Modeling the plastic relaxation onset in realistic SiGe islands on Si(001)

Physical Review B - Condensed Matter and Materials Physics

Volumn 78, Issue 18, 2008, Pages

  Gatti, R ^a   Marzegalli, A ^a   Zinovyev, V A ^b   Montalenti, F ^a   Miglio, Leo ^a  

^a UNIVERSITY OF MILANO BICOCCA   (Italy)

^b INSTITUTE OF SEMICONDUCTOR PHYSICS   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 56349107056     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.78.184104     Document Type: Article

References (45)

1. V. A. Shchukin and D. Bimberg, Rev. Mod. Phys. 71, 1125 (1999). 10.1103/RevModPhys.71.1125
2. Y. W. Mo, D. E. Savage, B. S. Swartzentruber, and M. G. Lagally, Phys. Rev. Lett. 65, 1020 (1990). 10.1103/PhysRevLett.65.1020
3. D. J. Eaglesham and M. Cerullo, Phys. Rev. Lett. 64, 1943 (1990). 10.1103/PhysRevLett.64.1943
4. V. A. Zinovyev, G. Vastola, F. Montalenti, and L. Miglio, Surf. Sci. 600, 4777 (2006). 10.1016/j.susc.2006.07.047
5. J. Stangl, V. Holy, and G. Bauer, Rev. Mod. Phys. 76, 725 (2004). 10.1103/RevModPhys.76.725
6. G. Costantini, A. Rastelli, C. Manzano, R. Songmuang, O. G. Schmidt, K. Kern, and H. von Kanel, Appl. Phys. Lett. 85, 5673 (2004). 10.1063/1.1829164
7. F. Ratto, G. Costantini, A. Rastelli, O. G. Schmidt, K. Kernz, and F. Rosei, J. Exp. Nanosci. 1, 279 (2006). 10.1080/17458080600977782
8. G. Medeiros-Ribeiro, A. M. Bratkovski, T. I. Kamins, D. A. A. Ohlberg, and R. S. Williams, Science 279, 353 (1998). 10.1126/science.279.5349.353
9. E. Sutter, P. Sutter, and J. E. Bernard, Appl. Phys. Lett. 84, 2262 (2004). 10.1063/1.1669068
10. M. Stoffel, A. Rastelli, J. Tersoff, T. Merdzhanova, and O. G. Schmidt, Phys. Rev. B 74, 155326 (2006). 10.1103/PhysRevB.74.155326
11. G. Vastola, R. Gatti, A. Marzegalli, F. Montalenti, and Leo Miglio, in Self-Assembled Quantum Dots, edited by, Zhiming M. Wang, (Springer, Berlin, 2008), pp. 421-438.
12. F. K. LeGoues, M. C. Reuter, J. Tersoff, M. Hammar, and R. M. Tromp, Phys. Rev. Lett. 73, 300 (1994). 10.1103/PhysRevLett.73.300
13. F. M. Ross, J. Tersoff, M. C. Reuter, F. K. LeGoues, and R. M. Tromp, Microsc. Res. Tech. 42, 281 (1998). 10.1002/(SICI)1097-0029(19980915)42: 4<281::AID-JEMT7>3.0.CO;2-T
14. A. Rastelli, M. Kummer, and H. von Kanel, Phys. Rev. Lett. 87, 256101 (2001). 10.1103/PhysRevLett.87.256101
15. G. Capellini, M. De Seta, and F. Evangelisti, Appl. Phys. Lett. 78, 303 (2001). 10.1063/1.1339263
16. M. Floyd, Y. Zhanga, K. P. Driver, J. Drucker, P. A. Crozier, and D. J. Smith, Appl. Phys. Lett. 82, 1473 (2003). 10.1063/1.1558215
17. T. U. Schülli, M. Stoffel, A. Hesse, J. Stangl, R. T. Lechner, E. Wintersberger, M. Sztucki, T. H. Metzger, O. G. Schmidt, and G. Bauer, Phys. Rev. B 71, 035326 (2005). 10.1103/PhysRevB.71.035326
18. T. Merdzhanova, S. Kiravittaya, A. Rastelli, M. Stoffel, U. Denker, and O. G. Schmidt, Phys. Rev. Lett. 96, 226103 (2006). 10.1103/PhysRevLett.96.226103
19. A. Marzegalli, V. A. Zinovyev, F. Montalenti, A. Rastelli, M. Stoffel, T. Merdzhanova, O. G. Schmidt, and Leo Miglio, Phys. Rev. Lett. 99, 235505 (2007). 10.1103/PhysRevLett.99.235505
20. Z. Y. Zhong, W. Schwinger, F. Schaffler, G. Bauer, G. Vastola, F. Montalenti, and Leo Miglio, Phys. Rev. Lett. 98, 176102 (2007). 10.1103/PhysRevLett.98.176102
