Infrared phosphor-semiconductors

Infrared phosphor-semiconductors

SESSION Q: LARGE BAND then the ratios of the line strengths before and after irradiation should be (NA-- ND)/(N* - ND NR). From these results WEDE...

782KB Sizes 7 Downloads 98 Views

SESSION

Q:

LARGE

BAND

then the ratios of the line strengths before and after irradiation should be (NA-- ND)/(N* - ND NR). From these results WEDEPOHL found NR = 11 x lo15 cm-a. This value is higher than that deduced from the electrical measurements after irradiation but the difference is probably not significant owing to the difficulties of determining the strengths of the infrared lines accurately. Further details of the effect of irradiation on the properties of semiconducting diamond will be published later. Acknowledgments-The work described in this review has been carried out in Professor DITCHBURN’S laboratory at Reading and the contributions of different members of the group are indicated in the references. We are grateful to Dr. J. F. H. CUSTERS,Director of Research, Diamond Research Laboratory, Johannesburg for his interest and for providing the variety of polished diamonds used in the work. REFERENCES 1. CLARKC. D. J. Phys. Chem. Solids 8, 481 (1959). 2. STEPHENM. J. Proc. Phys. Sot. 71,485 (1958).

./. Phys. Chem. Solids

Pergamon

SEMICONDUCTORS

3. LAX M. and BUR~TEIN E

449

Phys. Rev. 97, 39 (1955).

4. WEDEPOHL P. T. Proc. Phys. Sot. B 70, 177 (1957). 5. CLARKC. D., DITCHBURNR. W., and DYER H. B. Proc. Roy. Sot. A 237, 75 (1956). 6. DYER H. B. and MATTHEWS I. G. Proc. Roy, Sot. A 243, 320 (1957). 7. CUSTERS J. F. H. and RAAL F. A. Nature,

Lond.

179, 268 (1957).

8. CUSTER~ J. F. H. Nature, Lond. 176, 173 (1955); Physica 18, 489 (1952). 9. WEDEPOHL P. T. Ph.D. (1958).

Thesis,

Univ.

of Reading

IO. MITCHELL E. W. J. and WEDEPOHLP. T. Proc. Phys. Sot. B 70, 527 (1957). Il.

ELLIOTT R. J., MATTHEWS I. G., and MITCHELL E. W. J. Phil. Mug. 3, 360 (1958).

12. CLARK C. D., DITCHBURN R. W., and DYER H. B. Proc. Roy. Sot. A 234, 363 (1956). 13. KEMMEY P. to be published. K. Z. Pkys. Chem. 14. JAMESH. M. and LARK-H• ROVITZ 198, 107 (1951). 15. CLARK C. D. Ph.D. Thesis, Univ. of Reading (1955). 16. MITCHELL E. W. J. I3rit.J. Appl. Pkys. 8,179 (1957).

Press 1959. Vol. 8. pp. 449-457.

INFRARED

Q-2

GAP

Printed in Great Britain

PHOSPHOR-SEMICONDUCTORS G. F. J. GARLICK University of Hull, England

Abstract-The development of sensitive photoconducting detectors for infrared radiation has made possible the study of luminescence emission from a new variety of solids including those of considerable interest as semiconductors. A review of progress over the past few years is given with special reference to the emission of zinc and cadmium sulphide phosphors, lead sulphide, lead telluride and mercury sulphide. The infrared emission found in zinc sulphide is ascribed to electron transitions from the valence band to the ground states of visible emission centers. In mercury sulphide the characteristics of the excitation and emission spectra suggest a different mechanism. This also applies to lead sulphide and lead telluride. New results on cadmium telluride madep- or n-type under controlled conditions show a number of emission bands extending to 2.6 p. Excitation and photovoltage excitation curves coincide with emission bands, there being no Franck-Condon shift. The results are given a tentative theoretical explanation. 1. INTRODUCTION

improve

knowledge

of

luminescence

processes

THE extension of luminescence studies to the infra-

in solids, but would also provide a new approach

in the It was hoped that investigation would not only

to semiconductor research by measurements of optical transitions associated with such phenomena as photoconduction and the photovoltaic effect.

red region

of

the

spectrum

author’s laboratory in 1952-3.

results GG

of

such

was begun

450

SESSION

Q:

