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MAGNETIC FIELD DEPENDENT RELAXATION TIME IN p-InSb AT LOW TEMPERATURES
J. Cheeke, G. Madore, A. Hikata
To cite this version:
J. Cheeke, G. Madore, A. Hikata. MAGNETIC FIELD DEPENDENT RELAXATION TIME IN p- InSb AT LOW TEMPERATURES. Journal de Physique Colloques, 1981, 42 (C5), pp.C5-689-C5-693.
�10.1051/jphyscol:19815106�. �jpa-00220974�
JOURNAL DE P H Y S I Q U E
CoZZcque C5, suppZ&ment au nO1O, Tome 42, octobre 1981 page C5-689
MAGNETIC F I E L D D E P E N D E N T RELAXATION T I M E IN
p-InSbA T LOW T E M P E R A T U R E S
J.D.N. t h e e k e , G . Madore and A. ~ i k a t a *
Ddpartement de Physique, Universit6 de Sherbrooke, Sherbrooke JIK Z R I ,
@&bee, Canada
'
Metals Research Laboratory, Brown U n i v e r s i t y , Provide?zce RI, U. S. A.Abstract.- We have observed a magnetic f i e l d dependent r e l a x a t i o n time i n p-InSb a t low temperatures (slOK) where t h e e l e c t r i c a l conduction i s by f r e e holes i n the valence band. The r e l a x a t i o n peak i s o n l y observed i n nondege- n e r a t e specimens f o r those a c o u s t i c modes which are p i e z o e l e c t r i c a l l y a c t i v e . The r e s u l t s are compared w i t h t h e a c o u s t o - e l e c t r i c theory o f Hutson and White and found t o be i n s u b s t a n t i a l agreement.
There have been many r e c e n t i n v e s t i g a t i o n s o f u l t r a s o n i c a b s o r p t i o n by shallow and deep i m p u r i t y centers i n semiconductors a t low temperatures, i n which e f f e c t s c h a r a c t e r i c t i c o f b o t h resonance and r e l a x a t i o n regimes due t o a b s o r p t i o n by impur- i t y centers have been observed
[I).
Our p r e l i m i n a r y r e s u l t s on p-InSb were a l s o i n t e r p r e t e d i n t h i s way (2). However more r e c e n t d a t a on the p o l a r i s a t i o n depend- ence o f t h e a t t e n u a t i o n , taken t o g e t h e r w i t h t h e s t r o n g c o r r e l a t i o n between r e s i s t - i v i t y and a t t e n u a t i o n r e s u l t s p o i n t s t o the p i e z o e l e c t r i c i n t e r a c t i o n between the u l t r a s o n i c wave and f r e e holes i n t h e valence band as being a t t h e o r i g i n o f t h e observed r e l a x a t i o n peaks. It appears t h a t t h i s i n t e r a c t i o n i s r e s p o n s i b l e f o r the magnetic f i e l d dependent a t t e n u a t i o n i n both t h e f r e e and bound c a r r i e r regimes, b u t o n l y the former case w i l l be t r e a t e d i n t h i s c o m u n i c a t i o n .Specimens o f p-InSb doped w i t h Germanium w i t h excess concentrations o f 10'"
2-10'5 and 8.1016 have been s t u d i e d i n t h e present work. The r e s i s t i v i t y measurements were made by t h e conventional 4 probe method i n p a r a l l e l magnetic f i e l d s . The u l t r a s o n i c measurements were made u s i n g standard techniques w i t h a Matec system and l i t h i u m n i o b a t e transducers grease bonded onto t h e specimen s u r f - c e s . A l l measurements were made i n a double c a l o r i m e t e r w i t h He exchange gas and a lakeshare c a p a c i t i v e diode i n the bore o f an 8T superconducting solenoid.
Yost o f t h e u l t r a s o n i c work was done i n perpendicular magnetic f i e l d s as t h e e f f e c t s were r a t h e r l a r g e r than i n p a r a l l e l f i e l d . V e l o c i t y measurements were made o n l y a t 30
MHz
f o r t e c h n i c a l reasons by t h e p u l s e o v e r l a p method w i t h a p r e c i s i o n o f aboutl o - '
i n Av/v.Typical experimental r e s u l t s f o r t h e a t t e n u a t i o n i n zero magnetic f i e l d as a f u n c t i o n o f temperature and frequency are shown i n f i g . 1 . The s c a l i n g o f t h e amplitude and
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19815106
JOURNAL DE PHYSIQUE
F i g u r e 2 F i g u r e 1
j
i
TEMPERATURE T ( K l I 5 6 7 8 9 10 11 I2 IS I4 I5 I6 I T 18 19 20 21F i g u r e 3 F i g u r e 4
p o s i t i o n o f t h e peaks with frequency c l e a r l y e s t a b l i s h e s t h i s as a r e l a x a t i o n peak.
