orp ti o n of germanium near the lattice edge', Phys. Rev., 97, 1 7 1 4.
Band structure
of
germanium and silicon
99
G . G . and ROBERTS , V . ( 1 955) 'Infra-red absorp tion of silicon near the lattice edge', Phys. Rev., 98, 1 865. L A X , B . , R OT H , L . M. and ZWERDLING, S. (1 959) 'Quantum mag neto-absorption phenomena in semi-conductors', J. Phys. Chem . So lids, 8, 3 1 1 . Opt ical transitions
M AC FA R L A N E ,
HERMAN, F . (1 957) 'Report on the second symposium on the phy s i cs of semi-conductors', J. Phys. Chem . Solids, 2, 72.
Indium antimonide
B A L K A N S K I , M . and W A L D R O N , R . ( 1 958) 'Internal photoeffect and exciton diffusion in cadmium and zinc sulphides', Phys . Rev., 1 12,
Band structure and optical transitions in zinc or cadmium sulph ides!
1 23 .
B A LK A N S K I , M . ( 1 959) Proprietes optiques des semi-conducteurs, 2 ,
32. Faculte des Sciences, Paris.
B A L K A N S K I , M . and D E S CLOIZEAUX, J. ( 1 960) 'Transitions op tiques au voisinage de la limite d'absorption dans le CdS', J. Phys.
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825 ; 22, 41 .
H . (1955) 'Photoconductivity of the sulphide, selenide and
21,
telluride of zinc or cadmium',
B UBE, R .
J.R.E. , 43, 1 836.
B uB E , R . H . ( 1 955) 'Temperature dependence of the width of the Proc.
band gap in several photocond uctors',
Rev., 98, 43 1 .
B U B E , R . H . ( 1 957) 'Analysis of photoconductivity applied to CdS type photoconductors', J. Phys. Chem. Solids, 1 , 234. Cox, J. T . , WAYLONIS, J. E. and HUNTER, W. ( 1 9 59) 'Optical Pro perties of ZnS in the vacuum U.V.', J. Opt. Soc. Am., 49, 807. VAN D ooRN, C. Z. (1954) 'Temperature dependence of the energy
gap in ZnS',
1 1 55.
G . ( 1 957) 'Optical absorption band edge in aniso
Physica, 20,
tropic crystals',
D R ESSE L H A U S ,
Phys.
1 35.
D u M KE , W . P . ( 1 9 57) 'Spontaneous radiative recombination in semi conductors', Phys. R ev . , 1 05, 1 39. K E L L E R , S. P . and P E TT I T , G. D. (1 959) 'Optical properties of acti Phys. Rev . , 105,
vated and unactivated ZnS single crystals',
526.
PIPER, W. W . (1 953) 'Some electrical and optical properties of syn thetic crystals of zinc sulphide', Phys . Rev . , 92, 23 . Phys.
Rev.,
1 15,
t The problem of band structure connected with binding in ZnS and CdS is described in Chapter V .
I 00
P I P ER ,
W.
Luminescence
in Crystals
W . , M A R P LE , D . T . F . and J O H N S O N , P . D .
( 1 9 5 8)
'O p ti
c a l properties o f hexagonal ZnS crystals', Phys. Rev . , 1 1 0, 3 2 3 .
P I P ER , W .
W . , J O I-I N S O N , P . D . a n d M A R P L E , D. T . F . ( 1 9 5 9) 'Tem
perature depen d ence o f the optical band gap in ZnS', J. Phys.
Solids, 8, 4 5 7 . N . A . ( 1 9 59) 'A study o f t h e intrinsic ab sorp t i o n spec tru m of zinc sulphide', Op tics and Spec troscopy, 7, 320. Ch em .
V L A S EN K O ,
1 1 . 1 . Elec tron-hole
recombination in germanium
Th eory of band- t o -band recombination S H O C K L E Y , W. a n d V A N ROOS B R OE K , W. ( 1 954) ' Ph o to n radiative reco m b i n a t i o n s of ele c tr on s and holes in germanium', Phys. Rev. ,
94, 1 5 58 .
Two-steps recombination o n a crystal defect
S H O C K LEY, W .
and R E A D , W. T . ( 1 9 52) ' Stati s ti cs of the recombina
t i o n of holes and
electrons',
For experi mental wo rk,
2. Ewles-Kri:iger
Phys . Rev . , 87, 8 3 5 .
see Ch apt e r
IX
(Electroluminescence).
emission spectrum
EW L E S , J . ( 1 9 3 8) ' Resolution and i nterpretation of the l um i n e sce nt spectra of some s o l i ds at low t e m p e ra t u r e s ' , Proc. Roy. Soc. , A
Early references
167,
34.
K R O G E R , F. A. ( 1 9 4 0) 'Lumi nescence
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R A N D A L L , J.
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S c HON ,
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'Zum Leuchtmechanismus d e r K ristallphosphore',
Zeits. fur Phys., 1 19,
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G R O SS , E . F . , G R I L L O T , E . and RAZBIRINE, deux series de spectre de l a fluorescence v e rt e a basse te mp e rature du cadmium pur', Comptes-Rendus A cad. Se. Paris, 250,
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B A N C I E - G R I LLOT, M . ,
B. S. ( 1 960) ' Infl u en ce d e la te m p e ratu re sur I e s
bandes d u
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de
C O L LT NS , R . 1 .
Optical transitions
101
( 1 959) ' Mechanism and defect res p o n s i b l e fo r ed ge
em ission in C d S ' , J. Appl. Phys. , 30, I 1 3 5 .
COLLINS ,
R . 1 . a n d HOPFTELD ,
e m i ssio n in C d S
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H. G. J. ( 1 9 5 7) 'The a tu r e of edge emission in Cd S', Physica, 23, 9 8 7 . D U TTON, D. ( 1 9 5 8 ) 'A niso t r o py of e dg e l u m i n escence in cad m i u m sulphide', J. Phys. Chem. Solids, 6 , 1 0 1 . H A L S TE D , R . E . , A P P LE , E . F . and P R E N E R , 1 . S . ( 1 9 5 9 ) ' T w o - s tage op ti cal exci tat i o n in s u l p h i d e phosphors ' , Phys. Rev. Letters, 2, 420. H O P F I E L D , 1. 1. ( 1 959) ' A theory o f e d g e e m i ss i o n phe n o m e n a i n CdS , ZnS a n d ZnO', J. Phys. Chem. Solids, 1 0 , 1 1 0. KLICK, C . C . ( 1 95 1 ) 'Low temperature l u m i n e s c enc e o f i n o rganic solids', J. Opt. Soc. Am., 41, 8 1 6. K L I C K , C . C . (1 953) 'Luminescence and absorpti o n in C d S at the absorption edge', Phys . Rev., 89, 274. K RO G E R , F. A . and M E Y E R , H. G. 1. ( 1 954) 'The edge emission of ZnS, Cd S and ZnO and its relation to the lattice vibrati o n s of these solids', Physica, 20, 1 1 49. L AMB E , J . , KLI C K , C . C . and D EXTER , D. L . ( 1 956) Nat u re of edge emission in cadmium sulphide', Phys. Rev. , 103, 1 7 1 5. REYNOLD S , D . C . ( 1 960) 'Temperature dependence of edge emission in cad mium sulphide', Phys. Rev., 1 18, 478 . SMITH, R . W . ( 1 957) 'Low-field electroluminescence in i n s u l ati n g crystals of cadmium sulphide', Phys. Rev . , 1 05, 900. ',
D I E M E R , G . , V A N G U R P , G.
1. and M EYER ,
n
'
J . and KLEINMAN, D . A . (1 959) 'Infrared reflectivity of zinc oxide', J. Phys . Chem. Solids, 11, 1 90. CO UTURE, L. and M ATHIEU, 1. P. (1 953) 'Spectre de diffu s i o n d es cristaux piezoelectriques. Blende', Comptes-Rendus A cad. Se. Vibrational energies in ZnS and Zn O
COLLINS , R .
Paris, 236, 37 1 .
H A A S , C . and M A T H I EU,
l o ngitudin a les et Rad., 15, 492.
J.
P.
t ransversales
C H O Y K E , W. J . , H A MILTON,
( 1 954) 'Spectre i n fra-ro uge et o n d e s dans les cristaux cubiques', J. Phys.
Edge emission in SiC
ized e d ge e m i ssion of
D. R.
and PATR I C K , L. ( 1 960) 'Pol a r 1 4 30.
S i C ' , Phys . Rev . , 1 17,
I 02
Luminescence in Crystals
L . (1 960) 'Polarization of the luminescence of d onor acceptor pairs', Phys. Rev., 1 17, 1 439. See also, in connection with the donor-acceptor theory for edge
PATRI C K ,
P RENER, J . S . an d WILLIAMS, F. E . ( 1 9 56) 'Associated donor acceptor luminescent cen t res , Phys. Rev., 101 , 1 427. PRENER, J. S . and WILLIAMS, F. E. ( 1 9 5 6) 'Theorie des centres luminogenes du type donneur-accepteur associes', J. Phys. Rad. , emission :
'
17, 669. WALLIS, R . F . , H ERMAN,
Spectr., 4, 5 1 .
R.
and M I LNES,
H.
W . ( 1 960) Ene rgy J. Molecular '
l evel s of an electron in the field of an i n fi nite d ipole',
Ill. Emission and absorption spectra o f the excitont
Ea rly references FRENKEL, J. ( 1 93 1) ' O n the t ransformation of light i n t o heat i n solids', Phys. Rev., 37, 1 7, 1 276. FRENKEL, J. ( 1 936) ' O n the absorption o f l ight a n d the trapping of electrons a n d holes in crystalline dielectrics' , Phys. Z. So wje t Union, 9, 1 58. Mon, N . F . (1938) 'Energy levels in real a n d ideal crystals' , Trans. Faraday Soc. , 34, 500. Mon, N. F. ( 1 938) 'On the absorption of light by crystals', Proc. Roy. Soc., A 167, 384. PEIERLS, R. (1 932) 'Zur T h�eo ri e der Absorptionspektren fester Korper', Ann. Phys. , 13, 955. WANNIER, G . H . ( 1 937) 'The structure of electronic excitation levels in insulating crystals', Phys. Rev., 52, 1 9 1 . Comprehensive papers on the exciton problem BA LKANSKI, M . ( 1 958) Etude sur le probleme de l'exciton, Ecole d ' Ete
I'Etat
Normale
Paris.
BALKAN S K I , M . ( 1 958) 'Etat actuel du probleme d e l'exciton', J. Phys. Rad., 19, 1 70 ; 22, 1 1 3 . G Ross, E . F . ( 1 956) 'O p t i ca l spectrum of exci tons i n t h e crystal lattice', Nuovo Cimento, 3, Suppl. no. 4, 672 (48 references). sur
Solide. Ecole
Superieure,
t The papers working chiefly about exciton diffusion and transfers by excitons are described in Chapter VIII.
Optical transitions
1 03
H A K E N , H . ( 1 9 58) Der heutige Stand der Exzitonenforschung in Halb
/eitern. Vieweg, Braunschweig.
Phys. A cta, 28, 307.
N I KITIN E , S. ( 1 955) 'Spectres de l'exciton dans les cristaux', Helvetica NI KITINE, S . (1 955) 'Spectres d'absorption de l'etat solide', J. Phys.
Rad. , 16, 40S.
NIKITINE, S. (1 959) 'Spectroscopie du corps solide et spectres de l'exciton', J. Phys. Chem. So li ds, 8, 1 90.
Some experimental work on the emission and absorption spect ra of the exciton in ionic semi-conductors; Cu20, CdS, Hgl2, Agl, &c . . . . A RK H A N G U E LS K A I A , V . A . and FEOFILOV, P . P . ( 1 9 56) 'Sur les bandes etroites dans le spectre de luminescence de quelques cristaux aux basses temperatures', J. Phys . Rad. 17, 824. B A N C I E - G R I LLOT, M . , G Ross, E . F . , GRI LLOT, E . and RAZ BIRIN E , B . S . ( 1 959) 'Investigation of linear fluorescence and absorption o f pure cadmium sulphide crystals a t a temperature of 4 ·2°K', Optika i Spekt., 6, 707. Op t ics and Spectros. , 6, 46 1 . G RILLOT, E . , G R I LLOT, M . , PEST E I L , P . and ZMER L I , A . ( 1 956) ' Spectre de fluorescence quasi-hydrogenoide (exciton) de sulfure de cadmium pur a 20°K', Compt es-Rendus Acad. Se. Paris, 242, 1 794. G RILLOT, E. ( 1 956) 'Fluorescence de I'exciton dans CdS pur', J. Phys. Rad. , 17, 822. G RI LLOT, E. (1 958) 'Sur le transfert d'energie par Ies excitons dans le sulfure de cadmium pur', J. Chimie Phys., 55, 642. G ROSS, E . F . and KARRIEV, N . A . ( 1 9 52) 'Optical spectrum of the exciton', Dokl. Akad. Nauk S.S.S.R., 86, 47 1 . G ROSS, E . F . and JACOBSON, M . A . ( 1 955) 'Absorption line spec trum in the cadmium sulphide crystal at liquid air temperature', J. Techn. Fiz. , 25, 364. G Ross, E . F. and JACOBSON, M . A. (1956) 'Emission spectrum of the exciton', Z. Tekhn. Fiz. S.S.S. R., 26, 1 369. G Ross, E. F. ( 1 956) 'Le spectre optique d u a la formation des ex citons dans les reseaux cristallins', J. Phys . Rad. , 17, 8 1 5. G ROSS, E . F . and ZAKHARTCHENIA, B . P . ( 1 9 5 7) 'Les effets lineaire et quadratique Zeeman et le d iamagnetisme de l'exciton du crista! de protoxyde de cuivre', J. Phys. Rad., 18, 68. G ROSS, E . F . , G R I LLOT, E . , ZAKHARTCHENIA , B. P. and BANCIE G R I LLOT, M . ( 1 959) 'Influence of a magnetic field on the blue ,
1 04
Luminescence in
Crystals
fl u o rescence l i nes and of the abso rption lines of ce r ta i n pure cad mium s u l p h i d e crystals at a te m p e ra ture of 4·2°K', Optika i Spekt., 6, 7 1 0. Opt ics a n d Spectros. , 6, 462. N I K I T I N E , S . , PERNY, G. an d S I ES K I N D , M . ( 1 954) 'Etude des s p e c t re s de l'exciton dans Cu 20 ' , J. Phys . Rad. , 15, 1 8 S . N I K I T I N E , S . ( 1 956) ' Etu d e des spectres de l'exciton aux tres basses temperatures', J. Phys. Rad. , 17, 8 1 7. ' S p ect res d ' exci t o n d es cristaux ioniques', J. Phys. Rad. , 19, 2 1 S. N I K IT I N E , S . ( 1 9 5 8) ' E tu d e experimentale et tentative d 'i n te rp reta tion d es spec t re s d'absorption fondamentalc des c r i s tau x purs' , J. Chimie Phys. , 55, 62 1 . N I K I T I N E , S . , R E I S S , R . and S I ES K I N D , M . ( 1 958) ' Classification des s pect r e s des co rps solides et leur o ri g in e cxcitonique', Comptes Rendus A cad. Se. Paris, 246 , 3 4 3 9 . N I K IT I N E , S . and S ! ES K I N D , M . ( 1 9 5 8 ) 'Etude c o m p a r a t iv e des spectres d'absorption, d'emission et de refiexio n de Hgl 2 rouge aux basses temperatures', J . Chimie Phys. , 55, 837. N I K I T I N E , S . , GRUN, J. B. a n d S ! ES K I N D , M. ( 1 96 1 ) 'Etude spectro
N ! K I T I N E , S . ( 1 958)
photometrique de la serie j aune de Cu 20 aux basses temperatures', J. Phys. Chem. Solids, 17, 292. P E R N Y , G . ( 1 9 56) 'Remarques concernant le spectre de l'exciton', J. Phys. Rad. , 1 7, 820. P ER N Y , G. ( 1 9 5 8 ) 'Spectres de l'exciton et polymorphisme de l ' i o d ure d ' a r gen t' , J. Chimie Phys. , 55, 650.
Theoretical work on the exciton A N DRE, P. (1 958) 'Etude theorique sur l'exciton dans le sulfure de cadmium' . Thesis, Faculte des Sciences, P a ri s . B A L K A N S K I , M . ( 1 9 59) Proprietes op tiques des semi-conducteurs, 2, 79. Faculte des Sciences, Paris. B A R R I O L , J . , N I K I T I N E , S. and S ! ES K I N D , M. ( 1 9 56) ' Ca l cu l des n iveaux d'energie de liaison d'un e x ci t o n dans un crista! u n ia x e' , Comptes-Rendus A cad. Se. Par is , 242, 790. D RESSELH A U S , G. (1 956) 'Effective mass ap p r o x i m at i o n for exci tons', J. Phys. Chem . Solids, 1 , 1 5 . D R ES S E L H A U S , G . (1 957) ' A b s o r p tio n coefficients for exciton ab s o rp t i o n lines', Phys. Rev . , 106, 76.
D Y K M A N , I . and
1 05
P E K A R , S . I . ( 1 9 52) ' E x c i t o n s i n i o n i c c rysta l s ' ,
I . ( 1 9 57) 'Theory of excitons i n
Dokl. Akad.
DYKMAN,
Optical transitions
Nauk S. S.S. R . , 83, 8 2 5 .
Akad. Na uk S.S. S. R., Ser Fiz. , 2 1 , 65.
i o n i c crystals', Jzvest.
'Intensity of optical a bso rp t i o n by excitons', 1 384. E LLIOTT, R. J. and LouooN, R . ( 1 9 59) ' Th eor y of fine structure on t h e absorp tion edge in sem i-cond uctors', J. Phys. Chem. Solids, 8, 382. H A K EN , H. ( 1 9 56) 'Theorie des excitons dans les cristaux pola i res ' , J. Phys. Rad. , 1 7, 826. H A K E N , H. ( 1 9 57) 'Berech nung der Energie des Exzito n e n g r u n d zustandes i m p ol aren Kristall n ach einem neuen Variation sver fah ren von Feynman', Z. Phys. , 147, 323. H A K E N , H . ( 1 958) ' D i e Thcorie des Exzi t o n s i m festen Ko rper', Forts. der Phys. , 6, 2 7 1 . H A K E N , H . and S C H OTTKY, W . ( 1 958) 'Die Behandlung des Exzitons nach der Vielelektronentheorie', Z. Phys. Chem. Frankfurt, 16, 2 1 8 . HELLER , W . R . and MARCUS, A . ( 1 9 5 1 ) 'A note on the pro p aga t i o n of excitation in an ideal ized crystal', Phys. R ev . , 84, 809. HOPFIELD , J. J . ( 1 960) 'Fine structure in the op t ical a b s o rpt i o n e d g e of an i sot r op i c c r y s t a l s ', J. Phys. Chem. Solids, 15, 97. M EY E R , H . G . J . ( 1 9 56) ' S o m e aspects of electron-lattice i n teraction in polar crystals', Thesis, Amsterdam, Physica, 22, 1 09. N I K ITI N E , S . ( 1 95 5) 'Theorie approchee du spectre de l 'exciton d ' u n crista! u n i axc', Comptes-Rendus A cad. Se. Paris, 240 , 1 4 1 5 . P E K A R , S . I . ( 1 958) 'Theory of electromagnetic waves in a crystal with exci t o n s ', J. Phys. Chem. Solids, 5, 1 1 . T H O M A S , D . G . , HoPFI ELD , J. J . and P OW E R , M . ( 1 960) 'Excitons and the ab so r p tio n edge of cadmium sulphide', Phys. Rev . , 1 19, 570. E L L IOTT, R. J. ( 1 957) Phys.
Rev.,
108,
Excitons in germanium and silicon
P . , QUARRI NGTON, J . E. a n d ' Fine structure i n the absorpti on e d ge spec trum of ger m a n i u m ' , Phys. Rev . , 108, 1 377. M A C FA R L A N E , G. G . , M c LEAN, T. P . , Q UA R R I N G T O N , J. E. a n d RoB E R TS , V . ( I 958) ' Fine structure i n the abs o r p t i o n e d ge spec t r u m o f s i l i c o n ' , Phys. Rev., 1 1 1 , 1 245. M A CFA R L A N E , G . G . , M c L E A N , T . R o B E R T S , V . ( 1 9 57)
106
Luminescence in Crystal.�
M c LE A N , T. P.
and Lo u o o N , R . ( 1 960) 'Exciton energy levels i n germanium a n d silicon', J. Phys. Chem . Solids, 1 3 , I . Z W E R D L I N G , S . , ROT H , L . M . and L A X , B . ( 1 958) 'Direct transition exciton and fine structure of the magneto-absorption spectrum in germanium', Phys. Reu . , 1 09, 2207. Excitons in aflvali ha/ides
and T A FT , E . ( 1 9 5 2) Jmpelfections in Nearly Pe1ject Crystals. Chapman and H a l l Ltd . , London. E B Y , J. E . , T E EG A R D E N , K . and D U TT O N , D . B . ( 1 959) ' U l tra violet absorption of alkali halides', Phys. Reu . , 1 1 6, 1 099. v o N H I P P E L ( 1 936) 'Einige prinzipielle Gesichtpunkte zur Spektro scopie der Ionenkristalle und ihre Anwendung auf d ie A l kalihalo genide', Z. fur Phys., 101, 680. KNOX, R. S. and l N C H A U S P E , N. ( 1 959) 'Exciton states i n ionic crystals', Phys. Rev . , 1 1 6, 1 09 3 . M o T T , N . F . a n d G U R N E Y , R . W . ( 1 948) Electronic Processes in Ionic Crystals, 88-1 00. Clarendon Press, Oxford . M uT o , T . ( 1 956) 'Structure de l'exciton de KCI', J. Phys. Rad., 17, 829. M U T O , T . , 0YAMA , S. and 0 K U N O , H. ( 1 958) 'Electronic structure of the exciton in ionic crystal', Prog. Theor. Phys., 20, 804. M uT o , T. ( 1 9 59) 'Exciton problem and a new approach to its elec tronic structure', Prog. Theor. Phys . , Suppl. 1 1 , 1 . S L A T E R , J . C . and S H O C K L E Y , W . ( 1 936) 'Optical absorption by the alkali halides', f._hy_s. R ev . , 50, 705. APKER, L.
Some references on the a and {3 bands B A S S A N I , F . a n d l N C H A U S P E , N . ( 1 957) 'Position of the "greek" bands in alkali halides crystals', Phys. Rev., 105, 8 1 9. D E L B E C Q , C . J . , P R I N GS H E I M , P . and Y U S T E R , P . ( 1 9 5 1 ) 'A new type of short wavelength absorption band in alkali h alides contain ing colour centres', J. Chem. Phys., 19, 574. D ELB E C Q , C. J . , P R I N G S H E I M , P . and Y U S T E R , P . ( 1 952) 'a and {3 bands in potassium iodide crystals', J. Chem. Phys. , 20, 746. D E L B E C Q , C. J. and P R I N G S H E I M , P. ( 1 9 5 3) 'Absorptio n bands and lines in irradiated L i F', J. Chem. Phys., 21, 794.
C HAPT E R V
Luminescence Centres in Phosphorescent Sulphides
I . CONSTIT UT I O N OF PHOSP H O R ESCENT S ULPHIDES
To obtain luminescent zinc sulphide the base material must first be obtained as pure as possible. To do this several methods are available : (a) Hydrogen sulphide is passed through a solution of zinc salt, the zinc sulphide precipitated, washed and dried in an oven. (b) Guntz and Grillot used as the sulphuretting agent sodium thio sulphate Na2S20 3 instead of H 2S which forms a disulphide ZnS2 which is unstable and decomposes to give ZnS at high temperatures. (c) Coustal used a direct reaction of the elements zinc and sulphur, an explosive process but one appropriate for the production of so called 'self-activated' sulphides. As necessary a salt of the activator impurity is added in a suitable quantity and often also a flux (e. g. 1 per cent NaCl) and the whole is usually fired at 900°- 1 ,200°C. If the firing takes place at a temperature below 1 020° C the zinc sulphide crystallizes in the cubic form (blende), above 1 ,020°C the hexagonal form (wurtzite) is produced . Cooling must be sufficiently rapid to have the wurtzite form persisting at room temperature. Lewchin has found wurtzite to be present in ZnS made at much lower temperatures f'>:! 650°C. The small difference between the properties of the two forms of zinc sulphide is remarkable. The emission bands are very similar ; for ZnS(Cu) the green-band maximum is a little displaced towards the yellow-green in the case of blende crystals, in agreement with the slightly smaller energy-band gap for this form. Both forms show phosphorescence (they appear to have the same groups of electron traps with additional groups in the case of wurtzite). The difference 1 07 1 . Preparation
,
1 08
Luminescence
between the
in
Crystals
funda mental o r lattice absorp t i o n edge positi o n s is a l s o structures the n eares t neighbour configurati o n i . e . a t e t rah e d ro n of s u l p h u r i o n s a round a zinc i o n (o r
very s m a l l . I n b o t h is the same,
)
v i ce versa .
The p rep a ra t o ry methods fo r cad m i u m s u l phide a re anal ogous, but only the hexagonal form (wurtzite) usually o ccu r s. The blend e form has been observed , but only i n excepti onal cases . The st u d y of crystal l i n e t ra n s fo r ma t io n s in ZnS is ge n e ral ly made by o ptic a l m i c ro scop y using polarized light : hexagonal crystals are bi refringen t , w h i l e cubic crystals are not. T h i s method is a n excellent one and was used by A . G u ntz as early as 1 923. Diffr a c t i on e x peri ments by means of X-rays have al so been p e rfo r m ed . More recently, an inter e s t i n g meth od has been proposed by van Wierin gen ( 1 953) and used by A ven a n d Parodi ( 1 960) i n o rder to study the influence o f activator i m puri t ie s (Cu, A g) on crys t a l st r u c ture . A fraction of a bou t I 0 4 M n 2 + w a s added to the s am ple and electron spin reson ance studies were carried out. It is w e ll known (page 1 24) that the r es onan c e spectrum of Mn 2 + embedd e d in a n h exa g on a l su l phid e possesses 30 l i n es but only 6 in the b l e n d e cas e. The energy d iffere n ce between t h e blende and wurtzite forms is cer tainly e x t re mely s mal l ; p e r haps the transition temperature, and m o re over the rate of t h e transition, i s affected by low co n cent ra t io n s of cop p e r . A ccord ing to A ven and Paro d i , heati n g for one hour at 1 , ro o c a c h iev e s the transformation blende-wurtzite for a concentra tion of c o p p e r c < 2 · 5 . 1 0 - 4 , while the blende s t r u ctu re p e r s i s t s if c > 7 · 5 . J 0 4 • M an g an ese p ro d u c es an anal ogous effect (K ro g er) but at l a rger concentrations. Addamiano a n d A v e n sugges t that the transition te m p e rat u re fo r very pure c rys t a l s is hi ghe r than the accepted val u e of 1 ,020°C. The occurrence of t he phase ch a n ge wurtzite-blende nee d s nuclea tion effects whose opt i m u m temperature lies between 700°C ( Aven and P aro di) and 900°C ( Kremheller) . These results seem in a gree m ent with Lewch i n ' s exper i m en t s .
2. Numerical values of the energy-band gap for phosphors of the ZnS type The fol l o w i n g t a b l e is t a k e n fro m t h e review by B u b e (Proc. J. R.E.) and gi ves t h e v a l u es fo r the fu n d a m e n t a l o p t ical absorption limit .A.11m as well as t h o se for t h e e q u i v a len t q u a n t u m e n e rgy hl'llm· This quan-
Luminescence centres
1 09
t u rn is near to the v a l u e E for the fo r b id d e n b a n d w i d t h b u t m o re
precisely we h ave
/n·um h1•um
=
=
Egap if the
ve r t i ca l ( n o ph o n o n s i n vo l ved) if th e transi t i o n is effected with s i m u l ta n e o u s
tra n siti o n is
Egap - Ephonon
p h o n o n abso rptio n .
The table also gives the value for the agai n s t tem peratu re
s l o pe f3 of t h e
cu rve Ega 1,( T)
T between l i q u i d a i r tempera t u re a n d l 30°C.
E�;a,,(T)
=
Egap(O) -(JT
TA BLE V. !
Fundamental absorption limits h •um (e V) at 293°K
""'" (1)
at 293°K
ZnS blende ZnS wurtzite CdS wurtzite ZnSe blende CdSe wurtzite ZnTe blende CdTe blende
3,410 3,350
{J (e VjO C)
? 5·5 X J O -• 5 x IO - ' 7 X JO-' 5 x Jo-•
3 · 64 3 - 70 2-43 2-60 1 · 74 2 15 1 ·42
5 , 1 00 4,770 7,1 1 5 5,780 8,7 1 0
? 4 x IO-'
The values
give n are those which occur most o fte n i n the li tera t u re . e d ge i s not so sh arply defi ned a n d h1 ·1 1 m c a n est i m a ted to 0· 1 e V . W e often fi x t h e a b s or p t i o n l i m i t as t h e
However, the absorption o nly be
w a ve l e n g t h for whic h the absorption coefficient is 1 00 m m 1 ( Fi g . V . I ) . The l i m i t is most probably a ss o ci a t e d with a n o n - vertica l (o r Num ber of e l e c trons per photo n
K (m m1 ) '
1
Fig.
A(A)
10 9 8 7 6 5 4 :> 2
'--'-
3300
V. I
(a )
3400
3500
(b)
Op t ical properties of an unactivated ZnS (wurt
zite) crystal at room temperature (after Piper) (a) absorp tion spectrum (h) photoconduction response spectrum
1 10
Luminescence in Crystals
indi rect) transition (involving phonon absorption) between the valence and conduction bands, the lowest levels of the latter being due to the s-states of zinc or cadmium (Dresselhaus) while the valence band has a more complex structure due to the mixing of the p- and s-states of the sul phu r ions. In a purely ionic model for zinc sulphide Zn2+S 2 - the v al e nce band will be due to the S2- ions while t h e con duction levels will be those for Zn2+ to which an electron has been added, i.e. those for Zn + (cf. Fig. 1!. 2 for the monovalent ionic c ry st a l KC!). The l ong-w a v e limit for mixed crystals of ZnS and Cd S shifts con tinuously in the di rec t i o n of greater wavelengths with i ncreasi n g cadmium concentration (H e nde rs on , Kroger, P r i n gs h e i m). A similar di sp l ac e m ent occurs fo r the l u m i n esce n ce emission bands (A. Guntz, Rothschild, &c.).
This shift is al most linear when the the percentage of Cd S
functions of
hv11m are pl o t t e d as w e i g h t relative to ZnS
e n e rgies by
(Fig. V.2).
This behaviour suggests a s m a l l o r i n si g n i fi c an t difference i n t h e nature of the absorpti o n t r an s i t i o n hvlim for ZnS and CdS (K roger) . It contrasts with the behav i o u r of germ a n i u m-s i l icon al loys.
Fig.
Zn S
Q O '!.
V . 2 Band gap
1. 0 '1.
6 0 '1.
S O '!.
a function of composition for
cadmium sulphides as
100 CdS
------ percentage of CdS by weight - - - - - molar percellfage of CdS
zinc
111
Luminescence centres
Larach, S h rad e r and Stacker have shown that the s h i ft is a l s o linear
i n zinc sulpho-selenides, b ut strongly concave (with the occurrence
of a mi ni m u m for an intermediate c o m p o s i t i o n ) ZnSe + ZnTe.
for ZnS + ZnTe and
The problem of the e n e rg y -ban d structure in ZnS or CdS is, as well stated i n a recent work by B. S egal l , a fo rmi d ab le computational p ro b le m , which i m p l i e s that the attempts made over several years using c onsid e ra b le means (such as c o m p u t i n g machines) are not yet concluded. We may refer to the work of Segal l (t h e Kahn and Kor ringa method of dec o m p o s i ti o n i n t o p la n e waves), that of J. Birman (quasi-cellular method u s i n g the effective charge on the i o n s as a p ara me te r) , that of F. E. Wi ll i am s (quasi-cellular method self-consis tent calcula t i o n of t h e electron distribution between zinc and s u l ph u r i on s) and that o f M . Balkanski ( g ro u p t heo ry me t h od ) . In t h e meantime we m i g ht hope to limit the p r o bl e m to the possi bility of q u al i t at ive consideration of the e ffec ti ve ionic charges a n d of th e percentages of ionic b ind i n g . However, fro m m a n y d iscuss i o n s w e fi n d that th e notion of an effec ti ve c ha rge h a s n o u n ique d e fi n i t i o n 3. Observations on the nature of binding in ZnS
and its introd uction i n the course of consideration of each problem effectively i n v o lves a p a r ticu la r definition. However, s u ch i d eas are quite useful if we d o not demand too rigorous an appr o ach . The tetrahedral structure of zinc su lp h i d e is suggestive of a co valent type of b i n d i n g . While a purely ionic sp ecific ati on would give Zn2+S2 , a p urely c ova l e n t st r ucture wo u ld c o rresp o nd to a n e q u a l d is t rib u tio n o f t h e e i g h t valence electrons between the Zn and S ato m s and would lead to the charge specifi cat i o n Zn2 - S 2 + (Pauling's 'formal cha rges ') . Caster, Knol and Prins have been able to show by X-ray diffraction studies that the zinc ions are positively charged and the s ul ph u r i o n s n egatively charged . St retchi ng the blende crystal along t h e ( 1 1 I ) axis would give p os i tiv e ch a rge s o n t h e Zn pl an es and ne gati ve ch a rge s o n the S pl a n e s . To a first a pp r o x im a t i o n we might place ZnS among the ionic c rys tals since the static (K) and h igh - fre q u e ncy (K0) d iel ec t r i c con
stants are different :
K = 8·3 ;
K0
= 5 ·07
The Frohl ich relation between K a n d K0 on the
one hand and
the
1 12
Luminescen ce in Crystals
wave n u m bers of the l o ngi t u d i n a l and transverse o p t i cal v i brati o n s t h e l a ttice v z a n d � · : respectively o n th e o t h e r h a n d h a s been wel l t es t e d . F r o m J. P. Math i eu et al. we have of
,.,
--
l't
= 349
c m ·- l
274 cm 1
=
1 ' 74 · �
At t h e s a m e t i m e t h e param eter C
=
_}
K J- = Ko
'
K0
1 ·280
� which
K
_ _ _
occu rs i n the
theory of p o l a r o n s i s , fo r e x a m ple, m u c h s m a l l e r fo r Z n S a n d CdS
than
NaC I .
Table
TABLE Y .2
of t:a!ues for parameter
Crystal
C (Pekar) for various ionic crys tals
NaCI KCI KBr KI ZnS CdS ZnO Cu,o
K
5·8 4·78 4-8 1 5·2 8·3
1 1 ·6 1 2·0 9
K0
c
n•
2 33 2· 1 7 5 2·36 2·65 5 07 =
0·257 0 · 25 1 0·2 1 7 0· 1 8 5
0·0767 0 · 0864 0 · 1 74 0 · 1 39
3 88 4 0
5 · 85
m e a s u r e of the d egree c f i o n i c bin d i ng, the small value for ZnS and CdS su ggests a marked covalent a sp e c t of b i n d i n g i n t h e s e s o l i d s . We the refore wri t e t h e i on i c charge a s 2 e * , wh ere e* i s positive b u t is less t h a n e, and this i s the effect ive charge o n t h e z i n c i o n s . F r o m measu rements of t h e piezoe l e c t r i c c o n s tant B o rn and then Saksena h ave d e d u c ed 2e*. B o rn gives 2e* 0 · 3 e and Saksena 2e* 0·68c. These values now a pp e a r to be too s m a l l . Le Corre A l t h o ugh i t w o u l d be w r o n g to u se C as a true
=
=
( 1 9 5 5) took acco u n t of n o n-ce n t ral forces a n d the d e fo rmati o n of the
i o ns i n a crystal , and fro m t h e piezoelectric characteristic ded uced 2c*
==
1 · 4e. H.
Poulet a ppl ied the Szigeti fo r m u l a : K- Ko
=
(K0+2)2 (2e*)2
where, togeth er with p revious notation,
;;c2 i/if,.,2
c i s t h e velocity o f light, V the M the red uced mass of the zinc and sul phu r ion pai r. Us i n g the val ues of all th e s e q u a n t i tives the val ue 2e* 0·88e.
volume o f t h e unit cel l , and =
Luminescence
ce n t res
I I3
fo rmula uses the Lorentz-Lorenz e ffective field w h i c h an approximation, but H. Poulet obtained a good agreement between the experimental states for the Raman spectru m of zinc blende and the calculated characteristics u sing the above val ue fo r The
Szigeti
i s o nly
t h e effective charge.
We may therefore conclude that a value of the effective charge 2e* about unity (75 per cent ionic bindi n g) seems to be appl icable to ZnS. The i onic cha racter o f t h e b i nd i ng i s p robabl y a b o u t the s a m e i n CdS , while, as shown by the Pau ling tables o f e l ectro negat i vi t y , t his type of b i n d i n g wi l l decrease when s u l p h u r i s replaced b y selen i u m and above a l l b y tel l u r i u m . of
Remark : Szigeti's fo r m u l a i s a good approx imation, but i t is s t i l l o n l y a n approximation. Let us m a k e a comparison with t h e effec t i ve charge o f t he i o n s in the alkali halides : T A B L E V.3
e • je 0 93 0 80
0 87
LiF NaF KC!
0 69 0·87
KI Rbi
In lectures given i n 1 959-60 at the University o f Paris , N . Inchaus pe
developed the fo llowing point of view : It seems most probable tha t in
compound such as LiF the real charge of the ions is very little d i fferent from e, and thus l i kely that Szigeti's formula lead s to val ues of e* that are a
a
l ittle too small . If the same thing holds in ZnS, the effective charge 2e*
will be
nearer u n i ty than the above value of 0 · 8 8 e * .
I l . L U M I NESCENCE CENTRES A N D E M I S S I O N S PECTRA F O R Z n S AND Cd S
F o l l o w i n g Pi per and Will ia m s ( 1 958), we shall first reproduce t h e p o rti on of the p eri o dic table o f the elements which is rel e v a n t to the
class o f usual sem i-co n d u ct o rs a n d phosphors a n d to their activati n g
or co a cti v a t ing
i m p u ri ti e s
.
T A B L E Y.4
IB
liB
IIB
IVB
AI Cu
Zn
Ga
Ag Au
Cd Hg
In
Ge
B
c
Si
Sn
VB N p As Sb
VIB
VIIB
s Se Te
Cl Br I
Luminescence in Crystals
1 14
From this we can deduce that In silicon and germanium, P, As, Sb introduce donor levels i m pu rities ; A I , Ga, In are acceptors. I n SiC, N and P are donors, B and AI acceptors (see Chapter IX, page 26 1 ) . I n the phosphors of the Z n S type, m a d e by t h e combination of an element from column liB and an element from column VIB : (a) the usual activating impurities Cu, Ag, Au substituted for Zn, C d , Hg are in acceptor positions ; it is the same for P, As, Sb substi tuted for S, Se, Te ; (b) AI, Ga, In and the halogens Cl, Br, I are in donor positions. 1.
Copper
as
an activator
From experience it is found that in ZnS copper prod uces two main emission bands, a green band at about 5,230 A (2· 3 7 eV) and a blue one at about 4,450 A (2·79 eV) . Bands also occur in the infra-red (Garlick and Dumbleton) and also a red band wh ich is produced by higher copper concentrations and fo r which groups of copper ions arc probably responsible (Froelich). If we introduce increasing amounts of CdS into ZnS phosphors the above bands are shifted . For pure CdS the equivalent of the blue band is now at 0·82 p ( 1 · 5 1 eV) and that of the green band at 1 ·02 ,a ( 1 ·22 eV) These band shifts contrast strongly with the case of thallium in the alkali halides. While in the latter the luminescence can, to a first approximation, be a t trib u ted to interlevel transitions of the Tl + ion, .
ZnS
Con ducUon b a n d 3 7 0 eV
m o P.
4450 A
Valen ce band
Con duction band
l'a !ence b a n d
Fig. V.3 Positions ofenergy levels giving the characteristic
emission bands for copper activator centres in ZnS and CdS (wurtzite) Classical level scheme (Rieh/-SchOn-Klasens)
115
the i n teractio n with the c ry s ta l lattice being treated as a perturbation, in the c a s e of copper activations we cannot identify the transitions with levels of the copper ion . As emission always follows the recom bination of a conduction electron with the centre, it is often the prac tice to represent the centre processes of Fig. V . 3 by transitions to their ground states from the bottom of the conduction band . This is rather simplified and we shall see that the emission does appear to involve excited states of the centres at small depths below the con duction band. However, this does not affect the various conclusions below. We see rather that the separatio n of the centre ground states from the valence band is almost constant, while that from the con duction band alters.t The former is the same for silver-activated ZnS or CdS (Grillot and Guintini). The valency of copper as an emission centre. The absence of elec tron spin resonance for ZnS(Cu) 1 01 x phosphors and moreover the mea surement of magnetic suscepti- 0 bility as a function of temperature show that the emission centre is - 1 due to Cu + ions. For neutral copper atoms (Z 29) an odd - z number of electrons is present 3 o 0·1 0 ·2 0 ·3 0·4 o s o s 0 1 1/r(.K) and cancellation of all spins is Fig. V.4 Magnetic suscep tibility impossible, that is, the atom is paramagnetic. The same applies X of ZnS (9 . J 0 -6 Cu) as a func to Cu 2 +, but in contrast Cu+ is tion of temperature T (Bowers & Melamed) diamagnetic. Experiment shows ( Fig. V.4) that the susceptibility of ZnS(Cu) is sensibly independent of temperature (Bowers and Melamed). A notable experiment due to Prener and Williams shows also that, no matter how it is introduced into the lattice, copper does not by itself form a luminescence centre. They prepared ZnS by acting on a zinc s al t with hydrogen sulphide, the zinc salt being made from zinc previously irradiated with neutrons to produce the reaction : ZnG4(n, y) --+ Zn65 --+ 65Cu (by K electron capture with half-life of 250 days) Luminescence centres
=
t The separation is the same for blende as for wurtzite , the small spectral shifts observed being attributable to the change in the width of the forbidden energy band.
1 16
Luminescence in Crystals
S o m e copper i s formed in this way i nside the sul p hid e a fter firin g . However, the emission ba n d s are unaltered by its presence and so we conclude it is n o t the activator for th e s e bands. There is some doubt about expl a n a ti o n s of these effects. The copper may not be at a suitable site i n the c r y st a l lattice (i .e. n o t a s s oci a ted with a don or centre a cc o r d i ng to Wi lli a m s) o r perhaps, fo ll o wi n g an i o ni c model Zn Z + S 2 , it occu rs as Cu2+ a n d not Cu+ (Kl ick a n d Schulman) . W h a tever the nature of the b i n d i n g assumed for ZnS, most workers agree that copper i ntrod uces new l e vel s situ ated se v e ral tenths of an elec tr o n vol t above the top of the valence band . Usi n g the purely ionic model ( Klasens), the replacement of Zn 2 + by Cu+ r e d uce s the bo n d stren gths to the s u rroun ding s u l p h u r ions and increases the electro static energy for the e lec t ro n s on these ions. This p ro d u c es bands at a height e2 IKd above the valence band (K is d ielectric constant of the s u l p hi d e and d the nea rest neighbour distances in the lattice) . I f o n the other hand a pu rely coval ent bi n ding is assumed (Williams), then repl acement of Zn (Z = 30) by Cu (Z 29) a l l o ws only three of t h e fou r te t r a hed r al l y direct covalent bands to be c o mpleted around the c o p p e r This gives rise t o an acceptor level which according to the Bethe m o de l will be at an e ne rgy 1 3 · 5 eV/K2 above the v al ence band. The s i m i l ar co ncl usi on for both the above ap p r o a c h es is thus pro ba b l y a v a l i d o n e . D e t a i l e d i n ve s tigat i o ns consider the occ u pa n cy of the centre, the role played by the 'flux' in p r e p a rat i o n and the difference between 'blue' and 'green' emission centres. From the work of E. Grillot it would appear that introduction of oxygen pr o d u ce s the green emissio n centres. A h a l ogen replacing sul phur (i n tro du c ed by t h e flux during firing) will d o the same (F. E. Willi ams). The centre c a n therefore be represented to a fi rst approxi mat i o n by a p a rt i al l y covale n t ' molecule' fo r me d by cop p e r the su r r o u n d i n g sulphur atoms and those of oxygen or a h a l o ge n associated with the group (with the e x cept io n of fl uorine, which because of i t s h igh electronegativity d o e s n o t favo u r coval ent b o n d i n g). Som e discussion on recen t models for luminescen ce centres in ZnS( Cu) . A s i m p l e pi c tur e o f the association between the copper ion and the h a l o ge n ion is given by Williams and Prener's model of associated donor-acceptor cen tres (see below, Fig. V.9). This kind of as s o ci a ti o n req u i res that approximately eq u a l concentra t i o n s of the a ct iv a t or and o f t h e halogen (c o a c tiv a t or) h ave been deliberately introduced into the su l ph i d e . For such experimental cond i tions the i n tensity of the ,
=
.
,
Luminescence centres
1 17
green band is much h i gher than the inten s ity of the blue band (see v a n Gool a n d Cleiren, 1 960) : th i s supports the ass u m p ti o n t h a t t h e green band i s due to th e a sso c iated d o n or- a cc e p t o r sy s te m . On the o th e r h a n d , an ex c es s of c o p p er g i ve s t h e b l u e copper fluoresce nce. This fact leads to the assumption that the blue band i s not due to an association between the activator and the h al o gen ions (see, h owever, K r o ger and Helligman, 1 948). T h e p e a k p o s i t io n o f both bands is unaffected (within experi mental l i m i ts) by the chem ical natu re of the h aloge n i o n , fo r in s t a n c e, Cl or I : the h al o gen effect is d ue to i ts s u bstitu t i o n a l charge - e in the latti ce. K r o ger and Dikhoff ( 1 950) have sh own that t h e trivalent elemen ts AI, Ga, In may be used as c oac t i va t o r ions instead of t h e h al ogens . The m echan i sm of th e coactivation i s probably a pp r o x i m a t el y the same. However, t h ey seem to introduce donor levels with depths slightly larger than the halogens (by 0·04 to 0·08 eV) a n d a d i s p la ce ment of the emission toward s longer wavelengths is observed . When such an accuracy is p o ssible many contradictions appear between the experimental results reporte d by diferent wo rkers . The numerous expe rime n t s performed by E. a n d M . G ri l l o t h av e given evidence for the fact that oxyge n i ons m ay behave qualita tively in the same way as the above c o a ct i vato r s . It is quite certai n that the incorporation of oxygen leads t o donor l evel s i n m any semi c o nd u c to rs , and the same occurs probably in zi n c s u l p h i de. I ndeed , the part played by oxygen in the improvement of electroluminescent p h o sphors also supports th i s assumpt ion (see page 255). When neither halogen nor A I , Ga or In is pre s e n t, the gree n e m i s sion i s fa vou red b y rather s mall concentrations of c o p p e r a n d t h e b l u e o n e b y large co n cen t ra t i on s ; the l i m i t depends on t h e amo u nt of oxygen present in the s u l p h i de. This behaviour is the same as that reported above for coactivated p h o sp h o rs . The fo ll owi n g level s che me summarizes the above discussion. We must em ph as i ze that m a ny fu rther ex p e rim e nts are needed for sup porting or for aband o n i ng it, but we th i n k that i t m a y be a g o o d fi rs t approximation. I t is p rop o s e d t h a t the same ground state, due to Cu + i o n s , p l ays its p ar t in both blue and g ree n centres in zinc sulphide. B u t the green emiss i o n occu rs from a transition arising from the donor level in tro d uced by the oxygen or the c o ac t i vat o r ions ; the bl ue emission is E
1 18
Luminescence in Crystals
p r od u ced , either in a transition d i rectl y from the conduction band or i n a transition from an excited level of the centre ; th is excited level must be shallower than th e donor level involved in the green emis s ion (Fig. V . S) . van Gool ( 1 96 1 ) s uggests that an a s socia t i o n with lattice defects i s re s po n s i b l e for the blue e m i ss i o n . Con duction band
Blue em1ssion
i I
:w
I
donor level
Green em1ssion
--
Fun damenta l ' h a cceptor level I Cu i I
V
Valence band
V . 5 A model recently proposed for blue and green emission centres in ZnS(Cu) (G. Curie and D. Curie) W is the energy necessary for exciting the centre in electroluminescence hv is the energy involved in the infra-red quenching
Fig.
The assumption tha t the same gr o u n d state occu rs for both em is sion b a n d s is s upp o rted by the following evidence : (A) In electrol uminescent cells u sing Zn S(Cu), no change of colour is prod uced when hi ghe r vol tages are applied (Fig. I X . S) ; t h is be h aviour is opposite to t h a t of p hos p h o rs c o n t a ini ng different acti vators. Thus the energy W fo r exciting blue and green centres is
On the contrary, the cl as si ca l level scheme (Fig. V.3) s u ggests that the blue band grows in in te n si ty with voltage faster than the green band, and this conclusion is not supported by experimental evidence. (B) The same energy hv occ u rs in the i nfra - re d quenching of both emission bands ( F i g . VII . 1 3). G a r l ic k and B r ow ne h ave shown that the infra-red quenching spectra a re i d e n t i c a l with the excitation
about
the same.
On the o t h e r hand, the classical Riehl-Schon-Kiasens scheme
bands.
e x pl ai n s more easily the difference of temperature q ue nch i ng between
the blue and green emissions : the blue emission d isappears at a tem perature 1 00° to 1 50° lower than for the green one. However, this may also be expl a i ned with Fig. V . S by using a remark due to
I I9
Luminescence centres
Roberts and Williams ( 1 9 50) : quenching occurs when the thermal activati o n of an electron from the excited level of the centres freeing it into the cond uction band occurs before the light-emission tran sition. This activation i s produced at lower temperatures for the blue centres . In addition, the Cu level is split by the asymmetry of the electric field
in the crystal (J. L. Birman). In our opinion, this spl itting i s
probably n o t very much larger than t h e splitting of t h e valence band levels, i.e. some
I Q-2
eV. If this is true, it is much smaller than t h e
widths of the emission bands.
2. Silver and gold as activators
While the copper activator is close to zinc in the period ic table, s i lver
and gold are the higher 'homologues' of copper. The activation pro
cess is probably analogo us, i . e . s ubstitution of the metal i n a zinc site
and formation of a partial ly covalent molecule. The fo l l owing table gives the l ocation of the two main emission bands for zinc and cad m i u m sulphides.
T A B L E V.5 Cu Cu Ag Ag Au
Type 'I' Centres
in ZnS (wurtzite) in ZnS (blende) in ZnS (w u rtzi t e) in ZnS (blende) in ZnS (wurtzite)
Au in Cu in Ag in Au i n
5,230 A 5,350 A 4,760 A 4,960 A 5,300 A 5 ,500 A 1 0,2oo A 7 , 800 A t i , 5oo A
ZnS (blende) CdS (wurtzite) CdS ( ) CdS ( )
Type 'Il' Centres
4,450 A 4,600 A 4,370 A 4,500 A 4,700 A 4,800 A 8,200 A 7, 1 60 A s ,oo
A
Most of the emissio n band s of CdS are in the i n fra-red . of CdS(Ag), centres of type
In the case II always give a red emiss ion, but to
obtain high emission efficiency firing m ust be made at the rather low temperature of 600° -800°C (E. Grillot) . In addition, the i ncorporation of a large amount of si lver into cadmium sulphide produces
a visible red emission, peaked at 6, 200 A
(Fonda) . We agree with a suggestion from van Gool, ascribing this emission to centres d escribed by the model of Lam be and Klick (see
Fig. V.9). The homologous band in ZnS is l ikely to be situated i n the ultra-violet region (near 3,900
A).
I n several respects the beh aviour o f si lver-activated samples
1 20
Lum inescence in Crystals
a ppears to b e slightly d i fferent fro m t h a t o f Cu- a n d Au-activated zi n c s u l phi d e phosphors. The reason for these differences is not wel l u nderstood. Until q u i t e recent w o r k , the lo n g wa v e ba n d ( ty pe ' I ' c e n t res ) of silver-activated Zn S was not o b se rve d Henderson, Ran by a n d H a l s t e a d h ave gi ve n evidence for the occ u r rence o f this band , -
.
h v leV J
JSOO
. 1.000
I. S OO
25
0
20 1.0 6 0 %Cd 5
Fig. V.6 Position of emission p eaks as a function of com position for zinc- cadmium su lp hides at room temp erature . Molewlar percentages of CdS Gap Cu
Ag
= = =
band gap green band due to copp er main band of silver (blue emission)
intensity re m ai n s small compared to the main blue-violet (typ e 'II ' centres) . I t is relatively e nh a n ce d at temperatures above room temperatu re : in this way, H. Payen d e la Garanderie, of the au t h o r s laboratory, has confi rmed the results of Henderson a n d eo-wo rkers, a n d shown that i t i s i ndeed the ho mologous band of the 7,800-A band of Cd S .
b u t i ts band
'
3 . R a d i a tiv e recombination due t o vacancies
(Krogcr)
' U n activated' or rather 'self-activated' zinc sulphide s h o ws a bl ue emission . When i t does not a rise from u nsuspected t ra ce s of coppert t Traces (� 1 0 • pts pe r ZnS) of Cu, Ag, &c., can be detected by ra d i ochem ical ( 1 955), p . 7 1 .
a n a l ysis : E. G R I L LOT, Congres Soc . Sav.
Luminescence
cen tres
121
i t i s o ften at t ri b u ted to zinc vacancies . At room tem p e ra t u re the emission p e a k s at 4, 520 A (Kroger and Di khoff)t a n d i s very c l o s e to the peak for copper and e ven fo r s i l v e r a cti vat o rs . We therefo re a s k if t h ey do not arise fro m the same process in each ca s e . H o w ever, Larach and Schrader have sh o w n t h a t the maxim u m fo r the bl ue emissio n of self-activated Z n S m o v e s to l onger wavel e n gths a s the temp�rature is l owered (4, 5 60 A at 90�K), while the b l u e emi s s i o n d u e t o copper is s h i ft e d in the o pp o si t e directio n (4,380 A at 90° K ) . When imp urity activator concentrations exceed I 0-6 or 1 0 -s p arts pe r ZnS or C d S , the emission attributed to va can c i es d isappears i n fa vour o f that due t o the i mp uri t i e s. In CdS the metal vacancy emission is peaked n e a r 7,600 A ; t h u s , e x a ctl y in t he same way as in ZnS , c o nfusio n is poss ible wi t h t h e s i l ver-acti vated e m is s i o n .
I n a dd i tio n , a c o n nect i o n h a s b ee n s o meti mes t h e sulphur vacancies and o ther emissi o n b a n d s .
proposed
betwee n
M elamed ascri bes the visible red emission of CdS(Ag) (6,200 A ) ,
b y an e x ce s s of silver, t o the sulphur vaca n c i es . A priori, em iss io n can also be ascribed t o i nters t i tial Ag+ i on s , or to p a i rs of A g + ions : in t he near future, p olariz at i o n experiments wil l give the p o ss ibi l i ty of d i s tinguishing between these different models . We s h o u l d remember that the analogous emission i n Z n S occu rs a c t iv ate d
this
The sulphur v a ca n ci e s
at 3 , 900
A.
h ave also been suggested a s play i n g a p a r t
i n the emission at 6, 700 A o f ZnS(Cu) wi th an excess o f co p p e r (Froelich). T h is emission is commonly refe r r ed to a s the ' red' e m i s s i o n (because the maximum of the emi t te d energy is i n the red p a r t of the spectru m) or as 'orange-red' (becau se the word des cri be s the colour of the emission as observed). The p o s s ibl e models for the cor responding centres have been recently reviewed a nd discussed by Aven and Potter ( 1 9 5 8) . Pairs of cqpper ions are involved in these cen t re s , but they may be associated with a sulphur vacancy. 4.
Manganese (Mn 2+) as an activator
As an activator in ZnS p ho sp h o rs manganese gives a characteristic yellow-orange em i s s i o n . Its behaviour is d i fferent from th o s e d ue to C u , Ag and Au activa tors. Although photoco n d uction can be at
t This figure is for wurtzite ZnS. 4,690 A.
In blende
(Lewchin, 1 96 1 ) the pea k
is s i t uated
1 22
Luminescence in Crystals
excited i n ZnS(Mn), particularly
if 3 ,650 A rad iation is u sed , t h e a series of di s crete absorption bands (see Fig. V.7), by i rradiation in one of these b a n d s (e.g. w i t h 4 , 358 A H g line)
M n 21 i o n p r o d u c es
and
3 66 3
4047 4 3 5 8
47n?
;\. (A )
F i g . Y . 7 Absorption spectrum of a ZnS-MnS phosphor (F. A . Kroger)
(2 p e r cent)
a fluorescence unaccompanied by photoconduction or p ho sp h o r escence of long duration is produced, the d e cay being sensibly inde pendent of temperature. The emission is d ue to t r a ns i t i o n s with i n t h e M n 2 + ion, t he main transiti o n being d ue to a ch a n g e i n spin of one of the five 3 d electrons (see Fig . V.8). The stable configuration of a neutral m an ga n e s e atom is as follows : M n l s2 2s2 2p6 3 s 2 3p 6 3d5 4s 2 The energy-level system for the free manganese ion M n 2 + ( l s2 3d5) gives the spherically symmetrical 6S state a s th e gro u n d state, i n which all 3d electron spi ns are parallel , while t h e first excited state is 4 G having one of the spi n s reversed . T h e series of levels for the i o n is as follows : 6S, 4 G, 4p, 4D , 4F The energy sep ara t i on between the ground and the first excited state is 3 · 32 eV. The excited state 4P is only a little h i gh e r . The excited state 3d44s is 3d5 46 some 7 · 2 eV above the g ro und state and , as Kroger a s su m ed , it cannot be involved in the observed emission . Johnson a nd Williams have d ete r mi n ed the magnetic 6s 3d5 dipole moment for Mn2+ in the ground Fig. V.8 The transition and in the excited states for the ion in a 4G +- 6S in the Mn2+ ion ZnF2 l a t t i c e , and have found t ha t it is m u ch weaker by about o ne B o h r m a g n e to n i n the excited state, which i n d icates a lower m u l t i p l icity i n t h e excited state (probabl y '1 G). •
•
•
1 23
Luminescence centres
fo r the g ro u n d state 6S is extremely small I 0 - 3 c m - 1 • This sp l i t t i n g is larger fo r the excited state 4G; but theoretical calculations, which have been m a d e by d iffere n t authors (Tanabe a n d Sugano, Clogston, &c.) lead t o the co n cl u s io n that it The crystal li e l d splitti n g
�
rem ai ns small enough to describe the emitting level as arising from the 4G state of the free ion. The emission due to MnZ+ ions is often in the yellow-orange regi o n , as is the case for ZnS-Mn and ZnF2-Mn. However, a notable exception is wi l l e m ite Zn2SiOcMn, where the emission is g ree n (the same is true of C aF 2- M n).t These differences are attributed to a different interaction between the MnZ + ion and the s ur r o u ndin g lat tice which can be described by a confi gu ra ti on coordinate scheme as for Tl + ions in KCI. Only in the case of wil l e m ite has this been d on e (Kiick and S ch u lm a n , Vlam - see Chapter III. l ) . Emission
TAB LE
V.6
peaks for the Mn Z+ ion luminescent&
Mn ' + free ion Mn2 + in ZnS Mn2 + in ZnF M n 2 + in zn.SiO,
3,730 A 5,850 A 5,950 A 5,200 A
The transition due to s p in reversal is normally forbidden. The sp i n
orbit co up li n g makes it p o s s i b le to have a mixture of 6S and 4P s tates ( Leveren z) and the p ro b a b i l i ty of such a t ra n s i t i o n i s stron gly d epend
e n t on lattice interaction ; the more the binding is covalent the more probable it becomes. T A B L E V.7
Excited state life
times for Mn 2 +
M n 2 + in ZnF2 Mn 2 + in Zn 2Si0, Mn • + in ZnS
centres
0·1 sec 0·0 1 3 sec
P h o sph o rs activated by Mn2+ ions p rovi de ideal subjects for elec tron spin resonance studies (Kastler, Hershberger, Uebersfeld, &c.). 0·00 sec
t The manganese emission is also orange or yellow in halophosphates phos phors (see page 62), in calcium and cadmium silicates (Fonda), &c. However, since the free ion transition would be, if observed, in the u ltra-vio let part of the spectrum, all colours are theoretically possible for Mn 2 + embedded into diferent crystals. A red emission is found with Zn3(P0,)2-Mn ; a search for a bl ue emission has been made by E. Lind for CaF2 + BeF2(Mn) phosphors .
