Ellipsometry Results

This chapter covers the two ellipsometry result pages:

• Psi
• Delta

These pages do not report reflectance or transmittance directly. They describe how the polarization state changes after interacting with the stack.

Relative to R / T / A, Psi / Delta are more phase-sensitive and polarization-sensitive, so they are more useful for parameter-sensitivity analysis, fine thickness correction, and angle selection.

Analysis Entry

Focus

This chapter covers three points:

1. the availability conditions and physical meaning of Psi / Delta
2. curve interpretation in single-run and Sweep modes
3. how curve changes map back to thickness, refractive index, and incident angle

Example Setup: 65° Coherent Ellipsometry Case

The screenshots in this chapter use a minimal “default ITO coating at 65° incidence” ellipsometry case. This keeps the built-in default structure while making the one change required to show why the stock model is not ellipsometry-ready and how to fix it.

This example uses:

1. The default structure as the starting point, with no extra layers and no material-file replacement.
2. One structural change in Structure: turn off Inco. for the second layer (Substrate) so every enabled layer is coherent.
3. The default wavelength-sweep settings in Optics: 400 -> 900 nm, step 5 nm.
4. Incident Angle = 65°. This is a much more realistic oblique-incidence setting for ellipsometry than 0°, and it provides stronger parameter sensitivity.
5. Both Psi and Delta enabled in the Ellipsometry detector group.
6. The top-toolbar Run button.

Availability conditions

The prerequisites here are stricter than for ordinary result pages.

The current implementation requires both of the following:

1. Psi and/or Delta must be enabled in the Optics detector list.
2. Every enabled layer in the structure must remain coherent.

That “every layer must be coherent” rule applies to:

• top-level regular layers
• enabled layers inside a Layer Group

If any enabled layer is marked Incoherent, the app raises a validation error and treats Psi / Delta as invalid.

The reason is physical: ellipsometry relies on coherent interference. Once part of the stack is switched to incoherent propagation, Psi / Delta no longer have the same clear interpretation, so the app blocks that configuration.

So when you see any of the following:

• a validation error before Run
• Psi / Delta staying disabled in the result tree
• No data on the result page

check for enabled incoherent layers first.

Physical interpretation of Psi and Delta

Ellipsometry is commonly written as the complex reflection ratio:

ρ = rp / rs = tan(Ψ) · exp(iΔ)

The two pages in the app correspond to the two quantities in that expression:

A practical shortcut is:

• Psi tells you which polarization component is stronger, and by how much
• Delta tells you how far the two components drift apart in phase

You should normally read both together, not in isolation.

Psi page

When wavelength mode is Sweep, the most common Psi result is a wavelength-dependent curve.

Check the following:

1. decide whether the overall trend is rising, falling, or nearly flat
2. identify any knees, plateaus, peaks, or valleys in the wavelength band that matters
3. map that behavior back to the structure and decide whether the change looks global or localized

Common interpretation patterns:

• an almost uniform vertical shift often points to a more global parameter change, such as average thickness or dominant refractive-index level
• a local feature moving within a limited band usually means the interference condition itself has shifted

If you are fitting to a target, compare the shape in the critical band first, not just a single wavelength point.

Delta page

Delta is the phase-difference result, so it is often more sensitive to thickness, interfaces, and dispersion than Psi.

When reading Delta, focus on:

1. whether the curve stays continuous
2. where the slope accelerates or relaxes
3. whether the feature positions move in sync with Psi

Compared with Psi, Delta more often shows:

• a larger visible response from a smaller parameter change
• sharper local features in narrow wavelength bands
• stronger sensitivity to fitting mismatch

That is why Delta is often the stricter curve during parameter inversion. It tends to reveal disagreement between model and target earlier.

Combined interpretation of Psi and Delta

Reading only Psi or only Delta is risky. The safer workflow is to treat them as two projections of the same physical response.

Combined interpretation:

1. Psi: judge the broad amplitude-side behavior
2. Delta: verify whether the phase-side behavior shifts with it
3. if both curves move in the same wavelength region, a core interference condition is probably shifting
4. if only one curve changes strongly, the active parameter may affect amplitude and phase asymmetrically

A practical fitting order is:

• use Psi to lock the broad direction
• use Delta to tighten the fine adjustment

Delta usually constrains the solution more strongly, but it is also more sensitive to small mismatch.

Sweep mode

Psi / Delta reuse the same result container logic as the basic result pages, so they follow the same view-switching rules.

The current implementation is:

Display rules:

1. if you are sweeping wavelength and the sweep has more than 2 parameters, the chart can disappear and only the table remains
2. in scalar mode, the app tolerates one extra dimension and only forces a table once the sweep exceeds 3 parameters

So if the chart/table toggle disappears, check the sweep dimensionality first. That is usually expected behavior.

Parameters to inspect first

If you are using ellipsometry to infer the stack, these are usually the first parameters worth testing:

1. Film thickness
   Thickness changes move interference features directly, so they often shift Psi / Delta knees, peaks, and valleys.
2. Refractive-index dispersion
   If the material file or dispersion model is inaccurate, the mismatch often appears as a wavelength-dependent offset rather than a simple global shift.
3. Incident angle
   Ellipsometry is highly angle-sensitive. Confirm that the angle in Optics is the intended one before interpreting the curves.

A stable fitting order is usually:

1. lock the incident angle and wavelength range
2. use Psi to establish the broad match
3. use Delta to tighten the detail
4. only question the material model or stack topology after both curves refuse to align

Common errors and checks

No data after enabling Psi/Delta

Check these first:

1. whether you actually ran Run
2. whether at least one of Psi or Delta is enabled
3. whether any enabled layer in the structure is still incoherent

Validation error after enabling Psi/Delta

This is usually not a chart problem. It means the app is blocking the combination of ellipsometry detectors with incoherent layers.

Check these first:

1. top-level regular layers marked Incoherent
2. Layer Group internal layers marked Incoherent

As long as one enabled incoherent layer remains, the validation error will continue.

Small visible differences

Do not keep guessing from the chart. Instead:

1. switch to the table view and read exact values at the critical wavelengths
2. narrow the wavelength range to the band you care about
3. compare it against Reflectance / Transmittance in the same band

Mismatched Psi and Delta trends

That is not automatically an error. It often means:

• the current parameter affects amplitude and phase differently
• the model is more sensitive in one response channel than the other

Do not draw conclusions from one curve alone. Read both as a pair.

Next step

If the current task is to turn Psi / Delta into sweep strategy and parameter-sensitivity judgment, continue with Ellipsometry Analysis. If the current task moves to local fields and local absorption position, continue with Depth Detector Analysis.