Multiband and multidimensional quantum transport

Abstract

We give an overview of a numerically stable and efficient method for computing transmission coefficients in semiconductor heterostructures using multiband band structure models. The multiband quantum transmitting boundary method (MQTBM) has been successfully implemented for the empirical tight-binding model, the effective bond orbital, the k·p model, and the pseudopotential method. It has been used extensively in the investigation of band structure effects such as valley mixing and band mixing. We use a GaAs/AlAs double barrier heterostructure and an InAs/GaSb/AlSb interband tunnel device to illustrate the applications of this method to the phenomena of X-point tunneling, hole tunneling, and interband magneto-tunneling. We then review a closely related method, the open-boundary planar supercell stack method (OPSSM), as a means for treating 3D quantum transport in mesoscopic tunnel structures. The flexibility of the method allows us to examine a variety of physical phenomena relevant to quantum transport, including alloy disorder, interface roughness, defect impurities, and 0D, 1D, and 2D quantum confinement, in device geometries ranging from double barrier heterostructures to quantum wire electron waveguides. As examples, we examine double barrier structures with interface roughness, resonant tunneling through self-organized InAs quantum dots, and MOS tunnel structures with non-uniform ultra-thin oxide layers.