Luminescence
1 24
in
Crystals
A n appl ied m a g n e t i c fi e l d H s p li ts ea c h energy l e v e l by a Zee m a n effect i n to 21+ I c o m p o n e n ts with sp a c i n gs 8.£
_!}:_:If
g4mnc while a h i gh-freq uency field ( fre q u e n c y l') is applied i n a p er p e n d icular d i rect i o n t o :it. The t ra n s i t i o n p r o bab i l i t y between two adjace n t l e v e l s i s a m a x i m u m when .no i s o f such a magnitude to give
a resona nce
=
hv
For t h e gr o u n d s tate ( J
=
D. E
5/2), five tra n s i t i o n s c a n occu r, b u t the
same applies to each at r es o n an ce .
Hershbergcr a n d Leifer h ave exa m i n ed t h i rty-two p h o s pho rs acti va ted by m a n ganese. They fi rst l o o k e d a t the e l e ctr o n res o n a n ce a bs o rp t i o n fo r the u n e xc i ted p h o s p h o rs a n d their results confi rm t h e assu med s y m m e t ry of the ground state (i . e . 6S) with an isotropic
g value of about 2 . However, a ma rked hyperfi ne structure some
t i me s occ urs .
Since the n uclear spin of manganese is I = 5/2, a hyperfi ne spec t rum with six components occurs . This is found for dilute aqueous
solutions c o n t a i n i ng M n 2 + ions (Kip) an d also for ZnS(Mn) (ble n d e fo rm) .
This stru c tu re is easily e x pl a i n e d u s i n g t h e H am i lto n ia n HMn> +
g4 eh Jf' + A S . I
nmc
i nvolvi ng cou p l i ng between nuclear spin I and electron s p i n S. I f
M is the electronic magnetic q u antu m nu mber and m that for the
n u cle us , then we have the selection rules
8.M
=
I
;
8.m
=
0
from w hich we have six a bs o r p ti o n lines corresponding to the 21+
1
=
6 values o f m .
o b s erved , and this has be e n expl ained by a th e o ry due to Abragam a n d Pryce which a s sum e s a n asymmetric electric field around the M n 2 + (pe rhaps d u e For h ex ag o nal ZnS, thirty l i nes have been
t o a vacancy) . This prod uces a correction of an ax i al a n d non spherical k i n d to the Hamiltonian o f the form
HM.n• + = e x p r e s si o n above + D[S. 2 - ! S(S + 1 )]
The selection
rule
!1 M
=
1 thus all ows five se r ies of lines for each
o f the six hyp e rfi n e structure lines (i . e . for each of the
m values) .
Thus Hershbe rger was able to acc ou n t fo r the th irty li nes observed .
Luminescence centres
The c h a n ge i n the electron resonance s p ectra
when the
1 25
p ho s p ho r
is exci ted has also been investigated . A. Ka stl e r had already shown
the in terest wh ich existed in applying the resonance tech nique for
the exci ted state. However, since He rsh b e rge r used 3 , 650 or 2 , 5 3 7 A r a d i a t i o n which p r od uce s photoconductivity, even in ZnS(Mn), and
not radiation l y i n g in a characteristic absorption band of the man
effects due to the conduction electro n absorption oc magneti c field). These mask the sp i n effects (which of course occur o n ly at c e rt a i n magnetic
ganese, large
cur ( e v e n without t h e a pp li e d res o n ance
field v al u es ).
I l l . O P T I C A L T RA N S I T I O N S I N V O L V I N G
I.
LOCA LIZED LEVELS
Luminescence centres a n d electron traps in
crystal phosphor
a
photoco n d u c t i n g
Let us first recall the d efinitio n s
given i n the introd uction : (i) Luminescence centres are the energy levels respo n s i b l e for the spectrum of the emitted luminescence. (ii) Electron traps are metastable levels resp on s ibl e for phosphor escence after excitatio n has finished .
an atom or in a luminescent crystal such as KCI(TI) , where the emitter sy s te m is 'quasi-atomic' (Tl + to a first approxi mati o n), it is easy to know whether or not a metastable state is involved . Thus the levels 1P1 and 3P1 of the thallium are emission levels with s h o rt life time s , but 3P0 constitutes an electron trap because the J v a l u e is zero In
as for the ground state 1 80•
In a photoconducting crystal such as ZnS(Cu), b ot h the cen tres a n d traps are localized levels
in the forbidden p ositi ve holes .
capture free electrons and free
energy gap and ca n T h e distincti o n be
tween them is no longer s o cl e arly marked and d epends on thei r
rel ative captu re cross-secti ons for t he two d i ffere n t types of ca rriers ,
a.
fo r conducti o n electrons and
CIA for positi v e h oles in the v a l e nce
band . We obtain a recombination centre for electrons and h o l es if a level has
a. R:!
a11 a n d an electron trap if a.
been possible t o say for
the given
> a11.t S o far it has a l ways whether a given l evel
co nditions
a trap o r a recombination centre. However, the be d ep en d e n t o n experimental co n di t i o n s . Thus copper t For traps in C d S t h e ra ti o of the capture cross-sections for t h e two types of carrier i s of t h e order of 1 00,00 (R. H. Bube). will behave as
h avi o u r is
very
Luminescence in Crystals
1 26
in
germanium gives three acceptor levels (accepting I , 2 or 3 elec trons to complete the tetrahedral covalent bonding around the cop per) situated at 0·04 eV and 0·32 eV above the valence band and at 0·26 eV below the conduction band (Woodbury and Tyler). The level at 0·32 eV behaves as a\ recombination centre in N-type ger manium at room temperature. However, while the capture cross section for holes is almost independent of temperature, that for the electrons a. depends on a thermal activation with energy 0·2 eV (this activation is necessary to obtain the configuration in which the cap ture transition is most likely). At liquid air temperature, therefore, this level becomes a positive hole trap. Such effects have not been found for ZnS : however, Arpiarian and also Gergely have shown that in ZnS(Au+ Ni, Co or Fe) the respective capture probabilities for the centres Fe, Ni and Co (with or without radiative emission), i .e. their functioning as 'killer' centres or luminescence centres, de pends on the temperature and also on their concentrations. This behaviour is, however, rather exceptional. In general, as shown by Fig. 5 of the Introduction, a level which is normally empty and lying near to the conduction band behaves as an electron trap, while a level normally occupied and near to the valence band behaves as a positive hole trap . A level approximately midway between the bands acts as a radiative or non-radiative re combination centre. This can be demonstrated by the following qualitative argument which is from P. Aigrain : Suppose that _the matrix element representing the capture prob ability for a conduction electron by a localized level is given by cpk = vk exp (ik . r) This can be written e n 1p(r)- -:(A . grad)?fk dr
J
mc 1
1p(r) can be resolved into a series of Bloch fu nctions of the type 1p(r) =
2:A k'1'k' exp (ik' . r) k'
As in Chapter IV, the term Ak' only gives an appreciable m atrix ele ment for k' k. This means that the transition probability is only large when the coefficient A k' is large. During phosphorescence the cond uction electrons diffuse to the bottom of the conduction band for which we assume k 0. The =
Luminescence centres
1 27
radiative ca pture of these electrons by the level 7p(r) will have a prob ability of the fo rm Pcnpture OC I Ak= O 1 2 which is large if A k o is large. For a trap near to the conduction band the coefficient A k � o fo r the bottom of the band will generally be large while the contribu tions of the Bloch functions to the valence band will be small, which gives a high probability for conduction electron capture and a low probability for the electron to fall into one of the holes in the valence band . For a d eeper level the large A ,, values correspond to energies if(k) situated h i gher up in the band (as far above its bottom as the localized level is below). However, if the level is sufficiently localized and its F o u r i e r transform sufficiently extended , the coefficients Ak�o can have su fficient amplitudes to allow capture with a signifi cant probability. I f, however, the level is too deep and its Fourier transform not extensive, then Ak= O will be negligible and that wiJ I also apply to the capture probability. Quantitative calculation of the radiative capture probability has been made by Parodi for a hydrogenlike level. Capture in such a level appears to lead to observable transitions in germanium and certainly in silicon . 2. Various types o f centres in photoconducting phosphors
Three types of model can be assumed for the centres in a photo conducting phosphor : (a) Centres near to the conduction band. These centres are simply deeper than typical electron traps, and transitions to the valence band although less probable than those from the conduction band to these centres still have an appreciable probability. This model was postu lated for CdS by Lambe and Klick and for certain bands of ZnS(Cu, S m) by V. V. Antonov-Romanovsky. First of all, a conduction elec tron is captured in the localized level and then this electron falls into a hole in the cond uction band, this last and radiative transition giving emission. Most workers consider that special conditions must apply for such transitions to occur. This really arises from the intuitive feeling that the very low positive hole mobility in phosphorescent sulphides mitigates against them (the 'macroscopic' hole mobility in CdS is R:f I 0 4 while that of the electrons lies between 10 and 1 00 cm 2/volt sec).
1 28
Luminescence in: Crystals
Acco rd i n g to Sch o n the centres resp o n s i b l e fo r the Ewlcs -Kroger
emission (Chapter IV, paragraph II.2) are of this type. (b) Centres near to the valence band. This is the 'classical' model for copper centres in zinc sulphide (Riehl-Schon-Klasens) . Copper pro duces a level in the forbidden energy band several tenths of an elec tron volt above the valence band which has a high probability for positive hole capture (it is assumed that a hole diffusing through the valence band is immediately captured by the centre when it lies below it in the band diagram). The centre also is allowed a significant car: ture probability for conduction electrons, and this gives rise to luminescence as observed by a transitio n to the centre ground state from the bottom of the conduction band. Fig. V.3 was drawn on the basis of this model. (c) Centres in volving a ground state (I) near the valence band and an excited state (!!) near to the conduction band. After the discussions given earlier we can see that the level s I have a high hole capture probability and levels II a high electron capture probability. After capture has taken place in each type, emission can take place by a transition of the electron from level I to level II. The only condition is that the temperature is not too high, so that electrons are not freed by activation from the type II levels before the transition can take place. We can affirm that if such centres exist, the probability of radia tive capture will be higher than for the o ther types of centres considered in the two models of (a) and (b) above. Williams and Prener suggested the following idea : Copper with nuclear charge Z = 29, one less than zinc with Z = 30, produces, as already seen, a level j ust above the valence band. The coactivator chlorine with Z 1 7, one more than sul phur with Z = 1 6, introduces a 'donor' level j ust below the conduc tion band. These levels are equivalent to those denoted by I and II respectively above, and they arise from a centre produced by copper i n association with chlorine. The association arises simply from the electrostatic attraction between the two impurities. This idea assumes a halide flux to have been used in preparation of the sulphide. This model was discussed on page 1 1 6 for zinc sulphide. The transition probability will be very sensitive to the amount of overlap between the levels I and II and is essentially determined by the covalent character of the binding. The quantitative calculation is very complex a n d has not yet been compl e t e d . =
Luminescence centres
1 29
The emission from cubic zinc sulphide crystals is not polarized, even if po lari ze d radiation is used for ex c itat i on , but t h e emission from he x ag o n a l Zn S and CdS single crystals, acti v a te d by Cu, Ag, Au, is polarized p re fere nti all y with E pe rp en d icu l a r to the op tical z-axis (Birman and Le mp icki). Th is result can be ex pl ai n e d with a n y of the above models if we assume that a level s i t u ate d near the valence or the c o n d ucti o n b a n d
Polarizatio n of the fluorescence emission of impurity-act ivated phos
plzors.
A
8
c
f Em ission Fig. V.9 Various centre models
The Lambe and Klick model; emission occurs when a captured electron recombines with a hole in the valence band B ' Classical' model of Riehl, Sclzon and Klasens; emis sion occurs when a conduction electron is captured by an empty centre c Associated donor-accep tor centre; hole capture in the ground state I and electron capture in the excited state II is followed by transition of the electron from /I to I giving emission ( Wil!iams-Prener model)
A
has the same symmetry as the n e igh bo u ri n g band . Jt seems t ha t t h i s valid, a t least a s an approximation. More e l abo r a t e computations, t ak i ng into account the differences between the sym metry of a shallow lo cal ize d level and the n eigh bouri n g band, are necessary in o rd e r to use p ol ariz ati o n experiments for choosing be tween the three models of Fig. V.9. Sometimes, dichroism effects appear (the radiation with El.z is more stro n gl y absorbed i n the c rys tal than the radiation with El lz) and c o n ce a ls the above effects (Keller and Pettit). hypothesis is
1 30
I.
Luminescence in Crystals
BIBLIOGRAPHY Structure of the sulphide phosphors
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1 38
K R O G E R , F . A . and Y I N K , H . J . ( 1 956) ' T h e i ncorporation of fo reign atoms in c rystal l i n e solid s ' . S y m p os i u m Garmisch-Partenkirchen, September 1 956. M EL A M E D , N . T . ( 1 9 5 7 ) 'Sulph u r vacancy e m i s si o n i n ZnS phos phors', Phys. Rev . , 1 07, 1 727.
R I EH L , N. a n d 0 RTM A N N , H. ( 1 956) l o c . cit. D isplacement in opposite directions of the blue emission peaks for Cu activated and self-activated ZnS V A N G o o L , W. A m s t e rd a m
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,
.
S H RADER, R . S . a n d LARACH, S . ( 1 9 5 6) E ffect of tem p e r at ure o n t h e spectral d i s t rib u t i o n of b l u e emission band s of ZnS : I a n d ZnS : Cu , I', Phys. Rev . , 1 03, 1 899. '
m angan es e t FOND A , G . R . ( 1 9 50) 'Dependence of emission s p e c t ra of phosphors upon activator concentration and tem p erature' , J. Opt. Soc. A m . , 40, 347. F O N D A , G . R. ( 1 957) ' I nfluence of the activator e n v i ro n m e nt u p o n the spectral e m i ssion of phosphors', J. Opt. Soc. A m . , 47,
Luminescence of phosphors activated by
877.
K Li c K , C . C. ( 1 9 5 5) 'Manganese as a l u m i n esce nce centre ' , British J. Appl. Phys.,
6,
Suppl. 4, S 74.
K L I C K , C. C. and S c H U L M A N , J. H. ( 1 9 5 7) 'Luminescence in solids', Solid State Physics, 5, 97- 1 72. Academic Press, New York. K R b G E R , F. A . ( 1 940) Lumi n es cen ce in s o l i d s containing mangan ese' . Thesis, Amsterdam. K R O G E R , F. A. ( 1 948) Some Aspects of the L um in es cen ce of Solids, 57- 1 05, 1 74-9 7 . Elsevier, Amsterd am . LEVERE N Z , H . W . (1 956) 'Luminescence dans les solides electro n i q u e me nt actifs', J. Phys. Rad. , 17, 6 1 2. L I N D , E . L . ( 1 9 5 5) 'A new blue-emitting phosphor with manganese activator', S p ri n g M eetin g the Electrochemical So ciety, Cincin nati, 1-5 May 1 955. WILLI AMS, F . E . ( 1 953) 'Solid state l um i n escence' , A dvances in Electron ics, 5, 1 48 . A ca dem i c Press, New York. '
,
'i" See also the b i b l i ography on 'Wi llem ite phosphors' (Chapter III).
1 39 Luminescence centres Paramagnetic resonance in plzosphors activated by manganese A B RA G A M , A . and P R Y C E , M . H. L. ( 1 9 5 1 ) 'Theory of the nuclear hy p e rfi n e structure of param agnetic reso n a nce spectra i n c ry s tal s ',
Proc. Ray. Soc. , A 205, 1 3 5 . H E R S H B E R G E R , W . D . a n d LEI F E R , H . N . ( 1 952) ' Paramagnetic resonance i n phosph o rs', Phys. Rev., 88, 7 1 4. H E RS H B E R G E R , W . D . ( 1 9 5 6) 'Magnetic effects i n p h o sph o rs under i ll umina t i o n , J. Chem . Phys. , 24, 1 68 . H E R S H B E R G E R , W . D . ( 1 956) 'Resonance paramagnetique s u r les phosphores', J. Phys. Rad. , 17, 672. K A STLE R , A . (1 954) O p tical methods of atomic orientation and their applications', Proc. Phys . Soc. London, A 67, 853. K ELLE R , S . P . , G ELLES , I . L . a n d SMITH, W . V . ( 1 9 58) 'Paramag n e ti c resonance absorption in M n -activated hex a go n al ZnS', Phys. Rev., 1 10, 850. LAMBE, J. a n d K I K U CH I , G . ( 1 960) P a ramagn e t i c resonance of Cd Te ( M n ) a n d C d S ( M n ) , Phys. Rev., 119, 1 256. U E BERSFE L D , J . and C O M B R I SSON, J . ( 1 953) R e s onance paramag netique electronique' , J. Phys. Ra d. , 14, 1 04. U E B E R SFELD , J . ( 1 9 5 4) 'Sur la structure h y p e rfine de la resonance p a r a m agn eti q u e dans quelques s u bs ta n ce s fi u o re s ce ntes J. Phys. Rad. , 15, 1 26. '
'
'
'
'
',
S e e also th e bibliography on escent zinc sulphide' (§I).
'
C r y s t a ll i n e
transformations on lumin
Magnetic susceptibility of ZnF2(Mn 2 +) JoHNSON , P . D . and WJ LLI A M S , F . E . ( 1 949) 'Some magnetic pro pe rties of m anganese activated l u minescent solids', J. Chem. Phys. , 17, 43 5. On
splitting of levels for Mn 2 + embedded in crystals ( 1 9 5 8) ' Structure of the metastable state of Mn2+ and Fe3 +', J. Phys. Chem. Solids, 7, 20 1 . TANABE, Y . a n d S U G A N O , S . ( 1 954) 'On the a bsorp ti o n spectra of complex ions', J. Phys. Soc. Japan, 9, 769. the
CLOGSTON, A . M .
Ill.
Optical transitions between localized levels
1. Probability of electron-hole recombination
E A G L E S , D . M . ( 1 960) O p ti ca l a b s o rp t ion a n d '
r e c o m b i n a t i on
1 40
Luminescence in Crystals
se m i - co n d uc to rs due to transitions between h y dr o ge n impurity levels and the c o n d u c ti o n b a n d , J. Phys. Chem . Solids, 16, 76. PA R O D I , 0. ( 1 958) 'Recombinaison radiative de trous libres avec des electrons li es a des centres d'impurete dans le germanium', Ecole d'Ete sur l'Etat Solide. Ecole Normale Superieure, Paris. See also Chapter IV, §II. l . radiation in
l i ke acceptor
'
Luminous efficiency and cross-sections for trapping and reco mbin a t ion
V . V. ( 1 956) 'Sur le rendement de la l u mi n e sce n ce dans les phosphores c ri s tall i n s , J. Phys. Rad. , 17, 692, 694. B UB E R . H . ( 1 957) A n a l y s is o f p h otocond uctivity applied to cad mium su l p h i d e typ e p h o toconducto rs', J. Phys. Clzem . Solids, 1 , 234. S J O U - S I O u - I o u N (1 956) D ete r m i n a t i o n of the effective cross-sections of capture and recomb i n a t i o n i n t h e ph o sp h o r Z n S ( C u , C o) ' , Op tika i Spek tr., 1, 264. A N T O N O V - R O M A NOVS K Y ,
'
,
'
-
'
semi-conductors C AR L S O N , R . 0 . ( 1 957) D o u b l e a cc e p t o r behaviour of zinc in sili con ' , Phys. Rev . , 108, 1 390. S H U L M A N , R. G . and W Y L U D A , B . J. ( 1 956) 'Copper in germanium : recombination c e n t re a n d trap p in g ce nt re , Plzys Rev . , 102, 1 455. WOOD BURY , H . H. a n d T Y L E R , W . W . ( 1 957) 'Triple acceptors in germanium', Plzys. Rev., 105, 84.
Multiple acceptors in
'
-
'
Visible em iss io n
due to iron-group
.
elements and their enhancing effect
on luminescence
N. ( 1 956) 'Existence d'un effet inte n s ifi c ate ur des ele fer et situati o n du n iveau de Fermi dans les s u l fu r e s lu minescents' , J. Plzys. Rad. , 17, 674. A V I N O R , M. ( 1 960) 'Vis ible emission of n i ck e l a ct i v a te d CaS', J. Chem . Plzys . 32, 62 1 . B LO Z H E V I C H , A . l . , Z A V RA H I N A . G . and L A V R O V , A . V . ( 1 9 59) 'The p ro p ert i e s of ZnS(Mn, Ni) phosphors under cathode-ray ex citation', Op t ics and Spectr., 7, 290. GERGELY, G Y . ( 1 956) 'Effet des extincteurs sur les spectres d'absorp tion et d ' e m i s s i o n d es sulfures de zinc actives a !'argent', J. Phys. Rad. , 1 7 , 679. A RP I A R I A N ,
m e n t s du groupe du
-
,
,
Luminescence centres
141
TOLSTO I , N . 'The
A . , T K A CH OU K , A . M . and T K A CH O U K , N . N . ( 1 957) fl as h - l i k e burst of l uminescence in Z n S (N i )' , Optika i Spektr. ,
2, 7 59.
O n the kil ling
effect of iron-group elements : see Chap te r VIII, §III.2.
Possible states of iron in crystals
C LOGSTON, A . M . ( 1 958) 'Structure of and Fe 3 + ' , J.
the m etas table state of M n 2 +
Phys. Chem . Solids, 7, 20 1 . Low, W . an d W E G E R , M . (1 960) 'Pa ramag n et ic resonance and opti cal spectra of divalent iron in cubic fields', Phys. Rev., 118, 1 1 1 9, 1 1 30. 2. Polarization of the fluorescence emission from i mpuri ty centres in zinc sulphide or cadmium s ul phi d e crystals B I R M A N , J . L. (1960) 'Polarization of fluorescence in CdS and ZnS single c r y s t a l s ' , J. Electrochem. Soc. , 107, 409. G R I B K O V , V . I . a n d ZHE V A N D R O V , N . D . (1 960) ' Po la ri z at i o n o f lumi n e sce n ce of ZnS monocrystals', Optika i Spektr. , 8, 275. KELLER, S. P. and PETTIT, G. D. ( 1 9 59) 'Optical p ro p e rt ies of acti vated and u nactivated hexagonal ZnS single crystals', Phys. Rev . , 1 15, 526. LEMP I C K I , A. (1 960) ' P o l a ri zati on of l u mi ne s ce n ce in ZnS and CdS single crystals', J. Electrochem . Soc., 107, 404. WARS CHAUER, D . M . and REYNOLDS, D . C . (1 960) 'Mechanically exci t e d emissi o n in cadmium s ulp h i d e ' , J. Phys. Chem. Solids, 13, 25 1 .
Splitting of the fundamental Cu-level in ZnS crystals B I RMAN, J . L . ( 1 96 1 ) 'Electro n ic structure of the centres i n Zn S', Phys. Rev. , 121, 1 44.
CHAPTER
VI
Electron Traps, Phosphorescence, Thermoluminescence
l.
D E F I N IT I O N O F T R A P S - M E A N Ll FE TI M E S EFFECTIVE C R O S S - S E CT I O N S
1 . Definitions
Electron traps are me tas ta b le states or le v e ls in wh i c h electrons ca n be capture d and rema i n fo r s i gn i fi c an t times between excitation (a b so r p t i o n of exciti n g radi a t i o n) and emission o f l u mi n e scence . They are t he l e v e l s re s po n si bl e fo r the pers ist e n ce of p h o sp h o r e sce n ce while the centres are the levels which determine the lu mi nescence spectra (cf. Introd uctio n and Chapter V, §lii) .
An electron raised i n t o an excited state (i. e . into the c ondu cti o n band in the case of a pho t o c o nd u ct i n g phosphor) can (a) r e c o mb i n e with i t s o riginal centre givi n g fluorescence emis sion ;
(b) fall i nto a tr a p ; it will
e s cape
after a mean l i fe time r a n d ca n
then recombine with an empty centre giving phospho rescence
e m i s si o n at a t i m e r a ft e r the o riginal e xci tatio n . The electron freed fro m a trap may, alternatively, be retrapped, and in this case the ultimate ph o s p ho resce nce will be delayed. The th e r m al activation energy E required to liberate a trapp ed electron is known a s t h e trap d ep t h , the energy being received by p ho n o n i n t er ac t i o n wi t h t h e surro u n din g s . I f p is t h e p ro b a bi l i ty of liberating the t ra p p e d e l e ct ro n p e r se c o n d, th en r = 1 /p and p
log.
=
r =
S
e - E/kT
k - I og s
E
T
We give s o m e typical numerical values of r for various trap depths
ass u m i n g s
=
1 09/sec and T
=
l 8 °C : 1 42
Electron traps, Phosphorescence, Thermoluminesccnce
I
TAB LE Vl . l T
1 43
E
0·52 eV 0·62 eV 0·725 eV 0·805 eV
sec
1 min 1 hou r 1 day
Tr aps responsible for phosphorescence observed at room tempera t ure for such an s val ue have thus depths between 0·5 and 0·8 eV. The mean life at various temperatures for S = 1 09/sec a n d E = 0·65 eV (an i m po r ta n t case i n Z n S (C u) where such traps cause the room temperature phosphorescence of the order of minutes) is as follows : T
T
T A B LE
- 10o·c
- so"c 1 day
I ,600 days
J s•c
3 min
VI.2 so•c
4 sec
t oo•c 0·25 sec
1 so·c
0·03 sec
Thus a trap i m po r t a nt in phosphorescence at ordinary temperatures is not so at temperatu res 1 00°C away on each side (Lewchin) . 2. Thermal activation of trapped electrons
The above e x p o ne n t i al e x press io n for r, with s a constant, is wel l supported by experiment . There are not many d i rect verifications
0 -
-5
ID I
L
0
Fig. V T . J
0·5
__ L
Variation of the life times of three groups of traps in
CaS(Bi) with temperature
1 44
Luminescence in Crystals
avai l a ble such as those g i v e n by t h e
cu rves
of
Fig. VI . l , but t h e r m o as a bas i s
luminescence-cu rve theory consta n t l y u s e s t h i s e xp re s si o n
no contradictions. a given trap d ep t h E, s d o e s not a p pear t o vary m u c h w i t h temperature T, a t least it d o e s n o t a ffe c t the li nearity of t h e log r vs. 1/T graphs (a proportionality b e twee n s and T would not affec t the linearity) . We c a n therefore u sually assume s(T) is a consta n t in the i n t e rpre t a ti on of e x pe ri m e nta l res ults. However, even in the same p h o s p h or s d oes not n e ce ss ar i l y have the same v a l u e for traps of different d ep ths . Such variations in s with E have not been very much studied . O nl y s values of about 108 to 1 0 9/s e c h ave been us e d for different groups of traps as, for example, t h o s e due to copper in zinc su l p h i d e . In germanium and si l i co n , higher val u es of s of the o rder of 1 011 to I O H/sec h av e been i n d icated (Haynes, M. Lax), b u t there are few systematic studies
a n d t h i s leads to For
available.
escape of t ra pped electrons. However, as soon as a thermal activation is a s sum e d , all t he different theories must i n v o l v e a Bol tzmann factor in the p ro babi l i ty p. We give now a semi-classical //,/ / . ap pr o ach to the pr ob l e m of activa tion of trapped electrons. C onsi d e r a tra pp i ng model with levels equidistant in· energy from each other, the s p ac i n g b e in g ln·c Different workers have envisaged different processes for the
2 (1 ·0
j£
l h Yc , h vc
(i .e. oscillators
of characteristic
frequ e n cy vc) . By successive ab E so rption of phonons of energy hvc th e t rap s ystem re a che s hi gh e r and Fig. VI.2 Progressive excitation higher excited levels, that is, t he of an electron !rapt s u rro u n d i n g ions have increasing v i b rati o n al energies. When the trap is in a certain sta te jhvc the electron will be freed (Fi g . VI.2) . The absorption proba bili ty for a trans i t io n loth -+ (k -+- l ) t h level
t An analogous calculation for a chemical reaction requ iring a similar activa tion of molecules has been given by NI K I TI N E , E. E. ( 1 957) 'On deviations from the Boltzmann distributions i n the dissociation of diatomic molecules', Dokl. Akad. Nauk S.S.S. R . , 1 16, 584.
Electron traps, Phosphorescence, Thermoluminescence
wi l l be
p r o p ort i on a l t o
the number of phonons I
A = a eh��/kT-_ 1) (
T h e em i ss i on probabi l i ty (return fro m (k + I ) t o
R
=
a(l+(ehv,}T_Jj)
o f frequency
1 45
h vc :
k ) w i l l be
We thus obtain a set o f d i ffe rent i al equations :
dn0
CfT
-A =
An0
- (A + R)
nu l l dt = A ni - 2 - (A + R)
d
-
11j
1+R
n;
where nk is the number of traps in the state k. If the system extends to k = oo, t h e n there is an e q u i l i b r i u m solution
n1 = n0 e -ilw,;kT and the occurrence of the Bol tzma nn factor i n t h e probability p i s e as il y e xp la i n e d : i t is given b y the B oltzmann factor and is t h e n u m b e r of t rap s in t h e state j. However, this elementary approach is incorrect since the t rap s a re e m pt ie d as soon as they reach the jth state, which c au s es a pert u rba tion of the Boltzmann distribution. The set of e q u at i o n s must b e modified thus : = Ani - 1 (a-j- R)n n0
=
co n s t .
,
{�7
}
a is the p r o b ab i lity of t h e transition of t h e trapped elec t r o n from the jth state into the cond uctio n b a n d Between the nk traps in t h e kth s tate a n equilib riu m w i l l be estab li she d in which they d e cay exponentially w i t h time : nk Xk e-"1 p being the smallest root of the characteristic d ete r m i na n t of the mod ified set of differential eq u a t i ons We thus have (ehv,fkT - 1 ) 2 - U + 1 lhv,/kT p oc where
.
=
.
=
env./kT +A- l oc
which is o b vi o u s l y of the form p = s e - E/kT where
e
E
=
(j j- l )hvc
1 46
Luminescence in Crystals
3. Thermodynamic expression of Williams and Eyring (The 'Absolute R a te The o ry ' )
For constant volume the free e ne rg y F of a system (given by
F = U- TS with the usual no ta t i o n) p l a ys the role of the thermo d y n a m i c potential. It follows that the rate of a chemical reaction, h e re t h e escape of trapped electrons and a monomolecular react i o n , d epends o n a thermal activation which will depe n d on the variation D.F in the fr ee e n e r gy a cc or d i n g t o a B o l tz m a n n factor K e D.S!k . e - D. U!k1' p = K e - D.Pik1' =
where D. U is the activation energy and fiS the activation en tropy . The coefficient K has the form xv1, a n d so p = xv1 eM!k e - Mf!kT, the factor e::,.s;k (a s s u m i ng S k log W) being the probability that the s ys te m , having o b tai ned the necessary activation energy, wil l rea c h the configuration fro m which the electron is freed ; v1 is the thermal vibratio n fre q u e ncy for this configuration and x is a ' trans mission coefficient' . These various factors are all lu mped together in the constant s, v 1 is of the order of 1012 to 1 0 1 3/ sec, not ne ce ss aril y of the same order as s, to which we so met i m �e s w r o ngl y give the name ' e s ca pe fre q u e ncy ' since o nly Vt me ri ts that name. When s is m a rked ly less t h a n Vt, x is small and D.S < 0. =
4 . R elat i on between the escape probability
T h i s relati o n ,
p and the effective capture
of the trap d ue to Mott, is ob ta in e d by u se of t h e law of de tai l ed
cross-section
a
balancing. S u p p o s e there a re
n0
traps per c.c of w h ich n are e mp ty and n0 - n n e le c t r o n s in t h e conduction band w i t h
and that there are t he r m a l vel o c i t y u where occ u pied ,
ll
=
J
3kT m
(tmu2
=
'}kT)
The number of electrons captured p er sec o n d by e a c h trap is given by anu and the n u mber captu red per sec o nd by any of the n e mp t y traps is
fo r equ i l i b r i u m . Now
Electron traps, Phosphorescence, Thermoluminescence
But t h i s ratio is a l so
gi ve n from above by ./!_ and so
!!.
(f
1 47
au
2nn1(kT) \! 6n - E/kT e h3
i f w e assume p s e - E!k2' and a to be a co n s tant we have at ord i n a ry temperatures the nu m e ri ca l re l ati o n
and
=
For copper-activated zinc s ulph id e for wh i ch s R:j 1 08 to 1 09 / s ec
:!_ R:j 1 · 5 . 1026
will l i e between I 0 1 8 and I Q 1 7 cm 2 • For such cross-sections a n d for concentrations of c o n d uc t io n e le c t ro n s n R:j 1 0 1 7 /c.c, the m e an fre e p at h s of e l e c tro ns b e fo re c a p t u re w i l l be g i ve n by (f
,
,
r;
l = _!_ an
reach or exceed one centimetre. The experiments of G udden and Pohl o n the saturation of the p ri m ary p hot oc u r re nt i n zi nc blende lead to p aths of this order of magnitude. I n ge rm a n i um evidence has been given of values of s and a that may be larger by m o re than t hree or four orders of magnitude t han the above. For instance, the p o s i t i v e hole trap due to copper, opera tive at liquid air temperatu re (page 1 2 6), has a c r o ss s ec t i o n a R:j I Q - 1 3 cm2 (Newman and Tyler) ; for th e electron trap, d u e to Sb +, a R:j I 0 - 1 2 cm2 ( K o e n i g) M. Lax has given t o such traps with such l a rge cross-sections the name of g ia n t trap s . The correspond i n g values of the parameters are not very different fr o m t h e fre q u e n and c a n
,
-
.
'
'
paths a re n o t ac tua lly found except when high electric appli ed . The occurrence of thermal lattice vibrations (ph o n o n i n te rac ti o n s) and s c atteri n g and capture by i mp ur i ty and l a ttice defects limit the mean free path far more than capture in t ra ps It is likely that the natural zinc blende crystals selected by G udd e n and Pohl were m o re perfect t h a n s yn t h eti c c ry s tals currently available.
cies of
thermal vibrations and are perhaps
fi el ds are
even larger.
Such long
.
I I . D ECAY
OF L U M I NE S C E N C E
of l umine scence process, that with kinetics of th e first o rd e r (m o n om o lecu l a r m ech a ni sm) a n d th a t h av i n g second-order kinetics (bimolecular m ech a ni s m) 1 . Monomolecular a n d bimolecular mechanisms
We usually distinguish two kinds
.
Luminescence in Crystals
It is generally accepted, but not quite correct, to use these terms, taken from chemical kinetics, as synonymous for such processes. A bimolecular reaction is one i n which two molecules combine. In photoconducting luminescent solids there occurs in all cases a 'bimo lecular recombination' of electrons and empty centres, but the kinetics may be of first or of second order, depending on the particular con ditions. However, if this is generally understood, then the term bimolecular can still be applied to the particular case of a second order kinetics recombination . (A) First-order kinetics. The number of e xcited elec t rons 11 decreases according to a c o n st a n t probability law 1 48
" h giVes · wh Jc n
then
dn - = - IX d t
· th e 1 ummescence · mtens1ty · · I= n0 e cx1 , and smce 1l
dn
I = Io e -cxt (B) Second-order kinetics. The probability for reco m b i n a ti o n i s pro portional to the number of available centres dn - = -IXn dt n and so n decreases hyperbolically with time n
dt'
no (1 +n01Xt)
the luminescence decay then being given by dn ! I= � IX1l 2
thus
=
-
=
where a = VI01X
' dt '
The decay thus becomes more rapid as the excitation intensity is increased . Kinetics offluorescence. The above kinetics can only apply to fluor escence (see definition in Introduction) since their foundation does not consider the intermediate process of trapping. When luminescence is due only to transitions within the l um i n escence centres the monomolecular mechanism applies. If the optical transition is permitted (dipole), the mean life time in the excited state IX- 1 is of the order of t o-s sec, the mean l i fe time for transitions
Electron traps, Pho�phorescence, Thermoluminescence
1 49
in isolated atoms. However, we find forbidden transitions of much longer life time, for example for uranyl salts ( I 0 4 to I Q 3 sec), i n ternal transition in Mn2+ i o n s (lo a sec in ZnS, IQ 2 in willemite, Zn2Si04 ; cf. page 1 23). In the case of the long duration fluorescence of the M n 2 +, which is more or less independent of temperature, this is often mixed with a short-period phosphorescence due to shallow electron traps and having a strong temperature dependence (Fonda). However, even in this case of internal emission transitions the l u m inescence processes would really only be confined to the centre if a low-intensity excitation occurs in its characteristic absorption bands and if the crystal possesses no defects or impurity except the activator impurity. In actual practice the kinetics of fluorescence are sometimes more complicated (Louchtchik, Antonov-Romanovsky and eo-workers) . We have discussed above (see page 36) the pheno mena occurring in KCJ(Tl). In ZnS(Mn) the traps are not meta stable levels of the Mn2 _1_ ion (Lewchi n and Tunitskaia) : an excitation occurri ng in the characteristic bands of manganese (4,358 A) pro duces a small photoconduction effect and thus these traps are hardly filled : on the contrary, excitation using 3,650 A radiation involves a large photoconduction effect and marked filling of these traps occurs. In the same way, it is possible to find evidence for an electron hole recombination in the uranyl salts (experiments by Lewchin, Gutan and Karzhavina, using cathode-ray excitation), while as a general rule (ultra-violet excitation) the case of uranyl salts gives one of the most characteristic examples of a simple exponential decay ft uorescence. In the case of sulphide phosphors of the ZnS(Cu) type, the short duration emission seems to involve first of all a monomolecular decay with a life time characteristic of transitions in isolated atoms, the t ransition occurring in emission centres (Kallmann), t and finally an approximately bimolecular decay with a life time of the order of I Q 5 sec due to electrons, previously liberated, recombining with emission centres. All this is followed by a slower decay ( l 0 4 to I Q 2 sec) with complex kinetics and which is really a short-period phosphorescence due to traps of 0·3 or 0·4 eV in depth . Finally, there follows a long-period phosphorescence. t See Chapter X, page 303 ; e<-particle scin t i llations in zinc sulphide.
Luminescence in Crystals
1 50 2.
Kinetics of phosphorescence in photoconducting phosphors
To describe phosphorescence d ecay the preceding differential equa tions must be replaced by systems of differential equations containing several variables. Let n be the number of trapped electrons and
v
the number of con
d uction band electrons. The kinetics of phosphorescence depend on the spatial r ela t i on s between l u minescence ce n t r es and traps and on
the m o t i o n o f the c o n d u c t i o n electro n s .
Suppose t w o n e i gh b o u ri ng centres a re
about I 0 6 to I 0 5
cm
I0 6
cm
apart :
(A)
If t h e traps are located near to the centres (less than
away) and o n ly very small movement of e lec t r o n s occurs from trap
to centre, and vice versa, then we may consider each 'centre and
n e i ghbour in g trap' as an independent unit giving a constant recom
bination constant with time. First-order kinetics then apply and traps o f mean life time
-r
release electrons acco rding t o the relation 1l
= llo e t!<
The short life time centre level is thus replenished by electrons fro m traps in a similar way to t h e case i n radioactivity where a short-lived element (say radon) is formed by b reak-up of a long-lived element (radium). There is an equilibrium condition in which the activities o f the two elements are equal, but their abundances very different (in
the ratio of their life times). In phosphorescence of this type the number dv of electrons recom bi ni n g with centres equals the number arriving from traps : dv
=
dn
with the c o n d i t i o n v
n
life time in conduction b a nd
life time in tr a p s
The l u m i nescence intensity is g iv en by 1
=
9� dt
=
02 e '
i
1
t;.
and an exponential decay law res ults . This is e qu al ly valid if in stead
of a conducti o n band we have an exci ted state of a centre, the trap being a metastable state. If a distribution of trap depths is present,
ncn
d-r being the number filled initially with life times between -r an d
-r + d-r, then
I=
J
""
0
ncn '
e-t/T d -r
(l)
151
(B) If the traps are s pat ial ly independent of t h e centres and electro n displacements are la rge enough for recombination with any of a large number of centres (i.e. > w-s cm), the recombination probability is proportional to the number of empty centres and second-order kinetics apply. Consider the case for traps of one mean life tim e (r) only. Let n0 be the total number of traps per c.c, n the n u m be r of fi ll e d traps and thus (n0 - n) the number of empty traps. Let v be the number of con d uction electrons and N the number of empty centres. If all cen tres are normally o ccupi e d and are emptied by e xcitat i o n , then N = n + v. We can then write Electron traps, Phosphorescence, Thermolumines c ence
dv
dt
=
n
- - acNV - at(n0 - n)v 7:
d - = at(n0 - n)v - dn
n
t
7:
I = acNv and (ac is the effective cross-section of centres m ultipl i ed by the thermal velocity of the electrons ; a, is the similar product for the empty
traps). We can obtain a ri g o r o u s analytical solution only when ac = a, = a, wh tch corresponds t o equilibrium between the con duc tio n band a n d traps :
n an0r ( I Ian0 is the effective life time for electrons in the cond uction band).
The two differential eq uations above give dn dt
which has the solutions n
n2 = - n0r
r = t+noto '.
Y
=
I
a(t + t0) where t0 is an integrati o n constant equal to r for saturatio n excita tion, i.e. all traps filled at t 0. The luminescence i n t ensity I = a(n +v)v decays according to the simple law =
I=
const.
The equilibrium conditions are n o t necessarily valid throughout the decay, but are applicable after about w-s sec of decay.
(t+ to)2
! 52
Luminescence in Crystals
This l a w is valid for
the solution ass u m i ng e q u i l i brium even if
a
distribution of trap depths is present. When the shallow t rap s reach equilibrium with d ee p e r
traps the system behaves as if the mean l ife time i s s in g l e va l u e d a n d eq u al to th at of the d ee pe r t rap s. Thus the decay tends towards a fi nal form , I oc r 2, according to the particular phosphor and excitation mechanism involved . This res u l t is n o t in agreement with ex p eri m en t . Often and at elevated temperatu res we observe for ZnS(Cu) ph o sp h o rs w hich g i ve a linear l og f- l og t plot with a slope greater t h an two . Th is constitutes one argument a gai ns t t he b i m o le c u l a r for m u l a tio n . H owe v er, this can always be attr i b u ted to si mplified a s s u m p t i o n s i n trod uced i nto the
A diro witch's theory. A d i r o wi tch has considered the case fo r t raps a si n gl e mean life time r, but where the capture cross-sections o f em p ty ce n tres and traps are n ot the same ( ac :;z: a t) . A r i g o r o u s solution is no lo n ge r possible, but Adirowitch ha s given an a p pr oxim ate solution for e q u i l i br i u m conditions . He shows that a gr ap h of log I as a fu n ct i o n of l o g (t f-!0) h as an inflexion and that th e re is an extensive ra n ge over which I follows a B e c q u erel type of
calcu lations. w i th
relation :
I=
The table below
o f t h e rat .1 o p y
t
y
=-=
(t + to)1'
g ives various values of the i ndex p for d i ffe rent values a,
- -
Dr.
�
_c o ns t : _
TABLE Vl.3 2
3
5
10
50
1 ·0 1
100
500
This type of fo rm u la is often a very goo d description of the d ec ay of a nu mber o f p ho sp h o rs over a considerable range. However, se v e ral o bjecti o n s have been made to Adirowitch's th e o ry, among them being the fo l l o w i n g : (i) The val u e s of y are o fte n u nac cep ta b l e , e.g. C o u sta l fo u n d p 0·43 fo r a zinc s ulphid e p h o sph or at liquid air tempera ture which necessitates a y value greater than 1 ,000. (ii) In t he case of a p h o s p h o r co n tain i ng we l l - s e pa rat ed groups of tra ps the Becquerel formula is no longer suitable and a 'kink' is observed i n the log I vs. log t cu rv e (see Fig. V1.3). 2·5
2· 3
2
1 · 75
1 ·6 3
1 ·47
1 · 34
0·97
0·8
Electron traps, Phosp!torescence, T!termoluminescence
I SJ
D iffere n ti al eq u a ti o ns similar to those g i ven above but rather more
have been considered , for example, by Schon, by B ro s e r a n d by Urbach , which include in the bi molecular kinetics (i) th e distribu tion of tra p lng Il ( arb;�rJry u n 1 t S ' life times, I (ii) non-rad iation recomc o mp l ex
and Broser-Warminsky
binations, (iii) positive hole mi g ra ti o n
in t h e valence band , their captu re by activa
! � �� ' 1 1
\
t
tor centres and the lo9 t cc 0 1 2 :>. 4 t r a n s fe r p r o c e s s e s Fig. VI . 3 Decay of a wurtzite type wh i ch re s ult. ZnS( Cu) phosphor obtained by A . Guntz In conclusion, it is clear that the inte rp retati on of ph o sp h ore scen ce decay is so complex that the decay cannot be used to i n fe r t h e s p ecifi c mechanism or p r o ce s s e s in volved . The early workers t h ou ght that i t was sufficient to d i s t i n g u i s h betwee n eq uatio ns of the type dn - = -rx dt lead i n g to a si mple
n
e xp one n t i a l
decay, and
dn -= n
- (:1./l
dt
l e ad i n g to a power law decay I oc t 2 • However, each i ndividual (by suitable as s u mp tio n s about distributions and filling of traps) b e interpreted in terms of a m o no - o r bi -mo lecu l ar m ech a n i s m . For i n s tan ce , the Becquerel type o f formula (as above) can be given a 'monomolecular' in t erp re tati o n if we assumet a d istribution of trap l i fe times of the form
resu lt can
In a specific case we obtain for p = 2 a h y perb o li c decay which corresponds to that fo r a b i m olec u l ar mechan i s m wi t h a s i n g l e trap depth (we shall use this result later) . H o weve r, in spi te of these rem ark s, other experimental data do t For a discussion of phosphorescence mechanisms see 'Questions actuelles en luminescence cristalline', Revue d'Optique, Paris (1 956), pp. 39-48 .
1 54
d
Luminescence in Crystals
give i n i c a t i o n s of the particular kinetics of p h o s p h o resce nce. T h u s i n the case of ZnS(Cu) phosphors : ( I ) No disagreement has been found between the trap distributions o btai n ed fro m decay cu rves at d i ffe re nt fixed temperatu res by assump tion o f m o n o m ole c ular kinetics and the trap distri butions indicated more directly by thermoluminescence cu rves . (2) A l t hough electrons are raised into cond uction levels by excita t i o n ( a s shown by the occurrence of marked p h otoco n d uction closel y related to the luminescence) d uring phosph orescence these electrons h ave e n e rgie s only of the order of kT (polarons). Now it is usually assu med that t h e fraction o f conduction electro n s captured by crystal d e fects is much greater Energet1c e l e ctron when the electrons are slow (see Fig. VI.4). Thus in an imperfect crystal, such as Z n S(Cu) , we may Slow electron E 'C>L k T assume t hat the 'floor' of the con duction band has irregularities, each of these being due to a defect. Fig. VI.4 Electron potential in the Shockley has s h own that we can conduction band. E is the kinetic consider the energetic position of energy of the electron the bottom of the cond uction band to provide an effective potential in which the electron is 'immersed'. The fast electrons will be unaffected by the irregularities, but slow electrons will be stopped . So we see that in phosphorescence the con d uction electron displacements are very small but can become large if (i) the crystal is reasonably perfect, (ii) a strong accelerating electric field is present, (iii) the electron energies are much greater than kT, i.e. for excita tion, optical stimulation, or for electroluminescence. (3) Electron retrapping has been found to be small during normal phosphorescence decay (not more th a n 10 p e r cent of the escaping electrons being retrapped), but it is much more marked for optical stimu lation (more than 50 per cent for deep traps and almost 1 00 per cent for shallow traps). These figures are only the o rders of magn i tude for the effects in ZnS(Cu) and are valid at long decay times, i.e. when most of the traps are empty. The ret ra ppi n g effect is much less marked when most of the traps are occupied . In addition, it has been found th a t the better the crystal l ine sta t e of the p h os p h o r t h e greater a re the ret rapping effects.
£! �
1 55
(4) The traps responsible for long-period phosphorescence in ZnS(Cu) phosphors occur when the 'green' centres due to copper impurity are introduced and the simplest assumption is that traps and centres are closely related , both being due to the introduction of copper. We are thus led to conclude that monomolecular kinetics will apply (i.e. traps localized around emission centres and excited elec trons showing very small displacements). All this assumes excitation of electrons directly from centres which is true for ZnS(Cu) phos phors excited by 3,650 A radiation. The electron excited from the centre falls into a neighbouring trap and si milarly returns from that trap to the same centre to give emission. This allows the approxima tion to a monomolecular mechanism. However, if excitation takes place in the fundamental absorption band of the crystal lattice, conditions are no longer the same. If the resulting electron and positive hole migrate independently of one another they will fill a trap and empty an emission centre respectively, the two not being in general near to each other. In this case the phos phorescence will be more characteristic of a bimolecular mechanism. Th is is the case for zinc sulphide excited by radiation of wavelengths less than 3,350 A, or in the case of cadmium sulphide less than 5 , 1 00 A. As a result we can arrange the following table : Electron traps, Phosphorescence, Thermo!wninescen ce
T A B LE VI.4 Dependence of recombination kinetics for electrons and empty centres in a photoconducting phosphor on experimental conditions
Nature of process__
__ !
I
Electrons freed from traps Long-period phosphorescence and by thermal activat i on : thermolumint raps close to centres escence Electrons freed from traps S timulation : or centres by optical excitation of activation luminescence
Excitat ion in fundamental ShO
Elcctrolu m inescencc injection emission
I
I I
Electron
Recombination kinetics
< 1 Q • cm Small
Approximately m onomolecu l a r
Larger
Complex : mono molecular with perturbations
La'""
Complex : bi molecular with perturbations
Very large > 1 0 • cm
Approximately bimolecular 1
1 56
Lum inescen ce in Crystals
3. Investigations of trap distributions by analysis of experimental decay
curves I(t) The analysis is usu all y made by use of the formula I(t)
J
oo no, 0
e t;r dr
T
which for th e monomolecular mechanism relates the distribution of traps filled by e x c i ta ti o n llor(r) to the pho sp h o r e sce n ce intensity I(t). A s i n the table above, we ass ume the monomolecular mechanisms to be val id for the l o n g-period phosph orescence, which appears to be so for ZnS(Cu) phosphors . To be more exact, we assume a pertur bation of a bimolecular kind which e xp lai n s the photoconduction characteristics but which is too s m al l to affect the luminescence. We look bri e fl y at the e n d of this ch a p te r at what h app ens if the mechanism is not mono-molecular to a g oo d a pp ro xi m at i o n . In experiment I(t) is measured over a re a s o n abl y long time so that the pa rti cul ar traps involved are nearly a l l emptied . This type of ex periment has been carried out systematically fo r ZnS(Cu) p h o s pho rs by J. Saddy. I(t) at o rdin a ry temperatu res must b e measured over the time interval from a fraction of a second up to about three hours. I f, for instance, only the first half-hour of d e cay is measured, the results are of little s i gnifi c ance i n o b tai nin g the trap distribution. Durin g these ti mes t h e p h ospho res c e n ce intensity falls c o ns i de rab l y. Use of the n a k e d eye with a visual pho t o m eter is possible because of the large s e ns i t i v i ty range of the eye. If a photomultiplier is used t h e sensitivi ty range of the apparatus has to be ch a nged often . As an other p o ssibi lity o n e can use the method of Lenard and Kuppenheim and obtain the ligh t sum remaining after time t :
S(t)
�
J 00 /(1) I)
dt
=
J 00 0
llor
e t/r d r
a method p a r t ic u l a r ly a p p r op ri at e to CaS(Bi) p hos p h o r s which c o n tain traps with mean li fe tim es greater than a month. In these c a s e s the filling of traps c or r e sp o n d s to a 'light sum' st o re d i n the ph os ph o r , but this is released so slowly that the observed phosphorescence represents o n l y a s mal l fraction of it. A sudden warming will free electrons from all traps and give r i s e to thermoluminescence. A p ho t o v o l t aic cel l p l aced in front of the p h o s p ho r will indicate by a
m e te r deflection of an electrometer an electric cha rge proportional to the l i ght s u m rel eased by wa r m i n g .
Electron traps, Phosphorescence, Thermn/uminescencc
! 57
After o n e or o ther of these experi ments h as been carried o u t the determination of the trap depths i s made in three stages : (a) An analysis of the distribution
n0.(r)
of mean life times
of the
trapped electrons.
(b) A
t rans fo rmati o n
depth d istribution
(c) I n te rpreta t i o n
of th i s distribution ntr(r) to give the trap
no,(£).
of the res u lts.
(a) To obtain from J(t) or S(t ) the quantity n0r(-r) r e q u i r e s the in version of a Lapl ace transformation. Th i s becomes i n te re s t i n g when we try to find a form fo r n tr(r) which gives a decay l aw for wh ich we
have an analytical fo rm. There d o not seem to be m ach i nes for inver sion of the Laplace transformation such as exist for inversion of the
Fourier tran sformation (harmonic analysers) . In practice, we are reduced to using the method of calcul ation previously employed by Lenard and Kuppenheimer.
In
order to get
some idea of the p roblem, consider S(t) . We replace
the integral , us i ng an approximation, by a sum of exponential terms
S(t) :2: ntr(r) e-1/• 6.-r In other word s, we break down the experimental decay curve into a series of exponential terms . We shal l not describe the process of resolution into these terms, a current p ractice in nuclear p h ysi c s t ,
but simply make the following observation :
The exponential terms for radioactive decay h ave a real sign i fi
their exponents r a r e the mean life times of the constituents. same r values wh ich are n o t usually very numerous. In the present case the exponential terms are o n ly a convenience in cance ;
Different workers will obtain the
calculation ; the resultant trap distri bution, which for sulphides is
of exponential term s of r depend on the precision involved i n t h e resol u tion. It is wrong to consider the values as the life times of t h e trapped electrons. They simply provide p o int s through which a graph of
continuous, has only one meaning. The number and the values
n0,(-r)
may be draw n .
of t he convergence of the calculated distribu of component terms becomes larger and larger gives the proper assurance of the validity of the ded uced d istribution. {b) The trap depth E and not the mean l i fe time r is a better T h e i nvestigation
tions as the n u m ber
t J ouoT-CURI E , I. (1 946) Les Radio-Elements naturels, p. 1 5.
Hcrmann, Paris.
1 58
Luminescence in Crystals
characteristic to define a t r ap since the mean life time de p e n d s on the temperature at which decay takes place : the ch ange from
n0r (r)
E
and so
=
I = s e ·- E.'kl'
to nop(E) is made by putting nor: d E = noT dr r
k T log (sr) and d £
=
dr kTr
To obtain the fo r m of th e trap d istribution it is sufficient to p l o t the prod uct no-r(r) . r as a function of log r. I n order to obtain the trap depths it is n ecessary to obtai n s. The m o s t accurate way to do this is to follow the behaviour of each c group of traps by m ea s uri n g the decay at d ifferent temperatures (cf. Fig. VI . l ). s may also be obtained from t h e r m o l u m in escence exp eriment s . (c) Results. The t ra p distri bution usually occurs as a co ll ec t i o n of approximately 'Gaussian' groups (see Fi g . VI.S). E ac h of t h e s e groups can be assigned a value of E L � · _L_ 0I corresponding to that of its -- 1 0 Z 3 log 1 (S) maximum. Fig. VI . 5 Trap distribution in a ZnS( Cu) phosphor with the decay curve Mean life times and trap depths in ZnS(Cu) (wurtzite) . If we of F{f · Vl.3 denote the v a ri o us maxima of the groups of traps in Fig. VI. S by A, B, C and D respectively, then at r o o m temperature we h av e
,r
log r(s)
__
__
0·5 (for A), 0·9 (for B), 2·2 (fo r C), a n d 3 (for D)
and if s � 109 sec-1 the corresponding trap dept h s are =
0·5, 0·57, 0·65 and 0·7 eV respectively .
In this s p e c i fi c
case the gap between groups B and C is particu larly marked , whence the 'ki nk' in the curve of Fig. VI.3, but the
Electron traps, Phosphorescence, Thermo!uminescence
1 59
same groups A, B, C a n d D are found for all long afterglow zinc sulphide phosphors . There arc other groups, but they are so deep that they contribute l ittle to the decay at room temperature. They can be found by means of thermoluminescence curve experiments, but they would have been noticed i f the decay had been measured at other temperatures. N. B. The above method of finding trap distributions assumes that the decay is monomolecular to a first approximation. If the decay i s bimolecular then there are no satisfactory formulae available. How ever, even in this case we can, apparently, go on using the monomole cular formulae ( I above) without introd ucing serious errors. Consider the case where a bimolecular treatment is needed and for a single trap depth. The actual trap distribution corresponds to a single mean life time t0 with a corresponding trap depth E given by J -
fo
-- - - s e
··
Ii1'k1'
If, as seen previously, we assume the same captu re cross-sections for centres and traps and neglect non-radiative transitions and positive hole migration, then decay of phosphorescence follows a simple bi molecular law 1 const. (t+ to) 2 =
and if excitation prod uces saturation, then ! 0 is the mean life time of the trapped electrons. Ignoring the actual luminescence mechanism in such a phosphor, the experimenter interprets the decay in terms of a monomolecular mechanism and obtains an apparent life time dis tribution for the trapped electrons :
noT(r)
=
!_ e t,/T
To
and ded uces the trap depth distribution : noB oc
n0.(r) . r
=
1
-
T
e-t,/T
t0 , i .e. at The maximum of this apparent distribution occurs at T the position corresponding to the actual trap depth E. Thus the apparent distribution obtained differs from the real distribution , but the maxima for each coincide. This conclusion is only valid if the initial excitation satu rates the trapping states. =
Lumincsc('ICC in Crystals
l (iO ITT.
M ET H O D
THE
C U RV E S
OF
T H E R M O L U M I N ESCE NCE
(OR G LOW C U RVES)
Description of the method
This method, le ss precise than t h at of analysis of decay curves, is 1.
more convenient and more rapid. It was first pr oposed by F. Urbach and then by K atz and Solomoniouk, but its use is now extensive d u e to the researches of Ra n d al l and Wilkins. The method i s as follows : ( I ) The phosphorescent solid is first excited at a low initial tem perature T;, low enough fo r the traps to be investigated, not to lo se their electrons. (2) The solid is w a r m e d at a rate fi w h i ch is made as u n ifo rm as p o ssi bl e The traps empty as the temperature rises, the 'shal low' ones first, .
0
liS eV
:o J
0·72 eV
O SO eV
2so
Fig. VI . 6 Thermoluminescence curve of a long afterglow ZnS(Cu) phosphor. The trap depths involved are indi cated at each maximum. The letters A , B, c, D denote the f{roups of traps similarly indicated in Fig. Vl.S obtained from decay curves A t ooc the sensitivity of the apparatus was increased
sevenfold
The groups A , B and c are complex and sometimes can be reso lv ed into subgroups (see Fig. Vl. 7)
each temperature T those with life times of a fraction of a
second or so are principally responsible for the observed thermoand at
Electron traps, Phosphorescence, Thermo/um inescence
161
l uminescence. I f there is only one trap d e p th , then the thermo luminescence is very weak at T = T; ; b u t then increases with T, reache s a m a xi m u m for th e temperature of thermoluminescence, T*, an d then decreases to zero as the traps are all e m p ti ed . If the trap distribution c o ns i s t s of separate groups of trap depths, then these groups are o b se rv ed as thermoluminescence maxima. The p r o b le m is : K n o wing the te m pe ra tu re T* of max i m u m therm o l u m i n escence, what is th e trap depth E i nvolved . Urbach gave the approxim ate n u merical relation E
- -50
T*(°K)
ded uced from experiments on KCl(Tl) : this form ula gives the righ t order of m ag ni t u d e of E for a n u m ber of ph osphors. 2.
