抄録
By dimensional analysis, it is confirmed that a cumulative local size xy for one-dimentional irreversible submonolayergrowth of point islands [J. G. Amar and M. N. Popescu, Surf. Sci. 419, 239 (2001)] is expressed bya function of scaled gap length Y and dimensionless deposition time R1/3θ, where R is the ratio of the monomerdiffusion rate to the deposition rate and θ is coverage. Using asymptotic analysis for xy as the limit R Ishow that xy/sav I = 1/B ∫ 1 ϕY uα tanh (YBu−α) du, where B is a certain monotonically decreasing function ofthe variable R1/3θ, α is dynamical exponent of nucleation length and sav is average size. At both of the numericalresult of xy/sav and the approximate analytical evaluation for the integral I with Taylor expansion in YB for theintegrand, correction term for Y Y−3( or limit of xy/sav as is shown to be proportional to (R1/3θ)−3/4,and the analytical evaluation is in good agreement with the numerical result in R1/3θ 400. Finally, I findanother evaluation for I with the expansion in α to improve the deviation in 100 R1/3θ < 400.