Behavior of crystalline silicon under huge electronic excitations: A transient thermal spike description

Nuclear Instruments and Methods in Physics Research B 267 (2009) 2719–2724

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Behavior of crystalline silicon under huge electronic excitations: A transient thermal spike description A. Chettah a, H. Kucal b, Z.G. Wang b,c, M. Kac b,d, A. Meftah a, M. Toulemonde b,* a

LRPCSI, University of Skikda, route d’El Hadaiek, BP 26, 21000 Skikda, Algeria CIMAP Laboratory, CEA-CNRS-ENSICAEN and Université of Caen, BP5133, 14070 Caen-cedex 5, France c Institute of Modern Physics, CAS, 363 Nanchang Road, Lanzhou 730000, PR China d Institute of Nuclear Physics PAN, Radzikowskiego 152, 31-342 Krakow, Poland b

a r t i c l e

i n f o

Article history: Available online 23 June 2009 PACS: 61.80.Jh 61.80.Lj 61.82.Fk

a b s t r a c t Recent experimental works devoted to the phenomena of mixing observed at metallic multilayers Ni/Si irradiated by swift heavy ions irradiations make it necessary to revisit the insensibility of crystalline Si under huge electronic excitations. Knowing that Ni is an insensitive material, such observed mixing would exist only if Si is a sensitive material. In order to extend the study of swift heavy ion effects to semiconductor materials, the experimental results obtained in bulk silicon have been analyzed within the framework of the inelastic thermal spike model. Provided the quenching of a boiling (or vapor) phase is taken as the criterion of amorphization, the calculations with an electron–phonon coupling constant g(300 K) = 1.8  1012 W/cm3/K and an electronic diffusivity De(300 K) = 80 cm2/s nicely reproduce the size of observed amorphous tracks as well as the electronic energy loss threshold value for their creation, assuming that they result from the quenching of the appearance of a boiling phase along the ion path. Using these parameters for Si in the case of a Ni/Si multilayer, the mixing observed experimentally can be well simulated by the inelastic thermal spike model extended to multilayers, assuming that this occurs in the molten phase created at the Ni interface by energy transfer from Si. Ó 2009 Elsevier B.V. All rights reserved.

1. Introduction When a swift heavy ion penetrates matter it interacts with the electrons and nucleus of the target atoms. At low energies (keV/amu), the ion energy is mainly deposited via elastic collisions with the target atoms (nucleus) leading to direct atomic displacements. At high energies (MeV/amu) the ion deposits its kinetic energy mainly by electronic stopping, i.e. by excitation and ionization of the target atoms along its trajectory, while direct atomic displacements by elastic collisions do not play a significant role anymore. During the last two decades, many papers have been devoted to study the different modifications induced by electronic excitations and ionizations in many of radiolysis resistant target materials such as metals [1–3], insulators [1,4–6] and even semiconductors [7–16]. The analysis of these modifications are interesting from two points of view: from fundamental physics in order to understand the exact mechanism of the high electronic excitation and from applied research, because of a growing interest in methods for producing nanostructures [17] or quantum wells and quantum dots [7–10].

* Corresponding author. Fax: +33 231 45 47 14. E-mail address: [email protected] (M. Toulemonde). 0168-583X/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2009.05.063

Though great progress has been achieved in experiments, the exact physical mechanism of the high electronic excitations leading to track formation in materials is still widely discussed. However, defect annealing and defect creation in pure metals have been successfully described by the inelastic thermal spike model (i-TS) with electron–phonon interaction [2,18–24] assuming that the damage appearing only above an energy threshold deposition, results from the quenching of a molten matter along the ion path [2,19]. The value of the electron–phonon coupling constant, characterizing the rate of the energy transfer from the electron to the lattice, was derived from the electrical conductivity of the considered irradiated metals [2,19]. Furthermore, the formation of ion tracks in crystalline inorganic insulators has also been explained by the i-TS model [24]. These tracks are due to a rapid quenching of a matter in which the energy transferred to the lattice has overcome either the energy necessary to reach a quasi-molten phase in an amorphisable material or the cohesive energy for a non-amorphisable one. In this case, the electron lattice mean free path, directly linked to the electron–phonon coupling constant, is considered as a parameter. Its value appears to be correlated to the band gap energy of the considered material. Most of semiconductor materials seem to be difficult to amorphize by swift heavy ions [7–10,15]. Evidence of track formation has been reported in several compound semiconductors like GeS,

