Energy dissipation in submicrometer thick single-crystal silicon cantilevers

This paper discusses four kinds of mechanical energy losses in ultrathin micro-cantilevers of 60 nm, 170 nm, and 500 nm in thickness: thermoelastic loss, air damping, support loss, and surface loss. For the cantilevers with thickness H < 500 nm and length L > 10 μm, thermoelastic loss is negligible. But it becomes significant when the beam thickness H > 500 nm and the length L < 10 μm. The cantilevers are very liable to air damping, hardly operated at pressure higher than 10^-3 mbar. In a high vacuum (<10^-3 mbar), air damping is negligible, the support and surface loss play an important role. The shorter the cantilevers, the larger the support energy loss. For the cantilevers with L/H < 100, the quality factors (Q factors) are limited by the support loss. When the length L > 30 μm, the Q factors of the cantilevers are proportional to their thickness, i.e., surface loss dominates the mechanical behavior. Annealing the cantilevers of 170 nm thick at 1000 °C for 30 s under an ultrahigh vacuum (UHV) condition results in an over one order-of-magnitude increase of the Q factor, up to about 2.5 × 10⁵ for cantilevers of 30-90 μm in length. The improvement of the Q factor was found to be associated with the deoxidization of the surface, as corroborated by X-ray photoelectron spectroscopy (XPS). With the promising mechanical behavior, the cantilever can easily be actuated by a laser beam (beam size: about 300 × 100 μm², wavelength: 680 nm) with power down to less than 40 μW, corresponding to 480 nW, i.e., 1.64 × 10¹² photons/s, irradiated on a cantilever surface (60 × 6 μm²). This provides a rather simple way to operate the ultrathin cantilevers dynamically in UHV. Atomic scale force resolution (4.8 × 10^-17 N) at 300 K is also expected with these cantilevers.