Energy dissipation in submicrometer thick single-crystal silicon cantilevers

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 thickness 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.