An intrinsic stress scaling law for polycrystalline thin films prepared by ion beam sputtering

The intrinsic stresses of Al, Ti, Fe, Ta, Mo, W, Ge, Si, AlN, TiN, and Si3N4 films prepared by ion beam sputtering were investigated at low Td/Tm values. The intrinsic stress is compressive and its origin is explained in terms of the ion peening model. Knock-on linear cascade theory of forward sputtering is applied to derive a simple scaling law with the film’s physical properties. The results show that the stress is directly proportional to the elastic energy/mole, given by the quantity Q=EM/(1−ν)D, where E is Young’s modulus, M the atomic mass, D the density, and ν Poisson’s ratio. Stress data taken from the literature for a variety of materials deposited by low-pressure magnetron sputtering, and rf and ion beam sputtering also fit the correlation with Q. Furthermore, the model predicts a square-root dependence on the incident ion energy, suggesting that the stress is momentum rather than energy driven.