A multi-band, multi-level, multi-electron model for efficient FDTD simulations of electromagnetic interactions with semiconductor quantum wells

Abstract

We report a new computational model for simulations of electromagnetic interactions with semiconductor quantum well(s) (SQW) in complex electromagnetic geometries using the finite-difference time-domain method. The presented model is based on an approach of spanning a large number of electron transverse momentum states in each SQW sub-band (multi-band) with a small number of discrete multi-electron states (multi-level, multi-electron). This enables accurate and efficient two-dimensional (2-D) and three-dimensional (3-D) simulations of nanophotonic devices with SQW active media. The model includes the following features: (1) Optically induced interband transitions between various SQW conduction and heavy-hole or light-hole sub-bands are considered. (2) Novel intra sub-band and inter sub-band transition terms are derived to thermalize the electron and hole occupational distributions to the correct Fermi-Dirac distributions. (3) The terms in (2) result in an explicit update scheme which circumvents numerically cumbersome iterative procedures. This significantly augments computational efficiency. (4) Explicit update terms to account for carrier leakage to unconfined states are derived, which thermalize the bulk and SQW populations to a common quasi-equilibrium Fermi-Dirac distribution. (5) Auger recombination and intervalence band absorption are included. The model is validated by comparisons to analytic band-filling calculations, simulations of SQW optical gain spectra, and photonic crystal lasers.

Keywords:

• Finite-difference time-domain method
• nanophotonic devices

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. In general, the Δl = 0 selection rule is not strictly correct. However, it is an excellent approximation [20], especially close to the zone center which can reduce significant computational overhead.

2. In general, the scattering between various sub-bands would depend on the phonon energy. Moreover, scattering may not exactly follow the simplistic picture of occurring between the bottom of the two sub-bands However, the approach here is phenomenological in that it serves to thermalize the carrier distributions to a common lattice temperature.

3. Equation (1) is valid for nonparabolic band structures in general. In order to account for asymmetry, we need to write two polarization equations for each transition energy value E as E(k_t) ≠ E(−k_t).