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[Bo Da](https://orcid.org/0000-0002-0785-8662), [Jiangwei Liu](https://orcid.org/0000-0003-2580-7401), Mahito Yamamoto, Yoshihiro Ueda, Kazuyuki Watanabe, Nguyen Thanh Cuong, Songlin Li, [Kazuhito Tsukagoshi](https://orcid.org/0000-0001-9710-2692), [Hideki Yoshikawa](https://orcid.org/0000-0002-7389-8865), [Hideo Iwai](https://orcid.org/0000-0002-0250-4937), [Shigeo Tanuma](https://orcid.org/0000-0003-2628-9941), Hongxuan Guo, Zhaoshun Gao, Xia Sun, Zejun Ding

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[Virtual substrate method for nanomaterials characterization](https://mdr.nims.go.jp/datasets/3e86e1c1-3034-4e33-b4bd-3b3872296ffe)

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Virtual substrate method for nanomaterials characterizationARTICLEReceived 5 Oct 2016 | Accepted 14 Apr 2017 | Published 26 May 2017Virtual substrate method for nanomaterialscharacterizationBo Da1,2,3, Jiangwei Liu1, Mahito Yamamoto4, Yoshihiro Ueda5, Kazuyuki Watanabe5, Nguyen Thanh Cuong1,4,Songlin Li4, Kazuhito Tsukagoshi4, Hideki Yoshikawa2, Hideo Iwai2, Shigeo Tanuma2, Hongxuan Guo6,Zhaoshun Gao7, Xia Sun8 & Zejun Ding8Characterization techniques available for bulk or thin-film solid-state materials have beenextended to substrate-supported nanomaterials, but generally non-quantitatively. This isbecause the nanomaterial signals are inevitably buried in the signals from the underlyingsubstrate in common reflection-configuration techniques. Here, we propose a virtualsubstrate method, inspired by the four-point probe technique for resistance measurement aswell as the chop-nod method in infrared astronomy, to characterize nanomaterials withoutthe influence of underlying substrate signals from four interrelated measurements.By implementing this method in secondary electron (SE) microscopy, a SE spectrum(white electrons) associated with the reflectivity difference between two different substratescan be tracked and controlled. The SE spectrum is used to quantitatively investigate thecovering nanomaterial based on subtle changes in the transmission of the nanomaterial withhigh efficiency rivalling that of conventional core-level electrons. The virtual substrate methodrepresents a benchmark for surface analysis to provide ‘free-standing’ information aboutsupported nanomaterials.DOI: 10.1038/ncomms15629 OPEN1 International Center for Young Scientists, National Institute for Materials Science, Tsukuba, Ibaraki 305-0047, Japan. 2 Surface Chemical Analysis Group,Nano Characterization Unit, National Institute for Materials Science, Tsukuba, Ibaraki 305-0047, Japan. 3 Magnet Materials Group, Center for MaterialsResearch by Information Integration, National Institute for Materials Science, Tsukuba, Ibaraki 305-0047, Japan. 4 International Center for MaterialsNanoarchitectonics, National Institute for Materials Science, Tsukuba, Ibaraki 305-0044, Japan. 5 Department of Physics, Tokyo University of Science,Tokyo 162-8601, Japan. 6 Center for Nanoscale Science and Technology, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA.7 National Institute for Materials Science, Tsukuba, Ibaraki 305-0047, Japan. 8 Department of Physics, University of Science and Technology of China, Hefei,Auhui 230026, China. Correspondence and requests for materials should be addressed to B.D. (email: DA.Bo@nims.go.jp) or to H.Y.(email: YOSHIKAWA.Hideki@nims.go.jp) or to S.T. (email: TANUMA.Shigeo@nims.go.jp).NATURE COMMUNICATIONS | 8:15629 | DOI: 10.1038/ncomms15629 | www.nature.com/naturecommunications 1mailto:DA.Bo@nims.go.jpmailto:YOSHIKAWA.Hideki@nims.go.jpmailto:TANUMA.Shigeo@nims.go.jphttp://www.nature.com/naturecommunicationsNanomaterials are materials at the smallest scale andnear the forefront of research in natural sciences.Nanomaterials show great potential to revolutionizeindustry, medicine and computing, and improve our under-standing and conservation of nature. Various types of nanoma-terials have been subjected to many chemical and physicalanalyses typically applied to bulk or film solid-state materials1–3.However, most of these analysis tools are unsuitable for substrate-supported nanomaterial samples because of the influence ofunderlying substrate signals, particularly for techniques usingreflection configuration4. Even electron-based approaches,represented by surface analysis techniques such as X-rayphotoelectron spectroscopy and Auger electron spectroscopy(AES), whose probing depths are at the nanoscale level, have beenlimited by this problem. Surface analysis techniques, whichtypically use reflection configuration are powerful tools toquantitatively obtain elemental composition and chemical-stateinformation of materials5–7 and have been applied to intactsubstrate-supported nanomaterial samples8–10. Not surprisingly,only qualitative information about nanomaterials can be obtainedusing traditional operating procedures because of the influencefrom substrate signals. Such a substrate contribution cannotsimply be removed by purposely decreasing the probing depth,because doing this causes the obtained information to be relatedto the properties of the surface atomic layer of the nanomaterial,rather than the overall properties of the entire nanomaterial.Generally, the overall properties of the entire nanomaterial canonly be measured by techniques using transmission configu-ration. Therefore, for techniques using reflection configuration,there is a need for a new method that is able to obtaininformation about entire nanomaterials without influencefrom substrate signals even when the nanomaterial is supportedby a substrate.The method that is currently most widely used to extractnanomaterial information from measurements obtained forsubstrate-supported nanomaterial samples can be summarizedas a two-point probe method, in which traditional data-processing techniques, such as spectrum subtraction and ratioing,are applied to two interrelated spectra measured for a coveringnanomaterial and bare substrate to highlight the spectral featuresrelated to the nanomaterial. However, using a two-point probemethod, the influence from substrate signals can only beweakened rather than completely removed, so the informationobtained about a nanomaterial is not quantitative. Indeed, eventhe influence from substrate signals can be completely removed,electron-based surface analysis techniques face one moreproblem; that is, strong secondary electron (SE) background atlow energies. Regardless of the sample size, the strong intensity ofSEs generally observed in spectra measured below 50 eV results ina lack of spectral features because of the SE cascade. Althoughsignals at such low energies should be the best platform to studyelectron–electron (e–e) interactions in materials and hold greatpotential to characterize materials11,12, they are completely buriedin the strong SE