Desorption of gold nanoclusters from gold nanodispersed targets by 200 keV Au5 polyatomic ions in the elastic stopping mode: Experiment and molecular-dynamics simulation

Nuclear Instruments and Methods in Physics Research B 267 (2009) 2503–2514

Contents lists available at ScienceDirect

Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb

Desorption of gold nanoclusters from gold nanodispersed targets by 200 keV Au5 polyatomic ions in the elastic stopping mode: Experiment and molecular-dynamics simulation C. Anders a, I. Baranov b,*, S. Della-Negra c, V. Domaratsky b, M. Fallavier d, A. Novikov c, V. Obnorsky b, K. Wien e, S. Yarmiychuk b, G. Ziegenhain a, H.M. Urbassek a a

Universität Kaiserslautern, Physics Department, Erwin-Schrödinger-Strasse, 67663, Kaiserslautern, Germany V.G. Khlopin Radium Institute, 2nd Murinskii Ave. 28, 194021 St.Petersburg, Russia Institut de Physique Nucléaire, CNRS-IN2P3, 91406 Orsay Cedex, France d Institut de Physique Nucléaire, CNRS-IN2P2, Universite Claude Bernard, Lyon I, 69622 Villeurbanne Cedex, France e Institut für Kernphysik der Technische Universität Darmstadt, Schloßgartenstraße 9, 64289 Darmstadt, Germany b c

a r t i c l e

i n f o

Article history: Received 21 July 2008 Received in revised form 4 May 2009 Available online 27 May 2009 PACS: 79.20.Rf 61.82.Rx 36.40.c Keywords: Nanoislet metal target Cluster projectiles Nanocluster ejection

a b s t r a c t Au nanoislet targets (£ 2–60 nm) were bombarded by 200 keV polyatomic ions (40 keV/atom), which P P deposit their energy mainly in the nuclear stopping mode: (dE/dx)n = 30 keV/nm and (dE/dx)e = 2 keV/nm. The matter desorbed in the form of nanoclusters was registered by TEM. The total transfer of matter was determined by neutron-activation analysis. The total yield of the ejected gold reached high values of up to 2.6  104 atoms per Au5 ion. The major part (2  104 atoms per ion Au5) of the emission is in the form of nanoclusters. The results are compared with the data of similar experiments with 1 MeV Au5 (200 keV/atom) and other projectiles. The analysis of the experimental data and the comparison to molecular-dynamics simulation results of the desorption process show that the desorption of Au nanoislets is induced by their melting, build-up of pressure and thermal expansion. Ó 2009 Elsevier B.V. All rights reserved.

1. Introduction The interaction of ion irradiation with nanoparticles and nanostructured surfaces raises interesting fundamental questions. In contrast to the interaction with flat surfaces of bulk targets, the size of the irradiated nanoobjects may play a major role. Nanoparticles have a limited number of atoms, many of whom form part of the surface. This has interesting consequences, which may be termed a ‘size effect’. In a nanoislet (NI), the energy deposited by an ion will be (in first approximation) proportional to the path length of the ion; if the ion is not fully stopped in the NI, the energy deposition will thus be proportional to the NI diameter, £, which we take as the measure of the NI size. However, the number of atoms in the NI is proportional to £3, and hence the deposited energy density (averaged throughout the NI) is £2. Thus, with decrease of £, phase transitions in the NI (melting, atomization) will depend on the NI size.

* Corresponding author. Tel.: +7 812 545 43 70; fax: +7 812 297 80 95. E-mail address: [email protected] (I. Baranov). 0168-583X/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2009.05.010

In bulk materials, regions of high energy density (collision spikes), which may have been created by ion impact, may quickly cool due to heat transport to the surroundings. This mechanism will be strongly suppressed in NIs, due to the deteriorated heat contact with the substrate onto which the NIs are deposited. In the case of metals, such as the metal Au studied here, electrons may play an important role in energy dissipation into the surrounding; in the case of NIs supported on an insulating substrate, electrons can hardly conduct energy away from the NI. In this sense, the physics occurring in irradiated NIs is actually simpler than in bulk targets; while the irradiating ions deposit their energy both in the atomic (elastic stopping) and electronic (inelastic stopping) subsystem of the NI, after a time of thermal equilibration and energy exchange between the two subsystems, the energy is spread out homogeneously in the NI; this makes the study of the ensuing processes easier. In irradiated bulk targets, on the other hand, the two subsystems will generally not reach equilibrium, since the strong spatial gradients in energy deposition will continuously conduct energy away. An important procedure to obtain information on ion interaction with solids is given by the measurement of emitted (sputtered

2504

C. Anders et al. / Nuclear Instruments and Methods in Physics Research B 267 (2009) 2503–2514

or desorbed) material. Such emission may occur in the form of monatomic atoms, but also by clusters. Actually, in several studies it has been found that (more or less) intact NIs may be desorbed from surfaces under ion impact; these clusters will in the following be called nanoclusters (NCs) in order to differentiate them from the NIs on the substrate surface. In the following we collect some important information on previous work on NI desorption.

