ABSORPTION AND LUMINESCENCE EXPERIMENTS IN SEMICONDUCTOR SUPERLATTICES

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EXPERIMENTS IN SEMICONDUCTOR SUPERLATTICES

M. Voos

To cite this version:

M. Voos. ABSORPTION AND LUMINESCENCE EXPERIMENTS IN SEMICONDUC- TOR SUPERLATTICES. Journal de Physique Colloques, 1984, 45 (C5), pp.C5-489-C5-498.

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J O U R N A L D E PHYSIQUE

Colioque C5, suppl6rnent au n04, Tome 45, avril 1984 page C5-489

ABSORPTION AND LUMINESCENCE EXPERIMENTS IN SEMICONDUCTOR SUPERLATTICES

M . Voos

Groupe de Physique des ~ o ~ i d e s * de ZrEcoZe NormaZe Supgrieure, 24 rue Lhomond, 75231 Paris Cedex 05, France

R6sumB - Nous prBsentons i c i des r B s u l t a t s expBrimentaux obtenus rBcemment 2 p a r t i r de mesures o p t i q u e s f a i t e s s u r des super-r6seaux semiconducteurs. Ces 6 t u d e s o n t donnB des i n f o r m a t i o n s i n t s r e s s a n t e s s u r l e s p r o p r i s t 6 s B l e c t r o n i - ques de c e s systBmes B deux dimensions q u i o n t o u v e r t un nouveau champ de r e c h e r c h e en physique des semiconducteurs

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A b s t r a c t - We p r e s e n t h e r e some e x p e r i m e n t a l r e s u l t s o b t a i n e d r e c e n t l y on semiconductor s u p e r l a t t i c e s from o p t i c a l measurements. These s t u d i e s g i v e i n t e r e s t i n g i n f o r m a t i o n s on t h e e l e c t r o n i c p r o p e r t i e s o f t h e s e two- d i m e n s i o n a l systems which have opened up a new f i e l d of i n v e s t i g a t i o n s i n semi c o n d u c t o r p h y s i c s

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I - INTRODUCTION

Semiconductor s u p e r l a t t i c e s , which have been proposed by E s a k i and Tsu / I / , c o n s i s t of t h i n a l t e r n a t e l a y e r s of two semiconductors which, g e n e r a l l y , c l o s e l y match i n l a t t i c e $ o n s t a n t . I n t h e s e p e r i o d i c s t r u c t u r e s , t h e t h i c k n e s s of t h e l a y e r s r a n g e s from 10 A t o a few hundred A a b o u t , s m a l l e r t h a n o r comparable t o t h e e l e c t r o n mean f r e e p a t h , b u t l a r g e r t h a n t h e i n t e r a t o m i c s p a c i n g . Thus, t h e c o n s i d e r e d system i s two-dimensional, a t l e a s t i n f i r s t a p p r o x i m a t i o n , and quantum e f f e c t s can be e x p e c t e d , changing t h e e l e c t r o n i c s t r u c t u r e of t h e h o s t m a t e r i a l s and g i v i n g r i s e t o unusual p r o p e r t i e s . The d i f f e r e n t band gaps Eg of t h e h o s t semiconductors c r e a t e a one-dimensional p e r i o d i c p o t e n t i a l i n t h e z d i r e c t i o n p e r p e n d i c u l a r t o t h e p l a n e of t h e l a y e r s . T h i s l e a d s t o t h e c r e a t i o n of an a r t i f i c i a l p e r i o d i c i t y , which i s l o n g e r t h a n t h e atomic s p a c i n g and i s s u p e r p o s e d t o t h e n a t u r a l p e r i o d i c i t y of t h e c r y s t a l . This p o t e n t i a l c a u s e s a f o l d i n g of t h e B r i l l o u i n zone, r e s u l t i n g i n a s e r i e s of q u a n t i z e d subbands i n b o t h t h e c o n d u c t i o n and v a l e n c e b a n d s , a s shown i n F i g . 1 . One can c o n s i d e r t h a t t h e c a r r i e r s a r e c o n f i n e d i n quantum p o t e n t i a l w e l l s and t h a t t h e i r motion i s q u a n t i z e d i n t h e z d i r e c t i o n , t h e c o n d u c t i o n ( v a l e n c e ) subbands such a s E l , E2..

.

Two t y p e s o f s u p e r l a t t i c e s , I and 11, have been e x t e n s i v e l y i n v e s t i g a t e d .

