Silicon cantilevers locally heated from 300 K up to the melting point: Temperature profile measurement from their resonances frequency shift

When heated, micro-resonators present a shift of their resonance frequencies. We study specifically silicon cantilevers heated locally by laser absorption and evaluate theoretically and experimentally their temperature profile and its interplay with the mechanical resonances. We present an enhanced version of our earlier model [Sandoval et al., J. Appl. Phys. 117, 234503 (2015)], including both elasticity and geometry temperature dependency, showing that the latter can account for 20% of the observed shift for the first flexural mode. The temperature profile description takes into account thermal clamping conditions, radiation at high temperature, and lower conductivity than bulk silicon due to phonon confinement. Thanks to space-power equivalence in the heat equation, scanning the heating point along the cantilever directly reveals the temperature profile. Finally, frequency shift measurement can be used to infer the temperature field with a few percent precision.