For the first time ion beams in the elastic stopping mode were used for the desorption of nanoclusters from nanoislet targets in [1]. In this work, the NI and NC size spectra could be determined for polyatomic Au5 cluster impact with 6 MeV total energy, as well as the total matter transfer per ion, the limiting size (£max). Compared to monoatomic ions, five-atom cluster ions with heavy atoms (Au) may deposit higher elastic energy. Similar experiments

Table 1 Parameters of nanoisland targets and yields of gold (total and in the form of nanoclusters). Target

Substrate temperature at the target preparation (°C)

Mean islet size (d ± r), nm

Percentage of target area occupied by islets (c)

Mean nanocluster size (d ± r), nm

Mean polar angle*, degrees, and exponent factor k

Yield of nanoclusters (ncl./ion Au5)

Transfer of Au by NCs (at./ion Au5)

Total yield (at./ion Au5)

#1 #2 #3

20 °C 20 °C 180 °C

12 23 32.6

220 °C

#5

350 °C

3.7±1.9 6.0±3.7 4.3±2.0 10.0±6.5 4.1±2.0 13.0±6.0 3.5±1.7 12.9±6.1

37 37 37 30 37 32 37 37

3.3 2.1 0.6 0.6 0.3 0.1 1.2 0.01

5.0  103 1.5  104 1.6  103 1.8  104 6.2  102 6.8  103 1.5  103 3.9  102

8.9  103 2.1  104 2.6  104

#4

3.8±1.7 5.5±2.3 4.4±2.6 11.4±6.0 5.2±2.0 15.5±9.2 7.1±4.3 29.3±16.6

*

44 55

(1.2) (1.2) (1.2) (1.4) (1.2) (1.3) (1.2) (1.2)

Mean polar angle – half of the polar angle, corresponding to the solid angle where 95% of nanoclusters are desorbed.

Fig. 1. (a)–(e) TEM images of Au islet layers for the targets ##1–5.

6.6  103 1.4  103

2505

C. Anders et al. / Nuclear Instruments and Methods in Physics Research B 267 (2009) 2503–2514

with the corresponding sets of NI Au targets, measuring the same parameters were made with 1 MeV (200 keV/atom) Au5 ions [2], i.e. with 5 times lower energy than in [1], and with 38 keV Au1 ions [3], where the total energy losses for elastic stopping were 95%, for inelastic losses – 5%, the limiting size and the total range of the ejected Au NCs being 14 nm. Several other investigations referring to the elastic stopping mode should also be mentioned. Papers [4–6] are devoted to the formation of craters, penetration of gold and transfer of the latter from thin discrete films on Si substrates, as well as from nanoislet gold targets under bombardment by mainly 1.5 MeV Au1 ions with total losses for elastic stopping 80% and inelastic 20%, with the total range in gold 100 nm, as well as by 32 keV Au1, i.e. in the mainly elastic stopping mode. Other results include TEM measurements of size distributions of the ejected nanoparticles, though neither initial size distributions of target nanoislets (Au1 32 keV), nor their absolute yields were measured.

In the present paper measurements similar to those made in [1,2] are presented with 200 keV (40 keV/atom) Au5 ions. These have 5 times lower energy than the projectiles in [2] and 30 times lower energy than in [1]. In agreement with their relatively low initial velocity 1.4  107 cm/s, they lose their energy mainly in elastic collisions. Our investigation and the comparison with previous results make it possible to obtain information on the emission mechanism of NCs by ions in the mode of mainly elastic stopping. 2. Experimental technique 2.1. Nanodispersed targets Five NI gold targets with islets ranging from 2 to 60 nm in size were used. The mean size of the islets varied from 4 to 30 nm. The substrates were made of Al covered with a 15–20 nm carbon film. NI layers were deposited by thermoevaporation of gold in vacuum

200 keV Au5 ion beam

Collector 6 mm

Gold nanoclusters

45

Target

Types of collectors Al foil for neutron activation analysis

TEM-grid mosaic

5 mm

Beam entry

Beam entry ent

Fig. 2. Scheme of the experiment with the 200 keV Au5 ion beam.

Table 2 Limiting sizes of NC ejected by ions with different energies mainly in the elastic stopping mode. Ions

Au5 Au5 Au5 Au1

Total energy, keV

Energy per atom, keV

Total energy losses in elastic processes at the ion stopping in Au, keV

Total energy losses in inelastic processes at the ion stopping in Au, keV

On entering of the ion into Au nanoisland (dE/ dx)n keV/ nm

(dE/ dx)e keV/ nm

Velocity of the ion (107 cm/ s)

6000 1000 200 38

1200 200 40 38

5253 (87.6%) 928 (93%) 188.8 (94.4%) 36 (95%)

747 (12.4%) 72 (7%) 11.2 (5.6%) 2 (5%)

49 45 30 5.8

11 4.5 2 0.4

7.7 3 1.4 1.3

Range of ions (in Au, nm)

Limiting size of NC, nm (number of atoms in the NC)

Energy per atom (eV/at)

Reference

78 17.6 6 5.8

86 (2.0  107) 40 (2.0  106) 24 (4.8  105) 14 (8.5  104)

0.32 0.50 0.47 0.45

[1] [2] Presentwork [3]

2506

C. Anders et al. / Nuclear Instruments and Methods in Physics Research B 267 (2009) 2503–2514

according to the procedure described in Refs. [7,8] (see Table 1) and were characterized by means of transmission electron microscopy (TEM). Fig. 1(a)–(e) shows TEM images of the islet layers of all the 5 targets. We draw attention to the rather high substrate temperature (350 °C) under which target #5 was prepared. 2.2. Target irradiation and determination of the amount of the ejected gold The scheme of the experiment is given in Fig. 2. The targets were irradiated by 200 keV Au5 polyatomic ions at the Van de Graaf accelerator of the Institute of Nuclear Physics in Lyon. The ions bombarded the target at a = 45o to the surface. The calculated values of the nuclear and electronic stopping powers of 200 keV Au5 ions – estimated as the sum of the values for five 40 keV Au ions in gold – are according to SRIM 2003 [9]: (dE/dx)n = 29.6 keV/nm and (dE/dx)e = 2.0 keV/nm. This demonstrates that the projectiles lose 94.4% of their initial energy by elastic stopping and only 5.6% of the energy is given to electrons, Table 2. The projectile range estimated from these values is 6 nm. We note that (i) the recoil atoms are themselves subject to electronic stopping; we estimate that roughly 50% of the projectile energy will ultimately be given to electrons; (ii) the SRIM stopping forces given above apply to the clusters entering the target; since stopping is energy dependent, the stopping forces will vary during projectile slowing down.

