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.

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The real-time and accurate measurement of tip-sample interaction forces in Tapping Mode Atomic Force Microscopy (TM-AFM) is a remaining challenge. This obstruction fundamentally stems from the causality of the physical systems. Since i) the input of the dynamic systems propagates to the output with some delay, and ii) , multiple different inputs can generate the same output, there exist no measurement or estimation technique that can estimate the force input of the systems in real-time without phase and amplitude distortion. However, an approximate and delayed estimation can still be possible. This article presents a general-purpose algorithm which aims to estimate an approximation of the force input of TM-AFM with minimum delay and error. For this reason, first, the input estimation problem is converted to an ill-posed state observation problem. Then, a Tikhonov-like regularization technique is applied to eliminate the ill-conditioning and estimate the force input using a linear Kalman filter. The proposed input observer is remarkably robust, real-time in the order of the sampling frequency, and applicable for any Linear Time Invariant (LTI) system with a (semi-) periodic process. Simulation and experimental results show that using the proposed algorithm with a wide-band AFM probe; one can determine the tip-sample forces with only a few percent error and a delay in the order of sampling time. Unlike the existing force estimation techniques for AFM, this algorithm does not require any prior knowledge of the force-distance relationship which can be very beneficial for the closed-loop control of AFM.@en

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.

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Due to the harmonic motion of the cantilever in Tapping Mode Atomic Force Microscopy, it is seemingly impossible to estimate the tip-sample interactions from the motion of the cantilever. Not directly observing the interaction force, it is possible to damage the surface or the tip by applying an excessive mechanical load. The tip-sample interactions scale with the effective stiffness of the
probe. Thus, the reduction of the mechanical load is usually limited by the manufacturability of low stiffness probes. However, the one-to-one relationship between spring constant and applied force only holds when higher modes of the cantilever are not excited. In this paper, it is shown that, by passively tuning higher modes of the cantilever, it is possible to reduce the peak repulsive force.
These tuned probes can be dynamically more compliant than conventional probes with the same static spring constant. Both theoretical and experimental results show that a proper tuning of dynamic modes of cantilevers reduces the contact load and increases the sensitivity considerably.
Moreover, due to the contribution of higher modes, the tuned cantilevers provide more information on the tip-sample interaction. This extra information from the higher harmonics can be used for mapping and possibly identification of material properties of samples.@en