MAGNETO-OPTICS IN MODULATION-DOPED QUANTUM WELLS

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MAGNETO-OPTICS IN MODULATION-DOPED QUANTUM WELLS

T. Rötger, J. Maan, P. Wyder, F. Meseguer, K. Ploog

To cite this version:

T. Rötger, J. Maan, P. Wyder, F. Meseguer, K. Ploog. MAGNETO-OPTICS IN MODULATION- DOPED QUANTUM WELLS. Journal de Physique Colloques, 1987, 48 (C5), pp.C5-389-C5-392.

�10.1051/jphyscol:1987583�. �jpa-00226787�

MAGNETO-OPTICS IN MODULATION-DOPED QUANTUM WELLS

T.

ROTGER, J. C. MAAN, P. WYDER, F. MESEGUER* and K. PLOOG' * M a x - P l a n c k - I n s t i t u t f u r F e s t k b r p e r f o r s c h u n g , H o c h f e l d -

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Les s p e c t r e s de photoluminescence e t d ' e x c i t a t i o n de p u i t s quantiques

2

modula- t i o n d e dopage t y p e n dans d e s champs magn'etiques j u s q u t & 22 T montrent que l e s d i s t a n c e s inter-sous-bandes changent de manisre p'eriodique avec l e champ. Nous montrons que ce comportement e s t d6 au t r a n s f e r t d f ' e l e c t r o n s e n t r e des sous-bandes

1

e x t e n s i o n s p a t i a l e d i f f e r e n t e , q u i modifie l e p o t e n t i e l de charge d f e s p a c e . La v a r i a t i o n d f i n t e n s i t ' e d e luminescence observ'ee e n f o n c t i o n du champ e s t 'egalement expliqu'ee p a r ce modsle.

Photoluminescence and e x c i t a t i o n s p e c t r a i n n-modulation-doped quantum w e l l s w i t h 3 occupied subbands i n magnetic f i e l d s up t o 22 T show t h a t t h e i n t e r s u b b a n d d i s t a n c e s change w i t h f i e l d i n a p e r i o d i c manner. This behaviour i s shown t o be due t o t h e t r a n s f e r of e l e c t r o n s between subbands w i t h d i f f e r e n t s p a t i a l e x t e n s i o n , t h e r e b y modifying t h e space charge p o t e n t i a l . The observed v a r i a t i o n of t h e luminescence i n t e n s i t y w i t h f i e l d i s a l s o explained by t h i s model.

I n modulation-doped quantum w e l l s ( M D Q W ' S ) [ I ] both p r o p e r t i e s of undoped quantum w e l l s ( s i z e q u a n t i z a t i o n ) a s w e l l a s t h a t of modulation-doped s i n g l e h e t e r o - j.unctions ( t r a n s p o r t p r o p e r t i e s ) a r e combined. I n r e l a t i v e l y t h i c k GaAs l a y e r s between doped GaAlAs l a y e r s a two-dimensional e l e c t r o n gas i s formed a t t h e i n t e r - f a c e s , l i k e i n s i n g l e h e t e r o j u n c t i o n s , which allows magnetotransport experiments [ 2 j . On t h e o t h e r hand, i n t h e same'samples one can perform photoluminescence measure- ments [3-71, because c o n t r a r y t o h e t e r o j u n c t i o n s t h e e l e c t r o n and h o l e wavefunctions o v e r l a p s u f f i c i e n t l y t o have a s u b s t a n t i a l o p t i c a l a b s o r p t i o n [ 8 j .

Our measurements were done on n-modulation-doped GaAs/GaAlAs m u l ~ i p l e quantum w e l l s [ 9 ] w i t h a l a r g e GaAs x e l l width (500

a ) ,

^{and a} c a r r i e r concenzration of

1.6*1012 cm2. I n t h e s e wide w e l l s , a t t h e s e d e n s i t i e s t h e subband e n e r g i e s f o r t h e lowest two subbands a r e mainly determined by t h e s t r o n g band bending and a r e l o c a l i z e d a t t h e two i n t e r f a c e s as i n a double h e t e r o j u n c t i o n .