G ~ A S - A ~ , G ~ ~ - ~ A S s t r u c t u r e s c o r r e s p o n d / 2 / t o t y p e I , and t h e s i t u a t i o n i s schemati- c a l l y d e s c r i b e d i n F i g . 1 . The GaAs c o n d u c t i o n band edge i s a t lower energy t h a n t h a t of A1,Gal-,As, w h i l e i t s v a l e n c e band edge i s a t h i g h e r energy t h a n t h a t of

A 1 Gal-,As. x The GaAs l a y e r s a r e t h u s p o t e n t i a l w e l l s f o r b o t h e l e c t r o n s and h o l e s which a r e c o n f i n e d i n t h e s e l a y e r s . I n InAs-GaSb s t r u c t u r e s 1 3 1 , which b e l o n g t o t y p e I1 s t r u c t u r e s , t h e InAs c o n d u c t i o n band edge l i e s a t lower e n e r g y t h a n t h e GaSb v a l e n c e band edge, a s s c h e m a t i z e d i n F i g . 2 ( a ) . The InAs and GaSb l a y e r s s e r v e a s p o t e n t i a l w e l l s f o r e l e c t r o n s and h o l e s , r e s p e c t i v e l y . E l e c t r o n s and h o l e s a r e spa-

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t i a l l y s e p a r a t e d , b u t photon a b s o r p t i o n o r emission a r e n e v e r t h e l e s s p o s s i b l e because t h e e l e c t r o n and h o l e wavefunctions o v e r l a p . Furthermore, e x p e r i m e n t a l i n v e s t i g a t i o n s have shown / 4 / r e c e n t l y t h a t HgTe-CdTe s u p e r l a t t i c e s , which belong a t f i r s t s i g h t t o type I s t r u c t u r e s , have i n f a c t q u i t e d i f f e r e n t c h a r a c t e r i s t i c s from t h o s e of GaAs-AlGaAs s y s terns.

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F i g u r e 1 : S c h e m a t i z a t i o n o f a semiconductor s u p e r l a t t i c e c o n s i s t i n g h e r e i n a l t e r - n a t e l a y e r s of GaAs and AlxGal-xAs. The t o t a l t h i c k n e s s of t h e s u p e r l a t t i c e i s g e n e r a l l y of t h e o r d e r of 1 urn, and t h a t of t h e s u b s t r a t e i s t y p i c a l l y 500 pm. Also shown i s t h e v a r i a t i o n of t h e conduction and v a l e n c e bands i n such a s t r u c t u r e i n t h e z d i r e c t i o n p e r p e n d i c u l a r t o t h e l a y e r s . S e v e r a l conduction ( E l , E2) and v a l e n c e ( H I , h l , H2, h 2 ) subbands a r e r e p r e s e n t e d h e r e , where H1 and H2 correspond t o heavy- h o l e s , w h l l e h l and h 2 a r e l i g h t - h o l e subbands. The s u p e r l a t t i c e band gap i s Eo = El - H I .

I n a d d i t i o n t o t h e s p a t i a l s e p a r a t i o n of e l e c t r o n and h o l e s , t h e r e i s a n o t h e r impor- t a n t d i f f e r e n c e between GaAs-A1,Ga ,As and Ids-GaSb s u p e r l a t t i c e s . The e l e c t r o n e f f e c t i v e mass i n InAs (0.023 mo) );/ i s much l i g h t e r t h a n i n GaAs (0.066 mo) 151, which l e a d s t o s t r o n g e r t u n n e l i n g i n t e r a c t i o n s between InAs l a y e r s t h a n between GaAs l a y e r s . Thus, i n InAs-GaSb s t r u c t u r e s , even f o r r a t h e r l a r g e v a l u e s of t h e l a y e r t h i c k n e s s e s (% 200 i), t h e El subband h a s / 3 / an a p p r e c i a b l e width AE1 i n t h e z d i r e c t i o n , w h i l e AE1 i s o f t e n n e g l i g i b l e i n GaAs-AlxGal-xAs s u p e r l a t t i c e s .

Furthermore, due t o t h e l a r g e heavy-hole e f f e c t i v e mass i n 1 1 1 - V compounds

(% 0 . 3 mo) 1 5 1 , t h e width of t h e H1 subband i n t h e z d i r e c t i o n , AH^, i s approximate- l y e q u a l t o z e r o .

I t i s n o t p o s s i b l e t o review h e r e a l l t h e o p t i c a l s t u d i e s performed on semiconductor s u p e r l a t t i c e s , and we w i l l o n l y d e s c r i b e some of t h e r e s u l t s which have given i n t e - r e s t i n g i n f o r m a t i o n s on t h e i r e l e c t r o n i c p r o p e r t i e s . We w i l l focus on

GaAs-A1,Gal-xAs and I d s - G a S b s u p e r l a t t i c e s , which a r e t h e most e x t e n s i v e l y i n v e s t i - g a t e d s t r u c t u r e s , and we w i l l a l s o d e s c r i b e b r i e f l y some a s p e c t s of HgTe-CdTe super- l a t t i c e s . However, i t s h o u l d be n o t e d t h a t o t h e r s u p e r l a t t i c e s , such a s

In,Gal-,As-InP 161 and GaSb-AlSb / 7 / systems f o r example, a r e now b e i n g i n v e s t i g a t e d .

