Voltage scale for electro-thermal runaway

Contact problems account for 40{\%} of all electrical/electronic failures [1]. Current crowding leads to intense local heating in both bulk [2] and thin film contacts [3], and is a concern to high power microwave sources, pulsed power systems, field emitters, thin film devices, and interconnects, etc. We investigate electro-thermal instability (ET) due to the increase in electrical conductivity as temperature increases, which may lead to thermal runaway at fixed voltage. We deduce a voltage scale for ET onset [4], $V_{s} =\sqrt {\kappa /{\sigma }'_{0} } $ [in volts], where $\kappa $ is the thermal conductivity [in W/(m-K)] and ${\sigma }'_{0} $ is the rate of change of the electrical conductivity with respect to temperature [in 1/(ohm-m-K)]. $V_{s} $ depends only on material properties and is independent of geometry or the operating voltage. It measures the intrinsic tolerance of the material to ET. The calculated $V_{s} $ are consistent with the well-known properties of several common materials, such as Si, Ge, C (graphite), and SiC [4].\\[4pt] [1] \textit{Review of Federal Programs for Wire System Safety}, NSTC Final Report, 2000. [2] Zhang, PhD dissertation, UM, Ann Arbor (2012). [3] Zhang et al., IEEE TED 59, 1936 (2012); J. Phys. D: Appl. Phys. 46, 065502 (2013); ibid 46, 209501 (2013); IEEE JEDS (in the press, 2013). [4] Lau, et. al., PPPS Proc 2013.