To a v o i d t h e u s u a l l y poor q u a l i t y o f t h e " i n v e r t e d " Ga.As/GaAlAs i n t e r f a c e [ 2 ] , t h e a c t u a l samples used were s l i g h t l y asymmetric a s can be seen i n t h e i n s e t of Fig. 1. N e v e r t h e l e s s , s i n c e t h e p o t e n t i a l i s mainly determined by t h e e l e c t r o s t a - t i c s , t h e a c t u a l b a n d s t r u c t u r e i s v e r y s i m i l a r t o a symmetric w e l l [ 6 , 1 0 1 w i t h two almost d e g e n e r a t e subbands l o c a l i z e d ar, t h e i n t e r f a c e s and a t h i r d subband c e n t e r e d i n t h e w e l l .

We performed luminescence and e x c i t a t i o n measurements a t 1.7 K i n a magnetic f i e l d p e r p e n d i c u l a r t o t h e sample s u r f a c e (z-di.rection) between 0 and 22 T. For t h e luminescence, we used e x c i t a t i o n wavelengths around 1.60 eV ( s l i g n t l y above t h e bandgap of G a A s ) t o avoid e l e c t r o n h e a t i n g . A s shown i n Fig. 1 , t h e luminescence shows two main peaks: a s h a r p e r one ( A ) s i t u a t e d a t 1521 meV a t B=O, and a b r o a d e r one ( B ) a t 1506 meV. We a s s i g n peak A t o a t r a n s i t i o n between t h e e l e c t r o n subband E2 and t h e h i g h e s t hole l e v e l Ho, which i s t h e only one occupied a t low temperatures, and peak B t o one between t h e quasi-degenerate Eo and E l , and

Ho.

The h o l e l e v e l , b e i n g common f o r a l l e l e c t r o n - h o l e t r a n s i t i o n s allows us t o determine d i r e c t l y i n t e r s u b b a n d d i s t a n c e s .

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987583

C5-390 JOURNAL

DE

PHYSIQUE

With i n c r e a s i n g magnetic f i e l d , luminescence peak energy i n c r e a s e s , and one s e e s a c l e a r s p l i t t i n g o f peak A i n t o s e v e r a l Landau l e v e l s ( L L ' s ) UI, t o about 2.7 T; a t h i g h e r f i e l d s t h e luminescence comes only from t h e lowest LL, due t o t h e r m a l i z a t i o n . Furthermore t h e peak e n e r g i e s do not i n c r e a s e any more as t h e

GaAs AIAs G a A l k

1.50 1,51 1.52 1,53 I ~ ~ ~ ~ I ~ ~ ~ ~ I ~ ~ ~ ~ I ~ ~ ~ ~

0 5 1 0 1 5 20 25

E~urninescence IeV1 Mognetic field [TI

Fig. 1 : Photoluminescence s p e c t r a a t Fig. 2: S o l i d c i r c l e s : Luminescence peak T = 1 . 7 K and d i f f e r e n t mag- p o s i t i o n s a s a f u n c t i o n of magne- n e t i c f i e l d s . The p o s i t i o n s t i c f i e l d . Very weak t r a n s i t i o n s of t h e lowest e x c i t a t i o n peaks a r e i n d i c a t e d by s m a l l e r symbols.

a r e marked by arrows. The in- Open c i r c l e s : E x c i t a t i o n peaks.

s e t shows t h e p o t e n t i a l d i a - gram of t h e samples used h e r e .

c y c l o t r o n energy, a s expected ( E L w ( ~ ) = ELum(B=O)+hwc/2), but d e v i a t e from it i n a s t e p - l i k e manner, t h e s t e p s becomlng more pronounced with i n c r e a s i n g f i e l d , a s shown i n Fig. 2. The most s t r i k i n g f e a t u r e , however, i s t h a t t h e s e p a r a t i o n between t h e peaks A and B d e c r e a s e s from 1 5 meV a t B=O t o 10 meV a t about 1 7 T. I n a d d i t i o n

above t h i s f i e l d , t h e i n t e n s i t y o f peak B, which had been much l e s s t h a n A a t a l l lower magnetic f i e l d s , i n c r e a s e s s t r o n g l y and becomes 3x t h e i n t e n s i t y of A a t 20 T.

