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TUNNELING FROM QUASI 2D ELECTRONIC STATES INTO CONTINUUM- AND BOUND STATES
IN GaAs/GaAlAs-HETEROSTRUCTURES
J. Smoliner, R. Lassnig, E. Gornik, G. Weimann, K. Ploog
To cite this version:
J. Smoliner, R. Lassnig, E. Gornik, G. Weimann, K. Ploog. TUNNELING FROM QUASI 2D ELECTRONIC STATES INTO CONTINUUM- AND BOUND STATES IN GaAs/GaAlAs- HETEROSTRUCTURES. Journal de Physique Colloques, 1987, 48 (C5), pp.C5-479-C5-482.
�10.1051/jphyscol:19875101�. �jpa-00226683�
TUNNELING FROM QUASI 2D ELECTRONIC STATES INTO CONTINUUM- AND BOUND STATES IN GaAs/GaAlAs-HETEROSTRUCTURES
J. SMOLINER, R. LASSNIG, E. GORNIK, G. WEIMANN* and K. PLOOG*"
Institut fiir Experimentalphysik, Universitat Innsbruck, Technikerstrasse 25, A - 6 0 2 0 Innsbruck, Austria
"~orschungsinstitut der Deutschen Bundespost, Am Kavalleriesand 3 , D-6000 Darmstadt, F . R . G .
t l
Max-Planck-Institut fiir Festkbrperforschung, Heisenbergstrasse 1, 0-7000 Stuttgart 80, F.R.G.
A b s t r a c t - O s c i l l a t o r y s t r u c t u r e i s observed i n forward b i a s e d dI/dV and d21/dV2 c u r v e s of conventional GaAs/GaAlAs h i g h e l e c t r o n m o b i l i t y t r a n s i s t o r samples a t l i q u i d helium temperature using modulation t e c h n i q u e s . These o s c i l - l a t i o n s c a n be e x p l a i n e d by Fowler-Nordheim t u n n e l i n g . From t h e p o s i t i o n of t h e o s c i l l a t i o n s t h e conduction band d i s c o n t i n u i t y i s determined a s a f u n c t i o n of t h e aluminum c o n c e n t r a t i o n X . F o r samples having an a l u n i n u n c o n c e n t r a t i o n between 0.3 and 0.4 a v a l u e of AE /AE = 0.61 i s found. F u r t h e r t h e d e p t h of t h e deep donor l e v e l s i n t h e G a A l f I s w%s determined t o be 130 meV below t h e con- d u c t i o n band. I n most r e c e n t experiments t u n n e l i n g between subbands i n t h e GaAs and GaAlAs i s observed.
I n t r o d u c t i o n
Recently n-GaAs/GaAl~s/n-GaAs s t r u c t u r e s have been s t u d i e d e x t e n s i v e l y i n o r d e r t o understand b a r r i e r p r o p e r t i e s . Watanabe e t a l . / l / have used a c a p a c i t a n c e - v o l t a g e
(CV) p r o f i l i n g t e c h n i q u e , which was developed by Kroemer / 2 / , t o measure t h e band gap d i s c o n t i n u i t y . They found A E ~ / A E t o b e 0.62, t a k i n g a c o r r e c t i o n f o r t h e i n t e r - f a c e charge d e n s i t y i n t o account. Arxold and coworkers /3/ used thermionic emission d a t a t o determine t h e b a r r i e r h e i g h t . A conduction band d i s c o n t i n u i t y of 65 % of t h e band gap d i s c o n t i n u i t y f o r aluminum c o n c e n t r a t i o n s o f 54 8 , 70 % and 100 % c o u l d be deduced from h i s d a t a . Hickmott e t a l . /4/ have combined c u r r e n t - v o l t a g e (IV) and CV measurements on n GaAs/Ga~lAs/n+GaAs c a p a c i t o r s with d i f f e r e n t G a A l A s l a y e r t h i c k - n e s s e s t o determine t h e conduction band d i s c o n t i n u i t y . T h e i r r e s u l t f o r AE /AE was 0.63 + 0.03. Furthermore t h e y have c a l c u l a t e d t h e e f f e c t of band bending, s u e ?o n e g a t i v e c h a r g e i n t h e undoped GaAlAs. Resonant Fowler-Nordheim t u n n e l i n g through a n - ~ a A s / ~ a A 1 ~ s / n + ~ a ~ s s i n g l e b a r r i e r h e t e r o s t r u c t u r e was observed f i r s t by Hickmott e t a l . /S/. I n t h i s s t r u c t u r e e l e c t r o n s t u n n e l from an accumulation l a y e r through a t r a p e z o i d a l b a r r i e r . O s c i l l a t i o n s were observed i n t h e I V c h a r a c t e r i s t i c s and could be e x p l a i n e d q u a n t i t a t i v e l y by t h e t h e o r y of r e s o n a n t Fowler-Nordheim t u n n e l i n g /6,7/.
