Efficient Fourier space quantum dot k ⋅ p for wurtzite systems including smooth alloy profile and spatially varying elastic and dielectric constants

Abstract

We present methods to calculate the electronic structure of wurtzite quantum dot systems with continuous alloy profiles within Fourier-space-based k⋅p theory. We incorporate spatially varying elastic and dielectric constants in strain and piezoelectric potential calculations. A method to incorporate smooth alloy profiles in all aspects of the calculations is presented. We demonstrate our methodology for the case of a 1-dimensional InGaN quantum dot array and show the importance of including these spatially varying parameters in the modeling of devices. We demonstrate that the convergence of the lowest bound state energies is for good approximation determined by the largest wave vector used in constructing the states. We also present a novel approach of coupling strain into the k⋅p Hamiltonian, greatly reducing the computational cost of generating the Hamiltonian.