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EXCITONS IN SMALL PERIOD GaAs/GaAlAs SUPERLATTICES
B. Lambert, A. Chomette, F. Clerot, B. Deveaud, A. Regreny, Gérald Bastard
To cite this version:
B. Lambert, A. Chomette, F. Clerot, B. Deveaud, A. Regreny, et al.. EXCITONS IN SMALL PERIOD GaAs/GaAlAs SUPERLATTICES. Journal de Physique Colloques, 1987, 48 (C5), pp.C5-533-C5-536.
�10.1051/jphyscol:19875114�. �jpa-00226697�
EXCITONS IN SMALL PERIOD GaAs/GaAlAs SUPERLATTICES
B. LAMBERT, A. CHOMETTE, F. CLEROT, B. DEVEAUD, A. REGRENY and G.
BASTARD*Centre National dlEtudes des T6lecommunications, LAB/ICM/MPA, 22300 Lannion, France
' ~ r o u p e de Physique des Solides d e 1'Ecole Normale ~ u ~ & r i e u r e ~ , 24, Rue Lhomond, F-75231 Paris Cedex 05, France
L16nergie de liaison de l'exciton dans des super-rCseaux GaAs-GaAlAs de petites periodes est dCterminCe au moyen de l'excitation de la photo-luminescence et de la photoluminescence en fonction de la temperature. L16nergie de liaison de l'exciton lie au trou lourd decrort avec la periode du super r6seau. Les rCsultats expgrimen- taux sont en accord avec un calcul variationnel.
Abstract
We report the optical determination of exciton binding energies in small period GaAs/Ga0.,A10.3As superlattices by means of low temperature photoluminescence exci- tation spectroscopy and photoluminescence spectroscopy as a function of temperature.
The heavy-hole exciton binding energy decreases with superlattice period. Our expe- rimental findings are in agreement with a variational calculation.
Optical properties of semiconductor quantum wells (QW) are now increasingly documented [l-91. Due to their quasi-two-dimensional nature, excitons in QWs of GaAs sandwiched between G a ~ ~ - x ) A l x A s layers have binding energies (Bls) greater than bulk ones [l- and give rise to excitonic photoluminescence lines up to room temperatures [l, 5-7
.
When the width of the GaAlAs barriers decreases, neighbouring wells become electronically coupled and the electron and hole gases progressively loose their 2-D character. They are able to move in the direction perpendicular to the layers [l01 and their eigenenergies form minibands. In these structures, called small period superlattices (SL), low temperature luminescence spectra reveal excitonic lines [l11 corresponding to heavy and light hole excitons.
In this paper we report the results of photoluminescence (PL) and photoluminescence excitation (PLE) spectroscopies on several small period GaAs/ GaAlAs superlattices with near equal well and barrier thicknesses and compare the binding energies thus obtained for heavy-hole excitons with the results of a variational calculation.
Starting from isolated QW situation where the exciton is confined in the wells, the heavy-hole exciton binding energy is found to decrease with decreasing superlattice period and to tend to about
4
meV when the SL period tends to zero. This limit is quite close to the value of the exciton binding energy in bulk GaAs.The samples studied here were all grown in a Riber molecular beam epitaxy system.
