The tunneling current characteristics and transient response of double-barrier semiconductor structures are simulated for different barrier and quantum-well widths, barrier heights, operating bias voltage, and ambient temperatures, using the equation for the Wigner distribution function. The numerical results suggest the following: (a) There is a particle buildup inside the quantum well prior to the resonant current peak as the applied bias is varied: (b) the number of resonant energy levels seen in the simulation agrees with its proportionality to the square root of the product of the barrier height and quantum-well width: (c) the resonant peak width is larger for higher resonant energy levels than for the lower resonant energy levels in agreement with the different degree of localization of these levels; (d) at T=77 K, the current slowly increases with bias at lower bias than for T=300 K, with higher peak-to-valley ratio at T=77 K, presumably due to a much sharper convolution of the tunneling density and resonant energy level width; and (e) a higher degree of localization and existence of numerically resolved resonant energy level, in the case of asymmetrical barrier widths, occurs when the thicker barrier is located in the side with lower electron potential or higher voltage bias; no negative differential resistance was observed when these barrier widths were interchanged in our simulation. The superior accuracy of an alternative finite difference scheme, coupled with the Cayley form for the time evolution operator, in this type of numerical simulation is briefly discussed.

Jensen, K. L., & Buot, F. A. (1989). Numerical simulation of transient response and resonant-tunneling characteristics of double-barrier semiconductor structures as a function of experimental parameters. Journal of Applied Physics, 65(12), 5248–5250.