Optimizing precision of rotating-analyzer ellipsometers

TLDR

Theoretical uncertainty equations for rotating‑analyzer ellipsometers are derived for shot‑noise‑limited, detector‑noise‑limited, and ideal‑detector conditions. The study finds that ideal‑detector systems achieve minimal uncertainty with circularly polarized reflected light, while shot‑ and detector‑noise‑limited setups require a compromise between circular polarization and transmitted flux; uncertainty behavior varies with |ρ|, suggesting avoidance of the pseudo‑Brewster angle for detector‑limited cases, and demonstrates that a compensator is essential for dielectric surfaces but not for metals, achieving a theoretical relative precision of ~1×10⁻⁵ for silicon and gold across the visible and near‑UV range.

Abstract

General equations describing the theoretical uncertainty in the measurement of the complex reflectance ratio, ρ, are given for rotating-analyzer ellipsometers operating under shot-noise-limited, detector-noise-limited, and incident power-fluctuation-limited (ideal-detector) conditions. In the latter case, uncertainty is minimized when the light reflected from the sample surface is circularly polarized. For shot-noise- and detector-noise-limited configurations, minimum uncertainty is obtained as a compromise between the conditions that yield circularly polarized reflected light and those that maximize the transmitted flux. As |ρ| → 0, the uncertainty decreases linearly in |ρ| for ideal-detector systems, approaches a constant limiting value for shot-noise-limited systems, and becomes arbitrarily large for detector-noise-limited systems, which suggests that measurements at the pseudo-Brewster angle should be avoided in the latter case. A compensator is essential to achieve high precision on dielectric surfaces, but is generally not needed for metals. The theoretical relative precision to which the complex dielectric function can be obtained for silicon and gold over the visible and near-uv optical range is of the order of 1 × 10−5, which is comparable to that attainable by high-precision reflectance techniques.