Reliable k⋅p band structure calculation for nanostructures using finite elements

Abstract

The k · p envelope function method is a popular tool for the study of electronic properties of III-V nanostructures. The equations are usually transferred to real-space and solved using standard numerical techniques. The powerful and flexible finite element method was seldom employed due to problems with spurious solutions. The method would be favorable for the calculation of electronic properties of large strained nanostructures as it allows a flexible representation of complex geometries. In this paper, we show our consistent implementation of the k · p envelope equations for nanostructures of any dimensionality. By including BurtForeman operator ordering and ensuring the ellipticity of the equations, we are able to calculate reliable and spurious solution free subband structures for the standard k·p 4×4, 6×6 and 8×8 models for zinc-blende and wurtzite crystals. We further show how to consistently include strain effects up to second order by means of the Pikus-Bir transformation. Finally, we analyze the performance of our implementation using benchmark examples.

Unified simulation of transport and luminescence in optoelectronic nanostructures

“…However, standard k · p methods fail to incorporate effects from material interfaces and remote k-points. Details of the formulation and implementation are discussed in [24].…”

“…The eigenvalue problem associated with k · p envelope equations for wells, wires and dots and its numerical solution is elaborated in [24].…”

Optical properties and optimization of electromagnetically induced transparency in strained InAs/GaAs quantum dot structures

“…The asymmetry parameter present in the Burt-Foreman formalism but not in the Luttinger-Kohn formalism is shown to lead to changes in approximately Ϯ25 meV in the electronic band structures of InAs/GaAs. 18 Optoelectronic properties of InGaAs zinc-blende quantum dot with varying shape and size based on k ជ · p ជ theory have already been studied by Schliwa et al 19 and Veprek et al 20 However, so far, only a small selection of all possible transitions have been studied. In this work we apply the eightband model based on Burt-Foreman formalism derived in Ref.…”

Physics-based simulation of a core-multishell nanowire light emitting diode

“…The device simulator implements a microscopic and coupled solver for computing transport and luminescence in photonic semiconductor devices with quantized regions [4], [5]. It has been successfully applied to the analysis of quantum disk nanowire LEDs [6].…”