Numerical simulations of confocal Raman spectroscopic depth profiles of materials: a photon scattering approach

Abstract

We present a simple model that uses a novel photon scattering approach to predict the depth profile response obtained when confocal Raman spectroscopy is applied both to silicon and to a number of related polymeric materials of varying optical clarity. This paper first provides an overview of the models proposed to date to demonstrate the evolution in understanding of the confocal Raman response of semi-transparent materials, based upon geometrical optics. A new model is then described that is based upon the twin notions of a permanent extended Raman illuminated volume and the degree of extinction of the incident and Raman scattered photons from the whole of the illuminated volume as it is gradually moved further into, or defocused above, the sample. The model's predictions are compared with empirical data from previous studies of a range of semi-crystalline polymers with different scattering properties and, by means of contrast, with that of a silicon sample. We show that, despite its inherent simplicity, the physics this model utilizes is able successfully to predict the form of the depth profile for each material, something that has not been achieved by any model previously proposed, and that the parameters used in the model scale with independent physical measurements. Finally the model is used to account for the fact that useful Raman spectra can be obtained when the laser is focused as much as 40 µm above the sample surface.

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