Carbon in GaN as a nonradiative recombination center

Trap-assisted nonradiative recombination has been shown to limit the efficiency of optoelectronic devices. While substitutional carbon ($\mathrm{C_N}$) has been suggested to be a nonradiative recombination center in GaN devices, a complete recombination cycle including the two charge-state transition levels has not been previously described. In this work, we investigate the trap-assisted recombination process due to $\mathrm{C_N}$ in GaN, including multiphonon emission (MPE), radiative recombination, trap-assisted Auger-Meitner (TAAM) recombination, as well as thermal emission of holes. Our study shows the key role of TAAM processes at the high carrier densities relevant for devices. We also reveal the carrier-density regimes where thermal emission and radiative recombination are expected to play an observable role. Our results highlight that carbon concentrations exceeding $\sim$10$^{17}$ cm$^{-3}$ can have a noticeable impact on device efficiency, not just in GaN active layers but also in InGaN and AlGaN. Our comprehensive formalism not only offers detailed results for carbon but provides a general framework for assessing the multiple processes that participate in trap-assisted recombination in semiconductors.