Determination of the spring constants of the higher flexural modes of microcantilever sensors

Parkin, John D.; Hähner, Georg

doi:10.1088/0957-4484/24/6/065704

Cited by 6 publications

(6 citation statements)

References 35 publications

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“…Experiments were performed with a commercial Bruker Dimension FastScan AFM system (Bruker, Santa Barbara, CA, USA). In our setup, a custom-built, smooth parallel plate microchannel of height ≈100 μm and length 4.5 mm was used [ 27 , 29 – 30 ]. An accurate value of the channel height was obtained by contacting the free end of a cantilever on the bottom surface of the channel with the channel aligned parallel to the cantilever length and measuring the distance to the top of the channel by lifting the cantilever with the AFM microstepper motor until it contacted the top surface of the channel.…”

Section: Methodsmentioning

confidence: 99%

“…It is therefore desirable to have a universal force tool that can exert well-defined forces on all types of cantilever sensors independent from their physical and chemical properties. A microfluidic flow tool has been previously employed in connection with cantilever spring constant determination [ 27 – 30 ], and it was shown that forces due to the flow from a microfluidic channel can be exploited to determine the dynamic flexural spring constants [ 29 ] as well as the torsional and lateral spring constants [ 30 ]. In the following, we describe a method to determine the static flexural spring constant for cantilevers of any geometric shape.…”

Section: Introductionmentioning

confidence: 99%

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Contact-free experimental determination of the static flexural spring constant of cantilever sensors using a microfluidic force tool

Parkin

Hähner

2016

Beilstein J. Nanotechnol.

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SummaryMicro- and nanocantilevers are employed in atomic force microscopy (AFM) and in micro- and nanoelectromechanical systems (MEMS and NEMS) as sensing elements. They enable nanomechanical measurements, are essential for the characterization of nanomaterials, and form an integral part of many nanoscale devices. Despite the fact that numerous methods described in the literature can be applied to determine the static flexural spring constant of micro- and nanocantilever sensors, experimental techniques that do not require contact between the sensor and a surface at some point during the calibration process are still the exception rather than the rule. We describe a noncontact method using a microfluidic force tool that produces accurate forces and demonstrate that this, in combination with a thermal noise spectrum, can provide the static flexural spring constant for cantilever sensors of different geometric shapes over a wide range of spring constant values (≈0.8–160 N/m).

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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Contact-free experimental determination of the static flexural spring constant of cantilever sensors using a microfluidic force tool

Parkin

Hähner

2016

Beilstein J. Nanotechnol.

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“…The static deflection u(x) depending on the applied fluidic forces was determined with a home written MATLAB ® routine by generalizing the results reported in [35,41] for the force profiles extracted from Elmer and the flexural rigidity of each cantilever. The flexural spring constants were obtained beforehand independently as described in [42]. Note that the static equilibrium bent shape u(x) could also be determined with other methods: for example via interferometry or by taking a photograph if the cantilever and its deflection are large enough.…”

Section: Determination Of the Bent Shape U(x) And The Spring Constantsmentioning

confidence: 99%

Calibration of the torsional and lateral spring constants of cantilever sensors

Parkin

Hähner

2014

Nanotechnology

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A method suitable for the calibration of the spring constants of all torsional and lateral eigenmodes of micro-and nanocantilever sensors is described. Such sensors enable nanomechanical measurements and the characterization of nanomaterials, for example with atomic force microscopy.The method presented involves the interaction of a flow of fluid from a microchannel with the cantilever beam. Forces imparted by the flow cause the cantilever to bend and induce a measurable change of the torsional and lateral resonance frequencies. From the frequency shifts the cantilever spring constants can be determined. The method does not involve physical contact between the cantilever or its tip and a hard surface. As such it is noninvasive and does not risk damage to the cantilever.Experimental data is presented for two rectangular microcantilevers with fundamental flexural spring constants of 0.046 and 0.154 N/m. The experimentally determined torsional stiffness values are compared with those obtained by the Sader method. We demonstrate that the torsional spring constants can be readily calibrated using the method with an accuracy of around 15%.Calibration of the torsional and lateral spring constants of cantilever sensors 2

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“…The recent rise in popularity of bimodal and multifrequency imaging [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40] , which provide high-resolution nanomechanical mapping of heterogeneous materials by exciting two or more cantilever eigenmodes, has extended the need for accurate cantilever calibration to its higher eigenmodes 41,42 . To date, the large uncertainty in highermode amplitudes and stiffnesses has impeded proper operation and quantitative data interpretation in multifrequency AFM.…”

Section: Introductionmentioning

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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Determination of the spring constants of the higher flexural modes of microcantilever sensors

Cited by 6 publications

References 35 publications

Contact-free experimental determination of the static flexural spring constant of cantilever sensors using a microfluidic force tool

Contact-free experimental determination of the static flexural spring constant of cantilever sensors using a microfluidic force tool

Calibration of the torsional and lateral spring constants of cantilever sensors

Calibration of higher eigenmodes of cantilevers

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