LARGE

BAND

The present paper attempts to provide a critical and up-to-date review of progress in the production and measurement of infrared emitting phosphors and of the resulting advances in knowledge of luminescence and related phenomena. Some of the work has already been published(1-4) but the more complete account below includes much work which has not been previously reported. Luminescence effects in solids may be confined to luminescence centres or may involve energy transfer and storage outside such centres. Examples of both are found in infrared emitting phosphors, e.g. molecular systems like iodine or transition element activators like Co2+ ions show luminescence of a confined form, while such infrared emitters as zinc and cadmium sulphides, mercury and lead sulphides, cadmium telluride and cuprous oxide show emission which is closely related to charge carrier motion in the solid, i.e. with photo- and semiconduction. These different types are dealt with in separate sections below. In attempting to look for infrared emitting phosphors new techniques of radiation detection have had to be adopted. Advantage was taken of the availability of lead sulphide and lead telluride photoconducting cells. The use of these together radiation-narrow band tuned with “chopped” amplifier techniques have enables us to explore the region up to 5 TVwith sensitivities not too far below those attainable with photomultipliers in shorter wavelength studies. 2. PHOSPHORS OF NON-PHOTOCONDUCTING

GAP

SEMICONDUCTORS Ey&tion

Emission CLBr I

2.5 Wavelength,

EI~Li;c$on

cbj:_J

/A

Emission ICI. IBr

A

0.5

1.0

1.5 Wavelength,

2.0

2.5

/_I,

FIG. l(a) Excitation and emission spectra of solid halogens. l(b) Excitation and emission spectra of solid halogen compounds (after DUMBLETON @)).

TYPES

2.1. The solid halogens Quite early in our investigations DUMBLETON’~) discovered near infrared emission from the solid halogens and inter-halogen compounds (fluorine excepted due to its very low solidification temperature). Their excitation and emission spectra are given in Figs. l(a) and l(b). More recently FRANKS(~) remeasured the spectra for iodine and also investigated the absorption and diffuse reflection spectra and temperature dependence of emission. From these, and using the method of KLICK and SCHULMAN’~) he was able to construct the energy configurational diagram of Fig. 2 and to compare his curves (shown by solid lines) with those proposed much earlier for molecular iodine vapour by MULLIKEN. t6) It is interesting to note

FIG. 2. Energy configurational co-ordinate diagram for solid iodine (full curves) compared with previous results for vapour state (broken lines) (after FRANKS@)). -solid iodine - - - - vapour (after MULLIKEN(~)).

that the infrared excitation and emission correspond to transitions between ground and second excited states of the molecule. However, an absorption but no emission was found at 1.12 p corresponding to transitions to the first excited state. The absence of emission is expected from the curve for the lu state in Fig. 2. We were unable to find any relation

SESSION

Q:

LARGE

BAND

GAP

451

SEMICONDUCTORS

between luminescence and the phutoconduction characteristics for iodine reported by MOSS{” except perhaps indication from absorption curvea that the two processes are competing ones for the absorbed quanta.

those for manganese ~y~~ow~~g~ emission) and cobalt (3 p regiun). We have so far failed to detect any emission from ZnS-Ni2+ phosphors in the region up to 5 p and at temperatures down to 77°K.

In zinc sulphide addition of a few parts per million of cobalt produces relatively deep electron traps (8) but in larger concentration this activator %ills” the normal visible emission completely. However, an infrared emission characteristic of transitions in the 3d shell of the Co2+ ions is observed and this reaches an optimum efficiency for a concentration of about one part Coz+ per thousand ZnS. Mutual perturbation of activator ions causes a drop in efficiency above these concentrations. It is of interest to note that the above concentration limit corresponds roughly to the appearance of dipole,-dipole broadening effect in the paramagnetic resonance spectra of such

As shown some years ago by Russian workers(“) cuprous oxide specimens can be excited to give an emission at 1 p. Since cuprous oxide is important as a semiconductor, considerable attention was devoted to it in the author’s laboratory. The results were previously reviewed in 1956uQ) and an energy band scheme, correlating the phatoconductian photovoltaic and luminescence characteristics shown in Fig. 4, proposed. This is given in Fig. 5 together with a modified scheme proposed more recently by BLOEM (11) following his more extensive measurements and discovery of another emission region at 0.7-0.8 p predicted by the author.uO) The emission bands of cuprous oxide have a

FIG. 3, Excitation, diffuse r&ection and emission spec=a for cobaft activated zinc sulphide(after Du~~To~~~b)~.

