Calculations of Energy Band Structure of GaAs, GaSb and GaP Crystals as a Function of Temperature Using the Semiempirical Tight Binding Method

Abstract

Abstract In this paper, the band structure of gallium group of III-V semiconductor has been calculated with temperature, the semi-empirical tight binding method was used to calculate the band structure and the matrix elements were calculated for both models sp^3 and sp^3 s^*. A computer program in MATLAB was designed to calculate the energy eigenvalues for the wave vector points in the first Brillouin zone between high symmetry points to form energy bands. The effect of temperature on the energy band of these group of crystals has been studied by changing the values of the lattice constant under the influence of temperature according to the Pierron relation and thus calculating the change in the length of the bond with temperature, which in turn affects the change in the values of the elements of the Hamiltonian matrix. The energy gap and refractive index were calculated at points of high symmetry as a function of temperature. The results showed a decrease in the energy gap values of GaAs, GaSb and GaP crystals with increasing temperature. Then the experimental Varshni relation was used to calculate the change in the energy gap values of these crystals and the results obtained from current study were compared with the results of Panish and Bellani, where the results showed that a model sp^3 s^* gives better results than the model sp^3.As well as the calculations of the refractive index of these crystals using the Moss formula showed that the refractive index will gradually increase with increasing temperatures.

Keywords

• energy bands,,
• ,،,؛semiconductor bands,,
• ,،,؛energy gap with temperature,,
• ,،,؛refractive index