Nanoscale modification of WS_2 trion emission by its local electromagnetic environment
Noémie Bonnet, Hae Yeon Lee, Fuhui Shao, Steffi Y. Woo, Jean-Denis Blazit, Kenji Watanabe, Takashi Taniguchi, Alberto Zobelli, Odile Stéphan, Mathieu Kociak, Silvija Gradecak-Garaj, Luiz H. G. Tizei
NNanoscale modification of WS trion emission by its localelectromagnetic environment No´emie Bonnet, Hae Yeon Lee, Fuhui Shao, Steffi Y. Woo, Jean-DenisBlazit, Kenji Watanabe, Takashi Taniguchi, Alberto Zobelli, OdileSt´ephan, Mathieu Kociak, Silvija Gradecak-Garaj, ∗ and Luiz H. G. Tizei † Universit´e Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405, Orsay, France Department of Materials Science and Engineering,Massachusetts Institute of Technology,77 Massachusetts Ave, Cambridge, MA, 02141, USA Research Center for Functional Materials,National Institute for Materials Science,1-1 Namiki, Tsukuba 305-0044, Japan International Center for Materials Nanoarchitectonics,National Institute for Materials Science,1-1 Namiki, Tsukuba 305-0044, Japan (Dated: February 15, 2021) a r X i v : . [ c ond - m a t . m e s - h a ll ] F e b bstract Structural, electronic, and chemical nanoscale modifications of transition metaldichalcogenide monolayers alter their optical properties, including the generation ofsingle photon emitters. A key missing element for complete control is a direct spatialcorrelation of optical response to nanoscale modifications, due to the large gap inspatial resolution between optical spectroscopy and nanometer resolved techniques,such as transmission electron microscopy or scanning tunneling microscopy. Here,we bridge this gap by obtaining nanometer resolved optical properties using electronspectroscopy, specifically electron energy loss spectroscopy (EELS) for absorptionand cathodoluminescence (CL) for emission, which were directly correlated to chem-ical and structural information. In an h-BN/WS /h-BN heterostructure, we observelocal modulation of the trion (X − ) emission due to tens of nanometer wide dielectricpatches, while the exciton, X A , does not follow the same modulation. Trion emis-sion also increases in regions where charge accumulation occurs, close to the carbonfilm supporting the heterostructures. Finally, localized exciton emission (L) detectionis not correlated to strain variations above 1 % , suggesting point defects might beinvolved in their formations. Transition metal dichalcogenides (TMDs) of the form MX (where M = W, Mo, andX = S, Se) with the 2H phase are semiconductors with indirect bandgap in bulk, anddirect bandgap in monolayer [1]. Photoluminescence (PL) due to exciton decay is thenbrightest for monolayers. Their particular excitonic spin-valley physics, created by thelack of inversion symmetry, the strong spin-orbit coupling [2], and the reduced coulombscreening, have recently attracted great interest. Up to now, spectral changes in PL have notbeen linked to specific nanometer structural or chemical modifications in TMD monolayers,despite the observation of single photon emitters (SPE) in these materials. These SPE areof particular interest for their temporal stability, narrow spectral linewidths [3–6] indicatinga low coupling to phonons, and possibility to create them selectively in space [4, 6], whichplaces them as strong candidates for applications in quantum optics.Near band-edge optical resonances of TMD monolayers are governed by excitonic transi- ∗ [email protected] † [email protected] A andX B , occur at the K point in reciprocal space and are split by spin-orbit coupling. Emissionspectra of TMD monolayers, such as from PL spectroscopy, contain excitons (X A ) [8], trionsthat can be negatively- (X − ) [9] or positively-charged (X + ) [10], and other lower energy lines,previously attributed to defects [8] or potential changes due to strain [11–13]. Some of thesehave been shown to be single photon emitters [3, 5], which occur at energies below the X − emission, and are often referred as L peaks (for localized excitons) [5, 14, 15]. Nanometerscale modulation of the dielectric environment of WSe through a gated h-BN/grapheneheterostructure creates moir´e bands [16]. These bands were attributed to local changes ofthe single particle bandgap, but not directly measured. Local measurements of the absorp-tion of these heterostructures (where WSe is buried in layers of h-BN and graphene) or theidentification of the of nanoscale emitters in TMDs require at least an order of magnitudeincrease in the spatial resolution in measurements of the local structure and the chemistry tobe coupled with optical measurements. Electron spectroscopies, such as electron energy lossspectroscopy (EELS), cathodoluminescence (CL) have the potential to address the obstacleof measuring the optical properties at deep sub-wavelength scales [17].Here, we used transmission electron microscopy techniques including highly monochro-mated EELS, CL, high angle annular dark field (HAADF), and diffraction imaging to corre-late sub-10 nanometer optical absorption and luminescence spectral mapping to structuraland chemical mapping. We show that the trion and other localized (L) light emission en-ergy and intensity can vary on scales down to tens of nanometers in WS monolayers whileexciton emission intensity remains unchanged. In short, three effects are revealed: local-ized trion emission intensity increase at constant absorption rate due to either 1) chemicalchanges in tens of nanometer patches or 2) to charge accumulation in a metal-insulator-semiconductor heterostructure combined with near-field emission enhancement; and 3) thepresence of a bright emission, attributed to L, below the trion energy, highly localized inspace. These effects, sketched in Fig. 1a, are linked to local charge density variations andto near-field enhancement and not to the generally evoked local strain modification. In ad-dition, the spatially-constant absorption, coupled to nanoscale-resolved CL, shows that thetrion emission intensity increases due to a locally faster decay rate.X A , X − , and the localized emission possibly linked to defects have been observed withCL in TMD monolayers before [18–20], utilizing specific sample heterostructures, but with3nly hundreds of nanometer spatial resolution. More importantly, previous reports of EELSmeasurements on TMD monolayers did not reach spectral resolution comparable with opticalabsorption experiments to allow for facile interpretation [21–24]. An alternative technique,scanning tunnelling microscopy induced luminescence (STM-lum) allows the detection lightemission from TMD monolayers [25, 26]. Despite the impressive atomic resolution achieved[26], the strong influence of the STM tip on optical spectra hinders their use as an nanoscaleequivalent of PL.The samples used here are made from WS monolayers exfoliated from bulk material,and encapsulated in h-BN (5 and 25 nm thick on each side). The heterostructures createdare then deposited on a conductive carbon film (ten of nanometer thick) with 2 µ m-wideholes, itself supported on copper TEM grids (see the Methods section for details on samplepreparation). The encapsulation offers high CL emission rate due to the increased interactionvolume with the fast electron beam. The high charge-carriers density then produced enablesCL detection [18–20]. High purity and homogeneity in the h-BN layers are critical to getspectral line shapes comparable to those using pure optical means. Four samples wereanalyzed, with a typical surface area of 150 µm .Experiments were performed in a scanning transmission electron microscope (STEM),in which spatially resolved data are acquired by scanning a subnanometer electron beam,retrieving images (2D arrays with an intensity value in each pixel) and datacubes (2D arrayswith a spectrum or a diffraction pattern at each pixel), see Fig. SI3. Energy filtered mapscan be produced by cuts of these datacubes at different energies. Structural information wasretrieved from atomic scale images (Fig. 1a inset) and strain mapping through diffractiondatacubes (Fig. SI2). For more information, see the Methods section.Fig. 1b presents the typical optical information that can be collected using CL and EELSon WS monolayers with the samples kept at 150 K. CL and EELS spectral resolution usedwere 8 and 26 meV, respectively, for the measurements presented here.CL can be directly compared to off-resonance PL [27], where the emission from X A andX − (X + occurs only in negatively gated WS [10]) is observed for the WS monolayer. Anoverview of the energies measured for X A and X − CL emission is plotted as histograms inFig. 1c-d (more histograms corresponding to the localized L emission and exciton energiesin EELS are shown in Fig. SI11), where the survey areas are of few µ m each (represented bya different color). The measurements average around 2.049 eV and 2.011 eV (with full width4t half maxima (FWHM) 13 meV and 19 meV, respectively), showing agreement betweenensemble of CL measurements across a sample with macroscopic optical measurements (typ-ical variations are of 20 to 30 meV for X A emission and absportion in regions above 10 µ m [8, 14, 28, 29]). Regions with broader ( ∼
