HAL Id: jpa-00224309
https://hal.archives-ouvertes.fr/jpa-00224309
Submitted on 1 Jan 1984
HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
VOLUME DEPENDENCE OF OPTICAL
TRANSITIONS IN GaAs : PHOTOMODULATED REFLECTIVITY
M. Hanfland, K. Syassen, N. Christensen
To cite this version:
M. Hanfland, K. Syassen, N. Christensen. VOLUME DEPENDENCE OF OPTICAL TRANSITIONS IN GaAs : PHOTOMODULATED REFLECTIVITY. Journal de Physique Colloques, 1984, 45 (C8), pp.C8-57-C8-60. �10.1051/jphyscol:1984811�. �jpa-00224309�
JOURNAL DE PHYSIQUE
Colloque C8, suppl6ment au n O 1 l , Tome 45, novembre 1984 page C8-57
VOLUME DEPENDENCE OF OPTICAL TRANSITIONS I N GaAs :
PHOTOMODULATED REFLECTIVITY
M. Hanfland, K. Syassen and N.E. Christensen*
Physikatisches I n s t i t u t , U n i v e r s i t t l t DUsseZdorf, 0-4000 DUsseZdorf I, F.R.G.
*Max-PZanck-Institut fiir FestkUrperfor6chung, 0-7000 S t u t t g a r t 80, F.R.G.
R'esumg - Nous avons b t u d i k , par une mkthode spectroscopique de r e f l e x i o n -dulge e t en u t i l i s a n t l a technique de 1 'enclume d diamant, l e comportement des gaps Eo e t E l en GaAs. On a dgterminii aussi l a r e l a t i o n pression-volume (PV) j u s q u ' d 170 kbar d l ' a i d e de l a d i f f r a c t i o n des rayons X 6 haute pression. La dgpendance de l ' h e r g i e o p t i q u e de t r a n s i t i o n en f o n c t i o n du volume ( c o e f f i c i e n t s 1 in g a i r e s e t quadratiques) e t l a r e l a t i o n PV expgrimentale sont comparges aux r c s u l t a t s obtenus p a r l e c a l c u l r e l a t i v i s t e s e l f - c o n s i s t a n t LMTO-ASA de l a s t r u c t u r e de bande.
A b s t r a c t - Photomodulated r e f l e c t i o n spectroscopy i n combination w i t h t h e diamond c e l l technique has been used t o study t h e pressure dependence o f the Eo and E l gaps i n GaAs. I n a d d i t i o n , t h e pressure-volume (PV) r e l a t i o n up t o 170 kbar i s determined by h i g h pressure x-ray d i f f r a c t i o n . The dependence o f t h e o p t i c a l t r a n s i t i o n energies on volume change ( l i n e a r and q u a d r a t i c c o e f f i c i e n t s ) as w e l l as t h e experimental PV r e l a t i o n a r e compared t o r e s u l t s o f s e l f c o n s i s t e n t r e l a t i v i s t i c LMTO-ASA band s t r u c t u r e c a l c u l a t i o n s .
I - INTRODUCTION
The development o f the diamond a n v i l c e l l (DAC) has s t i m u l a t e d t h e renewed i n t e r e s t i n experimental and t h e o r e t i c a l i n v e s t i g a t i o n s o f pressure e f f e c t s on t h e band s t r u c t u r e o f semiconductors. Absorption, photoluminescence, and resonant Raman techniques have been used t o measure c r i t i c a l p o i n t t r a n s i t i o n s (see e.g. Refs. 1-4) and the extended pressure range has made p o s s i b l e t h e d e t e c t i o n o f n o n l i n e a r
pressure dependences o f energy gaps (see e.g. Ref. 1 ) . Most o f t h e e x i s t i n g data have been obtained f o r t h e lowest d i r e c t gap Eo. I n t h i s r e p o r t we describe a new technique f o r o b t a i n i n g i n f o r m a t i o n on energy gaps w i t h t h e DAC by u t i l i z i n g photo- modulated r e f l e c t i o n s p e c t r o ~ c o p y . ~ - ' The method i s a p p l i e d t o study t h e Eo and E l gaps o f GaAs. I n a d d i t i o n , t h e l a t t i c e parameter o f t e t r a h e d r a l GaAs i s measured by h i g h pressure x - r a y d i f f r a c t i o n up t o 170 kbar. Using t h e experimental PV r e l a - t i o n , we determine the volume dependence o f t h e o p t i c a l gaps. The experimental data ( b o t h PV r e l a t i o n and o p t i c a l t r a n s i t i o n s as a f u n c t i o n o f volume) are compared t o r e s u l t s o f r e l a t i v i s t i c LMTO-ASA c a l c u l a t i o n s a l s o presented here.
