EFFECT OF MAGNETIC FIELD ON BALLISTIC HEAT-PULSE SCATTERING IN n-TYPE GERMANIUM

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EFFECT OF MAGNETIC FIELD ON BALLISTIC

HEAT-PULSE SCATTERING IN n-TYPE

GERMANIUM

T. Miyasato, M. Tokumura, F. Akao

To cite this version:

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JOURNAL DE PHYSIQUE

CoZZoque C6, supplgment au n o 12, Tome 42, de'cembre 1981 page C6-658

EFFECT OF MAGNETIC FIELD ON BALLISTIC HEAT-PULSE SCATTERING IN

n-TYPE GERMANIUM

*

T. Miyasato

,

M. Tokumura and F. Akao

The I n s t i t u t e of S c i e n t i f i c and Industrial Research, Osaka University, Suita 565 Osaka, Japan

Abstract

-

The scattering of ballistic heat-pulse propagating along the

100 axis of lightly Sb or As doped Ge has been studied as a function

7 - 7 -

of (100) magnetic field and the heater temperatures ranging from

4.6

to

8.6

K for Sb doped Ge (6.6 to 9.3 K for As doped ~e). It is shown that the transmitted ballistic heat-pulse intensity detected by CdS thin film bolometer increases with increasing magnetic field up to

60

kG with sample temperatures ranging from 1.8 to 4.2 K, and the behavior depends on the concentration of donor atom even at such a low concentration region. The behavior of the detected ballistic heat-pulse amplitude is compared with a calculation based on the Suzuki-Mikoshiba theory, taking into the shrinkage effect of the donor wave function and the resulting change of the value of the valley-orbit splitting.

1.Introductian.- The donor atoms of V-group in Ge have shallow donor levels, and the ground state of which splits into the lowest singlet (A ) and the

I

higher laying triplet (T ). This is called the valley-orbit splitting, and

2

the separation of which is denoted by 44, with the values of 0.32 meV for Sb doped Ge and 4.23 meV for As doped Ge. The donor electrons in the ground state of many-valley semiconductor such as Ge or Si are coupled with the acoustic phonons through a deformation potential coupling. When the magnetic field is applied,the energy level of the ground state undergoes the Zeeman splitting, and the shrinkage effect of the donor wave function should be con- sidered simultaneously. Concequently, the value of

46

and the cut-off

function are changed by the magnetic field.

2.Experimental Technique and Procedure.- CdS thin film bolometer(1) was uscd for the detection of ballistic heat-pulse. The Au-thin film was evaporated onto one surface of the sample as a heater. The phonon flux emitted from the Au-heater travels ballistically in the sample and arrives at the - C ~ S film. The release of the electrons in the trapping centers of CdS by this heat- puIse phonons gives rise to the variation of the electric resistance. The observed pulse amplitude, that is measured as a peak resistance change in CdS bolometer, represents the transmitted phonon power. The experimental results of the pure Ge showed the change of the signal height of 2-3

%,

which means that the magnetic field effect on the generating and detecting systems can be neglected in the present experiments.

*present address : Department of Physics, University of Lancaster, Lancaster LA1 4YB,

England

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j.Experimenta1 Results.- The experimental results for Sb doped Ge is shown in Fig.1, and those for As doped Ge are shown in Fig.2 and 3, and summarized

as follows:(i)~n Sb doped Ge, the signal echo height increases with the magnetic field for all heater temperature Th's, and the ratio of the change in the signal echo height increases with increasing Th. (ii)~n As doped Ge, the signal echo height decreases at 5 kG and then increases in 1 . 5 ~ 1 0 ~ 4~s/cmJ

I5

doped sample, but monotonically increases in 0.9~10 ~s/cm' doped sample. Namely, there is a concentration dependence in such a low concentration

region.

