Q-factor control of a microcantilever by mechanical sideband excitation

Abstract

We demonstrate the coupling between the fundamental and second flexural modes of a microcantilever. A mechanical analogue of cavity-optomechanics is then employed, where the mechanical cavity is formed by the second vibrational mode of the same cantilever, coupled to the fundamental mode via the geometric nonlinearity. By exciting the cantilever at the sum and difference frequencies between fundamental and second flexural modes, the motion of the fundamental mode of the cantilever is damped and amplified. This concept makes it possible to enhance or suppress the Q-factor over a wide range. V C 2011 American Institute of Physics. [doi:10.1063/1.3650714] Cantilevers have numerous scientific and technological applications and are used in various instruments. In sensing applications, the sensitivity is related to the Q-factor, and this has motivated researchers to increase the Q-factor of mechanical resonators, in particular, in dissipative environments. Among the techniques that have been employed are applying residual stress, 1 parametric pumping, 2 and selfoscillation by internal 3 and external 4 feedback mechanisms. When increasing the Q-factor in these ways, energy is pumped into the mechanical mode and the resonator heats up. The opposite effect leads to cooling of the resonator and attenuation of its motion. 5 By pumping energy out of the mechanical resonator into a high quality-factor optical or microwave cavity, several groups have shown reduction of the effective temperature of the vibrational mode from room temperature to millikelvin temperatures. 6-14 Such cooling schemes are now employed to bring down the mode temperature to below an average phonon occupation number of one, providing a promising route to study the quantum behavior of a mechanical resonator. [15][16][17] In analogy to cavity optomechanics, where an optical or a microwave cavity is used to extract energy from the resonator, we employ a mechanical cavity to damp the mechanical mode. Here, the fundamental flexural mode of the cantilever is the mode of interest, and the mechanical cavity is formed by the second flexural mode of the same cantilever, which is geometrically coupled to the fundamental mode. In this paper, we demonstrate the presence of this coupling by strongly driving the cantilever on resonance, while monitoring its broadband frequency spectrum. Sidebands appear in the spectrum, which are located at the sum and difference frequencies of fundamental and second modes of the cantilever. Driving the cantilever at these sidebands results in positive or negative additional damping, which is demonstrated in this paper.Cantilevers are fabricated from low pressure chemical vapor deposited silicon nitride by electron beam lithography and isotropic reactive ion etching in a O 2 /CHF 3 plasma. 18 The dimensions are length  width  height ¼ 39 lm  8 lm  70 nm. An optical deflection technique, similar to the one employed in atomic force microscopy, is used to detect the cantilever motion. Figures 1(a) and 1(b) show the cantilever and ...

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