AFM cantilever, contact mechanics, and electrostatics calibration in the off-resonant dynamic regime

S. Raghuraman, N. Domingo, S. Jesse
Oak Ridge National Laboratory,
United States

Keywords: atomic force microscope, contact mechanics, electrostatics


Many routine as well as advanced emerging atomic force microscopy (AFM) methods rely on the very sensitive coupling between the AFM tip and cantilever to electrostatic or mechanical induced forces or, in many instances, a combination of them. Techniques like Electrical-, Kelvin Probe-, Piezo-response-, and Contact Resonance Force microscopies and their spectroscopic variations are common examples. In many of these cases, extracting quantitative and well calibrated data remains an open challenge. Complications arise in part because, even though the intended driving force is different, the measurable, which is the deflection or displacement of the cantilever, is the same. Therefore, it can become very difficult to distinguish signal origins as they can add and convolve. Without a method to reliably determine and deconvolve multiple signal origins, measurements can be unreliable and misleading, and conclusions based on them incorrect. Further complexities emerge because these techniques are often operated at resonant frequencies of the AFM probe which require solving more difficult governing equations, exacerbates the role of non-linearities at the tip-surface junction, and limits one to only operate at the mechanical modes of the probe system thus dramatically limiting the frequency range of phenomena that can be studied. Calibration approaches based on resonant modes bring with them these challenges and tend to require substantial simplifying assumptions for practical applications. At the other extreme, the community often relies on static measurements for calibration (e.g. force distance curves). Some insight into measurement sensitivities and mechanical properties (like equivalent spring constants) can be extracted. However, the information from static measurements does not extrapolate well to dynamic or resonant cases and is insufficient to address even the most basic free parameters needed for calibrating electrical, mechanical, and electromechanical interactions including: tip-sample stiffness, non-linearities in tip-sample stiffness, and capacitance gradients of the different components of the AFM probe. We have developed a simple and straightforward method that bridges the extremes described above to reliably determine important parameters defining and differentiating electrostatic and electromechanical contributions in AFM measurements. By performing calibrations in dynamic but off-resonance conditions, simple closed form solutions to governing equations can be derived, inverted, and applied to arrive at a small number of required calibration constants. Here, we present this approach, provide several examples of its use and application, and show the derived parameters can be extended to improve interpretation of resonant measurements as well.