On the properties of hot electrons in semiconductor quantum wells

Abstract

The appearance of negative differential resistance (NDR) associated with the abrupt optical phonon emission threshold in low-dimensional systems is discussed on the basis of three simple transport models. First, a streaming solution of the Boltzmann equation is obtained for when there is an absence of any scattering other than optical phonon emission. Then a solution in which electron-electron scattering maintains a Maxwellian distribution below, and only below, the emission threshold is shown to yield NDR. Finally a solution is obtained for the case of strong electron-electron scattering. A composite solution, consisting of a linear combination of these three models, based on the assumption of a relaxation time for electron-electron scattering is thought to be the most realistic. The result is that weak NDR appears when the electron-electron scattering is of the same magnitude as the optical phonon emission rate. The field at which runaway occurs is calculated, and a discussion of the observational effects of runaway is made. It is pointed out that in some cases the role of upper sub-bands will be to produce a quantum hot-electron effect on the current. It is also remarked that localisation of states at sub-band edges appears to provide yet another mechanism for NDR.