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ABSOLUTE CROSS SECTIONS FOR ONE-PHONON
RAMAN SCATTERING FROM SEVERAL
INSULATORS AND SEMICONDUCTORS
J. Calleja, H. Vogt, M. Cardona
To cite this version:
J O U R N A L DE P H Y S I Q U E
CoZZoque C6, suppZ6ment au no 12, Tome 42, de'cembre 1981 page C6-487
ABSOLUTE CROSS SECTIONS FOR ONE-PHONON RAMAN S C A T T E R I N G FROM SEVERAL INSULATORS AND SEMICONDUCTORS
J . M . C a l l e j a , H. Vogt and M. Cardona
Mm-PZanck-Institut fiir Festktirpexforschng, Heinsenbergstr. 1, 7000 Stuttgart 80, F. R. G.
Abstract.- Using the Brillouin-Raman method we have measured the Raman scattering efficiencies for the Pphonons of GaP,ZnTe,ZnSe, ZnS as well as CaF2,SrF2,BaF2. The results for the zincblende- type materials allow us to calibrate in absolute scattering effi- ciency units the resonance Raman curves found in the literature. From the calibrated resonances the deformation potentl/al d is deduced on the basis of a parabolic band model. For the f lgorides the scattering efficiency is attributed to the edge exciton. The deformation potential of the
r15
valence band following from this interpretation is compared with pseudopotential and LCAO calcu- lations.1.Introduction.- Raman resonances of semiconductors in the neighbour- hood of interband critical points have usually been studied by measur- ing the Raman scattering efficiency SR in relative, arbitrary units as function of photon energy.' A full understandinq of the Raman process, however, requires the knowledge of absolute values of SR. Such values yield information on electron-phonon coupling constants or deformation potentials.
'
'
Here we investigate with the Brillouin-Raman technique the Raman scattering efficiency of four typical zincblende-type materials (Gap, ZnTe,ZnSe,ZnS) and three fluorides (CaF2,SrF2,BaF2). The latter have non-dispersive Raman polarizabilities and are often used as standards for Raman measurements.
2.Experimental Method.- We determined SR by measuring the Raman-Bril- louin scattering efficiency ratio SR/SB and calculating S from data measured independently by other experimental t e ~ h n i q u e s . ~ ~ U s i n g a five-pass piezoelectrically scanned Fabry-Perot interferometer we re- corded Raman and Brillouin lines under exactly identical scattering conditions. S /S was obtained from the relative intensities inte-
R B
grated over the full linewidth.
3.Results.- Raman polarizabilities a
,
scattering efficiencies SRI and differential cross sections d d / d R at 1.92 eV are listed in Table 1.
a
is defined by :JOURNAL DE PHYSIQUE
where the indices refer to the cubic axes,
X
is the dielectric suscep- tibility, and U the relative displacement of the two sublattices in- volved in the Raman vibration.Table 1. Raman polarizabilities Q
,
scattering efficiencies SR, and differential cross sections d 6 / d a at 1.92 eV (6471 W).
material
/a/
( ~ ~ 1S,( I ~-~sr-'crn-' ) d~ / d R ( I ~ - ~ ~ c m ~ s r - I per primitive cell)Gap ,L0 2 5 Gap ,TO 2 3 ZnTe
,
L0 2 4 ZnSe, L0 7.0 ZnS ,L0 2.5 CaF2 0.47+0.09 SrF2 0.61+0.05 BaF2 0.84+0.08Within the indicated limits of accuracy the Raman polarizabilities of the fluorides turn out to be constant in the visible spectrum. There- fore we quote the average of the values obtained for 5 different laser lines.
The data for the zincblende-type materials were used to cali- brate the resonance curves found in the literature. ' Examples are given in Figs. 1 and 2. The solid curves in these fiqures are theore- tical fits. The underlying formulas2 mainly take into account the con- tribution of the direct gap Eo, E o + A o to the Raman polarizability and allow to deduce values of the deformation potential do from the cali- brated resonances. In Table 2 we compare these values with LCAO and pseudopotential calculations.
-
TO theory"
%
g,A
I%]
ralative values-
-t - 3 w 6 -.
-
-
-
u ) . 10-'-I n t h e c a s e o f t h e f l u o r i d e s we a t t r i b u t e t h e whole o f a t o t h e s t r o n g e d g e e x c i t o n d o m i n a t i n g t h e o p t i c a l ab- s o r p t i o n s p e c t r u m . W e have: 6
a
= N e f f do ( 2 ) 4 Et, - where a. i s t h e l a t t i c e con- s t a n t , N e f f t h e " e f f e c t i v e e l e c t r o n d e n s i t y " , a n d E. t h e e x c i t o n e n e r g y . L i k e i n t h e c a s e o f z i n c b l e n d e t h e d e f o r m a t i o n p o t e n t i a l do i s i n t r o d u c e d a s : dEo d o = - a-
0 ( 3 ) du3 V a l u e s o f do f o l l o w i n g from Eq. ( 2 ) , t h e o p t i c a l a b s o r p t i o n s p e c t r u m , a n d o u r e x p e r i m e n t a l d a t a a r e a l s o l i s t e d i n T a b l e 2 a n d compared w i t h t h e r e s u l t s of LCAO a n d p s e u d o p o t e n t i a l c a l c u l a t i o n s . T a b l e 2 . D e f o r m a t i o n p o t e n t i a l do ( i n eV) o b t a i n e d by v a r i o u s methods. m a t e r i a l Raman LCAO p s e u d o p o t e n t i a l Gap 2 7 39.4* 26.5*;26.3* ZnTe 3 7 24.4* 28* ZnSe 12 28.1" 21.6*;27* ZnS 4 30.4* 30.5*;25* Car2 4 9 38 - 8 45.1 SrF2 5 0 37.8 37.8 BaF2 6 6 34.2 30.0*
v a l u e s o b t a i n e d by o t h e r a u t h o r s ( s e e R e f . 6 ) 1 . W . R i c h t e r , S p r i n g e r T r a c t s i n Modern P h y s i c s , V o l . 78 ( S p r i n g e r Ver- l a g , H e i d e l b e r g , 1976) 2. M. Cardona,Atomic S t r u c t u r e a n d O p t i c a l P r o p e r t i e s o f S o l i d s , e d . b y E . B u r s t e i n (Academic P r e s s , New York, 1972) p. 514M. Cardona, M.H. G r i m s d i t c h , a n d D. Olego, L i g h t S c a t t e r i n g i n So- l i d s , e d . by J . L . Birman a n d H.Z. Cummins (Plenum P r e s s , N e w York, 1979) D. 249
3. M . H . . ~ E i m s d i t c h a n d A. Ramdas, Phys. Rev. B
c,
3139 (1975) 4 . B.A. W e i n s t e i n a n d M. Cardona, Phys. Rev. B8 ,
2795 ( 1 9 7 3 ) 5 . R.L. S c h m i d t , B.D. McCombe, a n d M. Cardona, Phys. Rev. B2,
746( 1 975)
R.L. Schmidt a n d M. Cardona, P h y s i c s o f S e m i c o n d u c t o r s , e d . by F . G . Fumi ( T i p o q r a f i a Marves, Rome,1976) p. 239
