TY - JOUR
T1 - Fragmentation approach to the point-island model with hindered aggregation
T2 - Accessing the barrier energy
AU - González, Diego Luis
AU - Pimpinelli, Alberto
AU - Einstein, T. L.
N1 - Publisher Copyright:
© 2017 American Physical Society.
PY - 2017/7/24
Y1 - 2017/7/24
N2 - We study the effect of hindered aggregation on the island formation process in a one- (1D) and two-dimensional (2D) point-island model for epitaxial growth with arbitrary critical nucleus size i. In our model, the attachment of monomers to preexisting islands is hindered by an additional attachment barrier, characterized by length la. For la=0 the islands behave as perfect sinks while for la→ they behave as reflecting boundaries. For intermediate values of la, the system exhibits a crossover between two different kinds of processes, diffusion-limited aggregation and attachment-limited aggregation. We calculate the growth exponents of the density of islands and monomers for the low coverage and aggregation regimes. The capture-zone (CZ) distributions are also calculated for different values of i and la. In order to obtain a good spatial description of the nucleation process, we propose a fragmentation model, which is based on an approximate description of nucleation inside of the gaps for 1D and the CZs for 2D. In both cases, the nucleation is described by using two different physically rooted probabilities, which are related with the microscopic parameters of the model (i and la). We test our analytical model with extensive numerical simulations and previously established results. The proposed model describes excellently the statistical behavior of the system for arbitrary values of la and i=1, 2, and 3.
AB - We study the effect of hindered aggregation on the island formation process in a one- (1D) and two-dimensional (2D) point-island model for epitaxial growth with arbitrary critical nucleus size i. In our model, the attachment of monomers to preexisting islands is hindered by an additional attachment barrier, characterized by length la. For la=0 the islands behave as perfect sinks while for la→ they behave as reflecting boundaries. For intermediate values of la, the system exhibits a crossover between two different kinds of processes, diffusion-limited aggregation and attachment-limited aggregation. We calculate the growth exponents of the density of islands and monomers for the low coverage and aggregation regimes. The capture-zone (CZ) distributions are also calculated for different values of i and la. In order to obtain a good spatial description of the nucleation process, we propose a fragmentation model, which is based on an approximate description of nucleation inside of the gaps for 1D and the CZs for 2D. In both cases, the nucleation is described by using two different physically rooted probabilities, which are related with the microscopic parameters of the model (i and la). We test our analytical model with extensive numerical simulations and previously established results. The proposed model describes excellently the statistical behavior of the system for arbitrary values of la and i=1, 2, and 3.
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U2 - 10.1103/PhysRevE.96.012804
DO - 10.1103/PhysRevE.96.012804
M3 - Article
C2 - 29347254
AN - SCOPUS:85026477359
SN - 2470-0045
VL - 96
JO - Physical Review E
JF - Physical Review E
IS - 1
M1 - 012804
ER -