Plasma and Fusion Research: Regular Articles

Volume 14, 3402049 (2019)

Characterization of He Induced Nanostructures
Using SEM Image Analysis∗)
Hirohiko TANAKA, Shin KAJITA1) and Noriyasu OHNO
1)

Graduate School of Engineering, Nagoya University, Chikusa-ku, Nagoya 464-8603, Japan
Institute of Materials and Systems for Sustainability, Nagoya University, Chikusa-ku, Nagoya 464-8603, Japan(Received 26 December 2018 / Accepted 3 February 2019)

Helium induced nanostructures on tungsten were characterized by applying basic statistical analysis techniques to scanning electron microscope (SEM) images. As the analysis targets, pinhole- and fuzz-dominantsurfaces irradiated with diﬀerent ion fluences were employed. Although two-dimensional Fourier analysis of thenormalized brightness of SEM images clarified several characteristic features, their diﬀerences are small to distinguish the dominant nanostructures. On the other hand, probability density functions (PDFs) of the normalized
brightness indicate that hole- and fuzz-dominant surfaces have long tail and Gaussian-like shape, respectively. By
using several indexes with considering the black and white saturation, it was found that kurtosis and KullbackLeibler divergence could provide reasonable judgement as the characterization index.
c 2019 The Japan Society of Plasma Science and Nuclear Fusion ResearchKeywords: image analysis, statistical analysis, SEM, two-dimensional fast Fourier transform, probability density
function, kurtosis, Kullback-Leibler divergence, pinhole, fuzz
DOI: 10.1585/pfr.14.3402049

1. Introduction
Tungsten (W) is thought to be the most promising material for the divertor target that should be irradiated withthe high heat and particle fluxes in future magnetic fusion
devices. From past researches, although W has quite low
sputtering rate, helium (He) plasma irradiation could provoke several kinds of surface modifications such as bubbles, pinholes, and fiberform nanostructures called fuzz,even if the incident ion energy was much smaller than the
sputtering threshold [1]. Up to now, the fuzz-formation
condition was deeply investigated and was found to bestrongly related to the incident ion energy, surface temperature, and ion fluence [2]. Fuzzy nanostructure changes
several surface physical characteristics, e.g., high light absorptivity [3] and large surface area [4] due to an increaseof the porosity [5]. Further, similar nanostructures are also
found to be formed on other metals such as iron [6], vanadium [7], platinum, and so on [8–10]. In order to utilize theunique characteristics of the fuzzy surface for an industrial
application field, morphology-change conditions of several
metals are energetically being surveyed.
The novel growth process of fuzzy structure has been
attracted attention from modeling perspective. Density
functional theory (DFT) and molecular dynamics (MD)were used for the nucleation of He clusters and bubbles anddislocation formation [11–14], and morphology changes
were demonstrated using multi-scale simulations by theauthor’s e-mail: h-tanaka@ees.nagoya-u.ac.jp∗) This article is based on the presentation at the 27th International Toki
Conference (ITC27) & the 13th Asia Pacific Plasma Theory Conference(APPTC2018).

combination of MD and Monte Carlo (MC) simulations[15, 16]. Even though those simulations still have a challenging issue that they can only deal with a limited timeand space, formations of initial protrusion and short finestructures were demonstrated.
To bridge the experiments and simulation, it is necessary to compare the grown structure quantitatively; fractal analysis has been conducted using scanning electron microscope (SEM) micrographs, transmission electron microscope (TEM) micrographs, and gas adsorption
isotherms [17–19]. It was found that initially formed pinholes have a fractal feature in the size-number relation andthe fuzzy structure has a multi-fractal feature. It is of interests to further develop method to extract the specific characteristics of fuzzy structures grown by He plasma irradiation.
In this study, we applied basic statistical analysis techniques based on two-dimensional (2D) fast Fourier transform (FFT) and probability density function (PDF) to SEM
images. As the He ion fluence increases, the fuzzy surface
was formed with accompanying changes of several statistical features. By introducing characterizing statistics and ameasuring scale of PDFs, pinhole- and fuzz-dominant images were distinguished. Such techniques are easy to apply. Thus, these techniques could be easily shared among
researchers and would be utilized for the parameter survey
from a number of samples.
In Sec. 2, analyzed SEM images will be explained.
Then, these images will be analyzed in Sec. 3. Finally, thisstudy will be summarized in Sec. 4.