F i g u r e 2 : S c h e m a t i c e n e r g y diagram o f a n InAs-GaSb s u p e r l a t t i c e . Ecl (Ec2) and Evl (Ev2) a r e t h e c o n d u c t i o n and v a l e n c e band e d g e s o f GaSb ( I n A s ) . E l and H I a r e r e s p e c t i v e l y t h e ground c o n d u c t i o n and v a l e n c e subbands of t h e s u p e r l a t t i c e . Semi- c o n d u c t i n g ( a ) and s e m i m e t a l l i c ( b ) s i t u a t i o n s .

I1 - OPTICAL ABSORPTION AND LUMINESCENCE

A b s o r p t i o n e x p e r i m e n t s done a t h e l i u m t e m p e r a t u r e s i n GaAs-A1xGal-xAs s u p e r l a t t i c e s grown by m o l e c u l a r beam e p i t a x y (MBE) h a v e g i v e n s t r o n g e v i d e n c e f o r c a r r i e r c o n f i - nement i n t h e GaAs p o t e n t i a l w e l l s / 2 , 8 / . T y p i c a l d a t a a r e shown i n F i g . 3 which p r e s e n t s t r a n s m i s s i o n ( i . e . a b s o r p t i o n ) and e x c i t a t i o n s p e c t r a 181. E x c i t a t i o n s p e c t r o s c o p y , which g i v e s t h e same i n f o r m a t i o n s a s o p t i c a l a b s o r p t i o n , c o n s i s t i n s c a n n i n g t h e e x c i t i n g l i g h t w a v e l e n g t h from a dye l a s e r w h i l e t h e d e t e c t i n g s p e c t r o - m e t e r i s s e t a t a n e n e r g y where t h e sample e x h i b i t s l u m i n e s c e n c e , i . e . h e r e a t

1.525 eV ( s e e F i g . 3 ) . P e a k s a r e f o u n d a t e n e r g i e s c o r r e s p o n d i n g t o p o s s i b l e t r a n s i - t i o n s shown i n t h e i n s e t o f F i g . 3 a s a r e s u l t o f p h o t o n a b s o r p t i o n by t h e c o r r e s p o n - d i n g e n e r g y l e v e l s f o l l o w e d by r a p i d r e l a x a t i o n o f t h e e x c i t e d c a r r i e r s t o t h e l u m i n e s c e n t l e v e l w h e r e t h e y r e c o m b i n e r a d i a t i v e l y . I n f a c t , t h e p e a k s i n F i g s 3 ( b ) and 3 ( c ) a r e c h a r a c t e r i s t i c o f l i g h t a b s o r p t i o n by f r e e e x c i t o n s 1 2 1 , a n d , t h e o b s e r v e d o p t i c a l t r a n s i t i o n s a r e i d e n t i f i e d i n F i g . 3 where t h e n = l e - hh p e a k , f o r i n s t a n c e , i s a t t r i b u t e d t o a b s o r p t i o n by a f r e e e x c i t o n c o r r e s p o n d i n g t o t h e n = 1 e l e c t r o n ( E l subband) and heavy-hole ( H I subband) s t a t e s shown i n t h e i n s e t . C a r r i e r c o n f i n e m e n t i s c l e a r l y o b s e r v e d s i n c e , i n b u l k GaAs, t h e a b s o r p t i o n s p e c t r u m p r e s e n t s 1 2 1 o n l y a f r e e e x c i t o n peak a t 1.515 eV, namely a t lower e n e r g y t h a n t h e t r a n s i t i o n s s t u d i e d h e r e . The e n e r g y p o s i t i o n o f t h e peaks i n F i g . 3 i s i n good agreement w i t h c a l c u l a t i o n s o f t h e c o n d u c t i o n and v a l e n c e subband e n e r g i e s performed i n a s i m p l e model where t h e GaAs l a y e r s c o r r e s p o n d t o n o n - i n t e r a c t i n g quantum w e l l s h a v i n g a f i n i t e d e p t h 121. A d d i t i o n a l a b s o r p t i o n e x p e r i m e n t s 1 2 1 i n s i m i l a r s u p e r -

l a t t i c e s d e m o n s t r a t e t h a t , when t h e GaAs l a y e r t h i c k n e s s i s d e c r e a s e d , t h e f r e e e x c i t o n p e a k s move t o h i g h e r e n e r g i e s and t h e d i s t a n c e between t h e s e p e a k s i n c r e a s e s , a s c a n be e x p e c t e d i n a s i m p l e quantum w e l l model. From s u c h i n v e s t i g a t i o n s , t h e d i s c o n t i n u i t y AEc (AE,) o f t h e c o n d u c t i o n ( v a l e n c e ) band a t e a c h i n t e r f a c e h a s been found 121 t o b e e q u a l t o 225 meV (30 meV) :or x % 0 . 2 . T h i s was o b t a i n e d by f i t t i n g t h e e n e r g y p o s i t i o n s o f t h e o b s e r v e d t r a n s i t i o n s i n s e v e r a l s u p e r l a t t i c e s h a v i n g d i f f e r e n t GaAs l a y e r t h i c k n e s s e s t o s i m p l e c a l c u l a t i o n s c o r r e s p o n d i n g a g a i n t o non- i n t e r a c t i n g quantum w e l l s of f i n i t e d e p t h s 121. More s o p h i s t i c a t e d 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 i n t h e e n v e l o p e f u n c t i o n a p p r o x i m a t i o n 1 9 1 of t h e s u p e r l a t t i c e band

