Infrared optical constants and roughness factor functions determination: the HTHRTR method

Abstract

This method was developed to determine the complex infrared optical constant of a single free-standing partially absorbing plate as wellas a thin solid film eposited on it. The method is based on exact formulas for normal transmittance T and near-normal reflectance R of the substrate as well as the film-substrate double layer. Coherent multiple reflections throughout the film and incoherent multiple reflections in the substrate as well as the intensity losses on the rough surface are taken into account. The influence of various data on the solution of the inverse problem is discussed by a contour map study. The method is explained using examples of both- and single-side-polished silicon wafers where the transmission and reflection roughness factor functions H(T),H(R) are determined for the rough surface. The thin-film example has been the silicon oxide film formed on the single-side-polished silicon substrate by chemical vapor deposition.

Infrared absorption of n-type tensile-strained Ge-on-Si

“…The validity of this method has been verified by deriving the optical constants of SiO 2 in the mid-and far-IR regime from the raw transmission data of SiO 2 thin films on SSP Si substrates reported in [9]. The derived absorption coefficient and real part of refractive index using our method are in good agreement with the results in [9].…”

“…The broad oscillations in the wavelength range of 1-5 μm are produced by the multilayer interference effect. Because of the wavelength-dependent scattering caused by the backside roughness of SSP Si and impurity IR absorption in Si [8,9], the transmittance of SSP Si substrates deviates from the theoretical value of ∼55% in the wavelength range of 1.3-22 μm. In particular, the dips in the transmission spectra at ∼9 and ∼16.5 μm correspond to the absorption due to oxygen and carbon in the Si substrate, respectively [10,11].…”

“…Then with a combination of transfer matrix analysis and the Kramers-Kronig relation we were able to derive the absorption coefficient as well as the real part of refractive index for the tensile-strained n Ge thin films deterministically using an iterative self-consistent regression approach [7]. The validity of this method has been verified by deriving the optical constants of SiO 2 in the mid-and far-IR regime from the raw transmission data of SiO 2 thin films on SSP Si substrates reported in [9]. The derived absorption coefficient and real part of refractive index using our method are in good agreement with the results in [9].…”

Analysis of Low-k Dielectric Thin Films on Thick Substrates by Transmission FTIR Spectroscopy

“…coherent (C)) expression for a thin film on a thick substrate, and then, using heuristic arguments, argued that the derived IC expression becomes exact in the low resolution limit (such as 4 cm −1 ). At roughly the same time, Klansek-Gunde and Alexandrov 26,27 independently utilized the same IC technique to derive analytical expressions for both the transmittance and reflectance of a thin film on thick substrate, and then demonstrated that the two equations could be numerically solved to experimentally extract the optical constants of a thin film. They further extended the IC technique by considering the practical case of surface scattering for single side polished substrates.…”

High-responsivity thermoelectric infrared detectors with stand-alone sub-micrometer polysilicon wires

“…Then the reflection and transmission spectra of each sample were recorded using an FTIR (Fourier transform infrared spectroscopy) system. A contour map of reflection and transmission spectra for a range of n and k (real and imaginary parts of the refractive index) was created and overlapped with the experimental results [30,31]. Out of the possible solutions, a meaningful initial estimate was used to choose the correct solution [32].…”