Atomic force microscopy cantilever simulation by finite element methods for quantitative atomic force acoustic microscopy measurements

Measurements of vibrational spectra of atomic force microscopy (AFM) microprobes in contact with a sample allow a good correlation between resonance frequencies shifts and the effective elastic modulus of the tip-sample system. In this work we use finite element methods for modeling the AFM microprobe vibration considering actual features of the cantilever geometry. This allowed us to predict the behavior of the cantilevers in contact with any sample for a wide range of effective tip-sample stiffness. Experimental spectra for glass and chromium were well reproduced for the numerical model, and stiffness values were obtained. We present a method to correlate the experimental resonance spectrum to the effective stiffness using realistic geometry of the cantilever to numerically model the vibration of the cantilever in contact with a sample surface. Thus, supported in a reliable finite element method (FEM) model, atomic force acoustic microscopy can be a quantitative technique for elastic-modulus measurements. Considering the possibility of tip-apex wear during atomic force acoustic microscopy measurements, it is necessary to perform a calibration procedure to obtain the tip-sample contact areas before and after each measurement.