Transport and heating of electrons in semiconductors with a one-dimensional superlattice

Abstract

On the basis of the Boltzmann equation with a new model collision integral that takes into account the redistribution of energy and momentum of all degrees of freedom of the electron, we have constructed and investigated a three-dimensional model of electron transport in one-dimensional semiconductor superlattices (SL’s). The current-voltage curves (CVC), mean energies, and effective temperatures of the electrons have been found for vertical and longitudinal transport. In contrast to one-dimensional models, the approach developed here allows one to take into account and describe not only longitudinal electron heating, but also electron heating transverse to the current. For vertical transport, transverse heating substantially alters the position, magnitude, and width of the current maximum. For longitudinal transport, electron heating that is non-quadratic in the field arises along the superlattice axis even in the approximation of a linear current-voltage characteristic. The possibility of describing electron transport in a superlattice using a mixed Fermi distribution with an isotropic temperature is analyzed.