Thermo-optical bistability in silicon micro-cantilevers

Abstract

We report a thermo-optical bistability observed in silicon micro-cantilevers irradiated by a laser beam with mW powers: reflectivity, transmissivity, absorption, and temperature can change by a factor of two between two stable states for the same input power. The temperature dependency of the absorption at the origin of the bistability results from interferences between internal reflections in the cantilever thickness, acting as a lossy Fabry-Pérot cavity. A theoretical model describing the thermo-optical coupling is presented. The experimental results obtained for silicon cantilevers irradiated in vacuum at two different visible wavelengths are in quantitative agreement with the predictions of this model.

Force microscopy cantilevers locally heated in a fluid: Temperature fields and effects on the dynamics

“…After proper calibration, a set of 5 photodiodes (A to E, including the 2-quadrants photodiode C used to measure deflection) allows the measurement of the incident light power of each beams P green 0 , P red 0 , of the reflected one P green r and P red r , and of the light transmitted through the cantilever P green t and P red t . Indeed, a few micrometers thick silicon cantilever is semi-transparent for those wavelengths, its absorption coefficient results from the interferences within the cantilever and is expected to vary during the experiment through the temperature 22,36 . Since light diffusion is negligible in this experiment, those measurements allow deducing the total absorbed power P a by the cantilever during the whole measurement.…”

“…As silicon is semi-transparent for visible light, the cantilever reflectivity results from the interferences between the multiple reflections within its thickness 36 . The refractive index of silicon is changing significantly with temperature, thus the interference state and the resulting reflection coefficient R vary with ∆T .…”

“…The temperature rise mea- Reflectivity R of the three cantilevers measured in vacuum as a function of the temperature rise ∆T at the laser spot position. R results from multiple interferences in the cantilever thickness, and depends on temperature through the refractive index of silicon 36 .…”

“…Kr is obtained by solving the linearized Navier-Stokes equations with the temperature, density, and viscosity of air described by Eqs. (6) and(36). Owing to the larger volume involved in the flow in the viscous regime (lower Re values), the force is less sensitive to the temperature rise.…”

Thermal noise of a cryo-cooled silicon cantilever locally heated up to its melting point

“…• Finally, the absorbed power is also unknown, since during the experiment we measure the total injected power P = P 1 + P 2 , with no control over the absorption A 1 and A 2 (which can be different for each heat source and temperature dependent [33]). It is similarly not possible to know the repartition of the laser power into the two sensing beams, as it could be not equal for B 1 and B 2 .…”