A numerical Schrödinger–Poisson solver for radially symmetric nanowire core–shell structures

We present here a general purpose numerical Schrödinger–Poisson solver for radially symmetric nanowire core–shell structures for electronic and optoelectronic applications. The solver provides self-consistent solutions of the Schrödinger equation and the Poisson equation in cylindrical coordinates, for nanowire core–shell structures with radial compositional variation. Quantized energy levels as well as their associated electron wavefunctions and populations can be obtained from the solutions. Individual equation solvers were verified by comparison with scenarios where analytical results exist; verification of the self-consistent solution process was done by comparing results in the large radius limit with numerical solutions for a rectangular slab structure. We apply this solver to compute the charge/capacitance–voltage characteristics for a nanowire field effect device with wrap-around gate. It is shown that quantum confinement and the low dimensionality can give rise to, for representative nanowire FETs considered, ∼30% reduction in gate capacitance compared to the classically predicted value, and is ∼1/3 of the geometrical barrier limited capacitance.