transition ions, dispersed in solids. Fig. 3 shows the excitation, diffuse reflection and emission spectra of ZnS-Co2* phosphors and indicates the close correlation between absorption and excitation. We are hoping to have single crystal specimens available in the near future which will enable us to make much more quantitative investigations of the details of the emission centres and their interaction with the surrounding lattice, One interesting problem to be solved is that we have not observed the infrared emission for cobalt ions dispersed in any other matrix although similar diffuse reflection spectra have been observed (e.g. Co=* dispersed in a borax bead or in a zinc silicate lattice). A further interesting problem is to determine why the corresponding emission about 1 p for iron-activated zinc sulphide is relatively feeble compared with

0

o-5

1.0

Wavelength,$V.

l-5

FIG. 4. Efectrkal and optical properties of cuprous oxide. A. Optical transmission, B. Photoconduction response

spectrum,

C. hrninescence

tnun, D. Emission spectm.

excitation

spec-

452

SESSION

Q:

LARGE

BAND

GAP

SEMICONDUCTORS

Conduction

FIG. 5. Energy band schemes for cuprous oxide: modified scheme due to BLOEM,(“) (b) proposed GARLICK.(‘~)

doublet nature and the forbidden gap levels of Fig. 5 are thought to arise from lattice defects, a copper vacancy giving rise to the 1 p emission. More copper-rich specimens contain oxygen vacancies which provide levels, one of which is assumed to be associated with the shorter wavelength emission.(ll) In cuprous oxide we have a relatively tractable material for such investigations. More detailed studies are still required, e.g. the relation between types of carrier and the several luminescence processes and comparison of carrier life time measurements in photoconduction with luminescence decay times over a wide temperature range. 3.2. Lead sulphide Lead sulphide is well known as a member of the photoconductor group lead sulphide-selenidetelluride. Infrared emission from lead sulphide was first reported by Russian workers.02) We subsequently measured the spectral distribution of the emission(l) and more recently R. A. Fatehally, of the author’s laboratory, measured the excitation spectrum for the emission. The excitation and emission spectra for a typical specimen are given in Fig. 6, together with the photoconduction response spectra. It will be seen that one emission band appears where photoconduction response is falling off with increasing wavelength and that this band moves to longer wavelengths with a fall in

(a) by

temperature as does the photoconduction response curve. So far doping of specimens with impurity has failed to produce different emission bands. The band observed is most intense in specimens prepared to give maximum photoconduction efficiency, i.e. in specimens which are p-type produced by oxidation of n-type material under closely specified conditions.03) We assume from detailed consideration of results that the emission arises from electron transitions between levels very close to the bottom of the conduction band and the top of the valence band, charge carriers being trapped before these transitions occur. This would appear to be supported by BLOEM’S work on defect levels in lead sulphide.04) It would be interesting now, as in the case of cuprous oxide above, to make measurements of carrier and luminescence decay times at various temperatures in order to correlate photoconduction and emission processes. 3 3. Mercury sulphide Mercury sulphide in the form of red cinnabar has been known for a long time as a photoconductor. In recent years HAMILTON of the author’s laboratory succeeded in making single crystals of the material of higher purity than natural crystals. The emission of mercury sulphide is shown in Fig, 7 together with examples of mixed cadmiummercury sulphide.‘l)

SESSION

Q:

LARGE

3.0

2.5

BAND

2.0

GAP

SEMICONDUCTORS

1.7

1.5

Wavelength,

4.53

l-2

/A

FIG. 6. Excitation, emission and photoconduction response spectra for a typical lead sulphide specimen.

zinc and cadmium sulphides, the emission for mercury sulphide is due to transitions in anion rather than cation vacancies, it being difficult to retain mercury in the lattice during preparation. We hope to re-explore the matter by reheating single crystals made by Hamilton’s techniques in mercury vapour under controlled vapour pressure and temperature conditions. Again more effort to try and correlate photoconduction and luminescence characteristics is indicated. 3.4. Zinc and cadmium sulphides FIG. 7. Emission spectra of cadmium-mercury sulphide phosphors and excitation spectrum for mercury sulphide. A. CdS; B. CdS(70%)-HgS(30%); C. CdS(25%) -HgS(75%); D. HgS at 290°K; E. HgS at 90°K; F. Excitation spectrum for D.

