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Analysis of dynamic cantilever behavior in tapping mode atomic force microscopy.
PubMed
Deng, Wenqi; Zhang, Guang-Ming; Murphy, Mark F; Lilley, Francis; Harvey, David M; Burton, David R
2015-10-01
Tapping mode atomic force microscopy (AFM) provides phase images in addition to height and amplitude images. Although the behavior of tapping mode AFM has been investigated using mathematical modeling, comprehensive understanding of the behavior of tapping mode AFM still poses a significant challenge to the AFM community, involving issues such as the correct interpretation of the phase images. In this paper, the cantilever's dynamic behavior in tapping mode AFM is studied through a three dimensional finite element method. The cantilever's dynamic displacement responses are firstly obtained via simulation under different tip-sample separations, and for different tip-sample interaction forces, such as elastic force, adhesion force, viscosity force, and the van der Waals force, which correspond to the cantilever's action upon various different representative computer-generated test samples. Simulated results show that the dynamic cantilever displacement response can be divided into three zones: a free vibration zone, a transition zone, and a contact vibration zone. Phase trajectory, phase shift, transition time, pseudo stable amplitude, and frequency changes are then analyzed from the dynamic displacement responses that are obtained. Finally, experiments are carried out on a real AFM system to support the findings of the simulations. © 2015 Wiley Periodicals, Inc.
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Computational model for noncontact atomic force microscopy: energy dissipation of cantilever.
PubMed
Senda, Yasuhiro; Blomqvist, Janne; Nieminen, Risto M
2016-09-21
We propose a computational model for noncontact atomic force microscopy (AFM) in which the atomic force between the cantilever tip and the surface is calculated using a molecular dynamics method, and the macroscopic motion of the cantilever is modeled by an oscillating spring. The movement of atoms in the tip and surface is connected with the oscillating spring using a recently developed coupling method. In this computational model, the oscillation energy is dissipated, as observed in AFM experiments. We attribute this dissipation to the hysteresis and nonconservative properties of the interatomic force that acts between the atoms in the tip and sample surface. The dissipation rate strongly depends on the parameters used in the computational model.
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On the origin of amplitude reduction mechanism in tapping mode atomic force microscopy
NASA Astrophysics Data System (ADS)
Keyvani, Aliasghar; Sadeghian, Hamed; Goosen, Hans; van Keulen, Fred
2018-04-01
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.
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Confocal Raman spectroscopy and AFM for evaluation of sidewalls in type II superlattice FPAs
NASA Astrophysics Data System (ADS)
Rotter, T. J.; Busani, T.; Rathi, P.; Jaeckel, F.; Reyes, P. A.; Malloy, K. J.; Ukhanov, A. A.; Plis, E.; Krishna, S.; Jaime-Vasquez, M.; Baril, N. F.; Benson, J. D.; Tenne, D. A.
2015-06-01
We propose to utilize confocal Raman spectroscopy combined with high resolution atomic force microscopy (AFM) for nondestructive characterisation of the sidewalls of etched and passivated small pixel (24 μm×24 μm) focal plane arrays (FPA) fabricated using LW/LWIR InAs/GaSb type-II strained layer superlattice (T2SL) detector material. Special high aspect ratio Si and GaAs AFM probes, with tip length of 13 μm and tip aperture less than 7°, allow characterisation of the sidewall morphology. Confocal microscopy enables imaging of the sidewall profile through optical sectioning. Raman spectra measured on etched T2SL FPA single pixels enable us to quantify the non-uniformity of the mesa delineation process.
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Atomic Force Microscope Mediated Chromatography
NASA Technical Reports Server (NTRS)
Anderson, Mark S.