15 meV, black histogram in Fig 1c-d) and narrower( ∼ − R − T , where R and T are the optical reflectivityand transmission [8]) spectra of h-BN encapsulated WS at 150 K shows a one-to-one matchbetween features (see Fig. SI1 and the Methods section for a discussion on EELS and opticalabsorption). The features seen in the EELS spectrum presented in Fig 1b are exciton peaks.In addition to X A and X B , two others are detected: X ∗ A , the excited state of X A , and X C which arises from strong absorption due to band nesting around the Q point [32]. Theenergy positions of X A and X B measured in EELS are plotted as histograms in Fig. SI10and Fig. SI11, showing the mean value of X A and X B to be 2.101 eV and 2.502 eV (withFWHM 24 meV and 25 meV, respectively).With this understanding of CL (EELS) as nanometer counterparts of PL (absorption),we can now describe our typical observations of deep sub-wavelength intensity variations,with examples shown in Fig. 2. X − and L peak intensities can vary locally in scales oftens of nanometers, while the X A peak intensity is relatively uniform. Fig. 2a and c showan example of this local intensity change for the X − and the L emission, which can occurfor areas as small as 30x30 nm . Spectra averaged in such small regions (Fig. 2e) showvarying peak heights. This behavior is not homogeneous across a single h-BN/WS /h-BNheterostructure or between different samples, and has been observed in regions of a fewhundred nanometers across. A similar increase in X − intensity is observed close to edges ofthe carbon support (which appear as brighter regions in HAADF images, as in the upperright of Fig. 2b), which is in direct contact with the thicker (20 nm) h-BN layer (the sampledetails are described in the Methods section), but not with the WS layer. Indeed, filteredemission maps at the trion energy (Fig. 2d) have stronger intensities close to the edge, asobserved systematically in other holes of the same heterostructure (see Fig. SI6) and of5 .0 2.5 3.0 Energy (eV) I n t e n s i t y CLEELSX - X A X A* X B X C X A Stokes Shift b da c h-BNWS2h-BN impuritieschargeaccumulationconductivecarbonphotons X A -- --- - - X - LX - En e r g y ( e V ) D i ff e r e n t a r e a s C o un t s X - En e r g y ( e V ) C o un t s D i ff e r e n t a r e a s X A FIG. 1.
Nanoscale optics of WS monolayers: (a) Sketch of the main results: a WS mono-layer (orange) encapsulated by two h-BN flakes (purple, 20 and 5 nm thickness) partially supportedby a holey carbon film (gray) shows three emission lines: A excitons (X A , red), trions (X − , cyan)and localized emitters (L, blue). X − emission intensity increases close to the carbon support edgesand around tens of nanometer residues patches throughout the WS monolayer. The inset showsan atomically resolved image of the WS in the heterostructure (the scale bar is 2 nm). (b) Typicalelectron energy loss spectra (EELS, orange) and cathodoluminescence (CL, purple). The X A , X B ,X C , and X − peaks are labeled. The extra absorption between X A and X B is attributed to the2s excited state of X A , marked X ∗ A . The difference between X A emission and absorption maximais marked as Stokes shift. The curves intensities are normalized to match the X A maxima. (c) Histogram of the A exciton energy, measured by Gaussian fitting of the CL X A peak at each po-sition contained in 6 different regions. (d) Histogram of the trion energy, measured by Gaussianfitting of the same CL data as (c). Each color represents a distinct region of between 1 and 2 µ m surface area containing hundreds of pixels, that would be only few pixels if measured by opticaldiffraction-limited methods.
00 nm I n t e n s i t y ab c d I n t e n s i t y Energy (eV) I n t e n s i t y X A X - Energy (eV) I n t e n s i t y X - L
200 nm
500 nm
200 nm X A ef
13 213 2 4 5 X A X - L X - FIG. 2.
Nanoscale emission intensity variations: (a)
HAADF image of the area measuredin (c) and (e), (b)
HAADF image of the suspended area measured in (d) and (f). (c)
L emitters(left), X − (center) and X A (right) intensity maps, where small localized spots are seen for L andX − . (d) X − intensity map showing trion enhancement next to the carbon support edge. (e) CLspectra corresponding to highlighted regions in (c). (f )
CL spectra corresponding to highlightedregions in (d). The intensity in (e) and (f) was normalized by the maximum of the cyan spectrumto conserve the intensity changes of all peaks. The intensity in (c) and (d) was normalized bydividing by the maximum of each integrated datacube. The shaded regions in (e) and (f) markwhere intensities were integrated for (c) and (d). different samples. Spectra close to the edge (cyan curve in Fig. 2f) show stronger trionemission in comparison to those in the suspended region (red curve in Fig. 2f). At firstglance, these emission modifications could have the same origin. Yet, they occur at differentscales Figs. 3 (tens of nanometers) and 4 (above a hundred nanometers) further entailing adetail analysis.In suspended regions where the X − intensity varies locally while X A intensity remainsconstant (Fig. 3a-b and Fig. SI4), the typical spatial extension where enhanced trionemission is observed is of the order of tens of nanometers. As a function of position acrossdifferent bright spots, the X − and X A intensities change independently (Fig. 3b), with nomeasurable energy shift. The typical size of these regions brings to mind the possibility ofdiscrete light emitters, such as individual point defects, as observed in h-BN in the past [33]7sing CL. The trion formation and decay probabilities are known to depend on the localdensity of available free carriers, which can be modified not only by the presence of defects,but also by the local dielectric environment. HAADF images (Fig. 3d) of these regions showintensity variations, indicating the presence of extra matter either on the heterostructures’interfaces or surfaces. Core loss EELS shows that in addition to the expected chemicalspecies (S, B, and, N), traces of impurities including Si, C, and O are also detected. Silicon,carbon, and oxygen impurities are expected residues from the sample preparation duringthe exfoliation of layers.Blind source separation spectral analysis (see Methods, and Fig. SI5) shows that acomponent with Si, C, and O content is anti-correlated to the appearance of localized X − emission maxima: a map of this component is shown in Fig. 3c. The localized trionemission occurs in the areas which lack this residue-related component (marked by dashcircles in Fig. 3). These same patches appear as minima in an HAADF image (Fig. 3d,which is proportional to the projected atomic number; see Fig. SI5b, Fig. 2a-b, and theMethods section). Their presence do not prevent the excitation transfer from the h-BN tothe monolayer, indicating they are thin (as also suggested by EELS). h-BN/TMD stackscan be very clean [34], but they contain some thin interface residue and bubbles. Theseadditional surrounding dielectric patches change the local electromagnetic environment ofthe WS monolayer.Around holes in the carbon support of the sample, the X − to X A ratio also increases(Fig. 4a-b and Methods). On top of the carbon support the X A emission increases, with adrastic decrease of the X − to X A ratio. A series of emission spectra acquired starting fromthe suspended region up to the hole’s edge along three different line profiles show the contin-uous increase in X − and X A emission. This evolution in emission occurs without observablemodification of the absorption spectra (Fig. 4c-e, right panels). The same behavior occursin most of the analyzed holes in the carbon support (three other examples are shown in Fig.SI6). A correlation between strain (Fig. 4a shows the (cid:15) yy component) and these modifica-tions has not been detected (the bright lines occur due to structural changes including afold and the carbon support edge).In addition to the X − intensity increase, its peak emission energy varies towards the edgeof the support (white curved arrow in Fig. 4d and Fig. SI6): initially the peak redshiftsby about 20 meV over a distance of 200 nm, and as its intensity increases, the redshift is8 .40.60.81.0 I n t e n s i t y I n t e n s i t y I n t e n s i t y ab cd Si - EELS X -
100 nm1.95 2.00 2.05 2.10Energy (eV) P o s i t i o n ( n m ) X - X A FIG. 3.