21. J. P. Hirth and J. Lothe, Theory of Dislocations (Krieger, Malabar, 1992).
22. M. Peach and J. S. Koehler, Phys. Rev. 80, 436 (1950). 10.1103/PhysRev.80.436
23. B. J. Spencer and J. Tersoff, Phys. Rev. B 63, 205424 (2001). 10.1103/PhysRevB.63.205424
24. J. F. Justo, A. Fazzio, and A. Antonelli, J. Phys.: Condens. Matter 12, 10039 (2000). 10.1088/0953-8984/12/49/303
25. A. T. Blumenau, M. I. Heggie, C. J. Fall, R. Jones, and T. Frauenheim, Phys. Rev. B 65, 205205 (2002). 10.1103/PhysRevB.65.205205
26. I. N. Remediakis, D. E. Jesson, and P. C. Kelires, Phys. Rev. Lett. 97, 255502 (2006). 10.1103/PhysRevLett.97.255502
27. E. Van der Giessen and A. Needleman, Modell. Simul. Mater. Sci. Eng. 3, 689 (1995). 10.1088/0965-0393/3/5/008
28. R. Gracie, J. Oswald, and T. Belytschko, J. Mech. Phys. Solids 56, 200 (2008). 10.1016/j.jmps.2007.07.010
29. B. Devincre, L. P. Kubin, C. Lemarchand, and R. Madec, Mater. Sci. Eng., A 309-310, 211 (2001). 10.1016/S0921-5093(00)01725-1
30. T. Belytschko and R. Gracie, Int. J. Plast. 23, 1721 (2007). 10.1016/j.ijplas.2007.03.003
31. J. W. Matthews and A. E. Blakeslee, J. Cryst. Growth 27, 118 (1974).
32. R. Hull in Properties of Silicon Germanium and SiGe: Carbon, edited by, Erich Kasper, and, Klara Lyutovich, (University of Stuttgart, Germany, 2000), pp. 21-39.
33. A. K. Head, Proc. Phys. Soc. London, Sect. B 66, 793 (1953). 10.1088/0370-1301/66/9/309
34. H. T. Johnson and L. B. Freund, J. Appl. Phys. 81, 6081 (1997). 10.1063/1.364357
35. R. Gracie, G. Ventura, and T. Belytschko, Int. J. Numer. Methods Eng. 69, 423 (2007). 10.1002/nme.1896
36. J. Zou, X. Z. Liao, D. J. H. Cockayne, and Z. M. Jiang, Appl. Phys. Lett. 81, 1996 (2002). 10.1063/1.1506414
37. J. Tersoff, Phys. Rev. B 37, 6991 (1988). 10.1103/PhysRevB.37.6991
38. J. Tersoff, Phys. Rev. B 39, 5566 (1989). 10.1103/PhysRevB.39.5566
39. A. Marzegalli, F. Montalenti, and Leo Miglio, Appl. Phys. Lett. 86, 041912 (2005). 10.1063/1.1856145
40. A. Marzegalli, F. Montalenti, and Leo Miglio, J. Phys.: Condens. Matter 17, 7505 (2005). 10.1088/0953-8984/17/48/004
41. While introducing a 3 ML WL does not require any additional cost in the atomistic simulations, so that we considered its presence, inserting a three-layer Ge subdomain in the FEM calculation forces the creation of a dense mesh within this thin region. Since the WL has a negligible effect on the island stress field (Ref.) (as also demonstrated by the comparison between atomistic and FEM results), we avoided this additional computational cost in the FEM calculations by placing the island directly on the Si substrate. We also checked that neglecting the WL does not produce any significant variation in the critical volume for dislocation insertion.
42. K. Tillmann and A. Förster, Thin Solid Films 368, 93 (2000). 10.1016/S0040-6090(00)00858-0
43. F. Glas, Phys. Rev. B 74, 121302 (R) (2006). 10.1103/PhysRevB.74.121302
44. As discussed when describing the PK and the MF approaches, the presence of free surfaces causes a faster decay of the dislocation field. This allowed us to find converged values of Etot considering relatively thin substrates. For the results reported in Sec. 4, a Si substrate thickness of 2000 nm turned out to be more than sufficient.
45. D. C. Houghton, J. Appl. Phys. 70, 2136 (1991). 10.1063/1.349451