Film Color
Predict interference colors for clear oxide films by thickness, density, and substrate. Transfer matrix optics and CIE 1931 color science, plus a PVD coating color reference.
Interference color
Pick a material, density and substrate, then drag the thickness slider or click the map.
Standard: typical ALD or sputtered film, f ≈ 0.85
Slider range adjusts to material's interesting window. Type larger values to explore higher orders.
The physics behind the colors
Why thickness controls color
As film thickness increases, the two reflected beams (from the top and bottom of the film) cycle in and out of phase. At phase difference δ = π, the wavelength is maximally reflected and defines the perceived color. Thicker films produce longer-wavelength (redder) colors, then the sequence repeats in higher orders with less contrast.
Why density shifts the spectrum
Amorphous or porous films (sputter-deposited at high pressure, PECVD) incorporate void space, reducing effective refractive index via effective medium theory. A TiO₂ film at n = 2.10 (porous) needs about 29% more thickness to give the same color as a dense rutile film at n = 2.70. Optical measurements of n are a practical indicator of film quality and packing density.
Why the substrate matters
Reflection at the film/substrate interface (r₁₂) depends on the index contrast. A metallic substrate (silver, gold) produces a large, complex r₁₂ that modulates the interference deeply. Gold's absorption onset at ~520 nm imparts a warm tint to films on gold, even at zero thickness. Porous or Lambertian white/black substrates reduce interference contrast while adding a background tint.