Trion modification due to local surface patches: (a) X − intensity map. Theintensity was normalized by the maximum of trion emission. (b) Spectral profile along the arrowin (a), where intensity modulation of X − occurs. (c) Residue content extracted using a blind sourceseparation algorithm on the EELS datacube. The residue is present due to the monolayer transferprocess. (d)
HAADF image acquired in parallel with the EELS datacube image used to generate(c), with dark regions appearing to the lack of residue. X − maxima occur where the residue is notpresent. followed by a final abrupt shift back to its initial energy, over a distance of 50 nm, and alarger intensity increase. The energy shifts lead to broader emission X − histograms comparedthe X A (orange curves in Fig. 1c-d). Where this effect is observed, the X A emission andabsorption energy do not follow the variations observed for the X − . However, along withthis characteristic shift of the trion, other energy shifts are observed, which the X A doesfollow (Fig. 4c and Fig. SI6). These will be disentangled in the discussion.Finally, close to the carbon support edge, one also observes localized emissions whichmatch the lower-energy transitions referred to as L in literature [8, 10, 14, 15] (Fig. 4,9 n t e n s i t y ab cd Emission Absorption
500 nm S t r a i n ( % ) P o s i t i o n ( n m )
500 nm P o s i t i o n ( n m ) X - e
35 meV
Lcarboncarbon c d ec d e ε yy X - P o s i t i o n ( n m ) X -
25 meV X A X A FIG. 4.
Trion and L increase due to charge accumulation in a conductor-insulator-semiconductor interface: (a)
Strain map of (cid:15) yy component. The brightest lines correspondto a fold (top line) and the edge of the carbon membrane (curved line). (b) X − intensity map,normalized by the maximum of trion emission. (c-e) CL (left) and EELS (right) spectra alongeach arrow marked in (a) and (b). In both (c) and (d) the trion peak redshifts then shifs back to itsinitial energy when approaching the carbon membrane (represented by a dotted line), as explainedin the text. (e) A lower energy emission, marked by L 35 meV below the X A emission, which doesnot shift in energy is observed. It is attributed to localized excitons. vertical profiles e in Fig. 4a-b). This emission can be separated from that of the trion sincetheir energy splittings to the X A are different: X A - X − is 35 meV on average while X A -L is 45 meV. This particular energy splitting is systematically observed for this localizedemission on the edge of the carbon support (observed on 21 measurements of 14 local emittersfrom two different samples). Its intensity is usually brighter than that of the trion, with anintensity ratio of I L /I X A = 3.4 on average, while it is of 1.3 for I X − /I X A . The width of theL emission is about the same as that of the X − , respectively 31 and 33 meV, but larger thanthat of the X A is 17 meV, on average. The appearance of L emission could not be directly10inked to patterns in strain maps.The ensemble of observations concerning the trion can be explained by making a hypoth-esis based on local changes of the free electron density and of the dielectric environment.Trion emission intensity can be controlled by gating of III-V [35] and TMD [9] semicon-ductors, which controls the density of free electrons; conversely, chemical doping can alsomodify this quantity [36]. Unintentional doping in MoS has been shown to increase trionemission [37], while a similar increase in WS has been attributed to a larger concentrationof defects [38]. Substrate modification has also demonstrated an effect on the trion emissionintensity in WS monolayers [39]. In view of these reported observations, we attribute thelocalized trion emission increase described in Fig. 3 to an augmentation of the local freeelectron density due to the absence of the surface contaminants. It has also been observedthat strain (0.6 % and above) applied to WS monolayers [40] could induce trion intensitymodification. Strain maps of regions around holes in the support do not show a correlationto the trion increase pattern (Fig. SI7). Our strain measurements are not precise below 1%for the buried WS monolayer (see Methods), so small deformations cannot be excluded.Finally, X A emission energy is not modified by the local dielectric patches. It is known thatthe optical bandgap of TMD monolayers is weakly influenced by the dielectric environment[16], as both the single particle bandgap and the exciton binding energy shift in tandem (tofirst order).At first sight, one could invoke a similar interpretation to the increase in the X − /X A emission ratio close to the carbon support edge, that is, an effect of the local dielectricenvironment of the monolayer. However, given the sample geometry, the carbon support isnot in contact with the monolayer, but separated by 20 nm of h-BN (the lower layer in theheterostructure), a thickness far larger than the extent of the exciton wavefunction outsidethe monolayer [7]. More importantly, the amorphous carbon of the TEM grids is conductive,which is one of the reasons for their routine use in TEM, and it would quench light emissionfrom the monolayers (TMD monolayer deposited directly on TEM grids do not emit lightin CL experiments).It is exactly this conductive character of the carbon support that enters into play here.Our hypothesis is that the carbon support, h-BN, and WS heterostructure forms a metal-insulator-semiconductor (MIS) capacitor, as the WS is in contact with the carbon supportaway from measurement area. Therefore, free carriers at the center of the suspended region11distant from the carbon support) have different potential profiles than those in proximityto the carbon support. This changes the free carrier density at the center of the hole andaround its edges, resulting in the different X − /X A emission ratio. Rough estimates showthat the capacitance created by a 20 nm h-BN (considering its bulk dielectric function),given the difference in workfunction between amorphous carbon and WS , can induce chargedensities of the order of 1x10 cm − . A 3 . cm − increase in the electron density inWS (achieved by a 40 V gate voltage) has demonstrated an increase of the X − absorptionintensity and a redshift of about 20 meV [9]. This energy shift matches the magnitude ofthat observed in Fig. 4c. In short, we interpret the redshift and higher emission rate as anincrease in the trion population due to higher free electron concentration.A second effect is observed, in addition to the redshift of the trion energy over 200 nmwhen approaching the carbon support; a blueshift of the trion which is in fact a shift back toits initial energy far from the carbon membrane. Along with this shift, an intensity increaseat distances below 50 nm from the edge of the membrane is clearly visible. This is at firstcounterintuitive, as the former MIS capacitor explanation implies a continuous redshift withintensity increase. This second shift cannot be explained by a local change of the opticalbandgap, since the energy of X A remains constant