We propose two models of electron tunneling from metal to a semiconductor via traps. In addition to the electrons below the metal Fermi level, the models also include the thermally activated electrons above the Fermi level. The first model is called generalized thermionic trap-assisted tunneling (GTTT), which considers tunneling through both triangular and trapezoidal barriers present in metal insulator semiconductor (MIS) structures. The second model is called thermionic trap-assisted tunneling (TTT), which considers tunneling through triangular barriers present in modern Schottky junctions. The GTTT model is shown to predict the low field leakage currents in MIS structures with nitrided oxide as insulator, and the TTT model is shown to predict the reverse gate leakage in AlGaNGaN high electron mobility transistors. © 2006 American Institute of Physics.