Tracing temperature in a nanometer size region in a picosecond time period

ABSTRACT Irradiation of materials with either swift heavy ions or slow highly charged ions leads to ultrafast heating on a timescale of several picosecond in a region of several nanometer.

This ultrafast local heating result in formation of nanostructures, which provide a number of potential applications in nanotechnologies. These nanostructures are believed to be formed when

the local temperature rises beyond the melting or boiling point of the material. Conventional techniques, however, are not applicable to measure temperature in such a localized region in a

short time period. Here, we propose a novel method for tracing temperature in a nanometer region in a picosecond time period by utilizing desorption of gold nanoparticles around the ion

impact position. The feasibility is examined by comparing with the temperature evolution predicted by a theoretical model. SIMILAR CONTENT BEING VIEWED BY OTHERS TEMPERATURE EVOLUTION OF

DENSE GOLD AND DIAMOND HEATED BY ENERGETIC LASER-DRIVEN ALUMINUM IONS Article Open access 07 September 2022 AN APPROACH FOR THE MEASUREMENT OF THE BULK TEMPERATURE OF SINGLE CRYSTAL DIAMOND

USING AN X-RAY FREE ELECTRON LASER Article Open access 03 September 2020 ULTRAFAST MULTI-CYCLE TERAHERTZ MEASUREMENTS OF THE ELECTRICAL CONDUCTIVITY IN STRONGLY EXCITED SOLIDS Article Open

access 12 March 2021 INTRODUCTION The interaction of energetic ions with materials is the basis of a wide range of applications, such as surface analysis, surface modification, ion

implantation and so on. Recently, nanostructures produced by single ion impact is attracting a wide attention because of its potential applications. When a swift heavy ion (SHI) penetrates a

solid the ion excites solid electrons. The energy of the excited electrons is then transferred to the lattice via electron-phonon coupling and provides ultrafast local heating along the ion

path. Eventually, a cylindrical damage region of diameter several nm, a so-called ion track, may be created when the electronic energy loss is larger than a material dependent threshold

value1. Such ion tracks are used for DNA sequencing2, templates for the synthesis of micro- and nanowires3 and waveguide-mode biosensors4 and so on. The formation mechanism of ion track is

explained by a so-called inelastic thermal spike (i-TS) model1. In the i-TS model, the evolution of the temperature distribution around the ion path is described by classical heat equations

for the electronic and atomic subsystems. It is generally assumed that the ion track is formed when the atomic temperature rises beyond the melting point of the material3. Because such

heating occurs in a highly localized region of nanometer size on a time scale of ~10 ps, it is very difficult to confirm the assumption by tracing the temperature during the track formation.

Similar ultrafast heating can be also realized by the irradiation of pulsed lasers. When a solid target is illuminated with a pulsed laser, the solid electrons are excited and the deposited

energy is transferred to the phonon system on a picosecond time scale. This phenomenon is the basis of laser ablation which has been widely used for the deposition of a wide range of

materials. The laser ablation is often described by the so-called two temperature model5,6, which is basically the same model as the i-TS model. Recently it was demonstrated that ultrafast

heating in localized region can be realized by combing the pulsed laser and local plasmon resonance7. When gold nanoparticles are illuminated by a pulsed laser at their plasmonic resonance,

the laser power is deposited into the electronic subsystem of the nanoparticles through the plasmon resonance. The deposited energy is then transferred to the atomic subsystem via

electron-phonon coupling. This is called pulsed laser plasmon-assisted photothermal heating6 and is a promising heat source of nanometer size in ultra-fast time frames. Theoretical studies

showed that the temperature of nanoparticles rises ~1000 K in a nanosecond time period8 although the measurement of the actual temperature is very difficult. More recently, it was found that

individual slow highly charged ions (HCI) produce surface modifications (either hillock, pits or craters) on a nanometer scale when the potential energy carried by HCI is larger than a

material dependent threshold value9,10,11,12,13,14. These modifications result from the large potential energy (_e.g._ ~16 keV for Xe30+) carried by slow HCI. The potential energy is first

deposited to the surface electrons in a nanometer region and then transferred to the atomic system. This leads to ultrafast local heating around the ion impact position. The observed

potential energy threshold for hillock formation was well reproduced by the i-TS calculation assuming that the hillock is formed when the temperature rises beyond the melting point15. All

these phenomena are similar in the sense that the initial energy deposition to the electronic subsystem results in ultrafast local heating of the atomic subsystem. Although theoretical

studies predict the evolution of temperature distribution there has been no direct temperature measurement of such ultrafast local heating. Based on the molecular dynamics (MD) simulations

that determine the surface desorption energy of gold nanoparticles16, we propose a novel method to trace temperature in highly localized region on a ultrafast time scale. Thin films

deposited with gold nanoparticles are irradiated with swift heavy ions and the desorption of nanoparticles around the ion impact position is observed using transmission electron microscopy

