# Thermal effects in point contacts

• Yu. G. Naidyuk
• I. K. Yanson
Part of the Springer Series in Solid-State Sciences book series (SSSOL, volume 145)

## Abstract

It is well known that the electron contribution to the thermal conductivity dominates in the metals. As a consequence, the thermal conductivity of pure metals is one or two orders of magnitude higher than that of semiconductors or dielectrics. If the relaxation time of electrons is identical for electrical and thermal processes, then electrical and thermal conductivity is connected by the well-known Wiedemann—Franz law [Kittel (1986)]. Theoretical treatment of the heat transfer through a point contact in the ballistic regime when a temperature gradient is applied to the contact instead of (or together with) a potential difference was done by Bogachek et al. (1985b). In the zeroth-order approximation, the heat flux was calculated analogously to the ballistic injection of electrons as
$$Q(T) = \frac{{{{\pi }^{2}}}}{3}{{\left( {\frac{{{{k}_{{\rm B}}}}}{e}} \right)}^{2}}\frac{T}{{{{R}_{0}}}}\Delta T,$$
(7.1)
where ΔT = T 2T 1 is the difference between temperatures on both sides of contact T 1 and T 2, and R 0 is the Sharvin resistance. If we determine the thermal resistance of a point contact as R T = ΔT/Q, then
$$\frac{{{{R}_{0}}}}{{{{R}_{T}}}} = \frac{{{{\pi }^{2}}}}{3}{{\left( {\frac{{{{k}_{{\rm B}}}}}{e}} \right)}^{2}}T = {{L}_{0}}T,$$
(7.2)
where L 0 is the Lorenz number. That is the Wiedemann—Franz law is valid for point contacts as well.

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