Removing interference-based effects from the infrared transflectance spectra of thin films on metallic substrates: a fast and wave optics conform solution

Abstract

A hybrid formalism combining elements from Kramers-Kronig based analyses and dispersion analysis was developed, which allows removing interference-based effects in the infrared spectra of layers on highly reflecting substrates. In order to enable a highly convenient application, the correction procedure is fully automatized and usually requires less than a minute with non-optimized software on a typical office PC. The formalism was tested with both synthetic and experimental spectra of poly(methyl methacrylate) on gold. The results confirmed the usefulness of the formalism: apparent peak ratios as well as the interference fringes in the original spectra were successfully corrected. Accordingly, the introduced formalism makes it possible to use inexpensive and robust highly reflecting substrates for routine infrared spectroscopic investigations of layers or films the thickness of which is limited by the imperative that reflectance absorbance must be smaller than about 1. For thicker films the formalism is still useful, but requires estimates for the optical constants.

Beer's Law – Why Absorbance Depends (Almost) Linearly on Concentration

“…[19] He discussed limiting cases based on an analogue of eqn. (14), and came to the same principal conclusions as we did, i. e. Beer's law should hold good for small "vertheilungsdichten" and lose its justification for stronger absorptions and higher concentrations. Even if Planck did neither derive Beer's law explicitly nor an expression for the molar attenuation constant, we think that his insights should have deserved much more than having gone unheeded for so long.…”

“…Accordingly, the absorbance peak is originally practically symmetric and located at its oscillator position for the small concentrations c = 0.05 and 0.5 mol/l, suggesting that the approximation contained in eqn. (14) and thereby Beer's law should hold well in this range. As a consequence, there is no noticeable difference between the thousandfold absorbance for c = 0.05 mol/l (black curve) and the hundredfold absorbance for 0.5 mol/l in Figure 1 (red curve, which practically covers the black curve completely).…”

“…We have recently investigated how eqn. (14) performs as approximation of eqn. (8) and found that the differences are very small as long as the oscillators are comparably weak, like for organic and biological matter in the infrared spectral range.…”

“…Recently, also deviations from the (Bouguer-) Lambert part of the (Bouguer-)Beer-Lambert law due to wave optics-based effects like interference became a focus of attention in this context ("electric field standing wave artefacts"). [11][12][13][14] Respectively, blue shifts and asymmetric broadening in absorbance spectra seem to be nothing out of the ordinary, cf., e. g., Figure 1 in the excellent tutorial about the Beer-Lambert law by Mäntele and Deniz. [15] However, how much the individual influences contribute to the spectral deformation would have to be investigated in each particular case.…”

Beer's Law‐Why Integrated Absorbance Depends Linearly on Concentration

“…In particular, any alteration of the electric field intensity inside the medium must be due to absorption. If the electric field intensity changes locally, e. g., by interference effects ("electric field standing wave effect"), [38][39][40] scattering, plasmonic enhancement or electromagnetic coupling [27,41,42] the simple connection between the dielectric function and absorption index is invalidated, and the linear relationship between concentration and (integral) absorbance is therefore revoked. The details of the derivation of the sum rules are discussed in the supporting information and ref.…”