Growth of fiberform nanostructures on metal surfaces by helium plasma irradiation

Since helium (He) atoms are one of the by-products of nuclear fusion reaction (nuclear fusion between deuterium and tritium), interaction between He ions and materials, tungsten (W) in particular, has been investigated experimentally, because W is the most plausible candidate material for divertor in fusion devices, where the heat load is concentrated. Initially, investigations had been done using high energy ion beams. Formation of high density He bubbles has been identified on W after the irradiation with 8 keV $He +$ ions¹ even when the He ion fluence, $Φ He$⁠, was less than $10 21 m − 2$⁠. This could be understandable because the energy was greater than the threshold energy of He for the displacement of W atoms. Later, it was found that He bubble growth can occur even when the incident ion energy, $E i$⁠, is much lower than the sputtering threshold, and the necessary energy for the bubble formation is shown to be less than 10 eV.² 

The surprising thing is that when certain conditions for, $E i$⁠, $Φ He$⁠, and the surface temperature, $T s$⁠, are satisfied,^3,4 fiberform nanostructures are formed, and the surface becomes completely black. It is noted that the conditions are likely to be met under the strike point in the divertor. Figures 1(a) and 1(b) show cross-sectional scanning electron microscope (SEM) micrographs of W fiberform nanostructures. The fiberform nanostructure is called fuzz. As shown by a transmission electron microscope (TEM) image in Fig. 1(c), the width of the nanostructure is several tens of nm and contains many He bubbles inside the fibers.¹⁴⁶ The size of He bubbles is less than 20–30 nm in diameter, and the size of bubbles and width of fibers are known to increase as increasing the surface temperature.^5,6

It has been revealed that the formation of fuzz changes various physical properties. The porosity of the fuzzy layer was measured by measuring the mass and thickness of the fuzzy layer.⁷ The porosity increases with increasing $Φ He$⁠, and it becomes about 95% when the thickness of the fuzzy layer, $h fuzz$⁠, is about 3  $μ$m. It was also found that the density of fuzzy layer is not uniform but it gradually decreases in the height direction.⁸ The surface area increases by the formation of fuzz and reaches 20–30 times higher than that of a flat surface when $h fuzz$ is several $μ$m.⁹ In terms of the interaction of particles (ions and electrons), the sputtering rate decreases by about an order of magnitude,⁷ particle reflectivity decreases, resulting in an increase in the power transfer coefficient;¹⁰ secondary electron emission (SEE) decreases by about 50% and is reported to be uncorrelated with the direction of electron bombardment.¹¹ In addition, the field electron emission is found to increase significantly compared to the unirradiated surfaces, and the field enhancement factor is confirmed to increase to $∼$1000.^12,13 The work function increases by about 0.5 eV.¹⁴ The thermal conductivity, which determines the interaction with heat, was found to decrease by at least two orders of magnitude from the thermoreflectance method.¹⁵ Other than that, the optical reflectance decreased to almost zero from ultraviolet (UV) to near infrared (NIR) (more than 99%),¹⁶ and the optical emissivity increased as a result.¹⁷ 

These material property changes raise concerns for the material lifetime in nuclear fusion reactors, because the erosion processes become complicated by the existence of fuzz. Fuzz growth is a particular concern in fusion devices from a perspective of long-term operation, because it may occur on the divertor for a short period of time, i.e., within less than an hour. Therefore, extensive studies have been performed on W because of the interest in fusion research. On the one hand, there are several positive aspects as plasma facing components in fusion reactors. The decrease in the sputtering yield decreases the erosion by sputtering. In addition, it has also been found that the crack formation due to intermittent heat loading is inhibited by the formation of fuzz.¹⁸ On the other hand, the formation of fuzz can have a significant negative effect on thermal responses. Since the thickness of the nanostructures is only a few micrometers at most, the surface temperature does not increase with a steady heat load. However, intermittent heat loads can lead to significant differences between temperature responses with and without the fuzzy layer. Pulsed laser irradiation experiments on fuzz in vacuum (a pulse width of $∼$0.5 ms)¹⁹ and on fuzz simultaneously irradiated with pulsed or steady state plasma²⁰ showed that melting traces on the surface with an excessive surface temperature increase. In addition to an anomalous temperature rise and melting, the frequency of arcing increases when the surface is covered with fuzz.^21,22 An arcing on a material that is exposed to plasmas is called unipolar arc, because it occurs between a material (cathode) and the plasma, unlike the usual arcing that occurs between a cathode and an anode. When a localized arcing occurs, a large amount of W is emitted, which can cause significant damage to materials and may also be a source of impurities in fusion reactors. In particular, since fuzz is extremely fragile mechanically, it can form dusts and droplets as was observed in response to ignition of arcing,²³ which is a major concern for the reactor operation.

As mentioned above, fuzz is an important issue in nuclear fusion research. Figures 2(a) and 2(b) show the number of fuzz related publications per year and journal, respectively. It is noted that there are relevant papers that are not included in Fig. 2. For example, since the term fuzz has not been used commonly before 2010, the number of publications is almost zero, although there are several important relevant papers. However, we can see the trend of the number of fuzz related publications here. The number of relevant published papers began to increase around 2010, with 80–100 papers published annually since 2017. Mainly, the research field is in the nuclear material researches and relevant basic material researches published in such as Journal of Nuclear Materials, Nuclear Fusion, and Nuclear Material and Energy. In addition, since it is expected to be used also for various applications, there are several dozen papers published in applied physics field such as in Journal of Applied Physics and Applied Surface Science.

In this Tutorial, we will focus on fuzz and discuss our understanding to date and the issues that need to be solved in the future. We also present applications of fuzz as gas sensors and photocatalysts. In Sec. II, we first show fuzz growth on W, mainly because there are extensive experimental studies on W. Section III discusses fuzz on W alloys and various metals, and Sec. IV summarizes modeling and simulation works up to date. Then, open issues and future prospects of fuzz are discussed.

