Envelope Function Approximation (EFA) Bandstructure Calculations for III-V Non-square Stepped Alloy Quantum Wells Incorporating Ultra-narrow (~5Å) Epitaxial Layers

Abstract

We describe Envelope Function Approximation (EFA) bandstructure calculations based on a 4-band electron (EL), heavy-hole (HH), light-hole (LH) and split-off hole (SO) effective mass Hamiltonian, with Burt-Foreman hermitianisation, which can handle III-V quantum well structures that incorporate ultra-narrow epi-layers. The model takes into account the coupling of EL, HH, LH and SO bands and is suitable for describing quantum wells tuned to the 1.0 - 1.55 µm window exploited by optical fibre communication devices. We have used the multi-band solver to calculate the bandstructure of an illustrative InGaAsSb-AlGaSb non-square quantum well that incorporates 6Å potential “spikes” in its well region. Calculations based on the Burt-Foreman hermitianised Hamiltonian and those based on a Hamiltonian with standard “symmetrised” hermitianisation are presented and compared. When coupling to the conduction band is excluded from the calculation, the latter formulation leads to anomalous electron-like curvature of the dispersion curves for our spiked non-square quantum well structure.

Modeling Energy Bands in Type II Superlattices

“…It is worth mentioning that, to reduce the size of the problem to be solved, the 8 × 8 Hamiltonian can be block diagonalized into two 4 × 4 Hamiltonians by choosing an appropriate transformation matrix based on a new set of basis states. More details can be found in [31]. To use FEM analysis to solve the multiband effective mass in Equation 15, it is instructive to use either the Galerkin or variational approach, as both lead to the same final expression.…”

Non-square quantum well growth for reduced threshold current in tensilely strained lasers operating at 1.52m

“…In this work, an 8-band effective mass Hamiltonian based on the k×p method is used to describe the coupled QW electron (EL), heavy-hole (HH), light-hole (LH) and split-off-hole (SO) states. By use of a unitary transformation, this 8x8 Hamiltonian is block diagonalized (decoupled) into two 4´4 Hamiltonians whose wavefunctions are given by [16]…”

“…Equations 7and 8are solved by basis function expansion in terms of solutions, obtained by an accurate shooting method, of the corresponding single band problems. Details of the calculation are given in [16].…”

Simulation of quantum wells with ‘spikes’ and ‘dips’

“…Although rectangular quantum wells (QWs) have been widely investigated, only few studies have been carried out for non-square QWs (Devaux et al 1997;Shen et al 1998;Kaduki and Batty 2000;Kaduki et al 2003). The introduction of either high-bandgap ('spikes') or low-bandgap ('dips') layers in conventional rectangular QWs influences significantly the QW properties and provides supplementary flexibility in engineering the intra-and interband energy level separation.…”