Analysis of amplification of thermal vibrations of a microcantilever

We examine the conditions under which the small amplitude of thermal vibrations of cantilevers typically used for atomic force microscopy and sensor applications can be enhanced through a feedback mechanism. Using a simple mathematical model with two independent measurable physical parameters, a time delay τ and a gain factor G, we show that for certain values of these two parameters, such amplification is feasible. Experimental measurements of the two parameters when amplification succeeded show that these fall in the range predicted by the calculations.