BAND GAP VARIATION OF GALLIUM SELENIDE UNDER HIGH PRESSURE

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BAND GAP VARIATION OF GALLIUM SELENIDE UNDER HIGH PRESSURE

Michel Gauthier, A. Polian, J Besson

To cite this version:

Michel Gauthier, A. Polian, J Besson. BAND GAP VARIATION OF GALLIUM SELENIDE UNDER

HIGH PRESSURE. Le Journal de Physique Colloques, 1984, 45, �10.1051/jphyscol:1984813�. �hal-

03059390�

JOURNAL D E PHYSIQUE

Colloque C8, suppldment au nO1 1, T o m e 45, novembre 1984 page C8-65

BAND GAP V A R I A T I O N OF G A L L I U M S E L E N I D E UNDER H I G H PRESSURE

M. Gauthier,

Polian and J . M . Besson

Physique des Milieux h 8 s Condensls, U n i v e r s i t l P . e t M . Curie, 7 5 2 3 0 Paris Cedex 0 5 , France

Resume - Af in de rendre compte de l a variation sous pression de l a b a n d e i n t e r d i t e de GaSe, nous proposons u n modele dans lequel l a nature lamellaire de ce compose e s t explicitement u t i l i s e e . Ce mo- dele complete par l e s r e s u l t a t s de calcul de s t r u c t u r e de bandes e s t en t r e s bon accord avec l e s r e s u l t a t s experimentaux.

Abstract - Taking into account the lamellar s t r u c t u r e of GaSe, we reproduce i t s complex band gap variation under pressure. The model j o i n t with recent band s t r u c t u r e calculation f i t s very well with experimental data.

Ga Se is layered 1 1 1 - V I semiconductor. The variation of its absorption coefficient under pressure is complex : Although the indirect absorption edge monotonicaly decreases with pressure, the direct gap first decreases up to 1.3 GPa and then increases at higher pressure. We can account for these variations with a simple model in which we assume that :

i) the interlayer and interlayer regions are completely independant.

ii) the deformation potentials depend only upon the nature of the electronic levels.

In order to compare this model with experimental data, we have determined the variation under pressure of the intra-and interlayer distances.

COMPRESSIBILITY

The disconnection of the intra and interlayer regions is the key to our description of the evolution of the cristallographic parameter C under pressure. We write :

dc = dci + ^dc P a n d : x C = $ x . + - P

c X~

with xi - ¹ = Bi = C (n)pn

- ^dP

n Boi i ' Xi

X-l= B

c B(n)Pn

- ^{a d~}

P P n o p p XF ^P

where

c : cristallographic parameter

c : thickness of one layer of compressibility x in the c direcsion

P P

c

- c interlayer distance in the c direction (compressibility x.) P

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984813

C8-66 JOURNAL DE PHYSIQUE

Experimental data were obtained by using a microphotographic method in the diamond anvil cell (D.A.C.). Figure 1 shows the fit between experimental data and this

.

- THEORlE

9 2 .

88 ^-

I

5 10 15

EXPERIENCE

THEORlE

Fig. 1 Length v a r i a t i o n of G a Se u n d e r pressure (cristallographic parameter c)

Fig. 2 Schematic band structure of G a Se.

- E 1 splitting of the s-p gallium levels at the r ^point.

- ^E'(') splitting of the P XY

I gallium levels at the M point.

I E B C splitting of the

-

^-

- . - I E ~ ~ ; e n , u m levels in the

I vzlence and c o n d u c t i o n bands.

- E l B C splitting of the P Z

I ! gallium l e v e l s in the conduc-

I I tion band.

model. We have found (6,O 2 0,2) Gpa-' and (59,2 2 ²⁾ Gpa-' for the intra and intercompressibilities. The ratio xi(@)/ x (0) " 10 is in good agreement

P

with previous Raman results (1). It is not necessary to invoke a phase transition to explain the strong initial decrease of the c parameter.

ABSORPTION COEFFICIENT

The atmospheric pressure band structure is shown in figure (2). The splirting E(') at the r ^{point (E"') at the M} point) of the s.p. gallium levels (p at M)

XY is due to the intralayer interaction. S~littings EBV, EBc at (ElBc at the M point) of the selenium levels (PZ gallium levels at M) are due to the inter- layer interaction. Electronic levels (s-p, p ) localised in a layer are assumed

XY

to depend only on the intralayer distance ; The PZ levels pointing in the inter- layer region depend only on the interlayer distance. So with the notations of figure 2 :

for the direct gap and :

for the indirect one.

dE(l) dEl(l)

All linear deformation potentials - , - - -

^{d E ~ d E ~ c ~} and - ^{dE'gc are}

dc dc dci ' dc

i dc.

P P

assumed to be constant and negative.

In order to compare this model with experimental results, we have performed transmission measurements in a D.A.C. with the electrical field perpendicular to the

axis of the sample.

The direct gap was obtained after substraction of the indirect absorption by using the Elliot-Toyozawa model (3).

Figures 3 and 4 show the fit of the model to experimental data. The pressure

coefficients for the two gaps are

JOURNAL DE PHYSIQUE

P ( GPa 1

F i g . 3 a n d 4

V a r i a t i o n o f t h e d i r e c t g a p ( u p p e r f i g u r e ) a n d i n d i r e c t g a p

( l o w e r f i g u r e ) o f G a S e u n d e r p r e s s u r e .

d~(l)

with -

- ^{(2,41 f 0,02) eV} (s-p gallium levels)

All these results are consistent and the pressure coefficients for the two gaps are in good agreement with previously published values (4).

In conclusion, we can note that the behaviour of electronic levels under pressure in Ga Se may be quantitatively explained by its lamellar properties. The initial decrease of the direct gap is due, according to this model, to the high compressi- bility at P

0 of the interlayer region, and the strong decrease of the interlayer compressibility leads to an increase of the direct gap for high pressure.

REFERENCES

1 - T.J. WIETING, Sol. Stat. Com. 12, 931, (1973) 2 - ^{M. SCHLUETER} , Nuovo. Cim. B12, 313, (1973)

A. BOURDON,Th$se, Paris, (1983)

3 - Y. TOYOZAWA, Prog. Theor. Phys. 20, 53, (1958)

R. LETOULLEC, N. PICCIOLI, J.C. CRERVZN, Phys. Rev. B22, 6162 (1980) 4 - A. BOURDON, M. MEJATTY, R. LETOULLEC, J.M. BESSON

Proc. 13 th I.C.P.S. Ed. par F.G. FUMI Rome (1976) p. 1283.

J.M. BESSON, K.P. JAIN, A. KlrHN,

Proc. 12 th I.C.P.S. Ed. par M.H. PILKUHN, STU'ITGART (1974) p. 987.