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Volumn 53, Issue 1, 1996, Pages 359-388

Scale invariance and dynamical correlations in growth models of molecular beam epitaxy

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EID: 2342613966     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.53.359     Document Type: Article
Times cited : (163)

References (84)
  • 6
    • 85035236813 scopus 로고    scopus 로고
    • references therein.
    • references therein.
  • 22
    • 85035233099 scopus 로고    scopus 로고
    • to mitigate any confusion, we note that the convention in defining the primed and unprimed variables in this reference is opposite to that used here.
    • to mitigate any confusion, we note that the convention in defining the primed and unprimed variables in this reference is opposite to that used here.
  • 46
    • 0000675372 scopus 로고
    • The nabla2(nabla h)2 nonlinearity of Eqs. ( refgeneral) and ( refldseq) was first introduced into growth equations by T. Sun, H. Guo, and M. Grant [Phys. Rev. A 40, 6763 (1989)] as a conserved KPZ nonlinearity with the noise η considered a completely conserved noise η equiv ηD. In contrast, the deposition noise is unconserved in the MBE growth situation as emphasized in Refs. citelds,vill.
    • (1989) Phys. Rev. A , vol.40 , pp. 6763
  • 54
    • 85035233263 scopus 로고    scopus 로고
    • J.M. Kim and S. Das Sarma (unpublished); J. Krug
    • J.M. Kim and S. Das Sarma (unpublished); J. Krug (unpublished).
  • 55
    • 85035241044 scopus 로고    scopus 로고
    • J. Krug and H. Spohn, in Solids Far From Equilibrium, edited by C. Godrèche (Cambridge University Press, Cambridge, England, 1992); references therein.
    • J. Krug and H. Spohn, in Solids Far From Equilibrium, edited by C. Godrèche (Cambridge University Press, Cambridge, England, 1992); references therein.
  • 58
    • 85035241743 scopus 로고    scopus 로고
    • The same is true for all the higher order linear models of the [Formula Presented] type with n ge2, all of which have α'=1 and α = (n - 1/2), making kappa = (2n -d -1) for n ge 2 and d = 1+1 or 2+1. Note that in d=2+1 the [Formula Presented] linear model has a logarithmic anomalous scaling exponent with kappa = [Formula Presented].
    • The same is true for all the higher order linear models of the nabla2n type with n ge2, all of which have α'=1 and α = (n - 1/2), making kappa = (2n -d -1) for n ge 2 and d = 1+1 or 2+1. Note that in d=2+1 the nabla4 linear model has a logarithmic anomalous scaling exponent with kappa = 0+.
  • 60
    • 85035208502 scopus 로고    scopus 로고
    • While the scaling collapse of Fig. 6 for the BD model does not have the high quality of the corresponding SOS scaling collapses in Figs. 3 and 4, saturation of the scaling function is clear in Fig. 6 and the deviations for y= 0.1 to 1.0 are attributed to the intrinsic width and defect formation effects, well known to be important for non conservative growth, and demonstrate a problem of using a single valued height function to describe BD growth. See Refs. citedlgk,cjl_lag,krugspohn, for example. par
    • While the scaling collapse of Fig. 6 for the BD model does not have the high quality of the corresponding SOS scaling collapses in Figs. 3 and 4, saturation of the scaling function is clear in Fig. 6 and the deviations for y= 0.1 to 1.0 are attributed to the intrinsic width and defect formation effects, well known to be important for non conservative growth, and demonstrate a problem of using a single valued height function to describe BD growth. See Refs. citedlgk,cjl_lag,krugspohn, for example. par
  • 61
    • 85035206386 scopus 로고    scopus 로고
    • We note that the correlation lengths in the simulations yielding α' and z' are small [ξ([Formula Presented]) sim 30 60 for the data of Fig. 5(a)] compared to the largest system size (L=200) used to extract an L independent value for γ in Fig. 7(a), so the comparison between γ and z' may not be completely justified due to finite size effects. In particular, we note that for L=50 in the d=1+1 results for S(k) [so that L approx ξ([Formula Presented])], γ approx 2.3, the finite size effect making γ more consistent with z'. Because growth in 2+1 dimensions is not as constrained as it is for d=1+1 (there are more diffusional opportunities for an atom in higher dimensions), it seems reasonable that such effects are reduced.
    • We note that the correlation lengths in the simulations yielding α' and z' are small [ξ(tmax) sim 30 60 for the data of Fig. 5(a)] compared to the largest system size (L=200) used to extract an L independent value for γ in Fig. 7(a), so the comparison between γ and z' may not be completely justified due to finite size effects. In particular, we note that for L=50 in the d=1+1 results for S(k) [so that L approx ξ(tmax)], γ approx 2.3, the finite size effect making γ more consistent with z'. Because growth in 2+1 dimensions is not as constrained as it is for d=1+1 (there are more diffusional opportunities for an atom in higher dimensions), it seems reasonable that such effects are reduced.
  • 64
    • 85035207164 scopus 로고    scopus 로고
    • We attempted to fit the P(s) distribution to the stretched exponential form, but very few step height values occur even for very long simulations both in the D=10,20 DT model and the Family model, and such an exercise is not statistically meaningful.
    • We attempted to fit the P(s) distribution to the stretched exponential form, but very few step height values occur even for very long simulations both in the D=10,20 DT model and the Family model, and such an exercise is not statistically meaningful.
  • 65
    • 85035194256 scopus 로고    scopus 로고
    • J.M. Kim (private communication).
    • Kim, J.M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.