Drift model of resonant tunneling in superlattices including a time delay simulating electron scattering mechanisms

Abstract

The current oscillations in semiconductor superlattices under domain formation, which are due to a recycling of the domain boundary, contain additional spikes of much higher frequency than the fundamental oscillations. While the recycling of the domain boundary covers a larger number of periods of the superlattice, these spikes are due to a relocation of the domain boundary, which is a charge monopole, by one period. The number of spikes within one period of the fundamental oscillation can therefore serve as a measure for the number of periods, which are involved in the recycling motion. The theoretical model used in the simulations of the dynamics of the domain boundary has been outlined in Ref. [2]. In addition we have included a time delay in the drift term (proportional to the tunneling probability through a given barrier) so that the drift term is evaluated at a previous time, (t-τtun). This accounts for the nonzero tunneling time τtun that is estimated as the scattering time due to the interaction between electrons and Coulombic impurities, interface defects and optical and acoustical phonons. Delay effects occur when the average time that the monopole spends crossing a SL period (roughly, the oscillation period divided by number of wells) is comparable to the tunneling time. Our simulations show that the time delay results in high-frequency spikes similar to those experimentally observe. In the following figure we show the time evolution of the current, (a), and the electric-field profiles at the times depicted in the inset, (b).