A p p l i c a t i o n o f a magnetic f i e l d has a dramatic e f f e c t on t h e peak p o s i t i o n as i n d i c a t e d i n f i g . 2 , where a t 30 MHz t h e peak i s s h i f t e d by several degrees by f i e l d s o f t h e o r d e r o f a few Tesla. V e l o c i t y measurements f o r t h e same specimen i n i d e n t i c a l c o n d i t i o n s a r e shown i n f i g . 3 . Again t h e form o f t h e Av/v (T) curve i s c h a r a c t e r i s - t i c o f a r e l a x a t i o n process and t h i s curve i s s h i f t e d i n i d e n t i c a l f a s h i o n by a magnetic f i e l d . The behaviour c l e a r l y i n d i c a t e s t h e existence o f a magnetic f i e l d dependent r e 1 a x a t i o n time.
S i m i l a r measurements were made on t h e r e s i s t i v i t y i n t h i s temperature and f i e l d range and these r e s u l t s a r e shown i n f i g . 4 . A t t h e h i g h e r temperatures (T > 7K) we a r e a b l e t o i d e n t i f y t h e E X conduction regime due t o f r e e holes i n t h e valence band.
The slope o f t h e curves i n f i g . 4 gives a i o n i s a t i o n energy E, a 10 meV. A t lower temperatures ( T <
6K)
a f t e r a p o s s i b l e t r a n s i t i o n through an c 2 i m p u r i t y band regime we pass i n t o t h e E, hopping conduction regime w i t h €,20,2 meV. The general form o f t h e r e s u l t s and t h e values o f t h e a c t i v a t i o n energies a r e i n good agreement w i t h previous work on s i m i l a r specimens (3). One should a l s o note i n f i g . 4 t h a t t h e r e l a x a t i o n time obtained from the usual r e l a x a t i o n formula and t h e peak p o s i t i o n has a form s i m i l a r t o t h a t o f t h e r e s i s t i v i t y w i t h approximately t h e same a c t i v a t i o n energy A % 10 meV. This i n d i c a t e s a very close c o r r e l a t i o n between the r e s i s t i v i t y and a t t e n u a t i o n mechanisms.Besides t h e magnetic f i e l d dependence, i m p o r t a n t i n f o r m a t i o n i s provided by t h e p o l a r i s a t i o n dependence o f t h e a t t e n u a t i o n peak. I t i s found t h a t t h e r e i s o n l y a r e l a x a t i o n peak f o r those modes which a r e p i e z o e l e c t r i c a l l y a c t i v e , t h a t i s l o n g i - t u d i n a l waves along (111) and transverse waves along (1 10) w i t h (001) p o l a r i s a t i o n . As the peak i s always found i n t h e c o n d u c t i v i t y regime, t h i s s t r o n g l y suggests t h a t t h e observed e f f e c t s a r e due t o t h e p i e z o e l e c t r i c i n t e r a c t i o n between t h e u l t r a s o n i c waves and f r e e holes i n the valence band. This i n t e r a c t i o n has been s t u d i e d i n g r e a t d e t a i l i n t h e a c o u s t o - e l e c t r i c e f f e c t , and i n f a c t i n i t s s i m p l e s t form t h e theory p r e d i c t s r e l a x a t i o n and d i s p e r s i v e e f f e c t s s i m i l a r t o those observed here, p r i n c i p a l l y due t o t h e d i e l e c t r i c r e l a x a t i o n frequency w c - u / e ( a = e l e c t r i c a l c o n d u c t i v i t y and E = d i e l e c t r i c c o n s t a n t ) associated w i t h t h e f r e e c a r r i e r space charge b u i l t up by t h e p i e z o e l e c t r i c f i e l d s . This simple theory (4) gives f o r t h e a t t e n u a t i o n a:
where K2 = electromechanical coup1 i n g constant v, = sound v e l o c i t y .
C5-692 JOURNAL DE PHYSIQUE
We a r e t h u s l e d t o a s s o c i a t e wc w i t h 1 / ~ o f f i g . 4 . However as n o t e d p r e v i o u s l y (2) w h i l e t h e a c t i v a t i o n e n e r g i e s f o r T and p observed e x p e r i m e n t a l l y a r e i n r e a s o n a b l e agreement, t h e f i e l d dependent p r e f a c t o r s a r e n o t . A d e t a i l e d a n a l y s i s o f t h i s p o i n t i s underway b u t i t appears t h a t one o r b o t h o f two c o r r e c t i o n f a c t o r s must be c o n s i - dered. F i r s t l y as s t r e s s e d by s e v e r a l workers (5)
,
cr = l / p o n l y f o r m a g n e t i c f i e l d s p a r a l l e l t o t h e c u r r e n t d i r e c t i o n w h i c h means t h a t t h e a t t e n u a t i o n d a t a m u s t be o b t a i n e d f o r p a r a l l e l f i e l d s b e f o r e an e x a c t comparison w i t h t h e s i m p l e t h e o r y can be made. Secondly t h e l a t t e r s h o u l d be m o d i f i e d t o t a k e i n t o account c a r r i e r "de- bunching" e f f e c t s due t o t h e i r t h e r m a l d i f f u s i o n , c h a r a c t e r i z e d by a d i f f u s i o n frequency wD-
v i / O where t h e d i f f u s i o n c o n s t a n t 0 = p k T/q, w i t h p = c a r r i e r mobi 1 i t y6
and q = e l e c t r o n i c charge. Then t h e m o d i f i e d f o r m f o r t h e a t t e n u a t i o n becomes (4) :
D e t a i l e d comparison w i t h t h i s more s o p h i s t i c a t e d t r e a t m e n t must a w a i t t h e experiment- a l d e t e r m i n a t i o n o f t h e p a r a l l e l f i e l d a t t e n u a t i o n and t h e H a l l e f f e c t under i d e n t i c - a l c o n d i t i o n s . However a p r e l i m i n a r y c a l c u l a t i o n u s i n g r e a s o n a b l e v a l u e s f o r t h e m o b i l i t y shows t h a t t h e q u a l i t a t i v e v a r i a t i o n o f u as a f u n c t i o n o f IA, T and H as w e l l as t h e o r d e r o f magnitude o f t h e peak h e i g h t can be v e r y w e l l e x p l a i n e d b y t h i s model
.
A number o f f u r t h e r experiments a r e planned i n o r d e r t o d i s t i n g u i s h between t h i s model and t h e i m p u r i t y a b s o r p t i o n model (2). We p l a n t o t e s t t h e l a t t e r b y l o o k i n g f o r a resonance regime a t h i g h e r f r e q u e n c i e s and l o w e r temperatures; p r e l i m i n a r y r e s u l t s a t 700 MHz down t o 1.3K have been n e g a t i v e on t h i s p o i n t . Secondly we hope t o make a q u a n t i t a t i v e t e s t o f t h e p r e s e n t f r e e c a r r i e r a b s o r p t i o n model by p a r a l l e l f i e l d a t t e n u a t i o n and H a l l e f f e c t measurements; i n t h i s case t h e r e would be no f r e e parameters i n t h e t h e o r e t i c a l e x p r e s s i o n s g i v e n above.
I n c o n c l u s i o n a v a i l a b l e d a t a on t h e u l t r a s o n i c a t t e n u a t i o n i n p-InSb a t l o w temper- a t u r e s suggests a r e l a x a t i o n process due t o 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 t h e f r e e c a r r i e r s . Such an e f f e c t has n o t been observed b e f o r e a t low temperatures t o o u r knowledge; t h e p a r t i c u l a r i t y o f t h i s case as compared t o t h e u s u a l room t e m p e r a t u r e regime (4) i s t h a t t h e c a r r i e r d e n s i t y i s e x t r e m e l y s m a l l , %10" cm-3 f o r T a l O K . I f we o b t a i n a q u a n t i t a t i v e v e r i f i c a t i o n o f t h e model as o u t l i n e d above we hope t o a p p l y t h e method t o t h e d e t e r m i n a t i o n o f t h e e l e c t r o n i c parameters o f semiconductors, as w e l l as t o i n v e s t i g a t e t h e phenomenon i n o t h e r p i e z o e l e c t r i c semiconductors.
Acknowledgements: This work was supported by t h e N a t u r a l Science and Engineering Research Council o f Canada and the Groupe de Recherches s u r l e s Semiconducteurs e t D i e l e c t r i q u e s . One o f t h e authors (AH) would l i k e t o thank the Physics Dept a t Sherbrooke U n i v e r s i t y f o r welcoming him f o r several summers. Another (JDNC) wishes t o thank P r o f . and t h e
R.
Maynard f o r t h e i r h o s p i t a l i t y d u r i n g t h e p r e p a r a t i o n o f t h e manuscript. The authors a r e g r a t e f u l t o D r . Gremaud f o r h i s h e l p and understand- i n g i n producing the f i n a l copy.References:
(1) See f o r example papers i n "Phonon s c a t t e r i n g i n Condensed M a t t e r " H.J.Moris ed., Plenum Press, New York, 1980
( 2 ) JDN Cheeke, G.Madore and A.Hi kata, S o l i d S t a t e Comnunications 1981 ( I n Press)
(3) E.M.Gershenzon, I . ~ . ~ u r i l e n k o and
L.B
.Li tvok-Gorskaya, Sov. Phys. Semicond., 8, 768, 1974-
(4) A.R. Hutson and D.L.White, J . App. Phys.,
-
33, 40, 1962(5)
