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

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 voltage
V
dependent
\propto \exp (bV)
, when
T
is 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 V
m
, times for temperature runaway when voltages larger than V
m
were applied, and instabilities in the negative differential resistance ranges. Some significant differences were found as σ
1
rises much faster with temperature than σ
2
. 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 σ
2
than in the σ
1
case of conductivity. Transition to a branch line V-I characteristic and filament formation can occur in the σ
2
case at considerably higher temperatures than in the σ
1
case.