In the early 1970's

Ibach made the low energy electron diffracting experimentation on the surface of semiconductor [ZnO etc.. The surface polarop in the crystals was of considerable interest. Evans

Mills and Sak studied theoretically the surface polaron in polar crystals for the first time. Evans et al. investigated the effect of bulk LOphonon on the surface polaron. Gu et al. discussed ideal surface polaron and the weak and intermediate coupling polaron in semi-infinite polar crystal. There is a weak coupling between electrons and BO SA phonons but a strong coupling between electrons and SO phonons for many kinds of polar semiconductors. For α

s

>

2.5

it belongs to the strong coupling.In this paper

the properties of the surface electrons in polar semiconductor

which is coupled both with SO BO and SA phonons

are studied. The effective Hamiltonian and the renormalization masses of the surface electrons are derived by using a linear-combination-operator and Lagrange multiplier method.The Hamiltonian of the electron-phonon system can be written as(la). We introduce the creation and annihilation operator B and B by (3) and carry out the unitary transformation U

1

and U

2

. The ground state wave function of the system is φ=φ(p)|0

>

. In the unitary transformation

U

1

with

A

1

=0

A

2

=

A

3

=1 corresponds to the weak coupling between electrons and BO SA phonons and the strong coupling between electrons and SO phonons.We now consider two limit cases.1. The electron is near the surface

i.e. z

<

<

uL

-1

. In this case

we have (20) and (21).2. The electron goes very deep into the bulk

i.e. z

>

>

uL

-1

In this case

we get (23) and (24).The effective Hamiltonian

the self-trapping energy

the image potential and the rencrmalization masses cf the surface electrons in the two limit cases are discussed.