Atomic force microscopy cantilever simulation by finite element methods for quantitative atomic force acoustic microscopy measurements

Espinoza‐Beltrán, F.J.; Muñoz-Saldaña, J.; Torres-Torres, D.; Torres-Martínez, R.; Schneider, Gerold A.

doi:10.1557/jmr.2006.0379

Cited by 17 publications

(11 citation statements)

References 21 publications

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“…Compared to an experimental SAM verification scheme that must make assumptions about the beam dynamics and contact mechanics, FEA allows the tip-sample contact to be simplified to a system of elastic springs. In principle, FEA could be used to directly calculate the contact stiffness from experimental contact resonance frequencies [21][22][23]. However, the variability amongst different cantilevers would necessitate a unique model for every cantilever used.…”

Section: Feasibility Of Analytical Analysis Of Higher-eigenmode Cr Spmentioning

confidence: 99%

Low-force AFM nanomechanics with higher-eigenmode contact resonance spectroscopy

Killgore

Hurley

2012

Nanotechnology

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Atomic force microscopy (AFM) methods for quantitative measurements of elastic modulus on stiff (>10 GPa) materials typically require tip-sample contact forces in the range from hundreds of nanonewtons to a few micronewtons. Such large forces can cause sample damage and preclude direct measurement of ultrathin films or nanofeatures. Here, we present a contact resonance spectroscopy AFM technique that utilizes a cantilever's higher flexural eigenmodes to enable modulus measurements with contact forces as low as 10 nN, even on stiff materials. Analysis with a simple analytical beam model of spectra for a compliant cantilever's fourth and fifth flexural eigenmodes in contact yielded good agreement with bulk measurements of modulus on glass samples in the 50-75 GPa range. In contrast, corresponding analysis of the conventionally used first and second eigenmode spectra gave poor agreement under the experimental conditions. We used finite element analysis to understand the dynamic contact response of a cantilever with a physically realistic geometry. Compared to lower eigenmodes, the results from higher modes are less affected by model parameters such as lateral stiffness that are either unknown or not considered in the analytical model. Overall, the technique enables local mechanical characterization of materials previously inaccessible to AFM-based nanomechanics methods.

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Section: Feasibility Of Analytical Analysis Of Higher-eigenmode Cr Spmentioning

confidence: 99%

Low-force AFM nanomechanics with higher-eigenmode contact resonance spectroscopy

Killgore

Hurley

2012

Nanotechnology

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“…The free resonance frequencies for the fitted experimental cantilever are compared with the experimental ones and with those obtained by using Finite Element Process (FEA) [36], see Table 1.…”

Section: Resultsmentioning

confidence: 99%

“…, where a ∼ 11nm was obtained using the methodology by [46], M tip = 170.33GPa [36] and the proposed model, an indentation modulus mapping is obtained, see Figure 7. This mapping was computed using the results shown in Figure 6(c), (d), (e) and (f) and the database shown in Figure 5.…”

Section: Resultsmentioning

confidence: 99%

Stochastic excitation for high-resolution Atomic Force Acoustic Microscopy imaging: a system theory approach.

Cruz-Valeriano¹,

Arciniega²,

Landaverde³

et al. 2019

Preprint

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In this work, a high-resolution Atomic Force Acoustic Microscopy imaging technique is shown in order to obtain the local indentation modulus at nanoscale using a model which gives a quantitative relationship between a set of contact resonance frequencies and indentation modulus through a white-noise excitation. This technique is based on white-noise excitation for system identification due to non-linearities in the tip-sample interaction. During a conventional scanning, a Fast Fourier Transform is applied to the deflection signal which comes from the photo-diodes of the Atomic Force Microscopy (AFM) for each pixel, while the tip-sample interaction is excited by a white-noise signal. This approach allows the measurement of several vibrational modes in a single step with high frequency resolution, less computational data and at a faster speed than other similar techniques. This technique is referred to as Stochastic Atomic Force Acoustic Microscopy (S-AFAM), where the frequency shifts with respect to free resonance frequencies for an AFM cantilever can be used to determine the mechanical properties of a material. S-AFAM is implemented and compared to a conventional technique (Resonance Tracking-Atomic Force Microscopy, RT-AFAM), where a graphite film over a glass substrate sample is analyzed. S-AFAM can be implemented in any AFM system due to its reduced instrumentation compared to conventional techniques.

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“…These resonance frequencies were fitted according to a database, which was computed using the free cantilever model described in Equation 21 and the particle swarm optimization algorithm [33][34][35][36], in order to obtain the geometrical parameters for the experimental cantilever. The database describes each cantilever according to length L, width a, thickness b, inertia moment I = ab 3 /12, linear mass m = ρA, where A is the crosssectional area of the cantilever and ρ = 2330 kg/m 3 [37] is the density of the cantilever. The database has 10000 cantilevers where L ∈ [440,500] µm, a ∈ [40,50] µm, b ∈ [1,3] µm.…”

Section: Transfer Function For a Cantilever In Contactmentioning

confidence: 99%

Stochastic excitation for high-resolution atomic force acoustic microscopy imaging: a system theory approach

Valeriano

Gervacio-Arciniega

Flores

et al. 2020

Beilstein J. Nanotechnol.

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In this work, a high-resolution atomic force acoustic microscopy imaging technique is developed in order to obtain the local indentation modulus at the nanoscale level. The technique uses a model that gives a qualitative relationship between a set of contact resonance frequencies and the indentation modulus. It is based on white-noise excitation of the tip–sample interaction and uses system theory for the extraction of the resonance modes. During conventional scanning, for each pixel, the tip–sample interaction is excited with a white-noise signal. Then, a fast Fourier transform is applied to the deflection signal that comes from the photodiodes of the atomic force microscopy (AFM) equipment. This approach allows for the measurement of several vibrational modes in a single step with high frequency resolution, with less computational cost and at a faster speed than other similar techniques. This technique is referred to as stochastic atomic force acoustic microscopy (S-AFAM), and the frequency shifts of the free resonance frequencies of an AFM cantilever are used to determine the mechanical properties of a material. S-AFAM is implemented and compared with a conventional technique (resonance tracking-atomic force acoustic microscopy, RT-AFAM). A sample of a graphite film on a glass substrate is analyzed. S-AFAM can be implemented in any AFM system due to its reduced instrumentation requirements compared to conventional techniques.

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Atomic force microscopy cantilever simulation by finite element methods for quantitative atomic force acoustic microscopy measurements

Cited by 17 publications

References 21 publications

Low-force AFM nanomechanics with higher-eigenmode contact resonance spectroscopy

Low-force AFM nanomechanics with higher-eigenmode contact resonance spectroscopy

Stochastic excitation for high-resolution Atomic Force Acoustic Microscopy imaging: a system theory approach.

Stochastic excitation for high-resolution atomic force acoustic microscopy imaging: a system theory approach

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