Thermal Characterization of Bi-Material Microcantilevers: Thermal Conductance and Microscale Convection

Bi–material atomic force microscope cantilevers have been used extensively over the last 15 years as physical, chemical, and biological sensors. As a thermal sensor, the static deflection of bi–material cantilevers due to the mismatch of the coefficient of thermal expansion between the two materials has been used to measure temperature changes as small as 10−5 K, heat transfer rate as small as 40 pW, and energy changes as small as 10 fJ. Bi–material cantilevers have also been use to measure “heat transfer - distance” curves a heat transfer analogy of the force–distance curves obtained using atomic force microscopes. In this work, we concentrate on characterization of heat transfer from the microcantilever. The two quantities that we focus on are the thermal conductance of the cantilever, Gcant (units WK−1), and the thermal conductance due to microscale convection from the cantilever to the ambient fluid, Gconv (units WK−1). The deflection of the cantilever to changes in its thermal environment is measured using the shift in position, on a position sensitive detector, of a laser beam focused at the tip of the cantilever. By determining the response of the microcantilever to (1) uniform temperature rise of the ambient, and (2) change in power absorbed at the tip, the thermal conductance of heat transfer from the cantilever can be determined. When the experiment is performed at low enough ambient pressure so that convection is unimportant (¡ 0.1 Pa), Gcant can be measured. When the experiment is performed at atmospheric pressure the heat transfer coefficient due to convection from the cantilever can be determined.