Self consistent solution of a multi-band k.p Hamiltonian and Poisson´s equation using a plane wave expansion method

Conventionally finite difference methods are used to solve a multi-band k.p Hamiltonian in quantum well and heterostructure systems where a self consistent solution of Poisson´s equation is important, due e.g. to the presence of a Type II band line-up, with electrons and holes confined in separate layers. Following similar methods to density functional theory we describe a plane wave expansion method to efficiently solve a multi-band k.p Hamiltonian self consistently, including a fast Fourier space solution of Poisson´s equation. We demonstrate the efficiency of the method by considering the potential in an InGaAs/InGaAsP/InP 1.5 μm laser.