High Field Mobility and Diffusivity of Electron Gas in Silicon Devices

In this paper the Boltzmann equation describing the carrier transport in a semiconductor is considered. A modified Chapman-Enskog method is used, in order to find approximate solutions in the weakly non-homogeneous case. These solutions allow to calculate the mobility and diffusion coefficients as function of the electric field. The integral-differential equations derived by the above method are numerically solved by means of a combination of spherical harmonics functions and finite-difference operators. The Kane model for the electron band structure is assumed; the parabolic band approximation is obtained as a particular case. The numerical values for mobility and diffusivity in a silicon device are compared with the experimental data. The Einstein relation is also shown.