background. To quantitatively understande–e interactions and characterize materials, the first step is toextract useful information from the SE signals. However, this stepis particularly difficult for a two-point probe method where weakfeatures in core-level signals are identified against backgroundwith the naked eye. There is a growing consensus that it isimpossible to extract pure nanomaterial information particularlyat low energies from just two spectra using simple algebrawithout any prior knowledge about distinguishing spectralfeatures. Because the two-point probe method cannot providequantitative information about a nanomaterial, it seems that amethod with more probe points, like the four-point probemethod, may overcome this limitation. In fact, the feasibility ofthis logic has been demonstrated in various fields; for instance,the four-point probe method has been successfully implementedin materials science to precisely determine the electrical resistanceof solid-state matter by excluding contributions from parasiticcontact resistances13, and also in radio astronomy as thechop-nod method14 to detect faint astronomical sources byground-based telescopes despite the bright, variable skybackground. Learning from these successful examples, werealize that the four-point probe method could be a trigger formore efficient use of electron-based surface analysis techniqueson nanomaterials.In this work, we propose the virtual substrate method, which isan extension of the four-point probe method to nanomaterialsscience, to study substrate-supported nanomaterials withoutinfluence from substrate signals even at low energies. Using thevirtual substrate method in electron-based surface analysistechniques, the equivalent transmission configuration experimentcan be realized from a combination of four interrelatedmeasurements in reflection configuration. Furthermore, uncou-pling our reliance on core-level signals, the virtual substratemethod enables us to extract information from seeminglyfeatureless spectra. Therefore, the full energy range (white)spectrum, mainly including SEs, can be treated as a usefulsignal. This perspective is quite different from the establishedsurface analyses that target characteristic peaks in a narrow-rangespectrum.ResultsThe concept of the virtual substrate method. Although thevirtual substrate method is not restricted to surface analysis, theimplementation of this principle shown in Fig. 1 is based onsurface electron spectroscopy techniques. The raw spectrarepresent the evolution of a primary electron beam inside asample driven by the interaction of the sample with movingelectrons. From the viewpoint of mathematics, the energy spec-trum J0(E) of a normally incident electron beam can be describedby a special vector with one non-zero element representing theincident electron energy. First, a measurement of a bare substrate(substrate A) is considered, where the substrate acts as thescatterer that emits the reflected electrons and SEs. Such a processis essentially a modification of J0(E), transforming themonochromatic incident electrons into the emitted whiteelectrons. Therefore, the scattering process can be described bythe matrix R, and the reflected spectrum from the substrate canbe written as JS(A)(E)¼RJ0(E).Next, we consider the case where a nanomaterial is placed onthe top of the substrate, which is also the configuration used forconventional reflection spectroscopy. The electron beam is firstincident on the nanomaterial and produces SEs and partiallyreflected electrons, which can be described by the material-dependent matrix RN, so the reflection spectrum can be denotedas RNJ0(E). In addition to this reflection process, a transmissionprocess also occurs, which is denoted by the material-dependentmatrix TN. These transmitted electrons with spectrum TNJ0(E)then interact with the underlying substrate and lead to thereflected spectrum RTNJ0(E). These substrate-reflected electronssubsequently pass through the nanomaterial on the top ofthe substrate, creating the new spectrum TNRTNJ0(E). In thiswork, we only consider the approximation to the first order;that is, we neglect any further reflection between the nanomaterialand substrate. Furthermore, we can approximate TN as unityfor high-energy incident electrons (the first TN starting fromthe right in TNRTNJ0(E)), which physically corresponds to thecomplete transmission of high-energy electrons through theultra-thin nanomaterial. Therefore, the measured spectrum forARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms156292 NATURE COMMUNICATIONS | 8:15629 | DOI: 10.1038/ncomms15629 | www.nature.com/naturecommunicationshttp://www.nature.com/naturecommunicationsa nanomaterial on a substrate can be written asJN Að Þ Eð Þ ¼ RNJ0 Eð ÞþTNRJ0 Eð Þ: ð1ÞPhysically, this means that in a single measurement (that is,conventional reflection measurement), the obtained spectrum forthe substrate-supported nanomaterials include contributionsfrom several sources: (i) RNJ0(E), the reflection from thenanomaterial and typically SEs originating from the interactionof the high-energy monochromatic incident electrons and thenanomaterial and (ii) TNRJ0(E), the transmitted spectrumoriginating from the substrate-reflected electrons RJ0(E). Thisgreatly complicates the data processing and prevents extraction ofthe full information of the target nanomaterials. In a traditionaltwo-point probe measurement (represented by the processesinside the red dashed box in Fig. 1a), measurements areperformed on both the substrate and substrate-supportednanomaterial. For the reasons discussed above, the substratereflection is measured separately and the second term in equation(1) can be written as TNJS(A)(E). Thus, we will haveJN Að Þ Eð Þ ¼ RNJ0 Eð ÞþTNJSðAÞ Eð Þ; ð2Þwhere JN(A)(E) and JS(A)(E) are the measured spectra for thesubstrate-support nanomaterial and bare substrate, respectively.RN and TN are the reflection and transmission matrices for thenanomaterial, respectively. These matrix elements are quantita-tively linked to the e–e interaction. Therefore, by solving RN andTN using linear equations, we can obtain complete informationabout the target nanomaterial.However, even neglecting all off-diagonal elements of TN (thatis, for an ultrathin nanomaterial such as mono- or bilayergraphene), the number of unknown variables, that is, ri,j (j¼ j0)for matrix elements of RN in a given column referring to primaryincident electron beam energy and ti,j (i¼ j) for matrix elementsof TN on the principal diagonal, is twice the number of equationsin equation (2). That is, there is only one equation with twounknowns at a given energy. Therefore, to obtain a solution, weneed an additional set of measurements, which can be obtainedby collecting another set of measurements using a differentsubstrate. As shown in Fig. 1a, we then perform the traditionaltwo-point