Influence of the law of electrical conductivity on thermal switching and breakdown

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Abstract
Influences of the law of electrical conductivity σ on thermal switching and breakdown events were investigated. The conductivities selected were\sigma_{1}\propto \exp(aT), or\sigma_{1}\propto \exp(-B/T), and also voltageVdependent\propto \exp (bV), whenTis temperature and a, B, and b are constants. Simple models, thin film, and cylindrical specimens were considered. The influence of σ was examined by comparing steady-state V-I characteristics, the values of maximum voltages Vm, times for temperature runaway when voltages larger than Vmwere applied, and instabilities in the negative differential resistance ranges. Some significant differences were found as σ1rises much faster with temperature than σ2. Thus current filaments were very narrow when\sigma_{1}\propto \exp(aT), but orders of magnitude wider when\sigma_{1}\propto \exp(-B/T). For a given current, much larger temperature rises occur in the σ2than in the σ1case of conductivity. Transition to a branch line V-I characteristic and filament formation can occur in the σ2case at considerably higher temperatures than in the σ1case.

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