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GeSb, InP, InSb [12–14]. For crystalline Si and Ge amorphous track appears only when irradiated by C60 clusters [25–31]. This paper will deal with a specific study of silicon which is of importance for many applications. 2. Experimental knowledge of Si irradiated in the electronic energy loss regime 2.1. Damage creation In contrast to specific compound semiconductors [13,14], there is no experimental evidence that monoatomic swift heavy ions produce tracks in crystalline Si. It is therefore considered as insensitive to the electronic excitation [25–27]. Indeed in bulk silicon at 80 K or 300 K, irradiated with various monoatomic ions in the electronic energy loss regime (Ar to U ions, at energies between 5 and 25 MeV/u, leading to Se of 4–25 keV/nm) no specific effect has been observed [25–27] and the observable damage in Si in the 4–28 keV/nm energy deposition range was attributed to nuclear collisions [27]. The lack of track observation in the bulk in Si, may be explained by the possibility of perfect epitaxial re-crystallization [16]. Experimental tracks for Si observed in thin films have been obtained only by irradiation with 20–40 MeV C60 fullerenes [28–31]. In single crystalline silicon irradiated at room temperature by C60 fullerenes with energies of 20, 30 and 40 MeV, leading to electronic energy loss values (Se) equal to 35.5, 48 and 57 keV/nm, respectively, amorphous tracks were found to have respective diameters of 5.5, 8.4 and 10.5 nm. Assuming a linear dependence of the track cross section versus Se, an amorphous track threshold value, was deduced to be equal to 28 keV/nm. This latter value is larger than any delivered by monoatomic ions. Finally, for silicon irradiated at 300 K by Cn carbon clusters at constant velocities (0.8 MeV per carbon with n = 1 – 8, leading to Se from 1 to 8 keV/nm), damage production at the surface has been observed [32]. The defects appear for Se larger than 5 keV/nm, and their number increases with Se. On the other hand, in the Se range between 1 and 5 keV/nm, the damage production decreases as previously observed in metallic material [33]. Therefore, a surface damage threshold value was deduced to be equal to 5 keV/nm. At the first glance, the behavior of silicon seems to be different from that of the conducting [2,33] and of the other amorphisable insulating materials [6,24] which usually have a unique electronic energy loss threshold value. Nevertheless, quite recently it has been shown that LiF (a nonamorphisable insulator) may present two thresholds of damage creation, one at a lower Se value for extended defects and another at a larger Se value, corresponding to a strong change in the material density [34,35]. In the framework of the i-TS model, these two thresholds were ascribed to two different responses of the irradiated material: one at a low value of Se resulting from the quenching of a molten phase and the other at a larger Se as a consequence of the quenching of a boiling (vapor) phase. The idea of two different responses of the LiF will be the guide line for the analysis of the silicon behavior under swift heavy ion irradiation.

2.2. Mixing with metallic materials Recent works devoted to the phenomena of mixing observed for metallic multilayers deposited on Si under swift monoatomic ions irradiation require revisiting the insensibility of crystalline Si. Indeed, defect recovery and recrystallisation may hamper information about the track appearance in Si. On the other hand, if we assume atomic intermixing as an irreversible process, the interface mixing induced by the swift heavy ions is an interesting tool to investigate the atomic transport process and the property of sili-