(TEM). The feasibility of this method will be examined by comparing the observed radius in which the nanoparticles are expelled with the i-TS model calculations. RESULTS DESORPTION OF GOLD

NANOPARTICLES Figure 1(a) shows an example of TEM bright field images of a gold-deposited amorphous SiO2 (a-SiO2) film (thickness 20 nm) observed before irradiation. There are many gold

nanoparticles formed by the gold vapor deposition. The areal density, _N_, of these nanoparticles was measured to be 1.9 × 1012  particles/cm2. The size distribution of these nanoparticles

was derived from the observed TEM images and shown by closed circles in Fig. 2. The distribution shows a Gaussian-like well-defined peak with a peak radius of 1.0 nm and a width of 0.9 nm. A

similar size distribution with a peak radius of 2.2 nm and a width of 1.6 nm was also observed for the gold nanoparticles deposited on amorphous SiN (a-SiN) films (thickness 30 nm) as shown

by open circles in Fig. 2. The size difference between a-SiO2 and a-SiN is attributed to the smaller diffusivity of gold adatoms on a-SiO2 surfaces compared to a-SiN. Figures 1(b) shows an

example of TEM bright field images of the gold-deposited a-SiO2 film observed after irradiation with 420 MeV Au ions. The irradiation was performed on the rear surface, _i.e._ from the

opposite side of the gold deposition (will be referred to as “rear surface irradiation”). Ion tracks are clearly seen as bright spots with a diameter of about 2 nm. The ion tracks were also

observed using high-angle annular dark field scanning transmission electron microscopy (HAADF-STEM). The profiles of the observed track images are shown for both TEM and HAADF-STEM in Fig.

3. The TEM profile has an oscillatory structure caused by Fresnel diffraction, indicating the difficulty of deducing quantitative information from TEM images. On the contrary, the HAADF-STEM

profile can be directly linked to the density profile. The observed HAADF-STEM profile shows a core-shell structure, namely a low density core (radius 1.6 ± 0.3 nm) surrounded by a high

density shell (outer radius 6 ± 1 nm). This is in good agreement with the observation using small angle x-ray scattering17. According to the two thresholds model17,18 (see also Supplementary

information), the present result suggests that the energy per atom surpasses the melting energy (0.38 eV/atom17) at _r_ < 6 ± 1 nm and boiling energy (1.7 eV/atom17) at _r_ < 1.6 ± 

0.3 nm. Looking at the vicinity of the ion track closely (Fig. 1(b)), the gold nanoparticles seem to disappear from the surrounding area of the ion tracks. Such disappearance of the gold

nanoparticles was also observed for the front surface irradiation. The distance between the ion track and the closest gold nanoparticle was measured for each ion track. The observed closest

distance, _R_c, represents the radius of the region where nanoparticles disappeared. The distributions of the measured closest distances for the samples irradiated on the front surface

(solid circles) and the rear surface (open circles) are shown in Fig. 4. The average of the closest distance, <_R_c>, is 6.3 ± 0.6 and 7.2 ± 0.7 nm for the front and rear surface

irradiations, respectively. This suggests that 2.4 and 3.1 nanoparticles, on average, are removed by single Au ion impact. In order to confirm this, the distribution of closest distance was

calculated assuming that there was no removal of nanoparticles around the ion tracks. The probability that the closest nanoparticle is found in a region [_R_c, _R_c + _dR_c] is given by if

the gold nanoparticles are not desorbed by the ion irradiation. The distribution was calculated with the observed _N_ (1.9 × 1012  particles/cm2) and shown by a solid line in Fig. 4. The

calculated distribution has a peak at a distance of ~3 nm, which is much smaller than the observed ones (6.3 and 7.2 nm). This clearly indicates that nanoparticles are really removed from

the vicinity of the ion impact position. The removed nanoparticles were collected by a thin foil placed in front of the gold-deposited surface of the sample. This collector foil was also

observed using TEM. An example of the TEM images is shown in the inset of Fig. 1(b). Very precisely circular gold particles with a radius close to those of the deposited gold nanoparticles

