A SIMPLE-MODEL FOR THE FORMATION OF COMPRESSIVE STRESS IN THIN-FILMS BY ION-BOMBARDMENT

A simple model is proposed to explain the formation of compressive stress in thin films deposited with simultaneous bombardment by energetic ions or atoms. Consideration of a steady state in which stress formation by knock-on implantation of film atoms is balanced by thermal spike excited migration of implanted atoms shows that the stress sigma is proportional to [Y/(1 - nu)]E1/2/(R/j + kE5/3), where E is the ion energy, R the net depositing flux, j the bombarding flux, k a material-dependent parameter, Y the film material Young's modulus and nu the Poisson ratio. This formula is used to explain seemingly contradictory experimental results in the literature. For small values of the normalized flux j/R the stress is proportional to the square root of the ion energy. Larger values of the normalized flux cause the stress to go through a maximum with increasing ion energy, and a power law decrease in stress with ion energy is predicted for large normalized fluxes.