ISO 23729:2022

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

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ISO 23729:2022(E)
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© ISO 2022
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Published in Switzerland
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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
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ISO 23729:2022(E)
Foreword
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This document was prepared by Technical Committee ISO/TC 201, Surface chemical analysis,
Subcommittee SC 9, Scanning probe microscopy.
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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.
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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)
r
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ISO 23729:2022(E)
S = I ⊖ P (4)
r
It should be noted that S is the least upper bound on the actual surface, and not necessarily equal to S.
r
Since I = S ⊕ P,
SS⊇ (5)
r
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
r
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
...