Quantitative material characterization by ultrasonic AFM

In an atomic force microscope equipped with a micromachined cantilever tip, the cantilever vibration spectra in contact with the sample were found to be strongly dependent on the excitation power. However, if the excitation power is small enough, the resonance peak width decreases and the peak frequency increases to a certain limiting value. In this condition the tip–sample contact is kept linear, and satisfactory agreement between the measured and calculated frequency is obtained, assuming a constant contact stiffness; the agreement is further improved by taking into account the lateral stiffness. More quantitative information on the elasticity of the sample is obtained from the contact load dependence of the frequency, where contact stiffness of a non-spherical tip shape is derived from the Sneddon–Maugis formulation, and the tip shape index is estimated by an inverse analysis of the load–frequency relation. A further advantage of evaluating not only the vertical but also the lateral stiffness is demonstrated on a ground silicon wafer by simultaneous measurement of deflection and torsional vibration.