Using Monte Carlo Method for Calculating Phonon Images

In this paper a Monte Carlo method has been used to calculate the phonon images of a number of semiconductor cubic crystals from III-V and II-VI groups (higher symmetry) and orthorhombic crystals (lower symmetry). An algorithms a MATLAB codes has been prepared for the calculation of phase velocities, slowness surfaces and group velocities and the formation of the phonon images which required a large number of points in the reduced Brillion zone, these points has been transformed to the group velocity space by solving the Christoffel equation for each of these points, a projection in a given direction is obtained, each incident pluses is transformed to gray level to form the final image. A comparison between the Monte Carlo and systematic methods has been done for the calculated images.