In the early 1970's Ibach has made low energy electron diffracting(LEED)experiments on ZnO and other semiconductor surfaces. The surface polaron in crystals have been of considerable interest. Sak and Evans studied theoretically the surface polaron in polar crystals. In the 1980's Gu

et al

. discussed the weak and intermediate coupling surface polaran in semi-infinite crystals.Gu

et al

. investigated further the strong coupling surface polaron.In fact

so far research of the surface polaron only was restricted to the calculation of ground state energy. Huybrechts studied the properties of the internal excited state of the optical polaron by using the linear combination operator method.Gifeisman

et al

. calculated the wave functions of first excited state using perturbation theory. The excited state energy of bound Frhlich polaron was evaluated using the Fock approximation of Matz and Burkey by Lepine.A new variational wave function to describe the ground state and the excited states of a bound polaron is proposed by Devreese. Using the effective-mass approximation and the variational method the ground-state and first-excited state energy of a polaron in a polar-crystal slab

due to the interactions of the electron with the BO and SO phonons

are calculated self-consistently by Lu and Li. Qin and Gu investigate temperature dependence of the electron self-energy in the polar-crystal slab using Green-function method. In calculation

they consider the effect of the excited states on the electron self-energy and find the ground-state energy be about 11% lower than that of bulk polaron. A variational calculation is performed by Sahoo to obtain the ground state and the first excited state of the Frhlich bipolaron in a multidimensional polar crystal. Chun

et al

.discussed the hydrogenic impurity binding energy of the ground and the excited state in a cylindrical quantum wire by using Landau and Pekar variational method. However

using a Huybrechts's method

the properties of internal excited state of the polaron has not been investigated so far. In this paper

the effective Hamiltonian

the vibration frequency and the excitation energy of strong coupling surface polaron are calculated by using the linear combination operator and unitary transformation methods. Two limiting cases of coordinate z are discussed. The results show that for strong-coupling surface polaron the excitation energy will increase with increasing the electron-phonon coupling constant α

S

(α

L

)and the vibrational frequency of phonon ω

S

(ω

L

).