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

TL;DR

This study investigates silicon cantilevers heated locally up to their melting point, using resonance frequency shifts to measure temperature profiles with high precision, combining theoretical modeling and experimental validation.

Contribution

The paper introduces an improved model for silicon cantilever temperature profiles that accounts for elasticity, geometry, and thermal effects, enabling accurate temperature inference from resonance shifts.

Findings

Temperature profile can be accurately measured via resonance frequency shifts.

The model accounts for 20% of the frequency shift due to geometry changes.

High-precision temperature inference is achievable from frequency measurements.

Abstract

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 a enhanced version of our earlier model [F. Aguilar 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 a 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.