ACOUSTOELECTRIC INTERACTION IN p-InSb AT LOW TEMPERATURE

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ACOUSTOELECTRIC INTERACTION IN p-InSb AT LOW TEMPERATURE

J. Cheeke, G. Madore

To cite this version:

J. Cheeke, G. Madore. ACOUSTOELECTRIC INTERACTION IN p-InSb AT LOW TEMPERATURE. Journal de Physique Colloques, 1981, 42 (C6), pp.C6-569-C6-571.

�10.1051/jphyscol:19816165�. �jpa-00221243�

JOURNAL DE PHYSIQUE

CoZZoque C6, suppte'ment au n012, Tome 42, de'cembre 1981

ACOUSTOELECTRIC INTERACTION IN p-InSb AT LOW TEMPERATURE

J . D . N . Cheeke and G. Madore

Dgpartement de Physique, Universite' de Sherbrooke, Sherbrooke, Prov. QuSbec, Canada J1K 2R1

A b s t r a c t .

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There have been many r e c e n t u l t r a s o n i c s t u d i e s of resonance, r e l a x a t i o n and magnetic f i e l d e f f e c t s a s s o c i a t e d w i t h a b s o r p t i o n by i m p u r i t i e s i n p t y p e semicon- d u c t o r s a t low t e m p e r a t u r e s ( 1 ) . Our f i r s t r e s u l t s on p-InSb were i n t e r p r e t e d i n t h i s way (1) ( 2 ) . However more r e c e n t r e s u l t s t o b e p r e s e n t e d h e r e suggest t h a t t h e r e l a x a t i o n and low t e m p e r a t u r e magnetic f i e l d e f f e c t s observed i n t h i s system a r e i n f a c t due t o a p i e z o e l e c t r i c i n t e r a c t i o n w i t h f r e e o r bound c a r r i e r s .

The experiments were c a r r i e d o u t i n t h e u s u a l way w i t h a Matec 6600 system and PAR two channel Boxcar i n t e g r a t o r . LiNb03 30 MHz t r a n s d u c e r s were g r e a s e bonded t o t h e p o l i s h e d f a c e s and a double c a l o r i m e t e r was used f o r temperature s t a b i l i t y and c o n t r o l . Experiments were c a r r i e d o u t on Ge doped InSb specimens w i t h concen- t r a t i o n s of 1014, 2 . 1 0 ~ ~ and 8 . 1 0 ~ cm-3. Only t h e f i r s t w i l l be d i s c u s s e d h e r e , t h e second showing s i m i l a r r e s u l t s and t h e t h i r d , which appears t o b e d e g e n e r a t e , shows no unusual behaviour.

T y p i c a l r e s u l t s f o r t h e r e l a x a t i o n peak a r e shown i n F i g u r e 1. The peak h e i g h t and p o s i t i o n s c a l e w i t h w , such t h a t UT-1 w i t h T = =,(H) e A / k ~ T , A

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Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19816165

C6-5 70 JOURNAL DE PHYSIQUE

subsequent r e l a x a t i o n , a r e l a x a t i o n peak i s p r e d i c t e d by t h i s t h e o r y , of t h e form:

where = e l e c t r o m e c h a n i c a l coupling c o e f f i c i e n t

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Vso = sound v e l o c i t y , w = U / E = d i e l e c t r i c r e l a x a t i o n frequency, 0 = d . c . e l e c t r i - c a l c o n d u c t i v i t y , E = s t a t i c d i e l e c t r i c c o n s t a n t , w = a p p l i e d a n g u l a r frequency, wD = V s o 2 / ~ , D = uk T/e, t h e E i n s t e i n r e l a t i o n w i t h y = c a r r i e r m o b i l i t y . The i m -

B

p o r t a n t term i n t h e r e l a x a t i o n i s t h a t i n v o l v i n g w and t o f i r s t approximation t h i s g i v e s a simple r e l a x a t i o n r = w -l. T h i s corresponds roughly t o what i s observed a l t h o u g h t h e r e i s some t r o u b l e w i t h t h e magnetic f i e l d dependence of t h e p r e f a c t o r of .r. Using known v a l u e s of t h e above parameters and u s i n g a m o b i l i t y determined from t h e 77K H a l l e f f e c t measurements a numerical c a l c u l a t i o n g i v e s good agreement between t h e above e x p r e s s i o n and t h e experimental r e s u l t s a s r e g a r d s peak a t t e n u a - t i o n and frequency, temperature and magnetic f i e l d dependence.

