Preventing overfitting in infrared ellipsometry using temperature dependence: fused silica as a case study

Abstract

The dispersive linear optical properties of materials are frequently described using oscillator models, where the oscillators represent interactions between light and various material resonances (vibrational, free-carrier, interband, etc.). The state-of-the-art measurement of the complex refractive index is variable-angle spectroscopic ellipsometry (VASE), where additional measurement angles and the measured depolarization of light provides much more information compared to simpler measurements such as single-angle reflectance and transmittance. Nevertheless, even state-of-the-art VASE data can be hard to uniquely fit using oscillator models, and the resulting models may be hard to interpret physically. Here, we demonstrate the use of an additional degree of freedom, temperature, to improve the accuracy, uniqueness, and physicality of oscillator models of materials. Our approach relies on the well-understood temperature dependence of material resonances, and in particular vibrational resonances in amorphous SiO2, which are expected to change monotonically from room temperature to hundreds of degrees C. We performed VASE measurements at different temperatures, independently fitted the data at each temperature, and then confirmed that our models are unique and physical by monitoring the temperature dependence of the resulting fitting parameters. Using this technique, we generated highly accurate and precise data sets and material models describing the mid-infrared complex refractive index of three different grades of fused SiO2, which can then be used for modeling of mid-infrared optical components such as thermal emitters.