# Ellipsometry
**Ellipsometry** is an optical technique that measures the change in the polarization state of light upon reflection from (or transmission through) a sample, and uses that change to determine properties such as thin-film thickness, refractive index, roughness, and composition. The measured quantities are the ellipsometric angles Ψ and Δ, defined through the ratio of the complex Fresnel reflection coefficients for p- and s-polarized light:
\[ \rho = \frac{r_{\mathrm{p}}}{r_{\mathrm{s}}} = \tan(\Psi)\, e^{i\Delta} \]
where tan Ψ is the amplitude ratio and Δ is the difference in phase shift between the two polarization components[1](https://journals.sagepub.com/doi/10.1366/12-06883). The technique is nondestructive and contactless, requires no sample preparation, and is sensitive enough to detect changes of a single atomic layer in a silicon oxide film[1](https://journals.sagepub.com/doi/10.1366/12-06883).
| Key fact | Detail |
|---|---|
| Measured quantities | Ψ (amplitude ratio of p and s reflection) and Δ (phase difference), via \( \rho = r_{\mathrm{p}}/r_{\mathrm{s}} = \tan\Psi\, e^{i\Delta} \)[1](https://journals.sagepub.com/doi/10.1366/12-06883) |
| Indirect method | Sample properties are obtained only through modeling analysis; thickness and refractive index are fitted, not read directly[2](https://arxiv.org/abs/1210.1076) |
| Sensitivity | Precision of about 0.01–0.02° in Ψ and Δ gives theoretical thickness sensitivity on the order of 0.01 nm[1](https://journals.sagepub.com/doi/10.1366/12-06883) |
| Thickness range | Transparent or low-absorbing films from less than a nanometer to several micrometers with broadband sources; lasers extend the maximum to several centimeters[1](https://journals.sagepub.com/doi/10.1366/12-06883) |
| Main variants | Single-wavelength ellipsometry (SWE) and spectroscopic ellipsometry (SE); Mueller ellipsometry for anisotropic or depolarizing samples[3](https://www.nist.gov/publications/thin-film-ellipsometry-metrology) • [1](https://journals.sagepub.com/doi/10.1366/12-06883) |
| Reference standards | PTB offers SiO2-on-Si(100) standards of nominal 6, 70, 160, 400, and 1000 nm, with expanded uncertainty of about 0.6 nm at 6 nm and about 5 nm at 1000 nm[4](https://www.ptb.de/cms/en/ptb/fachabteilungen/abt5/fb-52/ag-523/layer-thickness-and-crystalline-standards.html) |
| Standardization | IEC TR 63258:2021 provides a practical protocol for evaluating nanoscale film thickness by ellipsometry[5](https://www.iso.org/cms/%20render/live/en/sites/isoorg/contents/data/standard/07/54/75422.html?browse=tc) |
## Principle
When linearly polarized light strikes a surface, the components parallel (p) and perpendicular (s) to the plane of incidence acquire different amplitude changes and phase shifts, so the reflected beam generally becomes elliptically polarized. An [ellipsometer](https://www.edgepedia.org/ellipsometer) measures the resulting Ψ and Δ[1](https://journals.sagepub.com/doi/10.1366/12-06883). For a layer-covered substrate, the general relation is (Ψ, Δ) = f(ε₀, ε₁, ε₂, d, λ, θ), where λ is the wavelength, θ the angle of incidence, d the film thickness, and ε₀, ε₁, ε₂ the dielectric properties of the ambient, layer, and substrate. Since λ, θ, ε₀, and ε₂ are known, two properties, generally d and the refractive index n, can be extracted from one measurement[1](https://journals.sagepub.com/doi/10.1366/12-06883).
The sensitivity of the phase measurement comes from an interferometric effect: light reflected at the first interface of a layer interferes with light reflected at the second. This also sets a limit, the maximum film thickness measurable must be less than the coherence length of the light source[1](https://journals.sagepub.com/doi/10.1366/12-06883).
