Renormalization of Optical Transition Strengths in Semiconductor Nanoparticles due to Band Mixing

TL;DR

This paper demonstrates how quantum confinement and band mixing in semiconductor nanoparticles significantly suppress electron-photon interaction strengths, requiring an energy-dependent renormalization of the Kane momentum for accurate optical property predictions.

Contribution

It introduces an effective energy-dependent Kane momentum to account for band mixing effects, improving the accuracy of optical property calculations in semiconductor nanoparticles.

Findings

Band mixing causes significant suppression of electron-photon coupling.

Neglecting band mixing can overestimate absorption and emission rates by about a factor of 2.

The proposed renormalization aligns theoretical models with quantum confinement effects.

Abstract

Unique optical properties of semiconductor nanoparticles (SN) make them very promising in the multitude of applications including lasing, light emission and photovoltaics. In many of these applications it is imperative to understand the physics of interaction of electrons in a SN with external electromagnetic fields on the quantitative level. In particular, the strength of electron-photon coupling determines such important SN parameters as the radiative lifetime and absorption cross section. This strength is often assumed to be fully encoded by the so called Kane momentum matrix element. This parameter, however, pertains to a bulk semiconductor material and, as such, is not sensitive to the quantum confinement effects in SNs. In this work we demonstrate that the quantum confinement, via the so called band mixing, can result in a significant suppression of the strength of electron interaction with electromagnetic field. Within the envelope function formalism we show how this suppression can be described by introducing an effective energy-dependent Kane momentum. Then, the effect of band mixing on the efficiencies of various photoinduced processes can be fully captured by the conventional formulae (e.g., spontaneous emission rate), once the conventional Kane momentum is substituted with the renormalized energy-dependent Kane momentum introduced in here. As an example, we evaluate the energy-dependent Kane momentum for spherical $\rm{PbSe}$ and $\rm{PbS}$ SNs (i.e., quantum dots) and show that neglecting band mixing in these systems can result in the overestimation of absorption cross sections and emission rates by a factor of $\sim$2.