THE METHODOLOGY OF SIMULATING PARTICLE TRAJECTORIES THROUGH TUNNELING STRUCTURES USING A WIGNER DISTRIBUTION APPROACH

Understanding and describing steady-state and transient tunneling behavior are necessary for determining the fundamental transport properties and speed performance limits of electronic devices based on field emitter arrays. The Wigner distribution approach is used as a first step in developing a theoretical and calculational methodology applicable to a wide class of quantum tunneling problems. The tunneling behavior in nanostructure field emitters is fundamentally similar to the tunneling behavior in other tunneling structures, e.g., resonant tunneling diodes (RTD's), where a large amount of experimental data exist. A modified relaxation time approximation is used for the scattering. Self-consistency is implemented, for the first time in fully time-dependent calculations, to investigate both the steady-state and transient behavior in RTD's. Of particular interest is their ultra-fast switching times (approximately 0.1 ps), which is comparable to that promised in micrometer scale vacuum devices based on field emitter arrays. A methodology for constructing quantum "particle trajectories" is presented with the long-term goal of incorporating them into a particle Monte Carlo simulation. The trajectories for an RTD are presented and their behavior, as a function of scattering and self-consistency, is shown to be consistent with the steady-state current-voltage/quantum well electron density characteristics of the RTD, and with the response of the RTD to a sudden bias switch. The trajectories also exhibit a conservation-of-energy-like behavior. The trajectory formulation is thus shown to be potentially useful for incorporating into a multidimensional particle Monte Carlo simulation of quantum-based devices in which the tunneling region is small compared to the dimensions of the device, as is the case with heterojunctions and nanostructure field emitters.