A 2 mm diaphragm limited the beam of projectile ions. The intensity of the projectile beam, which passed through the diaphragm, was measured by means of a Faraday cup placed behind the target directly before and after irradiation (the target was removed during the measurements). The fluence of the ions on a 4 mm2 target area was 2  1010 ions (5  1011 cm2) in order to stay in the ‘static’ regime, i.e., to avoid any major changes in the target structure induced by the bombardment. To collect NCs, 10 spots on 3 targets from one set were irradiated, the NCs being collected onto the corresponding set of TEM grids covered by 15-20 nm carbon films. The grids are arranged on a T-shape collector (see Fig. 2(a)) to be examined by TEM in order to determine the size distributions of NCs, dNclust/dD (D is the NC size, D > 2 nm) and the density of NCs collected per lm2 to determine the angular distribution as well as the total number of desorbed NCs. For the neutron-activation analysis the total number of Au atoms were collected onto Al foils (Fig. 2(b)) with a fluence of 2  1010 cm2. The total yield of the desorbed NCs as well as the total yield of the ejected gold was calculated counting on a 200 keV Au5 projectile hitting the area of the substrate occupied by NIs: Y = Ntot/(Nproj  c/cos(a)); here Ntot is the total number of NCs or total number of Au atoms emitted from the target, Nproj is the number of projectiles incident on the target, c is the surface coverage with NIs (see 1), and a = 45o is the projectile incidence angle (Fig. 2). The two latter factors were introduced to correct for the

Fig. 3. (a)–(e) TEM images of Au nanoclusters ejected by 200 keV Au5 ions from the targets ##1–5.

2507

C. Anders et al. / Nuclear Instruments and Methods in Physics Research B 267 (2009) 2503–2514

fact that not every projectile hits a NI (factor c) and that the apparent surface area irradiated by an oblique ion beam becomes enlarged (factor 1/cos(a)).

TEM images of NIs and NCs respectively for target #4 with a higher magnification than for targets #1, 2, 3 and 5 for easier comparison of the shape of these particles. Fig. 4 shows the size distributions of NIs on 5 targets and those of NCs ejected from them. For the targets #3, 4 and 5 these distributions have two maxima, which are formed due to the character of growth of an islet film [10]. For all the targets irradiated in the experiment, ejection of intact NIs was observed. For the targets with the mean islet size of 4–6 nm (targets #1 and 2), the size distribution of NCs coincides with that of the NIs on the targets and for the target #3 they almost coincide.

3. Experimental results 3.1. Size distributions of the desorbed nanoclusters

110 100 90 80 70 60 50 40 30 20 10 0

140 Target #1 d=(3.8 +-1.7) nm

d=(3.7 +- 1.9) nm

120 100 Counts

Counts

Fig. 3(a)–(e) shows TEM images of the Au NCs ejected by 200 keV Au5 ions from the targets # 1–5. Figs. 1 and 3(d) show

80 60 40 20 0

2

4 Islet size,nm

6

8

0

24

6

8

Nanocluster size, nm 300

400 Target #2 d=(5.5 +-2.3)nm

350

d=(6.0 +-3.6)nm 250 200

250

Counts

Counts

300

200 150

150 100

100 50

50

0

0 0

246

8

10

02

12

46

Islet size, nm 80

12

14

350 Target #3 d=(4.4 +-2.5)nm d=(11.3 +-6.0) nm

60

d=(4.3 +-2.0) nm d=(9.9 +-6.4) nm

300 250 Counts

Counts

8 10 Nanocluster size, nm

40

200 150 100

20

50 0

0 02468

10 12 14 Islet size,nm

16

18

20

22

0

4

6

8

1 01 21 4 1 61 Nanocluster size, nm

82

0

2 22

4

200

80

d=(4.0 +-2.0) nm d=(13.0+-6.0) nm

Target #4 d=(5.2 +-1.9) nm d=(15.4 +-9.1) nm

70 60

150

50

Counts

Counts

2

40 30

100

50

20 10

0

0 0

5

10

15

20

25

30

0

35

5

10

20

25

30

3000

200

2500

Target #5 d=(7.0 +-4.2) nm d=(29.2 +-16.6)nm

d=(3.5 +-1.7) nm d=(12.8 +-6.1) nm

2000 Counts

150 Counts

15

Nanocluster size, nm

Islet size,nm

100

1500 1000 500

50 5 0

0 0

5

10

15

20

25 30 35 40 Islet size,nm

45

50

55

60

65

0

5

10 15 Nanocluster size,nm

20

25

Fig. 4. Size distributions of islets on the targets ## 1–5 and nanoclusters ejected from these targets and gathered on the collectors.

C. Anders et al. / Nuclear Instruments and Methods in Physics Research B 267 (2009) 2503–2514

The size distributions of the desorbed nanoclusters vanish at sizes > 20 nm. However, there are particular cases of larger NCs up to 24 nm (Fig. 4, targets #4 and #5). The angular distribution of the ejected gold was estimated on the basis of the distribution of the surface density of the collected NCs. The angular distributions of the ejected gold NCs are peaked normally to the surface; for larger NCs the distributions are narrower, Fig. 5. The angular distributions of the NCs in the incidence plane of the beam and normally to this plane appeared to be similar, see Fig. 6. This points that the momentum of a 200 keV Au5 ion is small and does not affect the angular distribution of the NCs. The angular distribution has been found to be well described by the function: dn/dX = g(h)exp(k  h)  cos(h), where h is the desorption polar angle and k = 1.21.4 is the exponent factor reflecting the steep slope of a branch of the angular dependence. We use this analytical representation for the analysis of the experimental data concerning the collection of material on the TEM grids and Al foils.

