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