Mechanical property measurements enabled by short-term Fourier-transform of atomic force microscopy thermal deflection analysis

Contact resonance atomic force microscopy (CR-AFM) has been used in many studies to characterize variations in the elastic and viscoelastic constants of materials along a heterogeneous surface. In almost all experimental work, the quantitative modulus of the surface is calculated in reference to a known reference material, rather than calculated directly from the dynamics models of the cantilever. We measured the cantilever displacement with very high sampling frequencies over the course of the experiment and captured its oscillations that result from thermal energy. Using short-term Fourier transformations, it was possible to fit the thermal resonance peak of the normal displacement to track the frequency and Q-factor of the cantilever during an experiment, using a similar process to that used to calibrate the normal bending stiffness of cantilevers. With this quantitative data, we have used the dynamic mechanics models relating the contact stiffness of the tip/cantilever pressing into a surface with the oscillation frequency of the cantilever and show that they did not accurately model the experiment. Several material combinations of tip and sample were examined; tip size and cantilever stiffness demonstrate that existing models cannot capture the physics of this problem. While concrete solutions to use analytical models to interpret CR-AFM data have not been found, a possible solution may include revisiting the analytical model to capture a potentially more complex system than the current model, improved matching the cantilever/sample stiffness to obtain a larger variation in contact stiffness with frequency, or investigating the use of higher-order modes that may achieve this improved match.