HAL Id: jpa-00221676
https://hal.archives-ouvertes.fr/jpa-00221676
Submitted on 1 Jan 1981
HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
THE MULTIVALUED DISTRIBUTION OF
ELECTRONS BETWEEN EQUIVALENT VALLEYS
M. Asche, H. Kostial, O. Sarbey
To cite this version:
M. Asche, H. Kostial, O. Sarbey. THE MULTIVALUED DISTRIBUTION OF ELECTRONS BE-
TWEEN EQUIVALENT VALLEYS. Journal de Physique Colloques, 1981, 42 (C7), pp.C7-323-C7-
328. �10.1051/jphyscol:1981739�. �jpa-00221676�
Colloque C7, supplément au n°10, Tome 42, octobre 1981 page C7-323
Résumé.- Dans le Si-n la distribution multiforme d'électrons chauds entre des vallées équivalentes conduit à. la formation de domaines de haut champ en vertu de la conductivité négative dif- férentielle du type N et de la formation de structure des couches avec des champs opposés de Sasaki pour des températures au-des- sous de 50 K.
THE MULTIVALUED DISTRIBUTION OF ELECTRONS BETWEEN EQUIVALENT VALLEYS
M. Asche, H. Kostial and O.G. Sarbey*Zentralinstitut fur Elektronenphysik dev AdW der DDR, Berlin, Germany.
*Institut fiziki AN USSR, Kiev, USSR.
Abstract. - In n-Si the multivalued distribution of hot electrons among the valleys (mde) leads to static high field domains on account of N-type ndc and to layers of opposite Sasaki fields for temperatures below 50 K.
1. Introduction. - The subject of the present investigations can be described in the following way: when in a finite sample the current j is directed according to Fig. 1, on account of the conductivity
f 1S
anisotropy in the single valleys there are opposite currents 1
v'
and j y x
v' besides the contributions of both pairs of valleys to i . When there appears a field F* by fluctuation it originates par-
allel currents j * ' ' and i'v
2) but opposite components j'^ ' and
(2\ y y *
j'
v'. Because of these fluctuations, in a heating field the elec-
trons of the second pair of valleys gain more energy and those of the first one will be cooled. In the case of intervalley transitions
Fig. 1: Fields and currents for the equivalent valleys
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1981739
C7-324 JOURNAL DE PHYSIQUE
o f t h e e l e c t r o n s w i t h t h e a s s i s t a n c e o f phonons t h i s l e a d s t o a h i g h e r p o p u l a t i o n o f t h e p a i r o f v a l l e y s 1 i n comparison t o t h e v a l l e y s 2. T h e r e f o r e a l l c u r r e n t c o n t r i b u t i o n o f t h e v a l l e y s 1 a r e i n c r e a s e d , b u t t h o s e o f v a l l e y s 2 a r e decreased.
~f j
('1 -
(2)< j a + j a ( 2 ) t h e f l u c t u a t i o n becomes d i m i n i s h e d ,Y
( 1 ) j y f o r JY
-
jy(2)>l;(1) i t r i s e s . T h i s means t h a t a new + j yasymmetric s t a t e o f t h e semiconductor becomes r e a l i z e d , which i s c h a r a c t e r i z e d by t h e presence o f an e l e c t r i c f i e l d t r a n s v e r s e t o jx
( S a s a k i - f i e l d ) . Of course, i n t h e same way a f l u c t u a t i o n o f t h e o p p o s i t e s i g n has t o be regarded. T h e r e f o r e i n t h e case o f j y ( l )
-
j Y (2)> jl(')
+
j;(2) a symmetric s t a t e w i t h e q u a l e l e c t r o n d e n s i t i e s i n b o t h t h e p a i r s o f v a l l e y s i s u n s t a b l e , and t h e s t a b l e Y s o l u t i o n on t h e o t h e r hand i s d e t e r m i n e d by t h e boundary c o n d i t i o n s . The t h e o r y /1/ p r e d i c t s t h a t b o t h p o s s i b l e asymmetric s t a t e s ( w i t h d o m i n a t i n g p o p u l a t i o n i n t h e f i r s t o r second p a i r o f v a l l e y s , r e s p e c t i v e l y ) c o e x i s t i f i n t e r v a l l e y s c a t t e r i n g on t h e s u r f a c e i s l a c k i n g ; t h e sample decays i n t o two l a y e r s w i t h o p p o s i t e s i g n o f t h e t r a n s v e r s e f i e l d and t h e w a l l between them extends a l o n g t h e c u r r e n t d i r e c t i o n and l i e s i n t h e m i d d l e o f t h e sample i f t h e l a t t e r i s p e r f e c t l y homogeneous and e x a c t l y o r i e n t a t e d .2. R e s u l t s .
