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Analysis of charge, mass and energy of large gas cluster ions and applications for surface processing
Nuclear Instruments and Methods in Physics Research B 241 (2005) 599–603 www.elsevier.com/locate/nimb
Analysis of charge, mass and energy of large gas cluster ions and applications for surface processing D.R. Swenson
*
Epion Corporation, 37 Manning Road, Billerica, MA 01821, United States Available online 29 August 2005
Abstract In a previous study averages of +3.2 charges, 64 keV energy and 10,400 atoms were measured for a high intensity Ar gas cluster ion beam [D.R. Swenson, Nucl. Instr. and Meth. B 222 (2004) 61]. At this energy multiple collisions with Ar gas atoms are observed to progressively abrade the clusters. The mass loss is consistent with a simple theory that assumes thermalization of the collision energy followed by evaporation. The measurements are important for cluster–surface interactions because they allow cluster energy and dose to be measured for multi-charged clusters. It is shown that higher energy clusters that cause larger craters are more affected by the cluster–gas collisions, and this effect can be beneficial when using a cluster beam to smooth a surface. Ó 2005 Elsevier B.V. All rights reserved. PACS: 36.40.Wa; 39.90.+d; 36.40.Qv; 34.90.+q Keywords: Cluster charge; Cluster–atom collisions; Cluster energy; Cluster mass
1. Introduction Cluster–gas collisions have been the subject of several recent papers,1 but there have been no studies for large, multi-charged clusters that are typical of commercial gas cluster ion beams (GCIB). For such large clusters the standard techniques are not adequate because they measure m/q *
1
Tel.: +1 978 215 6305; fax: +1 978 670 9119. E-mail address: [email protected] See Refs. [18–25] cited in [1].
ratios leaving the mass and charge ambiguous. In a recent paper I reported the first measurements of charge state q, energy E, and mass m for very large Ar clusters as are commonly used in GCIB processing of surfaces [1]. In that paper the average charge of the clusters was determined by q ¼ I=aeC, where I is the beam electrical current measured by a Faraday cup, C is the flow rate of particles in the beam, as measured using a modified Daly detector and applying particle counting techniques, and a was the measured relative detection efficiency. The experimental apparatus also
0168-583X/$ - see front matter Ó 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2005.07.183
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D.R. Swenson / Nucl. Instr. and Meth. in Phys. Res. B 241 (2005) 599–603
included TOF and electrostatic spectrometer measurements, all for the same pico-ampere-level sample2 of a high intensity Ar GCIB [2] that was accelerated with 30 kV accel potential. This so named ‘‘QEM’’ technique was used to look for the presence of multiply charged clusters in the beam and to study the effect of cluster–gas collisions. The data from the experiment consists of measurements of q, and spectra of velocity v and E/q that were measured for various thicknesses of Ar gas that was introduced into a cell immediately upstream of the instruments. The averages v and fE=qgave are determined from the spectra, and averages of cluster mass and energy are given ¼ 2E=v2 . The derived by E ¼ qfE=qgave and by m averages are strictly valid if the various distributions are uncorrelated. In this paper I further analyze the data from this experiment and show that a simple heuristic analytical model can predict the main features of the data. A more detailed Monte-Carlo simulation is also compared to the results and to the analytical model, and it is used to investigate the limitations of the experimental technique, particularly to what degree correlations affect the average values derived using the QEM technique. The theory developed can be used to understand and predict the effect of gas–cluster collisions on surface processing.
2. Technique The main features of the data from the QEM experiment can be understood with a surprisingly small number of assumptions: (1) the cluster charge on acceleration q0 was the same as that measured at the lowest gas target thickness; (2) the cluster–gas impact velocity is that of the cluster after accelerapffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi tion and is given by v ¼ 2q0 eU =N 0 ma where q0 and N0 are the charge and number of atoms in the cluster at acceleration, ma is the monomer mass, and U is the acceleration voltage; (3) the cluster– gas collision cross section is pr2 (r is the cluster
2
The QEM technique was limited to pico-ampere samples because the maximum count rate of the particle detector was 100 MHz.