**Indirect analysis.** Ellipsometry does not yield thickness or optical constants analytically from Ψ and Δ. Instead, a model of the layer stack is built, theoretical spectra are calculated, and model parameters are adjusted until calculated and measured values agree, usually by minimizing a figure of merit such as a mean-square error[1](https://journals.sagepub.com/doi/10.1366/12-06883) • [6](https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=902197). For nonabsorbing single layers, a Cauchy model, \( n(\lambda) = n_0 + A/\lambda^{2} + B/\lambda^{4} \), relates refractive index to wavelength, and its three coefficients plus the thickness are fitted simultaneously[6](https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=902197). Model choice matters: in one grating-profile study, a trapezoidal model gave fitted line widths fluctuating by 5 nm and thickness by 10 nm with observation angle, while a two-lamella model varied by less than 1.5 nm and 2 nm respectively, and model inadequacy does not necessarily show up in the goodness of fit[1](https://journals.sagepub.com/doi/10.1366/12-06883).
## Instrument types
A standard ellipsometer has two optical arms with the sample between them: a polarization state generator (polarizer plus source) and a polarization state analyzer with a detector[1](https://journals.sagepub.com/doi/10.1366/12-06883). Instruments fall into two families. In null ellipsometers, the optical elements are rotated until the detected intensity vanishes, and Ψ and Δ are read from the element orientations; these were the first instruments developed in the late 19th century and remain accurate, but are hard to extend spectroscopically because the retarder is dispersive[1](https://journals.sagepub.com/doi/10.1366/12-06883). Non-null instruments modulate the intensity and extract the ellipsometric angles by harmonic analysis; they divide into rotating polarizer/analyzer, rotating compensator, and phase-modulated designs, each with distinct strengths. Rotating polarizer/analyzer systems are quasi-achromatic with wide spectral range but measure Δ inaccurately near 0° or 180°; rotating compensators capture the full Stokes vector and 12 Mueller matrix elements; phase-modulated systems (tens of kilohertz) offer excellent signal-to-noise from the vacuum ultraviolet to the near infrared but use a temperature-sensitive photo-elastic modulator[1](https://journals.sagepub.com/doi/10.1366/12-06883).
Commercial instruments differ in technique and in the complexity of the models used to evaluate thickness and refractive index, which affects the accuracy of thickness determinations; the two main measurement techniques are single-wavelength and spectroscopic ellipsometry[3](https://www.nist.gov/publications/thin-film-ellipsometry-metrology).
## Single-wavelength versus spectroscopic
Single-wavelength ellipsometry, typically at one fixed wavelength and angle, is relatively inexpensive and works well when a single film on a substrate is to be measured; it is particularly effective for films from a few nanometers to a few hundred nanometers thick[7](https://www.asminternational.org/results/-/journal_content/56/ASMHBA0001295/BOOK-ARTICLE/). [Spectroscopic ellipsometry](https://www.edgepedia.org/spectroscopic-ellipsometry) measures two independent values at each wavelength across a spectrum, giving more information than conventional reflectometry and enabling thickness determination with improved precision[1](https://journals.sagepub.com/doi/10.1366/12-06883). Common sources cover roughly 250 nm in the ultraviolet to about 2500 nm in the near infrared; the far ultraviolet is most sensitive to ultrathin layers, interfaces, and low-index-contrast films, while the near infrared is needed for strongly visible-absorbing materials and for optical conductivity dominated by free carriers[1](https://journals.sagepub.com/doi/10.1366/12-06883). [Infrared spectroscopic ellipsometry](https://www.edgepedia.org/infrared-spectroscopic-ellipsometry) extends the method to chemical specificity: in one NIST study of polymer multilayers, thicknesses from infrared ellipsometry agreed with [X-ray reflectivity](https://www.edgepedia.org/x-ray-reflectivity) to within 1–2 nm[6](https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=902197).
