Departmental Bulletin Paper 極小モデルに基づいた薄膜点状島初期成長のスケーリング理論

中井, 日佐司

30 ( 1 )  , pp.71 - 78 , 2018-02-01 , 電気通信大学
For the both of Kinetic Monte-Carlo (KMC) and rate equations (RE) based on irreversible sub monolayergrowth of point islands in substrate spatial dimension d = 2, 3 and 4 as the limit R , I find that monomerdensity N1 and island density N have N1 = −1 ˆ() and N = −1 ˆN (), where R is the ratio of the monomerdiffusion rate to the deposition rate, is coverage and is the scaling factor determined by the detail of thesystem. The function ˆ and ˆN are universal functions independent of R and d, and calculated in the minimalmodel for submonolayer epitaxy by Tang [L. -H. Tang, J. Phys. I France 3, 935 (1993)]. As result, = (R)1/2was obtained for the both KMC and RE in d = 2, 3 and 4, where is the capture number of diffusing monomer.Finally, for RE in d > 4 as the limit, I show N1 and N have function form as same as the form in d 4.

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