Three-dimensional scattering-assisted tunneling in resonant-tunneling diodes.

Abstract

A quantum model and simulator for resonant tunneling diodes that includes three-dimensional (3D) scattering-assisted tunneling processes is reported. The 3D phase-breaking or quasi-phase-breaking scattering processes considered are polar scattering by optical phonons, deformation potential scattering by acoustic phonons, interface roughness scattering, and alloy scattering. The simulator solves Schr\"odinger equation in 3D using an expansion in terms of sequential scattering events. The average transmission and reflected currents are then calculated using an (analytic) ensemble average over the scatterers. We assume that the scattering events are uncorrelated and use a semiclassical phonon field. The relaxation approximation is not used. Back scattering is included so that the current is conserved. An important feature is that the 3D analysis permits one to account for the variation of the perpendicular momentum of the electron in the scattering process. This variation of the perpendicular momentum and the dependence of the scattering process upon the initial perpendicular momentum are the source of the broadening of the transmission coefficient.Simulation results are reported for a 34/34/34 and a 50/50/50 double-barrier heterostructure. The dominant scattering mechanisms in these devices are polar phonon scattering and interface roughness scattering. Polar phonon-assisted tunneling is revealed in the transmission coefficient by the presence of secondary resonant transmission peaks due to emission and absorption of optical phonons. At low temperature (4.2 K) this emission-assisted tunneling introduces a noticeable bump in the current voltage characteristics of the diode in agreement with a previous one-dimensional quantum model and low-temperature experimental data. At room temperature, however, 3D polar scattering introduces a much larger broadening of the transmission peak in the 50/50/50 structure than can be predicted by a one-dimensional model. A strong broadening is also introduced by interface scattering for monolayer terraces of 70 \AA{} average width, emphasizing the importance of the interface quality. Up to 6 and 20 multiple sequential IR scattering events are required for the transmission coefficient to fully converge for the 34- and 50-\AA{} barrier diodes resulting in a transmission coefficient versus energy with a characteristic asymmetric shape.However, the diode IV current converges typically in only three sequential IR scattering events. As expected the effective broadening introduced by these scattering mechanisms reduces the peak current and increases the valley current of the current voltage characteristic of the resonant tunneling diodes in agreement with experimental data.