The yield of desorbed NCs was estimated taking into account the angular distribution in accordance with the procedure described in [8] and was from 3 NCs per Au5 ion for NCs with the mean size of 3.7 nm (target #1) up to 0.1 NCs per ion for those with a mean size of 13 nm (target #4), see Fig. 7 and Table 1. For

1600

Target #3 -nanocluster size ~4.3 nm -nanocluster size ~10 nm

1400 -2

3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 2

4

6

8

10

12

14

Nanocluster size. nm Fig. 7. Absolute yields of the gold nanoclusters ejected by 200 keV Au5 ions from the targets ## 1–4.

3.2. Yields of the ejected gold

Nanocluster density, µm

4.0

Yield. nanocl./Au5

2508

1200 1000 800 600 400 200

the hottest target #5 (350 °C) the yield is lower; this is probably due to the increase of both the NC sizes and their adhesion to the surface and hence the results for target #5 have to be regarded with some caution. The total transfer of gold is given in Table 1 for all the 5 targets. When due account is taken of all the factors contributing to the error (precise monitoring of the ion beam, exact determination of the number of the collected gold by neutron-activation analysis etc.), the total error of the yield measurement is estimated to be 35%. It is evident from the table that depending on the mean sizes of the NIs on the target the total yield value varies from 1.4  103 to 2.6  104 atoms/Au5. With the assumption of spherical clusters, we can estimate that the main part of the gold is transferred in the form of intact nanoclusters for the targets #1, 2, 3 and 4 (see Table 1). The desorbed NCs have an ideally smooth and round shape, see Fig. 3(a)–(e). Comparison of Figs. 1 and 3(a)–(e), as well as 1d and 3d, shows that NC desorption is accompanied by melting of NIs on the targets.

0 -60

-40

-20

0

20

40

60

4. Analysis of experimental data

Angle of ejection, degree Fig. 5. Distribution of the surface density of the collected gold nanoclusters desorbed from the target #3 depending on the angle, at which the center of a TEMgrid is seen from the center of the target area irradiated.

- long collector size - short collector size

Nanocluster density, µm

-2

1200

600

0 -60

-40

-20

0

20

40

60

Angle of ejection, degree Fig. 6. Surface density of the collected gold nanoclusters desorbed from the target #3 in the longitudinal (long side) and transverse (short side) directions relative to the plane of the ion beam normal to the surface.

We estimate the energy released by 200 keV Au5 ions in NIs in the size range of 3–24 nm and consider their subsequent fate. This size range is considered since NI ejection is observed only in this range, even though experiments have been performed for NI size distributions extending up to 30–60 nm (targets #4 and #5). Our analysis is based on the comparison of the ion range (6 nm) with the NI diameter, and on the average energy delivered to a NI atom; depending on whether this energy is larger than the energy needed for melting (0.41 eV/atom) or even larger than the energy needed for NI atomization (3.75 eV/atom), the NI suffers different fates. (a) In NI with £ > 24 nm, the projectile can be completely stopped and delivers its total impact energy to the NI. Thus the energy deposited per atom is <0.41 and the NI is only heated. Experiment shows that desorption of these NIs is not observed (Fig. 4, targets #4 and 5). (b) NIs with £ = 12–24 nm are melted but will not be destroyed, since the energy released by a 200 keV Au5 ion is lower than 3.75 eV/atom (atomic binding energy in gold) but higher than 0.41 eV/atom (the energy necessary for melting gold). (c) When the NI size becomes <12 nm they can both get destroyed or melted depending on the length of the trajectory of the Au5 projectile inside the NC. Therefore the energy

C. Anders et al. / Nuclear Instruments and Methods in Physics Research B 267 (2009) 2503–2514

per atom is either higher or lower than 3.75 eV. Note that with decreasing NI size £, the number of atoms in the NI decreases £3, while the deposited energy will be proportional to the ion path length in the NI and hence be limited by £. That is why the probability of NI destruction (sputtering) increases sharply and that of melting decreases with decreasing NI size. Destroyed NIs contribute to the total transfer of the gold atoms onto the collector. NIs having a size <6 nm are destroyed by 200 keV Au5 ions with high probability; their atoms are sputtered and scattered at 4p. (d) However, nanoclusters with £66 nm appear in the experimental size distributions, Fig. 4. Where do they come from? We propose that while the NC hit by the projectile is destroyed, its fragments may hit the surrounding NCs on the substrate surface and impart them enough energy to desorb from the surface. The amount of energy imparted to neighboring NIs depends primarily on the areal density of NCs on the substrate surface; when NCs are close to each other, fragments may have a high probability to hit them and induce their melting. We propose that the desorption of NIs is connected with their melting. As a result of the shape change associated with melting and due to the concurrent reduction of the surface area of the NI, energy is released, a part of which may be transformed into kinetic energy of the created NC, shifting its center of mass away from the substrate. We note that an analogous mechanism has been proposed in [11] in order to explain the interaction of a liquid drop with a liquid surface in a micro-gravity environment. We shall investigate this mechanism in detail in the following section using atomistic simulation.