probe measurement with an additional substrate(substrate B) to obtain another system of linear equations, suchthatJN Bð Þ Eð Þ ¼ RNJ0 Eð ÞþTNJSðBÞ Eð Þ: ð3ÞWith the number of variables now equal to the number ofequations (equations (2) and (3)), we can solve the matrices RNand TN and thereby obtain complete information for a targetnanomaterial.Combining equations (2) and (3) determined according to thefour-point probe method, we will haveJDN Eð Þ ¼ TNJDS Eð Þ; ð4Þwhere JDN(E) and JDS(E) are the difference spectra, which can beobtained by subtracting two measured spectra for a substrate-supported nanomaterial (JN(A)(E) and JN(B)(E)) and two spectrafor the substrates (JS(A)(E) and JS(B)(E)). The mathematicalexpression of JDN(E) is TN(RA�RB)J0(E), while that ofJDS(E) is (RA�RB)J0(E), where RA and RB are matrix descrip-tions of the reflection process of substrate A and B, respectively,and can be further simplified as TNdRJ0(E) and dRJ0(E),respectively, where dR represents a ‘virtual substrate’ whosecontribution is equivalent to the responses of two substratesto injected electrons (dR¼RA�RB). It is obvious that JDS(E)and JDN(E) are the responses of the bare substrate system andSubstratea bNanomaterialNanomaterialNanomaterialNanomaterialSubstrate B Substratex, Intensity (a.u.)y, Intensity (a.u.)z, Electron energy (eV)Substrate A Substrate A Substrate BJS(A) (E )JN(A) (E ) JN(B) (E )JS(B) (E )JN(A)(JS(A), JN(A))(JS(B), JN(B))JS(A)EiJN(B)JS(B)RN J0(0, RN J0)TNFigure 1 | Visualization of the virtual substrate method. (a) Schematic diagram of the virtual substrate method implemented in surface analysis.A combination of four interrelated spectra measured for two slightly different bare substrates (JS(A), JS(B)) and a target nanomaterial supported on thesetwo substrates (JN(A), JN(B)) is used in the virtual substrate method. Different groups defined as ‘substrate’ and ‘nanomaterial’ (surrounded by black boxes)are classified from the spectra measured for the bare substrate or nanomaterial. A traditional two-point probe measurement is indicated by a red dashedbox. (b) Visual representation of the virtual substrate method using a 3D coordinate system, where two spectra obtained using a traditional two-pointprobe measurement are plotted in pairs orthogonally along the x- and y-axes and share one electron energy axis (z-axis). Two spectra measured for baresubstrates (blue and green dots) are plotted in the x-z plane (substrate plane), and the other two spectra measured for the nanomaterial supported on thesubstrates (blue and green dots) are plotted in the y–z plane (nanomaterial plane). According to the virtual substrate method, the covering nanomaterialinformation is included in the lines that pass through two points whose x and y coordinates are the intensities of the two spectra in the traditional two-pointprobe measurements for different substrates at a given energy. The intercept of these lines, RNJ0(E), is plotted in the y–z plane (nanomaterial plane) asred dots. One line (purple) at energies Ei is plotted together in the x–z and y–z planes (thin purple lines) along with the deviations in these shallow lines(thick cyan line). At Ei, two known points (JS(A), JN(A)) and (JS(B), JN(B)) obtained by traditional two-point probe measurements with different substrates andthe intercept point (0, RNJ0) are presented as large black dots.NATURE COMMUNICATIONS | DOI: 10.1038/ncomms15629 ARTICLENATURE COMMUNICATIONS | 8:15629 | DOI: 10.1038/ncomms15629 | www.nature.com/naturecommunications 3http://www.nature.com/naturecommunicationsnanomaterial/substrate system, respectively, to the virtualsubstrate, which are not related to the concrete substrate usedin these systems. The physical meaning of the two differencespectra JDS(E) and JDN(E) then becomes apparent; they are theinitial and final states, respectively, for white electrons with theexpression dRJ0(E) travelling through a nanomaterial. Therefore,the ratio JDN(E)/JDS(E) (that is, TNdRJ0(E)/dRJ0(E)) directlyreveals the quantitative e–e interaction information for matrixTN. TN is typically a lower triangular matrix that can simply besplit into two matrices:TN ¼t1;1t2;1 t2;2� � � � � � . ..tn;1 tn;2 � � � tn;n0BBB@1CCCA¼t1;1t2;2. ..tn;n0BBB@1CCCA þ0t2;1 0� � � � � � . ..tn;1 � � � tn;n� 1 00BBB@1CCCA:ð5ÞThe first matrix, which includes only the elements on theprincipal diagonal, reflects the elastic electron transmissioninformation of the nanomaterial. Elements ti,j (i¼ j) are theelastic electron transmission of the nanomaterial, which convergeto 1 as the index (electron energy) increases. The second matrixincludes only those elements ti,j (i4j) below the principaldiagonal and is a sparse matrix whose non-zero entries arelocated in two major regions. One major region is confined toa diagonal band below the main diagonal, providing informationabout inelastic scattering processes. The lower bandwidth ofthis region depends on the electron energy and nanomaterialthickness. The other major region is located far from the maindiagonal near the bottom left corner of the matrix and describesthe production of SEs in inelastic scattering processes, whoseintensities directly reflect the energy loss behaviour of thenanomaterial. For an ultra-thin target nanomaterial, suchas mono- or bilayer graphene, the TN matrix mainly containscontributions from the first matrix term and can be treated as theelastic electron transmittance of the target nanomaterial. Fora thick target nanomaterial, such as few-layer graphene (n45),the second matrix term is dominant, reflecting the accompanyingsecondary electron emission (SEE) at low energy and providingenergy loss information about the target nanomaterial.In fact, there is another more intuitive way to demonstrate theprinciple of the virtual substrate method. As shown in Fig. 1b, therelationship between the measured spectra (JS(A), JN(A), JS(B) andJN(B)) and the determined elements in the matrices TN and RNcan be visualized as a finite number of lines that pass through thetwo points (JS(A), JN(A)) and (JS(B), JN(B)). These intersection pointsin the lines correspond to every energy in the measured spectra,whose slope and intercept are TN and RNJ0(E), respectively.According to this relationship, when the intensities of fourinterrelated raw spectra in the form of the two points (JS(A), JN(A))and (JS(B), JN(B)) are considered inputs, then the slope andintercept of the determined lines, TN and RNJ0(E), respectively,are the outputs, and include only the properties of thenanomaterial. A more intuitive description is that the virtualsubstrate method converts a line determined from the absoluteintensities of four interrelated raw spectra at a given energy inmeasurable space into a point in parameter space (slope–interceptparameterization of a straight line), where the slope (that is,diagonal elements of TN) and intercept (that