Discontinuity of the surface polaron

Using the Feynman's path integral method, energies and masses are calculated for various types of a surface polaron. It is shown that, when the electron-surface phonon interaction becomes strong, surface optical phonon yields continuous change from free to self-trapped states. On the other hand surface acoustic phonon yields discontinuous change for the deformation type interaction and continuous change for the piezoelectric interaction. All these results reflect the character of the force range of the electron-surface phonon interaction.