Capture of adatoms by clusters in thin film deposition

The adatom diffusion and capture by clusters are considered as a random-walk problem. The method of solution is developed. Green's function for a square substrate lattice is obtained. This permits one to give a general solution for a steady-state adatom distribution around clusters and for Halpern's arrival probability. This solution is applicable for calculating capture numbers of some small capture centres. An interpolation formula for the capture number, as dependent on the perimeter length of the capture centre, is proposed for λ a. The adatoms fluxes to the 10 and 11 steps on the surface are calculated. The fluxes are anistropic but the anisotropy disappears with λ/a → ∞. The applicability of the steady-state approach is discussed. It is shown that this approximation is valid for low adatom density. The adatom fluxes to monatomic and diatomic immobile clusters are calculated under conditions when these clusters cannot be treated as capture centres. The conservation equations for these clusters are formulated whereby two different configurations of three-atomic clusters are taken into account.