Nonlinear thermal model of a heterojunction-based light-emitting diode

A mathematical nonlinear thermal model of a heterojunction-based light-emitting diode (LED) is considered; the model makes it possible to estimate the nonuniformity of the current and temperature distributions in the active region of the heterostructure with the LED efficiency and the temperature dependence of the thermal-conductivity coefficient in the structure taken into account. A numerical-analytical iteration method is used to solve a set of equations that includes solving a nonlinear time-independent equation of thermal conductivity with the density of electrical power converted to heat dependent on the LED efficiency and an equation of electrothermal feedback, under conditions of a constant value for the average current density over the active region of the structure. The results of theoretical and experimental studies into the dependence of the $p$–$n$ junction-to-case thermal resistance on the forward current are represented for high-power light-emitting diodes.