---
title: "Spectroscopic Ellipsometer Interactive Lab | Sandbox Physics"
description: "Can reflected polarization tell film thickness and refractive index apart?"
canonical_url: "https://sandboxphysics.com/labs/spectroscopic-ellipsometer/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/spectroscopic-ellipsometer/"
last_modified: "2026-11-03"
---

IN20 · Thickness changes reflected polarization

# Spectroscopic Ellipsometer

**Can reflected polarization tell film thickness and refractive index apart?** Several wavelengths and angles often help separate thickness from refractive index because each changes the reflected polarization differently. A single color can repeat the same response at several thicknesses. Matching the substrate index or strongly absorbing the returning light can leave thickness poorly determined even with a good fit.

Rotate two optical arms, keep intensity scans and reference calibration, then compare competing film fits across wavelengths and angles.

> Interactive simulation: open this page in a web browser to change the parameters and run the model.

Model assumptions

A coherent, flat isotropic single layer lies between air and a known lossless substrate of index 1.7. Film index and extinction are constant over the finite measured band; this is a teaching material, not a material database or a roughness model. Harmonic fields use exp of spatial phase minus time phase and right-handed local p/s/propagation bases. Ellipsometric ratio is full-vector p reflection over s reflection; the existing tangential-field p coefficient requires a sign adapter. Twenty-four compensator/analyzer states and six externally characterized unit-Stokes reference states calibrate receiver rows from raw ADC counts; a separate elliptical reference checks them. Stable reference/sample flux, perfect source-polarizer angle and ideal exposure timing are assumed. Sample phase is recovered only with adequate circular sensitivity and reflection. A bounded multi-start fit uses saved complex ratios; competing minima and weak thickness sensitivity remain visible. Candidate neighborhoods are numerical comparisons, not confidence intervals. Film thickness is enlarged 25,000 times; field glyphs and scan replay are slowed. Anisotropy, depolarization, roughness, finite bandwidth and source drift are omitted.

### Intensity scans determine the polarization change

### Raw central intensity scan

$A/{}^\circ\quad;\quad N_{\mathrm{ADC}}/\mathrm{counts}$

Turquoise: compensator at zero degrees; violet: forty-five degrees. The marker and physical display replay one stored exposure.

### Choose incidence angle

### Amplitude angle $\Psi$

$\lambda_{\mathrm{vac}}/\mathrm{nm}\quad;\quad\Psi/{}^\circ$

### Phase difference $\Delta$

$\lambda_{\mathrm{vac}}/\mathrm{nm}\quad;\quad\Delta/{}^\circ$

Phase wraps leave a gap.

Filled marks come from raw reduction; dashes or open marks show one candidate, with each selected-angle panel scaled independently.

Competing films, reference checks and saved scans

#### Thickness profile at the candidate optical constants

$d/\mathrm{nm}\quad;\quad\log_{10}L$

$L=\frac1N\sum_j\frac{|\rho_{\mathrm{fit},j}-\widehat\rho_j|^2}{1+|\widehat\rho_j|^2}$

Distinct numerical candidates

| $d/\mathrm{nm}$ | $n$ | $\kappa$ | Cost |
| --- | --- | --- | --- |

The profile holds candidate optical constants fixed; it is not a confidence interval or a full marginalization over correlated parameters. Several starting points reduce local-minimum risk but do not prove global uniqueness.

Frozen raw scans

| Record | Conditions | Calibration | Fit |
| --- | --- | --- | --- |

Exports retain all reference/dark/check and sample ADC counts, commanded angles, relative exposure times, seeds, conventions, model family and fitted candidates. Preview changes leave kept raw and processing snapshots unchanged.

Physics tutorial

## Read the phase before choosing a film

**Background** A thin film sends back light from its upper and lower boundaries. Their relative timing changes the polarization of the reflected beam.

**Why it matters** Two films can give nearly the same brightness yet change the reflected electric-field ellipse differently.