-
Our experiments were performed w i t h quadershaped samples of n - S i w i t h 5 x 1013< ND<5 x 1014 cme3 and NA< 2 xloi3
cm3 w i t h t h e l o n g a x i s p a r a l l e l t o <.110>. The measurements were p e r - formed f o r temperatures between 20 and 77 K. The e x i s t e n c e o f mde was observed f r o m 20 K u p t o 5 0 K.As a f i r s t e f f e c t of mde (Fig. 2a) t h e c u r r e n t v o l t a g e c h a r a c t e r - i s t i c s e x h i b i t r e g i o n s o f c u r r e n t s a t u r a t i o n f o r T 5 5 0 K. They a r e c r e a t e d by domains of a h i g h s t a t i c e l e c t r i c f i e l d f o r F > F c which appear on account of N-type ndc f o r t h e c o n d i t i o n of mde + ) and can be e x h i b i t e d by t h e p o t e n t i a l d i s t r i b u t i o n a l o n g t h e sample. The v a l u e s o f t h e e l e c t r i c f i e l d s i n t h e domains depend on t h e l a t t i c e
+)
r e a l p i c t u r e o f mde f o r n - S i w i t h j a l o n g (110) d i f f e r s from t h e s c e t c h o f F i g . 1 by t h e t h i r d p a i r o f v a l l e y s on t h e < 0 0 1 ) a x i s . I n o r d e r t o demonstrate t h a t t h e ndc observed i s n o t connected w i t h a r e d i s t r i b u t i o n o f c a r r i e r s f r o m these v a l l e y s i n t o b o t h t h e o t h e r p a i r s experiments w i t h u n i a x i a l p r e s s u r e were performed /2/ as w e l l as Monte C a r l o c a l c u l a t i o n s /3/.s t r e n g t h s Fc m a r k e d b y a r r o w s ( t h e c u r r e n t d e n s i t i e s f o r 27 K a r e m u l t i p l i e d by 1 0 )
F i g . 2 b r V o l t a g e d i f f e r e n c e b e t w e e n o p p o s i t e p r o b e s on ( i 1 0 ) - s u r - f a c e s ( d i s t a n c e 0,19 cm) v e r s u s m a g n e t i c i n d u c t i o n a p p l i e d a l o n g (001)
t e m p e r a t u r e c h o s e n a n d f o r 27 K f o r i n s t a n c e t h e y a r e a b o u t 70
-
80 V/cm I n t h e h i g h f i e l d d o m a i n a n d a b o u r 4 0 V/cm i n t h e l o w f i e l d r e g i o n . F u r t h e r o n a s t o be s e e n f r o m F i g . 2 a t h e c r i t i c a l f i e l d Fc n e c e s s a r y f o r t h e a p p e a r a n c e o f mde r i s e s w i t h T. From t h e v a l u e of F c o n c l u s i o n s w i t h r e s p e c t t o t h e i n t e r v a l l e y s c a t t e r i n g p r o c e s s e s
C
can b e d r a w n /3/.