For pure mercury sulphide it will be seen that the emission band is single and, as in the case of lead sulphide, moves to longer wavelengths with decreasing temperature. The excitation spectrum is similar to that of lead sulphide but the position of the emission is well outside the absorption edge and well beyond the usual limit of photoconduction response. Although for the mixed cadmiummercury sulphides a complete range of solubility is shown and although the emission band shifts uniformly with mercury content, the excitation spectra show a more complex behaviour. BROWNE@) suggests that, in contrast to the usual emission for

Following the initial discovery of infrared emission in zinc sulphideu) BRO~NE(~) has made a much more extensive investigation of the emission in the zinc-cadmium sulphide system. Typical emission and excitation spectra are shown in Figs. 8 and 9 respectively. A series of important conclusions have been reached from his results which provide the bases of a much more comprehensive theory of zinc sulphide phosphors: (1) The emission bands do not shift much in position from zinc to cadmium sulphide in contrast to the shift of the usual emission bands from the visible into the near infrared region. This suggests that they are associated with perturbed levels of the valence band (characteristic of anions). (2) The excitation bands for infrared emission coincide with the quenching spectra for the visible emission and photoconduction. This supports the conclusion in (1) above.

454

SESSION

Wavelength,

Q:

LARGE

BAND

SEMICONDUCTORS

Wavelength, /A

/I.

FIG. 8. Infrared emission spectra of zinc and cadmium sulphide phosphors. (a) ZnS (b) ZnS (50%)-CdS (c) CdS (after BROWNS@)).

GAP

FIG. 9. Excitation spectra for infrared emission for zinc and cadmium sulphide phosphors (after BRO~NE(~)).

(50%)

(3) The relation of infrared emission excitation conditions to phosphor preparation conditions suggests that the important luminescence centres in these phosphors are due to cation vacancies.

in the study of the anomalous dependence of the decay time of the infrared emission on temperature (see later for cadmium telluride). The latter is constant up to a certain temperature beyond which it increases rapidly due to the depopulation of the (4) It is possible to explain both visible and levels by thermal activation of positive holes into infrared emission in terms of transitions to and from the cation vacancy levels as given by BROWNE’S the valence band. At present the above models are not completely satisfactory and we are planning energy band scheme, shown in Fig. 10(a). further experiments on the luminescence and From further consideration of BROWNE’S results electrical properties of single crystal specimens. in relation to more recent measurements on cadmium telluride in this laboratory by R. A. Fatehally and data on this group as photoconductors obtained by BuBE,~~) we prefer the model shown in Fig. 10(c) which is a modified form of that due to BUBE shown in Fig. 10(b). The levels lying close to the valence band are brought into evidence

3.5. Cadmium tell&de The zinc, cadmium and mercury sulphides are characterized by a hexagonal lattice structure (zinc sulphide can also of course exist in the zinc-blende form) but the basic lattice unit is tetrahedral. Cadmium telluride exists in the zinc-

(b)

FIG. 10. Energy band models for luminescence in zinc and cadmium sulphide phosphors: (a) due to BRO~NE,(~) (b) due to BT_JBE,(‘~) (c) modified model (all energy values in eV).

SESSION

Q:

LARGE

BAND

blende form but with the same basic lattice unit as for the above phosphors. However, its luminescence shows different features from the other phosphors and provides interesting new information on a II-VI compound which is already of considerable interest as a photo- and semi-conductor. It has been extensively studied from the point of view of emission by R. A. Fatehally of the author’s laboratory and independently, with marked differences in results, by DE NoBEL.~‘) Cadmium telluride is synthesized with relative ease from its constituent elements, but to make specimens of controlled constitution and departure from stoichiometry (p- or n-type) is more difficult. We found it most suitable to adopt the preparation techniques developed by KRUEGERand DE NOBEL~Q and by VAN DOORN and DE NOBEL~Q) using a controlled vapour pressure of cadmium over the previously prepared specimen, and with a selected temperature to obtain p- or n-types. We also deliberately “doped” some specimens by small additions of, e.g., chlorine (as HCl vapour) or copper. Fig. 11 gives R. A. Fatehally’s results for

11

!

ribs.