Start with the essentials

- **Focus question**: When do several colors and angles distinguish thickness from refractive index?
- **One-sentence intuition**: A measured polarization change constrains an optical model; several wavelengths can separate film candidates that coincide at one color.

### Core mathematical model

#### The complex ellipsometric ratio

$$
\rho=\frac{r_p}{r_s}=\tan\Psi\,e^{\mathrm i\Delta}
$$

The reflection amplitudes use right-handed local p, s and propagation axes. Psi specifies their amplitude ratio and Delta their phase difference. A detector observes intensities at known compensator and analyzer angles.

#### One transparent-film round trip

$$
\beta=\frac{2\pi d}{\lambda_{\mathrm{vac}}}\sqrt{N^2-\sin^2\theta},\qquad N=n+\mathrm i\kappa
$$

The phase convention is spatial phase minus time phase. A round trip contributes twice beta. For a transparent film, adding a whole round-trip cycle repeats the single-color reflection. Absorption attenuates the returning field.

### Common difficulties

#### A small residual can have several solutions

**Typical misconception** The lowest displayed cost proves a unique thickness.

**Better mental model** The film model may contain several similar minima or a broad weak-sensitivity region. The numerical comparison tolerance is not a confidence interval.

#### A linear analyzer can lose part of the phase

**Typical misconception** Rotating a single polarizer always gives the full polarization ellipse.

**Better mental model** The compensator converts circular sensitivity into a measurable intensity change. Parking it can make the reference matrix rank deficient.

### Run the experiment

1. 01

   #### Watch one exposure

   Pause the replay and compare the physical analyzer display with the marker on the raw scan.

   **What to observe:** Both refer to the same stored detector count and commanded analyzer angle.

2. 02

   #### Compare one color with several

   Choose the repeated-thickness preset, then restore several wavelengths and angles.

   **What to observe:** Several thicknesses can fit a single color. Additional conditions usually separate those branches.

3. 03

   #### Change the receiving optics

   Drag the compensator or analyzer mount to change its zero offset, then measure new reference states.

   **What to observe:** A hardware change invalidates the old calibration. Six known input states calibrate the receiver; a different ellipse checks it.

4. 04

   #### Remove the lower reflection

   Compare the index-matched and strongly absorbing presets.

   **What to observe:** A film can become insensitive to thickness because the lower interface vanishes or its returning light becomes too weak.

Physical conclusion

Keep the intensity scans and reference calibration, then compare competing film descriptions and their residuals.

## Related experiments and articles

How physics instruments measure · Reading path

### How physics instruments measure

Articles on this path that use this experiment, followed by the other experiments they suggest.

1. [Article **How an ellipsometer reads thin-film thickness from reflected light**](https://sandboxphysics.com/stories/instruments/spectroscopic-ellipsometer/)

Waves & optics · Starter path

## From one ray to interference measurement

Start with refraction, find where the ray picture stops working, then use interference to measure tiny distances.

[Start here → **Optical Boundary Explorer** Turn the incident angle and watch reflected and transmitted power trade off. Then switch to the critical-angle scene. Observe · 11 min](https://sandboxphysics.com/labs/optical-boundary-explorer/)

1. [1 Optical Boundary Explorer](https://sandboxphysics.com/labs/optical-boundary-explorer/)
2. [2 Rainbow Caustic Observatory](https://sandboxphysics.com/labs/rainbow-laboratory/)
3. [3 Camera Obscura](https://sandboxphysics.com/labs/camera-obscura/)
4. [4 Coherent Wave Composer](https://sandboxphysics.com/labs/coherent-wave-composer/)
5. [5 Young Double-Slit Bench](https://sandboxphysics.com/labs/young-double-slit-bench/)
6. [6 Michelson Precision Lab](https://sandboxphysics.com/labs/michelson-precision-lab/)

[View the full path →](https://sandboxphysics.com/topics/waves-and-optics/#starter-path)