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Quantum and Classical Molecular Dynamics Studies of the Threshold Displacement Energy in Si Bulk and Nanowires

Published online by Cambridge University Press:  31 January 2011

Eero Holmström ,
Arkady Krasheninnikov  and
Kai Nordlund
Eero Holmström
Affiliation:
eero.holmstrom@helsinki.fi, University of Helsinki, Helsinki Institute of Physics, Helsinki, Finland
Arkady Krasheninnikov
Affiliation:
arkady.krasheninnikov@helsinki.fi, University of Helsinki, Department of Physics, Helsinki, Finland
Kai Nordlund
Affiliation:
kai.nordlund@helsinki.fi, University of Helsinki, Helsinki Institute of Physics, Helsinki, Finland
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Abstract

Using quantum mechanical and classical molecular dynamics computer simulations, we study the full three-dimensional threshold displacement energy surface in Si. We show that the SIESTA density-functional theory method gives a minimum threshold energy of 13 eV that agrees very well with experiments, and predicts an average threshold displacement energy of 36 eV. Using the quantum mechanical result as a baseline, we discuss the reliability of the classical potentials with respect to their description of the threshold energies. We also examine the threshold energies for sputtering in a nanowire, and find that this threshold depends surprisingly strongly on which layer the atom is in.

Keywords

ion-solid interactionsion-implantationelectron irradiation
Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 1181: Symposium DD – Ion Beams and Nano-Engineering , 2009 , 1181-DD05-02
Copyright
Copyright © Materials Research Society 2009

