2008/05/30 by Lionel Sittler, Sittler Lionel, Lionel, Sittler
Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech #nanoparticles nucleation surface interactions
paper · pdf · doi:10.48550/arxiv.0805.4744
to be publish in journal to Thin Solid Films
openalex publication_date 2008/05/30 · arxiv created 2010/06/15 · arxiv updated 2010/06/16 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
In this paper we propose a solution for the time evolution of the island density with irreversible aggregation and a time dependent input of particle in the space dimensions d=1,2. For this purpose we use the rate equation resulting from a generalized mean field approach. A well-known technique for growing surfaces at the atomic scale is molecular beam epitaxy (MBE). Another approach is the pulsed laser deposition method (PLD). The main difference between MBE and PLD is that in the case of MBE we have a continuous rate of deposition F of adatoms on the surface whereas in the case of PLD the adatoms are deposited during a pulse of a laser which is very short in comparison to the time span T between the pulses. The generalized mean field theory is a useful model for both MBE and PLD with the most simple approximation, point-like island. We show that the parameter T distinguishes the MBE regime from the PLD regime. We solve the rate equation for the PLD regime. We consider the time evolution of the density of immobile islands. For large time t≫ T, the PLD regime dominates the MBE regime and we find that the density of immobile islands grows as t1/2 whereas for MBE we find the known behavior of the density, t1/3 for d=2 and t1/4 for d=1. We illustrate this result with Monte-Carlo simulations for d=1,2.