When should I use interference colors vs spectral fringes?

Use interference color charts for quick visual estimates of films 50-550 nm thick on silicon substrates. For films outside this range or when higher precision is needed, use spectral interference fringe analysis.

Why is refractive index important for thickness calculation?

Film thickness calculations depend critically on the refractive index (n). An error of 0.1 in n can cause 5-10 percent thickness error. Always use measured n values when available.

What thickness range works for each measurement method?

Color chart method: 25-550 nm. Spectral interference: greater than 150 nm. Single-wavelength ellipsometry: 1-500 nm. Spectroscopic ellipsometry: 0.5 nm to several micrometers.

How accurate are interference-based thickness measurements?

Spectral fringe spacing: 2-5 percent for uniform films. Color chart: 10-20 nm. Spectroscopic ellipsometry: 0.1-1 nm for well-characterized systems.

Ellipsometry & Interference Thickness Calculator

Estimate transparent film thickness using spectral interference fringes, color charts, or ellipsometry parameters

Measurement Method

Auto-Update

Film Material Select preset or enter custom n

Refractive index at measurement wavelength.

Refractive index must be ≥ 1

Angle of Incidence 0° = normal incidence

Angle must be between 0° and 89°

Fringe Wavelengths Two adjacent fringe peaks or valleys

λ₁ (shorter wavelength)

λ₂ (longer wavelength)

Include uncertainty ± nm

Use peaks (maxima) or valleys (minima) consistently. Must be adjacent fringes.

Both wavelengths required; λ₂ must be greater than λ₁

Observed Interference Color SiO₂ on Si, white light

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Click the color closest to what you observe (thickness in nm).

💡 Illuminant: This chart assumes D65 (daylight, 6500K). Under fluorescent or incandescent lighting, colors may shift by 10–15 nm. Best viewed under natural daylight or D65-calibrated illumination.

Select a color swatch to estimate film thickness

Or Enter Thickness Directly

Film Refractive Index

Color chart calibrated for SiO₂ (n≈1.46). Other materials require scaling.

p-polarization: E-field in plane of incidence. s-polarization: E-field perpendicular (●).

⚠️ Thickness ambiguity: Single-wavelength ellipsometry has periodic solutions every λ/(2n·cos θ') ≈ 200–250 nm. Use the Color Chart tab first to estimate which order your film is in.

Film Refractive Index

n (film)

k (film)

Refractive index must be ≥ 1

Dispersion Model Optional

Use Cauchy dispersion: n(λ) = A + B/λ²

Substrate

n_s

k_s

Wavelength & Angle

λ (nm)

θ (°)

Common angles: 70° (standard), 75° (near Brewster for Si).

Angle must be between 0° and 89°

Measured Ellipsometric Angles

Δ (Delta, °)

Ψ (Psi, °)

ρ = tan(Ψ)·e^iΔ = r_p/r_s. Δ: phase shift (0–360°). Ψ: amplitude ratio (0–90°).

Both Δ and Ψ are required

Cycle Order (m) For films > 200 nm

D_cyc = λ / [2√(n²−sin²θ)]. Use Color Chart to estimate which order your film is in.

Results

Display in Å

Estimated Film Thickness (t)

— nm

Optical Path (2nt)

— nm

Fringe Order

—

Verification tip: For critical measurements, compare results across methods or validate with a calibrated step standard.

Understanding Optical Interference in Thin Films

When light reflects from a transparent thin film on a substrate, interference occurs between reflections from the film's top surface and the film-substrate interface. This interference creates characteristic colors (for white light) or spectral fringes (for broadband spectroscopy), enabling non-destructive thickness measurement.

Key requirement: The film must be optically transparent and have a different refractive index than the substrate.

Spectral Interference Fringe Method

When measuring reflectance versus wavelength, a thin film produces periodic oscillations (fringes). The thickness is calculated from the spacing between adjacent maxima or minima:

t = λ₁λ₂ / [2n(λ₂ − λ₁)cos θ']

Where θ' is the refracted angle inside the film (Snell's law: n·sin θ' = sin θ).

Color Chart Method

For SiO₂ films on silicon substrates viewed under white light, the observed interference color corresponds to specific thicknesses:

First order (0–300 nm): Tan → brown → purple → blue → green → yellow
Second order (300–550 nm): Orange → red → violet → blue → green

Ellipsometry Basics

Ellipsometry measures changes in light polarization upon reflection:

Δ (Delta): Phase difference between p- and s-polarized components
Ψ (Psi): Amplitude ratio angle, tan(Ψ) = |r_p/r_s|

The fundamental ellipsometry equation: ρ = tan(Ψ)·e^(iΔ) = r_p/r_s

Material Refractive Index Reference

Material	n @ 633 nm	Applications
SiO₂ (thermal)	1.46	Gate dielectric, passivation
Si₃N₄	2.00	Diffusion barrier, AR coating
TiO₂	2.4	High-n AR coating layer
Al₂O₃	1.63	Protective coating, ALD
MgF₂	1.38	Low-n AR coating layer
PMMA	1.49	Resist, planarization
Photoresist	1.54	Lithography

References

Tompkins, H.G. & McGahan, W.A. (1999). Spectroscopic Ellipsometry and Reflectometry. Wiley.

Fujiwara, H. (2007). Spectroscopic Ellipsometry: Principles and Applications. Wiley.

Heavens, O.S. (1991). Optical Properties of Thin Solid Films. Dover.

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