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Atomic and Electronic Structure of Germanium Clusters at Finite Temperature Using Finite Difference Methods

Published online by Cambridge University Press:  10 February 2011

James R. Chelikowsky
Affiliation:
Department of Chemical Engineering and Materials Science, Minnesota Supercomputer Institute, University of Minnesota, Minneapolis, Minnesota 55455, USA
Serdar ÖĞüt
Affiliation:
Department of Chemical Engineering and Materials Science, Minnesota Supercomputer Institute, University of Minnesota, Minneapolis, Minnesota 55455, USA
X. Jingc
Affiliation:
Department of Chemical Engineering and Materials Science, Minnesota Supercomputer Institute, University of Minnesota, Minneapolis, Minnesota 55455, USA
K. Wu
Affiliation:
Department of Computer Science, Minnesota Supercomputer Institute, University of Minnesota, Minneapolis, Minnesota 55455, USA
A. Stathopoulos
Affiliation:
Department of Computer Science, Minnesota Supercomputer Institute, University of Minnesota, Minneapolis, Minnesota 55455, USA
Y. Saad
Affiliation:
Department of Computer Science, Minnesota Supercomputer Institute, University of Minnesota, Minneapolis, Minnesota 55455, USA
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Abstract

Determining the electronic and structural properties of semiconductor clusters is one of the outstanding problems in materials science. The existence of numerous structures with nearly identical energies makes it very difficult to determine a realistic ground state structure. Moreover, even if an effective procedure can be devised to predict the ground state structure, questions can arise about the relevancy of the structure at finite temperatures. Kinetic effects and non-equilibrium structures may dominate the structural configurations present in clusters created under laboratory conditions. We illustrate theoretical techniques for predicting the structure and electronic properties of small germanium clusters. Spefically, we illustate that the detailed agreement between theoretical and experimental features can be exploited to identify the relevant isomers present under experimental conditions.

