High field mobility and diffusivity of an electron gas in silicon devices

In this paper we consider the Boltzmann equation describing the carrier transport in a semiconductor. A modified Chapman‐Enskog method is used, in order to find approximate solutions in the weakly non‐homogeneous case. These solutions allow us to calculate the mobility and diffusion coefficients as functions of the electric field. The integral‐differential equations derived by means of the above mentioned method are numerically solved using 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 of the mobility and diffusivity in a silicon device are compared with experimental data. The Einstein relation is also shown.