TEM micrographs of W samples exposed to He plasmas with different $Φ He$ are shown in Fig. 3(a) (⁠ $0.6× 10 25 m − 2$⁠) to Fig. 3(e) (⁠ $5.5× 10 25 m − 2$⁠).¹⁶ It is seen that $h fuzz$ increases with $Φ He$⁠. Initially, rough structures are formed on the surface. The surface top layer (⁠ $∼$100 nm thick) is fully packed with He bubbles [Fig. 3(a)], followed by the formation of protrusions [Fig. 3(b)]. Then, fiberform nanostructures are started to be observed from Fig. 3(c). From thermal desorption spectroscopy (TDS), He content in fuzz was estimated to be He/W = (13 $±$4)at.%.²⁴ It is believed that the formation and growth of He bubbles are the key process for the growth of fuzz. As shown in a schematic of Fig. 4, the growth of bubbles formed protrusions, and swelling process due to the inclusion of He atoms and bubbles with increasing the porosity is likely related to the initial growth process. The details of the growth process will be discussed later in Sec. IV.

From experiments in the linear plasma devices NAGDIS-II and PISCES-B, it has been shown that $T s$ and $E i$ are important conditions for the fuzz growth. Figure 5 summarizes the growth condition of fuzz in terms of $T s$ and $E i$⁠. The gray colored area and hatched area represent the conditions where fuzz growth and bubble growth are identified, respectively. In Fig. 5, bubbles mean pinholes observed on the surface rather than nanobubbles observed by TEM. The fuzz formation requires $T s$ of 1000–2000 K and $E i$ of greater than or equal to 20–30 eV. Another important parameter is $Φ He$⁠, and Fig. 6 shows the summary of $h fuzz$ vs $Φ He$ organized by Petty et al.²⁵ It has been shown experimentally that $h fuzz$ is proportional to the square root of $Φ He$⁠,²⁶ suggesting that some diffusion-like process limits the growth of the fuzz layer. Also, by plotting $h fuzz$ as a function of $Φ He$⁠, it was revealed that the intersection point with the horizontal is not always zero, indicating the existence of an incubation fluence (typically $Φ He , 0=2.5× 10 24 m − 2$⁠) that precedes the fuzz growth.²⁷ It is noted that fuzz growth has been reported not only from high density (⁠ $> 10 18 m − 3$⁠) linear plasma devices, but also from magnetron sputtering devices, where the plasma density is lower.²⁸ A difference from the higher density devices is in the fact that fuzz was identified even when $Φ He$ is lower than or comparable to the incubation fluence of $Φ He , 0=2.5× 10 24 m − 2$ in magnetron sputtering devices.²⁹ 

In the initial phase of the morphology changes, i.e., when the fluence or the energy of the incident ions is low, dependence on the crystal orientation of the fuzz growth can be detected, although no clear dependence remains when fuzz is fully grown. Ohno et al. investigated the initial morphology changes and crystal orientations by the combination of electron backscatter diffraction (EBSD) and SEM observation,³⁰ as shown in Fig. 7. In Ref. 30, $E i$ was chosen to be 25 eV, which is close to the threshold energy for the fuzz growth. Clear wavy structures were found on the {101} face, while the surface was kept flat on {102}, {407}, and {203} faces with pinholes on the surface. Similar results were reported by Parish et al. using SEM-EBSD,³¹ in which morphology changes on W exposed to a He plasma up to a He fluence of $4× 10 24 m − 2$ at $T s=1130 °$C were investigated around the {001} plane. They categorized the morphology changes to smooth, pyramidal, wavy and terraced, and revealed the relation between the types of morphology changes and crystal orientation. It was shown that pyramids were formed near- $⟨001⟩‖$normal direction (ND) grains, wavy/terraced were formed near $⟨114⟩$ to $⟨112⟩‖$ND grains, and the surface remained smooth near $⟨103⟩‖$ND grains.

The difference between Refs. 30 and 31 appeared on the {001} plane, where wavy and pyramid structures were observed, respectively. In another report, He irradiation on single crystal W showed that initial morphology changes on {001} plane was less than that on the {101} plane.³² Near-{001} planes, the morphology change was different (flat, pyramidal, and wavy). One clue is in the dependence of crystal orientation on the interval of undulation formed at temperatures below the threshold temperature for fuzz formation studied in detail by Sakamoto et al.^33,34 It was found that the crests of undulation align with the $⟨100⟩$ direction. In other words, the {001} plane can be more stable than the other planes. At the moment, it is not yet clear how these morphology change occur, though slip and adatom diffusion are candidates for this.

Crystal orientation of isolated nano-tendrils from W fuzz has been investigated using transmission Kikuchi diffraction.³⁵ It was shown that there was no preferential crystal orientation in the long axis (growth direction) for W fuzz. However, the preferential growth direction was identified on rhenium (Re) and ruthenium (Ru) fuzz.³⁶ On Re and Ru fuzz, fibers have no bifurcation, and curved wires grew $c$-axis direction in a hexagonal closed packed (HCP) crystal structure.

There are processes that counteract the growth of fuzz: sputtering and high-temperature annealing. The sputtering yield decreases by an order of magnitude when fuzz is formed on the surface,⁷ as mentioned in introduction, probably because the sputtered atoms are trapped again by the fuzzy structure. However, since the growth rate continuously decreases with increasing $h fuzz$⁠, while sputtering rate does not decrease more than one order of magnitude, the effective growth rate approaches zero. The saturation in fuzz growth can be clearly identified especially when the sputtering effect is significant. The threshold energy for He ions to sputter W atoms is approximately 105–110 eV.³⁷ The saturation thickness is determined by the balance between the growth rate and the sputtering yield³⁸ and decreases from 7 to 8  $μ$m at 200 eV to less than 1  $μ$m at 400 eV.³⁹ It could be changed if the prompt redeposition of sputtered particles would occur.⁴⁰ It is noted that the sputtering can also occur even when $E i<100$ eV. Petty et al. discussed that a small amount of background impurity, which can be usually neglected, cannot be neglected to determine the thickness²⁵ when $Φ He$ is significantly greater than $10 27 m − 2$⁠.