Type
Research Article
Copyright
Copyright © Materials Research Society 1996

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References

1. Physics and Chemistry of Small clusters, edited by Jena, P., Rao, B. K., and Khanna, S. N. (Plenum, New York, 1987).Google Scholar
2. Jarrold, M. F., Science 252, 1085 (1991); J. M. Alford R. T. Laaksonen, and R. E. Smalley, J. Chem. Phys. 94, 2618 (1990).Google Scholar
3. Bloomfield, L. A., Freeman, R. R., and Brown, W. L., Phys. Rev. Lett. 54, 2246 (1985).Google Scholar
4. Honea, E. C., Ogura, A., Murray, C. A., Raghavachari, K., Sprenger, W. O., Jarrold, M. F., and Brown, W. L., Nature 366, 42 (1993).Google Scholar
5. Cheshnovsky, O., Yang, S. H., Pettiette, C. L., Craycraft, M. J., Liu, Y., and Smalley, R. E., Chem. Phys. Lett. 138, 119 (1987).Google Scholar
6. Glassford, K., and Chelikowsky, J.R., Phys. Rev. B43, 14557 (1991).Google Scholar
7. Chelikowsky, J.R., Glassford, K., and Phillips, J.C., Phys. Rev. B44, 1538 (1991).Google Scholar
8. Raghavachari, K., J. Chem. Phys. 84, 5672 (1986).Google Scholar
9. Raghavachari, K., Phase Transitions 24–26, 61 (1990)Google Scholar
10. Raghavachari, K. and Rohlfing, C. M., J. Chem. Phys. 94, 3670 (1991).Google Scholar
11. Binggeli, N. and Chelikowsky, J. R., Phys. Rev. B 50, 11764 (1994); N. Binggeli, J.L. Martins, and J.R. Chelikowsky, Phys. Rev. Lett. 68, 2956 (1992).Google Scholar
12. Hohl, D., Jones, R. O., Car, R., and Parrinello, M., Phys. Rev. Lett. 55, 2471 (1985); D. Hohl, R. O. Jones, R. Car, and M. Parrinello, J. Chem. Phys. 89, 6823 (1988).Google Scholar
13. Kawai, R. and Weare, J. H., Phys. Rev. Lett. 65, 80 (1990).Google Scholar
14. Yi, J.-Y., Oh, D. J., Bernholc, J., Phys. Rev. Lett. 67, 1594 (1991).Google Scholar
15. Kumar, V. and Car, R., Phys. Rev. B 44, 8243 (1991).Google Scholar
16. Chelikowsky, J.R., and Cohen, M.L.: “Ab initio Pseudopotentials for Semiconductors,” Handbook on Semiconductors, Editor: Landsberg, Peter, (Elsevier, 1992), Vol.1, p. 59.Google Scholar
17. Ballone, P. and Andreoni, W., Phys. Rev. Lett. 60, 271 (1988); R. Car, M. Parrinello, and W. Andreoni, in Microclusters, edited by S. Sugano, Y. Nishina, and S. Ohnishi, Springer Series in Materials Science Vol.4 (Springer-Verlag, Berlin, 1987), p. 134; P. Ballone, W. Andreoni, R. Car, and M. Parrinello, Europhy. Lett. 8, 73 (1989).Google Scholar
18. Rötlisberg, U., Andreoni, W., and Giannozzi, P., J. Chem. Phys. 96, 1248 (1991).Google Scholar
19. Kubo, R., Rep. Prog. Theor. Phys. 29, 255 (1966).Google Scholar
20. Risken, H., The Fokker-Planck Equation, (Springer-Verlag, Berlin), 1984.Google Scholar
21. Biswas, R. and Hamann, D.R., Phys. Rev. B 34, 895 (1986).Google Scholar
22. Examples of Langevin dynamics can be found in Adelman, S.A., and Garrison, B.J., J. Chem. Phys. 65, 3751 (1976); J.D. Doll, and D.R. Dion, J. Chem. Phys. 65, 3762 (1976); J. C. Tully, George H. Gilmer, and Mary Shugard, J. Chem. Phys. 71, 1630 (1979), and references therein.Google Scholar
23. Binggeli, N., and Chelikowsky, J.R., Phys. Rev. B 50, 11764 (1994).Google Scholar
24. Nosé, S., Mol. Phys. 52, 255 (1984); W.G. Hoover, Phys. Rev. A 31, 1695 (1985).Google Scholar
25. Kirkpatrick, S., Gelatt, C.D., and Vecchi, M.P., Science 220, 671 (1983).Google Scholar
26. Hohenberg, P. and Kohn, W., Phys. Rev. 136, B864 (1964); W. Kohn and L.J. Sham, Phys. Rev. 140, A1133 (1965).Google Scholar
27. Perdew, J. P. and Zunger, A., Phys. Rev. 23, 5048 (1981).Google Scholar
28. Feynman, R. P., Phys. Rev. 56, 340 (1939).Google Scholar
29. Chelikowsky, J.R., and Cohen, M.L.: “Ab initio Pseudopotentials for Semiconductors,” Handbook on Semiconductors, Editor: Landsberg, Peter, (Elsevier, 1992), Vol.1, p. 59.Google Scholar
30. Troullier, N. and Martins, J. L., Phys. Rev. B 43, 8861 (1991).Google Scholar
31. Kleinman, L. and Bylander, D.M., Phys. Rev. Lett. 48, 1425 (1982).Google Scholar
32. Chelikowsky, J.R., Troullier, N., and Saad, Y., Phys. Rev. Lett., 72, 1240 (1994), J.R. Chelikowsky, N. Troullier, K. Wu, and Y. Saad, Phys. Rev. B 50, 11355 (1994), X. Jing, N. Troullier, D. Dean, N. Binggeli, J.R. Chelikowsky, K. Wu, and Y. Saad, Phys. Rev. B 50, 12234 (1994).Google Scholar
33. Fornberg, B. and Sloan, D., “A review of pseudospectral methods for solving partial differential equations”, in Acta Numerica 1994 (Iserles, A., ed.), Cambridge Univ. Press, pp. 203267.Google Scholar
34. Parlett, B.N. and Saad, Y., Linear Algebra and Its Applications 88/89, 575 (1987).Google Scholar
35. Saad, Y., Numerical Methods for Large Eigenvalue Problems, (Halstead Press,1992).Google Scholar
36. Ortega, J.M., Introduction to Parallel and Vector Solutions of Linear Systems (Manchester University Press, 1992).Google Scholar
37. Hunter, J. M., Fye, J. L., Jarrold, M. F., and Bower, J. E., Phys. Rev. Lett. 73, 2063 (1994).Google Scholar
38. Jing, X., Troullier, N., Chelikowsky, J.R., Wu, K. and Saad, Y., Solid State Comm. (in press).Google Scholar
39. Binggeli, N., and Chelikowsky, J.R., Phys. Rev. Lett. 75, 493 (1995).Google Scholar