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Ralfy Kenaz, Saptarshi Ghosh, Pradheesh Ramachandran, [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), Hadar Steinberg, Ronen Rapaport

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[Thickness Mapping and Layer Number Identification of Exfoliated van der Waals Materials by Fourier Imaging Micro-Ellipsometry](https://mdr.nims.go.jp/datasets/ce7fc56a-c0f5-40cb-9cbe-92fde83aafde)

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Thickness Mapping and Layer Number Identification of Exfoliated van der Waals Materials by Fourier Imaging Micro-EllipsometryThickness Mapping and Layer NumberIdentification of Exfoliated van der WaalsMaterials by Fourier ImagingMicro-EllipsometryRalfy Kenaz,* Saptarshi Ghosh, Pradheesh Ramachandran, Kenji Watanabe, Takashi Taniguchi,Hadar Steinberg, and Ronen Rapaport*Cite This: ACS Nano 2023, 17, 9188−9196 Read OnlineACCESS Metrics & More Article Recommendations *sı Supporting InformationABSTRACT: As performance of van der Waals heterostructuredevices is governed by the nanoscale thicknesses andhomogeneity of their constituent mono- to few-layer flakes,accurate mapping of these properties with high lateralresolution becomes imperative. Spectroscopic ellipsometry isa promising optical technique for such atomically thin-filmcharacterization due to its simplicity, noninvasive nature andhigh accuracy. However, the effective use of standardellipsometry methods on exfoliated micron-scale flakes isinhibited by their tens-of-microns lateral resolution or slowdata acquisition. In this work, we demonstrate a Fourierimaging spectroscopic micro-ellipsometry method with sub-5μm lateral resolution and three orders-of-magnitude faster dataacquisition than similar-resolution ellipsometers. Simultaneous recording of spectroscopic ellipsometry information atmultiple angles results in a highly sensitive system, which is used for performing angstrom-level accurate and consistentthickness mapping on exfoliated mono-, bi- and trilayers of graphene, hexagonal boron nitride (hBN) and transition metaldichalcogenide (MoS2, WS2, MoSe2, WSe2) flakes. The system can successfully identify highly transparent monolayer hBN, achallenging proposition for other characterization tools. The optical microscope integrated ellipsometer can also map minutethickness variations over a micron-scale flake, revealing its lateral inhomogeneity. The prospect of adding standard opticalelements to augment generic optical imaging and spectroscopy setups with accurate in situ ellipsometric mapping capabilitypresents potential opportunities for investigation of exfoliated 2D materials.KEYWORDS: spectroscopic ellipsometry, van der Waals materials, mechanical exfoliation, hexagonal boron nitride,transition metal dichalcogenides, thickness mapping, modelingINTRODUCTIONEver since mechanical exfoliation of single-layer graphene fromgraphite,1 the two-dimensional (2D) inventory has expandedconsiderably to include hexagonal boron nitride (hBN) andtransition metal dichalcogenides (TMDs) with strong in-planeand weak out-of-plane van der Waals (vdW) molecular bonds.In such vdW layered structures, thickness (and thus layernumber) is a crucial parameter for realizing many exotic effects,such as superconductivity,2 exciton and exciton-polaritonBose−Einstein condensation,3−5 generalized Wigner crystals,6tunnel barriers7,8 and exotic correlated states.9−20 Yet, anaccurate, fast and noninvasive method capable of performing insitu lateral mapping of angstrom-level thicknesses is stillmissing. To date, such layer numbers and their sub-nanoscalethicknesses are primarily estimated by optical microscopy, andsubsequently evaluated by Raman spectroscopy or atomic forcemicroscopy (AFM).21,22The effective thickness of a flake depends on multiple factorssuch as presence of physisorbed organic molecules and otherReceived: December 26, 2022Accepted: May 1, 2023Published: May 8, 2023Articlewww.acsnano.org© 2023 The Authors. Published byAmerican Chemical Society9188https://doi.org/10.1021/acsnano.2c12773ACS Nano 2023, 17, 9188−9196Downloaded via 220.150.145.156 on May 27, 2023 at 01:36:19 (UTC).See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.https://pubs.acs.org/action/doSearch?field1=Contrib&text1="Ralfy+Kenaz"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Saptarshi+Ghosh"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Pradheesh+Ramachandran"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Kenji+Watanabe"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Takashi+Taniguchi"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Hadar+Steinberg"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Hadar+Steinberg"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Ronen+Rapaport"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/showCitFormats?doi=10.1021/acsnano.2c12773&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsnano.2c12773?ref=pdfhttps://pubs.acs.org/doi/10.1021/acsnano.2c12773?goto=articleMetrics&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsnano.2c12773?goto=recommendations&?ref=pdfhttps://pubs.acs.org/doi/10.1021/acsnano.2c12773?goto=supporting-info&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsnano.2c12773?fig=tgr1&ref=pdfhttps://pubs.acs.org/toc/ancac3/17/10?ref=pdfhttps://pubs.acs.org/toc/ancac3/17/10?ref=pdfhttps://pubs.acs.org/toc/ancac3/17/10?ref=pdfhttps://pubs.acs.org/toc/ancac3/17/10?ref=pdfwww.acsnano.org?ref=pdfhttps://pubs.acs.org?ref=pdfhttps://pubs.acs.org?ref=pdfhttps://doi.org/10.1021/acsnano.2c12773?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://www.acsnano.org?ref=pdfhttps://www.acsnano.org?ref=pdfhttps://creativecommons.org/licenses/by/4.0/https://creativecommons.org/licenses/by/4.0/https://acsopenscience.org/open-access/licensing-options/adsorbents,23,24 air gaps at substrate−flake interfaces,25 as wellas exerted pressure that can alter bond length andconsequently the thickness.26 These along with differences ingradients of the attractive and lateral forces on the material andthe substrate,27 and anomalies due to tip−sample inter-actions28,29 are common causes for misinterpreting thethickness values using an AFM instrument, which might alsobe invasive especially in the more-accurate contact mode.30Optical microscopy provides a simpler way for estimating theexfoliated flake’s layer number, and not the actual thickness,based on the color contrast.21,31 However, it involvesuncertainties at times due to dependence on human cognition.Another challenge faced by optical microscopy is the hightransparency of mono- and few-layer hBN which makes theiridentification a challenging proposition (a maximum of 2.5%white-light contrast is achievable for monolayer hBN).32,33 Assuch, the layer number of an hBN flake is typicallycharacterized by Raman spectroscopy, as its thickness altersthe width and position of phonon modes in the Ramanspectra.32,33 However, the signal and its dependence onthickness is extremely weak, thus requiring long integrationtimes while also varying considerably among samples.32,33 Asfor graphene and TMDs, Raman spectroscopy is widelyaccepted as the ideal method for distinguishing among layernumbers,22,34,35 although exposing the material to varying laserpowers might result in increase in the lattice temperature bystrong optical absorption, which corresponds to shifts in theRaman frequencies.36,37Spectroscopic ellipsometry offers a noninvasive yet highlysensitive optical technique for accurate thickness measure-ments, relying on the incident light to penetrate through thepartially absorbing thin-film.38 The technique can also extractthe optical properties from 2D vdW materials.39,40 Spectro-scopic ellipsometry was successfully used in measuring variousthicknesses of highly transparent hBN with angstrom-levelprecision, from monolayers33 to much thicker flakes (>100nm).41 However, current spectroscopic ellipsometers arelimited to off-axis illumination for oblique angles of incidence,and even with integrated focusing optics, they cannot achieve aspot size smaller than ∼50 μm,42 thus rendering themunsuitable for mapping smaller lateral dimensions which aretypical of exfoliated vdW flakes.To counter this issue, imaging ellipsometers integrate opticalmicroscopy by addition of an objective lens and a 2D detectorarray to their hardware, increasing the lateral resolution to afew microns.41,43−48 However, this method is constrained to asingle wavelength at a single incidence angle at-a-timemeasurements, resulting in very long data acquisition timesfor spectrally and angularly resolved information,49 thus alsorequiring a very stable sample. Acquisition at multiple angles ofincidence is