Another process that counteracted fuzz growth is the thermal annealing process. It has been found that fuzz can be reintegrated to surface even at temperatures much lower than the melting point of 3700 K.^41–43 Typically, a 500-nm-thick fuzzy layer was reintegrated to the surface by a 30-min thermal annealing at a temperature of $∼$1400 K. The annealing rate exponentially increases with the annealing temperature. De Temmerman et al. summarized the available experimental data and modeled the annealing rate with double exponential Arrhenius-type functions.⁴⁴ It was shown that trends of the temperature dependence of the annealing rate change around $∼$1550 K. Even without erosion by sputtering, the thickness saturates by the equilibrium between the growth rate and the annealing rate.⁴⁵ In a fusion reactor environment, annealing during the transient heat load accompanied by instabilities called edge localized modes (ELMs) can be influential for the saturation fuzzy layer thickness.⁴⁴ 

Woller et al. discovered that large-scale structures of tens of micrometers in size, called nano tendril bundles (NTBs), can be formed by He irradiation.⁴⁶ They discussed that the radio frequency (RF) bias of the target and the broad ion energy are related to the growth process. Furthermore, NTBs were found to form (Fig. 8) when a small amount of impurity, such as argon, neon, and nitrogen, was added to He gas, suggesting that the redeposition of W released by sputtering is important.^47,147 The role of impurity in the growth of a large-scale structure 10- $μ$m in size has also been discussed with the existence of small amount of carbon (0.01%).⁴⁸ Woller et al. made a comparison between EBSD images and SEM and optical micrographs of the samples that has two separate regions where full fuzz growth and NTB growth are dominant, respectively.⁴⁹ They showed that NTB growth occurs easier on the surface that has {101} than the surface with other orientations. It was discussed that the results supported surface diffusion or W adatom mobility enhanced by ion bombardment plays a key role in the NTB formation.

It has been revealed that the NTBs significantly decrease the onset electric field of the field electron emission and increase the field electron emission current.⁵⁰ Because the field electron emission can lead to the initiation of unipolar arcing,⁵¹ understanding of growth process of NTB will be important for fusion experiments.

In addition, in recent years, it has been found that fuzz grows at orders of magnitude higher rates than the normal growth rate during He irradiation with metal atoms/ions deposition, and visible fuzzy nanostructures with a thickness of about 1 mm are formed after about 30–60 min of irradiation.⁵²  Figures 9(a) and 9(b) show an optical micrograph and an SEM image of the large-scale fiberform nanostructures (LFNs). It can be seen that fiberform nanostructures with a width of several tens of nm are intertwined to form the large-scale structure. This result suggests that the presence of metal atoms deposited on the surface causes the growth of LFNs via different process and growth rate than conventional fuzz.

Enhanced growth of fuzz with auxiliary W deposition has also been identified in a magnetron sputtering device⁵³ in addition to linear plasma devices.^54,55 The thickness of fuzzy layer does not follow the square root of $Φ He$ anymore with additional deposition. In the magnetron sputtering device, 8- $μ$m-thick fuzz was formed when $Φ He$ was less than $10 25 m − 2$⁠. Considering that such thick fuzzy layer can be formed only when $Φ He$ is $∼ 10 27− 10 28 m − 2$ in pure He plasmas,²⁵ one can say that additional deposition increases the growth rate by orders of magnitudes. On LFNs shown in Figs. 9(a) and 9(b), the structures grew not mainly in the height (normal to the surface) direction but in the surface direction (parallel to the surface) after the height reached 0.1 mm, which corresponded to the sheath thickness, and the growth rate in the surface direction was estimated to be $∼$7  $μ$m/s.⁵⁶ It is noted that the growth rate does not saturate nor decrease with $Φ He$⁠.

Figure 10 summarizes the thickness or height of nanostructures grown in He plasmas. For conventional fuzz, the thickness increases with square root of $Φ He$ and saturates probably because of sputtering. The thickness could not exceed 10  $μ$m even if $Φ He$ was greater than $10 27 m − 2$⁠. The height of NTBs is 10–40  $μ$m when $Φ He$ is the order of $10 25 m − 2$⁠. With auxiliary deposition, the thickness reached $∼$7  $μ$m at $Φ He∼ 10 26 m − 2$ in Magnum-PSI⁵⁴ and 8  $μ$m at $Φ He∼ 10 25 m − 2$ in a magnetron sputtering device.⁵³ When LFN growth occurred, the height reached 200  $μ$m in the initial phase of deposition experiments (LFN growth) even at $Φ He$ of $10 25 m − 2$⁠. The thickness reached 1 mm when $Φ He$ was $4× 10 25 m − 2$⁠. The growth of LFNs was identified when the W/He ratio was greater than 0.04%, and the growth rate could be altered by the ratio of W/He.

In the initial phase of the LFN growth, the height of fibers increases exponentially in time.⁵⁶ Thus, one can say that bottom-growth process such as tin whiskers,⁵⁹ which was formed by in-plane compressive stress, cannot explain the exponential growth. Also, from the crystal orientation analysis of Ru and Re fuzz, it was found that the fibers are straight and the growth direction is always in the $c$ axis direction of a hexagonal closed packed (HCP) crystal structure.³⁶ It is thought that the adatom formed by the deposition of metallic atoms on the fiber surface diffused on the fiber, and epitaxial growth occurs on the tip of the fiber.

Concerning the exponential growth up to 0.1 mm, one potential explanation is the effects of electric field around the fibers. When the height of the fiber is much shorter than the sheath thickness, the trajectories of ions to the surface were not influenced by the fibers. However, when the height is comparable to or greater than the sheath thickness, the electric field formed around the fibers likely attract the metal and He ions.⁵² That will accelerate the numbers of adatoms formed on the fiber surface. Although the detailed mechanisms for enhanced fuzz growth with deposition has yet to be fully understood, understanding of the enhanced growth process will shed light on the study of the fuzz growth mechanism.

Helium plasma irradiations to doped W and W alloys have been performed from an early stage. Baldwin et al. irradiated He plasmas to doped W grades— $La 2 O 3$ (1 wt. %), Re (5 wt. % and 10 wt. %), and TiC (1.5 wt. %).⁴¹ Kajita et al. used doped W with undersized atomic species (Fe 2 at. % and Cr 2 at. %).³² Fuzz was grown on all the doped W samples in the same manner as pure W cases. Concerning Re, quantitative comparison in the growth rate of fuzzy layer showed additional Re has an inhibiting effect on growth.⁶⁰ Because transmutation of W to Re is expected in fusion reactors, it is thought to have a beneficial effect.

