Growth of islands in two dimensions by irreversible aggregation of particles with a biased diffusion

The effects of the biased diffusion of particles on the growth of islands for a model of deposition, diffusion and irreversible aggregation of particles forming islands in two dimensions is studied. The direction of the bias is perpendicular to the growth direction of islands and these islands act as obstacles for the diffusing particles that collide with the lateral sides of islands without sticking. Due to the biased diffusion the islands are composed by the agglomeration of monomer chains. Using Monte Carlo simulations we found that the island density exponent continuously increases from to 1/2 when the bias parameter lambda increases from lambda = 1 to infinity, but the chain density exponent Xe congruent to 1/3 is independent of lambda. For lambda = infinity, the fully directed diffusion case, an expression for the nucleation rate can be obtained which is in agreement with the numerical results.