especially important for multilayered structuressince each angle traverses a different optical path, providingunique ellipsometric information that is crucial for optimizingsensitivity to the unknown parameters.38,50In this paper, we perform spectroscopic ellipsometrymeasurements on exfoliated micron-scale vdW flakes withour recently developed Fourier imaging spectroscopic micro-ellipsometry method.51 Our spectroscopic micro-ellipsometer(SME) integrates spectroscopic ellipsometry into genericoptical microscopy configuration, working in an on-axisconfiguration with a sub-5 μm lateral resolution (one order-of-magnitude higher compared to focused-beam spectroscopicellipsometers).42,52 Its high data acquisition rate allowsrecording broadband ellipsometric data at multiple angles ofincidence simultaneously at a given lateral position within afew seconds, making it at least three orders-of-magnitude fastercompared to imaging ellipsometers, improving the practicallyachievable level of sensitivity and accuracy in process.Utilizing these advantages of the SME, we demonstratehighly accurate, angstrom-level precise thickness mapping andconsequent layer number identification of exfoliated vdWflakes from different genres, including conductive graphene,various semiconductor TMDs and wide band gap dielectrichBN. Successful ellipsometric identification of a highlyFigure 1. (a) Schematic of the SME. WLS: White light source, FS: field stop, P: polarizer, C: compensator (quarter-wave retarder), M:mirror, DSM: D-shaped mirror, FP: Fourier plane, FPL: Fourier plane lens (on a flip mount - for interchanging between sample-imagingmicroscopy mode and the Fourier plane imaging ellipsometry mode), IL: imaging lens, A: analyzer (polarizer), SPG: spectrograph with a 2Ddetector array. (b) Multiple-angle reflection of polarized white light from the sample results in sample-dependent variations on thepolarization state per incident angle, namely, transformation of linear polarization E( )in to elliptical polarization E( )out . Previously measurednearby SiO2 thickness and the optical constants from the literature for the measured 2D material are used in the model for extraction of theflake thickness.ACS Nano www.acsnano.org Articlehttps://doi.org/10.1021/acsnano.2c12773ACS Nano 2023, 17, 9188−91969189https://pubs.acs.org/doi/10.1021/acsnano.2c12773?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsnano.2c12773?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsnano.2c12773?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsnano.2c12773?fig=fig1&ref=pdfwww.acsnano.org?ref=pdfhttps://doi.org/10.1021/acsnano.2c12773?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-astransparent monolayer hBN flake (0.32 nm thick) showcasesthe high sensitivity of the SME. In particular, we investigate thehomogeneity of exfoliated MoSe2 mono- and bilayers byaccurate mapping of the local thickness variations across theirmicron-scale surface areas with high lateral resolution. Suchmapping of in-plane homogeneity is crucial for estimatingthickness variations and deviation in optical properties arisingfrom localized strain, which can be identified by spectroscopicellipsometry exclusively.RESULTS AND DISCUSSIONThe schematic of the spectroscopic micro-ellipsometer(SME)51 and the illustration for the flake measurement areshown in Figure 1. High numerical aperture (NA) objectivelenses provide acquisition of more angular data up to higherangles of incidence, together with a better lateral resolution(smaller spot size), thus are preferred for the SME. Afterlocating the flake of interest under the objective lens (NA =0.9) of the SME in microscopy mode (see Figure 1a), the SMEis switched to ellipsometry measurement mode. Measurementsare performed first on the substrate just outside the peripheryof the flake and subsequently on the flake, obtaining thespectrally and angularly resolved spectroscopic ellipsometrydata of both points (or areas in case of mapping experiments).The thickness of the oxide layer in the vicinity of the flake isdetermined by the SME and is used in the model when fittingfor the thickness of the residing flake, as seen in Figure 1b, andis assumed to not fluctuate considerably under the flake (seeSupporting Information (SI) section S3). Next, depending onthe flake material, the complex refractive index values obtainedfrom