(eV)
c=
Simple theory of the thermoluminescence curve due and Wilkins
This theory assumes a monomolecular m ech a n is m it s te m s from th e eq u a tio n :
ph o sph ore s ce nce , i . e .
dn
n
I=
to Randall
as u sed above fo r
dn
where n is the number of traps filled at time t and -r is the mean life time of the t rapp ed e l e c t ron s , I b ei n g the thermolumi nescen ce i n dt
-:z:,
dt
Previously -r was a cons ta n t, the temperature being fixed , i n cre ases with t h e t i m e t accor d in g to the relation
tensity. T
and so
and
n
-r
also varies :
dT
=
fJ d t
I = s e -- li/k'l '
is given by the i n teg ra tio n T
n
"-"'
n0 bei n g
h eat i n g) .
[ J>rzi) dt]
n0 c x p
d TJ [ IT 0 (at beginn ing
the number of filled t r a ps at time t n0
exp
�,=
The thermoluminescence intensity
given by -
I( T)
= noS exp
( - E/kT) exp
but n o w
-
I(T) at
[-J:.s
.
\ c
T ,·
".'k1' -
=
(J
of
the temperature T is
e x p ( - E/kT)
��
in
Luminescence
1 62
Crystals
con stant warmi n g ra te need not be uscd t and th e work of T. in a d i ffe re n t h e at ing reg i m e (heating in 'bursts') . However, T* for maximum emission de p e n d s on the rate A
Louchtchik sh ows t he interest
gives by numerical i n teg ra t io n the complete
of heating and we shall here assume fJ to The above formula
be
constant.
form of the thermoluminescence c u rve , but the calculations arc laborious and often an attempt is made to deduce the d epth E fro m T* . T* is found by s ett in g d l/d T 0 a n d t h i s give s E
=
- B/ = se
k1'•
(2)
E is thus a n implicit function of T*, the relation between th e m b ei n g d efined by t he parameter e (Jjs. From numerical calculations this relation can be obtained with sufficient acc u racy (better than I per cent) and we ca n write =
o - To((J/s) E (e V) = T*( K) K((J/s)
t he values of
following
T0 and K being table : 0
=
Jo-• JO -• JO-• 10 ' • JoJO-• 1 0 10
/3/s (°K)
For ZnS(Cu)
K (°K/e V) 833 725 642 577 524 480 44 1 408
0 -1 1
phosphors ,
graphically and g ive n
T A BLE V I.5
10-12 J 0 -13 JO-" S JO -l
J
formula E ::
obtained
in t he
T0 (° K) 35 28 22 17
13
10 7 6
6
379
5
353 331 312
where s is
(3)
5
4
a b o ut 1 09
sec - 1, t h e
T* /500 gives the right order of values fo r
Urbach
relatively
t More recently (1958), M. SchOn has shown that the use of a heating rate that 1 / T is a linear function of the time t, i.e.
such
d(I/T)
functions.
=
- /3 dt
leads to integrations that may be easily carried out in terms of simple exponential
1 63
high warming rates of about 1 o K j s ec t H o we v e r , s l o w e r w a r m ing is o fte n used to get a better separation of the different gro ups of traps and to be less affected by thermal capacity effects . For (3 R: 0·01 ° K/ s ec E R: T* /400. The formula (3) is precise, but the major problem lies in the determination of s. Electron traps, Phosphorescence, Thermoluminescence
.
,
3.
Thermoluminescence curve measurements using two different warming rates
Booth, Bohun and also Parfi a n o vitch have shown independently that the need to know s can be avoided if one uses two different warming rates, {31 and {32, to o btai n E. The same trap depth then re s ults in two different values of T*, i.e. T1 * a n d T2* . If {31 > (32, then T1* > T2* . B y u s i ng t h e eq u a ti o n (2) a b o ve the elimination of s g i ve s from which E can be o b t a i n e d
w ri te (A . Wrzesinska)
log £
sk
.
T.2 * log
=-
If
(%� �:;�)
we now want to know s we ca n
= log
*2
(32
·
T! * 2 1 * log _(31_
Unfortunately the above method, which is m os t convenient, is not very precise, since T* varies so little with warming r at e : E can only be estimated with a 20 or 30 per cent accuracy. T1 * .: T2*
··
As in s ecti o n II, fo r the decay we can obtain the thermol uminescence equations based on a bimolecular m ech anis m and then show that the assumption of monomolecular basis as in the Randall-Wilkins the ory does not lead to any serious errors in determining the trap distribution . W e assume a single trap depth and equal capture cross-sections for centres and traps. We use the differential equatio n as for decay (see
4. Observations on thermoluminescence equations
t Randall and Wilkins have shown that the mean life T is little different from
I sec at the glow temperature T• : E
=
kT* Ioge s[l +f(s,
.8)]
This is a coincidence, valid in ZnS for high values of the heating rate, but it is not generally valid. The formula E = kT log, (s) (obtained by putting f(s, fi) fom!Ula is better.
=
0)
is a poor approximation. Urbach's simple
Luminescence in Crystals
page 1 5 1 above). However rapid the warming rate, the phosphor temperature will be sensibly constant for the time ( � ro-s sec) taken t o establish equilibrium between the trapped electrons and those in the conduction band . We thus use the equation dn n2 1 64
=
Since we now have T, and also as a result integral of the equation m u st be w r i t t e n dt
11
=�
dt
----�-- =
l-t-J1
0
-n0-r:
I+ J 'l'
r,
no
varying with time,
the
( - E/kT) dT/(3
s exp
Assuming excitation saturates the traps initially, the thermolumines cence intensity I = I dnjdt I and at t i me t or temperatu re T: l( T)
lloS
7:
7'•
H/k1' / [I + L>·
( - E/kT) d T/(3
The temperature fo r the emission ma x i m u m a n d so =
1[ J
e
exp
exp ( - E/kT) d T/(3
is
r
given by d l/d T =
p( J by the factor This relation differs from that of �[I+ J:.S exp ( EjkT) dT/(3J E
I+
T
T
.s
=
s ex
0,
E/kT*) (2a)
(2)
where n* is the number of electrons left in traps at T*. The thermo luminescence curve is not quite symmetrical and the change from T to T* does not correspond exactly to the relation n* = n0/2. How ever, the difference is not large and T* is only changed by a per cent or so by the above factor (A. Wrzesinska). So we see that the application of monomolecular formulae (3) to T* gives an approximately correct value for the maximu m of the trap distribution, but if the whole curve is plotted , then the bimolecular formula gives a wider apparent distribution than really exists. T. Louchtchik in his book Crystal Phosphors has given many numerically obtained thermoluminescence curves for mono- and bi molecular theory and for various values of E, S and (3. He has also investigated the va riation o f radiative emission probability with tem perature =
17(T) =
1Jo
l + C exp --
(
-
--
W/k T )
Electron traps, Phosphorescence, thermoluminescence
i 65
in relation to its effect on thermoluminescence curves. In the region where thermal quenching is large the temperatures T* of maximum thermoluminescence emission have lower values tban where thermal quenching is absent. The shift can reach as much as 1 0°, wliic1l is greater than the error in measuring T* . For monomolecular processes we can make the simple correction for thermal quenching :
but the correction becomes complex in the b i m o l ec u l a r case. I f thermal quenching i s marked ( T * > 200 o r 300°C for ZnS), the traps involved do not show up in the thermoluminescence curve. By use of the same kind of mathematical approximations as those in Adirowitch's theory for decay (i.e. the 'quasi-stationary' approxi mation), Louchtch i k and eo-workers have extended their calculations to the bimolecular mechanism when the ratio y atfac of the elec tron cross-sections for traps and centres is not unity. When the re trapping probability is much larger than the recombination proba bility (y ?> 1), a quasi-monomolecular approximation is obtained . Thus in the region for y > 1 , the Randall-Wilkins fo r m u l a gives rather good results, as a general rule, for the case of saturation ex citation. But if y is appreciably smaller than unity, the peak glow temperatures calculated by Louchtchik are somewhat higher.
J(T)obscrved
=
J( t )rcal · 'Y)(T)
=
IV.
D A TA
O N E LE C T R O N T R A P S
IN
V A RI O U S
P HOSPHO RS
The mean values of E for different groups of traps as formed by various workers indicate a close correlation between thermolumines cence curves and phosphorescence decay curves. Similar trap depths are apparently found in spite of the particular m et ho d of preparation of the sulphides. Thus Joukova has found that the use of fluxes such as LiCl, NaCI or KCI modifies the relative i mp or tan c e of the different groups of traps but not their mean depths. We give here some results of this. (a) A group of traps with E about 0·28 eV occurs which is indepen dent of the activator centre : this can be explained in terms of a hydrogenlike model of localized states (Bethe m o del). According to this model the electron moves in a field due to a substitutional charge -+ e in the lattice (possibly a sulphur vacancy) . In the ground state it 1. ZnS(Cu) phosphors
Luminescence
in
will mo v e in a Bohr orbit of rad ius a Ka0 (a0 0·53 A) a nd its energy is - R/K2 (R 1 3 - 5 eV), a value which gives t h e t rap depth below the conduction band In a covalen t c rys tal K is the dielectric c o ns ta n t of the medium. In an ionic crystal the static (K) and optical (K0) diel e c t ri c constants are different a nd the i o nic pol a rizati o n must be c o ns i dered Thus an effective dielectric constant K. is introduced giv e n by 1 66
Crystals
=
=
=
.
.
The orbital radius
is
a
K.a0 and the t h e rm al activation energy is =
=
E=
K -2
R e
The o p tical activation ene rgy is (see Chapter V I I )
hv or
=
a p p r o x imately
;.(fi k-� -!6 *)
T A B L E VI.6
Numerical values for various K
ZnS
8·3
1 1 ·6( ?) 1 2 ( ?)
CdS ZnO Cu,O
9
Ko
= nz
5 ·07 5·85 3· 88 4·0
ionic
crystals
Ke
E (e V)
hv (e V )
7·25 6·48
0·26
0·47
6·93
8·88
0 28 0· 1 7
·
0·38 0 26
In ZnS, CdS and ZnO thermoluminescence gives peaks correspond to 0·28, 0· 1 7 and 0·26 eV. In Cu20 the activation energy for semi conduction in dicates a level with E = 0·32 eV (acceptor level) Thus the agreement with experiment is very good, in fact so good that it ing
0·32
0·50
.
must be fortuitous. The above values were found by R. Freymann and his collab o rat o rs for the activation en e rg i es involved in Debye-type dipolar abs o rp ti o n (b) A grou p of traps with E � 0·4 eV fou nd by Garlick and also by Wallick to be pron ou nce d in fine grain size sulphides and attributed to surface t raps (c) An assembly of trap groups associated with introduction of .
copper.
.
Electron traps, Phosph orescence, Thermoluminescence
1 67
The model wh ich is d es c ri b e d below leads to the following trap depths :t T A B L E VI.7
Trap depths E and the corresponding mean life times r at room temperature (18°C), computed for s = 109 sec 1 E (e V) 0·48 (A) 0·50 0·53 (B) 0·565 0·61 (C) 0·63
{ {
-r(s)
0·2 0·45 1 ·5 6·0 38
81
{
0·68
60
2,500 1 20,00
(D) 0·7 1 5 0·8 1 5
The gro ups (A), (B) and (C) are generally not resolved into the subgroups predicted by the model (see Figs. VI.5 and VI.6). Such a Thermoluminescence zoo
150 100
r ·� -7o' c E = 0 1. 6 e V
r'= 1 7s'c [= 0 · 2 1 e V r'= 1 1.5°C E = 0 ·28 e V
r; - 6o'c E = 0 ·48 eV
I r '= - s o ' c t E = 0 50 e V
t
r"= - 3 5 ' C E = 0·53eV
i�-25 ° C f= 0·5 6eV
T� +10'C E = 0·63eV I\0
T � + 95°C E = 0 83cV
50
� 200°
-150 °
- 1 00°
. 50°
+ 50°
V1.7 Glo w curve of a ZnS(Cu) phosphor fired at 1, 150'C. Heating rate {J = 0 · 06' /s. The trap dep ths are computed by the formula (see page 162)
Fig.
E (e V) =
T*('K) - 7 433 ·
-
-
i" At present the traps which have been found from the therm olum inescence curve are (a) the traps correspondin g to the six nearest neighbours ; (b) for larger distances the most important groups, i.e. those common to blende and wu rtzite-type phosphors.
1 68
Luminescence in Crystals
reso l u ti o n o f t h e g l o w p e a k s needs a convenient choice of the rate of
h e a ti n g
a d d i t i on , this rate must be maintained at a constant with a d e g re e of accuracy. The t raps with E R:> 0·8 eV Jose their electro ns very slowly at room tem perature a n d g i ve rise to no appreciable phosphorescence. How ever, the groups with E 0·57 and 0 · 6 1 to 0 · 6 8 eV (which occur in b o t h cubic and h ex a go n al Z n S ) and with E 0 · 72 eV ( i n hexagonal ZnS) give the long d u ration phos p h o res ce n ce o f ZnS at ordinary
(J ;
in
v a l u e d uri n g the gl o w ex p e ri m e n t
=
=
tem peratures .
These traps ca n be a s s o c i a ted wi t h the charge + e of the level of (a) a b o v e pertu rbed by the nearness of the copper centre which func tion s as a second s u bsti t u tional cha rge + e when i t is ionized (i.e. a ft e r e x c i t a ti o n ) . Us i ng t he hydrogenlike model, this trap model de s cribes the t rapped electron as captu red in t h e field of two po si ti v e c ha r ges ( + c) A a n d B, one bei n g a s u l p h u r vacancy (A ) a n d the other (B) bei ng the s i n g l y i o nized l u m i nescence ce n t re at a z i n c site. The d ep t h of s u c h a t ra p is gi ven approx i ma t e l y by hl'
R:>
R e2 - + -K. 2
KrA JJ
where K . i s t h e effective dielectric constant as defined p revio usly i n
K is the static dielectric constant. The term e2/KrA B R/K2 when there is a second charge +e at a d i s ta n ce rAB from the first. The same perturbation is effective in the expression for the optical activation energy, which is thus the same d e g re e of approxi mation : (a) above a n d
gi ves the p ert urb ati o n of the simple trap depth E
hv
=
-- + KJ{0 KrAB
R
e2
The above formulae are not accurate. A more rig oro u s treatment h as been given ( D . C u ri e , 1 9 57), using the LCAO m et ho d for describ R:>
i n g the trapped electro n .
K nowing the coord i n ates o f the zi n c a n d s u l p h u r atoms i n
the cube rA B as
(blende) or hexagonal ( wu rtzi t e) l a ttices , it is s i m p le to o b t a i n
shown in t h e tab le .
We n otice the agreement between t h e calculated and observed E. In particular we find also that the same distance rA B ap p li es to the two d i ffe ren t crystalline
values for the thermal activation energy forms and th e r . 1 li
=
same trap depths. In addition, for wurtzite the distance
5r0/3 g i v es t h e co r respo n d i n g t rap depth of 0 · 72 eV, givi n g the
T A B L E VI.8
Trap depths according to the hydrogen molecular-ion model Blende
- -- -1 --
Number of sites
- ---
4
12
I
--- - -
� ----
I
i
i
16
12
rA n
I
vTT7J
,1 1 9/3 3
24 12
24
i
�
I
I
1
i I
i
----1 ----
Number
of sites
-
4 I
6 9 9 3 9
6
18 3
7
1 i
rA n
----
I
5/3
I
vTT7J
! vfi
!
I
�
i
7/3
I I I ! I
3
I
V89/3
v'97;3
V35/3
i
1 1 /3
Vil / 3
1I
1
E (e V) -
0·8 1 5 0·7 1 5
1
-
hv
-
o-68 o-63 0· 6 1
6
12
-
-
-- .
(e V)
-
0 55
0·54 0·53
0 96 0·84
0· 5 1
.
---- -
E
(e V )
0 4 75 0·42 5 o-4 1 o-39
----
0· 34 0 · 34 0 335 0·33 o- 32
0 585
0· 56
0 315
The distances r, w are given i n u n i ts of r 0 2 35 A for ZnS a n d n0 r0 is the distance between nearest neighbours.
CdS ;
=
liagonat
Princtp a f cube
"
'\ > A, ----+� ' I I
:
I
I
j .A
A1
A,
,
WuriZ!fe
Fig. V I . 8 Position of nearest neighbour sulphur atoms re/arilJe to zinc atmm in the b/ende and wurtzite lattices
of ZnS
A
sulphur
B
zin c
--
h v (e V )
0 395
Hez agon a l BJ.I!.
s6
-
0· 60 0· 5 3 o-5 1 o-48 0·46 0-45 0·445 0 · 44 0·4 3 0·425 0-42 0 41 o·4D
0·38 0·36 0·355 0·35
o·575
- --
- -- - -
-
0 · 60 5 0 ·59 5
0·52
·
-
0·72 0·67 0 65 0·63 0·62
0·565
- --
-- - - - -
-
o-8o o 75
v 4 3/ 3 i 0· 50 -vm /3: o-49 v 1 -:i : 0·48
3
I
! ------ ---
2 52
A
fo r
1 70
Luminescence in Crystals
longer phosphorescence for the wurtzite lattice phosphor than for the blende lattice specimens. In the blende crystals the zinc and sulphur atoms are arranged in a face-centred cubic lattice, while in wurtzite they occur on a compact hexagonal lattice. In blende, as i n wurtzite, a zinc at o m B (see Fig . V1.8) is surrounded by fou r sulphu r atoms at a distance r0, forming a tetrahedron with zinc at the centre. In wurtzite, however, the four sulphur atoms are not equivalent. If the hexagonal axis is vertical , then three of the atoms A , A2 a n d A 3 , form an equilateral triangle i n th e horizontal plane while the fourth A ' i s directly above the zinc atom a distance r0 away along the axis. If b 8r0/3, the spacing along the hexagonal axis, the sulphur atom A" b el o w b has a di s ta n c e rAB 5r0/3, and this gives the extra trap depth 0·72 eV. (d) Finally, for ZnS a number of very shallow traps exist (£ 0· 1 eV) which have very short life times for electrons except at very low temperatures (N. Riehl). =
=
=
The traps in CdS are shallower than in ZnS and less well separated because of the higher value of K. It seems possible to resolve o nl y the following groups : E 0·475 eV, E � 0·42 eV, E � 0·35-0·39 eV, E � 0· 1 7 eV This seems to be in agreement with Bube's, with Broser-Warminsky and with Boer's experimental results. In order to obt ai n the best agreement between calculated and experimental values, one must accept a lower value of the parameter s in CdS than in ZnS : s � 108 sec - 1 in CdS s � 1 09 sec 1 in ZnS 2. CdS phosphors
=
The total number of deep traps (r > 1 minute) i n zinc and cadmium sulphides seems to be of the order of 1 015 per cm3 (H. Kallmann, Spruch and Sucov). The number of shallow traps is probably larger by one or two orders of magnitude. Some experiments give evidence for a considerable amount of retrapping in short-lived traps. These figures may be compared with the number of l u m inescence centres. In a zinc sulphide phosphor activated with copper at the op ti m um concentration of 2· 1 0 ·1 g Cu/g ZnS, the number of centres is a b o u t 4· 1 0 1 8 per cm 3.
Electron traps, Phosphorescence, Thermoluminescence
171
Calcium sulphide is one of the oldest known phosphorescent ma terials having a fine violet luminescence and a very long afterglow (Balmain's p aint). Its composition is no t well defined and it u s ually contains some CaO, CaC03 and CaS04• Traps of many different depths are usually found for this phosphor . T h e pri nc i pal groups deduced from phosphorescence light sums at room temperature (Lenard), have mean life times of 1 07, 1 05·6 and 1 03· 3 sec correspond ing to trap d ep t hs (s R;j 101 0/sec) of 1 , 0·9 and 0·8 eV. These appear to be independent of activator centre concentration (Lenard and Kuppenheim). The thermoluminescence peaks at a temperature of about 400°K, but there are indications of a trap group with T * R;j 550° C giving E R;j 1 ·2 eV , the mean life times being of the order of centuries at room temperature. The latter group seems to be associated with the introduction of bismuth impurity (A . F. Wells). 3. CaS(Bi) phosphors
We have already given the energy-level sc h eme for the thalli u m i on
4.
KCI(Tl) phosphors
(see Fig. II.3). While the states 3P1 and 1P1 give ri se to t he princip a l absorption and emission bands, t h e states 3P0 and 3P2 are metastable and form the t rapping levels. Ab s orp tion at 2,500 A raises the ion from the ground state 1 S0 to the excited s tate 3P1, from whence the electron can fall back to the 1S0 state with em i ssion at 3,050 A or be captured into the metastable state 3P0 (or be transferred to the 1P1
state). A thermal or suitable op tical activation can raise the TI + ion fro m the trapping st ate 3P0 to the state 3P1 t o give subsequen t emission 1 (3P1 - S1). Such a trap system will give an essentially monomolecular mechanism for phosphorescence which will follow an exponential law with a s ingle l ife ti me r. Bi.inger and Flechsig measured the light sum S(t) and for certain c rystals of KCl(Tl) (which they called 'good' crystals) found that S(t) = S0 e - t/T+const. the latter constant being due to the effect of deeper traps. The life time satisfies the usual relation with
E
=
0·67
eV and s
l
=
e - Efk1'
2·9 X 1 09 sec- 1• In the so-called 'good' T
=
s
1 72
Luminescence in Crystals
fro m t h e very shallow a n d very d ee p tra p s ) a grou p life time very closely centred on a s i n gle value was found. Howeve r, if this group is wi de due to d i ffe re n t interactions of d iffe re n t Tl + ions with th e crystal lattice, then the decay is no longer of simple e xpo ne n ti al form . Bi.i n ger a n d Fl ec h s ig called crystals with such groups of traps 'bad' crystals . Thermolu minescence curves p rovide m o r e preci s e info rmatio n . Fo r l ow Tl + ion concentrations only two maxima appear (see Fig. VI .9), which are much l a rge r than those o f phosph orescent s u l p h i d e s The most importa nt of t h e se occurs at T* 300°K (� �2·5°/sec) an d the form u l ae (3) of section III e n a b l e this to be identified with the trap crystals (a part
with
a
'
'
.
=
1
T (" K )
Thermoluminescence curve for KC/(TI) (thallium concentration 0·05 per cen t : � 0·83°K/sec) (After Johnson and Williams)
Fig. VI .9
=
i nvestigated by B ii nger a n d Flechsig and t h e i r value of s is co n fi rmed The second maximum at T* = 205 °K gives E � 0 · 4 eV. J o h n s o n and Williams have shown that these traps are due to the metastable states 3P0 and 3P2 of t h e thallium ion. They s tu d i e d the variation of thermoluminescence in te n s i ty with thallium ion concen tr a t i o n which varies in the same way as the luminescence, a n d on this they based their conclu si o n s When the concentration is h igh other thennoluminescence maxima occur, i n partic ul ar a peak at T* 250°K due to pairs of adj acent Tl+ i o ns (F. Seitz) . Only s peci m e n s of KCl(Tl) p re p a re d fro m the melt show such trap distributions having a res t ricted and well-defined number of groups. P . Pringsh e im h as p repare d differen t s pe ci m e n s by pre cip i t at i on from saturated a q u e o u s solutions which show an excellent l um i n e scenc e but the thermoluminescence shows no pron o u nce d maxima which i nd i cates a wide d i stribution of tra pp i n g leve l s . .
,
.
=
,
1 73
Electron traps, Pho sphorescence, Thernwfuminescence
5.
Thermolumincscence o f alkali halides
with
If
the temperature is raised, colour centres of F, M, R types, &c.
colour
centres
(va ca ncie s with one or more ch a rge carriers) lose their electrons a n d be h ave like electron trap s . I f the freed electrons reach luminescence
a thermolu m i n escence peak resu l ts . T h e observed emis s i o n is usually i n t h e ultra-violet o r i n the blue regio n of the spectru m and may be due to t ransitions in V centres or in i mpu ri ty cen t re (see page 64). The thermoluminescence is: a cc o mp a n i ed by remarkable effects, but these are d i fficu l t to i n terp re t : (A) T h e thermal activation of a co l ou r centre ca use s a bleach i n g o f the c or resp ond i n g ab s orpt i o n band a t the same temperatu re as t h a t for thermol uminescence (Prin g s he i m an d Y us te r , T. Louchtch i k , &c.). (B) The ultimate capture of the liberated electron by a vaca n c y gives rise to a n o t her a b s o rptio n band (at the expense of th e fi rst) . (C) Th e capture of the electron in a V centre (pos it i ve i o n v ac a n cy co ntai n i n g a p os itive hole) c a us es a b leac hi ng of V centre absorp t i o n simultaneously with t h e bl e ac h i ng of the o r igi n a l colour centre ban d . Similar effects h ave been observed i n conventional ph o s p h o rs such as ZnS and CdS ( Hal pe ri n and Garlick), but the abs o r pt i on bands d u e to traps in the sul p hi des are in the infra re d between I and 3 ,a ra t h e r than in the vis ib l e as for colour centres in alkali h a l i de s ( D) As far as the emission spectra are concerned an electro n c o min g from an F centre, for ex a mp le can recombine wi th differen t l u m i n esc e nce centres. Thus thermoluminescence e m i s s i o ns of d i ffer ent c olo u rs may arise from th e the r m al emp ty i n g of the same trap (Bo n fi gl ioli Brovetto and Cortese) . On the other hand, the emptying of different traps may be followed by the recombination of th e conduction electrons and of holes in the same l u minescence centre ; and so we obta i n different thermolumines cence peak s with th e same emission spectra (Halperin , K r i s t i a n p o l l e r et al.). Here we give a typ i ca l e x a m pl e : In KCl the F-band absorption is at 2·55 eV in t h e gre e n y e l lo w region and so a KC! c rys tal with colour centres has a deep blue or r athe r magenta colour. Bose a n d Sharma bomb a rd ed KC! with cathode rays at liquid air temperature but n ot many F ce n t res were prod uced , the crystals acquiring a rose tint d u e to u n i d e n t i fied c o l o u r centres, th en
.
,
,
-
1 74
Luminescence in Crystals
cence curve
centres . By heati n g the crystals at a u n i form rate a thermol u m i nes w a s recorded (see Fig. V LI O) with two m a i n pe a k s at T* 205°K an d T* 620°K. When the first peak was passed th rough the rose coloration dis appeared and at the same time the 'magenta' colour characteristic of =
=
recapture of electrons in vacancies to form F centres was observed . This coloration persisted up to 620°K, when the crystal bleached during the emission of the second glow peak. If we take 620°K as the thermoluminescence temperature corre sponding to the thermal activation of F-centre electro n s , then u se of
1 00
200
300
400
500
600
Fig. VI. I O Thermo luminescence curve
700
T(K )
of KC/ (no t!wl !ium) after cathode-ray excitation at 90 'K({J = 5 ° -6" /se cl (After Bose and Sharma)
the relation E = T* /500 gives E � 1 ·2 eV, assuming s 1 010 sec 1• Other workers (Parfianovitch) have suggested an s value of I OU s ec t which gives E � 1 · 8 eV, and this is theoretically preferable. t We thus have : F-band absorption in KCl at 0·55 fl hv � 2·3 eV F-band emission in KCl at 1 ·00 ft Jrv 1 ·4 eV Thermal activation energy £ � 1 ·8 eV The thermal energy E is marked ly l es s than the optical activation energy of 2·3 eV as predicted by Mott. =
-
,
=
t The configurational coordinate model (see Chapter VII) leads to the equality being obeyed for an E value of 1 · 8 eV rather than 1 · 2 eV.
in
Electron traps, Phosphorescence, Tlzermo!uminescence
1 75
B I B LI O G R A P H Y I.
Mean life times and cross-sections o f electron trapst
R . and SEITZ, F . , editors (1 948) , and especially the following papers : G A R L I C K , G . F . J . (1 948) 'Some studies on electron traps in phos phors', Cornell Symposium, 87. U R B A C H , F . ( 1 948) 'Storage and release of l i gh t by p h o s p ho rs , Cornel/ Symposium, 1 1 5 . WI LLIAMS, F . E . ( 1 948) 'The mechanism of rate processes in the luminescence of solids', Cornell Symposium 337.
General referen c es
Corne/1 Symposium, F O N D A , G .
'
,
( 1 9 50) ' Remarques sur le mecanisme de la phosphores cence dans les cristaux', J. Phys. Rad., 11, 1 79 . C U R I E , D . ( 1 9 5 1 ) 'Essai d'utilisation de la mecan ique ond ulatoire e n phosphorescence', J. Phys. Rad., 12, 920. C U R I E , D . ( 1 952) C apture et recapture electroniq ues en p h osp h ores cence', Ann. de Phys. , 7, 749. C U R I E , D . (1 955) 'Sur la loi fondamentale de sortie des pieges', Comptes-Rendus Acad. Se. Paris, 240, 1 6 14. E L L I C K S O N , R. T . ( 1 953) 'Electron t r ap p i n g states in p h o s p h ors J. Opt. Soc. A m . , 43, 1 96. G A R L I C K , G . F . J . and G I BS O N , A. F . ( 1 948) 'The electron t rap mechanism of luminescence in sulphide and silicate phosphors', Proc. Phys. Soc . , A 60, 574. G A R L I C K , G . F . J. and GmsoN, A . F. ( 1 949) L u m i n es c en c e of photoconducting phosphors', J. Opt. Soc. A m 39, 935. GARLI C K , G . F . J . ( 1 949) 'Phosphors and 'phosphorescence', Repo rts Progress in Phys., 12, 34. G A RLI C K , G. F. J. ( 1 955) 'Absorption, emission, and storage of energy in phosphors', British J. Appl. Phys., 6, Suppl . 4, S 8 5 . LEWCHIN, V. L . ( 1 956) 'Influence s u r la loi de declin de la phos phorescence de l'existence de plusieurs systemes de pieges et du phenomene de recapture', J. Phys. Rad., 17, 684. C U R I E , D.
'
',
'
.,
t The publications that have to deal more precisely with a particular subject, or 'the theory of multiphonon transitions', and so on . . . , will be found under the correspond ing t i tle of the bibl iography.
such as 'the decay law i n sul phide phosph ors', or 'the glow curves',
1 76
Luminescence in Crystal\'
R A N D A LL , J . T . and W ! L K I N S , M . H . F . ( 1 945) 'Phosphorescence and e lect r o n traps', Proc. Roy. Soc., A 184, 366. W I L LI A M S , F . E . ( 1 949) ' Review of the interpretations o f lu m i ne s cence p h e n o m e n a ' , J. Op t . So c . A m . , 39, 64 8 . W I S E , M . E. ( 1 95 1 ) ' Fr e e elect ro n s , tra p s a n d glow i n crystal ph os phors', Physica, 1 7, 1 0 1 1 . On Williams and Eyring's ' A bsolute Rate Theory' G LASSTO N E , S . , L A I D L E R . K . J . a n d E Y R I N G , H . ( 1 9 4 1 ) The Theor r of Rate Processes, 1 4, 1 95 . McG raw- H i l l , New York. W I LLI A M S , F. E. and E Y R J N G , H. ( 1 947) ' Mech a n i sm of t h e l u m i n es c e nce o f s o l i d s ' , J. Chem. Phys . , 1 5, 289.
relation b e t ween the probability p of escaping from the trap and capture cross-section a M aTT, N . F . and G U R N E Y , R . W . ( 1 948) Electronic Processes in Ionic Crystals, 1 0 8 . Clarendon Press, Ox for d .
Th e
the
( 1 956) 'Sur le re n d e m e nt de la lumine s ce n ce dans les p h ospho r e s c rist a l l i n s ', J. Phys. Rad. , 17, 692, 694. C U RI E , D . ( 1 9 5 2) 'Libres parcou rs des electrons dans 1es cristaux. Effets d'electroluminescence et ph e no m e ne s de ruptu re diel ec trique' , J. Phys. Rad. , 13, 3 1 7. ' R o s E , A . ( 1 9 5 1 ) 'An outl i n e of some ph otoconductive processes , R . C. A . Review, 12, 362. R o s E , A . ( 1 9 5 5) ' R ecombinati o n processes i n insulators and sem i c o n d u c t o rs ' , Phys. Rev . , 97, 322. S cH i:i N , M. ( 1 9 5 6) 'Le mode!e d es bandes dans les s u l fu re s phos phorescents c r i stal li ns ' , J. Phys. Rad. , 17, 689. S i o u - S w u- I o u N ( 1 9 5 6) ' D e termi n a t i o n of the effective cross-sec tio n s of capture and recombination in the ph o s p h o r ZnS(Cu, Co)', Cross-sections for traps in sulphide plzosphors
A NTONO V - R OMANOVS K Y , V . V .
Optika i Spek tr. , 585, and ( 1 9 5 6) ,
1,
264. See also 8 1 8.
1 06,
Doklady A kad. Nauk ( 1 955), 103,
Some referen ces on traps in germanium and silicont H A Y N E S , J. R. and H O R N B E C K , J. A. ( 1 953) ' T e m p o ra ry silic o n a n d ge r m a ni u m ', Phys. Rev.', 90, 1 52. t Traps
with an h i gh
cross-section only.
traps i n
Electron traps, Phosphorescence, Thernwluminescence
germanium below
L77
( 1 9 58) 'Recombination of t h e r ma l e l ec tr o n s i n n t y p e l 0°K', Phys. Rev., 1 10, 9 8 8 . LA X , M . ( 1 959) 'Gaint traps' , J . Phys. Chem. Solids, 8, 52. L A x , M. ( 1 960) 'Cascade capture of electrons i n sol i d s ' , Phys. Rev., 1 19, 1 502. N EWMAN, R. and T Y L E R , W. W. ( 1 959) ' Ph o toconduction in ger m a n i u m A dvances in Solid State Physics, 8, 49. A cad . P ress, New York. KOEN I G , S . H .
-
',
ll.
Decay of luminescence
A general discussion C U R I E , M . ( 1 946) Fluorescen ce et Phosphorescen ce, 1 1 7 -2 3 . H e r man n , P a ri s C U R I E , M . a n d C U R I E , D . ( 1 956) Quest ions actuelles en lum in e.1 cen n: crista/line, 3 9 -4 8 . Revue d ' Optiq ue, Paris. M OTT, N. F . a n d G U R N E Y , R. W. (1 948) Electronic Pro cesses in Io n ic Crystals, 209 - 1 9 . C l a r e n d o n Press , O x ford . P R I N GS H E I M , P . ( 1 949) Fluorescence and Phosphorescence, 566 - H 2 . Interscience Pub . , New York. S E I T Z , F . ( 1 939) ' A n i n terp ret a tion of crystal l u m i n es c e nc e Trans . Faraday So c . , 35, 74. See also the discussion section , by DE GROOT, w . , G U R N E Y , R . w . , KROGER, F . A . , R A N D A L L , J . T . , R O T H · SC H I L D , S . , &c. .
',
Fluorescence and short-period phosphorescencet B RODY, S . S . ( 1 957) 'I nstrument to m eas u re fluorescence l i fetimes i n the mill imicrosecond region', Rev. Scientific Jnstr. , 28 , 1 02 1 . D REESK A M P , H . a n d B U R T O N , M . ( l 959) ' Measurement of fast l u min escence decay times', Phys. Rev. Letters, 2, 45. G A R L I C K , G. F. J . a n d WILKI NS, M. H. F. ( 1 9 4 5 ) ' S h o rt period phosphorescence and electron traps', Proc. Roy. Soc., A 184, 408 . G A RLI C K , G . F . J. and GIBSON, A . F . ( 1 947) ' D e c ay of l um i nes cence d ue to fo rbidden optic al t r a n s i t i o n s Na ture, 1 60, 303. G A V I O L A , E . ( 1 927) 'Ein Fl uorometer : Apparat zur Mess u n g von Fluoreszenzabklingungszeiten', Z. fur Phys. , 42, 8 5 3 . G A VIOLA , E . a n d P R I N GS HE I M , P . ( 1 927) 'Zur Frage nach dem Obergang von Fluoreszenz i n Phosp h o reszenz', Z . fiir Phys., 43, 3 84. ',
t See also
the bibli ography on Radio l u m i nescence and Scin til lations.
1 78
Luminescence in Crystals
G o u o u , G . ( 1 942) 'La mod ulation de la l umi e re en haute freq uence par l e s on des s t ati o n n ai res u l t ra - s o n o re s . A p p l i c a t i on a la m e s u re
des durees de vie des substances ftuorescentes'. Thesis, Paris.
J A BL O N S K I , A. ( 1 935) ' O ber den Mechanism us der Photolumineszenz
von Farbstoffphosphoren' , Z. fur Plzys. , 94, 3 8 . A . (1 936) ' O ber d i e Abklingungsgesetze d e r po l a ri sie r t en F l u or esze n z ' , Z. fur Phys . , 95, 53 ; 103, 526. L E W I S , G. N . and K A S H A , M. ( 1 944) ' P h o s p h o re s c e n ce and the tri p l e t state', Am. Chem. Soc. J. , 66, 2 1 00. P E R R I N , F. ( 1 929) 'La fl u o res ce n c e des sol utions. I nd uction molecu laire. Polarisation et d u ree d'emission. Photochimie' . Thesis, Paris. T O L S TO I , N. A. a n d F E O F I L O V , P. P . ( 1 947) 'The Ta u- meter' , Dokl. Akad. Nauk S.S. S. R . , 58, 3 89. T O LSTO I , N. A. and F E O F I L O V , P. P. ( 1 948) 'The decay of vario us s ubstances (Mn p h o s ph o rs , uranyl c o m po u n d s, u r a n i u m g l a s s e s ) ' , Dokl. Akad. Nauk S. S. S . R . , 59, 235 . T O LSTO I , N . A . a n d F E O F I L O V , P . P . ( 1 952) ' E m i s s i o n spectr u m and de c a y of ruby', Dokl. A kad. Nauk S. S. S. R., 85, 5 5 1 . T O LSTO I , N . A . ( 1 9 56) ' Q u el q ues methodes et r e sul ta t s de l'etude c i ne tiq ue de la luminescence et de la photoconductibilite', J. Phys. J A BLONS K I ,
R . W . ( 1 92 1 ) 'The time interval between absorption and of light in fluorescence', Proc . Ray. Soc . , A 99, 362.
Rad. , 17, 80 1 .
Wooo ,
e mi ss i o n
Some referen ces
salts B ECQUEREL, J . (1 9 1 1 ) 'Sur la duree de la p h o s p h o res ce n ce des sels d ' uran yle' , Comptes-Rendus A cad. Se. Paris, 152, 5 1 1 . D ELORME, R . a n d PERRIN, F . (1 929) 'D urees d e fluorescence d es sels d ' ur anyl e soli des et d e I eu rs s ol u ti on s' , J. Phys. Rad. , 10, 1 77. H A L L , L . a n d DIEKE, G. H. ( 1 9 57) 'Fluorescent lifetimes of uranyl s al t s at different t e mp e r at u r e s ' , J. Opt. Soc. Am., 47, 1 092. L EWCHIN, V. L . ( 1 937) 'A s t u d y of absorption and luminescence spectra of u ranyl salts a n d their solutions', Acta Phys. Chim. U. S. S. R . , 6, 661 . L E W CH I N , V . L . , G UTAN, V . B . and K A R Z H A V I N A , E . N . ( 1 959) 'On the possibility of re c ombi n at io n processes in t h e luminescence of tungstate a n d u ra n yl c o m p o u n d s ' , Optika i Spektr. , 6, 372 ; Optics and Spectr. , 6, 234. V A V ILOV , S . I. and LE W C H I N , V . L. ( 1 928) 'Studien zur K en n tn is on the decay of uranyl
Electron traps, Phosphorescence, Thermoluminescence
der Natur der
48, 397.
Photolumineszenz von
1 79
U ran y l s a lz en ' , Z. fur Phys.,
The decay of manganese-activated phosphors F o N D A , G . R . (1 939) 'Characteristics of silicate phosphors', J. Phys. Chem., 43, 561 . G E R GELY , G Y . ( 1 950) 'Rise and decay of w i l l em i te l u minescence' , J. Op t . Soc. Am., 40, 3 56. J O H N S O N , P . D. (1939) 'Decay of willemite and ZnS phosphors', Phys. R ev , 55, 8 8 1 . K R O G E R , F . A . a n d H O O G E NSTRAATE N , W. ( 1 948) 'Decay and qu e n chi n g of fl u o re s ce n ce in willemite', Physica, 14, 425 . L E V I AL D I , A . a n d L U Z Z A T I , V . (1 947) ' S u r un s il i cate de cadmi u m l u m i n escen t ' J. Phys. Rad., 8, 306, 341 . L E W C H I N , V . L . and TUNITS K A I A , V . F . ( 1 960) 'The n a t u re and kinetics of r a d i at i o n processes in ZnS ( Mn) phosphors d ur i n g ex citation', Optika i Spektr., 9, 223 ; Optics and Spec t r . , 9, 1 1 8 . N A GY, E . ( 1 9 5 1 ) L u mi n e s ce nce phenomena in zinc sulphide phos phors', A cta Phys. Hung. , 2, 89. .
,
'
See also, in connection with traps in ZnS(Mn) phosphors LEW CHIN, V. L. a n d TUNITSKAIA , V . F. (1 960) 'Thermolumines cence and the localized levels of ZnS(Mn) phosphors', Optics and Spectr., 8, 350. Short-period fluorescence of ZnS phosphors (J0-7-J0-8 sec) B ITTMAN, L . , FURST, M . a n d KALLMANN, H. ( 1 9 52) 'Decay time, fluorescence efficiency and energy storage properties for various substances with y-ray and a:-particle excitation', Phys. Rev., 87, 8 3 . TREGUI E R , L . a n d KoECHL I N , Y . ( 1 9 59) 'Nouvelles etudes sur les proprietes phys i qu es des scintilateurs organiques et mineraux', R app or t C.E.A. DE/SE No. I 199-147. Experiments on the decay ofphosphorescent emission, in zinc sulph ide and other phosphors A N T O N O V - RO M A N O V S K Y , V . V. { 1 935) Abkli n g un g von Zink pho s p h o re n in einzelnen Krystallen', Phys. Z. Sow. Union, 7, 366. A N T O N OV - ROMANOVS K Y , V . V . (1937) 'Mesures quantitatives sur l a decroissance de la phosphorescence du phosphore ZnS a des temperatures diverses', Comptes-Rendus Acad. des Sciences, Moscou, 17, 95. · '
I 1\0
Luminescence
A N T O N O V - ROMA NOVSK Y , V . V .
in
Crystals
( 1 942) 'The m e c h a n i s m of l u m i nes 6, 1 20 ; 7, 1 53 . B L O K H I N Z E W , D . ( 1 937) ' D i e Ki netik d e r Phosphoreszenz', Phys . Z. Sow. Union, 12, 586. C U R I E , M . ( 1 9 3 5) ' S u r l a l o i hyperbolique d u declin de la phos ph orescence' , Comp tes-Rendus Acad. des Sciences Paris, 201 , 142. C U R I E , M . ( 1 9 3 6) ' S u r les t h e o ri es de la phosphorescence' , Comptes Rendus A cad. des Sciences Par is , 202, 75 1 . C u R I E , M . ( 1 939) ' Ph o sp h o resc e n t glasses . Decay o f p h osphores cence' , Trans. Fa raday Soc . , 35, 1 1 4. ELL I C KSON, R . T. a nd PARKER, W. L . ( 1 946) ' T h e decay of infra-red sensitive p h o s p h ors ' , Corneli Symposium, 327. Wi!ey, New York. F O N D A, G. R. ( 1 945) ' F ac t o rs affecting phosphorescence decay of the ZnS phosphors', TrailS. Electrochem. Soc., 87, 3 3 9 . D E G ROOT, W . ( 1 9 3 9 ) ' Lu m i nescence d e c a y a n d rel a t e d ph en o m e n a ' , Physica, 6, 275. D E G ROOT, W . ( 1 940) ' M is ce ll a n e o u s observations on the rise and d e ca y o f the l u mi n e scenc e of various p h os ph ors' , Physica, 7, 432. G U N T Z , A . ( 1 92 6 ) 'Sur le s u l fu re d e zi n c p ho s p h ores ce n t' , Ann. de Ch im . , 5, 1 57, 3 6 3 ; 6, 5. Thesis, Paris, 1 92 5 . K L A S E N S , H . A . and W I S E , M . E. ( 1 946) 'The decay of ZnS phos p h o rs ' , Nature, 158, 306. K U P P ENHEIM, H . ( 1 923) ' 0 ber die B es Ui n d i gkeit der Phosphor eszenzzentren', Ann. der Phys. , 70, 8 1 , 1 1 3 ; 72, 564. LENARD , P. and H A U S S E R , W . ( 1 9 1 2) ' 0 ber das Abklingen der P h o sph ore s zen z' , Heidelberg Ber. , 12. LE W C H I N , V. L. ( 1 9 3 6) ' Re ch e rch e s sur la decroissance de la lumi n e sce n ce et le mecanisme d'emissi on de differentes substances', Acta Phys. Polonica, 5, 30 1 . L E W C H I N . V . L . ( 1 9 5 6) ' Influence sur la l o i d e declin de la phos p h o rescence de !'existence d e plusieurs s ys te m e s de pieges et d u phcnomene d e recapture', J. Phys. Rad. , 1 7, 684. N I C H OLS, E. L . a n d M E R R I T T , E. ( 1 908) ' T h e phenomenon of phos p hore s c e nce considered from the s t andp o i n t of the dissociation t h e o ry ' , Phys. Rev., 27, 367. S A D D Y , J. ( 1 9 47 ) 'Contributions a !' etu d e de la photoluminescence du sulfure de zinc', Ann. de Phys., 2, 4 1 4. Thesis, Paris, 1 946. S CHLEED E , A. ( 1 943) Der An- und A bklingverlauf und die Licht ausbeute in A bhiingigkeit \'Oil Erregung und A bsorption. M u n ic h . cen ce of phosphors', Journal of Phys., U.S. S. R.,
Electron traps, Phosphorescence, Thermolum inescencc
U RDACH, F. , HEMMENDINGER, asymptotic
behaviour
SrS(Ce, S m ) ' ,
H . and P E A R LM A N ,
of s pon t a neo u s
J. Opt. Soc. Am.,
39,
675.
and
D.
fo rced
IRI
( 1 949) 'The d ecay
of
On Adirowitch's theory and Becquerel's fo rm ula (1 953) Einige Fragen zur Theorie der Lumineszenz der Kristalle, 1 1 9-86. Akad cmie-Verlag, Berl i n . A D I ROWITCH, E . I . (1 956) ' L a formule de B ecq u e r e l e t l a l o i elemen taire du d e c l i n de la l u minescence des p ho s p h o re s c ri sta l l i n s ' , J. Phys. Rad. , 11, 705 . A NTONOV- ROM A NO VS K Y , V . V. ( 1 9 56) - Discuss i o n of t h e above A D I RO W I T C H , E . I .
paper.
C URIE, M. (1 956) - Dis c u s si on of the above paper. G UNTZ, A . (1 926) 'Sur le sulfure d e zinc phosphorescent' . Thesis, Paris,
1 18.
VERGUNAS, F . I . ( 1 9 56) ' Decay law o f zinc sulphide phosp h o rs i n the nei gh b ou rh o o d of th e thermal quenching temperature i n terval ' , Optika i Spektr., 1, 4 1 6.
On Schon's theory of luminescence transitions R . (1952) ' Dber die m i t Phosphor eszenz verk n ii p fte Le i t fah i gkei t v o n CdS-Einkristallen ' , Z. fur Phys., 1 33, 340. B R OS E R , J. and B ROSER· W A R MI NS K Y , R . ( 1 955) ' Luminescence a n d electrical c o nd uctiv i ty of cryst al ph o s ph o rs ' , British J. Appl. Phys. , 6, Supp l. 4, S 90. Duuoc, C . A. (1 955) ' Non-li n ea ri ty in photoco n d u c t i n g p h o s p h o rs ' , Brit ish J . Appl. Phys., 6, Suppl. 4, S 1 07. M osER, F . an d URBACH, F. ( 1 957) ' Lumine s ce n ce of silver bro m o iodide crystals', Phys. Rev., 106, 852. S cH O N , M . ( 1 9 5 1 ) ' O ber die Strahlungslosen Ubergange in Sulfid p hosp h oren ' , Z . Nat urfo rsch . , 6a, 25 1 . S CHON, M . ( 1 954) 'Photoleitung und Lu m i n e s z e n z i n Kristal len d e r ZnS-Gruppe', Physica, 20, 930. B R O SE R , I . and WARMINS K Y ,
On
the complexity of the mechanism ofphosphorescence (superposition of 'monomolecular' and 'bimolecular' k inetics , or 'multimolecular'
mechanism)
CURIE, M . and C U R I E , D . (1956) Questions actue!les en luminescence crista/line, 48. R evu e d'Optique, Paris. 0
1 82
Luminescence in Crystals
(1 956) 'Etude theorique et experimentale de quelques pro prietes des pieges a electrons et des centres luminogenes dans les sulfures', J. Phys . Rad., 17, 699.
C U RI E , D .
H. A. ( 1 9 5 1 ) ·some remarks and questions on the mech anism of phosphorescence', Co mm . Heidelberg-Mosbach Sym posium, 7-9 July 195 1 . NAIL, N . R . , PEARLM A N , D . a n d U R B A C H , F . (1 946) 'Photolumi nescence of some sulphide phosp h ors as a function o f intensity', Cornell Symposium , 1 93. W i l ey , New York. WISE, M. E. ( 1 95 1) 'Free electrons, traps and glow in c rys t a l ph os phors', Plzysica, 17, 1 0 1 1 . See also : PRIMA K , W. (1 955) 'Kinetics of processes distributed in activation energy', Phys. Rev., 1 00, 1 677. S H O C K L E Y , W. and B A RDEEN, J. ( 1 9 50) 'Energy bands and mobili ties in monoatomic semicond uctors', Phys. Rev., 77, 407. K LASENS ,
Computation of the trap distribution by means of the experimentally observed decay law l(t) or S(t) C U R I E , D . (1 949) 'Sur la distribution des pieges a electrons dans les sulfures de zinc et de calcium', Comptes-Rendus A cad. Se. Paris, 229, 1 93. C UR I E , D . (1 949) ' In te rp ret at i on des courbes experimentales de d ecl i n de la phosphorescence des sulfures', Comptes-Rendus A cad. Se. Paris, 229, 1 321 . CURIE, D . (1952) 'Capture et recapture electroniques en phosphores cence', A nn . de Phys., 7, 749. Thesis, Paris, 1 95 1 .
R . (1 928) 'Handbuch der experimental Phys i k, Phosphoreszenz-Fluoreszenz', 1 1 6-20, 1 251 3 1 , 1 87-9. N A Z A R I A N , G . M . (1952) 'The determination of electron trap dis tributions from phosphorescence decay measurements', J. Opt. So c . Am., 42, 288 . R A N D A L L , J . T . and W I L K I N S , M . H . F . ( 1 945) 'Phosphorescence and electron traps', Proc. Roy. Soc., A 184, 366. S A D D Y , J . (1947) ' C o n t ri b u ti ons a !' e t u d e de la photoluminescence du sulfure de zinc', Ann. de Phys., 2, 4 1 4. Thesis, Paris, 1 946. S A D D Y , J. (1 959) 'Sur le declin d e la phosphorescence d es s ulfu res
LENARD , P . , S CHMIDT, F . , TOM A S C H E K ,
de zinc', J.
Phys. Rad. , 20,
890.
Electron traps, Phosphorescence, Thermo luminescence
1 83
Evidence for recapture phenomena in phosphors C U R I E , D . ( 1 950) R e m arq u e s sur le mecanisme de la phosphores cence d a ns l e s c ri staux , J. de Phys . , 11, 1 79. CURIE, D. (1 950) 'Preuves e xp erim e n tale s d e la recapture elec tro n i que dans les sulfures ph o sph o res ce nts cristallins', Comptes Rendus Acad. Se . Paris, 230, 1400. G A R L I C K , G. F. J. ( 1 946) 'Some studies of electron traps in phos phors', Corn ell Symposium, 87. Wiley, New York . G A R L I C K , G . F . J . a n d G I BS ON , A . F . ( 1 948) 'The electron trap m ec h an i s m of lumi nescence i n s u l ph i d e and s i l icate phosphors', Proc. Phys. So c . , A 160, 587. LEWCH I N , V . L . (1 948-56) 'Influence s u r la loi de declin d e la p h o s phorescence de !'existence de plusieurs sy ste me s de pieges et du pb e n o mene de rec apt u re , J. Exp. Theor. Phys. U. S.S. R., 18, 82, 1 49 ; J. Phys. Rad. , 17, 684. M A T T L E R , J. a n d C U R I E , D. (1950) 'Comportement des p i e ge s a ele c tro n s dans les p h e n o m e n e s d'electroph otol umi nescence' ' Comptes-Rendus Acad. Se. Paris, 230, 2086. '
'
'
Ill. On the study of trap distribution by means of the glow curvest
Development of th e method K AT Z , M . L . (1 954) Ouspiekni Fizitch . Nauk, 52, 660 (n u m e ro u s re fe re n ces). R AN D A L L , J . T . and WILK I N S , M. H . F. (1 945) 'Phosph o rescence and electron traps', Proc. Roy. Soc. , A 184, 366. U R B A C H , F. (1 930) 'Zur Lu mi nes ze n z der Alkalihalogenide', Wiener Ber., ITa, 139, 363. URBACH, F . (1 946) 'Storage and release of light by phosph o rs', Cornell Symposium, 1 1 5. Wiley, New York. More recent work BOHUN, A . ( 1 954) 'Thermoemission u n d P h o toem iss i o n von Na triumchlorid', Czechosl. J. Phys . , 4, 9 1 . B O O T H , A . H . ( 1 9 54) 'Calculation o f e l ec tro n trap depths from t h erm ol u m i n escen ce maxima', Canad. J. Phys . , 32, 214. C U R I E , G . and CURIE , D . : (1955) 'Sur la d e term i n a ti o n des t Here are given only references of papers concern i ng the gl ow cu rve method . results on t rap d i s t r i b u t i o n s i n a part i cular phosphor, see §IV.
For t h e
1 84
Lum inescen ce in Crystals
p r o fo n d e u rs des pieges a e l e c t r o n s p a r thc r m o l u m i nesce nce', J.
Phys. Rad. , 16, 1 99. C U R I E , G. an d CURIE, D. ( 1 9 6 0) 'A n u meri ca l t a b l e for c o m p u tation o f trap d e p th s by the thermoluminescence experim e n t ' S p ri n g M eeting, The Electroche m . S o c . , Ch i ca g o 1 -5 May 1 960. H A A K E , C. H. ( 1 957) ' Critical com ment on a method for d eterm i n i n g el ectron trap d ep t h s , J. Opt. Soc. A m 47, 649. H ALPERI N , A . a n d B R A N E R , A . A . ( 1 960) ' Eval uation of thermal a ct iv at i o n e n e rgi es fr o m g l ow cu rv e s , Phys. Re v . , 1 1 7, 408 . ,
,
'
. ,
'
LOUCHTCHT K , Tech . ( 1 955) ' Crystal loph o s p h o rs ' , 1 7- 8 8 .
Acad. Fiz. and Astronomy, Tartou.
LOUCHTCH I K , Tech . a n d Z A I T O V , relaxation processes
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F. N. ( 1 958) 'On t h e k i netics !ss!. po Lumin.,
crystal phosp h o rs',
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A . ( 1 954) 'The determ ination of the d ep th o f electro n traps i n crystal phosph o rs ' , J. Exp. Theor. Phys. S. S. S. R . , 26, 696. S c H O N , M . ( 1 9 5 1 ) 'Bemerku ngen zu r A uswertu ng der G l ow-Ku rven von Kristallphosphoren', Naturwiss . , 10, 23 5 . S c H O N , M . ( 1 9 58) B e m e r k u n ge n zu r T h e o ri e d e r Glow-Kurven',
P A RF ! A N O V I T C H , J .
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W RZESI N S K A ,
On
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' themwstimulated current curves'
S . and V O I G T , J . ( 1 958) '0ber die Auswertung von Leitfahigkeitsglowkurven', A nn. der Phys., 2,
B OER, K. W . , 0BERL ANDER,
1 30.
B RO S E R , J.
a n d W A R M ! N S K Y , R. ( 1 952) ' 0 ber die mit Phosphor eszenz v e rk niipft e elektrische Le i t fa h igk ei t von Cds-Ei nkri stal len', Z. fiir Phys. , 133, 340. B R O S E R , I . and BROSER- W A R M I N S K Y , R . ( 1 9 55) 'Luminescence and electrical c o n d u ct ivity o f crystal p h o s p h o rs', British J. App!. Phys. , 6 , Suppl. 4 , S 90, B u s E , R . H . ( 1 95 1 ) 'A c o m p a ra t i v e s t u d y of p h o t o c o n d uc t ivity a n d l u m i n e s ce n c e ' , Ph rs. R e i ' . . 8.1, :1 9 .1 .
Electron traps, Phosphorescence, Thermoluminescence
B UBE, R . H.
tel l u ride
( 1 955)
1 85
' P h o toco n d uctivity of t h e s u l p h i d e , se l e n i d e a n d
of zi n c or
cad m i u m ' , Pro c . l. R . E. , 43, 1 8 3 6 .
CURIE, G . and CURIE, D .
( 1 9 5 4)
( 1 9 60) l o c . cit.
'Photocond uctivity i n phosph o r s ' , Report No . NR-015-207. Un i ve rs i ty of B ro o k l yn . G ARLICK, G . F. J . a n d G IBSON, A . F . ( 1 947) ' El ect ro n traps and D RO P K I N , J. J .
dielectric ch a n ge s in phosphorescent s o l id s ' , Proc. Roy. Soc., A
188, 485.
R. C . and M E Y E R , C . F . ( 1 946) 'Therm o l u m i n escence and cond uctivi ty o f phosphors', J. App l. Phys. , 1 7, 743 .
H ERMAN,
On the 'exo-electron emission glo w curve' A . ( 1 9 5 4) 'Em ission aus n ic h t m eta l l i s c h e n K ristallen' , Czechosl. J. Phys. , 4, 2. BOHU N , A. ( 1 956) ' D i e Exoelektronen Emission von Ront g en bestrah l tc n S u l fi d c n ' , Czechosl. J. Phys., 6, 628. B o H U N , A. a n d DoLES K I , J. ( 1 9 5 9) ' D i e Exoel ektronen und Therm o elektronen E m i ss i o n b c i ei nige n Haloge n i d e n ' , Czechos!. J . Phys. ,
BOHU N ,
9, 578.
HANLE, W . ( 1 9 5 7 ) 'Exoelektronenemission und Phys. A ustria ca , 10, 339.
L u m i n e s ze n z ' , A c t a
K R A M E R , J. ( 1 957) ' Ex o e le k t r o n e n nach Bestra h l u nge n ' , A ustriaca, 1 0,
LINTNER, K.
327.
( 1 9 5 7)
A ustriaca, 10, 3 1 5 .
' D as P r o bl e m
der Exo e l ek t r o n en ' ,
A ::ta Phys . A cta Phys.
IV. Trap depths in different phosphors
ZnS(Cu) BUBE, R . H . ( 1 9 50) 'Luminescence and t rapp i n g in zinc s u l p hi d e pho s p ho rs with a n d wi t h o ut copper activato r', Phys. Rev., 80, 655 .
R . H . ( 1 953) ' El ectro n i c transitions in t h e l u m i n escence o f ZnS p h o sp h o rs ' , Phys . Rev . , 90, 70. C U R I E , D. ( 1 952) 'Capture et recapture electroniques en p:1 o sphor esce n ce ' , 1 5, 25, 4 3 -4 . Thesis, Pa ri s . G A R LI C K , G . F. J. ( 1 946) 'Some studies of e l ect r on traps in p h o s phors', Camel! Symposium, 1 08-9 . Wiley, New York. G n . LSO N , J. L . ( 1 9 5 4) ' S o m e p rop e r t ies of electro n traps i n a Zn S(Cu) phosp h o r', .!. Opt. Soc. A m . , 44, 3 4 1 . B U BE,
1 86
phors', J.