were observed, indicating that gold nanoparticles were desorbed as liquid droplets without fragmentation from the surface of a-SiO2 by the ion irradiation. Similar desorption of gold

nanoparticles upon ion impact was also observed for the gold-deposited a-SiN films. The measured distributions of the distance between the ion track and the closest nanoparticle are shown by

solid and open triangles for front and rear surface irradiations, respectively, in Fig. 4. The average closest distances were derived to be 9.3 ± 0.9 and 9.9 ± 1.0 nm for front and rear

surface irradiations, respectively. It is noteworthy that the nanoparticle cleared region is larger in the case of the rear surface irradiation compared to the front surface irradiation for

both a-SiO2 and a-SiN. This will be discussed later in this paper. If the density of the nanoparticle is infinitely large, the measured closest distance _R_c between the track center and the

surrounding nanoparticles is equal to the radius of the nanoparticle cleared region, _R_. The actual density is, however, finite. As a result, the measured closest distance is larger than

_R_. The relation between <_R_c> and _R_ can be derived using a Poisson law. The probability that the closest nanoparticle is found in a region [_r, r_ + _dr_] is given by where _r_ is

the distance from the track center. The average of the closest distance is calculated by, Using Eq. (3), _R_ was estimated from the observed <_R_c> and _N_. The results are summarized

in Table 1. Anders _et al._ studied the desorption mechanism of nanoparticles using MD simulations16. They simulated the motion of hemispherical gold nanoparticles (radius 3.6 nm) placed on

a surface when the gold atoms are energized. The simulation was performed for various initial kinetic energies given to the gold atoms ranging from 0.13 to 1.03 eV/atom. They found that the

nanoparticles are desorbed within a short time period of several ps without fragmentation when the initial kinetic energy exceeds a threshold energy, _E_d = 0.4 eV/atom. Their detailed

investigation showed that the desorption is triggered by melting of nanoparticles, which leads to expansion of the nanoparticles and results in the desorption. This is in accordance with the

present observation that the gold nanoparticles were desorbed as liquid droplets without fragmentation. In view of their result, present observation indicates that the energy deposited on

the atoms exceeds 0.4 eV/atom in the region closer than _R_ around each ion impact position. It is noteworthy that the observed nanoparticle cleared radii for a-SiO2 (5.1 ± 0.6 and 6.0 ± 0.7

 nm, see Table 1) are very close to the shell radius of the observed track (6 ± 1 nm). This indicates that the threshold energy for track shell formation is close to the threshold energy for

desorption (_E_d = 0.4 eV/atom). Actually, the threshold energy for track shell formation was estimated to be 0.38 eV/atom for a-SiO217,19. This suggests that the proposed method of the

temperature tracing works well. COMPARISON WITH THE RESULT OF I-TS CALCULATION The evolution of the temperature distribution around the impact position was calculated using the i-TS model.

In the i-TS model, the heat diffusion in time _t_ and space _r_ (radial distance from the ion path) is described by the following differential equations1, where _T__e,a__, C__e,a_ and

_K__e,a_ are the respective temperature, specific heat and thermal conductivity of the electronic and atomic subsystems, _g_ is the electron-phonon coupling parameter, _A_(_r, v, t_) is

energy input into the electronic subsystem from the electronic energy loss and _v_ is the ion velocity. The energy lost by the projectile ion is sheared between electrons and then gradually

transferred to atoms by the electron-phonon interaction. The parameter _g_ is related to the electron-phonon mean free path λ. For a-SiO2, this parameter is well established, _i.e. λ_ = 3 

nm17,19. With this mean free path, the i-TS model reproduces observed track radii in a-SiO2 very well17,19. Unlike with a-SiO2, the electron-phonon coupling parameter for a-SiN is not well

known. For crystalline Si3N4, λ can be estimated to be 4.3 nm from the empirical relation between λ and band gap energy (5.3 eV for Si3N4)20. Considering the fact that λ for amorphous

materials is significantly lower than that for the same material in its crystalline phase, we use λ = 3 nm for a-SiN. This was chosen so that the observed track radii in a-SiN21,22 can be

reproduced (see Supplementary information). With the above mentioned parameters, the evolution of the temperature distribution around the ion impact position was calculated using the i-TS

model. Figure 5 shows the result of a-SiO2. The horizontal line indicates the threshold energy for desorption (_E_d = 0.4 eV/atom16). The energy deposited on the atoms exceeds the threshold

