Abstract
The open-boundary planar supercell stack method treats three-dimensional quantum transport in mesoscopic 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 the 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 that can be solved. We demonstrate the effectiveness of the seven-diagonal pre-conditioning algorithm by applying it to the studies of interface roughness in double barrier resonant tunneling structures and tunneling characteristics of n + poly-Si/SiO2/p-Si with ultra-thin oxides undergoing dielectric breakdown.
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