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

Abstract

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 147nm and 304nm, 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

Preparation of Graphene-Supported Microwell Liquid Cells for <em>In Situ</em> Transmission Electron Microscopy

“…Immerse the PMMA-coated graphene in a Petri dish filled with DI water (Figure 3a). NOTE: The number of layers of graphene can be determined using feasible techniques 32,33 . 2.…”

Highly accurate determination of heterogeneously stacked Van-der-Waals materials by optical microspectroscopy

“…With the optical system being accurately described, different 2D materials in Van-der-Waals heterostructures can be discriminated while simultaneously determining their number of layers by combining both mentioned evaluation schemes, i.e. the contrast-based 5 (in this particular case absolute reflectance instead of contrast is deployed) and the wavelength-shift based method 8 . The applicability of this strategy is demonstrated for the extreme case of graphene-hBN heterostructures, where the influence of individual layers on reflected light is weak due to their extraordinary small thickness (graphene: 3.35 Å 2 ; hBN: 3.33 Å 15 ).…”

“…Optical spectroscopy is used for characterizing ultra-thin films down to atomic layers. It has been shown that in particular reflectance spectroscopy is well-suited for detecting single atomic layers of 2D materials like graphene (Gr) [1][2][3][4][5][6] , hexagonal boron nitride (hBN) 3,7,8 or transition metal dichalcogenides (TMD) 3,[8][9][10] like MX2 (M = Mo, W; X = S, Se, Te). For this purpose, reflectance spectra of a dielectric layer stack in combination with a superimposed ultra-thin layer are acquired and the deviation between both reflectance spectra is evaluated in form of contrast spectra 5 .…”

“…It has been shown that in particular reflectance spectroscopy is well-suited for detecting single atomic layers of 2D materials like graphene (Gr) [1][2][3][4][5][6] , hexagonal boron nitride (hBN) 3,7,8 or transition metal dichalcogenides (TMD) 3,[8][9][10] like MX2 (M = Mo, W; X = S, Se, Te). For this purpose, reflectance spectra of a dielectric layer stack in combination with a superimposed ultra-thin layer are acquired and the deviation between both reflectance spectra is evaluated in form of contrast spectra 5 . The optical contrast between 2D materials and subjacent (or overlying 11 ) layer stacks can be used for determining the number of layers and is tailored by choosing appropriate combinations of materials and film thicknesses (i.e.…”

“…tailoring optical pathways). This is achieved by predicting the reflectance behavior of the layer stack via analytical calculations while considering the optical properties of each individual layer 5,12 . Additionally, a spectral shift of distinct extreme values in reflectance spectra can be analyzed to gain information about the number of layers of a 2D material as well 8 .…”