Modeling growth of one-dimensional islands: influence of reactive defects

An ab initio approach to anisotropic alloying into the Si(001) surface

By employing density functional theory calculations, we explore the initial stage of competitive alloying of co-deposited silver and indium atoms into a silicon surface. In particular, we identify respective adsorption positions and activation barriers governing their diffusion on a dimer-reconstructed silicon surface. Furthermore, we develop a growth model that appropriately describes diffusion mechanisms and silicon morphology with the account of silicon dimerization and the presence of C-type defects. Based on the surface kinetic Monte Carlo simulations, we examine the dynamics of bimetallic adsorption and elaborate on the temperature effects on the submonolayer growth of an Ag-In alloy. A close inspection of adatom migration clearly indicates effective nucleation of Ag and In atoms, followed by the formation of orthogonal atomic chains. We show that the epitaxial bimetallic growth might potentially lead to exotic ordering of adatoms in the form of anisotropic two-dimensional lattices via orthogonally oriented single-metal rows. We argue that this scenario becomes favorable provided above room temperature, while our numerical results are shown to be in agreement with the experimental findings.

Dynamic scaling of island size distribution in submonolayer one-dimensional growth

The dynamic scaling of the island size distribution (ISD) in the submonolayer growth regime of low-dimensional nanostructured systems is a long standing problem in epitaxial growth. In this study, kinetic Monte Carlo simulations of a realistic atomistic lattice-gas model describing the one-dimensional nucleation and growth of Al on Si(100):2×1 were performed to investigate the scaling behavior under varied growth conditions. Consistent with previous predictions, our results show that the shape of the scaled island size distribution can be altered by controlling the temperature and the C-defect density. The shifts in the scaled ISD are opposite to each other with temperature depending on the density of C-defects. For low C-defect density, a shift from a monomodal to a monotonically decreasing distribution as temperature increases is observed. We attribute the monomodal distribution to enhanced nucleation and aggregation whereas a monotonically decreasing distribution is attributed to restricted aggregation with defects playing only a minor role. At higher C-defect density, we show that the scaled ISD shift is from a monotonically decreasing to a monomodal distribution with increasing temperature. We argue that the reversal of the shift is due to competing effects introduced by high C-defect concentration. In addition, results show that the ISD is generally insensitive to flux variations and that at a high coverage regime the shift in the scaling behavior vanishes. Lastly, we posit that the shift in the scaled ISD indicates the departure of the island density's temperature dependence from predictions of classical nucleation theory.

Analytic scaling function for island-size distributions

We obtain an explicit solution for the island-size distribution described by the rate equations for irreversible growth with the simplified capture rates of the form σ(s)(Θ)∝Θ(p)(a+s-1) for all s≥1, where s is the size and Θ is the time-dependent coverage. The intrinsic property of this solution is its scaling form in the continuum limit. The analytic scaling function depends on the two parameters a and p and is capable of describing very dissimilar distribution shapes, both monomodal and monotonically decreasing. The obtained results suggest that the scaling features of the size distributions are closely related to the size linearity of the capture rates. A simple analytic scaling is obtained rigorously here and helps to gain a better theoretical understanding of possible origins of the scaling behavior of the island-size distributions.

Natural scaling of size distributions in homogeneous and heterogeneous rate equations with size-linear capture rates

We obtain exact solutions of the rate equations for homogeneous and heterogeneous irreversible growth models with linear size dependences of the capture rates. In the limit of high ratios of diffusion constant over deposition rate, both solutions yield simple analytical scaling functions with the correct normalizations. These are given by the cumulative distribution function and the probability density function of the gamma-distribution in homogeneous and heterogeneous cases, respectively. Our size distributions depend on the value of the capture rate a in the reaction of joining two mobile monomers A1 (A1 + A1 → A2) or the monomer attachment to the reactive defect B (A1 + B → AB). In homogeneous cases, the size distribution is monotonically decreasing regardless of a. In heterogeneous growth, the distribution is monotonically decreasing when a ≤ 1 and monomodal when a > 1. The obtained solutions describe fairly well the experimental data on the length distributions of Al, Ga, In, and Mn adatom chains on Si(100)-2 × 1 surfaces.