Application of the Green's function method to lattice vibrations in thin films

The Green's function method is used to investigate the lattice vibrations in a simple cubic thin film with nearest neighbour interactions. Appropriate Green's functions for the study of the surface waves for (001) and (011) orientations of the surface are determined. For a thin film with two parallel (001) free surfaces the atomic force tensors at the surface are modified in order to satisfy the rotational invariance condition. The surface waves are determined and a detailed discussion is made for the long wave-length limit k_y = 0 and k_x ? 1. For a given k_x there is a critical thickness below which only an antisymmetrical solution can exist. For the (011) orientation only the case of a single free surface is discussed.