Enhancement Efficiency of Calculation of the Phonon Images for GaP Piezoelectric Crystal

Abstract

In this paper an improved phonon imaging for GaP has been calculated, this crystal is one of III-V group. In the presence of piezoelectric properties, the computation treatment is based on increasing the number of points in the reduced Brillouin zone and increasing the size of the phonon image matrix. The phonon images can be calculated by large number of points in the reduced Brillouin zone which represent the wave vectors and these vectors can be transformed to group velocity vectors using Christoffel equation, these set of group velocity vectors can be projected in a certain direction to form the phonon image. A program was prepared in MATLAB language to calculate these images by determining the number of points in the reduced zone and determining the size of the matrix that represents the phonon images in addition to the direction of the projections. To calculate the phonon images in the presence of the effect of the piezoelectric properties, it is through the presence of the k44 factor, which indicated of the influence of the piezoelectric properties on the phonon images. The results showed that the size of the image matrix is more effective factor than the number of points in the reduced Brillouin zone especially when the number of points is greater than 8×〖10〗^5 points, and when the number of points less than 〖10〗^4 points all the obtained phonon images is not clear.