This paper investigates the closed-loop dynamics of the Tapping Mode Atomic Force Microscopy using a new mathematical model based on the averaging method in Cartesian coordinates. Experimental and numerical observations show that the emergence of chaos in conventional tapping mode AFM strictly limits the imaging speed. We show that, if the controller of AFM is tuned to be faster than a certain threshold, the closed-loop system exhibits a chaotic behavior. The presence of chaos in the closed-loop dynamics is confirmed via bifurcation diagrams, Poincaré sections, and Lyapunov exponents. Unlike the previously detected chaos due to attractive forces in the AFM, which can be circumvented via simple changes in operation parameters, this newly identified chaos is seemingly inevitable and imposes an upper limit for the closed-loop bandwidth of the AFM.@en

The development of acoustic subsurface atomic force microscopy, which promises three-dimensional imaging with single-digit nanometer resolution by the introduction of ultrasound actuations to a conventional atomic force microscope, has come a long way since its inception in the early 1990s. Recent advances provide a quantitative understanding of the different experimentally observed contrast mechanisms, which paves the way for future applications. In this Perspective, we first review the different subsurface atomic force microscope modalities: ultrasonic force microscopy, atomic force acoustic microscopy, heterodyne force microscopy, mode-synthesizing atomic force microscopy, and near-field picosecond ultrasonic microscopy. Then, we highlight and resolve a debate existing in the literature on the importance of the chosen ultrasound excitation frequencies with respect to the resonance frequencies of the cantilever and the observed contrast mechanisms. Finally, we discuss remaining open problems in the field and motivate the importance of new actuators, near-field picosecond ultrasonics, and integration with other techniques to achieve multi-functional non-destructive three-dimensional imaging at the nanoscale. @en

The origin of amplitude reduction in Tapping Mode Atomic Force Microscopy (TM-AFM) is typically attributed to the shift in resonance frequency of the cantilever due to the nonlinear tip-sample interactions. In this paper, we present a different insight into the same problem which, besides explaining the amplitude reduction mechanism, provides a simple reasoning for the relationship between tip-sample interactions and operation parameters (amplitude and frequency). The proposed formulation, which attributes the amplitude reduction to an interference between the tip-sample and dither force, only deals with the linear part of the system; however, it fully agrees with experimental results and numerical solutions of the full nonlinear model of TM-AFM.@en

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

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

The characterization of buried nanoscale structures nondestructively is an important challenge in a number of applications, such as defect detection and metrology in the semiconductor industry. A promising technique is Subsurface Scanning Probe Microscopy (SSPM), which combines ultrasound with Atomic Force Microscopy (AFM). Initially, SSPM was used to measure the viscoelastic contrast between a subsurface feature and its surrounding medium. However, by increasing the ultrasonic frequency to >1 GHz, it has been shown that SSPM can also measure acoustic impedance based contrasts. At these frequencies, it becomes difficult to reliably couple the sound into the sample such that the AFM is able to pick up the scattered sound field. The cause is the existence of strong acoustic resonances in the sample, the transducer, and the coupling layer-the liquid layer used to couple the sound energy from the transducer into the sample-in combination with the nonlinearity of the tip-sample interaction. Thus, it is essential to control and measure the thickness of the coupling layer with nanometer accuracy. Here, we present the design of a mechanical clamp to ensure a stable acoustic coupling. Moreover, an acoustic method is presented to measure the coupling layer thickness in real-time. Stable coupling layers with thicknesses of 700 ± 2 nm were achieved over periods of 2-4 h. Measurements of the downmixed AFM signals showed stable signal intensities for >1 h. The clamp and monitoring method introduced here makes scattering based SSPM practical, robust, and reliable and enables measurement periods of hours.@en