The l a t t i c e parameter o f GaAs was measured i n a DAC u s i n g an a n g l e - d i s p e r s i v e powder d i f f r a c t o m e t e r . Samples were embedded i n a methanol-ethanol pressure medium and pressures were determined from t h e r e d - s h i f t o f t h e ruby R - l i n e fluorescence (0.365 8 / k b a r s ) . The experifiental setup f o r photonodulated r e f 1 e c t i o n spectroscopy i n a DAC i s based on a m i c r o o p t i c a l system described elsewhere.' L i g h t from a Xe a r c o r tungsten lamp i s passed through a 0.3 m g r a t i n g spectrometer and then focused o n t o t h e i n t e r f a c e between sample and a l c o h o l pressure medium i n s i d e the c e l l . The i n t e n s i t y o f t h e r e f 1 ected 1 i g h t i s modulated by simul taneousl y f o c u s i n g a chopped l a s e r beam a t a d i f f e r e n t photon energy (0.5 mW a t 628 nm o r 441 nm, chopping
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984811
C8-58 JOURNAL DE PHYSIQUE
frequency f~ = 78 Hz) o n t o t h e sample. The m o d u l a t i o n mechanism c o n s i s t s of a change i n t h e macroscopic e l e c t r i c f i e l d a t t h e sample s u r f a c e by t h e p h o t o i n j e c t i o n o f c a r r i e r s . 5 - 7 The in-phase m o d u l a t i o n i s d e t e c t e d by p a s s i n g t h e d e t e c t o r s i g n a l t h r o u g h a l o c k - i n amp1 i f i e r tuned t o f ~ . A p p r o p r i a t e f i l t e r i n g b l o c k s t h e l a s e r s t r a y l i g h t from r e a c h i n g t h e d e t e c t o r . The GaAs samples (n-type d o p i n g l e v e l -1017) had a t h i c k n e s s o f a b o u t 15 Dm.
I 1 1 - CALCULATIONS
The PV r e l a t i o n o f GaAs i s c a l c u l a t e d i n t h e s e l f - c o n s i s t e n t LMTO scheme by i n t r o - d u c i n g "empty spheres" and u s i n g t h e l o c a l d e n s i t y a p p r o x i m a t i o n (LDA) f o r exchange- c o r r e l a t i o n e f f e c t s ( C e p e r l e y - A l d e r d e s c r i p t i o n w i t h r e l a t i v i s t i c c o r r e c t i o n s ) . l o
The r e l a t i v i s t i c c o r r e c t i o n s do n o t i n f l u e n c e t h e ground s t a t e p r o p e r t i e s s i g n i f i - c a n t l y . However, t h e band gaps i n v o l v i n g s - l i k e s t a t e s ( e . g . t h e d i r e c t Eo gap a t r )
t u r n o u t t o be even s m a l l e r compared t o n o n - r e l a t i v i s t i c LDA c a l c u l a t i o n s (0.25 eV versus 1.1 eV - 1.2 eV f o r Eo). T h i s i s due t o t h e p a r t i c u l a r l y l a r g e ( n e g a t i v e ) m a s s - v e l o c i t y s h i f t f o r s - l i k e c o n d u c t i o n band s t a t e s . The d i s c r e p a n c y i s remedied by a d d i n g s h a r p l y peaked e x t r a p o t e n t i a l s on t h e atomic s i t e s and on t h e "empty sphere" s i t e s . These l o c a l i z e d , p o s i t i v e p o t e n t i a l s a c t e s s e n t i a l l y o n l y on s-states.
They a r e a d j u s t e d t o match t h e normal p r e s s u r e experimental gaps a t t h e T, L and X p o i n t s . The e x t r a p o t e n t i a l s , added t o t h e l o c a l - d e n s i t y p o t e n t i a l a t a l l stages o f s e l f - c o n s i s t e n t i t e r a t i o n , were t a k e n t o be independent o f volume.
