Generalized <i>A</i>(<i>n</i>)<i>BC</i> Recombination Model in Semiconductors with Multilevel Defects

The ABC model has been widely used to describe the carrier recombination rate, in which the rate of defect-assisted recombination is assumed to depend linearly on excess carrier density Δ<i>n</i>, leading to a constant recombination coefficient <i>A</i>. However, for multilevel defects that are prevalent in semiconductors, when Δ<i>n</i> varies, we find that the carrier capture and emission of defects can change the defect density distribution in different charge states, which makes the <i>A</i> coefficient depend on Δ<i>n</i> and become a function <i>A</i>(<i>n</i>). Therefore, the recombination rate should depend nonlinearly on Δ<i>n</i>. However, in many recent computational studies on multilevel defects, only carrier capture was considered, while carrier emission from defect levels was neglected, causing incorrect charge-state distribution and misleading linear dependence of the rate on Δ<i>n</i>, especially for multilevel defects with shallow levels. Taking V_Ga-O_N in wurtzite GaN and Pb_I in perovskite CsPbI₃ as examples, our calculations showed that neglecting carrier emission can cause the recombination rate to be underestimated by more than 8 orders of magnitude when Δ<i>n</i> is 10¹⁵ cm^-3. Our findings suggest that recent studies on carrier recombination assisted by multilevel defects should be revisited with carrier emission considered, and the widely used ABC model should be reformulated into the <i>A</i>(<i>n</i>)<i>BC</i> model.