LOW TEMPERATURE ANOMALIES OF ELECTRON PROPERTIES AND QUANTUM SIZE OSCILLATIONS IN THIN LAYERS OF Bi-Sb ALLOYS

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LOW TEMPERATURE ANOMALIES OF ELECTRON

PROPERTIES AND QUANTUM SIZE

OSCILLATIONS IN THIN LAYERS OF Bi-Sb ALLOYS

Yu.F. Komnik, E. Bukhshtab, Yu.V. Nikitin

To cite this version:

JOURNAL DE PHYSIQUE

Colloque

C6, supplbment au

no 8,

Tome

39,

aozit

1978,

page

C6-1142

LOW TEMPERATURE ANOMALIES OF ELECTRON PROPERTIES AND QUANTUM S I Z E O S C I L L A T I O N S

I N T H I N LAYERS OF

Bi-Sb

ALLOYS

Yu.F.Komnik, E.I.Bukhshtab and Yu.V.Nikitin

Physico-Technical I n s t i t u t e o f Low Temperatures, U?crSSR Academy o f Sciences, 47, Lenin Prospect, Kharkov, 310164, USSR

Rdsum6.- La transition semi-mdtal- conducteur n'existe pas dans Bil-xSbx en couches minces.

Cependant, le nombre de porteurs de charges augmente pour

X >

0.07, concentration

P

laquelle

un dtat semi-conducteur surgit dans les cristaux massifs. On a ddcouvert une augmentation de

la concentration des porteurs avec l'amincissement des couches. Ces anomalies sont lides

P

l'influence de la courbure du potentiel de couche au voisinage des surfaces. On a observe des

oscillations de rgsistance en fonction de lt6paisseur

et de la composition de l'alliage,

oscillations dues

B

l'effet quantique dimensionnel.

Abstract.- It has been found for Bi

Sb alloys that no semimetal-semiconductor transition

occurs in thin films and the charge k?rigr concentration grows at

X >

0.07, where the semi-

conductive state arises in bulk crystals. The growth of carrier concentration with a decrea-

se in the film thickness is observed. The anomalies are related to the effect of the film

potential bending near the surface. The resistance was observed to oscillate with varying

film thickness and alloy composition due to the quantum size effect.

It is known that the spectrum properties

of Bi

Sb crystals change smoothly with

X

growth:

I-X

X

the band overlap decreases and at

X

2

0.065 the

transition to a narrow-gap semiconductor is obser-

ved. In Bi

Sb films the electric properties

l-X X

depart from the bulk crystal ones mainly due to a

small thickness'l. The effect of thickness and

composition on resistance p, magnetoresistance coef-

ficient Ap/pH2 and Hall coefficient

was studied

on epitaxial thin Bi

Sb films at 4.2 K. Two

l-X

X

types of samples were used

: l)

of variable compo-

sition with fixed thickness, and 2) of variable

thickness with fixed composition.

It was found for samples of variable com-

position

(0.01 < X <

0.20), 3000-20000

I!

thick,

that at low

X

the electric characteristic variation

agrees qualitatively with changes in the electron

spectrum of bulk 'Bi

l-xSbx crystals

:

as the band

overlap decreases,

p

and

1%1

grow; however, with

a further

X

increases the resitance passes through

its maximum at

X

2

0.08 and then falls.

[ R ~ I

has

its peak at

X %

0.055. The magnetoresistance

coefficient Ap/pH2, describing a change in the

charge carrier mobility

y

in a compensated metal,

falls monotonically at

X >

0.02 (in the region

X %

0.02 there is -a

Ap/pH2 maximum and the cor-

responding mobility peak which seems to be due to

the vanished gap

E

in the band structure). A fall

g

in

p

and

1 ~ ~ 1

along with a monotonic decrease of

A ~ / ~ H ~

in the composition region, where a semi-

conductive state occurs i? bulk crystals, can be

accounted for by the absence of the semimetal-

semiconductor transition in thin films and by the

growth of the charge carrier concentration

17

with

increasing

X.

This conclusion supported by the

calculations of charge carrier concentration and

mobility using the two-band model fourmulae and

experimental quantities p, Ap/pH2 and

%.

It

appears that the dependence of charge carrier con-

centration on

X

has a minimum at

X %

0.06, where

decreases with increasing film thicknesses.

The studies on samples of a variable thick-

ness (400

<

L

< 11000

L)

and

0 < X <

0.14 com-

positions revealed that with decreasing L resis-

tance grows regularly, though as thickness reaches

certain magnitude,

p

starts to drop manifesting an

anomalous size effect. The region of dropping

p

expands with the growth of Sb contents (at

X =

0,

0.02, 0.035 the thickness corresponding to the

onset of drop is 2200, 5000 and 6000

I!

) .