or changes marginally, both in absorptionand emission (Fig. 4d) across the whole range. A simple reduction of the charge densitywould explain the shift back to initial energy, but not the increase in emission. We attributethis second shift and increase in intensity to a locally higher density of optical modes, whichincreases the decay rate due to the Purcell effect, where both the X − and X A are modified.A substantial increase in the emission intensity of molecules has been known to occur inclose proximity to metallic structures [41].In fact, such enhancement induces shorter exciton and trion lifetimes, leading directlyto higher emission rates. It also explains the shift back in energy, which is related to thesubsequent decrease of the trion population. We note that this is followed by an increaseof X A emission, which is stronger on top of the carbon support (Fig. 4c, above the whitedashed line), where the trion emission is reduced (Fig. 4d and SI6). We interpret this asa consequence of the reduction of the X A lifetime, which increases its emission rate anddecreases the trion formation probability. Here, we note that absorption intensity does notincrease, ruling out a larger emission intensity simply due to a larger excitation rate. Thatis, at a constant excitation rate, the total number of exciton and trion formation is fixed,12eading to a competition between their emission intensities.More specifically, the hypothesis of a trion blueshift due to strain is excluded becausestrain would also blueshift the X A emission and absorption energies, since it would changethe WS optical bandgap. Notably, in other regions X A emission and absorption are observedto change locally, as in the profiles in Fig. 4c and Fig. SI6. These energy shifts are followedby the X − , but they do not preclude the general behavior demonstrated in Fig. 4d. Strainmapping (Fig. SI8) along the profiles in the regions where the X A energy (and X − ) variesdoes not allow one to attribute the energy profiles solely to strain. Shear and tensile strainand in-plane rotation are observed, but a one-to-one correspondence between these and theenergy variations was not detected in Fig. SI8 and Fig. SI9.Finally, we return to the L emission observation. Strain maps of the monolayer closeto the carbon support edges show that it is strained (see Fig. SI9 and Fig. SI8). Thestrain pattern is not simply that of a suspended membrane covering a circular hole, as onemight initially expect. Indeed, regions close to the support edges show they can be undercompression, including those where trion emission is increased. We interpret this as a resultof the strain created during the heterostructure transfer.This complex strain profile brings to mind the multiple observations of single photonemitters in TMDs [3–6], specifically WSe , which are currently attributed to the formationof localized excitonic states due to confinement. Previous experiments in suspended layers [3]and layers deposited over nanopillars [4, 6] show that strained layers lead to the formation ofthese single photon source. We do not observe a one-to-one correspondence of the appearanceof L emission and strain maps. These emitters can be distinguished from trions based ontheir energy (they appear as distinct peaks in the binding energy histograms in Fig. SI10)and have spatial localization below 100 nm, similarly to single photon emitters detected in h-BN using CL [33]. These and other localized emitters in TMDs warrant further explorationat the nanometer and atomic scales.In addition to allowing us to validate some hypothesis concerning energy shifts, theabsorption and emission profiles shown in Fig. 4 give a local measure of the Stokes shift,the energy difference between emission and absorption of the same transition (X A here).In molecular systems this energy difference occurs due to the interaction with phonons. Insemiconductors, in addition to phonon interaction, other phenomena can intervene, such asdoping, strain, and substrate-related effects. The Stokes shift measured for our samples is13f the order of 40 meV. This is much larger than the smallest reported values for bare orh-BN encapsulated WS monolayer [8, 29]. We attribute this difference to sample quality(source of WS or the heterostructure preparation), which further motivates future EELSand optical absorption experiments on the same objects.The results presented here demonstrate the existence of nanometer scale localized lightemission in relatively structurally homogeneous TMD monolayers, which can be attributed tovariations of the free electron density in the material caused by surface residue modifying thedielectric environment locally. Trion mapping on TMDs could also be used as local dielectricsensor, similar to the suggestion by Xu et. al [16] based on optical reflectivity. From anotherperspective, the creation of nanoscale emitters indicate that dense arrays could be engineeredby manipulation of the surface, such as by way of patterning. Finally, a lack of correlationbetween L emitters and strain above 1% indicates that strain alone is not sufficient fortheir generation. Possibly, point defects are necessary to generate them, as suggested bythe detection of single photon emitters in h-BN encapsulated WSe placed on dielectricpillars only after 100 keV electron-irradiation [6]. As such, nanoscale electron microscopyand spectroscopy can offer a way to generate and characterize atomic-scale defects, andto monitor the change in optical response in real-time towards better understanding ofnanoscale emitters in TMDs. [1] K. F. Mak, C. Lee, J. Hone, J. Shan, and T. F. Heinz, Atomically thin MoS : A new direct-gapsemiconductor, Phys. Rev. Lett. , 136805 (2010).[2] X. Xu, W. Yao, D. Xiao, and T. F. Heinz, Spin and pseudospins in layered transition metaldichalcogenides, Nat. Phys. , 343 (2014).[3] P. Tonndorf, R. Schmidt, R. Schneider, J. Kern, M. Buscema, G. A. Steele, A. Castellanos-Gomez, H. S. van der Zant, S. M. de Vasconcellos, and R. Bratschitsch, Single-photon emissionfrom localized excitons in an atomically thin semiconductor, Optica , 347 (2015).[4] C. Palacios-Berraquero, D. M. Kara, A. R.-P. Montblanch, M. Barbone, P. Latawiec, D. Yoon,A. K. Ott, M. Loncar, A. C. Ferrari, and M. Atat¨ure, Large-scale quantum-emitter arrays inatomically thin semiconductors, Nature Comm. , 1 (2017).[5] T. P. Darlington, C. Carmesin, M. Florian, E. Yanev, O. Ajayi, J. Ardelean, D. A. Rhodes, . Ghiotto, A. Krayev, K. Watanabe, et al. , Imaging strain-localized exciton states innanoscale bubbles in monolayer WSe at room temperature, Nat. Nano , 854 (2020).[6] K. Parto, K. Banerjee, and G. Moody, Irradiation of nanostrained monolayer WSe for site-controlled single-photon emission up to 150 k (2020), arXiv:2009.07315 [physics.app-ph].[7] A. Molina-S´anchez, D. Sangalli, K. Hummer, A. Marini, and L. Wirtz, Effect of spin-orbitinteraction on the optical spectra of single-layer, double-layer, and bulk MoS , Phys. Rev. B , 045412 (2013).