Measurement of Film Thickness from Lattice Absorption Bands

Abstract

Many compound semiconductors and insulators exhibit characteristic infrared lattice absorption bands which can be quantitatively described by classical dispersion theory. When the dispersion parameters are known, the thickness of an absorbing film on a nonabsorbing substrate can be determined from a measurement of the lattice absorption. For thin films the dispersion parameters can differ from the values appropriate to bulk single crystals; however, it is shown that the parameter most susceptible to variation can be obtained directly from the measured absorption band without knowledge of the film thickness. It is also shown that the integrated optical density (the area under the band plotted as optical density vs. wave number) is a linear function of thickness when the refractive index of the substrate is unity, but departs from linearity as the substrate refractive index increases. The appropriate equations and a method for determining film thickness from a measured absorption band are given. The discussion is illustrated by data for thin films on Si substrates.