edge



l-0



GAP

SEMICONDUCTORS

455

specimens (notably In and Ag as in the experiments of KR~GJZR and DE NOBEL) we were able by electrical measurements to determine the specimen type and approximate carrier concentrations (as given in Fig. 11). No Franck-Condon shift between excitation and emission bands is found for cadmium telluride and coincidence with excitation bands for photoconduction and photovoltaic effects is also found. This would appear to indicate that cadmium telluride has a predominantly homopolar binding. Measurements of refractive index by apparent depth measurements using an infrared microscope have been made by J. Hough of the author’s laboratory. Results indicate little difference between the optical and static dielectric constants and confirm the assumption of homopolar binding. This is a somewhat different conclusion from those reached separately by DE NOBEL~‘) and by GOODMAN. Addition of copper chloride produces a new emission peak at 1.35 p. This suggests that copper behaves as an acceptor impurity providing a

I

2.0

1.5 Wavelength,

2.5

TV

FIG. 11. Typical emission spectra of cadmium telluride specimens. 11 = n type; p = p type; Numbers 14-18 signify approximate log,, carrier concentration.

the emission spectra of various specimens. Five different bands are found in undoped specimens, their occurrence depending on specimen type as shown. It seems clear that the longer wavelength bands occur when energy states in defect centres have their normal electron population increased by increasingly “n-type” preparation conditions. By using various electrode materials on the

level (or levels) near to the valence band, the necessary electron being supplied by the chlorine inclusion. The latter by itself produces more n-type behaviour in otherwise p-type specimen (see curves of Fig. 11) with some shift of the longer wavelength band peaks being evident. This could be explained by the perturbation due to chlorine substitution in the lattice. DE NOBEL has shown that the rate of

456

SESSION

Q:

LARGE

BAND

cooling of specimens after preparation has a marked effect on properties. He uses a rapid rate, ostensibly to avoid aggregation of lattice vacancies, but it would seem to encourage the formation of large strain regions in the specimens. He only observes the two shorter wavelength emission bands of Fig. 11. We employed much slower cooling for our specimens. However, further work on the effect of cooling rate is important and also on doping with elements such as gold and indium as carried out by DE NOBEL. Decay time measurements by R. A. Fatehally have revealed an anomalous variation with temperature as shown by BROWNE(~) for zinc and cadmium sulphides. A quantitative theory for this behaviour has now been developed and will be published later. It enables the complex decay characteristics to be correlated with the efficiencytemperature relations for each band and also prompts further measurements on carrier life times in the single crystal specimens now available to us. With respect to the energy band diagram for cadmium telluride the correlation between emission bands and specimen type (n or p) suggests that increase in electron population fills the vacancy levels already existing. It might be assumed with some safety that the two shorter wavelength emission bands are characteristic of transitions involving cation vacancies. Longer wavelength bands might be due to higher-lying levels in those vacancies or to levels of the anion vacancies (cation and anion being used to distinguish cadmium and tellurium respectively although the ionic charge on each in the lattice may be very small under

GAP

SEMICONDUCTORS

predominantly homopolar conditions). Detailed results from R. A. Fatehally’s work suggest the energy diagram of Fig. 12(b). In Fig. 12(a) we give a tentative energy band scheme proposed by DE NoBEL.~‘) There are similar features in the two diagrams although DE NOBEL requires fewer levels in the forbidden zone than we do to explain his results. His cation vacancy levels when combined would provide one of the centres of our model and would explain three of the observed emission bands of Fig. 11 (1.3, 0.78 and 0.54 eV) and the occurrence of only one of them in p type specimens (1.3 eV) since a low Fermi level position would obtain. A new band in the emission for copper activation, would also be expected by inspection of DE NOBEL’S results. If, as is found in our results (see Fig. 11) copper impurity causes a suppression of the usual emission bands of cadmium telluride then we may assume that it is likely to be sited in the cadmium vacancies. To explain the 1.06 and 0.48 eV emission bands is more difficult although from Fermi level considerations we would expect the 1.06 eV band to occur in most specimens and the 0.48 eV band only in n-type specimens. Reference to DE NOBEL’S results rules out the possibility of these levels being due to interstitial cadmium (this would in any case be absent in ptype specimens). The occurrence of these levels may be due to vacancy aggregates in our specimens which were cooled slowly after preparation compared with the rapid quenching of DE NOBEL'S specimens. We hope to have more single crystal studies completed soon. Until then, the model shown must be regarded as tentative.

