Stochastic modeling of film porosity in thin film deposition

Abstract

This work focuses on modeling of film porosity in thin film deposition using stochastic differential equations. A deposition process is modeled via kinetic Monte Carlo (kMC) simulation on a triangular lattice. The microscopic process events involve atom adsorption and migration and the film growth allows for vacancies and overhangs to develop inside the film. Appropriate definitions of film site occupancy ratio (SOR), i.e., fraction of film sites occupied by particles over total number of film sites, and its fluctuation are introduced to describe film porosity. Deterministic and stochastic ordinary differential equation (ODE) models are also derived to describe the time evolution of film SOR and its fluctuation. The coefficients of the ODE models are estimated on the basis of data obtained from the kMC simulator of the deposition process using least-square methods. Simulation results demonstrate the applicability and effectiveness of the proposed film porosity modeling methods in the context of the deposition process under consideration.