Universal dispersion model for characterization of optical thin films over a wide spectral range: application to hafnia

Abstract

A dispersion model capable of expressing the dielectric response of a broad class of optical materials in a wide spectral range from far IR to vacuum UV is described in detail. The application of this universal dispersion model to a specific material is demonstrated using the ellipsometric and spectrophotometric characterization of a hafnia film prepared by vacuum evaporation on silicon substrate. The characterization utilizes simultaneous processing of data from multiple techniques and instruments covering the wide spectral range and includes the characterization of roughness, nonuniformity, transition layer, and native oxide layer on the back of the substrate. It is shown how the combination of measurements in light reflected from both sides of the sample and transmitted light allows the separation of weak absorption in films and substrates. This approach is particularly useful in the IR region where the absorption structures in films and substrates often overlap and a prior measurement of the bare substrate may be otherwise necessary for precise separation. Individual phenomena that contribute to the dielectric response, i.e., interband electronic transitions, electronic excitations involving the localized states, and phonon absorption, are discussed in detail. A quantitative analysis of absorption on localized states, permitting the separation of transitions between localized states from transitions between localized and extended states, is utilized to obtain estimates of the density of localized states and film stoichiometry.