Efficient quantum dot $\mathbf{k}\cdot\mathbf{p}$ in wurtzite systems including spatially varying elastic and dielectric constants and smooth alloy profile

TL;DR

This paper introduces Fourier-space methods for calculating the electronic structure of wurtzite quantum dots with spatially varying properties, improving accuracy and efficiency in modeling such systems.

Contribution

It presents a novel approach to incorporate spatially varying elastic, dielectric, and alloy profiles into quantum dot electronic structure calculations, reducing computational costs.

Findings

Accurate modeling of quantum dot states with spatially varying parameters.

Convergence of energy states depends on the maximum wave vector used.

Coupling strain into the Hamiltonian reduces computational cost.

Abstract

We present Fourier-space based methods to calculate the electronic structure of wurtzite quantum dot systems with continuous alloy profiles. 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 1D InGaN quantum dot array and show the importance of including these spatially varying parameters in the modeling of devices. We demonstrate that convergence of the lowest bound state energies is to good approximation determined by the largest wave vector used in constructing the states. We also present a novel approach of coupling strain into the $\mathbf{k}\cdot\mathbf{p}$ Hamiltonian, greatly reducing the computational cost of generating the Hamiltonian.