Helium plasma irradiation using a thin film deposited on a W substrate has revealed an interesting feature. Doerner et al. performed He plasma irradiation using a thin film of an isotope-enriched W (⁠ $∼$92.99% $182$W) deposited on the surface of a bulk W sample with the natural abundance of the isotopes.⁶¹ It was revealed that the depth profiles of the atoms in the thin film showed that mixing of W atoms from bulk to the surface occurred. They concluded that the results indicate enhanced mixing of W atoms due to the dynamic behavior of He bubbles. Strong mixture during fuzz growth has also been identified on W film on bulk Mo⁶² and Ru and Re thin film on bulk W.⁶³ 

After the discovery of fuzz structures on W, similar nano-scale structures were found on other metallic materials.⁴ Shapes and scales vary by each material and useful insight can be obtained from comparisons of their structures.^64–67 As seen in Fig. 11, typical fuzz, fiberform nanostructure with a diameter of 20–30 nm and a thickness of few micrometer, can be seen on W, molybdenum (Mo), titanium (Ti),⁶⁸ and iron (Fe),⁶⁸ and various precious metals⁶⁷ with a typical He ion fluence of greater than $10 25 m − 2$⁠. A thin fuzzy layer appears on the surface of niobium (Nb) and tantalum (Ta) when the ion fluence was sufficiently high (⁠ $∼ 10 26 m − 2$⁠). Fuzz also forms on Re and iridium (Ir) and grows faster than W fuzz under similar irradiation conditions.⁶⁵ The thickness of the fuzzy layer of Re and Ir reaches 10–100  $μ$m with the He ion fluence of $∼2× 10 25 m − 2$⁠. In addition, the formation of fuzz on zirconium (Zr) and hafnium (Hf) was also observed.⁶⁹ 

Fiber on cone shape appears on silver (Ag) and palladium (Pd). On Ag and Pd surfaces, fiberform nanostructures formed only on a tip of cone shape structures. The nanocone formation by He plasma irradiation has been identified on various materials including beryllium,⁷² chromium (Cr),⁷³ titanium, stainless steel,⁶⁸ and silicon.⁷⁴ Nishijima et al. performed He irradiation to Cr in several linear devices and concluded that deposition of a small amount of heavier impurities (Mo or Ta) was the seed for preferential sputtering leading to the nanocone formation. Shi et al. also concluded that the deposition was inevitable for the formation of silicon nanocones and actively changed the amount of molybdenum deposition on silicon to control the size and the aspect ratio of nanocones.⁷⁵ Concerning the fiber on cone structure, the growth mechanism is not yet clear, but the nanofiber at the tip could be made of impurities. First, the cone shape is formed on surface by sputtering, then impurity species diffuse on surface and agglomerate on the tip of the cone, because the impurity-rich tip is less likely sputtered. Finally, the impurity species on the cone form the fiber.

Some materials are hard to show fiberform nanostructures. Compared to the fiberform nanostructures, the nanostructures of gold (Au) and platinum (Pt)⁶⁵ have thicker and straight shapes. We call them as rod-like structures. Fiberform nanostructures formed on Ta in the NAGDIS-II device.⁷¹ However, because it requires a high He fluence and the sputtering yield is low, Ta is a suitable material for the specimen masks and materials exposed to plasmas in He plasma irradiation experiments.

For both the upper and lower boundaries, the He behavior in lattice could be related. As was discussed in Sec. II, the formation of He bubbles is required for He-induced growth of nanostructures, and $T H$ is an important parameter for the growth of He bubbles.⁷⁶ For the He bubble formation, numbers of He atoms should be migrated and agglomerated at one site. In general, temperature is a strong factor in the migration of He atoms/clusters. If the temperature is too low, these He migrations are less likely. As the He bubbles with the appropriate size grow in the surface top layer, surface morphology changes occur.

The elastic modulus of materials such as shear modulus, bulk modulus, and Young’s modulus can be another key parameter. The importance of the shear modulus has been discussed in terms of the viscoelastic model,^77–79 where viscous flow of W to the tip of the fiber plays a key role for the fuzz growth. Although adatom diffusion has recently become more popular to explain the growth process, the elastic modulus still seems to be an important parameter from an experimental point of view. Figure 12(b) summarizes the He plasma induced morphology changes as a function shear modulus of the materials at $T H=0.25−0.5$⁠. In this figure, materials can be categorized into three groups in terms of the tendency to the fuzz growth: easily formed, only thin layer, and no fuzz. This categorization shows that the fuzz structure growth is preferrable on materials with higher shear modulus. It should be noted that the temperature dependence of the shear modulus can also be important. The error bars represent the minimum and maximum values of shear modulus at $T H=0.25−0.5$⁠. The fuzz preferrable materials show larger error bars.

In addition to the above factors, sputtering yield is another important parameter, as was discussed in Ref. 71. For example, concerning aluminum and cupper, where fuzz has yet to be identified, the sputtering yield is $∼$0.08 when $E i=100$ eV. Considering that the sputtering yield of W by He is $∼$0.015 even at $E i=500$ eV, where only a thin fuzzy layer (⁠ $∼$300 nm) could form due to the equilibrium between growth and sputtering,³⁹ the significant sputtering may complicate the fuzz growth or narrow the conditional window.

There is currently no numerical simulation that can fully reproduce the formation and growth of fuzz. Although a direct comparison between simulations and experiments has been difficult yet, the role of simulation is to investigate physical processes from the theoretical viewpoint that cannot be directly observed in experiments and to clarify the mechanism of fuzz formation. The physical processes under He plasma irradiation are complicated and a representative case of multi-scale multi-physics processes. Therefore, there are a wide variety of simulation methods to be used,⁸⁰ and some new methods have been developed for research on fuzz.

Figure 13 shows physical processes at the surface and inside W exposed to a He plasma. We describe the relationship between the physical processes involved in fuzz formation and simulation methods suitable for them. When reading or using simulation methods and results, it is important to first recognize whether the calculation is an atomistic model, a coarse-grained model, or a continuous-field model. Atomic models are not always first-principles models, while coarse-grained models and continuous-field models tend to be empirical models. At that time, it is important to carefully find out what kind of mechanism is assumed as driving forces. Here, typical methods of atomistic simulations used for plasma–material interaction (PMI) are binary collision approximation (BCA), molecular dynamics (MD), density functional theory (DFT), and kinetic Monte–Carlo (KMC). These methods should be used properly according to each process in Fig. 13.

Helium atoms are irradiated from the plasma with an energy of 10 eV to several keV. The He atoms scatter the atoms composing a target material, while a part of He atoms are reflected back into the plasma region and the other He atoms stay inside. To investigate this incident process of He, BCA has been often used. In BCA, the dynamics of multi-particles is approximated as the iteration of two-body collisions between an incident atom and rest target atoms. The incident atom is called projectile culturally. The projectile gradually loses its kinetic energy due to collisions with many target atoms and eventually stops. When the energy transfer from a projectile to a target atom due to a collision is higher than the threshold energy, $E rc$⁠, the target atom is regarded to be kicked out. The atom kicked out is called recoil or knock-on atom, and it begins to move according to the same routine as the projectile. As a result, the trajectories of projectiles and recoils are obtained like a cascade scattering. When recoils are ejected from a surface, they are counted as sputtered atoms. This is a better approximation when the kinetic energy of the projectile is high and the scattering cross section is small.

