Thermo-optical bistability of micro-cantilevers

The attenuation length of visible light in silicon is of the order a few µm, which is comparable to the thickness of the µ-cantilevers used for Atomic Force Microscopy (AFM). The light beam used to measure the deflection is therefore often not zero on the bottom face of the lever, where it can be reflected and interferes with the incident wave. Concretely, the lever is for the light field an absorbing Fabry-Pérot cavity, which interference state is a function of the cantilever thickness, the wavelength, and the optical index of silicon. This interference state drives the value of the reflectance, absorbance and transmittance of the lever. The reflectivity may for example vary by a factor of 2 for very weak variations (less than 100nm) of the thickness.

The absorbed fraction of the light radiation corresponds to a heat source at the extremity of the lever, and in the stationary state this heat flux is dissipated by convection in the surrounding fluid, thermal conduction along the lever toward its support, and thermal radiation. In vacuum, thermal conduction is the dominant process, and quickly end up in very high temperatures (several hundreds of degrees for a few mW of incident power).

The optical index of silicon depending on temperature, so does the interference state of the light field in the cantilever thickness. This interference state driving itself the absorption of light, it retroacts on the heat flux, hence on temperature. We thus have a closed loop between absorption and temperature, that may induce a non-monotonic, or even instable, behavior: when the absorption is a steep increasing function of temperature, if the light power raises, the heat flux follows, so does the temperature, increasing the absorption, thus the heat flux, and so on. We observe in some cases a hysteretic behavior between high and low temperature branches when the input power is cycled. Temperature jumps of few hundred degrees can be measured during the hysteresis cycle. We will detail the mechanism of this thermo-optical bistability.