Heat Transfer From Freely Suspended Bimaterial Microcantilevers

Bimaterial 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 bimaterial 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 $10−6K$⁠, heat transfer rate as small as 40 pW, and energy changes as small as 10 fJ. Bimaterial cantilevers have also been used 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 the characterization of heat transfer from the microcantilever. The thermomechanical response of a bimaterial cantilever is used to determine the (1) thermal conductance of a bimaterial cantilever, and (2) overall thermal conductance from the cantilever to the ambient. The thermal conductance of a rectangular gold coated silicon nitride cantilever is $Gc=4.09±0.04μWK−1$⁠. The overall thermal conductance from the cantilever to the ambient (at atmospheric pressure) is $Ga=55.05±0.69μWK−1$⁠. The effective heat transfer coefficient from the cantilever to the ambient (at atmospheric pressure) is determined to be $≈3400Wm−2K−1$⁠.