Electron subband structure in strained silicon UTB films from the Hensel–Hasegawa–Nakayama model – Part 2 efficient self-consistent numerical solution of the k · p schrödinger equation

A self-consistent Schrödinger–Poisson model for the calculation of the electron subband structure of ultra-thin body (UTB) devices for arbitrary substrate orientation is presented. The proposed approach is based on a two-band k · p Hamiltonian and takes the band nonparabolicity and arbitrary strain into account. Despite its small matrix size compared to full-band approaches, an excellent description of the band structure over a wide range of the Brillouin zone is assured. Furthermore, emphasis is put on the efficiency and accuracy of the numerical, two-dimensional k-space integration of the subband distribution functions. For this purpose, the Clenshaw–Curtis method which is based on non-equidistant interpolation nodes is employed. Simulation results of (0 0 1) and (1 1 0) oriented silicon UTB double gate devices demonstrate the suitability of the proposed numerical method. For Si body thicknesses in the nanometer regime, the presence of band structure effects which are not captured by a one-band model are clearly demonstrated.