refs 53−55 are used in the model, and the thickness ofthe flake is fitted for. The obtained thickness value of the flakeis used to determine the number of layers. Due to differentexperimental methods used in the literature to extract theoptical constants, they might not exactly coincide with those ofthe flakes measured by the SME. However, these possibledeviations in optical constants do not interfere with the abilityof the model to predict the number of layers of the measuredflakes.The optical microscope images of monolayer (1L), bilayer(2L) and trilayer (3L) graphene with illustrated 5 μm diameterSME measurement spots are shown in Figure 2a (these flakeswere also used in our previous work51). Figure 2b plots theSME data from a single measurement on the monolayergraphene, consisting of ellipsometric parameters Ψ and Δ at551 wavelength points between 500 and 775 nm, and at 52different angles of incidence between 30.50° and 60.50°. Thechange in light polarization reflected from the sample isrepresented by parameters Ψ and Δ (Ψ is related to theFigure 2. (a) Optical microscope images of monolayer (1L), bilayer (2L) and trilayer (3L) graphene flakes on 285 nm SiO2/Si withillustrated 5 μm diameter SME measurement spots. (b) Single-measurement SME data on the monolayer consisting of spectrally andangularly resolved Ψ and Δ values. The model is illustrated in the plot legend, with inputs of SME measured SiO2 thickness and grapheneoptical constants from the literature, resulting in best fit at the graphene thickness value of 0.32 nm. The same procedure is repeated forbilayer and trilayer graphene. (c) The parameter uniqueness plots by the SME for monolayer, bilayer and trilayer measurements pointing tographene thicknesses of 0.32 nm, 0.61 nm and 1.00 nm, respectively (RMSE: root-mean-square error). (d) The Raman spectra measured onthe same flakes confirm their mono-, bi- and trilayer natures measured by the SME.ACS Nano www.acsnano.org Articlehttps://doi.org/10.1021/acsnano.2c12773ACS Nano 2023, 17, 9188−91969190https://pubs.acs.org/doi/suppl/10.1021/acsnano.2c12773/suppl_file/nn2c12773_si_002.pdfhttps://pubs.acs.org/doi/10.1021/acsnano.2c12773?fig=fig2&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsnano.2c12773?fig=fig2&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsnano.2c12773?fig=fig2&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsnano.2c12773?fig=fig2&ref=pdfwww.acsnano.org?ref=pdfhttps://doi.org/10.1021/acsnano.2c12773?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asFigure 3. SME derived thicknesses of mono- (1L), bi- (2L) and trilayer (3L) flakes of (a) graphene, hBN, (b) MoS2, WS2, MoSe2 and WSe2.Figure 4. (a) Optical microscope image (contrast-enhanced for better visibility) of monolayer, bilayer and trilayer hBN with illustrated 5 μmdiameter SME measurement spots in blue, orange and yellow, respectively. (b) AFM image of the hBN flake with the red line marking thetransition from the monolayer hBN to the substrate and (c) the height profile of the red line showing a thickness of ∼0.4 nm, confirming themonolayer nature of the flake region. (d) The measured Raman spectra of the mono-, bi- and trilayer hBN. (e) The parameter uniquenessplots by the SME pointing to thickness results of 0.34 nm, 0.63 nm and 0.97 nm for monolayer, bilayer and trilayer hBN, respectively.ACS Nano www.acsnano.org Articlehttps://doi.org/10.1021/acsnano.2c12773ACS Nano 2023, 17, 9188−91969191https://pubs.acs.org/doi/10.1021/acsnano.2c12773?fig=fig3&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsnano.2c12773?fig=fig3&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsnano.2c12773?fig=fig3&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsnano.2c12773?fig=fig3&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsnano.2c12773?fig=fig4&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsnano.2c12773?fig=fig4&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsnano.2c12773?fig=fig4&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsnano.2c12773?fig=fig4&ref=pdfwww.acsnano.org?ref=pdfhttps://doi.org/10.1021/acsnano.2c12773?