Calculation of The Electronic Energy Band Structure of GaAs Crystal Using The Semiempirical Tight Binding Method
In this paper, the semi-empirical tight binding method for the nearest neighbors in the first Brillouin zone has been used to calculate the energy band structure of GaAs crystal which have zinc blend ZB structure, the band structure has been calculated by using sp^3 model which have 9 parameters and sp^3 s^* which have 13 parameters, both these models are used to calculate the main characteristic of both valence and conduction bands. The matrix elements were determined using the method followed by Cohen and Vogl, by identifying points in the wave vector space within the reduced Brillouin zone between the points of high symmetry and calculating the eigenvalues of all these points by building a computer program in MATLAB to form the energy band structure. The effective mass m^* along the direction  for the lowest conduction bands has been calculated. A comparison between the sp^3 model used by Cohen and the sp^3 s^* model used by Vogl has been made. The energies of the band structure at points the high symmetry Γ and X obtained from the study were compared with the results of the published research. The results showed that there is a difference in the energy gap between sp^3 and sp^3 s^* models and there is good agreement between the band energies at high symmetry points between these two models and the published results.
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