Investigation of position detectors for atomic force microscopes

This paper presents different possibilities of determination of cantilever deflection using the beam theory and finite element method. It is proved that the cantilever can be described as an elementary beam with the force point within the neutral fibre, and its deflection can be determined according to Euler-Bernoulli beam theory. The determined analytical relationship between the inclination angle of the cantilever beam and displacement of its end is used for further calculations of the output signal of the atomic force microscope (AFM) position detector optical lever. Such position detectors as an interferometer, optical lever, and focus sensor are compared for application in an AFM. Analytical and numerical position detector models are developed here for determination of characteristic curves of detector output signals and their sensitivities. The comparison shows that the interferometer is by far the most sensitive and the optical lever is similarly sensitive to the focus sensor. Furthermore, a combined deflection-detection system that contains a homodyne Michelson interferometer and an optical lever is discussed.