Measurement of thermal constriction resistance in micro-contacts formed by indentation of metals

Abstract

Heat transfer across contacting surfaces has been widely investigated through theoretical and experimental studies as a consequence of increasing demand in the thermal management industry. The contacting surfaces consist of micrometer-scale asperities. When heat enters the contact, it is constricted by these asperities, giving rise to the thermal resistance. This phenomenon is studied as heat entering or leaving a half space through a circular contact area at its boundary. The resulting expressions describe thermal constriction resistance in terms of surface and material properties, as well as the applied load and the contact area. Under applied pressure, asperities deform by truncation at their apex, increasing the real contact area and thereby reducing the thermal resistance. In contrast to many studies in the literature that focus on two-dimensional contact formation, this study investigates three-dimensional contact surfaces created by indentation. A sharp cube corner diamond indenter tip is penetrated into the softer metallic sample, deforming the sample material and generating a volumetric contact area for heat transfer. The experimental setup for the investigation of thermal contact consists of a homemade indenter system. It enables controlled positioning of the indenter tip into the sample while measuring the temperature of the tip and the load. An experimental procedure is followed to determine the thermal constriction resistance at different indentation depths, involving an oscillatory motion of the indenter tip, producing alternating contact and noncontact periods. The resulting tip temperature response is analyzed using the lumped capacitance model. The rise portion of the tip temperature is fitted to the exponential function, and the time constant is extracted. Then, constriction resistance is obtained using the proposed effective heat capacity, which is different for each tip-sample contact pair. The experimental procedure is applied to four different metallic samples, consisting of two copper and two gold samples with different thermophysical properties. The results are compared across samples, and the effects of applied load and depth on thermal constriction resistance are analyzed. The dependence of the constriction resistance on depth and load exhibits a saturation behavior, consistent with the simulation results. In addition, the effect of graphene on thermal constriction resistance is also investigated by performing experiments on graphene-coated copper and copper substrate under identical experimental conditions. Although no significant reduction in the measured time constants is observed for graphene in the load range of the experiments, other two dimensional materials may offer improved performance and require further investigation. Lastly, the choice of the indenter tip material is of particular importance. Diamond exhibits both high thermal conductivity and high stiffness. Investigating the thermal contact behavior of a single diamond asperity can provide insights into its potential use as a thermal interface material (TIM). Such an application could enable efficient heat transfer for plug-in contacts without the wetting of the surface by conventional paste-based TIMs.