حساب تركيب حزمة الطاقة الإلكترونية لبلورة GaAs باستخدام طريقة الربط المحكم شبه التجريبية

الملخص EN

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 sp3 model which have 9 parameters and sp3s∗ 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 ?∗ along the direction [111] for the lowest conduction bands has been calculated.

A comparison between the sp3 model used by Cohen and the sp3s∗ 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 sp3 and sp3s* models and there is good agreement between the band energies at high symmetry points between these two models and the published results.