Tunneling through Thin Films with Traps

Tunneling currents through barriers containing one-dimensional potential wells with effective cross-sectional areas are calculated by using the WKB connection formulas to extend the wave functions of the incident free electrons to the other side of the barrier. The lifetime of electrons in the potential wells is assumed to limit the rate at which electrons may tunnel through the barrier. It is proposed that the qualitative features of this calculation may be applicable to tunneling currents through metal-insulator-metal thin-film sandwiches when the insulating film contains defects capable of trapping electrons. It is found that if the quasi-stable levels of the potential well lie near the Fermi level of the metal, for small voltages applied across the insulator, then the current may be greatly increased by the presence of these potential wells and most of the current will flow at energies near the quasi-level. A sample calculation was done to demonstrate these features for a square well in a rectangular barrier. A possible extension of this model allows the current to be proportional to the product of the densities of states in the metals on both sides of the barrier.