I V - RESULTS AND DISCUSSICfi
The experimental PV d a t a f o r GaAs a r e shown i n F i g . 1. From u l t r a s o n i c experiments up t o 2 k b a r one f i n d s Bo = 747 k b a r and BA = 4.67," where Bo and BA a r e i s o t h e r m a l b u l k modulus and i t s p r e s s u r e d e r i v a t i v e a t 1 bar, r e s p e c t i v e l y . ide adopt t h i s v a l u e f o r Bo, because a d e t e r m i n a t i o n f r o m x - r a y d a t a would be l e s s a c c u r a t e . A f i t o f a B i r c h e q u a t i o n t o t h e e x p e r i m e n t a l d a t a y i e l d s BA = 4.44 ? 0.1. The d i f f e r e n c e be- tween t h e p r e s e n t PV r e l a t i o n and t h e f r e q u e n t l y used FTurnaghan e x t r a p o l a t i o n o f t h e u l t r a s o n i c r e s u l t s i s 3.5% a t 170 kbar. The c a l c u l a t e d PV r e l a t i o n ( s o l i d 1 in e i n Fig. 1 ) i s i n c l o s e agreement w i t h t h e e x p e r i m e n t a l d a t a . The e q u i l i b r i u m l a t t i c e parameter (5.650 f l ) d i f f e r s b y o n l y 0.05% f r o m t h e e x p e r i m e n t a l value. Bo i s c a l - c u l a t e d t o be 728 kbar, which i s 2.5% s m a l l e r t h a n t h e room-temperature v a l u e of Ref. 12. A l s o , t h e s l o p e BA = 4.4 agrees we1 w i t h t h e p r e s e n t experiment. F o r com- p a r i s o n , Froyen and Cohen13 o b t a i n a. = 5.57 I , Bo = 725 k b a r and B; = 3.82 i n t h e i r f i r s t p r i n c i p l e 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 o f t h e ground s t a t e p r o p e r t i e s o f GaAs.
Photomodulated r e f l e c t i o n s p e c t r a o f GaAs near t h e E l gap a r e shown i n F i g . 2. The s t r u c t u r e observed a t 1 b a r i s s i m i l a r t o t h a t r e p o r t e d by i l i l s s o n 6 , e x c e p t f o r a s l i g h t l y broadened response p o s s i b l y due t o a h i g h e r d o p i n g l e v e l i n o u r case. The peaks a t 2.893 eV and 3.152 eV a r e a t t r i b u t e d t o t h e E l gap and i t s s p i n - o r b i t s p l i t companion a t E l + A1 i n analogy t o t h e assignment used i n e l e c t r o r e f l e c t a n c e
s t u d i e s . ' " The v a l u e o f A1 i s 0.253 eV + 0 . 0 1 eV as compared t o 0.227 eV f r o m Ref.
14. The d e ~ e n d e n c e o f E l and E l + A 1 on volume change i s shown i n F i g . 3. The s o l i d l i n e s correspond t o t h e r e s u l t s o f l e a s t squares f i t s u s i n g t h e q u a d r a t i c e x p r e s s i o n E(V) = E(Vo) + b(AV/Vo) + C ( A V / V ~ ) ~ , where V o . i s t h e normal p r e s s u r e volume. The c o e f f i c i e n t s b and c a r e g i v e n i n Table 1, which a l s o l i s t s o u r e x p e r i m e n t a l d a t a o b t a i n e d f r o m photomodulation spectroscopy a t t h e Eo gap. The c a l c u l a t e d band gaps have been f i t t e d i n a s i m i l a r manner and t h e r e s u l t i n g c o e f f i e c i e n t s a r e i n c l u d e d i n Table 1.
Comparison o f e x p e r i m e n t a l and c a l c u l a t e d r e s u l t s l e a d s t o t h e f o l l o w i n g conclusions:
( i ) The p r e s e n t e x p e r i m e n t a l d a t a f o r t h e Eo gap d e v i a t e n o t i c e a b l y f r o m those of Ref. 1, n o t o n l y i n t h e magnitude o f t h e l i n e a r c o e f f i e c i e n t b, b u t a l s o i n t h e d i r e c t i o n o f t h e nonl i n e a r behavior. The v a l u e o f b f r o m t h e LMTO c a l c u l a t i o n and f r o m t h e r e c e n t 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 of Chang e t a1 . I 5 d i f f e r by about +4%
and -6%, r e s p e c t i v e l y , from t h e e x p e r i m e n t a l value. The LMTO c a l c u l a t i o n reproduces t h e s u p e r l i n e a r c h a r a c t e r i s t i c o f t h e volume dependence. ( i i ) The l i n e a r c o e f f i c i e n t s
F i g . 1 - Pressure-volume r e l a t i o n o f GaAs. Closed c i r c l e s : e x p e r i m e n t a l d a t a ; s o l i d l i n e : LMTO c a l c u l a t i o n ; dashed l i n e : M u r n a g h a n - e x t r a p o l a t i o n o f u l t r a s o n i c d a t a ; open c i r c l e : Ref. 11.
PHOTON ENERGY (eV)
VOLUME CHANGE ( A V / \ ~ . ~ O ' )
F i g . 2 - Photomodulated r e f l e c t i o n F i g . 3 - The El gaps o f GaAs as a f u n c - s p e c t r a o f GaAs near t h e E l gaps. t i o n o f volume change.
