Enhanced Visibility of MoS2, MoSe2, WSe2 and Black Phosphorus: Making Optical Identification of 2D Semiconductors Easier

We explore the use of Si3N4/Si substrates as a substitute of the standard SiO2/Si substrates employed nowadays to fabricate nanodevices based on 2D materials. We systematically study the visibility of several 2D semiconducting materials that are attracting a great deal of interest in nanoelectronics and optoelectronics: MoS2, MoSe2, WSe2 and black phosphorus. We find that the use of Si3N4/Si substrates provides an increase of the optical contrast up to a 50%-100% and also the maximum contrast shifts towards wavelength values optimal for human eye detection, making optical identification of 2D semiconductors easier.


Introduction
Mechanical exfoliation has proven to be a very powerful tool to isolate two-dimensional material out of bulk layered crystal [1]. The produced atomically thin layers, however, are randomly deposited on the substrate surface and are typically surrounded by thick crystal which hampers the identification of the thinner material.
Optical microscopy is a perfect complement to mechanical exfoliation as is a reliable and non-destructive method and it allows distinguishing the atomically thick layers from their bulk-like counterparts. This technique is valid despite the reduced thickness of 2D materials. They can be seen through an optical microscope with the naked eye, because of the wavelength dependent reflectivity of the dielectric/2D material system [2][3][4][5][6]. This dependence can be exploited to easily identify and isolate 2D material single layer flakes by modifying the substrate dielectric thickness and permittivity. In addition to increasing the visibility, the use of different substrate materials may improve the performance of the produced devices if the chosen substrate has good dielectric properties.
In this work we systematically study the visibility of several 2D materials with potential applications in electronics and optoelectronics, such as MoS 2 , MoSe 2 , WSe 2 and black-phosphorus (BP) [7][8][9][10][11]. The performed experiments and analysis are general, and can be applied to any kind of 2D materials. Here, we explore the use of silicon nitride (Si 3 N 4 ), a high k dielectric material (κ ~ 7) commonly used in the semiconductor industry, as a substitute of the silicon oxide layer, which is almost exclusively used nowadays to fabricate nanodevices based on 2D materials. We show how the use of silicon nitride strongly enhances the optical contrast of 2D semiconductors, making the identification of ultrathin sheets easier. Moreover, by using a Si 3 N 4 spacer layer of 75 nm in thickness, the optical contrast reaches its maximum value at a wavelength of 550 nm (which is the optimal wavelength detection of the human eye) [12], while 285 nm of SiO 2 spacer layer (the standard in graphene and MoS 2 research nowadays) has its maximum contrast value at 460 nm, in the deep-blue/violet part of the visible spectrum.
Apart from the enhanced visibility, the use of Si 3 N 4 as spacer layer also has the potential to improve the electrical performance of nanoelectronic devices due to its high dielectric constant (almost twice that of SiO 2 ) that can help to screen Coulomb scatterers and, thus, to improve the mobility [13]. Additionally, the use of Si 3 N 4 do not present any disadvantage with respect to SiO 2 layers in terms of processing as Si 3 N 4 is compatible with most common semiconductor industry processes. Moreover, Si 3 N 4 substrates can be used for other fabrication processes different than mechanical exfoliation, such as CVD [14][15][16] (because of its high thermal stability) and inkjet printing [17][18][19] as its surface chemistry has the potential to be tuned using similar recipes to those used for SiO 2 substrates. In summary due to the good dielectric performance of Si 3 N 4 and its deposition compatibility with other semiconductor industry processes, we believe that the use of Si 3 N 4 as spacer layer for 2D semiconductor applications will become popular in the near future.

Experimental Section
Two-dimensional semiconductor samples are prepared using a recently developed deterministic transfer process [20]. First, we mechanically exfoliate bulk MoS 2 , MoSe 2 , WSe 2 or black phosphorous using clear Nitto tape (SPV 224). Bulk crystals were synthetic (grown by vapor transport method) in all cases except the MoS 2 crystal that was obtained from naturally occurring molybdenite (Moly Hill mine, Quebec, QC, Canada). The freshly cleaved flakes are then deposited onto a viscoelastic poly-dimethylsiloxane (PDMS) substrate. Subsequently, the flakes are transferred onto two different silicon substrates: one with a 285 nm thick SiO 2 oxide layer on top and another one with a 75 nm thick Si 3 N 4 layer. The latter thickness was chosen after the theoretical analysis explained in Section 3 in order to maximize the contrast at a wavelength of 550 nm.
Few-layer flakes are identified under an optical microscope (Nikon Eclipse LV100) and the number of layers is determined by a combination of quantitative optical microscopy and contact mode atomic force microscopy (used instead of tapping mode to avoid artifacts in the thickness determination). The optical properties of the nanosheets have been studied with a modification of a home-built hyperspectral imaging setup, described in detail in Reference [21].