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asamplitude ratio between the s- and p-components of thepolarized light, whereas Δ is the phase difference betweenthem, see ref 51 for more details). Importantly, this whole setof data is acquired with just four exposures (at differentmeasurement polarization settings), in a total measurementtime of around 45 s (see Materials and Methods).The measured oxide thickness by the SME and the complexrefractive index of graphene obtained from ref 54 are used inthe model to fit for the flake thickness, as shown in Figure 2bfor the monolayer graphene. The same procedure is repeatedfor bilayer and trilayer graphene flakes. Figure 2c shows theparameter uniqueness plots for all three measurements,normalized to their corresponding minimum values. Theseplots represent the error (in normalized RMSE or root-mean-square error) between the experimental data and the modelwhen the model is scanned for the flake thickness parameter.The global minimum of each curve provides the best fitbetween the ellipsometric data (i.e., Ψ and Δ) and the model,which for the monolayer occurs at graphene thickness of 0.32nm. This is in good agreement with the theoretical thickness of0.34 nm for single-layer graphene.56 Similarly, thicknesses of0.61 and 1.00 nm are obtained for the bilayer and trilayergraphene respectively, again in agreement with the literature.28Each measurement on mono-, bi- and trilayer graphene isrepeated 10 times to demonstrate the instrumental accuracy ingraphene thickness results. Standard deviations of ∼0.02 nmare obtained for all the three sets of measurements. Finally, theRaman spectra of the same flakes are measured (with laserexcitation wavelength of 514.5 nm). Figure 2d plots thenormalized and vertically displaced (for better visibility)Raman spectra of the graphene flakes, confirming the findingsof the SME. The ∼2.5 peak intensity ratio of the 2D-band tothe G-band (I2D/IG) and the symmetric 2D-band at ∼ 2690cm−1 with a full width at half-maximum (FWHM) ∼ 33 cm−1provide an exclusive signature for monolayer graphene.57−59Similarly, I2D/IG ∼ 1.1, 0.67 intensity ratios and asymmetric2D-bands with FWHM ∼ 53, 62 cm−1 show the typicalfeatures of bilayer and trilayer graphene, respectively.58−60The same procedure performed on graphene is repeated onmono-, bi- and trilayer candidates of hBN, MoS2, WS2, MoSe2and WSe2 (the TMD flakes, measurements and Ramananalyses are elaborated in section S1 of the SI). Figure 3plots a summary of the measured thicknesses for all theexfoliated vdW flakes residing on 285 nm SiO2/Si substrates,where the bi- and trilayer flakes are expected to be integermultiples of the monolayer.61 As shown, very good agreementswith the single-layer thicknesses of 0.32 nm for hBN62 andindividual values between 0.6 and 0.7 nm for TMDs (MoS2 -0.67 nm,63,64 WS2 - 0.65 nm,65 MoSe2 - 0.7 nm66 and WSe2 -0.67 nm63,67) are found for 1L, 2L and 3L, as in the graphenemeasurements. All flakes are also analyzed by Ramanspectroscopy for their layer numbers, which show goodagreement with the SME results (see SI section S1 forTMDs). The thickness errors provided by the fit algorithm forall materials and all number of layers range from ±0.001 nm to±0.006 nm, two orders-of-magnitude smaller than the finalthickness values. As these numbers are too small to be visibleon the plot and also to have any effect on the final results, theyare considered negligible.A major aspect in the ellipsometry measurement of a flake’sthickness is understanding the thickness fluctuation of thesubstrate oxide layer, as the exact oxide thickness valueunderneath the flake may have an effect on its thickness resultthrough modeling and fitting of the ellipsometric data. Thisoxide thickness fluctuation was measured in our recent paper51on a same type of silicon wafer used in this work (see Materialsand Methods). The maximal fluctuation in the oxide thicknesswas measured to be ±0.21 nm. The error bars in measuredflake thicknesses resulting from this maximum oxide thicknessvariation are plotted (see Figure S6) and discussed in sectionS3 of the SI. As seen, they are found to be relatively small andnot interfering with the accuracy of layer number identi-fication.Among the flakes investigated, hBN holds specialimportance due to its high transparency (especially itsmonolayer) under optical microscope. An advantage of theSME over currently used methods is demonstrated byperforming thickness measurements of an exfoliated hBNflake residing on a silicon substrate with 285 nm SiO2, asshown in Figure 4. Incidentally, the mono-, bi- and trilayerswere