Surface chemical analysis — Atomic force microscopy — Guideline for restoration procedure for atomic force microscopy images dilated by finite probe size

This document describes a procedure for the quantitative characterization of the probe tip of an atomic force microscope (AFM) probe and a restoration of AFM topography images dilated by finite probe size. The three-dimensional shape of the probe apex is extracted by image reconstruction using suitable reference materials. This document is applicable to the reconstruction of AFM topography images of solid material surfaces.

Analyse chimique des surfaces — Microscopie à force atomique — Lignes directrices relatives au mode opératoire de restauration des images de microscopie à force atomique dilatées par la taille finie de la sonde

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Published
Publication Date
12-Jul-2022
Current Stage
6060 - International Standard published
Due Date
05-Feb-2022
Completion Date
13-Jul-2022
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ISO 23729:2022 - Surface chemical analysis — Atomic force microscopy — Guideline for restoration procedure for atomic force microscopy images dilated by finite probe size Released:13. 07. 2022
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INTERNATIONAL ISO
STANDARD 23729
First edition
2022-07
Surface chemical analysis — Atomic
force microscopy — Guideline for
restoration procedure for atomic force
microscopy images dilated by finite
probe size
Analyse chimique des surfaces — Microscopie à force atomique —
Lignes directrices relatives au mode opératoire de restauration des
images de microscopie à force atomique dilatées par la taille finie de
la sonde
Reference number
ISO 23729:2022(E)
© ISO 2022
---------------------- Page: 1 ----------------------
ISO 23729:2022(E)
COPYRIGHT PROTECTED DOCUMENT
© ISO 2022

All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may

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Published in Switzerland
© ISO 2022 – All rights reserved
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ISO 23729:2022(E)
Contents Page

Foreword ........................................................................................................................................................................................................................................iv

Introduction .................................................................................................................................................................................................................................v

1 Scope ................................................................................................................................................................................................................................. 1

2 Normative references ..................................................................................................................................................................................... 1

3 Terms and definitions .................................................................................................................................................................................... 1

4 Symbols (and abbreviated terms) ..................................................................................................................................................... 3

5 Mathematical morphology modelling ........................................................................................................................................... 3

6 Procedure of restoration of AFM topography images .................................................................................................. 4

6.1 General ........................................................................................................................................................................................................... 4

6.2 Calibration of measuring systems......................................................................................................................................... 4

6.3 Environment requirements ........................................................................................................................................................ 5

6.4 Extraction of probe tip shape using certified reference materials .......................................................... 5

6.5 Estimation of probe tip shape by blind reconstruction ..................................................................................... 5

6.6 Reference materials ........................................................................................................................................................................... 6

6.7 Probe shape characteristic and curvature radius .................................................................................................. 6

6.8 Validity test for topography image restoration ........................................................................................................ 6

Annex A (informative) Example studies .......................................................................................................................................................... 7

Annex B (informative) Results of interlaboratory comparison ...........................................................................................12

Bibliography .............................................................................................................................................................................................................................15

iii
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ISO 23729:2022(E)
Foreword

ISO (the International Organization for Standardization) is a worldwide federation of national standards

bodies (ISO member bodies). The work of preparing International Standards is normally carried out

through ISO technical committees. Each member body interested in a subject for which a technical

committee has been established has the right to be represented on that committee. International

organizations, governmental and non-governmental, in liaison with ISO, also take part in the work.

ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of

electrotechnical standardization.

The procedures used to develop this document and those intended for its further maintenance are

described in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the

different types of ISO documents should be noted. This document was drafted in accordance with the

editorial rules of the ISO/IEC Directives, Part 2 (see www.iso.org/directives).

Attention is drawn to the possibility that some of the elements of this document may be the subject of

patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of

any patent rights identified during the development of the document will be in the Introduction and/or

on the ISO list of patent declarations received (see www.iso.org/patents).

Any trade name used in this document is information given for the convenience of users and does not

constitute an endorsement.

For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and

expressions related to conformity assessment, as well as information about ISO's adherence to

the World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT), see

www.iso.org/iso/foreword.html.

This document was prepared by Technical Committee ISO/TC 201, Surface chemical analysis,

Subcommittee SC 9, Scanning probe microscopy.

Any feedback or questions on this document should be directed to the user’s national standards body. A

complete listing of these bodies can be found at www.iso.org/members.html.
© ISO 2022 – All rights reserved
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ISO 23729:2022(E)
Introduction

Atomic force microscope (AFM) is a method for imaging surfaces by mechanically scanning their

surface contours, in which the deflection of a sharp probe tip sensing the surface forces, mounted on a

compliant cantilever, is monitored. AFM belongs to a family of scanning probe microscope (SPM) and

is of increasing importance for the characterization of materials surfaces at the nanoscale. Therefore,

precise and quantitative measurement of three-dimensional (3D) surface topography at the nanoscale

by AFM is highly demanded by researchers and engineers in the various fields of academia and industry.

