Efficient multi-band k•p calculations of superlattice electronic and optical properties using plane waves

Abstract

Solving the multi-band k•p Schrödinger equation for a quantum-confined heterostructure using a reciprocal space plane wave approach presents several advantages compared to conventional real space approaches such as the finite difference or element methods. In addition to allowing analytical derivation of the heterostructure Hamiltonian, a desired level of accuracy in the computed eigenstates can generally be achieved using significantly reduced basis set size compared to equivalent real space calculations. This reduces the size of the Hamiltonian matrix that must be diagonalised to compute the electronic structure, thereby accelerating numerical calculations. Here, we demonstrate how the built-in periodicity of plane waves also allows to efficiently compute – for an arbitrary multi-band k•p Hamiltonian – superlattice (SL) miniband structure, using a calculational supercell consisting only of a single SL period. As an example we analyse the origin of the high radiative recombination rate in "broken-gap" InAs/GaSb SLs, of interest for applications in mid-infrared inter-band cascade light-emitting diodes.