found on a single flake at different locations as marked inthe optical microscope image in Figure 4a. The optical contrastof the image has been amplified considerably using imageprocessing tools to make the monolayer a bit more visible.However, it is to be noted that such tools are normallyunavailable with a stand-alone optical microscope generallyused for locating flakes, making the task rigorous. Even withsuch amplifications, the monolayer boundary is hardlydiscernible and only apparent in the AFM image in Figure4b. The normalized and vertically displaced Raman spectra ofthe hBN flakes are plotted in Figure 4d. The relatively low-intensity and noisy peak centered at ∼1369 cm−1 is the Ramansignature for monolayer hBN.32 Similar peak positions ofbilayer and trilayer hBN between 1365 and 1366 cm−1 weredemonstrated in the literature.32 These weak signals and tinyspectral shifts compared to their spectral widths inhibit Ramanspectroscopy from confidently distinguishing between bi- andtrilayers of hBN. In comparison, the AFM analysis performedon the monolayer hBN shows a thickness of ∼0.4 nm which isclose to the reported values, as seen in Figure 4c. However,evidently, the AFM height profile for the monolayer is alsonoisy and thus less reliable. Comparatively, the SME providesthickness results with much better confidence, as inferred fromthe parameter uniqueness plots shown in Figure 4e. The SMEclearly distinguishes between mono-, bi- and trilayers of hBNwith thickness results in agreement with integer multiples ofthe monolayer thickness of 0.32 nm.62 These results clearlydemonstrate the high sensitivity and superiority of thethickness measurements by the SME.To showcase the reliability and sensitivity of the SME formapping thickness variations of flakes, thickness mapping scanson monolayer and bilayer of MoSe2 are performed. Figure 5ashows the optical microscope image of the exfoliated MoSe2flake on 285 nm SiO2/Si substrate with monolayer and bilayerregions. The marked bilayer area of 20 × 20 μm2 is mappedwith a spot size of 5 μm and a step size of 2.5 μm (49 points),and the monolayer area of 7 × 9 μm2 is mapped with a stepsize of 1 μm (15 points). The local thickness variations in thebilayer and the monolayer mapping measurements are plottedin Figure 5b,c. The mean values of 1.266 and 0.603 nm withdeviations of ±0.04 nm and ±0.01 nm are obtained in themapping measurements of bilayer and monolayer areas,respectively. In order to understand the nature of thesethickness variations, repeatability measurements are performed10 times on the same points in bilayer and monolayer areas toobtain the instrumental thickness accuracy, resulting in aACS Nano www.acsnano.org Articlehttps://doi.org/10.1021/acsnano.2c12773ACS Nano 2023, 17, 9188−91969192https://pubs.acs.org/doi/suppl/10.1021/acsnano.2c12773/suppl_file/nn2c12773_si_002.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acsnano.2c12773/suppl_file/nn2c12773_si_002.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acsnano.2c12773/suppl_file/nn2c12773_si_002.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acsnano.2c12773/suppl_file/nn2c12773_si_002.pdfwww.acsnano.org?ref=pdfhttps://doi.org/10.1021/acsnano.2c12773?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asdeviation of ±0.005 nm for both layers. In addition, thicknessvariations that might be caused by the substrate oxidethickness fluctuations are found to be ±0.005 nm for bothmono- and bilayer MoSe2 (see SI section S3). Therefore, forboth mono- and bilayer mappings, the thickness variations mayoriginate from either the flake’s landscape or from the variationof the local optical properties as a result of localized strain68(reflected in the thickness results). A compressive strain can becaused by the PDMS assisted dry transfer of the flakes onto thesilicon wafer and is normally estimated through shifts of the E2g1mode in the flake’s Raman spectra.69,70 It is important to notethat the position-dependent thickness variations caused by thelateral inhomogeneity of the flake do not influence thequantization of layer numbers. This mapping of theinhomogeneity of an exfoliated vdW flake is exclusive forspectroscopic ellipsometry, which is successfully performed onthe micron-scale flake by the SME with high lateral resolutionand high accuracy (via the high data acquisition rate).Finally, the substrate-independent performance of ourmethod is proven with a number of measurements performedon exfoliated graphene, WS2 and hBN flakes residing on siliconwafers with a different SiO2 thickness of 90 nm, showingresults that are consistent and as accurate to those discussedabove (see section S2 of the SI).CONCLUSIONSIn this work, a fast and highly sensitive Fourier imagingspectroscopic micro-ellipsometry method with high lateralresolution and data acquisition rate is used for accuratethickness mapping and thus layer number identification ofvarious exfoliated vdW materials. The described apparatus canbe seamlessly integrated as an add-on unit with any experimentinvolving high lateral resolution spectroscopic imaging setup oroptical microscope, allowing for accurate in situ spectroscopicellipsometry measurements.Six different types of vdW materials are measured, and twodifferent substrates are used to prove the sample- andsubstrate-independent performance of the proposed method.The spectroscopic micro-ellipsometer (SME) could consis-tently identify among mono-, bi- and trilayers of theinvestigated materials with sub-angstrom precision. Especially,the SME could discretely identify monolayer hBN on 285 nmSiO2/Si substrate, which is a challenging proposition for othercharacterization techniques. Repeatability measurements per-formed on various flakes exhibited minimal uncertainty in layerthicknesses, quantizing the layer number reliably at everyiteration of measurement. Additionally, the lateral inhomoge-neity of a flake comprising of mono- and bilayer areas wasmapped to assess sub-angstrom thickness variations. Mappingsuch minute variations might provide opportunities tocorrelate thickness variations with local strain and with localmeasurements such as optical spectra and electrical transport.These results are a significant step toward an automatedsystem capable of mapping the thickness homogeneity andallocating the exact layer number to residing flakes within awafer area. Especially, the method can be used for locatingmonolayer hBN by automated scanning around other thinhBN flakes, as single-layer hBN tends to be found in their closeproximity. A sensitive mapping capability of optical homoge-neity with high lateral resolution should be useful for broadapplications in nanotechnology and nanoscience, such ascharacterizing vdW devices and nanoscale metamaterials,investigating crystal structure of nanoparticles and even forprobing of biological samples for variation of optical properties.MATERIALS AND METHODSSample Preparation. Various vdW materials were tape exfoliatedand transferred by polydimethylsiloxane (PDMS) assisted dry transfermethod onto silicon chips with a 285 nm SiO2 (P-type ⟨100⟩ primegrade silicon wafers from NOVA Wafers with a nominal thermal oxidethickness of 2850 Å).63 Based on the contrast under an opticalmicroscope, possible candidates for mono, bi- and trilayers wereidentified for graphene, hBN and TMDs (MoS2, WS2, MoSe2 andWSe2), to be eventually measured with the SME for their thicknesses.Finding candidates for monolayer hBN in optical microscope wasextremely challenging and required multiple iterations. Theinvestigated flakes were pre-annealed in forming gas before micro-ellipsometry measurements to remove surface adsorbents as well asthe entrapped water molecules between the flake and the substrate(150 °C for the TMDs, 300 °C for graphene and hBN). Organicadsorbates are normally trapped during PDMS assisted transfer offlakes onto silicon substrate and are squeezed into small pocketsthrough a self-cleaning effect.69 These are normally reflected as brightspots or wrinkles in the AFM images. However, as can be seen fromFigure 5. (a) Microscope image of an exfoliated MoSe2 flake with marked areas on bilayer (square) and monolayer (rectangle) regions. Thethickness mapping results by the SME of the (b) bilayer and (c) monolayer areas with respective (x1, y1) and (x2, y2) coordinates.ACS Nano www.acsnano.org Articlehttps://doi.org/10.1021/acsnano.2c12773ACS Nano 2023, 17, 9188−91969193https://pubs.acs.org/doi/suppl/10.1021/acsnano.2c12773/suppl_file/nn2c12773_si_002.