s t r u c t u r e p r o v i d e s , i n f a c t , s i m i l a r r e s u l t s . Luminescence e x p e r i m e n t s h a v e a l s o b e e n performed i n s u p e r l a t t i c e s grown by MBE 1 8 1 and by m e t a l o r g a n i c c h e m i c a l v a p o r

d e p o s i t i o n / l o / . F i g . 3 ( a ) g i v e s t y p i c a l r e s u l t s o b t a i n e d 1 8 1 i n t h e same s t r u c t u r e a s t h e one used i n t h e a b s o r p t i o n e x p e r i m e n t s d e s c r i b e d p r e v i o u s l y . From t h e absorp- t i o n and e x c i t a t i o n s p e c t r a , t h e two luminescence l i n e s i n F i g . 3 ( a ) a r e a s s i g n e d t o t h e r e c o m b i n a t i o n o f f r e e e x c i t o n s i n v o l v i n g t h e n = 1 e l e c t r o n s t a t e and t h e n = 1 heavy and l i g h t - h o l e s t a t e s , r e s p e c t i v e l y . It i s noteworthy t h a t , i n such s t r u c t u r e s where t h e i m p u r i t y d e n s i t y i s low (NA - ND ". 10" - 10" ~ m - ~ ) , t h e luminescence spectrum does n o t show i n t e n s e l i n e s i n v o l v i n g i m p u r i t i e s w h i l e , i n b u l k GaAs w i t h a s i m i l a r i m p u r i t y c o n c e n t r a t i o n , i t i s dominated / 1 I / by e x t r i n s i c recombination p e a k s , b u t t h i s d i f f e r e n c e w i t h b u l k GaAs i s n o t u n d e r s t o o d .

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F i g u r e 3 : Luminescence ( a ) , a b s o r p t i o n (b) and e x c i t a t i o n s p e c t r a ( c ) o f a GaAs;A10.3Ga0.7As s u p e r l a t t i c e c o n s i s t i n g of 25 GaAz l a y e r s whose t h i c k n e s s i s 188 A , w h i l e t h a t of t h e A10e3Ga0.7As l a y e r s i s 19 A . I n t h e i n s e t a r e shown p o s s i - b l e o p t i c a l t r a n s i t i o n s i n such a s t r u c t u r e . Here n = l e , 2e c o r r e s p o n d s t o t h e E l , E2 subbbands, and n = 1 hh, 2 h h , 1 l h , 2 l h c o r r e s p o n d t o t h e H I , H z , h l and h2 subbands shown i n F i g . ] . I n such a s t r u c t u r e , o p t i c a l t r a n s i t i o n s a r e allowed f o r An = 0. ( A f t e r R e f . 8 ) .

O p t i c a l a b s o r p t i o n e x p e r i m e n t s have been done i n PE-grown InAs-GaSb s u p e r l a t t i c e s 1121 f o r l a y e r t h i c k n e s s e s r a n g i n g from 15 t o 30 A about. They g i v e e v i d e n c e f o r t h e e x i s t e n c e o f a s u p e r l a t t i c e s t r u c t u r e , b u t no f r e e e x c i t o n t r a n s i t i o n s have been o b s e r v e d , which i s n o t s u r p r i s i n g b e c a u s e t h e s p a t i a l s e p a r a t i o n of e l e c t r o n s and h o l e s i s n o t f a v o r a b l e t o t h e f o r m a t i o n o f f r e e e x c i t o n s 191. The a b s o r p t i o n e d g e , which i s found t o depend on t h e l a y e r t h i c k n e s s , d e t e r m i n e s t h e s u p e r l a t t i c e band gap Eo = El - H I . By comparing t h e s e d a t a t o t h e t h e o r e t i c a l v a r i a t i o n of Eo w i t h t h e l a y e r t h i c k n e s s c a l c u l a t e d by t h e LCAO method / 1 3 / , one o b t a i n s Es ". 150 meV, where Es i s t h e d i f f e r e n c e between t h e InAs c o n d u c t i o n band edge and t h e GaSb valen- ce band edge a t e a c h i n t e r f a c e . B e s i d e s , luminescence e x p e r i m e n t s have been p e r f o r - med i n InAs-GaSb s u p e z l a t t i c e s 1141 where t h e InAs and GaSb l a y e r t h i c k n e s s e s were r e s p e c t i v e l y d l = 30 A and d2 = 50 1. The o b s e r v e d s p e c t r a , which a r e shown i n F i g . 4 , l i e around 250 meV, and a r e t h e r e f o r e a t much lower energy t h a n t h e band gaps / 5 / o f b u l k InAs (410 meV) and GaSb (815 meV), i n d i c a t i n g t h e f o r m a t i o n of subbands i n t h e s u p e r l a t t i c e . I n t h i s s y s t e m , LCAO c a l c u l a t i o n s of t h e s u p e r l a t t i c e band s t r u c t u r e /13,15/ g i v e AE1 = 60 meV, w h i l e AH1 ". 0. T h e r e f o r e , t h e h o l e d e n s i t y of s t a t e s i s a c t u a l l y two-dimensional, b u t t h a t of e l e c t r o n s i s n o t s t r i c t l y two- d i m e n s i o n a l a s a r e s u l t of t h e non-zero width of E l . Taking i n t o a c c o u n t t h e a c t u a l e l e c t r o n and h o l e d e n s i t i e s o f s t a t e s , a s w e l l a s t h e c a l c u l a t e d o p t i c a l m a t r i x element which, i n t h e s e s t r u c t u r e s , depends /16/ on k,, t h e o r e t i c a l f i t s of t h e main l i n e i n F i g . 4 show t h a t i t i s due, o v e r t h e whole t e m p e r a t u r e range i n v e s t i g a t e d , t o band-to-band r e c o m b i n a t i o n between f r e e e l e c t r o n s i n t h e El subband and f r e e h o l e s