is, RNJ0(E)) canbe considered the equivalent transmitted electron spectrumand equivalent reflected electron spectrum for a free-standingtarget nanomaterial, respectively. It should be noted that thisSubstratea cbdeF. CupE-gunSample10510310110–110–30.0 200.0 400.0Electron energy (eV)Intensity (pA)2K5 keVEN(E)N(E)/TFCMACMAAu4K 6KΔS=S(A)–S(B) ΔN=N(A)–N(B)ΔN/ΔSSubstrate AVirtual substrate Virtual substrateSubstrate B Substrate A Substrate BS(A)White electronN(A) N(B)S(B)S (A)S (B)N (A)N (B)NanomaterialRaw spectraDifference spectraTransmitted spectraElectron energyIntensityJS (A) (E)JS (B) (E )JN (A) (E )JN (B) (E)JΔS (E )JΔN (E)TΔN/ΔS (E)Figure 2 | Implementation of the virtual substrate method in Auger electron spectroscopy. (a) Experimental setup for AES. (b) Raw electron energyspectrum EN(E) (red) and restored spectrum N(E)/TFCMA (blue). (c) Top: four real experiment configurations, S(A), S(B), N(A) and N(B).Middle: equivalent experiment configurations DS and DN in which virtual substrates (see main text) are used. Bottom: Equivalent experiment configurationDN/DS in which white electrons (see main text) are used as a probe. (d) Application of the virtual substrate method to graphene/gold. (e) Spectra for thethree major steps in a virtual substrate measurement: four raw spectra (JS(A), JS(B), JN(A) and JN(B)), two difference spectra (JDS and JDN) and onetransmitted spectrum (TDN/DS).ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms156294 NATURE COMMUNICATIONS | 8:15629 | DOI: 10.1038/ncomms15629 | www.nature.com/naturecommunicationshttp://www.nature.com/naturecommunications‘intuitive description’ is valid only for thin layers, where it isappropriate to neglect the inelastic contribution.White electrons in the virtual substrate method. Besidesremoving the influence from substrate signals, implementingthe virtual substrate method in electron-based techniques alsoenables the use of an energy-dispersive full spectrum as a probeto investigate the properties of a target nanomaterial at differentenergies simultaneously. Figure 2a shows an AES setup witha cylindrical mirror analyser (CMA) including a Faraday cup.Focused electrons are incident on a sample, and emittedelectrons are deflected into a CMA, generally with an uncleartransmission function (TFCMA), which is accurately measuredhere15. Considering the modification by TFCMA, a measuredAES spectrum (gold) can be restored back to the moment justbefore entering the CMA detector (Fig. 2b). According to thisrestored spectrum, the number of SEs increases dramatically asthe electron energy decreases, which implies that this reflectedSE spectrum has the potential to be used as a probe tostudy substrate-supported nanomaterials. In this method, thenanomaterial is back-illuminated by the reflected SE spectrum asa white electron probe analogous to the widely used whiteX-rays16. But unlike white X-rays, when white electrons are usedas a probe, the information carried by the white electrons inthe SE energy range is obscured by the undesired electronsignals produced by energy loss or the formation of new SEs ininelastic collisions, while white electrons of higher energy travel ina target nanomaterial. Therefore, the energy channels in themeasurement are approximately rather than fully separated whenthe reflected SEs from the underlying substrate are used as a whiteelectron probe. In this case, the underlying substrate acts asa backscatterer of the monochromatic electron beam with fullydispersed energies, forming the white electrons. The transmissionof white electrons through the nanomaterial enables thee–e interactions of the nanomaterial supported by the substrateto be studied with ultimate efficiency; however, the initial energydistributions of these white electrons are difficult to measure inreflection configuration because of the influence of the reflectionfrom the nanomaterial. Implementing the virtual substratemethod in AES measurements, white electrons originating fromsubstrate-reflected electrons, can be controlled to quantitativelyinvestigate the covering nanomaterial by realizing an equivalenttransmission configuration measurement from a combinationof four interrelated measurements in reflection configuration,as shown in Fig. 2c. This method uses four interrelatedmeasurements in reflection configuration for the two baresubstrate (S(A) and S(B)) and a target nanomaterial supportedon two substrates (N(A) and N(B)). Four interrelatedspectra, JS(A), JS(B), JN(A) and JN(B), can be obtained fromthese measurements correspondingly. According to the virtualsubstrate method, spectrum subtraction is implemented bysubtracting two spectra associated with different substrates(substrate A and B) to give a difference spectrum (JDS(E) andJDN(E) for the bare substrate system and nanomaterial/substratesystem, respectively), in which an inevitable issue in reflectionconfiguration—SEs excited because of the attenuation of themonochromatic incident electron beam—is completely removed.If there is a virtual substrate whose contribution is equivalentto the deviations of the spectra separately measured on thetwo different substrates at low energy, JDS(E) and JDN(E) canbe viewed as the output from equivalent measurements inreflection mode for the bare virtual substrate (DS) and thetarget nanomaterial supported on the virtual substrate (DN),respectively. In this case, JDS(E) containing SEs excited in thevirtual substrate and emitted from the surface can be used as awhite electron probe. In contrast, JDN(E) contains an attenuatedwhite electron probe that passes through the nanomaterialtogether with the accompanying SEs. Therefore, by measuringthese two difference spectra, the initial and final states for thewhite electron travelling through a nanomaterial can be obtainedby neglecting the blocking effect of the nanomaterial on theincident electron beam. Furthermore, the transmissioninformation as a function of electron energy is the ratio ofthe two difference spectra, termed the transmitted spectrumTDN/DS(E), (that is JDN(E)/JDS(E)) which can be viewed as theoutput from an equivalent measurement in transmissionconfiguration (DN/DS), in which the white electron is used as aprobe to quantitatively investigate nanomaterials based on theirsubtle changes in the transmission of a nearly transparentnanomaterial. It should be noted that the virtual substrate methodis suitable to remove the reflectivity difference between asubstrate-supported nanomaterial and bare substrate for mostanalysis tools in reflection configuration, whereas the whiteelectron probe used to raise efficiency is only applicable toelectron-based techniques.Practical application of the virtual substrate method. A prac-tical application of this virtual substrate method using graphene asa representative nanomaterial is shown in Fig. 2d. Here we used apolycrystalline metal substrate composed