Abstract
The tunnelling current j( V) and the logarithmic conductivity σ( V) ≡ (1/ j)(d j/d V) are calculated for exactly solvable one-dimensional models of metal-insulator-metal structures. When the tunnelling probability is calculated by the MWKB method, the logarithmic conductivity exhibits a single peak at a value of the applied voltage equal to the barrier height. When the tunnelling probability is calculated exactly this peak is shifted to a higher value of the applied voltage and additional peaks appear at even higher values of the applied voltage, depending on the thickness of the insulating film. This additional structure in σ( V) is due to “resonances” in the tunnelling probability which may or may not survive in three a dimensional calculation.
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