Where θ is the original "detection" phase angle and α is the phase angle used in the spectral (or interferogram) rotation. The new "in-phase" [M(σ)cos(α+θ)] and "quadrature" [M(σ)sin(α+θ) ] spectra from the phase rotation enhance signals from different depths of the sample depending on the values of α. The third approach to depth profiling analysis using the phase data is to calculate the phase spectrum θ(σ) from the simultaneously collected in-phase and quadrature spectra by using Equation(3-8). The phase difference obtained from the comparison of extinction angles in the continuous phase rotation plot method can be also obtained more directly and with less manipulation from the phase spectrum.
The measurement of the absolute PA phase is limited by the ability to reproduce the instrument phase from reference to sample. Nevertheless, the phase differences between different bands in a spectrum are highly reproducible. For this reason, the phase difference ΔΦ has been made the focus of conceptually simple, general theoretical mode, which are particularly applicable to discretely laminar materials with distinctive marker bands for each layer as mathematically described by Equation (3-6) and (3-7) for the two specific cases in Section 3.3.3. In the phase difference models the relevant variables (thickness, optical absorptivity, thermal diffusivity, modulation frequency, etc.) are related to each other by the PA phase information. Thus quantitative determination of these physical parameters is also made possible through the use of the models and the S2ΦM FT-IR PAS technique.
3.3.6 Step-Scan Phase Modulation (S2ΦM) FT-IR PAS: Experimental PAS Reference. Since only the absorbed IR light generates thermal waves and contributes to PA detector signals, the PA single-beam spectrum is an uncorrected "absorption" spectrum of the sample. The variations over the spectral region in source intensity, beam splitter efficiency, and detector response must be corrected using a reference sample that absorbs strongly at all wavenumbers. A common practice in both continuous- and step-scan PAS depth profiling is to use a strongly absorbing glassy carbon (or a highly concentrated carbon black-filled rubber, minimum carbon content 60%) as a reference. Since the reference absorbs strongly at all wavenumbers in the mid-IR region, its magnitude spectrum can be used as a reference to normalize PA spectra, correcting all those variations mentioned above. In addition, since almost all absorption occurs at surface of the strong absorber, it can be used as a surface reference for calibrating the phase of a step-scan phase modulation depth profiling experiment. When this reference is in place, the relative ΦM phase setting button, as shown in Figure 3.6, is pressed to maximize PA signals in the in-phase (I) channel and subsequently the quadrature (Q) channel is minimized. After this phase angle calibration is done, the ΦM phase setting will be kept unchanged for running a sample under the same modulation frequency. The resulting in-phase spectrum of the sample will therefore enhance the surface absorption features and the quadrature spectrum will enhance those from the substrate or deeper part of the sample.
Software Setup Screen. The OMINC SST setup screen for a S2ΦM experiment is shown in Figure 3.6. All the S2ΦM related experiment parameters can be set in this window. The Start button allows a short setup scan (64 points around the ZPD or centerburst) using the setup parameters and displays the result in this window. The phase angle calibration button is located on the bottom right corner and must be pressed when the glassy carbon black reference is placed in the PA cell. This setup screen also allows users to adjust PA gain setting on top of the PA cell to optimize the signal before collecting data.
3.3.7 FT-IR PA Depth Profiling Examples The theory, experimental, and spectral analysis approaches for FT-IR PA depth profiling have been discussed in previous sections. In this section, applications of these approaches will be demonstrated in depth profiling analysis of some multi-layered samples. Modulation frequency-resolved and phase-resolved S2ΦM FT-IR PAS will be emphasized as they are presently the most popular approaches in practical applications. In addition, continuous-scan PAS will also be demonstrated as a very valuable diagnostic tool despite the ambiguity with spectral interpretation because of its simplicity and speed of data acquisition. By monitoring characteristic band intensity variation over a range of mirror velocities, it is also possible to achieves some useful spectral depth profiling results. A few other depth profiling approaches used in FT-IR PAS, as reported in literature, such as time-resolved FT-IR PAS, 2D FT-IR PAS and PAS linearization are not covered in this chapter. Generalized 2D FT-IR PAS will be briefly discussed in Chapter 7.
PMMA on ABS. This sample consists of a 0.9μm layer of poly(methyl-methacrylate) (PMMA) on a thicker layer of poly(acrylonitrile:butadiene:styrene) (ABS). Continuous-scan PAS spectra taken at a series of optical velocities (0.0158-0.63cm/sec) are shown in Figure 3.7. It can be seen that at high optical velocities, modulation frequencies are high, the sampling depths are subsequently shallower, and therefore PAS spectra are dominated by the surface PMMA layer. The picture is reversed as the velocities and the corresponding modulation frequencies decrease. At low velocities, the sampling depth is deep and the relative contribution from the thin surface layer is minor, thus the spectra are dominated by the bands of the bulk ABS layer.
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