Luminescence in Crystals
H O O G E N ST R A A T E N , W .
( 1 9 5 3) 'The chemistry of Soc., 100, 356.
traps in
ZnS phos
W. (1958) 'Electron traps in zinc sulphide phos phors', Thesis, Amsterdam. J O U K O V A , H . V . (1952) 'Influence of the fusible a d d i t i o n on traps in ZnS(Cu)', Dokl. Akad. Nauk S.S. S. R., 85, 1 8 1 . M ARTIN, W . ( 1 957) 'Beeinfiiissung der Lumineszenzeigenschaften von P ho sp h o ren durch H2 +-I o n en , Z. fiir Phys., 147, 582. SMITH, A. W . and TURKEY! CH, J . ( 1 95 2) ' A study of electron traps in ZnS phosphors', Phys. Rev., 87, 306. W A L LI C K , G. C. ( 1 9 5 1 ) 'Size effect in the lumi nescence of ZnS phos ph o rs , Phys . Rev., 84, 375. Electrochem .
H oo GENSTRAATEN,
'
'
On the model for t h e traps which is described in t h e text CURIE, D. (1956) 'Niveaux d'impurete dans les cristaux (mode!e
hydrogenoide)', J. Phys. Rad. , 17, 1 6. ( 1 957) 'Modeles pour Ies divers types de pieges dans le sulfure de zinc phosphorescent. Liberation thermique et optique des electrons pieges', J. Phys. Rad. , 1 8, 2 1 4. C UR I E , G . , ARPIARIAN, N . , G U ERE T , P . and C U R I E, D . ( 1 960) 'On the hyd ro gen l ike model for traps in zinc sulphide', Spring Meeting, The Electrochem. Soc., Chicago, 1 -5 M ay 1 960.
C U RI E , D .
-
and 0 R T M A N N , H . (1 955) ' O ber Elektronen-Anlagerungs geringer energetischer Tiefe in Zinksulfid', Z. Natur forsch., lOa, 896.
Very shallow traps in zinc sulphide
stellen
RIEHL, N .
sehr
'Contribution a !'etude de la stimulation de la par !'i nfra-ro uge', Ann. de Phys., 15, 388. LEW C H I N , V . L . and 0RLOV, B . M . ( 1 959) 'Investigation of the thermal activation energy ofph o t o s ti m u l a t ed flashes i n ZnS(C u , Pb) phosphors', Optics and Spec tr , 1, 330.
ZnS(Cu,
Pb)
C U R I E , G . ( 1 960)
phosphorescence
.
ZnS(Cu, Co) H A A K E , C . H . (1957) 'Critical comment on a method for determining
electron trap depths', J. Opt. Soc. A m . , 47, 649. W. and K L A S E N S , H . A . ( 1 953) 'Some pro-
H OO G E NSTRA ATEN,
Electron traps, Phosphorescence, Thermoluminescence
perties o f zinc sulphide activated with copper and cobalt', J. Elec 187
trochem. Soc., 100, 366. L . and TUNITSKAIA , V . F . ( 1 9 57) ' The influence of the wavelength of exci ting l i ght and the nature of trapping levels in Zn S (C u , Co) phosphors on trappi ng level occupation', Optika i Spektr. , 2, 350.
LEW C H I N , V .
0BERLANDER, S . and V O I GT, J . ( 1 958) ' 0 ber die Auswertung von Leitfahigkeitsglowkurven', Ann. der Phys . , 2, 1 30 . B R O SER , I . and W A R M I N S K Y , R . ( 1 952) ' 0 ber die mi t Phosp h or eszenz verkniipfte elek tri sch e Le i tfiihi gk e i t von Cad miu msulfid k ri stalle n ' , Z. fur Phys . , 1 33, 340. B U B E , R. H. (1 955) 'Photoconductivity and crystal i m perfect i ons in cad mi um sulphide crystals', J. Chem. Phys., 23, 1 8 .
CdS
B O ER , K . W . ,
P . , S C HMIDT, F. and TOMAS CHE K , R . (1 928) 'Phos phoreszenz-Fluoreszenz', Hand. der exper. Phys. , 1 1 6-20, 1 2 5-3 1 .
CaS(Bi)
LENAR D ,
( 1 944) M inistry of Home S ecurity Report, R.C.C. 1 1 9. Work described in GARLI C K , G. F . J . ( 1 949) Luminescent materials, 7 1 -6. Clarendon Press , Oxford . W R Z ES I N S K A , A . ( 1 956) 'Impurity-activated crystalline phosphors. Their production and thermolurninescence curves', A cta Phys. Polonica, 15, 1 5 1 .
1 87-9.
WELL S , A . F.
L E W C H I N , V . L . and FAIZI, N. K . ( 1 960) ' I n v e sti gation of the e n ergy of thermal activation of the flash and of trapping levels in C a S phosphors', Optics and Spectr. , 8, 458. CaS(Cu) and CaS(Sm) p!wsphors
Number of traps in zinc, cadmium or calcium sulphide phosphors C U R I E , D . ( 1 952) ' Li bres parcours des electrons dans les cristaux,
effets d'electroluminescence et phenomenes de rupture dielec tri que ' , J. Phys. Rad., 13, 3 1 7. K A L L M A N N , H. and S PRU CH , G . M . (1 9 56) 'Number of traps and behaviour of excited electrons in luminescent materi al s', Phys. H . and
Rev., 103, 94.
CdS phosphors', Phys. Rev.,
K ALLMANN,
S ucov, E .
(1 958) ' Ene rgy storage in ZnS and
109,
1 473 .
KC!(TI)
B U N GE R , W .
a nd
Z.
W . ( 1 93 1 ) ' 0 b e r d ie A b k li n g u ng eines TI Z u s at z u n d i h re Tcmperatu rabhangigkei t ' ,
FLECHSIG,
KC! P h o s p h o rs m i t
fur Phys., 67, 42.
E w L E s , J . and J o s H I , R . V .
( 1 960)
a c t i va ted p o tassi u m ch l o ride
'The l u mi n escence of thallium
p h o s p ho rs ' , Proc. Roy. Soc., A 254,
] O H N S O N , P . D . a n d W I LL I A M S , F . E. ( I 953) ' E lec tr o n traps i n the thalliu m-act ivated p o tas s i um chloride ph os p h or ' , J. Chem . Phys. , 2 1 , I 25. P R I N GS H E I M , P . ( 1 942) 'Fluorescence a n d pho sphore s c e n c e o f t h alli u m -act: vated p otas si u m h a l i d e p h o s ph o rs ' , Rev. Mod. Phys. , 14, I 3 2 . S E J T Z , F . ( 1 939) ' A n i n t e rp ret a t i o n of crystal l u m i n escen ce ' , Trans. Farada r Soc. , 35, 79. 3 58 .
Tlzermoluminescence and bleaching of alkali h a !ides with colour centre B ONFI GLIOL I , G . , B R O V ETTO , P . and CORTESE, C. (1 959) 'F a n d V centres th e r m o l u m in e s c ent recombination', Phys. RetJ., 1 14, 95 1 , 956. H A LP E R I N , A . , B R A N E R , A . A . a n d A L E X A N D E R , E . ( 1 9 57) 'Thermo Iurninescence of X-ray coloured KC! si n gl e cry s t a l s ' , Phys . Rev., 1 08, 928, 932. H A LPER I N , A . and K R I ST I A N P O L LE R , N. ( I 958) 'Thermolumines cen ce spectra of X - r ay col oured KC! c ry s tal s ' , J. Opt. Soc. Am. , 48, 996. H A LP ER I N , A . , K R I S T I A N P O L L E R , N. and B E N - Z V I , A. ( 1 9 59) 'Tbermoluminescence of X-ray colou red NaCI cry s t a l s ' , Phys. Rev., 1 1 6, l C18 l . L o u cHTCH I K , T e ch . ( 1 956) ' I n ves ti ga tio n of t h e capture centres in c rys tal s by tr.ermal irrad iation', J. exp. Teor. Fiz. S.S.S.R., 30, 488. P A R FI A N O V I T C H , I . A. ( 1 957) 'On the energy of thermal ionization of t ra ppi n g centres in a l kali h a l ide p h os p h o rs ' , Optika i Spektr. , 2, 592. P R I N GS H E I M , P. a n d YUSTE R , P. ( 1 950) 'Absorption bands and l uminescence o f Li F irrad i a te d at low temperatures', Phys. Rev. , 7 8 , 293 . S H A R M A , J . ( 1 952) ' C o l o u r centres a n d thermoluminescence in alkali h a l i des', Phys. Rev . , 85, 692.
l. f C C / 1 () I J l J
UjJ.) ,
1
I L U.JjJ/l() / C'.) (. t.:/ i L. C ,
1 l l l.; l l l l U i i-U f l l l l t . ) l. L I I L L
J
U/
S H A R M A , J . ( 1 9 56) 'Thermoluminescence properties o f some alkali halides', Phys. Rev., 101, 1 295.
Bleaching of infra-red absorption bands in CdS
H A L P E R I N , A . and G A R L I C K , G . F . J . ( 1 955) 'The absorption s pec
trum o f excited crystals of cadmium sulphide', Proc. Phys. Soc. ,
B 68, 758.
CHAPTER V I I
Thermal and Optical Activation of
Trapped Electrons: Quenching Effects
I.
T R A P S , T H E R M A L A CT I V A T I O N A N D O P T I C A L STI M U LATI O N I N THE CONFI G U RATI ONA L C O O R D I NA T E M O D E L
1 . Description of the escape from traps This type of model is particularly applicable when t rapp i n g p rocesse<; are confined toge th e r with luminescence transitions within an atomic or ionic activator centre : the example of KCI(Tl) has already been q uoted. The energy of t h e trapping state in interaction with the lattice is given by a configu rational coord inate curve o/!U(r) when the system is in the ground state and by o/t•(r) when i t is raised into the short lined excited state from which a luminescence transition may take place. We can also employ a configurational diagram when the electrons escaping from traps enter the cond uction ban d . Certain difficulties met with in studying the capture cross-sections of traps suggest the assumption that capture and subsequent activation involve the transi tion through a very shallow level. In this case 1'17!0(r) applies to the ground state and %-•(r) to the shallow excited level and the re is no p r oblem in applying the configurational coordinate m o d el If, on the other hand, the emptying of traps raises the electron directly into the conduction band, fo llo wi ng R. Kubo we can use %-•(r) to denote the potential energy of the system 'trap + lattice' when the e lect ro n h a s just left the trap and is in the cond uction band. The 'ionization continuum' is then given by all the energies l y i n g above the curve. The calculations made by Kubo show that the thermal activation from %'U(r) to %-•(r) can occur in two different ways : A t high temperatures t h e activation can be treated classically. If T is the intersection point of the two curves ct!g(r) and U?t•(r) (see Fig. VIT . l ), then to obtain the escape from the t rap, T must be reached .
1 90
191
Thermal and optical activation
from the minimum A . This necessitates an energy Er, which is equal to the height of th e p o i n t T above A.
Actually the two curves u
d o not cross at
T but come very close to
ro
Fig. V I I . l Escape of trapped electron described
in terms
of the configurational coordinate model E0 : thermal activation energy for escape from trap low temperatures Er: thermal activation energy at high temperatures hv: optical activation energy
..
at
each o th er This is because two levels approaching eac h other prod uce a mutual perturbation inversely p r o p o rtio na l to their distance apart (see Fi g VII.2). However, no di ffic u lty i s raised : the p o i n t T corre-
ul.
Fig. VII.2
, .
r
sponds to a very high state of ionic vi brati o n the wave functions having a mp l i tu d es approaching the classical am plitu d e Near T the t ransit ion fro m one cu rve to the other has a high p robability.
If we n o w use the express i o n of W i l l i a m s a n d Ey ring fo r t h e probabi l i ty p fo r escape from a trap, i .e.
e AS/k e - ET/k2' we have x little different from unity. Unless the en t r o py /:S of activation is abnormally l a rg e , p = s e - ET/kT, with s o n l y a li ttl e different from the thermal vibration fre quencies, � 1 0 1 3 sec- 1, according to this mechanism . A t low temp eratures acti vatio n takes place by the s mal les t p os s i b le energy, i.e. to B (Fig. VII. l ) , w hic h has t h e same value at the min i mum 0 of t h e curve for the excited state. Transition fro m B to 0 can then take place by a tunnel effect. The necessary activation energy is then only E0, the height of the min im u m 0 above A, and is smaller t h an that above (ET) . However, the trans mission coefficient x is now small compared to unity. In th i s case the probability of e s ca pe is given by p
with
s0 now m uch
=
s m a l ler
p
Xl't
=
So e -
f:,/!·2"
than thermal vibration frequencies. After
p re v i o u s l y this would seem to be the case for ZnS , CaS and KC!(Tl), o rd in ary temperature being what we have called a ' l ow temperature' above, while the 'high temperature' con d itions may a pp l y to the traps in germanium and silicon as explored by Haynes and Lax. what has been discussed
2.
Optical activation energies
A ccord i n g to the Franck-Co n d o n p r i n c i p l e the escape from a trap effected by absorption of a quantum lzv equal in energy to the ve r tical distance AB' of th e curves in Fig. VII. l . If the level "l/�(r) is localized, there will be an ab s orp tio n band in the spectrum at fre
is
quency v. If this level is, however, the bottom of the conduction band ,
t h e n absor p tio n will occur for all frequencies greater t h a n v, hence a wide band with a t hre sho l d around the value l'. hv is the optical ionization energy of the trap w h i l e E0 (or ET) is th e
thermal activation energy.
If the two curves of Fig. VII. l have a relative d i sp l acem e n t r0, then E0• It follows that in an ionic crystal the optical activation is, as a general rule, g r e a te r than the thermal activation energy E0 (low temperature value). I n some cas es r0 is very small and the difference hY- E0 is very smal l . The d i spl a ce m e n t r0 is m o s t significant in ionic c rysta l s as seen fo r KCI (Tl) (page 38) a n d i t fo l l ows for mainly
hv >
electrostatic reas o n s . Overlap of i o n s is greater i n t h e e x c i ted s t a t e .
For a trap treated i n t erm s of a hy d ro gen l i k e model t h e same applies (cf. p age 1 66). The th e rm a l activation E0 occurs with rem o val of the Conduction ban d
hv L o ca lised !e v e !
Fig. VII.3 Thermal ionization energy E0 and optical energy hv in an ionic crystal
ionic polarization due to the trappe d el ectron , but in o p tica l activa tion the polarization does not have time to di s app e a r and the energy
hv - E0 is n o t recovered until later.t
In a covalent crystal the d i splacement r0 is rea l l y s m a l l if
I n th i s case the opt i c al activation process is to the u
not zero .
m i n i m u m 0 of <¥1 •
r
Fig . VII.4 Case of zero displacement between configura tional coordinate curves. Thermal activation energy the same as optical activation energy hv
E0 is
and hv E0• In contrast we cannot co m p a re hv a n d the 'high tem peratu re' thermal activation energy ET, and it is eas i ly seen that con figurational curves can be d rawn so that ET ca n be smaller o r great�r =
t h a n hv. Experimentally it is very difficult to relate a p a rticu l a r observed optical absorption band with a p a rt i c u l a r thermal act i v a t i o n energy t Except in th is chapter, where
make a distinction between Eo and Er, we
simply:denote the thermal act ivation energy by E, wh ich is o b t a i ned i n experi men t . we
Luminescence in Crystals
1 94
for trapped electro ns, and this is especially so when t h e re is ionization of the trapped electrons without an i n ter m e d i ate excited level tran sition. In this case v gi ves the threshold of the band and not its m aximum We give here so m e ex a mp l es : (i) For F ce nt re s in KC!, if the th e rm a l g l o w pea k at 620°K is due to em p tying of F centres, then In' = 2·3 eV ; E0 1 · 8 eV (ii) For the me ta s tabl e state 3P0 of thallium i n K C I , for which E0 0·67 eV, the optical activation energy is a pp ro x i m ate l y given by a stimulation band at 1 · 1 5 ft ( l ·07 eV) accord i ng to data from John son and Will iams. If the explanation of this band is correct, then hv 1 ·07 eV ; E0 0 6 7 eV The energy is t h at requ i red to raise the Tl + ion from the trapping state to the e x c i ted state 3P1 • With an energy of 4 to 5 eV (2, 500 A excitation), the trapped electrons may be liberated into the cond uc tion band of the KC! crystal. Experi mentall y F centres are th en found which indicates a transit of electrons through the conduction band . (i ii ) In ZnS(Ag) phosph ors Lambe and Klick h ave shown the exi st e n ce at liquid air temperature of a stimulation band at 2·6 p (0·47 eV). It is tempting to suggest a correlation between th i s band and the most im portant groups of traps wi t h E = 0·28 eV, i.e. _ hv 0· 47 eV ; E0 0 28 eV However, no stimulation band is found to correlate with the groups at 0· 50, 0·57, 0·65 and 0·72 eV, &c., which occur in ZnS(Cu). Wh a t is observed is a broad stimulation band in the infra red at about 1 · 3 fl (0·96 eV). The difference between the optical and therm al d epth s has th e right sign, however, the photon activation of the trapped elec trons is not likely to be the result of a d irect photon abso rption in the traps but rather of an absorp tion transition involving other levels in the phosphor, followed by an energy trans fer This pr obl em is st i l l u n der discussion. (iv) In ger m a niu m , which is not an ionic crystal, the optical and thermal activation energies of do n or l evel s (h yd roge n l ike) are very close in value. Th ey are a little less so in silicon. Picus, Bu rstein and H e nvis give for i mp uri t i es P, As and Sb in silicon : .
=
=
=
=
·
,
=
=
·
.
Eo (eV) /lv (eV)
P
0·045 0·050
As
0·049 0·05 3
Sb
0·039 0·04?
1 95
Thermal and optical activation
(v) Urbach cites a case where the difference is small, although it involves an ionic crystal (perhaps r0 is very small). In the high ly stimulable phosphors SrS(Eu, Sm) the infra-red stimulation is sensi tized by Sm, giving a band with a maximum at 1 ·02 f-l ( 1 ·2 eV), which also gives a deep trap having a glo w peak at 650°K. This corresponds to a thermal activation energy of about 1 ·2 eV, the experimental accuracy n ot being great enough to establish the exact identity be· tween the two val ues or in which sense the difference might exist. 3.
Description of effects shown by the highly stimulable alkaline earth sulphides (containing two activator impurities)
The sulphides concerned are of the type
The host material can be CaS, SrSe, &c. Europium or ceri um can be replaced by manganese or copper while samarium may be replaced S rS(Eu, Sm) ;
SrS(Ce, Sm)
by bismuth.
cerium, yellow for manganese an d orange-red for europium, these bein g known as th e principal or dominant activators. The secondary activator samarium gives an orange-red band which is thus usually obscured by the emission of the first activator. The effects are particularly striking in the case of S rS(Ce, Sm) be cause of the m arked difference in colour of the emissions of the two activators. We shall describe them in some detail . The usual emission under ultra-violet excitation is the green for
The green emission shows little persistence and during t h e decay a feeble orange-red emission is also seen. As in decay, the thermo luminescence is green for the shallower traps and o r ange red for the deep traps, i.e. at higher temperatures ; this indicates that the deep traps are introduced by the samarium. The stimulability of the phosphor is due to the samarium, which is thus called a sensitizer. It is shown by stimulation spectra (see Fig. VII. 5) that the spectrum is characteristic of samarium and indepen dent of the particular dominant activator. The stimulation spectrum is the curve which shows the maximum value reached by the emission intensity h. during the stimulation pro cess as a function of the wavelength (.A) of the stimulating infra-red radiation. However, the colour of the stimulated emissio n is charac te ristic o f the princi p al acti vato r. The g ree n cerium e m i ssion agam -
m a s k s t h e o ra n ge-red emission of the samari u m . The effect has
m i l i tary a p p l i c a t i o n s ( i n fra- red sign a l l i n g a n d i m age converters) . For
this
t h e S r S ( E u , S m ) p h o s p h o r is used
because the green emissi o n of
S rS(Ce, Sm) i s too easily seen at a d i s tance
the light e mi s s i on from the act i most conveniently d escri b e d as o ccurrin g be
Th e tran sitions r e spon s i b l e for
vators are probably
.
tween l evels of the activator i o n s . T h i s is at least true for the ground
s t ate. The excited l evel is very shall ow with re s p ec t to th e conduction band . The
luminescence processes in these
p h o s p h ors are accom
panied by photoconduction p h en o me n a and the ce n t r es are ionized
(Keller and Pet t i t) .
T h e un excited ceri u m and sama ri u m i o n s occu r in t h e pho s p h or a s 1-;.
•
+
l
07
0·8
0·9
1·0
1·1
_ _._ _ �-" --•---
Fig. VII . 5
Eu Ce
- ---1 2
-'-
1·3
14
"--'-
A. (microns)
Stimulation spectra of SrS(Eu, Sm) and SrS(Ce, Sm)
(After B. O'Brien)
Ce3 + a n d Sm 3 + which is the u s u a l v a l en cy state for rare earths.
The
n e u t ra l ceri u m a to m has the followin g el e ctron i c configuration : Ce : and the t ri v ale n t i o n :
.
.
.
4f 1 5s2 5p6 5 d1 6s2
4/ 1 5s2 5p6 The fun d amental state of Ce3 + is t h e doublet 2Fo;2, 2F1;2. whose s e p ar a t i o n is a b out 0 · 20 eV ( K rog e r and Bakker). T h i s doublet l e ad s Ce3 + :
.
.
.
to a d o u bl e p e ake d e m i ssio n s p e ctru m . t -
On the o t h e r hand , the europium atom , wh ich
rare earth series,
might
Eu :
have the c on fi guratio n : .
.
.
4/6 5s2 5p 6 5d 1 6s2
t Th e crystal field spl i t t i n g
of
is the
sixth in t h e
the levels is probably smal ler.
but in fact the stabi lity is higher if the 4f sh e l l is hal f-fil led with 7 electrons and the internal ion is th us d ivalen t : Eu 3 + : . . . 4f6 ( b a sic level 7 F0) Eu 2 + : . . . 4f 7 • • • (basic level 8S,1z) Paramagnetic resonance experiments show that indeed in the SrS phosphors cerium occurs as Ce3 + and eu ropium as Eu 2 + (W. Low) . Experiments by A ntonov-Romanovsky, Dubinin and Trapeznikova support the conclusio n that the Eu 2 + ions are ionized d u ring the excitation. For Eu 2 + the observation of p a ra m agn e tic resonance ab sorption can be made at room temperature since the relaxati on times in an S-state are rather large, while Ce3 + and SmH give paramagnetic resonance only at low temperatures and Eu 3 + is in the n o n -para magnetic state 7F0• As a result a decay of the intensity of the room •
�
� �
..c:,
1·20
•
•
Conduction band
sm++
_l_
3· 5 4
':u:' '
Con duction band � "'
F 712 ce«• ' 2 Fs/2
Va lence band
/
si
:u �
sm++
Sr S ! Ce , S m )
3 5 1.
: 2 10
__ e s 7/ 2 E u. .
Valence band
Sr S ! E u , S m l
Fig. VII . 6 Models for luminescence emission and infra red stimula tion in SrS(Ce, Sm) and SrS(Eu, Sm)
(From Keller,
Mapes and
Cheroj()
temperature paramagnetic resonance absorption is observed when the phosphor SrS(Eu, Sm) is excited by ultra-violet rad iation . The nature of the samarium trapping states is less well known . But we might accept the hypothesis of Keller, Mapes and Cheroff d e scribing it as a Sm3+ ion which has captured an electron (Sm 3 + -+ Sm2+) A ccording to these authors, the 1 -micron infra-red absorption leads to the ionization of the Sm trap and ejection of the electron into the conduction band followed by light emission from the activator ions. No perturbing or quenching phenomena occur under irrad i ation at this wavelength . T h e interpretation of stim ulation effects has raised several problems which are in sight of solutions. While samarium gives rise to the same stimulation band i n both SrS(Ce, Sm) and S r S (Eu , S m ) wi th a m a x i m u m a t 1 ·02 ;t , the
1 98
Luminescence in Crystals
th ermoluminescence peak observed at 650° K fo r the sulphide acti vated by e ur o pi u m is not observed for that activated by cerium. Instead , a shallower tra p occu rs , givi n g a p e ak at 420°K . W e might ask wh e ther there is any connection betwee n t h e o p ti ca l traps' (Sm l e ve l s ) res p o n s i ble for stimulation and the t h erma l traps' (levels resp o n s i ble for the thermal gl o w pea k s) It is simpler to assume that in both SrS( Ce , Sm) and SrS(Eu, S m ) phosphors the metastable l evel d u e to Sm is th e same but that thermal q u e n ch i ng masks the '
'
.
1 : r,
I I! i
I
Fig.
VII . 7
O. r· S (Ce, S ITl )
6 50
T (°K)
Thermoluminescence curves of SrS(Eu, and SrS(Ce, Sm) phosphors
Sm)
(After F. Urbach)
thermoluminescence peak at 650°K i n t h e first case but not in the �econd. The g ro un d state of Eu 3 + will be a b o v e the valence band at a heigh t near t o that for Ce3 +, but the ground state of Eu2 + will b e somewhat higher. T h u s a l arge activation energy will be re q u i red for freei n g of h ol e s in SrS (E u , Sm) than in SrS(Ce, S m) and so thermal qu e nchi n g (as shown b e l o w) will not occur u n t i l higher temperatures a re reached in t he former case.
The stimulation e fficie n cy of Zn S (Cu ) at room t em pe ratu re is rat h e r poor. However, evidence for the occurrence of a stimulation flash when an e xc i t e d ph o sp h or is submitted to an i n fra-re d irradiation has been given as e arly as in Lenard's wo rk The maximum of the st im u latio n spectrum is situated at 1 ·3 p. Another stimulation ba n d (0·6-0· 8 11) occurs at sho r t e r wav elengths and adjoins the excitation re gi o n The 1 · 3-p band is correlated with th e o p tica l activation of the 0· 5-0· 8-eV traps, whi ch are c o n n e c ted with the green centres (see 4.
Stimulation and quenching spectra of zinc and cadmium sulphides
.
.
Thermal and optical activation
1 99
page 1 55). The green emission is thus st i m ula te d but not the blue one (Garlick and Browne). The abse nce of structure in this band is in marked contrast with the structure of the trap distribution, which is revealed by th e glow c u rves and 1;. t he d ec ay cu rv es . The 0·6-0·8-,u b a nd is ascribed t o t he em p tyi ng of donor levels deeper than the t rap s . At l iquid air temperature the stimulation is s tronge r . To the 1 · 3-,u ba n d is then ad d e d a second peak in th e stimulation spectrum , at 1 ·2 f l (Garlick and Mason). I n addition, a long wave band now occurs at 2·6 ,u and is correlated with the activation of electrons from shallow levels. The emptying of 0 · 8 0 · 9 1 0 1 ·1 1 · 2 1 · 3 1- 4 1 · 5 1 · 6 shallow traps is much easier .\. I micron s ) than the emptying of deep Fig. VII . 8 Stimulation spectrum of tra p s . ZnS(Cu, Pb) at room temperature Apart from the 1 - 3-,u p ea k , The same bands are observed in the stim ulation spectra for both ZnS(Cu), without Pb, but their in blue a n d green emission are tensity is 10 to 20 times smaller identical (Garlick and Browne). In s u l phi de p hosphors, infra-red quenching phenomena occ u r also ; they a re co m petitive with the stimulation p rocess. The q uen c hing is most e as i l y studied when the infra-red is applied during the ultra violet excitation (Fig. VII. l 4), while the stimulation is better observed during t h e p hosphorescence d ecay, i.e. when a l ong time - often several hours - elapses between the end of the e xcitat i o n and the i n fra-red i r ra d i at i on . The same 1 ·3- a n d 0·6-0· 8-,u radi atio n s that a re specifically active in stimulation p rod uce also the maximum q ue n chi n g effects,t but the que n ching is equally well observed for the blue band and the green band. It is a scribed to the obstruction of the copper centres by an electron co m in g fro m t he su lp h u r levels in th e valence band (see t According to G . Mcijer, these for the infra-fl!d em ission .
band� coincide also with the exci tation band�
2 00
below, Fig.
VII . 1 3).
Luminescence In
in
Crystals
the case of the 1 · 3-J-L irradiation this t ra n s i ti o n
need s a th ermal activation
of
about 0 · 4
eV (Broser and Broser
Warminsky, Bube and Tutihasi). The q u e nc h ing is more pronounced a t 290°K than at liquid air temperature. The in t e rp re ta ti o n of thi s thermal activation can be looked for i n a t w o s t ep excitation process. First of all the 1 · 3-tL infra-red p h o t o n r a ises a val e n c e band electron into a metastable s u l p h u r level S * . T h e n , starti ng from th is configu rati o n , a therm al transition obstructs t h e l u m i n escence centre. This hypothetical metastable lev e l was fi rst i n t rod uced to expla i n t h e two-s tage extinction e ffect s o f i n fra-red light a n d electric fields o n the Gudden and Pohl p h e n o m en o n (M. Curie, 1 946). I n m odern l a n guage, the optical activation l e adi n g to this level can be described a s an i n t r a b a n d tran s i t i o n i n s i d e the val ence band (see page 83). In com peti tion with t he q u e nc h ing process a n energy transfer may a l s o occ u r from the S* level to any o f the traps. I n t h i s case the s t i m u l a t i o n fl as h is prod uced . Thus t h e mech anism which is proposed here l ead s to an e x p l a n at i o n of t h e s i m i larity b e t w ee n the quenching and stimulation spectra. Lewchin and Orlov and Garlick and Mason have shown th a t if the sti m u l ation e xpe ri m en t is performed at various temperatures T a fter an excitation at a given temperature T0, the i nte ns ity of the flash i ncreases with T: -
-
I = Io e - E/kT of electrons from traps, possibly the occurrence of the a b o ve t ra n s fe r needs thus a preliminary thermal activation. The activation e n e rgy E d ep en d s on the nature of the trap and is indepen d e n t of the w av el e n g t h of the s t i m u la ti n g radiation (Lewchin and
T h e r e l ea s e
,
O rl ov) .
S i mila r p h e n o m e na
occur in cadmium s ul p h id e ph osp h o rs Ho w the sti m u l a t i o n and q uenchi n g b a n d s a re slightly d i spl a ce d to ward s l a rger wavel e n gt h s . .
ever,
TABLE VII . !
The short wavelength s t i mulation
band The deep trap stimulation and quenching band
The La m be and K l ick st i m u la t i cm band
Peak position in ZnS 0·75 I ·3
2 · 1>
fL 1' I'
Peak position in CdS
0·80 1 ·4
2· 8
!•
I' fL
Thermal and opt ical
act iva t io l l
20 I
ZnS(Cu, Pb) sensitized for infra - red radiation. G. F o n d a has s h o w n that the i nco r p o ra tion of Pb i n a Zn S (C u ) phosph o r leads to a s t ro n g en h an c e m e n t of its infra-red stimulability. At first sig ht one might think that l ead , in the same way as samarium in the pre ced i n g paragraph, is correlated with a dee p trap ping level ; the o p ti cal activation of this l ev el by the infra-red p h o t o n , followed by light emission from the ce n t re s , would gi ve an e xp l a n a tion of the stimulability. However, this i d e a must be rej e cted because the stimulatio n spec t ra of ZnS(Cu) and Z n S (C u , Pb) have t h e s a m e s h a p e (G. Curie) . O n Condu ctton band
s
Fig.
•
Cu · level
-- -
--
' O ·I. eY
--- 11;- --- '
Va len c e b a n d
VII .9 Proposed level sch eme for the stimulation and in ZnS(Cu) and ZnS(Cu, Pb) phosphors
quenching phenomena
The 1 ·3-p. radia t ion raises the valence band ele ctro ns to a me /astable sulphur leve l S*; starting from this con
figuration, an energy transfer to the traps can occur (stimulation), or a thermal activation blocking access to the centre (quenching). In addition, in a ZnS( Cu, Pb) phosphor the free holes in the valence band are trapped in the Pb cen tres , whence an increased probability of light em ission occurs ( H. Kallmann)
the contrary, the s h a p e of the stimulation spectrum of a samari u m sensitized sulphi d e i s characteristic o f the n a t u r e o f t h e sensitizcr. I n ZnS(Cu, P b) the s t i mu lation intensity (height o f th e spectrum) is m e rely increased by the addition of lead . Thus in Zn S (C u , Pb) the ab s o rpti o n of t h e infra-red photons m ost l i kely inv o l ve s the same t ra n s iti on as in ZnS(Cu), i.e. an i n tra-ba n d activation to the S*-Ievel, fol lowed b y an energy t ra n s fe r to t h e t raps.
Luminescence in Crystals
202
This mech anism does not depend on the i n corp o rati o n of Pb. The s t i mu l atin g action of this acti vator is then s i m ply ascribed to a large c ro ss - s e c ti o n for electron-hole radiative recombination in the lead c ent re (H. Ka l l ma nn) . The emission due to the lead activa to r is in the green regio n of the visible spectrum as for the main ba n d of copper, but spectral dis tribution measurements show di fferences. The maxi mum of the Pb b an d is situated at 0· 5 1 fl, w h i l e that of the Cu band peaks at 0�523 fl· During t h e stimulation of emission the spectrum of P b only is ob served (G. F o n da V. L. Lew ch i n ) ,
.
I I . NON- R A D I AT I V E CAPT U RE B Y I M P U R ITY STATES , THER M A L AND OPTI C A L Q UENCHING OF L U M I NESCENCE 1 . Non-radiative capture by traps
The n o n-radiative capture of an electron b y a trap , with dissipation o f t h e excess e n e rg y as pho n o ns a n d n o t a s p h o to n s ca n be de s c r ibe d u s i n g Fig. VII . I by a pro c e s s inverse to t h a t of thermal activatio n . An electro n i n i t i a ll y in the excited state OZt• falls t o the ground state UJfu with the e m i s si o n of vibrational quanta in the crystal lattice. At h igh temperatures t h i s transition necessitates a thermal activation energy E* from th e minimum 0 of the excited state to the neighbour h o o d of T where the transition between the curves for the two states 0/tu and 0/• is highly p ro b ab l e We thus o b t a in a probability for the non-radiative transition or capture : Pcap. = s e - E•fkT, where E* ET - E0• This is the classical approach first described by Mott. At lower tem pe rat u res non-radiative capture i nvolves a transition from the one state OZ/6 to t h e other Oft u by t u n n elling at the height of the minim u m 0. Pear. q uasi-constant. ,
.
=
,
In
both
cases the
ratio of
the pr o b ab i l i t i es
g i v e n by t h e same exponential factor p
--
Pcap.
et:
e
Pcap. and
P(c>capc)
wil l be
l'., lk1'
Thus it is the thermal ionization energy for low temperatures (E0) is involved i n a p p l y i n g t h e J a w of detai led balancing (see Chapter v r , §l.4). wh ich
203
Thermal and optical activation
2.
Thermal quenching of luminescence
The intensity of luminescence during excitation falls if the tempera ture is raised sufficient2y ; emission of lattice vibrations occurs in competition with the photon emission. If Pr is the probability of luminescence emission and Pnr the proba bility of a non-radiative transition, then the luminescence is propor tional to the ratio
1] =
P
which is called the luminescence efficiency. It is ass umed that Pr is sensibly independent of temperature, while Pnr rises rapidly with temperature. (A) Thermal quenching according to the theory of Mott and Seitz. This is applicable when the radiative and non-radiative transitions com pete within the confines of the luminescence centres ; this is the case for KCI (Tl). If we look again at the configurational co ordinate curves U(eV)
Fig. VII . I O
Mechanism for non-radiative transitions in the configurational coordinate theory (Mo!t)
of Fig. II. S , obtained by F. E. Will iams to account for the absorption and emission bands, we can produce them until they reach their 'intersection' T (see Fig. VII . 8). At low temperatures there may be some non-radiative transitions, but they will only become important about 5 00°K where quer.ching occurs. The efficiency is well repre sented by 1J
=
l+C �-.e·;k1. ,
The experimental activation
where C is a constant.
e n e rgy
£*
""
0·60 e V is
m
good
204
Luminescence in Crystals
agreement with the val u e of 0 · 69 eY obta i n ed by extrapol ating t h e configurational coordinate curves. This model will apply when the minimum 0 of t he excited state falls within the limits of the ground state curve Cf/0• Th i s gives a lumi I
{arbitrary units}
I
E * = 0, 6 0 c V
s I·
0 00 3
Fig.
YII. l l
0 002
. . · ---
Efficiency of 3,050 A
T-
emission
f KCI(Tl)
o
function of temperature (Johnson and Williams)
as a
nescent solid at low e n o u gh temperatures with q u e n ch i ng at higher tem p e rat u re s and is the case considered by Mott. I f in contrast to this the minimum 0 lies outside the ground state curve it co rresponds to a m e ta st ab l e state from which a lu m i n escence transition is not possible. The 'de-excitation' occ u rs by a thermal activati on OT (see Fig. VII . 1 2) followed by phonon emission as the only possible tran sition so that the material is non-luminescent. We Vi
U l
uc
A bsnrpl10h
emi SSIOn -·· -·-- ---------
Fig. (a)
YII. l 2
'H '
/'
Two
(Seitz) fo r a
t L_ :
dinate curves: non-luminescent solid
-
(b)
-- ---
arrangements of configura t ional or
r
co
Klick and Russe/1) a luminescent solid, but one with a high probabilityfor non-radiative transitions
(b) ( Dexter,
205
Thermal and optical act iva tion
do not know if this a pp lies to an actual so l i d ; i n a n y case it i s neces sary to assume a very large displacement b etween the ex c i te d state and the ground state equili b rium positions. Returning to the arrangement of curves assumed by Mott, Dexter, Klick and R usse ll have observed that if absorption leads to a tran sition from 0?/0 to a poin t high up on 0?/� and near in energy to the inter-section T, then in order to reach 0 from which the lumniescence transition occurs, the crysta l has a large c h ance of p assing through the configuration co r res p o n ding to the point T. No activation energy is n eeded in this case to reach T and so a low emission probabi l i ty will result even at low temperatures. The conditi ons for this arrangement to occur are easily seen to obtain when the vibrational frequencies for the centre are the same i n the ground and excited sta t es There must then be between t h e mean absorption and emission frequencies the following relation : hvo (emision) R:j !hvo (absorption) As a general observation we see that a large dis p lacemen t between gro und and excited states (giving a marked Stokes's l aw effect) will involve a high p ro b a b il i ty of non-radiative transitions (i .e. p o o r luminescence efficiency) . (B) Thermal quenching in phosphorescen t sulphides. The first theory o f thermal quenching in phosphorescent photoconductors introduced the direct non-radiative recombination between conduction-band electrons and holes in the valence band (Moglich and Rompe, 1 940). If the p robability for phonon emission is of the form + I ), then .
I n = eliwfkT_ 1
a(n
where il is the mean number of phonons present at t h e particular temperature. The prob ab ilit y of simultaneous emission of g phonons is proportional to the p roduc t
Now
g
=
�:P
Pnr
ex:
TI
and is of the order of 50- 1 00 in CdS and 1 00 to
1 50
in Zn S. At t emperatu res at which spontaneous emission is n egligibl e Pnr
ex:
17 =
(�Y I
l + CP
' ' '
"-
'
.)
'' I � I I ' '
Experiment shows that a n expression o f this form i s i n good agree ment with experiment, but g R: 10 instead of 50 to 1 00 (Peyrou). I t would seem that non-radiative transitions o f the Moglich and Rompe type will only occur at relatively high temperatures (R: 1 ,000°K), while at temperatures where the efficiency is low (300° to 500°K) they will occur via defects (Rompe, 1 9 52). The generally accepted Schon-Kiasens scheme of Fig. VII. l 3 furnishes a simple and interesting explanation of thermal quenching in the sulphides. An electron in the valence band can enter a luminescence centre by a thermal activation of energy W. The electron previously removed from the centre by excitation cannot now return and after diffusing in the conduction band for a while will finally recombine via some C e n tre
Fig.
Va lence band ( sulph ur) VII. l 3 Schon-Klasens model for thermal quenching of luminescence in sulph ide phosphors
defect or other (eventually in a killer centre such as iron, nickel or cobalt if these are present). If there are a sufficient number of defects available the thermal activation process will determine the probability of quenching and we have 1 C e - Wf k1' 1J =
being of the same form as in the theory of Mott and Seitz, b ut with a different interpretation placed on the energy W. The same transition W can occur by absorption of an optical photon hv : this explains the quenching effect of infra-red radiations (see page 1 99). This phenomenon may be considered as photon ab sorption effect in the sulphur atoms (M. Curie, 1 923), leading to a filling of the centres. This description in terms of the energy band scheme was first given by P. Brauer. T h i s q u e nching (s e e Fig. VTT. I 4) may occur ei ther by one optical
Ju:m wt and
opttcui
activation
207
transition only (0· 6-0·8-JL band in ZnS) or by a two-step process needing a thermal activation ( 1 · 3-JL band in ZnS). Discussion of the various models. The idea which ascribes both thermal and optical quenching to the same kind of transitions looks rather 1
uv
I
UV + IR
: S limula lion
-- - � - - -
'
-·--
fluenchmg
0
Time
Fig. Vll . l 4 Luminescence under constant excitation. Effect of infra-red stimulation followed by permanent quenching effect
tempting . Unfortunately, it does not seem to be supported by experi mental evidence. The similarity of the infra-red ex tin ction spectra for both blue and green emission bands in ZnS (Garlick and Browne) is in marked con trast to the observed difference between their respective thermal ex tinctions : it is well known that thermal quenching occurs about 1 50° higher for the green band than for the blue band.t I
100
0
+ 1 00
+ 200
+ 3 00
oc
Fig. VII. 1 5 Temperature dependence of the luminescence of a ZnS(Cu) phosphorfor excitation by 3,650 A radiation (F. A. Kroger) t For instance, the fall in the luminescence intensity begins near ooc for the blue band of a given phosphor, and near 1 50°C for the green band. However, large differences are found between these values for different samples : this fact proves t h a t the non-radiative electron-hole recombinations occur in the defect;; of the crystal and not by band-t o-band recombinat ions.
Luminescence
208
in
Crystals
I n t h e p resent s t a te of affairs, if we accept the above mechanism for the i n fra red activation, we must place the blue and green e mi ttin g copper centres at the same h eig h t above the valence band, while if we accept the Schon-Klasens mechanism for the thermal quenching, we -
Conduction ba n d Excite d
associa t e d
Fundamental copp er level
level
hv
Fig.
Valence b a n d
V I I . I 6 Thermal and op tical quenching ac c ording to the mode l for centres p roposed in Fig. V.5
Optical quenching is assumed to o c cur a cc o rding to ' Brauer s and Schon-Kiasen's de l thermal quench ing occurs when the thermal activation W happens rhe light-emitting transition (Roberts and Wi//iams) .
mo
while
before
We emphasize that, of course, at sufficiently high tem the filling of th e ground state by therma l activa tion also occurs
peratures
have to place the green level higher than th e b l ue o n e (s ee Chapte r V, Figs . V . 3 and V . 5). Further studies are needed in order to choose be tween these d ifferent m o d els . Electroluminescence s tud ie s support the assumption of the same g rou n d state o cc u r ri n g in both centres, i.e. Fig. V.S. I l l . T H E T H E O R Y OF M U LT I P H O N O N T R A N S ITIONS
We denote by multiphonon transitions the simultaneous a b s o rp ti o n or emission of a l a r ge number of thermal vib ra t i o n quanta. These tran sitions have been much investigated by th eoreti ci a n s over the last de cade. The author believes that the co mm o n sense' view of progressive a cti v ati o n or de-activation via defects (see page 144) corresponds more closely t o reality. Nevertheless, these theories of multiphonon t ra n si t i on s apart from their intrinsic interest, offer a chance of clarifying the ideas discussed above. We use the same notation as in s ect i o n III.4 of ch ap te r II. Consider the t ra nsi ti o n (by thermal a c ti v a t i o n) between the gr o u nd state o/fu in wh ich the vibration of the ions is characterized by a q u a n tu m n urn '
,
Thermal and op tical
ber
m
and the excited
state in which the vibrational state is
quantum then is a s s um e d
209
n.
The
to be t h e s a m e i n t h e gro u n d an d exci ted
states.
The
act ira t ion
with
tran s i tio n takes place
absorption of p
=
m-n
W e introduce a n a b s orp ti o n operator (phonon a n n i h i l a t i o n )
ay;m
=
quanta.
Vm1Jlm - 1
a n d a n e m i s s i o n operator ( ph ono n c re a t ion ) T h e m a t r i x ele m e n t
a*y;m vm-J-=ly;m : =
1
relative to the opera to r
f 1Pn(r r0)ay;m(r) dr
=
=
Vm
a
is
f1Pn(r r0)1Jlm -I(r) dr
VmA nP - I (S)
J1 be i n g a normal Laguerre fu n ction of t h e configuratio n a l parameter
The matrix eleme n t of the operator a* is V m+ l A nP+ 1 (S) . When S is zero, i . e . no displacement r0 betwee n the two oscil lators 6!fu and o/le, the only n o n-zero A n" is that for p 0. Thus the matri x e l e m e n t of the operator a is only different for p I (absorption of a q u a n t u m ) an d that for a* only for p - 1 (emission of a q u a n t u m ) . S.
=
=
=
U (r!
Fig. VII. I 7 Thermal activation and non-radiative capture hy an impurity level: transition from a vibrational level m to vibrational /eve/ n
However,
when S is n o t zero all th e A's a re different from zero .
Thus the operators a and a nu m b e r of ph o n on s p
a * permit both absorption and emission o f
when the oscillators o/tu a n d o/t• are d i s pl a ce d rela tive to each oth e r (r0 ;;e 0). The gre a t e r the S t okes's s h i ft, 2Stu;J ,
Luminescence in Crystals
210
between emission and absorption of ra d iati o n , the greater the c h a n c e of no n-radiative t ran s i ti o ns . t The transition probability due to the o pe ra t or a is
Pa
=
m
m =p n�o
where
e moc I A np-· l(S) I 2 -.;---
e - tna
u
r;. lkvjkT. The summatio n is Lebedeff formula. We obtain
made
=
Pa
ea/ '!.
P a - e paf � e I e o
_
Se
ot
(cx/-l fp - 1 •>
by neglecting the terms linear in S (S small).
+
number of phonons present at T: Pa
=
pVii(n + l )
n
ii
1] -p/2
ex p
[
by
(sir11 (a/2))
=
S
If i'i
=
_!_l is t h e mean
ea -
S(2n + I )].!;, - I[2 Svn(n + I )]
The t ra n s ition probability due to the operator Pa•
use of the M yl l e r
a * is similarly
exp [- S(2n + I )]lp + I[2SVn(ii + I )]
The a d iabati c approximation for the m ovemen t of the ions shows
that the actual operator to consider is not a but (a -a *) / V 2. I f S is small the contribution of a t o the thermal activation probability p will be sufficiently l a rge c o mp are d with that of a * for the latter to be n eg l ec t ed . We can t h us assume p :: p" a n d similarly the non radiative capture probability Pcap. :: Pu•· These fo rmulae are d ue to H uang and Rhys, Pekar and K r ivo g l a z , Vasileff, Kubo and Toyozawa, &c. Using the asymptotic forms for !11, we ob t a i n at l o w te m pe ra tu re s Pa oc exp ( pliwjkT) Pa• oc quasi-constant while at high temperatures Pa oc e xp [ - /iw(p + S)2/4SkT] Pa• oc exp [-liw(p-S)2/4SkT]
,
t We must emphasize that no discrepancy ex i s ts between this as se r tio n which takes into account the case of d i fferen t centres with different values of r0, an d 'Vavilov's law' - as corrected by Louchtchik for solid crystal phosphors - which states that the luminescence efficiency is a steplike function of the wavelength of the exciting radiation ; it is a constant when the exciting radiation is changed, but remains wi thi n the same absorpt ion band of a g iven centre. See page 49 for the case of KCI(Tl) and page 227 for t h e case of ZnS phosphors.
21 1
Thermal and optical activation
The activation energies in three of t hese e q ua ti o n s can b e identified E0, Er and E* = Er- E0 respectively in agreement with the general consid e rati ons of the p re ce ding se cti o n s . with
B I B LIOG R A P H Y I.
Thermal activation and optical stimulation of trapped electronst
'Thermal depth' and 'optical depth' of traps
CuRIE,
D . (1 954) ' Su r l e m od el e h y d r o g en oid e d es p ieg e s (m odele de
Comptes-Rendus Acad. Se. Paris, 238, 579. ( 1 956) 'Niveaux d ' imp urete dans les cristaux (mo d ele hydrogenoide)', J. Phys. Rad., 17, 1 6. CuRIE, D . ( 1 9 57) 'Modeles pour les divers types d e p i eges dans le sulfure de zi n c phosphorescent. Liberati o n thermique et o pt ique des el ec tr o ns p i e ge s ' , J. Phys. Rad. , 18, 2 1 4. C U R I E , G . , A R P I A R I A N , N . , G U E R E T, P . and C U R I E , D . (1 960) 'On t h e hydr o g en -li ke model for traps in zinc sulphide', S p ri n g Meet ing, The Electrochem. Soc., Chicago, 1-5 May 1 960. Kuao, R. ( 1 952) 'Thermal ion izati o n of trapped electrons', Phys. Rev., 86, 929. LEHO V E C , K. ( 1 953) ' E n e rgy of trapped electrons in i o n i c solids' , Phys. Rev., 92, 253. M oTT, N . F . and G U R N E Y , R . W . ( 1 948) Electronic Processes in Ionic Crystals, 85, 1 60-2. P E K A R , S . I . ( 1 954) Untersuchungen uber die E/ektronen theorie der Kristalle, 1 09-84. Akademie-Verlag, Berlin. S J MPSON, J . H. ( 1 949) 'Charge distribution and energy levels of trapped electrons in ionic solids', Proc. Roy. Soc. , A 1 97, 269. URBACH, F . ( 1 948) ' Sto rage and release of l ight by p h o s p h o r s ' , Cornell Symposium, 1 32. Wiley, New York. B et h e) ' ,
C U R I E , D.
Thermal and optical depths in alkali ha/ides; see Chapter
VI.
Thermal and optical depths in silicon E . , P r c u s , G . , HENV I S , B . and W ALLIS, R . ( 1 9 56) 'Ab sorption s p ec tra of impurities in si l i c o n ' , J. Phys . Chem. So lid1·, 1, 65, 75 .
B U RSTEIN ,
t
See
also the b i b l i ography of § TU :
'The
theory of m u l t iphonon t ransitions'.
212
Luminescence in Crystals
SrS(Eu, Sm) and SrS(Ce, Sm) phosphors
See, in Cornell Symposium, the following papers : E L L I C K S O N , R . T . and P A R K E R , W . L . ( 1 948) 'The d ecay of i n fra red sensi tive phosphors', Cornell Symposium, 3 2 7 . W il e y , New York. O ' B R T E N , B. ( 1 9 48 ) 'Infra-red sensitive phos phors', Cornell Sym posium , 1 4 1 . Wiley, New York . P E A R L M A N , D . , N A I L , N . R . and U R B A C H , F . ( 1 9 4 8 ) 'Stim ulati o n of s o m e s u l phide phosph ors', Cornet! Symp os ium , 358. Wiley, New York. URB A CH , F. ( 1 948) 'Storage and release o f light by phosphors', Cornell Symposium, 1 1 5 . Wiley, New York. URB A C H , F . , HEMMENDINGER, H . , and PEARLM AN, D. ( 1 948) 'Ab so rpti o n , storage, and release of light by infra-red sensitive p hos phors', Cornell Symposium, 279. Wiley, New York.
Other papers B R A U ER , P . ( 1 946-47) ' I n fra-red sensitive phosphor SrS(Eu, Sm)', ' Z. Naturforsch., l, 70 ; 2a, 238. BRAVER, P . ( 1 9 5 0) 'Rise i n brightness of infra-red sensitive phos pbo rs ', J. Opt. Soc. Am., 40, 353. GARLI C K , G . F . J . an d M AS O N , D . E . ( 1 9 4 9) 'Electron traps and infra-red stimulation of ph o sp h o rs ', J. Electrochem. Soc., 96, 90. K E L L ER , S . P . , M A PES, J. F. and CHEROFF, G. ( 1 9 57) 'Studies on some i n fra-red stimu lable phosphors', Phys. Rev . , 108, 663. K E L LE R , S. P. and PETTIT, G . D . ( 1 9 5 8 ) 'Quenching, stimulation a n d exhaustion studies on some i n fra-red stimulable phosph ors' , Phys. Rev . , 1 1 1 , 1 53 3 . K ELLER , S . P . ( I 9 59) 'Stimulated i n fra-red emission from S m centres in S rS phosphors', Phys . Rev. , 1 1 3, 1 4 1 5 . S T E I N B E R GER , I . T . , B R A U N , E . A . and A L E XA N D E R , E . ( 1 9 5 7 ) 'Gudden-Pohl and mem o r y effects in an infra-red stimulable phos phor', J. Phys. Chem . Solids, 3, 1 3 3 . Paramagnetic resonance of SrS(Eu, Sm) phosphors D U B I N I N , V . G . a n d T R A P E ZN I K O V A , Z. A . (1 9 60) 'An electron paramagnetic resonance investigation of the valence change of the activat o r d u ring e xci tatio n in the p h o sph o r SrS(Eu , Sm)', Optika i Spektr. , 9, 360 ; Op tics and Spectr. , 9, 1 87.
Thermal and optical activation
21 3
W . ( 1 9 5 5) 'Pa r a ma g n e ti c resonance spectrum of some d o u b l y a cti vated phosphors', Phys. Rev . , 98, 426.
Low,
Stimulation and quenching i n ZnS, CdS and CaS phosphors B E C K E R , A . ( 1 945) Ob er die Phosphoreszenz-Til gung', z. Natur forsch., 2a, 1 00. B E C K E R , A . ( 1 949) 'Phosphoreszenz-Tilgung', Z. fiir Phys . , 1 25, 475, '
694.
( 1 944) 'Zur Frage der oberen Temperaturgrenze des Phosphoren', Naturwiss., 32, 3 2 . B R OSER , I. and B ROSE R-WA R M I NS K Y , R. ( 1 9 56) 'Sur l e s c h e m a cnerge t i q u e des cristau x phosphorescents', J. Phys. Rad. , 1 7, Le uc h t e n s vo n
B R AUER , P.
79 1 .
I . and S C H U L Z , H . J . ( 1 960) 'A comparative study of infra red emission and other optical and electrical properties of ZnS(Cu) s i ngle crystals', Spring Meeti n g, The Electrochem. Soc., Chicago, 3 May 1 9 60. B RO W N E , P. F. ( 1 956) 'Infra-red luminescence of zinc and cad m i u m sulphide phosphors', J. Electronics, 2 , 1 1 - 1 2. B U B E , R . H . ( 1 955) 'Infra-red qu enchi ng and a unified d escripti o n of photoconductivity phenomena in cadmium s u lphid e and selenide', Phys. Rev., 99, 1 1 05. B U LL , C . and MASON, D. E. (195 1 ) 'The determination of the dis tribution of electron trapping states in phosphors', J. Opt. Soc. Am. , 41 , 7 1 8 . C u R I E , M . ( 1 92 1 -23) 'Action des rayons i n fra r oug e s e t r o ug e s sur les substances phosphorescentes', Comptes-Rendus A cad. Se. Paris, 1 72, 272 ; 174, 5 50. Thesis, P ari s , 1 923. C U R I E M. ( 1 946) Fluorescence et Phosphorescence, 1 30-6 . H e r m a n n BROSER ,
-
( 1 955) 'Mouvement des electrons d e conductibil ite luminescence cristalli ne', J. Phys. Rad. , 16, 77. ,
,
Paris.
C u R I E , D.
en
phosphores ce n c e par ! 'infra-rouge', A nn . de Phys. , 1 5, 3 88. Thesis Paris, 1 959. D R O P K I N, J . ( 1 954) 'Photoconductivity in phosphors', R eport No . NR-015-207. University of Brooklyn. G A R L I C K , G . F . J . and M AS O N D . E. ( 1 949) 'Electron traps and infra-red stimulation of phosphors', J. Electrochem. Soc., 9 6 , 90. CURIE, G.
( 1 960) 'Contribu t i o n a ! ' e t u d e de l a stimulation de la
,
H
2I4
G I L L S O N , J . L.
Luminescence in Crystals
( 1 956) 'Some properties of electron traps in a ZnS(Cu) p h o sph o r ', J. Op t . Soc. A m . , 44, 34 1 . K A LLM A N N , H . and KRAM E R , B . ( 1 9 5 2) ' I nd uc ed co nd uctivi ty and light emission in different l u m i n esce n t type powders', Phys. Rev., 87, 9 1 . K A LL M A N N , H . , K R A ME R , B . and PERLM UTTER, A . (1 953) ' I n d uce d conductivity in luminescent pow d e rs ' , Phys. Rev., 89, 700. K A L LM A N N , H . ( 1 9 56) 'Stimulation op t iq ue dans Ies s u lfu res de zinc et de cad m i u m ' , J. Phys. Rad. , 17, 787. K A LLM A N N , H . and S P R U C H , G . M . ( 1 9 56) ' Number o f traps and behaviour of excited el ect ro n s in luminescent materials', Phys. Re v . ,
103, 94.
and S u c o v , E. ( 1 958) 'Energy s torage in ZnS and CdS p ho sp ho rs ' , Phys. Rev., 109, 1 47 3 . L A M B E , J . ( 1 9 5 5) 'Cadmium s ul p h id e with silver a c tiva t or' , Phys. Rev. , 100, 1 586. L A M B E , J . and K L I C K , C . ( 1 9 56) 'Les modeles d e centres lumina gen es dans Ies s u lfure s ' , J. Phys. Rad. , 17, 663 . L E N A R D , P . , S CH M I D T , F . and T O M A S C H E K , R . ( 1 928) 'Ausleuch tung und Tilgung', 'Phosphoreszenz-Fluoreszenz', Hand. der exper. Phys. , 11, 745-8 5 3 . P R I N GSHEI M , P . ( 1 949) Fluorescence and Phosphorescence, 545-56. Intersc. P ub . , New York. R E B A N E , K . K . ( 1 958) 'Photostimulation of Z n S (C u) phosphors', Issl. po Lumin . , 7, 357 ; Bull. A cad. Se. S. S. S. R . , 21, 546 ; Columbia Technical Translations, 21, 542. TUTIHASI, S . ( 1 9 5 6) 'Quenching of photocond uctivity in cadmium s u l ph ide ' , J. Opt. Soc. Am., 46, 443 . Y I G E A N , F . and CURIE, D . ( 1 9 5 1 ) 'Action extinctrice des radi a tions de grandes l o n geu rs d'ondc en clectroluminescence', Comp tes Rendus A cad. Se. Paris, 232, 8 1 9, 9 5 5 . KALLMANN, H .
ZnS(Cu,
Pb) phosphors R . ( 1 9 46)
' P re p a rati on and characteristics of zinc sul sensitive to infra-red' , J. Opt. So c . Am., 36, 382, G A R L I C K , G. F . J. (1 949) Luminescent Materials, 1 58-62. Cl a rend on Press, Oxford . K A L LM A N N , H . ( 1 956) loc. cit. L E W C H I N , V. L . and 0 R L O V , B. M. ( 1 9 5 9) 'Investigation of the
FONDA, G.
phide p h o s ph o r s
Thermal and optical activation
215
phosphors', Optika i Spektr., 1, 530 ; Optics and Spectr., 1, 330. See also LEW C H I N , V. L. and FAIZI, N. K. (1960) ' I nv e s ti gat i on of the flash and of trapping levels in CaS p ho sp h o rs ' , Optics and Spectr. , 8, 458 .
thermal activation energy ofphotostimulated flashes i n ZnS(C u , Pb)
(use of a configurational coordinate
II. Thermal quenching of luminescence d i agra m)
The theory
of Mott and
Seitz
and G URNEY, R . W. ( 1 94 8) Electronic Processes in Ionic Crystals, 2 1 9-24. Cla ren d o n Press, Oxford . S EI T Z , F. (1 939) 'An i n terp retat i on o f c rystal luminescence', Trans. Faraday Soc., 35, 79. MoTT, N. F .
