Measurement of stress-optic coefficients for metals in the visible to near-infrared spectrum with spectroscopic ellipsometry

Abstract

• A feasible method is proposed to get stress-optic coefficients of metals with ellipsometry. • The stress-optic coefficients of Cu film from 380 to 1000 nm are measured with spectroscopic ellipsometry. • The relation between stress-optic coefficients and wavelengths of Cu are apparently nonlinear. The measurement of stress-optic coefficients is of great importance in photoelasticity which can be used in many fields, such as stress measuring and nondestructive testing. In this paper, the stress-optic coefficients of Cu film were measured in the visible to near-infrared spectral range by spectroscopic ellipsometry. In order to determine the stress-optic coefficients, a measuring principle is proposed by the combination of the classic 4 × 4 Matrix method of ellipsometry and the stress-optic law. According to this principle, we establish a quantitative relation between the ellipsometric parameters (Ψ, Δ) and stress, which is related to stress-optic coefficients. The ellipsometric parameters of a thin film/substrate assembly by sputtering Cu on polyimide (PI) were experimentally measured under various stress conditions. Fitting the proposed measuring principle to experimental data, the stress-optic coefficients of Cu film in the visible to near-infrared spectral range were obtained. This research provides insights into stress measuring of metal films, which is widely needed in many application fields such as chip processing.