Rigorous prediction of Raman intensity from multi-layer films.

In the Raman probing of multilayer thin film materials, the intensity of the measured Raman scattered light will be impacted by the thickness of the thin film layers. The Raman signal intensity will vary non-monotonically with thickness due to interference from the multiple reflections of both the incident laser light and the Raman scattered light of thin film interfaces. Here, a method for calculating the Raman signal intensity from a multilayer thin film system based on the transfer matrix method with a rigorous treatment of the Raman signal generation (discontinuity) is presented. This calculation methodology is valid for any thin film stack with an arbitrary number of layers with arbitrary thicknesses. This approach is applied to several thin film material systems, including silicon-on-sapphire thin films, graphene on Si with a SiO capping layer, and multilayer MoS with the presence of a gap between layers and substrate. Different applications where this method can be used in the Raman probing of thin film material properties are discussed.