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PHONON SCATTERING BY Cr IONS IN GaAs AND THE EFFECT OF UNIAXIAL STRESS
A. Ramdane, B. Salce, L. Challis, M. Locatelli
To cite this version:
A. Ramdane, B. Salce, L. Challis, M. Locatelli. PHONON SCATTERING BY Cr IONS IN GaAs AND THE EFFECT OF UNIAXIAL STRESS. Journal de Physique Colloques, 1981, 42 (C6), pp.C6- 244-C6-246. �10.1051/jphyscol:1981670�. �jpa-00221606�
JOURNAL DE PHYSIQUE
CoZZoque C6, suppZdment au n012, Tome 42, ddcembre 1981 page C6-244
PHONON S C A T T E R I N G BY Cr I O N S I N G a A s AND THE E F F E C T OF U N I A X I A L STRESS
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A. Ramdane, B. S a l c e , L . J . C h a l l i s and M. L o c a t e l l i
Department of Physics, Nottingham University, Nottingham NG7 2RD, U.K.
* Service B T, CENG, 85X, 38041 GrenobZe Cedex, France
' A b s t r a c t : Thermal c o n d u c t i v i t y m e a s u r e m e n t s i n t h e r a n g e 50mK t o 100K on n;
p and S I Sam l e s o f C r doped GaAs show t h a t crZ+ o n l y s c a t t e r s phonons a t 2 5 GHz w h i l e Erg+ h a s s e v e r a l r e s o n a n t f r e q u e n c i e s i n t h e r a n g e 2 0 t o 700GHr.
Measurements u n d e r u n i a x i a l s t r e s s i n d i c a t e v e r y a n i s o t r o p i c b e h a v i o u r q u a l - i t a t i v e l y c o n s i s t e n t w i t h a J a h n - T e l l e r model f o r cr3+.
2 + S u b s t i t u t i o n a l C r a p p e a r s t o e x i s t i n GaAs i n t h e t h r e e i o n i c s t a t e s C r , cr3+
and cr4+. cr4+ h a s a n o r b i t a l s i n g l e t ( 3 A21 g r o u n d s t a t e and c a n n o t s c a t t e r phonons s t r o n g l y ( n e i t h e r c o u l d C r l + i f i t e x i s t e d ) b u t t h i s i s n o t n e c e s s a r i l y t h e c a s e f o r
crZ+ a n d C r 3 + . We h a v e i n v e s t i g a t e d t h e phonon s c a t t e r i n g by making t h e r m a l c o n d u c - t i v i t y m e a s u r e m e n t s down t o 50mK and u n d e r u n i a x i a l s t r e s s . The z e r o s t r e s s work i s a n e x t e n s i o n o f e a r l i e r work /I/ and a f u l l r e p o r t on t h e 1 4 s a m p l e s i n v e s t i g a t e d w i l l a p p e a r e l s e w h e r e /2/.
The t h e r m a l c o n d u c t i v i t y K c o r r e l a t e s w i t h t h e e l e c t r i c a l c h a r a c t e r i s t i c s and v a l u e s f o r n, p a n d s e m i - i n s u l a t i n g ( S I 1 s p e c i m e n s a r e shown i n f i g 1 . The d a t a a r e p l o t t e d a s t h e r m a l r e s i s t i v i t y ( W = 1 / K 1 d i v i d e d by t h e r e s i s t i v i t y c h a r a c t e r i s t i c o f undoped GaAs t o e m p h a s i s e t h e s c a t t e r i n g an'd t h e u p p e r s c a l e shows t h e f r e q u e n c y o f t h e d o m i n a n t phonons i n t h e h e a t c u r r e n t ( h v % 4kT) a t t r i b u t a b l e t o C r . The weakly p - t y p e (GA781) and S I s a m p l e GA735Ce) a r e n o t d i s s i m i l a r i n b e h a v i o u r a b o v e 100mK a n d t h e s m a l l e r t h o u g h s t i l l v e r y s u b s t a n t i a l s c a t t e r i n g i n T I 4 i s c o n s i s t e n t w i t h t h e f a c t t h a t t h e C r c o n c e n t r a t i o n i s a b o u t 2 0 t i m e s s m a l l e r t h a n i n t h e o t h e r 2 s a m p l e s . T h e r e i s a l s o e v i d e n c e o f r e s o n a n t s c a t t e r i n g a t &GHZ i n S I GaAs w h i c h i s a b s e n t i n t h e p - t y p e m a t e r i a l b u t a p p e a r s t o b e t h e o n l y r e s o n a n t s c a t t e r i n g i n n - t y p e m a t e r i a l c o n t a i n i n g a r o u g h l y s i m i l a r amount o f C r . S i n c e t h e C r i n n - t y p e m a t e r i a l s h o u l d b e v e r y l a r g e l y i n t h e cr2+ s t a t e we c o n c l u d e t h a t t h i s i o n i s r e s p o n s i b l e f o r t h e low f r e q u e n c y s c a t t e r i n g . So Cr2+ c a n o n l y s c a t t e r phonons s i g n i f i c a n t l y a t ~ ~ G H Z . The a b s e n c e o f t h i s s c a t t e r i n g i n w e a k l y p - t y p e m a t e r i a l ( c r 3 + a n d Cr4+1 a n d i t s p r e s e n c e i n S I m a t e r i a l ( c r 2 + a n d c r 3 + ) i s c o n s i s t e n t w i t h t h e p r o b a b l e v a l e n c e s t a t e s g i v e n . The s c a t t e r i n g a b o v e 100mK i n p - t y p e a n d S I m a t e r i a l seems a t t r i b u t a b l e t o Cr3+ a n d f r o m t h e p o s i t i o n s o f t h e maxima i n W/W we d e d u c e t h a t t h e s c a t t e r i n g i s r e s o n a n t a t 2 1 , 80, 1 5 0 , 400 a n d 690GHz s u g g e s t i n g a
f a i r l y c o m p l e x l e v e l scheme. T h e v a l u e s a t 150 a n d 400 GHz are b r o a d l y c o n s i s t e n t w i t h v a l u e s o b t a i n e d b y t u n n e l j u n c t i o n s p e c t r o s c o p y / 3 / .
