From the photoluminescence of SiC microcrystals uniformly covering a rectangular mesa of the high transition temperature $T_c$ superconductor ${\text{Bi}}_2{\text{Sr}}_2{\text{CaCu}}_2{\text{O}}_{8+\delta }$, the local surface temperature $T\left(\mathit{r}\right)$ was directly measured during simultaneous sub-THz emission from the $N\sim {10}^3$ intrinsic Josephson junctions (IJJs) in the mesa. At high bias currents $I$ and low bath temperatures $T_{\mathrm{bath}}\lesssim 35$ K, the center of a large elliptical hot spot with $T\left(\mathit{r}\right)>T_c$ jumps dramatically with little current-voltage characteristic changes. The hot spot does not alter the ubiquitous primary and secondary emission conditions: the ac-Josephson relation and the electromagnetic cavity resonance excitation, respectively. Since the most intense sub-THz emission was observed for high $T_{\mathrm{bath}}\gtrsim 50$ K in the low $I$ bias regime where hot spots are absent, hot spots cannot provide the primary mechanisms for increasing the output power, the tunability, or promoting the synchronization of the $N$ IJJs for the sub-THz emission, but can at best coexist nonmutualistically with the emission. No $T\left(\mathit{r}\right)$ standing waves were observed.

• Received 23 October 2012
• Revised 11 October 2013

DOI:https://doi.org/10.1103/PhysRevB.89.054503