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MAGNETIC FIELD ( H : T E S L A l

o , l o ~ 0.0 l.? 2.0 3 0 4.0 S O 6.0 7 0 80

F i g u r e 1 F i g u r e 2

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It i s now i n t e r e s t i n g t o r e g a r d t h e low temperature behaviour (T < 7K) where t h e mobile c a r r i e r s a r e t h e r m a l l y f r o z e n o u t and t h e e l e c t r i c a l conduction i s by

A

A a . a ( n 1 - a t 0 1

I d b / s n l A ~ ~ l l l ] LONG WAVE

p - l n s b I O " % ~

1 . 2 7 0 M H z 7J.T ^{"A A A +}

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hopping of c a r r i e r s between compensated i m p u r i t y s i t e s . I n t h i s temperature r e g i o n we observe an important d e c r e a s e of a t t e n u a t i o n w i t h a p p l i e d magnetic f i e l d . A s i n d i c a t e d f o r one c a s e i n F i g u r e 2 t h i s magnetic f i e l d e f f e c t f o l l o w s t h e same se- l e c t i o n r u l e a s f o r t h e r e l a x a t i o n peak. We t h u s deduce t h a t t h e i n t e r a c t i o n mecha- nism i s a g a i n p i e z o e l e c t r i c , a l t h o u g h a numerical c a l c u l a t i o n c l e a r l y shows t h a t t h i s a t t e n u a t i o n d e c r e a s e i s n o t t h e t a i l of t h e r e l a x a t i o n peak. I n f a c t t h e

s i t u a t i o n corresponds p h y s i c a l l y t o t h a t d e s c r i b e d by Chaikovskii and G i t i s (4), who modify t h e Hutson and White treatment f o r t h e c a s e of hopping conduction. For w > w t h i s g i v e s a- c t e U. A t p r e s e n t i t i s not e a s y t o t e s t t h i s r e l a t i o n r e - g a r d i n g t h e temperature dependence a s t h i s i s q u i t e weak and t h e r e s i d u a l a t t e n u a - t i o n i s unknown. However t h e magnetic f i e l d v a r i a t i o n of t h e a t t e n u a t i o n is i n good agreement w i t h t h a t e s t i m a t e d from t h e above e x p r e s s i o n a l t h o u g h a t p r e s e n t we o n l y have r e s u l t s f o r t h e DC magnetoresistance. The c r u c i a l t e s t w i l l b e pro- vided by comparing t h e f i e l d dependence of t h e a t t e n u a t i o n w i t h t h e a c magnetore- s i s t a n c e . T h i s s t u d y i s c u r r e n t l y being undertaken.

I n summary t h e p r e s e n t r e s u l t s a r e i n good agreement w i t h t h e a c o u s t o e l e c t r i c t h e o r y f o r i n t e r a c t i o n w i t h f r e e and hopping c h a r g e c a r r i e r s . F u r t h e r experiments a r e i n p r o g r e s s i n a n a t t e m p t t o d i s t i n g u i s h unequivocally between t h i s model and t h a t i n v o l v i n g a b s o r p t i o n by i s o l a t e d i m p u r i t y c e n t r e s .

This work was supported by t h e N a t u r a l Science and Engineering Council of Canada and t h e Groupe d e Recherches s u r l e s semiconducteurs e t d i s l e c t r i q u e s . We a r e g r a t e f u l t o A. Hikata f o r p a r t i c i p a t i o n i n some of t h e e a r l y experiments.

REFERENCES

1 ) K. Lassman and o t h e r p a p e r s i n Phonon s c a t t e r i n g i n condensed m a t t e r ( e d i t e d by H . J . Maris) Plenum P r e s s New York (1980).

2) J . D . N . Cheeke, G. Madore and A. Hikata, S o l i d S t a t e Communications 38, 755, (1981).

3 ) A.R. Hutson and D.L. White, Jour. App. Phys. 33, 40, (1962).

4) I . A . Chaikovskii and M.B. G i t i s , S o v i e t P h y s i c s S o l i d S t a t e

2,