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c 2019 The Japan Society of Plasma
Science and Nuclear Fusion Research

Plasma and Fusion Research: Regular Articles

Volume 14, 3402049 (2019)

Fig. 1 Analyzed SEM images of W samples: (a) W1, (b) W2,and (c) W3. Insets show magnified figures with the color
scale from μ − 1.5σ to μ + 1.5σ.

2. Analyzed SEM Images
We analyzed three W samples irradiated with He
plasmas at diﬀerent fluences in the linear plasma device
NAGDIS-II [19]. Figure 1 shows the analyzed SEM images: W1, W2, and W3, which are viewed from the normal
direction to the surface. The He ion fluences of W1, W2,
and W3 are 6 × 1024 , 1.8 × 1025 , and 4.7 × 1025 m−2 , respectively. Sample information and irradiation conditions
are summarized in Table 1 of Ref. [19]. On W1 surface,a number of pinholes can be found. As increasing the fluence, thicker convex structures appear in addition to pinholes (see Fig. 1 (b)), and then, fuzzy nanostructure covers
the surface (see Fig. 1 (c)).
Brightness (I) of these images is 8-bit grayscale whichhas 256 tonal steps from I = 0 (black) to 255 (white). The
analyzed size of each image is 1080 pixels in vertical direction and 1600 pixels in horizontal direction.

3. Image Analyses
As the basic technique for the image analysis, 2D FFTand PDF analyses were applied. For analyzing SEM images, it should be taken into account that the mean of theFig. 2 2D power spectra of In of (a) W1, (b) W2, and (c) W3
along kh and kv .

brightness and the contrast can be changed depending on
SEM devices, and beam and detector settings. Furthermore, saturations in the brightness can occur dependingon the settings.
In this study, to minimize the eﬀects, the normalized
brightness, In ≡ (I −μ)/σ, was used for the analyses, where
μ and σ are the mean and the standard deviation of I in
all pixels, respectively. Eﬀects from the black and whitesaturation for 2D FFT and PDF analyses will be discussed
later. Insets in Fig. 1 are magnified images with the color
scale from μ−1.5σ to μ+1.5σ. Their characteristic featuresassociated with the analyses will be discussed in Sec. 3.1.

3.1 2D FFT
2D FFT analysis is widely used for identifying the
crystalline nature particularly on TEM images [20, 21].
We investigated whether the 2D FFT analysis could finda dominant nanostructure from SEM images.
Figures 2 (a, b, c) shows 2D power spectra of In of
W1, W2, and W3. Before the application of the 2D FFT,
Hanning window was applied to minimize the edge effect. Horizontal and vertical axes indicate the wave numbers, kh and kv , along horizontal and vertical axes in Fig. 1,

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Volume 14, 3402049 (2019)respectively. Because a 2D power spectrum has a point
symmetric profile, kv < −20 µm−1 range is not displayedin Figs. 2 (a, b, c).
At around (kh , kv ) ∼ (±3, 0) µm−1 in Fig. 2 (a), there
are unemphatic small peaks, indicating that there is avertical-stripe component with a characteristic length of∼1/3 µm. Actually, in the inset in Fig. 1 (a), concavoconvex structures seem to be elongated not in the horizontal direction but in the vertical direction. This would reflect
a stripe formation on single crystal W surfaces in the initial
phase of He plasma irradiation [22]. In addition, profile ofthe 2D power spectrum of W3 seems to be slightly elongated to the kh kv > 0 direction, implying that characteristic
length in the right oblique direction is slightly shorter thanthat in the left oblique direction. However, in any case, thespectral shape roughly looks like a concentric pattern.
Figure 3 (a) is azimuthally averaged power spectra ofFigs. 2 (a, b, c) along k = (kh2 + kv2 )1/2 . A little convex of
W1 at k ∼ 3 µm−1 is attributed to the above-mentioned
vertical-stripe structures. A shoulder of W1 exists at
k ∼ 10 µm−1 = (0.1 µm)−1 , and the wave number corresponds to the inverse of the typical diameter of pinholes(∼0.1 µm) shown in the inset in Fig. 1 (a). Such shoulder is observed when similar-size structures are nonperiodically distributed [23]. Thus, it is found that pinholes
are distributed nonperiodically. The power spectra of W3
has large component at smaller k range, indicating that thefuzz forms a larger-scale rough surface compared with thetypical size of pinholes on W1. Actually, submicrometer
structures can be found in the inset in Fig. 1 (c). Theselarger-scale structures have no periodicity, because there isno spectral peak. The power spectrum of W2 looks like anintermediate between power spectra of W1 and W2. This