4,Discussion and Conclusions.- ( a ) ~ n e r ~ ~ of ground state: When the magnetic field is applied along the (100) axis of n-type Ge, the equivalence of the four conduction band minima is kept and the degeneracy of the triplet state is not removed except for the spin splitting. I n this configuratiyn, 4 4 i s changed through the shrinkage of the donor wave function by the magnetic field, and the magnetic field dependence of

46

for this configuration was given by Lee et al(2). The cut-off function in the donor electron-phonon interaction is also changed through this shrinkage. Therefore, the phonon scattering by donor electrons through process unaccompanied with donor spin

reversal is strongly affected due to the shrinkage effect. (b)~cattering of heat-pulse in n-type Ge under magnetic field: The phonon relaxation rate in the ballistic heat-pulse propagation along the (100) axis under (100) magnetic field is calculated on the basis of ref.(j) and shown in ref.(4). The calculated curves are shown in Fig.5 for As doped Ge, and in Fig.4 for Sb doped Ge, and summarized as follows. For Sb doped Ge, the calculated results by this theory (denoted by B) show opposite sence to the experimental results,

and for As doped Ge, the calculated curve shows smaller change compared with

1 I I 'the experimental results. Ge:Sb, n=0.4x10' 5~b/cm. I T - 8 . u .

(c)scattering by the homopolar-

20 ' To-1 . 8 K

.

.-.-

-

pair: The phonon scattering by

homopolar pair(5,6,7) was calcu-

= 4 ' 6 lated using approprate parameters

lo

-

_{for Sb doped Ge, and shown in}

Fig.4 by A. As seen from these

00 -

curves, it is necessary to take Ge:Sb, n=0.4xl0'

f//Q/

[I 00)

,

T Inwu,. fi To-1 . 8 K

.

/:'.-ph=b.4 K

-

I

-

" A*'

,&.-

.-.-

homopolar pair(5,6,7) was calcu- m . I *

0.90

0 10 20 30 40 50 kG

Magnetic F i e l d .

Fig. 1 : Magnetic field dependence of transmitted

heat- pulse(^

mode) amplitude in ~b(n=0.4xl0l5/cm~) doped Ge. Sample temperature Tp1.8 K, heater temperature Th's are 4.6, 6.4 and 6.8 K.

1

into consideration the scattering of phonons by homopolar-pair even

in such a very low concentration region in addition to the scattering by the neutral shallow donors. Acknowledgements: We would like

to express our deep thanks to

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C6-660 JOURNAL DE PHYSIQUE I 1

4-4

Ge;As, n-1.5~10 ~s/cm', $//$//[I001

,

T mode, Th=8.5 K 1 I I

.

Magnetic Field.

Fig. 2 : Magnetic field dependence of transmitted heat-pulse(~ mode) amplitude in ~s(n=

1 .5x1

o1

4/cm3) doped Ge

.

0.90

0 10 20 30

40

50

kG Magnetic Field.

discussions and encouragements. References.- (1 )~.~shiguro & S.

~ o r i t a : ~ ~ ~ l . ~ h ~ s . ~ e t t . ~ ( 1 9 7 4 )

533. (2)~.Lee, D.M.Larsen & B.

Lax: J.Phys.Chem.Solids 24(1977) 181 7. (~)~.~uzuki & N.Mikoshiba

: J.P~~S.SOC. ~~n.28(1970)1248, (4)~.~i~asato, M.Tokumura, M. Toguchi & F.Akao:J.Phys.Soc.~

(1981)1986. ('j)~.~.~ortel:J. Phys.C 2(1976)707. (6)~.~oba- yashi & K.Suzuki:Phys.Rev.z (1

979)

3278. (7)~.suzuki: private communication.

Fig. j : Magnetic field

dependence of transmitted heat- ~ u l s e ( ~ mode) amplitude in Sb (n=0,9xl015/cm3) doped Ge. Sample temperature is 1.8 K,

and heater temperatures are 6.6 and 9.7 K. Theoretical curve was calculated based on Suzuki-Mikoshiba theory using appropriate parameters for Th=

6.6

K.

I

A.Scattering by homopolar pa!

Fig.

4

: Theoretically calcu-

0.9

l*Ool

0 10 20 30 40 donor. 50 kG 2

3

1 . 2

phonons by homopolar pair, and lower curves show that of scattering by neutral shallow donor electron(~uzuki-~ikoshiba theory). To explain the experimental results fully, it will be necessary to consider both scatterings.

magnetic ~ield. '

I I

GerSb, Calculated ourves for 4x1 0' 4~b/om3doped eemple

.

'

-