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TWO-EXCITON PROCESS RESONANT RAMAN SCATTERING IN InSe
N. Kuroda, Y. Nishina
To cite this version:
N. Kuroda, Y. Nishina. TWO-EXCITON PROCESS RESONANT RAMAN SCATTERING IN InSe.
Journal de Physique Colloques, 1981, 42 (C6), pp.C6-332-C6-334. �10.1051/jphyscol:1981697�. �jpa-
00221634�
JOURNAL DE PHYSIQUE
Cottoque C6, supptgment au no 12, Tome 42, dgcembre 1981 page c6-332
TWO-EXCITON PROCESS RESONANT RAMAN SCATTERING IN InSe
N. Kuroda and Y. Nishina
The Research I n s t i t u t e for Iron, S t e e l and Other Metals, Tohoku University, Sendai 980, Japan.
A b s t r a c t . - Resonant Raman s p e c t r a o f n o n p o l a r o p t i c a l phonons i n t h e l a y e r compound InSe have been measured i n t h e A - e x c i t o n r e g i o n a t 1 . 8 K and 77 K. O u t - o f - p l a n e phonons e x h i b i t t h e i r r e s o n a n c e d i s p e r s i o n s t y p i c a l o f t h e o n e - e x c i t o n p r o c e s s . The i n - p l a n e phonon e x h i b i t s a d i s p e r s i o n which can be e x p l a i n e d e x c l u s i v e l y i n terms o f t h e t w o - e x c i t o n p r o c e s s where t h e A- and t h e C - e x c i t o n s e r v e s i m u l t a n e o u s l y a s t h e r e s o n a n c e i n t e r - m e d i a t e s t a t e s . The r e s u l t s show t h a t t h e o u t - o f - p l a n e phonons i n d u c e o n l y i n t r a b a n d e l e c t r o n i c s c a t t e r i n g s , whereas i n - p l a n e o n e s do i n t e r b a n d s c a t t e r i n g s a l o n e .
1. Experiment.- Measurement h a s been performed i n t h e back s c a t t e r i n g geometry by means o f a c o n v e n t i o n a l p h o t o n c o u n t i n g method. E i g h t o s c i l l a t i o n l i n e s o f an A r - i o n l a s e r a r e used a s t h e l i g h t s o u r c e . The l a s e r beam i s i n c i d e n t normal t o t h e c l e a v e d s u r f a c e o f a 3R(y)- InSe c r y s t a l which i s immersed i n l i q u i d h e l i u m a t 1.8 K o r i n l i q u i d n i t r o g e n a t 77 K.
R e s u l t s . - There a r e f o u r n o n p o l a r o p t i c a l phonons i n 3R(y) - InSe
, , r:, r:
andr3
3 b e i n g a l l a c t i v e f o r Raman s c a t t e r i n g 1 ) and o b s e r v e d1 1 8 , 234, 43 and 182 cm-I a t 1 . 8 K , r e s p e c t i v e l y . F i g u r e 1 shows r e s o n a n c e d i s p e r s i o n s of c r o s s s e c t i o n s of t h e s e phonons a t 1 . 8 K.