i n t h e H1 subband. I n a d d i t i o n , t h e s u p e r l a t t i c e band gap, Eo, o b t a i n e d a t 2 K from s u c h a f i t i s e q u a l t o 262 meV, i n s a t i s f y i n g agreement w i t h t h e t h e o r e t i c a l v a l u e 19,131 (280 meV). As c a n b e s e e n i n F i g . 4 , when T i s reduced below 300 K , t h e lumi- n e s c e n c e s p e c t r u m e x h i b i t s a t a i l o r a bump on i t s low-energy s i d e which i n d i c a t e s t h e e x i s t e n c e of e n e r g y s t a t e s i n t h e s u p e r l a t t i c e band gap. They may c o r r e s p o n d t o i m p u r i t i e s whose b e h a v i o r i n s u p e r l a t t i c e s h a s been s t u d i e d t h e o r e t i c a l l y by B a s t a r d 1171. They may a l s o a r i s e 1141, a s o b s e r v e d i n G a t l ~ - A l ~ G a l - ~ systems 1181, from i n t e r f a c e d e f e c t s l o o k i n g l i k e s u r f a c e roughness and c o r r e s p o n d i n g t o t h i c k n e s s f l u c t u a t i o n s w i t h i n e a c h l a y e r . However, a t t h i s s t a g e , i t does n o t seem p o s s i b l e t o d e t e r m i n e which p r o c e s s e s a r e r e s p o n s i b l e f o r t h i s low-energy t a i l .

PHOTON ENERGY hv ( m e V )

F i g u r e 4 : Luminescence s p e c t r a o b s e r v e d i n an I d s - G a S b s u p e r l a t t i c e a t d i f f e r e n t t e m p e r a t u r e s . ( A f t e r Ref. 1 4 ) .

I11 - MAGNETO-ABSORPTION EXPERIMENTS

At f i r s t , i t i s i m p o r t a n t t o n o t e t h a t E s a k i e t a l . have s u g g e s t e d 13,131 t h a t a semiconductor-semimetal t r a n s i t i o n s h o u l d t a k e p!ace i n InAs-GaSb s u p e r l a t t i c e s when t h e l a y e r t h i c k n e z s becomes of t h e o r d e r of 100 A. When t h e l a y e r t h i c k n e s s i s s m a l l e r t h a n 100 A ( F i g . 2 ( a ) ) , t h e El subband, mainly l o c a l i z e d i n t h e InAs l a y e r s , i s a t h i g h e r energy t h a n t h e H1 subband, which i s c o n f i n e d i n t h e GaSb l a y e r s . T h e r e f o r e , t h e s u p e r l a t t i c e band g a p , Eo = El - H i , i s p o s i t i v e and c o r r e s p o n d s t o a s e m i c o n d u c t i n g s i t u a t i o n which was s t u d i e d i n t h e p r e v i o u s s e c t i o n . When t h e l a y e r t h i c k n e s s i s i n c r e a s e d , El i s lowered and Hi i s r a i s e d , i n f i r s t a p g r o x i m a t i o n a s i n a s i m p l e quantum w e l l . When t h e l a y e r t h i c k e n s s i s l a r g e r t h a n 100 A a b o u t , H I i s a t h i g h e r e n e r g y t h a n El and El - HI i s n e g a t i v e ( F i g . 2 ( b ) ) , t h e c o r r e s p o n d i n g

s t r u c t u r e b e i n g s e m i m e t a l l i c . I n s u c h a s i m p l e model 1191, e l e c t r o n s t r a n s f e r from H1 t o E l , namely from GaSb t o InAs l a y e r s , and t h e Fermi l e v e l , EF, l i e s between E l and Hi, c l o s e t o H1 b e c a u s e of t h e l a r g e heavy-hole mass.

