Three-dimensional quantum transport by supercell method: Numerical acceleration and applications

The open-boundary planar supercell stack method treats three-dimensional quantum transport in mesoscopic tunnel structures in a numerically stable and efficient manner. The method formulates quantum mechanical scattering problems for the supercell geometry as sparse linear systems, which can be solved by iterative methods. Recent improvement in solution algorithm using a seven-diagonal pre-conditioner has resulted in over two orders of magnitude of numerical acceleration, bringing more flexibility in the range of problems we can tackle. We will discuss applications to interface roughness in double barrier resonant tunneling structures and tunneling characteristics of ultra-thin oxides undergoing dielectric breakdown.