ISO 11775:2015
(Main)Surface chemical analysis — Scanning-probe microscopy — Determination of cantilever normal spring constants
Surface chemical analysis — Scanning-probe microscopy — Determination of cantilever normal spring constants
ISO 11775:2015 describes five of the methods for the determination of normal spring constants for atomic force microscope cantilevers to an accuracy of 5 % to 10 %. Each method is in one of the three categories of dimensional, static experimental, and dynamic experimental methods. The method chosen depends on the purpose, convenience, and instrumentation available to the analyst. For accuracies better than 5 % to 10 %, more sophisticated methods not described here are required.
Analyse chimique des surfaces — Microscopie à sonde à balayage — Détermination de constantes normales en porte-à-faux de ressort
General Information
Standards Content (Sample)
INTERNATIONAL ISO
STANDARD 11775
First edition
2015-10-01
Surface chemical analysis — Scanning-
probe microscopy — Determination of
cantilever normal spring constants
Analyse chimique des surfaces — Microscopie à sonde à balayage —
Détermination de constantes normales en porte-à-faux de ressort
Reference number
©
ISO 2015
© ISO 2015, Published in Switzerland
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ii © ISO 2015 – All rights reserved
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Symbols and abbreviated terms . 2
5 General information . 4
5.1 Background information . 4
5.2 Methods for the determination of AFM normal spring constant . 5
6 Dimensional methods to determine k . 5
z
6.1 General . 5
6.2 k using formulae requiring 3D geometric information . 5
z
6.2.1 Method . 5
6.2.2 Measuring the required dimensions and material properties of the cantilever . 7
6.2.3 Determining k for the rectangular cantilever . 8
z
6.2.4 Determining k for the V-shaped cantilever . 8
z
6.2.5 k for the trapezoidal cross-sections . 9
z
6.2.6 k to account for coatings . 9
z
6.3 k using plan view dimensions and resonant frequency for rectangular
z
tipless cantilevers .10
6.3.1 Determining k .10
z
6.3.2 Uncertainty .11
7 Static experimental methods to determine k .11
z
7.1 General .11
7.2 Static experimental method with a reference cantilever .11
7.2.1 Set-up .11
7.2.2 Determining k .
z 12
7.2.3 Uncertainty .14
7.3 Static experimental method using a nanoindenter .15
7.3.1 General.15
7.3.2 Determining k for a tipped or tipless cantilever .15
z
7.3.3 Uncertainty .16
7.4 Measurement methods .18
7.4.1 Static deflection calibration.18
8 Dynamic experimental methods to determine k .18
z
8.1 General .18
8.2 Dynamic experimental method using thermal vibrations using AFM .18
8.2.1 Determining k .18
z
8.2.2 Uncertainty .20
Annex A (informative) Inter-laboratory and intra-laboratory comparison of AFM cantilevers .21
Bibliography .24
Foreword
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The committee responsible for this document is ISO/TC 201, Surface chemical analysis, Subcommittee
SC 9, Scanning probe microscopy.
iv © ISO 2015 – All rights reserved
Introduction
Atomic force microscopy (AFM) is a mode of scanning probe microscopy (SPM) used to image surfaces
by mechanically scanning a probe over the surface in which the deflection of a sharp tip sensing the
surface forces mounted on a compliant cantilever is monitored. It can provide amongst other data,
topographic, mechanical, chemical, and electro-magnetic information about a surface depending
on the mode of operation and the property of the tip. Accurate force measurements are needed for
a wide variety of applications, from measuring the unbinding force of protein and other molecules
to determining the elastic modulus of materials, such as organics and polymers at surfaces. For such
force measurements, the value of the AFM cantilever normal spring constant, k , is required. The
z
manufacturers’ nominal values of k have been found to be up to a factor of three in error, therefore
z
practical methods to calibrate k are required.
z
This International Standard describes five of the simplest methods in three categories for the
determination of normal spring constants for atomic force microscope cantilevers. The methods are
in one of the three categories of dimensional, static experimental, and dynamic experimental methods.
The method chosen depends on the purpose and convenience to the analyst. Many other methods may
also be found in the literature.
INTERNATIONAL STANDARD ISO 11775:2015(E)
Surface chemical analysis — Scanning-probe microscopy —
Determination of cantilever normal spring constants
1 Scope
This International Standard describes five of the methods for the determination of normal spring
constants for atomic force microscope cantilevers to an accuracy of 5 % to 10 %. Each method is in one
of the three categories of dimensional, static experimental, and dynamic experimental methods. The
method chosen depends on the purpose, convenience, and instrumentation available to the analyst. For
accuracies better than 5 % to 10 %, more sophisticated methods not described here are required.
2 Normative references
The following documents, in whole or in part, are normatively referenced in this document and are
indispensable for its application. For dated references, only the edition cited applies. For undated
references, the latest edition of the referenced document (including any amendments) applies.
ISO 18115-2, Surface chemical analysis — Vocabulary — Part 2: Terms used in scanning-probe microscopy
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 18115-2 and the following apply.
3.1
normal spring constant
spring constant
force constant
DEPRECATED: cantilever stiffness
k
z
quotient of the applied normal force at the probe tip (3.2) by the deflection of the cantilever in
that direction at the probe tip position
Note 1 to entry: See lateral spring constant, torsional spring constant.
Note 2 to entry: The normal spring constant is usually referred to as the spring constant. The full term is used
when it is necessary to distinguish it from the lateral spring constant.
Note 3 to entry: The force is applied normal to the plane of the cantilever to compute or measure the normal
force constant, k . In application, the cantilever in an AFM may be tilted at an angle, θ, to the plane of the sample
z
surface and the plane normal to the direction of approach of the tip to the sample. This angle is important in
applying the normal spring constant in AFM studies.
3.2
probe tip
tip
probe apex
structure at the extremity of a probe, the apex of which senses the surface
Note 1 to entry: See cantilever apex (3.3).
3.3
cantilever apex
end of the cantilever furthest from the cantilever support structure
Note 1 to entry: See probe apex (3.2), tip apex (3.2).
4 Symbols and abbreviated terms
In the list of abbreviated terms below, note that the final “M”, given as “Microscopy”, may be taken
equally as “Microscope” depending on the context. The abbreviated terms are:
AFM Atomic force microscopy
FEA Finite element analysis
PSD Power spectral density
SEM Scanning electron microscopy
SPM Scanning probe microsco
...
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