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Title: Nondestructive and noncontact method for determining the spring constant of rectangular cantilevers

Abstract

We present here an experimental setup and suggest an extension to the long existing added-mass method for the calibration of the spring constant of atomic force microscope cantilevers. Instead of measuring the resonance frequency shift that results from attaching particles of known masses to the end of cantilevers, we load them with water microdrops generated by a commercial inkjet dispenser. Such a device is capable of generating drops, and thus masses, of extremely reproducible size. This makes it an ideal tool for calibration tasks. Moreover, the major advantage of water microdrops is that they allow for a nearly contactless calibration: no mechanical micromanipulation of particles on cantilevers is required, neither for their deposition nor for removal. After some seconds the water drop is completely evaporated, and no residues are left on the cantilever surface or tip. We present two variants: we vary the size of the drops and deposit them at the free end of the cantilever, or we keep the size of the drops constant and vary their position along the cantilever. For the second variant, we implemented also numerical simulations. Spring constants measured by this method are comparable to results obtained by the thermal noise method, as wemore » demonstrate for six different cantilevers.« less

Authors:
; ; ;  [1];  [2];  [2]
  1. Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz (Germany)
  2. (Germany)
Publication Date:
OSTI Identifier:
20953427
Resource Type:
Journal Article
Resource Relation:
Journal Name: Review of Scientific Instruments; Journal Volume: 78; Journal Issue: 4; Other Information: DOI: 10.1063/1.2720727; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND TECHNOLOGY; ATOMIC FORCE MICROSCOPY; CALIBRATION; DEPOSITION; DEPOSITS; NOISE; NONDESTRUCTIVE TESTING; SIMULATION; SURFACES; WATER

Citation Formats

Golovko, Dmytro S., Haschke, Thomas, Wiechert, Wolfgang, Bonaccurso, Elmar, Department of Simulation, University of Siegen, Am Eichenhang 50, 57076 Siegen, and Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz. Nondestructive and noncontact method for determining the spring constant of rectangular cantilevers. United States: N. p., 2007. Web. doi:10.1063/1.2720727.
Golovko, Dmytro S., Haschke, Thomas, Wiechert, Wolfgang, Bonaccurso, Elmar, Department of Simulation, University of Siegen, Am Eichenhang 50, 57076 Siegen, & Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz. Nondestructive and noncontact method for determining the spring constant of rectangular cantilevers. United States. doi:10.1063/1.2720727.
Golovko, Dmytro S., Haschke, Thomas, Wiechert, Wolfgang, Bonaccurso, Elmar, Department of Simulation, University of Siegen, Am Eichenhang 50, 57076 Siegen, and Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz. Sun . "Nondestructive and noncontact method for determining the spring constant of rectangular cantilevers". United States. doi:10.1063/1.2720727.
@article{osti_20953427,
title = {Nondestructive and noncontact method for determining the spring constant of rectangular cantilevers},
author = {Golovko, Dmytro S. and Haschke, Thomas and Wiechert, Wolfgang and Bonaccurso, Elmar and Department of Simulation, University of Siegen, Am Eichenhang 50, 57076 Siegen and Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz},
abstractNote = {We present here an experimental setup and suggest an extension to the long existing added-mass method for the calibration of the spring constant of atomic force microscope cantilevers. Instead of measuring the resonance frequency shift that results from attaching particles of known masses to the end of cantilevers, we load them with water microdrops generated by a commercial inkjet dispenser. Such a device is capable of generating drops, and thus masses, of extremely reproducible size. This makes it an ideal tool for calibration tasks. Moreover, the major advantage of water microdrops is that they allow for a nearly contactless calibration: no mechanical micromanipulation of particles on cantilevers is required, neither for their deposition nor for removal. After some seconds the water drop is completely evaporated, and no residues are left on the cantilever surface or tip. We present two variants: we vary the size of the drops and deposit them at the free end of the cantilever, or we keep the size of the drops constant and vary their position along the cantilever. For the second variant, we implemented also numerical simulations. Spring constants measured by this method are comparable to results obtained by the thermal noise method, as we demonstrate for six different cantilevers.},
doi = {10.1063/1.2720727},
journal = {Review of Scientific Instruments},
number = 4,
volume = 78,
place = {United States},
year = {Sun Apr 15 00:00:00 EDT 2007},
month = {Sun Apr 15 00:00:00 EDT 2007}
}
  • A direct method for the evaluation of the torsional spring constants of the atomic force microscope cantilevers is presented in this paper. The method uses a nanoindenter to apply forces at the long axis of the cantilever and in the certain distance from it. The torque vs torsion relation is then evaluated by the comparison of the results of the indentations experiments at different positions on the cantilever. Next, this relation is used for the precise determination of the torsional spring constant of the cantilever. The statistical analysis shows that the standard deviation of the calibration measurements is equal tomore » approximately 1%. Furthermore, a simple method for calibration of the photodetector’s lateral response is proposed. The overall procedure of the lateral calibration constant determination has the accuracy approximately equal to 10%.« less
  • No abstract prepared.
  • We describe a method to calibrate the spring constants of cantilevers for atomic force microscopy (AFM). The method makes use of a ''piezosensor'' composed of a piezoresistive cantilever and accompanying electronics. The piezosensor was calibrated before use with an absolute force standard, the NIST electrostatic force balance (EFB). In this way, the piezosensor acts as a force transfer standard traceable to the International System of Units. Seven single-crystal silicon cantilevers with rectangular geometries and nominal spring constants from 0.2 to 40 N/m were measured with the piezosensor method. The values obtained for the spring constant were compared to measurements bymore » four other techniques: the thermal noise method, the Sader method, force loading by a calibrated nanoindentation load cell, and direct calibration by force loading with the EFB. Results from different methods for the same cantilever were generally in agreement, but differed by up to 300% from nominal values. When used properly, the piezosensor approach provides spring-constant values that are accurate to {+-}10% or better. Methods such as this will improve the ability to extract quantitative information from AFM methods.« less
  • 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,more » 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.« less
  • There are many atomic force microscopy (AFM) applications that rely on quantifying the force between the AFM cantilever tip and the sample. The AFM does not explicitly measure force, however, so in such cases knowledge of the cantilever stiffness is required. In most cases, the forces of interest are very small, thus compliant cantilevers are used. A number of methods have been developed that are well suited to measuring low stiffness values. However, in some cases a cantilever with much greater stiffness is required. Thus, a direct, traceable method for calibrating very stiff (approximately 200 N/m) cantilevers is presented here.more » The method uses an instrumented and calibrated nanoindenter to determine the stiffness of a reference cantilever. This reference cantilever is then used to measure the stiffness of a number of AFM test cantilevers. This method is shown to have much smaller uncertainty than previously proposed methods. An example application to fracture testing of nanoscale silicon beam specimens is included.« less