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 experimentally temperature profile its interplay with the mechanical resonances. enhanced version our earlier model [F. Aguilar Sandoval et al., J. Appl. Phys. 117, 234503 (2015)] including both elasticity geometry dependency, showing that latter can account for 20% observed first flexural mode. The description takes into thermal clamping conditions, radiation at high temperature, lower conductivity than bulk due to phonon confinement. Thanks space-power equivalence in heat equation, scanning heating point along cantilever directly reveals profile. Finally, frequency measurement be used infer field few percent precision.