The incorporation of quantum mechanics into ensemble Monte Carlo simulation

As device sizes become smaller and begin to reach the quantum limits, quantum effects in these devices are expected to dominate device operation. Currently, the best developed simulation techniques are classical, where the most robust and reliable of these techniques is the ensemble Monte Carlo approach. A major setback to these classical techniques is that they are unable to incorporate quantum effects associated with the wave nature of the electron and, as such, are expected to fail when used in simulations of quantum devices. Although fully quantum mechanical approaches to device simulation do exist, they lack the ability to incorporate scattering into the system without the use of approximations. To this end, new methods are proposed to incorporate quantum effects into already trusted ensemble Monte Carlo simulations. First, the effective potential and the role it plays in introducing confinement effects in EMC are discussed. The effective potential's inability to model tunneling leads to the more complicated method of the Wigner quantum Monte Carlo to correctly calculate tunneling in EMC. Finally, a new method of incorporating non-local scattering is presented.; The first method developed here is that of the effective potential, which demonstrates efficient and accurate incorporation of confinement effects associated with the wave nature of the electron into classical simulations. However, it is also shown that the effective potential is unable to model tunneling. To achieve tunneling, a Monte Carlo based on the Wigner function is developed. This new method allows the simulation of fully quantized structures, with a full description of the scattering in the problem. Using this method, the operation of the resonant tunneling diode is studied. A novel method for including non-local scattering (including the intra-collisonal field effect and collision broadening) into the Monte Carlo is presented. It is found that these non-local scattering effects are small and can be ignored.; Finally, this Monte Carlo based on the Wigner function is employed to discuss the source of hysteresis seen in resonant tunneling devices. By including the scattering in the problem correctly, it is possible to properly discharge the quantum well in the diode and, therefore, prevent the build-up of charge, which theoretically causes hysteresis. This leads to the conclusion that the hysteresis seen experimentally is due to external circuit components used in the current-voltage measurements.