Analytical models of electron leakage currents in gallium nitride-based laser diodes and light-emitting diodes

The electrical-to-optical power conversion efficiencies of the light-emitting devices based on gallium nitride (GaN) are seriously limited by electron leakage currents due to the relatively low mobility and activation ratio of holes. However, there have been few theoretical models on the behavior of the leakage current with an increasing total current. We develop an Ohmic-law-like method to describe the transport behaviors of the systems with electron and hole currents simultaneously. Based on reasonable assumptions, the ratio of the leakage current to the total current is related to the differential resistances of the devices. Through the method, we develop analytical models of the leakage currents in GaN-based laser diodes (LDs) and light-emitting diodes (LEDs). The ratios of the leakage currents with total currents in LDs and LEDs are shown to increase, which explains the sublinear behaviors of the luminescence-current (LI) curves of the devices. The theory agrees well with the numerical simulation and experimental results in larger current ranges in comparison to the traditional ABC model. The above analytical model can be used to fast evaluate the leakage currents in GaN-based LDs and LEDs.