radius) which scales as N2a where N is the number of atoms in the cluster and a is determined by the nature of the packing (a = 1/3 for hard sphere packing) [3]; (4) the mass loss rate is such that the number of atoms lost by the cluster in a collision with a background atom is the ratio of the collision energy to the binding energy per atom in the cluster j0 (j0 assumed constant); (5) ‘‘Non-gas cell’’ mass loss ND occurs before and independent of the gas cell mass loss. The cluster mass as a function of target thickness P is then given by 1 2 !ð12a Þ pq0 eU ra ð12aÞ N ¼ ðN 0 N D Þ ð1 2aÞ P N 0 j0 N aa ð1Þ
which includes the mass dependence of the gas collision cross section. The calibration of cluster size ˚ and Na = 1500) was meato mass used (ra = 24 A sured for neutral clusters by electron diffraction as given by Farges et al. [4]. The Monte-Carlo model is used to investigate the distributions of q, E and m in the cluster beam. The model has a log–normal initial mass distribution [5]. Ionization is assumed to occur in multiple singly ionizing events, and the mass dependence of the ionization cross section is included [6]. ND is assumed to have a normal distribution and the size and width was fit to the data at the lowest P. The fit to the data and the effect of the gas collisions is simulated cluster-by-cluster using the same assumptions as Eq. (1). It was assumed that q was constant unless N was reduced to zero and then the charge was lost from the beam. With this model it is possible to fit the E/q and the TOF spectra as well as the other data. Average values and E are calculated directly and also by using m the assumptions of the QEM method.
3. Results and discussion Eq. (1) was fit to the data of [1] assuming that it was valid for N by optimizing ND and j0. With a = 1/3, the best fit yields the values: ND = 3820 and j0 = 69 meV. The value of j0 is close to a theoretical prediction of 80 meV for neutral clusters with N = 5000 [7,8]. Fig. 1 compares the
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Fig. 1. Comparison of the theoretical calculations to the data of [1] as function target thickness P (Ar atoms cm2) for (a) average energy E (keV) and (b) average size N (Ar atoms).
analytical and Monte-Carlo fits to the data for N and for E as a function of P (for convenience I use units of Ar atoms cm2). In the case of N the correlations in the distributions do not significantly affect the calculations, as is also the case for E for low P, but as P increases the relative error in E caused by correlations grows to a maximum of 0.40. The correlations between q, E and m are caused by the mass dependence of the ionization and the gas collision cross sections, and by the v2 dependence of the mass loss per gas collision. In the absence of gas collisions E/q is constant and correlations do not affect the calculation of E, but as P increases, higher velocity clusters are abraded faster causing correlations. A more complete mathematical treatment is beyond the scope of the present paper. Fig. 2 shows good agreement for the MonteCarlo prediction of the evolution of the E/q spectrum as a function of P. There is evidence of an accelerated loss of I for small E/q at large P. It appears that below 10-keV/q, charge-loss processes such as charge exchange, scattering or Coulomb explosion, are enhanced for small cluster remnants (below 3 keV/q the electrostatic spectrometer is unreliable because the detection efficiency is low). These effects are also responsible for the low values of q at high target thickness [1].
Fig. 2. Comparison of theoretical calculations (dotted lines) to the data of [1] (solid lines) for the E/q distribution of cluster current density (arbitrary units) for various target thicknesses P (Ar atoms cm2).