In this

case A ~ / ~ H ~

and

IR I

increase monotonically with L

H

in the whole range of thicknesses. To illustrate

the anomalous size effect, Figure la shows the

change of conductivity a and magnetoresistance

coefficient A p / p ~ ~

with thickness. It is known that

a

is proportional to

p

and Ap/pH2 to

y2,

meanwhile

the behaviour of these characteristics with varying

thickness is quite opposite. The anomalous size

e f f e c t is caused by a growth of charge c a r r i e r c o n c e n t r a t i o n a s t h e f i l m t h i c k n e s s d e c r e a s e s . The c a l c u l a t i o n by formulae f o r t h e two-band semimetal model shows t h a t t h i s change may be d e s c r i b e d by t h e r e l a t i o n rl = rl

+

AIL'

,

where a % I f o r f i l m s i n t h e s e m i m e t a l l i c r e g i o n of compositions redu- c i n g t o 0 . 5 a t X

%

0.14. For g r e a t t h i c k n e s s e s t h e dependence q ( ~ ) v a n i s h e s . The t h i c k n e s s a t which t h i s o c c u r s grows with X. The m o b i l i t y in- c r e a s e s too ( F i g u r e I b ) , however, a t s m a l l L t h e r e i s a r e g i o n , where y i s thickness-independent.

F i g . 1 : V a r i a t i o n w i t h t h i c k n e s s of c o n d u c t i v i t y (curve 1 ) magne t o r e s i s t a n c e c o e f f i c i e n t (2)

,

charge c a r r i e r c o n c e n t r a t i o n (3) and mean c h a r g e m o b i l i t y

(4) i n Bi Sb f i l m s a t X = 0.035. l-X X

The anomalies observed

- t h e growth of

c a r r i e r c o n c e n t r a t i o n w i t h X i n t h e "semiconducti-

ve" r e g i o n of compositions and t h e c o n c e n t r a t i o n growth w i t h a d e c r e a s i n g f i l m t h i c k n e s s

-

may b e accounted f o r by t h e f i l m p o t e n t i a l bending near t h e s u r f a c e , which induces t h e average charge c a r r i e r c o n c e n t r a t i o n t o grow i n t h e f i l m . This growth i s governed by t h e e x t e n t of inhomogeneity i n t h e f i l m p o t e n t i a l , which i n c r e a s e s w i t h redu- c i n g f i l m t h i c k n e s s and w i t h r i s i n g Sb c o n t e n t s i n

t h e a l l o y f o l l o w i n g t h e d e c r e a s i n g band o v e r l a p i n t h e spectrum, i n c r e a s i n g e l e c t r o n wavelength and s c r e e n i n g r a d i u s .

Samples of v a r i a b l e t h i c k n e s s w i t h f i x e d composition and of v a r i a b l e composition w i t h f i x e d t h i c k n e s s d i s p l a y e d r e s i s t a n c e o s c i l l a t i o n s induced by t h e quantum s i z e e f f e c t (QSE). S i z e q u a n t i z a t i o n

nM

d i c t a t e s allowed magnitudes of momentum p Z =

-

S

.

L I n t h e f i r s t c a s e t h e o s c i l l a t i o n s a r e due t o t h e changing w i t h t h i c k n e s s number of allowed s t a t e s w i t h i n t h e Fermi energy, w h i l e i n t h e second c a s e

due t o t h e Fermi l e v e l motion w i t h r e s p e c t t o t h e system of allowed s t a t e s d i c t a t e d by t h i c k n e s s L.

max

The dependence px (X) deduced from t h e QSE (Figu- max

r e 2) i s c h a r a c t e r i z e d by t h e p Z drop i n t h e s e m i m e t a l l i c r e g i o n of compositions and by t h e

max

p , growth i n the"semiconductive" r e g i o n , which

i s i n q u a l i t a t i v e agreement w i t h c a l c u l a t e d depen- dences

for

c a r r k c o n c e n t r a t i o n s an i n d i c a t e s t h e

absence of t h e semimetal-semiconductor t r a n s i t i o n i n S i I-X Sb X f i l m s . T h i s s u g g e s t s t h a t t h e r e s u l t s obtained should be r e l a t e d t o small f i l m t h i c k n e s s , i . e . c r y s t a l l i m i t s i n one dimension.

F i g . 2 : Composition dependence of maximum e l e c t r o n momentum p y x governing quagtum-size o s c i l l a t i o n s i n Bi l-X Sb X f i l m s 3000-9000 A t h i c k . S o l i d c i r c l e s : pmaxderived from r e s i s t a n c e o s c i l l a t i o n s w i t h t g i c k n e s s v a r i a t i o n ; open c i r c l e s : ptax based on r e s i s t a n c e o s c i l l a t i o n s w i t h v a r y i n g a l l o y compo- s i t i o n .

References

/ l / Komnik, Yu.F. and Andrievsky, V.V., F i z . Nizk. Temp.

1

(1975) 104.