Optimizing precision of fixed-polarizer, rotating-polarizer, sample, and fixed-analyzer spectroscopic ellipsometry

Area of Science:

• Optical Physics
• Materials Science
• Metrology

Background:

• Ellipsometry is a powerful technique for characterizing thin films and surfaces.
• Understanding measurement uncertainty is crucial for accurate material property determination.
• Existing models often simplify noise conditions, potentially limiting precision.

Purpose of the Study:

• To derive general equations for theoretical uncertainty in complex reflectance ratio measurements.
• To analyze uncertainty under both shot-noise-limited (SNL) and detector-noise-limited (DNL) conditions for PP(r)SA ellipsometers.
• To determine optimal polarizer and analyzer azimuths for minimizing uncertainty.

Main Methods:

• Development of theoretical equations for measurement uncertainty.
• Calculation of optimum fixed-polarizer and fixed-analyzer azimuths as a function of ellipsometric parameters (psi, D).
• Analysis of uncertainty behavior under SNL and DNL conditions.

Main Results:

• Uncertainty decreases linearly with psi approaching 0 under SNL conditions.
• Uncertainty approaches arbitrary large values under DNL conditions as psi approaches 0.
• Optimal azimuths were calculated for both SNL and DNL systems.

Conclusions:

• Compensators are not required for high precision on dielectric surfaces under SNL conditions.
• Measurements at small psi values should be avoided under DNL conditions.
• Discrepancies from optimal azimuths were analyzed for SNL systems.