Quantitative Determination of Complex Dielectric Function of Amorphous Silicon Dioxide on Silicon Substrate from Transmission Spectrum

Abstract

Infrared spectroscopy is a powerful tool for characterizing the molecular bonding structures of oxide films. Using parametric analysis, we could determine both real and imaginary parts of the complex dielectric function of oxide thin films supported on a substrate. In this work, the complex dielectric function of a silicon dioxide thin film on a silicon substrate in the infrared region (400 -1400 cm À1 ) was determined quantitatively by fitting an optical model for the transmittance of an air/silicon/insulator/air laminated structure to experimental data. The adsorption due to the ionic vibration of siloxane bonding was parameterized with the sum of Lorentz damping oscillators convoluted with a Gaussian distribution. The incidence angle of light was changed from nearly normal (5 off) to oblique (55 -65 off), and all of the data was simultaneously fitted. Transverse optic and longitudinal optic functions were calculated from the dielectric function. Good agreement was found between the peak frequency of each function and that calculated by another method.

Ionic Vibration Spectrum of Nanocrystalline MEL Pure Silica Zeolite Film

“…The differences of the functional shapes and the absorption intensities between the nearly normal (5° off) incidence spectrum and the oblique incidence spectra are due to the excitation of longitudinal (LO) coupling mode of ionic vibration in addition to transverse optical (TO) coupling mode, as described by Berreman effect . After a numerical analysis, a good agreement between the theoretical model (eq 7 of ref ) and the experimental data was found as shown in Figure . We have to note that, in this analysis, the fitting range was taken at the 4000–400 cm –1 region, and the refractive index due to the electronic polarization was also determined by fitting to the experimental data.…”

Molecular Bonding Structure of Alkylene-Bridged Organosilicate Glass Films

“…In the case of th-SiO 2 , j takes the indices for the four oscillator modes of R, SS, AS 1 , and AS 2 . Width of each oscillator mode become broad compared to that of crystalline glass and g takes Gaussian distribution as denoted by ,, g j false( normalξ − normalν j − normalT normalO false) = 1 2 normalπ normalσ j exp ( − false( normalξ − normalν j − normalT normalO false) 2 2 normalσ j 2 ) The Gaussian convoluted Lorentz oscillator is abbreviated to L–G oscillator. Integrated oscillator strength of j th mode is denoted by ⟨ F j ⟩ = ∫ 0 ∞ F j ( ξ ) g j ( ξ − ν j − T O ) d ξ Theoretically, the ε can be calculated from optical responses such as reflectance and transmittance of the materials.…”

“…After samples were purged in N 2 ambient for 5 min, relative transmittance of the stacked glass-film/Si-substrate against that of bare Si wafer was recorded. The bare Si wafer was selected carefully to match the absorption of the Si substrate of the samples . Spectrum resolution was taken at 4 cm –1 to avoid the fringe pattern due to the internal reflection in the Si substrate …”

“…Fourier transform infrared (FT/IR) spectroscopy is a powerful tool to investigate the molecular bonding structures of oxide films as extensively performed for the thermally grown silica, − sol–gel-derived silica, − chemical vapor deposition silica, ,, and others. For amorphous or optically isotropic dielectric films, its intrinsic absorption is described by a complex dielectric function normalε = normalε normale normall + normalε normali normalo normaln + normalε normalp normalr which is the sum of the electronic component (ε el ), ionic component (ε ion ), and permanent polarization component (ε pr ).…”

“…However, the spectrum is frequently discussed in an arbitral unit, and the result is strongly affected by geometrical effect such as the incidence angle of light, 45 film thickness, 29,31 film density, 41,42 and multiple internal reflections in the film and substrate. 29,31,37 To avoid these geometrical effects, one of the authors established a quantitative analysis method to calculate the ε ion . 37,43 By use of this parametric analysis method, both real and imaginary parts of the ε ion can be determined separately, without using KramersÀ Kronig transformation.…”