energy when the distance from the impact position _r_ is smaller than 7 nm. This local heating continues for more than picosecond. The similar calculation was performed for the a-SiN

irradiated with the 420 MeV Au ion. The obtained critical radius within which the deposited energy exceeds the threshold energy for desorption is 7.6 nm. These calculated critical radii are

roughly in agreement with the observed nanoparticle cleared radii _R_, indicating that the i-TS model reproduces the temperature distribution during the track formation. It is also

noteworthy that i-TS calculation also reproduces the observed track radius. From Fig. 5, it can be seen that the energy deposited on atoms exceeds the energy to boil (1.7 eV/atom for

a-SiO217) and the energy to melt (0.38 eV/atom17) at _r_ smaller than 1.7 and 7.2 nm, respectively. These radii are in good agreement with the observed track core and shell radius, 1.6 ± 0.3

 nm and 6 ± 1 nm, respectively, for a-SiO2. Finally the difference in the nanoparticle cleared radius between the front and rear surface irradiations is discussed. A possible origin of the

observed difference is the effect of high-energy secondary electrons (so-called δ-rays) produced by the projectile ions. The δ-rays carry away the deposited energy and do not contribute to

heating the place of production but do contribute in the deeper region. As a result, the deposited energy is smaller than the energy loss in the entrance region and increases with depth. The

evolution of the deposited energy along the ion path was calculated using Monte Carlo simulations23. Figure 6 shows the result of the MC simulations for 420 MeV Au ions travelling through

a-SiO2. The result of each simulation is shown by small dots and the averaged result is shown by solid circles. The result was fitted by an exponential function and is shown by a solid line.

The deposited energy at the entrance surface is 20.4 keV/nm and increases with depth. Eventually, it reaches equilibrium at ~15 nm. The deposited energy at the exit surface of the 20-nm

a-SiO2 film is 23.7 keV/nm, which is about 16% larger than that of the entrance surface. Using these deposited energies, the radii of the region where the energy per atom exceeds _E_d were

calculated to be 6.4 nm and 7.0 nm at the entrance and exit surfaces, respectively, for a-SiO2. These radii are slightly larger than the observed results, 5.1 ± 0.6 and 6.0 ± 0.7 nm (see

Table 1), but the difference between the front and rear irradiation is well reproduced. For a-SiN, the calculated radii are 6.9 and 7.6 nm at the entrance and exit surfaces, respectively,

showing good agreement with the observed ones, 7.5 ± 0.9 and 8.1 ± 1.0 nm (see Table 1). These results demonstrate that the desorption of gold nanoparticles can be used to measure the

temperature of the localized area of nm size in a short time period. In passing we note that similar measurements of nanoparticle desorption from a-SiN films of different thicknesses upon

impact of 0.72 and 1.1 MeV C60 ions were performed using different kinds of nanoparticles, platinum and gold nanoparticles with different sizes. In spite of very different experimental

conditions, the observed nanoparticle cleared radii agree with the i-TS calculations. This supports that the present approach is a robust method. In conclusion, gold nanoparticles were

deposited on a-SiO2 and a-SiN films and irradiated with 420 MeV Au ions. The irradiated samples were observed using TEM and HAADF-STEM. The ion tracks produced by the ion irradiation are

clearly seen and the gold nanoparticles are found to be cleared from the vicinity of each ion track. The radii of the nanoparticle cleared regions were derived to be 5.1 ± 0.6 and 6.0 ± 0.7 

nm for front and rear irradiation of a-SiO2, respectively and 7.5 ± 0.9 and 8.1 ± 1.0 nm for a-SiN. The radius of the region where the energy deposited on the atoms exceeds 0.4 eV/atom,

which is the threshold energy for the desorption of gold nanoparticles predicted by the MC simulations, was calculated using the i-TS model. The calculated radii are in reasonable agreement

with the observed nanoparticle cleared radii both for a-SiO2 and a-SiN. The observed difference in the nanoparticle cleared radius between the front and rear surface irradiations was

attributed to the effect of δ–rays and quantitatively reproduced by the i-TS calculations in combination with MC simulations of δ–rays. The present result demonstrates that the desorption of

gold nanoparticles can be utilized for the temperature measurement in a nanometer size region in a picosecond time period. More detailed temperature distribution may be deduced using

nanoparticles of other materials with different melting points (see Supplementary information). METHODS PREPARATION OF SAMPLES Self-supporting a-SiO2 (thickness 20 nm) and a-SiN (thickness

