In the early 1970s

Ibach carried out low-energy electron diffraction experiments on ZnO and other semiconductor surface.Sak

Evans and Mills studied theoretically the surface polaron in polar crystals

the Hamiltonian of the electron and surface phonon interaction was derived. Gu et al. discussed the ideal surface polaron and the weak

intermediate-coupling polaron in a semi-infinite polar crystal. Mills indicated that when electron moves in the surface vicinity of the crystals

the electron and surface optical phonon interaction produces a polarization cloud around the electron

whereas because of the electron surface acoustic phonon coupling the electron have been trapped at the surface vicinity motion.Theoretical results show that the surface layer of crystals may be regarded as pure 2D crystals if the distance from the surface is smaller than the radius of polarons.The effect of bulk phonons can be neglected

while surface acoustic and surface optical phonons are taken into account in the surface layer. Ueba discussed the properties of the electron

which is a interaction with both the surface optical and acoustic phonons in the surface phonon field. Toyozawa studied the quasi-particle

the acoustic deformation potential (ADP) polaron

formed by the interaction of electrons with acoustic lattice vibration using the concept of the deformation potential.Recently Zhao Cui-lan et al. investigated the properties of surface polaron of interaction with the deformation potential.From the point of view of confined electron

studying electron via the deformation potential interaction with acoustic phonon is more significant.The properties of surface polaron in polar crystals

which is a weak-coupling with surface optical and surface acoustic phonons

was studied. In the paper

the renormalization mass of the surface polaron is derived using Tokuda’s improved linear-combination operator and the Lagrange multiplier and the variational method. Two limiting cases are discussed.