Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-28T01:10:22.041Z Has data issue: false hasContentIssue false

Quantum atomistic simulations of silicon and germanium

Published online by Cambridge University Press:  31 January 2011

Carlos P. Herrero
Affiliation:
Instituto de Ciencia de Materiales, Consejo Superior de Investigaciones Científicas (C.S.I.C.), Campus de Cantoblanco, 28049 Madrid, Spain
Get access

Abstract

Quantum atomistic simulations of crystalline silicon and germanium have been carried out by the path-integral Monte Carlo method. The interatomic interactions were modeled by Stillinger–Weber-type potentials, with parameters adequate to quantum simulations. Quantum zero-point motion together with anharmonicity of the interatomic potential led to a lattice expansion of 7 × 10−3 Å for both Si and Ge. Results for the equation-of-state (volume versus pressure) and for the thermal expansion coefficient agreed well with experimental results for both materials at T > 100 K and for hydrostatic pressures up to 100 kbar.

Type
Articles
Copyright
Copyright © Materials Research Society 2001

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Biswas, R. and Hamann, D.R., Phys. Rev. Lett. 55, 2001 (1985).CrossRefGoogle Scholar
2Dodson, B.W., Phys. Rev. B 35, 2795 (1987).CrossRefGoogle Scholar
3Broughton, J.Q. and Li, X.P., Phys. Rev. B 35, 9120 (1987).CrossRefGoogle Scholar
4Tersoff, J., Phys. Rev. B 37, 6991 (1988).CrossRefGoogle Scholar
5Kaxiras, E. and Pandey, K.C., Phys. Rev. B 38, 12736 (1988).CrossRefGoogle Scholar
6Kluge, M.D. and Ray, J.R., Phys. Rev. B 37, 4132 (1988).CrossRefGoogle Scholar
7Wang, C.Z., Chan, C.T., and Ho, K.M., Phys. Rev. B 40, 3390 (1989).CrossRefGoogle Scholar
8Cook, S.J. and Clancy, P., Phys. Rev. B 47, 7686 (1993).CrossRefGoogle Scholar
9de la Rubia, T. Díaz and Gilmer, G.H., Phys. Rev. Lett. 74, 2507 (1995).CrossRefGoogle Scholar
10Car, R. and Parrinello, M., Phys. Rev. Lett. 55, 2471 (1985).CrossRefGoogle Scholar
11Biernacki, S. and Scheffler, M., Phys. Rev. Lett. 63, 290 (1989).CrossRefGoogle Scholar
12Pavone, P., Karch, K., Schütt, O., Windl, W., Strauch, D., Giannozzi, P., and Baroni, S., Phys. Rev. B 48, 3156 (1993).CrossRefGoogle Scholar
13Pavone, P. and Baroni, S., Solid State Commun. 90, 295 (1994).CrossRefGoogle Scholar
14Rignanese, G.M., Michenaud, J.P., and Gonze, X., Phys. Rev. B 53, 4488 (1996).CrossRefGoogle Scholar
15Ashcroft, N.W. and Mermin, N.D., Solid State Physics (Saunders College, Philadelphia, PA, 1976).Google Scholar
16Srivastava, G.P., The Physics of Phonons (Adam Hilger, Bristol, United Kingdom, 1990).Google Scholar
17Kazimorov, A., Zegenhagen, J., and Cardona, M., Science 282, 930 (1998).CrossRefGoogle Scholar
18Cardona, M., Phys. Status Solidi (B) 220, 5 (2000).3.0.CO;2-K>CrossRefGoogle Scholar
19Feynman, R.P., Statistical Mechanics (Addison-Wesley, New York, 1972).Google Scholar
20Gillan, M.J., in Computer Modelling of Fluids, Polymers, and Solids, edited by Catlow, C.R.A., Parker, S.C., and Allen, M.P. (Kluwer, Dordrecht, The Netherlands, 1990); Gillan, M.J., Philos. Mag. A 58, 257 (1988).Google Scholar
21Ceperley, D.M., Rev. Mod. Phys. 67, 279 (1995); 71, S438 (1999).CrossRefGoogle Scholar
22Ramírez, R. and Herrero, C.P., Phys. Rev. B 48, 14659 (1993).CrossRefGoogle Scholar
23Herrero, C.P., Solid State Commun. 110, 243 (1999).CrossRefGoogle Scholar
24Ramírez, R. and Herrero, C.P., Phys. Rev. Lett. 73, 126 (1994); Herrero, C.P. and Ramírez, R., Phys. Rev. B 51, 16761 (1995).Google Scholar
25Noya, J.C., Herrero, C.P., and Ramírez, R., Phys. Rev. B 56, 237 (1997).CrossRefGoogle Scholar
26Stillinger, F.H. and Weber, T.A., Phys. Rev. B 31, 5262 (1985).CrossRefGoogle Scholar
27Noya, J.C., Herrero, C.P., and Ramírez, R., Phys. Rev. B 53, 9869 (1996).CrossRefGoogle Scholar
28Laradji, M., Landau, D.P., and Dünweg, B., Phys. Rev. B 51, 4894 (1995).CrossRefGoogle Scholar
29Binder, K. and Heermann, D.W., Monte Carlo Simulation in Statistical Physics (Springer-Verlag, Berlin, Germany, 1988).CrossRefGoogle Scholar
30Physics of Group IV Elements and III-V Compounds, edited by Madelung, O., Landolt-Börnstein, New Series Group III, Vol. 17a (Springer-Verlag, Berlin, Germany, 1982).Google Scholar
31Hall, R.O.A., Acta Crystallogr. 14, 1004 (1961).CrossRefGoogle Scholar
32Shah, J.S. and Straumanis, M.E., Solid State Commun. 10, 159 (1972).CrossRefGoogle Scholar
33Reeber, R.R., Phys. Status Solidi (A) 32, 321 (1975).CrossRefGoogle Scholar
34Yim, W.M. and Paff, R.J., J. Appl. Phys. 45, 1456 (1974).CrossRefGoogle Scholar
35Singh, H.P., Acta Crystallogr. 24A, 469 (1968).CrossRefGoogle Scholar
36Murnaghan, F.D., Proc. Natl. Acad. Sci. U.S.A. 30, 244 (1944).CrossRefGoogle Scholar
37McSkimin, H.J. and Andreatch, P. Jr., J. Appl. Phys. 35, 2161 (1964).CrossRefGoogle Scholar
38McSkimin, H.J. and Andreatch, P. Jr., J. Appl. Phys. 34, 651 (1963).CrossRefGoogle Scholar
39Anderson, O.L., J. Phys. Chem.Solids, 27, 547 (1966).CrossRefGoogle Scholar
40Karch, K., Dietrich, T., Windl, W., Pavone, P., Mayer, A.P., and Strauch, D., Phys. Rev. B 53, 7259 (1996).CrossRefGoogle Scholar
41Reeber, R.R. and Wang, K., J. Mater. Res. 15, 40 (2000).CrossRefGoogle Scholar
42Williams, J.J., Kramer, M.J., and Akinc, M., J. Mater. Res. 15, 1780 (2000).CrossRefGoogle Scholar
43Herrero, C.P. and Ramírez, R., Phys. Rev. B (in press).Google Scholar
44Debernardi, A. and Cardona, M., Phys. Rev. B 54, 11305 (1996).CrossRefGoogle Scholar