E x p e r i m e n t a l d a t a a t 77 K a r e a l s o p l o t t e d i n t h e same f i g u r e , where t h e y a r e s h i f t e d by 1 3 meV towards h i g h e r photon e n e r g i e s on a c c o u n t of t h e t h e r m a l s h i f t of t h e e n e r g y gap. T h i s p r o c e d u r e i s j u s t i f i e d by t h e f a c t t h a t t h e damping c o n s t a n t o f t h e A - e x c i t o n i n c r e a s e s o n l y by 30 % w i t h i n c r e a s e i n t e m p e r a t u r e from 1 . 8 K t o 77 K. Two o u t - o f -
2 3
p l a n e phonons,
rl
andr l ,
a r e s t r o n g l y enhanced by t h e r e s o n a n c e o f e x c i t a t i o n o r s c a t t e r e d p h o t o n s w i t h t h e 1 s s t a t e of t h e A - e x c i t o n l y i n g a t 2.547 eV. On t h e o t h e r hand, t h e i n - p l a n e phonon,r3,
3 e x h i b i t s i t s r e s o n a n c e enhancement by an o r d e r o f magnitude weaker t h a n t h e tworl
phonons.3 . D i s c u s s i o n . - A group t h e o r e t i c a l a n a l y s i s shows t h a t any
rl
mode i s a l l o w e d f o r i n t r a b a n d s c a t t e r i n g s w i t h i n Z (A), Z4(B) o r Z 4 (C)5 8 6
v a l e n c e bands and f o r t h e i n t e r b a n d s c a t t e r i n g between Z4(B) and Z4(C)
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1981697
Fig. 1: E x p e r i m e n t a l and t h e o r e t i c a l r e s o n a n c e d i s p e r s i o n s of n o n p o l a r o p t i c a l phonons i n l a y e r e d 3R(y)-InSe a t 1 . 8 K.
2.2 2.4 2.6 2.8 3.0 3.2
PHOTON ENERGY ( e V )
b a n d s ; any
r 3
mode can p a r t i c i p a t e i n any i n t e r b a n d s c a t t e r i n g and i n i n t r a b a n d s c a t t e r i n g s w i t h i n Z4(B) and Z4(C) bands. I n t h e q u a s i c u b i c model c o n c e r n i n g t h e s e Se p - l i k e v a l e n c e b a n d s , n o p r o b a b i l i t y i sfound f o r t h e i n t e r b a n d s c a t t e r i n g by a T1 phonon n o r f o r t h e i n t r a - band s c a t t e r i n g by a
r 3
phonon. Hence anyr l
phonon can p a r t i c i p a t e o n l y i n t h e i n t r a b a n d s c a t t e r i n g , whereas anyr3
phonon can p a r t i c i - p a t e o n l y i n t h e i n t e r b a n d s c a t t e r i n g . T h i s s e l e c t i o n r u l e i s i n aremarkable c o n t r a s t t o t h e c a s e o f z i n c b l e n d e s t r u c t u r e c r y s t a l s i n which A and B v a l e n c e bands a r e d e g e n e r a t e , t h e r e b y t h e TO phonon p a r t i c i p a t e s i n b o t h i n t r a b a n d and i n t e r b a n d s c a t t e r i n g s . ' ) The Z4(B) v a l e n c e band i n InSe i s r a i s e d i n e n e r g y a s h i g h a s 1.209 eV above t h e Z5,6(A) v a l e n c e band by a s t r o n g u n i a x i a l c r y s t a l l i n e f i e l d . 3 ) Thus t h e p r e s e n c e of t h e B - e x c i t o n can be n e g l e c t e d a s f a r a s t h e r e s o n a n c e e f f e c t i n t h e A - e x c i t o n r e g i o n i s c o n c e r n e d . The C - e x c i t o n i s
s e p a r a t e d by 0 . 3 4 4 eV from t h e A - e x c i t o n by t h e s p i n - o r b i t i n t e r a c t i o n of Se p o r b i t a l s . The f o l l o w i n g arguments show t h a t t h e C - e x c i t o n
x , Y
a s w e l l a s t h e A - e x c i t o n p l a y s an e s s e n t i a l r o l e a s t h e r e s o n a n c e i n t e r m e d i a t e s t a t e t o g i v e r i s e t o t h e s c a t t e r i n g by t h e
r 3
