Temperature dependence of the force sensitivity of silicon cantilevers

Abstract

The resonance frequency and internal friction Q Ϫ1 of the first eigenmode of microfabricated silicon cantilevers are measured in the temperature range of 15-300 K. The analysis shows that variation of Young's modulus is responsible for the temperature dependence of the resonance frequency, whereas the dependence of the geometrical dimensions can be neglected. Accordingly, the data can be fitted by the Wachtman equation, yielding a Debye temperature ⌰ D ϭ634 K. The temperature variation of internal friction Q Ϫ1 is analyzed in terms of Zener's theory of thermoelastic damping. Due to the temperature dependence of the thermal expansion coefficient ␣, thermoelastic damping is expected to vanish at 20 K and 125 K. A minimum of internal friction is observed at 20 K, whereas the minimum at 125 K appears to be hidden by other dissipation effects. A maximum of internal friction at 160 K is observed, which is an activation peak due to phonon scattering by atomic-scale defects. The best force sensitivity is achieved at 20 K, where a factor of 10 is gained compared to room temperature.

Advances in Thermoelastic Damping in Micro- and Nano- Mechanical Resonators: a Review

“…Advances in the study of thermoelastic damping 3.1. Experimental study of thermoelastic damping Gysin et al [27] measured the resonance frequency ω and internal friction damping was expected to vanish at 20K and 125K. A minimum of internal friction was observed at 20K, whereas the minimum at 125K appeared to be hidden by other dissipation effects.…”

“…The intrinsic dissipation mechanism can be regarded as phonon-phonon interaction, namely the scattering of acoustic phonons with thermal phonons. [27] …”

Near-self-imaging cavity for three-mode optoacoustic parametric amplifiers using silicon microresonators

“…dominating cause of acoustic mode frequency drift [42,43]. The near-linear relation [41] ΔYT∕ΔT ≈ −7 MPa∕K allows the mode frequency to be used as a temperature probe.…”

Advances in mechanical detection of magnetic resonance

“…The underlying sources of intrinsic cantilever dissipation remain under intense investigation both experimentally and theoretically. [185][186][187][188][189][190][191][192][193][194] Rast et al have shown that annealing single crystal silicon cantilevers in ultrahigh vacuum can improve their mechanical quality factors by an order of magnitude. 195 Nevertheless, achieving subattonewton sensitivity may require moving beyond single-crystal silicon oscillators.…”