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

Basile Pottier (1) , Felipe Aguilar (2) , Mickaël Geitner (1) , Francisco Melo (3) , Ludovic Bellon (1)

1 Phys-ENS - Laboratoire de Physique de l'ENS Lyon
2 Departamento de Ciencias Naturales y Tecnología, Universidad de Aysén
3 Departamento de Fisica [USACH Santiago]

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.

Domaines: Vibrations [physics.class-ph]; Thermique [physics.class-ph]; Instrumentations et Détecteurs [physics.ins-det]; Micro et nanotechnologies/Microélectronique; Science des matériaux [cond-mat.mtrl-sci]; Mécanique statistique [cond-mat.stat-mech]

Basile Pottier, Felipe Aguilar, Mickaël Geitner, Francisco Melo, Ludovic Bellon. Silicon cantilevers locally heated from 300K up to the melting point: temperature profile measurement from their resonances frequency shift. Journal of Applied Physics, 2021, 129, pp.184503. ⟨10.1063/5.0040733⟩. ⟨ensl-03032421v2⟩