3 phonon.The time dependent t h i r d o r d e r p e r t u r b a t i o n t h e o r y f o r t h e r e s o n a n t Raman t e n s o r i n v o l v i n g e x c i t o n e f f e c t h a s been d e v e l o p e d i n t h e l a s t s e v e r a l y e a r s . I n t h e c a s e where i s o t r o p i c Wannier e x c i t o n s w i t h a f i n i t e damping s e r v e a s t h e r e s o n a n c e i n t e r m e d i a t e s t a t e s , t h e Raman t e n s o r i s g i v e n by
C6-334 JOURNAL DE PHYSIQUE
where Plw and-liw' a r e photon e n e r g i e s of i n c i d e n t and s c a t t e r e d l i g h t s , r e s p e c t i v e l y , h w o t h e e n e r g y o f t h e phonon i n v o l v e d i n t h e s c a t t e r i n g , R* t h e e f f e c t i v e Rydberg of an e x c i t o n , a. t h e Bohr r a d i u s , 17 t h e damping c o n s t a n t ,
E a ( ~ ) t h e e n e r g y gap between t h e a(B) v a l e n c e band and t h e c o n d u c t i o n band, P a ( B ) t h e o p t i c a l m a t r i x e l e m e n t and D t h e
aB d e f o r m a t i o n p o t e n t i a l . The summation o v e r a = 8 t e r m s o f eq. (1) g i v e s t h e Raman t e n s o r o f t h e o n e - e x c i t o n p r o c e s s , and t h e summation o v e r a f 13 t e r m s g i v e s t h a t of t h e t w o - e x c i t o n p r o c e s s . Raman c r o s s s e c t i o n s , IR(5w)
1'
f o r t h e t h r e e phonons have been c a l c u l a t e d from e q . (1) w i t h R* = 15 meV, q = 7.6 meV, EA = 2.562 eV and E C =2 2
2.906 ev3) assuming DAA(T1) = DCC(P1), DAA(r:) = D ~ ~ ( I . : ) and ~ ~ ~ ( r : ) =
D ~ ~ ( ' : ) . The b e s t f i t t o e x p e r i m e n t a l p o i n t s a r e o b t a i n e d w i t h t h e
2 3
r a t i o s o f Du(T1) : ~ ~ ( l ' : ) : DAC(r3) = 1 : 0.9 : 1 . 5 a s shown i n f i g u r e 1. T h e o r e t i c a l c u r v e s f o r two
rl
phonons c a l c u l a t e d i n terms-
of t h e o n e - e x c i t o n p r o c e s s e x p l a i n t h e s t r o n g r e s o n a n c e enhancement o b s e r v e d .
hey,
however, a p p r e c i a b l y d e v i a t e from e x p e r i m e n t a l v a l u e s a s t h e photon e n e r g y v a r i e s away from r e s o n a n c e , s u g g e s t i n g t h ep r e s e n c e of a background which i s somewhat dependent on photon energy.
The t h e o r e t i c a l c u r v e f o r t h e
r 3
3 phonon, on t h e o t h e r hand, i sc a l c u l a t e d i n t e r m s o f t h e t w o - e x c i t o n p r o c e s s i n v o l v i n g t h e A- and C- e x c i t o n s t a t e s i n a c c o r d w i t h t h e s e l e c t i o n r u l e mentioned above. The c u r v e shows t h a t t h e r e s o n a n c e enhancement i s c o m p a r a t i v e l y s m a l l b u t t h e c r o s s s e c t i o n s h o u l d be k e p t r a t h e r h i g h and n e a r l y c o n s t a n t f o r photon e n e r g i e s between t h e two e x i c t o n s t a t e s . T h i s p a r t i c u l a r f e a t u r e i s e x c e l l e n t l y r e p r o d u c e d by t h e e x p e r i m e n t a l c r o s s s e c t i o n i n t h e whole photon e n e r g y r e g i o n examined i n t h e p r e s e n t work.
R e f e r e n c e s
1 ) N. Kuroda and Y . N i s h i n a , S o l i d S t a t e Commun. 28, 439 (1978).
2 ) R. Trommer and M. Cardona, Phys. Rev. B
2,
1 8 n (1978).3) N. Kuroda, I . Munakata and Y. N i s h i n a , S o l i d S t a t e Commun. 33, 687 (1980).
4 ) R. Zeyher, C.S. Ting and J . L . Birman, Phys. Rev. B l0, 1725 (1974) 5) F. B e c h s t e d t , R. E n d e r l e i n , A. Kolpakov and K . P e u k e r , Phys. S t a t .
S o l . (b)
