Electron-phonon scattering and high-field transport in $n$-type Si

The transport problem for warm and hot electrons in silicon is formulated using a simple, nonparabolic band model. The electronic distribution function is written in terms of an extended diffusion approximation which allows for a certain amount of "streaming" of the distribution in momentum space. The solution of the Boltzmann equation is reduced to the solution of a coupled set of ordinary second-order differential equations which are well suited for iterative numerical techniques. By comparing experimental and numerical data we can assign realistic values to electron-phonon coupling constants and a good overall fit is obtained for several types of experiment.