A Method for Calculating the Spring Constant of Atomic Force Microscopy Cantilevers with a Nonrectangular Cross Section

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

doi:10.1021/ac048828h

Cited by 42 publications

(42 citation statements)

References 16 publications

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“…Indeed, the theoretical spring constant for rectangular cantilevers with trapezoidal cross section is given by k a eff = 3EI / l 3 (Table I) with I the second moment of inertia. 28 Alternatively, from Q tuning one obtains the experimental cantilever spring constant k b eff (Table I). 3 Hence from the first resonance frequency of the cantilever (obtained from the maximum of the PSDs as in Fig.…”

Section: Resultsmentioning

confidence: 99%

Influence of surface modification on the quality factor of microresonators

2012

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Influence of surface modification on the quality factor of microresonators Ergincan, O.; Palasantzas, G.; Kooi, B. J. Take-down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Noise measurements were performed to determine the quality factor (Q) as a function of gas pressure P for microresonators in cantilever form with systematically modified surfaces. In the free-molecular regime, which is dominated by internal energy losses, Q was substantially decreased by more than an order of magnitude with increasing surface roughness. At higher pressures, within the molecular regime, Q showed the typical inverse linear dependence on pressure Q ∼ P −1 . However, in the molecular regime the Q factor also showed a strong dependence on surface morphology as indicated by surface area calculations using measured roughness data and compared to those obtained from Q ∼ P −1 plots.

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Section: Resultsmentioning

confidence: 99%

Influence of surface modification on the quality factor of microresonators

2012

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“…We apply a dimensional approach [23] to calculate the static spring constant c L stat of a cantilever with a point load acting on its free end:…”

Section: Static Spring Constantmentioning

confidence: 99%

Bidirectional quantitative force gradient microscopy

et al. 2015

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“…For example, I = wt 3 /12 is the equation describing the moment of inertia for a rectangular cantilever beam where w, and t are its width and thickness. Beams with a trapezoidal cross-section may also be analyzed by dimensional means [6]. Often, V-shaped cantilevers are used as well, and solutions for the dimensional determination of k have been developed based on a parallel beam approximation [7].…”

Section: Introductionmentioning

confidence: 99%

SI-Traceable Spring Constant Calibration of Microfabricated Cantilevers for Small Force Measurement

2006

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A variety of methods exist to measure the stiffness of microfabricated cantilever beams such as those used as mechanical sensors in atomic force microscopy (AFM). In order for AFM to be used as a quantitative small force measurement tool, these methods must be validated within the International System of Units (SI). To this end, two different contact techniques were used to calibrate the spring constant of a cantilever beam. First, a dynamic indentationbased method was used to measure the spring constant of a rectangular cantilever beam. These results were then compared against an SI-traceable spring constant measurement from an electrostatic force balance (EFB). The measurements agree within experimental uncertainty and within 2% for spring constants greater than 2 N/m. The use of this cantilever beam as a transfer artifact for in situ AFM cantilever calibration was then evaluated in comparison to the thermal calibration method. Excellent agreement is seen between these techniques, establishing the consistency of the thermal and dynamic indentation methods with SItraceable contact cantilever calibration for the rectangular cantilever geometry tested.

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A Method for Calculating the Spring Constant of Atomic Force Microscopy Cantilevers with a Nonrectangular Cross Section

Cited by 42 publications

References 16 publications

Influence of surface modification on the quality factor of microresonators

Influence of surface modification on the quality factor of microresonators

Bidirectional quantitative force gradient microscopy

SI-Traceable Spring Constant Calibration of Microfabricated Cantilevers for Small Force Measurement

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