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1981670
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Fig I: Reduced h e ~ h f - i u M y WIW, 06 G&:Ch.
B o t h cr2+ a n d Cr3+ a r e b e l i e v e d t o u n d e r g o J a h n - T e l l e r e f f e c t s . I n t h e s t a t i c l i m i t t h e T2 s t a t e s o f t h e Td c r y s t a l f i e l d o f 5 cr2+ a r e s p l i t by t e t r a g o n a l J a h n -
T e l l e r d i s t o r t i o n s t o l e a v e a g r o u n d s t a t e o r b i t a l s i n g l e t 5 ~ 2 f o r e a c h o f t h e t h r e e w e l l s w h i c h i s t h e n s p l i t by s e c o n d o r d e r s p i n - o r b i t i n t e r a c t i o n . T h i s c a n a c c o u n t f o r t h e EPR d a t a /4/ b u t n o t f o r t h e phonon s c a t t e r i n g o b s e r v e d h e r e w h i c h i s f o r b i d - d e n i n t h i s l i m i t / 2 , 5 / . T u n n e l l i n g b e t w e e n t h e w e l l s m i x e s t h e i r s t a t e s a n d phonon s c a t t e r i n g i s now a l l o w e d b e t w e e n l e v e l s s e p a r a t e d by 36? w h e r e 61 i s t h e t u n n e l l i n g f r e q u e n c y /5/. The l e v e l s s h o u l d b e v e r y s e n s i t i v e t o a p p l i e d o r random s t r a i n w h i c h p r o d u c e s r e l a t i v e s h i f t s i n t h e e n e r g i e s o f t h e w e l l s . However t h e phonon s c a t t e r i n g c u t s o f f o n c e t h e s e s h i f t s e x c e e d t h e t u n n e l l i n g s p l i t t i n g s o no s c a t t e r i n g c a n o c c u r much a b o v e 36,,. From t h e d a t a i n f i g 1 we c a n c o n c l u d e t h e r e f o r e t h a t 2 2GHz a n d s o t h e Ham r e d u c t i o n f a c t o r y 2 0 . 0 0 1 . The p i c t u r e i s much l e s s c l e a r f o r cr3+. The Td g r o u n d s t a t e i s 4 ~ 1 and EPR d a t a s u g g e s t t h a t t h e J a h n - T e l l e r d i s t o r t i o n r e s u l t s i n 6 o r t h o r h o m b i c a l l y p l a c e d w e l l s /6/. The s i z e o f t h e r e d u c t i o n f a c t o r s a n d s o t h e r e l a t i v e s i z e s o f t h e f i r s t a n d s e c o n d o r d e r s p i n - o r b i t s p l i t t i n g s a r e n o t known a n d t h e d e s c r i p t i o n i s c o m p l i c a t e d by t h e p o s s i b l e c l o s e p r o x i m i t y t o 4 ~ 1 o f s t a t e s f r o m e x c i t e d c o n f i g u r a t i o n s /7/.
