Hisashi NAKAI (中井 日佐司)

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.

Numerical solutions and an error estimation formula for gap ys between an island with size s and another island in one-dimensional submonolayer growth are presented. The origin of the error is assumed to be the numerical integral computation included in an equation for the ys. In order to evaluate the error for YM, which is the numerical approximation of ys, numerical integrations in the equation of ys are calculated with composite trapezoidal rule using 1/2M, M and 2M of number of equal divided interval. As a result, the error of the gap for M = 213 of the divided number is a onethird for the difference Ys M/2 Ys M . Similarly, the error for the numerical solution of the island size distribution Ns M is the 1/4.2 of Ns M/2 Ns M and was less than 7 × 10--9. My size-distribution result is compared to both the results of literature on the kinetic Monte-Carlo simulation and the rate equation.