© 2015 Elsevier Ltd. The generation of multiple leakage current paths in metal-insulator-semiconductor (MIS) structures with a HfO2/Al2O3-based nanolaminate grown by the ALD technique as insulator material was investigated. The devices were stressed at selected constant voltages in order to achieve accurate values for the occurrence time of every single breakdown event in a time range spanning around 120 s. The final result of the degradation experiment is a current-time characteristic with well-defined current steps. It is shown that using an equivalent circuit model formed by an array of series and parallel resistances we are capable of replicating the current increase exhibited by the investigated structures. Taking into account the obtained results for the discrete failure events, the model is extrapolated to the quasi-continuous breakdown case, which provides an even simpler relationship for the leakage current evolution. In this connection, an approximate expression for the time required to reach a given current level is proposed.