Apart from sputtering, the incident process is also involved in the penetration depth of He from the surface, which is culturally called range. The penetration depth of He corresponds to the initial position of thermal diffusion of He in materials. Of particular importance, in metals with lattice structures, He atoms often penetrate deeply by channeling. Note, however, that some conventional BCA codes can only handle either amorphous structure or crystalline structure.

There seems to be a misunderstanding that BCA is sometimes called the Monte–Carlo method, which is a general term for methods that use random number for simulations and numerical calculations. The random numbers are used for the following two parts in the BCA code. One is to determine the initial positions of projectiles. The other is to generate a target atom for each collision. In the past, the BCA code developed for computers with limited memory cannot retain all the atomic positions of a target material. Therefore, when one collision is over, the collision target atom is deleted from computer memory in order to reduce a total memory usage. At the next step, the next collision target atom is generated using random numbers according to the density of the target material. This is probably one reason why the BCA is sometimes called the Monte–Carlo method. The other reason why the BCA is sometimes called the Monte–Carlo method is probably because it is confused with the binary collision model⁸⁶ in particle-in-cell (PIC) simulation in which the trajectory of each collision is determined by using random numbers. On the other hand, the important point of BCA is that in each collision the trajectories of projectiles and target atoms are solved without random number and are uniquely determined as a function of the kinetic energy of projectiles and an impact parameter. Moreover, on recent computers with a larger memory resource, recent BCA codes such as AC $∀$T^87,88 retain all atomic positions in a target material, and then any structured material can be treated. Namely, the Monte–Carlo method is only to determine incident positions.

The large memory resources of modern computers also make it easier to simulate complicated surface geometries. Retaining the data of about one billion atoms, it is possible to handle full-scale fuzz-like structures of $100 3 nm 3$⁠. BCA for the full-scale fuzz-like structure is useful for investigating the effect of nanoscale fibers and their gaps, rather than simply considering the fuzz layer as a low-density uniform material. Nakamura et al.⁸⁹ made a semi-elliptical hole on the surface. Klaver et al.⁹⁰ simulated fuzz by stacking ellipsoids in a network. Similarly, Yang et al.⁹¹ simulated a fuzz by stacking cylinders in a network. For instance, sputtering yield becomes lower than that of a flat surface because recoils re-deposit on fibers.

After He atoms are implanted to materials, a key issue is the formation of He bubbles. Let us choose the calculation method depending on whether we need static property or dynamic property. To investigate the nucleation of He bubbles in materials, the binding energy of He atoms, which is the energy gain when a He atom moves from an independent interstitial site to a clustering site, is often used and is estimated according to the electronic state calculation using DFT.^92,93 Here, if the binding energy of He atoms is positive, agglomerated He atoms in W are energetically more stable than independent He atoms at interstitial sites. From Fig. 14, the binding energy of He atoms clustering at an interstitial site increases, while that at a mono-vacancy site decreases. However, both of the binding energies remain positive at 2.0–2.5 eV even when the number of He atoms in the cluster is greater than eight. This suggests that the agglomeration of He atoms into a larger He bubble will continue. The mechanism why He atom can agglomerate in W is considered as follows. Noble gas atoms, which have an electronically closed shell structure, receive repulsion from electrons in metals. It is stable for them to self-aggregate and to create a space with a low electron density in the metal.⁹⁴ Such evaluation of the binding energy of He atoms by DFT is also useful for metals other than W.⁶⁴ From Fig. 14, it is clear that He atoms can agglomerate in various elements [W, Mo, Cr, Ta, Nb, vanadium (V), and Fe], which have a body-centered cubic (BCC) structure. In addition, He agglomeration was also confirmed by using DFT for Ir and Au which have a face-centered cubic (FCC) structure.⁹⁵ 

MD simulations are often used to investigate dynamical phenomena such as the deformation processes of W due to He bubbles. One of the successful results of MD is a visual demonstration of loop punching. According to the simulation results,^98,99 when the size of a He bubble reaches several nm, W atoms around the He bubble are pushed out. The W atoms are not emitted separately but are collectively shifted in the $⟨111⟩$ direction. At this time, the lattice mismatch that appears around the pushed atoms is observed as a dislocation loop. By this emission, the pressure in the He bubble is released.

As a He bubble grows near the surface, dislocation loops are emitted toward the surface. As a result, the surface is lifted. When the pressure inside the He bubble is high, part of the lifted surface bursts, which is called bursting. However, according to MD,^100,101 the size of the pinhole created by the bursting is less than 1 nm. Still, almost all He atoms escape through pinholes in a few picoseconds. Therefore, the height of the surface that can be lifted is at most about the size of a He bubble. This is not enough to explain fuzz growth. In addition, the size of pinholes created by the bursting in MD is an order of magnitude smaller than experimental observations.

Here, we note that the steps achieved by a typical MD in recent computer systems is up to $10 8$ per a day, which corresponds to about 10 ns. Therefore, although MD can treat rapid processes such as the diffusion of He and H atoms in material and the loop-punching due to the stress of a He bubble, slower processes such as the thermal annealing and structure relaxation of W are difficult to simulate with MD. For the same reason, MD also hardly treats the process of bubble connection, in which the motion of W atoms causes a slow change in the shape of He bubbles from a dumbbell-shaped to a larger spherical shape.

Since He bubbles can be generated far deeper than the penetration depth of the injection process, the diffusion of He atoms is important for the distribution of He bubbles. The diffusion process of He atoms in W is involved in the distribution of He bubbles and the generation of surface roughness. According to DFT estimates, the migration barrier energy of He in W with a BCC lattice is $ΔE=0.04−0.06$ eV.^94,102 This is less than one-third of the migration barrier energy of 0.2 eV for hydrogen atoms. Moreover, the migration barrier energies of Ne and Ar, which are noble gases, are about the same as or less than the migration barrier energy of hydrogen atoms.

