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):$2\times 1$ 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.

Figure 1

Schematic of the atomistic lattice-gas model used to simulate the scaled ISD. The Si(100):$2\times 1$ surface is modeled as a 2D lattice where each cell represents a lattice site corresponding to an adsorption site on Si(100). The black and gray circles are $C$-defects and Al adatoms, respectively. The crossed lattice (with mark X) sites are forbidden zones (energetically unfavorable) for diffusion and nucleation. Detachment and diffusion events and their corresponding energy barriers are as follows: (A) the detachment of adatom A from a $C$-defect site (0.30 eV), (B) the detachment of adatom B from a dimer $(s=2)$ nucleated on a $C$-defect (1.50 eV), (C) the detachment of adatom C from even-sized islands $(s\ge 3)$ nucleated on the $C$-defect (0.45 eV), (D) the detachment of adatom D from odd-sized islands $(s\ge 3)$ nucleated on the $C$-defect (0.45 eV), (E) the detachment of adatom E from a homogeneous dimer $(s=2)$ (1.30 eV), and (F) the free adatom F diffusion on the parallel (0.305 eV) or perpendicular (0.466-eV) direction with respect to Si-dimer rows.

Figure 2

The scaled ISDs are monomodal for different temperatures for the irreversible growth model. Simulation parameters: $F={10}^{-4}\mathrm{ML}{\mathrm{s}}^{-1},N_{\mathrm{def}}=0.01/\mathrm{site}$, and $\theta =0.05\mathrm{ML}$.

Figure 3

The scaled ISD for the reversible growth model at various temperatures $\left(T\right)$ and $C$-defect densities $\left(N_{\mathrm{def}}\right)$. Simulation parameters: $F={10}^{-4}\mathrm{ML}{\mathrm{s}}^{-1}$ and $\theta =0.05\mathrm{ML}$.

Figure 4

The scaled ISD at different coverages and temperatures. Simulation parameters: $F={10}^{-4}\mathrm{ML}{\mathrm{s}}^{-1}$ and $N_{\mathrm{def}}=0.01/\mathrm{site}$.

Figure 5

The scaled ISD for different deposition fluxes at various temperatures. Simulation parameters: $N_{\mathrm{def}}=0.01/\mathrm{site}$ and $\theta =0.05\mathrm{ML}$.