Analysis of the exciton–LO-phonon coupling in single wurtzite GaN quantum dots

Abstract

In this study, we analyze the interaction between excitons and longitudinal-optical phonons (LO phonons) in single, wurtzite GaN quantum dots (QDs) by means of micro-photoluminescence $(\ensuremath{\mu}\mathrm{PL})$ spectroscopy. We report on Stokes-shifted emission lines measured for hundreds of single QDs. A decrease of the Huang-Rhys factor $(\ensuremath{\sim}0.5\text{--}0.01)$ is observed with increasing QD emission energy that can be modeled in an adiabatic approximation applying two-particle eight-band $\mathbf{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{p}$ wave functions. In order to obtain the QD dimensions and shape needed for these calculations, we conduct a scanning transmission electron microscope (STEM) analysis, not only focusing on the QD dimensions, but also on alloying effects. The QD height is identified as the most detrimental parameter for the exciton-LO-phonon interaction in strongly polar QD systems based on nitrides. Additionally, we extract the LO-phonon energy for a significant number of individual QDs from our $\ensuremath{\mu}\mathrm{PL}$ data set scaling in-between the bulk values for the QD (GaN) and the matrix material (AlN). Such a large variation of the LO-phonon energy cannot be explained by the alloying effects attested by our STEM analysis. Hence, the exciton-LO-phonon interaction resides in a volume that encloses the QD in the growth direction and a fraction of the matrix material depending on the QD height. We approximate this exciton-LO-phonon interaction volume by a sphere with a constant diameter of $2.6\phantom{\rule{0.16em}{0ex}}\ifmmode\pm\else\textpm\fi{}\phantom{\rule{0.16em}{0ex}}0.2$ nm.