It is not possible to estimate the diffusion coefficient just by using the DFT. The diffusion coefficient is given as a function of the temperature by $D(T)= D 0exp(−ΔE/ k bT)$⁠. We either estimate the pre-factor $D 0$ of the diffusion coefficient using transition state theory^103,104 or estimate the mean squared displacement observed from an actual diffusion trajectory in MD. For the latter case, $D 0$ and $ΔE$ are determined by the Arrhenius plot. In fact, the MD simulations reported that $D 0=5.35× 10 − 8 m 2/ s$⁠, $ΔE=0.13$ eV,¹⁰⁵ and $D 0=3.36× 10 − 8 m 2/ s$⁠, $ΔE=0.0623$ eV,¹⁰⁶ where these difference was caused by the difference of potential models. The estimations suggested that the diffusion speed of He atoms is faster than that of hydrogen atoms. In addition, it is important that He atoms can diffuse even if they form a cluster such as a dimer and a trimer. Moreover, both MD¹⁰⁵ and DFT showed that the diffusion speed of a dimer is faster than that of a single atom.

The fact from experiments that fuzz formation required $∼ 10 24 m − 2$ in He fluence is important. To simulate the He fluence as same as experiments is impossible for MD because of the short elapse time of at most 1  $μ$s. In general, the incident flux in experiments is in the range of $10 20− 10 24 m − 2 s − 1$⁠, while the incident flux in MD is often set to $10 28 m − 2 s − 1$ or higher. However, it is not recommended to choose the incident flux extremely higher than in the experiment, because the distribution of He bubbles should depend on the incident flux. When the incident flux is high, He atoms easily cluster in shallow areas, while when the incident flux is low, the He atoms diffuse deeply before clustering. Therefore, the ideal simulation is to achieve the He fluence as large as possible while using an incident flux close to experimental conditions.

One of the strategies for this problem is to use a high-performance computing (HPC). Hammond et al.^107–109 employed the MD with massively parallel computing. Their MD was able to reduce the incident flux to $10 25 m − 2 s − 1$ and to achieve $10 19 m − 2$ in He fluence. On these realistic conditions, the dependence of the He bubble distribution on the incident flux was investigated in detail. Moreover, the size of pinholes due to He bubbles reached about 4 nm (see Fig. 15), which is larger than the size of pinholes just after the bursting mentioned above (<1 nm). Namely, after the pinhole bursts, it takes a long time before it becomes large enough to be observed by an SEM.

In addition, a technical solution to achieve high helium fluence is the hybrid simulation of MD and KMC.^110,111 The diffusion and agglomeration of He atoms are solved fast by KMC on a grid system with a width of several Å, and the deformation of W materials due to the high pressure of He bubbles is solved by MD. In the algorithm, KMC and MD are switched alternately at a regular interval. The hybrid simulation could achieve $10 22 m − 2$ in the He fluence under the condition that the incident flux is $10 22 m − 2 s − 1$⁠, although it depends on the calculation time. In the simulation, it is needed to convert the data of atomic positions to the data of a discretized grid. The grid cell is classified into a W bulk cell, a He bubble cell, and a vacuum cell. For example, the region where a He bubble exists in MD is converted to a He bubble cell. When a He bubble bursts, the cell changes into a vacuum cell. In the KMC on these grid cells, He atoms can move on W cells. If a He atom reaches a vacuum cell, the He atom is vanished, which corresponds to the desorption of He atoms. If a He atom reached a He bubble cell, the He atom is regarded as trapped and then the He atom is added into the MD as an atomic particle. This hybrid simulation can treat swift processes of W atoms such as bursting and loop punching (⁠ $∼$10 ps/process). However, the slow processes of W atoms, such as thermal relaxation and surface diffusion, cannot be sufficiently represented. As a result, unfortunately, the hybrid simulation of MD and KMC can represent the formation of small surface roughness, but not enough for fuzz formation.

An unsolved problem for fuzz growth is the moving process of W atoms. In particular, it is not well understood what kind of mechanism causes the transport of W atoms in the normal direction to the surface. Conversely, assuming the normal transport, it is possible to create a coarse-grained model for growth that has $t$ dependence in the fuzz height. Lasa et al.¹¹² assume that the driving force of normal transport is a loop punching and rupture (bursting), and Martynenko¹¹³  et al. assumed that the driving force is the gradient of W adatom concentration.

Here, let us consider that sputtering is also a candidate for the normal transport of W atoms. As mentioned in the section on the injection process, because the injection energy of He is lower than the sputtering threshold energy, it has been thought that sputtering hardly occurs. Therefore, in most simulations for slow deformations of W, such as the MD and hybrid simulations discussed in the previous subsection, He atoms are directly implanted into materials without calculating the injection process. Another reason for avoiding the calculation of the injection process in MD is that the time step must be set short in order to handle fast-moving incident atoms, which requires a longer calculation time.

However, in the atomic scale viewpoint, the recoil cutoff energy $E rc$ to knock on a W atom is expected to generally decrease on rough surfaces compared with a bulk region, and then the sputtering can occur even in low incident energy. In order to treat the incident process, the above hybrid simulation has been extended to the BCA-MD-KMC hybrid simulation,¹¹⁴ in which the incident process is solved by using BCA in addition to MD for material deformation and KMC for helium diffusion. In a recent work,¹¹⁵ the hybrid simulation achieved the total fluence of $1.0× 10 24 m − 2$ under the flux of $1.4× 10 22 m − 2 s − 1$⁠. As a result, the growth of the fiberform structure was represented as shown in Fig. 16.

A key point in the hybrid simulation is that $E rc$ is given by $E c n / 8$⁠, where $E c$ is the cohesive energy of bulk and $n$ is a coordination number for each atom. Namely, $E rc$ becomes smaller than $E c$ when $n$ is smaller than the coordination number of bulk W, 8. From the MD part, $n$⁠, which reflects the deformed material structure, is estimated. By this model, W atoms located at a rough surface can be sputtered by the He atom whose incident energy is 100 eV or less. Actually, the number of sputtering events was low when the surface was flat, while the number of sputtering events increased after the bursting of He bubbles made the surface rough. Some of the sputtered W atoms are re-deposited at the tips of the surface, and the net sputtering yield is kept low at $∼ 10 − 4$⁠. Finally, the height of the fiberform structure reached about 40 nm. At least in the hybrid simulation, the sputtering and the re-deposition were dominant mechanisms for the normal transport of W atoms. These mechanisms are consistent with the fact that deposition enhanced the LFN growth.

