Influence of surface stress on the resonance behavior of microcantilevers

McFarland, Andrew W.; Poggi, Mark A.; Doyle, M.; Bottomley, Lawrence A.; Colton, Jonathan S.

doi:10.1063/1.2006212

Cited by 123 publications

(114 citation statements)

References 14 publications

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“…They also form integral components in micromechanical and nanomechanical devices. One such application involves the atomic force microscope (AFM), [1][2][3][4][5][6][7][8][9][10][11][12][13] which employs a micron sized cantilever as its force sensing element. Due to their widespread use, the mechanical behavior of cantilever beams and plates has been studied extensively.…”

Section: Introductionmentioning

confidence: 99%

“…The out-of-plane deflection of a cantilever transducer is analyzed in a large number of these studies, and is a cornerstone of many applications. [1][2][3][4][5][6][7][8][9][10][11][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][36][37][38] One important aspect that has received relatively little attention involves the coupling of in-plane loads to the out-of-plane deflection of cantilever plates. Such a mechanism can potentially lead to buckling, and is thus of particular relevance to the design of instrumentation and structures employing these devices.…”

Section: Introductionmentioning

confidence: 99%

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Buckling of a cantilever plate uniformly loaded in its plane with applications to surface stress and thermal loads

Lachut

Sader

2013

Journal of Applied Physics

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Sn and Nb modified ultrafine Ti-based bulk alloys with high-strength and enhanced ductility Appl. Phys. Lett. 102, 061908 (2013) A comparative study of two molecular mechanics models based on harmonic potentials J. Appl. Phys. 113, 063509 (2013) Viscoplastic analysis of cyclic indentation behavior of thin metallic films J. Appl. Phys. 113, 063510 (2013) The increase in conductance of a gold single atom chain during elastic elongation J. Appl. Phys. 113, 054316 (2013) Additional information on J. Appl. Phys. Buckling of elastic structures can occur for loads well within the proportionality limit of their constituent materials. Given the ubiquity of beams and plates in engineering design and application, their buckling behavior has been widely studied. However, buckling of a cantilever plate is yet to be investigated, despite the widespread use of cantilevers in modern technological developments. Here, we address this issue and theoretically study the buckling behavior of a cantilever plate that is uniformly loaded in its plane. Applications of this fundamental problem include loading due to uniform temperature and surface stress changes. This is achieved using a scaling analysis and full three-dimensional numerical solution, leading to explicit formulas for the buckling loads. Unusually, we observe buckling for both tensile and compressive loads, the physical mechanisms for which are explored. We also examine the practical implications of these findings to modern developments in ultra sensitive micro-and nano-cantilever sensors, such as those composed of silicon nitride and graphene. V C 2013 American Institute of Physics.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Buckling of a cantilever plate uniformly loaded in its plane with applications to surface stress and thermal loads

Lachut

Sader

2013

Journal of Applied Physics

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“…2,16 There should be no dramatic change in cantilever stiffness caused by changing the fluid environment from air to water. Changes in the resonant frequency correlating to a change in the surface stress on a cantilever have been observed; 17 however, the changes are small compared with the frequency shift caused by the mass loading effect that a liquid such as water has on a beam and the mechanism driving these changes is still debated. 18 As will be discussed in Sec.…”

Section: Introductionmentioning

confidence: 99%

A method for atomic force microscopy cantilever stiffness calibration under heavy fluid loading

Kennedy

Cole

Clark

2009

Review of Scientific Instruments

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This work presents a method for force calibration of rectangular atomic force microscopy ͑AFM͒ microcantilevers under heavy fluid loading. Theoretical modeling of the thermal response of microcantilevers is discussed including a fluid-structure interaction model of the cantilever-fluid system that incorporates the results of the fluctuation-dissipation theorem. This model is curve fit to the measured thermal response of a cantilever in de-ionized water and a cost function is used to quantify the difference between the theoretical model and measured data. The curve fit is performed in a way that restricts the search space to parameters that reflect heavy fluid loading conditions. The resulting fitting parameters are used to calibrate the cantilever. For comparison, cantilevers are calibrated using Sader's method in air and the thermal noise method in both air and water. For a set of eight cantilevers ranging in stiffness from 0.050 to 5.8 N/m, the maximum difference between Sader's calibration performed in air and the new method performed in water was 9.4%. A set of three cantilevers that violate the aspect ratio assumption associated with the fluid loading model ͑length-to-width ratios less than 3.5͒ ranged in stiffness from 0.85 to 4.7 N/m and yielded differences as high as 17.8%.

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“…In this case,  = 10 is known,  and o  are the two unknowns to be determined. Because the original axial load (or surface stress) can be determined during an experimental calibration process by measuring the shift of a resonant frequency [9], this inverse problem solving technique for two variables can correspondingly be applied to the case that adsorption induces no surface stress. …”

Section: Resultsmentioning

confidence: 99%

The inverse problem of sensing the mass and force induced by an adsorbate on a beam nanomechanical resonator

Liu

Zhang

2016

AIP Conference Proceedings

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Abstract. The mass sensing superiority of a micro/nanomechanical resonator sensor over conventional mass spectrometry has been, or at least, is being firmly established. Because the sensing mechanism of a mechanical resonator sensor is the shifts of resonant frequencies, how to link the shifts of resonant frequencies with the material properties of an analyte formulates an inverse problem. Besides the analyte/adsorbate mass, many other factors such as position and axial force can also cause the shifts of resonant frequencies. The in-situ measurement of the adsorbate position and axial force is extremely difficult if not impossible, especially when an adsorbate is as small as a molecule or an atom. Extra instruments are also required. In this study, an inverse problem of using three resonant frequencies to determine the mass, position and axial force is formulated and solved. The accuracy of the inverse problem solving method is demonstrated and how the method can be used in the real application of a nanomechanical resonator is also discussed. Solving the inverse problem is helpful to the development and application of mechanical resonator sensor on two things: reducing extra experimental equipments and achieving better mass sensing by considering more factors.

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Influence of surface stress on the resonance behavior of microcantilevers

Cited by 123 publications

References 14 publications

Buckling of a cantilever plate uniformly loaded in its plane with applications to surface stress and thermal loads

Buckling of a cantilever plate uniformly loaded in its plane with applications to surface stress and thermal loads

A method for atomic force microscopy cantilever stiffness calibration under heavy fluid loading

The inverse problem of sensing the mass and force induced by an adsorbate on a beam nanomechanical resonator

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