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 = r<sub>p</sub>/r<sub>s</sub> and τ = t<sub>p</sub>/t<sub>s</sub>, 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) CIO, 67 (1993)1; it can be simplified to ε = ε<sub> 1</sub> sin<sup>2</sup> θ<sub>1</sub>/(COS<sup>2</sup> θ<sub>1</sub>− ρ/τ), where ε<sub>1</sub> is the dielectric constant of the ambient medium and θ<sub>1</sub> is the angle of incidence. Stability of the solution with respect to noise in the data is analyzed.
© 1994 Optical Society of America
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)