2013-01-01
The atomic force microscope (AFM) is used to inject a sample, provide shear-driven liquid flow over a functionalized substrate, and detect separated components. This is demonstrated using lipophilic dyes and normal phase chromatography. A significant reduction in both size and separation time scales is achieved with a 25-micron-length column scale, and one-second separation times. The approach has general applications to trace chemical and microfluidic analysis. The AFM is now a common tool for ultra-microscopy and nanotechnology. It has also been demonstrated to provide a number of microfluidic functions necessary for miniaturized chromatography. These include injection of sub-femtoliter samples, fluidic switching, and sheardriven pumping. The AFM probe tip can be used to selectively remove surface layers for subsequent microchemical analysis using infrared and tip-enhanced Raman spectroscopy. With its ability to image individual atoms, the AFM is a remarkably sensitive detector that can be used to detect separated components. These diverse functional components of microfluidic manipulation have been combined in this work to demonstrate AFM mediated chromatography. AFM mediated chromatography uses channel-less, shear-driven pumping. This is demonstrated with a thin, aluminum oxide substrate and a non-polar solvent system to separate a mixture of lipophilic dyes. In conventional chromatographic terms, this is analogous to thin-layer chromatography using normal phase alumina substrate with sheardriven pumping provided by the AFM tip-cantilever mechanism. The AFM detection of separated components is accomplished by exploiting the variation in the localized friction of the separated components. The AFM tip-cantilever provides the mechanism for producing shear-induced flows and rapid pumping. Shear-driven chromatography (SDC) is a relatively new concept that overcomes the speed and miniaturization limitations of conventional liquid chromatography. SDC is based on a sliding plate system, consisting of two flat surfaces, one of which has a recessed channel. A fluid flow is produced by axially sliding one plate past another, where the fluid has mechanical shear forces imposed at each point along the channel length. The shear-induced flow rates are very reproducible, and do not have pressure or voltage gradient limitations. SDC opens up a new range of enhanced separation kinetics by permitting the sample confinement with submicron dimensions. Small, highly confined liquid is advantageous for chromatographic separation because the separation rate is known to scale according to the square of the confined sample diameter. In addition, because shear-driven flows are not limited by fluid velocity, shear-driven liquid chromatography may provide up to 100,000 plate efficiency.
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The SERS and TERS effects obtained by gold droplets on top of Si nanowires.
PubMed
Becker, M; Sivakov, V; Andrä, G; Geiger, R; Schreiber, J; Hoffmann, S; Michler, J; Milenin, A P; Werner, P; Christiansen, S H
2007-01-01
We show that hemispherical gold droplets on top of silicon nanowires when grown by the vapor-liquid-solid (VLS) mechanism, can produce a significant enhancement of Raman scattered signals. Signal enhancement for a few or even just single gold droplets is demonstrated by analyzing the enhanced Raman signature of malachite green molecules. For this experiment, trenches (approximately 800 nm wide) were etched in a silicon-on-insulator (SOI) wafer along <110> crystallographic directions that constitute sidewalls ({110} surfaces) suitable for the growth of silicon nanowires in <111> directions with the intention that the gold droplets on the silicon nanowires can meet somewhere in the trench when growth time is carefully selected. Another way to realize gold nanostructures in close vicinity is to attach a silicon nanowire with a gold droplet onto an atomic force microscopy (AFM) tip and to bring this tip toward another gold-coated AFM tip where malachite green molecules were deposited prior to the measurements. In both experiments, signal enhancement of characteristic Raman bands of malachite green molecules was observed. This indicates that silicon nanowires with gold droplets atop can act as efficient probes for tip-enhanced Raman spectroscopy (TERS). In our article, we show that a nanowire TERS probe can be fabricated by welding nanowires with gold droplets to AFM tips in a scanning electron microscope (SEM). TERS tips made from nanowires could improve the spatial resolution of Raman spectroscopy so that measurements on the nanometer scale are possible.
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Material properties of viral nanocages explored by atomic force microscopy.
PubMed
van Rosmalen, Mariska G M; Roos, Wouter H; Wuite, Gijs J L
2015-01-01
Single-particle nanoindentation by atomic force microscopy (AFM) is an emergent technique to characterize the material properties of nano-sized proteinaceous systems. AFM uses a very small tip attached to a cantilever to scan the surface of the substrate. As a result of the sensitive feedback loop of AFM, the force applied by the tip on the substrate during scanning can be controlled and monitored. By accurately controlling this scanning force, topographical maps of fragile substrates can be acquired to study the morphology of the substrate. In addition, mechanical properties of the substrate like stiffness and breaking point can be determined by using the force spectroscopy capability of AFM. Here we discuss basics of AFM operation and how this technique is used to determine the structure and mechanical properties of protein nanocages, in particular viral particles. Knowledge of morphology as well as mechanical properties is essential for understanding viral life cycles, including genome packaging, capsid maturation, and uncoating, but also contributes to the development of diagnostics, vaccines, imaging modalities, and targeted therapeutic devices based on viruslike particles.
