Micromechanical cantilevers used in atomic force microscopy are characterized by the geometry, the elastic modulus E and the quality factor Q . The sensor can be regarded as a rectangular bar clamped on one side and free on the other. In contrast to a simple harmonic oscillator a cantilever has different eigenfrequencies ω n and a mode-dependent spring constant D n . Using the fluctuation-dissipation theorem we developed a simple model to calculate the thermal noise on each eigenmode for a free cantilever. With this result we can decide whether measuring on higher eigenmodes increases the force sensitivity.
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Rast et al. (2000) studied this question.
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