With the development of the material science and experimental technology

the properties of the surface polaron in semi-infinite crystals have been of considerable interest.Many investigators studied the properties of surface polaron in semi-infinite crystals in many aspects by a variety of theoretical and experimental 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 longitudinal optical (LO) phonon mode.The properties of crystals having only one LO phonon branch have been studied by a great variety of techniques.However

a large number of polar crystals

with several atoms per unit cell

have more than one LO phonon branch.For example

in cuprite compounds such as CuO

2

/there are two LO phonon modes.SiO

2

GaAs

1-x

P

x

and a large number of perovskite’s crystals (SrTiO

3

LiNbO

3

BaTiO

3

etc) have more than two LO phonon modes.The pelaron problem with many LO phonon branches has been studied by Matsura and Lepine.The properties of the polaron and the magneto-pelaron in a polyatomic polar crystals are investigated by the present authors.However

so far

research of the properties of surface polaron in polyatomic semi-infinite crystals considering both the electron-bulk-longitudinal optical-phonon and electron-surface-optical-phonon interaction

has been very scarce.Recently

the properties of the excited state of surface polaron in polyatomic semi-infinite

which are the strong-coupling with surface optical phonon and the bulk longitudinal optical phonon

are studied by using a linear-combination operator and unitary transformation method by the present authors. For the bulk polaron

the weak and intermediate coupling theories are applicable for electron-bulk LO phonon coupling constant α

L

<

6

whereas for the surface polaron

this confinement is about 2.5.Hence

when the electron-SO phonon coupling constant satisfied α

s

>

2.5

the strong-coupling theory must be applied. There is a weak coupling between the electron and the bulk LO phonon

but a strong coupling between the electron and the SO phonon for many polar crystals.So far

the research of this aspect is very scarce. The properties of the excited state of surface polaron in polyatomic semi-infinite crystal

which are the strong-coupling with surface optical phonon and the weak-coupling with bulk longitudinal optical phonon

are studied by using a linear combination operator and unitary transformation method.Results show that the ground state energy and the first internal excited state energy of surface pelaron in polyatomic semi-infinite crystal

which are the strong-coupling with surface optical phonon and the weak-coupling with bulk longitudinal optical phonon not only includes the coupling contribution between electron with different LO phonon and SO phonon branches

but also exists only an extra contribution due to crossed terms between the different SO phonon bran-ches

and the excitation energy not only includes the coupling contribution between electron and different SO phonon branches

but also exists only an extra contribution due to crossed terms between the different SO phonon branches.The excitation energy is independent of the bulk longitudinal optical phonon.