con. Evidence for atomic mixing induced by electronic energy deposition in metallic layers deposited on Si has been reported by Leguay [36]. Although, Sinha et al. [37] come to the conclusion that metallic layers do not mix with the Si crystalline substrate, recent experimental work shows the contrary [38–41]. For example Sisodia et al. [38] suggest that irradiation with swift heavy ions causes some mixing at interface of Ti/Si that could be expected as in the case of Ti/Ni [36] since one of the materials is sensitive to swift heavy ions. Mixing appears even for Ni deposited on Si which is rather unexpected since the two materials are, to our knowledge, insensitive to monoatomic ion irradiation. Indeed, a high mixing rate was found for Ni layers on Si irradiated by 350 MeV Au26+ [39–41], being several times larger than that for irradiation by 400 keV Au in the nuclear collision regime. Moreover the threshold of mixing was determined by Kraft et al. [41] in the following range of energy loss, 9–16 (28–47) keV/nm for Si (Ni), respectively, being easily attained with swift heavy ions. The aim of this paper is to present an approach leading to a coherent description of the silicon behavior under high electronic excitation in a large range of electronic stopping power between 5 and 55 keV/nm, considering the following experimental results: two different Seth threshold values, one for surface damage production and the other for latent track formation and a mixing at a Ni/Si interface that appears with monoatomic ions in between the two experimental thresholds. The study will be done within the framework of the inelastic thermal spike model [13,19,24,42] initially developed to describe the sensitivity of metals [43] and insulators [44] under swift heavy ion irradiation. Although this model is open to criticism [45], it is the most elaborate in providing certain quantitative predictions regarding track formation [19,42]. Moreover, our description will complete the recent application of the inelastic thermal spike model by Szenes et al. [46], Dhamodaran et al. [14] and by Kamarou et al. [13] to semiconductors, assuming the similar basic mechanism of track formation for different kinds of materials. Furthermore, it has been shown that the inelastic thermal spike model can explain the mixing at the interface (see e.g. [47,48]). The energy locally deposited by electronic energy loss in matter is quickly shared among the electrons by electron–electron interactions and then transferred to the atoms by electron–phonon interactions. This causes an increment in the lattice temperature that can exceed the melting temperature. Therefore, if one of the components is sensitive to the electronic energy loss, the melting phase will appear at the interface of bi-layers system and the mixing between two different materials could occur due to the high diffusivity of components in a liquid phase [48–50]. Consequently, one can suppose that intermixing could be attributed to interdiffusion in the molten ion track, provided that, at least one of the components is sensitive to Se deposition. Concerning the metallic layers deposited on Si, atomic mixing by electronic energy deposition has been shown for Ni, Ti, and Fe, respectively [33,38,41,47,48]. Taking into consideration that Ni is an insensitive material, the mixing between Ni and Si would exist only if the Si is sensitive under high electronic excitation induced by ions. The paper is organized in following manner: firstly, the behaviour of the silicon irradiated by swift heavy ions is analyzed in the frame of the thermal spike model in order to obtain a reasonable description of experimental results mentioned above. Secondly, the 3D numerical simulations of the possible interface melting for Ni/Si system are presented.

3. Thermal spike model 3.1. Numerical analysis The two important parameters of the model are the electron– phonon coupling constant and the electronic diffusivity, unknown

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for Si to our knowledge. The numerical simulations of several experimental data (the electronic energy loss threshold of damage creation by ions and the radius of amorphous tracks induced by cluster beams) provide the values of these two parameters. Even if the values of De and g have to be proved and discussed, the first object of the simulation was to carry out the sensitivity of the silicon to heavy ion irradiation. As we know, huge energy deposition through high electronic excitations/ionizations results in a very short, local and very high excitation of the solid [51]. During this so-called inelastic thermal spike process, the energy transfer relating to the heat diffusion in the electronic and lattice subsystems can be described by the following coupled differential equations in a cylindrical geometry [2,19–24]:

  @T e 1 @ @T e rK e ðT e Þ ¼  gðT e  T a Þ þ Aðr; t; v Þ; r @ @t @r   @T a 1 @ @T a C a ðT a Þ rK a ðT a Þ ¼  gðT e  T a Þ; r @ @t @r

C e ðT e Þ

Table 1 Lattice thermal parameters of silicon. Melting point Tm = 1683 K Vaporization temperature Tv = 2953 K qs = 2.32 g/cm3 Solid density at 300 K Liquid density at Tm ql = 2.50 g/cm3 Latent heat for fusion at Tm Hf = 1797 J/g Hv = 13,722 J/g Latent heat for vaporization at Tv Lattice specific Ca (J/g K) Ca = 0.1354 + 4.486  103 T  5.207  106 T2 (60 K 6 T < 300 K) Ca = 0.7007 + 1.469  104 T + 3.183  108 T2 (300 K 6 T 6 Tm) Ca = 1.045 (T > Tm) Lattice thermal conductivity Ka (W/cm K) Ka = 1042 T1.158 (60 K 6 T 6 Tm) Ka = 0.14 (Tm < T 6 Tv) Ka = 8.76  105 T1/2 (T > Tv)

