epl draft Dissipation of micro-cantilevers as a function of air pressure and metallic coating

In this letter, we characterize the internal dissipation of coated micro-cantilevers through their mechanical thermal noise. Using a home-made interferometric setup, we achieve a resolution down to 10 m/ √ Hz in the measurement of their deflection. With the use of the fluctuation dissipation theorem and of the Kramers-Kronig relations, we rebuilt the full mechanical response function from the measured noise spectrum, and investigate frequency dependent dissipation as a function of the air pressure and of the nature of the metallic coatings. Using different thicknesses of gold coatings, we discuss the source of the internal viscoelastic damping. Microsized cantilevers are present in many applications, ranging from chemical and biological sensors [1] to atomic force microscopy (AFM) [2]. They are also used as a basic brick of microelectromechanical systems (MEMS). As mass detectors for example, they can be functionalized for the adsorption of specific chemical compounds by proper coating of their surface: the mass increment is detected as a resonance frequency shift. Gold coating is widely used due to the large selection of materials that can be adsorbed via thiol chemistry [1, 3]. Besides, from a gold layer, electrically conducting layers can be patterned and integrated into the cantilever for local heating [4], magnetomotive actuation [5] or piezoresistive readout of the deflection [6]. The sensitivity of the resonant cantilever when used as a mass sensor depends on the spectral resolution, thus of its quality factor Q defined as the ratio of stored vibrational energy over energy lost per cycle of vibration [7]. The greatest sensitivity will thus be reached with the smallest dissipation. The functionality of MEMS, AFM probe or mass sensors is based on the deformation of the cantilever. Thermally induced mechanical fluctuations determine the ultimate deflection sensitivity of these sensors and represent one of the most important noise sources. They are linked to the damping of the system, as shown by the fluctuation dissipation theorem (FDT) [8]. Smaller damping (a)Email: [email protected] will thus lead to reduced thermal noise, thus increasing the sensitivity and usability of the probes. It is therefore of prime importance to understand and characterize the dissipation sources in these systems. Great effort has been put into describing the effect of ambient pressure and cantilever coating on their resonant behavior, both experimentally [9–14] and theoretically [15–17]. For example, Sandberg [13] investigated the effect of gold coating on the quality factor of a resonant cantilever and showed that in vacuum Q is severely reduced by the deposition of even a thin gold film (100nm), especially for higher order modes. Considering only structural damping, Saulson [15] proposed a viscoelastic model, in which the power spectrum density (PSD) of thermal induced deflection presents a characteristic 1/f like trend. In a previous work [14], we introduced a simple power law to describe the frequency dependence of this viscoelasticity on a gold coated cantilever, and a model that includes Sader’s approach to describe the coupling with the surrounding atmosphere [17, 18]. We showed that the damping is only due to the coating when viscous dissipation vanishes in vacuum. Understanding the source of this coating induced viscoelasticity will undoubtedly help in designing more sensitive and accurate cantilever based sensors and microprobes. However, measuring the thermal noise or small damping over a wide range of frequency is a great challenge, and very few experiments [14, 18–21] have succeeded so far in directly measuring fluctuations out of resp-1 en sl -0 06 36 83 9, v er si on 1 28 O ct 2 01 1