[8] A. Arora, N. K. Wessling, T. Deilmann, T. Reichenauer, P. Steeger, P. Kossacki, M. Potemski,S. M. de Vasconcellos, M. Rohlfing, and R. Bratschitsch, Dark trions govern the temperature-dependent optical absorption and emission of doped atomically thin semiconductors, Phys.Rev. B , 241413 (2020).[9] A. Chernikov, A. M. van der Zande, H. M. Hill, A. F. Rigosi, A. Velauthapillai, J. Hone, andT. F. Heinz, Electrical tuning of exciton binding energies in monolayer WS , Phys. Rev. Lett. , 126802 (2015).[10] M. Paur, A. J. Molina-Mendoza, R. Bratschitsch, K. Watanabe, T. Taniguchi, and T. Mueller,Electroluminescence from multi-particle exciton complexes in transition metal dichalcogenidesemiconductors, Nat. Comm. , 1 (2019).[11] A. Castellanos-Gomez, R. Rold´an, E. Cappelluti, M. Buscema, F. Guinea, H. S. van der Zant,and G. A. Steele, Local strain engineering in atomically thin MoS , Nano Lett. , 5361(2013).[12] R. Schmidt, I. Niehues, R. Schneider, M. Dr¨uppel, T. Deilmann, M. Rohlfing, S. M. De Vas-concellos, A. Castellanos-Gomez, and R. Bratschitsch, Reversible uniaxial strain tuning inatomically thin WSe , 2D Materials , 021011 (2016).[13] R. Frisenda, M. Dr¨uppel, R. Schmidt, S. M. de Vasconcellos, D. P. de Lara, R. Bratschitsch,M. Rohlfing, and A. Castellanos-Gomez, Biaxial strain tuning of the optical properties ofsingle-layer transition metal dichalcogenides, npj 2D Materials and Applications , 1 (2017).[14] J. Jadczak, J. Kutrowska-Girzycka, P. Kapu´sci´nski, Y. Huang, A. W´ojs, and z. Bryja, Probingof free and localized excitons and trions in atomically thin WSe , WS , MoSe and MoS inphotoluminescence and reflectivity experiments, Nanotechnology , 395702 (2017).[15] M. Koperski, M. R. Molas, A. Arora, K. Nogajewski, A. O. Slobodeniuk, C. Faugeras, andM. Potemski, Optical properties of atomically thin transition metal dichalcogenides: observa- ions and puzzles, Nanophotonics , 1289 (2017).[16] Y. Xu, C. Horn, J. Zhu, Y. Tang, L. Ma, L. Li, S. Liu, K. Watanabe, T. Taniguchi, J. C. Hone, et al. , Creation of moir´e bands in a monolayer semiconductor by spatially periodic dielectricscreening, Nat. Mat. , 1 (2021).[17] A. Polman, M. Kociak, and F. J. G. de Abajo, Electron-beam spectroscopy for nanophotonics,Nat. Mat. , 1158 (2019).[18] S. Zheng, J.-K. So, F. Liu, Z. Liu, N. Zheludev, and H. J. Fan, Giant enhancement of cathodo-luminescence of monolayer transitional metal dichalcogenides semiconductors, Nano Lett. ,6475 (2017).[19] G. Nayak, S. Lisi, W. Liu, T. Jakubczyk, P. Stepanov, F. Donatini, K. Watanabe,T. Taniguchi, A. Bid, J. Kasprzak, et al. , Cathodoluminescence enhancement and quench-ing in type-i van der waals heterostructures: Cleanliness of the interfaces and defect creation,Phys. Rev. Materials , 114001 (2019).[20] A. Singh, H. Y. Lee, and S. Gradeˇcak, Direct optical-structure correlation in atomically thindichalcogenides and heterostructures, Nano Res. , 1 (2020).[21] L. H. Tizei, Y.-C. Lin, M. Mukai, H. Sawada, A.-Y. Lu, L.-J. Li, K. Kimoto, and K. Suenaga,Exciton mapping at subwavelength scales in two-dimensional materials, Phys. Rev. Lett. ,107601 (2015).[22] C. Habenicht, M. Knupfer, and B. B¨uchner, Investigation of the dispersion and the effectivemasses of excitons in bulk 2H-MoS using transition electron energy-loss spectroscopy, Phys.Rev. B , 245203 (2015).[23] H. C. Nerl, K. T. Winther, F. S. Hage, K. S. Thygesen, L. Houben, C. Backes, J. N. Coleman,Q. M. Ramasse, and V. Nicolosi, Probing the local nature of excitons and plasmons in few-layerMoS , npj 2D Materials and Applications , 1 (2017).[24] J. Hong, R. Senga, T. Pichler, and K. Suenaga, Probing exciton dispersions of freestandingmonolayer WSe by momentum-resolved electron energy-loss spectroscopy, Phys. Rev. Lett. , 087401 (2020).[25] R. J. Pe˜na Rom´an, Y. Auad, L. Grasso, F. Alvarez, I. D. Barcelos, and L. F.Zagonel, Tunneling-current-induced local excitonic luminescence in p-doped WSe monolayers,Nanoscale , 13460 (2020).[26] B. Schuler, K. A. Cochrane, C. Kastl, E. S. Barnard, E. Wong, N. J. Borys, A. M. chwartzberg, D. F. Ogletree, F. J. G. de Abajo, and A. Weber-Bargioni, Electrically drivenphoton emission from individual atomic defects in monolayer WS , Science Advances ,10.1126/sciadv.abb5988 (2020).[27] Z. Mahfoud, A. T. Dijksman, C. Javaux, P. Bassoul, A.-L. Baudrion, J. Plain, B. Dubertret,and M. Kociak, Cathodoluminescence in a scanning transmission electron microscope: Ananometer-scale counterpart of photoluminescence for the study of ii–vi quantum dots, J. ofPhys. Chem. Lett. , 4090 (2013).[28] P. V. Kolesnichenko, Q. Zhang, T. Yun, C. Zheng, M. S. Fuhrer, and J. A. Davis, Disentan-gling the effects of doping, strain and disorder in monolayer WS by optical spectroscopy, 2DMaterials , 025008 (2020).[29] I. Niehues, P. Marauhn, T. Deilmann, D. Wigger, R. Schmidt, A. Arora, S. M. de Vascon-cellos, M. Rohlfing, and R. Bratschitsch, Strain tuning of the stokes shift in atomically thinsemiconductors, Nanoscale , 20786 (2020).[30] R. Hambach, Theory and ab-initio calculations of collective excitations in nanostructures:towards spatially-resolved EELS , Ph.D. thesis (2010).[31] M. Kociak and L. Zagonel, Cathodoluminescence in the scanning transmission electron mi-croscope, Ultramicroscopy , 112 (2017).[32] A. Carvalho, R. Ribeiro, and A. C. Neto, Band nesting and the optical response of two-dimensional semiconducting transition metal dichalcogenides, Phys. Rev. B , 115205 (2013).[33] R. Bourrellier, S. Meuret, A. Tararan, O. St´ephan, M. Kociak, L. H. G. Tizei, and A. Zobelli,Bright UV single photon emission at point defects in h-BN, Nano Lett. , 4317 (2016).[34] S. Haigh, A. Gholinia, R. Jalil, S. Romani, L. Britnell, D. Elias, K. Novoselov, L. Ponomarenko,A. Geim, and R. Gorbachev, Cross-sectional imaging of individual layers and buried interfacesof graphene-based heterostructures and superlattices, Nature materials , 764 (2012).[35] F. J. Teran, L. Eaves, L. Mansouri, H. Buhmann, D. K. Maude, M. Potemski, M. Henini, andG. Hill, Trion formation in narrow GaAs quantum well structures, Phys. Rev. B , 161309(2005).[36] N. Peimyoo, W. Yang, J. Shang, X. Shen, Y. Wang, and T. Yu, Chemically driven tunablelight emission of charged and neutral excitons in monolayer WS , ACS Nano , 11320 (2014).[37] A. Neumann, J. Lindlau, M. Nutz, A. D. Mohite, H. Yamaguchi, and A. H¨ogele, Signatures ofdefect-localized charged excitons in the photoluminescence of monolayer molybdenum disul- de, Phys. Rev. Materials , 124003 (2018).[38] Y.-C. Lin, S. Li, H.-P. Komsa, L.-J. Chang, A. V. Krasheninnikov, G. Eda, and K. Suenaga,Revealing the atomic defects of WS governing its distinct optical emissions, Adv. Func. Mat. , 1704210 (2018).[39] Y. Kobayashi, S. Sasaki, S. Mori, H. Hibino, Z. Liu, K. Watanabe, T. Taniguchi, K. Suenaga,Y. Maniwa, and Y. Miyata, Growth and optical properties of high-quality monolayer WS ongraphite, ACS Nano , 4056 (2015).[40] M. G. Harats, J. N. Kirchhof, M. Qiao, K. Greben, and K. I. Bolotin, Dynamics and efficientconversion of excitons to trions in non-uniformly strained monolayer WS , Nat. Photon. , 1(2020).