C . C . a n d RUSSELL, D . A . ( 1 955) 'Criteri o n fo r t h e occurrence of l um i n esce n ce ' , Phys. Rev., 1 00, 603 . J O H N S O N , P . D . a n d WILLIAMS, F . E . ( 1 952) 'Energy levels and rate p r oc e ss e s in the thallium activated potassium chloride phosphor', More recent papers
DEXTER, D . L . , KLICK,
J. Chem. Phys. , 20, 1 24. (1 9 5 5) Cristallophosphores, 64-88 . Editi o n s Acad. Fiz. and A st rono my, Tarto u . M E Y E R , H . J . G. (1 956) 'Some aspects of electron-lattice in teracti o n in polar cryst al s ', 39, 50. Thesis, Amsterdam. REBANE, K . K . (1 958) 'On the criterion for the occurrence of lumi
LoucHTCH I K , Tech .
nescence', Issl. po Lum in . , 7, 62. K . K . , V A L E , G . K . and ZUNDE, B. Y. ( 1 960) 'Radia tionless transitions in the luminescence centres of alkali h alidc phosp ho rs ', Issl. po Lumin., 12, 77.
S CHWARZ,
B I RUS, K . , M 6 GLICH, F. a n d ROM PE, R . (1 943) ' U ber e i n i ge d i e Kristallphosphore und Isolatore n bet re ffe n de F rage n ' , Phys. The theory of Peierls, Frenkel, Moglich and Rompe
Zeits., 44, 1 22. J. (1 936) 'On the ab so rp ti o n of l i g ht and th e trapping of electrons and holes i n c r ystallin e dielectrics', Phys. Z. Sowjet Union, 9, 1 58 . M 6 G LI CH , F . and ROMP E , R . ( 1 940) ' U ber Til g u n g von L u m i neszenz durch VielfachstOsse', Z. fur Phys. , 1 15, 707 ; 1 1 7, 1 1 9. P E I E R L S , R . ( 1 932) ' Z u r Theorie der Absorptionsspektren fester Korpcr', Ann. der Phys. , 13, 905. FRENKEL,
216
discussions
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about the above theories F . A . ( 1 948) Some Aspects of the Lumin escen ce of Solids , I 74-252. Elsevier, Amsterdam. P E Y R O U , C. ( 1 948) ' Lu m i nes ce n ce des sulfures d e zi nc-cad m i u m , transitions electroniques sans emission de Jumiere, c h o c s m u ltipl es', Ann. de Phys . , 3, 459. Thesi s, Paris, 1 947. Some
KRbGER,
of defects in the non-radiative electron hole recombination me chanism A D I R O W I T C H , E. I . ( 1 948) ' Radia t i o n less transitions in a pertu rbed Evidence for the interven tion
crystal lattice', Dokl. A kad. Nauk S. S. S. R . , 63, 6 3 5 . I . ( 1 953) Einige Fragen zur Th eo r ie der Lumineszenz der Kristal!e, 202-49 . Akademie-Verlag, Berlin. G R I L LO T , . M. ( 1 9 56) ' Facte u r s extincteurs de l a fl u o resce n ce de CdS(Ag)', J. Phys. Rad. , 17, 682. Ga r m i sch-Partenkirchen Lum in e sc e n c e Symposiu m , 1 95 6 . R O M P E , R . ( 1 9 5 2) A rbeits tagung Festkorper Physik, 94. 1 9 52.
A D I ROWITCH , E .
Thermal quenching i n sulphide phosphors A R K H A N GELS K A I A , V. A . ( 1 9 54) ' I n fra - red l uminescence and ki n e t i cs of semi-conductor p rocesses with CdS i n the range of temperature q ue n chi ng' , Dokl. Akad. Nauk S. S.S.R., 100, 233. B R AUER , P. ( 1 944) 'Zu r Fr a ge der oberen Temperaturgrenze des Leuchtens von P h os p h o ren ' , Naturwiss. , 32, 32. B R A U E R , P . ( 1 953) 'Temperaturmessung mit Leuchtstoffen', Techn. wiss. Abhand!. Osram -Gesells . , 6, 72.
BROSER, I .
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G ARLICK ,
Thermal and optica l
activation
G . F . J . ( 1 949) Luminescent Materials,
Press, Oxford .
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G A R LI C K ,
G.
F. J.
99
217
1 1 2 . C l a rc n d o n
( 1 9 5 5) 'Absorpti o n , e m i ss i o n J.
a n d sto rage Appl. Phys. , 6, Suppl. 4,
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H A LPERI N , C .
perature Phys.
Rev., 1 13, 1 2 1 6.
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H I L L , C . G . A . and K L A S E N S , H . A . ( 1 949) ' T he
infl uence o f tem
J. Electrochem . Soc. ,
H . A . , R A M S D E N , W . and C H O W Q U A NT I E ( 1 948) 'The relation between efficiency and exci ting i nt e n s i t y for zinc s u l p hi d e p h o s p h o rs ', J. Opt. Soc. Am., 38, 60. K L A S E N S , H . A. ( 1 9 5 8 ) 'The i ntensity-dependence of p h o toconduc ti o n and l u m i n e sce n ce of ph o t o c on d uct o r s in the s t a t i o n a ry s ta te ' , J. Phys. Chem. Solids, 7 , I 75. K L A S E N S , H . A. ( 1 9 5 9 ) 'The temperature dependence of t h e fl u o res cence of photoconductors', J. Phys. Chem. Solids, 9, 1 8 5 . K RO G E R , F . A . ( 1 948) Some Aspects of the Lumin escence of Solids, 1 76. Elsevier, Amsterdam . K R O GE R , F . A . , H o o G ENSTRA A T E N , W. , BoTTEM A , M . and B o T D E N , T . P . J . ( 1 9 4 8 ) 'The influence of t e m p e ra tu re q ue n c h i n g on the decay of fluorescence', Physica, 1 4 , 8 1 . K LASENS,
and
D E 0 R O O T , W . ( 1 950) 'The i n fl uence of t h e
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K R O GER , F . A .
L E W CH I N , V. A .
and
R E B A N E , V. N . ( 1 959) 'Comparative study o f
light sums and temperature q u e nch i n g of Zn S(Ag) p ho s p h o r excited by (3-rays and light' , Optika i Spek t r . , 7, 236 ; the storage of
Optics and Spectr. , 7, 1 49 .
tions on s u pe rl i n e a r
N AIL,
N.
l u m in e s ce n ce ', J.
R . , URBACH,
F.
and P E A R LM A N , D . ( 1 949) ' New o bserva
Opt. So c . A m . ,
39,
d ' em i s s i o n d ' u n sulfu re d e zi n c active a u c u i vre, d a n s d 'extinction thermique p a r ti e l l e ' , Comp tes- Rendus A cad.
690.
P A Y E N DE LA 0 A R A N D E R I E , H. and C U R I E , D . ( 1 9 59) 'Spectre
248, 3 1 5 1 .
la
r e gi o n
Se . Paris,
218
RIEHL, N .
Lum inescence in Crystals
( 1 9 39) ' U ber einen neuen
Effekt
an
l u m i neszierendem
ZnS', Z. jar techn. Phys. , 20, 1 52 . R I E H L , N . ( 1 949) 'The temperature dependence of t h e i n te ns i ty o f fluorescence o f Z n S i n rel ation to other pr ope rt i es , Dokl. Akad. Nauk S. S. S. R . , 67, 245 . ROBERTS, S. and W I LL I A M S , F . E . ( 1 950) 'Theory of the l u m in e s cence of s ulp h i d e phosphors', J. Opt. Soc. A m . , 40, 5 1 6 S CHON, M . ( 1 9 5 1 ) ' Ober die strahlungslosen O bergan ge i n S u lfid ph o s ph ore n , Z. fiir Natwforsch ., 6 a , 25 1 . S CHON, M . ( 1 953) ' O be r die strahlungslose Oberga nge d e r Elek tronen im Gitter der Kristallphosphore', Techn. wiss. Abhandl. der Osram-Gesel!s., 6, 49. S cHON, M . ( 1 954) 'Photoleitung und Lumi neszenz in K r i s tal l e n der Zn S G r u ppe Physica, 20, 930. URBACH, F . , N AI L R. and PEARLMAN, D. (1 949) 'The observation of temperature d is t ri b u tio n s and of thermal radiation by means of a non-linear phosphor', J. Opt. Soc. Am., 39, 1 0 1 1 . VERGUNAS , F . I . and GAVRILOV, F . F . ( 1 947) 'The thermal quench ing of the photoluminescence of ZnO', Dokl. Akad. Nauk S. S. S. R . , 57, 3 1 ; J. Eksp. Teor. Fiz. S. S. S.R. (1950) , 20, 224. Y ASTREBOV, V. A. ( 1 947) 'Temperature d e p end e n ce of flu o rescence J. Elosp. Teor. Fiz. S. S. S. R . , 17, 1 40 ; J . Phys. S. S. S. R . , 1 1 , 3 . '
.
'
-
',
,
',
Ill. The theory o f multiphonon transitions
A I GRAIN, P. (1956-57) 'Defauts dans les sem i-conducteurs'. Lectures given at the Faculte des Sciences, Paris (unpublished) . C U R I E , D . ( 1 9 5 8 ) 'Sur les transitions m u l t ip l e s et !'ionisation ther mique des niveaux l o calises clans le modele des courbes d e c o n fi g u r at i o n , Comptes-Rendus A cad. Se. Paris, 247, 1 843 . G UMMEL, H . a n d L A X , M . ( 1 955) 'Thermal ionization and capture of e lect r o ns t rap pe d in s emi co n d u c tors , Phys. Rev . , 97, 1 469. H U A N G , K. and RHYS, A. ( 1 9 50) 'Theory of light a bs orption and non-radiative t ra n s i t i o ns in F-ccntres', Proc. Roy. So c . , A 204, 406. KRIVOGLA Z, M. A. ( 1 956) Co m pariso n of the theory of the lumi nescence of solid bodies with experiment', Optika i Spektr., t, 54. KUBO , R. (1 952) 'Thermal ionization of trappe d electrons', Phys. Rev., 86, 929. KUBO, R. an d TOYOZAWA, Y. ( 1 955) 'Application of the method of gen erating fu n c t i o n to radiative and n o n ra d i a t i ve transitions '
-
'
'
-
Thermal and oplical activation
219
of a tra pped el e c t ro n i n a crystal', Prog. Theor. Phys. Japan, 1 3,
1 60.
( 1 9 54) ' T h e o ry of rad i a t i o n less t ransitions i n F 181. M EY E R , H . J . G . ( 1 9 56) ' S o m e aspects o f electron-lattice interaction in polar c rys t al s ' , 42-55. Th e s i s , Amsterdam . O ' D W Y E R , J . J . and H A R P E R , P . G . ( 1 9 57) ' Non-radiative transi tions of trapped e l ect r o n s i n polar cry st a ls ' , Phys. Rev . , 105, 399. T R I FL A J , M. ( 1 9 5 5) 'Thermal and n o n - r a di a t ive tra n s i t i o n s of elec t ro n s at imperfections in i onic c rys ta ls ' , Czechosl. J. Phys. , 5, 1 3 3 . V ASI LEFF, H . D . (1954) ' The rm a l ionization o f im p u rities in pol a r c rys tals . I. F o rmal theory', Phys. Rev. , 96, 603 . V ASILEFF, H . D . (1 955) 'Th e rmal ionization of i m p u ri t i e s in p ol a r crystals. Il. Application to interstitials in cubic Zn S', Phys. Rev . , 97, 89 1 . M EY E R , H . J . G.
c e n t re s ' , Physica, 20,
CHA PTER
VIII
Energy Transfer, Sensitization
and Concentration Quenching Energy t r a n s fer occurring i n l u minescence d u ri n g abs o rp t i o n
and
em i ss i o n is not s imply confi ned to the same ce ntre. Energy transfe r d u rin g fluorescence between molecules o f a gas o r in organic solu
tions h a s be e n e xt e ns i v e l y studied, but s uch transfer plays an i m p o r
tant ro le in solid s ; a notable example is the p h enomen o n of sensitiza
tion.
The sensitization effect was discovered in SrS(G d , S m) by To m a
s c he k a n d in C aS ( S m , Bi) by Rothsch i l d . In r e ce n t years n um ero u s studies o,f the effect have been made, particularly by B o td en and
Krog er, Butler, Dexter and Schul man, Fonda, Froelich , Jani n and Crozet, Ginther and Lea ch .
Take, for e x ample , the ph o spho r Ca(P0.1kf- Ce ( sen s itizer) + M n
(ac tiva to r) i n v estigate d b y Botden .
Calciu m phosphate a c tiv at ed by man gan e s e has a red fluorescence
when exci ted hy cathode rays, but is not excited by ultra-violet rad ia tion
(2, 500 A) . T h e latter falls outside the characteristic absorption
of t h e M n 2 + ion. Ac t ivated by cerium alone, ultra-violet excitation
(2,500 A) prod uces an u l tra-vio l et fluorescence (at abo u t 3 , 500 A) due to transi tions i n the Ce3 + ion. The ground s tate is the doublet 2 F5;z-2 F; ;2 and the excited state is most likely d e rive d from the 2 D3;2
and
2 D:.;z
s t ate s of t h e Ce 3 + i o n s , s pl i t by the e l ect ri c field in the
crysta l . In Ca(P04MCe , Mn) the abs or pt i o n due to Ce3+ ions in the
2,500-A regi o n is not altered by t h e presence of man g ane s e . However, 2, 500-A excitation now p ro d uce s both the ultra-violet emission of the Ce3+ ions and the red emission of the M n 2 + ions. Abso rption
is by
the Ce3 + i o n s , but is followed by transfe r of energy to the M n 2+ i o n s
which occu rs b y a resonance p ro cess . 220
Energy transfer and sensitization
22 1
I . R E S O N A NCE T R A N S FER B ETWEEN ATO M S WITH OVERLAP P I N G E LECT R I C FI E L D S Reso nance occurs between two configurations : 1Jli w h ere S
is ex cited and A not excited (S* A) S is 'de-excited' and A ex ci te d (SA *) t S and A representing the s en s i t ize r and act i vat o r centres respectively. 1Jl t where
w' s hv
Fig. VI I I . I
WA
WS
Resonance transfer
of energy
S: ground state of sensitizer, S * its excited state A: ground state of activator, A* its excited state Excitation passes from S to A (S * is 'de-excited' and A excitecf) without electric charge transfer between S and A
The
g(ws')
probability
PsA and
of the transfer S* -- A *
=
g(wA)
f f g(ws')g(wA) I
MI
per u nit time is
2 d ws
'
given by
d wA' d(h1•)
being statistical weighting factors . The m a t rix ele
ment M for the t ra n si t i o n is of the M =
f
form
'ljl;OH'Ij11
dr
where oH is the coulombic interaction between S an d A, i .e . same operator as th at responsible for Van der Waal s forces
oH =
KR3
R2
.
rAJ
it is the
for the dipole-dipole interactio n approximatio n . K is the dielectric cons ta nt of th e matrix medium. R is the d istance between the nuclei of S and A, rs is the distance of the electrons of S from the nucleus t The achievement of a configuration in which resonance is possible may in in this case the transfer efficiency will be tem
volve a thermal activation energy : pera tu re dependen t .
222
Luminescence in Crysta/.1·
of S (the sum of the distances i f there are severa l electrons) and s i m i l a rly fo r A · T h e matrix element M i s thus given b y
r
M =
by introd ucing t he
J
-- M s . MA
- -
matrix M s
t h a t M A for the a c ti v at o r
.
Ms
=
of
t h e s ensitize r d ipole moment and
-eJ1Ps•rs1psdrs
a n d s i m i l a rl y for M ..t . T h e mean val ue o f M is t h e n given by
and so
Ps A
=
I MI 4n 2
1
�
=
x:h�-6. � l Ms I
h ' KzRe X
� J JJ g(ws') I
�
.
I
MA
I�
}
J
M s ! 2 d ws' g(wA) I MA 1 2 d w A d(hv)
There is n o quesdon of c alcu l a ti ng these i ntegrals ; we use the emis si o n spectrum of S* and the ab so rptio n spectrum of A respectively as d ete r m i n ed experimentally. It is co nv e nie n t to introduce on the one hand the form of these spec t ra normalized to unit area [e s(hv) and o:A(hv)] a n d on the other h a n d the normalization constants . IfT s is the mean life time of S* before emission a n d the effective absorp tion cross-section of A is a A , t he n PsA
=
h 4c4 64n5 K2R6 r: s
We c a n write
P s .1
0
(hv) 4
d (hv)
=
where R0 is know::1 as the transfer distance and is interpreted as t hat for which 1 PsA = r:s
For R < R0 tra ns fer occurs before S has a chance to be 'de-excited' by emission. In ttis l a s t formula we have introduced the measured life time which is different from the life time before emission by a fac t o r rJ s . i . e. Ts(moasmcd) 'Y/S. TS(bcforc emission) =
Thus
Energy transfer and sensitiza tion R o6
h �c4
- 64:<:5 K2
GA 1] S
J
"'
o
22]
t: s(h v )a-A(hv) d (/n ) (h v) -1 '
The overlap between the spectra e s and IXA is usually better if S a n d A are identical . Thus the transfer between the Ce3 + sensitizer a n d t h e M n Z + activator in CalP04)2 is effected by a series of transfers b e tween cerium ions u ntil the excitation reaches a cerium ion near to a manganese ion. Botden and Kroger reserve the term transfer fo r the basic resonance process and call the general process the energy transport. In the particular example above the transfer d i stance be tween two CeH ions is estimated to be R0 � 35 A. In organic solutions spectral overlap is more marked and fo r fl uorescein ions in solution R0 � 70 A. We can think of associated pairs SA for which the overlap of t: s and IXA would be better than the overlap of es and as. It would be interesting to study the kinetics of energy transfer in such a case. The theory of sensitization has been developed by Kall man and London, by F. Perrin, by Vavilov and that used here by Th . Forster and by Dexter and Schulman. The case of forbidden transitions. In the above case we assumed dipole-dipole interactions, i.e. transitions in S and A were both al lowed. This gives the dependence of PsA on distance as 1 /R6 as i n Van der Waal s interaction o f this kind .
PsA(dd)
oc
I
R6 If the transition in the activator ion is of electric quadrupole type, the dependence on distance will be determined by a dipole-quad ru pole Van der Waals interaction and P sA (dq ) oc
I Rs
1
and if both transitions are of quadrupole type we have
PsA(qq)
oc R1 0
Dexter and Schulman have sh own that such transfers will occur with a significant probability. If a is a quantity of the order of the activator dimensions, then
(q_)2
PsA(dq) � R PsA (dd)
224
in
Luminescen ce
Crystals
which is a b o u t 1 / 1 0 fo r near-neighbou r positi o n s
In
the latter case
so that t h e
t h ose for
PsA (qq) P s A(dd) R=< R the life time -r: s i s i tself increased 2 -r: s(q) R=<
(�)4 (�)
r s (d)
in the ratio :
a
(qq) t ran s fer di stances are essentially of the same order a s (dd) t r a nsfe rs , while ten times higher activator concentra
t i ons are effective in
(dq) transfers. c o n t ras t to a l l this, when the activator transition is of magnetic d i p o l e n a t ure Dexter fi n d s t h at r es o n a n ce t ransfers only occur for such h igh concentrati o n s t h a t tr an s fe r w i l l o cc u r by electron exchange In
p rocesses . II.
OTHER TYPES
OF
ENERGY TRANSFER
WITHOUT CHARGE
D I S P L A CEMENT
l f the a ct iva t o r centre A emits ra d iat i o n which can be absorbed and a secondary fluorescence will o ccu r from B. In gases the effect is inevitable a n d is most important. We can recall t h e recent experiments o f A. Kas tler, J. Brossel and J . P. Ban· a t on the appare n t l i fe time of the 63P1 s t a te of mercury atoms excited by 2,537-A re s o n a n c e rad iati on : this life t ime measured by paramagnetic res onance t ec h n i q u es (du ration of coherence) is consid erably in c re ase d by m ul t ip l e d i ffu s i o n when the mercury pres s u re is increased . I n ino rganic p h o s p h o r s the r e ab s o rp t i o n effect is always p ossible and often d i fficult to eliminate. The m o s t i m po rt a n t p r a c t ical case is that when the activators A and B are identical . The interaction be t wee n the l uminescence centre and n e i g hb o u ri n g ions is often so large as to gi v e a c o n side r ab le Stokes shift , an d then the overlap of ab sorption and emi s s i o n spectra is negligible. I n sensitization effects even a s m al l overlap of t h e es a n d IXA spectra is s uffi ci e n t to e ffe c t resonance transfer, but if o n e of t h e activator transitions is forbidden , wh ich is o ften th e case, then t h e r e a b s o r p t i o n effects may becom e v e ry sm al l . The case of zinc sulphide phosphors. A s a general r u l e a p e rfec t zinc su lphide crystal sam ple is a l m o s t t ra n sparent t o its own visible 1 . Reabsorption o f emitted light
excite an o t h e r emission centre B, then
,
Energy transfer and sensitization
225
emission. However, for most powdered Z n S phosphors, the radiati ons from 4,000 to 5,400 A are slightly absorbed : this results in the ex citation of a short duration p h o sph o rescen ce ( Len a r d 's ' M o m ent a n anregu n g' ) . Ritschl has succeeded i n o b se rv i ng it under excitatio n by green li gh t (5,350 Tl-line an d 5,46 1 H g- l ine), but with a small inten s i ty and only when a special experiment is arranged to observe i t . On the other hand, the reab s orp ti o n o f the infra-red e m i ss i o n of ZnS i s not negligible ; s i mil arly the red emission of ZnS(Cu, G a ) is reabsorbed and leads to the exci tation of the infra-red emission b a nd s (Halsted , Apple a n d Prener) . Since 1 8 89 (B . Waiter) it has b e en assumed that to ex plain concentra 2. Transfer by electronic exch a nge between neighbouring atoms
tion quenching of l uminescent molecules p ai rs or aggregates of m ole
cules are formed which are supposedly non-luminescent. Johnson an d Williams have made a systematic study of this quenching mech anism in inorganic p h os p h o rs . Th ey assume that an activator c entre is n o t luminescent if there i s a no t h e r at the nearest z p o i n t s o f th e
The approach of an activator B to within a d i stance r of an a c t i vator A c an perturb the res p ecti ve p r ob a bil i ti es of rad i a t i ve e m i s si o n Pr an d non-radiative energy d i s s i p a ti on Pnr o f A . Since the overlap i nteg ral surrounding lattice.
v a ri es
e xp o nen ti al l y with
They then
f
'tpA 'tpB
r, J o h n so n
P nr
=
s
and Wiliamst postu l a t e t h a t
(- �c;!)
E(r) E(co)(I - e-o:r) the v a ri a t i o n of the effici e ncy =
give
exp
dr
'YJ
as a fu n cti on of ac t i v at o r concentration fo r the fo l l o w i n g : 22 in ZnF2(Mn) w i t h z with z 1 50 i n KCI(TI) 4,000 in Zn S(Cu) w i t h z I n t h e latter ca s e the h i gh value of z reflects the l o w =
Pr/(pr+Pnr) =
=
=
activator
"f The physical ideas o f this mo del are t h e sa m e as in t h e 'shell model' explaining the concentration q uenching of fluorescence in solutions, but mathematical formulation i s d i ffe ren t (see especially Jablonski, 1 957).
the
for
Luminescence in
226
Crystals
concentrc.tion, about 2 X w-·i Cu per ZnS for optimum efficiency. lea C.s to a d i stanc e b e twe en n eigh b ou rin g centres of about 1 00 A. It seems d ifficul t to accept t h i s size of t he extension of i ndi vidual centres, but by assuming the m o de l of Johnson and Williams, that pairs of c entre s form the qu e n c h i n g centres, we can assume that for extinction it i s not ne ce s s ary for all th e luminescence centres to form pairs. I t i s sufficient that t h e excitation energy of an isolated a c t i vat or .:an be transferred to one of these pairs (e i t her by re so na n c e This
In the case of gases and of o rga n i c solutions, c o ll i s io n s between l uminescent and q u e n chi ng molecules will e n ter into trans fe r pro cesses. Such collisions can be eliminated fro m considerations of luminescent crystals. or hole m igration) .
I l l . T R A N S F E R O F E N E R G Y BY P O S I T I V E H O LE M I G R A T I O N
The movement o f positive holes i n photocond ucting p h o s p hors gives an explamtion of energy t ran s fe rs over re l a ti ve l y l a r ge d i s ta n ce s . I.
Positive hole motion was first used (Riehl) to e xp lai n the excitation of l u mi n e s cen ce activator centres by ra di atio n absorbed in the funda mental a b s o r p ti o n band of the c rys tal lattice (in ZnS-wurtzite ;;. < 3 , 3 50 A ; i n CdS .A. < 5 , 1 00 A) a n d E l ectron not in an ab s orp ti o n band due t o th e • ce n t res . The excitation creates positive holes in t h e valence band and t h ese th e n d i ffus e i n t o the neighb o u rh ood of the centres. If the el ec tro n in the centre falls into the hole, then this gives a st ate of Cen tre excitation w i th the centres empty a n d conduction electrons available for re c o mbin a ti o n with th e centres and pro o- - - - - - - d uction of luminescence emission. Riehl's excitation mechanism
Ho!e
If traps exist close to the centres, then
of in the Riehl m ec h a ni s m they will not be a centre a;ier absorp tion of p re fe re n t i al ly filled by excited electro n s radiation lying within the ( fundamental absorption band s ee t h e p a r ag rap h on phosphorescence of a crystal lattice (Riehl) kinetics). Fig. VII ! . 2 Excitation
Energy transfer and sensitization
22 7
The quantum efficiency of the luminescence is a b o u t 20-30 per cent under excitation by Riehl's process. It is a constant when the wavelength of the e xc i t in g rc.diation is cha nge d and remains in the fundamental absorption region of the crystal (Antonov-Romanovsky and Al e n t s e v). On the oth e r hand , when the ex ci ti n g radiation falls i n the p roper absorption band of t h e C u c ent re , the efficiency i s higher a n d often approaches un ity. 2. The Schon-Klasens theory of energy transfer between two centres
Consider the 'de-activation' cf a lumin e sce n ce centre (e.g. Cu i n ZnS) by a 'killer' centre (such as Ni). We have, then : (a) Thermal activation of an electron from the valence band into an empty copper centre which needs an e n e rgy W which d e t e rm ines the probability of the transfer.t (b) Movement of the positive hole c re a te d i n t h e valence ban d . (c) A n electron from the :J.ickel centre falls into, i . e. a n n i h i l ates , the positive hole and leaves the nickel centre e m pty. We do not normally assume reso nance t ra nsfer to occu r i n these phosphors because the trans N1 fer distances are too great. The qu e nchi n g or 'killer' Cu action of nickel is easily ob c a w served at concentrations of I o-a g Ni per g. ZnS which corresponds to an average distance between 'killer' Fig. VIIJ . 3 Energy transfer by hole centres of 400 A. For re- migration according to the Riehi-Schon sonance this would have to Klasens mechanism be of the order of 35 A . T h e discovery of t h e phc tomagnetic e ffe ct i n CdS h as p rovided
t In recent studies on the analogous problem of the t ransfer between blue (Zn vacancies) and green (copper) centres in ZnS(Cu, Cl) phosphors, Mel amed (1 958) has given evidence for the possibility of s uch a transfer to occur even at very low temperatures (4°K). This fact lea ds to the assumption that the excitation itself pro d uces holes in the valence band and the thermal activation W is not necessary ; radiation of >. = 3 ,450 A was us!d for this excitation and was th u s not able to excite electrons directly from the valence band to the c o ndu c t i o n band according to Riehl's mechanism, but probably able to ra i s e electrons to empty localized levels in the fo rb idden band. However, if the temperature is h igh enough and thermal a c t i va t i on occu rs, the efficiency of the t ransfer p r ocess is enhanced .
228
Luminescence
in Crystals
o f h o l e motion. However, in CdS the Ki k o i n p ote n of the o rder of a few microvolts, while in germanium they exceed 10 m il l ivolts. The h o le mobility is thus very small . Experi m e n tal s t u d ies h ave given a v a l u e of th e ambipolar diffusion coeffidi rect evidence
tials are
cie n t :
D
2
. .
It is
fo u n d
that
=
=--=
e
-- . ·
- · t-
I" ""=' 2 . I 0 4 c m /s e c p e r vol t/cm i n CdS while i n germ ani um /1-
""='
2,300 cm/sec per volt/cm
If we assume a carrier life time of I 0 5 sec in Cd S , we can obtain
Fig. Y I I I . 4 Photoelectromagnetic effect (Kikoin effec t) The spec im en is irradiated on its surface, holes and elec trons difuse in t o the crystal: if the difusion current is defle c ted by application of a magne tic fieldparallel to the illuminated
D
surface then a potential diference appears width of the specimen
across the
fro m p , and fi n a l l y the d i ffu s i o n length L fro m the Ei n s te i n relation :
We find tha t which
L
L
""
= .,/ D-e
750
A
i n CdS
i s m uch smaller t h a n that in germanium L ""=' l /50 cm
but is s t i l l s u ffi cient to j u s t i fy the effects of hole migrati o n . Tn t h e m a i n w e c a n s a y that
Energy transfer and sensitization
229
(a) in photoconducting ph o sph o rs c ha rge mi grati o n will pred o mi
nate in e n er gy transfer ; (b) i n p h o s phors with t ran si tio n s within well-defined centres (such as rare ea r th i m pu ritie s ) resonance transfer will pre d omi n a te . This i s o n ly a rough ap p r o x i m a t i o n and t h e d i fferent modes of t r a n s fer can o ccu r at the s a m e t i m e.
TV.
ENERGY TRANSFER
M I G R A TI O N
BY EXCITON
We now r e t u r n t o t h e transfer process between a s e n s i t i zer S a n d an activator A. A nother p r o c ess i n which a n e l ectro n o n S ret u r ns to its g r o u nd state, w hi l e that o n A is ra i sed to an ex c i ted state, can be
described in t w o stages : (a) the return of the e l ec t r o n on S c r e a te s an exci t o n which diffuses to A ; (b) the exciton i s absorbed at A and raises an e le ctr o n i n to the excited state.
c a n assume the emiss i o n of an actual exciton wh i c h can be d e tec ted by its d i ffus i o n or a virtual exciton, i.e. t h e re is no co n s e rv a tion of energy in two p ro cess e s a and b (s i mply energy conservation over the w h o l e transfe r process) . These two c as es have been con sidered by H. H ake n . Transfers by re al excitons are naturally m o re interesting ; the i ntro d ucti on of virtual excitons is no more than a m a th em a tical d evice to describe the matrix elements o cc u rri n g in t h e evaluati o n of t h e t ra n s fe r p rob a b il i ty . A n o table e x pe ri me n t by Broser and Balkanski shows the possi bility of the action of excitons at large dist an ce s fro m t h ei r p o i n t o f creation . They irradiated one part o f a platelet o f Cd S t h ro u gh a n ar ro w window in an o p a q u e screen. The rad iati o n was of too low a quantum energy to b r i d ge the energy ' gap ' of the c rys t a l and t h er e fore to p rod uce ph otocondu ctivity. However, i t can p r o d u ce excitons w hi c h diffuse and fi nally d is socia t e at impuri ty levels and l i berate el e ct r o ns and holes. Thus p h o t o c on d u ct ion is o b se rv e d in the regi on of t h e c rys ta l where t h e e xc i t o n s d i s s o ci ate . At a distance x from the i r ra di a ted area the e x ci t o n d e n sity in the steady state is - :r:fL p = Po e We
The observed
photocu rrent varies with separati o n of t h e el ect rodes
Luminescence in Crystals
230
g i ve directly
relation of the above form . value for th e exciton diffusion
from the illuminated area according to a
length :
The measurements
a
0·23 cm in CdS Experiments show that the e x ci t a t i o n spectrum for the p h oto c o n d uc tion has h y d r o ge nlike features and is identical with t h e absorpti on spectra attributed to exciton formatio n . I n a d d i ti o n , a pp lic a tio n o f L
=
Pla tele t of Cd S
Opaque screen
Experimental arrangement used by I. Broser and M. Balkanski The platelet of CdS is irradiated through the window W and a plwtocurrent is observed between tire electrodes e and e' Fig.
an
VIII . 5
electric field does not modify the d iffu s i o n process showing that
a ge n t
neutral entities are involved. It i s difficult to prove that the diffusing
is n o t a photon, i.e. that p hotoconductivity is not excited by fluorescence. However, a di s ti n c tion can be made if non steady state ex p eri m e nt s are made, the form o f th e si g n al being dif ferent for each case (M. Balkanski and A. Fortini). a secondary
Using
a quantum energy greater than the crystal band gap,
an
intense photoconduction is observed due to free el ectro n and hole creation. Excito n mi g rati on over large distances is only possible in very pure and defect-free cry s tals . It i s p a rtic u l arl y sensitive to the presence o f s u r fa ce s t a t e s . B I B LI O G RAPHY
B OTDEN, T. P. J . a n d KROGER, F. A. (1 948) ' En e rgy transfer in s ensitized Ca3(P0�) 2 : Ce, Mn an d CaSi03 : Pb, Mn', Physica, 14, 5 5 3 . Sensitization phenomena
Energy transfer and sensitization
23 1
BoTDEN, T . P . J . ( 1 9 52) 'Transfer and transport of energy by reson a nce processes in luminescent solids', Ph i!. Res. Rep., 6, 425 ; 7, 1 97 .
The si s , Utrecht. B RAUER, P . ( 1 9 5 1 -52) 'Tragheitserscheinungen beim Au s l eu c h t e n sensibilisierter P h o s p h o re n ' , Ann. der Phys., 9, 225 ; 10, 282. B UTLE R , K. H. ( 1 953) 'Al kaline e art h p h o s ph o r s (Ca, S r, Bah(P04) 2 : So, M n ' , J. Electrochem. Soc. , 100, 250. CROZET, A . , F I G U E T , J . and JANIN, J. ( 1 9 5 3 ) 'Etude de quelques p ropri e t e s o p tiq u es de CaO(Pb, Sm) et CaO(Pb, Pr)', J. Phys. Rad.,
14, 1 2 S . D EXTER, D. L . ( 1 953) A theory of sensitized luminescence in solids',
F o ND A , G . R . ( 1 9 5 5) 'Energy transfer in calcium h alo ph osp hat e phosphors', British J. Appl. Phys., 6, Suppl. 4, S 69 . FROEHLICH, H . C . and MARGOLIS, J . M . (1951) 'The fluorescence of Ca a(P 04) 2 : Ce, Mn', J. Electrochem. Soc., 98, 400. FROEHLI C H , H . C. (1 953) ' S e n s itized electroluminescent re s po ns e', '
J. Chem. Phys., 21, 836.
J. Opt. Soc. Am., 43, 320. G I NTHER , R. J. ( 1 9 54) 'Sensitized luminescence of CaF 2 (Ce, M n ) ' , J. Electrochem. Soc., 101, 248 . J A N I N , J . and C ROZET, A . ( 1 9 52) 'Contribution a l ' e t u d e des pro p rietes o p ti q u e s de chaux activee au Plomb et au Plomb + Man ganese', J. Phys . Rad. , 13, 9 1 .
K ROGER , F . A . ( 1 949) 'A proof of the associated-pair theory for sensitized luminophors' , Physica, 15, 80 1 . LEACH, R . ( 1 958) ' En e rgy transfer and sensitization i n single crystal p hosphors', J. Electrochem. So c. , 105, 27. M ERRILL, J. B. and S CHULMAN, J. H. ( 1 948) 'The C aSiOiPb, M n) p h o s p ho r ' , J. Op t . Soc. Am., 38, 47 1 , 8 1 7. PRINGSHEIM, P . (1 949) Fluorescence and Phosphorescence, 545-7. Interscience Pub . , New York. R OTHSC H I L D , S . ( 1 932-36) ' O b er einen Fall v o n sensibilisierter Phosphoreszenz', Naturwiss. , 20, 850 ; Phys. Z. , 35, 557 ; 37,
757.
J . and KLI CK, C . C . ( 1 95 0) 'A study of the mechanism of sensitized luminescence of solids (in particular Ca Si0 3 : Pb, Mn)', J. Electroch em . Soc., 97, 1 23. S CHULMAN, J. H., G I N T H E R , R . J . and CLAFFY, E . W . ( 9 5 3 ) 'Pro perties of CaSi03 phosphors', J. Opt. Soc. Am., 43, 3 1 8 .
S CHULMAN, J . H . , G INTHER , R .
1
232
Luminescence in Crystals
S E N ( 1 9 59) 'Some aspects of the luminescence of CaF 2(Ce, Mn) and KC! + TlCl p hosphors'. Thesis, Indian Institute of Technology, Kharagpur. TEREN I N E , A. and PUTZEI K O , E. ( 1 958) 'Sensibilisation optique des semi-conducteurs par la chlorophyll c et pigments ap pare n t e s , J. S U N I T CHA N D R A
'
Chimie Phys. , 55, 68 1 .
R . ( 1 944) 'Innermolekulare Sensi bil isierung von Leuchtstoffen', Reichsber. d. Phys . , 1, 1 39.
T O M A S C HE K ,
A comprehensive paper
C . and S c HULM A N , J . H . (1 957) 'Lu minescence So lid State Phys ics 5, 1 22 . Academic Press, New York.
K LI C K C . ,
in
solids',
,
I.
Resonance transfer processes
Pioneer work
and LO N D O N , F . ( 1 929) ' O bcr quantenmechanische Energieiibertragung zwischen atomaren Systemen', Z. fiir Phys.
K ALLMANN, H .
Chem. , B 2, 207.
P ER R I N , F .
(1932) 'Theorie quantique des transferts d'activation entre molecules de meme espece. Cas des solutions fluorescentes', Ann. de Phys. 17, 283. V AVILO V , S. I . (1 943) 'A theory of concentration quenching of fluorescence in solutions', J. Phys. S. S. S. R., 7, 1 4 1 . ,
More
recent work
D EXTER ,
D . L. ( 1 953)
J. Chem. Phys. , 21,
'A
theory of sensitized luminescence in solids',
836.
D . L. and S C H U L M A N , J . H . ( 1 9 54) 'Theory of concentra tion quenching in inorganic phosphors', J. Chem . Phys. , 22,
D EX T E R ,
1 063.
F i:i R S T E R , T . ( 1 9 46)
'Energiewanderung und Fluoreszenz', Naturwiss. ,
33, 1 66 .
Fi:iRSTER, T .
( 1 948) 'Zwischenmolekulare Energicwanderung und Fluoreszenz', A nn. der Phys. , 2, 55. H o o GENSTR A A T E N , W . (1 958) 'Non-electronic energy migration in phosphors', Halbleiter und Phosphore, 285. Vieweg, Braunschweig. Symposium Garmisch-Partenkirchen, September 1 956. K L I C K , C. C. and S cH U LM A N , J. H. ( 1 957) 'Luminescence i n s o lid s Solid State Physics, 5 , 1 3 1 . Academic Press, New York. ',
Energy transfer and sensitization
23 3
11.1. Reabsorption of the emitted light
In gases, liquids or organic scintillators B I R K S , J . B . ( 1 9 53) Scintillation Counters, 73-8, 9 1 - 1 0 1 . M c Gr aw Hil Co. , New York. GUIOCHON, M. A . , B L A M O NT, J. E. and B ROSSEL, J. ( 1 957) 'Sur la coherence d u ph en o me n e de diffusion multiple de l a lumiere dans la resonance opti que ' , J. Phys. Rad. , 18, 99. KASTLER, A . , BROSSEL, J. and B A R R AT, J. P. ( 1 957) 'Diffusion de la l umi ere dans la resonance opti que '. Conferences Societe Fran9aise de Physique, 26 October 1 957. LAVOREL , J . (1 957) 'Effect of energy m i grati o n on fluorescence in dye s o l ut i ons ' , J. Phys. Chem . , 61, 864. LAVOREL, J . ( I 958) 'J n fi u e nce de la concentration de substances fiuorescentes sur l ' efficacitc d e s inhibiteurs de fluorescence', J. de Chimie Phys., 55, 9 1 1 .
fn so lid crystal phosphors H A L S TED , R. E . , APPLE, E. F . and PRENER, J . S . (1958) ' Ra d ia t i ve energy tran sfer in ZnS', Phys. Rev. Letters, 1, Z 505. KLI CK, C. C. and S CHULMAN, J. H. ( 1 957) loc. cit., 1 1 9. RITSCHL, R. ( 1 947) 'Untersuchungen iiber die Lumineszenzerre gu ng von ZnS-Cu Phosphor durch Jangwelliges Licht' , Ann. der Phys., 6, 207 . 11.2. Concentration
qu e n chi ng in crystal phosphors
D . L. and S CHULMAN, J. H . ( 1 9 54) 'Theory of concentra tion q u ench i ng i n i n o rga nic p h o s p h o r s ' , J. Chem . Phys., 22, 1 063. E W LES, J . ( 1 930) 'The n ature and size of the l u m i n e s ce n t centre', Proc. Roy. Soc., A 129, 509. EwLEs, J. a n d LEE, N. ( 1 953) 'Dependence of the luminescent effi ciency on the concentration o f the activator ; the size of the l u mi n es c en c e ce ntre s ', J. Electrochem. Soc., 100, 392. JOHNSON , P . D. and WILLIAMS, F. E . ( 1 950) 'The interpretation of the d ep e n d en ce of l u m i nescen t effi ci e n cy on activator c o n ce nt ra tion', J. Chem. Phys. , 18, 1 477. WILLIAMS, F . E. ( 1 955) 'Theory of activator systems i n l u min e s cen t solids', British J. Appl. Phys. , 6, Suppl. 4, S 97. (See also the Dis cussion S ect i o n . ) D EXTER ,
234
Luminescence in Crystals
discussion of concen tration qu en ch ing in organic and dy es LAVOREL, J . ( 1 9 5 8) loc. cit. P R I N GS H E I M , P. ( 1 949) Fluorescence and Phosphorescence, 349-6 1 . For
a
revie w and
ph osphors
Interscience Pub . , New York. W ALTER, B . (1 889) ' Die Anderung des F l uores ze n zve rmo ge n s der Ko n ze n t r a t ion , Ann. der Phys., 34, 3 1 6 ; 36, 502.
m
it
'
A fe w references about the 'shell model' F R A C KO W I A K , M . ( 1 957) 'Decay of phosphorescence of rigid solu
tions',
A cta Phys. Polonica,
16, 63 ; Bull. A cad.
Po lo n a ise des Se. ,
A. ( 1 954) 'Q uenching of p h o tol u mine sc e n ce of solu , A cta Phys. Polonica, 13, 1 75 . J A B LONS K I , A . (1 957) 'Yield of p h o tolu mi ne s ce n ce of so l u ti o ns ' , Bull. A cad. Polonaise des Se. , I l l , 5, 5 1 3 . P ERRI N , F . (1 924) 'Loi de decroissance du pouvoir fluorescent en fonction de la c on ce ntrati o n , Comptes-Rendus Acad. S e . Paris, III,
5 , 809.
ti o n s
J A B LO N S K I , '
V A V I LO V , S . I . ( 1 943)
theory of concentration quenching of fluorescence in s o lu ti on s , J. Phys S.S. S . R . , 7, 141 . '
1
178, 1 978.
'A '
.
Ill. Transfers involving the movement of positive holes
KLASENS, H. A . (1 9 4 6) 'Transfer of energy between centres in zinc sulphide ph o sph o rs' , Nature, 158, 4 8 3 . M ELAMED , N . T . (1958) 'Energy transfer in ZnS(Cu, Cl) p ho s p h o rs 1 . lliehl- Schon-Klasens modelt
J. Phys. Chem. Solids, 7, 146. R r EH L , N. and ScHbN, M . ( 1 939) 'Der L e uch t m echan is mu s von Kristallphosphoren', Z. fiir Phys . 1 14, 682. S cHbN, M. ( 1 942) 'Zum Leuchtmechanismus der Kristallphosphore', ',
,
Z. fur Phys., 119, 463 . WrsE, M . E . and KLASENS, H .
(1 948) 'Fluorescence efficiency , J. Opt. Soc. Am., 38,
and hole migration in zinc s u lp h i de s A.
'
226.
t Here are given only references concerning the physical basis of the model . For the references which are related to the applications of the model to phosphor escence decay, thermal quenching, k i l ler effects, and so on s ponding bibliography.
.
.
.
, see the corre
Energy transfer and sensitization
235
Efficiency of photoluminescence in zinc sulphide phosphors (see also
'cathodoluminescence' a n d 'electroluminescence') N. ( 1 949) 'The quantum efficiency of some crystal p h o s p h o rs' , Dokl. Akad. Nauk S. S. S.R., 64, 479. A LENTSEV, M. N . ( 1 956) 'Dependence of the luminescence o u tp u t of the phosphor ZnS(Cu) on the wavelength of the exciting light', Optika i Spektr. , I, 240. ANTONOV - R OMANOVSKY, V. V. ( 1 9 56) 'S u r le rendemen t de la l u m i n e scen ce dans l e s phosphores cristaUi ns', J. Phys. Rad. , 1 1, A LENTS E V , M.
694.
G E RGELY, G Y . ( 1 9 57)
' O ber die kalorimetrische Bestimmung der Phosphors', Z. Physikal. Chem.
Lumineszenz-Ausbeute von ZnS
Leipzig,
207, 8 1 .
2. On the killer effect of Fe, Ni, Co
in ZnS t
N . and C U R I E , D . ( 1 9 52) 'Niveaux electroniques d a n s les corps phosphorescents cristallins a centres po i s on s (Fe, Ni, Co)', Comptes-Rendus Acad. Se. Paris, 234, 75. ARPIARIAN, N . ( 1 9 53) ' S u r le deplacement d u niveau de Fermi par effet de temp e ra tu re d ans les sul fure s ph o s pho re s cents a centres po i so n s', J. Phys. Rad. , 14, 552. B UBE , R. H . , L A R A C H , S. and S HR AD E R , F . E. ( 1 9 5 3) 'The mech anism of i mp u rity poisoning in ZnS(Mn) by Fe, Ni and Co', Phys. Rev., 92, 435. GARLICK, G. F . J . an d GIBSON, A. F . ( 1 9 49) 'Lu minescence of photoco nductin g phosphors', J. Opt. Soc. Am., 39, 9 3 5 . K R YL OV A , E . S . (1 950) 'The mechanism of the luminescence o f ZnS(Cu, Co)', J. Eksp. Teor. Fiz. S.S.S.R., 20, 905. LEVY, L . A. a nd WEST, D. W . ( 1 939) 'The d ifferential action of Ni, Fe and C o upon the fluorescence an d phosphorescence of ce rtai n ZnS phosphors when excited by X-rays' , Trans. Faraday Soc., 35, A RP I A R I A N ,
1 28 .
J. ( 1 947) ' C o nt ribu tio n a !'etude de la photoluminescence du sulfure de zinc', Ann. de Phys., 2 , 4 1 4. Th e si s , Paris, 1 946. SADDY, J. and A R P I ARIAN, N. ( 1 9 50) 'Comparaison des actions ex tinctrices du nickel et d u cobalt sur les sulfures de zinc lumines ce nts ' , Comptes-Rendus Acad. Se. Paris, 230, 1 948.
SADDY,
t For other effects, see Chapter V, §Ill. I .
236
Luminescence in Crystals
F . ( 1 95 1 ) ' S tr a h l u ngslo se Elektroniibergange in Kris tallen', Z. flir Phys., 130, 477. VINOKOUROV, L . A. ( 1 9 52) 'The quenching of ZnS(Cu, Co)', Dok/. Akad. Nauk S.S.S.R., 85, 529. S Ti: C K M A N N ,
Hole migration, energy transfers and photomagnetoelectric effects in sulphide phosphors
(1958) 'Transferts d'energie dans les cristaux luminescents 607. D I E M E R , G . and H O O GENSTRAATEN, W. (1 957) 'Ambipolar and exciton diffusion in CdS crystals', J. Plzys. Clzem. of Solids, 2, 1 1 9. FRESQUET, M . ( 1 95 5) 'Etude de l'effet photo-magneto-electrique sur le sulfure d e c a d m iu m' . D ipl 6me d'Etudes Superieures, University of Paris. C U RI E , D .
mi n e rau x ' , J. Chimie Phys., 55,
IV. Energy transfer by exciton diffusion B ALK A N S K I , M . and WALDRON, D . ( 1 958) 'Internal photoeffect and exciton diffusion in Cd S and ZnS', Phys. Rev., 1 12, 1 23 . B A L K A N S K I , M . ( 1 9 58) 'Sur l e m ecanisme d u transport d ' e ne r g ie ' , J. Plzys. Chem. Solids, 6, 40 1 .
I . and B RO S E R - W A RM I N S K Y , R . ( 1 958) ' 0 ber den Mechan i smus der Energie-wanderung in CdS-Kristallen', J. Phys. Clzem.
BROSER,
Solids, 6, 3 8 6 .
and H o o GE N S T R A ATEN, W . ( 1 9 57) loc. cit. E. ( 1 958) ' S u r le transfert d ' en e rgie par les excitons dans le sulfure de cadmium pur', J. Chimie Phys., 55, 642. H A K E N , H. ( 1 958) 'Sur la t h e o r i e des excitons et le u r role dans les transferts d ' e n e r gi e a l ' eta t solide', J. Chimie Phys., 55, 6 1 3 . D IEMER , G . G RILLOT,
CHA PTER
IX
Electroluminescence and Electrophotol uminescence
The prod uction of luminescence solely by the action of an applied electric field on a material is known as electroluminescence. The various effects known to date for crystall ine solids can be d ivided into two main categories as follows : 1. 'Pure' or 'intrinsic' electroluminescence (the Destriau effect), which is the result of the sole action of the applied electric field, as in elec troluminescent cells or panels. These are made by dispersing a suit able phosphor powder in a suitable dielectric in a condenser system, an alternating field being applied to the electrodes. 2. Electro/uminescence due to charge carrier injection . This is the emission produced by injection of charge carriers through a recti fying contact such as a 'eat's whisker' contact on a crystal or a P-N junction . A cu rrent passes, the luminescence intensity being approxi mately proportional to this current. In contrast, for intrinsic electro l uminescence the phosphor need not be in con tact with the electrodes and no net current passes through the crystals. The term electrophotoluminescence was origi nally reserved for the G udden and Pohl effect, i.e. for the transient luminescence occurri ng when an el ectric field is applied to a phosphor previously excited by, say, ultra-violet or X-radiation. A number of effects produced by the action of electric fields on photoluminescence may be grouped under this term , some of them permanent, the field causing quenching or sti mulation of emission during photo-excitation. 1.
I . ' P U R E ' O R ' I NT R I N S I C ' E L E CT R O L U M I NE S C E N C E
Introduction : description o f phenomena Historical. The circumstances of the discovery of electrol uminescence
are worthy of mention
here. In 1 93 6 G. 237
Destriau completed his
Lum inescence in Crystals
238
D octo rate Thesis at the
Radium Institute in Paris. It was concerned produced by a particles i n zinc sulphides. The experiments showed that the fluctuations i n a-particle range were larger when me a s u re d by the sci ntillation method than by any other metho d, e.g. using io n i z a ti o n chambers . Destriau explained this d i f ference by the fact that the fluctuations in the number of excited centres d ue to each rx particle and i n the sci ntillation yield cor r e l at e d with the fluctuations in pa rt i c l e range. In the course of this work h e wished t o compare t h e ionization o f the crystal lattice by an i n te n se electric fiel d with that prod uced by the Cl. particles : i t was i n this way that he saw the i l l u m i nation of the s ul phide u nder t h e acti o n o f the field and in the absence of a-particle excitation . with
scintillations
Metal p l a te IA )
-
"'.. .. .. --
---
__
Meta l p l a te
181
Sulphide
/
Con ducting
G l a ss
Sheet
o f m1ca
.
.. . .. . .. ,/
Mm
_ _____ ___
i
1
IlL
Co n duct1ng
film
1 n a r a /dJte
A
Fig. IX. l Various kinds of electroluminescent cells Cell originally used by G. Destriau
Electroluminescent lamps using conducting glass Malller for study of effect of tempera ture on electroluminescence. A high concentration ofzinc sulphide to dielectric binder is arranged. To avoid charge injection effects the transparent electrode is a thin sheet of mica and the mixture ZnS + araldite is deposited on the non- con duct ing face
c Cells used by J.
B
Electroluminescence
and e!ectrophotolwninescence
2.39
Production of electroluminescent 'cells'. The first ce ll s constructed by D e s t ri a u were very delicate. The phosphorescent s u l p h i d e was i n c lud e d in a liquid dielectric (cas t or o i l) a n d the transparent electrode necessary to see the emissio n was a sh eet of m ica covered with salt
water. The development of conducting g l ass or micat enables more robust cells to be made which are used in c o mmerc i al applications (electro luminescent l a m p s) . Th e zi n c s ulp hid e is e m b e d d e d in a p l ast ic d i electric (e.g. a rald ite or p o ly s ty re n e) or in a c e ra m i c . A co n d e n ser is m a d e by p u t t i n g s u c h a d ielectric l ay e r betwee n two e l ectro d e s , o n e o f c o n d u c t i n g gl ass o r mica a n d the o t h er a deposited metal layer o r b y metal foil . The thickness of the dielectric layer is a b o u t 0· 1 m m . Us ually abo u t 2 00 V is app lied to the cell giving an a v e rage field of 20,000 Vfern. Howeve r, the field inside the sulphide crystal g ra i ns will d e p end on the d ielectric . If a v oltage V is applied to the cell of thickness d, th e n Em = Vjd, th e mean field . For spherical grains of ZnS of d i el ec t ri c constant K1 in a dielectric of dielectric constant K2, th e field Ez n s in the g r ai n s is giv e n by Ezns
3K2
= Em · 2K2 + K1- v(K1 - K 2)
v is the fraction of the total volume o c c up i e d by the sulp h ide grains. Actually the c rys tals are an gul a r in fo rm and their internal field is very far fr o m homogeneous, even l eavin g a s i d e t h e p ro bl e m of pot e nti a l barriers in or on the crystal grains. Emission spectra. In gen eral , we find the same luminescence emission bands as in photoluminescence, for ex am p le , the blue and green bands of zinc s u l p h i d e . The posi tio n s of the re sp e cti v e maxima of the different bands show o n ly mi n o r c h a n ge s with the kind of excitation. For example, when the a p plied field is in c rea s e d , d e fi ni te di spl a ce m e n t s occur towards the red which are due to the Stark e ffect on the luminescence cen t re s . However, th e relative intensities of the different emission b a nd s can s h o w considerable v a ri ati o n s (Fig. IX.2).
where
t To make conducting gl ass (U.S. Pat. No. 2-522, 5 3 1 1 9th Sept. 1 950) a glass plate is heated to ab ou t 600° and then on its surface is sprayed a hydrochloric acid solution of stannic chloride containing a little antimony trichloride. There then forms on the surface a thin, very adhesive and transparent layer of tin oxide of small resistance (about a few ohms over the cell surface).
240
Luminescence in Crystals
figure, th e blue emission band of a ZnS(Cu) e n h an ced relative to the green band in the electro luminescence s p ect ru m or in cathodoluminescence c o m pared with the p h o t o lumin e s ce n ce spectrum. For insta nce, D e s t r i a u and Ivey
,
Often , a s shown in this
phosphor can be
l
80 !
I I I
I
60 40
4 0 ..
20
20 -
o L·
1.�00
5000
6000
5500
I I I I I I I I
I
---
_,
/
5000
>. i l l
I
I
5500
F i g . I X . 2 Emission spectra of a sulphide phosphor in photoluminescence (do tted curve) and in electrolumin escence (full line)
6000
.>. i l l
ZnS(Cu) with 'blue' and 'green' centres. Applied field frequency 20 c/s B ZnS(Cu, Mn) with green (Cu) and orangC'-ye!!o 11' ( Mn) hand>. Applied field frequen cy 50 c/s A
(After J.
Matt/er and T.
Ceva)
h ave de sc rib e d a sulph ide i n wh ich the two b a n d s had s i milar i nten si t ies u nder 3 , 6 50-A rad iati o n ; h owever, the b l u e b a n d b ec a m e pre
the temperature is
is quenched the typ e of excitation. When t h e fre qu e n cy o f the a p pl i e d fi e l d i s i n c re a s ed t h e intensity of both bands increases ; but the green band soon shows a satura tion effect while the blue band c o n t i n u e s to i nc rea s e Thus generally a ZnS(Cu) e l ect r ol u mi nescen t phosphor which shows a dominant green band at a frequency of 50 o r 60 cycles /s ec sh ows a b l u e emis-
,
i n cr e as ed , the bl ue band
d o mi n an t in electrolumi nescence.
When
before the green band whatever
.
Electroluminescence and electrophotolu minescence
24 1
sion at the frequency of about 2,000 cycles/sec. We shall return later to these saturation phenomena. Variation of brightness with applied voltage. Th e variation is very marked (exponential) . Destriau p ro p o s e d in 1 937 an empirical formula of th e following form : a V+ b L L0 exp (1)
(
=
then, on the form :
s u gges t i o n
of J ean Perrin, he
)
u sed o n l y t h e m o re
s i m ple
The a gr ee m e n t of the e x p re s s i on i n equation (2) with experimen t is sufficiently good over several decades of light intensity L. The im portance of t h i s expression is that it can be given a very simple interpretation and leads to that actually assumed for t h e phe n o menon of electroluminescence : that is, excitation of the luminescence centres by the collisions of accelerated electrons.
(2 )
,
0
0 2 0 · 1, 0 6
-v;, fectrvt volts
Fi g . lX.3 Variation of luminance L of electroluminescent plzosphors ZnS(Cu) and ZnS(Mn) with applied voltage V (After G. Destriau)
When an electron with charge e traverses a path x in t h e d i rection of the field E, it acquires a kinetic e n e rgy : Ektn eEx If W i s t h e energy fo r an accelerated electron to excite or i o n i ze a =
Luminescence in Crystals
242 l umi nescence
centre in collision, the pa t h x m us t be great enough for
that is
>
x
£kin > W
I
W
with
=
eEl
I f ;'( de n o t e s that mean free path for t he accelerated electrons, the fraction of electrons with paths greater than l is
f= The
b r i g h t n es s L
exp
( �) -
is proportional to this L
with
oc
exp
( -�)
b =
w 6';
,
frac t i o n / that is
Of course, the field E inside the c ry s ta l will not be exactly propor tional to the applied fiel d . In addition, o t h er factors than the fraction f wil l affect the brightn ess . This is why the fo r m ul a (2) c ann o t be exact. Nevertheless , i t m u s t be conceded that i t is t h e proportion / of the accelerated electrons wh ich determines t h e luminescence emission . Besides the factor f exp ( - b/E ) , w e must introduce into the ex p re s s i on for L the n umb e r n(E) of accelerated electrons ; the probability p that the collision of a sufficiently energetic elec tron with a ce n tre will res ult in the excita t i o n of the latter ; t h e e ffi ci en cy 'rJ of the resultant ra di a ti ve re co m b i n a t i o n s =
We can therefore
w rit e
L(E)
=
n(E) .j(E) . p17
.