We have i n v e s t i g a t e d conventional Ga~s/GaAlAs/GaAs h e t e r o s t r u c t u r e s , where e l e c t r o n s t u n n e l from a two dimensional e l e c t r o n g a s (2DEG) through t h e GaAlAsbarrier i n t o a shallow a l l o y e d ohmic c o n t a c t /8/. P e r i o d i c s t r u c t u r e i s observed i n t h e dI/dV c h a r a c t e r i s t i c s of t h e s e samples, which can be explained u s i n g aFowler-Nordheim
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19875101
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t u n n e l i n g theory. We used t h i s d a t a f o r t h e f i r s t time t o c a l c u l a t e t h e conduction band d i s c o n t i n u i t y AE from t h e p o s i t i o n of t h e observed o s c i l l a t i o n s .
Experimental
Three t y p e s o f GaAs/GaAlAs/Ga~s samples were used i n o u r experiments ( s e e Table II5 A l l samples had a p-doped GaAs l a y e r , with a n a c c e p t o r c o n c e n t r a t i o n o f
1 . 0 ~ 1 0 , followed by a GaAlAs s p a c e r , t h e n n-doped GaAlAs and f i n a l l y a cap l a y e r of undoped GaAs. The c o n t a c t s t o t h e 2DEG were made u s i n g a n AuGe a l l o y (Au:Ge =
= 8 : l ) . A g a t e c o n t a c t was formed by a shallow d i f f u s i o n of AuGe i n t o t h e GaAlAs l a y e r . The b a r r i e r t h i c k n e s s db was determined from CV measurements t a k i n g t h e d i s - placement of t h e 2DEG from t h e G a A s / ~ a ~ l ~ s i n t e r f a c e i n t o account. A l l I V , dI/dV, and dZI/dV2 measurements were made using a 4-terminal a c conductance b r i d g e with a modulation frequency o f 140 Hz.
A l l samples showed an o s c i l l a t o r y behaviour i n t h e f i r s t and second d e r i v a t i v e s of t h e I V c h a r a c t e r i s t i c s measured a t 4.2 K, which can be e x p l a i n e d by Fowler-Nord- heim t u n n e l i n g . The s t r e n g t h of t h e o s c i l l a t i o n s was d i f f e r e n t on a l l samples, due t o t h e i r r e p r o d u c i b l e depth and a b r u p t n e s s of t h e shallow a l l o y e d ohmic c o n t a c t s . Another r e a s o n f o r t h e weak appearence of t h e o s c i l l a t i o n s i s t h e r e l a t i v e l y s t r o n g impurity s c a t t e r i n g i n t h e b a r r i e r .
R e s u l t s
The b a n d s t r u c t u r e (Fig. 1 ) was c a l c u l a t e d a f t e r S t e r n / g / . For t h e c a l c u l a t i o n of t h e t u n n e l i n g c u r r e n t a one e l e c t r o n p i c t u r e was a p p l i e d . I n a p r e l i m i n a r y ana- l y s i s e f f e c t i v e mass e f f e c t s and any r e s i d u a l charge i n t h e s p a c e r were n e g l e c t e d . Shubnikov-de Haas measurements have shown t h a t t h e e l e c t r o n c o n c e n t r a t i o n Ns s a t u r a - t e s w i t h g a t e v o l t a g e i n forward b i a s . A s i m i l a r e f f e c t was observed by Hirakawa /10/.
Since t h e change i n e l e c t r o n c o n c e n t r a t i o n w i t h g a t e v o l t a g e V , i n forward b i a s , i s s m a l l , Ns i s approximately independent of t h e a p p l i e d v o l t a g e . Under t h e s e condi- t i o n s we have used a q u a s i - f r e e p a r t i c l e approximation f o r t h e t u n n e l i n g c u r r e n t from t h e 2D-bound s t a t e , which s i m u l a t e s t h e e v o l u t i o n of t h e bound wavepacket by a f r e e incoming wave a t t h e same energy. For t h e c u r r e n t of a p a r t i c l e i n t h e a t h e l e c t r o n subband one o b t a i n s /IT/:
Here T(E ) d e n o t e s t h e t r a n s m i s s i o n r a t e of a f r e e p a r t i c l e with energy Ea, and t h e p r e f a c t o a s d e s c r i b e t h e e f f e c t i v e incoming p a r t i c l e f l u x . T h i s f l u x i s approximately g i v e n by t h e s i m u l a t e d v e l o c i t y devided by t h e confinement width. The t u n n e l i n g c u r r e n t i s d i r e c t l y p r o p o r t i o n a l t o t h e t r a n s m i s s i o n c o e f f i c i e n t of t h e b a r r i e r . The t r a n s m i s s i o n i s t h e n c a l c u l a t e d n u m e r i c a l l y using a piecewise l i n e a r b a r r i e r a f t e r Wayne e t a l . /12/.