of alternating micron-sized single-phase grains with different crystallographic orienta-tions instead of different substrates. Generally, the uncertaintyrange of relative orientations for one type of metal grains should bewithin 0.5�, while the relative orientation between two types ofmetal grains should be larger than 4� (Supplementary Fig. 1).A typical virtual substrate method operation involves three majorsteps (Fig. 2e, Supplementary Figs 2–5). First, four raw spectra aremeasured by selecting incident positions on different crystal-lographic orientations in the bare substrate and similar regionscovered by graphene sheets. Second, difference spectra are calcu-lated by subtracting paired spectra with the same experimentalconfiguration. Third, the transmitted spectrum is obtained from theratio of the two difference spectra. In addition, theoreticalapproaches are used to remove the disturbance from Augerelectrons and accompanying SEs when focusing on transmissioninformation (Supplementary Note 1, Supplementary Figs 6–8). Itshould be noted that the reliability of these selected incidentpositions was verified by the consistency of the raw spectra mea-sured at these positions before transferring the target nanomaterialsheets onto half of them, and the relative errors should be within5%. Atomic force microscopy was used to confirm the absence ofwrinkles in the covering nanomaterial layer. The criteria forselecting these measurements points are presented inSupplementary Note 2 and Supplementary Figs 9–13. Generally,short-term repeated measurements for multiple cycles withmicrometre distances between different measurement sites wereused to minimize the influence of changes in the stability of theinstrument over time and sample inhomogeneity.Elastic electron transmission. The virtual substrate method wasfirst investigated using mono- and bilayer graphene. The elastictransmission of mono- and bilayer graphene over the entireenergy range is presented in Fig. 3. To confirm the effectivenessof the virtual substrate method, we compared the elastictransmission obtained using different theoretical approaches. Theextended Mermin method17 was used to calculate the electroninelastic mean free path (IMFP) of monolayer graphene from acorresponding energy loss function determined by the WIEN2kpackage18. Using a standard straight-line approximation19 for theattenuated signal from IMFP only, the elastic transmission Tn ofNATURE COMMUNICATIONS | DOI: 10.1038/ncomms15629 ARTICLENATURE COMMUNICATIONS | 8:15629 | DOI: 10.1038/ncomms15629 | www.nature.com/naturecommunications 5http://www.nature.com/naturecommunicationsn-layer graphene can be estimated byTn ¼ expð� nd0=lIMFP� cos yÞ; ð6Þwhere d0 is the thickness of graphene (0.335 nm), lIMFP is theIMFP of monolayer graphene and y is the emission angle.The results obtained by this method agree well with thoseobtained from the virtual substrate measurements, except for theenergy range of 10–200 eV because of the lack of a multiplescattering effect. For bilayer graphene, excellent agreement isachieved over the entire energy range because of thecompensation of the diffraction effect, mainly provided by theerrors introduced by using the dielectric function of thewell-known jellium model to describe the electrical propertiesof single-crystal graphene. Using the Monte Carlo (MC)method20, the elastic interactions of electrons with carbonatoms are predicted by considering the zigzag trajectory ofelectrons inside graphene. The MC method shows excellentagreement with the virtual substrate measurements over theentire energy range for monolayer graphene, with some deviationfrom 10 to 300 eV for bilayer graphene. Time-dependent densityfunctional theory (TDDFT)21 calculations were performed toinclude the influence of the two-dimensional crystal. The elastictransmission predicted by TDDFT corresponded well with thevirtual substrate measurements and theoretical predictionsof the MC method for monolayer graphene and exhibited adeviation of B15% at high energies (4300 eV) for bilayergraphene. Other experimental techniques were also used tomeasure elastic transmission. The virtual substrate measurementsshow excellent agreement with existing electron point sourcemicroscopy at 66 eV22 and 100 eV23 and with elastic transmissionmeasurements performed in this work using the AES overlayermethod24 at 2.3 eV (gold surface plasmon), 78 eV (Si LVV Augertransition) and 503 eV (O KLL Auger transition). It should benoted that the data point at 2.3 eV is the attenuation of surfaceplasmons of gold (approximately equalling the attenuation ofelectrons) by graphene sheets, which was estimated from theintensities of surface plasmon gain peaks observed at a surfaceplasmon energy above the vacuum level in difference spectra forn-layer graphene/gold (n¼ 4, 6, 11 and 14) with an incidentelectron energy of 10 keV (Supplementary Fig. 5d).Characterization of nanomaterials. For few-layer graphenesheets, accompanying SE features appear in the transmittedspectra (Fig. 4a) together with the transmitted spectra roughlyestimated by very-low-energy electron diffraction (VLEED) forsingle-crystal graphite25 and low-energy electron microscopy(LEEM) for eight-layer graphene on SiC (ref. 26). Althoughtransmission data from VLEED and LEEM are related to the0 200 400 600 0 200 400 600Electron energy (eV)1.00.80.6Elastic transmission, TΔN/ΔS0.40.20.0Monolayer BilayerExp. 10 keVExp. 15 keVCal. EMCal. MCCal. TDDFTExp. LEEPS (22,23)Exp. Overlayer-SPExp. OverlayerFigure 3 | Elastic transmission of mono- and bilayer graphene. Elastictransmission (TDN/DS(E), that is JDN(E)/JDS(E)) of monolayer graphene andbilayer graphene measured by the virtual substrate method for primaryelectron energies of 10 and 15 keV. The elastic transmission was calculatedby the extended Mermin (EM), Monte Carlo (MC) and time-dependentdensity functional theory (TDDFT) methods. The total transmission wasmeasured by low-energy electron point-source (LEEPS) microscopy22,23corrected to the elastic transmission by the MC method. The elastictransmission was measured by the overlayer method for graphene/gold at2.3 eV, associated with gold surface plasmons (overlayer-SP), and forgraphene/SiO2 samples at 78 and 503 eV (overlayer).432101.00.50.00.20.10.00 10 20 30 40 500 10 20 30 40 50Transmitted spectra (a.u.)Transmission (a.u.)EELS (a.u.)DSEP (keV–1)Electron energy (eV)Energy loss (eV)1 L4 L6 L11 L16 L(3)(1)(2)(2)1 L2 L5 L>10 L1 L2 L4 L8 L12 LVLEED (25)LEEM (26)0.80.40.110 (2)(2)5 20 25 30 35 40�abFigure 4 | Material characterization using the virtual substrate method.