I n t e r e s t i n g i n f o r m a t i o n s h a v e been o b t a i n e d from f a r - i n f r a r e d (FIR) magneto- a b s o r p t i o n e x p e r i m e n t s 120-221 performed i n MBE-grown InAs-GaSb s u p e r l a t t i c e s (S1, S2) whose InAs and GaSb t h i c k n e s s e s a r e g i v e n i n T a b l e I. I n t h e s e e x p e r i m e n t s t h e f a r - i n f r a r e d t r a n s m i s s i o n o f t h e s e samples was s t u d i e d a t f i x e d p h o t o n e n e r g i e s a s a f u n c t i o n of t h e m a g n e t i c f i e l d B, which was p e r p e n d i c u l a r t o t h e p l a n e of t h e l a y e r s , t h e i n f r a r e d r a d i a t i o n b e i n g n e a r normal i n c i d e n c e t o t h e l a y e r s . F i g u r e 5 g i v e s t y p i c a l t r a n s m i s s i o n s p e c t r a i n sample S1, showing t h a t t h e t r a n s m i s s i o n s i g n a l v e r s u s B e x h i b i t s pronounced o s c i l l a t i o n s . I n F i g . 6 a r e shown, a s a f u n c t i o n of B, t h e i n f r a r e d photon e n e r g y p o s i t i o n s of t h e t r a n s m i s s i o n minima ( i . e . absorp-

t i o n maxima) o b t a i n e d from t h e o b s e r v e d o s c i l l a t i o n s ( F i g . 5 )

F i g u r e 5 : T r a n s m i s s i o n s p e c t r a v e r s u s B f o r d i f f e r e n t i n f r a r e d w a v e l e n g t h s ( A f t e r Ref. 2 0 ) .

As c a n b e deduced from s i m p l e t h e o r e t i c a l a n a l y s e s 120-221, t h e p h o t o n e n e r g i e s , h v , a t which t h e s e minima o c c u r depend a l m o s t l i n e a r l y on B. E x t r a p o l a t i o n t o B = 0 r e s u l t s i n hv = 0 f o r t h e l i n e n o t e d C R , hv = - 39 meV f o r t h e l i n e s l a b e l l e d 1 , 2 , 3 . . . , and hv = - 16 meV f o r t h e l i n e n o t e d 0'. The CR l i n e ( F i g . 6 ) i s a t t r i b u t e d t o e l e c t r o n c y c l o t r o n r e s o n a n c e , i . e . t o t r a n s i t i o n s from t h e l a s t f i l l e d t o t h e f i r s t empty Landau l e v e l o f E l . The c u r v e s c o n v e r g i n g t o hv = - 39 meV a r e a s s i g n e d t o i n t e r b a n d t r a n s i t i o n s from H1 t o El Landau l e v e l s a t k, = 0. The l i n e 0 ' i s a s s o c i a - t e d t o s i m i l a r i n t e r b a n d t r a n s i t i o n s o c c u r i n g a t t h e s u p e r l a t t i c e B r i l l o u i n zone boundary i . e . a t k, = n / d , where d i s t h e s u p e r l a t t i c e p e r i o d i c i t y . These i n t e r b a n d t r a n s i t i o n s a r e r e p r e s e n t e d i n F i g . 7 ( a ) which g i v e s t h e band s t r u c t u r e o f a s u p e r - l a t t i c e a l o n g k, w i t h and w i t h o u t m a g n e t i c f i e l d i n t h e s e m i m e t a l l i c model. As mentioned p r e v i o u s l y , t h e El s u b b a n d , which i s below H I , h a s a f i n i t e w i d t h AEl , b u t t h a t o f HI i s e s s e n t i a l l y z e r o . Under a m a g n e t i c f i e l d , El and H I e x h i b i t b o t h a s e r i e s o f Landau l e v e l s moving upward and downward, r e s p e c t i v e l y , when B i s i n c r e a - s e d . I t i s c l e a r t h a t e a c h Landau l e v e l o f H1 s h o u l d g i v e r i s e t o a s i n g l e peak i n t h e d e n s i t y of s t a t e s ( F i g . 7 ( b ) ) . However, El i s f l a t a t k, = 0 and k Z = n l d , s o t h a t t h e r e s h o u l d b e two p e a k s i n t h e c o r r e s p o n d i n g d e n s i t y o f s t a t e s f o r each Landau l e v e l . I f t h e s e l e c t i o n r u l e s f o r i n t e r b a n d t r a n s i t i o n s a r e t a k e n t o be Ak, = 0 and AN = 0 , where N i s t h e Landau i n d e x , two s e t s o f t r a n s i t i o n s can b e e x p e c t e d , a t k, = 0 and .rr/d, r e s p e c t i v e l y , a s s c h e m a t i z e d i n F i g . 7 ( a ) , where t h e i n t e r b a n d t r a n s i t i o n s a t k, = 0 a r e n o t e d 1 , 2 and t h o s e o c c u r i n g a t k z = n l d a r e l a b e l l e d 0 ' , 1 ' .

