Compare reflectivity measurements with a model

Start a measured-reflectivity comparison by matching the sample geometry and illumination. Then inspect the residuals—the supplied signal minus the model—before selecting parameters to fit. A close-looking overlay alone can hide a systematic mismatch.

A reproducible Mo/Si practice example

This exercise uses synthetic, noiseless reflectivity generated by EUV Insight. The source stack has 40 Mo/Si bilayers, a 6.96 nm period and Mo fraction Γ = 0.4 on silicon, with Si facing the beam. Densities are 10.22 g/cm³ for Mo and 2.33 g/cm³ for Si. All interfaces are smooth; incidence is normal and illumination is unpolarized.

The starting model uses a 6.90 nm period with everything else held fixed. The file contains 81 wavelengths from 12.4–14.6 nm, with reflectivity in fractions. No noise or uncertainty is added. This is a fitting exercise, not evidence of agreement with a manufactured mirror.

Import a spectrum or angular scan

1. Open the starting mirror in Pro and confirm the example. Go to Measurements and choose the downloaded CSV.
2. Set Coordinate unit to nm, the coordinate column to wavelength_nm, and the signal column to R_fraction.
3. Choose Fraction (0–1), Reflectance R, Unpolarized and an incidence angle of 0° from normal. Leave the uncertainty column as None for this noiseless file.
4. Record “EUV Insight synthetic Mo/Si example” in the source field. Select Import measurement. Keep signal scale at 1, background at 0 and angle offset at 0°.
5. Review the overlay and residuals. Select only bilayer period in Fit parameters, with bounds 6.85–7.05 nm, then select Fit selected parameters.

For your own measurements, use the actual acquisition settings. Spectral coordinates may be nm or eV. An angular scan uses degrees from the surface normal and a fixed wavelength. Import the signal as fractions or percent consistently, including any supplied 1σ uncertainties.

Inspect the residuals and the fitted candidate

The residual plot below shows how the period mismatch appears across the band. After fitting just that parameter, the model recovers the known input period within the displayed precision.

Use Apply fitted candidate only after reviewing the result; the current stack is preserved until you apply it. You can undo the applied fit. Pro also provides a residual CSV and a run bundle for recording the inputs and result.

What to check with real measurements

• Verify layer order, substrate, material data, polarization and the angle convention before changing geometry.
• Check normalization and background. The app applies corrected signal = scale × (raw − background); the background control is in fraction units.
• Supply positive 1σ uncertainty for every point or none. With uncertainties, fitting weights residuals by those values; otherwise it gives each point equal weight.
• Look for residual structure across wavelength or angle. A pattern can reveal a mismatch but does not uniquely identify its physical cause.
• Start with a small parameter set and physically supported bounds. A parameter ending at a bound deserves review.

For background on using residual plots to assess a model, see the NIST guide to model validation.

Current fitting limits

The app fits one dataset at a time with 1–4 selected parameters and three deterministic local-search starts. It does not establish a unique structure or provide parameter confidence intervals. Instrument-resolution convolution and joint fitting of multiple measurements are not currently included.

For a deposited film with appropriate measured n and k, import those optical constants before comparing curves. Use independent metrology to constrain interpretations of thickness, density and interfaces.