Optical measurement of thermal contact conductance between wafer-like thinsolid samples

This paper presents a noncontact optical technique for measuring the therma l contact conductance between wafer-like thin solid samples. The technique is based on heating one solid surface by a modulated laser beam and monitor ing the corresponding temperature modulation of the other solid surface acr oss the interface using the reflectance of a probe laser beam. The phase la g between the two laser signals is independent of the optical properties of the samples as well as the laser intensifies, and can be related to the th ermal contact conductance. A detailed theoretical analysis is presented to estimate the thermal contact conductance as well as the thermophysical prop erties of the solids from the phase lag measured as a function of the modul ation frequency. Closed-form solutions in the high-frequency limit are deri ved in order to provide a simple estimation procedure. The effect of misali gnment of the two lasers is studied and the conditions for robust measureme nts are suggested. As a benchmark for this technique, the thermal conductiv ity of a single crystal silicon sample was measured to within two percent o f reported values. The thermal contact conductance was measured for Al-Si s amples, each about 0.22 mm thick, in the pressure range of 0.8-10 MPa. In c ontrast to traditional contact conductance measurement techniques that requ ire steady-state operation and insertion of thermocouples in thick solid sa mples. the noncontact dynamic optical technique requires much less time and is particularly well suited for electronic packaging materials that are ty pically in the thickness range of 0.1-5 mm. In addition, localized conducta nce measurements are now possible with a spatial resolution of about four t imes the thickness of the solid and can be used to detect interfacial voids and defects.