The Landau l e v e l s and H ] , N o f El and H i , r e s p e c t i v e l y , can be c a l c u l a t e d u s i n g a s i m p l e t h e o r e t i c a l model /19-221. To o b t a i n El , N , t h e InAs c o n d u c t i o n band non- p a r a b o l i c i t y i s t a k e n i n t o a c c o u n t on t h e b a s i s o f t h e s i m p l i f i e d v e r s i o n o f t h e Kane model 119-221, l e a d i n g t o t h e f o l l o w i n g r e l a t i o n :

F i g u r e 6 : P o s i t i o n of t h e t r a n s m i s s i o n minima a s a f u n c t i o n of t h e i n f r a r e d photon energy and B (+,e). The s o l i d l i n e s correspond t o t h e o r e t i c a l f i t s a s d e s c r i b e d i n t h e t e x t . The curves n o t e d 1 , 2

...

where Eg i s t h e band gap of bulk InAs and i s e q u a l / 5 / t o 410 meV. DN i s given by :

Here wc = e ~ / m , * i s t h e e l e c t r o n c y c l o t r o n frequency i n bulk InAs, m t b e i n g i t s band edge mass e q u a l / 5 / t o 0.023 mo. B e s i d e s , a l l t h e e n e r g i e s a r e measured from t h e conduction band e d g ~ o f bulk InAs. Furthermore, HI ,N = H I - (N + 112) Muv, w i t h o, = e ~ / m $ where m, = 0.33 mo i s t h e GaSb heavy-hole e f f e c t i v e mass 151.

For CR t r a n s i t i o n s , hv = El ~ + 1 - E ~ , N , N b e i n g such t h a t EF i s between E ~ , N and El , N + l . For i n t e r b a n d t r a n s i t i o n s a t k, = 0 , hv = E l N - HI , N with t h e p r e v i o u s s e l e c t i o n r u l e s . F i t s of t h e experimental d a t a t o t h i s simple model a r e p r e s e n t e d i n F i g . 6 and g i v e t h e v a l u e s of El and H 1 a t B = 0 which a r e l i s t e d i n Table*l f o r samples S1 and S2. Also given i n Table 1 i s t h e s u p e r l a t t i c e e l e c t r o n mass m which has been determined from t h e CR d a t a . I t i s c l e a r t h a t m * i s l a r g e r than t h e band edge mass of bulk InAs, and i t has been shown 1201 t h a t t h i s i s due t o t h e InAs c o n d u c t i o n band n o n - p a r a b o l i c i t y . This demonstrates t h a t e l e c t r o n s a r e a c t u a l l y c o n f i n e d i n t h e InAs l a y e r s . I n a d d i t i o n , i t should be noted t h a t El - Hi i s n e g a t i - v e , a s expected i n a s e m i m e t a l l i c s i t u a t i o n . Using t h e same model, t h e i n t e r b a n d t r a n s i t i o n s a t k, = ~ r / d can be a l s o c a l c u l a t e d , r e p l a c i n g E l by El + AE1 i n Eq.2.

I n F i g . 6 a r e p r e s e n t e d t h e o r e t i c a l f i t s of t h e d a t a f o r N = 0 ' . They y i e l d AE1 a t B = 0 whose v a l u e , o b t a i n e d 121,221 from t h e s e s t u d i e s , i s given i n Table 1 f o r b o t h samples. Table 1 g i v e s a l s o t h e v a l u e s of E l , El and AE1 c a l c u l a t e d by t h e LCAO method /13,15/ showing t h a t t h e 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 u l t s compare favora- b l y i n b o t h samples.

F i g u r e 7 : ( a ) S c h e m a t i c band s t r u c t u r e o f a s e m i m e t a l l i c InAs-GaSb s u p e r l a t t i c e a l o n g kZ

.

T a b l e 1 : T h i c k n e s s of t h e I d s ( d l ) and GaSb (d2) l a y e r s f o r samples S 1 and S2.

The e x p e r i m e n t a l * a n d t h e o r e t i c a l v a l u e s of E l , H i and AE1, and t h e measured e l e c t r o n c y c l o t r o n mass m a r e a l s o shown h e r e .

The o b s e r v a t i o n o f a n e g a t i v e e n e r g y gap i s c o n s i s t e n t w i t h t h e proposed semi- m e t a l l i c n a t u r e o f t h e s e s u p e r l a t t i c e s 13,131, and t h e s e s t u d i e s h a v e p r o v i d e d t h e

f i r s t e x p e r i m e n t a l d e t e r m i n a t i o n i n t h e s e s t r u c t u r e s o f t h e subband e n e r g i e s El and Hi, and a l s o of AE1. I n a d d i t i o n , t h e measurement o f AE1 d e m o n s t r a t e s t h a t t h e e l e c t r o n s y s t e m i n s u c h InAs-GaSb s u p e r l a t t i c e s e x h i b i t s a t h r e e - d i m e n s i o n a l c h a r a c - t e r , d e v i a t i n g t h e r e f o r e from t h e s t r i c t t w o - d i m e n s i o n a l i t y c o r r e s p o n d i n g t o un- c o u p l e d quantum w e l l s . F i n a l l y , i t i s p e r h a p s w o r t h m e n t i o n i n g t h a t s i m i l a r e x p e r i - ments done i n s e m i c o n d u c t i n g InAs-GaSb s u p e r l a t t i c e s e x h i b i t o n l y t r a n s i t i o n s due t o c y c l o t r o n resonance.

