Renormalization of optical transition strengths in semiconductor nanoparticles due to band mixing
We report that 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. Lastly, as an example, we evaluate the energy-dependent Kane momentum for spherical PbSe and 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 ~2.