(a) Top: transmitted spectra for one-, four-, six-, 11- and 14-layer graphenefor primary electron energies of 10 keV (dashed lines) and 15 keV(solid lines). Insets show the transmitted spectra at 15 keV without anoffset. Bottom: electron transmission spectrum (TVLEED)25 measured byvery-low-energy electron diffraction (VLEED) and transmission data(TLEEM)26 estimated from the reflectivity spectra (TLEEM¼ 1� RLEEM)obtained from low-energy electron microscopy (LEEM). (b) Top: electronenergy-loss spectra (EELS) for one-, two-, five- and several-layer grapheneshowing p and pþs plasmons27. Bottom: differential surface excitationparameter (DSEP) spectra for the few-layer graphene/gold system. Theshaded region is the energy loss below the work function of graphite(j¼4.6 eV). For straight comparison, the work function of graphite relativeto the cylindrical mirror analyser was determined a priori.ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms156296 NATURE COMMUNICATIONS | 8:15629 | DOI: 10.1038/ncomms15629 | www.nature.com/naturecommunicationshttp://www.nature.com/naturecommunicationssurface properties of graphite and graphene rather than theoverall properties of graphene like those obtained by the virtualsubstrate method, strong, consistent fluctuations of electronenergy caused by the diffraction of the crystal potential at certainenergies are observed in all the transmitted spectra. Peaks at 2.3and 4 eV and the plateau at 12–20 eV (highlighted by redarrows (3), (1) and (2), respectively) appear only in the virtualsubstrate measurements. All of these features become morepronounced as the number of sheets increases because of thespecific accompanying SE contribution; however, they originatefrom different mechanisms. For instance, peak (1) relates to thes–s* transition in graphene. The increase in peak height andsharpness with sheet number reflects the competition of cascadeSE peaks between graphene and the underlying gold substrate(a broad plateau at approximately 8 eV). The plateau structure(2) is associated with pþs plasmon excitation in graphenelayers. To prove this association, the plasmon spectrum of a free-standing graphene film measured by electron energy-lossspectroscopy (EELS)27 and the theoretical prediction of thedifferential surface excitation parameter (DSEP), includingcoupling excitation with the underlying substrate, are presentedin Fig. 4b. The plateau structure in the virtual substratemeasurements occurs at the exact energies corresponding to thepþs plasmon energies observed in the EELS and DSEP spectraminus the work function j of graphene sheets (4.6 eV28); j of thesample with respect to the CMA was already considered todetermine the onset of the spectra. This result demonstrates thatplasmons excited by electron energy-loss decay via the generationof single electron–hole pairs act as a source of SEs. No featuresrelated to p plasmon excitation are found, indicating that pplasmon decay does not contribute to SEE. Peak (3), assigned tothe gain of a surface plasmon quantum of gold, is caused byemitted SEs that gained a surface plasmon quantum in theeffective surface plasmon area after overcoming j as the reversereaction of supersurface electron scattering29.DiscussionAlthough multi-point probe measurements have been used toobtain information from measured spectra for many yearsalready, like multi-spectral approaches using Auger electronmicroscopy30, the concept behind the virtual substratemeasurement presented in this work is a new development. Infact, besides the accompanying SE features in transmitted spectra,the electronic properties of a target nanomaterial determined bya virtual substrate measurement can also be used as a descriptorfor nanomaterial characterization. To demonstrate this, virtualsubstrate measurements were performed for investigatingmono- and bilayer molybdenum disulfide (MoS2) samples,which have different electronic properties in the low energyrange as identified by optical spectroscopy31. The determinedtransmitted spectra for mono- and bilayer MoS2 are presented inFig. 5. Consistent fluctuation of electron energy caused by acombination of inelastic scattering, accompanying SE and thediffraction effect is observed in the transmitted spectra for mono-and bilayer MoS2 over the whole energy range, except for between2 eV and 5 eV, as highlighted by blue arrows. When the electronenergy exceeds 2 eV, the intensity of transmitted spectra formonolayer MoS2 decreases gradually with increasing electronenergy until the energy reaches about 5 eV. For bilayer MoS2, theintensity of transmitted spectra decline sharply until thisbehaviour suddenly stops at about 2.5 eV. This variationbetween mono- and bilayer MoS2 may be caused by differente–e interactions near the band gap energy, different out-of-planeproperties, or different interfacial properties when mono- andbilayer MoS2 contact with the gold substrate (these mechanismswill be discussed elsewhere). Such variation in measuredtransmitted spectra can be used as an indicator in electron-beam techniques to distinguish substrate-supported mono- andbilayer MoS2. Furthermore, the differences between mono- andbilayer MoS2 are more obvious when organizing thesetransmitted spectra in the form of IMFP by reversing equation(1); that is, lIMFP¼ � (nd0)/(ln Tn� cos y). The determinedIMFPs for mono- and bilayer MoS2 agreed well over the wholeenergy range, except for between 2 eV and 5 eV, which isconsistent with the observed transmitted spectra.The experimental conditions required for a virtual substratemeasurement are similar to those of traditional measurementsexcept for the substrate on which the target nanomaterial issupported. A tailor-made substrate is important in the virtualsubstrate method; in this work, the substrate is polycrystallinegold. In fact, strict requirements for the substrate are onlynecessary for highly precise, high-speed quantitative studies oftarget nanomaterials. To obtain low-precision measurements,virtual substrate measurements can be performed using almostany two substrates with different element composition, surfacemorphology, and crystal quality. However, polycrystalline metal1.00.80.60.46050403020100.1 1 10 100Electron energy (eV)0.1 1 10 100Transmitted spectra (a.u.)IMFP (Å)Electron energy (eV)S1 1 LS1 2 LS2 1 LS2 2 LS1 1 LS1 2 LS2 1 LS2 2 LabFigure 5 | Electronic properties of monolayer and bilayer MoS2.