Carrier spreading and diffusion coefficient in n‐Si

We have solved the transient {k} and space dependent Boltzmann equation in n‐type silicon. The transient distribution function f(k,z,t) is obtained in the k space and along the direction of the applied electric field (along the z axis). The material is assumed to be homogeneous so that the Poisson equation is not taken into account. Hence we can follow the spreading of a packet of carriers initially located around z=0. By a simple integration over the whole k space we obtain f(z,t), v(z,t), and e(z,t). The longitudinal diffusion coefficient is computed using the slope of the variance of the carriers’ positions.