Gaussian oscillator model of the dielectric constant of SiO2 thin film in infrared range
Authors: Liu Hua-Song  , Yang Xiao  , Wang Li-Shuan  , Jiang Cheng-Hui  , Liu Dan-Dan  , Ji Yi-Qin  , Zhang Feng  , Chen De-Ying  ,   Tianjin Key Laboratory of Optical Thin Film, Tianjin Jinhang Technical Physics Institute, HIWING Technology Academy of CASIC, Tianjin 300308, China;,   National Key Laboratory of Science and Technology on Tunable Laser, Institute of Opto-Electronics, Harbin Institute of Technology, Harbin 150080, China
Published: December 2020

SiO2 thin film is one of the most important low refractive index materials in the area of optical thin films. It is always used in the design and preparation of many kinds of multilayer films. The dielectric constant of the SiO2 thin film is a key characteristic for design of the multilayer thin film. The composite Gaussian oscillator model is one of the most important dispersion models for the dielectric constant of the amorphous SiO2 in the anomalous dispersion regime in the infrared range. More and more researchers have focused on the number and the physical meaning of the oscillators in the composite oscillator. A method to determine the SiO2 thin film oscillator quantity was proposed. In this method, the quantity of oscillator peaks was equivalent to the oscillator number of chemical composition, based on the factor analysis technology of chemometrics. Concretely, the composite oscillators of the dielectric constant were equivalent to the mixture, and the independent oscillators were equivalent to the compositions of the mixture. The absorbance of the mixture changed with the physical thickness of the thin film. Eight SiO2 film samples with different thickness were prepared on the Si substrate by the ion beam sputtering deposition. The infrared transmittances of the eight samples were used as elements in the spectral matrix. There were nine Gaussian oscillators in the range of 400-4000 cm-1, which was determined by the factor analysis technology. The dielectric constant of the SiO2 thin film in this range was obtained by the inverse calculation from the spectral transmittance. It provides the inverse calculation result for the dielectric constant of the SiO2 thin film with a specific physical meaning. By analyzing the dielectric constant in the range of 400-900 cm-1, the symmetric stretching vibrational frequency and the in-plane rocking frequency of the Si-O-Si bond of the SiO2 thin film can be obtained. Compared with fused silica, the symmetric stretching vibrational frequency increased while the rocking frequency was reduced. In fact, the frequency shifts are caused by the strain of the thin film. By analyzing the dielectric constant in the range of 900-1500 cm-1, four anti-symmetric stretching vibrational frequencies of the Si-O-Si bond in the SiO2 thin film were obtained. They have a certain corresponding relation with the anti-symmetric stretching vibrational frequency of the Si-O-Si bond in the fused silica. What's more, by analyzing the dielectric constant in the range of 3000-4000 cm-1, the water-cut (or hydroxyl) chemical defects in the films were confirmed. The chemical defects can influence the dielectric constant in the whole infrared range.