Analysis of amplification of thermal vibrations of a microcantilever

We examine the conditions under which the small amplitude of thermal vibrat ions of cantilevers typically used for atomic force microscopy and sensor a pplications can be enhanced through a feedback mechanism. Using a simple ma thematical model with two independent measurable physical parameters, a tim e delay tau and a gain factor G, we show that for certain values of these t wo parameters, such amplification is feasible. Experimental measurements of the two parameters when amplification succeeded show that these fall in th e range predicted by the calculations. (C) 2001 American Institute of Physi cs.