Fig. 3 Azimuthally averaged power spectra of (a) In and (b) artificially saturated and then normalized In of W1 (solid),
W2 (dashed), and W3 (dotted) along k.

would be caused by the coexistence of pinholes and initialstructures of fuzz.
In order to investigate the eﬀect from the black andwhite saturation for these power spectra, artificially saturated images were analyzed. In this calculation, pixels
with I less than μ − 1.5σ and over than μ + 1.5σ were replaced with −1.5σ and 1.5σ values, respectively. These artificially saturated images, which correspond to the insets
in Fig. 1, were normalized again and then analyzed withthe 2D FFT. Figure 3 (b) shows the power spectra of theartificially saturated images. There is no clear diﬀerence
between Fig. 3 (a) and Fig. 3 (b), indicating that a certain
level of the black and white saturation is not a problem forthe 2D FFT analysis.
From the analysis results, we found several characteristic features in three samples. However, because pinholes
and fuzz have no periodicity, it is not easy to distinguishthese structures from 2D FFT analysis.

3.2 PDF
Next, we applied the PDF analysis. Figure 4 shows
histograms of brightness I of three samples. They havepeaks near the middle of the 256 tonal steps. Histograms ofW1 and W3 become quite small at both ends. On the other
hand, the histogram of W2 has small peaks at I = 0 and
255, being attributable to the black and white saturation.
Because the edge peaks largely aﬀect the below-mentioned
PDF analysis result in contrast to the power spectra, bothends of all histograms (∼2% in each end) were removed
before the following analysis.
Figure 5 is semilogarithmic plots of PDFs as a function of In . Integration of each PDF is equal to unity. PDF
tails are located within the range of −5 ≤ In ≤ 5 except fora tail with a small amplitude in positive In region of W1. In
each figure, the standard Gaussian distribution (μ = 0 and
σ = 1) is overplotted as a reference.
We can find significant diﬀerences between Figs. 5 (a,b) and Fig. 5 (c). The PDFs of W1 and W2 have tails in
the negative In region with large amplitudes due to the existence of pinholes, which have darker colors (In < 0). The

Fig. 4 Histograms of brightness of W1 (solid), W2 (dashed),
and W3 (dotted).

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Fig. 6 (a) Skewness and (b) kurtosis of W1 (solid), W2(dashed), and W3 (dotted) as a function of Ins .

Fig. 5 PDFs of (a) W1, (b) W2, and (c) W3 as a function of thenormalized brightness. Black dashed lines indicate thestandard Gaussian distribution.

PDFs of W1 and W2 in the positive In region have also
larger amplitudes compared with the Gaussian distribution.
This is mainly caused by brighter regions from the edge of
pinholes and convex structures, because SEM image hashigher brightness at the edge of structures due to secondary
electron emissions from the edge face. In contrast, the
PDF of W3 has no long tail and resembles the Gaussian
shape due to the complicated fuzzy nanostructures. From
Fig. 5, it is suggested that pinholes and fuzz could be distinguished by comparing the PDF with the Gaussian distribution.
For characterizing a PDF, skewness (S ) and kurtosis(K) are convenient indexes and often used in edge plasma
field [24]. They are defined by (I − μ)3
=
In3 ,
(1)
S ≡
3
σ


