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Electrical effects of non-uniform temperature distribution in current carrying conductors Anwar, Mohammad Zahural

Abstract

Anomalous electrical behaviour may appear in the d.c. and a.c. characteristics of metals or semiconductors in which the current is determined by both voltage and temperature. Theoretical investigations have been carried out by assuming different models of heat flow and the conditions for the appearance of thermal breakdown and Negative Resistance (NR) have been obtained for both metals and semi-conductors. For purely longitudinal heat flow, NR is predicted for metals while for semi-conductors, the d.c. characteristic is of the "breakdown" type without NR. On the other hand, the radial heat flow model predicts NR for semi-conductors and the conductivity modulation due to the radial temperature distribution causes a concentration of current-density along the axis, giving rise to the "thermal pinch" effect. For metals, this model does not predict NR and the resistivity modulation confines the current-density within a small depth from the surface giving rise to the "thermal skin effect". NR is also predicted for the model considering longitudinal heat flow with surface heat loss, the d.c. λ-K thermal theory, in semi-conductors whereas for metals, the theory does not predict NR. For the applicability of the λ-K thermal theory, the specimen must be thin enough to ensure an isothermal cross-section. The a.c. impedance of the specimen with a small a.c. voltage superimposed on the d.c. bias has been obtained for the λ-K thermal theory. Theoretical analysis shows that a non-zero surface loss parameter λ is essential for attaining NR in semiconductors. Experiments were performed with metals and semiconductors in an attempt to check the d.c. and a.c. λ-K thermal theories. Comparison of the experiments with the theory shows that for semi-conductors, the λ-K thermal theory is valid for current-density J ≤20 amps.cm-² while for metals, it is valid for J ≤5 x 10⁴ amps.cm-². The measured a.c. characteristics at both low and high frequencies are interpreted on the basis of the a.c. λ-K thermal theory but over the intermediate frequency region, the theory offers no explanation for the "circular arc" locus of impedances observed experimentally for both metals and semi-conductors. The present investigation enables one to determine the character of heat flow from measurements of the electrical characteristics of the specimen and also to distinguish the thermal effects which may be present in other experiments (e.g. on the "magnetic pinch").

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