2509

one particular case (Einit = 0.39 eV) the simulation length had to be increased to determine whether the cluster desorbs. We obtained the following results: (a) Desorption mechanism: After the initial energization, the energy is equilibrated in the cluster, it may melt and possibly finally

5. Simulation set-up and results In order to study whether the desorption process invoked here is realistic, we performed molecular-dynamics simulations. Specifically, the desorption process of a AuN NI containing N = 6000 atoms off a substrate surface. The Au–Au interaction potential is chosen of a many-body form [12–14]; this potential reproduces the melting temperature of Au, Tmelt = 1338 K. A hemispherical cluster was constructed by cutting it out of a Au crystal; it hence originally possesses an fcc crystal structure. Its (100) base plane contains 486 atoms. Before the start of the simulation, the NI is allowed to relax to relieve all internal stresses. The NI is set on a substrate, which is modelled according to a graphite surface. Since details of the atomistic nature of the graphite surface are assumed to play only a minor role in the desorption process studied here, we model the surface as a flat plane. It interacts via a Morse potential

VðzÞ ¼ D exp½2aðz  zeÞ  2D exp½aðz  zeÞ

ð1Þ

with each cluster atom (z is the distance of a cluster atom to the surface plane), to provide both the attractive forces which initially bind the cluster to the surface and repulsive forces which are important in the desorption process. The Morse potential parameters (D = 0.153 eV, ze = 2.6 Å, a = 2.6/Å) are taken from [15]; note that basically only the lowest Au layer of the cluster is bonded to the substrate in this potential. We let the cluster relax on the surface; it maintains its hemispherical form. The adsorption energy towards the substrate amounts to ND = 74 eV. The simulation is started at time t = 0 by giving each cluster atom an energy Einit, which we vary in the range of 0.13–1.1 eV; we call this the energization. The energization is realized by giving each atom the same kinetic energy with random direction of the velocity. We follow the processes occurring until 30 ps; only in

Fig. 8. Cross-sectional snap shots of the Au6000 cluster after energization to different energies Einit per atom. Colour denotes temperature in K. The substrate surface is at the bottom of the figure: (a) Einit = 0.13 eV at time t = 30 ps after energization. The hemispherical cluster stays at the surface. (b) Einit = 0.39 eV at time t = 170 ps after energization. The cluster assumes a spherical shape, but remains bound to the surface. (c) Einit = 0.8 eV at time t = 42 ps after energization. The spherical cluster has desorbed off the surface.

2510

C. Anders et al. / Nuclear Instruments and Methods in Physics Research B 267 (2009) 2503–2514

desorb off the surface. Fig. 8 shows the results of cluster energization for three different values of Einit. For the smallest energization (Fig. 8(a)), the temperature is not sufficient to induce melting; the cluster maintains its hemispherical form and rests on the surface. For the largest value (Fig. 8(c)), the cluster desorbs off the surface; it has been molten and acquires a spherical shape. In the intermediate case shown in Fig. 8(b), the cluster does melt and becomes spherical, but it does not leave the surface.

Fig. 9 displays several snapshots showing the desorption case of Fig. 8(c). At the earliest time, t = 1 ps, the crystalline cluster has started melting. A major change happens at 3 ps: The inner part of the cluster has left the surface, while the outer cluster rims still are close to the surface. Note that the figure only shows a crosssectional view; the three-dimensional shape is obtained by rotating the figure around the middle axis of the cluster. The reason for this change of shape is the build-up of a high pressure in the

Fig. 9. Time series of cross-sectional snapshots displaying the desorption process of a Au6000 cluster after energization to energy Einit = 0.8 eV per atom. Color denotes temperature in K. The substrate surface is at the bottom of the figure. (For interpretation of the references in colour in this figure legend, the reader is referred to the web version of this article.)

2511

C. Anders et al. / Nuclear Instruments and Methods in Physics Research B 267 (2009) 2503–2514

center of the cluster. This pressure is called ‘thermoelastic’ and its origin can be understood from the tendency of the cluster to expand with temperature. Consequently, the cluster starts expanding in all directions. However, in ‘downward’ direction, the cluster is repelled from the substrate; this eventually leads to the momentum inducing cluster desorption, and to the asymmetrical shape seen. In Fig. 10, we display the pressure distribution inside the energized cluster (same event as Fig. 9). The high energization leads to

the build-up of a large compressive pressure in the cluster; at this high energization, it has had no time to expand in order to relax the thermoelastic pressure and hence is under high compressive stress. Pressure relaxation (called ‘unloading’) starts at the surface and travels as a rarefaction wave towards the cluster center, leading to large tensile pressures in the cluster center. In a reference simulation of a cluster energized in vacuum (not deposited on a surface), we even observed the temporary formation of a void in the cluster center. However, the vicinity of the surface changes the picture; at this interface, the pressure always remains compressive due to the repulsion of cluster atoms from the substrate. As a consequence, a net momentum is imparted to the cluster in the direction normal to the surface, which leads to desorption. We note that a similar mechanism has been proposed [16]. – and later accompanied by molecular-dynamics simulations [17]- for the desorption of biomolecules by ionizing radiation, and has been termed the ‘popcorn mechanism’ The sudden nature of desorption and its origin in thermal expansion and thermoelastic pressure would allow to use this terminology also in the present case. At time t = 10 ps (Fig. 9(c)) the cluster has already entirely left the surface. It now has reached a disk-like shape, while retaining its curvature. The ensuing snapshots show that the cluster performs ‘flapping’ oscillations, where the rim moves up and down with respect to the cluster center of mass. Simultaneously, the cluster attempts to acquire a spherical shape, which is finally reached at t = 42 ps (Fig. 8(c)). Note that the oscillatory motion is damped quite quickly; damping is due both to the viscosity of the liquid and to the action of the surface tension. (b) Dependence on energization: Fig. 11 displays the time evolution of the center-of-mass distance z to the substrate. Clearly, for the lowest energization, the cluster center of mass does not move; this is in accordance with Fig. 8(a), which shows that the cluster remains crystalline. For Einit = 0.26 eV, the cluster attempts to move away from the surface, but finally ends again adsorbed on the surface. We verified that it maintained its hemispherical shape. An energization of 0.39 eV leads to the borderline case visualized in Fig. 8(b). Here the cluster assumes a spherical shape; by necessity it moves its center of mass away from the surface. However, the energy of this motion does not suffice to desorb it from the surface. All the larger energizations lead to cluster desorption. Fig. 12 allows to discuss in detail the channels into which the total energy Etot = NEinit given to the cluster is distributed as a func-