O-64 ,I VCd 1.354

l-174

t

._

(G)

(b)

FIG. 12. Energy band schemes for cadmium telluride: (a) due to DE NOBEL, (b) scheme deduced from our own results.

SESSION

Q:

LARGE

BAND

It will also be valuable to divert some effort to a further study of cadmium selenide since this is intermediate between the zinc-cadmium sulphides and cadmium telluride. In early studies of cadmium selenide we found emission at 1.35 eV and 1.03 eV the total band gap being 1 a74 eV. However, we found no smaller energy emission bands further into the infrared at that time. BUBE’S results for quenching of photocurrents in cadmium sulphide show quenching bands at 1.2, 1.05 and 0.79 eV which are difficult to correlate with the emission bands with which there is marked overlap. Clearly, new observations on emission and conduction in single crystals are desirable to examine these differences. We have also measurements proceeding on cadmium-mercury telluride mixed crystals. 4. CONCLUSION

Luminescence research has now reached the stage where specimens are available in which emission properties can be correlated with other characteristics such as photoconduction. Such specimens are already of considerable importance as semiconductors. Infrared emission studies could be extended to various solids not dealt with above. For example, we have had no opportunity so far to apply our techniques to doped germanium and silicon crystals having forbidden zone levels likely to involve transitions in the energy region covered by our detectors. It would also be interesting to look for infrared electroluminescence as distinct from the injection and recombination emission already measured in this region for

J. Phys.

Chem. Solids

Pergamon

SEMICONDUCTORS

457

germanium, etc. With the likely development of efficient detectors such as indium antimonide and doped germanium in the near future it should be possible, with the help of very low temperatures, to extend the field of luminescence studies to much longer wavelengths. REFERENCES M. J. Proc. Phys. 1. GARLICKG. F. J. and DUMBLETON Sot. B 67, 442 (1954). 2. (a) DUMBLETONM. J. Proc. Phys. Sot. B 68, 53 (1955); (b) Brit. J. Appl. Phys. Suppl. 4, S.88 (1955). 3. BROWNEP. F. ‘J, Electronics 2, 1, 95 (1956). 4. FRANKSJ, Proc. Phys. Sot. B 70, 892 (1957). 5. KLICKC. C. and SCHULMANJ. H. -7. Opt. Sot. Amer. 42, 910 (1952). 6. MULLIKENR. S. Rev. Mod. Phys. 4 (1932). in the Elements. 7. Moss T. S. Photoconductivity Butterworths, London (1952). W. r. Electrochem. Sot. 100, 356 8. HOOGENSTRAATEN (1953). 9. LASHKAREV V. E. and KOSSONOGOVA K. M. Dokl. Akad. Nauk. SSSR 54, 125, (1946). 10. GARLICKG. F. J. Photoconductivity Handbuch der Physik 19, 316. Springer, Berlin (1956). 11. BLOEMJ. Philips Res. Rep. 13, 167 (1958). 12. GALKIN L. N. and KOROLEVN. V. Dokl. Akad. Nauk. SSSR 92, 529 (1953). 13. SMITH R. A. Advanc. Phys. 2,321 (1953) (Review). 14. BLOEMJ. Philips Res. Reg. 11, 273 (1956). 15. HAMILTOND. R. Brit. r: Apbl. Phys. 9, 103 (1958). 16. BUBER. H. Proc. Inst. Radio Ewrs. 43.1836 (1955). 17. DE NOBELD. Dissertation, Leid& (May 1958‘). ’ 18. KRUGERF. A. and DE NOBELD. r. Electronics 1, 2, 190 (1955). 19. VANDOORNC. Z. and DE NOBEL D. Physica 22, 338 (1956). 20. GOODMANC. H. L. r. Electronics 1,2, 115 (1955).

Press 1959. Vol. 8. pp. 457-461.

TEMPERATURE

Q.3

GAP

Printed in Great Britain

DEPENDENCE OF THE OPTICAL BAND GAP IN ZnS

W. W. PIPER,

P. D. JOHNSON

General Electric Research Laboratory, 1. INTRODUCTION

and D. T. F. MARPLE Schenectady,

New York

dependence of the band gap of ZnS(r) is in part due to the effects of lattice dilata-

crystals under hydrostatic pressure.t2) It has been found that above room temperature the expression derived by FAN(~) for the shift due to electron-

tion,

phonon coupling in polar crystals can account for

THE temperature

as determined

by measurements

on single