4. Conclusions 4.1. Implications for surface processing with GCIB The high temperatures and pressures generated in cluster surface impacts are unique features of GCIB surface processing. They result from the collective effects of a cluster collision and give rise to shallow craters (fragments abraded from the
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D.R. Swenson / Nucl. Instr. and Meth. in Phys. Res. B 241 (2005) 599–603
clusters have less of a physical effect, even though the energy per atom may be the same as in the cluster, because they are dispersed and do not interact). In most applications a large GCIB dose is applied and the resulting surface morphology is determined by the physical characteristics of the craters and their surface density. Thus the critical parameters that are required to understand and predict GCIB surface processing are the m and v (or E) of the clusters and the area density of the cluster impacts (calculated using I and qÞ. The QEM technique allows averages of these parameters to be measured. That higher velocity clusters are abraded much more rapidly than lower velocity clusters has important consequences for surface processing. Fig. 3 is a prediction, using Eq. (1), of the energy of Ar clusters with N = 10,000, ND = 3800, q = +3 as a function of P for various U. It shows that low beam line pressure must be maintained in order to transport high energy clusters intact. On the other hand, when smoothing a surface is the objective, the gas collisions have the beneficial effect of preferentially attenuating the higher energy clusters that can roughen a surface. The ultimate smoothness of the surface depends on the maximum crater sizes produced. With perspicacious use, gas collisions can yield higher smoothing rates
because higher values of U and q0 can be used, resulting in higher cluster beam currents; while the buffering effect of the collisions limits the maximum cluster–surface impact energy. Fig. 4 shows the Monte-Carlo simulation of the evolution of the energy distribution in the beam of [1], as P increases. Initially the cluster charge distribution included clusters with as great as q = +12, and energies of 360 keV. With gas collisions such high-energy clusters are changed into low energy clusters and the distribution will produce better ultimate surface smoothness but lower etch rates. 4.2. Implications for cluster physics A much clearer picture of the basic physics of high intensity Ar GCIB is now appearing. Previously measurements of N/q using TOF showed that the average N/q decreased from 30,000 for singly charged clusters to as low as 3000 as the current of ionizing electrons was increased, and it was not known whether they were 30,000 atom clusters with +30 charge or 3000 atom clusters with one charge or something in between.3 Now we know that, in the center of such a beam, the N/q is 3250 and it consists of clusters with q ¼ 3:2 and N of 10,400. These clusters have an average radius ˚ and average velocity of 5.6 km/s. Typically of 46 A they undergo many collisions with thermal Ar atoms during their time of flight to the surface. At each collision the gas atom is absorbed into the cluster and the collision energy is thermalized in the cluster. The average range of an Ar atom ˚ by the wellin the cluster is predicted to be 7 A known code SRIM [9]. The heated cluster then cools by evaporating enough monomers or fragments to regain equilibrium; initially the clusters lose an average of 130 atoms in a collision. The cluster charge is tightly bound and cluster N/q only decreases. The monomers or fragments are ejected with low thermal energies and because they 3
Fig. 3. Theoretical predictions of cluster energy E (keV) as a function of target thickness P (Ar atoms cm2) for various acceleration voltages U (kV) assuming a cluster charge state of +3.
These results were obtained with the conditions of the QEM experiment described in [1]. Using other nozzle-skimmer, ionizer configurations and sampling the entire beam, we have seen the N/q ratio change from 30,000 to less than 1000 Ar atoms per charge.
D.R. Swenson / Nucl. Instr. and Meth. in Phys. Res. B 241 (2005) 599–603
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surface can be profoundly affected by these abrasive collisions.
Acknowledgments I thank M.E. Mack for helpful discussions and the management of Epion A. Kirkpatrick, B. Libby, M.E. Mack and J. Hautala for their support of this work.
References
Fig. 4. Monte-Carlo prediction for the distribution of cluster energy E (keV) of the clusters for various target thicknesses P (Ar atoms cm2).
retain the velocity of the center-of-mass, they can remain in the beam. As a consequence the cluster abrasion effect may not be seen using pressure gauge Faraday cups or by using thermal power meters. Since the cluster mass is much greater than that of the gas atom, the cluster velocity is little changed by the collisions and hence cluster abrasion is also difficult to detect with TOF. However, the rate at which the GCIB etches or smoothes a
[1] D.R. Swenson, Nucl. Instr. and Meth. B 222 (2004) 61. [2] M.E. Mack, R. Becker, M. Gwinn, D.R. Swenson, R.P. Torti, R. Roby, in: Proceedings of the 14th International Conference on Ion Implantation Technology, Taos, New Mexico, 2002, IEEE, 2003. [3] H. Deutsch, K. Becker, T.D. Ma¨rk, Int. J. Mass Spectom. Ion Proc. 144 (1995) L9. [4] J. Farges, M.F. De Feraudy, B. Raoult, G. Torchet, Ber. Bunsenges. Phys. Chem. 88 (1984) 211. [5] J.M. Soler, N. Garcı´a, O. Echt, K. Sattler, E. Recknagel, Phys. Rev. Lett. 49 (1982) 1857. [6] F. Bottiglioni, J. Coutant, M. Fois, Phys. Rev. A 6 (1972) 1830. [7] B.W. van de Waal, J. Chem. Phys. 90 (1989) 3407. [8] P. Slavı´cˇek, R. Kalus, P. Pasˇka, I. Odva´rkova´, P. Hobza, A. Malijevsky´, J. Chem. Phys. 119 (2003) 2102. [9] J.F. Ziegler, J.P. Biersack, computer program ‘‘SRIM-200320’’. Available from: (2003).
