VARIATION OF THE ENERGY SPECTRUM OF BISMUTH, ANTIMONY AND THEIR ALLOYS UNDER STRONG UNIAXIAL TENSION

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VARIATION OF THE ENERGY SPECTRUM OF BISMUTH, ANTIMONY AND THEIR ALLOYS

UNDER STRONG UNIAXIAL TENSION

N. Brandt, E. Bogdanov, V. Kulbachinsky, N. Minina

To cite this version:

N. Brandt, E. Bogdanov, V. Kulbachinsky, N. Minina. VARIATION OF THE ENERGY SPECTRUM OF BISMUTH, ANTIMONY AND THEIR ALLOYS UNDER STRONG UNIAXIAL TENSION.

Journal de Physique Colloques, 1978, 39 (C6), pp.C6-1108-C6-1109. �10.1051/jphyscol:19786491�.

�jpa-00217974�

JOURNAL DE PHYSIQUE Colloque C6, suppliment au no 8, Tome 39, aoat 1978, page ~ 6 - 1 1 0 8

V A R I A T I O N

OF

THE ENERGY SPECTRUM

OF

BISMUTH, ANTIMONY AND T H E I R ALLOYS UNDER STRONG U N I A X I A L T E N S I O N

N.B. Brandt, E.V. Bogdanov, V.A. Kulbachinsky, N.Ya. Minina.

Physics Department, Moscow State University, Moscow, U. S. S. R.

RBsum6.- Soumis 1 une t e n s i o n u n i a x i a l e s u i v a n t l ' a x e b i n a i r e ou b i s s e c t e u r , B i , Sb e t l e u r s a l l i a g e s perdent 116quivalence d e s t r o i s p a r t i e s de l e u r s u r f a c e d e Fermi. Dans c e s c o n d i t i o n s on a observe l e s t r a n s i t i o n s Blectroniques dans Bi e t dans l ' a l l i a g e B i Sb de type n.

0 , 9 2 4 0 , 0 7 6

Abstract.- B i , Sb and t h e i r a l l o y s under t e n s i o n along t h e b i n a r y and b i s e c t o r axes show inhomoge- neous changes i n p r e v i o u s l y e q u i v a l e n t p a r t s of t h e Fermi s u r f a c e . As a r e s u l t , e l e c t r o n i c phase t r a n s i t i o n s occur i n B i and B i

0 . 9 2 2 07'6 n-type a l l o y s under s u f f i c i e n t l y l a r g e s t r e s s e s ( Q 0.3 + 0.6 X).

With t h e h e l p of a method t h a t allows s t r o n g deformations l i k e u n i a x i a l tension i n l a r g e c r y s t a l s / 1 , 2 / , changes i n t h e energy spectrum were i n v e s t i - gated f o r B i , Sb and t h e i r a l l o y s under t e n s i o n along b i n a r y C and b i s e c t o r C axes of t h e sample

2 1

up t o a deformation of 4 . 7 5 % f o r B i and Bil-xSbx a l l o y s , 'and up t o a . 2 3 % f o r Sb. The energy spec- trum of t h e s e m a t e r i a l s was s t u d i e d w i t h t h e h e l p of t h e Shubnikov de Haas e f f e c t . The dependences of extremal c r o s s - s e c t i o n s S of Fermi s u r f a c e on ap- p l i e d load a, f u l l y c o i n c i d i n g f o r small U, w i t h analogous dependences f o r B i 1-X Sb X a l l o y s i n t h e s e m i m e t a l l i c region, a r e shown i n f i g u r e 1.

i n t h e d i r e c t i o n of e l o n g a t i o n was E = 0.025 %

XX

kg-', and i n t h e p e r p e n d i c u l a r d i r e c t i o n E =

-

^{0.015 % kg-'.} YY

I n c o n t r a s t with an h y d r o s t a t i c compression,or compression along t h e t r i g o n a l a x i s , a d i f f e r e n t type of change i n e l l i p s o i d s 1 and 2,3 i s observed, which i s connected w i t h t h e disappearance of 3rd or- d e r synrmetry and a break oP e l e c t r o n extrema a t pre- v i o u s l y e q u i v a l e n t L.points. The r e s u l t s of calcu-

l a t i o n s , e v a l u a t i n g changes i n t h e B i spectrum un- d e r s t r e s s , c a r r i e d o u t on t h e b a s i s of Abrikosov's model 131, a r e shown i n f i g u r e 2.

Fig. 2 : R e l a t i v e displacement of t h e e n e r g band edges i n B i f o r U = I7 kg. n

-

^{U =} 0, b

-

^Ufb2,

c

- 011

^Cl.

