Daniell method for power spectral density estimation in atomic force microscopy

Labuda, Aleksander

doi:10.1063/1.4943292

Cited by 5 publications

(3 citation statements)

References 61 publications

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“…An automated calibration method [ 61 ] was used to obtain the stiffness of the first eigenmode ( k c1 = 43.2 N/m), which was then used as a basis of calibration for the second eigenmode stiffness k c2 = 818 N/m by a recently established calibration protocol [ 62 ]. Next, a thermal power spectral density [ 63 ] of the cantilever was acquired close to the surface (within a few hundred nanometers) to determine the remaining cantilever properties ( f c1 , f c2 , Q c1 , Q c2 ). For this calibration step, the proximity to the surface is important.…”

Section: Resultsmentioning

confidence: 99%

Generalized Hertz model for bimodal nanomechanical mapping

Labuda¹,

Kocuń²,

Meinhold³

et al. 2016

Beilstein J. Nanotechnol.

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104

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SummaryBimodal atomic force microscopy uses a cantilever that is simultaneously driven at two of its eigenmodes (resonant modes). Parameters associated with both resonances can be measured and used to extract quantitative nanomechanical information about the sample surface. Driving the first eigenmode at a large amplitude and a higher eigenmode at a small amplitude simultaneously provides four independent observables that are sensitive to the tip–sample nanomechanical interaction parameters. To demonstrate this, a generalized theoretical framework for extracting nanomechanical sample properties from bimodal experiments is presented based on Hertzian contact mechanics. Three modes of operation for measuring cantilever parameters are considered: amplitude, phase, and frequency modulation. The experimental equivalence of all three modes is demonstrated on measurements of the second eigenmode parameters. The contact mechanics theory is then extended to power-law tip shape geometries, which is applied to analyze the experimental data and extract a shape and size of the tip interacting with a polystyrene surface.

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Section: Resultsmentioning

confidence: 99%

Generalized Hertz model for bimodal nanomechanical mapping

Labuda¹,

Kocuń²,

Meinhold³

et al. 2016

Beilstein J. Nanotechnol.

Self Cite

104

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“…The spectrogram method performed on a PPP-CONTR cantilever at a distance L spot from the cantilever base. (a) The PSD of the cantilever thermal motion (computed by the Daniell method 33 ) was measured at various distances across the cantilever to create (b) a spectrogram where the spectral density is represented in a gray scale. (c) The torsional peak can be identified and fit with a SHO model to determine the amplitude variance A 2 rms as a function of distance across the cantilever.…”

Section: B Spectrogram Calibration Methodsmentioning

confidence: 99%

Static and dynamic calibration of torsional spring constants of cantilevers

Labuda

Cao

Walsh

et al. 2018

Review of Scientific Instruments

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A method for calibrating the dynamic torsional spring constant of cantilevers by directly measuring the thermally driven motion of the cantilever with an interferometer is presented. Random errors in calibration were made negligible (<1%) by averaging over multiple measurements. The errors in accuracy of ±5% or ±10% for both of the cantilevers calibrated in this study were limited only by the accuracy of the laser Doppler vibrometer (LDV) used to measure thermal fluctuations. This is a significant improvement over commonly used methods that result in large and untraceable errors resulting from assumptions made about the cantilever geometry, material properties, and/or hydrodynamic physics of the surroundings. Subsequently, the static torsional spring constant is determined from its dynamic counterpart after careful LDV measurements of the torsional mode shape, backed by finite element analysis simulations. A meticulously calibrated cantilever is used in a friction force microscopy experiment that measures the friction difference and interfacial shear strength (ISS) between graphene and a silicon dioxide AFM probe. Accurate calibration can resolve discrepancies between different experimental methods, which have contributed to a large scatter in the reported friction and ISS values in the literature to date.

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“…Figure 4: Spectral density of the first three eigenmodes of the AC240 cantilever from Figure 3. These data were calculated from a 2 s time series using the Daniell method 52 of PSD estimation to avoid bias and reduce effects of spurious noise peaks. Then, the spectra were corrected by the respective 𝛽 𝑛 computed by Eq.…”

Section: A Experimental Setupmentioning

confidence: 99%

Calibration of higher eigenmodes of cantilevers

Labuda

Kocuń

Lysy

et al. 2016

Review of Scientific Instruments

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A method is presented for calibrating the higher eigenmodes (resonant modes) of atomic force microscopy cantilevers that can be performed prior to any tip-sample interaction. The method leverages recent efforts in accurately calibrating the first eigenmode by providing the higher-mode stiffness as a ratio to the first mode stiffness. A one-time calibration routine must be performed for every cantilever type to determine a power-law relationship between stiffness and frequency, which is then stored for future use on similar cantilevers. Then, future calibrations only require a measurement of the ratio of resonant frequencies and the stiffness of the first mode. This method is verified through stiffness measurements using three independent approaches: interferometric measurement, AC approach-curve calibration, and finite element analysis simulation. Power-law values for calibrating higher-mode stiffnesses are reported for several cantilever models. Once the higher-mode stiffnesses are known, the amplitude of each mode can also be calibrated from the thermal spectrum by application of the equipartition theorem.

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Daniell method for power spectral density estimation in atomic force microscopy

Cited by 5 publications

References 61 publications

Generalized Hertz model for bimodal nanomechanical mapping

Generalized Hertz model for bimodal nanomechanical mapping

Static and dynamic calibration of torsional spring constants of cantilevers

Calibration of higher eigenmodes of cantilevers

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