We investigated the effect of adding the fi eld-dependent recombination process, namely fi eld-enhanced trapping, to the generation-recombination processes of charge carriers that model current oscillations in semiconductors. The main new features arising from this modifi cation are identifi ed in bifurcation diagrams with the electric fi eld as the control parameter. The characteristic of the bifurcation diagrams is a function of impurity energy. Thus, we generated a set of bifurcation diagrams for a range of the impurity energy and applied bias. The energy dependence of the bifurcation diagrams is discussed considering the context of the competition between the generation-recombination mechanisms impact ionization and fi eld-enhanced trapping.