One of the imaging artefacts of AFM topography measurements is caused by the finite size and shape at

the apex of an AFM probe used for the scanning. Such a dilation effect due to the probe shape can cause a

significant error in the precise analysis of 3D surface morphology. Especially for the critical dimension

(CD) analysis of fine devices at the nanoscale, there is a need for probe-shape artefact to be corrected

in a reproducible and quantitative way. Thus, the demand for the establishment of an international

standard on the guideline for a reliable restoration procedure of dilated AFM images is high.

This document describes a quantitative procedure for the restoration of AFM height images dilated by

finite probe size and shape. It includes the quantitative characterization of AFM probe apex in use and

the restoration of AFM topography images using the actual probe shape.
© ISO 2022 – All rights reserved
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INTERNATIONAL STANDARD ISO 23729:2022(E)
Surface chemical analysis — Atomic force microscopy
— Guideline for restoration procedure for atomic force
microscopy images dilated by finite probe size
1 Scope

This document describes a procedure for the quantitative characterization of the probe tip of an atomic

force microscope (AFM) probe and a restoration of AFM topography images dilated by finite probe size.

The three-dimensional shape of the probe apex is extracted by image reconstruction using suitable

reference materials. This document is applicable to the reconstruction of AFM topography images of

solid material surfaces.
2 Normative references

The following documents are referred to in the text in such a way that some or all of their content

constitutes requirements of this document. For dated references, only the edition cited applies. For

undated references, the latest edition of the referenced document (including any amendments) applies.

ISO 11775, Surface chemical analysis — Scanning-probe microscopy — Determination of cantilever normal

spring constants

ISO 11952, Surface chemical analysis — Scanning-probe microscopy — Determination of geometric

quantities using SPM: Calibration of measuring systems

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.

ISO and IEC maintain terminology databases for use in standardization at the following addresses:

— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at https:// www .electropedia .org/
3.1
dilation

one of the two basic operators of mathematical morphology, whose basic effect on a binary image is to

gradually enlarge the boundaries of regions of foreground pixels
Note 1 to entry: The dilation (⊕) of a set A by a set B is defined as follows:
AB⊕= ()Ab+
bB∈

Note 2 to entry: By dilation, areas of foreground pixels grow in size while holes within those regions become

smaller.
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ISO 23729:2022(E)
3.2
erosion

one of the basic operators of mathematical morphology, whose basic effect on a binary image is to erode

away the boundaries of regions of foreground pixels
Note 1 to entry: The erosion (⊖) of a set A by a set B is defined as follows:
AB−= ()Ab−
bB∈

Note 2 to entry: By erosion, areas of foreground pixels shrink in size, and holes within those areas become larger.

3.3
mathematical morphology

theory and technique for the analysis and processing of geometrical structures, based on set theory,

lattice theory, topology, and random functions, which is commonly applied to digital images

Note 1 to entry: See Reference [4]
3.4
probe

structure at or near the end or apex if the cantilever designed to carry the probe tip (3.8)

[SOURCE: ISO 18115-2:2021, 5.109]
3.5
probe characterizer
tip characterizer

structure designed to allow extraction of the probe tip (3.8) shape from a scan of the characterizer

3.6
probe shape characteristic
PSC

relationship between the probe profile width and the probe profile length for a given probe projected

onto a defined plane
[SOURCE: ISO 13095:2014, 3.10]
3.7
probe shape function
PSF

matrix representing a three-dimensional shape of a probe tip (3.8) used for AFM imaging

3.8
probe tip
tip
probe apex

structure at the extremity of a probe (3.4), the apex of which senses the surface

[SOURCE: ISO 18115-2:2021, 5.120]
3.9
reconstruction

estimate of the sample’s (or tip’s) surface topography determined by removing from the image the effect

of the tip’s (or sample’s) shape and other measurement artefacts
[SOURCE: ISO 18115-2:2021, 5.132]
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ISO 23729:2022(E)
4 Symbols (and abbreviated terms)
The symbols and abbreviated terms are:
AFM Atomic force microscopy
I A function describing the measured topography image of a sample by AFM; z(x,y)
S A function representing the true topography image of a sample; s(x,y)
T A function representing the shape by a probe apex of AFM; t(x,y)

S A function representing the reconstructed topography image of a sample by AFM; s (x,y)

r r

P A function describing the reflection of the probe shape T through the origin; p(x,y) = -t(-x,-y)