ð1aÞ ð1bÞ

where T(e,a), C(e,a) and K(e,a) are the temperature, the specific heat, and the thermal conductivity for the electronic (e) and atomic (a) subsystems, respectively. A(r, t, m) is the energy density deposited on the electrons by an ion as defined in [52] that decreases when the projectile velocity m increases. This is the so-called ‘‘velocity effect” [53]. The thermodynamic parameters for the electron subsystem are described in [19] for metals and in [24,42] for insulators. For semiconductors the values of these parameters should be consistent with those previously ascribed to insulators or metallic materials. All the lattice thermodynamic parameters in solid and liquid phases are taken from equilibrium measurements [54–57]. The lattice thermal diffusivity above the vaporization temperature increases with the square root of the temperature (see [58]). The electron–phonon coupling factor g [2,59] is directly linked to the electron mean free path k by following relation k2  De(Te)Ce(Te)/g where De is the electronic thermal diffusivity [60]. In semiconductors, De(300 K) and g will be the two free parameters as done for a semi-metallic materials [23], with De(300 K) in between 150 and 2 cm2/s [2,24]. As compared with the simplified version of the thermal spike model [61], we have performed a complete numerical solution of the two equations, allowing the energy transfer between the electronic subsystem of the two materials in contact. Our calculations allow us to predict the track sizes whatever the incident projectile velocity [62]. The stopping energy loss values have been calculated with TRIM95 code [63].

track radii and the corresponding electronic energy loss threshold are fitted to the experimental data obtained after fullerene irradiation of silicon [28,29,32]. This procedure allows us to determine the g and De values for silicon. The best fit is realized for g = 1.8  1012 W/cm3/K and De = 80 cm2/s assuming that the amorphous track radius is formed when the energy deposited surpasses the energy necessary for boiling as visualized in Fig. 1. The threshold value for boiling Sveth (cluster) = 25 keV/nm in a nice agreement with experimental equal to 28 keV/nm [28–31]. With the melting criterion and taking into account these values of De and g, the molten phase arises at an electronic stopping power threshold, Sm eth (cluster) = 3.5 keV/nm (Fig. 1, Rm at an energy of 0.07 MeV/u) not far from the experimental result (5 keV/nm) [32]. 3.3. Interface mixing In the previous section the electronic and lattice temperatures have been calculated in a plane perpendicular to the ion path and considered to be constant along this path. In order to explain the interface mixing linked to the evolution of the temperature in a multilayer system the exchange of the energy between layers has to be included. This was done by Wang et al. [49] for the Ni–Ti system and applied to Fe–Au and Fe–Al by Chettah et al. [50]. The model developed by Szenes [61] has been discarded because it does not take into account energy exchange in the electronic

12

g = 1.8 10

12

-3

W cm K 2

D (300K) = 80 cm s

10

-1

-1

e

R

The thermal lattice parameters used for Si are presented in Table 1 (see [57]). The formulas, giving the temperature dependence of Ca and Ka, result from a fit to the experimental data. The system of two coupled Eqs. (1a) and (1b) has been numerically solved as proposed in [2,19] providing the evolution of the electronic temperature versus time t and radius r as well as the temperature of the lattice and the energy deposited to the lattice for given g and De value. In order to calculate track radii two criteria of track formation have been considered: either the molten or vapor phase. We presume that a track is formed when the energy called Eat transferred to the lattice surpasses either the energy necessary to melt Eatm or to boil or evaporate Eatv and each phase should develop only above v specific values of the electronic energy loss thresholds, Sm eth and Seth respectively. Moreover, Rm = R(Eat > Eatm) and Rv = R(Eat > Eatv) correspond respectively to the sizes of the cylinder in which the molten or the boiling phases appear along the ion path. The calculated

Radius (nm)

3.2. Damage formation: track radii R

8

m

m

(E = 5 MeV/u)

(E = 0.07 MeV/u) R (E = 0.04 MeV/u) v

6

4

R (E = 5 MeV/u)

2

v

0

20

40

60

80

dE/dx (keV/nm) Fig. 1. Calculated track radii versus Se for g = 1.8  1012 W cm3 K1, De = 80 cm2 s1 and for different values of incident energy. The experimental values of amorphous track radii (full circles) with the experimental errors bars (15%) are also reported [28,29]. Rv corresponds to the boiling (vapor) criterion and Rm to the molten criterion. E = 5 MeV/u corresponds to ion irradiation and E = 0.07 MeV/u for fullerene cluster irradiation.

