<p>The article proposes a physical and mathematical model of the current–voltage characteristic (CVC) of light-emitting diode structures with quantum wells based on high band gap semiconductors using the Sah–Noyce–Shockley recombination mechanism. The article also describes the mechanism of the current–voltage characteristic generation at high forward current densities. It is demonstrated that the deviation of the current–voltage characteristic from the exponential dependence at high current densities is associated with the formation of a built-in electric field between the quantum wells inside the space charge region and, as a consequence, with an additional voltage drop. The distinctive feature of the model is that recombination in quantum wells does not occur through local centers but between the semiconductor zones in quantum wells. The developed model can be used to provide sound explanations for a set of experimental facts.</p> Graphical abstract <p></p>