L.J. Kirsch, J. Killgore, G.J. Rodin, F. Mangolini
University of Texas at Austin,
United States
Keywords: AFM indentation, tip geometry, contact mechanics
Summary:
Even though atomic force microscopy (AFM) is extensively used for assessing mechanical properties at the nanoscale, obtaining accurate and precise quantitative Young’s modulus measurements from force-indentation curves remains a significant challenge. One major source of uncertainty stems from improper assumptions about the AFM tip geometry. While contact mechanics models with simplified indenter geometry models (e.g. cone, paraboloid, or power law type geometries) are often employed to fit force-indentation data, real AFM tips are typically more complex and piecewise in nature. In addition to fitting the force-indentation curve, the characteristic parameters for the tip geometry must be determined by fitting profiles extracted from electron microscopy images or blind tip reconstruction. Typically, bounds for this fitting are arbitrarily chosen to visually encompass the overall tip geometry. However, because simplified models can never perfectly capture the true tip geometry, these bounds can significantly influence the fitted geometry parameters and, thus, the resulting Young’s modulus values derived from force-indentation analysis. These observations raise two key questions: (i) What magnitude of error is introduced by improper tip geometry models? (ii) How should bounds be chosen during tip geometry fitting to ensure accurate mechanical property quantification? To address these issues, we generate synthetic force-indentation data using well-defined construction tip geometry profiles (i.e., paraboloid and power law). This data is then fit assuming incompatible indenter shape functions (i.e., conical and paraboloid geometries respectively) while systematically varying the bounds used for fitting tip profiles to extract the characteristic geometry parameters. Using bounds uninformed by the force-indentation data results in large errors for derived Young’s modulus values (sometimes exceeding 100%) when the bounds are far from the relative indentation depth. Conversely, fitting the tip boundaries up to the maximum indentation depth or maximum contact radius drastically reduces relative error (e.g., 23% and 6% respectively using a conical indenter model on data produced with a paraboloid). Although fitting up to the maximum contact radius requires simultaneous fitting of the tip geometry and force-indentation curve, this technique most effectively minimizes error in Young’s modulus quantification. Applying these techniques to experimental AFM force-indentation curves produced on polydimethylsiloxane (PDMS) in a minimal-adhesion environment with parabolic AFM tips yields similar qualitative trends in derived Young’s moduli. Specifically, fitting up to the maximum contact radius produces accurate Young’s modulus values, regardless of the assumed tip geometry. These findings highlight the importance of considering relevant corresponding indentation length scales, namely the maximum contact radius, when fitting AFM tip profiles. Regardless of the indenter geometry model used, these guidelines can enhance the accuracy of quantitative AFM nanomechanical measurements.