Self-consistent rate theory for submonolayer surface growth of multicomponent systems

The self-consistent rate theory for surface growth in the submonolayer regime is generalized from mono- to multicomponent systems, which are formed by codeposition of different types of atoms or molecules. The theory requires the introduction of pair density distributions to enable a symmetric treatment of reactions among different species. The approach is explicitly developed for binary systems and tested against kinetic Monte Carlo simulations. Using a reduced set of rate equations, only a few differential equations need to be solved to obtain good quantitative predictions for island and adatom densities, as well as densities of unstable clusters.

Figure 1

Number densities of $A$ and $B$ adatoms, and stable islands as a function of the coverage $\Theta =Ft$ for $i=1$ and various combinations of $x_A$ and $D_A/D_B$. Results from the self-consistent rate theory are given by solid lines.

Figure 2

Number densities of (a) stable islands $N$, (b) $A$ adatoms, and (c) $B$ adatoms as a function of the coverage $\Theta$ for a case of mixed dimer stabilities, where $AA$ and $AB$ dimers are stable while $BB$ dimers are unstable with zero binding energies. Results from the self-consistent approach (solid lines) with ${\mu }_{BB}=0.1$ are compared with KMC simulations (symbols).

Figure 3

Densities of (a) stable $AA$ dimers, (b) stable $AB$ dimers, and (c) partial nucleation rates $2D_A{\sigma }_1^{AA}{\left(n_A\right)}^2$ (open symbols) and $(D_A+D_B){\sigma }_1^{AB}{n}_A{n}_B$ (filled symbols) as a function of the coverage $\Theta$ for mixed dimer stabilities as in Fig. 2. In (a) and (b) the symbols refer to KMC results, and in (c) they are used for the assignment of the lines to the parameters. In all figure parts, the lines represent results of the self-consistent rate theory.