(a) Transmitted spectra for mono- and bilayer MoS2 obtained at a primaryelectron energy of 20 keV. Two different MoS2 sheets supported on the samebatch of substrates, denoted as S1 and S2, were used in virtual substratemeasurements with energy ranges of up to 12 eV in 0.1 eV increments and120 eV in 0.5 eV increments, respectively. (b) Corresponding inelastic meanfree path (IMFP), lIMFP, of mono- and bilayer MoS2 for a primary electronenergy of 20 keV.NATURE COMMUNICATIONS | DOI: 10.1038/ncomms15629 ARTICLENATURE COMMUNICATIONS | 8:15629 | DOI: 10.1038/ncomms15629 | www.nature.com/naturecommunications 7http://www.nature.com/naturecommunicationssubstrates are the best choice for highly precise, high-speedquantitative studies of target nanomaterials because of theirsimilar surface barrier and degree of interaction with the coveringnanomaterial. For instance, a hole-patterned SiO2 substrate hasalso been used to investigate multilayer graphene by virtualsubstrate measurements. Four spectra measured for flat and holeregions of the SiO2 substrate without and with a coveringgraphene layer are used in this measurement instead of spectrameasured for two different types of gold grains. The results of thismeasurement were broadly in line with those obtained fora graphene/polycrystalline gold system, but had very lowprecision. This demonstrates that we are able to design othertailor-made substrates in accordance with specific conditions;however, tailor-made substrates that can produce nearly identicalreflected SE spectra at two determined measurement points arenecessary to perform virtual substrate measurement.For research purposes, the target nanomaterial can betransferred onto the tailor-made substrate; however, for industrialpurposes, it is usual to study a target nanomaterial on a givensubstrate (any arbitrary substrate). Stringent demands for thesubstrate are essential to extract pure information of targetnanomaterials with high precision through virtual substratemeasurements. These stringent demands for the substrate arebound to restrict the scope of this technique in wider applications,especially industrial ones. However, there are exceptions even inindustry; for instance, the virtual substrate method will be a veryefficient tool to quantitatively investigate passive films on stainlesssteel, which is a typical nanomaterial/polycrystalline substratesystem. In fact, there is another way to implement this virtualsubstrate method by which almost any given nanomaterial/substrate combination with a substrate that is not completelyuniform, like a single crystal, can be investigated just froma ‘monochromatic’ SEM image without any designed substrate,and even without selecting measurement points. In thisspectral imaging approach, the pixels of a SEM image formedby detected electrons at a given energy are considered as pixelsized ‘fictitious grains’ and used to perform the virtual substratemeasurement as described in Supplementary Note 3 andSupplementary Fig. 14. This new approach has allowed us tostudy a target nanomaterial on a given substrate as long as itdisplays fairly stable intensity distributions in a SEM image.A limitation of this approach is the huge amount of datagenerated during measurement; however, it does represent apossible future direction for the virtual substrate method.In summary, the virtual substrate method represents abenchmark to provide ‘free-standing’ nanomaterial informationfrom measurements of substrate-supported samples, which, inprinciple, can be easily implemented in many more reflection-configuration techniques than surface analysis techniques anddoes not demand extra investment in equipment. Implemented inelectron-based surface analysis techniques, this method expandsthe energy scale of analysis down to several electron volts andthus allows one to quantitatively probe the e–e interactions of ananomaterial and observe ‘hidden’ electronic energy transfer toand from a nanomaterial on a substrate, which is visualized asemitted SE features in equivalent ‘transmitted’ spectra. Further-more, using ordinary SE signals, the virtual substrate methodoutrivals conventional methods based on core-level signals insignal-to-background ratio by orders of magnitude. Thus, thevirtual substrate method holds great potential for manufacturemonitoring and quality control.MethodsSubstrate preparation. Gold layers were evaporated on Si (100) substrates withthin titanium buffer layers using electron-beam evaporation (RDEB-1206K, R-DECCo. Ltd., Ibaraki, Japan), as shown in Supplementary Fig. 1. The thicknesses of thetitanium and gold metal layers were 5.0 and 200.0 nm, respectively, and they weredeposited at rates of 0.05 and 0.2 nm s� 1, respectively. The chamber pressurewas B1.0� 10� 5 Pa. After evaporation, the samples were annealed by rapidthermal annealing (QHC-P410, ULVAC-RIKO Inc., Kanagawa, Japan) undera N2 atmosphere at 300 �C for 30 s.Graphene fabrication. Graphene flakes were produced on the gold substrates bymechanical exfoliation32 as shown in Supplementary Figs 2 and 4. The number ofgraphene layers was estimated by atomic force microscopy and further confirmedby Raman spectroscopy, particularly for mono- and bilayer graphene33.Virtual substrate measurement. The raw spectra in the virtual substratemeasurements were measured at room temperature with a scanning Augerelectron spectroscope (SAM650, ULVAC-PHI, Kanagawa, Japan) with a CMA(Supplementary Figs 3 and 5). The take-off angle of the instrument was 42.3±6�.The incident electron beam current for these raw spectra was B0.87 nA, ascalibrated with a Faraday cup before the measurements. The raw spectra wereaveraged from eight different sample regions (B490 nm2) on the bare substrate aswell as on graphene samples with different numbers of layers.Condition number of the measurement. From the error propagation analysis ofthe expression of the transmitted spectrum TDN/DS¼ JDN/JDS in a virtual substratemeasurement, the relationship between the relative errors in the raw spectra as theinput and the transmitted spectrum as the output can be simply obtained asDTDN=DSTDN=DS¼ JSðAÞJDSDJSðAÞJSðAÞþ JSðBÞJDSDJSðBÞJSðBÞþ JNðAÞJDNDJNðAÞJNðAÞþ JNðBÞJDNDJNðBÞJNðBÞ; ð7Þwhere DJS(A), DJS(B), DJN(A) and DJN(B) are small given changes in the raw spectraand DTDN/DS is the resulting change in the transmitted spectrum. The relativeerrors in the raw spectra, such as DJS(A)/JS(A), DJS(B)/JS(B), DJN(A)/JN(A) andDJN(B)/JN(B), are enhanced JS(A)/JDS, JS(B)/JDS, JN(A)/JDN and JN(B)/JDN times in thetransmitted spectrum TDN/DS, respectively. The condition number of the virtualsubstrate measurement for the initial error in a specific raw spectrum equals theratio of this raw spectrum to the corresponding difference spectrum; for instance,JS(A)/JDS, JS(B)/JDS, JN(A)/JDN and JN(B)/JDN are the condition numbers of thistechnique for the initial errors in JS(A), JS(B), JN(A) and JN(B), respectively. Tostudy mono- and bilayer graphene, the condition numbers of the virtual substratemeasurement using the presented tailor-made polycrystalline gold substrate(with a relative orientation of B4� between the two types of gold grains, as shownin Supplementary Fig. 1) have similar values regardless of the initial errors in theraw spectra measured on the bare substrate or covering graphene. The conditionnumber is B15 for an energy level o100 eV and B10 in the energy rangeof 100–600 eV. Although the virtual substrate measurement is an ill-conditionedsystem with a high condition number, the condition number can be artificiallyreduced to 4–6 by using two gold grains with larger relative orientations of 10–12�.Transmission