Because of the inh o m oge n eity of the field inside the crystal , and the va riatio n of this d u ri n g a v o l t age cycle , we cannot apply s u c h a s i mple fo rmula to describe accu rat ely the relation b e t ween L a n d V. I n sp i te of this, t h e semi-empirical expressions of simple fo r m have some i nterest. As a modification of eq u ati o n (2), D e s t r iau proposed the follow ing: L
=
L0 V " cxp
( -;)
(3)
Fol l o w i n g Zal m , Dicmer a n d K l ascns ( 1 9 54) , many auth o rs h ave
E/ectroluminescence and electrophoto/uminescen ce
used the following formula :
L0 exp -
or again that of Al frey and Taylor : L
=
(
(
243
(4)
(5)
-
This formula is interpreted by assuming that the luminescence emission results mainly from the existence of a potential barrier of the Mott-Schottky type, where the field E is proportional to V V. The ag reem ent of the form ula (4) with experiment is o fte n tog 1 0 L L
=
L0 Vn exp
Nevertheless, Le h m a n n ( 1 960) has shown that if the 6 crystal grai n s o f zi nc s u l p h i d e are sepa r ate d accord ing to their di a m e te r, the lum i n 4 escence d u e to gra i n s of t h e 3 same dimension i s less t h an the luminescence for the whole po w d e r in the relation of (4) . 1 He has also shown that the l � minescence of a single par4 5 V -tlcle of phosphor follows t h e votts relation involvi n g exp ( -b/V) . . . . . F1g. IX.4 Vanatwn of /ummance L of a and no�that mvolvmg exp ZnS(Cu)phosphor with applied voltage V ( - b/ V V) . For an isola te d (After Zalm, Diemer and Klasens) particle one need not assume the existence of a Mott Scho t tky barrier, but such particles give less e m iss i on than those i n c o nta ct with the electrod e s (D. Curie, 1 953). It must also be true t hat for small voltages the field is no t sufficient to pro duce electroluminescence except in the surface barrier (th e Mott-Schottky b a r ri e r or an intrinsic barrier). H o we v er, at high voltages the luminescence emission can occur from the whole of the crystal. According to a sugges tion from Thornton, for an electroluminescent cell of the usual type, the relation in clud i ng exp ( - b/V V) is valid at small voltages and the relation including exp ( - b/ V) is applicable to high voltages This is very obvious in the res ults of the experiments of Antonov-Romanovsky ( 1 959). B -
very good (Fig . I X . 4 ) .
.
.
-
.
s�000
244
Luminescence in Crystals
As expected from all the above empi ri cal formulae, there is no threshold for the electrol uminescence effect : when the e miss ion is no l o nge r visible to the naked eye it can still be detected by means o f a p h o to m u l t ipl ie r and it can be shown that the change with v o ltage goes on without a discontinuity (Destriau and Domergue) . The ap parent observed th reshold d e pen d s on the s e nsi t iv i t y of the detector. log10 l 5
3 -
100
./Vvolts
Fig. IX.5 Parallel variation of the green and blue emission bands of a ZnS(Cu) phosphor with applied voltage
(J. Matt/er and T. Ceva) To obtain this data rigorously the displacement of the bands as the voltage is varied must be allowedfor. Inter position of blue or green fillers in fron t of the measuring photomultiplier does not give the exact parallelism
The case of sulphides with several activators. Di ffe rent emission bands be h ave in a di ffe re n t way with applied voltage. For i n st ance in ZnS(Cu, Mn) the band associated with copper predominates at low vo l ta ge s and that due to the manganese at high v olta ges In contrast, the green and blue bands of ZnS(Cu) change in a similar way, s howi ng that the same energy W is required to excite the two d i ffe re n t kinds of centres due to copper (Fig. 1 X. 5). ,
.
Electro!uminescence and e!ectrophotoluminescence
245
Brightness waves. We obtain a n i n sigh t into the mechanism o f electro luminescence by presenting sim ul tan e ou sly on a double beam oscillo graph screen t h e e mis si o n bri gh tn ess wave and the volt a ge wave If in the dielectric around the crystal t he r e exists a s i nus oidal field E0 of frequency f = wj2n, Destriau has shown in his early investiga tions that the field E in the zinc sul p h i d e leads E0 in phase with an -
.
angle 4> g i ve n by
4>
2
4n
where K is the dielectric constant and p the resistivity of the s u l ph ide. The magnitudes of both fields are given by tan
=
=
E = E0 cos rf> Later on, Destriau and I vey showed that the field £0 is itself lag ging behind the applied voltage V, by an amount which is com plex in interpretation and s ubj ec t to a ssu mpt io n s about the shape of the c rystals, &c. However, if the rel ative amount of s u lp h id e embedded in th e mass of dielec t ric is small, E0 is i n phase wi th V and the differ ence in p has e between the internal field and V is simply equal to rj>. Experime nt shows clearly a shift in a lead i ng direction of the bri gh t n ess maximum with respect to the voltage maximum.
Brilliance
Voltage
Brilliance
Z n S ( Cu )
Time
Zn S ( M n )
Fig. IX .6 Brightness waves obtained for ZnS(Cu) and ZnS(Mn) in an alternating applied field (G. Destriau)
246
Luminescence in Crystals
The resistivi ty p varies during t h e voltage cycle, and in contrast to the maximum, the minimum of the brightness is often found in phase with the zero of the voltage V. The simple form of the brightness waves obtai ned for ZnS(Mn), where there is direct excitation of the l uminescence centres, without ionization, contrasts with the occurrence of a secondary brightness maximum observed almost always for the ZnS(Cu) phosphors where the centres are ionized. The secondary maximum is related to elec trons which recombine with the centres after a delay, for example, because they have been trapped ; the intercrystalline contacts also have an effect on the brightness o f this maximum. If a steady voltage is applied to the cell the internal field becomes zero, and a weak continuous emission results. This is characteristic of pure electroluminescence. Phosphors used in electro!uminescence. Zinc sulphides showing-a good electroluminescence are relatively rare. At the voltages used, which are often much smaller than those causing dielectric breakdown, the acceleration of electron s from thermal energies up to those of several electron volts necessary for excitation of the centres is a relatively rare event. Recipes have been given for the preparation of good phosphors. We shall discuss these after looking a little more at the mechanism of the phenomena. Most often zinc sulphide activated by copper, silver or man ganese is used . The respective emission bands are in the green and the blue regions for copper and in the blue for silver and the yel low-ora n ge region for manganese. Addition of cadmium sulphide to zinc sulphide causes the emission bands to be displaced towards longer wavelengths (see page 1 20) ; however, generally the electroluminescence of solid solutions of ZnS and CdS is not as good as that for ZnS (Zalm). The electrolumin escence of cadmium sulphide has been observed, but under condi tions which more nearly approach dielectric breakdown than i n ZnS (K . W. Boer and Kummel, G. Diemer) ; in other experiments, electro luminescence arises by the injection of charges followed by electron hole recombination (R. W. Smith). It is likely that cadmium sulphide is too good a conductor for the internal field to be high, except in the neighbourhood of breakdown voltages.
Electroluminescence and electropho toluminescence
247
A. W ac h te l ( 1 960) has �thown that for a ZnS + HgS phosphor, activated with c o pp e r, a red electroluminescence can be o b t a ined wh i c h c o m pl etes the g a mu t of colo u rs which ca n he obtai ned i n
electroluminescence.
To have a greater fl exibility in t h e realization of various colo u rs , a si mpl e process is available (H. F. Ivey) ; it i s sufficient to e m b ed the electroluminescent s ul p h i d e in a dielectric which has been co l o u r ed by an o rg a ni c dye. The latter is n o t usually electroluminescent bu t acts as a colour filter for the light emitted by t h e sulphides. In most sulphides, oxides and silicates of zinc (willemites activated by manganese) the Destriau e ffect is obs erved . Thei r emission is green. In this group we should include th e selenides a n d tel lurides of zinc and cad miu m. The efficiency and application of e!ectroluminescent cells. E l ectro luminescence is the direct conversion of electrical energy in to visible light. However, t he e ffici ency Output I l u m e n /watt 1 is low, which is e a s i l y ex 20 p l ai ne d by the theory of centre excitation by collisions of a c celerated electrons since this 10 p rocess has a low probability. The efficiency reach e s an 5 op ti m u m value for a given 1. voltaget which depends on 3 the size of the s u l p h i de g ra i n s , 2 on the construction of t h e cell and on the applied field frequency. lvey and Lehmann 200 3 0 0 400 500 700 1 000 Volts 100 have obtained values ap fficiency of a ZnS(Cu) cell E IX.7 Fig. p ro achi n g 1 5 lumens per watt. a fraction of applied voltage (lvey and as It is t ho u gh t that th i s value Lehmann) may be doubled. Because of the low effic ien cy , appl i cati on s are limited at present to d i s p o siti o n s with low brightness such as safe lamps, dashboards, &c. The lighting of a room by means of a ceiling or walls e nti rely made of electroluminescent cells p r ovi d e s in a direct way th e adva n t ag e of indirect ligh t i n g : the absence of dazzles, shadows, &c. Moreover, if
t I n contrast, when the brightness i s proportional t o the frequency (absence of saturation effects), the effic iency is independent of frequency (W. Lehmann).
248
Luminescence in Crystals
cells wi th d ifferent activators are used , the colour of the luminescence can be changed at will by al te r ing the voltage or the frequency of the supply.
The excitation process for the luminescence centres involves three parts (Piper and Wi ll i am s D. Curie) : (a) The raising of electrons for acceleration into the conduction band. (b) Acceleration of some of the s e el ectron s by the fiel d . (c) C o ll is ion of these electrons with centres causi ng the excitation or ionization of the latter. Finally, the radiative or non-radiative recombination of electrons with centres wil1 occur. We now consider in turn these different processes : (a) Raising of electrons into the conduction band. These electrons come from donor levels which are deeper than the traps (which are empty in the unexcited sulphide) but not as deep as the centre levels. We can assume that their depth is about 1 or 1 ·2 eV. The question is, are these levels emptied by thermal activation or by the action of the field ? If a purely thermal activation occurs, the electroluminescence would be depeEdent on the temperature and involve a high activa tion energy, but this is not the case (Fig. IX.8). It must be due to a direct emptying of the donor levels by the field which is, as obvious, incapable of exciting the centres directly. Piper and Williams have shown that for such emptying of the donor levels an electric field of about 200,000 V/cm would be neces sary ; such a field could not occur t h rou gho u t the interior of the crystal but would probably exist in the potential barrier (Mott Schottky or intrinsic). A ccord in g to an idea of Frenkel, the field and the ph o n on s mutu ally assist each other in prod ucing ionization of the levels i n the fol lowing way : if t:J.e depth of the level is s in the absence of the field, the probability of ionization per second is 2. Discusion of the electroluminescence mechanisms
,
p
s exp
(
wh ich is very small if s is large. In t h e presence of the field E the depth is re d u ce d to e* s -f(E) =
=
Efectro luminescence and electrophotoluminescence
249
and the prob ability of ionization becomes p
s exp
(
During the first few cycles of the applied field on the cell the bright ness is very low (F. Vigean and D. Curie). Gradually the electrons fall into the traps which at the beginning are empty, and the ionization of the latter by the same process as above s o o n plays a dominant role in L
200
=
200
Z n S ! Cu i Gre en
150
150
100
100 50
50 0
Zn S i �" I
- 1 50
l OO 50
Fig.
IX.S
0
50
100
150 °[
- 1 00
_[_
•
Variation of brightness of electroluminescent sulphides with temperature (J. Matt/er) A rise in tempera ture decreases the mean pa th of elec trons between thermal collisions and tends to prevent their acceleration: in contrast the liberation of donor level electrons into the conduction band by the field is made easier. The two effects act in opposite directions. In addi tion norma/ thermal quenching of emission occurs. Haake has shown how corrections may be made to obtain the effects really due to the electroluminescence processes
: r. r:
� �
the supply of electrons to the conduction band. Thornton and Haakc have shown that the thermal activation of the trap of depth e 0· 3 eV which gives the electroluminesccnce L must be repl aced by a thermal activation with an energy e* which varies with the voltage and the frequency of the applied field, s* being of the order of a few hun dredths of an electron volt, sometimes greater, but always l es s than e . (b) Acceleration of the electrons by the field. The condition for an electron to accelerate is that it must gain energy more rapidly in the field than it loses by interaction with phonons ; if s is the energy of > such an electron : =
field
phonon:;
Luminescence in Crystals
250
I f w is the path between two p honon encounters, at the end of the w, the electron e x c ha n g e s with t h e p honon an e n e r gy hv. We c a n write the c o n d i t io n for acceleration in the fo rm d u e to Frolich and pa t h
Mott :
eEw >
/zv[l+ exp (lzvJkT)-1]
w is n o t at all well known for zinc sulphide ; i t is the order of 1 0 7 c m for the thermal electrons but this Jack of info rmation does n o t permit any p re ci s e discussion at the moment about the fi e l d i nt en s i ty capable of prod ucing t h e accelera tion. Nevertheless, we can be sure that most of the the rm al electrons a re not accel e rated by fiel d s less than 1 00,000 V/cm. Some of them Unfortunately
probably o f
-<.
1 0- 5 c m -
-- ·
- ---
�
Trap or 1 0.7cm
'-� Therm al e n ergtes reg10n
A ccelerac,on re.r;1nn
Fig. IX.9 Path of an accelerated electron in the
wil l a lw ay s be able to reach an energy of the order of several te n ths of an el ectr o n volt because of the fluctuations : for instance, at the end o f a pat h greater than the mean length w or at the e nd of a suit able interaction in which e n e rgy is received from the phonons rath e r than l o st to them. conduction band
The imp o rtant p o i nt is as follows : in ionic crystal s the mean free p a t h rise s grad uall y and is p rop o rtional to the energy of the elec t r o ns t Thus an electron which begins to be accelerated and crosses the critical zone at about a tenth of an electron volt has a mean path greater than 10-a cm, and the process of acceleration continues even i n fields of the o rde r of 20,000 V/cm. On the other hand the interactions, which are sensibly i s o t ro p ic at low energies, only o c c ur with low-angle s c a t te rin g at hi gh e r energies .
I I t rises even faster at
high energies where
w cc
£2•
25 1
and the path finishes by being a straight line effectively in the direc tion of the field. Thus, in an ionic crystal in an electric field of the order of tens of thousands of volts per centimetre, we can distinguish two electron groups : (a) the greater part of the electrons remaining at thermal energies, with an electronic temperature greater by a few degrees than the lattice temperature (this temperature does not show any effective increase except when the conditions for dielectric breakdown are approached) ; (b) some electrons, effective initially by favourable fluctuations in interactions, have a considerable temperature. The introduction of the idea of the electronic temperature into electroluminescence is due to Nagy and Goffaux. We should notice that the expression given previously for the fraction of electrons with mean paths to greater than /: Electroluminescen ce and electrophotoluminescence
f = exp
( -�)
is the same as postulating a Boltzmann distribution for the group of hot electrons :
f = exp - �
= eEx
(
)
kT,
where T, is of the order of 4, 700°K for x = 1 o-s cm and E 40,000 V/cm. x and T. are not limited by the thermal interaction wh i ch in this energy region no longer prevents the electron from being accelerated indefinitely. In particular, the loss of energy at a donor level or at a full trap when ionization of either occurs is a generator of avalanches for which the multipl ication factor is natu ral ly m u ch less than that for avalanches leading to breakdown. The stopping of the electron by a luminescence centre with excita tion of the latter is a relatively rare phenomenon : in the example above, to have an energy W of 2·4 eV (the value for a quantum of green light), the electron must be accelerated over a path six times greater than the mean path ;'(, where f e-6 1 /400. Only very rarely will an accelerated electron obtain sufficient energy to excite an electron from the valence band and to form a free electron hole pair. This is why no dielectric breakdown occurs. kT,
=
=
=
Luminescence in Crystals
252
(c) £>:citation of the centres by impact of a fast electron. I m p ac t of a fast electron with a l u mi nes cence centre involves the loss of the whole or part of its energy and the release of an electron from the centre into the conduction band (see Fig. IX. I O). Both electrons will have after impact some residual motion i n the field direction. They will be in the same state as an electron begi nning its acceleration and will be moved far from the original centre by the action of the field. This is borne out by Zalm's experiments . He applied a u ni d i rectional field to an electroluminescent copper-acti vated zinc sul phide (the field o s ci l l at i n g between zero and a maximum
Fig. lX. l O Schematic picture
for
electro/uminescence
D
Conduction band
c
Luminescence centre
d Shallow donor leve l
due
c
mechanism accelerated e /ectron
of excitation to
impacts
T Ionizatio n of donor by electric field I I A cceleration o f some e lec t rons raised into conduction band (!-path o e lec tron remain ing at thermal velocity) m Ejection of electron in it ia lly in centre due to impact of an accelerated electron
/
value) . The maximum of the brightness wave does not occur at the field maximum but at the time when the field is ze ro and when the electrons return to their original centres (Fig. IX. l l). However, in the ca s e of ZnS(Mn) pho s p hors when the centres are mostly excited but not ionized the emission maximum occurs only a short time after the field maximum is reached, t he displacement being clearly due to the life time of the excited state of the centre. Electroluminescence produced by fast electrons in the bulk of the ph o sphor is rather like cathodoluminescence, i.e. the traps are only slightly populated and the emission bands modify in the s ame way when compared to p h o to luminescence, &c. (this remark is due to Klasens). However, th ere are certai n di ffe r e n ce s , notably the much lower value of the excitation
253
energy, the much higher ionization density and the removal of elect rons from the neighbourhood of the empty centres by the electric field. Ele ctroluminescence and electrophotoluminescence
Recombination offreed electrons with empty centres: effect of applied field frequency on electroluminescence. For each cycle of the applied
field the donor ionization, electron acceleration and ionization of centres begins Brillia nce Z n S ( Cu i afresh. Within fairly wi d e limits the light sum in each cycle is constant and the brightness is p r opo r tio n al to V'Jitage the applied field frequency (J. M attle r , However, Zn S IMnl at hi gh frequen cies saturatio n Brillia n ce effects occur w hi ch are more marked for the green band Fig. IX. l l Brightness waves due ro a than for the blue band in unidirectional appliedfield (P. Zalm) ZnS(Cu) phosphors. If the frequency is too high the electrons liberated in any half-cycle have not recombined before the following half-cycle occurs. The brief calculation below, though rather over-simplified,t leads to a formula which shows good agreement with exp e ri me n t. Since the freed electrons are removed some distance from the centres in the excitation process we can assume a hyperbolic recombination pro cess. If n(t) is the number of excited electrons remaining after time t. then
1946).
no ( t ) = ( 1 +.n0at ) where a is a constant, a n d n0 the number of electrons initially excited . I n a time t = I /2f (f is the applied field frequency) the light sum S n
is proportional to
and the brightness is given by
so that
or
n0-- n( I /2f) B = S . 2f
B
..!_ B
oc
oc
n o 2rx (l +n0a/2/) ---
n02a
2f
actual fact, all the electrons are not excited into the con d uction band a t the same instant.
t In
254
Luminescence in Crystals
1 /B is a l i near function of 1 /f I f a: is large, i.e. if the life time of conduction electrons is short compared with the period of the ap· plied field, then the straight-line g raph of the relation will pass Blue b a n d through the ori gi n and B will be proportional to f. At low frequen cies (below 50 c/s), systematic devia Green ba n d tions occur from this relation due to polarization effects. The internal field is mu ch smaller than the applied field and depends on the 10 1 5 10[)0 frequency. These effects can be de Fig. IX. l 2 Variation of in scribed in terms of relations given tensifies of blue and green bands previously : of an electroluminescent ZnS(Cu) tan cfo = 2/Kpf E0 cos cfo ; hosphor with applied field fre E
Thus
-
p quency
=
The various regions present
in an
scope and electron m icroscope studies . The above theory suggests that there should be three regi o n s of i n terest in a n electroluminescent electrolumin escen t ma terial: m icro
layer :
(i) A region of h igh field strength (superficial or intergranular
potential barriers) greater than 1 05 V/cm where direct ioniza tion of traps or donor levels occurs due to the high field. This effect increases the number of conduction elec t rons (ii) A region in which these electrons are accelerated and excite the luminescence centres where the field is greater than 1 04 V/cm. In tllis region the luminescence emission occurs. At low volt ages it occurs in the potential barrier, but at high voltages it extends right across the crystal grains. (iii) A dark region where the field is low, less than 104 V/cm. Electrons removed from centres and donor levels move into this region, their energies remaining at thermal equi l ibrium values. They can only return to the second region when the field reverses. They become trapped in the present regio n and this causes delayed recombination. Microscopic observations on zinc su l phide grains indicate a very heterogeneous pattern of electroluminescence in contrast to the uni form emission under ultra-violet excitation. S ome crystals remain u n e x c i ted w h i l e o t h e r s sh o w a reasonably u n i form e m i ssion over the .
E!ectroluminescence and electrophotoluminescence
255
whole grain. O t hers, particularly the larger sizes, and presumably im perfect , show bri g ht spots of emission due to local inhomogeneity in the field . The exis te nce of these bri ght spots is beyond question. However, G. Destriau observed that the apparent brightness of these spots, c ompared to the brightness of the continuum, is considerably en hanced when the observation is made with a micro scope : it is well known that the ratio of the vis ibility for a spot and an extended luminous surface is g iven by Vspot
G2
where G is the microscope magnification. To see the continuous b ack g ro u nd emission G must be less than 1 00, otherwise on ly bri gh t s pots are observed . P. Goldberg (1 960) has described experiments with the elect ro n m ic roscope . Electroluminescent zinc su l phides s h ow , q u ite s y ste m a t ic ally , 'etch pits' indicative o f in h o m o g e n eity (possibly disloca ti o ns) which g ive s an i ncrease i n cond uction electron co nc ent ra t i ons , the d e n s i t y of these pi t s b e in g 1 0 to 1 00 times h i g h e r than i n non
Vsurfaco
=
electroluminescent specimens. This is pe rhaps the first observation of any systematic d i ffere nce between electroluminescent and non electrolum inescent zinc s u l ph id e s . Techniques for improvement of electroluminescent phosphors. To ob tai n good electroluminescent zinc s u lphide g ood crystal l ization is necessary. The crystals must have d onors for generati on of the acce l erated electrons but few traps. Phosphors showi n g a good 'Destriau' effect usual ly show little phosphorescence. An electroluminescent zinc sulphide can be made by the addition of donor levels or creatio n of potential b arri ers and r e g io n s of high field s tre ngth . Thus Destriau and Saddy refired zinc sul phide in an o x i dizi n g atmosphe re or with an admixture of zinc oxid e , the latter giving relatively shallow donor levels. Lehmann has d escribed t he p reparation of e le c t ro l umi nescent cells by m ix i n g a non- electrolumi n escent zinc su l p hi d e with metal particles or a semi -con d ucto r such as Cu2S. The optim u m concentrations of l umi n es c ence activators for elec troluminescent sp eci mens are hi gher than for pho tolum i nescence . In view of the low p robabili ty of the impact ionization process, this would be e x p ec t e d . For ZnS(Cu) phosphors the optimum concentration
Luminescence in Crystals
256
of copper for photoluminescence is about 2 x I 0 - 4 g Cu per g ZnS (A. Guntz), while optimum concentrations for electroluminescence are of the order of 10-3 g Cu per g ZnS. The content of copper is limited by the effect of the higher concentrations in producing a grey powder and also by the fact that the copper will not enter the crystal lattice. Refiring of zinc sulphide with copper added is a 'formation' process sometimes used. H. Froelich has shown that 'sensitization' for electroluminescence can be produced by a second activator impurity, e.g. copper can be included in ZnS(Mn). The latter can be excited without copper pre sent but needs a higher threshold field (see Fig. IX.3). Z n S(M n ) sensitized with copper can be excited by quite low fields and the emis sion bands of manganese and of copper appear at the same time i f the concentration of manganese is small. At high Mn concentrations only the manganese emission band occurs. J. Mattler and T. Ceva have found some ZnS(Cu, Mn) phosphors to show the following effects as the applied field is increased : at low voltages the intensity of the manganese band rises slowly, then reaches a critical point, after which it rises rapidly with the field. At low voltages the excitation is probably due to the sensitizer, but at higher voltages direct excitation occurs. It is doubtful whether associated Cu(Mn) pairs occur ; the most likely process is hole migration from the copper to the man ganese centres, thus emptying the latter in readiness for recombina tion. Some organic materials show light emission in an applied field (e.g. gonacrin and acridin orange) (A. Bernanose et al.). In many ways the behaviour is like that in the Destriau effect. The brightness voltage relation is of exponential form (e-Bilj and the brightness waves lead the voltage oscillations, and so on. Reference should be made to the publications of Bernanose and also to the writer's article 'Theories of Electroluminescence' . IT .
ELECT R O L U M I NESCENCE D U E TO CHA R G E C A R R I E R INJECT I O N
Injection of charge into a crystal can give rise to light emission but differing in characteristics from those of 'intrinsic' electrolumin escence as follows : (a) The effect is observed for direct current flow and persists for as
Electroluminescence and electrophotoluminescence
257
long as the current flows. In the Destriau effect build-up of the internal field (polarization) causes the emission to fall to zero. (b) The light intensity is proportional to the current. Electroluminescence due to charge injection arises from different mechanisms from those of the 'intrinsic' effect. In one group of phenomena an injection occurs from an electrode into the cry s tal e.g. electrons in a su rface barrier with a strong applied field. The electrons are accelerated and excite luminescence centres as in the intri n s i c case. Only the source of electrons is differ,
ra ) Appli ed vo ltage
E l e ctron
'
in; e c tion
·, " ..
//
/
"" )? Radiattve recombinations '
' ,
/
Fig. IX. 1 3 Energy-band diagram for a P-N junction (a) without applied field (b) field applied in forward direction: injection of mino rity carriers inferred from radiative recombination (Lehovec, Accardo and Jamgochian)
ent. Such effects can be observed in single crys tal s of suitably acti vated zinc sulp hi d e, or in thin films, in contact w ith elect rodes In the second group light emission occurs at a P-N junction (Fig. IX. B). If operated in the forward direction electrons from the N-type material pass into the P-type and find empty centres or re combine directly with positive holes having suffered no acceleration. If t he junction is operated in th e reverse or 'blocking' direction a high-potential gra di en t appears at the junction and carrier accelera ti o n can occur. Completely different effects from those of the pre vious group occur. However, both groups show the characteristic behaviour des cri b ed in (a) and (b) above. .
J. .•
I.
L I I I l l t i L .) t. C U C. L
tll
1. 1 _) ",) / £ 1 / ,\
Electroluminescence in single crystals or thin films of zinc sulphide between electrodes in contact with them
The first i nv est igation s were made by Piper and W i l l iam s ( 1 952) . In the 'intrinsic' electroluminescence of normal type with b ri gh t n ess w ave le a d in g the v o l t age, a n o t h e r b ri gh tnes s wave in p ha s e with the appl i ed voltage was found (see Fig. IX. l 4). The emission spectra are the same in each case but the i n phas e component occurs at hi gh er voltages and rises more rap idly with v o lta ge than the out-of-phase component. Frank! has shown that the brigh tness of the i n p h as e emission is p rop o rt i o n al to the cu rre n t addition to
-
-
,,, I I I I I
l ' Out of phose '
I
component
r
Fig. IX. l 4 Out-of-phase and in-phase comp onents of electroluminescence in relation to applied field (Piper and Williams)
flowing. It most likely arises from field emission at the cathode fol lowed by th e usual processes of electroluminescence.t It has been observed in ZnS(Cu) (green and blue emission) and i n ZnS(Mn), &c. Such effects can be obtained in p owde r-typ e electroluminescent cells when these have only a small proportion of b i n d e r dielectric (cf. Fig. IX. l). Electroluminescence at low fields. Using thin films, Thornton ( 1 959) has ob ta i n e d electroluminescence fro m ZnS(Cu) with an applied voltage of only 1 ·5 V, that is, less than the mean energy of the e m i tte d photons (2· 6 eV). T hi s is rather like the e xc i ta ti o n of cathodolumin escence by l ow e n ergy electrons (see page 292). In o rd e r to exp l ain this effect the nature of the electrode and its work function must be -
t We might call this effect an injection-controlled electroluminescence (in the same way as Cusano and Williams referred t o p hoto-electrol uminescence as radiation-controlled electroluminescence).
Electrolwninescence and e!ectrophotoluminescence
259
known ; perhaps there is a positive hole injection which empties the emission centres or the electron s penetrate the sulphide with enough energy to excite the centres. Whatever the mechanism, it seems un li kely that the electrons are accelerated in the sulphide.
Boer and Kummel and also Diemer have observed electrolumines cence in cadmium sulphide at fields near to breakdown values. R. W. Smith observed emission in unactivated cadmium sulphide having indium electrodes, the field in the crystal being less than 1 ,000 V/cm . At room temperature band-to-band recombination of electrons and h oles occurs and at liquid air temperature the Ewles-Kroger type of 2.
Electroluminescence of cadmium sulphide in weak applied fields
E/ectro / u m t n e scence
Transmission
1 0 0 '/, 0
,,s·on·
L
·
Fig.
77°K
:,zo o
1 0 0 '/,
5 �no
IX. l 5
fle ctro lumin e scen ce ' --, _
Tra-nsfnission
300 ° K
Emission spectrum for electron-hole recom bination in cadmium sulphide (R. W. Smith) A t 77oK band-to-band recombination (near absorption edge) and Ewles-Kroger luminescence (peak at longer wavelengths) are observed A t 300oK the Ewles-Kroger emission is quenched and on�y band-to-band recombination is seen
emission also appears. Indium provides an ohmic contact so that electrons can be injected at the cathode (A. Rose). Smith also as sumes that certain 'formed' spots or points at the anode can give posi tive hole injection and so luminescence arises from electron-hole recombination in the volume of the crystal. At the anode points there are pockets of yellow luminescence and in these regions th� field is hi gh Smith found that the intensity of the green emission was pro portional to the current flowing and that the 'brightness waves' were in phase with the applied field. .
3. Electroluminescence of silicon carbide
Luminous effects in rectifiers made of silicon carbide have been much studied . The first i nvestigations were those of 0 . Lossew (1 928-40) .
260
· �
Luminescence in Crystals
The usual arrangement is a crystal of carborund um pr o v ided with a point-plane electrode system (eat's whisker). In other systems two plane electrodes have been used . Lossew found that when a voltage was applied in the reverse direction a 'Luminescence type I' appeared as luminous points near to the eat's whisker, but for the opposite or forward direction case a 'Luminescence type 11' appeared in an extensive region of the crystal. The type I emission is attributed to field emission effects at the point contact and it is not seen when plane electrodes are used . Type 1 1 emission is d ue to the phenomenon of charge injection at a j u nction (Lehovec, Accardo and Jamgochian). It is only found when the crystal has a s u r face layer of different pro perties from those of its volume. For example, in a P-type crystal with an N type surface the type li luminescence appears when the junction is biased in the forward direction (Fig. Brillia n c e IX. l 3), that is, when the N type surface is negative. Lehovec, Accardo and Jamgochian have shown that above a certain threshold cur rent the luminescence L is proportional to the incre Volt a g e mental current : L = a(I-!0) Fig. IX. I 6 Brightness waves for a SiC The 'brightness waves' are in rectifier (G. and D. Curie) phase with the current (G . N.B. No out-ofphase component and D . Curie). For a long time the structure of silicon carbide has been little understood because of the large fractions of impurities usually pre sent in the crystal. Slowly it has been un ravelled, mainly due to the work of Kroger and Lely (Garmisch , 1 9 56). I n many ways silicon carbide resembles zinc sulphide. The more common form is hexagonal with an optical absorption edge at 4,200 A (2 95 eV) at room temperature.t When pure, the hexagonal crystals are colourless. They are obtained by sublimation at a -
·
vertical transition in the band model with emission of a phon on of 0·09 eV t The energy-ban d gap is 2·86 eV, but the
ener� (Choyke and Patrick, 1 957).
absorption limit corresponds to a non
26 1
very high temperature (2,500°-2,600°C). At lower temperatures (T < 2,200°C) a cubic form is obtained with absorption edge at 4,400 A at room temperature, giving the crystals a yellowish colour. Silicon and carbon both occur in group IV of the periodic table. The elements of group V, nitrogen and phosphorus, produce donor levels, those of group Ill, aluminium and boron, produce acceptor levels. Hexagonal SiC crystals are coloured green by nitrogen and phosphorus and blue by aluminium and boron. Luminescence emission bands have been found in the blue and green regions and are attributed to associated donor-acceptor pai rs, and in the orange region due to excess of nitrogen. For the earlier crystals investigated the preparation was not controlled carefully and gave either wholly type P or type N crystals, or samples with surface junctions. Now such junctions have been deliberately produced and have made an accurate study of electroluminescence processes poss ible (L. Patrick and W. J. Choyke). They involve partly a band-to band recombination of electrons and holes and partly recombina tions inimpurity centres. Recently, intrinsic electrolurninescence has been observed in silicon carbide by J. Weizburg (1960). A crystal showing the above effects when arranged as a rectifier was placed in a field of 1 06 V /cm and insulated from one electrode by a sheet of mica so that no charge injection could take place. The field was intense enough to ionize the surface donor levels and to accelerate the conduction electrons to produce electroluminescence. Electroluminescence and e!ectrophotoluminescence
During electrolytic oxidation of various metals luminescence is some times observed, particularly for aluminium electrodes.t For d.c. con ditions emission occurs at the metal acting as anode and occurs in a thin insulating oxide layer in which the field is nearly 107 V/cm , which corresponds to a potential different of 1 00 V across I 0 5 cm . Acceleration of electrons and excitation of centres occur, the emis s i on being characteristic of impurities in the alumina layer. Often it is yellow-orange and due to manganese impurity. The emission intensity is proportional to the current (/) and van Gee! has shown that it increases with the oxide layer thickness (d) in the following way : L al(el'd- I)
4. Luminescence in electrolysis
=
t Emission has also been found for Zr, Zn, Ta, Mg and W electrodes .
Lum inescence in Crystals
262
where a and b are constants . This indicates the occurrence of electron avalanches. An initial electron prod uces eb"' e l ect ro ns over the path length x a n d s o for the total t h ickn e s s
L
J:
(eM - 1 )
I n a n al te rnatin g field scintillations occur when the aluminium is cc
eb"' dx
cc
either anode or cathode. van Gee! points out that there a re many ways of e x plai n i n g these scintillations and that different effects occur ac c o rding to the nature and concentration of the impurities prese n t When the aluminium is the anode field emission effects c a n be a ssu m e d but when acting as cathode it mig h t be assumed that the thin o xi d e layer produced in the p rec ed i n g h a l f-cycle is n ot homo geneous and consists of a n N typ e region near to the electrode and a P-type region a dj acen t to the el ect ro lyte G. and D . Curie have fo u n d that the brightnes s waves' are in phase with the app l ie d fiel d . The oxide l ayer was so thin that no luminescence was visible under u ltra-violet radiation or c atho d e ra y excitation. With thick layers van Gee! h as found an app reciable phase shift for the emi s si o n relative to the field in the le a d i n g d i rec ti o n .
,
-
.
'
-
.
Al th o ugh germanium has been the subject of so many precise inves ti gati on s c ompared with the more usual luminescent solids, it i s i n this s olid that so c o mp le x a nd various a collectio n of phe n o m e n a i s fo u nd We have already briefly described the electron-hole, band-to band r ecombina ti o n emission (Chapter IV, §IJ) obtained by injec t i o n of electrons into a P-type region or holes into an N-type region (Haynes and B ri ggs R. Newman). These workers us ed P-N junc tions, but i nj ectio n can also be p r oduced at metal contacts. The re combination is u sually of an i nd i re ct kind (simultaneous emission of p h o ton and ph onon) At room t emp erature the emission maximum is at 0·68 eV (about 1 · 8 p) : at li q u i d air temp e ra tu re it is at about 0·72 eV (about 1 ·7 p), which co rre sp on ds to the shift in the band ga p
5. Infra-red electroluminescence in germanium
.
,
.
with temperature. The lowest minimum of t he conduction band c o rresponds to the B ril l o uin zone edge and electron-hole reco mb i nati o n (with k = 0) is only pos sible by an indirect t ra nsit i o n (see Fig IV.2). However, the re is a second minimum at k 0. When the temperature is high e n ough to give some elec tro n s at t h i s m i n i m u m then d i rect recombination .
=
,
Electroluminescence and electrophotoluminescence
263
occ u rs with peak emiss i o n at ab o u t 0· 8 1 eV ( 1 · 5 /1) . The i n tensity of t h is second band rises with temperature and i nvol ves an activation energy of 0· 1 6 eV (see page 84). Recombination via imp u rity centres is ge ner al ly non-radiative in germani u m (so -calle d deathnium centres). Band- to -band recombina tion emission is o nly observed for high c urrents (up to 1 amp) and specimens seem to have few non-radiative centres. Thus bimolecular r ecomb in at io n predominates. However, certain centres give radiative recombination, e .g . an electron is captured in an empty centre and t hen the cen tre is refil led by a hole and at least one of t h ese transiEmtsston
07
t Vt a t n
term edtary · centres
+
From b a n d to hand
eV
Fig. IX. l 7 Radiative recombination in germanium with dislocations functioning as centres (C. Benoit a la Guillaume) Spectral distribution measured at 95 °K
tions may be made with photon emission. This is so for centres located on dislocations (C. Benoit a la Gu i ii au me) which give a g roup of bands at about 0·5 eV (2· 5 /-l) (see Fig . IX. 1 7). It is also the case for copper in ge r m a n i u m (see page 1 26). An electron and a hole fal l i nto this centre and then make a radiative reco m b i n at ion givi n g a n e mi s si o n a t 0·6 eV (2· 1 p.). We m i ght ask why a band-to-band recombination which i s bi m olecul a r leads to an emission i n t e n s i ty proportional to the cur rent and not to its square. Now t he rate of re com bi nat ion is prop or tional to the product of electron (n) and hole (p) densities : R
=
n;-
264
Luminescence in Crystals
R, b e i n g the recombination rate and 1li the carrier d e ns ity in i n trin s i c germanium for which n p n;. If e l ectro n s are inj ected in to st ron gly 'd o p e d ' crystals the hole density is essentially constant a nd np (second-order kinetics) is sen sibly proportional to n (first-order kinetics re s u lt) . Injection into in tri ns i c m a terial als o gi v e s emission proportional to t h e current, though with s om e deviations at h i gh current densities. O p tica l ab s o rpti o n studies show that a state is reached in which the p ro du c t np is p roport i o n al to the c u r r en t (R. Newma n) . The above will apply when band-to-band reco mbination predo m i n a tes. but when rec o m bi n a t i o n via c e n t re s i s the main process =
=
E
Fig. IX. 1 8 Structure of valence band maximum in ger manium. Thejump of a hole from the band V2 (light holes) to the band V1 (heavy holes) occurs with infra-red emission
(Ben o i t) and there is co mpetiti o n between the two processes, the in tensity of t h e total luminescence L is p r op o r tion al to the cu rr e nt : L kl. H owever, if L1 is the i n tensity of the band-to-band emission and L2 that fo r recombination in centres, then L1 aJ2 b ut L2 kl- a1 2 Luminous effects due to 'hot' holes in germanium. P. Aigrai n and C. Be n o i t a la G uillaume have sh o w n that it i s relatively easy to a ccel e r ate holes of small effective mass in ge rm a n i u m (s ee Fig. IX. l 8) . The apparatus used was described in C hap ter IV ( F i g . IV.4), a point con tact giving h o l e injection into N-typ e germanium. The u p p e r valence band ( V1) with small c urv a tu re corresponds to heavy holes of mass R: }m0 • The lower band ( V2), with large curvature n ear to k = 0, i nvolves ' l i gh t ' holes of about 0·04m 0 effective m a ss (m 0 is mass of free el ectr on ) . A field of 1 ,000 V/cm is sufficient to =
=
=
Electroluminescence and electrophotoluminescence
26 5
accelerate the latt e r a n d equ i lib riu m between the light and heavy holes is d es troye d . T h e ligh t holes can thus be raised in the V2 band to a wave numb e r k and they can then pass over to the V1 band with emission of radia tion. The emitted pho t o n energy is given by the di s tance between the bands V1 and V2 for the k value re ached by th e hole. An infra-red emi ss i o n res ul t s . The band V2 wi th larger curvature near k 0 th an the band V1 ten ds to become parallel to it at h igh k values. Th e s ep a rati o n for k in th e (1 1 1 ) di rectio n is about 0· 1 9 eV (Kane). It i s also found that acceleration in th e (1 1 1 ) direction g ive s emission peaki n g at 0 · 1 9 e V (6· 5 fl wavelength) (J. Pa n ko v e) . Pankove has studied emission from the s u rface of germ a n i u m (by putting an ohmic contact and an i nj ecti on contact cl os e to each other at the Weierstrass p oi n t in the a rra n ge ment of Fig. IV.4). An al ogo u s effects to the a b o ve are observed , but the h igh field necessary to accelerate the light h o les is pro vid ed by the i nve rs ion layer at the ge rma n i um s urface . The 'ho t' holes which have been accelerated a l s o emit the r m a l radiations a t l o n ge r wavelengths t h a n t h e above (J. K e s s l er) . =
Electroluminescence effects due to charge i nj ection through a P-N j unction or emission from field accelerated ch a rges have been ob s erved in (a) 111-V semi-conductors such as indium antimonide ( Moss a n d Ha wk ins) or gal l ium a rs e nid e ; (b) some diamonds of type 11 ( Kra utz ; Wolfe and Wo o ds) ; (c) cuprous oxide Cu20 (Frerichs and H an dy) . 6. Other investigations
Ill.
ELECT R O P H OTO L U M I N E S CE N C E
If an electric fiel d is applie d t o certain p h o sph o rs previously exci ted by ultra-violet radiati o n , X-rays or cathode rays, &c., t h en a b urs t of light is observed. This effect has been mainly i nvestigated in sul p h i d e p h os p hors of the type ZnS(Cu) or ZnS(Mn). G udden and P o h l used a constant ap p l i ed field and this was quickly a nnu lled by the i n te r n al field, the emissio n b e i n g of s ho rt d u ration. However, a 1 . The Gudden and Pobl effect (1920)
266
Luminescence
in
Crystals
switching otf and on of the field could produce a dozen or more s uccessive li g h t pulses . In an alternating field the emission lasts long enough for the form of the 'brightness waves' to be studied (G. Destriau an d J. Mattler) . Their amplitude decreases rapidly while their p h a s e difference rela tive to the field given by 4n tan 4>
tends to zero as the conductivity decreases. If t h e field is removed a nd then reapplied, no more emission is observed unless several minutes elapse between cut-off and re app l icati o n . This effect pro vides an indication of the retrapping in shallower traps during the interval (J. Mattler and D. C urie). It is usually assumed that the Gudden and Pohl effect is an empty ing of traps by the applied field, while electroluminescence is a field excitation of luminescence centres. Let us consider a simple electrolu minescent effect. Electrons accelerated by the field E over a pa th len gth x can empty traps of depth : =
<
Kpw
--
However, in pr a cti ce very few traps are emptied in this way. The light sums obtained in th e Gudden and Pohl effect c.re very small. The change in trap population is insignificant. Destriau has, however, found several indications of a small decrease in the par ts of glow curves representing very shallow traps. This supports the basic idea of the mechanism of the Gudden and Pohl effect, but there is also a clearly ind icated enha ncement of the thermal glow due to deep traps (recapture process during Gudden and Pohl effect). T h e l igh t pulse can be observed several hours after excitation has been removed. It certainly cannot be associated with deep traps which did not lose their electrons during this interval. It is most likely due to an emptying of traps of very short life time which are involved in a re t rappin g process for electrons e s caping fro m deep traps. This may be the reason why the effect is relatively feeble. Many sulphides which do not show the Destriau effect (excitation by field alone) exhibit the Gudden and Pohl effect. The electric field can be applied du ring excitation and the emission is always more intense. The brightness can be doubled or tripled a t the moment when th-e field is applied and there is also a light fla s h Wtraps
eEx
Electroluminescence and electropho toluminescence
267
when it is rem oved . However, these effects are superimposed on per manent quenching or stimulation of l umi n e scence by the field (s ee bel o w) . I. T. S t einbe rge r, Braun and Alexander have shown that th e Gudden and Pohl effect also occurs in s u l ph id e s which a re very sensi tive to infra-red radiation, e.g. SrS(Eu, Sm) (see page 1 95). If the ph osp h o r is previously excited, then the light-pulse in tensity is much greater if the el ect ric field is applied during infra-red stimulation than during normal afterglow. This agai n shows that t h e re is no d irec t effect of the field on the deep traps, but an effect on shallow t raps which are be i n g constantly replenished by retrapping of electrons
from deep traps. As fo r intrinsic electroluminescence, the emi s sio n occurs predomi nantly at pl aces in the crystals where the field is high . This is so at low vo l ta ges , but emissi o n probably extends thr ough o ut the crystal volume as the voltage is raised to high values.
Fo r an excited ZnS(Cu) phosphor (X-ray or ultra-violet e x citatio n ) the luminescence is d en o te d by L0 in abs e nce of a fi el d (see Fig.
2 . Permanent quenching
l ight Lo 11
of luminescence in ZnS(Cu) by electric fields
outp ut
- - -
------
_ _ _ _
during which ts applted
�--
Ti m e
fie ld
Time
from X -ray Jrr a rf, a CIOn
Fig. IX. I 9 Quenching of luminescence due to an electric field
IX. l 9) . Now an alte rna t ing field E is ap p l i ed during excitation ; the brightness falls to L1 and we can write Lo- L l -c
where -r is th e quenching factor. Destriau and Mattler have shown that curves of r(£) at different temperatures T can be su pe ri m p o se d =
Lt
----·
268
Luminescence in Crystals
on each other by a simple change of ordinate scale (see Fig. IX.20). Thi s seems to show that the effect is due to a compet itio n between ra d iative transitions and non-radiative t rans i t i o n s due to the ap p li e d 1
!:L.!:._, L1
=
2 1·5 71 ° [
0
Fig.
IX.20 V
voltage
20
Variation
l. O
80
50
1 00 V I volts I
of quenching fector T
with
applied
at diferent temperatures (G. Destriau and J. Matt/er)
field. If P:P and Pnr are the respective probabilities for these transitions per unit time, then we can obtai n si mple relations as follows : L0 (no field)
T h e rati o
L1
(field on)
oc
r( £)
L1
oc
Pr+�:r(T) :) Pr
; Pm·(
-+ Pm(E )
�nr(E)
Pr-rPm (T) has the necessary form to expl a i n Fig. IX.20. However, from Fig. 1X.20 it is seen that in addition Pnr(E) d ep en d s also on temperature : =
= /(£ )
.g(T)
and a thermal activation e xp res s io n is suggested for (D. Curie) . For m an y years this q u e nchin g effect has r eceiv e d little attention, most of the interest bei n g in enhancement due to electric fields (see §3) and the q u en ch i n g mechanism is not yet understood. Some ana-
Pnr(E)
g(T)
logy with infra-red quenching might be made. The infra red produces quenching by activation of valence-band electrons and temperature plus an electric field may do the same. The above qu en ch i ng effects have been found in microcrystalline powder-form sulphides i f an alternati n g fi e l d is used with ' ce l l s ' con structed in the same way as Blue light for study of the Destriau effect. L IQUid Another type of extinction effect has been reported by Hershinger and others, using a CdS crystal in contact with electrodes under conditions su(phide similar to those for injection Emitted light emis sio n When the excita Fig. IX.21 Quenching effect during ex tion is not homogeneous, citation by strongly absorbed radiation e.g. using lattice or intrinsic (Hershinger, Daniel, Schwarz and Lasser) exciting rad iati o n , then the effect is observed (see Fig. IX.2 1). The excitation is confined to the surface and the less mobile holes remain in this region, which is then the only one with empty centres. If the field is so applied that the irradiated surface is negative (cathode), the electrons are moved away and cannot recombine with the empty centres or the holes, which gives rise to an extinction effect. The latter can be almost complete and occurs for quite reasonable field strengths (d.c.). Electroluminescence and electropho toluminescence
t
Cadmium
�
269
gl'"
.
3. Permanent enhancement of luminescence by electric fields
The theory of electroluminescence would suggest this possibil i ty. I f a phosphor has insufficient donor levels t o provide conduction elec trons in the absence of photo-excitation, then it will show very weak electroluminescence. However, if the phosphor is excited to give a large number of conduction electrons, then field application during excitation will enhance the number of excited centres. This might be called radiation-controlled electroluminescence or photo-electro luminescence (Williams and Cusano). The first kind of enhancement effect was found by G. Destriau and M. Destriau (1 954). They used zinc sulphide powders immersed in a dielectric and with an alternating applied field, the arrangement being similar to that of an electroluminescent 'cell'. X-ray excitation was
Luminescence in Crystals
270
used and phosphors of the type ZnS( M n), ZnS-CdS(Mn), ZnS-CdS (Mn, X) where X is gold or cobalt. However, these effects are n ot ex pli cab l e by the above mechanisms. They occur for quite weak field s for which electron acceleration would be rather unl ikely. In any case L tgh t output L,
------
lo
I
'
Ttm e during whtch field tS app lt ed
Fig. IX.22 Enhancement
T•mdrom
irra diation
of luminescence by an electric field
the curve for the variation of enhancement wi th applied voltage V is different from the e xpo n en t i al relation for electroluminescence due to impact excitation. The enhancement shows a satu ration which is similar to that for the current through an ionization chamber as very
Fig. I X . 2 3
Variation of enhancement ratio with applied
voltage (G. Destriau and J. Matt/er) When ionization density is high (()( p articles) the trend to wards saturation only occurs a t very high vo ltages
a function of field . We may assume that a m i gra ti on of charge carriers (holes and electrons) occurs due to the field, without accelera tion, and these can then 'excite' cen t res which would not be avai lable i n the absence of a field .
Electroluminescence and electrophotoluminescence
27 1
Using a notation similar to t hat ad o p te d previo u sly (see §2) let Pr be the radiative transition probabil i ty and Pnr be the n o n-rad iative pr o b a b i l i ty . I n the presen t instance Pnr is not affected much by the field (q ue n chi n g effect neg l i gi bl e i n t h e p a r ti c u l a r phosphors), bu t the latter introduces an additional radiative emission p rob a bi l it y P,(£). We might assume P, to depend on the number of centres excited by X-rays with the field absent and Pr(E) p r oportion al to t h e number of extra centres capable of being excited by the ch a rge carriers when the field is applied . The luminescence L is then gi ve n by L0 (n o fiel d )
cc
p
rl
P,+P,(E) Pr + P,(E) +Pnr The enhancement ratio p is given by Lt/L0• The maximum enhance ment co rrespo n d s to an efficiency of unity and a relation can be established as follows : L 1 (fie ld on )
Pmax - p
cc
L 1 - L0 L1max-L 1
P., .(E)
This relation varies with applied voltage V as a 3/2 p o we r law (G. Destriau) . The m a n ga n es e centres excited by the field show the s a m e emission as for X-ray or ultra-violet excitation. The enhancement for a given sulphide is m o re intense, the greater the p rimary excitation . Thu s an increase in contrast results from a p p licati o n of the field . The number of c h arge c a rrie rs ca p a b le o f diffusing in t he field is thus greater for higher excitation densities . The effect is n o t observed i n ZnS(Cu) phosphors. When ionization o f the centres occurs [a n d no t i nte rna l excitation as for ZnS(Mn)) non-radiative recombination of electrons and holes predominates. Even with ZnS(Mn) phosphors the effect is not observed with 3 ,650 A excitation, bu t it is fo u n d fo r X-ray and cathode- ra y excita tion (electrocathodoluminescence, P. M. Jaffe) and with <X-particle e xcitati o n (J. Mattler) . The total ligh t emission for Z n S( M n) or ZnS-CdS(Mn) phosphors excited by <X partic l es is enhanced by the field . However, J. Mat tl e r and J. M e s s i er have shown t ha t the peak heights of the <X- p a rti c l e scintillations are not i n cre a sed by the field. It is the weak scintillations and the b ack g r o u nd noise emission which are enhanced. For this re aso n the e n hancement effect c a n n o t be appl ied to scinti l l ation
2 72
Luminescence in Crystals
counters. H owever, it throws light on the scintillation mechanism. The intense scintillations result fro m excitation of all the centres along the ionization channel (see page 307) a n d cannot be enhanced, but the smaller scintillations and the background (perhaps from areas outside the channel) are enhanced . Similarly for 3 ,650 A excitation, no enhancement is observed but only quenching (the only likely effect since the quantum efficiency is about 100 per cent without the app l i e d field) . G obrecht and Gumlich have shown that ZnS(Mn) shows enhancement (however feeble) under ultra-violet radiation for irradiation falling in the fundamental absorption region which indicates movement of both signs of carriers is necessary to prod uce the effect - the holes empty cen t re s and elec t rons then fall into the centres with photon emission. It has been shown recently that infra-red radiation produces per manent enhancement effects i n the same sulphides wi th an a nalogous mechanism (F. Pingault, P. Jaszczyn). In all the above effects marked retrapping and 'memory' effects occur, the enhancement being higher after previous i n fra-red i rradia tion or applied fiel d . 4. Photoelectroluminescence (Williams and Cusano)
With a single crystal or thin film of ZnS(Mn), ZnS-CdS(Mn), &c., i n contact with electrodes allowing charge injection (§ 11. 1 ) we obtain electroluminescence controlled by irradiation, both with d.c. and a.c. fields. The effect occurs with X-rays but is more marked under ultra violet irradiation. The only thing in common with the effects above is that they are observed in ZnS(Mn), but in ZnS(Cu) a quenching effect occurs. (The experiments are made on sulphides in which electroluminescence is feeble without simultaneous excitation.) In ZnS(Mn) phosphors the yellow-orange band due to the manganese is enhanced, while the bl ue band associated with 'self-activated' zinc sulphide is quenched. The enhancement ratios can be quite h i g h , 1 00 to 500 times co m pared with 1 0-1 5 times, in the preceding phenomena. The variation with voltage i ndicates a somewhat different process (see Fig. IX.24) . No effect is found at low voltages, but above a certai n threshold the effect increases rapidly right up to the dielectric breakdown re gion The enhancement occurs when the metal electrode acts as a cathode. In Cusano's experiments the contacts are not ohmic hut rectifying.
.
Electrolum inescen ce am/ electrophotolum inescence
the absence of excitation t he electron injection in th e cathode region is small, but X-ray or ultra-violet exci tat i on produces a posi t i ve space charge in this r egion (el ec tron s are then sh i fte d while holes are t rapped), which produces further i njection of electrons. The elec trons are accelerated in t he resul ti n g intense field ( 100,000-300,000 Vfern) a n d can then excite the manganese centres. Cusano showed that the same mechanism operates as i n electro l u minescence by m easu ri n g the rati o L/ I of the emission i n t e n s i ty to 273
In
\ \ \ \
\
8
l um1nescent
\
\
e m t S S IOf1
4 \
\
\
I I
3 \
\
\
\ \
Meta l electrode
1 Current I Ji A I
\
8
Metal electrode
Fig. IX.24 Photoelectroluminescence. Variation of emis sion and current through sulphide with applied voltage (Cusano and Williams) Note diflerence between these curves and those of Fig. IX.23. They arise from two quite diferent types of enhancement effects
the current density through the layer. The ratio has the same max i 1 ft lambertfmA/cm2) in electroluminescence and i n photoelectroluminescence. One emission photon i s produced pe r 5,000 excited electrons. A pe rm anent photoelectroluminescence effect is found with phos phors of the type ZnS(As), ZnS(P) and ZnS(Sb), but not by field ex citation of the As, P or Sb luminescence centres. The emissions of the latter show quenching effects and it is the b lue or 'self-activated' band which shows enhancement. The activators arsenic, phosphorus and antimony give centres which are ionized in the exci t ation pro ces s . mum v al ue ( �
Luminescence in Crystals
Their c r oss- s ec t io n s for electron capture are very small. As a result they remain ionized when the appl ied field moves the electrons into an unexcited regi o n of the crystal. The role of these activators is thu s to p roduce a p os it ive space charge near to the cathode to assist carrier i njec ti o n , the electrons then being accelerated by the field and finally e xci ti ng the blue emitting centres (zi n c v aca n cies). 274
5. Application of electroluminescence in the development of image Electric field e n h a n c e m e n t of
luminescence gives poss i bi l iti e s fo r image ampl ification . At p rese n t the best pe r for m a n ce is obtained by a system comprising a photoconducting cel l of CdS coupled to a n electroluminescent panel (see Fig. JX.25). amplifiers
il t � r Cd S
Fig. IX.25
{t
Schematic
Lz
t
diagram of image amplifier com
photoconductive cell (CdS) and an electrolumin escent cell (ZnS) V1 and V2 are voltages applied to respective cells : V is overall voltage. A t junction of the two cells is an opaque layer to prevent optical feedback from ZnS to CdS
prising
a
The principle of the a m plifie r is as follows : I n the absence of ambient illumination the applied v oltage V is across both C d S and ZnS layers and the amount of electrolumines cence emission is small . If, however, the CdS layer is illuminated, the p o t en ti a l across it falls due t o t he p h o t o cond u ct io n and that across the ZnS layer is increased, giv i n g a rise in brightness of the emission. The expon ential change in e m i s s ion with voltage is an important fact or . In practice the processes are more complicated . This type of amplifier will not work with a constant ap plie d voltage ( u n less the exciting light is chopped) since it uses co n ventio n al electrolumines cent layers which only work with al te rn at i ng fields. There are also capacity effects involved . If C1 is t h e c a p a c i t y of the Cd S l a yer and C2 that of the ZnS l ayer,
Electroluminescence and electrophotoluminescence
275
Z1 and Z2 are their respective impedances and V1 a n d V2 their respec tive voltages, then we have, with V the o v e ra l l voltage, V=
V2
V1 + V2 Zz
The a d m i tt an ce of the photoconductive layer is
1
Zl
g1 is p r o p orti o n a l
=
gr -r]W I
•
c
1
to the i n t e n s i ty L1 of the i nc i d e n t a d m i tta nce o f th e electrol u m i nesce n t l ayer is
rad i a t i o n .
The
= gz +jw Cz
but we can neglect g2• The emission intensity L2 of t he elect rol umin escent layer is given by L2
=
Lw
exp
(- ) " vz
b a s e d on the above expressions by Diemer, Klasens a n d van S ante n lead to the following : (a) Lz oc Lr However, if L1 becomes too large, L2 tends towards a s a t u r ati o n limit. (b) The index y is independent of the applied field frequency, but a change in frequency shifts the region over which the relation in (a) holds. At low levels of illumination (L1) the device can operate at low frequencies, but at higher il l u m i n ation levels higher frequencies are necessary. (c) The maximum value of the 'amplification coefficien t' L2/L1 rises rapidly with applied voltage, but the value of y faiJs . To obtain a l inear relation between L2 and L1 h i gh operating voltages are used . In some Fig. IX.26 Log L2 as a func applications a high gamma factor is tion of log L1 (G. Diemer, H. A . needed (y � 1 ) ; (it can be as high as Klasens and J. G . van Santen) 1 0 to 30) and then low voltages must be used . The amplification is, however, small a nd several amplifiers m u st be used in series operation. A m p l i fi c a t i o n fa c to rs as high as 50 or 1 00 h ave been repo rted . Calculatio ns
'2 7 6
Luminescence in Crysta ls
General articles (i n ch r on o lo gi c al o rd e r)
B I B LI O G RAPHY
D ESTRIAU, G . ( 1 947) 'The new ph e n o m en o n of el ect r o ph o t o l u m in es cence and its p o s s ibili ti e s for the investigation of crystal l att i ce ' , Phi!. Mag., Ser. 7, 38, 700, 774, 8 8 0. W I L L I A M S , F . E. ( 1 9 53) ' S o l i d state l u m i n e sce n ce ' , A dvances in Electronics, 5, 1 56 . D ESTRIAU, G . a n d I v E Y , H . F . ( 1 9 5 5) 'Eiectrol umi nescence and related to p ics ' , Proc. I. R.E., 4 3 , 1 9 1 I .
HENDERSON, S . T . ( 1 9 5 5) 'Electroluminescence', Research (London), 8, 2 1 0.