Analysis of charge, mass and energy of large gas cluster ions and applications for surface processing D.R. Swenson
*
Epion Corporation, 37 Manning Road, Billerica, MA 01821, United States Available online 29 August 2005
Abstract In a previous study averages of +3.2 charges, 64 keV energy and 10,400 atoms were measured for a high intensity Ar gas cluster ion beam [D.R. Swenson, Nucl. Instr. and Meth. B 222 (2004) 61]. At this energy multiple collisions with Ar gas atoms are observed to progressively abrade the clusters. The mass loss is consistent with a simple theory that assumes thermalization of the collision energy followed by evaporation. The measurements are important for cluster–surface interactions because they allow cluster energy and dose to be measured for multi-charged clusters. It is shown that higher energy clusters that cause larger craters are more affected by the cluster–gas collisions, and this effect can be beneficial when using a cluster beam to smooth a surface. Ó 2005 Elsevier B.V. All rights reserved. PACS: 36.40.Wa; 39.90.+d; 36.40.Qv; 34.90.+q Keywords: Cluster charge; Cluster–atom collisions; Cluster energy; Cluster mass
1. Introduction Cluster–gas collisions have been the subject of several recent papers,1 but there have been no studies for large, multi-charged clusters that are typical of commercial gas cluster ion beams (GCIB). For such large clusters the standard techniques are not adequate because they measure m/q *
1
Tel.: +1 978 215 6305; fax: +1 978 670 9119. E-mail address: [email protected] See Refs. [18–25] cited in [1].
ratios leaving the mass and charge ambiguous. In a recent paper I reported the first measurements of charge state q, energy E, and mass m for very large Ar clusters as are commonly used in GCIB processing of surfaces [1]. In that paper the average charge of the clusters was determined by q ¼ I=aeC, where I is the beam electrical current measured by a Faraday cup, C is the flow rate of particles in the beam, as measured using a modified Daly detector and applying particle counting techniques, and a was the measured relative detection efficiency. The experimental apparatus also
0168-583X/$ - see front matter Ó 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2005.07.183
600
D.R. Swenson / Nucl. Instr. and Meth. in Phys. Res. B 241 (2005) 599–603
included TOF and electrostatic spectrometer measurements, all for the same pico-ampere-level sample2 of a high intensity Ar GCIB [2] that was accelerated with 30 kV accel potential. This so named ‘‘QEM’’ technique was used to look for the presence of multiply charged clusters in the beam and to study the effect of cluster–gas collisions. The data from the experiment consists of measurements of q, and spectra of velocity v and E/q that were measured for various thicknesses of Ar gas that was introduced into a cell immediately upstream of the instruments. The averages v and fE=qgave are determined from the spectra, and averages of cluster mass and energy are given ¼ 2E=v2 . The derived by E ¼ qfE=qgave and by m averages are strictly valid if the various distributions are uncorrelated. In this paper I further analyze the data from this experiment and show that a simple heuristic analytical model can predict the main features of the data. A more detailed Monte-Carlo simulation is also compared to the results and to the analytical model, and it is used to investigate the limitations of the experimental technique, particularly to what degree correlations affect the average values derived using the QEM technique. The theory developed can be used to understand and predict the effect of gas–cluster collisions on surface processing.
2. Technique The main features of the data from the QEM experiment can be understood with a surprisingly small number of assumptions: (1) the cluster charge on acceleration q0 was the same as that measured at the lowest gas target thickness; (2) the cluster–gas impact velocity is that of the cluster after accelerapffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi tion and is given by v ¼ 2q0 eU =N 0 ma where q0 and N0 are the charge and number of atoms in the cluster at acceleration, ma is the monomer mass, and U is the acceleration voltage; (3) the cluster– gas collision cross section is pr2 (r is the cluster
2
The QEM technique was limited to pico-ampere samples because the maximum count rate of the particle detector was 100 MHz.
