| This thesis addresses the quantum electronic transport properties of semiconductor nanostructures in the transient regime (Theme 1) and unconventional geometries (Theme 2), and the numerical algorithms to study them computationally. The transient regime properties are important in modeling fast-switching devices in digital electronics and high-frequency devices in sensing and telecommunications. In Theme 1, we start by overviewing the most important quantum master equations, then derive a quantum master equation for the device active region and couple it to the Poisson, Schrodinger, and current continuity equations in order to calculate the time-dependent charge density, current density, and potential profile of the nanostructure. Nanostructures are treated using the open system formalism. We introduce suitable initial conditions and discuss the role of scattering during the transient using a simple model. The results show that the longer the contact relaxation time, the shorter the transient. Furthermore, due to the initial depletion of electrons in the device, and depending on the strength of scattering injection into localized device states, the measured contact current and the device current can be very different initially due to charging/discharging. On the other hand, nanostructures with unconventional, curved geometries can be fabricated today in forms as complicated as helices. Curvature, coupled with a magnetic field, can have large effects on conductance, using mechanic or mechano-magnetic means for control. In Theme 2, we study the steady state, coherent quantum conduction in curved nanoribbons in a magnetic field. We transform the curvilinear Schrodinger equation into a tight-binding form and discuss the Hermiticity issues with the matrix Hamiltonian and the ways to deal with it. The method to solve the tight-binding Schrodinger equation introduces a preferable direction, which affects the choice of gauge that gives reasonable physical results. Consequently, we devise a local Landau gauge to help ensure that no artificial numerical reflection befalls the current-carrying states in the presence of a magnetic field. By applying this method to curved geometries with or without helicity, we observe conduction quenching and resonant reflections, among other features. |
