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We report on quaternary AlInGaN/InGaN multiple quantum well(MQW)light emitting diode structures grown on sapphire substrates. The structures demonstrate high quality of the p–njunctions with quaternary MQW. At low forward bias (below 2 V), the temperature dependent of current–voltage characteristics are exponential with the ideality factor of 2.28, which is in a good agreement with the model of the injected carrier recombination in the space charge region. This ideality factor value is approximately three times lower than for conventional GaN/InGaN light emitting diodes(LEDs). The obtained data indicate the recombination in p–njunction space charge region to be responsible for a current transport in LED structures with quaternary quantum wells. This is in contrast to InGaN based LEDs, where carrier tunneling dominates either because of high doping of the active layer or due to the high density of localized states.