In this letter, based on the beam theory and the thermal analysis of a bi-material cantilever, we demonstrate that the effective thermal conductance of the cantilever and the temperature at the tip of the cantilever can be determined by measuring the bending of the cantilever in response to two different thermal inputs: power absorbed at the tip and ambient temperature. The bi-material cantilevers were first introduced as a calorimeter to measure the heat generated in chemical reactions.[1] The same device was demonstrated to be sensitive enough to measure power as small as 100 pW or energy of 150 fJ in photothermal measurements. [2] They were also used as IR detectors [3,4,5] or as scanning thermal imaging probes.[6] Although the bi-material cantilevers are often used as temperature or heat flux sensors based on the beam bending due to the unequal thermal expansion of the two materials, the exact temperature at the tip of the cantilever is usually unknown. Directly measuring the temperature is difficult due to the small geometry of the cantilever structure. To find out the temperature of the cantilever, one should obtain the thermal conductance of the cantilever. However, since the thermal properties of two layers of the cantilever are dependent on their thickness, one cannot rely on theoretical calculation. In this letter, we develop a technique to determine the thermal conductance of the cantilever by measuring the bending of the cantilever in response to the variations of the absorbed power at the tip and the ambient temperature. A triangular silicon nitride cantilever coaled with 70 nm gold film is used in the current experiment. As shown in Fig.1 (a), a semiconductor laser beam is focused on the tip of the cantilever and reflected onto a position sensing detector (PSD). The deflection of the reflected laser beam spot on the PSD is used as a measure of the deflection of the cantilever. A part of the laser power is absorbed by the cantilever and thus creates a temperature rise at the end of the cantilever. The output of the PSD is converted into an X or Y signal corresponding to the position of the laser spot on the PSD and a sum signal proportional to the incident laser power.
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