Spring constant calibration of atomic force microscope cantilevers of arbitrary shape

Abstract

Compact metal probes: A solution for atomic force microscopy based tip-enhanced Raman spectroscopy Rev. Sci. Instrum. 83, 123708 (2012) Note: Radiofrequency scanning probe microscopy using vertically oriented cantilevers Rev. Sci. Instrum. 83, 126103 (2012) Switching spectroscopic measurement of surface potentials on ferroelectric surfaces via an open-loop Kelvin probe force microscopy method Appl. Phys. Lett. 101, 242906 (2012) Enhanced quality factors and force sensitivity by attaching magnetic beads to cantilevers for atomic force microscopy in liquid J. Appl. Phys. 112, 114324 (2012) Invited Review Article: High-speed flexure-guided nanopositioning: Mechanical design and control issues Rev. Sci. Instrum. 83, 121101 (2012) Additional information on Rev. Sci. Instrum. 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.

A virtual instrument to standardise the calibration of atomic force microscope cantilevers

“…The averaging process of this calibration initiative naturally generates the hydrodynamic function of that cantilever type, embodied in (what we term here) its -coefficient, see Section II [11]. This immediately enables non-invasive calibration of AFM cantilevers (of any geometry) using the Sader method [11] -the method requires only the cantilever's resonant frequency and quality factor in air.…”

“…By combining and appropriately averaging this dataset through use of a recent theoretical development of the "Sader method", described in Refs. [11][12][13], uncertainty in the measured spring constant is systematically reduced.…”

A method to measure nanomechanical properties of biological objects

“…25 Thus, they are almost applicable to our cantilevers, which have an aspect ratio of 3.3 6 0.1. Consequently, we upgrade the model of Dupas et al by using the results of Sader et al 27 To do so, we need to translate the corrections in resonance frequencies from Eq.…”

“…Sader et al 25 suggested that for a rectangular cantilever with an arbitrary aspect ratio, an imaginary component of the generalized hydrodynamic function H im can be approximated by a power law of the Reynolds number Re. The value of Re ¼ ð2pf q PBS b 2 Þ=ð4g PBS Þ, where g PBS is the viscosity of PBS.…”

“…For cantilevers with small aspect ratio, problems are exacerbated due to issues in providing analytical description of the hydrodynamic flow. 25 Currently, such cantilevers are among the most appropriate ones for probing compliant BOs. Thus, a comprehensive approach needs to be developed to accurately fit flexural resonances of compliant AFM cantilevers with a small aspect ratio 26 in contact with biological specimens in dissipative media.…”