Optical Contrast Calculation
In order to evaluate the potential of Si 3 N 4 to enhance the optical visibility of 2D semiconductors we have first calculated the optical contrast of monolayer MoS 2 , MoSe 2 and WSe 2 as function of the illumination wavelength for substrates with Si 3 N 4 and SiO 2 layers of different thickness. The model is based on the Fresnel law and more details can be found in the literature [2,3,[22][23][24][25]. Briefly, the optical contrast of atomically thin materials is due to a combination of: (1) interference between the reflection paths that originate from the interfaces between the different media and (2) thickness dependent transparency of the 2D material that strongly modulates the relative amplitude of the different reflection paths. These two effects combined lead to color shifts (dependent on the thickness of the 2D material) that can be appreciated by eye. Figure 1 displays colormaps that represent the optical contrast (defined as C = (I flake − I substrate )/(I flake + I substrate )) as a function of the illumination wavelength (vertical axis) and the thickness of the dielectric layer (horizontal axis). The references employed to extract the refractive indexes for the different materials employed in the calculation of the optical contrast are summarized in Table 1. One can clearly see how the optical contrast for Si 3 N 4 substrates is much higher than for SiO 2 .
Moreover, substrates with a 75 nm Si 3 N 4 layer have a maximum contrast at a wavelength around 550 nm, which is optimal for human eye detection. The strong optical contrast enhancement observed for 75 nm thick The result of the calculations displayed in Figure 1 illustrates the potential of Si 3 N 4 spacer layers with a thickness of 50 nm-100 nm to enhance the optical contrast significantly with respect to conventionally used

Hyperspectral Imaging
The optical contrast is measured at different illumination wavelengths with a modified hyperspectral imaging setup described in Reference [21]. The sample is illuminated with monochromatic light with the help of a monochromator. The measurement is carried out by sweeping the illumination wavelength from 450 nm to 900 nm in 5 nm steps, and acquiring an image with a monochrome camera at each wavelength step. The thickness of the studied flakes has been determined by atomic force microscopy prior to the hyperspectral imaging measurements (see Figure 2). Raman spectroscopy or photoluminescence can be also used to characterize and to determine the thickness of the exfoliated flakes on Si 3 N 4 surfaces [30], see Supporting Information for Raman spectra acquired for MoS 2 flakes on a 75 nm Si 3 N 4 /Si substrate and a comparison with the spectra reported for flakes on 285 nm SiO 2 /Si substrates [31,32]. is weaker within the visible part of the spectrum, whereas for Si 3 N 4 around 500-600 nm the monolayer contrast reaches the highest value.

Wavelength Dependent Optical Contrast
From the contrast maps at different wavelengths one can extract the wavelength dependence of the optical contrast for flakes with different thicknesses. Figure 4 summarizes the contrast vs. wavelength dependence measured for MoS 2 , MoSe 2 , WSe 2 and black phosphorus on both substrates. For all the studied materials the optical contrast is enhanced on substrates with Si 3 N 4 by a 50%-100%. The wavelength with the maximum optical contrast is also shifted: while on SiO 2 /Si substrates it is ~650 nm, on Si 3 N 4 the maximum contrast is at ~550 nm.

Conclusions
In summary, we have explored the use of Si 3 N 4 as dielectric layer for 2D semiconductor research. We      Figure S1. Real and imaginary parts of the refractive index of bulk MoS 2 , MoSe 2 and WSe 2 extracted from the complex dielectric constants displayed in Ref. [22] and Ref. [23] of the main text. We display these values here to facilitate future calculations on these materials.  The difference between the two Raman modes (E 1 2g and A 1g ) vs. the number of layers, extracted from (a). As a comparison the results reported for MoS 2 samples fabricated on 285 nm thick SiO 2 /Si substrates have been also plotted (data extracted from Ref. [31] and Ref. [32] of the main text).