Theory of metal-insulator-metal tunneling for a simple two-band model

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Abstract
The one‐band effective mass approximation for the dispersion relationship in the barrier of a metal‐insulator‐metal (MIM) tunnel junction fails if the barrier height is a considerable portion of the band gap of the insulator. This paper reports on results when the more realistic dispersion relation of Franz and Kane is used and displays the sensitivity of the tunnel effect to the band model. We illustrate some examples of the energy distribution of the current. Characteristic features of tunneling through trapezoidal‐like barriers will be discussed, including maxima in the logarithmic derivative curves, in the thermal I‐V characteristics, and the zero‐bias offset of the conductance minimum. Calculations are performed by integrating the tunnel equation numerically, and analytical approximations for this equation are also presented from which the effect of various parameters on the tunneling characteristic can be estimated.