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We present the simultaneous optical and thermal analysis of a freestandingphotonic semiconductor membrane made from wurtzite III-nitride material. Bylinking micro-photoluminescence ($\mu$PL) spectroscopy with Raman thermometry,we demonstrate how a robust value for the thermal conductivity $\kappa$ can beobtained using only optical, non-invasive means. For this, we consider thebalance of different contributions to thermal transport given by, e.g.,excitons, charge carriers, and heat carrying phonons. Further complication isgiven by the fact that this membrane is made from direct bandgapsemiconductors, designed to emit light based on an In$_{x}$Ga$_{1-x}$N($x=0.15$) quantum well embedded in GaN. To meet these challenges, we designeda novel experimental setup that enables the necessary optical and thermalcharacterizations in parallel. We perform micro-Raman thermometry, either basedon a heating laser that acts as a probe laser (1-laser Raman thermometry), orbased on two lasers, providing the heating and the temperature probe separately(2-laser Raman thermometry). For the latter technique, we obtain temperaturemaps over tens of micrometers with a spatial resolution less than$1\,\mu\text{m}$, yielding$\kappa\,=\,95^{+11}_{-7}\,\frac{\text{W}}{\text{m}\cdot \text{K}}$ for the$\textit{c}$-plane of our $\approx\,250\text{-nm}$-thick membrane at aroundroom temperature, which compares well to our $\textit{ab initio}$ calculationsapplied to a simplified structure. Based on these calculations, we explain theparticular relevance of the temperature probe volume, as quasi-ballistictransport of heat-carrying phonons occurs on length scales beyond thepenetration depths of the heating laser and even its focus spot radius. Thepresent work represents a significant step towards non-invasive, highlyspatially resolved, and still quantitative thermometry performed on a photonicmembrane.

Joined optical and thermal characterization of a III-nitride semiconductor membrane by micro-photoluminescence spectroscopy and Raman thermometry