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Characterization of external potential for field emission resonances and its applications on nanometer-scale measurements
NASA Astrophysics Data System (ADS)
Lu, Shin-Ming; Chan, Wen-Yuan; Su, Wei-Bin; Pai, Woei Wu; Liu, Hsiang-Lin; Chang, Chia-Seng
2018-04-01
The form of the external potential (FEP) for generating field emission resonance (FER) in a scanning tunneling microscopy (STM) junction is usually assumed to be triangular. We demonstrate that this assumption can be examined using a plot that can characterize FEP. The plot is FER energies versus the corresponding distances between the tip and sample. Through this energy–distance relationship, we discover that the FEP is nearly triangular for a blunt STM tip. However, the assumption of a triangular potential form is invalid for a sharp tip. The disparity becomes more severe as the tip is sharper. We demonstrate that the energy–distance plot can be exploited to determine the barrier width in field emission and estimate the effective sharpness of an STM tip. Because FERs were observed on Pb islands grown on the Cu(111) surface in this study, determination of the tip sharpness enabled the derivation of the subtle expansion deformation of Pb islands due to electrostatic force in the STM junction.
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Note: Automated electrochemical etching and polishing of silver scanning tunneling microscope tips.
PubMed
Sasaki, Stephen S; Perdue, Shawn M; Rodriguez Perez, Alejandro; Tallarida, Nicholas; Majors, Julia H; Apkarian, V Ara; Lee, Joonhee
2013-09-01
Fabrication of sharp and smooth Ag tips is crucial in optical scanning probe microscope experiments. To ensure reproducible tip profiles, the polishing process is fully automated using a closed-loop laminar flow system to deliver the electrolytic solution to moving electrodes mounted on a motorized translational stage. The repetitive translational motion is controlled precisely on the μm scale with a stepper motor and screw-thread mechanism. The automated setup allows reproducible control over the tip profile and improves smoothness and sharpness of tips (radius 27 ± 18 nm), as measured by ultrafast field emission.
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Tuning the metamagnetism in a metallic helical antiferromagnet
NASA Astrophysics Data System (ADS)
Ma, S. C.; Liu, K.; Ma, C. C.; Ge, Q.; Zhang, J. T.; Hu, Y. F.; Liu, E. K.; Zhong, Z. C.
2017-12-01
The antiferromagnetic (AFM)-ferromagnetic (FM) conversion in martensite was observed in Mn/Ni-substitution upon FM elements, such as Fe or Co, in MnNiGe helical antiferromagnets. Here, we report an AFM-FM conversion and consequently a sharp magnetic-field-driven metamagnetic martensitic transformation from paramagnetic (PM) austenite to FM martensite in the Ni- and Mn-substituted MnNiGe alloys with indium, a non-magnetic and large-sized main group element. Accordingly, a giant magnetocaloric effect such that a twofold increase of the magnetic entropy change in MnNi0.92GeIn0.08 and even a nearly threefold increase in the Mn0.92NiGeIn0.08 alloy is obtained with respect to the MnNiGe0.95In0.05 alloy. The origin of AFM-FM conversion and resultantly sharp magnetic-field-induced PM-FM metamagnetic transformation is discussed based on the first-principles calculations and X-ray absorption spectroscopic results.
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Effects of Structural Deformation and Tube Chirality on Electronic Conductance of Carbon Nanotubes
NASA Technical Reports Server (NTRS)
Svizhenko, Alexei; Maiti, Amitesh; Anantram, M. P.; Biegel, Bryan A. (Technical Monitor)
2002-01-01
A combination of large scale classical force-field (UFF), density functional theory (DFT), and tight-binding Green's function transport calculations is used to study the electronic properties of carbon nanotubes under the twist, bending, and atomic force microscope (AFM)-tip deformation. We found that in agreement with experiment a significant change in electronic conductance can be induced by AFM-tip deformation of metallic zigzag tubes and by twist deformation of armchair tubes. The effect is explained in terms of bandstructure change under deformation.
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Micromechanical contact stiffness devices and application for calibrating contact resonance atomic force microscopy.
