Theory of resonant tunneling through the insulator conduction band of a thin film metal-insulator-metal (MIM) heterojunction

An “atomic” model of an insulating barrier between two free-electron model metals is used to investigate resonant tunneling across the insulator in the presence of a medium to large, externally applied electric field (bias). The exact numerically calculated tunneling current exhibits a pronounced oscillatory bias dependence superposed on the dominant roughly exponential tunneling characteristic. The interpretation of these results in terms of an internal field emission or Fowler-Nordheim type tunneling subject to “periodic deviations” (or interferences) seems plausible and was suggested by Maserjian. To test this conjecture, a trapezoidal barrier model of our “atomic” model analyzed numerically. As expected, the trapezoidal barrier model could only qualitatively reproduce the oscillatory bias dependence of the barrier transmissivity and of the current. Furthermore this limited agreement depends on allowing the effective mass in the barrier to become a strictly adjustable parameter. This failure of the conventional model of the junction can be interpreted as follows: (i) For moderate external (bias) fields the trapezoidal barrier fails to account for the correct position dependence of the Blochwave vector in the insulator's conduction band, hence the correct interference conditions cannot be reproduced. (ii) For large external fields the band model itself begins to fail. An explanation of oscillatory bias dependence at the tunneling current in terms of splitting of the insulator's conduction band into a set of discrete Stark levels is suggested. It is demonstrated that a fit of the oscillatory tunneling characteristics in the “Fowler-Nordheim regime” is not a reliable technique to determine the effective mass in the thin insulating film of tunneling junctions over the energy interval containing the forbidden gap and the adjoining conduction-band.