I f t h e c o n c e n t r a t i o n of e l e c t r o n s N and t h e d e p l e t i o n charge N az-eknown, one
can c a l c u l a t e V d
SP' E , and E f ( F i g . 7) a f t e r S t e r n / g / . We have v a r i e d t h e band gap d i s c o n t i n u i t y <lrfo:! t h e measured v a l u e s of N,, N d , and d b , i n o r d e r t o f i t t h e p o s i t i o n of t h e c a l c u l a t e d minima of t h e d I / d v c h a r a c t e r i s t i c s t o t h e measured minima i n dI/dV. Fig. 2 shows a comparison betyeen t h e c a l c u l a t e d minima of
d ( l o g I ) / d V and o u r experimental d a t a f o r Sample 1360-4. A l l of t h e measured minima a g r e e w e l l with t h e o r y . The f i t , w a s c a r r i e d o u t on samples with aluminurn concen- t r a t i o n s of 30 8 , 36 % and 40 % . The measured b a r r i e r h e i g h t s f o r t h e t h r e e alu- minum c o n c e n t r a t i o n s were 226 meV, 272 meV and 304 meV r e s p e c t i v e l y . I t can be s e e n , t h a t t h e r a t i o of A E ~ / A E = 0.61 i s c o n s t a n t f o r a l l samples, which i s i n good agreement w i t h r e c e n t l y p u b l i s h e d r e s u l t s /l g - 5 / . The experimental e r r o r f o r A E , / A E ~ i s approximately k0.04, mainly due t o e r r o r s i n t h e d e t e r m i n a t i o n of the b a r r i e r t h i c k n e s s . A l t e r n a t i v e l y our c a l c u l a t i o n s c o u l d be used t o determine t h e d e p l e t i o n charge i f t h e b a r r i e r h e i g h t i s given. The main advantage of our method i s t h a t it needs no a b s o l u t e v a l u e s of t h e t u n n e l i n g c u r r e n t , s i n c e t h e b a r r i e r h e i g h t can be determined from t h e p o s i t i o n s of t h e o s c i l l a t i o n s a l o n e . T h i s means t h a t leakage c u r r e n t s and s e r i e s r e s i s t a n c e s have no i n f l u e n c e on t h e r e s u l t s .
A f t e r S t e r n / g / , t h e i o n i s a t i o n energy of t h e donor i s i d e n t i c a l with t h e Fermi l e v e l i f t h e GaAlAs i s h i g h l y doped and i f t h e r e i s o n l y one type of donor l e v e l i n
aluminum c o n c e n t r a t i o n For X-values 0.4 and h i g h e r , t h e r e l a t i v e c o n c e n t r a t i o n of deep donors i s l a r g e r t h a n 90 %. T h e r e f o r e , i n t h e c a s e o f h i g h doping, t h e Fermi l e v e l E f can be i d e n t i f i e d with t h e depth of t h e deep donor l e v e l EDb i f t h e concen- t r a t i o n of t h e shallow donors i s n e g l e c t e d . We found E t o be approximately 130 meV below t h e conduction band i n t h e GaAlAs f o r x = 0.4. T R ? ~ v a l u e i s lower t h a n S c h u b e r t ' s / l 3 / , which i s 140 meV, b u t one has t o keep i n mind, t h a t t h e r e s u l t may be s l i g h t l y i n f l u e n c e d by t h e r e s i d u a l c o n c e n t r a t i o n of shallow donors.
Most r e c e n t l y , we have i n v e s t i g a t e d t h e same t y p e o f samples a s d e s c r i b e d above b u t with a s e m i t r a n s p a r e n t Au-Schottky g a t e c o n t a c t . On t h i s samples t h e I V charac- t e r i s t i c s and i t s d e r i v a t i v e s were measured b e f o r e and a f t e r i l l u m i n a t i o n . Before t h e samples were i l l u m i n a t e d w i t h a r e d LED l i g h t p u l s e no s i g n i f i c a n t s t r u c t u r e was observed. A f t e r t h e samples were exposed t o l i g h t , we have observed o s c i l l a t i o n s i n t h e f i r s t d e r i v a t i v e of t h e I V c h a r a c t e r i s t i c i n forward and r e v e r s e b i a s .
