Fitting the AFM force–distance curves the correct way

Abstract Data fitting is an indispensable tool in modern metrology. However, as the models become more and more complex the most popular method, ordinary least squares regression, reaches its limit. As the relative uncertainty in the independent variable increases, we can no longer speak about an exactly known independent variable and an uncertain dependent variable. The increasing complexity of the measurement process may give rise to correlationsFurthermore correlations between data may become non negligible: typical sources are e.g. the use of reference samples or crosstalk between sensors. These problems can be treated with generalized least squares. A new algorithm–Optimum Estimate of Function Parameters by Iterated Linearization (OEFPIL) – has been recently suggested which can handle both a wide class of functions as well as general covariance matrices. We illustrate its application in the analysis of force distance curves in AFM which are used to evaluate the mechanical properties of samples such as the Young’s modulus and adhesion. In this work we apply the new algorithm and compare the results to other methods. The uncertainties obtained by OEFPIL are in good agreement with uncertainties obtained by the Monte Carlo method but can be obtained in a more straightforward way.