Thermomechanical deflection of microcantilever beams in scanning force microscopes

An analysis of the thermomechanical behaviour of a microcantilever beam for scanning probe microscope applications is presented in this paper. Analytical solutions are obtained for temperature distributions resulting from the measuring laser beam and microcantilever deflections caused by both thermal gradients and intermolecular forces. Calculations are made to investigate the individual as well as combined effects resulting from the temperature distribution and forces. It is found that in the region where the intermolecular force is large the mechanical deformation predominates and the thermal deflection plays only a negligible role. However, the thermal effects can become important in regions of weaker force. Thermal deflections increase linearly with the laser power level and hence can cause measurement errors when a laser power surge occurs within the design specifications. The temperature distribution and thermal deflections are dependent on the locations at which the laser beam is projected onto the cantilever. Thermal deflections are also more significant for microcantilevers made with materials of low thermal conductivities. Both thermal and mechanical deformations are sensitive to the geometric dimensions of the cantilever. To minimize the thermal deflections caused by the laser beam, a longer and thinner microcantilever should be used.