Direct and Fowler-Nordheim tunneling currents through oxide and dual layer silicon oxide-silicon nitride dielectrics are investigated for substrate and gate injection. The calculations include depletion effects in the heavily doped (n ϩ) polysilicon gate electrodes as well as quantization effects in the less heavily doped n-type substrates. The Wentzel-Kramers-Brillouin ͑WKB͒ effective mass approximation has been compared with exact calculations for the tunneling probability, and based on these comparisons it has been found that the WKB approximation is adequate for single layer dielectrics, but is not for the dual layer dielectrics that are the focus of this article. Using exact tunneling transmission calculations, current-voltage (I-V) characteristics for ultrathin single layer oxides with different thicknesses ͑1.4, 2.0, and 2.3 nm͒ have been shown to agree well with recently reported experiments. Extensions of this approach demonstrate that direct tunneling currents in oxide/nitride structures with oxide equivalent thickness of 1.5 and 2.0 nm can be significantly lower than through single layer oxides of the same respective thickness.