Simulation studies of the electrical response characteristics of 4H-SiC switches containing traps are reported in the absence of photoexcitation. The focus is on trap-to-band impact ionization and the role of hole injection from the anode. Simulations show that hole-initiated ionization can be more important than the electron-initiated process. The results also underscore the role of hole injection at the high applied voltages. Our one-dimensional, time-dependent model yielded reasonable agreement with measured current-voltage data spanning over three orders of magnitude, but only when impact ionization was taken into account. Finally, the simulations predicted undulations in the device conduction current density with respect to time, due to the dynamic interplay between impact ionization, spatial electric field values, and occupancies of the trap levels.