Electronic structure of semiconductor nanostructures: A modified localization landscape theory

Abstract

In this paper we present a modified localization landscape theory to calculate localized/confined electron and hole states and the corresponding energy eigenvalues without solving a (large) eigenvalue problem. We motivate and demonstrate the benefit of solving ${\hat{H}}^{2}u=1$ in the modified localization landscape theory in comparison to $\hat{H}u=1$, solved in the localization landscape theory. We detail the advantages by fully analytic considerations before targeting the numerical calculation of electron and hole states and energies in III-N heterostructures. We further discuss how the solution of ${\hat{H}}^{2}u=1$ is used to extract an effective potential $W$ that is comparable to the effective potential obtained from $\hat{H}u=1$, ensuring that it can for instance be used to introduce quantum corrections to drift-diffusion transport calculations. Overall, we show that the proposed modified localization landscape theory keeps all the benefits of the recently introduced localization landscape theory but further improves factors such as convergence of the calculated energies and the robustness of the method against the chosen integration region for $u$ to obtain the corresponding energies. We find that this becomes especially important for here studied $c$-plane InGaN/GaN quantum wells with higher In contents. All these features make the proposed approach very attractive for calculation of localized states in highly disordered systems, where partitioning the systems into different subregions can be difficult.

14 pages, 6 figures

References in corpus (4)

• Consistent set of band parameters for the group-III nitrides AlN, GaN, and InN
• Interrelation of structural and electronic properties of InGaN/GaN quantum dots using an eight-band k.p model
• Atomistic analysis of the impact of alloy and well-width fluctuations on the electronic and optical properties of InGaN/GaN quantum wells
• A comparison of atomistic and continuum theoretical approaches to determine electronic properties of GaN/AlN quantum dots