To i n v e s t i g a t e t h e s y s t e m f u r t h e r , m e a s u r e m e n t s h a v e b e e n made o f t h e d e p e n d e n c e o f t h e t h e r m a l c o n d u c t i v i t y on u n i a x i a l s t r e s s i n t h e t e m p e r a t u r e r a n g e 2-15K. No s i g n i f i c a n t e f f e c t was f o u n d i n n - t y p e m a t e r i a l and t h i s seems c o n s i s t e n t w i t h t h e d e s c r i p t i o n f o r cr2+ g i v e n a b o v e . S t r e s s s h o u l d i n c r e a s e t h e t r a n s i t i o n f r e q u e n c i e s t o v a l u e s c o m p a r a b l e w i t h t h o s e o f t h e d o m i n a n t phonons i n t h e h e a t c u r r e n t s o t h a t a d e c r e a s e i n t h e r m a l c o n d u c t i v i t y m i g h t o c c u r . The f a c t t h a t it d o e s n o t i s c o n s i s t - e n t w i t h t h e c u t - o f f i n s c a t t e r i n g c r o s s - s e c t i o n a t t h e s e h i g h f r e q u e n c i e s . D a t a f o r S I ( T I 4 1 and p - t y p e (GA781) s a m p l e s a r e shown i n f i g 2 f o r c o m p r e s s i v e s t r e s s e s a l o n g
<001> a n d < ? l o > d i r e c t i o n s . The b e h a v i o u r o f t h e two s a m p l e s i s v e r y s i m i l a r f o r
<DO?> s t r e s s e s a g a i n s u g g e s t i n g t h a t t h e s c a t t e r i n g i o n i s t h e same. I n T I 4 t h e s a t u r a t i o n v a l u e a t h i g h s t r e s s e s i s v e r y s i m i l a r t o t h a t o f undoped GaAs s u g g e s t i n g
C6-246 JOURNAL DE PHYSIQUE
t h a t t h e C r s c a t t e r i n g h a s b e e n c o m p l e t e l y q u e n c h e d . T h e a n i s o t r o p y r e f l e c t e d b y t h e c o m p a r a t i v e l y m o d e s t c h a n g e s p r o d u c e d by <110> s t r e s s i s v e r y s t r i k i n g and s u g g - e s t s t h a t < ? l o > s t r e s s l e a v e s a g r o u n d s t a t e w i t h i n w h i c h phonon s c a t t e r i n g c a n s t i l l o c c u r . T h i s seems q u a l i t a t i v e l y c o n s i s t e n t w i t h t h e s t r e s s s p l i t t i n g f o r Cr3+ n e a r t h e s t a t i c J a h n - T e l l e r l i m i t g i v e n i n r e f /6/. C o m p r e s s i v e <OD?> s t r e s s l e a v e s 2 o r t h o g o n a l l e v e l s l o w e s t s o t h a t phonon s c a t t e r i n g s h o u l d v a n i s h a t h i g h s t r e s s . C o m p r e s s i v e < I 1 0 2 s t r e s s l e a v e s 4 l e v e l s l o w e s t . T u n n e l l i n g c a n o c c u r b e t w e e n p a i r s s o phonon s c a t t e r i n g r e m a i n s e v e n a t h i g h s t r e s s . F u r t h e r m e a s u r e m e n t s and a n a l y s i s a r e i n p r o g r e s s t o t e s t t h i s d e s c r i p t i o n .
We a r e v e r y g r a t e f u l f o r s a m p l e s f r o m M J C a r d w e l l , P R J a y and D J S t i r l a n d and t h e P l e s s e y Co and f r o m T I s h i g u r o and H Tokumoto a n d t o many o f o u r c o l l e a g u e s p a r t - i c u l a r l y A S Abhvani, S P A u s t e n , C A B a t e s , L E a v e s , A M d e GO&, J R F l e t c h e r , P J King, L W P a r k e r and D J P o o l e r f o r v e r y h e l p f u l d i s c u s s i o n s . The work was s u p p o r t e d by t h e S c i e n c e R e s e a r c h C o u n c i l a n d t h e M i n i s t ' e r e d e s A f f a i r e s ~ t r a n g z r e s and o n e o f
u s (ARI i s v e r y g r a t e f u l t o t h e A l g e r i a n M i n i s t r y o f Hi'gher E d u c a t i o n and S c i e n t i f i c R e s e a r c h f o r a m a i n t e n a n c e g r a n t .
R e f e r e n c e s
/ I / C h a l l i s L J a n d Ramdane A, 1 9 8 0 , P r o c I n t Conf on Phonon S c a t t e r i n g i n Condensed M a t t e r , e d H M a r i s ( N e w York : Plenum) p p 121-4. Bury P, C h a l l i s L J , King P J , Monk 0 J , Ramdane A, Rampton V W a n d Wiscombe P C, 1 9 8 0 , P r o c I n t Conf on Semi- I n s u l a t i n g 1 1 1 - V Compounds [ N o t t i n g h a m ) , e d G J R e e s [ O r p i n g t o n : S h i v a P r e s s ] . /2/ C h a l l i s L J , L o c a t e l l i M, Ramdane A and S a l c e 8 , s u b m i t t e d f o r p u b l i c a t i o n . /3/ Hamdache M, K i n g P J , Murphy D T a n d Rampton V W , t o b e p u b l i s h e d .
/4/ K r e b s J J and S t a u s s G H, P h y s Rev B 16, 9 7 1 , 1 9 7 7 .
/5/ Abhvani A S , A u s t e n S P, B a t e s C A, P a r k e r L W and P o o l e r D J , s u b m i t t e d f o r p u b l i c a t i o n .
/6/ S t a u s s G H a n d K r e b s J J , P h y s Rev B 22, 2050, 1 9 8 0 . /7/ H e m s t r e e t L A a n d Dimmock J 0 , P h y s Rev 8 20, 1 5 2 7 , 1 9 7 9 .
