In the early 1970's

Ibach made the low energy electron diffracting experimentation on the surface of semiconductor ZnO etc..The suface polaron in the crystals was of considerable interest.Sak

Evans and Mills studied theoretically the surface polaron in polar crystals for the first time.Evans et al.investigated the effect of bulk LO phonon on the surface polaron.Gu et al.discussed the strong

weak and intermediate coupling surface polaron in semi-infinite crystals.The properties of the surface polaron has been calculated by many methods.In fact

so far research of the surface polaron only was restricted to the approximation and calculation where the interaction between phonons of different wave vectors in the recoil process was neglected.The properties of the surface polaron

which considers the corresponding interaction

have been discussed using the perturbation method by the present authors and co-workers.In this paper

the characteristic of the surface polaron in semi-infinite crystals is studied.The effective Hamiltonian

the effective mass and energy of interaction between phonons of the surface-polaron-in semi-infinite crystals-are derived using L.L.P method.The influences of the interaction between phonons of different wave vector in the surface polaron are discussed.The Hamiltonian of the electron-phonon system can be written as(1a).For motion parallel to the x-y plane

we introduce unitary transformation U

1

and U

2

.The ground state wave function of the system is ψ

>

=φ(ρ)

>

|0

>

.According to L.L.P method

we introduce(5).After some elementary calculation

the effective Hamiltonian of the surface ploaron in a plane parallel to the surface(9a)

the effective mass of the surface polaron(10)

the energy of interaction between phonons(11a)and the ratio of energy of interaction between-phonons and the energy of the surface polaron in x-y plane(12)are obtained.The properties of these quantities are discussed.