STARK EFFECT IN QUANTUM WELLS : RAMAN SCATTERING BY INTERSUBBAND TRANSITIONS

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STARK EFFECT IN QUANTUM WELLS : RAMAN SCATTERING BY INTERSUBBAND TRANSITIONS

K. Bajema, R. Merlin, F.-Y. Juang, S.-C. Hong, J. Singh, P. Bhattacharya

To cite this version:

K. Bajema, R. Merlin, F.-Y. Juang, S.-C. Hong, J. Singh, et al.. STARK EFFECT IN QUANTUM

WELLS : RAMAN SCATTERING BY INTERSUBBAND TRANSITIONS. Journal de Physique Col-

loques, 1987, 48 (C5), pp.C5-179-C5-182. �10.1051/jphyscol:1987535�. �jpa-00226739�

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STARK EFFECT IN QUANTUM WELLS : RAMAN SCATTERING BY INTERSUBBAND TRANSITIONS

K. BAJEMA, R. MERLIN, F.-Y. JUANG*, S.-C. HONG*, J. SINGH* and P.K. BHATTACHARYA*

Department of Physics, The University of Michigan. Ann Arbor, MI 48109-1120, U.S.A.

* ~ e p a r t m e n t

of

Electrical Engineering and Computer Science, The University of Michigan, Ann Arbor, MI 48109-2122, U.S.A.

N o u s a v o n s 6 t u d i e l l e f f e t d l u n c h a m p e l e c t r i q u e s u r l a t r a n s i t i o n i n t e r - s o u s - b a n d e c o + c , , d a n s u n p u i t s q u a n t i q u e G a A s - A 1 , , G a o 7 A s d e 264 A , p a r spectrometric R a m a n . L e s r e s u l t a t s e x p e r i m e n t a u x s o n t e n t r 6 s b o n a c c o r d a v e c l e s p r g d i c t i o n s t h e o r i q u e s . L a l a r g e u r d e s t r a n - s i t i o n s c o + c , e s t 3 p e u p r S s i n d e p e n d a n t e d u c h a m p b l e c t r i q u e , c o n - t r a i r e m e n t

a

1 1 6 1 a r g i s s e m e n t p r o n o n c e o b s e r v e p a r d e s r e s o n a n c e s b x c i - t o n i q u e s . C e p h 6 n o m S n e e s t a t t r i b u 6 3 u n e f f e t d e d e s o r d r e s t r u c - t u r e l .

T h e e l e c t r i c - f i e l d d e p e n d e n c e o f c,+c, i n t e r s u b b a n d t r a n s i t i o n s o f p h o t o e x c i t e d e l e c t r o n s h a s b e e n s t u d i e d i n a 264 A G a A s - A l O , G a o 7 A s q u a n t u m - w e l l s t r u c t u r e u s i n g R a m a n s p e c t r o s c o p y . E x p e r i m e n t a l r e s u l t s f o r t h e S t a r k s h i f t s a r e in v e r y g o o d a g r e e m e n t w i t h t h e o r e t i c a l p r e - d i c t i o n s . I n c o n t r a s t t o t h e e n h a n c e . d b r o a d e n i n g s h o w n b y e x c i t o n r e s o n a n c e s , t h e w i d t h o f c o + c , i s n e a r l y i n d e p e n d e n t o f t h e f i e l d . T h i s f e a t u r e i s a t t r i b u t e d t a e f f e c t s o f s t r u c t u r a l d i s o r d e r .

S t u d i e s o f t h e e f f e c t o f e l e c t r i c f i e l d s p e r p e n d i c u l a r t o t h e l a y e r s o n 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 q u a n t u m - w e l l s t r u c t u r e s ( Q W S 1 s ) h a v e r e c e n t l y a t t r a c t e d m u c h a t t e n t i o n . ' - 7 T h e i n t e r e s t i s m o t i v a t e d i n p a r t b y d e v i c e a p p l i c a t i o n s (e.g., h i g h - s p e e d o p t i c a l m o d u l a t o r s ) * w h i c h a r k b a s e d o n t h e p r o n o u n c e d s h i f t s o f h e a v y - h o l e e x c i t o n r e s o - n a n c e s i n d u c e d b y t h e f i e l d . E x p e r i m e n t a l l y , t h e S t a r k e f f e c t h a s b e e n i n v e s t i g a t e d i n G ~ A S - A ~ , G ~ ~ - ~ A S Q W S ' s b y u s e o f o p t i c a l a b s o r p t i o n , * p h o t ~ c u r r e n t , ~ e x c i t a t i o n s p e c t r o ~ c o p y , ~ a n d p h o t o l u m i n e s c e n c e 3 t e c h - n i q u e s . I n t h i s w o r k , w e r e p o r t a R a m a n s c a t t e r i n g ( R S ) s t u d y o f t h e e l e c t r i c - f i e l d d e p e n d e n c e o f c,+c, i n t e r s u b b a n d t r a n s i t i o n s o f p h o t o - e x c i t e d e l e c t r o n s [c,(c,) d e n o t e s t h e l o w e s t ( f i r s t - e x c i t e d ) w e l l s t a t e a s s o c i a t e d w i t h t h e c o n d u c t i o n band]. O u r r e . s u l t s a r e r e l e v a n t t o r e c e n t t h e o r e t i c a l w o r k s o n i n t e r s u b b a n d o p t i c a l a b s o r p t i o n s a n d o n t h e p o s s i b i l i t y o f u s i n g t h e s e e x c i t a t i o n s a s t h e b a s e s f o r f i e l d - t u n a b l e f a r - i n f r a r e d p h o t o d e t e c t o r s . S t a r k s h i f t s d e r i v e d f r o m o u r m e a s u r e m e n t s a r e i n v e r y g o o d a g r e e m e n t w i t h t h e o r e t i c a l c a l c u l a t i o n s . T h e c o + c , R a m a n p e a k s h o w s a n i n c r e a s e i n i n t e n s i t y w i t h a p p l i e d f i e l d d u e t o b r o k e n i n v e r s i o n s y m m e t r y , a n d a n e a r l y f i e l d - i n d e p e n d e n t

