The thoery of polarons near rough polar crystal surfaces is presented. The effec-tive Hamiltonian of the polaron is derived using the Lee-Low-Pines unitary transformation technique and considering the electron moving in the instantaneous field of the optical phonons. The image potential of the polaron arising from the interaction with both the longitudinal optical and surface optical phonons is obtained from the theory, while the image potential associated with the polarizations which have much higher 'vibrational' frequencies than thoes of optical phonons is added to the theory using its electrostatic limit. From the theory presented in this paper, it is predicated that the polaron outside the polar crystal will be localized near the surface, while the polaron inside the polar crystal will be repelled from the surface contrast to an early result, which predicates that polarons both outside and inside the crystal will be attracted to the surface [Evans and Mills, Phys. Rev. B8, 3981 (1972)].
