FIELD ION APPEARANCE SPECTROSCOPY AT SILICON SURFACES

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Submitted on 1 Jan 1986

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FIELD ION APPEARANCE SPECTROSCOPY AT SILICON SURFACES

W. Schmidt, M. Lovisa

To cite this version:

W. Schmidt, M. Lovisa. FIELD ION APPEARANCE SPECTROSCOPY AT SILICON SURFACES.

Journal de Physique Colloques, 1986, 47 (C2), pp.C2-157-C2-165. �10.1051/jphyscol:1986223�. �jpa-

00225656�

FIELD ION APPEARANCE SPECTROSCOPY AT SILICON SURFACES

W.A. SCHMIDT and M.F. LOVISA

Fritz-Haber-Institut der ~ax-~lanck-Gesellschaft, Faradayweg 4-6, 0-1000 Berlin 33, F.R.G.

Resumé

-

Potentiels d'apparition e t formes de d i s t r i b u t i o n s énergétiques in- m e s d ' i o n s ont été mesurés, pour 1 'hydrogène e t des gaz i n e r t e s ionisés par champ, prés e t au plan (111) de pointes émettrices de Si de type p e t

n .

A p a r t i r des r é s u l t a t s , deux modèles d'énergie potentiel 1 e sont proposés pour l e processus d'ionisation de champ. ( i ) Surface recouverte d'hydrogène atomique: pour l e Si-p, l ' e f f e t tunnel se produit vers l e s é t a t s l i b r e s des bandes de valence e t de conduction avec une photo-sensibilité vers l a bande de valence. Pour l e Si-n, l ' e f f e t tunnel se produit vers l e s é t a t s l i b r e s de l a bande de conduction. (ii) Surface propre: pour l e Si-p à 8C K sans lu- mière, l ' e f f e t tunnel se produit vers l e s é t a t s l i b r e s de surface suivi d'une recombination avec l e s trous de l a bande de valence e t d'un e f f e t tunnel vers l e s é t a t s de l a bande de conduction. Ces processus d ' é t a t s de surfaces sont accrus en présence de lumière. Pour l e Si-n à 80 K sans lumière, l ' e f f e t tunnel prend place seulement au bord de l a band de valence alors qu'avec lu- mière,les électrons qui passent dans l e s é t a t s de surface par e f f e t tunnel peuvent ê t r e excités vers l e s é t a t s de l a bande de conduction. I l y a l a preuve expèrimentale que la densité des é t a t s de surface e s t suffisamment élevèe pour f a i r e écran au champ électrique l o r s de 1 'i o n i s a t i o n de champ.

Abstract

-

Onsets and shapes of f i e l d ion integral energy d i s t r i b u t i o n s have been measured f o r hydrogen and i n e r t rjases which were f i e l d ionized a t and

close t o the (111) plane of p- and n-type Si emitter t i p s . From the r e s u l t s obtained two potential energy models a r e proposed f o r

the

f i e l d ionization process. ( i ) Surface covered wCth atomic hydrogen: f o r p-type Si tunnel ing occurs into empty s t a t e s of the valence and the conduction band with valence band tunnel ing being photo-sensitive. For n-type Si tunnel ing occurs into empty conduction band s t a t e s . ( i i l CZean surface: f o r p-Si a t 80 K y without 1 ig h t , tunnel ing occurs into empty surface s t a t e s fol loved by recombination with holes of the valence band and by tunneling into s t a t e s of the conduction band. Surface s t a t e processes a r e enhanced in the presence of l i g h t . For n-Si a t 80 K without l i g h t , tunneling only takes place a t the edge of the conduc- tion band, whereas with l i g h t , electrons which tunnel i n t o surface s t a t e s can be excited into conduction band s t a t e s . There i s experimental evidence t h a t the density of surface s t a t e s i s high enouoh t o considerably screen the elec- t r i c f i e l d f o r f i e l d ionization.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1986223

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INTROCUCTION

I n t h e f i e l d i o n i z a t i o n process o f an aton, which i s i n the presence o f a h i g h e l e c - t r i c f i e l d i n f r o n t o f t h e surface o f a sol i d , the tunnel i n 2 e l e c t r o n Toes i n t o an unoccupied e l e c t r o n i c s t a t e o f t h e surface o r t o a b u l k s t a t e . I t has been shown t h a t i n t e g r a l energy d d i t r i b u t i o n s o f f i e l d i o n i z e d gases obtained a t metal surfaces can be r e l a t e d t o t h e eneroy d i s t r i b u t i o n of t h e i r empty s t a t e s /1,2,3/. Only a few p r e l i m i n a r y r e s u l t s have been r e p o r t e d f o r i n t e g r a l energy d i s t r i b u t i o n s r e l a t e d t o the empty s t a t e s o f a semiconductor ( s i l i c o n ) surface /4,5/. I n these studies, emit- t e r s were i n the form o f vapour-grown whiskers, which, from t h e p o i n t o f view o f i n - t e r p r e t i n g t h e f i e l d i o n i z a t i o n mechanism, a r e o f l i t t l e value because o f t h e i r p o o r l y d e f i n e d doping. More c o n c l u s i v e r e s u l t s can be expected w i t h e m i t t e r m a t e r i a l c u t from l a r g e s i n g l y c r y s t a l s w i t h known and w e l l - d e f i n e d doping. I t i s t h e aim o f t h i s work t o study f i e l d i o n i z a t i o n a t s i l i c o n by measuring i n t e g r a l f i e l d i o n ener- gy d i s t r i b u t i o n s and, f o r t h e f i r s t time, t o - d e r i v e models f o r t h e i o n i z a t i o n pro- cess i n c l u d i n g t h e surface and the b u l k band s t r u c t u r e s under two c o n d i t i o n s : t h e clean S i surface and t h e S i s u r f a c e covered w i t h atomic hydrogen. Under both surface c o n d i t i o n s , the change o f t h e energy d i s t r i b u t i o n shape upon i l l u m i n a t i o n w i t h r e d l i g h t o f g r e a t e r than band gap energy has a l s o been i n v e s t i g a t e d .

II

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EXPERIMENTAL METHODS

From t h e t o t a l e m i t t e d f i e l d i o n image o f a s i l i c o n t i p , a beam o f about 5' d i v e r - gence from and c l o s e t o t h e c e n t r a l (111) plane was used t o measure t h e i n t e g r a l energy d i s t r i b u t i o n . The i o n beam was mass-selected by means o f a 60' magnetic çec-

t o r - f i e l d spectrometer and a r e t a r d i n g energy analyzer was behind t h e e x i t s l i t /2/.

The specimen used were [ I l l ] - o r i e n t e d S i s i n g l e c r y s t a l rods, 0 . 5 ~ 0 . 5 ~ 8 mm i n d i - mensions, which were c u t from p-type, 0.17 n cm m a t e r i a l , and from n-type, 0.005n cm m a t e r i a l

,

r e s p e c t i v e l y . I n order t o m i nimize t h e number o f d i s l o c a t i o n s introduced d u r i n g c u t t i n g , t h e rods were annealed a t 1550 K f o r 3 h i n vacuum, a f t e r they were o x i d i z e d a t 1325 K i n an oxygen Stream o f 15 ml/min. f o r l h , t o form a b a r r i e r a g a i n s t t h e l o s s o f doping. Etching o f t h e rods i n t o c y l i n d r i c a l shape f o r b o t h p- and n-type was done chemically i n a s o l u t i o n o f 1 Vol. p a r t o f 40 % HF p l u s 2 Vol.

p a r t s o f 65 % HN03. Chemical t i p p o l i s h i n g o f p-type, 0.17 fi cm r a t e r i a l was suc- c e s s f u l u s i n g a s o l u t i o n o f 9 Vol. p a r t s o f 65 % HN03 p l u s 7 Vol. p a r t s o f 40 % HF p l u s 14 Vol. p a r t s o f 96 % CH3COOH, whereas n-type m a t e r i a l could be p o l i s h e d i n t o a t i p w i t h the same s o l u t i o n as f o r e t c h i n g t h e rods. The S i specimen was squeezed

i n t o a p l a t i n u m tube which was spot-welded ont0 a h e a t i n g loop. Ohmic contacts b e t - ween S i and P t were e s t a b l i s h e d w i t h d i f f u s e d Al i n t h e case o f p-Si and w i t h Ni i n the case o f n-Si. The g e o m e t r i c a l l y estimated r e s i s t a n c e o f t h e specimen even a t 80 K was < 10 8 n l e a d i n g t o a p o s s i b l e v o l t a g e drop across t h e S i t i p o f < 0 . 1 V, provided a f i e l d i o n c u r r e n t o f < IO-' A.

Removal o f the oxide l a y e r from t h e s i l i c o n surface was done i n t h e f i e l d i o n mi-

induced hydrogen r e a c t i o n o f t h e c l e a n S i surface, which under hydrogen imaging con- d i t i o n s ( F i g . l a ) i s c o n t i n u o u s l y f i e l d desorbing (SiHf, S~H;, e t c .)/7,8/. Tests o f the c l e a n l iness o f t h e S i surface a f t e r hydrogen f i e l d treatment were made i n

UHV

by observing f i e l d e l e c t r o n emission. I t turned o u t t h a t h e a t i n g o f t h e specimen t o 500 K was necessary t o g e t a smooth p a t t e r n , which was s t a b l e up t o 620 K ( F i g . l b ) .

Fig. 1

-

( a ) S i surface imaged w i t h H2 a t 80 K, p-Si, F=14.5 V/nm. (b) F i e l d elec- t r o n image of t h e c l e a n Si surface a t 300 K, p-Si, F=2 V/nm. ( c ) Clean S i surface imaged w i t h Ne a t 80 K, p-Si, F=21 V/nm. (d) Enlarged c e n t r a l Si (111) plane taken from F i g . l c .

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Heating t o higher temperatures l e d t o a g r a i n y p a t t e r n p o s s i b l y due t o d i f f u s i o n o f b u l k i m p u r i t i e s t o t h e surface. A f i e l d i o n image o f t h e c l e a n Si surface u s i n g an i n e r t imaging gas l i k e Ne i s shown i n F i g . l c , d. There i s c e r t a i n symmetric emis- sion i n s i d e o f t h e c e n t r a l (111) t o p l a y e r , an observation which m i g h t be c o r r e l a t e d w i t h a r e c o n s t r u c t e d (111) surface. This phenomenon needs f u r t h e r i n v e s t i g a t i o n .

III

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RESULTS PND DISCUSSION

1. Surface Covered w i t h Atomic Hydrogen

Fig. 2a,c show t y p i c a l measured H2 i n t e g r a l energy d i s t r i b u t i o n s . The onsets o f t h e

+

d i s t r i b u t i o n s a r e i n d i c a t e d as s0F,and

E

6:'* r e s p e c t i v e 1 y. Since t h e p o s i t i o n o f the Fermi l e v e l i n t h e case o f t h e s i l i c o n surface i s i n question, t h e exact Fermi l e v e l onset was determined from H; enerpy d i s t r i b u t i o n s ~ e a s u r e d w i t h a inetal t i p . Using t h i s Fermi l e v e l onset as a reference, i t t u r n s o u t t h a t f o r p-Si t u n n e l i n ? occurs f i r s t l y a t EF and secondly about 2 V h i g h e r . F o r n-Si t h e r e i s o n l y one onset about 1 V above t h e EF reference.

From t h e measured H i i n t e g r a l energy d i s t r i b u t i o n s , a q u a n t i t a t i v e rode1 has been d e r i v e d f o r H2 f i e l d i o n i z a t i o n which i s shown i n F i g . 2b,d. As can be seen by com- parison f o r both p- and n-Si, t h e bands must be assumed t o be bent upwards. Thus, f o r p-Si t u n n e l i n g takes place i n t o empty valence band s t a t e s as w e l l as i n t o con- d u c t i o n band s t a t e s , whereas f o r n-Si t h e r e i s conduction band t u n n e l i n g o n l y . Band bending i n t o t h e same d i r e c t i o n f o r p- and n-Si implies, as a consequence, t h a t sur- face s t a t e s are n o t i n v o l v e d i n f i e l d i o n i z a t i o n o f hydrogen, because, i f they would p l a y a r o l e , t h e bands o f p- and n-type S i would have t o be bent i n opposite d i r e c - t i o n s /9/. Another p r o o f o f t h i s conclusion can be deduced from t h e experimental ob- s e r v a t i o n o f continuous f i e l d d e s o r p t i o n o f Si-H compound ions i n t h e presence o f Hz f i e l d i o n i z a t i o n . I n forming such ions, atoinic hydrogen, produced by t h e f i e l d , was assumed t o be t h e r e a c t i o n p a r t n e r f o r surface S i atoms. Under such c o n d i t i o n s , ob- v i o u s l y , t h e surface d a n g l i n g bonds a r e occupied w i t h atomic hydrogen. Then, surface energy l e v e l s a r e formed w e l l below t h e valence band maxirun / I O / .

It i s c l e a r from t h e band s t r u c t u r e ~ o d e l t h a t t h e bending o f t h e bands should be f i e l d dependent, g i v i n g a s h i f t o f t h e 6;' onset value f o r p- and n-Si t o h i g h e r values when t h e i o n i z a t i o n f i e l d i s increased. F i g . 3 shows t h e f i e l d dependence o f the band bending, 5 (see F i g . 2b,d), f o r n-Si a t 80 K, 0.005 n cm. It amounts t o 0.7 eV a t an estimated f i e l d o f F=14 V/nm and goes up t o over 1 eV a t a 4C % higher f i e l d .

I n t h e case o f p-Si, i l l u m i n a t i o n w i t h r e d l i g h t (1.9 eV energy a t Fax. i n t e n s i t y ) y i e l d e d a g r e a t e r nutrber o f counts i n the valence band p a r t o f t h e

H;

energy d i s t r i - b u t i o n . For n-Si no p h o t o - s e n s i t i v i t y o f t h e H l energy d i s t r i b u t i o n was observed.

2. CZean Surface

Fig. 4a,c show t y p i c a l i n e r t gas, here ~ . r + , in t e g r a l energy d i s t r i b u t i o n s obtained from f i e l d i o n i z a t i o n a t c a r e f u l l y cleaned S i e m i t t e r s a t 80 K w i t h o u t l i g h t . The

8 10 12 1 4 16 18

--

s

^[volt]

E

--

_II[ -- --- - - --

II

+Y

<++

119eV

5i.p-type.Ol7ncm H:

valence band 8OK.without Iight

100 200 3 0

rniintc

Fig. 2

-

( a ) Measured

H;

i n t e g r a l energy d i s t r i b u t i o n , p-Si a t 80 K , 0.17 cm, without l i g h t . ( b ) Flodel of t h e s u r f a c e band s t r u c t u r e f o r H z f i e l d i o n i z a t i o n a t p-Si adapted from t h e measured

H;

d i s t r i b u t i o n o f Fig. Za, and a d j u s t e d according t o t h e EF reference. ( c ) Peasured Hz

+

i n t e g r a l energy d i s t r i b u t i o n , n-Si a t 80 K , 0.005 n cm, without l i g h t . (d) Mode1 of t h e s u r f a c e band s t r u c t u r e f o r Hz f i e l d i o n i z a t i o n a t n-Si adapted from t h e measured H; d i s t r i b u t i o n of Fig. 2c and ad- j u s t e d according t o t h e EF r e f e r e n c e .

bulk

E _vac ---

+

; S r l e V

valence band

H;

51.n-type.0005ncm 8OK.vithait ltght

I

50 100

counts

C2-162 JOURNAL

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onsets o f t h e d i s t r i b u t i o n s a r e i n d i c a t e d as 6;FtA, and 6zB, r e s p e c t i v e l y . Again t h e r e f e r e n c e Fermi l e v e l was determined from an ~ r ' energy d i s t r i b u t i o n w i t h a me- ta1 t i p . With r e s p e c t t o t h i s reference, t u n n e l i n g occurs f o r p-Si f i r s t a t 0.3 V h i g h e r than EF and second a t 1.2 V higher than EF. For n-Si t h e r e i s one onset a t 0.8 V above EF.

Fig. 3

-

F i e l d dependence o f t h e band bending, 6

,

f o r Hz i o n i z a t i o n , n-Si a t 80 K, 0.005 Q cm; U=9.5 kV corresponds t o a f i e l d o f 14 V/nm.

It i s a s t r i k i n g feature o f t h e i n e r t gas energy d i s t r i b u t i o n f o r p-Si t h a t t h e second onset, which was found independent o f t h e f i e l d , i s much c l o s e r t o t h e EF reference than i n t h e case o f H2 f i e l d i o n i z a t i o n . Furthermore, under t h e chosen experimental c o n d i t i o n s a t which t h e top o f t h e valence band almost c o i n c i d e s w i t h t h e S i bu1 k Fermi l e v e l , t h e d i s t a n c e between t h e second onset and EF represents, w i t h i n t h e l i m i t s o f e r r o r ( * 0.1 V), t h e gap energy o f t h e bulk. These two f a c t s p o i n t t o a f i e l d i o n i z a t i o n model which excludes upwards bending o f t h e bands, b u t r e q u i r e s i n t r o d u c i n g surface s t a t e s which c u s t be > 5 ~ 1 0 ~ ~ c r n - ~ e ~ - ~ / l l / . I n F i g . 4b a model f o r i n e r t gas f i e l d i o n i z a t i o n a t t h e c l e a n surface o f p-type S i i s shown t h a t i s c o n s i s t e n t w i t h t h e measured d i s t r i b u t i o n . The bands a r e bent downwards due t o t h e presence o f surface s t a t e s . This band bending e x i s t s before t h e e l e c t r i c f i e l d i s switched on /9/ and i s o n l y s l i g h t l y reduced i n t h e presence o f t h e f i e l d . Thus, t o a major p a r t , t h e f i e l d i s screened by t h e surface s t a t e s . Since t h e f i r s t onset o f t h e measured energy d i s t r i b u t i o n , 6:FtA, i s found somewhat above t h e EF reference, a gap, A, between f i l l e d and empty s u r f a c e s t a t e s has t o be introduced, which consequently p o i n t s t o a r e c o n s t r u c t i o n o f the e m i t t i n g (111) plane 1121.

F i e l d i o n i z a t i o n a t low temperatures w i t h o u t e x c i t a t i o n due t o l i g h t a t t h e c l e a n surface of p-Si, t h e r e f o r e , takes p l a c e v i a t u n n e l i n g i n t o empty surface s t a t e s f o l - lowed by recombination w i t h holes i n the valence band and by t u n n e l i n g i n t o s t a t e s o f t h e conduction band.

condudion band

A?

S1.n-type.0005ncm surface .- 8OK.without iight

states

-

20 LO 60

counts

F i g . 4

-

( a ) Keasured ~ r + i n t e g r a l energy d i s t r i b u t i o n , p-Si a t 30 K, 0.17 Q _cm, w i t h o u t l i g h t . ( b ) Podel o f t h e surface band s t r u c t u r e f o r i n e r t gas f i e l d i o n i z a - t i o n a t p-Si adapted from t h e reasured Ar energy d i s t r i b u t i o n of F i g . 4a and ad-

+

j u s t e d according t o t h e EF reference. ( c ) Peasured Ar i n t e g r a l energy d i s t r i b u t i o n ,

+

n-Si a t 80 K, 0.005 8 cm, w i t h o u t l i g h t . ( d ) Yodel o f t h e s u r f a c e band s t r u c t u r e f o r i n e r t gas f i e l d i o n i z a t i o n a t n-Si adapted from t h e measured Ar enerçy d i s t r i b u t i o n i.

of F i g . 4c and adjusted according t o t h e EF reference.

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Fig. 4d shows t h e mode1 o f t h e surface band s t r u c t u r e f o r i n e r t gas f i e l d i o n i z a t i o n which i s adapted f r o r a measured Ar+ energy d i s t r i b u t i o n a t n-Si. Here, t h e bending of t h e bands i n t h e presence o f surface s t a t e s i s upwards w i t h o u t e l e c t r i c f i e l d /9/, and w i l l be o n l y s l i o h t l y increased i n t h e presence o f t h e f i e l d . It i s c o n s i s t e n t w i t h t h i s mode1 t h a t continuous t u n n e l i n g w i t h o u t e x c i t a t i o n o f ' t h e e l e c t r o n s a f t e r reaching t h e surface i s p o s s i b l e o n l y a t t h e edge o f t h e conduction band.

According t o these r o d e l r , a weak f i e l d dependence o f t h e 6O~+*onset f o r p-Si and t h e 1

6:B onset f o r n-Si i s expected, w i t h s h i f t s t o higher values i n both cases ( ) . V e r i - f i c a t i o n of these f i e l d e f f e c t s r e q u i r e s onset measurements o f h i g h p r e c i s i o n , which have n o t y e t been done.

I l l u m i n a t i o n w i t h r e d l i g h t (1.9 eV energy a t max. i n t e n s i t y ) i n t h e case o f ~ . r + f i e l d i o n i z a t i o n a t p-Si y i e l d e d a r a t i o o f 13 f o r t h e number o f counts a t satura- t i o n o f t h e energy d i s t r i b u t i o n w i t h 6:B onset t o the number of counts a t s a t u r a t i o n o f t h e energy d i s t r i b u t i o n w i t h a;~+'onset ( F i g . 5a). Without l i g h t t h i s r a t i o was 60 ( F i g . 4a). Obviously, i n t h e presence o f l i g h t the d e p l e t i o n o f t h e surface states, which c o n t i n u o u s l y accept electrons, i s more e f f e c t i v e , since l i g h t n o t o n l y creates more holes i n t h e valence band f o r recombination b u t a l s o e x c i t e s e l e c t r o n s from surface s t a t e s i n t o the conduction band.

1EF reference /EF reference

630 1 6 4 0 1

+ + +

5 0 4 - ^{5 1 2} -

3 7 8

- -

^{3 8 4} -

w "7

+ +

3 3

O

252 -

t - ï ^-

1 2 6

-

^{1 2 8}

-

S1.p-type.017ncm Sien-type.0005ncrn

BOK,red I~ght,i 9eV

O - _O

-

8 10 1 2 14 1 6 1 8 8 1 0 12 1 4 1 6 l e

- -

s

[volt1 -- S [volt1

a b

Fig. 5

-

( a ) Measured Ar+ i n t e g r a l energy d i s t r i b u t i o n , p-Si a t 80 K, 0.17

n

cm, w i t h red l i g h t . ( b ) Neasured Ar+ i n t e g r a l energy d i s t r i b u t i o n , n-Si a t 80 K, Q.CQ5 fi cm, w i t h r e d l i g h t . (Red l i g h t o f hv =1.9 eV a t r a x . i n t e n s i t y )

( l ) ~ h e r e p o r t e d decrease of t h e onset o f i n e r t gas d i s t r i b u t i o n s obtained w i t h S i whiskers /5/ c o u l d n o t be reproduced w i t h S i c u t from well-doped m a t e r i a l . An i n - t e r p r e t a t i o n f o r t h e f i e l d e f f e c t found w i t h whiskers has n o t y e t been found.

values, bo, b:,1 i s c o n s i s t e n t w i t h t h e f i e l d i o n i z a t i o n nodel o f n-Si ( F i g . 4d), be- cause e l e c t r o n s , which t u n n e l i n t o deep l y i n g empty s u r f a c e s t a t e s , can be e x c i t e d i n t o s t a t e s o f t h e c o n d u c t i o n band, a process which t a k e s p l a c e w i t h l e s s i n t e n s i t y t h a n t u n n e l i n g v i a s u r f a c e s t a t e s a t t h e edge o f t h e c o n d u c t i o n band. B u t t h e whole d i s t r i b u t i o n i s s h i f t e d t o h i g h e r v a l u e s by 0.6 V . T h i s s h i f t c o u l d be assumed simp- l y as a v o l t a g e drop, b u t i t appears d i f f i c u l t a t t h e moment t o g i v e a d e t a i l e d me- chanism. The s i t u a t i o n i s such t h a t one has a n - t y p e i n t e r i o r o f t h e c r y s t a l w i t h a p - t y p e s u r f a c e which i s r e v e r s e d - b i a s e d so t h a t e l e c t r o n s f l o w f r o m t h e p - s i d e t o t h e n - s i d e . A t t h e same t i m e , charge c a r r i e r s a r e generated due t o t h e l i g h t . To c l a r i f y t h i s p o i n t , f u r t h e r experiments a r e needed, e s p e c i a l l y u s i n g l i g h t o f l e s s t h a n band gap energy.

ACKNOWLEDGEMENTS

We would l i k e t o thank P r o f e s s o r J.H. B l o c k and Dr. L a j o s E r n s t f o r f r u i t f u l d i s c u s - s i o n s . We a l s o thank M. N a s c h i t z k i f o r v e r y h e l p f u l t e c h n i c a l a s s i s t a n c e . F i n a n c i a l s u p p o r t by Sonderforschungsbereich (SFB 6 1 ' 8 1 ) i s g r a t e f u l l y acknowledged.

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