Mueller-Matrix Ellipsometry

How do you measure the thickness of a film that is thousands of times thinner than a human hair — without ever touching it? The answer lies in polarization. When light reflects off a surface at an oblique angle, its p- and s-polarized components reflect with different amplitudes and phases, so the polarization ellipse of the light is reshaped by the encounter — hence the name ellipsometry. If thin films coat the surface, light rattling back and forth inside each layer imprints an interference signature onto that polarization change. Because the technique compares one polarization against the other, it is self-referencing: no absolute intensity calibration is needed, and film thicknesses can be resolved down to the sub-nanometer scale — from a single measurement of reflected light.

This sensitivity is why ellipsometry became a workhorse of the semiconductor industry: it is fast, non-contact, and non-destructive — ideal for monitoring wafers in a production line. Modern devices stack films aggressively, from gate dielectrics a few atoms thick to 3D-NAND memory built from a hundred or more alternating oxide/nitride layers, and infrared wavelengths are particularly well suited for probing these deep stacks. The utility below is a miniature IR ellipsometer: build a film stack on a silicon substrate (including repeated layer pairs), choose the wavelength range and angle of incidence, and compute the normalized Mueller-matrix elements M33 and M34 versus wavelength using the exact transfer-matrix solution of the multilayer Fresnel problem. All computation runs directly in your browser.