[41] P. Anger, P. Bharadwaj, and L. Novotny, Enhancement and quenching of single-moleculefluorescence, Phys. Rev. Lett. , 113002 (2006).[42] L. H. Tizei, V. Mkhitaryan, H. Louren¸co-Martins, L. Scarabelli, K. Watanabe, T. Taniguchi,M. Tenc´e, J.-D. Blazit, X. Li, A. Gloter, et al. , Tailored nanoscale plasmon-enhanced vibra-tional electron spectroscopy, Nano Lett. , 2973 (2020).[43] O. L. Krivanek, T. C. Lovejoy, N. Dellby, T. Aoki, R. W. Carpenter, P. Rez, E. Soignard,J. Zhu, P. E. Batson, M. J. Lagos, R. F. Egerton, and P. A. Crozier, Vibrational spectroscopyin the electron microscope, Nature , 209 (2014).[44] M. J. Lagos, A. Tr¨ugler, U. Hohenester, and P. E. Batson, Mapping vibrational surface andbulk modes in a single nanocube, Nature , 529 (2017).[45] R. Qi, R. Wang, Y. Li, Y. Sun, S. Chen, B. Han, N. Li, Q. Zhang, X. Liu, D. Yu, et al. ,Probing far-infrared surface phonon polaritons in semiconductor nanostructures at nanoscale,Nano Lett. , 5070 (2019).[46] J. A. Hachtel, J. Huang, I. Popovs, S. Jansone-Popova, J. K. Keum, J. Jakowski, T. C. Lovejoy,N. Dellby, O. L. Krivanek, and J. C. Idrobo, Identification of site-specific isotopic labels byvibrational spectroscopy in the electron microscope, Science , 525 (2019).[47] F. Hage, G. Radtke, D. Kepaptsoglou, M. Lazzeri, and Q. Ramasse, Single-atom vibrationalspectroscopy in the scanning transmission electron microscope, Science , 1124 (2020).[48] A. Losquin, L. F. Zagonel, V. Myroshnychenko, B. Rodr´ıguez-Gonz´alez, M. Tenc´e, L. Scara-belli, J. F¨orstner, L. M. Liz-Marz´an, F. J. G. de Abajo, O. St´ephan, and M. Kociak, Unveilingnanometer scale extinction and scattering phenomena through combined electron energy loss pectroscopy and cathodoluminescence measurements, Nano Lett. , 1229 (2015).[49] M. Couillard, G. Radtke, A. P. Knights, and G. A. Botton, Three-dimensional atomic structureof metastable nanoclusters in doped semiconductors, Phys. Rev. Lett. , 186104 (2011).[50] D. N. Johnstone, P. Crout, M. Nord, J. Laulainen, S. Høg˚as, EirikOpheim, B. Martineau,T. Bergh, C. Francis, S. Smeets, E. Prestat, andrew ross1, S. Collins, I. Hjorth, Mohsen,T. Furnival, D. Jannis, E. Jacobsen, AndrewHerzing, T. Poon, H. W. ˚Anes, J. Morzy,phillipcrout, T. Doherty, affaniqbal, T. Ostasevicius, mvonlany, and R. Tovey, pyxem/pyxem:pyxem 0.12.3 (2020).[51] F. de la Pe˜na, E. Prestat, V. T. Fauske, P. Burdet, T. Furnival, P. Jokubauskas, M. Nord,T. Ostasevicius, K. E. MacArthur, D. N. Johnstone, M. Sarahan, J. L¨ahnemann, J. Taillon,pquinn dls, T. Aarholt, V. Migunov, A. Eljarrat, J. Caron, S. Mazzucco, B. Martineau,S. Somnath, T. Poon, M. Walls, T. Slater, actions user, N. Tappy, N. Cautaerts, F. Winkler,G. Donval, and J. C. Myers, hyperspy/hyperspy: Release v1.6.1 (2020).[52] F. Pizzocchero, L. Gammelgaard, B. S. Jessen, J. M. Caridad, L. Wang, J. Hone, P. Bøggild,and T. J. Booth, The hot pick-up technique for batch assembly of van der waals heterostruc-tures, Nature Com. , 1 (2016).[53] T. Taniguchi and K. Watanabe, Synthesis of high-purity boron nitride single crystals underhigh pressure by using ba-bn solvent, Journal of Crystal Growth , 525 (2007).[54] O. St´ephan, D. Taverna, M. Kociak, K. Suenaga, L. Henrard, and C. Colliex, Dielectricresponse of isolated carbon nanotubes investigated by spatially resolved electron energy-lossspectroscopy: From multiwalled to single-walled nanotubes, Phys. Rev. B , 155422 (2002). A. Acknowledgments
This project has been funded in part by the National Agency for Research under theprogram of future investment TEMPOS-CHROMATEM (reference no. ANR-10-EQPX-50)and from the European Union’s Horizon 2020 research and innovation programme undergrant agreement No 823717 (ESTEEM3) and 101017720 (EBEAM). K.W. and T.T. ac-knowledge support from the Elemental Strategy Initiative conducted by the MEXT, Japan,Grant Number JPMXP0112101001, JSPS KAKENHI Grant Number JP20H00354 and theCREST(JPMJCR15F3), JST. This work has been supported by Region ˆIle-de-France in19he framework of DIM SIRTEQ”. We thank NION, HennyZ, and Attolight for the help-full interaction on the adaptation of the CL system to the NION sample chamber on theChromaTEM microscope and customization of the liquid nitrogen sample holder. We ac-knowledge the joint effort of the STEM team at the LPS-Orsay and, in particular MarcelTenc´e and Xiaoyan Li, concerning instrumental developments. We thank Ashish Arora andco-authors for kindly providing the optical absorption data on a WS monolayer encapsu-lated in h-BN. Luiz F. Zagonel is acknowledged for ideas and discussion on data analysis. B. Competing interests
MK patented and licensed technologies at the basis of the Attolight M¨onch used in thisstudy, and is a part time consultant at Attolight. All other authors declare no competingfinancial interests. 20 . SUPPLEMENTARY INFORMATION TO NANOSCALE MODIFICATION OFWS TRION EMISSION BY ITS LOCAL ELECTROMAGNETIC ENVIRONMENTA. Methods
Scanning transmission electron microscopy (STEM) imaging, diffraction, CL and EELSexperiments were performed on a modified Nion Hermes200 operated at 60 and 100 keV.In this microscope, subnanometer electron beams with sub 10 meV energy spread [42] canbe generated for high spatial resolution imaging, diffraction and spectroscopy. High energyand spatial resolution have been substantially improved over the last ten years due to newmonochromator technologies [21, 43–47]. The energy resolution of the EELS data presentedhere was between 20 and 30 meV (energy width of the primary electron beam). CL used aM¨onch system from Attolight [31], with an energy resolution of 8 meV (minimum separationbetween two discernible emission peaks). Combined EELS-CL experiments have been usedin the past to understand optical extinction and scattering in metallic plasmonic nanopar-ticles [48], but required much smaller requirements on the spectral resolution, due to thevery large linewidth of the plasmons. Sample were kept at 150 K using a liquid nitrogenHennyZ sample holder for spectroscopic experiments, except for EELS chemical mapping.The typical exposure time used for CL and EELS low-loss experiment were 300 ms, and forcore-loss and diffraction, 50 ms.Atomically resolved imaging and spatially resolved EELS chemical maps were acquiredon Nion UltraSTEM 200 operated at 100 keV, with the samples at room temperature. Allimages shown are high angle annular dark field (HAADF) images, in which the intensityis proportional to the projected atomic number, with W atoms showing as bright dots.The columns with two S atoms in projection are harder to pinpoint due to the backgroundcreated by scattering in the h-BN layers. Diffraction effects play a smaller role in HAADFimage intensity, so imaging with the h-BN slightly off-axis is beneficial to observe the singleWS monolayer embedded in 25 nm of h-BN, as demonstrated before for CeSi clusters in Simatrices [49]. Encapsulation has also ensured a high stability of the monolayers under 60keV and 100 keV electron irradiation, allowing imaging of free edges (Fig. 1a and Fig. SI2).Diffraction patterns were acquired