calculation. The MC and TDDFT methods were used to calculateelastic electron transmission without any adjusted parameters. In the MCcalculation34, the elastic scattering was determined by the Mott cross section basedon the muffin-tin model potential, and the inelastic scattering was determined bythe extended Mermin method, whose only input, the energy-loss function, wasprovided by the WIEN2k package. Furthermore, a quantum dynamic TDDFTcalculation35 that fully accounted for the carbon atoms of the target graphene andelastic/inelastic electron scattering was carried out for the same purpose. Theelectron transmission coefficient was calculated from the ratio of the time-averagedtransmitted current to incident current, and the elastic component was derivedusing the MC method, in which the proportion of elastic electrons was provided.Theoretical modification. Theoretical approaches were used to purify the elastictransmission information for mono- and bilayer graphene in the virtual substratemeasurements by considering the contributions from Auger electron emission,inelastic scattering and accompanying SEE (Supplementary Fig. 8). The Augerelectron contribution was removed from the transmitted spectra by subtractingscaled-down Auger peaks detected in the raw spectra. The inelastic scatteringprocess and accompanying SEE contributions were removed using a self-adaptiveiterative MC simulation programme that only exists when white electrons are usedas a probe in electron-based techniques, as discussed in Supplementary Note 1. Thecontribution of the surface potential barrier gap between the nanomaterial andsubstrate was removed using a square barrier model, where the constant electronicpotential in the interior of the sample was defined as the sum of the kinetic energyat the Fermi level (9.0 eV for gold and 20.2 eV for graphene) and j of the material(5.1 eV for gold and 4.2 for graphene).Data availability. The data sets generated during and/or analysed during thecurrent study are available from the corresponding author on reasonable request.ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms156298 NATURE COMMUNICATIONS | 8:15629 | DOI: 10.1038/ncomms15629 | www.nature.com/naturecommunicationshttp://www.nature.com/naturecommunicationsReferences1. Smith, D. J., Petford-Long, A. K., Wallenberg, L. R. & Bovin, J.-O. Dynamicatomic-level rearrangements in small gold particles. Science 233, 872–875(1986).2. Pan, Z. W., Dai, Z. R. & Wang, Z. L. Nanobelts of semiconducting oxides.Science 291, 1947–1949 (2001).3. 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The numerical TDDFT calculations were performed on supercomputersat the Institute for Solid State Physics, University of Tokyo and the Research Center forComputational Science, National Institutes of Natural Sciences Okazaki ResearchFacilities, Japan.Author contributionsB.D., H.Y. and S.T. supervised the project. B.D. designed the research and wrote themanuscript with important input from all authors. B.D., J.L., M.Y. and K.T. performedthe experiments. B.D., Y.U., K.W. and N.T.C. performed the calculations. All authorsdiscussed the results and commented on the manuscript.Additional informationSupplementary Information accompanies this paper at http://www.nature.com/naturecommunicationsCompeting interests: The authors declare no competing financial interests.Reprints and permission information is available online at http://npg.nature.com/reprintsandpermissions/How to cite this article: Da, B. et al. Virtual substrate method for nanomaterialscharacterization. Nat. Commun. 8, 15629 doi: 10.1038/ncomms15629 (2017).Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims inpublished maps and institutional affiliations.This work is licensed under a Creative Commons Attribution 4.0International License. The images or other third party material in thisarticle are included in the article’s Creative Commons license, unless indicated otherwisein the credit line; if the material is not included under the Creative Commons license,users will need to obtain permission from the license holder to reproduce the material.To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/r The Author(s) 2017NATURE COMMUNICATIONS | DOI: 10.1038/ncomms15629 ARTICLENATURE COMMUNICATIONS | 8:15629 | DOI: 10.1038/ncomms15629 | www.nature.com/naturecommunications 9http://www.nature.com/naturecommunicationshttp://www.nature.com/naturecommunicationshttp://npg.nature.com/reprintsandpermissions/http://npg.nature.com/reprintsandpermissions/http://creativecommons.org/licenses/by/4.0/http://www.nature.com/naturecommunications title_link Results The concept of the virtual substrate method Figure™1Visualization of the virtual substrate method.(a) Schematic diagram of the virtual substrate method implemented in surface analysis. A combination of four interrelated spectra measured for two slightly different bare substrates (JS(A), JS(B)) and  Figure™2Implementation of the virtual substrate method in Auger electron spectroscopy.(a) Experimental setup for AES. (b) Raw electron energy spectrum EN(E) (red) and restored spectrum N(E)solTFCMA (blue). (c) Top: four real experiment configurations, S(A White electrons in the virtual substrate method Practical application of the virtual substrate method Elastic electron transmission Characterization of nanomaterials Figure™3Elastic transmission of mono- and bilayer graphene.Elastic transmission (TDeltaNsolDeltaS(E), that is JDeltaN(E)solJDeltaS(E)) of monolayer graphene and bilayer graphene measured by the virtual substrate method for primary electron energies of 10  Figure™4Material characterization using the virtual substrate method.(a) Top: transmitted spectra for one-, four-, six-, 11- and 14-layer graphene for primary electron energies of 10thinspkeV (dashed lines) and 15thinspkeV (solid lines). Insets show the t Discussion Figure™5Electronic properties of monolayer and bilayer MoS2.(a) Transmitted spectra for mono- and bilayer MoS2 obtained at a primary electron energy of 20thinspkeV. Two different MoS2 sheets supported on the same batch of substrates, denoted as S1 and S2, Methods Substrate preparation Graphene fabrication Virtual substrate measurement Condition number of the measurement Transmission calculation Theoretical modification Data availability SmithD. J.Petford-LongA. K.WallenbergL. R.BovinJ.-O.Dynamic atomic-level rearrangements in small gold particlesScience2338728751986PanZ. W.DaiZ. R.WangZ. L.Nanobelts of semiconducting oxidesScience291194719492001ReedJ. P.The effective fine-structure const We thank Professor K. Goto, Professor W.S.M. Werner, Professor M.S. Xu, Professor M.M. Ma, Dr S.F. Mao, Dr Y.G. Li, Dr R.G. Zeng, Dr J. Hu, Dr C. Chen and Dr L. Sun for helpful comments and discussions. This research was partially supported by a Grant-in- ACKNOWLEDGEMENTS Author contributions Additional information