PubMed
Rosenberger, Matthew R; Chen, Sihan; Prater, Craig B; King, William P
2017-01-27
This paper reports the design, fabrication, and characterization of micromechanical devices that can present an engineered contact stiffness to an atomic force microscope (AFM) cantilever tip. These devices allow the contact stiffness between the AFM tip and a substrate to be easily and accurately measured, and can be used to calibrate the cantilever for subsequent mechanical property measurements. The contact stiffness devices are rigid copper disks of diameters 2-18 μm integrated onto a soft silicone substrate. Analytical modeling and finite element simulations predict the elastic response of the devices. Measurements of tip-sample interactions during quasi-static force measurements compare well with modeling simulation, confirming the expected elastic response of the devices, which are shown to have contact stiffness 32-156 N m -1 . To demonstrate one application, we use the disk sample to calibrate three resonant modes of a U-shaped AFM cantilever actuated via Lorentz force, at approximately 220, 450, and 1200 kHz. We then use the calibrated cantilever to determine the contact stiffness and elastic modulus of three polymer samples at these modes. The overall approach allows cantilever calibration without prior knowledge of the cantilever geometry or its resonance modes, and could be broadly applied to both static and dynamic measurements that require AFM calibration against a known contact stiffness.
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Micromechanical contact stiffness devices and application for calibrating contact resonance atomic force microscopy
NASA Astrophysics Data System (ADS)
Rosenberger, Matthew R.; Chen, Sihan; Prater, Craig B.; King, William P.
2017-01-01
This paper reports the design, fabrication, and characterization of micromechanical devices that can present an engineered contact stiffness to an atomic force microscope (AFM) cantilever tip. These devices allow the contact stiffness between the AFM tip and a substrate to be easily and accurately measured, and can be used to calibrate the cantilever for subsequent mechanical property measurements. The contact stiffness devices are rigid copper disks of diameters 2-18 μm integrated onto a soft silicone substrate. Analytical modeling and finite element simulations predict the elastic response of the devices. Measurements of tip-sample interactions during quasi-static force measurements compare well with modeling simulation, confirming the expected elastic response of the devices, which are shown to have contact stiffness 32-156 N m-1. To demonstrate one application, we use the disk sample to calibrate three resonant modes of a U-shaped AFM cantilever actuated via Lorentz force, at approximately 220, 450, and 1200 kHz. We then use the calibrated cantilever to determine the contact stiffness and elastic modulus of three polymer samples at these modes. The overall approach allows cantilever calibration without prior knowledge of the cantilever geometry or its resonance modes, and could be broadly applied to both static and dynamic measurements that require AFM calibration against a known contact stiffness.
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Angle-Dependent Atomic Force Microscopy Single-Chain Pulling of Adsorbed Macromolecules from Planar Surfaces Unveils the Signature of an Adsorption-Desorption Transition.
PubMed
Grebíková, Lucie; Whittington, Stuart G; Vancso, Julius G
2018-05-23
The adsorption-desorption behavior of polymer chains is at the heart of macromolecular surface science and technology. With the current developments in atomic force microscopy (AFM), it has now become possible to address the desorption problem from the perspective of a single macromolecule. Here, we report on desorption of single polymer chains on planar surfaces by AFM-based single molecule force spectroscopy (SMFS) as a function of the pulling angle with respect to the surface-normal direction. SMFS experiments were performed in water with various substrates using different polymers covalently attached to the AFM probe tip. End-grafting at the AFM tip was achieved by surface-initiated polymerization using initiator functionalized tips. We found that the desorption force increases with a decreasing pulling angle, i.e., an enhanced adhesion of the polymer chain was observed. The magnitude of the desorption force shows a weak angular dependence at pulling angles close to the surface normal. A significant increase of the force is observed at shallower pulling from a certain pulling angle. This behavior carries the signature of an adsorption-desorption transition. The angular dependence of the normalized desorption force exhibits a universal behavior. We compared and interpreted our results using theoretical predictions for single-chain adsorption-desorption transitions.
