Measuring and modeling thermal fluctuations at nanometer length scales

The size of mechanical, electrical, and optical devices continues to be reduced. As the length scales of such devices decrease, coupling to the external environment greatly increases. Thermal fluctuations due to momentum exchange between air molecules and micron scale devices under ambient conditions can effect the dynamics of a system. To illustrate this we use an atomic force microscope cantilever and detection system to measure background noise and thermal fluctuations of a micron size beam. The beam is modeled by a Langevin-type equation that is externally forced by a white-noise spectrum having an analytic as opposed to a statistical form. This model is compared with experimental data. It is found that at higher frequencies, a white-noise spectrum is not sufficient to model such a system. We modify the forcing spectrum so that it decays at higher frequencies and subsequently achieve closer agreement between the model and the experimental observations.