They consist of about 1 p of GaAs/Ga(l-x)AlxAs superlattice grown on a 0.7-pm-thick GaAs buffer. The aluminium concentration X is kept around 0.3. The well and barrier widths are determined by x-ray diffraction. The PL and PLE spectra are recorded with the samples merged in super-fluid Helium at about 2 K. The excitation
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19875114
C5-5 34 JOURNAL DE PHYSIQUE
i s p r o v i d e d by a n argon-ion-pumped t u n a b l e (h-h), d y e l a s e r a t power d e n s i t i e s of t h e o r d e r
L, l,
oo
of l - m f r o n t 1 s p e c t r o m e t e r w/cm2. f a c e i s The c o l l e c t e d p h o t o l u m i n e s c e n c e and d e t e c t e d and a n a l y s e d w i t h from a by GaAs t h e a no L17 (IOA/IOAI p h o t o m u l t i p l i e r and a s s o c i a t e d l o c k - i n . The q u a l i t y of t h e s u p e q l a t t i c e s is w i t n e s s e d cl by t h e s h a r p n e s s of t h e low t e m p e r a t u r e p h o t o l u m i n e s c e n c e l i n e s . For a l l t h e sample l i s t e d t h e f u l l w i d t h a t h a l f maximum of t h e low t e m p e r a t u r e PL l i n e i s s m a l l e r t h a n 5 meV and t h e S t o k e s s h i f t of t h i s l i n eA I A ) w i t h r e s p e c t t o t h e f i r s t peak of t h e
e x c i t a t i o n s p e c t r u m i s s m a l l e r t h a n 2.5 meV. T h i s S t o k e s s h i f t c o r r e s p o n d s e i t h e r Ih-h), 2 s E t o t h e one-monolayer i n t e r f a c e f l u c t u a t i o n s [ 1 2 J f o r t h e SLs w i t h l a r g e r p e r i o d s o r t o (l-h),
\
1 1 7 ~ / 2 0 ~ ) a b u l k - l i k e b e h a v i o u r i n t h e c a s e of t h e SLs w i t h v e r y s m a l l p e r i o d s , i n which t h e bl m a i n PL p e a k i s d u e t o some bounde x c i t o n s .
lf~O The low-temperature e x c i t a t i o n s p e c t r a of
A [ A I o u r samples e x h i b i t two v e r y d i f f e r e n t
k i n d s of s h a p e :
( i ) The PLE s p e c t r u m of a s u p e f l a t t i c e w i t h (h- 1, no 223 a l a r g e enough p e r i o d ( d ) 100 A) l o o k s l i k e
L;
t h e s p e c t r u m of a MQW [ l - 9 1 ( s e e F i g . l a ) and t h u s a l l o w s a d i r e c t d e t e r m i n a t i o n of Bls- Two w e l l r e s o l v e d peaks c o r r e s p o n d t o t h e h e a v y - h o l e a n d l i g h t - h o l e 1s e x c i t o n s . Between t h e s e two peaks a s t e p c a n be s e e n which is more o r l e s s w e l l r e s o l v e d depending on t h e sample and can be a t t r i b u t e d e i t h e r t o t h e e x c i t e d 2 s s t a t e o f t h e heavy-hole e x c i t o n [ g ] o r t o t h e o n s e t of t h e continuum [ l , 131. However assuming t h a t t h e i n t e r m e d i a t e s t r u c t u r e i sl~pO
t h e o n s e t of t h e continuum and t a k i n g f o rAIAI,
I I t h e 1s b i n d i n g e n e r g y Bls t h e d i s t a n c e between t h i s s t e p and t h e maximum of t h e F i g u r e 1 : Photoluminescence e x c i t a - heavy-hole peak i n v o l v e s a b o u t 1 meV of t i o n s p e c t r a of t h r e e samples. The u n c e r t a i n t y on Bls s i n c e t h e 2 s b i n d i n g d e t e c t i o n e n e r g y is s e t i n t h e low- e n e r g y (Bzs) h a s a v a l u e of a b o u t 1 meV e n e r g y t a i l of t h e heavy-hole e x c i t o n i n t h e 3-D c a s e (114 Bls) a s w e l l a s i nl i n e . t h e 2-D c a s e ( 1 / 9 B1,). T h i s p r o c e d u r e
y i e l d s a v a l u e o f B 1 , f o r a l l t h e s a m p l e s w i t h a p e r i o d g r e a t e r t h a n 50 A.
( i i ) The PLE s p e c t r a of t h e two samples w i t h t h e s m a l l e s t p e r i o d s a r e q u i t e d i f f e r e n t . Whereas t h e spectrum of sample n0417 ( F i g . l b ) s t i l l e x h i b i t s two peaks c o r r e s p o n d i n g t o t h e heavy-hole and l i g h t - h o l e e x c i t o n s , o n l y one peak, broadened on i t s high-energy s i d e , can be s e e n on t h e s p e c t r u m of sample n0447 ( F i g . l c ) .