F. J . ( 1 9 56) 'The electrical pro pe rties of phosphors', Progress in Semi-Conductors, 1, 99. Wiley, New York. M ATOSSI, F. ( 1 9 56) ' El ektr o l um in es ze nz und Elekt ro ph o t o l u m i n eszenz'. Vieweg, B rau n sch we ig . CURIE, D . ( 1 9 57) ' T he o ri es of e l ect r o l u rni nesce nce' , Progress in Semi-Conductors, 2, 25 1 . Wil ey, New York. IvEY, H. F. ( 1 9 57) 'Electroluminescence and field effects in phos p h o rs ' , J. Electrochem. Soc., 104, 740. G ARLI C K , G. F. J. ( 1 9 58) 'The elec tri cal p ro p erti es of phosp h ors ' , 'Licht und Materie', Hand. der Phys., 26, 8 9-1 1 0. S pri n ger, Berlin. H ENDERSON, S . T . ( 1 9 5 8) 'Electroluminescence', Brit. J. Appl. Phys. , 9, 4 5 . PIPER, W. W . and WILLIAMS, F . E . ( 1 9 5 8) 'Electroluminescence,' Solid State Physics, 6, 9 5 . Acad. Press , New York. I VEY, H. F. ( 1 959) 'Bibliography on electroluminescence and related t o p ic s' , I. R.E. Transactions on Electron Devices, ED 6, 203 (720
G A RLI CK, G .
references) .
I. Intrinsic electroluminescence 1 . Variation of luminescence with frequency and applied voltage. Effects of potential barriers A LFREY, G. F. a n d TAYLOR, J. B . ( 1 955) 'Electro1uminescence i n si n gle crystals of z i n c s ul p hi d e ' , Proc. Phys. Soc. London, 66B,
A NTONOV-ROMANOVSKY, V. V. ( 1 95 9) 'On the el ect ro l umi ne s ce n ce of powdered zinc sulphide layers', Czechosl. J. Phys., 9, 1 46. D ESTRIAU, G. (1 937) 'Recherches exp e ri me n tal e s sur l e s actions d u 775.
277
ch a mp electriq ue sur les sulfures ph o s ph o re sce n ts ' , J. de Chimie Phys., 34, 1 1 7. D ESTRI A U , G . ( 1 954) ' E mi ss io n spectra of electroluminescent mate rial s with multiple activators', J. Phys. Rad., 15, 1 3 . DESTR I A U , G . and DOMERGUE, L . (1 958) ' 0 b e r d i e Nichtexistenz einer An regungschwelle der Elektrol umi neszenz', Halbleiter wul Phosphore, 544. Vieweg, B raunschweig. F A VORIN, V. N. a n d POS K A CHEYEVA , L. P. (1 959) ' D ep e n d ence of the electroluminescent spectra of certain ph o s phors on the al ter n ati n g field i n te n si ty' , Optika i Spekt., 7, 706 ; Optics and Spectro scopy, 7, 420. Electroluminescence and electrophotoluminescence
D . and
( 1 954)
1umin es zenz verschiedener P h o s ph ore und ihre Abhang igk eit von der Starke und Frequenz des elektrischen Wech s elfeld es ' , Zeits.filr Phys. , 136, 6 1 2. GOLD B E R G , P . ( 1 959) ' P a rt i c l e size effects and the d i s t ributi on of b arriers in e1ect rolu m i ne s cen t zinc sulphide', J. Electrochem. Soc., 106, 34. G OL D B E R G , P . ( 1 960) 'Etch pits on e l e ctr o l u m i n esce nt zinc s ul p hi de crystallites' , Meeti ng on Colour Centres and Crystal Lu m i nescen ce , Turin, 8-1 1 S ep tember 1 960 . H A A K E , C . H. ( 1 9 56) 'Frequency d e p e n dence of electroluminescent b ri ghtnes s' , Phys . Rev., 101, 490. H A RM A N , G. G. and REYBO L D , R. L. (1 956) 'High fre q u ency in d uced electroluminescence in Z n S' , Phys. Rev., 104, 1 498. H O W A R D , B. T . , I V E Y , H . F . and LEHMANN, W . ( 1 954) ' Vo l tage dependence of electroluminescent brightness', Phys. Rev . , 96, 799. LEHMANN, W. (1 956) 'Frequency dependence of electroluminescent b righ tne ss o f i m pu ri t y-quenched ph o s p h o rs ' , Phys. Rev., 101, 489. LEHMANN, W. (1 958) ' P a rticl e size and efficiency of el ectr o 1um i nes cen t zin c s u lphide ph o s ph ors ' , J. Electrochem. Soc., 105, 585. LEHMANN, W . ( 1 960) ' V o ltage dependence and particle size distribu tion of electroluminescent p ho s ph o rs' , J. Electrochem. Soc. , 107, G O B R E CHT, H . , HAHN,
G U M L I C H , E.
'Die E1ektro-
( 1 9 5 5) ' Effe t des surtensions de resonance sur Ies con de n s ate urs electroluminescents', Comptes-Rendus Acad. Se. Paris, 240, 22 19. L U Y C K X , A . , VANDEW A U V E R , J . and R I ES , S . ( 1 958), ' D iel ec tri ca l properties of electroluminescent and ph o sp h o res cent zinc sulphides 20.
LUYC K X , A .
K
Luminescence in Crystals
278
and as sumptions on mechanism of electrolumi nescence', Ann. Soc. Scientifique Bruxelles, 72, 58. M ATTLER, J. and CEVA , T . ( 1 962) ' E l ectrolu m i n e s ce n ce of two-band zinc sulph i d e - voltage de pe nde nce of the spec tral distribution' , International M eeting on Luminescence, New York University, October 1 96 1 . Wi1ey , New York, 1 962, 537. P A Y N E , E . C . , M A GER , E . L . and J E R O M E , C . W. ( 1 950) 'Electro J u mi ne sce n ce . A new me t h o d of producing light', Appl. Eng. , 45, 688. R o u E RTS, S. ( 1 9 52) ' Field s t rength and tempera ture stud ies of electrol umi nescent powders i n d ielect ric med ia', J . Opt. Soc. Am., 42, 850. S TE I NBERGER , I. T. , B A R , V. and A L E X A N D E R , E. ( 1 9 6 1 ) 'Eiectro luminescence of zinc sulphide s i ngle crystals', Phys. Rev . , 121, 1 1 8. THORNTO N , W. A . ( 1 956) 'Electro lumin e scen ce in zinc sulp h ide ' , Phys. Rev . , 102, 38. ZALM, P., D I E M E R , G . and K L A S E N S , H . A . ( 1 954) ' Electro l u m i n es cent ZnS phosp h ors ' , Phi!. Res. Reports, 9, 8 1 . Z A L M , P . , DIEMER, G . and KLASENS , H . A . (1 955) ' So m e aspects of the voltage and frequency dep en d en c e of electroluminescent zin c s ulph ide', Phi!. Res. Reports, 10, 205 . Z A L M , P. (1 956) ' S ur l'electroluminescence d u sulfure de zinc (effet De s triau) ' , J. Phys. Rad. , 17, 777.
and CUR I E , D . ( 1 954) 'Ondes de brillance en electrolumi nescence et dans Ies effets 1umineux de surface', J. Phys. Rad. , 15, 61. D ESTRI A U , G . and M ATTLER, J . ( 1 945) ' A naly s e des ondes d e bril ]ance en electroluminescence', J. Phys. Rad. , 6, 227. D ES T R I A U , G . ( 1 955) 'Brightness waveforms in electroluminescence', Brit. J. Appl. Phys., Suppl. 4, S 2.9 D ES T R I A U , G. ( 1 956) 'On the effect of various metal electrodes on brightness waves in e l ect r ol um inescence ', Il. Eng., 51, 1 97. G O B R E C H T , H . , HAHN, D. and SEEM A N N , F . W. ( 1 955) 'Die Leuchtwellen bei der Elektrolumineszenzanregung von Phos ph o ren durch elektrische Wechselfelder', Z. fiir Phys . , 140, 432. H A H N , D. and S E E M A N N , F. W. (1 955) ' Z u r Temperaturabhangig-
2. Brightnes
CURIE, G.
waves
279
keit der Leuchtwellen der Elektrol u m i nesze nz', Z. fiir Naturforsch., lOa, 586. K LASENS , H . A . ( 1 958) 'Eiektrolumineszenz v o n S uspendierten Sul fidphosphoren', Halbleiter und Phosphore, 247. Vieweg, Braun schwe ig. LuYcKx, A . a n d STO K K I N K , A . J. ( 1 954) 'Some experimental results in e l ectro l u m ine s ce n ce', Brit. J. App!. Phys., Supp/. 4, S 57. M ATTLER, J. ( 1 956) 'Evolution des on des de brill a n ce en el ectro l umi nescence sous l'effet du ch a m p et de la tem pe ratu re' , .!. de Phys. Rad. , 17, 725. M A TO S S I , F . (1 955) 'Polarization e ffect s o n the b righ tne s s waves of electroluminescence', Phys. Rev., 98, 546. N U DELMAN, S. and M ATOS S I , F . ( 1 954) 'Electroluminescence with non-sinusoidal field s ' , J. Electrochem . So c . , 101, 546. Electroluminescence and electrophotoluminescence
3. The effect of temperature and trapping on electroluminescence G OBRECHT, H . , HAHN, D . and GUMLICH, H. E . ( 1 9 54) ' 0ber die Temperaturabhangigkeit der E le ktrol um i n es ze n z von ZnS und ZnO Phosphoren', Z. fur Phys., 136, 623 . HAAKE, C . H . (1 957) 'Trapping ac ti o n in electroluminescent zinc su lphid e phosphors', J. Opt. Soc. Am., 47, 88 1 . H A A K E , C . H . ( 1 957) 'Te mpe rat u re dependence of electrolumi nes cence', J. Electrochem . Soc., 104, 29 1 . }O HN S O N , P . D . , P I P E R , W . W . and WILL I A M S , F . E . (1 956) 'Effect of electron traps on elect rolu m ine scen ce ', J. Electrochem. Soc., 103, 22 1 . M ATTLER, J . ( 1 956) 'Action de la tem p e ra t u re sur l'e! e c tr o l u m in e s cence des sulfures', J. Phys. Rad. , 17, 42. V I GEAN, F. (1 953) 'Electroluminescence - la mo n te e initiale de l'electroluminescence produite par un c ham p alter n a tif', Comptes Rendus Acad. Se. Paris, 236, 1 1 5 1 . C U RI E , D. (1 952) 'Libres
mechanism of electroluminescence parcours des electrons dans les crista u x , effets d ' el ec t ro l u m in esce n ce et p h e n om e n e s d e ruptu re d ielec trique ' , J. Phys. Rad., 13, 3 1 7. C URIE, D . (1 953) ' Sur le m ec ani s m e de l'electroluminescence. I. Con
4.
The
siderations theoriques', J. Phys. Rad., 14, 5 1 0. le mecanisme de l'electroluminescence. H. A ppl ica tions au x fa its exp eri men taux', J. Phys. Rad., 14, 672.
CURIE, D . ( 1 953) 'Sur
280
Luminescence in Crystals
M. A . ( 1 956) 'L'clectroluminescence de monocristaux de sulfure de zinc', J. Phys. Rad., 11, 73 1 . GOFFAUX , R . (1956) 'Le mecanisme d e l'electroluminescence', J. Phys. Rad. , 11, 763. G OFFAUX , R. (1 957) 'Mecanisme de l'electroluminescence du sulfu re de zinc', J. Phys. Rad. , 18, 1 . G OFFA UX, R . ( 1 959) ' Proprietes e lect r o n i q u e s des poud res de Z n S e l ect ro l um i n esce n ts ' , J. Phys. Rad. , 20, 1 8 A . LEHMANN , W . (1 958) 'Electroluminescence o f zinc s ul p hi de phos phors as an equilibrium process', J. Opt. So c. A m . , 48, 647. LUYCKX, A . , VANDEWAUVER, J. and R I E S , S . ( 1 958) 'Studies on th e mechanism of electroluminescence', Technical Notes, University FRAN KL,
D . R . , B I R M A N , J . L . , NE UM A R K
,
G. F . and
LEMPI C K I ,
of Louvain, Be lgium MOREHEAD, F. F. ( 1 960) 'The m ech a ni s m a n d efficie n cy of electro1uminescence in ZnS phosphors', J. Electrochem. Soc. , 107, 28 1 . NAGY, E . {1956) 'Phenomenes d'electroluminescence', J. Phys. Rad. , .
773.
W . W . and WILLIAMS, F . E . ( 1 955) 'The mechanism of electro1uminescence of zinc sulphide', Brit. J. Appl. Phys. , Suppl. 4, s 39. PIPER, W . W . and WILLIAMS, F . E . (1 955) 'Theory of electrolumi nescence', Phys. ReP. , 98, 1 809.
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PIPER,
BA YET, M . , DELCROIX, J. L. and DENISSE, J. F. ( 1 956) 'La theorie cinetique des plasmas homogenes faiblement ionises', J. Phys. Rad ,
Additional references
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FROHLI CH, H. ( 1 947) 'On the theory of dielectric breakdown in solids', Proc. Roy. Soc . , A 1 88, 52 1 . 17,
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O' DWYER, J . J . ( 1 958) 'Dielectric breakd own i n solids', 360. S E I T Z , F . {1 949) 'On t h e theory of electro n Phys. R ev . , 76, 1 376.
A dvances in
Physics, 1,
m u l t i plicat i o n i n
crystals',
5. Sensitization of phosphors and new electroluminescent phosphors D EST R I A U , G . a n d S A D D Y , J . ( 1 945) Pre p ara t i o n de m at e ri a ux l uminescents p articul ierement sensibles a l'action des champs electriques' , J. Phys. Rad. , 6, 1 2 . '
Opt. Soc. Am., 43, 320.
FROELI C H , H . C. LEHMANN, W .
28 1
(1953) 'Sensitized electroluminescent response' , J.
Efectrofuminescence and electrophotofuminescence
(1 957) 'Contact electroluminescence', J. Electrochem.
(1960) 'CaS(Cu, Eu) electroluminescent phosphor', J.
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Electrochem. So c. , 107, 1 99.
W A C H T E L , A.
W A C H T E L , A.
(1960) '(Zn, Hg)S and (Zn, Cd, Hg)S electrolumines cent phosphors', J. Electrochem. Soc., 107, 682.
6. Electroluminescence in organic materials BERNANOSE, A . , COMTE, M . and VOUAUX, P. ( 1 953) ' S ur un nouveau mode d'emission lumineuse chez certains composes organiques', J. Chimie Phys. , 50, 64.
A . and VOUAUX, P. (1 953) 'Electroluminescencc organique : etude du mode d'emission', J. Ch im ie Phys. , 50, 26 1 . B ERNANOSE, A . ( 1 955) 'Sur le mecanisme de l'electro)uminescencc organique', J. Chimie Phys. , 52, 396. VouAU X , P . ( 1 956) 'Electroluminescence de certains co m pose s organiques . Thesis, Faculte de Pharmacie, Nancy. BERNANOS E ,
'
II. Electroluminescence due to charge carrier injection
1. Injection into ZnS D . and S E E M A N N , F . W. (1956) 'Der Einfiuss der Ladungs tragerinjektion auf die Wechselfeldelektrolumineszenz', Z. fur Phys., 146, 644. PIPER, W. W. and WILLIAMS, F . E . (1 952) 'Electroluminescence of single crystals of ZnS(Cu)', Phys. Rev. , 87, 1 5 1 . THORNTO N , W . A . (1 959) 'ac-dc electroluminescence', Phys. Rev. , HAHN,
1 13,
1 1 87.
T HORNTON, Phys.
W. A. (1 959) 'Electroluminescence at low voltages', A. ( 1 959) 'Electroluminescent thin films', J. Appl.
Rev., 1 16, 893.
1 23
T HORNTON , W . Phys. , 30,
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2. Electroluminescence of single crystals of cadmium sulphide
W. and KuMMEL, U. ( 1 952) ' O ber die Lumineszenz von Cadmium-sulfid Einkristallen in starken elektrischen Gleichfel dern', Z. Phys. Chem. , 200, 1 93.
(a) In relation to electrical breakdown
BoER, K.
Luminescence in Crystals
282
D I EM E R , G . ( 1 9 5 4 ) ' E l ec t ri c breakd own and light e m i s s i o n i n CdS single crystals', Phi!. Res. Rep . , 9, 1 09. W o o o s , J . ( 1 956) ' D e c h a rge d isrupt ive dans des monocristaux de CdS', f. Phys. Rad. , 1 7, 7 1 8 .
(b)
At
lo w fields
SMITH, R. W.
( 1 957)
105, 900.
' Low-fi eld e!ectrolumi nescence i n
crystals of cad m i u m s u l p h ide', Phys. Rev . ,
i n s u l a ti ng
I . T. ( 1 960) 'Further experimental evi d e nce of carrier i nj ec t i o n in CdS single crystals', J. Phys. Chem . Solids, 15, 354. W I LLIAMS, R. ( 1 960) 'Electric fi e l d ind uced light ab so r p t i o n in CdS', Phys. Rev., 1 17, 1 4 87.
Further references maj o ri ty
STEINBERGER,
K . , A C C A R.OO , C . A . and J A !1 G O C H I A N , E. ( 1 95 1 ) ' I n jected light emission of s i li c o n carbide crystals', Phys. Rev . , 83, 603. LEHOVEC, K . , A c C A R D O , C. A . and J A M GO C H I A N , E . ( 1 953) 'Light emission p r o d uce d by c ur re n t inj ected i n to a green silicon carbide crys tal ', Phys. Rev . , 89, 20. LELY, J . A . an d K R O G E R , F. A . ( 1 958) ' O pt i ca l properties of p u re and doped SiC', Halb!eiter und Phosphore, 5 14. Vieweg, Brau n s c hw e ig. LossEw, 0 . (1 928) ' L u mi n e sc e n t carborundum detector and detec tion effect and oscillations in crystals', Phi/. Mag. , 6, 1 024. PATRI C K , L. and C H O Y K E , W. J. ( 1 959) 'Impurity bands and elec tro luminescence in SiC p -n j u nc ti o ns' , J. Appl. Phys. , 30, 236. S c HoN, M. (1 953) 'On the luminescence of c a rbo ru n du m ( S i C) c rys t al s d u ring passage of current', Z. Naturforsch., Sa, 442. S z i GETI, G. (1 955) 'Electroluminescence of silicon carbide', Brit. J. Appl. Phys., Suppl. 4, S 56. WEISZBURG, J . ( 1 960) 'On the electrol uminescence of i n s u l at ed SiC crys t al s ' , A cta Phys. Hungarica, 11, 95. See also CHOY K E , W . J. an d PATRI C K , L . ( 1 957) 'Absorption of light in oc SiC near the band e d ge ' , Phys. Rev . , 105, 1 72 1 .
3. Electroluminescence of silicon carbide L1EHOV E C ,
Electroluminescence and e!ectrophotoluminesccnce
283
4. Luminescence in electrolysis A N DERSON, S . ( 1 943) 'Luminescence of valve metals d u ri ng electro l y t i c o x ida t io n ' , J. Appl. Phys., 14, 60 1 . FREYMA N N , R . ( 1 930) 'Etude des phenomenes l u mineux se pro duisant aux e l ec tr o des pendant ! ' el ec t r o l y s e ' , Dipl6me d'Etudes Superieures, Faculte d es Sciences, Pa ri s . Recherches et Inven tions,
1 1 , 36.
VAN
W . C H . (1 956) ' S ur la lu mi n esce n ce de couches d ' oxy d es o xy d at ion electrolytique', J. Phys. Rad. , 17, 7 1 4.
par
G EEL,
formees
A I GRAIN, P. (1 954) ' L i g h t emission from i nj ec t i n g contacts on ger manium in the 2/h to 6fh band', Physica , 20, 1 0 1 0. A I GRAIN, P . and BENOIT A LA G U I LL A U M E , C . ( 1 956) ' L'Ciectro l uminescence infra-rouge du ge r m a n i u m ' , J. Phys. Rad. , 17, 709. B E NOIT A LA G U I L L A U M E , C . ( 1 959) ' Contribution a ! 'e tu d e de la
5 . Electroluminescence o f germanium and silicon
reco mb i naiso n des porteurs en exces dans le
germ a niu m ' , Annales
de Physique, 13, 1 1 87. HAYNES, J . R. a n d BRIGGS, H. B. ( 1 952) 'Radiation prod uced in
ge rmanium and silicon by electron-hole recombin at i o n ' , Phys. Rev., 86, 647. H A Y NES, J . R . ( 1 955) 'New radiation resulting from recombination of holes and electro n s in ge rma n i u m ' , Phys. Rev., 98, 1 866. HAYNES, J. R. and WESTPHAL, W. C. ( 1 956) 'Radiation resulting fro m the recombination o f holes a n d electrons i n silicon', Phys. Rev. , 101, 1 676. NEWMAN, R. (1 953) 'Recombination radiation in ge r m a n i u m ' , Phys. Rev., 91, 1 3 1 3 . N EWMAN, R . ( 1 9 57) ' Rec o m b in atio n radiation from deformed and alloyed germanium p-n j u n ct i o n s at 80°K', Phys. Rev. , 105, 1 7 1 5. PANKOYE, J. I . (1 958) ' R a d ia ti v e surface effects in ge r m a n i u m ' , J. Phys. Chem. Solids, 6, 1 00. PANKOVE, J. I. (1960) 'Contribution a !'etude de I' emission infra rouge dans le g erm an i u m ' . Thesis, Paris.
6.
(1 957)
Investigations of other solids
149, 1 07.
FISCHER, A . FRERICHS,
'Electroluminescence of d iamond',
R. and HANDY, R . ( 1 959) Phys. Rev., 113, 1 1 9 1 .
cuprous oxide',
Z. for Phys. ,
'Eiectroluminescence in
284
Luminescence)n Crystals
KRAUTZ, E . and ZOLLFR A N K , G . (1957) 'Microscopic and oscil lo·
graphic investigations on the electroluminescence of insulating diamonds', Optik, 14, 446. Moss, T. S. and HA WKINS, T. H. ( 1 956) 'Radiation de recombinaison dans l'antimoniure d' i nd iu m', J. Phys. Rad., 17, 7 1 2. Moss, T. S . ( 1 957) 'Theory of the spectral distribution of recombi nation radiation from InSb', Pro c . Phys. Soc. London, 70 B, 247. WOLFE, R. and WooDs , J . (1957) 'Electroluminescence of semi conducting diamonds', Phys. Rev., 105, 92 1 . Ill. Electrophotoluminescence
J . ( 1 946) 'Etablissement de !'illumina fugace de certains sulfures. A pp li cat i on a l'electroradio graphie', J. Phys. Rad., 7, 259. D ESTRIAU, G. a n d MATTLER, J. (1952) 'Etude osci l!ograp h i qu e d e !'illumin ation fugace', J. Phys. Rad. , 13, 205. G u D DE N, B. and POHL, R. W. (1 920) 'Enhancement of phosph o res cence by electric fields', Z. Phys. , 2, 1 92. K O TER A , Y. and NARAOKA, K. ( 1 959) 'The Gudden-Pohl effect of ZnS (Cu) ', J. Electrochem. So c . , 106, 1 066. M A T O S SI , F . and NUDELMAN, S. ( 1 956) 'E[ectrophotoluminescent effects', J. Electrochem. Soc., 103, 1 22. MATTLER , J. and C U R I E , D . (1 950) 'Comportement des pieges a electrons dans les phenomenes d'electroluminescence', Comptcs Rendus Acad. Se. Paris, 230, 2086. STEINBERGER, I. T . , B RAUN, E . A. and A LEXANDER, E. (1 957) 'Giidden-P ohl and memory effects in an infra-red stimulable phos phor', J. Phys. Chem. Solids, 3, 1 3 3. VI GEAN, F . ( 1 95 1 ) 'Action extinctrice des radiations de grande lon gueur d'onde sur l'electrophotoluminescence. I. Re s u l tats experi me n taux' , Comptes-Rendus Acad. Se. Paris, 232, 8 1 9. V J GEAN, F . and CURIE, D. ( 1 95 1 ) ' A ctio n extinctrice des rad i ations de grande longueur d'onde en electrophotoluminescence. II. Essai d'interpretation', Comptes-Rendus Acad. Se. Paris , 232, 955.
1. The G udden -Pohl e ffect DESTRIAU, G . and M A TTLER , tion
The Gudden-Pohl effect during the excitation A LEXANDER, E . , Low, W . , STEINBERGER, I. T. and WEisz, S . Z .
(1 956) 'Effet des champs electriques continus sur la brillance de
285
substances luminescentes maintenues sous excitation', J. Phys. Rad., 17, 737. M ATOSSI, F . (1954) 'Interpretation of electroluminescent effects in an excited phosphor', Phys. Rev., 94, 1 1 5 1 . Electroluminescence and electropho toluminescence
2. Permanent quenching effects D ANIEL, P. J . , S cHWARZ, R . F . , LASSER, M .
and HERSHINGER,
L. W. (1 958) 'Control of luminescence by charge extraction', Phys. Rev., 111, 1 240. E.
DECHENE, G. ( 1 938) 'Modification de la brillance d'un ZnS phos phorescent sous !'influence d'un courant electrique', J. Phys. Rad. , 9, 1 09. DESTRIAU, G . and MATTLER, J . ( 1 948) 'Actions des champs elec triques alternatifs sur l'intensite de la l uminescence des sulfures irradies aux rayons X et deformations des bandes d'emission', J. Phys. Rad 9, 258. DESTRIAU, G . and M ATTLER , J. ( 1 9 50) Effet d'une elevation de temperature sur les phenomimes d'electroluminescence', J. Phys. Rad., 11, 529. KALLMANN, H. and M A R K , P. ( 1 957) 'De-excitation of ZnS and ZnCdS phosphors by electric fields', Phys. Rev., 105, 1 445. MATOSSI, F . (1 956) 'Theory of dynamic quenching of photoconduc tivity and luminescence', J. Electrochem. Soc., 103, 662. .,
'
3. Permanent enhancement effects CocHE, A . and HENCK , R . ( 1 959) 'Effets des champs alternatifs et
continus sur la luminescence de certains sulfures de zinc excites par un rayonnement Cl.', J. Phys. Rad , 20, 827. CURIE, D. (1 953) 'Sur !'interpretation d'experiences de photoconduc tibilite en champs eleves', Comptes-Rendus A cad. Se. Paris, 237, .
CUSANO, D . A . and WILLIAMS, F . E . ( 1 956) 'Photoelectroluminescence - electroluminescence controlee par les radiations', J. Phys. Rad., 17, 742. CusANO, D. A. ( 1 9 57) 'Photoelectroluminescence with visible re sponse', Phys. Rev., 106, 604. CusANO, D. A. ( 1 9 59) 'Photoelectroluminescence, electrolumines cence and related high field effects in zinc sulphide phosphor layers'. Thesis, Troy, New York, 1 959. 79 1 .
Luminescence
286
in
Crystals
D ES T R I A U , M . ( 1 954) ' S u r un nouvel etTet de sensibilisation de la
luminescence de certaines substances par les champs electriques',
G . , M A T T L E R , J . , D E S T R I A U , M. and G U M L I C H , H . E. ( 1 955) 'The enhancement effect of electric fields on some X-ray excited phosphors', J. E!ectrochem. Soc., 102, 682. D ESTRIAU, G. (1 957) 'Renforcement par les champs el e ctriques de la sensibi1ite aux rayons X de certains materiaux luminescents et photoelectroluminescence', Comptes-Rendus, 245, 1 797. DESTRIAU, G. (1 958) 'Sensibilisation, par des traces d'or, de mate ria ex pour l'effet e lectro r e n fo r9 a t eu r' , Comptes-Ren dus, 245, 1 9 1 3 . G O B R ECHT, H . an d G uM L I C H , H . E. ( 1 956) ' S u r le ren fo rcement et !'extinction par les champs e lectriqu e s alternatifs d e l a l u m i nes cence des su1fures de zinc actives aux manganese', J. Phys. Rad. , 17, 754. G O B R E C H T , H. and G U M L I C H , H. E. ( 1 960) ' U ber den Einfluss der Anregungswellenlange auf die Elektrophotolumineszenz', Z. Phys. ,
Co mptes-Ren dus A cad. Se. Paris, 238, 2298.
DESTRIAU,
G U MLICH , H. E. ( 1 956) ' C o n t ri b u tion a !'etude des effets extincteur et sensibi1isateur des champs electriques', J. Phys . Rad. , 1 7 , 1 1 7. G u M L I C H , H . E . ( 1 958) ' D i e Verstarku ng und Ausloschung der
158, 226.
Lumineszenz manganaktivierter Zinksulfide durch elektrische Felder', Thesis, Be r l i n . J A F F E , P . M . ( 1 959) 'Electric field enha n c e men t of cathodolumines cence (cathodoelectroluminescence)', J. E!ectrochem. Soc., 106, J. ( 1 956) ' Renforcement de la luminescence des scintilla par les champs electriques', J. Phys. Rad. , 17, 758. M A TTLE R , J . ( 1 959) 'Variation de l'effet electrorenfor9ateur avec la frequence des champs electriques', Comptes-Rendus Acad. Se. Paris, 249, 205 1 . M E S S I E R , J . and M A TTLER , J . (1 960) 'Action des champs elect riq u es alternatifs sur la luminescence des s ci n ti llations o: ' , Comptes
667.
tions
M ATTLER, o:
Rendus Acad. Se. Paris, 250, 3 822. F . E. (1 9 55) 'Theoretical basis for light-amplifying phos phors', Phys. Rev., 98, 547.
WILLIAMS ,
Enhancement effects with infra-red radiation P. B . (1959) 'L'extinction et le renforcement de la 1umi-
J A S Z CZYN,
287
nescence du ZnS(Mn) par !'irradiation par !'infra-rouge', Report No. 1 1 4-XIII, Acad. Polonaise des Sciences ; Optics and Spectro Electroluminescence and electropho toluminescence
scopy, 7, 69 1 . F . ( 1 959) 'Sur le nouvel etfet de sens ibilisation a !'action d es rayons X, par !'infra-rouge, des produits luminescents du type CdZnS(Mn, X)', Comptes-Rendus Acad. Se. Paris, 249, 248 .
PIN GAU LT,
4.
Solid state image amplifiers K LA S ENS , H . A . and V A N S A N T EN , J. G. ( 1 955) 'Solid
state image intensifiers', Phi!. Res. Rep., 10, 40 1 . B . and N I C O L L , F . H . ( 1 957) 'Solid state light amplifiers',
D I EMER, G . , KAZAN, J.
E. E . ( 195 6) 'Luminous and radiant power gains of light amplifying devices', J. Opt. Soc. Am., 46, 227. RosENTHA L , J . (1955) 'Theory and experiments on a basic element of a storage light amplifier', Proc. I.R.E., 43, 1 882. Opt. Soc. Am . ,
LOE B N E R ,
47,
887.
CHAPTER X
Cathodoluminescence, radiolumines cence, scintillations. Effects of high-energy radiation on
I.
C A T H O D O L U M I N E S CE N C E
Among the various kinds of luminescence, that excited by cathode rays would appear to have been the subject of most practical applica tions in recent years (e.g. cathode-ray tubes for oscilloscopes, mono chrome and colour television, radar, &c.). In contrast to the large amount of experimental effort in such applications relatively little attention has been given to a better understanding of the mechanisms of the phenomenon. We shall give the main attention here to this latter. High-energy radiations such as energetic electrons, X-rays, a, {3 and y rays, &c., passing through the phosphor excite or ionize the luminescence centres, this excitation or ionization being followed by visible emission from the centres. The radiative transition process is usually independent of the mode of excitation and we obtain, for example, in cathodoluminescence the same emission bands as in photoluminescence. However, more de tailed examination reveals definite shifts in the position of these bands, especially at high excitation densities. Moreover, the nature of the excitation is i mportant in the following ways : (a) In modifying the relative emission intensities in the different bands, this leading in certain cases (e.g. phosphors with several acti vators) to a change in the observed colour of luminescence. Thus in copper-activated zinc sulphide the blue band is often more intense than the green band under cathode-ray excitation than in photo luminescence ; an analogous change was observed in electrolumin escence (see page 270). (b) In modifying the relative probabilities of radiative and non288 1.
�
phosphorescent solids
Introduction
Cathodoluminescence and other topics
radiative recombination, i.e. the luminescence yield or efficiency of the phosphor. The energy conversion efficiency in cathodoluminescence lies gen erally between 5 and 25 per cent, while the quantum efficiency for a ZnS(Cu) phosphor excited by long wavelength ultra-violet light i s near to unity. t Leverenz has shown that the thermal quenching of luminescence occurs at somewhat higher temperatures i n cathode luminescence than in photo- Phosphorescence mtenrity luminescence, this being related to the higher density of excita 100 tion. (c) In modifying the filling of electron traps, i.e. the afterglow or persistence of the phosphor when excitation ceases. The per sistence is shorter after excitation 25 t 1 < 1 by high-energy radiation than Fig. X. l Comparison of de after photoexcitation (Fig. X. l). cay curves for the same ZnS Ultra-violet radiation will not CdS(Cu) phosphor after excita excite luminescence unless it lies tion by 3,650-A (curve A) and by in an absorption band of the 6 k V-electrons (curve B) phosphor. Thus in calcium tung (After Garlick) state the absorption edge is at about 2,400 A, so that luminescence is only feebly excited by the 2,537-A radiation of a mercury lamp ; addition of lead impurity enhances the excitation . It does not play the same role as, for ex ample, copper in zinc sulphide, the luminescence in CaW0.1 being characteristic of the wo4 group, but it moves the absorption limit to longer wavelengths so that absorption in the 2, 537-A region is much stronger. In contrast, cathode rays being of small penetration power are strongly absorbed, whatever their energy. A fraction of the absorbed energy is always transferred to the luminescence centres. Many materials are luminescent under cathode rays which show no emis sion for long or short wavelength ultra-violet excitation. Calcium tungstate with no lead inclusion is quite well excited by cathode rays, but not by ultra-violet radiation. 289
t The energy conversion efficiency is only about 70 per cent since an ultra violet photon must be absorbed to produce th� smaller ener� visible photon,
Luminescence in Crystals
290
ln radiographic screens using calcium tungstate the a d d itio n of the element lead , stro n gly absorbing the X-rays, seems to impro ve the luminescence excitation . Cathode-ray e x citatio n is accompanied by a stron g perturbation of the whole of the crystal lattice : even electrons in inner at omic shells are excited by the incident p a rticl e . The processes are much more complex than those in photo-excitation, where one considers only the valence and cond uction energy bands an d localized levels between t hese bands. Nevertheless, the efficiencies for certain z i n c sulp h i d es approach 20 to 25 per cent (Bril and Klas ens) and are of the same order as those for ultra-violet excitation in the fundamental abso rp tion band of the crystal lattice. As shown previously (see Chapter VIII), excitation involving the Riehl mechanism gives a smaller yield than that for long wavelength ultra-violet light . heavy
T A B LE X . l
Luminescence efficiencies and time constants of some cathodoluminescent phosphors (after Bril and Klasens)
(Excitation by 20-keV el ectrons 1 J.Lamp/cm2 c u rren t density : phosp hor in thick layer on glass)
Emission colour
Phosphor
ZnS ( I O - • Ag, Cl) 50 per cent ZnS, 50 per cent CdS (5 x I Q • Ag, Cl) Zn S (to • Cu, to-• AI) ZnS (O·Ot 5 Mn) ZnO(Zn) cawo. MgWO,
CaO, MgO, S i O , (3 per cen t Ti)
Zn,SiO,
(0· 004
M n)
Zn,(P0,)2 (0·03 M n ) Nai (0·0 1 Tl) -
-
- --
-
�
'
Blue
I
98 l um e ns'l watt
,
! !
Ye llow
Green
1 9·5
23 4
Yellow
2
Blue
7
G reen
8·5
U l tra-violet
···- - · -
·· ·
! -
-- -
4 x 10 •
w • sec
1 8 l umens/watt 25 lumens/watt 2 lumens/watt 5 lumens/watt
25
1 3 · 5 l u men s/wa t t
·
-
--
--
--
x
1 0 • sec
1 · 3 :< 1 0 2 sec
: 42 1 umcns/watt
-
sec
3 x I0 6 sec 4 x 1 0 " sec
5 l u mens/watt
8 2
- - -
Several componen t s 1 0 - • M I � "" Rc
92 lumens/watt
, '
7 3
Green Blue-vio l et Blu ish
Red
-.--··--'-
i1· ------Luminescence efficiency --Average . ! decay time Op�tcal I Energetic efficiency [ (per cent) [ efficzency --- - - i� 2- 1 J: 7
;
I
- �
25
x
6x -
J O ' sec to J O sec •
- - - - - · - ··
Cathodoluminescence and other topics
29 1
The large density of free electrons in cathode- ray excitation indi cates the p ossibi lity of non-radiative recombination invo l vi n g the Auger effect (Pincherle, L. Bess) : instead of a simpl e electron-hole recombination the excitation energy is given as kinetic energy to another electron . The effect certainly exists, but it is doubtful whether it is significant he re . Th e p rincip al p hos p hors of importa nce in cathodoluminescence are sulphides, selenides and telluri des of zinc and cadmi um, zinc oxide, silicates and tungstates of calcium, magnesium , zinc and cad mium , and the fluorides of magn esium and zinc. Table X. l gives some relevant data for the more usual phosphors. The intrinsic efficiency of a phosphor is given by the ratio luminous emitted energy 'f/ i energy absorbed in the body of the phosphor . It is clea r ly different from the measured screen efficiency given by the ratio l umi n o u s energy emitted 'f).,xp = incident e n ergi lf the screen is s u ffi ciently thick to absorb all the cathode rays but allowing the emission to emerge from it, then the difference between the two ratios is small ( � 1 per cent). We give in Table X. I the data obtained by Bril and Klasens. =
··
··
·-·-
··
-
-
-· ·
·
.
2. The general laws of cathodoluminescence (A) Phosphor screens of type used in cathode-ray tubes (deposited as a relatively thick microcrystalline layer)
The luminescence i n te n si ty L increases steadily with increase in elec tron beam current density and with the accelerating p o tential V for the electrons (Lenard). Although experimental co n ditions are not well defined in gene r al (non-collimated beam , focused or defocused), Strange and Henderson ( 1 946) extracted some si m p le relatio n s : = f(i) . ( V-
(1)
where f(i ) is an essentially linear function at first, then sh o wi n g a tendency to saturation for high b e am current densi t ies es pe cially at low penetration (low electron energy). The index q is esse n tially inde p endent of V and of i and remains so even where f(i ) ceases to be linear. L
V0)«
292
Luminescence in Crystals
Sometimes q is unity (Lenard), this often being the case for ZnS(Mn) and Zn2Si04(Mn) phosphors. More usually q is greater than unity and can reach or exceed two. It depends not only on the nature of the phosphor but also on the screen preparation, grain size and packing of the latter. V0 is a threshold potential known as the 'dead voltage' . Actually the phosphor can be excited for V < V0, but only very feebly.
(B) Cathodo/uminescence due to electrons of very low energy Since 1 909 Lenard and Sealand attributed the 'dead voltage' to a superficial contamination of the phosphor by impurities and defects giving rise to non-radiative transitions. Without special precautions in preparation, V0 can be 200-300 V, but by avoiding contamination Strange and Henderson reduced it to a few volts. In principle an electron of zero energy can penetrate into a phos phor where its kinetic energy will be given by the electron affinity x of Zero potentia l [mpty band
�4·2 eV Conduction b a n d
Valence b a n d
)
'' ''
Fig. X . 2 Electron affinity x of a crystal greater than The energy neededfor centre excitation allowing a zero energy incident electron to excite emission. Numerical values are for ZnO
the solid (Fig. X.2). If W is the energy necessary to excite a lumin escence centre, then emission will be produced if the electron energy e > W-x. If x > W, which seems to be the case in ZnS and ZnO, then zero energy electrons could produce emission. Shrader and Kaisel ( 1 954) succeeded in observing luminescence i n ZnO due to electrons with energies which, if not zero, were less than that of the emitted quantum, (Shrader and Kaise/)
293
Cathodoluminescence and other topics
In these experiments it should be noted that it is important to de posit the phosphor on a conducting base maintained at a constant potential and not on an insulating surface which will charge up and repel the incident electrons. In cathode-ray tubes the p racti ce of aluminizing can improve the efficiency by 50 to 100 per cent. (C) Screens in the form of a transparent film
or a
thin microcrystalline
Studer and Cusano have made cathode-ray tubes wi th a thin t ra ns parent layer as screen. Williams has indicated that besides their theo retical interest these sc ree n s have a much g re ater resolution an d optical contrast than conventional powder layers and have a more well-defined geometry. K o l l e r and Alden ( 1 957) have studied the exci ta ti o n of such a fi l m with el ectr o ns of i n c re asi n g e n e rgy The t h i ck n es s of these films be i n g of the ord e r of one micron , only electrons of small energy are completely s t o pp ed in the film : a 1 0-keV electron with a range of 2 f-l will be transmitted . Koller and Alden have shown that if the electrons are completely sto pp ed in t h e film, then the index q of e qu ati o n ( I ) ab ove is unity and a linea r response to electron energy occurs. It should th u s be asked if the various values of q are not due t o the perturbations produced by the nature of the screen in conventional cathode-ray tubes : thick powder layers involve non-unifo rmity of excitation, occurrence of space charge between grains, light losses, &c., while the basic process is still a linear one (M. and D. Curie 1955). Unfortunately the p u bl i sh ed experiments of Koller and Alden seem to have been confined to ZnS(Mn), i.e. specifically with man ganese centres. For this material Strange and Henderson fo un d q values of unity for powd e rs It would seem necessary to extend the measurements on thi n films wi t h different activators to see whether the l inear behaviour is characteristic of the fundamental excitation process. Experiments pertinent to this p oi nt of view were made b y G y. Gergely et al. (1959). They used thin microcrystalline layers of phos phors so that the absorption of the emitted light was negligible, but by contrast the microcrystals had an average thickness of 8 p., so that 10-keV electrons (range 2;;,) were stopped within each grain . Alth ough such experimental co nd i ti o ns were less s atis facto ry than those for the thin films of S tu d er and Cusano, Gergely was able to show that the layer
.
,
.
294
Luminescence
in
Crystals
was sensibly linear w i t h voltage, and m o re o ve r for a variety specimens o th e r than ZnS(Mn). Having co rrected for 'dead volt age' e ffec t s he showed that a simple rel ation applied : L = ·YJi V (2 ) where the efficiency 11 is i ndependent of V. He gave the following emission of
,
val ues fo r ?(
£:•:citation
TABLE X.2
e!Jiciencies for phosphor.1· studied by Gergely e t al. 'T]
Phosphor
(per cent) 8 ·5 1 7-8 19·5 14·6 1 6·6
Zn2Si04(Mn) ZnS(Ag) hex. ZnS(Ag) cub. ZnS(Cu) hex. ZnS(Cu) cub.
If the efficiency were equal to unity the li n ea ri ty would always occur. Since this is not so, it must be assumed t ha t a constant fraction of the absorbed energy is effective in exciting lumines ce n ce .
2 15
0·5
I
I
I
I
I
4
I
I
I
I
5
I
I
I
I
I
8
1 0 12 V i k V )
Fig. X . 3 Brightness of a ZnS(Ag) screen irradiated by a cathode-ray b eam as afunction of accelerating potential V (G. Gergely)
r
11
Experimental curve Calculated curve allowing for energy loss in layer
a 'dead'
29 5
Cathodo/uminescence and o ther topics
3. Penetration of fast electrons into matter and the excitation process
(A) Energy loss by electrons in matter
The retardation of i ncident electrons (pri maries) occurs by d e tach ment of electrons (sec o n d a rie s) from the crystal lattice atoms or ions. In their turn these secondaries continue the excitation or ionization process . In every case and above all at low voltages ( < 20 kV) some electrons emerge fro m the sol i d and an i mpo r ta n t fraction of energy is t h u s lost. Numerous wo rkers have s t u d i ed seco n d ary electron emis sion with s pec i a l reference to its energy and angular distributions w h i c h throw light on the deceleration process for th e pri m a ry elec trons. Reference may be made on t h i s subject to t he review articles by Garlick. We co n s i d e r here only t he deceleration process. M o s t of the studies i n this field make use o f the Thomson-Whiddington law :
where E is t he energy of the incident electron and Ex is its energy after t ra v ersi n g a path length x into the solid, a bei ng a c o ns t an t . The total p a t h length o r range R is given by Ex 0, i.e. fo r x R, a n d so E2 aR (4 ) This law is ap p ro xi m atel y valid for electrons of some tens of thou sands of volts : in the energy ra nge 40-50 keY in air. The theory l ea d s to the Bethe formula considering the n o n relativistic fo r m for these low e n ergi e s :
£ 2 - E,2
=
(3 )
ax
=
=
=
_
dEx
Ex
2nNZe 1
( 5) 2 I where N is the number of atoms per cubic centime tre Z t hei r atomic number, e the electronic charge, and I a mean ionization pote n t i al for the material. If the l o ga ri thmic term is neglected (made co n s ta nt) , this formula gives the T homs on-Wh idd i ng t o n law by integrati o n . Bethe's calculations apply to separate atoms. The electronic sy s tem i n a crystal p o se s p a rti c ul a r p r o blem s . For the inner shell electron s one may pre serv e t h e Bethe a s s ump ti o ns , but for valence electrons the atomic wave functions must be rep l aced by Bloch wave functions. Calculations have been made by Dekker and van der Ziel (1952). For energies greater than about 500 eV, the as s u mp t io n of Bethe's formula is j us tifie d . The theoretical calculation of electron range can in p ri n cipl e be made by i n tegrati n g the B ethe formula. Because of electron d iffu si on , dx
=
log
,
296
Luminescence in Crystals
this is not possible or realistic and a s em i em pi r ical formula has been proposed recently (C. Fe ldma n 1 960) wh i ch is valid for energies between 1 and 10 kV. (6) -
,
where n is a function which increases with the atomic number of the
element (n
�
2 for Z
=
24).
TABLE X . 3
Values (�( the constan ts b and n of equat ion certain conventional phosphors b
Phosphor
63 12
ZnS Zn2Si04 cawo.
17
6
for
11
2·4
2·7
3 ·0
n decreases slowly as the energy E increases : Katz and Penfold hav e p ropo s ed for aluminium (Z 1 3 thus n < 2)
J n actual fact,
R = 1 1 3£n with
=
for E > 0· 1 M eV , E being expressed here in MeV and R in ?mgstroms . n
=
1 ·265 - 0 · 0954£
(7 )
When n is greater than 2 at low energies, which is the case for the p ho sp h o rs then the Thomson-Wh id din gto n law is approached
at the h i gher energies ; in the {3-ray energy range one always uses the l inear formulation of th e range energy rel ati on For instance, in al u minium for E > 2·5 MeV th e Fea ther relation holds :
u sual
,
.
Rmgjcm' = 5 30 �rev - 1 06
Measurements for phosphors in this range do not appear to b e available. However, the range expressed in mg/cm2 varies little with the nature of the a bso rber r isi n g s l owly with Z.
(B) Electron difusion
The electrons in a ca t h ode ray beam of normal potential (5 to 50 keV) undergo considerable s catteri n g in s olid s compared with {3- rays and moreover compared with a-rays. Ehrenberg and Franks have studied the scatte ring of well-collimated electron beams inci de n t on a single crystal p h osp h or An a-particle or eve n a {3 p arti cle incident on a phosp h o r excites the emission centres along a cyli n d rical excitation channel. The ex periments of Ehrenberg and Fran k s show that for cath ode rays this channel geometry cannot be assumed, the excitation being w ithi n a -
.
-
297
spherical volume of secondary electrons. At low energies the surface of this sphere extends beyond the range of the primary electrons. Cathodoluminescence and other topics
Phosphor
Electron beam
Fig. X.4 Schematic diagram of excitation region in crystal phosphor due to electron penetration (Data of Ehrenberg
and Franks used by Garlick)
a
A -+ B -+ c Increasing electron energy. At low energies the e le c tro n beam excites a spherical
volume. At much higher energies a channel of excitation occurs especially when ener gies of Me V are reached
Fast electrons excite and ionize the luminescence centres. A fraction of the energy lost in the crystal lattice is finally transferred to these centres. For this a mechanism analogous to that proposed by Riehl and Schon for energy transfer can be assumed. It must be assumed generally that the luminescence under cathode ray excitation is due to a bimolecular recombination of conduction electrons with empty emission centres. However, the results of Strange and Henderson throw some doubt on this. For such phos phors as 'pure' ZnS, ZnS(Cu), ZnS(Ag), ZnS(Au), ZnS(Pb) they always found an exponential decay of luminescence with two com ponents, one with a decay time of about I 0-5 sec (o:) and the other with a decay time of 0·75 X 1 0 - � sec (/3) followed by a slow decay. The decay constants were insensitive to temperature. These data led them to propose an internal centre process without ionization. t Consider for a moment the retardation of a nuclear particle in (C) The excitation and emission processes
t A sensibly exponential decay can i n certa in cases result from a bimolecular recombination process (if one carrier is in large excess of the other). However, the hypothesis of excitation without ionization would give the in dependen ce of the life time of excitation density and the temperature. It must be noted that Strange and Henderson expressed caution about their interpretation.
Luminescence
in
Crystals
matter. One knows that it is necessary to consider the states of excita tion of the a t o ms or molecules of the ab s orba n t to account for the o bserved ioniz i ng p ow e r : thus i n air the energy lost by an o: o r f3 p ar ticle i n c re a ti n g one ion pai r is abo ut 3 5 eV , double the ioni zat i o n pote nt i al , which is 1 7 eV fo r nit ro ge n and 1 5 · 5 eV for oxygen. Thus molecules a re m ore l ikely to be excited than t o be ionized . The same a pp l i e s to luminescence centres in phosphors. There is no do ubt t hat c on s i de rab le ion izat i on is p rod u c e d in the c ry s t a l lattice by fast electrons, but when the number of ion pai rs created is very la rge co m p are d with the activator imp u rity concentra ti o n (i.e. density of luminescence cen t res) , their recombination with out radiative emission seems very probable. O ne cannot understand the relatively high luminescence efficiencies obtained if there is not centre e x ci ta t ion without ionization. One cannot u nd e rs tand why the efficiency should be independent of the density of electron-hole pairs. We therefore suggest that for l a rge excitation densities the lumines cence a ris e s m ainly fro m the fract ion of centres which are excited but not i o ni ze d by the primary and secondary electrons. After a certain time of decay , when the ex c it at ion d e nsity is sufficiently diminished, the electron-hole recombinations via l uminescence centres will a ga i n determine the em is si o n . 298
Screens of zinc and cadmium s u l p hi d e subjected to electron bom bardment slowly blacken and the luminescence efficiency falls. Light and pro l onge d exposure in a humid atmosphere produce the same effect. S i l i ca t e s and fluorides also show these 'fatigue' phenomena but to a lesser degree. Zinc or cadmium metal is deposited in the crys tal , but defects gi ving rise to non- rad i at i ve recombination centres are also p roduced . We return to this matter in s ec t ion IV below. In cathode-ray tubes the phosphor may also undergo ion bombardment. This can b e elim inated by use o f ion traps in the tubes. ( D) Phosphor deterioration ('electron burn')
I I . X - R A Y E X C I T AT I O N O F P H O S P H O R S
A l tho u gh the primary radiation consists o f pho t on s , the excitation is due to the fast secondary electrons produced by absorption : in this respect (of excitation mechanism) X-ray excited luminescence ap proach es more nearly to cathodoluminescence than to photolumin-
Cathodoluminescence and other topics
299
escence, s i nce the electron energies are of the same order of mag nitude. In t h e most favourable cases the quantum yield for photol u m i n e s ce nce is near to u n i t y ( n u m be r o f p h o t o n s emitted p e r photon a b sorb ed ) . This is effectively the case for ZnS(Cu) e x ci t e d by 3,650- A rad i a ti o n . For X-ray excitation the 'quantum yi e l d ' is much gre at e r t h an u n ity . Consider an X-ray tube running at 80 kV potential e m i t ti n g X-rays of m e an wavelength 0·2 A , the radiation being incident on a calcium tungstate screen (Coltman, Ebbighausen and Altar, 1 947). The e mi tte d light has a mean wavelength of 4,400 A . En e rge ti cal l y an X -ray p h o t o n could thus cause emission of 20,000 visible p h o t o ns. The intrinsic efficiency is at most 5 p e r cent ; each X-ray photon produces 1 ,000 visible quanta. Such a high value can only be under stood if sec o ndary electrons are produced in the excitation. The effi ciency appears t o b e app ro x i m a tel y i n d e pen d ent of t h e X-ray wave l e ngt h . Kallmann and D re s ne r (1959) have s h o wn d ire c t ly that the volume of the channel o f excitatio n is about proportional to t h e e nerg y of t h e incident beam. This proportionality remains t h e s a me even when the channel changes form (cf. Fig. X.4) : r o u gh l y cy l ind r i cal fo r 35-kV X-rays, it becomes a s ph ere for 3 ·5-kV X-rays.t In all cases, contrary to that in cathodoluminescence, the intrinsic e ffic i e n cy has no more than a lo o s e a s sociat i on w i t h the l ight output of the screen. In p ract ice , the screen absorbs only a small fraction of the incident X-rays, being s uffici entl y thick to h i n d er the e m e rge nc e of so m e of th e e mi tte d li g ht . This can be deduced from the results of C o l t m a n , Ebbighausen and Altar : The power of the incident X-ray beam is 7 1 4 ergsjcm 2/sec, o f which o n l y 86·2 ergsjcm2/sec are absorbed i n the screen, the rest b e i n g t r an s m i t t e d . E n e rg y emitted as li g h t amounts to 2·34 ergs/ c m 2js ec, from which a gross effici e n cy of 2·7 per cent is d e duce d . I f s om e 55 per cent of t h e li gh t actually gets out of t he screen, t h e n an intrinsic e ffici e n cy of 5 p e r cent is obtained. Klase n s ( 1 947) studied the light output of fluorescent screens ex cited by X-rays (Fig. X . 5) . If N0 is t h e number of incident X-ray p ho t on s , the number dN absorbed in a p ho sph o r layer of thickness
dx is
1" A channel of excitation is associated with each of the fast secondary electrons crea ted by the X-rays.
300
w h e re ft i s the absorption
coefficie nt of the screen material for the The lu m in escence emission is as s ume d equal to dN, which neglects s a tu rati on effects for i ncr e asi n g electron density. dL = rJ dN o If is the a b s orp tion coefficient for the emitted light and if one Luminescence in Crystals
X-rays.
X
X - rays
I I I I I I
-jdx(: 1
I I
Fig . X . 5
incident
emission from
I
I
D
011 a luorescent scree11 of thickness D
X-rays
to tal emission is
looks at the
I
1
same side as
the
L(hack o f scr�cn)
=
J�
that
of the
t)fL N0 e pJ; e ox
dx
inc i d e n t X-rays,
�),uN.'l [ J - e (t• +< llD]
This increases ten d in g towards saturation if D is increased indefinitely . This ap pli es in the case of certain re i n forci ng screens. ="
medical
,a + o
ra d i o g r a ph ic s c reen s) is
g ive n by '
The emission from the other side of the
This reach e s a where
L(rront)
=
maxi m u m =
These calculations ne gl ec t
J�
screen (usual case for '
1)ftNo e-vt e o
t),UNo e-oD _ e �'D] [
for a certai n screen
fl -0
_ log [t - log o ,u - o
thickness D
=
Dm
light diffusion w i thi n the screen : Klasens has shown that this can be taken care of in most cas es by a m od i fica D
tion
of the c oeffic i en t o.
m -
30 !
Cathodoluminescence and other topics
I n practice the efficiency of an X-ray screen is determined not only by the phosphor efficiency but also by the intensity of the X-ray absorption. For ZnS(Ag) the efficiency can reach 20 per cent and that L
8
Fig.
X.6
Light L emitted by
X-ray screen of increasing
thickness D
B
Viewed from back Vie wed rom front
f
of a CaW04 p ho s p h o r 5 per cent : however, by the proxim ity of a heavy element (lead or tungste n), which is strongly a b s o r bi n g the emission of the t u n gstate sc ree n can be made more i ntense. For the same reason it is more useful to use a ZnSCdS(Ag) pho s p h o r than ZnS. F
,
I l l . R A D I O L U M I N E S C E N C E - S C I NT I L L A T I O N S
The use of luminescence from zinc sulphide to detect radioactive rays i s coincident with the history of radioactivity, e.g. the spinthariscope of W. Crookes ( 1 903). Rutherford made a quantitative use of the scintillations produced bye<: particles in a zinc sulphide screen. A study of e<: particles scattered at different angles by nuclei made by Geiger and Marsden ( 1 908-1 3) compared with Rutherford's theory led to the nuclear model of the atom, using the scintillations technique. The subsequent development of Geiger-counter techniques and the Wilson cloud chamber led to the abandonment of this meth o d , prin cipally for the follo wi ng reasons : 1 . Historical
Luminescence in
Crystals
(i) the neces s i ty fo r d ark a d apta ti on of
the eye before measure ments, (ii) individual s c i n ti l l ati o ns pro d uc ed by {J- o r y-rays were us ually too feeble to be s e en . The modern form of the sc i n t ill ation coun t e r d epe n ds on the use of a p h o to elect ro n m ultipli er as ligh t de tecto r replaci n g the human eye (C ur ra n and Baker, 1 944). As the latter work remained classified until l 947 the first publicati on s on the su bj ect were those of Kallmann and his collaborators. In 1 947 B ro se r and Kallmann described the use of n aph t ha le n e crystals to count {J- a nd y-rays. Then followed liquid and p l a s ti c scintillators (in which luminescent substances were d i sperse d ) , all o w i n g l arge volume detectors for co s m ic rays. Since th e n there has been an ava l a nch e of devel opments. Thus in 1 952 Garlick was able t o cite 1 1 5 publications on t hes e counters in a re view article.
302
2. Characteristics o f the main crystalline scintillators
Reference may be made to special vol umes, such as th o se of C u n·a n or of Birks, and more re ce n t ly of D. Blanc, or t o the review by Gar l ick, Jordan or Morton for the arrangements and s peci al uses of the scintillation counter. We simply give here some ge ne ral o b se rva t ions .
Silver-activated zinc s ul phi d e is one of the most efficient p h o s p hors : several tens o f t h o u sa n ds o f p h oto ns are emitted per MeV of cx.-par ticle energy. There has been a l o ng discussion on this s ubj ec t sin ce ex p e rim e nts by Riehl su gges te d 80 per cent conversion e ffi cie n cy which was in conflict with the ory . However, the work of Klase ns showed that the efficiency did not exceed 20 per cent, which is q u it e h i gh but no more than that of cathodoluminescence. The decay time of Zn S (A g) is rather hig h , ex ceedi n g I 0 5 sec, which pro h i bi ts rap id p art i cle counting; this is not i m p o r t a n t for many cx.-p a rticl e measure ments, e.g. the natural rad i o act i ve sources i n common use. Zinc oxide has a d ecay time of I fJ- Sec but i ts e ffici ency is only about 20 per cent of that for zinc s ulp hi d e . O rga ni c c ry s tal s allow of rapid count i n g but their yield is even less favourable for cx. p article s ( 1 per cent or l es s) . NoTE . R ev e rti n g to ZnS, Kallmann showed t hat in addition to the usual decay of about I Q 5 se c duration, there was a fast c o m p o n e nt
(A) Detection of ex. p articles
303
Cathodoluminescence and other topics
lasting about I 0 7 s e c due to d ire c t excitation of e m is s io n centres without ionization (c f. page 1 49). T hi s ha s b ee n mea su red p recis el y at the Atomic Energy Co m m i s sion in Saclay by L. Treguier and Y. Koechlin. Exciting Z nS ( A g) by <1. particles, they found three components of decay : -r 7 x 10- 8 sec . Blue emission only T R:1 9 X 10_7 sec -r R: 1 ·3 x I 0-5 sec The <1. component of Strange and Henderson (se e page 297) these being followed by a slow phosphorescence. The time constant usually measured is in general the meant of the above, d e pen d i n g also on the various frequency responses of the associ ated c i rcui try. The u s e of suitable electronics, i n v o lvi n g fast amplifiers, &c. , a l lows th e shortest time response of the ZnS(Ag) phosphor to be selected .