## Mueller ellipsometry
Standard ellipsometry assumes the light beam remains completely polarized during the measurement; if the sample depolarizes the light, the measurement loses its physical meaning in the Ψ, Δ framework[1](https://journals.sagepub.com/doi/10.1366/12-06883). Mueller ellipsometry, also called polarimetry, uses the Stokes vector and the 4 × 4 Mueller matrix, which can describe any polarization state including partially polarized light, and is necessary for the complete characterization of anisotropic and depolarizing samples[1](https://journals.sagepub.com/doi/10.1366/12-06883). Depolarization also arises instrumentally from finite spectral resolution and beam focusing when characterizing samples smaller than a collimated beam, and must be included in the optical model to fit the data[8](https://www.sciencedirect.com/science/article/pii/S2211812816000298).
## Applications
Ellipsometry is used across material science, including semiconductors and photovoltaics, biology, and pharmaceuticals, and provides film thickness, optical constants, roughness, porosity, composition, and uniformity[1](https://journals.sagepub.com/doi/10.1366/12-06883). Because ellipsometers can be compact and mounted on vacuum chambers, chemical reactors, or bioreactors, measurements can be made in situ, characterizing a sample in real time under preparation conditions[1](https://journals.sagepub.com/doi/10.1366/12-06883). [In situ](https://www.edgepedia.org/in-situ) spectroscopic ellipsometry has demonstrated the film characterization precision required for process control in epitaxial semiconductor growth[9](https://www.sciencedirect.com/science/article/pii/S0961129097812860), and during sputter deposition of metallic multilayers it determines individual layer thicknesses to a fraction of an Ångstrom[10](https://www.sciencedirect.com/science/article/pii/S0040609097008754). Combined with rigorous coupled-wave analysis, in situ spectroscopic ellipsometry can track profile evolution of films growing inside lithographically patterned nanotrenches in real time[11](https://bishtref.com/articles/10.1116/6.0001937). Mueller ellipsometry has also been applied to nondestructive grating-profile metrology for in-line quality control in microelectronics[1](https://journals.sagepub.com/doi/10.1366/12-06883).
## Metrology and standards
Accurate determination of films thinner than 10 nm is a challenging task, and results from independent ellipsometric measurements on different instrument types have been compared for ultrathin thermally grown SiO2 films on silicon[3](https://www.nist.gov/publications/thin-film-ellipsometry-metrology). The NIST Standard Reference Materials for thin-film ellipsometry are based on conventional single-wavelength ellipsometry[3](https://www.nist.gov/publications/thin-film-ellipsometry-metrology). The [Physikalisch-Technische Bundesanstalt](https://www.edgepedia.org/physikalisch-technische-bundesanstalt), the German national metrology institute, offers nanometer layer-thickness standards for ellipsometer calibration consisting of thermal SiO2 layers on Si(100) substrates, with nominal thicknesses of 6, 70, 160, 400, and 1000 nm (5 nm and 100 nm planned); each carries a lithographic microstructure for independent step-height measurement with a scanning force microscope, and the expanded uncertainty (k = 2) is about 0.6 nm for the 6 nm layer and about 5 nm for the 1000 nm layer[4](https://www.ptb.de/cms/en/ptb/fachabteilungen/abt5/fb-52/ag-523/layer-thickness-and-crystalline-standards.html). At the international standards level, IEC TR 63258:2021, published in March 2021, gives a practical protocol for applying ellipsometry to nanoscale film thickness, aimed at minimizing data variation to improve reproducibility rather than specifying instruments[5](https://www.iso.org/cms/%20render/live/en/sites/isoorg/contents/data/standard/07/54/75422.html?browse=tc).
## History
The technique traces to the pioneering work of [Paul Drude](https://www.edgepedia.org/paul-drude) in the 19th century, who used polarized light in reflection to study the optical properties and thickness of very thin metallic films; he provided the theoretical basis, performed the first experimental measurements, and determined the optical properties of 18 metals by the null method[12](https://www.sciencedirect.com/science/article/abs/pii/S0040609003019540) • [1](https://journals.sagepub.com/doi/10.1366/12-06883). A 1963 symposium proceedings at the National Bureau of Standards collected early work on ellipsometry in the measurement of surfaces and thin films[13](https://nvlpubs.nist.gov/nistpubs/Legacy/MP/nbsmiscellaneouspub256.pdf). Since then, thousands of studies and industrial applications have been based on the technique or profit directly from its sensitivity[1](https://journals.sagepub.com/doi/10.1366/12-06883).
