Calibration of tapping AFM cantilevers and uncertainty estimation: Comparison between different methods

Abstract

We present a comparative study between three different methods for the spring constant calibration of silicon beam-shaped Atomic Force Microscope (AFM) cantilevers, used in tapping AFM mode in air. The geometries of these levers can be quite different from the standard rectangular cross section. We examine a method that combines the knowledge of cantilever dimensions and eigenfrequencies (Cleveland formula), the Sader method and we build cantilever models based on Finite Element Analysis (FEA). We demonstrate that with accurate measurement of dimensions, resonance frequency and quality factor, the Cleveland formula yields a combined cantilever stiffness uncertainty of approximately ±7% and the Sader method an uncertainty of ±5%. We also use FEA to show that when trying to approximate a realistic trapezoidal 3D tipped geometry, there exists a systematic overestimation in cantilever stiffness of ±2%, compared to when considering a simple rectangular cross section. Our constructed FE models are able to account for inhomogeneities in material properties as well as the influence of the added reflective coating in the cantilever stiffness estimation.