Chaos Affects Atomic Force Microscopes

Daniel S. Burgess

A pair of researchers at Purdue University in West Lafayette, Ind., have confirmed suspicions that deterministic chaos plays a role in dynamic atomic force microscopy (AFM) systems, introducing small but real uncertainty into the measurements. Although the consequences of the effect can be ignored for most applications of AFM, Arvind Raman and Shuiqing Hu note that they must be acknowledged as nanometrology advances.

Deterministic chaos is a source of error in dynamic atomic force microscopy (AFM). With the transition from the period-1 oscillation state in the noncontact regime to the tapping regime, chaotic tip oscillations introduce noise into an AFM system — here, imaging a sheet of highly ordered pyrolytic graphite. Courtesy of Purdue University School of Mechanical Engineering and Birck Nanotechnology Center.

In their experiments, Raman and Hu gradually increased the driving amplitude of the dither piezo for three types of microcantilevers in a Pico-Plus AFM from Molecular Imaging Inc. of Tempe, Ariz., to identify the transitions between oscillation states and the onset of chaotic behavior. Only very stiff cantilevers that were driven at very high frequencies did not display chaotic behavior at the transition between the noncontact and tapping regimes. They noted bifurcations in their data as the probes moved between oscillation states, suggesting that deterministic chaos, rather than a quantum mechanical phenomenon, was at work.

To evaluate the effects of chaos, they used silicon probes from Nano- World AG of Neuchâtel, Switzerland, in the instrument to image a sheet of highly ordered pyrolytic graphite. Driving the microcantilever at amplitudes where chaotic oscillations emerge, they found that uncertainty on the order of a couple of nanometers was introduced.

Error of this magnitude is not significant for most users of AFM, Raman and Hu concede, but they speculate that it will become commonplace for microscopists to need to measure nanoscale features. Understanding the chaotic processes, they suggest, enables users to select the optimal instrument setups and test conditions.

Physical Review Letters, Jan. 27, 2006, 036107.