Temperature dependence of the bound polaron in a polar crystal slab

Journal of Luminescence 40&41 (1988) 463—464 North-Holland, Amsterdam

463

TEMPERATURE DEPENDENCE OF THE BOUND POLARON IN A POLAR CRYSTAL SLAB

*

Jinying SUN

Institute of solid state Physics, Neimenggu University, Huhehaote, Neimenggu,P.R.C. Shiwel liii

Department of Applied Physics, Shanghai Jiao Tong University,

Shanghai,

P.R.C.

In considering both the electron interaction with the bulk longitudinal optical (La) phonon and the electron interaction with the surface optical (SO) phonon,we have obtained the temperature dependence of the ground state and the excited state energy and the effective mass of the bound polaron confined in a slab of polar

crystal by using Lee-Low-Pines variational technique and perturbative variational method.

zI~d

1. INTRODUCTION

thickness 2d occupying the space of

In the past, most work on polaron has been devoted to the calculation for the

and the space for zl>d is a vacuum, the potential is zero inside the slab and

temperature dependence of the energy and 1 ,2 in a three—dimen— the effective mass sional polar crystal, but no one has considerea the similar problem in a p0—

infinite outside the slab. In the fol— lowing, we limit ourselves to the region

IzI~dand assume that the donor is lo—

lar crystal slab taking into account the

Hasniltonian of the system can be written

electron-SO phonon interaction, In this paper, in considering both the

as HHe+Hph+HeLO+He_SO

electron—La phonon and the electron-SO phonon interaction,we have obtained the tern-

The last two term in (1) are the Ham— iltonian operatures for the electron-LO

perature dependence of both the ground state and the excited state energy of

(SO) phonon interaction taken from Pef.3~. Following the LLP method, after some

the bound polaron confined in a slab of

lengthy calculations,we obtain finally

cated at the center of the slab. The

2

~

lEi

2

polar crystal by using Lee-Low-Pinces variational technique and perturbative

~

variational method . We have also obtained the temperature dependence of the effective mass of the bound polaron in the

3. RESULTS AND DISCUSSION

slab.

*This

/

2

e ~~)+vB+VS

(2) e At last, we get the energy of the system.

We have done numerical computation for the weak coupling polar crystal InAs and have shown some results in Fig.1

2. THE HAMILTONIAN Consider

h

d

(1)

a polar crystal slab with

work was supported

by the

Science

0022—2313/88/$03.50 © Elsevier Science Publishers BY. (North-Holland Physics Publishing Division)

Foundation

of the Chinese

Academy of Sciences.

464

J. Sun, S. Gu

/

Temperature dependence of the bound polaron

________________________

0 0,0 ~

0.5

z/d

N= 30 VB~ T=200K

-1.0.

vB(vS)/aL~O

0,4

\\

0.2

1(a)

0.

FB+FS

0 O

10

20

e

/

the

,‘T~UQK ~ Zzrd/2

,,‘

V~—.-~

vB(vs)/thHO~L,o 200

600

effective

potentials

decrease

with

trend 15 consistent with the temperature behavior of the induced polarization 4. charge density For low temperatures, the ‘effective

1(b)

600 T(K)

400

I.

increasing temperature (Fig. 1(c)). This

—

0.0 0

a

400

FIG.2. The temperature dependence of in m*=m*rl÷a(FB+FS)]. effective mass factor (FB+FS) appearing

/ /

a

200

mass’ of electron in the x,yin plane rnincrease with motion T. As explained

~-

Pef.5 this increase can be attributed to

:—

the nonparabolicity of the polaron conduction band. At a higher temperature,

~

the uncorrelated motion of the phonons becomes

-0.8

an important

interaction FIG.1. The effective potential VB,VS vs. (a)tkse position of the electron z; (b)the number of InAs monolayers N; (c)the temperature T.

results

becomes

Fig.1(a),1(b) effective contributed

by the

non interaction

perature

and 1(c)

potential

results

electron—LO

(SO) pho-

is nOt related to the also

and the slab

relates

of the system.

It

to is

the

effective,which

of m~ (Fig.2).

REFERENCES and C,Podrigueg, 110 (1982) 105.

Phys.

the

VB(z,d,T)(VS(z,d,T))

of the electron but

showed that

less

in a decrease

1.V.K.Fedyanin Stat.Sol.(b)

thickness,

It

in a decrease of the coherence between the electron motion and the motion of’ the phonon, i.e., the electron—phonon

1(c)

position

factor.

z=d/2

tern—

shown that

2.

F.M.Peeters B31 (1985)

and J.T.Devrees, 1+890.

3.

J,J.Licari and R.Evrard, (1977) 2251+

1+. F.M.Peeters

Phys.Rev.

Phys.Pev.B15

and J.T.Devrees, Stat.Sol.(b)115 (1983) 285,

5.

Y.Osaka,J.Phys.Soc.Jap.21

Phys.

(1966) 1+23.