Kinetics of monolayer growth

Abstract

The kinetics of a monolayer growth is studied using the two-dimensional lattice gas model by means of the path-probability method (PPM) for nonequilibrium phenomena. Kinetic equations for the combined processes of relaxation (adsorption and desorption) and diffusion are derived analytically and solved for the first time in the square approximation of the PPM. Comparison of the square approximation with the point and pair approximations along with Monte Carlo simulation shows the effect of using a larger basic cluster than in the previous studies. When the square approximation is used, the growth rate results are much improved in both cases with and without diffusion and agree well with the Monte Carlo simulations results, except for very small values of the driving forceL=δμ/k _b T whereδμ is the chemical potential difference between the vapor and the solid phase. In the range where the agreement is good, there exists a region where the growth rateR is proportional to exp(−c/L with a constantc. This is the feature which is characteristic of two-dimensional nucleation-limited growth.