P A function representing the reconstructed image of the reflected-tip shape; p (x,y)

r r
R Tip radius
⊕ A symbol representing a dilation operation in mathematical morphology
A symbol representing an erosion operation in mathematical morphology
5 Mathematical morphology modelling

For quantitative morphology imaging of nano-objects, it should be noted that significant distortion in

imaging may occur if the surface of a nano-object has large corrugation compared to the size and shape

[5]

of the probe tip . When the sample surface is relatively flat on the atomistic scale, it is suitable to

express the influence of the probe shape on the AFM topography imaging by the convolution integral

with the probe shape. On the other hand, when the unevenness or roughness of the sample surface is

somewhat larger than the atomic size, it is more appropriate to express the AFM imaging by dilation

which is one of the fundamental operators of mathematical morphology, where the location on the top

apex of a probe tip approaching closest to or making a point contact with the sample surface is most

important. Interaction from any other area which does not make any contact or near-contact with the

sample surface is not considered. The operation of dilation is expressed by Formula (1):

z(x, y) = max{ s(x’, y’) – t(x’ – x, y’ – y) } = max{ s(x’, y’) + p(x – x’, y – y’) } (1)

Here, I = z(x, y) is a function describing the measured image of the top surface of the sample, while

S = s(x, y) is a function representing the true surface morphology. Meanwhile probe shape function

T = t(x, y) represents the probe shape describing the surface of the probe tip, where the coordinates

of the topmost point of the tip are set as the origin. Finally, P = p(x, y) means –t(–x, –y), describing the

reflection of the probe shape T through the origin, which may refer to reflected tip. The relationship

between the sample S, tip T, image I, and the reflected tip P can be written using the dilation operation

⊕ as shown in Formula (2):
I = S ⊕ (-T) = S ⊕ P (2)

On the contrary, the reconstruction of the actual surface morphology from the measured AFM image

and the probe shape function is expressed as an erosion operation (⊖) in the concept of mathematical

morphology. The reconstructed surface morphology S = s (x, y) is described by Formulae (3) and (4):

r r

s (x,y) = min{ z(x’, y’) – p(x’ – x, y’ – y) } = min{ z(x’, y’) + t(x – x’, y – y’) } (3)

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ISO 23729:2022(E)
S = I ⊖ P (4)

It should be noted that S is the least upper bound on the actual surface, and not necessarily equal to S.

Since I = S ⊕ P,
SS⊇ (5)

By the processing of the dilation and erosion operations, while scanning the AFM probe of the finite

size, the measured and reconstructed AFM images can be expressed as shown in Figure 1. As described

by Formula (5), there exist non-reconstructable regions or hole regions where the tip of the probe

cannot reach due to its finite size. Therefore, S is the best reconstruction because it is the surface of the

deepest penetration with the probe tip.
Key
1 tip shape
2 AFM imaged surface
3 reconstructed surface
4 hole (non-reconstructable) region

Figure 1 — Mathematical morphology modelling for AFM topography imaging (dilation

processing) and image reconstruction (erosion processing)
6 Procedure of restoration of AFM topography images
6.1 General

This clause describes the general procedure for the recovery of dilated AFM topography images.

Firstly, the AFM topography images of the reference nanostructures with given shapes, dispersed on

flat substrates, are acquired. Then, the probe shape function of the apex of an AFM probe in use is

determined by the numerical calculation. Then, by erosion operation using the probe shape function,

the most probable surface morphology shall be extracted from the observed AFM topography image of

an unknown actual sample (see examples in Annex A).
6.2 Calibration of measuring systems

Calibration of the measuring systems used for AFM topography imaging shall be carried out using

certified standards with proper intervals. For example, the calibration of X-, Y- and Z-axes piezoelectric

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ISO 23729:2022(E)

scanners are primary prerequisite for the precise topography imaging by AFM. The calibration of the

lateral scan axes, or X- and Y-axes of the measuring system, shall be done with one-dimensional (1D) or

two-dimensional (2D) lateral standards. Calibration of Z-axis of AFM shall be done by using a set of step

height standards in accordance with ISO 11952.

The deflection sensitivity and normal spring constant of a cantilever probe used for the measuring

system shall be calibrated properly in accordance with ISO 11775.
6.3 Environment requirements

It is recommended that the measurement be performed in controlled and stable conditions with

the temperature stable within ±1 °C or better to minimize the drift of the measuring system. It is

also recommended to carefully measure the drift rate of the measuring system in accordance with

ISO 11039.
6.4 Extraction of probe tip shape using certified reference materials

It is possible to reconstruct the probe tip shape of a force sensor from AFM topography images of

certified reference materials called a probe characterizer (or a tip characterizer), whose actual surface

morphology, I is well characterized. Using erosion operati
...

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