Thickness identification of thin InSe by optical microscopy methods

Indium selenide (InSe), as a novel van der Waals layered semiconductor, has attracted a large research interest thanks to its excellent optical and electrical properties in the ultra-thin limit. Here, we discuss four different optical methods to quantitatively identify the thickness of thin InSe flakes on various substrates, such as SiO2/Si or transparent polymeric substrates. In the case of thin InSe deposited on a transparent substrate, the transmittance of the flake in the blue region of the visible spectrum can be used to estimate the thickness. For InSe supported by SiO2/Si, the thickness of the flakes can be estimated either by assessing their apparent colors or accurately analyzed using a Fresnel-law based fitting model of the optical contrast spectra. Finally, we also studied the thickness dependency of the InSe photoluminescence emission energy, which provides an additional tool to estimate the InSe thickness and it works both for InSe deposited on SiO2/Si and on a transparent polymeric substrate.

This is the authors' version (post-peer reviewed) of the following article: Q. Zhao  like the quantitative analysis of transmission mode optical microscopy images and the apparent color of the flakes using a quantitative color chart. We believe that gathering this information together is helpful to promote the research on this novel 2D semiconductor.

Results and discussions
• Optical transmittance Thin InSe flakes are fabricated using mechanical exfoliation method from single crystal bulk InSe grown by the Bridgman method. [47] The InSe bulk crystal was firstly cleaved with Nitto tape (SPV 224) and then was transferred onto a Gel-film (WF 4 x 6.0 mil Gel-   Figure 1c (the top x-axis indicates the InSe thickness).
From the plot it is evident that the data, in the thickness range experimentally probed, follow a linear trend and we use linear regression to fit them. We find a slope of 1. dependence on the underlying substrate thickness, it is necessary to use the substrates with specific SiO2 thickness (in our case we provide a thickness color chart that will be valid for 270 nm SiO2/Si substrates).
• Optical contrast analysis The number of layers of InSe flakes that have been deposited on the SiO2/Si substrate can be further determined more accurately by quantitatively analyzing their reflection spectra. In Figure 3a, we show a schematic drawing of our four-media air/InSe/270 nm SiO2/Si optical system. The optical contrast (C) of the InSe flake on the SiO2/Si substrate can be calculated from the spectra measured on the bare substrate (Isub) and the one measured on the InSe flake (IInSe): The differential reflectance spectra are acquired in normal incidence with a modified metallurgical microscope (BA 310 MET-T, Motic) and experimental operation details have been described in our previous work. [17] The optical contrast of this kind of multilayer system can be also modelled with high accuracy using a Fresnel law-based model that takes into account the light reflected and where the subscript 0 refers to air, 1 to InSe, 2 to SiO2 and 3 to Si. Under normal incident The reflection Fresnel coefficient in a three media (the case of the bare substrate without being covered by InSe flake) is expressed as: Where sub index 0 is air, 1 is SiO2 and 2 is Si. Using equations (2) and (3), we can calculate the optical contrast by firstly calculating the reflected intensity of both situations as Then the optical contrast can be obtained through the following equation (5) that correlates the reflected intensity by the bare substrate (Rsub) with the reflected intensity by the InSe flake (RInSe) as: Interestingly, we found that using the thickness of the which the black line indicates the best fit to the present data points with the parameters are determined to be a = 3.25 ± 0.44 eV·nm 2 , b = 1.27 ± 0.01 eV. Our fit presents a good agreement with the results previously reported data in the literature. [28,34,35,[42][43][44][45] This is the authors' version (post-peer reviewed) of the following article: Q. Zhao

Conclusion
In summary, we have provided several fast and non-destructive complementary optical methods to evaluate the number of layer of thin InSe deposited on different substrates.
The results from the four proposed techniques are summarized in Table 1