Thermal Contact Conductance of Micromachined Interfaces

Woo-Bin Song and Joseph J. Talghader

The thermal contact conductance, G, is the most critical parameter in the study of heat transfer across interfaces. It is a measure of how much heat is able to flow across two surfaces in contact. For bulk materials (e.g. two metal rods stuck end-to-end) there are two primary paths for heat conduction between two interfaces at room temperature: one is solid-solid conduction through the contact points, and the other is conduction through an interstitial material, if there is one as shown in Figure 1. Measurements of these interfaces have shown that TCCs measured in vacuum are significantly lower than those measured with an interstitial gas, usually air. This behavior is typically attributed to the additional conduction paths offered by the air.

For micromachined devices, the roughness of interfaces is on the order of nanometers or angstroms, several orders of magnitude less than for bulk materials. We have done extensive testing of heat transfer in micromachined devices. A typical structure is shown in Figure 2 where we actuate a micromachined plate to the substrate and measure the heat dissipation across the interface. Our data shows suggests that trapped interstitial gas at nanometer roughness serves primarily to reduce the solid-solid contact area, overwhelming its traditional role in providing alternate conduction paths (see Figures 3 and 4).

Figure 1 - Conceptual diagram of a micromachined thermal contact interface (a) in vacuum and (b) in air. Evidence suggests that when a device is actuated to the substrate in (b), some of the air layer is squeezed between the plates before it can escape. The trapped air forces apart the plates in small areas and reduces the thermal contact conductance.

Figure 2 - Diagram(a) and optical micrograph(b) of a test structure used in this study to measure thermal contact conductance.

Figure 3 – The slope of a measurement of 1/(Resistance) vs, Current² is inversely proportional to the TCC. This measurement was done for a test device in air. The relatively flat curve is the measurement for the unactuated device, while the steeply sloped curve is for the snap-down condition. Note that the TCC measured in this manner (G under snap-down) is more than an order of magnitude greater than typical values seen with bulk metal interfaces.

Figure 4 - 1/R vs, I² for the test structure in Fig. 3 in vacuum. Note that the TCC in vacuum (G under snap-down) is significantly higher than the TCC in air from Fig. 3. This behavior is different from that of bulk interfaces. It implies that the interstitial fluid in actuated MEMS devices reduces the solid-solid contact area of the polysilicon-nitride interface. The alternate conduction path provided by the air is not efficient enough to overcome the reduction in contact area.