A. Chettah et al. / Nuclear Instruments and Methods in Physics Research B 267 (2009) 2719–2724

Electronic temperature (K) at radius r

1.210

5

(c) Ni at interface

(a) Ni Bulk

4

8,0x10 8.

4

4. 4,0x10

0,0 1.210

5

8,0x10 8.

4

(b) Si Bulk

4. 104 0,0 -17 10

(d) Si at interface

Radius (nm) 1 2 4 7 10 13

10 Energy per atom (eV/at) at radius r

subsystem. Heat diffusivity in this bi-layer system was simulated by a three dimensional code, which provides the evolution of the radial temperatures depending also on the distance from the interface between two layers. We have applied this procedure to analyze the Ni(70 nm)/ Si(bulk) system irradiated by Au ions of energy 1.77 MeV/u in order to test the validity of the estimated parameters g and De(300 K) for Silicon. The thermodynamic parameters of Si have been discussed above. For Ni, they have been taken from [19,49]. The electron–phonon coupling constant for Ni g = 1012 W/cm3/s was evaluated by [22] from the defect annealing. The calculation depth step from the surface and the radial step were both 1 nm. Some simulation results are displayed in Figs. 2 and 3. In Fig. 2 the electronic temperatures are presented for Ni (bulk and at interface) and Si (bulk and at interface). We note that the electronic temperature for Si at the interface reaches 110,000 K and is higher than that for bulk Si. On the contrary the electron temperature for Ni at the interface is lower than that for bulk Ni. Thus energy transfer from the electron subsystem of Ni to that of Si exists until a thermal equilibrium state is reached. Then the thermalized electrons release their energy to lattice by electron–phonon interactions. In Fig. 3 we have plotted the evolution of the energy deposited in the lattice for two cases: (1) Ni, Si in the bulk , (2) Ni/Si system. This energy is normalized by energy necessary for melting, being equal to Eatm = 0.71 eV for Ni and Eatm = 0.88 eV for Si. It is clear from Fig. 3 that for bulk Ni, this energy does not reach the energy necessary to obtain a molten phase in Ni. However, for Ni at the interface with silicon the liquid phase in Ni appears during a period of about 1012 s. For Si, the energy deposited in the lattice exceeds that needed to reach a melting phase in Si both for bulk and interface. Similar calculations have been done as function of electronic stopping power corresponding to irradiation with Kr ions of energy 260 MeV, Xe ions of 200 MeV and Ar ions of 120 MeV. In Fig. 4 we have plotted the ratio of the energy deposited normalized by energy needed to melt Ni and Si respectively versus the depth from the interface for some radial distances for Au and Kr irradiations. Both Ni and Si reach their melting point at the interface, which probably will allow atomic transport through the interface resulting in the observed mixing [41]. This interpretation is supported by the value of the estimated effective diffusion coefficients which are comparable with those for interdiffusion D in a li-

1 0.1

Radius (nm) 1 4 7 10 13

Eatm= 0.71 eV

(a) Ni Bulk

(c) Ni at interface

0.01 Eatm= 0.88 eV

1 0.1 (b) Si Bulk

0.01 -15 10

10

-14

(d) Si at interface -14

-13 -12 ddd 1x10 ddd 1x10

ddd 1x10

-13

ddd 1x10

-12

ddd 1x10

Time (s) Fig. 3. Evolution of the transferred energy per atom as a function of the time for various radial distances r: (a) bulk Ni, (b) bulk Si, (c) and (d) are, respectively Ni and Si at the interface of the layer system of Ni (70 nm) on Si irradiated by Au ions of energy 1.77 MeV/a at the temperature 80 K.

