A finite element analysis of surface-stress effects on measurement of the Si lattice parameter

Metrologia

Volumn 50, Issue 3, 2013, Pages 243-248

  Quagliotti, D ^a   Mana, G ^a   Massa, E ^a   Sasso, C ^a   Kuetgens, U ^b  

^a ISTITUTO NAZIONALE DI RICERCA METROLOGICA   (Italy)

^b PHYSIKALISCH TECHNISCHE BUNDESANSTALT   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

BULK MATERIALS; FINITE ELEMENT MODELS; INTERFEROMETER DESIGNS; OPTICAL INTERFEROMETRY; SOLID SURFACE; SURFACE LOADS; SURFACE STRESS; X-RAY INTERFEROMETERS;

FINITE ELEMENT METHOD; SILICON; SURFACE PROPERTIES;

LATTICE CONSTANTS;

EID: 84878885850     PISSN: 00261394     EISSN: 16817575     Source Type: Journal    
DOI: 10.1088/0026-1394/50/3/243     Document Type: Article

References (28)

1. 28Si crystal Phys. Rev. Lett. 106 030801
2. 28Si crystal for a new kilogram definition Metrologia 48 S1-13
3. 28Si x-ray interferometer Metrologia 48 S37-43
4. Kren P 2012 private communication
5. Ferroglio L, Mana G, Palmisano C and Zosi G 2008 Influence of surface stress in the determination of the (2 2 0) lattice spacing of silicon Metrologia 45 110-8 (Pubitemid 351220332)
6. Gibbs J W 1906 The Scientific Papers of J. Willard Gibbs vol 1 (London: Longmans Green) p 55
7. Shuttleworth R 1950 Proc. Phys. Soc. A 63 444-57
8. Cammarata R C 1994 Surface and interface stress effects in thin films Prog. Surf. Sci. 46 1-38
9. Desjonquères M C and Spanjaard D 1996 Concepts in Surface Physics (Heidelberg: Springer)
10. Makkonen L 2012 Misinterpretation of the Shuttleworth equation Scr. Mater. 66 627-9
11. Gurtin M E and Murdoch I 1975 A continuum theory of elastic material surfaces Arch. Ration. Mech. Anal. 57 291-323
12. Gurtin M E and Murdoch I 1975 Addenda to our paper: a continuum theory of elastic material surfaces Arch. Ration. Mech. Anal. 59 389-90
13. Gurtin M E and Murdoch I 1978 Surface stress in solids Int. J. Solids Struct. 14 431-40
14. Wolfer W G 2011 Elastic properties of surfaces on nanoparticles Acta Mater. 59 7736-43
15. Becker P and Mana G 1994 The lattice parameter of silicon: a survey Metrologia 31 203-9
16. Miyamoto Y 1994 Comparative study of Si(1 0 0) surface stresses with dimerized group-IV adatoms Phys. Rev. B 49 1947-51
17. Hara S, Izumi S, Kumagai T and Sakai S 2005 Surface energy, stress and structure of well-relaxed amorphous silicon: a combination approach of ab initio and classical molecular dynamics Surf. Sci. 585 17-24 (Pubitemid 40762466)
18. Delph T J 2008 Near-surface stresses in silicon(0 0 1) Surf. Sci. 602 259-67
19. Müller P and Saúl A 2004 Elastic effects on surface physics Surf. Sci. Rep. 54 157-258
20. Alerhand O L, Vanderbilt D, Meade R D and Joannopoulos J D 1988 Spontaneous formation of stress domains on crystal surfaces Phys. Rev. Lett. 61 1973-6
21. Payne M C, Roberts N, Needs R J, Needels M and Joannopoulos J D 1989 Total energy and stress of metal and semiconductor surfaces Surf. Sci. 211/212 1-20
22. Meade R D and Vanderbilt D 1990 Proc. 20th Int. Conf. on the Physics of Semiconductors (Thessaloniki, Greece, 6-10 August) (Singapore: World Scientific) p 123
23. Poon T W, Yip S, Ho P S and Abraham F F 1992 Ledge interactions and stress relaxations on Si(0 0 1) stepped surfaces Phys. Rev. B 45 3521-31
24. Garcìa A and Northrup J E 1993 Stress relief from alternately buckled dimers in Si(1 0 0) Phys. Rev. B 48 17350-3
25. Métois J J, Saúl A and Mueller P 2005 Measuring the surface stress polar dependence Nat. Mater. 4 238-42 (Pubitemid 40337218)
26. Itakura A N, Narushima T, Kitajima M, Teraishi K, Yamada A and Miyamoto A 2000 Surface stress in thin oxide layer made by plasma oxidation with applying positive bias Appl. Surf. Sci. 159-160 62-6
27. COMSOL Multiphysics® 4.3a
28. Ferroglio L, Mana G and Massa E 2011 The self-weight deformation of an x-ray interferometer Metrologia 48 S50-4