The divergence of e l e c t r o n extrema w i t h a r a t e

a&

meV

-

= as meV

1.3

-

(allc ) i s accom- au ^I

K

^{(ulk2) o r}

-

⁼ _kg

F i g

.

^{l : S:-} c r o s s - s e c t i o n of " e l l i p s o i d " I ; S:, panied by an i n c r e a s e of t h e i n t e g r a l :alue of t h e S:

-

c r o s s s e c t i o n s o f " e l l i p s o i d s " 2,3 ; Sh

-

c r o s s

s e c t i o n of h o l e " e l l i p s o i d " ; a

-

^{U [ / Cl, b}

-

^{all C,} overlapping vf bands a t L and T, which i s manifested i n t h e i n c r e a s e of t h e h o l e " e l l i p s o i d " ( f i g u r e 1 ) . Aschematic arrangement of e l e c t r o ~

-

h o l e " e l l i p - The n a t u r e of t h e dependence

7

AS (U) i n f i g u r e s o i d s " of the Fermi s u r f a c e r e l a t i v e t o t h e c r y s t a l - l a allows one t o suppose t h a t f o r ullc _and E,, % l o g r a p h i c axes and t h e d i r e c t i o n of e l o n g a t i o n i d 0.6 %, an e l e c t r o n i c phase t r a n s i t i o n occurs i n Bi.

shown i n t h e same f i g u r e . The amount of d e f a m a t i o n 141 which r e s u l t s i n t h e disappearance of t h e e l e c -

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19786491

tron "ellipsoid" I. The extrapolation of the data of figure Ib shows that the transition to a uniellip- soidal electron surface in Bi for a

11 occurs

^for

Exx % ^{l. 1} %.

Sharper electronic phase transitions were obser- ved in the alloy Bi Sb n-type (impurity Te

0 . 9 2 b 0 . 0 7 6

Q IO-~%) 151, in which the overlapping of energy bands at L and T does not exist, and the change in

the volumes of the electron surfaces was caused only by a redistribution of carriers at L extrema.

The dependences

-

AS _S (a) in this alloy for a

I I

^{C, and}

a

I I

C2 are shown in figures 3a, b respectively.

Fig.3 : S;

-

cross-section of "ellipsoid" 1; S;

,

S;

-

cross-sections of "ellipsoids" 2,3; c,d,e,f

-

different samples ; a

-

^a1

^{] c l ,}

^b

- 01 !c2.

'For the value ac=12 kg (E,,% 0.3%,~ %-0.2%)in the YY

n-type alloy Bi 0.924 Sb0.076 a transition to single ellipsoid, isoenergetic surface for a] lC2,and to a double ellipsoid,isoenergetic surface for ₀₁ IC1, takes place.In Bi as well as Bil-xSbx alloys no chan- ges in the anisotropy and tilt angles were observed.

Results of a study of the Fermi surface of Sb under tension along Cl and Cp axes, as well as a schematicarrangement of electron and hole "ellip- soids" in the basis plane of the crystal, are shown in figure 4. The applied deformation correspond to cxx = 0.015 % kgq1, E =

-

^0.0075 % kg-'. The chan-

YY

ge in the cross-sections of "ellipsoids" B(C) and E(F) corresponded to 2.2 %, -5.0 %

(a 11

^{C2) or}

-

^{2.3 %, 4.7 % (a}

11

^{C,) for o} = 11.5 kg. The general nature of the change in Fermi surface for Sb is ana- logous to that observed for Bi.

Fig. 4 : 1

-

minimal cross-section of electron

"ellipsoid" D; 2,3,4

-

minimal, intermediate and maximum cross-sections of hole "ellipsoid" A;

a

-

^{dIcl, b}

-

^{all C,.}

References

/l/ Brandt, N.B., Kulbachinsky, V.A., Minima, N.Ya., Schirokikh, V.D., V ICHP, High Temp. High Pres- sure,

1

(1975) 644.

/ 2 / Brandt, N.B., Kulbachinsky, V.A., Minima, N.Ya., Pisma, V ZhETF. 22, (19771, 173 (in Russian).

/ 3 / Abrikosov; B.A., J. Low Temp. Phys.

5

(1972)

315.

/4/ Lifshitz, L.M. ZhETF,

2

(1960) 1569 (iaRussian) /5/ Brandt, N.B., Kulbachinsky, V.A., Minima, N.Ya.,

Pisma, V ZhETF,

6

(1977) 637 (in Russian).