radius) which scales as N2a where N is the number of atoms in the cluster and a is determined by the nature of the packing (a = 1/3 for hard sphere packing) [3]; (4) the mass loss rate is such that the number of atoms lost by the cluster in a collision with a background atom is the ratio of the collision energy to the binding energy per atom in the cluster j0 (j0 assumed constant); (5) ‘‘Non-gas cell’’ mass loss ND occurs before and independent of the gas cell mass loss. The cluster mass as a function of target thickness P is then given by 1 2 !ð12a Þ pq0 eU ra ð12aÞ N ¼ ðN 0 N D Þ ð1 2aÞ P N 0 j0 N aa ð1Þ
which includes the mass dependence of the gas collision cross section. The calibration of cluster size ˚ and Na = 1500) was meato mass used (ra = 24 A sured for neutral clusters by electron diffraction as given by Farges et al. [4]. The Monte-Carlo model is used to investigate the distributions of q, E and m in the cluster beam. The model has a log–normal initial mass distribution [5]. Ionization is assumed to occur in multiple singly ionizing events, and the mass dependence of the ionization cross section is included [6]. ND is assumed to have a normal distribution and the size and width was fit to the data at the lowest P. The fit to the data and the effect of the gas collisions is simulated cluster-by-cluster using the same assumptions as Eq. (1). It was assumed that q was constant unless N was reduced to zero and then the charge was lost from the beam. With this model it is possible to fit the E/q and the TOF spectra as well as the other data. Average values and E are calculated directly and also by using m the assumptions of the QEM method.
3. Results and discussion Eq. (1) was fit to the data of [1] assuming that it was valid for N by optimizing ND and j0. With a = 1/3, the best fit yields the values: ND = 3820 and j0 = 69 meV. The value of j0 is close to a theoretical prediction of 80 meV for neutral clusters with N = 5000 [7,8]. Fig. 1 compares the
D.R. Swenson / Nucl. Instr. and Meth. in Phys. Res. B 241 (2005) 599–603
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Fig. 1. Comparison of the theoretical calculations to the data of [1] as function target thickness P (Ar atoms cm2) for (a) average energy E (keV) and (b) average size N (Ar atoms).
analytical and Monte-Carlo fits to the data for N and for E as a function of P (for convenience I use units of Ar atoms cm2). In the case of N the correlations in the distributions do not significantly affect the calculations, as is also the case for E for low P, but as P increases the relative error in E caused by correlations grows to a maximum of 0.40. The correlations between q, E and m are caused by the mass dependence of the ionization and the gas collision cross sections, and by the v2 dependence of the mass loss per gas collision. In the absence of gas collisions E/q is constant and correlations do not affect the calculation of E, but as P increases, higher velocity clusters are abraded faster causing correlations. A more complete mathematical treatment is beyond the scope of the present paper. Fig. 2 shows good agreement for the MonteCarlo prediction of the evolution of the E/q spectrum as a function of P. There is evidence of an accelerated loss of I for small E/q at large P. It appears that below 10-keV/q, charge-loss processes such as charge exchange, scattering or Coulomb explosion, are enhanced for small cluster remnants (below 3 keV/q the electrostatic spectrometer is unreliable because the detection efficiency is low). These effects are also responsible for the low values of q at high target thickness [1].
Fig. 2. Comparison of theoretical calculations (dotted lines) to the data of [1] (solid lines) for the E/q distribution of cluster current density (arbitrary units) for various target thicknesses P (Ar atoms cm2).
