Multi-mode noise analysis of cantilevers for scanning probe microscopy

A multi-mode analysis of micro-cantilever dynamics is presented. We derive the power spectral density of the cantilever displacement due to a thermal noise source and predict the cantilevers's fundamental resonant frequency and higher harmonics. The first mode in the multi-mode model is equivalent to the traditional single-mode model. Experimental results obtained with a silicon nitride cantilever at 300 K are in excellent qualitative agreement with the multi-mode model. The multi-mode model may be used to obtain accurate values of the cantilever properties such as the elastic modulus, effective mass, thickness and moment of inertia. (C) 1997 American Institute of Physics.