The other candidate of the normal transport is the effect called surface diffusion. The fundamental viewpoint of the surface diffusion is the migration of an adatom on flat surfaces.¹¹⁶ From the comparison among the migration barrier energy,^117,118 the diffusion of a W adatom on 110 surface is faster than the diffusion on other surface planes. From the estimation using MD,¹¹⁹ the migration barrier energy for a W adatom on the 110 surface $ΔE=0.89$ eV and its pre-factor $D 0=6.92× 10 − 7 m 2$/s, which does not seem to be slow. However, it should be noted that even if the diffusion of a single atom is fast, it will be clustered or trapped at the edge of steps. Then, the diffusion is slowed down, so that the adatoms on W surfaces are not moving permanently fast. In addition, it should be considered that the 110 surface does not dominate the surface of fuzz, which is winding in a nanometer scale.

If adatoms are clustered quickly or trapped somewhere, what matters is the frequency of formation of adatoms. From the MD simulation,¹²⁰ it seems that adatom can generate on the surface by increasing the concentration of He atoms in the shallow part of the surface. There is a possibility that the deposition of W atom is the cause of adatom formation. The sputtering and the re-deposition processes in the above hybrid simulation also can be regarded as the occurrence of the adatom formation. In growth of the LFN, aggressive deposition produces many adatoms.

However, it is difficult to even distinguish adatoms on rough surfaces, such as the surfaces of fuzz or the surfaces with bubbles burst. Then, it is probably appropriate to regard surface diffusion as a collective motion rather than as a migration of individual atoms. The statistical mechanical effects such as chemical potential¹¹³ and the effects of macroscopic physical quantity such as stress^77,121 can also be important factors. For instance, Chen et al. demonstrated, using a continuity simulation and linear stability theory, that the stress induced by the high pressure of He bubbles in nano-scale tips causes a long-wavelength surface morphological instability, and then the fiberform nanostructure was generated.¹²² Moreover, their model showed that a temperature influence and a He concentration influence on the incubation fluence, with the incubation fluence decreasing with increasing the temperature.¹²³ Here, the temperature dependence is the most interesting factor in fuzz growth and is often observed experimentally. However, atomic simulations from a microscopic viewpoint have too few degrees of freedom to clearly show the temperature dependence in fuzz growth. Continuous models from a macroscopic viewpoint are essential in this respect. Thus, the growth factors of fuzz is not fully elucidated. Candidates for the normal transport of W atoms will continue to be proposed and discussed.

The unique characteristic of the fuzz surface has various potential applications as functional materials. Here, we introduce two major candidate applications: gas sensors and photocatalysts.

For the gas sensor applications, there are three important “S”: sensitivity, selectivity, and stability. To improve the selectivity, additional catalytic nanoparticles should be examined. Nanoparticles may improve a sticking coefficient of the target gas molecules and enhance the reaction. Nickel, Pt, and Pd are the main candidates. If the sensitivity is well improved, it will improve the stability. With high-sensitive sensor materials, the sensor can be operated at lower temperatures, even at room temperature. In this case, the surface deformation is less likely and the stability is improved. In addition, operation at low temperatures is also beneficial for the power efficiency. For the universe of trillions of sensors, the power source is limited, thus low power gas sensors are essential.

Increases in the surface area and optical absorptance/absorbance by the formation of nanostructures on the surface is beneficial for photocatalysts.¹²⁶ Metals themselves cannot be photocatalysts; oxides of various metals such as V, Ti, Cr, zinc, tin, W, cerium are prosperous semiconductor photocatalysts.¹²⁷ 

Since fuzz was identified on W, two photocatalytic reactions are tested after oxidization, as far as we know: methylene blue (MB) (⁠ $C 16 H 18 N 3$SCl) decolorization reaction^68,128 and photoelectrochemical (PEC) characterization (photocurrent measurements).¹²⁹ 

Figure 20(a) shows time courses of MB concentration as a function of light irradiation time using the setup shown in the inset of Fig. 20(a). A $WO 3$ sample was placed in 2 ml of aqueous MB solution (10  $μ$mol/l) and exposed to visible light from a 300 W Xe lamp through an optical filter (long-pass optical filters with the edge wavelengths of 520 and 700 nm). It is noted that the decolorization progressed even though only near infrared light (>700 nm) was used for the irradiation. Concerning the MB decolorization, the surface oxidation fraction, which was measured by x-ray photoelectron spectroscopy (XPS), was an important factor. It was found that MB decolorization rate varied significantly with changing the oxidation fraction, and the reaction rate has a peak when the oxidation fraction was 60%.¹²⁸ The results suggested that the interface between W and $WO 3$ played an important role for the decolorization process. Also, oxygen vacancies, which are known to be influential factor for the photocatalytic performance, were found to be formed and stable in fuzzy $WO 3$⁠.¹³⁰ 

Although the MB decolorization process is a simple method to measure the photocatalytic process, it is not easy to judge if the decolorization is due to the absorption or decomposition reaction. Komori et al. have revealed from S K-edge x-ray absorption near edge structure (XANES) analysis on both of the samples before and after the MB decolorization process that the MB molecules have been actually decomposed.¹³¹ The $σ ∗$(S–C) peak in the XANES spectra decreased and a new peak from $SO 4 2 −$ was identified after the light irradiation; the results suggested that NIR light irradiation breaks S–C bonds in a MB molecule and the sulfur species are formed in the state of $SO 4 2 −$ ion.

PEC performances have been measured using oxidized fuzzy W with an optimized two-step oxidation annealing procedure.¹²⁹ The sample showed five times greater photocurrent density than the non-porous $WO 3$ sample from a W disc. Feng et al. investigated the PEC performance using oxidized fuzzy W with different $h fuzz$¹³² and optimized $h fuzz$ and oxidized temperature for the PEC performance. In the inset of Fig. 20(b), the setup for the PEC measurement is shown. A coiled Pt wire, an Ag/AgCl/sat. KCl electrode, and a prepared $WO 3$ sample were used as the counter electrode, the reference electrode (RE), and the working electrode, respectively, and a 0.5 M $H 2 SO 4$ solution was used for the electrolyte. Linear sweep voltammetry curves were obtained under chopped incident light. In Fig. 20(b), it was found that the $WO 3$ sample from a thin fuzz layer (15 min irradiation) W has 12 times higher performance than the one from thicker fuzz layer (30 min irradiation). It was discussed that recombination occurs before the produced electrons reach the conduction layer when $h fuzz$ is too thick.

