Bimaterial cantilevers have recently been used in, for example, the calorimetric analysis with picowatt resolution in microscopic space based on state-of-the-art atomic force microscopes. However, thermally induced effects usually change physical properties of the cantilevers, such as the resonance frequency, which reduce the accuracy of the measurements. Here, we propose an approach to circumvent this problem that uses an optical microcavity formed between a metallic layer coated on the back of the cantilever and one coated at the end of an optical fiber irradiating the cantilever. In addition to increasing the sensitivity, the optical rigidity of this system diminishes the thermally induced frequency shift. For a coating thickness of several tens of nanometers, the input power is 5–10 μW. These values can be evaluated from parameters derived by directly irradiating the cantilever in the absence of the microcavity. The system has the potential of using the cantilever both as a thermometer without frequency shifting and as a sensor with nanometer-controlled accuracy.
We theoretically study the dynamics of an atomic force microscope cantilever under various irradiation configurations of a laser. By conveying a stream of photons and its momenta, the laser beam whose geometrical intensity profile has a Gaussian form will exert a nonuniform radiation pressure on the cantilever surface and modify its vibration. The dependences of cantilever modeshapes on the laser spot position and waist reveal a possibility of diminishing or exciting a specific eigenmode. For cantilevers of ∼200 µm length, the vibration amplitude of higher-order eigenmodes can be increased 4–5 times. This implies the change in cantilever effective mass once the interaction with the ambient is taken into account. The study gives a deeper understanding of soft cantilever dynamics in liquids and can be applied in the modern measurement configuration where high frequencies are required.
We theoretically determine the optimum coating thickness for the greatest sensitivity of the bimaterial cantilevers considering the size effects of the metallic layer. A nonmonotonic deflection versus the coating thickness is seen when the size effects on the thermal conductivity and the stiffness are taken into account. The greatest sensitivity is seen at a lower value of the coating thickness in comparison to the values obtained in a recent experiment. For silicon cantilevers of thickness less than 3 μm, the greatest sensitivity is found for a coating to cantilever thickness ratio of 0.05–0.2 corresponding to the gold coating thickness of 40–150 nm. Especially, for much thicker cantilevers, e.g., up to 20 μm, the optimum coating thickness is not greater than 180 nm. For aluminum coating, the nonmonotonic behavior is not found, i.e., there is no optimum sensitivity in the range of available coating thickness, the thicker the coating thickness, higher the sensitivity. The obtained results could give useful information for the fabrication of cantilevers with the greatest thermal sensitivity.
A characteristic equation for the frequencies of the T‐shaped and overhang‐shaped cantilevers is derived for the first time. We show that there are optimum values of the overhang lengths and widths that maximize the frequency and the number of maxima is corresponding to the mode number. The frequency of higher‐order modes could be tuned by changing the overhang dimensions. Especially, a semi‐empirical formula for the coupling strength κ between cantilevers in an array is proposed where the strength presents a cubic decrease with the overhang width ξ and a linear increase with the overhang length η, κ=η/ξ3. There is a very good agreement between the proposed formula and the values obtained in recent experiments by other researchers.
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