Phase-field modeling of submonolayer growth with the modulated nucleation regime

Dong, Xianglei; Xing, Hang; Chen, C.L.; Wang, J.Y.; Kusaka, Jin

doi:10.1016/j.physleta.2015.06.021

Cited by 5 publications

(7 citation statements)

References 36 publications

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“…This is not an altogether surprising result, as all KMC simulations obtain this slope for irreversible aggregation. However, while some phasefield implementations 43 agree with this result, others 44,45 do not.…”

Section: Scaling Of Adatom and Island Densitiesmentioning

confidence: 68%

“…where τ is a time scale that determines the relaxation of the phase field to equilibrium and the right-hand side is the functional derivative of F with respect to φ. The free energy used here 43 is an extension of the expression proposed by Liu and Metiu 67 and has been used in other studies of epitaxial growth 44,45 on initially flat surfaces,…”

Section: A Solution Of Bcf Equationsmentioning

confidence: 99%

“…In previous implementations [43][44][45] of the phase-field method for submonolayer epitaxy, deposition was based on the random arrival of adatoms, and the nucleation rate of new islands was derived from the estimate λ n n 2 obtained from rate equations, 27,28,52 where λ n is an inverse time scale. This term is added to (14) as a new coupling for the phase field.…”

Section: A Solution Of Bcf Equationsmentioning

confidence: 99%

“…41,42 For our purposes, this method offers several advantages over the level-set method, including the ability to treat irreversible and reversible aggregation within a single framework, that is, without resorting to ad hoc, albeit sophisticated, schemes. 37 There have been several applications of the phasefield method to epitaxial systems, including growth in the submonolayer [43][44][45] and multilayer 45,46 regimes, on stepped surfaces [47][48][49] and spirals, 50 and on patterned surfaces. 51 Submonolayer epitaxy, the focus of our interest here, has been the most extensively studied regime, both experimentally and theoretically, 52 because scanning tunneling microscopy provides detailed information about island sizes and their distributions, which can be compared directly with predictions based on scaling theory to identify growth mechanisms and critical island sizes.…”

Section: Introductionmentioning

confidence: 99%

“…57 Previous work has focused either on island-size distribution functions for reversible and irreversible aggregation, but with uncertain results for island density scaling, 44 or solely on the scaling of island densities. 43,45 Here, we carry out a detailed examination of phase-field calculations of submonolayer epitaxy by determining exponents for adatom and island densities and, crucially, island-size distributions and demonstrate the crossover of these quantities from irreversible to reversible aggregation.…”

Section: Introductionmentioning

confidence: 99%

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Phase-field method for epitaxial kinetics on surfaces

Boer

Ford

Kantorovich

et al. 2018

The Journal of Chemical Physics

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We present a procedure for simulating epitaxial growth based on the phase-field method. We consider a basic model in which growth is initiated by a flux of atoms onto a heated surface. The deposited atoms diffuse in the presence of this flux and eventually collide to form islands which grow and decay by the attachment and detachment of migrating atoms at their edges. Our implementation of the phase-field method for this model includes uniform deposition, isotropic surface diffusion, and stochastic nucleation (in both space and time), which creates islands whose boundaries evolve as the surface atoms "condense" into and "evaporate" from the islands. Computations using this model in the submonolayer regime, prior to any appreciable coalescence of islands, agree with the results of kinetic Monte Carlo (KMC) simulations for the coverage-dependence of adatom and island densities and island-size distributions, for both reversible and irreversible growth. The scaling of the island density, as obtained from homogeneous rate equations, agrees with KMC simulations for irreversible growth and for reversible growth for varying deposition flux at constant temperature. For reversible growth with varying temperature but constant flux, agreement relies on an estimate of the formation energy of the critical cluster. Taken together, our results provide a comprehensive analysis of the phasefield method in the submonolayer regime of epitaxial growth, including the verification of the main scaling laws for adatoms and island densities and the scaling functions for island-size distributions, and point to the areas where the method can be extended and improved.

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Section: Scaling Of Adatom and Island Densitiesmentioning

confidence: 68%