The current-voltage characteristics of nf poly-Si/SiO2/p-Si tunnel structures containing nonuniform ultrathin oxide layers are studied using three-dimensional quantum mechanical scattering calculations. We find that, in general, roughness at the Si/SiO2 interface renders the oxide layer more permeable. In the direct-tunneling regime, interface roughness induces lateral localization of wave functions, which leads to preferential current paths. But in the Fowler-Nordheim tunneling regime it affects transport primarily through scattering. These two distinct mechanisms lead to opposite current density dependencies on island size. We have also examined oxide-embedded conducting filaments, and found that they act as highly efficient localized conduction paths and lead to dramatic increases in current densities. Depending on the filament length, our model can mimic experimental current voltage for ultrathin oxides having undergone either quasibreakdown or breakdown. We also found that the lower bias current densities in the structure with long filaments are greatly enhanced by resonant tunneling through states identified as quantum dots, and that this current enhancement is highly temperature dependent. We also report on the dependence of current-voltage characteristics on filament diameter size and filament density.