Quantitative elastic-property information with acoustic AFM: Measurements and modeling

To investigate nanoscale mechanical behavior, new approaches using dynamic modes of the atomic force microscope cantilever are being developed. One method, atomic force acoustic microscopy (AFAM), measures cantilever resonances in the acoustic-frequency range to obtain elastic-property information. We describe quantitative AFAM measurements and compare them to results from techniques like surface acoustic waves and instrumented indentation. With AFAM we examined a niobium film using two separate calibration samples and two cantilever geometries. Depending on the cantilever type we found M_Nb=105-114 GPa, in good agreement with literature values of M_Nb=116-133 GPa for bulk niobium and M_Nb=120±5 GPa obtained with surface acoustic waves. We also obtained AFAM values of M=54-81 GPa for the indentation modulus of an aluminum film. In comparison, literature values for bulk aluminum are M_Al=76-81 GPa, while other results on the same film yielded M_Al=78-85 GPa. To understand the results more thoroughly, we compare two methods of AFAM spectrum analysis. The analytical approach assumes a cantilever of uniform rectangular cross-section while the finite element model accounts for spatial variations in cantilever dimensions. The same data are interpreted with the two approaches to better understand measurement uncertainty and accuracy.