A voltage scale for electro-thermal runaway

Contact problems account for 40 percent of all electrical/electronic failures. Severe heating due to local current constrictions at thin film contacts [1-3] and at bulk contacts [2,4] is also a concern to high power microwave sources, pulsed power systems, field emitters, thin film devices and integrated circuits, and interconnects, etc. In this paper, we investigate one aspect of electro-thermal instabilities, namely, the increase in electrical conductivity as the temperature increases, as typical of semiconductors. This may lead to thermal runaway, at a fixed voltage. We deduce from the heat conduction equation a voltage scale, Vs [in volts], which characterizes thermal runaway. It is given by, Vs = sqrt(P/s), where P is the thermal conductivity [in W/m-K] and s is the rate of change of the electrical conductivity with respect to temperature [in 1/(ohm-m-K)]. Note that Vs depends only on material properties and is independent of geometry or the operating voltage. It measures the intrinsic tolerance of the material to electro-thermal instability. For various materials (Si, Ge, SiC) at room temperature, the typical values of P = (142, 58, 370) respectively, and s = (1.17, 0.104, 0.0003), yielding the values of Vs = (11, 24, 1100). Thus, SiC is the most resistant to thermal runaway for the same geometry and the same operating voltage, consistent with the well-known property of this material.