The noise of cantilevers

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 omega(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.