Calculating the Electrons Distribution Function for Gallium Arsenide at Low Fields by Solving the Boltzmann Transport Equation.

The electron distribution function for gallium arsenide GaAs was calculated by using the Boltzmann transition equation in the central valley , for a range of low fields relative to the threshold field (E0 = 5.95Kv/cm) (0.3-1)E0. To obtain the distribution function, the Boltzmann transport equation was solved using a mechanism that combines the analytical and numerical methods. Analytical method involving extension of the Legendre polynomial was used and the effect of polar optical scattering was introduced as the dominant scattering mechanism in this research, as well as the effect of an asymmetric energy band structure with spherical energy surfaces in the central valley. After obtaining a partial differential equation of the second order, it is solved numerically after separation process for the variables using the direct matrix method in energy space by building a mathematical program using MATLAB. In this study, a system with dimensions of 360 × 360 was built, and the rate of change in energy was taken as 0.001.The computational system was tested by applying low electric fields, and the distribution function that was obtained had a Maxwellian distribution at very low fields, and it shifted from the Maxwellian distribution at higher fields close to the threshold field, and the results obtained were agree with previous results. While this system did not give accurate results at the high-electric fields.