On the Determination of the Optical Constants of Very Thin (Lambda/50) Films

The improvement of a recently developed spectrophotometric method for the determination
of the complex refractive index (ñ) and physical thickness (d) of very thin films (d = Lambda/50, Lambda is the wavelength in the visible and near infrared) is presented. The thin film transmittance (Tf), front side reflectance (Rf) and back side reflectance (Rf') are used for the estimation of (ñ, d). Utilizing the nanothickness of the films, we derive analytical expressions for Rf, Rf' and Tf, by development of the Abelès characteristic matrix elements up to the 4th order in ñd/Lambda. An optimization procedure is used to estimate (ñ, d). Thus, the problem related to multiple or lack of solutions is overcome. The method is applied to Au films, deposited on transparent glass substrates. For comparison of the resulting (ñ, d), Veriable Angle Spectroscopic Ellipsometry is used as an independent technique.