Imaging stability and average tip-sample force in tapping mode atomic force microscopy

Abstract

In tapping mode atomic force microscopy (AFM), a cantilever is driven near its resonance frequency and intermittently strikes the sample while raster scanned across a surface. The oscillation amplitude is monitored via a feedback loop to construct topography maps of surfaces at the nanoscale. This paper deals with two major limits on scanning rates when operating in air: (1) the slow transient response of the cantilever and (2) instabilities associated with systems with high quality factors (Q). Due to the slow transient response, the AFM has difficulty in instantly responding to steps along the surface, resulting in the need for slower scan rates and higher gains to more accurately track the surface. However, the use of higher gains leads to more pronounced instabilities associated with high Q systems. By driving the cantilever well below its resonance frequency, stability of the system is greatly improved, resulting in better feature tracking and allowing for scanning at higher speeds with larger gains. Also, the impact of the cantilever spring constant and sample modulus on the response time was explored at different operating frequencies. The experimental results were further verified using numerical simulations of a tapping mode AFM experiment, in which a well-defined step was scanned and tracked via a feedback loop equipped with an integral gain. These simulations helped to elucidate the physics behind this improvement and the tip/sample forces associated with imaging far below resonance.