One of the problems to be overcome is that the photocatalytic property decreases during the MB decomposition or PEC water splitting.^128,132 Because it was found the degradation rate could be changed by the oxidation procedure,¹²⁸ it is necessary to optimize the structure and the oxidation process or put additional coating of thin film layer on the fuzzy surface.¹³³ 

Titania (⁠ $TiO 2$⁠) has been one of the most popular photocatalytic materials since the discovery of the Honda–Fujishima effect.¹³⁴ In addition to the water splitting, it has been used for various applications including air purification, sterilization, and cancer therapy.¹³⁵ 

After the fuzz growth condition on Ti has been revealed,^70,136 photocatalytic performances have been investigated on He irradiated Ti samples via hydrogen production reaction from aqueous methanol solution and ethylene decomposition, which is necessary for the transportation and storage of horticultural crops.¹³⁷ For the hydrogen production reaction, a nanostructured sample has revealed roughly three times greater photocatalytic performance.¹³⁸ This can be explained by the increase in the active surface area. For the ethylene decomposition, various fabrication methods have been investigated including thin film deposition on W fuzz and Ti thin film fuzzy samples.^133,139,140 However, the effect of the increase in surface area did not appear clearly; rather, the performance seemed more sensitive to the crystal structure. It was shown that anatase structure, which is known to be more active than rutile, can be formed on He plasma exposed samples with high ethylene decomposition efficiency and is stable even at higher calcination temperatures (>1000 K), though anatase is rarely formed on non-He-plasma-irradiated samples.¹⁴⁰ This suggested another aspect of He plasma irradiation effects in addition to the increase in surface area.

Hematite (⁠ $α$- $Fe 2 O 3$⁠) is a semiconductor with the bandgap energy of 2–2.2 eV and thought to be a promising material for oxygen evolution reaction (OER), which is a half-reaction to drive the water splitting.¹⁴¹ Based on an investigation of He plasma irradiation effects on Fe thin films,¹⁴² PEC performance of oxidized nanostructured Fe thin film has been measured.¹⁴³ 

The photocurrent density on a plasma exposed thin film for 20 min (SE) had 2–5 times higher than that on an unexposed film (UE), while a clearly nanostructured film exposed to the plasma for 50 min (LE) had lower performance than SE. From the electrochemical impedance spectroscopy, it was shown that SE and LE had 10- and 40-times greater surface area than that of UE, respectively. Thus, the increase in the photocurrent density was less than the increase in the active surface area. It was discussed that the presence of defects including maghemite phase (⁠ $Fe 3 O 4$⁠) could act as the recombination center. Also, the roles of secondary elements such as Sn, Si and Zn, and the presence of maghemite (⁠ $γ$- $Fe 2 O 3$⁠) identified on UE have been discussed.

Helium plasma irradiation effects on the photocatalytic performances have been investigated on other metallic oxides. Methylene blue decomposition by UV light irradiation was performed using fuzzy niobium oxides (⁠ $Nb 2 O 5$⁠).⁶⁶ Although no enhancement occurred on fuzzy samples, the performance increased with Pt support. Also, $H 2$ production from aqueous methanol solution using fuzzy vanadium oxides sample has been conducted, and it was shown that He plasma irradiation activated photocatalytic performance.¹⁴⁴ 

Dry processing can be used to form multiple thin film layers and add a small amount of novel metals such as Ag, Au, and Pd. Further studies with the combination of He plasma irradiation and thin film deposition, which can be a novel method for the fabrication of nanostructured heterogeneous photocatalysts,¹⁴⁵ are of interest. The He effect can also be beneficial in ways other than increasing surface area, such as the formation of stable anatase and oxygen vacancies. Fundamental understandings of the role of He implantation for photocatalytic materials are important.

In this Tutorial, we presented and discussed the growth process and growth condition of fuzz on various metals including W based on experiments and simulation, and progresses on the application of fuzz-based materials. Currently, both experimental and simulation studies are being actively conducted including the formation mechanism of fuzz and their effects on fusion reactors. In the past decade, the effects on fusion reactors have gradually become clear. However, it has not yet been determined whether or not the formation will proceed in a fusion reactor, and further research is needed, in particular, with regard to the temperature increase, energy increase, and redeposition effects associated with edge localized modes (ELMs). As detailed in Secs. II and IV, the growth mechanism is gradually becoming clear. As described in Sec. II, the formation of NTBs with a height of tens of micrometers and LFNs with a thickness of mm have been found in recent years. The verification and modeling of these formation processes is important and may lead to a new aspect of the understanding of fuzz growth.

In addition to the problems in fusion reactors, the fact that fuzz growth occurs on various metals, as described in Sec. III, will greatly broaden the range of industrial applications. Enhanced performances in gas sensors and photocatalytic materials have been already demonstrated, as described in Sec. V. As for photocatalytic materials, various metal oxides, nitrides, and sulfides of tungsten, tantalum, niobium, and vanadium are expected to replace $TiO 2$ as visible light responsive photocatalysts,¹⁴⁸ and it is important that cross-disciplinary research be further promoted. There is one hurdle in the process for industrial application research. With pure He plasma irradiation, a helium fluence of $10 25$– $10 26 m − 2$ is required for the fuzz growth to occur, and fuzz formation requires the use of devices that can generate high-density plasmas, such as divertor simulators. It has been reported that nanostructuring can also be performed in magnetron sputtering devices, but it requires about 10 h of time. If fuzz can be formed simply and in a short time, the possibilities for industrial application research will increase. The selection and development of an optimal plasma source and the development of a device that can withstand mass production by making full use of accelerated fuzz growth by deposition, etc., as described in Sec. II, are future issues.

One of the authors (S.K.) thanks Dr. M Tokitani and Professor Sakamoto at National Institute for Fusion Science for useful discussion about the crystal orientation dependence. This work was supported in part by a Grant-in-Aid for Scientific Research (Nos. 19H01874, 19H01882, 19K21870 and 21K18617), and Fund for the Promotion of Joint International Research (No. 17KK0132) from the Japan Society for the Promotion of Science (JSPS). A part of simulation is carried out on “Plasma Simulator” (NEC SX-Aurora TSUBASA) in NIFS with the support and under the auspices of the NIFS Collaboration Research program (No. NIFS22KISS027).

The authors have no conflicts to disclose.

Shin Kajita: Writing – original draft (lead); Writing – review & editing (lead). Atsushi M. Ito: Writing – original draft (equal); Writing – review & editing (equal). Kenzo Ibano: Writing – original draft (equal); Writing – review & editing (equal).

The data that support the findings of this study are available within the article.