Depth profiling by confocal Raman microspectroscopy: semi-empirical modeling of the Raman response

It has been well documented that the use of dry optics in depth profiling by confocal Raman microspectroscopy significantly distorts the laser focal volume, thus negatively affecting the spatial resolution of the measurements. In that case, the resulting in-depth confocal profile is an outcome of several contributions: the broadening of the laser spot due to instrumental factors and diffraction, the spreading of the illuminated region due to refraction of the laser beam at the sample surface, and the influence of the confocal aperture in the collection path of the laser beam. Everall and Batchelder et al. developed simple models that describe the effect of the last two factors, i.e., laser refraction and the diameter of the pinhole aperture, on the confocal profile. In this work, we compare these theoretical predictions with experimental data obtained on a series of well-defined planar interfaces, generated by contact between thin polyethylene (PE) films (35, 53, 75, and 105 microm thickness) and a much thicker poly(methyl methacrylate) (PMMA) piece. We included two refinements in the above-mentioned models: the broadening of the laser spot due to instrumental factors and diffraction and a correction for the overestimation in the decay rate of collection efficiency predicted by Batchelder et al. These refinements were included through a semiempirical approach, consisting of independently measuring the Raman step-response in the absence of refraction by using a silicon wafer and the actual intensity decay of a thick and transparent polymer film. With these improvements, the model reliably reproduces fine features of the confocal profiles for both PE films and PMMA substrates. The results of this work show that these simple models can not only be used to assist data interpretation, but can also be used to quantitatively predict in-depth confocal profiles in experiments carried out with dry optics.