Analytic inversion of combined reflection and transmission ellipsometric data is demonstrated. When the thickness is eliminated between the equations that give the reflection and transmission ratios ρ = rp/rs and τ = tp/ts, an algebraic equation for the unknown dielectric constant ε of the layer is obtained. After removal of some factors, this reduces to a linear equation in ε. The solution for unsupported films agrees with that previously obtained by Azzam [ J. Phys. (Paris) C10, 67 ( 1993)]; it can be simplified to ε = ε1 sin2θ1/(cos2θ1 − ρ/τ), where ε1 is the dielectric constant of the ambient medium and θ1 is the angle of incidence. Stability of the solution with respect to noise in the data is analyzed.
© 1994 Optical Society of America
Original Manuscript: September 7, 1993
Revised Manuscript: November 22, 1993
Manuscript Accepted: January 11, 1994
Published: July 1, 1994
John Lekner, "Determination of complex refractive index and thickness of a homogeneous layer by combined reflection and transmission ellipsometry," J. Opt. Soc. Am. A 11, 2156-2158 (1994)