}
=
(B)
.
Detection
These
rays,
of {I- and y-rays e s p e ci a l l y the y-rays, are l e s s absorbed than TA B L E X . 4
r:t.
particles :
The yields for {3 excitation of various scintil!ators Phosphor
cawo. CdW04 CaF2
Nai(TI) Anthracene
Stilbene Naphthalene
Naphthalene + 1 per cent anthracene Terphenyl in xylene Tetraphenylbutadiene in polystyrolene
Maximum of ' emission band
A
4,400 5,200 4,00 4,100 4,480 4,080 3 ,450
4 ,400 3,600
Yield in photons per Me V ,._, 1 0 ,00 ,. 20 00 ,. 5 00 ,._, 20,00 ,. 10,00 ,. 6,00 ,. 1 ,00 (visible)
:
in
Decay
time
sec
3 . 10 - ' 10-• 1 ·5 . 1 0 ' 2·5 . 1 0 ' + 6 . 1 0 8 >
3 . 10 · o-6 . w -• 6 . 1o •
5 ,00 2,00
4 . l o -- • t 4 . IO-• t
2,00
3 . 10-• §
t Mixed anthracene naphthalene crystals are more transparent to the ir em i t ted radiat ion than pure anthracene. t Liquid scintillator. § Plastic scintillator.
t Dependent on the ex perimen tal system, values between 0·2 an d tens of JLSCC onds are possi ble . It seems that the duration of the scintillation p ro du ced by an ex particle is some ten times shorter than that produced in cathodoluminescencc measured with the same system. The proportion of the rapid components is much greater.
Luminescence in Crystals
304
one therefore uses a material available in the form of la rge trans parent crystals. The liquid scintillators are less efficient than these. (C) Detection of cosmic rays The energy here is s o high that a poor efficiency does not matter. L i qu i d and plastic scintillators are part icu larly suitable. Plastic scintillators of 1 00-kg mass have been made. (D) Detection of heavy ions, fission fragments, &c. The response of zinc sulphide (for example) to machine-accelerated ions has been studied. Broser and Kallmann ( 1 948) have excited ZnS(Ag) with fission fragments fro m U238• Pulses of large size are obtained but only three times these produced by ex. particles from uranium. The efficiency is relatively low and e ffec ts of 'radiatio n d a m a ge are considerable. The response is n o t a linear fu n c t i o n of the p a rt icl e e n e rgy. '
(E) Detection of neutrons A fracti o n of the energy lost by fast neutrons in nuclear collisions is used to excite luminescence. In hydrogenous substances the excita t i o n occurs via the effects of recoil protons. The scintilla tor response is often comparable for neutrons and y-rays, which makes it difficult to distinguish between the two. For slow neutrons, an element such as boron may be incorporated into the pho sp ho r B 1 0 has a large reaction cross-section (n, ex.) of 550 barns for thermal neutrons, the resulting ex. particle pro v i d in g the scintillations. Lithium may also be used . .
B 1 0 + n � LF -+ cx.
or
Li6 + n � H 3 + cx.
The response of a scintillator is said to be linear when the pulse pro duced by each scintillation has a magnitude proportional to the energy of the incident particle (proportional counter) . This is gener ally t ru e when the ionization density is small : deviations from line arity occur at high ionization densities. Thus, in general, response to high-energy electrons is l in ear even for luminescent materials which do not show a linear response to cathode rays. In org ani c scintil lators show a s e n sibly linear response to protons and deuterons. In
3. Linearity o f response
Cathodoluminescence and other topics
305
contrast to this, the response to oc particles is not linear below ener gies of 10 to 1 5 MeV. At low energies ( < 5 MeV), the magnitude of the scintillations from silver-activated zinc sulphide is proportional to the resid ual Na i l H I
Pulse height
7000 6000 5000 �000 ) 000 2000
Anthracen•
.
.
1 00 0 0
50
100
4CO 500 600 [n.' '.Q V I kP.V I
Fig. X.7 Response of anthracene, stilbene and Nal(T[) scintilators to electrons (Jentschke, Ehy, Taylor, Remley and Kruger)
range of the oc particle (J. Anth o n y and G. Ambrosino). The same is true of calcium fluoride (Garlick and G. T. Wright) and also for anthracene (Birks). The simplest explanation of this is to assume that all centres are excited which lie in a channel of excitation of constant 2000
Pulse h e 1ght
li D O
Fig. X . 8
Q
2
4
6
9
10 1 2 1 1. 1 6
Energy
l ke V I
19 20
Response of Nal( Tl) to H2+ ions, deuterons and particles (Taylor, Remley, Jentschke and Kruger). Response to protons and deuterons essentially the same et
cross-section and length proportional to the residual range of the particle when it arrives at the crystal . A short phenomenological calculation by G. T. Wright ( 1 953) referred to by Garlick gives a sufficient account of the effects. Let e be the exciting energy per unit path length along the excita tion channel. We assume - as was done for cathodoluminescence -
306
only excitation
b l e probability of
that
the
Luminescence
in
Crystals
of c en tr e s without i o n ization
leads to a n appreci
e m i s si o n the i n te n s e ionization in
recombination when the den of electron-hole p a i rs is much larger than that of emission centres . The number o f excited molecules or lumi nescence c e n t re s de c a y s at a constant rate, with probability p for luminescence em i s s i o n a n d q fo r i n te r n al q u e n c h i n g (non-rad iative), w h i l e the i o n izat i o n i n v o l ve s a n o n-ra d i a t i v e bi mol e c u l a r reco m b i n a t i o n w i t h a rate fh:. G. T. Wright gives t h e r a t e o f e n e rgy d i s s i p a t i o n as fo l l ows : a
l u m i nescence
,
crystal lattice giv i n g n o n -rad iative
sity
��
- (p -H +f3s)s
while the luminescence em ission from a n element dx of the excitat i o n dL
channel is
If
F.0
=
g i ves
��
p
dx
J: s(t ) dt
i s t h e s p e cifi c e n e rgy loss o f the particle, then i n t e g r a t i o n
dL
=
The total l u m i n e s c en ce
no
=
reabsorption o f t h i s
E.
[r +_1_ . dx
dx
emission during the scintillati on, assuming emission, is x= II L= dL {J
p+q
f
I n g e n e ra l t h i s integrat i o n c a n only be carried o u t graphical l y . H o w
�� ,
ever, if
where E0
is s m al l ,
then l i n ear i ty may be assumed and
J � dE, i .e. �� large,
=
X=O
L = _!Eo p+q
the e n e r gy
of the i nc i d e n t particle.
I f,
on
the
l i n ea r i ty will occur, wh ich
are found experimentally. However, the th eory due to Wright d o es n o t explain the proportionality between L and R for l o w e n e r gy Cl. particles which may p e rh aps be associated with the saturatio n of the a v ai l ab le luminescence centres i n the excitation channel . contrary,
is
t h e n d eviatio ns fro m
-
Cathodoluminescence and other topics 4.
307
Size of the excitation channel, density of ionization and refilling of electron traps for the particular types of excitation
(A) A particle of high energy will cause considerable ionization den sities in the channel of excitation. The volume of the latter can be estimated by finding the number of luminescence centres excited by each p a rt i cle As carried out by Kallmann, Spruch a n d Dresner, one can d e t er m i n e the cross-section a of t he chan nel fro m t h e rise i n l umi nescence e xci te d by a constant stream of particles. Consider an a rea o f I cm2 with N i nc ide n t particles per seco n d . The fract i o n /st i l l i n t h e excited state a t t i me t is given by .
X'=
from which we get a luminescence which rises with a time constant
=
Na(l -f) .
Lmo.x( l - k e fJI) where k i s a constant. The length of channel is equal to the ran ge of
{J
Na :
L
the exciting charged particle. =
Examples (a) f3 particles of about 1 Me V energy (Sr 90). Range in ZnS about
1 m m such th at a powder screen shows partial transmission of {J particles. The diameter of channel according to Kallmann and Dresner is � 1 · 8 X 1 0-s cm . In a channel of volume 1 0 - 1 0 c m 3 there will be 1 00,000 excited electrons, giving an ionization density of the order of 1 015 electrons/cm3• (b) 35-ke V X-rays. Each secondary electron produces an excitation channel equal to its range, i.e. � 3 X w·- 4 cm. Diameter of channel � 9 x I 0-5 cm. Ionization density 1 0 15 to 1016 electrons per cm�. (c) 5·3-Me V et. particles (po/onium). Range in ZnS � 1 5 ,a, number of centres excited p e r et. particle 500,00. For 1018 centres/cm 3 (4 x I0 5 g Cu per g Z n S) the volume of channel is 5 x IQ-13 cm3• Radius of channel is I 0-5 cm, giving considerable ionization density � 1 0 1 8 electrons per cm3 or as much as 1 0 19 in the first i nstant follow ing excitation before electrons have had time to diffuse out of the channel. (d) Comparison with densities due to ultra-violet excitation. Consider a layer of zinc sulphide emitting 1 0 16 photons per secjcm2• For green light this corresponds to a luminescence of 2·5 l a m b e rt s (0· 8 candle/ c m 2) . Long wav e l e n gth ultra-violet radiation penetrates 0· 1 m m In .
308
Luminescence in Crystals
a layer of thickness 0· 1 mm and area 1 cm2 there will be 1016 recom binations per second, giving 1 0 1 1 free carriers (assuming a life time of I 0-5 sec) . The free carrier density will then be � 1013 electrons/ cm3• With the u s u a l s o u rces of excitation this value can vary between 1 0 1 1 and J O H .
(B) Fraction offilled traps Although total filling of traps ca n be ach ieved by ultra-violet light excitation the percentage filling for particle excitation is small ( � I to 5 per cent) . For example, even after a very intense <X-particle ex citation only a very feeble phosphorescence is observed. For electron or X-ray e xci ta tio n the filling of traps is a little greater than this. The d iameter of the excitation channel is much smaller than the d iffu sio n length of the electrons before trapping. This i ndicates that they will reco mbine preferentially wi th holes. I V . R AD I ATION D A M A G E I N
P H O S P H O R E S C ENT S O LI D S
Daylight pro d u ce s a blackening of zinc and more so of cadmium sulphide, attributed to freeing of metal (by breaking of atomic bonds) this being a pho tochemi cal action. The metal becomes colloidal and the damage is irreversible. The effect i nvolves liberation of electrons into the con d uction band , followed by their capture on zinc or cad mium ions. Gordon, Seitz and Quinlan ( 1 939) give the fol lowing reaction : Zn2+ � - e - -+ Zn+ 2Zn+ ->- Zn 2+-f- Zn
The blackening is more rapid for radiation of quantum energy ltv greater than the energy-band gap. This is why for d aylight irradiation it is seen more readily in mixed ZnS(CdS) crystals with a high pro portion of CdS. The effect is less marked when h1' is less than the b a n d gap energy and is related to localized level s, e.g. those i ntro duced by copper i m pu ri ty However, more effective than the phosphor composition is the influence of humidity. The electron liberation takes place within the crystals, but bond rupture occurs where the zinc sulphide is al ready partially dissociated and has a weaker binding energy Blackening -
.
309
is more rapid for wurtzite (hexagonal) than for blende (cubic) type crystals, the latter having greater chemical stability. - In electroluminescence the same process takes place with the same effect of humidity and is the principal cause of the deterioration of electroluminescent panels (Smith, Potter and A ven). If humidity is removed, the deterioration is less marked. It seems that the rotation of the sulphide grains produced by the internal electric field of the dielectric must equally lead to a lowering of luminescence efficiency. There is also perhaps a diffusion of impurities and lattice defects to the interior of the phosphor under the action of the applied electric field. High-energy radiations also produce the above phenomenon, but this is accompanied by other effects. Electrons accelerated in a cathode-ray tube rarely have energies sufficient to produce lattice vacancies and interstitial atoms. This requires an energy of about 8·7 eV in CdS (Kulp and Kelley, 1 960) and probably a higher value in ZnS (1 5 eV ?). This corresponds to a minimum threshold energy of bombarding electrons in CdS equal to 1 1 5 keV. When the energy exceeds this threshold value the incident electrons create centres in cadmium sulphide responsible for the edge emission at 5,200 A and also for the red band at 7,600 A.t These emission bands can 80 Z n S (Ag l therefore be attributed to 1 0 f! vacancies or interstitial atoms. To specify which model ap plies to each centre requires a number of additional ex 20 Cd S I C u l perimental data. 0 3 When the energy is less than Numb er of incident electrons that of the threshold, then besides the photochemical Fig. X.9 Deterioration of luminescence of various phosphors under steady cath destruction of the phosphor ode-ray excitation (J. Rottgardt) screen, F or colour centre formation occurs (particularly for radiation of small penetration Cathodoluminescence and other topics
-
t Cadmium sulphide showing ultra-violet excited emission bands before bom bardment shows the same under electron excitation , but the edge emission gradu ally disappears. L
310
Luminescence in Crystals
ex is te nce of t hi s effect in fluorite a b s o rp ti o n bands o cc u r rin g in the u l t ra - v i o l e t region . We assume, with Garlick, that these ce n t re s cause non-radiative transitions. The process does not ::a u s e such a rapid destruction of luminescence as that observed in zinc s ul p hide . I n c a th o d e- ray tube screens, ' s t i c k i n g ' of electro ns w i l l cause a reduction of luminescence due to electrostatic repu ls i o n o f i n c i d en t p r i mary electrons, but this can be eliminated by p r op e r aluminizing d e p th
confined to the s u rfac e l ay e rs) .
Hill
has shown directly the
the s c ree n . p artic le s p ro d u ce many defects. In the absence of informa tion on luminescent s ulph ides , we give data for �erni-conductors : of
Heavy
1 et. p a rtic l e of 5 MeV energy p r o d u ce s 1 00 v a c a ncy interstitial pairs 1 H2+ ion of 10 keV , , 20 , , , 1 p of 20 MeV 1 00 , ,
1
MeV
2,000
,
The l u m i ne s ce n c e efficiency thus fa l l s with the number N of in c i d ent of 2
n
,
The case for et. particles. The de s tru c t i o n of l u m i r_ es c e n ce centres by partic les.
et.
pa r t i cl es
c o n s i de re d i n very ea r ly work. Ru t h e rfo rd gave a t h e idea that each centre c o u l d o n ly be excited pa r ti cl e , as fo l l o ws :
was
formula, based on o nce by
a n et.
f_:!!
_!__( 1 - e -J.N)
where }. is a c o n s t an t, LN being the l u m i ne s c e n c e L0
=
}.N
<:fter bombardment by N p a rti c l e s and L0 the initial l u m i nescence. Currently it is ass u med that et. particles p r o d u c :: deep-lying de fec t traps which fu n c t i o n as non-radiat i ve recombination centres. Hanle and Rau ( 1 95 8) g i v e a fo r m u l a fo r ZnS as follow:; : 1 LN
l +AN
(I)
where A is a constant. The formula i s appl icable for deuterium ions (Martin, 1 957). For CdS, Br o s er and Wa r mi n sky p ro p o se d a d i ffe re n t formula : L N' L0
_:_
=
1 - log
( 1 + - )N/a a
N
(2)
is a constant. e q u at i o n ( 1 ) is more applicable when the d en si ty of e x c i t e d electrons is much larger than the activator concentration, wh i l e e q u a t i o n (2) a p p l i e s when the latter is of the same order as the
w here
a
It appears th a t
Cathodoluminescence and other topics
excited electron de nsi ty (in this case the bimolecular recombination o f electrons and holes in the centres following ionization can be radia tive, this being the assumption made by B rose r and Warminsky). 31 1
100% so
Fig. X. l 0
1 00
'200
300
1. 0 0
500 T {° C I
Thermal quenching of ZnS(Cu) phosphor ( W. Martin) ----- before irradiation after bombardment by 1013 H2+ ions/cm2
The defects or traps produced by bombardment are too deep to in the thermoluminescence of ZnS . However, their existence is confirmed by a study of thermal quenching which occurs at lower temperatures after irradiation (see Fig. X. I O). Infra-red q uenching
show up
--
Fig. X. l l
Te mpera ture
Tlrermoluminescence curves of ZnS(Cu) phosphor ( W. Martin) + + + + before irradiation after bombardment by 1014 H2+ ions • • • • after regeneration by 2 . 1016 electrons
oooooooooo
312
effects are specifically enhanced while infra-red stimulation practic ally d i s ap pe a r s (F. B a ndow, 1 9 5 6) . In contra st to a -par ti c l e irradia ti o n, that due to deuterons produces traps which are evident in th e rrnolu minesce nce (W. M a rti n, 1 957). After a bombardment by 1 0 15 electrons per cm2, the o ri g i n al thermoluminescence charac teristics a re resto red. This makes it do ub t ful whether the traps are due to ion di s place m en ts (defects or i n t erstit i al s), but the effect can be well explained u s i n g the trapping model described on page 1 68 . The i r ra d i atio n of Luminescence in Crystals
L
50 %
X. 1 2
0
20
1.0
60 Min utes
Rise of luminescence L of a ZnS( Cu) phosphor under ultra-violet excitation r Screen before neutron irradiation rr After 16 hours pile irradiation at Brookhaven with '" 5·8 . 10 1 6 neutrons per cm2 The slower rise indicates that many more levels have to be filled (Smith and Turkevich)
Fig.
ZnS by H2+ i o n s diminishes the n u mb e r of traps of d ep th 0·28 eV attrib u t ed to the capture of electrons by discrete substitutional im purity ch ar ges with an enhancement of electrons in traps of depth E R:-J 0·5 eV due to capture by doubly charged t rap sites. In this ex pla n at i o n one of the two ch a r ges i s p r o vide d by the incident H2 + ion. Pr o t o n s should
produce
very
effect.
Neutron d amage was stu d i ed by Smith and Turkevich. Neutrons p r o d u ce a l a r ge number of deep trap effects, but these do not show in the therm o l u mi nescence curves. Ho w ever, there is an o ve ral l reduc tion in thermoluminescence intensity (some 'glow' p eaks are more a ffected than others). Aga i n , thermal quenching effects occur at lower a
similar
Cathodoluminescence and other topics
313
temperatures after irradiation. The damage can be removed by heat ing for a few minutes at 900°C.
Transmutations in zinc sulphide phosphors Transmutations using IX particles. The reaction
Cu6 3 + He4 -- Ga66 + n
(r � 9·2 hours)
t
is known, but is very weak and almost unobservable for copper at impurity concentrations. Transmutations due to neutrons have been applied by E. and M . Grillot t o impurity centres in ZnS and CdS. With silver there are two reactions : Ag 1 0 7 (5 1 ·35 per cent) (n, y) Ag 1 0 8 (r = 2·33 min, fJ emission) (r = 44· 3 sec, y emitter) (n, n) A g lo7 A g1 09 (48·6 per cent) (n , y) Ag 11 0 (-r 270 days, K capture) (-r = 22 sec, fJ emitter) a = 1 ·4 barns Because of the life time the 270-day decay process is used in analysis. After pile irradiation at Saclay, a silver content of 2 x w s A gjg CdS was found. It was also shown that a part of the silver tended to re main on the surface of the phosphor grains, but about 80 per cent of the silver actually diffused into the crystal lattice. Copper detection. The following reaction is used : Cu6 3 (n, y) Cu64 (-r = 1 2· 8 hours p-, fJ+ emission and K capture) a = 2·7 barns Copper may be introduced into zinc sulphide by the following re actions of the lattice zinc Zn64 (n, p) Cu64 and Zn64 (n, y) Zn85 -- Cu65 by K capture An amount of copper greater than I0 - 5 g Cu per g ZnS may be measured but not smaller concentrations. This difficulty is not found for copper in cadmium sulphide. In contrast to the case of silver. nearly all the copper is substitutional in the lattice. znee +fJ+
=
400,000 years, p - emitter) 38·5 min, fJ+ emitter and K capture) After thermal neutron irradiation of the sulphide for several hours
CP5 (75·4 per cent) (n, y) CP6 CP7 (24·6 per cent) (n, y) CJ38 Detection of chlorine
(-r
(-r
=
=
3 14
in
Luminescence
Crystals
the chlorine can be distinguished from other ra dioactive i sotopes with a dosage precis i on better than I 0 - 6 cm Cl per g CdS. In practice , chlorine can be almost completely e l i m i nated initially from the sul phide, and then more copper t h an chlorine (5 times) i n t rod u ce d at 500° : it is not essential for the chlorine ions to provide activator cha rge compensation for the i n trod uct i on of Cu + ions to be possi b l e (E. and M. G rill ot) .
APPENDIX I Phosphors for monochrome and colour television
In 1 95 7 a symposium on the prob l e m s of colour television was held
in Paris. Reference may be made to the symposium pub lication, par ticularly to the contribution of H. A. Klasens and D. A. Bril. 1.
Introduction : the chromaticity diagram
I f we assume three pr i mary colo urs, red (A), green (B) and blue (C), then any colour may be defined by three quantities, X, Y and Z, which represent the respective amounts of A, B and C which mu s t be mixed to obtain a match to that colour. The qu an t i ties X
=
..
··-· ·
X
.
X+ Y+Z '
y
=
·
y--
- ··
•
X+ Y+Z '
z
=
z
-·--- ---
·
X+ Y+Z
are the t ri chr o m atic coordinates for the particular colour. They are governed by the iden tity
x+y+z
=
1
and so specification of two of them, x and y, w ill define the colour. Light sources of different spectral distributions can gi ve the same colour sensation : in c o n trast to the ear the eye does not seem capable o f anal ysi n g the freque n cy spectrum. The choice made by Maxwell consisted of the real p r i m ary radia tions : blue 0·457 p. green 0 · 528 p ; red 0· 6 3 0 p ; However, it was fo u n d that it was i mpossible to represent all real colours without a ccepti n g in ti m e negative values for the trichromatic coefficients. The I n te r n ational Committee on Illumination took unreal primary colours determined so that negati ve coefficients could not occu r .
These c o l o u r s are defined thus :
315
Cathodoluminescence and other topics
Red
0·700 p,
{X = 0·73 y = 0·27 z =O = 0·27
Green 0·546 p, f y = 0·72
= 0·01
= 0· 1 7 Blue 0·4358 p, y = 0·01 f = 0·82
If the amounts of these three colours are given, then a simple linear y 1
0·9 0·8
5200 p
0·7
5600
0·6
0·5
5700
58 00
5 900
0·4
6000
0 ·3
0·2
62 0 0 6400 6500 7 000
0·1 0·5
Fig.
06
0 ·7
X. 1 3 Chromaticity diagram showing position spectral colours and the point for 'illuminant C'
The point 0 represents waveleng th 5,240
of
a ZnS( Cu) phosphor of dominant A andpurity about 60 per cent
Luminescence in Crystals
316
substitution allows the coordinates for the trichromaticity to be determined. White light (daylight) known as illuminant C has the coor d in ates X = 0·3 1 , y 0·3 1 6. Dominant wavelength and purity. Consider a zinc sulphide phosphor (wurtzite) with a green emission band only. It is represented on t he chromaticity diagram by the point 0 with x = 0· 1 9 and y = 0·625. The straight line CO cuts the position of the spectral colour at a point P which determines t h e dominant wavelength. The colour 0 can be obtained by adding to the spectral colour P a certain amount of white C. The purity is defined as CO I CP. Different zinc sulphides, activated with copper and showing pre=
y 1
0·9
5200 5300
0·8 51 0 0
5400
0 ·7 5050 0 5
5500
E
5000
0·5
':i 6 0 0
0·4
5700
5 800
5900 6000
6200 6400 6600 7000
Te tevrsion white
0 ·3 0·2 0·1
0 0
03
Fig. X. l 4 Additive
o
E
i
0�
m x ture
05
0 6
of colours D
and E
Blue phosphor (Ca, Mg)Si03-Ti Yello w phosphor (0·855 Zn, 0·12 Be, 0·025 (Kroger, Bri/ and Dikho.f)
0 -7
Mn)2Si0,
Cathodoluminescence and other topics
317
dominantly a green band, have about the same dominant wavelength, but the purities are quite different. t 1
0 9
y
0·8 07
06
0·5
5 2 00
51 0 0
5300
5�00
5050
5000
0 4 03
0 2
L 8 50
4800
Fig. X. l 5
06
0 ·7
The Maxwell colour triangle used for colour television assessment A Red plwsplwr n Green plwsphor c Blue phosphor
t Leverenz gives in his book the colour diagram locations of ZnS + Cd.S with copper and silver activators. A remarkable application of such a diagram is to be found in the work of Kroger, Bril and Dikhoff (1 952), who show that a white colour cannot be obtained with a mixed ZnS Cd.S Ag Cu phosphor, whatever the relative proportions of constituents. In contrast, this can a lso be achieved with a mixture (0·8 6 Zn, 0 · 1 4 Cd)S(5 x 1 0 - 5 Ag, 5 x 1 0 - 5 Au, 3 x J O -' AI). It is also worth noting in the diagrams given by Kroger, Bril and Dikhoff that the point for ZnS(Cu) (blende form) is almost superposed on the point for (0·97Zn , 0·03 Cd)S- Cu (wurtzite). This shows that a change in colour in passing from wurtzite to blende can also be obtained by reducing the energy gap for wurtzite (cf. page 1 1 5).
Luminescence in Crystals
318
2.
Two-colour mixtures : monochrome cathode-ray tube screens (black and
white)
The colours obtained by addition of two colours D and E are repre sented by the points of the segment DE. A s u i tabl y chosen mixture of two phosphors can thus give white. A bl u e and a yellow-emitting phosphor can be used such as ZnS(Ag) (blue) and (0· 6 1 Zn, 0·39 C d)S A g (yellow), or (Ca, Mg)Si03-Ti ( b l ue) and (0· 8 5 5 Zn, 0· 1 2 Be)2SiOcMn (yel low) -
-
3. Th ree colour mixtures: colour television -
Additive su perp osition of the three colours A, B and C can give a anywhere within the triangle A BC, but using phosphors like th i s cannot give points outside the triangle. The loss of information p oi nt
resulting from this has been calculated ( 1 2 per cent) and it has been shown to be less than that in the usual colour mixing in printing processes (30 per cent). The choice thus provided b y the three summits of the Maxwell triangle is 0· 67 Red phosphor A = O· 3 3 Y Green phosphor B Blue phosp h o r C
{X = {X = 0·7 l {rx 0 · 1 4 = y
y
=
=
0·2 1
· O OS
The most difficult to obtain is the red phosphor. TABLE X . 5
Some phosphors used for colour television (Klasens and Bril) Red
Bl ue
Green
ZnSe(Cu) (0·20 Zn, 0·80 Cd) S (Ag) (0·97 Zn, 0·03 Cd)Se(Cu) Zn9(PO .).(Mn) Zn2Si0iMn) ZnS(Ag) blende wurtzite {Ca, Mg)S i09(fi)
X
0·66 0·67 0·67 0·67 0·20 0· 1 5 0· 1 5 0·16
y 0·34 0·33 0·33 0·33 0·72 0·05 0·03 0· 1 3
Different techniques for obtaining good colour have been pro
posed . The best result is obtained by using three separate tubes with
Cathodoluminescence and other topics
319
red, green and blue screens respectively and a sys tem for superposing the images in projection. The cost of this method is rather hi gh . The R . C . A . system uses a spot pattern of three different coloured phos phors, each colour receiving only t h e electron b e a m si gn a l appro priate to it. At a sufficient distance the mosaicity of the screen is not apparent.
1 candle/cm 2
APPENDIX II
= 1 stilb = n lamberts = 2,9 1 9 foot lamberts = n lumens emitted per cm2 of a surface o beyin g Lam bert ' s law
Relation between photometric units of luminescencet
I
millilambert
IQ 3
lumen emitted per cm2 of
= 0 · 9 2 9 foot lambert
=
a
surface
obeying
Lambert's law
=
1 0 effective lux or apos tilbs or blondels = 6·28 x 1018 eV/sec = 2·83 X 10 1 8 photons/
I watt = 685 l u mens
2·22 eV energy (maximum eye sensitivity .?. = 5,560 A equivalent to 2·22 eV)
sec for complete power conversion of photons of is a
B I B LI O G R A P H Y I. Cathodoluminescence
BRIL, A . and KLASENS, H . A . ( 1 9 5 2) 'Intrinsic efficiencies of phos phors under cathode-ray excitation', Phi/. Res. Rep., 7, 40 1 . CURIE, M . and C u R I E , D . ( 1 955) 'Cathodoluminescence', Cahiers Phys., 57-58, 72. GARLICK, G. F. J. ( 1 949) Luminescent Materials, 1 72-200. Claren don Press, Oxford. GARLI C K , G . F . J . ( 1 955) 'Cathodoluminescence', Proc. Inst. Radio Eng., 43, 1 907. GARLICK, G . F . J . ( 1 958) 'Cathodo and radioluminescence', Hand. der Phys., Licht und Materie, 1 1 1 . Springer, Berlin. 1.
General articles
t After H. W. Leverenz, A n Introduction to the Luminescence of Solids (J. Wiley, 1 950), p. 48 1 .
320
HIL L , C . G . A . (1955) 'Applied cathodoluminescence', Brit. J. Appl. Phys., 6, Suppl. 4, S 6. LEVEREN Z , H. W . (1 950) An Introduction to Luminescence of Solids, 1 9 5-21 2, 3 1 6-20, 427-52. Wiley, New York. WILLIAMS, F. E. (1 953) 'Cathode-ray tube screens', Advances in Electronics, 5, 1 62. Academic Press, New York. Luminescence in Crystals
BRIL, A. and KLASENS, H . A . (1952) 'New phosphors for flying-spot cathode-ray tubes', Phi!. Res. Rep., 7, 4 2 1 . GEOR GIADES- M A LHERBE (1 954) 'Contributions a !'etude experimen tale de la cathodoluminescence'. Thesis, Paris. GERGELY, GY . , HANGOS, I . , TOTH , K . , A D A M , J. and PozsGAY, G Y . (1959) 'The cathodoluminescence efficiency of thin micro crystalline layers', Z. for Physikal. Chem. , 210, 1 1 . GERGEL Y, G Y . (1959) 'The cathodoluminescence efficiency of thin microcrystalline layers. Part II. The intrinsic efficiency', Z. fur 2. Other articles, dealing principally with luminescence emission
Physikal.
Ch emie ,
( 1 9 60) 'Diffusion processes in electron bombardment 211, 274.
induced processes. Cathodoluminescence', Acta Phys. Hungarica,
GER GELY , GY.
12, 221 .
T . ( 1939) 'Band spectra o f cathodoluminescence',
Proc. Roy. Soc., A 173, 323. SHRADER, R. E. and K A I S E L , S . F . ( 1 954) 'Excitation of zinc-oxide phosphors by low energy electrons', J. Opt. Soc. Am., 44, 1 35. STRANGE, J . W . and HENDERSON, S. T . (1 946) 'Cathodolumines cence', Proc. Phys. Soc. Land. , 58, 369. HENDERSON, S .
F. J. and CUSANO, D. A. (19 5 5) 'Transparent phosphor coatings', J. Opt. Soc. Am., 45, 493.
STUDER,
A . J . and V AN DER ZIEL, A . ( 1 952) 'Production of secon dary electrons in solids', Phys. Rev., 86, 755. EHRENBERG, W. and F R A NK S , J . (1 953) 'The penetration of elec trons into luminescent material', Proc. Phys. Soc. Lond. , B 66, 1 057. FANO, U . (1 940) 'A theory of cathodoluminescence', Phys. Rev., 58, 3 . Articles dealing mainly with penetration o f electrons into crystals DEKKER,
544.
( 1 960) 'Range of 1-10 KeY electrons in solids', Phys.
Rev. , 117, 455.
F ELDMAN,
C.
Cathodoluminescence and other topics
32 1
and P EN FOL D , A . S . ( 1 95 2) 'Range-energy re lati on s for electrons and the d etermi nati o n of {3-ray en d-p o in t e n e rgi e s by absorpti o n ' , Rev. Mod. Phys., 24, 28. K OL L E R , L . R. and ALDEN, E . D. ( 1 9 5 1 ) ' Electr on penetration and scatteri ng in phosphors', Phys. Rev., 83, 684. KA TZ , L.
Non-radiative transitions due
to the Auger effect in crystals ( 1 9 5 7 ) 'Possible mechanism for radiationless recombination in semi-conductors', Phys. Rev., 105, 1 469. BEss, L . ( 1 958) 'Radiationless re c o m b i natio n i n phosphors', Phys. Rev., 111, 1 29. P IN C HE R LE, L . ( 1 955) 'Auger effect in semi-conductors', Proc . Phys. Soc. Lond., B 68, 3 1 9. B E SS , L.
11. X-ray excitation COLTM A N , J.
W . , E B B I GHA USEN , E. G . and A LTA R , W. ( 1 947) pro pe rti es of calcium tungstate X-ray screens', J. Appl. Phys., 18, 530. KALLMANN, H. and DRESNER, J. ( 1 959) ' E x ci ta ti o n of luminescent materials by ionizing rad i at io n ' , Phys. Rev., 1 14, 7 1 . K L AS E N S , H . A . ( 1 947) 'The light emi ssi o n from fluorescent screens irradiated by X-rays', Phi!. Res. Rep., 2, 68. LEVERENZ, H. W. ( 1 9 5 0) An Introduction to Luminescence of Solids, 1 67, 3 1 6, 42 1 -7. Wiley, New York. ' P h y s i ca l
m. Radioluminescence. Scintillations
1. The detection of particles by the scintillation counter General references B I R K S , J. B . ( 1 9 5 3 ) Scintillation Counters. P e rgam o n Press, London. B LANC, D. ( 1 9 59) Detecteurs de Particules, 1 8 8-220. Masson, P a ri s . C U R RA N , S . C . ( 1 9 5 3) Luminescence and the Scintillation Counter. B utte rwo rt h s , L on d on . D ETCEUF, J . F . , BLANC, D . and M A I GNAN, P . ( 1 952) 'Scintillateurs', J. Phys., 13, 5 6 7 . GARLI C K , G . F . J . (1 952) ' Lu mine s c e n t materials for sci n t illa tion counters', Progress in Nuclear Phys., 2, 5 1 . Pergamon Press, JORDAN, W . H. ( 1 9 52) ' D e tect i o n London.
Review of Nuclear Science, 1, 209.
of n u cl ea r particles',
A nnual
322
Luminescence in Crystals
M O RTO N , G . A . ( 1 952)
tronics,
4,
69.
'The scintillation counter', Advances
Organic and liqu id scintillators ( 1 958) 'Scintillation coun ti ng , '
Nucleonics, 16,
in
Elec
54.
Plastic scintillators PI CHAT, L . and KoE C H L I N , Y . ( 1 95 1 ) ' Mesures de radioactivite a ! aid e de s o !ides fluorescents non cristal lins', J. de Chimie-Physique, 48, 225. '
Inert gas scintillators K o c H , L. ( 1 960) 'Etude spectrale de la luminescence due a !'excitation des gaz rares par Ies rayons a.' , J. Phys . , 21, 1 69.
2. The mechanism
Books
of luminescence excited by high-energy radiation
M . ( 1 94 6) Fluorescence et Phosphorescence, 1 6 1 -75. Her mann, Paris. G A RLICK, G. F. J. (1 958) 'Cathodo and radioluminescence', Hand. der Phys., Licht und Materie, 1 1 1 -2 1 . Springer, Berlin. L E V E R EN Z , H . W . ( 1 950) An Introduction to Luminescence of Solids, 1 67, 3 1 6-2 1 , 420-7. Wiley, New York. CURIE,
Original
articlest
and A M B R O S I N O , G . ( 1 953) ' R ep on s e d'un ecran de sulfure de zinc aux rayonnements a d e ne r gi e inferieure a 5 MeV', Comptes-Rendus A cad. Se. Paris, 236, 1 774. EBY, F. S. a n d J ENTS C H K E , W. K. ( 1 9 54) 'Fluorescent response of Nal(Tl) to n u cl ea r rad iatio ns', Phys. Rev . , 96, 9 1 1 . l E NTSCH K E , W . K . , E B Y , F . S . , T A Y L O R , C . J . , R E M L E Y , M . E . an d K R U G E R , P . G . ( 1 95 1 ) 'The fluorescence efficiencies of some crys tals for electrons a n d heavy pa rti c l e s Phys . Rev., 83, 1 70. K A LL M A N N , H. an d D RE S N E R , J . (1 959) 'Excitation of l u m inescent materials by ionizing rad iation , Phys Rev. , 1 14, 7 1 . N O S E N K O , B . M . , S T R U K O V , N. A . and YAGUDAEV, M . D . ( 1 957) ' Luminescence of crystal pho s p h o rs on exc it ati o n by ions', Optika i Spektros . , 3, 35 1 . A NT H O N Y , J . P .
'
',
'
.
t To save space, references are not given to the work of Kallmann, Broser, Birks, Curran and Baker, and others before 1 95 1 : they can be found in the review articles listed in § I .
Cathodoluminescence and o th er topics
R E M L E Y , M. E . , JENTS CHKE, W. K. and K R U G E R , G . ( 1 95 1 ) 'Response of some scintillation crystals to heavy particles', Phys. Rev., 83, 1 69. TREGUIER , L. and KoECHLIN, Y. (1959) Nouve!les Etudes sur les TAYLOR, C. 1 . ,
323
P.
Rapport C.E.A., DE/SE No. 1 1 99-1 47. WRIGHT, G. T. (1953) 'Scintillation response of organic phosphors', Proprietes physiques des Scintillateurs Organiques et Miniraux,
WRIGHT, G. T. and G A R L I C K , G. F. 1 . (1 954) 'Characteristics of radioluminescence in crystals', Brit. J. Appl. Phys. , 5, 1 3 . Phys. Rev.,
91,
1 282.
IV. Radiation damage in crystals
(1 956) Col!oque sur !'action des rayonnements de grande energie sur les so/ides, organise sous la direction de Mile. Y. Cauchois. Paris, 1 956. B I L L I NGT O N , J . S. and CRAWFORD , J. H . ( 1 96 1 ) Radia tion Damage in Solids. Oxford University Press. CRAWFORD, J . H. and C L E L AN D , J. W. (1 957) ' Radiation effects in semi-conductors', Progress in Semi-Conductors, 2, 69. Heywood, London. FAN, H. Y. and LARK-HOROVITZ, K. (1956) 'Irradiation of semi conductors', Symposium Garmisch-Partenkirchen, September 1 956. Halbleiter und Phosphore, 1 1 3. Vieweg, Braunschweig. G UINIER, A. (1 957-58) Cours de Physique des So/ides. Faculte des Sciences, Paris. SEITZ, F . and KoEHLER, J . S . (1 956) 'Displacement of atoms during irradiation', Solid State Physics, 2, 305. 1 . General literature and review articles
Luminescent solids H ANLE, W. (1956) 'Beeinfti.issung von Leuchtstoffen durch energie
reiche Strahlung', Symposium Garmisch-Partenkirchen, Septem ber 1 956. Halbleiter und Phosphore, 1 39. Vieweg, Braunschweig. PRZIBRAM, K. (1 956) Irradiation, Colours and Luminescence. Perga mon Press, London.
2. Other articles BANDOW, F . (1 956) ' O ber die Wirkung von Kernstrahlen auf die optischen Eigenschaften von anorganischen Leuchtstoffen', Optik,
13, 259.
Luminescence in Crystals
324
B LEIL, C . E . , SNYDER, D . D . and S!HVONEN, Y . T . ( 1 958) 'Bom bardment of CdS crystals with 30- to 60-KeV electrons', Phys . Rev.,
1 1 1 , 1 522. I. and WARMINSKY, R . ( 1 9 5 1 ) 'Die Veranderung der Lumi
neszenz und der elektrischen Leitfahigkeit von CdS-Kristallen durch Bestrahlung mit ex-Teilchen', Z. fur Natwforschung, 6a, 85. G O R D O N , N. T . , S E I T Z , F . and Q U I N L A N , F . (1 939) 'The blackening of zinc sulphide phosphor', J. Chem. Phys. , 7, 4. G RILLOT, E. and GRILLOT, M . ( 1 955) 'Les microdosages radio chimiques dans l'etude des defauts de reseau', 80eme Congres des Societes Savantes. HANLE, W . and RAU, K . H . ( 1 9 52) 'Lichtausbeuten und Zerstorung von Leuchtstoffen bei Elektronen und Ionenstoss', Zeits. fur Phys. ,
B RO S E R ,
K U L P , B. A. and KELLEY, R. H . (1 960) 'Displacement of the sulphur atom in CdS by electron bombardment', J. Appl. Phys . , 31, 1 057. M A R T I N , W . ( 1 957) 'Beeinflilssung der Lumineszenzeigenschaften von Phosphoren durch H 2 +-Ionen', Z. fur Phys. , 147, 582. ROTTGARDT, J. ( 1 9 54), Z. angew. Phys. , 6, 1 60. SMITH, A. W. and TURKEV I C H , J. ( 1 9 54) 'Effect of neutron bom bardment on a zinc sulphide phosphor', Phys. Re v . , 94, 857. SMITH, A . W . ( 1 9 56) 'Effect of neutron bombardment on a zinc sul phide phosphor', Phys. R ev . , 101, 1 263. S M I T H , I. L . , POTTER, R. M. and AVEN, M. ( 1 960) 'Mechanism of depreciation of electroluminescent phosphors', The Electrochemi cal Society, Spring Meeting, Chicago, May 1960. 1 33,
297.
Symposium on 'Physical problems of colour television', Paris, July 1 957. Acta Electronica, 2, Nos. 1 -2, 1 - 149. KLASEN S , H . A. and B RIL, A. ( 1 957) 'Phosphors for colour tele vision', loc. cit., 143. KRoGER, F. A . , BRIL, A. and D I K H O FF , J . A. M. ( 1 9 52) 'A single component white luminescent screen for television tubes', Phi!.
V. Appendix
Res. Rep., 7, 24 1 .
LEVEREN Z , H . W . (1 950) 43 1 . Wiley, New York.
An Introduction to Luminescence of Solids,
General Bibliography
Recommended Books and Comprehensive Papers 1. Books giving general surveys of luminescence CURIE, M . (1 946) Fluorescence et Phosphorescence, 2 1 1 pp. Her manu, Paris . GARLIC K , G. F. J. (1954) Luminescent Materials. M ono graph s on the Physics and Chemistry of Materials, Frohlich and Mott editors , 254 pp. Clarendon Press, Oxford. GARLICK, G. F. J. {1 958) 'Luminescence', Hand. der Phys., Licht
und Materie, 26, 1 - 1 28. Sprin ger, Berlin. LEV I A LD I , A. ( 1 946) Luminescencia, 228 pp. Espasa-Calpe Argen tina , B uenos Aires. LEVEREN Z , H . W . ( 1 950) An Introduction to Luminescence of Solids,
569 pp. Wiley, New York.
PRIN GSHEIM, P. (1 949) Fluorescence and Phosphorescence, 794 pp.
Interscience Pub., New York. PRZI BRAM, K. ( 1 956) Irradiation Colours and Luminescence, Pergamon Press, London.
332
pp.
2. Recent symposia on luminescence (1 948) Preparation and Characteristics ofSolid Luminescent Materials,
Cornell Symposium, Fonda and Seitz edito rs , 459 pp. Wiley, New York. (1954) Conference on Lu m i n escence , Cavendish Lab oratory , Cam b rid ge , April 1 954. Published in (1 955) Brit. J. Appl. Phys. , 6, Suppl. 4, S 1 -S 1 20. (1956) Collo que International sur la luminescence des co rps cristallins anorganiques , Institut Henri-Poincare, Paris, May 1 956. M. Curie and G. Destri au editors. Published in Collection des Colloques Internationaux du C.N.R.S., No. 72 ( 1 956), J. Phys. Rad. , 17, 609-832. (1 957) Coll o qu iu m on Lu m i n escence , Tartu (Esthony). Published in (1 957) Bull. A cad. of Se. S.S.S.R. ; Columbia Tech n i cal Tr a ns la tions, 21, 475-786. 325
326
Luminescence in Crystals
( I 958) C oll o q u e sur Ies t r a n s fe rts d ' e nergic, I n s titut de Chimie Phy s i q u e , Paris, May 1 9 56. Published in ( 1 958) J. Chimie-Phys. ,
( 1 960) M e e ti n g on Colour Centres and Crystal Luminescence, Turin, 8- 1 1 S e pt e m b er 1 960. G. Bonfiglioli editor. ( 1 96 1 ) Luminescence of O rgan i c and Inorganic Materials, New York, 9- 1 3 October 1 9 6 1 . H. Kallmann editor. Published i n ( 1 962), Wiley, New Yo rk . Every Ye a r : Spring Meeting, The Electrochemical So ciety , Lumin escence Section (e n l a rge d abstracts avai lab le) . 55, 5 8 5-7 1 2 and 869-9 8 8 .
( 1 9 5 4) International Conference on S e m i - C o n d ucto rs , Amsterdam, 29 Ju n e 3 July 1 9 54. Pu b l i sh ed in ( 1 9 54) Physica, 20, 8 0 1 - 1 1 3 8 .
Some symposia on semi-conductors, containing papers on luminescence
( 1 9 56) Halbleiter und Phosphore, Garmisch-Partenkirchen, 28 A u gu s t- ! S e p t em ber 1 95 6 . M. Sch O n and H. Welker editors. Published i n ( 1 958), Vieweg and Sons, Brau ns ch we i g. ( 1 958) Solid State Physics in Electronics and T ele co mmu nicat i o ns , Brussels, 2-7 June 1 95 8 . Published i n ( 1 9 6 0) , Academic Press, London , New York. ( 1 9 5 8) Inte rnational C on fe re nce on Semi-Conductors, Rochester, 1 8-22 Au gu s t 1 9 5 8 . Pu b l ish ed in ( 1 959), J. Phys. Chem . Solids, 8. -
3. More theoretical works and comprehensive papers I . ( 1 95 1 ) Some Quest i o n s on the Theory of the
of Cry sta l s, State Editions for Technical and Theo re ti c al Literature, M o sc ow Len i ngra d . ( 1 9 5 3) Einige Fragen zur
A D I RO W I T C H , E . Luminescence
Theorie der Lumineszenz der Kristalle, 298 pp. Akademie-Verlag, B e rl i n -
M . a nd
cristalline, 86 pp. Revue d Op ti q u e P a ri s K u c K , C . C . a n d S CI-IULMAN, J . H . ( 1 957) ' Luminescence in solids', Solid S ta t e Physics, 5, 97- 1 72. Academic Press, New York. .
CURIE,
CURIE,
D.
( 1 956) Questions actuelles en luminescence '
,
.
F. A. ( 1 948) Some Aspects of Luminescence of Solids, pp. Elsevier, Amsterdam, New York, London, Brussels. K R O GE R , F. A. ( 1 956) 'Inorganic crystal phosphors', Ergebnisse der K R 6 GE R ,
310
Tech.
Exak ten Wissenschaften,
L o u CHTCHI K ,
29,
62- 1 44.
( 1 9 5 5) Crystallophosphors, 230
Acad . Fiz. an d Astronomy, Tartu, Esthony.
pp. Editions
Genera I Bibliography
F . E . ( 1 953) 'Solid state luminescence' , Advances in Elec tronics, 5, 1 37-68. 327
WILL! A M S ,
4. Related phenomena A I GRAIN, P. and ENGLERT, F. (1 958) Les Semi-conducteurs, 203 pp. Monographies Dunod, Paris. KITTEL, C . ( 1 95 6) Introduction to Solid State Physics, 2nd edition, 6 1 7 pp. Wiley, New York. MoTT, N. F. and GURNEY, R. W. (1 948) Ele ctron ic Processes in Ionic Crystals, 275 pp. Clarendon Press, Oxford. PEKAR, S . I . ( 1 9 5 1 ) Researches on the Electronic Theory of Crystals, State Edi t i o n s for Technical and Theoretical Literature, Moscow Leni n g rad . (1953) Untersuchungen iiber die Elektronen Theorie der Kristalle, 1 84 pp. Akademie-Verlag, Berlin. S E ITZ, F . ( 1 940) Modern Theory of Solids, 764 pp. McGraw-Hill Co. ,
New York.
SHOCKLEY, W . (1950) Electrons and Holes in Semi-Conductors , 558 pp. van No s tran d Co., New York.
See the corresponding b i bliography (Chapters IX and X).
5. Electroluminescence, cathodoluminescence and scintillations
Cerenkov radiation JELLEY, J. V. ( 1 958) Cerenkov Radiation and its Applications, 304 pp. Pergamon Press, New York.
On the photodielectric effect and the photodipolar Debye absorption FREYMANN, R . ( 1 9 5 6) 'L'absorption dipolaire de Debye', Cahiers de Physique , 667, 1 9-43. R o u x , J. ( 1 954) 'L'effet photod ielectriq ue', J. Phys. Rad. , 15, 1 76-8 8 . (1 956) 'L'effet photo d i e lectri qu e clans le sulfure et l'oxyde de zinc ', Ann. de Phys. , Ser. 13, 1 , 493-545. Thesis, Univers ity of Paris.
Masson, Paris.
Subject Index
Absorption, 24, 34, 36, 5 1 , 63, 8 3, 90, 1 09, 1 22, 226, 289 edge, 80-83, 87, 1 09 , 26 1 Activation energy, 2, 1 42, 1 43, 1 46 optical, 1 92, 1 93 , 1 96, 1 99 thermal, 1 9 1 , 1 92, 1 93, 1 98, 20 1 Activators, 5, 6, 1 1 3-25, 1 29, 1 55 phosphors with two, 1 95-202, 240, 267 Alpha-particle excitation, 302 Anharmonicity, 5 3 Anodic luminescence, 26 1 Associated donor-acceptor centres, 1 1 6, 1 28-1 29, 26 1 Attempt-to-escape frequency, 1 46 Band gap, see Energy gap Band structure, 79-8 3 , 1 09 Band-to-band transitions, 85, Beta-ray excitation, 296, 303 Bimolecular mechanism, 1 48 , 1 59, 1 64, 253 Black-and-white television , 318 Bleaching, 1 7 3-4 Blende, 8 1 , 1 08-9, 1 1 9, 1 69 Breakdown , 25 1 , 259 Brightness waves, 245, 253, 260
Charge compensation, 3 14 Chromium, 27 Coactivator, 1 14 , 1 1 7, 3 1 3 Cobalt, 7 , 270 Colour changes of phosphors, 1 74, 240, 248 , 288 television, 3 1 7- 1 9 Concentrational quenching, 225, 256 Configurational coordinates, 37-40 curves, 37-42, 46, 59-66, 1 90-3, 209 Controlled e!ectro!uminescence, 258, 259, 272-3 Cross-sections, 1 25, 1 45-7
259 151, 3 1 6,
258,
Cadmium sulph ide, 8 1 -8 3 , 8 7-88 , 9 1 , 9 7 , 1 09, 1 1 4, 1 20-1 , 1 70, 246, 259, 3 09 Calcium sulphide, 1 4 3 , 1 7 1 Cathodoluminescence, 28 8-30 1 , 309 efficiency of, 290, 294 Centres in ZnS, 1 1 3-25 killer, 7, 1 26, 227 luminescence, 5-7, 40, 1 25-9
Dead voltage, 29 1-2, 294 Decay of fluorescence, 4, 1 48-9, 297, 303 o f phosphorescence, 1 50-9, 1 67 , 1 7 1 , 289 Defects, 5-7, 63, 98, 206, 230, 255 Detection of fast particles, 302-5 Diffusion of charge carriers, 1 55 , 228 of excitons, 229-30 of light, 224, 230 Dipole moment, 1 1 - 1 2, 1 7, 23 -25, 46 oscillator, 1 9 Dominant wavelength , 3 1 5- 1 6 Donor levels, 7, 254-5
Edge emission , 84-90, 259 Effective charge, 1 1 1 - 1 3 Efficiency, 4, 64, 203 , 2 2 7-4 7 290, 294 Elcctro-cnhancement effect , 269-74 329 ,
Subject Index
330 E!ectroluminescence, 237-65 Electroluminescent cells, 23 8 Electron affinity, 3 3 , 292 bum, 298 exchange transfer, 224 temperature, 79, 25 1
traps, see Traps Electrophotoluminescence, 265-7 Emission s p e c t ra , 37, 4 3 , 44-55, 6 I , 66, 8 5 , 8 7 , 90, 1 I 3-23 , 240, 263 ,
288
E n e rgy b a n d s, 3 3 , 64, 7 9 - 8 4 , 94,
I 92, 205-6
Energy gap i n semi-conductors, 8 I , 84, 26 1
in sulphide phosphors, 8 1 , 1 09 Energy levels in KCI, 3 3-34 in ZnS, I I 4, 1 1 8- 1 9, I 22, 1 651 70 Energy loss of fast e l ectro n s , 295-6 Energy transfers, 220-30
Enhancing effect of Co, Fe, N i , I 26, 270 of electric fields, 269-74
of infra-red radiation, 272 Ewles-Kroger emission spectra, 8 6-90, 259 E xcita tion , d i rect, of centres, 1 55, 227
i n cathodoluminescence, 289-9 1 , 297-8 in electroluminescence, 1 1 8 , 24 1 244
G amma-rays excitation, 303 Germanium, 80-8 I , 84-86, 95, 1 47, 262-5
Glow curves, 1 60- 5 , 1 67, 1 72, 1 9 8
G u dden-Po h l effect, 265-7
Halophosphates, 62-63 H a m i l ton ia n (i n tera cti on electron
ra d i at i on ), 22
Hole m i g ra ti o n , 1 98 , 226-9
Hund's rule, 3 3
Image ampl ifiers, 274-5 I n fra-red in electro lumi nescence
germanium, 262-5 quenching, 1 1 8 , 206-8 sen s i t ive phosphors, 1 95-202, 267 stimulation, 1 90-6, I 99-202, 267 Intcrco mbination transitions, 26, 34 Interst i t i a l ions, 309 I ro n , 7, 1 26 KCl (Tl), 6, 3 1 -44, 52, 1 7 1 -2, 1 94 Killer centres, 7, 1 26, 227
Lambe and Klick's model, 1 27-9 Linear
response
of
scintillators,
304-6
Luminescence (definition), 1 cen tres, 5-7, 1 1 3 -29 , 1 55, 1 73-4, 226-7, 242, 256, 297- 8 criterion for the occurrence of, 204
i n the lattice, 1 55, 226-7 Excitation c han n e l , 297, 307-8 Excitons, 90-9 8 , 22 9 -30
M agnetic res o n ance, 1 1 5, 1 23
Extincti o n ,
M ang a n es e ,
see
Quenching
F-centres , 5 3 , 63 -66, 70, 1 73-4 Fermi level , 78 Fl u o rescence ( de fin i t ion ), 2 Fl ux, 1 07, I 1 6
Forbidden t ransitio n s , 2 5 -26 , 343 5, 1 23 Franck-Co n d o n p rinciple, 49 Free paths of electrons, 1 47, 1 5 5 of holes, 228
M-centres, 67 d ivalen t,
28 ,
60- 6 3 ,
1 2 1 -5 , 1 49, 24 1 , 245 , 249, 2 5 3 , 270, 272 tetravalen t , 28 Maxwe l l ' s e q u a tio ns , 1 5 2-7, 1 0, 34,
Mean l i fe,
1 42-3,
1 49, 1 67 , 1 7 1 , 228 , 290, 303
and effic iency , 4 Mech a n i s m of fl u o rescence, 2, 1 4 8 1 49 of phosphorescence, 2, 1 50-5
Subject Index
33 1
Mobility, 228 Momentum selection rule, 77-78
Retrapping, 1 42, 1 54, 266 Riehl-Schon-Klasens model
Monomolecular mechanism,
Rieh l ' s exci t ati o n mechan ism , 2 2 6-
1 47-
1 48, 1 50, 1 56, 1 59, 1 6 1 , 1 64-5 Multiphonon transitions, 208-1 1
centres, 1 1 4 , 1 28-9
for
227
Ruby, 26-28 Neutron detectio n , 304 effects on phosphors, 3 1 2, 3 1 3 Nickel, 7, 227
Non-photocond ucting
phosphors,
5, 32 35 Organic clectroluminescence, 25 6 scintillators, 303-5 Oscillator strengths, 68 exciton, 95
F-centres, 70 KCI(Tl), 70
Quadrupole mom e n t , 1 4, 2 1 , 25 Quantum efficiency, 227, 299 Concentrational ;
Infra-red ; The rm a l see
Scintillations, 27 1 , 3 0 1 -2, 306 Second a ry fl uore sce nce, 224-5 Selection rules, 25-26, 3 5 Sensitization, 1 95-8, 220-4 Sensitizer, 1 95 , 220
Silicon, 8 1 , 86, 1 94 Smakula's fo rmu l a , 68-70 Spin-flip t rans i tio n s 26, 28, 1 22 Stark effect on the exc i ton , 9 6 Stimu l a t i o n spectra, 1 95 -6 , 1 99 , 20 I Stokes's rule, 3 1 , 3 6, 4 1 , 89 Strontium sulphide, 1 9 5-8, 267 Substi tutional ions, 36, 1 I 3, I I 6, 1 65- 6 Surface states, 1 66, 254 ,
P-N j u n ct io n , 257, 26 1 Paramagnetism, I I 5 Phosphorescence (definition), 2 3 Photoco n d ucti ng phosphors, 6, 59, 76-98, 1 25 - 9, 1 5 0 - 5 Photoconductivity, 36, 76, 1 56 Photoelectroluminescence, 272-4 Photoluminescence, 1 , 240, 289, 299 Photomagnetoelectric effect, 228 Plastic scintillators, 303 Polarization in absorption , 67, 83, 1 29 in emission, 67, 88, 1 29 KCI(Tl), 43 CdS and ZnS, 8 3 , 88, 97, 1 29 Preparation of KC!(Tl), 32, 1 72 of sulph ide phosphors, I 07-8 Purity (of col o u r), 3 1 5- 1 6
Quench ing,
SiC, 8 1 , 87, 1 1 4, 25 9-6 1 Sci ntillation counters, 302-5
Rad i a t ion damage, 308- 1 4 Radiol u m i nescence, 3 0 1 Reabsorption o f e mi tted l ight, 224-5 Resonance transfer, 22 1 -4, 229
Television, Colour
see
Black-and-white ;
Thallium, 6, 3 1 -44, 52, 1 7 1 -2, 1 94 ,
303
Thermal quenching, 4, I 65, 202-8
Thermoluminescence,
1 7 1 -2, 1 73-4, 1 98 Transfers , 20 1 , 220-30
1 60- 5
,
1 67,
non-rad i ative, 4, 7, 202- 1 0 radi ative, 4 , 7 , 23-25, 44-55 Tr a p d ept h s , 2, 1 42-3 , 1 90 5 optica l , 1 90-5 thermal, 1 90-5 Trap d istribution s , I 65 74 Traps, 2-3 , 5, 7, 3 5 , 1 42-7, 1 56-9, 1 65-74, 1 90-5, 202, 255 Trich romatic coefficien ts, 3 I 4- 1 6 Tungstate p h os p h o r s , 59-60, 289290, 299, 303
Transitions,
Uranyl sa l t s , 4, 5 , 1 49
332
- ��-J -
Willemites, 28, 60-6 1 , 1 23 , 247, 290, 294, 3 1 8 Work functio n , 32 Wurtzite, 8 1 , 1 08-9, 1 1 9, 1 69 X-ray excitation , 298-30 1
Zn S : structure, 8 1 -82, 1 07- 1 3 ZnS(Ag), 1 1 9-20, 290, 294, 3 1 3, 318
-
ZnS(Cu), 1 1 4- 1 9, 1 53, 1 65-70,
207 , 226-7, 240- 1 , 243-5 , 247,
249 , 25 3-4, 258, 267-9, 290,
297, 3 1 1 - 1 3 , 3 1 5 ZnS(Mn), 1 2 1 -5, 1 49, 245, 249, 25 3 , 269-73, 290, 294, 3 1 8 i n fra-red sensitive ZnS, 1 98-202 vacancies in, 1 2 1 , 1 68 , 309 Zeeman effect on the exciton, 9798
