In the early 1970s

Ibach carried out low energy electron diffraction (LEED) experiments on ZnO and other semiconductor surface. The surface polaron in the crystals are of considerable interest. The behaviour of the electron phonon interaction near the surface or interface of a crystal has been studied by many investigators by means of various theoretical methods.Most polar crystals are diatomic and cubic and their crystal structure belongs to NaCl

CsCl or ZnS type.In these crystals there is one mode of the longitudinal optical(LO) phonon.The properties of crystals have been studied by a great variety of techniques

in the case of crystals having only one LO phonon branch.However

a large number of polar crystals

with several atoms per unit cell

have more than one LO phonon branch.For example

in cuprite such as CuO

2

there are two LO phonon modes and a large number of perovkites(SrTiO

3

BaTiO

3

LiNBO

3

...) also have more than two modes.Recently

there have been studied the polaron problem with many LO phonon branches.The properties of the surface polaron in polyatomic polar crystals are investigated using a linear combination operator and a simple unitary transformation by one of the authors.However

the influences of the electron interaction with both bulk longitudinal optical(LO) phonons and surface optical(SO) phonons on the effective potential of the surface polaron in polyatomic crystals has not been studied so far.The purpose of this paper is to explore the effect of the interaction between the electron with both LO and SO phonons on the effective potential of the surface polaron in polyatomic semi infinite crystals using a linear combination operator and a unitary transformation method.