Applicability of the effective medium approximation in the ellipsometry of randomly micro-rough solid surfaces

Area of Science:

• Materials Science
• Optical Physics
• Surface Science

Background:

• The effective medium approximation (EMA) is commonly used in spectroscopic ellipsometry (SE) to model surface roughness.
• EMA is applied to determine optical constants and estimate rough layer thickness from SE data.
• Current methods often assume root mean square (rms) roughness from atomic force microscopy (AFM) for EMA calculations.

Purpose of the Study:

• To theoretically investigate the error in optical constant estimation using the EMA model for various surface morphologies and materials.
• To analyze the deviation between EMA-derived roughness and AFM-measured rms roughness.
• To establish correlations between EMA roughness and surface morphological parameters.

Main Methods:

• Theoretical investigation of the EMA model's performance in spectroscopic ellipsometry.
• Analysis of surface roughness effects, considering both height and lateral irregularities.
• Comparison of EMA-derived roughness with atomic force microscopy (AFM) measurements.

Main Results:

• The EMA model's accuracy in determining optical constants is limited by its neglect of lateral surface irregularities, hindering high-precision results.
• EMA-derived roughness generally deviates from AFM-measured rms roughness.
• Correlated relationships between EMA roughness and surface morphological parameters were identified, showing material-dependent coefficients.

Conclusions:

• The EMA model's limitations in accounting for lateral surface features affect the accuracy of optical constant inversion and roughness estimation in SE.
• Understanding the deviations between EMA roughness and actual surface morphology is crucial for reliable SE data interpretation.
• This research provides insights for improved application and understanding of the EMA model in spectroscopic ellipsometry.