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 determined reflectance was compared to the calculated values. The first system consists of a single SiO2 layer with a thickness of 147 nm and 304 nm, respectively, and the second is a double layer stack consisting of a Si3N4 layer with a thickness of 54 nm and 195 nm, respectively, on top of an 11 nm SiO2 film. The Michelson contrast of single-layer graphene flakes on the latter layer stacks becomes very high (absolute value of more than 0.3) in the visible wavelength range. Additionally, in the UV-B range a large difference in the reflection of selected SiO2 layer thicknesses on silicon substrates with and without single-layer graphene on top is found with a decrease in the measured reflectance of up to 33%. The measured and calculated values showed a high conformity suggesting this approach usable for the calculation of reflectance and transmittance properties of arbitrary layer stack systems including thin conductive layers.