80

80

Einit (eV) 0.13 0.26 0.35 0.39 0.41 0.45 0.52 0.80 1.03

70 60

z (Å)

50 40

70 60 50 40

30

30

20

20

10

10

0

0

5

10

15

20

25

30

35

40

60

80 100 120 140 160

0

t (ps)

Fig. 10. Same as Fig. 9, but color denotes pressure in GPa. Positive pressure is compressive, negative pressure is tensile. (For interpretation of the references in colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 11. Distance of the center-of mass of the desorbing cluster as a function of time t after sudden energization to an energy Einit per atom. The right half of the figure shows the temporal evolution of the special case of Einit = 0.39 eV/atom, in which the cluster changes its form, but does not desorb.

2512

Etrans ¼ 600ðEinit  0:4 eVÞ:

7000

Etrans Etherm Ekin Epot Etot Etot/2 Emelt Evapor

6000

E (eV)

5000 4000 3000 2000 1000 0 0

b

1

0.2

0.4

0.6 Einit (eV)

0.8

1

0.4

0.6 Einit (eV)

0.8

1

Etrans Etherm Ekin Epot

0.8

E/Etot

0.6

0.4

0.2

0 0

0.2

Fig. 12. Partitioning of the energy in a cluster energized to an energy Einit per atom at the end of the simulation, t = 30 ps. Etot, total energy given to the cluster during energization; Epot, increase of potential energy; Ekin, kinetic energy; Etherm, thermal (random) part of kinetic energy; Etrans, center-of-mass translational part of kinetic energy. The lines Emelt and Evapor indicate melting and vaporization energies of the cluster. The line Etot/2 indicates equipartition of potential and kinetic energy, as it is observed for small energizations, Einit < 0.3 eV. (a): absolute energies (b) relative energies.

tion of the energization Einit; Fig. 12(a) shows the absolute energies, while Fig. 12(b) gives the energies relative to the total energy. The figure shows the contributions of kinetic and potential energy to the total energy; Epot and Ekin are symmetrical with respect to half the total energy, Etot/2, as they must. Furthermore, the kinetic energy is split up into two contributions, the translational energy of the center-of-mass motion of the cluster, Etrans, and the thermal energy (kinetic energy of random motion) inside the cluster. In order to put the energies into perspective, we introduce in Fig. 12(a) the melting energy

4500 4000 3500

Tend Einit/3k Tmelt Tvapor

3000 2500

ð2Þ

2000

where k is the Boltzmann constant, and an analogous vaporization energy Evapor, based on Tvapor = 3080 K. Fig. 12 demonstrates that the crystal starts melting at energizations Einit > 0.25 eV, where potential and kinetic energies start deviating from each other; for Einit > 0.5 eV, the entire crystal has become molten (cf. Fig. 8(b)). The difference between potential and kinetic energy reflects the latent heat of melting. Note that in an energy window around 0.4 eV, the kinetic energy does not increase, i.e., any increase in Einit is fully used to induce melting. Above Einit = 0.4 eV, the cluster desorbs from the surface and attains a definite translational energy. It can be fitted to a linear law,

1500

Emelt ¼ ð3=2ÞNkT melt ;

ð3Þ

Even at the highest energizations studied, Einit = 1 eV, the fraction of energy transformed into center-of mass motion only reaches values of 6.3%. The threshold found here corresponds to the energization needed for cluster melting. The attractive well binding the cluster to the substrate seems to play only a minor role. We note that we performed a series of reference simulation, in which we neglected the attractive binding of the NI to the substrate. In these no threshold to desorption was found; even at very small energizations (even below 0.3 eV), the cluster may desorb. In this case, cluster melting is decisive for desorption: As long as the cluster remains crystalline, atom motions remain small and the cluster may stay at the surface or leave it with only very small velocity. However, as soon as it melts, the surface tension tends to minimize its surface area, and the cluster will form a sphere; during this process cluster atoms hit the repulsive wall and energy is converted to translational energy of the cluster center-of-mass; but the energy conversion is found to be quite ineffective (only 1.4% even for the highest energizations). The borderline case of Fig. 8(b) would lead to desorption in the case of a purely repulsive interaction with the substrate. Note that the total energy imparted to the cluster when desorption may occur (>2400 eV) is large compared to the binding energy of the cluster to the surface (74 eV). It might be asked whether the release of surface energy which occurs when the cluster melts and forms a sphere helps in the desorption process. The specific surface energy of liquid Au at 2300 K has been measured to be around 0.62 J/m2; it slightly decreases with temperature and is of similar size as for solid Au [18,19]. We note that in our potential, the specific surface energy is well reproduced; we obtain 0.6 ± 0.08 J/m2. This value compares well with that obtained with other potentials [20]. Thus the initial surface energy of the hemispherical cluster (surface of 120 nm2) is around 450 eV. When the cluster forms a sphere (area of 100 nm2), it hence can lower its energy by a surface energy term of 75 eV. These values are confirmed by our atomistic molecular-dynamics simulations. We conclude that for weak attractions to the substrate, surface tension may contribute as an important driving force for desorption: As soon as the cluster melts, it attempts to acquire a spherical shape, thus pushing the cluster away from the surface (cf. Fig. 8(b)). Even in the present case, the energy gain by assuming a spherical surface (75 eV) is of the same order of magnitude as the cluster–substrate bond (74 eV) and may hence induce desorp-

T (K)

a

C. Anders et al. / Nuclear Instruments and Methods in Physics Research B 267 (2009) 2503–2514

1000 500 0 0

0.2

0.4

0.6

0.8

1

Einit (eV) Fig. 13. Final temperature Tend of the cluster at t = 30 ps after energization to an energy Einit per atom. The melting and vaporization temperatures of Au are indicated. The line Einit/3 k, where k is the Boltzmann constant, indicates the temperature reached in a harmonic solid (Dulong–Petit law).

