Optimization algorithm for rate equations with an application to epitaxial graphene

Journal of Physics Condensed Matter

Volumn 26, Issue 18, 2014, Pages

  De Boer, J Posthuma ^a   Ford, I J ^b   Kantorovich, L ^c   Vvedensky, D D ^a  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

^b UNIVERSITY COLLEGE LONDON   (United Kingdom)

^c KING'S COLLEGE LONDON   (United Kingdom)

Author keywords

graphene; optimization; rate equations

Indexed keywords

ALGORITHMS; OPTIMIZATION;

DIFFERENT MECHANISMS; EPITAXIAL GRAPHENE; NUCLEATION AND GROWTH; NUCLEATION THEORY; OPTIMIZATION ALGORITHMS; RATE COEFFICIENTS; RATE EQUATIONS; TEMPERATURE DEPENDENCE;

GRAPHENE;

GRAPHITE; IRIDIUM; RUTHENIUM;

ALGORITHM; CHEMISTRY; KINETICS; TEMPERATURE; THEORETICAL MODEL;

ALGORITHMS; GRAPHITE; IRIDIUM; KINETICS; MODELS, THEORETICAL; RUTHENIUM; TEMPERATURE;

EID: 84899449355     PISSN: 09538984     EISSN: 1361648X     Source Type: Journal    
DOI: 10.1088/0953-8984/26/18/185008     Document Type: Article

References (31)

1. Metiu H, Lu Y-T and Zhang Z Y 1992 Epitaxial growth and the art of computer simulations Science 255 1088-1092 (Pubitemid 23584371)
2. Venables J A, Spiller G D T and Hanbücken M 1984 Nucleation and growth of thin films Rep. Prog. Phys. 47 399-459
3. Vineyard G H 1957 Frequency factors and isotope effects in solid state rate processes J. Phys. Chem. Solids 3 121-127
4. Voter A F 2007 Introduction to the kinetic Monte Carlo method in Radiation Effects in Solids ed K E Sickafus et al (Dordrecht: Springer) 1-23
5. Madhukar A and Ghaisas S V 1988 The nature of molecular beam epitaxial growth examined via computer simulations CRC Crit. Rev. Sol. State and Mater. Sci. 14 1-130
6. Shitara T, Vvedensky D D, Wilby M R, Zhang J, Neave J H and Joyce B A 1992 Step-density variations and reflection high-energy electron diffraction intensity oscillations during epitaxial growth on vicinal GaAs(0 0 1) Phys. Rev. B 46 6815-6824
7. Evans J W, Thiel P A and Bartelt M C 2006 Morphological evolution during epitaxial thin film growth: formation of 2D islands and 3D mounds Surf. Sci. Rep. 61 1-128 (Pubitemid 44294396)
8. Curtiss C F and Hirschfelder J O 1952 Integration of stiff equations Proc. Natl Acad. Sci. 38 235-243
9. Bales G S and Chrzan D C 1994 Dynamics of irreversible island growth during submonolayer epitaxy Phys. Rev. B 50 6057-6067
10. Bales G S and Zangwill A 1997 Self-consistent rate theory of submonolayer homoepitaxy with attachment/detachment kinetics Phys. Rev. B 55 R1973-R1976
11. Popescu M N, Amar J G and Family F 1998 Self-consistent rate-equation approach to transitions in critical island size in metal (1 0 0) and metal (1 1 1) homoepitaxy Phys. Rev. B 58 1613-1619 (Pubitemid 128495557)
12. Tokar V I and Dreyssé 2013 Rigorous derivation of the rate equations for epitaxial growth J. Stat. Mech. 2013 P06001
13. Bartelt M C and Evans J W 1996 Exact island-size distributions for submonolayer deposition: influence of correlations between island size and separation Phys. Rev. B 54 R17359-R17362
14. Vvedensky D D 2000 Scaling functions for island-size distributions Phys. Rev. B 62 15435-15438 (Pubitemid 32373455)
15. Gallivan M A and Atwater H A 2004 Design of a film surface roughness-minimizing molecular beam epitaxy process by reduced-order modeling of epitaxial growth J. Appl. Phys. 95 483-489
16. Zangwill A 1988 Physics at Surfaces (Cambridge: Cambridge University Press)
17. Yildirim H, Kara A and Rahman T S 2007 Origin of quasi-constant pre-exponential factors for adatom diffusion on Cu and Ag surfaces Phys. Rev. B 76 165421
18. Kratzer P and Scheffler M 2002 Reaction-limited island nucleation in molecular beam epitaxy of compound semiconductors Phys. Rev. Lett. 88 036102
19. Castro Neto A H, Guinea F, Peres N M R, Novoselev K S and Geim A K 2009 The electronic properties of graphene Rev. Mod. Phys. 81 109-162
20. Loginova E, Bartelt N C, Feibelman P J and McCarty K F 2008 Evidence for graphene growth by C cluster attachment New J. Phys. 10 093026
21. Loginova E, Bartelt N C, Feibelman P J and McCarty K F 2009 Factors influencing graphene growth on metal surfaces New J. Phys. 11 063046
22. Loginova E and McCarty K F 2014 unpublished
23. Zangwill A and Vvedensky D D 2011 Novel growth mechanism of epitaxial graphene on metals Nano Lett. 11 2092-2095
24. Mulheran P A and Basham M 2008 Kinetic phase diagram for island nucleation and growth during homoepitaxy Phys. Rev. B 77 075427
25. Amara H, Bichara C and Ducastelle F 2006 Formation of carbon nanostructures on nickel surfaces: a tight-binding grand canonical Monte Carlo study Phys. Rev. B 73 113404 (Pubitemid 43462032)
26. Gao J, Yuan Q, Hu H, Zhao J and Ding F 2011 Formation of carbon clusters in the initial stage of chemical vapor deposition graphene growth on Ni(1 1 1) surface J. Phys. Chem. C 115 17695-17703
27. Chen H, Zhu W and Zhang Z 2010 Contrasting behavior of carbon nucleation in the initial stages of graphene epitaxial growth on stepped metal surfaces Phys. Rev. Lett. 104 186101
28. Saadi S, Abild-Pedersen F, Helveg S, Sehested J, Hinnemann B, Appel C C and Nørskov J K 2010 On the role of metal step-edges in graphene growth J. Phys. Chem. C 114 11221-11227
29. Wang B, Ma X, Caffio M, Schaub R and Li W-X 2010 Size-selective carbon nanoclusters as precursors to the growth of epitaxial graphene Nano Lett. 11 424-430
30. Lizzita S and Baraldi A 2010 High-resolution fast X-ray photoelectron spectroscopy study of ethylene interaction with Ir(1 1 1): from chemisorption to dissociation and graphene formation Catal. Today 154 68-74
31. Kim H, Mattevi C, Reyes Calvo M, Oberg J C, Artiglia L, Agnoli S, Hirjibehedin C F, Chhowalla M and Saiz E 2012 Activation energy paths for graphene nucleation and growth on Cu ACS Nano 6 3614-3623