Distortion in the thermal noise spectrum and quality factor of nanomechanical devices due to finite frequency resolution with applications to the atomic force microscope

Compact metal probes: A solution for atomic force microscopy based tip-enhanced Raman spectroscopy Rev. Sci. Instrum. 83, 123708 (2012) Note: Radiofrequency scanning probe microscopy using vertically oriented cantilevers Rev. Sci. Instrum. 83, 126103 (2012) Switching spectroscopic measurement of surface potentials on ferroelectric surfaces via an open-loop Kelvin probe force microscopy method Appl. Phys. Lett. 101, 242906 (2012) Enhanced quality factors and force sensitivity by attaching magnetic beads to cantilevers for atomic force microscopy in liquid J. Appl. Phys. 112, 114324 (2012) Invited Review Article: High-speed flexure-guided nanopositioning: Mechanical design and control issues Rev. Sci. Instrum. 83, 121101 (2012) Additional information on Rev. Sci. Instrum. The spring constant of an atomic force microscope cantilever is often needed for quantitative measurements. The calibration method of Sader et al. [Rev. Sci. Instrum. 70, 3967 (1999)] for a rectangular cantilever requires measurement of the resonant frequency and quality factor in fluid (typically air), and knowledge of its plan view dimensions. This intrinsically uses the hydrodynamic function for a cantilever of rectangular plan view geometry. Here, we present hydrodynamic functions for a series of irregular and non-rectangular atomic force microscope cantilevers that are commonly used in practice. Cantilever geometries of arrow shape, small aspect ratio rectangular, quasi-rectangular, irregular rectangular, non-ideal trapezoidal cross sections, and V-shape are all studied. This enables the spring constants of all these cantilevers to be accurately and routinely determined through measurement of their resonant frequency and quality factor in fluid (such as air). An approximate formulation of the hydrodynamic function for microcantilevers of arbitrary geometry is also proposed. Implementation of the method and its performance in the presence of uncertainties and non-idealities is discussed, together with conversion factors for the static and dynamic spring constants of these cantilevers. These results are expected to be of particular value to the design and application of micro-and nanomechanical systems in general.

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“…55. Use of a rectangular window enables the true device quality factor to be extracted from this measured value…”

Section: Determination Of the True Quality Factormentioning

confidence: 99%

Spring constant calibration of atomic force microscope cantilevers of arbitrary shape

Sader

Sanelli

Adamson

et al. 2012

Review of Scientific Instruments

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“…However, the Q factor correction for the Bartlett method (by inverting Eq. (3)) only applies to a rectangular window function, 39 which is very restrictive. Meanwhile, Q correction for the Daniell method (Eq.…”

Section: B Windowing Functionmentioning

confidence: 99%

“…The information about these parameters is contained in the power spectral density (PSD) of the cantilever's thermally driven stochastic motion. [28][29][30][31][32][33][34][35][36] Recent efforts have proved valuable in quantifying and correcting estimation biases [37][38][39] and predicting the variance 40,41 in measurements of cantilever parameters from measured PSDs.…”

Section: Introductionmentioning

confidence: 99%

Daniell method for power spectral density estimation in atomic force microscopy

Labuda

2016

Review of Scientific Instruments

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An alternative method for power spectral density (PSD) estimation--the Daniell method--is revisited and compared to the most prevalent method used in the field of atomic force microscopy for quantifying cantilever thermal motion--the Bartlett method. Both methods are shown to underestimate the Q factor of a simple harmonic oscillator (SHO) by a predictable, and therefore correctable, amount in the absence of spurious deterministic noise sources. However, the Bartlett method is much more prone to spectral leakage which can obscure the thermal spectrum in the presence of deterministic noise. By the significant reduction in spectral leakage, the Daniell method leads to a more accurate representation of the true PSD and enables clear identification and rejection of deterministic noise peaks. This benefit is especially valuable for the development of automated PSD fitting algorithms for robust and accurate estimation of SHO parameters from a thermal spectrum.

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“…It was verified for all cantilevers that the above parameters cause minimal spectral distortion due to finite sampling rate. 26 A typical lateral thermal noise spectrum for the first torsional mode of AIO cantilever B is shown in Figure 3.…”

Section: Thermal Methodsmentioning

confidence: 99%

A non-contact, thermal noise based method for the calibration of lateral deflection sensitivity in atomic force microscopy

Mullin

Hobbs

2014

Review of Scientific Instruments

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Calibration of lateral forces and displacements has been a long standing problem in lateral force microscopies. Recently, it was shown by Wagner et al. that the thermal noise spectrum of the first torsional mode may be used to calibrate the deflection sensitivity of the detector. This method is quick, non-destructive and may be performed in situ in air or liquid. Here we make a full quantitative comparison of the lateral inverse optical lever sensitivity obtained by the lateral thermal noise method and the shape independent method developed by Anderson et al. We find that the thermal method provides accurate results for a wide variety of rectangular cantilevers, provided that the geometry of the cantilever is suitable for torsional stiffness calibration by the torsional Sader method, in-plane bending of the cantilever may be eliminated or accounted for and that any scaling of the lateral deflection signal between the measurement of the lateral thermal noise and the measurement of the lateral deflection is eliminated or corrected for. We also demonstrate that the thermal method may be used to characterize the linearity of the detector signal as a function of position, and find a deviation of less than 8% for the instrument used.

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Distortion in the thermal noise spectrum and quality factor of nanomechanical devices due to finite frequency resolution with applications to the atomic force microscope

Cited by 12 publications

References 20 publications

Spring constant calibration of atomic force microscope cantilevers of arbitrary shape

Spring constant calibration of atomic force microscope cantilevers of arbitrary shape

Daniell method for power spectral density estimation in atomic force microscopy

A non-contact, thermal noise based method for the calibration of lateral deflection sensitivity in atomic force microscopy

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