Low-field electron runaway and spontaneous formation of two-beam velocity distribution in polar semiconductors

We show that high-energy electron injection into a polar semiconductor can lead to a spontaneous splitting of the electron beam into two distinct groups with different velocity distributions. While one group of electrons experiences thermalization in a given subthreshold field, the velocity and energy of the second group increases with distance due to the previously unknown low-field electron runaway effect. We investigate the dependence of the carrier distribution on the injection energy, and show that the overall distribution exhibits a partial population inversion with a distance-dependent energy gap between the thermalized and runaway electrons. The low-field runaway is a universal effect which is characteristic of nanoscale semiconductors where polar optical phonon scattering predominates and there is a large intervalley energy separation as in the group-III nitride heterostructures.