Generalized Thermal <i>J-V</i> Characteristic for the Electric Tunnel Effect

The thermal J-V characteristic for a tunnel junction is derived in terms of a generalized theory. The resulting functional form of the equations is similar to that of Stratton; however, in the present formulation, the physical parameters of the junction appear explicitly, and their effect upon the thermal characteristic is readily appreciated. In Stratton's work, the physical constants appear in the integrand of integral that can be solved only numerically. The theory is applied to symmetric and asymmetric junctions. For the symmetric case, it is shown that, at a given temperature, the percentage change Ĵ in the high-temperature thermal component of current from the low-temperature value increases initially with increasing voltage bias up to a maximum peak, and thereafter decreases rapidly. The voltage bias at which the component of thermal current maxima occurs is equal to the interfacial barrier height and, as such, permits what is probably the most accurate method of barrier height determination. Similar results are obtained for the asymmetric barrier; however, in this case, Ĵ depends upon the polarity of the voltage bias for V&amp;gt;φ1, and two Ĵ maxima occur at voltages corresponding to the two distinct interfacial barrier heights φ1 and φ2.