Simple Method for Determining Slowly Varying Refractive-Index Profiles from in situ Spectrophotometric Measurements

Reliable control of the deposition process of optical films and coatings frequently requires monitoring the refractive-index profile throughout the layer. In the present research a simple in situ approach is proposed that uses a WKBJ matrix representation of the optical transfer function of a single thin film on a substrate. Mathematical expressions are developed that represent the minima and the maxima envelopes of the curves transmittance versus time and reflectance versus time. The refractive index and the extinction coefficient depth profiles of different films are calculated from simulated spectra as well as from experimental data obtained during the PECVD (plasma-enhanced chemical vapor deposition) of silicon-compound films. Variation in the deposition rate with time is also evaluated from the position of the spectra extrema as a function of time. The physical and mathematical limitations of the method are discussed.