30 nm) films were purchased from Structure Probe, Inc. and Silson Ltd, respectively. The composition of the a-SiN film was determined to be Si0.47N0.53 using high-resolution Rutherford

backscattering spectrometry24, which is slightly Si rich compared to the stoichiometric Si3N4. A small amount of gold was vapor deposited on one side of the films at room temperature under a

vacuum of 10−4 Pa. The average thickness of the deposited gold is several tenth of nanometer. IRRADIATIONS AND TEM MEASUREMENTS The gold-deposited films were irradiated with 420 MeV Au ions

at normal incidence to a fluence of ~5 × 1010 ions/cm2 at the tandem accelerator facility of the Japan Atomic Energy Agency (JAEA). A carbon foil (20 μg/cm2) was placed in front of the

samples to acquire an equilibrium charge state. This carbon foil was also used as a collector foil, _i.e._ used to capture particles emitted from the target during irradiation. The

irradiation was performed either on the gold-deposited side (“front surface irradiation”) or on the rear side (“rear surface irradiation”) at normal incidence. In the rear surface

irradiation, a self-supporting a-SiO2 film was placed just behind the sample (facing to the gold-deposited surface) to capture gold nanoparticles emitted from the film during the

irradiation. Both the irradiated samples and the collector foils were observed using TEM (JEOL JEM-2200FS) equipped with a field emission gun operating at 200 kV. The images were taken by

GATAN Ultrascan 1000 CCD camera with a 2 k × 2 k pixel. For the observation of HAADF-STEM, the electron beam was converged to 0.5 nm in diameter and an annular dark detector covering over

120 mrad were used. ADDITIONAL INFORMATION HOW TO CITE THIS ARTICLE: Nakajima, K. _et al._ Tracing temperature in a nanometer size region in a picosecond time period. _Sci. Rep._ 5, 13363;

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Google Scholar  Download references ACKNOWLEDGEMENTS This work was performed under the shared use program of JAEA facilities. The authors are grateful to Drs. K. Narumi and Y. Saitoh for

fruitful discussion and thank the technical staff of the accelerator facilities at JAEA/Tokai for the 420-MeV Au-ion irradiation. This work was partly supported by JSPS KAKENHI Grant Number

26246025. AUTHOR INFORMATION AUTHORS AND AFFILIATIONS * Department of Micro Engineering, Kyoto University, Kyoto, 615-8540, Japan Kaoru Nakajima, Takumi Kitayama, Hiroaki Hayashi & Kenji

Kimura * Nuclear Science Research Institute, Japan Atomic Energy Agency, Naka, Tokai, 319-1195, Ibaraki, Japan Makoto Matsuda & Masao Sataka * Institute for Integrated Cell-Material

Sciences, Kyoto University, Kyoto, 606-8501, Japan Masahiko Tsujimoto * CIMAP-GANIL (CEA-CNRS-ENSICAEN-Université de Caen Basse Normandie), Bd. H. Becquerel, Caen, 14070, France Marcel

Toulemonde & Serge Bouffard Authors * Kaoru Nakajima View author publications You can also search for this author inPubMed Google Scholar * Takumi Kitayama View author publications You

can also search for this author inPubMed Google Scholar * Hiroaki Hayashi View author publications You can also search for this author inPubMed Google Scholar * Makoto Matsuda View author

publications You can also search for this author inPubMed Google Scholar * Masao Sataka View author publications You can also search for this author inPubMed Google Scholar * Masahiko

Tsujimoto View author publications You can also search for this author inPubMed Google Scholar * Marcel Toulemonde View author publications You can also search for this author inPubMed 

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author inPubMed Google Scholar CONTRIBUTIONS K.K. and K.N. conceived and conducted the study. T.K., H.H. and K.N. prepared samples. M.M., M.S. and T.K. performed the irradiations. M.

Tsujimoto observed the samples using TEM and HAADF-STEM. T.K. and H.H. performed data analysis. M. Toulemonde performed the i-TS calculations. S.B. performed MD simulations of δ-rays. K.K.

and M. Toulemonde wrote the paper in consultation with all authors. ETHICS DECLARATIONS COMPETING INTERESTS The authors declare no competing financial interests. ELECTRONIC SUPPLEMENTARY

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ABOUT THIS ARTICLE CITE THIS ARTICLE Nakajima, K., Kitayama, T., Hayashi, H. _et al._ Tracing temperature in a nanometer size region in a picosecond time period. _Sci Rep_ 5, 13363 (2015).

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