The magneto-luminescence i n t e n s i t i e s f o r peak A and B, both i n o+ and 0- c i r c u l a r p o l a r i z a t i o n , a r e shown i n Fig. 3 and compared t o t h e measured two-point magneto- r e s i s t a n c e . Except f o r B = l l t o 1 4 T , where a s p i n s p l i t t i n g seems t o manifest more s t r o n g l y i n t h e dc e l e c t r i c a l measurement, t h e luminescence i n t e n s i t i e s c l o s e l y follow t h e same behaviour a s t h e e l e c t r i c a l measurement.

We f u r t h e r m o r ~ . m e a s u r e d e x c i t a t i o n s p e c t r a (Fig. 2, open c i r c l e s ) by d e t e c t i n g both luminescence of peak A and peak B a s a f u n c t i o n of t h e e x c i t i n g r a d i a t i o n energy. T r a n s i t i o n s from HO t o a l l LL's of E2 a s w e l l as t h o s e i n v o l v i n g l i g h t h o l e s ( s i t u a t e d 'b4 meV above t h e corresponding heavy h o l e t r a n s i t i o n ) a r e observed.

A s a b s o r p t i o n can o n l y occur above EF, t h e e l e c t r o n LL involved must be t o t a l l y empty o r a t most p a r t i a l l y f i l l e d . I n t h e l a t t e r c a s e , where EF i s i n s i d e t h e LL i n q u e s t i o n , luminescence i s a l s o p o s s i b l e from t h e same l e v e l , and t h e luminescence and e x c i t a t i o n peaks should o v e r l a p w i t h i n t h e LL width, i . e . 1 t o 2 meV. This i s t h e case f o r t h e lowest e x c i t a t i o n peak and t h e luminescence from E2 0 (lowest LL, N=0, of E2) i n t h e whole magnetic f i e l d range above 2,7 T, t h e f i e l d ' a t which luminescence from h i g h e r LL's has t o t a l l y disappeared, and f o r N=l between 1 . 4 and 2.2 T. T h i s p i n n i n g of EF t o E2 0 f o r a long B i n t e r v a l i s i n c o n t r a s t with t h e u s u a l p i c t u r e of a Fermi energy &aking a more o r l e s s abrupt jump between l e v e l s a t each i n t e g e r f i l l i n g f a c t o r . This u s u a l p i c t u r e i m p l i c i t l y assumes t h a t t h e i n t e r - subband s e p a r a t i o n does not depend on t h e occupation of t h e subbands [ 11 ].

peaks A and B , both c i r c u l a r p o l a r i z a t i o n r e s o l v e d . A t low f i e l d s , t h e s o l i d l i n e shows t h e t o t a l i n t e n s i t y of peak A , t h e dashed l i n e only t h a t o r i g i - n a t i n g from LL 0.

b ) Magnetoresistance.

0 5 10 15 20 25 Magnetic field

[TI

I n o r d e r t o i n t e r p r e t t h e s e r e s u l t s , we c a l c u l a t e d t h e band bending and t h e energy l e v e l s by a simple s e l f - c o n s i s t e n t c a l c u l a t i o n by s a t i s f y i n g simultaneously P o i s s o n ' s and S c h r t i d i n g e r ' s equation. We o b t a i n two almost degenerate lower sub- band l e v e l s E o and E l , t h e corresponding charge d i s t r i b u t i o n s being concentrated on each of t h e t r i a n g u l a r w e l l s . The wave f u n c t i o n of t h e next subband, E2, spreads over t h e whole width of t h e QW.