S i m i l a r f a r - i n f r a r e d magneto-absorption e x p e r i m e n t s have b e e n done 1 4 1 r e c e n t l y a t 1.6 K i n a M3E grown HgTe-CdTe s u p e r l a t t i c e c o n g i s t i n g of 200 a l t e r n a t e l a y e r s of HgTe and CdTe whose t h i c k n e s s e s a r e 180 and 44 A, r e s p e c t i v e l y . The d a t a have a l s o been i n t e r p r e t e d i n terms of i n t e r b a n d t r a n s i t i o n s from v a l e n c e t o c o n d u c t i o n sub-

b a n d s , and from t h e s e i n v e s t i g a t i o n s i t h a s b e e n p o s s i b l e t o deduce t h e s u p e r - l a t t i c e band s t r u c t u r e a l o n g t h e growth a x i s . T h i s band s t r u c t u r e i s shown i n F i g . 8 ( b ) , t h a t o f b u l k HgTe and CdTe b e i n g r e p r e s e n t e d i n F i g . 8 ( a ) . These s t u d i e s show, i n p a r t i c u l a r , t h a t t h e c o n s i d e r e d s t r u c t u r e i s a q u a s i - z e r o e n e r g y gap semi- c o n d u c t o r , and p r o v i d e t h e f i r s t d e t e r m i n a t i o n o f t h e o f f s e t A between t h e HgTe and CdTe v a l e n c e bands which i s % 40 meV.

' 8

HgTe

F i g u r e 8 : ( a ) Band s t r u c t u r e o f b u l k HgTe and CdTe.

( b ) Band s t r u c t u r e a l o n g t h e growth a x i s o f t h e HgTe-CdTe s u p e r l a t t i c e i n v e s t i g a t e d i n Ref.4. E l , HH1, and h l a r e t h e ground c o n d u c t i o n , heavy-hole and l i g h t - h o l e s u b b a n d s . LH1 i s a l i g h t - h o l e subband d e r i v e d from t h e rth HgTe s t a t e s . ( A f t e r Ref. 4 ) .

I V - CONCLUSION

T h i s s h o r t r e v i e w i s c e r t a i n l y n o t e x h a u s t i v e , b u t d e s c r i b e s b r i e f l y some o p t i c a l s t u d i e s which have b e e n h e l p f u l t o u n d e r s t a n d t h e e l e c t r o n i c p r o p e r t i e s o f semi- c o n d u c t o r s u p e r l a t t i c e s . By c h o o s i n g t h e h o s t s e m i c o n d u c t o r s and t h e l a y e r t h i c k - n e s s e s , i t i s c l e a r t h a t one can grow a t a i l o r - m a d e m a t e r i a l w i t h a band s t r u c t u r e q u i t e d i f f e r e n t from t h a t o f t h e b a s i s s e m i c o n d u c t o r s . One can c e r t a i n l y c o n s i d e r t h a t t h e s e s y s t e m s , t o g e t h e r w i t h modulation-doped h e t e r o j u n c t i o n s , c o n s t i t u t e a new c l a s s o f two-dimensional s y s t e m s which h a s opened up a v e r y a c t i v e and impor- t a n t f i e l d o f r e s e a r c h i n s e m i c o n d u c t o r p h y s i c s .

ACKNOWLEDGEMENTS

The a u t h o r would l i k e t o t h a n k L.L. Chang and L. E s a k i from I B M and a l s o

J.P. F a u r i e and A . M i l l i o n from LIR-LET1 ( G r e n o b l e ) f o r h e l p f u l d i s c u s s i o n s and t h e s u p p l y o f t h e InAs-GaSb (IBM) and HgTe-CdTe (LIR-LETI) s u p e r l a t t i c e s i n v e s t i g a t e d i n h i s l a b o r a t o r y . He w i s h e s a l s o t o t h a n k h i s c o l l e a g u e s , G. B a s t a r d , Y . G u l d n e r , J . P . V i e r e n and P . V o i s i n who p a r t i c i p a t e d v e r y c l o s e l y t o t h e s t u d i e s performed on t h e s e s t r u c t u r e s a t t h e Groupe de P h y s i q u e d e s S o l i d e s de 1'E.N.S. He w a n t s , a l s o t o acknowledge t h e e f f i c i e n t and k i n d c o l l a b o r a t i o n o f J . C . Maan from t h e MPI i n Grenoble where h i g h - m a g n e t i c f i e l d e x p e r i m e n t s on InAs-GaSb s u p e r l a t t i c e s were done.

REFERENCES

* ~ a b o r a t o i r e a s s o c i 6 a u C.N. R. S.

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