C. Anders et al. / Nuclear Instruments and Methods in Physics Research B 267 (2009) 2503–2514

tion. However, at higher energizations, the ‘popcorn’ mechanism based on the thermal expansion of the cluster has a stronger influence. We note that we see no easy way to separate the effect of pressure from the surface tension in inducing desorption. Fig. 13, finally displays the temperatures measured in the cluster at the end of the simulation. A linear law – based on a harmonic solid (Dulong–Petit rule) – is well fulfilled for temperatures below the melting point. Melting in the cluster is observed to occur already at around 1130 K, well below the bulk melting point. This reflects the size effect of the melting phenomenon found in nanoparticles [21]. Above the melting point, the cluster temperature again increases in proportion with the energization, until a temperature of around 2340 K is reached for the highest energizations studied. 6. Discussion 6.1. Comparison to available models Let us first discuss in how far existing models may be used to explain our experimental results. Such models are based on: (1) the shock-wave, which might be generated by a 200 keV Au5 ion impact on the NI or on the substrate – this might be called a ‘‘trampoline effect” [22]; (2) the ‘‘lift-effect”, which considers intact ejection of NI to occur by the collective momentum imparted by substrate atoms sputtered by a 200 keV Au5 ion which entered the substrate under a nanoislet [23]; 3) the ‘‘recoil effect” discovered in [24]. It means that when under a non-central impact of a 200 keV Au5 ion on a NI hundreds of Au atoms get knocked out towards the substrate, a recoil momentum is imparted to the rest of the NI and accelerates it away from the substrate. However, it was shown in [24] that heavy gold NIs may not be shaken off by light carbon ions as a result of the shock wave (trampoline effect); for the same reason the lift-effect [23] does not work either in the carbon substrate (15–20 nm), on which heavy Au NIs of targets ##1–5 lie. These questions are considered in detail in [24]. The ‘‘recoil” effect was calculated using a classical molecular-dynamics method in [24] for 6 nm NIs. This channel was found to provide a 10% ejection probability of NIs when 72 keV Au400 ions penetrate the nanoislets. It may be applied to all the targets. However, its efficiency will not be high because it decreases with increasing NI size (mass). We note that we performed simulations to investigate the probability of NI desorption due to the ‘‘recoil effect” for 200 keV Au5 projectiles. In contrast to the case of 72 keV Au400 projectiles, no intact desorption event was found. This behaviour is due to the fact that a larger Au400 projectile acts rather like a massive ‘‘cannon ball”, which is able to impart a recoil momentum collectively to a NI, while a smaller (and faster) Au5 projectile may transfer energy to a NI by nuclear stopping, but only little center-of-mass momentum.

7. Explanation of experimental results The mechanism of NI desorption proposed here is based on the melting of NIs, the energy release due to reduction of the NI surface area and movement of its center of mass normally away from the substrate. It is also connected with the pressure build-up inside the NI due to the energy swiftly deposited by the projectile, the subsequent expansion of the NI and its pressure onto the substrate, which results in NI’s recoil from the substrate. In the following, we list the experimental results, which may be explained within the framework of the proposed mechanism. 1. For all the targets with different size distributions of NIs the angular distributions of the NCs are peaked normally to the surface. These angular distributions are explained by movement of

2513

the mass center and recoil of the desorbed NIs normally from the surface as soon as the NIs get melted and expand. Expansion of angular distributions with the decrease of NI sizes, Fig. 5, may be due to higher sensitivity of small NIs to the substrate surface structure. 2. Yields NIs/ion Y > 1. Under bombardment of all the 5 targets with the mean NI sizes from 4 to 30 nm by 200 keV Au5 ions we measured both total transfer of Au from the targets onto a collector per ion hitting a NI and the yields Y, i.e. the number of desorbed NCs per ion, Table 1. The yields Y for targets # 1 and 2 and for 3.8 nm and 5.5 nm NIs are 3.3 NC/ion and 2.1 NC/ ion, respectively. Yields > 1 indicate that NC’s are desorbed even though no projectile directly passed through them. In the framework of the proposed mechanism it is possible to explain Y > 1. When a 200 keV Au5 ion destroys a NI < 6 nm, the sputtered atoms may transfer the energy to the surrounding NIs on the substrate surface. The yield will depend on the energy deposited by the projectile ion in the destroyed NI and the density of NIs. on the substrate surface. 3. Limiting sizes and total size ranges of desorbed NCs. Table 2 gives data of 4 experiments on the desorption of gold NIs (3– 100 nm) by 6 MeV Au5 [11], 1 MeV Au5 [2], 200 keV Au5 [present work] and 38 keV Au1 [3] ions. It follows from the table that in all 4 experiments, NCs with the limiting size (£max) receive an energy density (energy per atom) which is close (slightly higher) to the energy necessary for melting of bulk gold (0.41 eV/atom). We note that the values of the energy per atom in the desorbed NCs with limiting sizes in Table 2 may be slightly underestimated for large sizes. The number of atoms in a NC is determined according to its lateral diameter. But the NC is desorbed in the melted state, and on the collector its height may be lower than the lateral diameter. Thus in [7] it was shown that the heights of desorbed Au NCI with the lateral sizes 10–15 nm (TEM measurements) were 5–10% lower (AFM measurements), but this deviation was within the error. Furthermore, the underestimation of this energy per atom for the NCs with £mean 86 nm may be connected with the uncertainty of determination of its height, as it is the only case when this largest NC had smooth but not round shape. The proposed mechanism thus makes it possible to understand the dependence of the limiting sizes £max of the desorbed NCs on the total deposited energy of projectile ions, Etot. Since the minimum energy per atom for melting NIs of various sizes is equal and the energy released by an ion may be assumed as proportional to £, we find

Etot  £3max :

ð4Þ

4. Fig. 7 shows the dependence of the yields Y (NC/ion) on NC sizes. Only for small sizes (up to 6 nm), yields Y > 1 are obtained; they belong to the NI size range where desorption of NCs occurs due to the destruction (complete sputtering) of neighboring NIs by a 200 keV Au projectile ion. For larger sizes, NCs may melt but not all of them will desorb.

