Dynamic Scaling of Island Size Distribution in One-Dimensional Nanowires:
a Kinetic Monte Carlo Study
Jason R. Albia ^{1*}, Marvin A. Albao^{1}^{1}Institute of Mathematical Sciences and Physics, University of the Philippines, Los Baños, Laguna, Philippines* presenting author:Jason Albia, email:jralbia@up.edu.ph Previous reports predicted that the dynamical scaling of island size distribution (ISD) can be tuned by controlling the growth conditions. Guided by experimental and theoretical works, we performed exhaustive kinetic Monte Carlo simulations of a suitable atomistic-lattice gas model describing the nucleation and growth of one-dimensional Al atomic chains (nanowires) on Si(100):2x1. We aim to determine the dependence of island size distribution (ISD) on varying growth conditions: temperature (T), C-defect concentration (C
_{c-def}), coverage (θ), flux rates (F). We mapped the Si(100):2x1 into 300 x 300 lattice size and use Bortz-Kalos-Lebowitz (BKL) algorithm to dynamically evolve the Al/Si(100) system. To make our model more realistic, we incorporated the C-type defects which have been experimentally observed as stable nucleation sites for adatoms. Consistent with previous predictions, our results show that there is a shift in the scaling behaviuor. For low C_{c-def}, the ISD shifted from monomodal to monotonically decreasing distribution as the temperature increases. We attribute the monomodal distribution to enhance nucleation and segregation whereas the monotonically decreasing behaviour is due to restricted aggregation. In contrast, for high C_{c-def}, the crossing over of the ISD is from monotonically decreasing to monomodal distribution as the temperature increases. We attribute the reversal in the shift in the scaling behaviour to the competing effects introduced by high C_{c-def}. At low temperature, the blocking effect of the C-defects on the diffusing adatom lead to formation of predominantly shorter islands thereby resulting to monotonically decreasing distribution. At high temperature when the system is more thermodynamically active, the frequent exchange of adatoms among islands tend to produce islands of uniform sizes thus resulted to monomodal distribution. In addition, simulation results show that ISD is generally insensitive to varying flux rates. This observation is attributed to high diffusion rate to flux rate ratio and the existence of the energetically forbidden regions. Lastly, we show that at low coverage value, the shift in the ISD behaviour is observable but for higher coverages the crossing over in the ISD vanishes. Keywords: nanowires, surface adsorption, surface defect, monte carlo methods, nucleation |