Local field corrections to the spontaneous emission in arrays of Si nanocrystals

TL;DR

This paper develops a theoretical model for local field corrections affecting spontaneous emission in silicon nanocrystal arrays, highlighting their dependence on fill factor and effective permittivities.

Contribution

It provides an analytical expression for the Purcell factor considering local field effects in silicon nanocrystal arrays, revealing their dependence on fill factor and permittivity models.

Findings

Local field corrections depend on nanocrystal fill factor.

Corrections are suppressed at high fill factors.

Different effective permittivities describe local field effects and density of states.

Abstract

We present a theory of the local field corrections to the spontaneous emission rate for the array of silicon nanocrystals in silicon dioxide. An analytical result for the Purcell factor is obtained. We demonstrate that the local-field corrections are sensitive to the volume fill factor of the nanocrystals in the sample and are suppressed for large values of the fill factor. The local-field corrections and the photonic density of states are shown to be described by two different effective permittivities: the harmonic mean between the nanocrystal and the matrix permittivities and the Maxwell-Garnett permittivity.