 
(I − μ)4− 3 = In4 − 3,
(2)
K≡
4
σ
where   means an average. Since the Gaussian distribution has S = K = 0, S and K values are utilizable forcomparison with the Gaussian. If a PDF had a large amplitude at positive/negative In tail region, S became positive/negative. Thus, the sign is important for S . On theother hand, positive and/or negative longer tail comparedwith the Gaussian produces K > 0. Shorter tails in positive
and negative directions make K negative.
Because the tail components are important for S andK calculations, the eﬀect from the black and white saturation should be taken into account. In order to confirm
whether these statistics could be utilized quasi-universallyfor SEM images, sensitivities of S and K against the saturation were investigated by artificially limiting the In range.
In the following, signals satisfying |In | > Ins were removed
and a normalized brightness was then recomputed before
the S and K estimations by introducing a saturation magnitude Ins .
Figure 6 shows the skewness and kurtosis as a function of Ins . At Ins = 5, where almost all data was used, S of
W1 is the largest in the three samples (see Fig. 6 (a)). Aschanging Ins , S of W1 maintains the largest, while sign ofS switches on W2 and W3 samples. Considering the sensitivities of S -sign on Ins , discrimination of surface nanostructures seems to be diﬃcult from S . On the other hand,
K of W1 and W2 are larger than that of W3 for all Ins cases.
Furthermore, except for small Ins cases, K of W1 and W2
are positive and that of W3 is negative. This is caused byexistence/nonexistence of the PDF tail. Therefore, K is apossible candidate for the characterization index.
As a diﬀerent candidate, Kullback-Leibler divergence(KLD) [25] is considered to compare the PDF with theGaussian. The KLD is a famous scale for measuring difference between two PDFs in probability and information
theory fields and is also called “information divergence”
and “relative entropy”. In plasma field, KLD was applied
to turbulent signals [26]. The KLD (DKL ) of a PDF (P)against a diﬀerent PDF (Q) distributing on the In axis isdefined as follows:

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Fig. 7 DKL (PSEM , G) of W1 (solid), W2 (dashed), and W3 (dotted) as a function of Ins .

AcknowledgementsP(In )DKL (P, Q) ≡P(In ) logdIn .
Q(In )−∞
 ∞ages, respectively, as if a certain level of brightness is saturated. Further, Kullback-Leibler divergence clearly indicates a resemblance with the Gaussian. In order to distinguish pinhole- and fuzz-dominant SEM images, the kurtosis and the Kullback-Leibler divergence would be useful.
For future work, it is of interests to apply the abovementioned techniques to a number of SEM images withvarious nanostructures. Application of such characterization indexes would make it easy for researchers to survey
parameter dependences. Further, above techniques could
be applied to surfaces made in a computer simulation.

(3)

The DKL value is nonnegative, and DKL becomes zero
when P and Q are the same. Although the KLD is also
called “KL distance”, this is not a distance function, because DKL (P, Q)  DKL (Q, P).
In order to compare between a PDF from a SEM
image (PSEM ) and the Gaussian (G), DKL (PSEM , G) andDKL (G, PSEM ) can be calculated. Ideally, integration range
in Eq. (3) is from −∞ to ∞. However, far-edge tails are notacquired in a PDF from a SEM image due to the limited
tonal range. Because P log(P/Q) = 0 and ∞ when P = 0
and Q = 0, respectively, DKL (PSEM , G) has a finite valueand DKL (G, PSEM ) becomes infinity if the integration range
contains a PSEM = 0 region. Therefore, DKL (PSEM , G) was
only calculated as a function of Ins , as shown in Fig. 7. Before the DKL calculation, signals satisfying |In | > Ins were
removed, and then the integral of the PSEM was calibrated
to be unity. In all Ins range, DKL (PSEM , G) of W3 is muchsmaller than those of W1 and W2. Thus, DKL (PSEM , G)
could be used for distinguish SEM images.

4. Summary
In order to characterize He induced nanostructures, weapplied two basic analysis techniques to SEM images: 2D
power spectrum and probability density function. To minimize the eﬀects from the diﬀerences in contrast and brightness levels of SEM images, the normalized brightness wasanalyzed with taking into account of the black and whitesaturation.
From the 2D power spectra, nondirectional and nonperiodic features of pinholes and fuzz are found. Because
diﬀerences of these spectra are not significant, this method
would be inadequate for distinguishing pinhole- and fuzzdominant structures with the non-periodic nature.
In contrast, probability-density-function shapes calculated from the brightness have a significant diﬀerence between pinhole- and fuzz-dominant surfaces. The former
surface has long tails in the PDF, while latter surface has
a Gaussian-like shape. As a result, positive and negative
kurtosis are observed in pinhole- and fuzz-dominant im-

This research was supported by JSPS KAKENHI(16H06139), a grant from the Hibi Science Foundation,and the NINS program of Promoting Research by Networking among Institutions (01411702).
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