8

Eat(max) / E atm

2722

(a)

8

Ni Si

6

6

4

4

(b)

Ni Si

Radius (nm) 1 2 4 7 10

Interface

2 0 -10

Interface

-5

2

0

5

10

0 -10

-5

0

5

10

Depth (nm) Fig. 4. Evolution of the maximum transferred energy versus the depth from surface of the layer of Ni (70 nm) on Si. (a) Irradiated by Au ions of energy 1.77 MeV/a at the temperature 80 K. (b) Irradiated by Kr ions of energy 1.5 MeV/a at temperature of 80 K.

quid rather than those for solid state diffusion. From the formula given by Kraft 2Dts ¼ k=pr 2t , where the coefficient k is the mixing coefficient as defined by Kraft et al. [41], rt corresponds to a radius of the melting zone and ts the duration of melting, the value of the D coefficient was evaluated for Ni/Si irradiated by Au and Xe [39,41] and is 103 cm2/s. Such a value is in agreement with that extracted by Srivastava et al. [48] and also with that corresponding to impurity diffusion in molten silicon [64] excited by a ns laser pulse. Moreover melting occurs above a certain threshold value in the electronic stopping power in Ni. In the present calculations no melting has been found for Ar ions in Ni while this is the threshold for the silicon. From the Fig. 4 the radius of melting zone in Ni at the interface is about 7 nm for Au irradiation, and 2 nm for Kr irradiation. By interpolation the threshold of Ni melting at the interface should appear between Ar and Kr ions. 3.4. Discussion

10

-15

-13

10

-17

10

-15

10

10

-13

Time (s) Fig. 2. Evolution of the electronic temperature as a function of the time for various radial distances r: (a) bulk Ni, (b) bulk Si, (c) and (d) are respectively Ni and Si at the interface of the layer system of Ni (70 nm) on Si irradiated by Au ions of energy 1.77 MeV/a at a temperature of 80 K.

Although many experimental results have been explained in the frame of this i-TS model, the overall agreement between experiment and i-TS calculations should not hide the hypothesis admitted in the simulation. Firstly, for the initial energy distribution on electrons we have considered an analytical expression proposed by ’Waligorski

A. Chettah et al. / Nuclear Instruments and Methods in Physics Research B 267 (2009) 2719–2724

et al. [65] and deduced from the Monte-Carlo calculations. Compared to [66,67] our initial energy distribution differs by less than 10% for an Al beam in silicon with energies ranging between 0.37 and 370 MeV/u. The nuclear stopping power was neglected on the basis of the experimental results given by Döbeli et al. [32]. Below the threshold of electronic damage creation by Cn cluster in Si, the damage induced by nuclear collisions decreases when increasing the electronic energy loss. For electronic energy loss larger than 5 keV/nm, it is assumed that the nuclear energy loss can be neglected in a first approximation except when it is experimentally observed [68]. Such assertion is supported by a recent work of Dallanora et al. [69] where it is shown that the nuclear effect on track etching is not effective even when nuclear energy loss is equal to the electronic energy loss. Secondly, it is not easy to define the thermodynamical parameters for electrons and holes in a semiconductor. This problem was treated e.g. by Klaumünzer especially in the case of Si [45, p. 303]. The conclusion is following: the electric field emerging from the electron and hole pair creation is very rapidly neutralized in a time less than 1 fs. However this neutralization is not complete and some track potential still exists in a time of 15 fs [70]. For insulators Baranov’s assumption [44] is applied: hot electrons in the conduction band will behave like hot electrons in a metal and a constant value of De (=2 cm2/s) was systematically used. This is valid for a large range of high electronic temperatures. Even with this crude approximation it was possible to promote a coherent view of the response of many insulators under swift heavy ion irradiation. Under this assumption, the i-TS calculations show that the larger the band gap energy of the irradiated material, the larger is the electron–phonon coupling [24,71]. Such a correlation is still an open question but allows quantitative predictions related to the sensitivity of insulators under swift heavy ion irradiation. For metallic material the electrons are considered as a quasifree electron gas with an initial value of De(300 K) = 150 cm2/s [43]. This approach provides a good description of many experimental results in metallic materials [2,19], with an electron–phonon coupling value which is very near the one that can be extracted from known physical characteristics of the metallic materials under consideration (e.g. from the electrical resistance). Therefore the deduced electronic thermal diffusivity De at 300 K for Si lies, as expected in between 150 and 2 cm2/s. In the present case the electron–phonon is considered as an unknown free parameter but linked to De through the electron–phonon mean free path. The calculated electronic temperatures can be compared to measurements done by Staufenbiel et al. [72]. In the case of gold beam of 3 MeV/u in silicon, the calculated temperatures are in reasonable agreement with measured ones (about 20% less). The difference could be ascribed to the ion track potential [68] or coulomb explosion [73] phenomena that we neglect in our case. On the other hand it has also been shown that the extracted values of the electron temperature from such measurements can vary by a factor of 2 for the same irradiated material [74,75] depending on the data analysis. Moreover, the comparison between experimental values and calculated ones are model dependant [75,76]. Thirdly, the thermodynamic parameters of the lattice, measured at equilibrium are utilized in the ps time regime, which means far from thermodynamic equilibrium. But this a – priori hypothesis, assumed in two systematic studies [19,24], provided a – posteriori coherent descriptions for numerous materials whether they are metallic or insulating. This a priori hypothesis was recently corroborated by a combined description of the track formation in amorphous SiO2 [77] by the inelastic thermal spike model and MD simulations. The atomic temperatures deduced from the MD sim-