C8-60 JOURNAL DE PHYSIQUE
Table 1 - C o e f f i c i e n t s ( i n eV) d e s c r i b i n g t h e volume dependence o f t h e Eo and E l gaps i n GaAs according t o the q u a d r a t i c expression given i n the t e x t .
...
...
E(VO) b C
Eo expa 1.452 -8.39f0.2 8 . 9 i 2
expb 1.450 -9.94 -7.0
c a l c a 1.452 -8.75 7.8
c a l c C -7.92
El expa 2.893 -5.88k0.2 -4.722
expC 2.900 -5.5
c a l c a 2.842 -5.82
c a i c a 3.057 -5.91
...
--- 6--- a ~ h i s work; Ref. I ( r e v i s e d ) ; ' ~ e f . 15;
d ~ e f . 16.
f o r t h e experimental E gaps agree c l o s e l y w i t h r e s u l t s obtained by electromodula- t i o n techniques.16 T h b c a l c u l a t i o n y i e l d s 1 in e a r c o e f f i c i e n t s i n excel l e n t agreement w i t h experiment. I t remains t o be i n v e s t i g a t e d , i f t h e present t h e o r e t i c a l approach a l s o reproduces the n o n l i n e a r volume dependence o f t h e E l gaps. ( i i i ) The experimental pressure c o e f f i c i e n t f o r t h e s p i n - o r b i t s p l i t t i n g A i s 0.19 t 0.05 eV/Mbar compared t o 0.3 + 0.1 eV/Mbar from Ref. 16. The c a l c u l a t i d value from t h i s work i s 0.125 eV/Mbar i n agreement w i t h Ref. 17. A more d e t a i l e d i n t e r p r e t a t i o n o f the p r e s e n t r e s u l t s wi 11 be g i v e n elsewhere.18
F i n a l l y , we p o i n t o u t t h a t t h e q u a l i t y o f r e s u l t s obtained by photomodulation spec- troscopy i n t h e DAC c r i t i c a l l y depends on t h e s e l e c t i o n o f samples g i v i n g the o p t i - mum response. With s u i t a b l e sample m a t e r i a l s t h e method should be a p p l i c a b l e t o o t h e r semiconductors, thus y i e l d i n g v a l u a b l e i n f o r m a t i o n on c r i t i c a l p o i n t t r a n s i - t i o n s above t h e fundamental gap and i n p a r t i c u l a r on t h e volume dependence o f t h e s p i n - o r b i t s p l i t t i n g .
REFERENCES
1. WELBER B., CAROONA M., KIM C.K., RODRIGUEZ S., Phys. Rev. B - 12 (1975) 5729.
2. YU P.Y., WELBER B., S o l i d S t a t e Commun. 25 (1978) 209.
3. OLEGO D., CARDONA M., MDLLER H., Phys. RG. B 22 (1980) 894.
4. AOKI A., SOOD A.K., PRESTING H., CARDONA M., S x i d S t a t e Comnun. 50 (1984) 287.
5. CARDONA M., Modulation Spectroscopy, e d i t e d by F. S e i t z , 0. T u r n b z l and H. Ehrenreich ca emic Press
6. NILSSON N.G., $:l iddS t a t e Con~n:~!~~*(1969) 479.
7. SHAY J.L., Phys. Rev. B 2 (1970) 803.
8. PIERMARINI G.J., BLOCK ST, BARNETT J.O., FORMAN R.A., J. Appl. Phys. 46 (1975) 2774.
9. SYASSEN K., SONNENSCHEIN R. , Rev. Sci . Instrum. 53 (1982) 644.
10. For more d e t a i l s see CHRISTENSEN N.E., Phys. RevTB, t o be p u b l i s h e d 11. RUOFF A.L., BAUBLITZ M.A., J. Appl. Phys. 53 (1982) 6179
12. MCSKIMIN H. J., JAYARAMAN A., ANDREATCH P. ,J. Appl . Phys. 38 (1967) 2362.
13. FROYEN S., COHEN M., S o l i d S t a t e Commun. 43 (1982) 447
14. THOMPSON A.G., CARDONA M., SHAKLEE K.L., mOLLEY J .C. Phys. Rev. 146 (1966) 601.
15. CHANG K. J. , FROYEN S. , COHEN M. L. , Sol i d S t a t e Comnun. 50 (1984) T65.
16. BENDORIUS R., SHILEIKA A., S o l i d S t a t e Comnun. 8 (1970)7111.
17. MELZ P.J., ORTENBURGER I.B., Phys. Rev. B 3 (1971) 3257.
18. HANFLAND M. , SYASSEN K. , CHRISTENSEN N. E. ,-to be pub1 i shed.
