AN ENERGY-TRANSPORT MODEL FOR SEMICONDUCTORS DERIVED FROM THE BOLTZMANN-EQUATION

An energy-transport model is rigorously derived from the Boltzmann tra nsport equation of semiconductors under the hypothesis that the energy gain or loss of the electrons by the phonon collisions is weak. Retai ning al leading order electron-electron collisions and elastic collisi ons (i.e., impurity scattering and the ''elastic part'' of phonon coll isions), a rigorous diffusion limit of the Boltzmann equation can be c arried over, which leads to a set of diffusion equations for the elect ron density and temperature. The derivation is given in both the degen erate and nondegenerate cases.