On the symmetry of efficiency-versus-carrier-concentration curves in GaInN/GaN light-emitting diodes and relation to droop-causing mechanisms

The internal quantum efficiency (IQE)-versus-carrier-concentration (n) curves of GaN-based light-emitting diodes have been frequently described by the ABC model: IQE=Bn2/(An+Bn2+Cn3). We show that this model predicts IQE-versus-n curves that have even symmetry. Phase-space filling makes the B and C coefficients concentration-dependent. We also show that IQE-versus-n curves that take into account phase-space filling possess even symmetry. In contrast, experimental IQE-versus-n curves exhibit asymmetry. The asymmetry requires a fourth-power or higher-power contribution to the recombination rate and provides insight into the mathematical form of the droop-causing mechanisms.