For h i g h enough t e m p e r a t u r e s ( s a y T
>
60 K), a s a r e s u l t of t h e i o n i z a t i o n of t h e e x c i t o n , t h e n a t u r e of l u m i n e s c e n c e changes from e x c i t o n t o band-to-band recombina- t i o n and t h e maximum of t h e PL l i n e , E p ~ ( T ) , f o l l o w s t h e v a r i a t i o n of t h e GaAs gap, E G ~ A ~ (T) ; t h a t is, i f A(T) = EpL (T)-
E G ~ A ~ (T), f o r T>
60 K A(T) r e a c h e s a p l a t e a u A. BIS c a n t h u s be d e t e r m i n e d by measuring t h e e n e r g y d i f f e r e n c eWe have used t h i s p r o c e d u r e on t h e f y r samples w i t h t h e s m a l l e s t p e r i o d s . The r e s u l t s o b t a i n e d f o r samples n0342 (30 A-30
1)
and 330 ( 3 91 -
391)
a r e v e r y c l o s e t o t h e v a l u e s d e r i v e d from PLE. On samples n0447 (10 AI10 A) and 417 (17 U 2 0 A ) , Bls i s found t o be e q u a l t o 3.8 meV and 3.5 meV. The heavy-hole e x c i t o n b i n d i n g e n e r g i e s f o r a l l t h e measured samples a r e r e p o r t e d on f i g u r e 2 : when t h e s u p e r l a t t i c e p e r i o d d e c r e a s e s , t h e w e l l and b a r r i e r w i d t h s b e i n g k e p t n e a r l y e q u a l , Bls d e c r e a s e s down t o a v a l u e c l o s e t o t h e GaAs b i n d i n g energy. An i n d i c a t i o n o f t h i s t r e n d was found by p h o t o l u m i n e s c e n c e e x c i t a t i o n under magnetic f i e l d [ 1 3 ] . To u n d e r s t a n d t h e b e h a v i o u r of t h e heavy-hole e x c i t o n s i n a s u p e r l a t t i c e a s a f u n c t i o n of t h e SL p e r i o d d , we have c a l c u l a t e d t h e i r b i n d i n g e n e r g y u s i n g a v a r i a t i o n a l approach 11151. I n t h e t r i a l wave f u n c t i o n we u s e t r i a l p a r a m e t e r s : one c o r r e s p o n d s t o t h e i n - p l a n e e x c i t o n r a d i u s and t h e o t h e r is l i n k e d t o t h e z e x c i t o n r a d i u s . F i g . 2 shows t h e c a l c u l a t e d v a r i a t i o n s of t h e 1s heavy-hole e x c i t o n b i n d i n g e n e r g y a s a f u n c t i o n of t h e SL p e r i o d d when t h e w e l l and b a r r i e r w i d t h s a r e e q u a l . When t h e p e r i o d t e n d s $0 z e r o Bls t e n d s t o t h e GaAs b u l k v a l u e . Bls r e a c h e s a maximum n e a r d W 140 A and t h e n d e c r e a s e s . The l a t t e r b e h a v i o u r is t h e same a s t h a t of s i n g l e QWs. The e x p e r i m e n t a l v a l u e s a r e a l s o r e p o r t e d i n Fig. 2 and t h e i r v a r i a t i o n s upon d a r e c o r r e c t l y r e p r o d u c e d by t h e c a l c u l a t i o n s .F i g u r e 2 : C a l c u l a t e d dependence of t h e Is heavy-hole e x c i t o n b i n d i n g e n e r g y Bls ( f u l l l i n e ) a s a f u n c t i o n of t h e SL p e r i o d d f o r e q u a l w e l l and b a r r i e r t h i c k n e s s e s and a n aluminium c o n c e n t r a t i o n X = 0.3 i n t h e b a r r i e r s . The s t a r s w i t h and e r r o r b a r a r e e x p e r i m e n t a l v a l u e s .
B, ImcVl
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