4. Conclusions 4.1. Implications for surface processing with GCIB The high temperatures and pressures generated in cluster surface impacts are unique features of GCIB surface processing. They result from the collective effects of a cluster collision and give rise to shallow craters (fragments abraded from the
602
D.R. Swenson / Nucl. Instr. and Meth. in Phys. Res. B 241 (2005) 599–603
clusters have less of a physical effect, even though the energy per atom may be the same as in the cluster, because they are dispersed and do not interact). In most applications a large GCIB dose is applied and the resulting surface morphology is determined by the physical characteristics of the craters and their surface density. Thus the critical parameters that are required to understand and predict GCIB surface processing are the m and v (or E) of the clusters and the area density of the cluster impacts (calculated using I and qÞ. The QEM technique allows averages of these parameters to be measured. That higher velocity clusters are abraded much more rapidly than lower velocity clusters has important consequences for surface processing. Fig. 3 is a prediction, using Eq. (1), of the energy of Ar clusters with N = 10,000, ND = 3800, q = +3 as a function of P for various U. It shows that low beam line pressure must be maintained in order to transport high energy clusters intact. On the other hand, when smoothing a surface is the objective, the gas collisions have the beneficial effect of preferentially attenuating the higher energy clusters that can roughen a surface. The ultimate smoothness of the surface depends on the maximum crater sizes produced. With perspicacious use, gas collisions can yield higher smoothing rates
because higher values of U and q0 can be used, resulting in higher cluster beam currents; while the buffering effect of the collisions limits the maximum cluster–surface impact energy. Fig. 4 shows the Monte-Carlo simulation of the evolution of the energy distribution in the beam of [1], as P increases. Initially the cluster charge distribution included clusters with as great as q = +12, and energies of 360 keV. With gas collisions such high-energy clusters are changed into low energy clusters and the distribution will produce better ultimate surface smoothness but lower etch rates. 4.2. Implications for cluster physics A much clearer picture of the basic physics of high intensity Ar GCIB is now appearing. Previously measurements of N/q using TOF showed that the average N/q decreased from 30,000 for singly charged clusters to as low as 3000 as the current of ionizing electrons was increased, and it was not known whether they were 30,000 atom clusters with +30 charge or 3000 atom clusters with one charge or something in between.3 Now we know that, in the center of such a beam, the N/q is 3250 and it consists of clusters with q ¼ 3:2 and N of 10,400. These clusters have an average radius ˚ and average velocity of 5.6 km/s. Typically of 46 A they undergo many collisions with thermal Ar atoms during their time of flight to the surface. At each collision the gas atom is absorbed into the cluster and the collision energy is thermalized in the cluster. The average range of an Ar atom ˚ by the wellin the cluster is predicted to be 7 A known code SRIM [9]. The heated cluster then cools by evaporating enough monomers or fragments to regain equilibrium; initially the clusters lose an average of 130 atoms in a collision. The cluster charge is tightly bound and cluster N/q only decreases. The monomers or fragments are ejected with low thermal energies and because they 3
Fig. 3. Theoretical predictions of cluster energy E (keV) as a function of target thickness P (Ar atoms cm2) for various acceleration voltages U (kV) assuming a cluster charge state of +3.
These results were obtained with the conditions of the QEM experiment described in [1]. Using other nozzle-skimmer, ionizer configurations and sampling the entire beam, we have seen the N/q ratio change from 30,000 to less than 1000 Ar atoms per charge.
D.R. Swenson / Nucl. Instr. and Meth. in Phys. Res. B 241 (2005) 599–603
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surface can be profoundly affected by these abrasive collisions.
Acknowledgments I thank M.E. Mack for helpful discussions and the management of Epion A. Kirkpatrick, B. Libby, M.E. Mack and J. Hautala for their support of this work.
References
Fig. 4. Monte-Carlo prediction for the distribution of cluster energy E (keV) of the clusters for various target thicknesses P (Ar atoms cm2).
retain the velocity of the center-of-mass, they can remain in the beam. As a consequence the cluster abrasion effect may not be seen using pressure gauge Faraday cups or by using thermal power meters. Since the cluster mass is much greater than that of the gas atom, the cluster velocity is little changed by the collisions and hence cluster abrasion is also difficult to detect with TOF. However, the rate at which the GCIB etches or smoothes a
[1] D.R. Swenson, Nucl. Instr. and Meth. B 222 (2004) 61. [2] M.E. Mack, R. Becker, M. Gwinn, D.R. Swenson, R.P. Torti, R. Roby, in: Proceedings of the 14th International Conference on Ion Implantation Technology, Taos, New Mexico, 2002, IEEE, 2003. [3] H. Deutsch, K. Becker, T.D. Ma¨rk, Int. J. Mass Spectom. Ion Proc. 144 (1995) L9. [4] J. Farges, M.F. De Feraudy, B. Raoult, G. Torchet, Ber. Bunsenges. Phys. Chem. 88 (1984) 211. [5] J.M. Soler, N. Garcı´a, O. Echt, K. Sattler, E. Recknagel, Phys. Rev. Lett. 49 (1982) 1857. [6] F. Bottiglioni, J. Coutant, M. Fois, Phys. Rev. A 6 (1972) 1830. [7] B.W. van de Waal, J. Chem. Phys. 90 (1989) 3407. [8] P. Slavı´cˇek, R. Kalus, P. Pasˇka, I. Odva´rkova´, P. Hobza, A. Malijevsky´, J. Chem. Phys. 119 (2003) 2102. [9] J.F. Ziegler, J.P. Biersack, computer program ‘‘SRIM-200320’’. Available from: