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Yoshiaki Hattori, [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), Masatoshi Kitamura

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[Identification of the monolayer thickness difference in a mechanically exfoliated thick flake of hexagonal boron nitride and graphite for van der Waals heterostructures](https://mdr.nims.go.jp/datasets/865db048-5b2e-43d5-9338-7dda8e2c5a73)

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Identification of the monolayer thickness difference in a mechanically exfoliated thick flake of hexagonal boron nitride and graphite for van der Waals heterostructuresNanotechnologyPAPER • OPEN ACCESSIdentification of the monolayer thickness differencein a mechanically exfoliated thick flake ofhexagonal boron nitride and graphite for van derWaals heterostructuresTo cite this article: Yoshiaki Hattori et al 2023 Nanotechnology 34 295701 View the article online for updates and enhancements.You may also likeAdsorption and epitaxial growth of smallorganic semiconductors on hexagonalboron nitrideM Kratzer, A Matkovic and C Teichert-Direct growth of hBN/Grapheneheterostructure via surface deposition andsegregation for independent thicknessregulationWenyu Liu, Xiuting Li, Yushu Wang et al.-Fabrication and characterization of InSbnanosheet/hBN/graphite heterostructuredevicesLi Zhang, Yuanjie Chen, Dong Pan et al.-This content was downloaded from IP address 144.213.253.16 on 14/05/2023 at 02:21https://doi.org/10.1088/1361-6528/accf23https://iopscience.iop.org/article/10.1088/1361-6463/ab29cbhttps://iopscience.iop.org/article/10.1088/1361-6463/ab29cbhttps://iopscience.iop.org/article/10.1088/1361-6463/ab29cbhttps://iopscience.iop.org/article/10.1088/1361-6528/ac8994https://iopscience.iop.org/article/10.1088/1361-6528/ac8994https://iopscience.iop.org/article/10.1088/1361-6528/ac8994https://iopscience.iop.org/article/10.1088/1361-6528/ac8994https://iopscience.iop.org/article/10.1088/1361-6528/ac6c34https://iopscience.iop.org/article/10.1088/1361-6528/ac6c34https://iopscience.iop.org/article/10.1088/1361-6528/ac6c34https://googleads.g.doubleclick.net/pcs/click?xai=AKAOjsu97PsqXK6juzPJOdHSuMoLqCNQm6nLFvd2IKbQ8zi5jmuRYhoyQy8Fda0uvLu-8565t7qqLWknUW13smRgLbTcsiwyS7yhAy1es42QM9QywcDAmeHSguZ6vNtPt_Tk63G3z4leWc_GCgQ7CwpSRNp4oHonxBJD6MuZQYvfuiFqa1Ew78Ah7XG0isuImwce6C5Z5GP6ZSVgyTtOr8fzm47Q42kjXoBoDun6A5XdKWtK3txVXeLT61zbUNrBEKnDvFsjEHGQZ_iCK93aJHkNro50DtoZ1vdQ10bWNw3aXhgjnQ&sai=AMfl-YT1cDj7J8Id4h9BNaRMXh7c8O-Ig2LbnKCWQ26RV-KAu6fYhyi07Nk7t_yPiOxJ9b14TRtPvSyUj1ifbvQ&sig=Cg0ArKJSzEjdzVVy0YTs&fbs_aeid=[gw_fbsaeid]&adurl=https://www.edinst.com/products/Identification of the monolayer thicknessdifference in a mechanically exfoliated thickflake of hexagonal boron nitride and graphitefor van der Waals heterostructuresYoshiaki Hattori1,∗ , Takashi Taniguchi2, Kenji Watanabe3 andMasatoshi Kitamura1,∗1Department of Electrical and Electronic Engineering, Kobe University, 1-1, Rokkodai-cho, Nada, Kobe,657-8501, Japan2 International Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1Namiki, Tsukuba 305-0044, Japan3Research Center for Functional Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba305-0044, JapanE-mail: hattori@eedept.kobe-u.ac.jp and kitamura@eedept.kobe-u.ac.jpReceived 25 December 2022, revised 11 April 2023Accepted for publication 21 April 2023Published 9 May 2023AbstractExfoliated flakes of layered materials, such as hexagonal boron nitride (hBN) and graphite with athickness of several tens of nanometers, are used to construct van der Waals heterostructures. Aflake with a desirable thickness, size, and shape is often selected from many exfoliated flakesplaced randomly on a substrate using an optical microscope. This study examined thevisualization of thick hBN and graphite flakes on SiO2/Si substrates through calculations andexperiments. In particular, the study analyzed areas with different atomic layer thicknesses in aflake. For visualization, the SiO2 thickness was optimized based on the calculation. As anexperimental result, the area with different thicknesses in a hBN flake showed differentbrightness in the image obtained using an optical microscope with a narrow band-pass filter. Themaximum contrast was 12% with respect to the difference of monolayer thickness. In addition,hBN and graphite flakes were observed by differential interference contrast (DIC) microscopy.In the observation, the area with different thicknesses exhibited different brightnesses and colors.Adjusting the DIC bias had a similar effect to selecting a wavelength using a narrow band-passfilter.Supplementary material for this article is available onlineKeywords: hBN, graphite, 2D materials, optical interferometry, differential interference contrastmicroscopy(Some figures may appear in colour only in the online journal)1. IntroductionVan der Waals heterostructure devices constructed fromlayered materials of various substances have been studiedintensively because of their novel electrical and opticalproperties. Layered materials can obtain an atomically flat,ideal interface and a precisely controlled number of layers.NanotechnologyNanotechnology 34 (2023) 295701 (10pp) https://doi.org/10.1088/1361-6528/accf23∗ Authors to whom any correspondence should be addressed.Original content from this work may be used under the termsof the Creative Commons Attribution 4.0 licence. Anyfurther distribution of this work must maintain attribution to the author(s) andthe title of the work, journal citation and DOI.0957-4484/23/295701+10$33.00 Printed in the UK © 2023 The Author(s). Published by IOP Publishing Ltd1https://orcid.org/0000-0002-5400-8820https://orcid.org/0000-0002-5400-8820https://orcid.org/0000-0003-3701-8119https://orcid.org/0000-0003-3701-8119https://orcid.org/0000-0003-1342-4796https://orcid.org/0000-0003-1342-4796mailto:hattori@eedept.kobe-u.ac.jpmailto:kitamura@eedept.kobe-u.ac.jphttps://doi.org/10.1088/1361-6528/accf23https://doi.org/10.1088/1361-6528/accf23https://crossmark.crossref.org/dialog/?doi=10.1088/1361-6528/accf23&domain=pdf&date_stamp=2023-05-09https://crossmark.crossref.org/dialog/?doi=10.1088/1361-6528/accf23&domain=pdf&date_stamp=2023-05-09http://creativecommons.org/licenses/by/4.0Van der Waals heterostructured devices are composed of amonolayer or layered materials several ten-nanometer thick.The typical materials are graphene, hexagonal boron nitride(hBN), and transition-metal dichalcogenide. The hetero-structure is constructed by stacking exfoliated flakes usingmechanical transfer techniques [1–7].The exfoliated flakes are prepared from bulk crystals withadhesive tape [8]. After mechanical exfoliation, the flakes aretransferred to a substrate. Since a large number of flakes withdifferent size, shape, and thickness are placed randomly on asubstrate, appropriate flakes for constructing a heterostructureare found in them. Generally, a large and flat isolated flakewith the same number of layers is ideal for use in hetero-structures. However, an exfoliated flake often has areas withdifferent atomic layer thicknesses. In addition, residues oftapes for exfoliation are present on the flake surface. Thesedisturb the construction of ideal interfaces in a hetero-structure. Thus, an optical technique that can provide highcontrast for finding ideal flakes is required for constructing adesirable heterostructure.The presence of a flake of a layered material placed on asubstrate can be visualized by optical microscopy from thedifference between the reflection intensity from the flakesurface and the substrate surface. In the first paper onmechanically exfoliated graphene, a thermally oxidized Sisubstrate with 300 nm-thick SiO2 layer was employed for thevisualization [8]. The visibility of an atomically thin flakedepends on the thickness of SiO2 layer by optical interference,where a 90- or 300 nm-thick SiO2 provides a large differencein reflection intensity [9, 10]. Therefore, a thermally oxidizedSi substrate with a 90 or 300 nm-thick SiO2 layer has beencommonly used in layer materials research.The reflection intensity is discussed based on the reflectance(R) governed by interference effects. To visualize a flake of alayered material on a substrate, the optical contrast is defined asCn = (Rn − Rsub)/Rsub = ΔR/Rsub = Rn/Rsub − 1 where n isthe number of layers for the layered material, Rn is the reflec-tance for the surface of the flake, Rsub is the reflectance for thesurface of the substrate, andΔR = Rn − Rsub. Since Rn and Rsubdepend on wavelength (λ), the observation at a wavelength thatRsub is small leads to the visualization of a flake with highcontrast [9–20]. For a Si substrate with a 90 or 300 nm-thickSiO2 layer, Rsub is small in the visible wavelength range and∼10% at λ = ∼550 nm [9, 10]. When observing a flake ofn = 1–5, Cn increases linearly with n [13, 14]. Therefore, n canbe estimated from the Cn value obtained by the observation.Another issue is to observe the difference in n for a thickflake of n > 5. Although ΔR for a thick flake is large, it isdifficult to recognize the difference in n for a flake since(Rn − Rn−1)/Rn is small. Hence, (Rn − Rn−1)/Rn rather thanCn is a suitable definition of contrast for the difference in n fora thick flake. Therefore, to visualize the difference in n, thethickness of a SiO2 layer should be adjusted so that Rn issmall.Some groups have been studying the visualization of anultra-thin film using a substrate with low reflectance, such as aAu/SiO2/Si [11, 12, 16–18] or SiNx/Si substrate[15, 19, 20]. A monolayer (1 L) hBN flake can be visualizedwith high contrast using such a substrate. A transparent hBNflake with a 1 L thickness of 0.333 nm is generally difficult tovisualize. One of the groups realized the C1 = 12% for 1 LhBN using an optimized SiNx/Si substrate with Rsub = ∼0%at a certain λ. The C1 = 12% value is larger than C1 = 2.5%for an optimized SiO2/Si substrate with Rsub = ∼10% [15].For a hBN flake with n atomic layer thickness, an area with a1 L difference in the flake with high contrast might beobserved by adjusting Rn to zero. Therefore, a study thatintentionally reduces Rn to zero is needed to visualize an areawith a thickness difference of a few atomic layers in a thickhBN flake.This study investigated the visualization of thick hBNand graphite flakes placed on SiO2/Si substrates by opticalmicroscopy to visualize areas with different numbers oflayers in a thick flake. A flake with a thickness of 4–100 nmis called a thick flake in this study. This is because hBNflakes, approximately 30 nm in thickness, and graphiteflakes, a few nm in thickness, are used in van der Waalsheterostructure devices [21–26]. Thus, this study focused onvisualizing thick flakes. The thickness of the SiO2 layerplays an important role in the visualization of a flake. Thus,for optimizing the SiO2 thickness, the optical reflectance fora substrate with a flake was examined through calculations.In the experiment, hBN and graphite flakes were observedusing a narrow band-pass filter and by differential inter-ference contrast (DIC) microscopy. The images capturedwith a digital camera are discussed in terms of the colorpredicted from the calculation.2. Experimental methods2.1. Sample preparationFigure 1(a) shows a schematic diagram of a flake consistingof a layered material placed on a SiO2/Si substrate examinedin this study. Thermally oxidized n-type Si (100) substrates,the bulk hBN crystals grown at high pressure and temperature[27], and Kish graphite (Graphene Supermarket) were usedfor the samples. The Si substrate with a 95 nm-thick SiO2layer was cleaned by sonication in acetone for 5 min and2-propanol for 5 min. The SiO2 thickness was adjusted to20–77 nm by chemically etching the SiO2 surface in a 48 wt%HF solution diluted to 5 vol% with deionized water. Afterexposing the substrate to UV/ozone for 15 min for clearing,single crystal thin flakes of hBN or graphite were prepared bymechanical exfoliation using scotch tape (BK-12N, Scotch)and transferred immediately to the substrate. Although theideal isolated thick and flat flakes with the same number oflayers can be obtained by the preparation, flakes that haveatomic steps were focused to study the identification of themonolayer thickness difference in a flake.2.2. CharacterizationFigure 1(b) shows the setup for the optical observation offlakes on a substrate. A flake of hBN or graphite was2Nanotechnology 34 (2023) 295701 Y Hattori et alobserved through an objective of 50× with a numericalaperture (NA) of 0.8 (LU Plan 50×, Nikon) under light froma halogen lamp in an optical microscope (LV150, Nikon).The image was taken using a monochrome 12-bit camera(CS-63M, Bitran) cooled to 10 °C or a color 8-bit camera(EOS Kiss X4, Canon). Superior images were obtained byadjusting the aperture stop so that the light disk at theobjective back focal plane was ∼80% of that for fully open.This corresponds to a substantial reduction in NA. A narrowband-pass filter was inserted in the optical path to investigatethe wavelength dependence. The full width at half maximum(FWHM) of the narrow band-pass filter was 10 nm. Theexperimental contrast was calculated from the digital valuesin the image photographed by the monochrome camera[12, 15]. A flake was observed by DIC microscopy using twolinear polarizers and a Nomarski prism without a narrowband-pass filter. The linear polarizers were arranged on crossNicol. The DIC bias (Δ0) was adjusted by changing theposition of the Nomarski prism. The reflectance spectra weremeasured using a spectroscope (BTC-110S, B&W Tek)equipped at the trinocular head of the microscope. Since thespatial resolution of the microscopic measurement is practi-cally less than 3 μm, the reflectance of the area only inside theflake was measured. The morphology of the substrate surfacewas observed by atomic force microscopy (AFM, NanoNavi,SII) with a Si cantilever (SI-DF3-R, SII Nano-Technology,Japan) in tapping mode at room temperature in ambient air(50% relative humidity, ∼20 °C). The root-mean-squareroughness of the SiO2 surface was typically 0.2 nm. Thethickness of the SiO2 film was estimated from the spectraobtained by ellipsometry (Auto SE, Horiba) and reflectancespectroscopy.2.3. Calculation of optical contrastThe reflectance spectra and photographs were acquiredthrough an objective lens. Therefore, the oblique incidenceshould be considered in the calculation. Reflectance R(λ) at awavelength λ is expressed asRr r d1sin, , sin cos 1020p2s20( )( )(∣ ( )∣ ∣ ( )∣ ) ( )òlql q l q q q q=´ +qusing θ0 is defined by sin θ0 = NA. Here rp(λ, θ) and rs(λ, θ)are the complex reflectivities for the p and s components ofthe incident light tilted from the surface normal with an angleθ, respectively [14, 18, 28–30]. NA was set to 0.7 for allcalculations. rp(λ, θ) and rs(λ, θ) were calculated based on amultilayer model using the transfer matrix method [13]. Themultilayer structure was composed of an hBN or graphitefilm, a SiO2 film, and a Si substrate, as shown in figure 1(a).The refractive indices of hBN and graphite were set to 2.2 andFigure 1. (a) Calculation model of a 2D flake on SiO2/Si substrate flake with atomic thickness differences. (b) Schematic diagram of thesystem. (c) Schematic diagram of thickness dependence of reflectance spectra for hBN. The reflectance spectra shift to longer λ with anincrease in hBN thickness. (d) Contrast of a 1 L hBN flake on SiO2/Si substrate as a function of λ and dSiO2.3Nanotechnology 34 (2023) 295701 Y Hattori et al2.6−1.3i [9, 31] in the calculation, respectively, where i is animaginary unit.When the sample was photographed under a light passingthrough a narrow band-pass filter, the reflectance detected bythe camera corresponds to the reflectance averaged for λ inthe range of λ′ − λFWHM/2 to λ′ + λFWHM/2. λ′ is the centralwavelength of the filter, and λFWHM is the FWHM. Thus, thedetected reflectance R̄( )l can be approximated asR R d1. 2FWHM 22FWHMFWHM¯ ( ) ( ) ( )//òlll l=l ll l¢-¢+The contrast of a flake with an n-layer thickness with regardsto a substrate is defined as Cn = Rn/Rsub − 1, as described inthe introduction. Here, Rn is the reflectance for the flakesurface, and Rsub is the reflectance for the surface of thesubstrate. Thus, the spectrum of calculated contrast isexpressed as C R R 1n n sub( ) ( ) ( )/l l l= - [12, 15]. However,the contrast of the area with k-layer thickness in a thick flakewith n-layer thickness is defined by Ck′ = −(Rk/Rn − 1).Similarly, the spectrum of the contrast calculated for Ck′ isexpressed as C R R 1 .k k n( ) ( ( ) ( ) )/l l l¢ = - -The color simulation for micrographs was performedfrom R(λ). R(λ) was converted to XYZ color space using thefollowing equations:XKNR I x d a, 3( ) ( ) ¯ ( ) ( )ò l l l l=LYKNR I y d b, 3( ) ( ) ¯ ( ) ( )ò l l l l=LZKNR I z d c3( ) ( ) ¯ ( ) ( )ò l l l l=LwhereN I y d d, 3( ) ¯ ( ) ( )ò l l l=Lx ,¯ ( )l y ,¯ ( )l and z̄ ( )l are the CIE color matching functions; Λdenotes the integration on [380 nm, 780 nm]; I(λ) is theilluminant; K is a constant. The light source of a halogen lampwas assumed to be black-body radiation of 3500 K. K isadjusted and is proportional to the exposure time to reproducethe photograph. The X, Y, and Z values are converted to thestandard RGB values.3. Results and discussionFigure 1(c) presents a schematic diagram of the Rsub, R1,Rn−1, and Rn spectra for a flake with an n-layer thicknessshown in figure 1(a). The wavelength at which the spectrumhas the minimum shifts to a long wavelength as the atomiclayer thickness is increased [17, 18]. This study focused onvisualizing a hBN flake rather than a graphite flake. This isbecause the visualization of a hBN flake, which is opticallytransparent, is more complex than that of a graphite flake,which is not transparent. First, the contrast for a 1 L hBNflake on a SiO2/Si substrate was examined to visualize areaswith a 1 L difference in a thick hBN flake discussed below.Figure 1(d) shows the contrast calculated for a 1 L hBN flakeon SiO2/Si substrate (C1) as a function of λ and SiO2thickness (dSiO2) [10]. As defined in section 2.3, the contrastis given by C1 = R1/Rsub − 1. On a SiO2 film with athickness of 60–140 nm or 260–330 nm, the contrast isapproximately ±3% at a certain λ [9].The contrast for a thick hBN flake was next examined. Inparticular, this study focused on the contrast of a hBN flakewith dBN = 40 nm (n = 120) as an example. Figure 2(a)shows the Cn calculated as a function of dBN and λ for dSiO2= 90 nm. The Cn increased as dBN was increased and reachedthe maximum at dBN = ∼60 nm since the Rsub is constant,which was attributed to the increase in Rn. For dBN = 40 nm,Rsub, R120, and C120 are calculated to be 11.13%, 58.59%, and426.6% at λ = 500 nm, respectively. A hBN flake of dBN= 40 nm in an image taken at λ = 500 nm should be brighterthan the substrate on which the flake is placed since C120 is apositive value. Ifthe flake has an area of 1 L thinner, R119 andC119 are 58.38% and 424.8%, respectively. The difference ofR120 and R119 was 0.21%, which was 0.0037 of R120= 58.59%. Thus, it is difficult to visualize a 1 L difference if ageneral 8-bit camera with linear sensitivity to light intensity isused. The difficulty is explained as follows. An 8-bit dataimage gives 256 shades expressed by digital integers (D) of 0to 255. The D is a value of ctI(λ)R(λ) as an integer where c isa camera constant, and t is the exposure time. The value of(R120 − R119)/ R120, 0.0037, is close to 0.0039 = 1/256.Therefore, the D value for R119 is equal to or one less thanthat for R120. This causes difficulty in visualization. Asdescribed in section 2.3, −(Rk/Rn − 1) is suitable for quan-titatively evaluating the difference in atomic layer thickness ina flake. Thus, the contrast for the difference in atomic layerthickness in a thick flake is defined as Ck′ = −(Rk/Rn − 1).According to the definition, the contrast of a 1 L thicknessdifference is expressed as C’n−1 = − (Rn−1/Rn − 1).Figure 2(b) shows the C’n−1 calculated as a function of dBNand λ for dSiO2 = 90 nm. For dBN = 40 nm, the C’120−1 valuewas 0.37% at λ = 500 nm. Figures 2(a) and (b) show that aSiO2/Si substrate of dSiO2 = 90 nm is suitable for visualizinga thick flake. In contrast, the SiO2/Si substrate is unsuitablefor confirming the area with the difference in atomic layerthickness in the flake. Figures 2(c) and (d) show the Cn andC’n−1 for 20 nm-thick SiO2 as a function of dBN and λ. TheCn value for 20 nm-thick SiO2 is lower than that for 90 nm-thick SiO2 over a wide range, including dBN = 40 nm. Incontrast, the absolute value of C’n−1 for a 20 nm-thick SiO2 islarger than that for a 90 nm-thick SiO2 over a wide range. Inparticular, the C’120−1 value was 12.2% at λ = 500 nm. Thesmall R120 value of 0.78% contributes to the large C’120−1. Inaddition, the C120 value was 98% at λ = 500 nm, and a hBNflake of dBN = ∼40 nm should be observed. Thus, a SiO2/Sisubstrate of dSiO2 = 20 nm is suitable for visualizing the areawith the difference in atomic layer thickness in the flake.As the calculation results in the above paragraph, Rsuband Rn are essential factors for visualizing a flake and an areawith the difference in atomic layer thickness in the flake,respectively. Thus, the spectra of Rsub and Rn were measuredexperimentally. Figure 3 shows the spectra of Rsub and Rnobtained from measurement and calculation. The calculation4Nanotechnology 34 (2023) 295701 Y Hattori et alresults indicated by the light colors roughly reproduce theexperimental spectra for all cases. The solid dark green andblue lines in the figure indicate Rsub for dSiO2 = 20 nm and95 nm, respectively. Rsub for the 95 nm SiO2 film was smallerthan that for the 20 nm SiO2 film, as shown in figure 3. Thered and black lines show Rn for 41 nm hBN on a 20 nm SiO2film and 6.3 nm graphite on a 77 nm SiO2 film, respectively.The SiO2 thickness was optimized to realize small Rn. Rn for athick hBN and a graphite flake on the optimized SiO2/Sisubstrate is close to zero at a certain λ.Figure 4 presents the results obtained for a 45 nm (136 L)hBN flake on a 20 nm SiO2 film by optical microscopy andAFM. Figure 4(a) is a color image taken under white light. Aflake with a navy-blue color was observed. Figure 4(b) is amonochromatic image taken under light passing through aband-pass filter of λ = 530 nm, corresponding to the dottedarea in figure 4(a). Some steps are shown in figure 4(b). Thisresult indicates that using an appropriate band-pass filtercontributes to the visualization of steps. In addition, theexposure time for capturing the image was adjusted for Rn,Figure 2. Contrast as a function of dBN and λ. (a) and (b) present Cn and C’n−1 for dSiO2 = 90 nm, respectively. (c) and (d) present Cn andC’n−1 for dSiO2 = 20 nm, respectively.Figure 3. Reflectance spectra of Rsub with different dSiO2 and Rn forhBN and graphite. The solid lines of light and dark colors indicatethe experiment and calculation, respectively. Rn for a thick hBN andgraphite flake on the optimized SiO2/Si substrate is close to zero atcertain λ.5Nanotechnology 34 (2023) 295701 Y Hattori et albeing different from that for Rsub since Rsub is higher than Rn.As a result, the D of the area of the substrate saturates and isfully white in the image. Figure 4(c) shows an AFM heightimage corresponding to the area enclosed by the solid blackline in figure 4(b). Figure 4(d) shows the two height profilesalong the green lines labeled A and B in figure 4(b). The stepheight is 0.30 nm and 0.57 nm for lines A and B, respectively,corresponding to the thicknesses of 1 L and 2 L, respectively.Thus, the downside area for lines A and B is an area ofn = 135 and 134, respectively. Figure 4(b) presents themeasured n values. The steps can be recognized in an imagetaken using a commercial color camera. Figures 4(e) and (f)show color images observed under light through a band-passfilter of λ = 520 and 590 nm, respectively. These images havenot been processed by software. For λ = 520 nm, the area of136 L has a bright color compared with the surrounding area.For λ = 590 nm, the area of 136 L has a dark color comparedwith the surrounding area. The brightness and darkness areexplained by C’n−1, as shown in figure 2(d). At dBN = 45 nm,the C’n−1 value is positive at λ = 520 nm and negative atλ = 590 nm, corresponding to the brightness and darkness,respectively.Figure 5 shows the C’n−1 spectra for dSiO2 = 20 nmobtained by measurements and calculations. The red andblack plots represent the experimental spectra for dBN= 41 nm and 45 nm, respectively. The solid lines with a lightcolor, by calculation, roughly reproduce the experimentalspectra. The difference between calculation and experimentalspectra may be caused by scattering light from the sur-rounding thick flake. For dBN = 41 nm, the experimentalspectrum has the maximum |C’n−1| of 12% at 570 nm. TheC’n−1 value for a 1 L difference in thickness is comparable tothe contrast of a 1 L hBN flake on the antireflection of siliconnitride substrate [14]. When a desirable flake is found from alarge amount of exfoliated flakes on a substrate, the flakeoften has small fragments or tape residues on the surface. Thepresent technique can also visualize them (figure S1).For figure 5, the SiO2 thickness, dSiO2, is fixed at 20 nm.Next, the dependence of dSiO2 on C’n−1 based on calculationresults for the realization of a large contrast was investigated.The maximum |C’n−1| in a wavelength range is used toevaluate the contrast since the C’n−1 value depends on λ. Theobservation of a flake is often conducted in a visible wave-length range using a halogen lamp. Thus, the maximum|C’n−1| was defined in the range of 450–750 nm as themaximum contrast, C’max. The wavelength range of λ <450 nm was excluded because of the low luminance of ahalogen lamp and the low sensitivity of a common camera inthe range.Figure 6(a) shows C’max calculated as a function ofdSiO2 and dBN. A contour map is useful for optimizing dSiO2so a flat hBN flake with a desirable thickness can be found.For example, the optimized dSiO2 for a thick hBN flake withdBN = ∼40 nm is approximately 20 nm. Thus, SiO2/Si sub-strates of dSiO2 = 20 nm were used in the experiment, asshown in figures 4 and 5. The λ for the maximum |C’n−1|depends on dSiO2 and dBN, where the white dotted linesindicate the contour lines. The dependence of λ is shown infigure S2. The map of the λ exhibits discontinuity since λ forFigure 4. Characterization of a 45 nm hBN flake on 20 nm SiO2 film.(a) Color photograph with white light. (b) Monochromatic image atλ = 530 nm, which corresponds to the dotted area in (a). (c) AFMheight image corresponding to the black line area in (b). (d) Heightprofile along the solid green lines in (b) or (c). (e) and (f) Colorphotographs at λ = 520 and 590 nm, respectively.Figure 5. Contrast spectra of C’n−1 of different dBN fordSiO2 = 20 nm. The dots and solid lines indicate the experiment andcalculation, respectively.6Nanotechnology 34 (2023) 295701 Y Hattori et alC’max is limited in the range of 450–750 nm. Figure S3 showsthe C’n−1 spectra for a certain dBN.A consumer color camera is often used when a hBN flakewith a desirable thickness is found. The color in an image of ahBN flake captured by a color camera can be predicted bycalculations. Such a predicted color is useful for finding ahBN flake. Figure 6(b) represents a color map calculated for ahBN flake on a SiO2/Si substrate as a function of dBN anddSiO2. The color gradually changes with dBN and dSiO2. Thecolor at dBN = 0 corresponds to that of the SiO2/Si substrate.For example, the color for dSiO2 = 20 nm is a wheat color atdBN = 0 and a navy color at dBN = 45 nm. The thicknesscorresponds to the sample shown in figure 4(a). The calcu-lated color roughly reproduces the color in the image capturedwith the actual digital camera. The data of C’max and colorsimulation of hBN for thicker SiO2 are shown in figure S4.A narrow band-pass filter enables the visualization of a 1L thickness difference in a thick hBN flake, as shown infigure 4(b). In this technique, a band-pass filter with theappropriate λ for dBN of a hBN flake was selected. Anothertechnique that does not require a narrow band-pass filter wasproposed. A DIC microscope also enables the visualization of1 L thickness difference. Figure 1(b) presents the setup forDIC microscopy. The optical components installed on acommercial reflected microscope were used for DICmicroscopy.Figures 7(a)–(c) shows an image of a 45 nm hBN flakeon 20 nm SiO2 film observed under white light using a DICmicroscope with different DIC bias, Δ0. The flake is the sameas that for figure 4. The observed color of the flake andsubstrate depends on Δ0, which an operator can adjust. Thecolor of the flake is black for Δ0 = 0, blue for Δ0= ∼750 nm, and wine-red for Δ0 = ∼300 nm. Figures 7(b)and (c) show that the flake has some areas colored with dif-ferent colors shown in figures 4(e) and (f). This result indi-cates the presence of atomic steps.Generally, DIC microscopy converts the gradient (Δ1) ofthe refractive index and/or the optical path length in anobservation specimen into intensity in an image. Therefore,when a thick hBN flake on a substrate is observed by DICmicroscopy, edges with thickness differences are highlightedin an image. The flake and substrate colors are black infigure 7(a) for Δ0 = 0. By contrast, the edges of thicknessdifference for the flake and wrinkles are highlighted by thewhite and yellow lines because of the large Δ1, respectively.Therefore, the shape of the thick hBN flake is recognized bythe white shape outlines. However, the presence of atomicsteps cannot be recognized in the image since the highlightedFigure 6. (a) Maximum |C’n−1| in the range of 450–750 nm as afunction of dBN and dSiO2. (b) Color simulation of hBN on a SiO2/Sisubstrate as a function of dBN and dSiO2.Figure 7.DIC microscopy of a 45 nm hBN flake on 20 nm SiO2 film.DIC photographs at Δ0 = 0 (a), 750 (b), and 300 nm (c). The flake isthe same as for figure 4. The atomic steps are visualized in DICmicroscopy without a band-pass filter by appropriate DIC bias. (d)Color simulation of hBN in the DIC image for dSiO2 = 20 nm as afunction of dBN and Δ0.7Nanotechnology 34 (2023) 295701 Y Hattori et allines of the atomic step edge were not observed. This resultsuggests that Δ1 of 1 L hBN is insufficient to change theintensity in the DIC image.DIC bias colorizes the flake and substrate in addition tothe highlighted lines of the thickness difference. The color ofthe flake and substrate in figure 7(c) for Δ0 = ∼300 nm iswine-red and yellow, respectively. Furthermore, the edges oflarge thickness differences are also highlighted in the image.The white edge lines in figure 7(a) were changed to green bythe DIC bias in figure 7(c). These colors that depend on Δ0are interference colors. In addition, DIC bias visualizes theatomic steps. Unlike the steps of large thickness difference,the presence of atomic steps can be recognized in figures 7(b)and (c) by the color difference, not outlines (figure S5). In thiscase, the color difference in atomic steps might be attributedto the sum of differences in R(λ) at various λ, as shown infigures 1 and 2. Thus, the color of the substrate and flake weresimulated. The intensity of each λ is dominated by Δ0 and R(λ), where the effect of Δ1 is included in R(λ). The lightintensity detected by a camera, IDIC(λ, Δ0), can be expressedby [32]I ctI R, sin . 4DIC 0 020( ) ( ) ( ) ( ) ( )/l D l l pD l=The light intensity with λ is zero at Δ0 = λl (l = 0, 1, 2, K).Therefore, a Nomarski prism is an optical component thatcontinuously tunes the light source spectrum with a trigono-metric function by the DIC bias. Consequently, images of aflake with colors depending on atomic layer thickness wereobtained by adjusting the DIC bias instead of using a band-pass filter.Figure 7(d) shows the color simulation of hBN in theDIC image for dSiO2 = 20 nm as a function of dBN and Δ0.The color for dBN = 0 corresponds to that for the substrate.The color was obtained using equation (4). The colorscorresponding to the substrate and the hBN flake infigures 7(b) and (c) are marked with red circles. The colorsobtained by the calculation are approximately the exper-imental colors in figures 7(b) and (c). The DIC bias of Δ0enhances the light of λ = Δ0/(l + 1/2) and weakens the lightof λ = Δ0/l. The DIC bias of 750 and 300 nm enhances 500and 600 nm light, respectively. The enhanced of λ = 500 nmis close to the wavelength of 540 nm for the maximumpositive contrast in figure 5. Consequently, the camera atΔ0 = 750 nm mainly detects light in the range of the positivecontrast and generates a similar image of figure 4(e). Simi-larly, the image at Δ0 = 300 nm can be explained.A similar investigation with a hBN flake on a SiO2/Sisubstrate of dSiO2 = 20 nm was also conducted for a graphiteflake on a SiO2/Si substrate of dSiO2 = 77 nm. Figures 8(a)and (b) show the photographs of a graphite flake with areas ofvarious thicknesses taken under white light and λ = 490 nmillumination, respectively. For the flake, the minimum dif-ference in the atomic layer thickness was 2 L. The step on thesurface of the graphite was observed compared with that ofthe hBN flake with a 2 L difference in figure 4(b). The clearobservation was attributed to the extinction coefficient in therefractive index of graphite [9]. Figure 8(c) shows the contourmap of C’n−1 for 77 nm SiO2 film as a function of dBN and λ.The |C’n−1| value for graphite is larger than that for hBN. TheC’n−1 for dgra > 5.5 nm and dgra < 5.5 nm is positive andnegative at λ = 490 nm, respectively. This explains thecontrast pattern in figure 8(b), where the brightness at theposition of 14 L (4.66 nm) and 20 L (6.66 nm) is higher thanthat of 16 L (5.33 nm) and 18 L (6.00 nm). Note that thepositive and negative contrast region in the contour map forC’n−2 is similar to that for C’n−1 (figure S6). Figure 8(d)shows the experimental C’n−1 spectrum for the differentgraphite flake of dgra = 4.66 nm having a 1 L thickness dif-ference with calculations. The black dots for the experimentindicate an enhancement of the contrast of 33% atλ = 510 nm, which is reproduced with the calculationrepresented with the solid line. Figure 8(e) shows the calcu-lated C’max as a function of dgra and dSiO2. The SiO2/Sisubstrate of dSiO2 = ∼75 nm is suitable for finding a flatgraphite flake with dgra = ∼5 nm. Figure 8(f) shows thesimulated color for graphite on SiO2/Si substrate as a func-tion of dgra and dSiO2. The color of the graphite and substrateis approximated with the simulation.4. ConclusionsWe attempted the visualization of thick hBN and graphiteflakes on SiO2/Si substrates, particularly the area with dif-ferent thicknesses. The reflectance of a thick flake on SiO2/Sisubstrate depends on the SiO2 thickness, and approaches zeroat a certain λ by adjusting the SiO2 thickness with respect tothe flake thickness. The reflectances of 41 nm hBN on 20 nmSiO2 and 6.3 nm graphite on 77 nm SiO2 were close to zero atλ = ∼530 nm. At the wavelength that the reflectance from anarea of a flake is close to zero, the contrast is sensitive to thethickness difference. Therefore, the difference in the atomiclayer thickness in the flake was visualized. The contrastspectra of a 1 L thickness difference were measured usingnarrow band-pass filters of various λ. The maximum absolutecontrast measured for a 1 L difference in thickness was 12%and 33% for 41 nm hBN on 20 nm SiO2 at λ = 570 nm and4.3 nm graphite on 77 nm SiO2 at λ = 510 nm, respectively.The high contrast is sufficient to evaluate the atomic thicknessdifference with a consumer eight-bit color camera.A rapid inspection technique that does not use a band-pass filter was proposed. Using the conventional setup ofDIC microscopy, the same h-BN flake on 20 nm SiO2 filmwas observed under white light illumination. The colors ofthe substrate and flakes in the DIC image are determinedmainly by the DIC bias and R(λ) because of the small dif-ference in the optical path length corresponding to the 1 Ldifference in thickness in the flake. In this case, DIC biasserves as an adjustable band-pass filter and restricts a lightsource spectrum to the wavelength determined by a trigo-nometric function. Therefore, the differences in atomicthickness were visualized similarly because of the sum ofthe difference in R(λ) for various λ. The colors of thesubstrate and flake in the photographed image wereapproximated by the calculation.8Nanotechnology 34 (2023) 295701 Y Hattori et alGenerally, thick exfoliated flakes used for van der Waalsheterostructures are obtained on a Si substrate with a ∼90 or∼300 nm SiO2 layer. This study shows that optimizing theSiO2 thickness instead of using a SiO2 layer with such athickness contributes to selecting a desirable flake from alarge number of exfoliated flakes on the substrate. The SiO2thicknesses optimized for ∼40 nm hBN and ∼5 nm graphitewas ∼20 and ∼75 nm, respectively. The hBN and graphiteflakes had purple and dark red-purplish colors in the digitalcamera image. The proposed observation technique is usefulfor constructing ideal van der Waals heterostructures.AcknowledgmentsThis work was partly supported by JSPS KAKENHI GrantNumbers 21K04195, 21H04655, Kansai Research Founda-tion, Chubei Itoh Foundation, Iketani Science andFigure 8. Characterization of the graphite flake on 77 nm SiO2 film. (a) and (b) Color photograph of white light and λ = 490 nm,respectively. The numbers in (a) indicate the layer number. (c) C’n−1 as a function of dBN and λ for dSiO2 = 77 nm. (d) Contrast spectra ofC’n−1 of different dGra for dSiO2 = 77 nm. The dots and solid lines indicate experiment and calculation, respectively. (e) Maximum |C’n−1| inthe range of 450–750 nm as a function of dGra and dSiO2, where the white dotted lines indicate the contour lines. (f) Color simulation ofgraphite on SiO2/Si substrate as a function of dGra and dSiO2.9Nanotechnology 34 (2023) 295701 Y Hattori et alTechnology Foundation, and Hyogo Science and TechnologyAssociation.Data availability statementAll data that support the findings of this study are includedwithin the article (and any supplementary files).ORCID iDsYoshiaki Hattori https://orcid.org/0000-0002-5400-8820Kenji Watanabe https://orcid.org/0000-0003-3701-8119Masatoshi Kitamura https://orcid.org/0000-0003-1342-4796References[1] Yao J D and Yang G W 2021 All-2D architectures towardadvanced electronic and optoelectronic devices Nano Today36 101026[2] Wang L, Huang L, Tan W C, Feng X, Chen L, Huang X andAng K-W 2018 2D photovoltaic devices: progress andprospects Small Methods 2 1700294[3] Zhou Y, Xu W, Sheng Y, Huang H, Zhang Q, Hou L,Shautsova V and Warner J H 2019 Symmetry-controlledreversible photovoltaic current flow in ultrathin All 2Dvertically stacked graphene/MoS2/WS2/graphene devicesACS Appl. 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Introduction 2. Experimental methods 2.1. Sample preparation 2.2. Characterization 2.3. Calculation of optical contrast 3. Results and discussion 4. Conclusions Acknowledgments Data availability statement References