Tunneling current from a metal electrode to many traps in an insulator

The tunneling current from a metal electrode to electron traps in insulating films which locate at a small distance from the electrode interface is calculated using the Bardeen tunneling-Hamiltonian formalism. The tunneling from the electrode to the traps is considered as an electron transition from the initial states in the electrode to many trap states in the insulating film. The electron in the electrode corresponding to the wave function of the initial state is assumed to be a free electron. The energy barrier between the metal electrode and the traps in the insulating film was taken into closer examination for considering the perturbation of the electron wave functions in the metal electrode and traps. In contrast to the band-to-band tunneling mechanisms, such as Fowler-Nordheim or true tunneling, the calculations show that the tunneling current into the traps largely depends on the temperature. The slopes of the tunneling current versus the applied electric field curves are steep and the logarithmic current increases linearly with increasing applied voltage. The tunneling current to traps having deeper bound state energy below the conduction band minimum of the insulator is much larger than the one to traps having shallower bound state energy.