Fast mechanical model for probe-sample elastic deformation estimation in scanning probe microscopy

We present a numerical approach for estimation of the probe-sample elastic deformation for higher contact forces and/or smaller probe apex radii in Scanning Probe Microscopy (SPM) measurements. It is based on a mass-spring model implemented on a graphics card in order to perform very high numbers of individual force-distance curves calculations in reasonable time, forming virtual profiles or virtual SPM images. The model is suitable for predicting the mechanical response of the probe and sample in SPM mechanical properties mapping regimes and for estimating the uncertainty sources related to probe-sample elastic deformation in dimensional nanometrology. As the model is based on using regular orthogonal mesh formed from the scanned surface topography, it can be also used as preprocessor for various pixel by pixel physical quantities calculations using Finite Difference Method, namely for the energy transfer between probe and sample, where a realistic probe-sample contact formation needs to be taken into account. Model performance is demonstrated via comparison to analytical solutions for simple contact mechanics tasks and its possibilities for SPM data interpretation are illustrated on measurements on simple reference structures, such as step edges or quantum dots.