We present results from numerical simulations of AlGaN/InGaN double‐heterostructure light‐emitting diodes. A highly convergent, fast, and memory efficient algorithm necessary for wide band‐gap device simulation was developed and is described here. Charge carrier tunneling currents and a band to impurity recombination mechanism are included. The results compare favorably to experimental results. The results demonstrate that the saturation of power at high currents, the high rate of increase in currents at high voltages, and the reduced broadening of the optical emission spectrum at high biases, with only band‐to‐acceptor recombination occurring in the active region, are due to carriers leaving the active region by thermionic emission rather than recombining. ©1996 American Institute of Physics.