title: Spring constant calibration of atomic force microscope cantilevers of arbitrary shape.
abstract: 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.
authors.affiliation: Department of Mathematics and Statistics, The University of Melbourne, Victoria 3010, Australia. jsader@unimelb.edu.au
authors.forename: John E
authors.initials: JE
authors.lastname: Sader
authors.forename: Julian A
authors.initials: JA
authors.lastname: Sanelli
authors.forename: Brian D
authors.initials: BD
authors.lastname: Adamson
authors.forename: Jason P
authors.initials: JP
authors.lastname: Monty
authors.forename: Xingzhan
authors.initials: X
authors.lastname: Wei
authors.forename: Simon A
authors.initials: SA
authors.lastname: Crawford
authors.forename: James R
authors.initials: JR
authors.lastname: Friend
authors.forename: Ivan
authors.initials: I
authors.lastname: Marusic
authors.forename: Paul
authors.initials: P
authors.lastname: Mulvaney
authors.forename: Evan J
authors.initials: EJ
authors.lastname: Bieske
mesh_terms: D002138:Calibration; D004548:Elasticity; D057446:Hydrodynamics; D055595:Mechanical Phenomena; D018625:Microscopy, Atomic Force / Q000295:instrumentation*; D035501:Uncertainty