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ulation are in agreement with those needed for the appearance of a molten phase or a boiling phase defined as criteria for track appearance in the frame of the i-TS model. We now consider whether the Ni/Si behavior is only an interface effect. Firstly, for silicon the existence of two thresholds, one for the damage creation appearing at 5 keV/nm with Cn beams, the other for the creation of amorphous tracks at 20 keV/nm with C60, suggests that it exists in two ways for damage creation. In the framework of the thermal spike, molten phase could appear in silicon when irradiated by ions (Fig. 1). Secondly, Ni is clearly insensitive to track formation since they were not observed after an irradiation by C60 beam at 40 MeV energy, corresponding to electronic energy loss of  86 keV/nm [78]. The i-TS calculations [22] with the electron–phonon coupling value deduced from nuclear defects annealing [78,79] for Ni corroborate this result. However in this ion regime mixing occurs at interface of Ni/Si for electronic energy loss larger than 25 (8) keV/nm for Ni (Si). Thus the melting of Ni would appear by energy transfer from the Si only at the interface with a mixing rate which is governed by the less sensitive material as expressed by Bolse et al. [80]. 4. Conclusion The behavior of silicon under intense electronic excitation has been qualitatively analyzed in the frame of the inelastic thermal spike model adapted for semiconductors. Within the framework of this model, we have seen that the track radii obtained for high electronic stopping powers result only from the quenching of a vapor phase and the surface damage from the quenching of a molten phase. Using the vapor criterion, the best fit was found with De(300 K) = 80 cm2/s and g(300 K) = 1.8  1012Wcm3 K1. This result would suggest that excited electrons in silicon might behave like electrons in a semi-metal (see [23]). The apparent low sensitivity of silicon under swift heavy ion irradiation seems to be due to an individual track, resulting from the quenching of a molten phase, re-crystallises when cooling and then cannot be observed as in the case of several other semiconductors [25–27]. Finally, according to our complete numerical calculations for silicon irradiated by ions, the amorphous tracks should appear only for very large values of electronic stopping power, experimentally not attained up to now. In multilayers, as Lieb et al. [39] have stated, experimentally mixing observation indicates melting of silicon with a concomitant fast and irreversible interdiffusion. However, in pure silicon perfect epitaxial re-crystallization may prevent the detection of the melting. These questions are still open and need to be experimentally explored in more details for Si and also for other semiconductors. Acknowledgements One of the authors (Z. G. Wang) is grateful to NSFC and the Chinese Academy of Sciences (CAS) for their financial support. M. Kac is grateful to European Commission through the Human Potential program Network EuNITT for their financial support (Contract No. HPRN-CT-2000-00047). References [1] See SHIM conferences series: the two last one are. Nucl. Instr. and Meth. B 267 (2009) ; See ICACS conferences series: the two last one are Nucl. Instr. and Meth. B 256 (2007). [2] C. Dufour, A. Audouard, F. Beuneu, J. Dural, J.P. Girard, A. Hairie, M. Levalois, E. Paumier, M. Toulemonde, J. Phys.: Condens. Matter 5 (1993) 4573. [3] H. Dammak, A. Dunlop, D. Lesueur, A. Brunelle, S. Della-Negra, Y. Le Beyec, Phys. Rev. Letzt. 74 (1995) 1135. [4] M. Toulemonde, F. Studer, Solid State Phen 30&31 (1993) 477. [5] S.M.M. Ramos, N. Bonardi, B. Canut, S. Della-Negra, Phys. Rev. B 57 (1998) 189.

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