8. Conclusions 1. We propose a novel mechanism of desorption of metal (Au) nanoclusters: Desorption is due to the melting, sudden buildup of pressure and the expansion of the NIs. 2. Regardless of the mode of the projectile stopping (elastic or inelastic) the characteristics of NI desorption are similar: desorbed NCs have a round shape as a result of melting, the angular distribution of desorbed NCs is peaked towards the surface normal, and the desorption yields are >1 for NCs with £ < 6–8 nm.

2514

C. Anders et al. / Nuclear Instruments and Methods in Physics Research B 267 (2009) 2503–2514

3. We propose that this mechanism may also apply for desorption induced by projectiles in the electronic stopping mode. In the latter case the size effect (NI stopping potential) influences also the energy, which is transferred from the excited electronic subsystem of the NI by hot electrons to the lattice atoms. 4. The limiting size £max (and the total size range) of desorbed NCs depends on the ion energy deposited in the NI, Etot, as be Etot  £3max. Acknowledgement The work has been performed under financial support of the International Science and Technology Center (project #2390). References [1] I. Baranov, A. Brunelle, S. Della-Negra, D. Jacquet, S. Kirillov, Y. LeBeyec, A. Novikov, V. Obnorsky, A. Pchelintsev, K. Wien, S. Yarmiychuk, Nucl. Instr. and Meth. B 193 (2002) 809. [2] I. Baranov, S. Della-Negra, M. Fallavier, S. Kirillov, Y. LeBeyec, A. Novikov, V. Obnorsky, K. Wien, S. Yarmiychuk, Nucl. Instr. and Meth. B 245 (2006) 184. [3] I. Baranov, S. Della-Negra, V. Domaratsky, A. Chemezov, S. Kirillov, A. Novikov, V. Obnorsky, M. Pautrat, H.M. Urbassek, K. Wien, S. Yarmiychuk, E. Zhurkin, J. Nanosci. Nanotechnol. 9 (2009) 4085. [4] B. Satpati, J. Ghatak, B. Joseph, T. Som, D. Kabiraj, B. Dev, P. Satyam, Nucl. Instr. and Meth. B 244 (2006) 157.

[5] B. Satpati, D. Goswami, U. Vaishnau, T. Som, B. Dev, P. Satyam, Nucl. Instr. and Meth. B 212 (2003) 157. [6] B. Satpati, D. Goswami, S. Roy, T. Som, B. Dev, P. Satyam, Nucl. Instr. and Meth. B 212 (2003) 332. [7] I.A. Baranov, V.V. Obnorskii, S.O. Tsepelevich, C.T. Reimann, Nucl. Instr. and Meth. B 146 (1998) 154. [8] I. Baranov, S. Kirillov, A. Novikov, V. Obnorsky, A. Pchelintsev, S. Yarmiychuk, Nucl. Instr. and Meth. B 183 (2001) 232. [9] J.F. Ziegler, J.P. Biersack, U. Littmark, The Stopping and Ranges of Ions in Solids, Pergamon, New York, 1985. [10] J.H. Fendler, (Ed.), Nanoparticles and Nanostructured Films: Preparation, Characterzation and Applications, Wiley-VCH, Wenheim, 1998. [11] I.M. Kirko, E.I. Dobychin, V.I. Popov, Sov. Phys. Dokl. 15 (1970) 442. [12] T.J. Colla, H.M. Urbassek, Nucl. Instr. and Meth. B 164–165 (2000) 687. [13] S. Zimmermann, H.M. Urbassek, Nucl. Instr. and Meth. B 228 (2005) 75. [14] S. Zimmermann, H.M. Urbassek, Nucl. Instr. and Meth. B 255 (2007) 208. [15] R. Smith, C. Nock, S. Kenny, J.J. Belbruno, M. Di Vece, S. Palomba, R.E. Palmer, Phys. Rev. B 73 (2006) 125429. [16] P. Williams, B. Sundqvist, Phys. Rev. Lett. 58 (1987) 1031. [17] D. Fenyo, B.U.R. Sundqvist, B.R. Karlsson, R.E. Johnson, Phys. Rev. B 42 (1990) 1895. [18] R.C. Weast, Handbook of Chemistry and Physics, 61 ed., CRC Press, Boca Raton, FL, 1980. [19] C.J. Smithells, Metals Reference Book, 5th ed., Butterworth, London, 1976. [20] E.B. Webb III, G.S. Grest, Phys. Rev. Lett. 86 (2001) 2066. [21] W. Luo, W. Hu, S. Xiao, J. Phys. Chem. C 112 (2008) 2359. [22] R. Webb, Appl. Surf. Sci. 59 (2004) 231. [23] R. Kissel, H.M. Urbassek, Int. J. Mass Spectrom. 208 (2001) 29. [24] I. Baranov, S. Della-Negra, V. Domaratsky, A. Novikov, V. Obnorsky, M. Pautrat, Chr. Anders, H.M. Urbassek, K. Wien, S. Yarmiychuk, E. Zhurkin, Nucl. Instr. and Meth. B 266 (2008) 1993.