for each beam position on the sample with typical con-vergence semi-angle between 3 and 5 mrad and the camera dwell time was 50 ms. Diffraction21apping analysis was done with the Pyxem [50] and Hyperspy [51] python libraries. Thequantity calculated is the displacement gradient tensor, corresponding to the difference be-tween the deformed vectors and a reference, where the reference is a calculated vector withthe reciprocal space length and orientation for unstrained WS . A right-handed polar de-composition was used to separate deformation and rotation. The angle of rotation was thenrecovered from the rotation matrix. Each deformed vector was defined with the barycen-ter of the diffraction spots, and the center of the direct beam was first aligned with across correlation method. The barycenter method is limited by illumination changes of thediffraction spots (due to diffraction on the thicker h-BN layers), limiting our current strainmeasurements to above 1%.The CL and EELS datacube spectral fitting was done with the Hyperspy bounded multifittool, using gaussian profiles. The Lorentzian profile was also tried since the EELS excitonpeak profiles should be close to lorentzian, but the results are not displayed here to keepcoherence for all curve fits. Most of the values found in the text are from mean spectraextracted from different regions of interest in each spectrum-image (these extracted spectrahave a much higher signal to noise ratio). The extracted spectra are fitted with gaussianprofiles, and the uncertainty associated is the standard deviation of the fit.
1. BSS+PCA analysis description
The blind source separation (BSS) technique consists of the separation of a mixed sig-nal into individual components. The algorithm used in this paper was the independentcomponent analysis (ICA) implemented in Hyperspy. In the ICA algorithm, the individualcomponents are additive, and treated as non-gaussian and statistically independent. Wechose 3 components, the first one contains the background, the h-BN and the carbon thatare correlated together. This carbon can be from contamination of the sample. The secondone contains the silicon and some carbon, and the third one contains mostly noise.
2. Sample preparation for electron spectroscopy and microscopy h-BN/WS /h-BN heterostructures were fabricated by using modified dry transfer method[52] then transferred to a TEM grid. WS was purchased from 2DSemiconductors and22igh quality h-BN synthesized by high pressure-high temperature method [53] was used.All constituted layers were first exfoliated onto a SiO /Si substrate using the scotch-tapemethod [1]. A PDMS (polydimethylsiloxane) mask spin-coated by 15 % PPC (polypropylenecarbonate) is used for polymer stamp. PDMS is made by using the 20:1 ratio of Sylgard184 pro-polymer to curing agent and kept at ambient conditions for overnight. To enhanceadhesion between PDMS and PPC, PDMS mask was treated by oxygen plasma (18 W) for5 min, before the spin-coating of PPC at 3000 rpm followed by heat treatment at 160 ◦ Cfor 10 minutes. This polymer stamp was mounted to the micromanipulator upside down. Abrief description of the procedures are described below.1. Pick-up exfoliated h-BN crystal from SiO /Si substrate by contacting polymer stampto the target crystal at 50 ◦ C for 1 minute and lifting the stamp.2. Repeat step 1 to pick-up the monolayer WS crystal and bottom h-BN layer subse-quently.3. Drop-down the stack (h-BN/WS /h-BN) on a new SiO /Si substrate by contact athigher temperature (120 ◦ C) for 10 minutes.4. Clean the PPC residue on the surface with acetone and IPA.5. Anneal the heterostructure to enhance the interlayer coupling between constituentlayers at 250 120 ◦ C) for 6 hours in Ar environment.6. Spin-coat with polymethylmethacrylate (PMMA, 495K, Microchem) over the het-erostructure at 3000 rpm followed by a heat treatment at 180 ◦ C for 5 minutes.7. Etch SiO /Si substrate by immerse the sample into KOH solution (1M) overnight.8. Transfer the sample to TEM grid (C-flat holey carbon grid with 2 µ m hole diameter)9. Remove PMMA residue by cleaning with acetone and IPA. B. EELS and optical absorption comparison
The electromagnetic response properties of materials are usually described by its dielectricfunction (cid:15) ( ω ) = (cid:15) ( ω ) + i ∗ (cid:15) ( ω ). However optical measurements, usually give access to the23omplex refractive index, ˜ n ( ω ) = n ( ω ) + i ∗ κ ( ω ). These two quantities are linked by therelation ˜ n ( ω ) = (cid:15) ( ω ), which also links their real and imaginary parts by (cid:15) ( ω ) = n ( ω ) − κ ( ω ) (cid:15) ( ω ) = 2 n ( ω ) κ ( ω ) , (1) κ is the extinction coefficient, which is linked absorption coefficient, α , by α = 4 πκλ , (2)with λ the wavelength of light. These two quantities, κ and α , are linked to the decrease ofthe total intensity being transmitted through a medium.A large part of optical absorption measurements are made from reflectivity, which givesaccess to reflectance, R: R = ˜ n − n + 1 = ( n − + κ ( n + 1) + κ , (3)from which (cid:15) ( ω ) and (cid:15) ( ω ) can be calculated using the Kramers-Kronig relation and a modeltaking into account the different dielectric layers in the sample under study.Complications arise from the model necessary to extract the complex dielectric function,which can lead to modifications of line shapes. Therefore, measurements of an absorbancespectrum A ( λ ) = 1 − R − T can be made, from which line shapes can be directly compared.However, this quantity is not a direct measure of any of the materials macroscopic constants.Of course, these can be extracted from the data.EELS from an object with dielectric function (cid:15) ( ω ) measures Im {− /(cid:15) ( ω ) } . Therefore, ingeneral, Kramers-Kronig transformation is required to retrieve (cid:15) ( ω ) and (cid:15) ( ω ). However,for atomically thin objects it can be proven that Im { (cid:15) ( ω ) } = (cid:15) ( ω ) is true. In this case, adirect comparison of (cid:15) ( ω ) measured by EELS for atomically thin layers and the calculatedvalue from optical reflectivity is justified. Being a direct measure of (cid:15) ( ω ), one can comparethe line shapes of EELS with those in optical absorbance spectra (Fig. SI1). However, acomparison of exact energy positions requires one to take into account the dispersion of thereal part of the dielectric function.As discussed in the text, the energy shifts observed can be due to sample heterogeneity(Fig. SI11 show that the EELS spectra shift by at least 20 meV within our samples). Butpart of it can also come from the dispersion of (cid:15) ( ω ). Nevertheless, we do not exclude fine24ifferences between the quantities measured in EELS and optical absorption, in the tens ofmeV range. The fact that EELS for atomically thin structures measures Im { (cid:15) ( ω ) } has onlybeen demonstrated at higher energies, with poorer energy precision (at 15 eV with 300 meVprecision for single wall carbon nanotubes [54]).25 . Supplemental figures Energy (eV) I n t e n s i t y OpticsEELS X A X B X C SOC
FIG. SI1.
