Diffusion of phonons through (along and across) the ultrathin crystalline films

Instead of usual approach, applying displacement-displacement Green's functions, the momentum-momentum Green's functions will be used to calculate the diffusion tensor. With this type of Green's function we have calculated and analyzed dispersion law in film-structures. A small number of phonon energy levels along the direction of boundary surfaces joint of the film are discrete-ones and in this case standing waves could occur. This is consequence of quantum size effects. These Green's functions enter into Kubo's formula defining diffusion properties of the system and possible heat transfer direction through observed structures. Calculation of the diffusion tensor for phonons in film structure requires solving of the system of difference equations. Boundary conditions are included into mentioned system through the Hamiltonian of the film-structure. It has been shown that the diagonal elements of the diffusion tensor express discrete behavior of the dispersion law of elementary excitations. More important result is that they are temperature independent and that their values are much higher comparing with bulk structures. This result favors better heat conduction of the film, but in direction which is perpendicular to boundary film surface. In the same time this significantly favors appearance 2D superconducting surfaces inside the ultra-thin crystal structure, which are parallel to the boundary surface