w i d t h . T h e l a t t e r f i n d i n g d i f f e r s f r o m t h e b e h a v i o r s h o w n b y e x c i t o n r e s o n a n c e s e x h i b i t i n g f i e l d - e n h a n c e d b r o a d e n i n g . ' D i s o r d e r o r i g i n a t e d i n s t r u c t u r a l d e f e c t s i s s h o w n t o a c c o u n t f o r t h i s d i f f e r e n c e .

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987535

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C5-180 JOURNAL DE PHYSIQUE

T h e sample used in our experiments w a s grown by molecular beam epitaxy on a Si-doped ( 0 0 1 ) G a A s substrate in the following sequence:

0.3-um Si-doped ( n = 2 ~ 1 0 ' ~ c m - ~ ) GaAs buffer l a y e r , 0.19-pm Al,,Ga,,As, thirty uncoupled G a A s wells with thickness L=264A (198-A-thick

Al,,Ga,,As barriers), and 0.19pm AlO3Ga,,As clad layer; unless i n d i c a - t e d , the layers are nominally undoped. A semitransparent Schottky contact w a s formed by evaporating Au t o build a 150-8-thick film on top of the sample. Raman spectra were recorded in the z ( x f , x ' ) z and z ( x f , y ' ) 2 backscattering configurations where z is normal t o the layers and x', y' are along [llO] and [liO] directions. The laser energy w a s tuned t o resonate with HH5. The estimated power density is P = 6 - 1 0 W C ~ - ~ .

Figure 1 shows R S data of the Q W S for different external d.c.

voltages

Vext.

The peak at 18.9meV ( V e x t = O ) is due to c,+c, intersubband transitions of electrons. A calculation using the band-gap d i s - continuities determined by Miller e t a1.9 predicts c,+cl=18.4meV. In

1 1 1 11 1 1 1 1 1 1 11 1 1 1 1 1 1

10 15 20 25

RAMAN SHIFT (meV)

Fig. 1:

Raman spectra of the QWS showing tahe c,+c, intersubband transition at different external voltages;

w =1.685eV is in the vicinity of the

~ k 5 exciton. T h e inset shows a s c h e - matic energy diagram ( n o t t o s c a l e )

the range of V e X t 1 s investigated, -3V1VextS0.9V, the FWHM (full-width at half m a x i m u m ) of c,+c,remained nearly constant at z3meV. With i n - creasing

I v e X t l ?

the intersubband peak growths in intensity and shifts t o higher e n e r g i e s , except for OIVe,

.

Since the shift and intensity must be even functions of the e?:E;:rc f i e l d , it f o l l o w s that -0.2V is the built-in voltage of the structure.

The observation of the c,+c, transition indicates t h a t the lowest subband in the s a m p l e is partially occupied. T h i s is due t o p h o t o e x c i - t a t i o n l o , a s revealed by results on the P-dependence of the scattering ( n o t shown). A c r u d e estimate based on parameters from the literature' gives a steady-state electron concentration 0 - 2 x l O ~ c m - ~ ( P = l O W c m - * ) .

In the range o f fields studied ( s e e below), the electron-hole recombination t i m e does not vary e n o u g h 3 a s t o explain the increase in intensity shown by c,+c, ( w h i c h might be attributed t o a larger

steady-state population). At z e r o f i e l d , c,fct is strictly forbidden in R S because the states have different parities. T h i s indicates t h a t the scattering enhancement results from parity-mixing due t o the field a s in field-induced absorption by forbidden excitons.'

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a n d c a l c u l a t e d c,+c, S t a r k s h i f t s .

ELECTRIC FIELD (kVcm-1)

T h e V e x t - d e p e n d e n c e o f t h e s h i f t o f c o + c l is s h o w n in Fig.