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acsnano.2c12773/suppl_file/nn2c12773_si_002.pdfhttps://pubs.acs.org/doi/10.1021/acsnano.2c12773?fig=fig5&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsnano.2c12773?fig=fig5&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsnano.2c12773?fig=fig5&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsnano.2c12773?fig=fig5&ref=pdfwww.acsnano.org?ref=pdfhttps://doi.org/10.1021/acsnano.2c12773?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asFigure 4b, the hBN flake is devoid of such features and appear to beclean, implying the annealing process has removed the organicadsorbates.Spectroscopic Micro-Ellipsometry Measurements. At eachlateral measurement point, the SME takes four consecutive first-orderimages of the objective lens Fourier (back focal) plane at differentpolarization settings, providing spectrally and angularly resolvedreflection intensity information, which is then processed to calculatethe ellipsometric data of the area. In the current configuration of ourmicro-ellipsometer, a good signal-to-noise measurement on a 2Dmaterial flake is achieved at around 45 s. This measurement time caneasily be decreased to get closer to 10 s by using a stronger lightsource and/or a more sensitive detector array. Our work ondevelopment of the SME51 gives a detailed discussion on its operationprinciple, data acquisition method, and instrumental performance.The ellipsometric data obtained from the substrate in the vicinity ofthe flake is modeled as Air/SiO2/Si layered structure and fitted for theoxide thickness to obtain its exact value. Then the flake data ismodeled as Air/Flake/SiO2/Si layered structure, and the previouslymeasured SiO2 thickness value is used in the model. The thin-filmthickness measurement accuracy of the SME was reported to be inexcellent agreement with a commercial ellipsometer in our previouswork.51For modeling and fitting, WVASE and CompleteEASE ellipsometrydata analysis software (J.A. Woollam Co., Inc.) are used. Since just thethickness of the flake is fitted for in a simple layered structure,following building of the relevant model for the sample, the thicknessfitting is nearly instantaneous, namely, negligible compared to themeasurement time per position.Characterization with Raman Spectroscopy and AtomicForce Microscopy. The Raman measurements are performed byRenishaw InVia Confocal Raman Microscope instrument in abackscattering geometry. The excitation laser has a wavelength of514.5 nm and the laser spot size is around 1 μm when using a 50×objective lens.The AFM measurement is performed by the scanning probemicroscope NTEGRA from NT-MDT company in tapping mode, andthe results are analyzed by Nova PX software (NT-MDT).ASSOCIATED CONTENT*sı Supporting InformationThe Supporting Information is available free of charge athttps://pubs.acs.org/doi/10.1021/acsnano.2c12773.Experimental data of transition metal dichalcogenide(TMD) flakes on 285 nm SiO2/Si substrate and ofvarious flakes on 90 nm SiO2/Si, as well as a discussionon the effect of oxide thickness fluctuations of thesubstrate. (PDF)AUTHOR INFORMATIONCorresponding AuthorsRalfy Kenaz − Racah Institute of Physics, The HebrewUniversity of Jerusalem, Jerusalem 9190401, Israel;orcid.org/0000-0002-3123-8068; Email: ralfy.kenaz@mail.huji.ac.ilRonen Rapaport − Racah Institute of Physics, The HebrewUniversity of Jerusalem, Jerusalem 9190401, Israel;orcid.org/0000-0001-7435-7924;Email: ronen.rapaport@huji.ac.ilAuthorsSaptarshi Ghosh − Racah Institute of Physics, The HebrewUniversity of Jerusalem, Jerusalem 9190401, Israel;orcid.org/0000-0002-0581-4877Pradheesh Ramachandran − Racah Institute of Physics, TheHebrew University of Jerusalem, Jerusalem 9190401, Israel;orcid.org/0000-0002-8690-7767Kenji Watanabe − Research Center for Functional Materials,National Institute for Materials Science, Tsukuba 305-0044,Japan; orcid.org/0000-0003-3701-8119Takashi Taniguchi − International Center for MaterialsNanoarchitectonics, National Institute for Materials Science,Tsukuba 305-0044, Japan; orcid.org/0000-0002-1467-3105Hadar Steinberg − Racah Institute of Physics, The HebrewUniversity of Jerusalem, Jerusalem 9190401, Israel;orcid.org/0000-0002-7409-5087Complete contact information is available at:https://pubs.acs.org/10.1021/acsnano.2c12773NotesThe authors declare no competing financial interest.ACKNOWLEDGMENTSRonen Rapaport acknowledges support from the IsraeliScience Foundation Grants 836/17 and 1087/22, and fromthe NSF-BSF Grant 2019737. 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