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References

REFERENCES

1 Smith, R. (ed.), Atomic & ion collisions in solids and at surfaces: theory, simulation and applications (Cambridge University Prss, Cambridge, UK, 1997).Google Scholar
2 Averback, R. S. and Rubia, T. Diaz de la, in Solid State Physics, edited by Ehrenfest, H. and Spaepen, F. (Academic Press, New York, 1998), Vol. 51, pp. 281–402.Google Scholar
3 Krasheninnikov, A. V. and Banhart, F. Nature Mater. 6, 723 (2007).Google Scholar
4 Loferski, J. and Rappaport, P. Phys. Rev. 111, 432 (1958).Google Scholar
5 Corbett, J. and Watkins, G. D. Phys. Rev. 138, 555 (1965).Google Scholar
6 Hemment, P. and Stevens, P. J. Appl. Phys. 40, 4893 (1969).Google Scholar
7 Marton, D. in Low Energy Ion-Surface Interactions, edited by Rabalais, J. W. (Wiley, Chester, 1994), p. 526.Google Scholar
8 Miller, L. Brice, D. Prinja, A. and Picraux, S. Phys. Rev. B. 49, 16953 (1994).Google Scholar
9 Miller, L. Brice, D. Prinja, A. and Pricraux, T. in Defects in Materials, MRS Symposia Proceedings No. 209, edited by Bristowe, P. D. Epperson, I. E. Griffith, I. E. and Liliental-Weber, Z. (Materials Research Society, Pittsburgh, 1991), p. 171.Google Scholar
10M.-Caturla, J. Rubia, T. Diaz de la, and Gilmer, G. H. in Materials Synthesis and Processing Using Ion Beams, MRS Symposia Proceedings No. 316, edited by Culbertson, R. I. amd, O. W. H. Jones, K. S. and Maex, K. (Materials Research Society, Pittsburgh, 1994), p. 141.Google Scholar
11 Miller, L. Brice, D. Prinja, A. and Pricraux, T. Radiat. Eff. Defects Solids 129, 127 (1994).Google Scholar
12 Sayed, M. Jefferson, J. H. Walker, A. B. and Cullis, A. G. Nucl. Instrum. Methods Phys. Res. B 102, 232 (1995).Google Scholar
13.Lucasson, P. in Fundamental Aspects of Radiation Damage in Metals, edited by Robinson, M. T. and Young, F. N. Jr. (ORNL, Springfield, 1975), pp. 42–65.Google Scholar
14 Andersen, H. H. Appl. Phys. 18, 131 (1979).Google Scholar
15 Jung, P. Phys. Rev. B 23, 664 (1981).Google Scholar
16 Nordlund, K. Wallenius, J. and Malerba, L. Nucl. Instr. Meth. Phys. Res. B 246, 322 (2005).Google Scholar
17For a review, see Jones, R. O. and Gunnarsson, O. Rev. Mod. Phys. 61, 689 (1989).Google Scholar
18 Gibson, J. B. Goland, A. N. Milgram, M. and Vineyard, G. H. Phys. Rev 120, 1229 (1960).Google Scholar
19 Uhlmann, S. et al. , Radiat. Eff. Defects Solids 141, 185 (1997).Google Scholar
20 Windl, W. Lenosky, T. J. Kress, J. D. and Voter, A. F. Nucl. Instr. and Meth. B 141, 61 (1998).Google Scholar
21 Mazzarolo, M. Colombo, L. Lulli, G. and Albertazzi, E. Phys. Rev. B 63, 195207 (2001).Google Scholar
22 Krasheninnikov, A. V. Miyamoto, Y. and Tomànek, D., Phys. Rev. Lett. 99, 016104 (2007).Google Scholar
23 Holmström, E., Kuronen, A. and Nordlund, K. Phys. Rev. B 78, 045202 (2008).Google Scholar
24 Stillinger, F. H. and Weber, T. A. Phys. Rev. B 31, 5262 (1985).Google Scholar
25 Tersoff, J. Phys. Rev. B 38, 9902 (1988).Google Scholar
26 Bazant, M. Z. Kaxiras, E. and Justo, J. F., (1997).Google Scholar
27 Justo, J. F. et al. , Phys. Rev. B 58, 2539 (1998).Google Scholar
28 Colli, A. et al. , Nano Letters 8, 2188 (2008).Google Scholar
29 Xu, S. et al. , Small 1, 1221 (2005).Google Scholar
30 Krasheninnikov, A. V. Nordlund, K. and Keinonen, J. Appl. Phys. Lett. 81, 1101 (2002).Google Scholar
31 Å.ström, J. A., Krasheninnikov, A. V. and Nordlund, K. Phys. Rev. Lett. 93, 215503 (2004).Google Scholar
32 Krasheninnikov, A. V. et al. , Phys. Rev. B 72, 125428 (2005).Google Scholar
33 Loponen, T. Krasheninnikov, A. V. Kaukonen, M. and Nieminen, R. M. Phys. Rev. B 74, 073409 (2006).Google Scholar
34 Sun, L. et al. , Phys. Rev. Lett. 101, 156101 (2008).Google Scholar
35 Nordlund, K. 2006, PARCAS computer code. The main principles of the molecular dynamics algorithms are presented in [60, 61]. The adaptive time step and electronic stopping algorithms are the same as in [62].Google Scholar
36 Tersoff, J. Phys. Rev. B 38, 9902 (1988).Google Scholar
37 Stillinger, F. A. and Weber, T. A. Phys. Rev. B 31, 5262 (1985).Google Scholar
38 Sole, J. M. et al. , J. Phys.: Condens. Matter 14, 2745 (2002).Google Scholar
39 Berendsen, H. J. C. et al. , J. Chem. Phys. 81, 3684 (1984).Google Scholar
40 Qian, G.-X. Martin, R. M. and Chadi, D. J. Phys. Rev. B 38, 7849 (1988).Google Scholar
41 Leung, W.-K. et al. , Phys. Rev. Lett. 83, 2351 (1999).Google Scholar
42 Al-Mushadani, O. K. and Needs, R. J. Phys. Rev. B 68, 235205 (2003).Google Scholar
43 Tang, M. Colombo, L. Zhu, J. and Rubia, T. Diaz de la, Phys. Rev. B 55, 14279 (1997).Google Scholar
44 Baraff, G. A. and Schluter, M. Phys. Rev. B 30, 3460 (1984).Google Scholar
45 Bar-Yam, Y. and Joannopolous, J. D. Phys. Rev. Lett. 52, 1129 (1984).Google Scholar
46 Car, R. Kelly, P. J. Oshiyama, A. and Pantelides, S. T. Phys. Rev. Lett. 52, 1814 (1984).Google Scholar
47 Car, R. Kelly, P. J. Oshiyama, A. and Pantelides, S. T. Phys. Rev. Lett. 54, 360 (1985).Google Scholar
48 Goedecker, S. Deutsch, T. and Billard, L. Phys. Rev. Lett. 88, 235501 (2002).Google Scholar
49 Puska, M. J. P.öykkö, S., Pesola, M. and Nieminen, R. M. Phys. Rev. B 58, 1318 (1998).Google Scholar
50 Centoni, S. A. et al. , Phys. Rev. B 72, 195206 (2005).Google Scholar
51 Nordlund, K. Runeberg, N. and Sundholm, D. Nucl. Instr. Meth. Phys. Res. B 132, 45 (1997).Google Scholar
52 Grein, C. H. J. Crys. Growth 180, 54 (1997).Google Scholar
53 Fulk, C. et al. , J. Electr. Mat. 35, 1449 (2006).Google Scholar
54 Vavilov, V. S. Patskevich, V. M. Yurkov, B. Y. and Glazunov, P. Y. Fiz. Tverd Tela 2, 1431 (1960).Google Scholar
55 Edmondson, P. D. Riley, D. Birtcher, R. C. and Donnelly, S. E. (2008), to be published.Google Scholar
56 Summers, G. P. Burke, E. A. and Walters, R. J. IEEE Trans. in Nucl. Sci. 40, 1372 (1993).Google Scholar
57 Ziegler, J. F. SRIM-2003 software package, available online at http://www.srim.org.Google Scholar
58 MacFarlane, R. E. RSIC, PSR-118 / NJOY (1979).Google Scholar
59 Huhtinen, M. Nucl. Instrum. Methods Phys. Res. A 491, 194 (2002).Google Scholar
60 Nordlund, K. et al. , Phys. Rev. B 57, 7556 (1998).Google Scholar
61 Ghaly, M. Nordlund, K. and Averback, R. S. Phil. Mag. A 79, 795 (1999).Google Scholar
62 Nordlund, K. Comput. Mater. Sci. 3, 448 (1995).Google Scholar