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AC LOSS IN AMORPHOUS GERMANIUM AT LOW TEMPERATURES
A. Long, W. Hogg, N. Balkan, R. Ferrier
To cite this version:
A. Long, W. Hogg, N. Balkan, R. Ferrier. AC LOSS IN AMORPHOUS GERMANIUM AT LOW TEMPERATURES. Journal de Physique Colloques, 1981, 42 (C4), pp.C4-107-C4-110.
�10.1051/jphyscol:1981419�. �jpa-00220816�
JOURNAL DE PHYSIQUE
CoZZoque C4, suppZ6ment au nOIO, Tome 42, octobre 1981 page C4-107
AC LOSS I N AMORPHOUS GERMANIUM A T LOW TEMPERATURES
A.R. Long, W.R. Hogg, N. Balkan and R . P . F e r r i e r
Department o f NaturaZ PhiZosophy, University o f GZasgow, GZasgow G I 2 8QQ, Scot land
Abstract.- The frequency, temperature and f i e l d dependencesofthe audio frequency AC l o s s i n a s e r i e s of s p u t t e r e d hydrogenated amorphous germanium samples a r e i n v e s t i g a t e d over t h e temperature range 1
-
10K. The r e s u l t s c o n f l i c t with t h e p r e d i c t i o n s of t h e model i n which e l e c t r o n s a r e assumed t o tunnel between l o c a l i s e d s t a t e s uniformly d i s t r i b u t e d i n space and i n energy.1. I n t r o d u c t i o n . The aim of t h i s work was to extend our previous measurements o f AC l o s s i n amorphous germanium, performed a t around l i q u i d n i t r o g e n temperature (1,2) t o very much lower temperatures. A t l i q u i d n i t r o g e n temperatures and above, t h e e l e - mentary theory o f e l e c t r o n hopping processes suggests t h a t t y p i c a l hopping e n e r g i e s w i l l be of magnitude a few kT, and hence a r e almost c e r t a i n t o involve multi-phonon processes, f o r which t h e matrix elements a r e n o t yetwellknown ( 3 , 4 ) . However i f measurements a r e made a t l i q u i d helium temperatures then t h e thermal e n e r g i e s involved a r e much smaller and s i n g l e phonon processes should dominate ( 4 ) . I t i s i n this low temperature regime t h a t IXv a r i a b l e range hopping i s observed i n impurity bands ( 5 ) and i n v e r s i o n l a y e r s (6). I t was our i n t e n t i o n t o study t h e AC l o s s a t l i q u i d helium temperatures t o see i f t h e i d e a s of v a r i a b l e range hopping a r e more s u c c e s s f u l i n explaining t h e new experimental d a t a than they were i n accounting f o r our previous observations ( 1 , Z ) .
2. P r e d i c t i o n s of t h e theory f o r AC l o s s by t u n n e l l i n g between l o c a l i s e d s t a t e s . The t h e o r i e s of AC l o s s i n amorphous germanium o r s i l i c o n i n v a r i a b l y assume a population of e l e c t r o n s t a t e s uniformly d i s t r i b u t e d i n energy and i n space, between which e l e c t r o n t r a n s f e r occurs by t u n n e l l i n g . The c a l c u l a t i o n s a r e usually performed i n t h e p a i r approximation and assume a r e l a x a t i o n time f o r e l e c t r o n t r a n s f e r between s t a t e s s e p a r a t e d i n energy by A and i n space by R o f t h e form
For reasons of s t a t e occupation, t h e l o s s w i l l be dominated by s t a t e s c l o s e t o t h e fermi l e v e l ( A / ~ T < 1 ) . Moreover i f each p a i r of s t a t e s i s assumed t o respond a s a Debye o s c i l l a t o r , then t h e maximum l o s s w i l l occur f o r an angular frequency % r - l . Taking t h e s e r e s u l t s t o g e t h e r implies an e f f e c t i v e hopping length a t an angular frequency w of
Considering t h e c o n t r i b u t i o n of each p a i r of s t a t e s independently it i s s t r a i g h t - forward t o deduce an AC c o n d u c t i v i t y
where g i s t h e d e n s i t y s t a t e s . This r e s u l t , f i r s t derived by Austin and Mott ( 7 ) , was confirmed using more d e t a i l e d s t a t i s t i c s by P o l l a k (8) and using a p e r c o l a t i o n approach by Butcher and Hayden ( 9 ) . I t p r e d i c t s a l o s s which v a r i e s d i r e c t l y a s t h e
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1981419
JOURNAL DE PHYSIQUE
Fig. 1. The Equivalence of F i e l d and Temperature i n changing conductance.
F i e l d curves a t 1 . 2 K , ( a ) 3KHz (b) 1KHz.
Temperature curves a t low f i e l d ( c ) 3KHz (d) lKHz
(Sample B5)
.
temperature, and has a frequency exponent s (when t h e l o s s i s expressed a s wS) given by
which should be approximately independent of frequency f o r wro << 1 and independent of temperature. Recently a more r e f i n e d c a l c u l a t i o n by Movaghar, Pohlmann and Sauer (10) has shown t h a t s may be a weak function of temperature.
3. Experimental Observations. For our i n v e s t i g a t i o n , we chose t o work with amorphous germanium samples s p u t t e r e d i n argon and argon/hydrogen atmospheres which can be prepared i n a more reproducible manner than evaporated samples. O u r samples were of sandwich configuration and measured using a simple AC bridge. Some DC p r o p e r t i e g m a s u r e d around l i q u i d nitrogen temperatures a r e given i n t a b l e 1. These, together with t h e higher temperature AC l o s s r e s u l t s a r e t o be discussed i n a forth- coming paper. The most i n t e r e s t i n g r e s u l t f o r our purposes i s t h a t t h e DC conduc- t i v i t y of t h e s e samples a t 77K v a r i e s by some 6 orders when hydrogen i s incorporated, which i s not f u l l y explained by t h e changes i n To, t h e temperature exponent i n t h e Mott T)a r e l a t i o n s h i p ( accurately obeyed by a l l t h e samples around 77K).
However when t h e AC l o s s i n these samples a t helium temperatures was measured, it was found t o vary very l i t t l e with hydrogen content (see t a b l e 1); a l l t h e c o n d u c t i v i t i e s measured a t t h e same temperature (4.2K) and frequency were within a f a c t o r of 2 of one another. The frequency exponents s (measured a t 4.2K) were again s i m i l a r from sample t o sample having values i n t h e region of 0.9. s was observed to be only a weakly decreasing function of temperature, varying f o r sample B5 f o r example from 0.88 a t 1.2K t o 0.84 a t 8K. These r e s u l t s a r e i n accord with t h e equations of 1 2. On t h e o t h e r hand t h e temperature dependence of t h e conductance
(G) a t a f i x e d frequency ( f i g u r e 1) does not agree with equation 3. G does not have a simple power law dependence on temperature, b u t becomes l e s s temperature dependent a s t h e temperature i s lowered.
I n a d d i t i o n t o these standard observations, we have detected a new low tempera- t u r e e f f e c t , a n AC f i e l d e f f e c t . A s the AC e l e c t r i c f i e l d F across our sample i s increased, t h e conductance, i n i t i a l l y independent of f i e l d , begins t o increase
( f i g u r e 2). The onset f i e l d a t which changes begin i n c r e a s e s w i t h temperature, and a t high f i e l d s t h e l o s s curves f o r d i f f e r e n t temperatures converge, with t h e l o s s becoming temperature independent. Similar f i e l d curves a r e observed over t h e f u l l range of frequencies a t which data was taken ( f i g u r e 2 ) . We were not a b l e , t o t h e accuracy of our d a t a , to d e t e c t any frequency v a r i a t i o n of t h e o n s e t f i e l d .
I t should be emphasised t h a t t h e v a r i a t i o n of conductance with f i e l d i s an AC e f f e c t , and i s not r e l a t e d t o t h e DC conductance. Although these samples i n v a r i a b l y have a f i e l d dependent DC leakage path i n p a r a l l e l with t h e AC l o s s , i n t h e measure- ments described t h i s leakage was never more than 10% o f t h e AC conductance a t low f i e l d s and could be s u b t r a c t e d from t h e d a t a t o leave t h e AC l o s s without introduc- i n g an e r r o r of g r e a t e r than a few p e r cent. The accuracy of t h i s conclusion is confirmed by the observation t h a t a s i m i l a r f i e l d e f f e c t i s observed a t a l l
-- k
0--
mA Fig. 2. The AC f i e l d
dependence of t h e conductance a t d i f f e r e n t frequencies and temperatures (Sample B 2 )
.
frequencies o f measurement, whereas t h e r e l a t i v e importance of t h e DC c o r r e c t i o n decreases with frequency.
An important c l u e a s t o t h e meaning o f t h e f i e l d e f f e c t i s provided when curves of G(F) a t a c o n s t a n t low temperature and G(T) a t low f i e l d a r e compared ( f i g u r e 1).
The s i m i l a r i t y between t h e s e s e t s o f d a t a suggest t h a t t h e energy changes a s s o c i a t e d with temperature (kT) and with t h e a p p l i e d f i e l d ( e F G f f ) a c t i n t h e same way. For t h e sample i l l u s t r a t e d , by comparing regions o f c o n s t a n t conductance and w r i t i n g eF%ff 5 kT, we may e s t i m a t e Reff a s (0.8
+
0.l)nm.Unfortunately complete enough s e t s o f temperature and f i e l d d a t a a r e n o t a v a i l - a b l e f o r a l l t h e samples. For t h e s e we e s t i m a t e Reff by determining t h e f i e l d a t which t h e conductance had i n c r e a s e d by 10% over i t s low frequency value (measured a t 4.2K and 3KHz) and using eFReff % kT. The Ref= values given by t h i s technique a r e given i n t h e t a b l e i n b r a c k e t s and s e r v e a s a good i n d i c a t i o n of t h e pronounced t r e n d i n our d a t a , which i s f o r Reff t o i n c r e a s e s t r o n g l y a s t h e hydrogen incorpora- t e d (measured by i t s concentration i n t h e s p u t t e r i n g gas) i n c r e a s e s .
