A one-dimensional solution of the Boltzmann transport equation including electron–electron interactions

In this article a technique is described for solving the one-dimensional spatially dependent Boltzmann transport equation with electron–electron interactions included in the scattering model. The analysis is illustrated by solving the Boltzmann transport equation over a potential profile typical of that found in the channel of a metal–oxide–semiconductor field-effect transistor. A comparison is made between the distribution functions obtained when electron–electron interactions are included and excluded from the scattering model. It is found that electron–electron interactions significantly increase the electron population at energies greater than are available from the electric field.