2 ? t o g e t h e r w i t h r e s u l t s o f c a l c u l a t i o n s . T h e o r y a n d e x p e r i m e n t a r e ~ n v e r y g o o d a g r e e m e n t if a l e n g t h o f 2.7um is u s e d t o c o n v e r t v o l t a g e s i n t o f i e l d s . In t h e c a l c u l a t i o n s , t h e e i g e n e n e r g i e s o f Q u a s i b o u n d e l e c t r o n s t a t e s w e r e o b t a i n e d n u m e r i c a l l y . W e u s e d t h e p r o c e d u r e d e - s c r i b e d in Ref. 5 t o a v o i d i m a g i n a r y c o r r e c t i o n s t o t h e e n e r g y d u e t o t u n n e l i n g , w h i c h a r e n e g l i g i b l e in o u r c a s e .

T h e o b s e r v a t i o n o f a n e a r l y f i e l d - i n d e p e n d e n t w i d t h o f c , + c l is a s i g n i f i c a n t f e a t u r e o f o u r r e s u l t s . T h i s b e h a v i o r d i f f e r s s i g n i f i c a n t - l y f r o m t h e reported' f i e l d - i n d u c e d e n h a n c e d b r o a d e n i n g o f e x c i t o n r e s o n a n c e s w h i c h is m a i n l y d e t e r m i n e d b y i n t e r f a c e r o u g h n e s s a n d i n - t e r - w e l l s i z e fluctuation^.^ S t r u c t u r a l d e f e c t s l e a d t o a c l e a r d i f - f e r e n t i a t i o n b e t w e e n t h e f i e l d - d e p e n d e n t w i d t h s o f e x c i t o n s a n d i n t e r - s u b b a n d t r a n s i t i o n s . T h e a r g u m e n t i s s i m p l e ; b r o a d e n i n g d u e t o f l u c - t u a t i o n s in t h e a v e r a g e w e l l - w i d t h L a n d a l s o d u e t o i s l a n d - r o u g h n e s s u n d e r c o n d i t i o n s o f l o c a l i z a t i o n l l is a p p r o x i m a t e l y g i v e n b y

r ( E ) = [ a R ( E ) / a L ] G L , w h e r e E i s t h e f i e l d a n d R i s t h e e n e r g y o f t h e c o r r e s p o n d i n g e x c i t a t i o n . F o r e x c i t o n s s

r

i n c r e a s e s w i t h E w h i l e it d e c r e a s e s f o r i n t e r s u b b a n d t r a n s i t i o n s . C a l c u l a t i o n s u s i n g t h e p a r a - m e t e r s o f o u r s t r u c t u r e a n d 6 L = 2 . 8 3 R ( o n e m o n o l a y e r ) g i v e r=0.4meV ( E = O ) a n d r = 0 . 3 m e V ( E = 1 2 k V c m - I ) . S i n c e 6 L d o e s n o t c o m m o n l y e x c e e d 3 - 4 m o n o l a y e r s , l l it is c l e a r t h a t o t h e r m e c h a n i s m s ( s u c h a s i m p u r i t y s c a t t e r i n g ) c o n t r i b u t e t o t h e c o + c , w i d t h .

T h i s w o r k w a s s u p p o r t e d b y t h e L i g h t w a v e T e c h n o l o g y P r o g r a m , N a t i o n a l S c i e n c e F o u n d a t i o n G r a n t No. E C E 8 6 - 1 0 8 0 3 .

R E F E R E N C E S

1. E.E. M e n d e z , G. B a s t a r d , L.L. C h a n g , L. E s a k i , H. M o r k o c , a n d R.

F i s c h e r , P h y s . Rev. B 2 6 , 7 1 0 1 ( 1 9 8 2 ) ; G. B a s t a r d , E.E. M e n d e z , L.L. C h a n g , a n d L. E s a k i , P h y s . Rev. B 2 8 , 3 2 4 1 ( 1 9 8 3 ) .

2. D.A.B. M i l l e r , D.S. C h e m l a , T.C. D a m e n , A.C. G o s s a r d , W. W i e g m a n n , T.H. W o o d , a n d C.A. B u r r u s , P h y s . R e v . L e t t . 5 3 , 2 1 7 3 ( 1 9 8 4 ) . 3. H.-J. P o l l a n d , L. S c h u l t h e i s , H. K u h l , E.O. G o b e l , a n d C.W. T u ,

P h y s . Rev. Lett. 55, 2 6 1 0 ( 1 9 8 5 ) .

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( 1 9 8 6 )

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C5-182 JOURNAL DE PHYSIQUE

7. L. ~ i G a , R.T. C o l l i n s , E.E. M e n d e z , a n d W.I. W a n g , P h y s . Rev.

L e t t . 5 8 , 8 3 2 ( 1 9 8 7 ) .

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L e t t . 46, 1 3 4 1 ( 1 9 8 1 ) .

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