Several methods are being researched to detect and characterize buried nanoscale structures in hard solid samples. The most common acoustic method is acoustic microscopy. An acoustic microscope is based on a single element transducer operating in pulse-echo mode. The acoustic waves are coupled into a sample using a liquid couplant (eg water) and the beam is focused using a geometric lens to obtain a good lateral resolution. Thus, the frequency is limited by the attenuation in the coupling layer (water 3.5\{dB}/{m} at 4 GHz) and the typically low transmission coefficients at the transducer-liquid couplant and liquid-sample interfaces. Here, we present a novel method for high frequency acoustic metrology of buried structures in solid samples. The concept consisted of a 4 GHz acoustic transducer integrated above the tip of a custom designed probe. It operated in pulse-echo mode, and used solid-solid contact with the sample without the need for liquid coupling layers. A prototype was built and successfully tested experimentally on samples consisting of silicon with 1D and 2D arrays ofmu\{m} sized features buried below 5-10{m} of PMMA or SiO2 top layers. Moreover, a good match was obtained between model predictions and measurements of the pulse-echo performance of the novel GHz acoustic metrology method. The technique features a penetration depth of O(10s ofmu\{m}), is nondamaging and is not hampered by optically opaque layers.

Many investigations have focused on steady-state nonlinear dynamics of cantilevers in tapping mode atomic force microscopy (TM-AFM). However, a transient dynamic model—which is essential for a model-based control design—is still missing. In this paper, we derive a mathematical model which covers both the transient and steady-state behavior. The steady-state response of the proposed model has been validated with existing theories. Its transient response, however, which is not covered with existing theories, has been successfully verified with experiments. Besides enabling model-based control design for TM-AFM, this model can explain the high-end aspects of AFM such as speed limitation, image quality, and eventual chaotic behavior.