A Wigner function study of quantum electronic transport in semiconductor tunneling structures

A Wigner function model was developed for the study of electron transport in semiconductors. The Wigner function was chosen because it correctly includes all quantum mechanics. The distribution resembles a phase-space distribution. Quantities of interest are easily calculated. Correlations are inherent in the distribution. The equation of motion resembles the Boltzmann equation, with the quantum corrections entering through a non-local potential. The Wigner distribution was found to be a frequency integral of the correlation Green's function G{dollar}sp{lcub}<{rcub}{dollar}, and the equations of motion were shown to be identical. The equation of motion was studied with simple wave packets tunneling through quantum barriers. The non-local potential was found to cause artificial reflections from the boundaries. An algorithm was developed to absorb these artificial reflections.; The wave packet studies calculated tunneling times for a wave packet to traverse a quantum barrier, for both single and resonant barrier structures. These were compared to various theoretical predictions of the tunneling time. The resonant barrier showed a peak in tunneling time caused by charge storage in the resonant state.; The resonant tunneling diode was modeled. The initial distribution of carriers in the model was calculated from a scattering state basis. This distribution was used in the equation of motion to solve for steady-state I-V characteristics and transient behavior of the resonant tunneling diode. The Wigner function correctly modeled the I-V curve. Transient switching was related to the charge storage time within the quantum well. Fully self-consistent potentials were added to the model. The I-V curve shows an intrinsic bistability in the negative differential conductivity region, resulting from redistribution of charge within the device. The transient behavior was studied with self-consistent potentials. The current transient shows decaying oscillations of large magnitude. Plasma oscillations and the ballistic inertia of the electrons cause the device to be inductive at frequencies below 2 THz, and charge storage within the quantum well causes capacitive behavior above that frequency. At very low applied biases, the current was found to have two components. High-momentum tails near the barrier contribute current with high conductance. After the tails are depleted, low conductance from tunneling current dominates. (Abstract shortened with permission of author.)...