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Angle-Dependent Atomic Force Microscopy Single-Chain Pulling of Adsorbed Macromolecules from Planar Surfaces Unveils the Signature of an Adsorption–Desorption Transition
PubMed Central
2018-01-01
The adsorption–desorption behavior of polymer chains is at the heart of macromolecular surface science and technology. With the current developments in atomic force microscopy (AFM), it has now become possible to address the desorption problem from the perspective of a single macromolecule. Here, we report on desorption of single polymer chains on planar surfaces by AFM-based single molecule force spectroscopy (SMFS) as a function of the pulling angle with respect to the surface-normal direction. SMFS experiments were performed in water with various substrates using different polymers covalently attached to the AFM probe tip. End-grafting at the AFM tip was achieved by surface-initiated polymerization using initiator functionalized tips. We found that the desorption force increases with a decreasing pulling angle, i.e., an enhanced adhesion of the polymer chain was observed. The magnitude of the desorption force shows a weak angular dependence at pulling angles close to the surface normal. A significant increase of the force is observed at shallower pulling from a certain pulling angle. This behavior carries the signature of an adsorption–desorption transition. The angular dependence of the normalized desorption force exhibits a universal behavior. We compared and interpreted our results using theoretical predictions for single-chain adsorption–desorption transitions. PMID:29712430
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Coupling of conservative and dissipative forces in frequency-modulation atomic force microscopy
NASA Astrophysics Data System (ADS)
Sader, John E.; Jarvis, Suzanne P.
2006-11-01
Frequency modulation atomic force microscopy (FM-AFM) utilizes the principle of self-excitation to ensure the cantilever probe vibrates at its resonant frequency, regardless of the tip-sample interaction. Practically, this is achieved by fixing the phase difference between tip deflection and driving force at precisely 90° . This, in turn, decouples the frequency shift and excitation amplitude signals, enabling quantitative interpretation in terms of conservative and dissipative tip-sample interaction forces. In this article, we theoretically investigate the effect of phase detuning in the self-excitation mechanism on the coupling between conservative and dissipative forces in FM-AFM. We find that this coupling depends only on the relative difference in the drive and resonant frequencies far from the surface, and is thus very weakly dependent on the actual phase error particularly for high quality factors. This establishes that FM-AFM is highly robust with respect to phase detuning, and enables quantitative interpretation of the measured frequency shift and excitation amplitude, even while operating away from the resonant frequency with the use of appropriate replacements in the existing formalism. We also examine the calibration of phase shifts in FM-AFM measurements and demonstrate that the commonly used approach of minimizing the excitation amplitude can lead to significant phase detuning, particularly in liquid environments.
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Nonlinear Dynamics of Cantilever-Sample Interactions in Atomic Force Microscopy
NASA Technical Reports Server (NTRS)
Cantrell, John H.; Cantrell, Sean A.
2010-01-01
The interaction of the cantilever tip of an atomic force microscope (AFM) with the sample surface is obtained by treating the cantilever and sample as independent systems coupled by a nonlinear force acting between the cantilever tip and a volume element of the sample surface. The volume element is subjected to a restoring force from the remainder of the sample that provides dynamical equilibrium for the combined systems. The model accounts for the positions on the cantilever of the cantilever tip, laser probe, and excitation force (if any) via a basis set of set of orthogonal functions that may be generalized to account for arbitrary cantilever shapes. The basis set is extended to include nonlinear cantilever modes. The model leads to a pair of coupled nonlinear differential equations that are solved analytically using a matrix iteration procedure. The effects of oscillatory excitation forces applied either to the cantilever or to the sample surface (or to both) are obtained from the solution set and applied to the to the assessment of phase and amplitude signals generated by various acoustic-atomic force microscope (A-AFM) modalities. The influence of bistable cantilever modes of on AFM signal generation is discussed. The effects on the cantilever-sample surface dynamics of subsurface features embedded in the sample that are perturbed by surface-generated oscillatory excitation forces and carried to the cantilever via wave propagation are accounted by the Bolef-Miller propagating wave model. Expressions pertaining to signal generation and image contrast in A-AFM are obtained and applied to amplitude modulation (intermittent contact) atomic force microscopy and resonant difference-frequency atomic force ultrasonic microscopy (RDF-AFUM). The influence of phase accumulation in A-AFM on image contrast is discussed, as is the effect of hard contact and maximum nonlinearity regimes of A-AFM operation.
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Autopilot for frequency-modulation atomic force microscopy.
PubMed
Kuchuk, Kfir; Schlesinger, Itai; Sivan, Uri
2015-10-01
One of the most challenging aspects of operating an atomic force microscope (AFM) is finding optimal feedback parameters. This statement applies particularly to frequency-modulation AFM (FM-AFM), which utilizes three feedback loops to control the cantilever excitation amplitude, cantilever excitation frequency, and z-piezo extension. These loops are regulated by a set of feedback parameters, tuned by the user to optimize stability, sensitivity, and noise in the imaging process. Optimization of these parameters is difficult due to the coupling between the frequency and z-piezo feedback loops by the non-linear tip-sample interaction. Four proportional-integral (PI) parameters and two lock-in parameters regulating these loops require simultaneous optimization in the presence of a varying unknown tip-sample coupling. Presently, this optimization is done manually in a tedious process of trial and error. Here, we report on the development and implementation of an algorithm that computes the control parameters automatically. The algorithm reads the unperturbed cantilever resonance frequency, its quality factor, and the z-piezo driving signal power spectral density. It analyzes the poles and zeros of the total closed loop transfer function, extracts the unknown tip-sample transfer function, and finds four PI parameters and two lock-in parameters for the frequency and z-piezo control loops that optimize the bandwidth and step response of the total system. Implementation of the algorithm in a home-built AFM shows that the calculated parameters are consistently excellent and rarely require further tweaking by the user. The new algorithm saves the precious time of experienced users, facilitates utilization of FM-AFM by casual users, and removes the main hurdle on the way to fully automated FM-AFM.
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Autopilot for frequency-modulation atomic force microscopy
NASA Astrophysics Data System (ADS)
Kuchuk, Kfir; Schlesinger, Itai; Sivan, Uri
2015-10-01
One of the most challenging aspects of operating an atomic force microscope (AFM) is finding optimal feedback parameters. This statement applies particularly to frequency-modulation AFM (FM-AFM), which utilizes three feedback loops to control the cantilever excitation amplitude, cantilever excitation frequency, and z-piezo extension. These loops are regulated by a set of feedback parameters, tuned by the user to optimize stability, sensitivity, and noise in the imaging process. Optimization of these parameters is difficult due to the coupling between the frequency and z-piezo feedback loops by the non-linear tip-sample interaction. Four proportional-integral (PI) parameters and two lock-in parameters regulating these loops require simultaneous optimization in the presence of a varying unknown tip-sample coupling. Presently, this optimization is done manually in a tedious process of trial and error. Here, we report on the development and implementation of an algorithm that computes the control parameters automatically. The algorithm reads the unperturbed cantilever resonance frequency, its quality factor, and the z-piezo driving signal power spectral density. It analyzes the poles and zeros of the total closed loop transfer function, extracts the unknown tip-sample transfer function, and finds four PI parameters and two lock-in parameters for the frequency and z-piezo control loops that optimize the bandwidth and step response of the total system. Implementation of the algorithm in a home-built AFM shows that the calculated parameters are consistently excellent and rarely require further tweaking by the user. The new algorithm saves the precious time of experienced users, facilitates utilization of FM-AFM by casual users, and removes the main hurdle on the way to fully automated FM-AFM.
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Autopilot for frequency-modulation atomic force microscopy
DOE Office of Scientific and Technical Information (OSTI.GOV)
Kuchuk, Kfir; Schlesinger, Itai; Sivan, Uri, E-mail: phsivan@tx.technion.ac.il
2015-10-15
One of the most challenging aspects of operating an atomic force microscope (AFM) is finding optimal feedback parameters. This statement applies particularly to frequency-modulation AFM (FM-AFM), which utilizes three feedback loops to control the cantilever excitation amplitude, cantilever excitation frequency, and z-piezo extension. These loops are regulated by a set of feedback parameters, tuned by the user to optimize stability, sensitivity, and noise in the imaging process. Optimization of these parameters is difficult due to the coupling between the frequency and z-piezo feedback loops by the non-linear tip-sample interaction. Four proportional-integral (PI) parameters and two lock-in parameters regulating these loopsmore » require simultaneous optimization in the presence of a varying unknown tip-sample coupling. Presently, this optimization is done manually in a tedious process of trial and error. Here, we report on the development and implementation of an algorithm that computes the control parameters automatically. The algorithm reads the unperturbed cantilever resonance frequency, its quality factor, and the z-piezo driving signal power spectral density. It analyzes the poles and zeros of the total closed loop transfer function, extracts the unknown tip-sample transfer function, and finds four PI parameters and two lock-in parameters for the frequency and z-piezo control loops that optimize the bandwidth and step response of the total system. Implementation of the algorithm in a home-built AFM shows that the calculated parameters are consistently excellent and rarely require further tweaking by the user. The new algorithm saves the precious time of experienced users, facilitates utilization of FM-AFM by casual users, and removes the main hurdle on the way to fully automated FM-AFM.« less