C7-326 JOURNAL DE PHYSIQUE
A n o t h e r e f f e c t observed f o r mde i s t h e decay o f t h e samples i n t o two l a y e r s w i t h o p p o s i t e s i g n s o f t h e t r a n s v e r s e e l e c t r i c f i e l d . T h i s was i n v e s t i g a t e d by a r r a n g i n g s e v e r a l probes on t h e (001)-surfaces p e r - p e n d i c u l a r t o t h e c u r r e n t d i r e c t i o n a l l o w i n g t o observe t h e p o s i t i o n o f t h e w a l l between t h e l a y e r s . As a consequence o f t h e l a y e r e d s t r u c t u r e t h e r e can appear a t r a n s v e r s e v o l t a g e d i f f e r e n c e between o p p o s i t e probes on t h e (310)-surfaces /4/.
W h i l e t h e c u r r e n t s a t u r a t e s i n a c e r t a i n r e g i o n o f F f o r a l l samples t h e t r a n s v e r s e v o l t a g e d i f f e r e n c e between b o t h t h e probes on (TIo) s u r f a c e s can n o t always be observed: t h e r e a r e samples i n which i t does n o t appear a t a l l i n t h e whole r e g i o n o f f i e l d s t r e n g t h s i n v e s - t i g a t e d , o t h e r s f o r which i t was measured a l r e a d y f o r F about F and
C
a t h i r d group where i t shows up f o r some f i e l d s t r e n g t h above F c These t y p e s o f b e h a v i o u r a r e caused by t h e p o s i t i o n o f t h e w a l l i n t h e r e g i o n o f t h e probes. I n t h e presence o f any inhomogeneity which d i s t u r b e s t h e symmetry t h e w a l l i s s h i f t e d f r o m t h e m i d d l e o f t h e sample towards one o f t h e s u r f a c e s and t h e n a v o l t a g e d i f f e r e n c e can be measured between b o t h t h e (x10) s u r f a c e s .
Another e f f e c t o f t h e mde i s t h e pronounced i n f l u e n c e o f t r a n s v e r s e magnetic f i e l d s on t h e c u r r e n t v o l t a g e c h a r a c t e r i s t i c s and t h e S a s a k i - f i e l d s .
F o r F> Fc t h e m a g n e t o c o n d u c t i v i t y o f t h e sample depends on t h e p o l a r i t y o f B when i n t h e absence o f t h e magnetic f i e l d t h e w a l l was n o t s i t u a t e d i n t h e m i d d l e o f t h e sample and i s n o t s h i f t e d symmetri- c a l l y by b o t h t h e p o L a r i t i e s o f B.
The f l e l d s t r e n g t h measured as t h e d r o p o f t h e p o t e n t i a l between an end c o n t a c t and probes on ( T l 0 ) - s u r f a c e s d i v i d e d by t h e d i s t a n c e e x h i b i t s s i g n i f i c a n t changes i n t h e r e g i o n o f weak magnetic f i e l d s
(Fig. 3 ) d e m o n s t r a t i n g how t h e H a l l f i e l d s w i t c h e s t h e w a l l between b o t h s i d e s o f t h e sample. T h e r e f o r e t h e p o t e n t i a l d i f f e r e n c e between o p p o s i t e probes r i s e s s t r o n g l y when i t was o n l y weakly pronounced i n t h e absence o f B. I n samples f o r which t h e r e was a l r e a d y a remarkable d i f f e r e n c e between t h e probes t h e magnetic f i e l d o f one p o l a r i t y changes i t o n l y a l i t t l e , b u t f o r t h e o t h e r p o l a r i t y t h e magnetic f i e l d s w i t c h e s t h e t r a n s v e r s e v o l t a g e d i f f e r e n c e t o one o f t h e o p p o s i t e s i g n and almost t h e same amount.