With i n c r e a s i n g magnetic f i e l d , t h e f i l l i n g f a c t o r v=nh/eB diminishes, and a s t h e LL's of t h e d i f f e r e n t subbands c r o s s each o t h e r , t h i s causes an o s c i l l a t o r y change i n t h e r e l a t i v e occupation of eaCh subband. A s t h e charge d i s t r i b u t i o n i n z - d i r e c t i o n f o r each subband i s d i f f e r e n t , t h i s changes t h e t o t a l charge d i s t r i b u - t i o n and t h u s t h e band bending, and consequently a l s o t h e energy eigenvalues. As t h e charge p a s s e s from E2 (extended d i s t r i b u t i o n ) t o E o and E l ( c o n c e n t r a t i o n on t h e e d g e s ) , t h e t r i a n g u l a r w e l l becomes s h a r p e r , and t h e s t r o n g e r confinement r a i s e s EO and E l w i t h r e s p e c t t o E2, which remains e s s e n t i a l l y pinned t o t h e band edge maximum. T h i s diminution of intersubband d i s t a n c e i s observed above 17 T (v=k, i . e . 2 LL's o c c u p i e d ) , where E2 i s t o t a l l y emptied. A t lower f i e l d s , however, t h e h i g h e r LL's of EO and E l a r e a l s o occupied. A t t h e p o i n t s where t h e y c r o s s E2 0, charge p a s s e s from t h e lower subband t o E2 w i t h i n c r e a s i n g f i e l d . As ex- plLined above, t h i s charge t r a n s f e r i n c r e a s e s t h e subband d i s t a n c e , i n a way a s t o counter-balance t h e moving away of t h e c r o s s i n g LL's, and both l e v e l s o v e r l a p over a f i n i t e f i e l d range, c a u s i n g EF t o be pinned t o E2 0. This i s experimentally indeed observed by t h e coincidence of t h e h i g h e s t l b i n e s c e n c e and t h e lowest e x c i t a t i o n peaks. As t h e e l e c t r o n s a r e e a s i l y t r a n s f e r r e d between t h e s e overlapping l e v e l s , a l l of them can c o n t r i b u t e t o peak A luminescence a s w e l l a s t o e l e c t r i c a l conduction. Under t h e s e circumstances t h e minimum i n t h e d e n s i t y of s t a t e s a t EF corresponds t o f i l l i n g f a c t o r s 4 , 8 , e t c . (two s p i n l e v e l s and t h e two almost de- g e n e r a t e lower subbands). This e x p l a i n s t h e p e r i o d o f magnetoresistance o s c i l l a - t i o n s t o be ~ ( 1 1 ~ ) = 0.060 T-1, which i s j u s t t h e double of t h e expected value f o r n = l . 6 * 1 0 ~ ~ g i v e n by low-field H a l l measurement and corresponding w e l l t o v=4 a t 17 T , where emptying of E2 i s observed. As t h e peak A luminescence i n t e n s i t y depends on t h e d e n s i t y of occupied s t a t e s i n t h e h i g h e s t l e v e l , t h e sane o s c i l l a t i o n p e r i o d i s observed.

I n c o n c l u s i o n , we have determined t h e subband e n e r g i e s ' o f modulation-doped quantum w e l l s w i t h 3 occupied subbands by luminescence spectroscopy, and have shown t h a t t h e intersubband d i s t a n c e changes with a magnetic f i e l d , depending on t h e r e l a t i v e occupation of t h e subbands. I n t h e range between 3 and 17 T , EF i s ?inned t o E2,g, which would not be p o s s i b l e i f intersubband d i s t a n c e s were c o n s t a n t . The same e f f e c t i n p r i n c i p l e a l s o occurs i n s i n g l e h e t e r o s t r u c t u r e s , although l e s s pronounced.

We t h a n k H. Krath f o r t h e e x c e l l e n t t e c h n i c a l a s s i s t a n c e .

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