EELS and optical absorption comparison:
EELS (orange) spectrum of a WS monolayer encapsulated with h-BN. A comparison to optical absorption (purple), from Arora etal. [8], shows a near perfect one to one correspondence, with the X A , X B and X C excitons shown.The extra absorption between X A and X B is attributed to the 2s excited state of X A . a b
20 nm -1 FIG. SI2.
Atomically resolved HAADF image and diffraction of a WS monolayer: (a) Atomically resolved image of a WS monolayer encapsulated in h-BN. The h-BN layer is barelyvisible due to off-axis imaging. (b) Diffraction pattern of the same sample showing the monolayer,a faint hexagon pattern of the first-order reflections marked by white arrows. The extra spots comefrom diffraction on the two h-BN crystals. mages SampleMirror
Electron source
Electron Beam
10 nm -1 Di ff ractionLight Emission Energy (eV) I n t e n s i t y I n t e n s i t y a LightdetectionEELSDi ff raction plane Imaging WS bc df e EELS CL
FIG. SI3.
Scheme of the experiment: as described in the main text the microscope usedfor spectroscopic measurements is equipped with an electron monochromator and light collectionsystem, to allow high resolution EELS and CL. In a scanning transmission electron microscope,a focused electron beam is used. Different signals can be acquired as a function of position,including structural information (diffraction and imaging) and spectroscopic (EELS and CL here).This information can be then correlated, allowing, for example, measurements of the Stokes shiftat a given position, or variations of the chemical composition. I n t e n s i t y a b c
500 nm 500 nm100 nm
FIG. SI4. X A intensity maps from main text: (a) X A intensity from same area as Fig. 2d, (b) X A intensity from same area as Fig. 3b, (c) X A intensity from same area as Fig. 4b. All mapshave been normalized by the maximum of X A emission in the spectral integrating range.
00 200 300 400 500Energy (eV)050100150 I n t e n s i t y x10 I n t e n s i t y I n t e n s i t y I n t e n s i t y I n t e n s i t y
100 nm
12 34ab cd ef
Si L
C-KB-K N-K
FIG. SI5.
Blind source separation (BSS) analysis of Fig. 3: (a)
BSS componenents spectra,at a normal scale on the left-hand part, and multiplied by 10 for lisibility on the right-hand part, (b)
HAADF image of the studied area, (c-f ) map of each three components in (a), (c) is 1, (d)is 2, (e) is 3, (f) is 4. The one shown in Fig. 3d, is component 1 containing some background,oxydized silicon, and carbon that are probably from the PDMS sample preparation. mission Absoprtion2.10 2.152.00 2.050250500750 P o s i t i o n ( n m ) I n t e n s i t y I n t e n s i t y a b cde f g I n t e n s i t y hi klj kl g h P o s i t i o n ( n m ) X - X - X - P o s i t i o n ( n m ) cd P o s i t i o n ( n m ) P o s i t i o n ( n m ) P o s i t i o n ( n m ) X A X A X - X - X - X - X - X - X -
500 nm
500 nm
500 nm
FIG. SI6.
Three regions showing similar behavior to that described in Fig. 4b: (a, e, i)
HAADF images of the three regions. (b, f, j) X − intensity maps similar to that in Fig. 2b, showingan increase in X − emission close to the hole edges. (c, d, g, h, k, l) Spectra from selected profilesin the three regions, showing the change in emission and absorption along the corresponding arrows.Spectra such as (c, h, k) are typically observed next to the carbon membrane support (representedby a dotted line the in the spectra), the others show a less typical behaviour.
00 nm r o t a t i o n ( r a d ) a bc d S t r a i n ( % ) S t r a i n ( % ) FIG. SI7.
Strain from same area as Fig. 3: (a)
MADF image, (b) , (cid:15) xx component of the straintensor, (c) (cid:15) yy component of the strain tensor, (d) rotation angle extracted from the rotation matrixwith polar decomposition. (cid:15) xy corresponding to shear strain is not displayed and shows similarfeatures as the rotation. The strain measurements below 1% show artefacts from the change inillumination in the diffraction spots. These maps illustrate that the diffraction measurements showonly small variations that do not explain the trion localization by itself.
00 nm S t r a i n ( % ) S t r a i n ( % ) a bc d r o t a t i o n ( r a d ) FIG. SI8.
Strain close to the carbon support in Fig. 4: (a)
MADF image, (b) , (cid:15) xx componentof the strain tensor, (c) (cid:15) yy component of the strain tensor, (d) rotation angle extracted from therotation matrix with polar decomposition. (cid:15) xy corresponding to shear strain is not displayed andshows similar features as the rotation. The strain measurements below 1% show artefacts fromthe change in illumination in the diffraction spots. These maps illustrate that the diffractionmeasurements show only small variations that do not explain the trion localisation by itself.
00 nm S t r a i n ( % ) S t r a i n ( % ) a bc d r o t a t i o n ( r a d ) FIG. SI9.
Strain close to the carbon support in Fig. 2b: (a)
MADF image, (b) , (cid:15) xx compo-nent of the strain tensor, (c) (cid:15) yy component of the strain tensor, (d) rotation angle extracted fromthe rotation matrix with polar decomposition. (cid:15) xy corresponding to shear strain is not displayedand shows similar features as the rotation. The strain measurements below 1% show artifactsfrom the change in illumination in the diffraction spots. These maps illustrate that the diffractionmeasurements show only small variations that do not explain the trion localisation by itself. .05 2.07 2.09 2.11 2.13Energy (eV)020406080100 X A -EELS a d
350 400 4500204060801002.01 2.03 2.05 2.07 2.09 2.11Energy (eV)0204060801000 20 40 60 80 100Energy (meV)020406080100 X B -EELS SOCX A -CL fb e X - -CL g Charg.energy c Stokesshift
FIG. SI10.
Histogram of measured energies and energies differences in different regions:(a) X A energy measured in EELS, (b) X A energy measured in CL, (c) X B energy measured inEELS, (d) X − energy measured in CL, (e) Stokes shift (corresponding to X
A,EELS - X
A,CL energy), (f )
Spin-orbit splitting (corresponding to X B - X A energy), (g) charging energy (corresponding toX A - X − energy). The energies are extracted from Gaussian fit of each pixel of each datacube. The12 datacubes were measured on the same day, on different areas of the same sample. The areas areof few µ m each. The colorcode refers to the different areas measured on the same heterostructurewithin holes in the amorphous carbon film. .95 2.00 2.05 2.1002468 a X A -EELS b X A -CL Energy (eV) 2.35 2.40 2.45 2.50 2.5502468 X B -EELS c X - -CL Energy (eV) Energy (eV)Energy (eV) d e L -CL
FIG. SI11.
Histogram of absorption and emission energies across all samples: