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.β70, 3967 (1999)] https://doi.org/10.1063/1.1150021 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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October 2012
Research Article|
October 17 2012
Spring constant calibration of atomic force microscope cantilevers of arbitrary shape
John E. Sader;
John E. Sader
a)
1Department of Mathematics and Statistics,
The University of Melbourne
, Victoria 3010, Australia
2Kavli Nanoscience Institute and Department of Physics,
California Institute of Technology
, Pasadena, California 91125, USA
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Julian A. Sanelli;
Julian A. Sanelli
3School of Chemistry,
The University of Melbourne
, Victoria 3010, Australia
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Brian D. Adamson;
Brian D. Adamson
3School of Chemistry,
The University of Melbourne
, Victoria 3010, Australia
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Jason P. Monty;
Jason P. Monty
4Department of Mechanical Engineering,
The University of Melbourne
, Victoria 3010, Australia
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Xingzhan Wei;
Xingzhan Wei
3School of Chemistry,
The University of Melbourne
, Victoria 3010, Australia
5Bio21 Institute,
The University of Melbourne
, Victoria 3010, Australia
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Simon A. Crawford;
Simon A. Crawford
6School of Botany,
The University of Melbourne
, Victoria 3010, Australia
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James R. Friend;
James R. Friend
7
Melbourne Centre for Nanofabrication
, Clayton, Victoria 3800, Australia
8
MicroNanophysics Research Laboratory, RMIT University
, Melbourne, Victoria 3001, Australia
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Ivan Marusic;
Ivan Marusic
4Department of Mechanical Engineering,
The University of Melbourne
, Victoria 3010, Australia
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Paul Mulvaney;
Paul Mulvaney
3School of Chemistry,
The University of Melbourne
, Victoria 3010, Australia
5Bio21 Institute,
The University of Melbourne
, Victoria 3010, Australia
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Evan J. Bieske
Evan J. Bieske
3School of Chemistry,
The University of Melbourne
, Victoria 3010, Australia
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a)
Author to whom correspondence should be addressed. Electronic mail: jsader@unimelb.edu.au.
Rev. Sci. Instrum. 83, 103705 (2012)
Article history
Received:
June 15 2012
Accepted:
September 18 2012
Citation
John E. Sader, Julian A. Sanelli, Brian D. Adamson, Jason P. Monty, Xingzhan Wei, Simon A. Crawford, James R. Friend, Ivan Marusic, Paul Mulvaney, Evan J. Bieske; Spring constant calibration of atomic force microscope cantilevers of arbitrary shape. Rev. Sci. Instrum. 1 October 2012; 83 (10): 103705. https://doi.org/10.1063/1.4757398
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