Center wavelength shift dependence on substrate coefficient of thermal expansion for optical thin-film interference filters deposited by ion-beam sputtering

Single-layer films of Ta2O5 and multilayer thin-film filters of Ta2O5 and SiO2 were deposited by ion-beam-sputter deposition. Postdeposition annealing of the structures resulted in increased optical thickness of the films, resulting in an upward shift in the wavelength of the transmission-reflection spectra. Modeling of the single-layer films by means of the effective media approximation indicates an increase in the void fraction of the film after annealing. This increase is consistent with an observed decrease in refractive index and an increase in physical film thickness. The multilayer structures, deposited on substrates of varying coefficient of thermal expansion (CTE), were annealed at various temperatures, and the change in the center wavelength was measured. The measured change is dependent on the annealing temperature and the substrate CTE, indicating that the increase in the void fraction is caused in part by thermally induced stress during the annealing process. A simple model is proposed that relates the void fraction present in the films after annealing with the substrate CTE and the annealing temperature.