4. I n t e r p r e t a t i o n i n terms of t u n n e l l i n g between l o c a l i s e d s t a t e s a t t h e f e d l e v e l . I n applying t h e theory of s e c t i o n 2 t o o u r d a t a , we start from t h e f e a t u r e most c l o s e l y i n agreement with theory, namely t h e temperature independent s value of 0.9. Using equation 4, this suggests a r0 value of around 1 0 - ~ ~ s . This i s s i m i l a r t o t h e values obtained from t r y i n g t o f i t AC d a t a a t higher temperatures (9, 101, and i s n o t easy t o e x p l a i n using r e a l i s t i c parameters, even i n t h e framework of t h e Miller-Abrahams (11) r e l a x a t i o n r a t e s . A more important o b s t a c l e becomes apparent however when t h i s r e s u l t i s a p p l i e d t o c a l c u l a t e
%ff
using equation 2.Taking e s t i m a t e s o f a-I of lnm from thickness dependent c o n d u c t i v i t y (12) o r 1.5nm from DC f i e l d e f f e c t (13) (both r e s u l t s assuming t h e v a l i d i t y of t h e Mott v a r i a b l e range hopping model), we g e t Reff values of 20 and 30nm r e s p e c t i v e l y , very much g r e a t e r than t h e f i e l d e f f e c t values o f Table 1. A l t e r n a t i v e l y , r e v e r s i n g t h e argument, accepting t h e bff values from t h e AC f i e l d e f f e c t , we o b t a i n an a-' f o r t h e pure f i l m of around 40 pm, which would correspond, using simple quantum mechanics t o an energy gap value of 24eV. Such a value i s obviously unphysical.
Moreover one would n o t expect from t h i s model such a r a p i d v a r i a t i o n of a-I with hydrogen content. (The o p t i c a l gap changes by some 100% over t h i s range o f hydrogenation (141, b u t t h e change i s i n t h e o p p o s i t e sense t o t h a t p r e d i c t e d by simple quantum mechanics from the
a'
d a t a ) .The temperature dependence and f i e l d e f f e c t d a t a cannot be explained e i t h e r using t h e i d e a s o f t u n n e l l i n g i n a uniform d e n s i t y of s t a t e s . A s we have a l r e a d y sugges- t e d , t h e low f i e l d l o s s should vary l i n e a r l y with temperature. The observed
temperature dependence would imply a narrow peak i n t h e d e n s i t y o f s t a t e s a t t h e F e d l e v e l of width % kT, which we consider p h y s i c a l l y u n l i k e l y . I n t h e high f i e l d
C4-1 10 J O U R N A L DE PHYSIQ'JE
l i m i t , t h e AC l o s s i s n o n - l i n e a r and d i f f i c u l t t o c a l c u l a t e . However we do n o t b e l i e v e t h a t t h e o b s e r v a t i o n s a r e i n a c c o r d w i t h t h i s m d e l .
Our c o n c l u s i o n t h e r e f o r e i s t h a t , a s w i t h t h e h i g h t e m p e r a t u r e d a t a ( 1 , 2 ) , t u n n e l l i n g o f e l e c t r o n s between s t a t e s u n i f o r m l y d i s t r i b u t e d i n s p a c e and i n e n e r g y c a n n o t p r o v i d e a n e x p l a n a t i o n o f t h e o b s e r v a t i o n s .
5. C o n c l u s i o n . Given t h a t t h e e f f e c t i v e hopping d i s t a n c e f o r p u r e f i l m s is o n l y o f t h e o r d e r o f lnm, w e p o s t u l a t e t h a t the AC l o s s we a r e measuring o c c u r s i n i n t i m a t e p a i r s o f s t a t e s w i t h o n l y weak c o u p l i n g between t h e p a i r s . I n o r d e r t o e x p l a i n why t h e s e s t a t e s r e s p o n d a t a u d i o f r e q u e n c i e s , w h i l e r e t a i n i n g a r e a s o n a b l e v a l u e f o r t h e i n t r i n s i c " a t t a c k f r e q u e n c y " T , - ~ , t h e p a i r s must b e c o u p l e d v i a a p o t e n t i a l b a r r i e r o f magnitude many t i m e s kT. T h i s model r e s e m b l e s t h e i d e a s which h a v e b e e n s u c c e s s f u l i n e x p l a i n i n g o u r n i t r o g e n t e m p e r a t u r e d a t a ( 1 , 2 ) and we hope to p u r s u e t h i s comparison i n f u t u r e work.
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