## References
1. [Enric Garcia-Caurel, Antonello De Martino, Jean-Paul Gaston, and Li Yan (2013). Application of Spectroscopic Ellipsometry and Mueller Ellipsometry to Optical Characterization. Applied Spectroscopy Reviews 67(1).](https://journals.sagepub.com/doi/10.1366/12-06883)
2. [Garcia-Caurel et al. (2012). Application of Spectroscopic Ellipsometry and Mueller Ellipsometry to Optical Characterization. arXiv:1210.1076.](https://arxiv.org/abs/1210.1076)
3. [P. Durgapal, James R. Ehrstein, Nhan Van Nguyen (1998). Thin-Film Ellipsometry Metrology. NIST.](https://www.nist.gov/publications/thin-film-ellipsometry-metrology)
4. [Layer Thickness and Crystalline Standards, Physikalisch-Technische Bundesanstalt (PTB).](https://www.ptb.de/cms/en/ptb/fachabteilungen/abt5/fb-52/ag-523/layer-thickness-and-crystalline-standards.html)
5. [IEC/TR 63258:2021, Nanotechnologies — A guideline for ellipsometry application to evaluate the thickness of nanoscale films, ISO.](https://www.iso.org/cms/%20render/live/en/sites/isoorg/contents/data/standard/07/54/75422.html?browse=tc)
6. [Methodology for Quantitative Measurements of Multilayer Polymer Thin Films with IR Spectroscopic Ellipsometry, NIST / Macromolecules 42(14), 2009.](https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=902197)
7. [Harland G. Tompkins (Motorola). Film Thickness Measurements Using Optical Techniques. ASM International.](https://www.asminternational.org/results/-/journal_content/56/ASMHBA0001295/BOOK-ARTICLE/)
8. [L. Halagačka, K. Postava, J. Pištora (2016). Analysis and Modeling of Depolarization Effects in Mueller Matrix Spectroscopic Ellipsometry Data. Procedia Materials Science 12.](https://www.sciencedirect.com/science/article/pii/S2211812816000298)
9. [Real-time process control with in situ spectroscopic ellipsometry. III-Vs Review 10(5), 1997.](https://www.sciencedirect.com/science/article/pii/S0961129097812860)
10. [Xiang Gao, Darin W. Glenn, John A. Woollam (1998). In situ ellipsometric diagnostics of multilayer thin film deposition during sputtering. Thin Solid Films 313–314.](https://www.sciencedirect.com/science/article/pii/S0040609097008754)
11. [In situ spectroscopic ellipsometry and rigorous coupled wave analysis for real time profile evolution of atomic layer deposited films inside SiO2 nanotrenches. Journal of Vacuum Science & Technology A 40(6), 2022.](https://bishtref.com/articles/10.1116/6.0001937)
12. [Expanding horizons: new developments in ellipsometry and polarimetry. Thin Solid Films (2003), ScienceDirect.](https://www.sciencedirect.com/science/article/abs/pii/S0040609003019540)
13. [Ellipsometry in the measurement of surfaces and thin films: symposium proceedings, Washington 1963. NBS Miscellaneous Publication 256.](https://nvlpubs.nist.gov/nistpubs/Legacy/MP/nbsmiscellaneouspub256.pdf)
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*Topic: Encyclopedia › Physical world and mathematics › Physics › Classical physics › Waves and optics › Optical technologies and instruments › Thin-film and coating optics › Coating characterization and metrology*
*Initially written Sep 17, 2026 · Reviewed: Oct 15, 2026 · Edited: Oct 15, 2026 · Last review: Oct 15, 2026*
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License: Edgepedia Community License 1.0, https://www.edgepedia.org/edgepedia/license