Furthermore t h e c a p a c i t a n c e a t z e r o v o l t a g e was i n c r e a s e d d r a s t i c a l l y . From t h e c a p a c i t a n c e measurements we conclude t h a t a c o n s i d e r a b l e number of e l e c t r o n s a r e l o c a t e d i n s i d e t h e G a A l A s , which r e s u l t s i n a formation of subbands. I n a d d i t i o n t h e d e p l e t i o n charge i n t h e GaAs i s decreased. Fig. 3 shows t h e b a n d s t r u c t u r e b e f o r e and a f t e r i l l u m i n a t i o n . I f v o l t a g e i s a p p l i e d t o t h e j u n c t i o n , e l e c t r o n s t u n n e l through t h e b a r r i e r i n t o empty subbands, and we a r e s u r e t h a t t h e observed s t r u c t u r e i n t h e dI/dV c h a r a c t e r i s t i c s i s due t o subband-subband resonance. Rough approximations have shown t h a t t h e p e r i o d i c i t y of t h e o s c i l l a t i o n s i n dI/dV (Fig. 4 ) have t h e c o r r e c t o r d e r of magnitude and 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 s a r e i n p r o g r e s s t o e x p l a i n t h e e f f e c t more p r e c i s e l y .
I n summary, we have measured I V , dI/dV, and d'I/dV2 c h a r a c t e r i s t i c s o f con- v e n t i o n a l h i g h e l e c t r o n m o b i l i t y t r a n s i s t o r s , where e l e c t r o n s t u n n e l from t h e 2DEG through a b a r r i e r i n t o a shallow a l l o y e d ohmic c o n t a c t . The observed o s c i l l a t i o n s i n t h e d 1 / d ~ c h a r a c t e r i s t i c s have t h e i r o r i g i n i n a Fowler-Nordheim t u n n e l i n g process, b u t a r e weaker t h a n p r e d i c t e d by t h e o r y , due t o t h e non i d e a l s i t u a t i o n i n o u r samples. A f i t of t h e t h e o r y t o t h e experiment a l l o w s a d e t e r m i n a t i o n of AE,/AE =
= 0.61 + 0.04, which a g r e e s w e l l w i t h t h e r e s u l t s p u b l i s h e d r e c e n t l y / l - 4 / . A s g f a r a s we know, t h i s i s t h e f i r s t a p p l i c a t i o n of Fowler-Nordheim t u n n e l i n g t o a determi- n a t i o n of t h e b a r r i e r h e i g h t . The deep donor l e v e l i n t h e GaAlAs i s found t o be
130 meV below t h e conduction band. F i n a l l y , r e c e n t experiments have shown evidence of subband-subband t u n n e l i n g i n ~ a ~ s / G & l ~ s h e t e r o s t r u c t u r e s , where subbands i n t h e GaAlAs a r e formed by i l l u m i n a t i o n .
Acknowledgements
T h i s work was sponsored by t h e S t i f t u n g Volkswagenwerk, P r o j e c t No. 1-61840.
The a u t h o r s a r e g r a t e f u l t o H. Kuen f o r h i s t e c h n i c a l a s s i s t a n c e , R. C h r i s t a n e l l , M. Hauser, M. Helm and R.A. Hopfel f o r v a l u a b l e d i s c u s s i o n s . F i n a l l y we want t o t h a n k S.A. Lyon f o r r e a d i n g t h e manuscript.
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Table I
Sample parameters: DGaAIAs i s t h e t h i c k n e s s o f t h e n-doped GaAlAs l a y e r , Dsp is t h e s p a c e r l a y e r t h i c k n e s s , db i s t h e b a r r i e r t h i c k n e s s , Ns i s t h e e l e c t r o n concentra- t i o n i n t h e 2DEG, Nd i s t h e d e p l e t i o n charge i n t h e GaAs, and NDb i s t h e doping o f t h e GaAlAs. X i s t h e aluminurn c o n c e n t r a t i o n i n %, and p i s t h e 2D-electron m o b i l i t y measured a t 77 K .
Fig. 1 : Bandstructure for a typical sample. The shallow alloyed gate contact reaches into the GaAlAs o n all samples used, so that the resulting barrier thickness is db.
I before ilfumina tion -
Fig. 3 : Scematic bandstucture of a typical sample (x=0.35) before and after illumination. After illumination the depletion charge is decreased, and several subbands ( E o ' . . ) may exist in the GaAlAs.
Fig. 2 : Comparison of the fitted theoretical d(logI)/dV (curve 3) and o f the experimental dI/dV curves (1 and 2).
Curve 2 is the same as curve 1 but shifted and amplified by a factor of 20.
The theoretical d(logI)/dV is plotted simply to allow the curve to fit on the same scale as the experimental one.
Fig.4 : Experimental dIldV curves measured before and after illumination.
Three oscillations. which are indicated by arrows, are clearly resolved both in forward and reverse bias. Curve 1 is shifted and amplified to fit on the same scale as curve 2.