-
T h i s s h i f t was examined i n d e t a i l a g a i n by experiments w i t h a d d i t i o n a l probes on (001)- s u r f aces.The dependence o f t h e t r a n s v e r s e v o l t a g e d i f f e r e n c e on magnetic f i e l d s t r e n g t h i s shown i n F i g . 2 b f o r s e v e r a l temperatures a t a
a l o n g < 1 1 0 ) i n d e p e n d e n c e on a m a g n e t i c i n d u c t i o n p a r a l l e l t o
<
0 0 1 )h e a t i n g e l e c t r i c f i e l d o f 1 0 6 V/cm. I n s t e a d o f t h e l i n e a r d e p e n d e n c e on B o b s e r v e d f o r weak e l e c t r i c f i e l d s , i n t h e p r e s e n c e o f mde t h e r e a r e two r e g i o n s t o b e s e e n : f o r s m a l l B t h e r e i s a s t e e p r i s e o f t h e v o l t a g e d i f f e r e n c e i n c o n t r a s t t o b i g B, f o r w h i c h t h e t r a n s v e r s e v o l t a g e d i f f e r e n c e i n c r e a s e s o n l y s l o w l y a s o b s e r v e d i n t h e common H a l l e f f e c t . When mde i s r e a l i z e d i n t h e w h o l e s a m p l e + ) t h e s l o p e o f t h e s t e e p r i s e is p r a c t i c a l l y i n d e p e n d e n t o f t h e f i e l d a n d t h e t e m p e r a t u r e . F o r T> 5 0 K o r
FZ
2 0 0 V/cm t h e s l o p e d i m i n i s h s a g a i n b e c a u s e t h e r e e x i s t s n o mde a n y m o r e b u t o n l y a n a n o m a l e o u s H a l l e f f e c t r e m a i n s i n a c c o r d a n c e w i t h t h e o r y /I/.-
') F o r F j u s t a b o v e Fc t h e s l o p e h a s n o t g a i n e d i t s m a x i m a l v a l u e b e c a u s e t h e l a y e r e d s t r u c t u r e o n l y e x i s t s i n t h e h i g h f i e l d d o m a i n , w h i c h s t i l l d o e s n o t e x t e n d t o t h e s p a c e b e t w e e n t h e p r o b e s .
C7-328 JOURNAL DE PHYSIQUE
3. C o n c l u s i o n .
-
The i n v e s t i g a t i o n o f t h i s s t r o n g l y n o n l i n e a r s y s t e m ( t h e dependence o f t h e v a l l e y p o p u l a t i o n on t h e h e a t i n g e l e c t r i c f i e l d ) d e m o n s t r a t e s t h e s p o n t a n e o u s symmetry b r e a k i n g c o n n e c t e d w i t h t h e m u l t i v a l u e d e l e c t r o n d i s t r i b u t i o n between e q u i v a l e n t v a l l e y s . B e s i d e s t h e Gunn e f f e c t t h e r e a l i z a t i o n o f s t a b l e a s y m m e t r i c s t a t e s on a c c o u n t o f mde i s a n o t h e r example f o r s y n e r g e t i c phenomena.The a u t h o r s acknowledge t h e p a r t i c i p a t i o n o f L.F.Kurtenok i n a p a r t o f t h e e x p e r i m e n t s .
/1/ Z. S. G r i b n i k o v , V. A. Kochelap, V. V. M i t i n , Zh. Eksper. Teor.
F i z .
59,
1828 (1970)/2/ M. Asche, H. K o s t i a l , 0. G, Sarbey, J. Phys. C
13,
L 645 (1980) /3/ 2. S. G r i b n i k o v , V. M, Iwashenko, V. V. M i t i n , 0. G. S a r b e y ,C h i s l e n n i i r a s c h e t mnogoznachnykh r a s p r e d e l e n i i e l e c t r o n o v po d o l i n a m v S i , p r e p r i n t 8, akademia nauk USSR, i n s t i t u t f i z i k i , K i e v (1981)
/4/ M. Asche, H. K o s t i a l , S o l . S t a t e Commun. ( 1 9 8 1 )
