Reactivity of heterogeneous surfaces: Modeling precursor–surface interaction using absorbing Markov chains

Abstract

Heterogeneous reactive surfaces involving a spatial distribution of reactive sites are ubiquitous in thin film growth, from defect nucleation to step flow growth. In this work, the interaction of gas phase species with heterogeneous reactive surfaces was explored using a model combining absorbing Markov chains and local balance equations. Through this model, single particle statistics can be extracted of the adsorption–diffusion–desorption/reaction process even beyond the transport-limited regime, where the surface coverage of adsorbates, and hence adsorbate–adsorbate interaction, is not negligible, and local rates can be connected with macroscopic quantities, such as the sticking probability and desorption rates. In the transport-limited regime, a similarity law was identified for the sticking probability for both step flow growth and nucleation on randomly distributed reactive sites in which the sticking probability is a function of the product of the local diffusion and reaction probabilities. Finally, the model can be applied to extract local reactivity maps providing the probability that a particle adsorbing on a given site reacts with the surface. This allows one to explore the development of capture zones and the impact of site-blocking and desorption on the local sticking probabilities.