Point defects, including intentional dopants, compensating impurities, and native point defects, as well as extended defects have a large impact on semiconductor devices and their performance. Some point defects are intentionally incorporated as dopants to provide free carriers or intentionally compensate material, and others serve as nonradiative and scattering centers that are deleterious to device performance. Shockley-Read-Hall (SRH) recombination is commonly used to determine the recombination rate associated with point defects when simulating devices. As the SRH model was developed treating only the capture processes of carriers with defects that scale linearly with carrier density, such as multiphonon emission and radiative capture, the defect-mediated recombination rates and currents it predicts are accurate only in the low-carrier-density regimes. Our recent experimental observation of hot electrons generated by trap-assisted Auger-Meitner recombination (TAAR) from a shallow impurity [Phys. Rev. B 111, 155308 (2025)], whose emission currents had a strong dependence on the operating device currents, raises a question regarding whether only a single type of capture and emission process can be ascribed to a given defect, or instead if several possible capture and emission processes with an appreciable rate must be considered for the same defect. In this work, we extend the conventional SRH analysis to include trap-assisted Auger-Meitner processes in defect-assisted recombination cycles (DARCs). The inclusion of TAAR processes in DARCs demonstrates that defect-mediated recombination rates and currents can scale quadratically with carrier density and can significantly deviate from the predictions of the conventional SRH model, especially in the higher-carrier-density regimes. We perform a case study for the recombination rates involving the ${\mathrm{Ca}}_{\mathrm{Ga}}$ impurities in $\mathrm{Ga}\mathrm{N}$ using our formalism, where ${\mathrm{Ca}}_{\mathrm{Ga}}$ is chosen because hot electrons from ee TAAR involving ${\mathrm{Ca}}_{\mathrm{Ga}}$ have been measured using electron emission spectroscopy. Implementation of DARCs using the analytical framework presented in this article can result in the increased accuracy of simulated defect-mediated recombination rates, especially for situations where there are large excess carrier densities such as in quantum-well-based light-emitting diodes and lasers.

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• Carrier generation & recombination
• Defects
• Optoelectronics
• Point defects
• III-V semiconductors
• LEDs
• Nitrides
• Semiconductor lasers