Generalized approach to design multi-layer stacks for enhanced optical detectability of ultrathin layers

The optical detectability of ultrathin conductive films (down to one atomic layer) can be enhanced by choosing distinct layer-stacks. A simple analytical approach using the transfer matrix method is applied for calculating the reflectance of arbitrary multi-layer stack systems with and without the ultrathin layer of interest on top in a wide wavelength range, including both the visible spectrum and the ultraviolet spectrum. Then, the detectability defined by the Michelson contrast was calculated. Performing these calculations for thickness variations of the individual layers in the stack allows determining optimum layer thicknesses, e.g., maximum overall contrast or maximum contrast for a given wavelength. To demonstrate the validity of the methodology, two thin film stacks were investigated, which use p-type silicon as a substrate material and partially covered by a single-layer graphene as a top layer. For each stack, two samples with different layer thicknesses were fabricated and their experimentally ...