# Nanoscale modification of WS2 trion emission by its local electromagnetic
environment

Noémie Bonnet  Université Paris-Saclay, CNRS, Laboratoire de Physique des
Solides, 91405, Orsay, France  Hae Yeon Lee  Department of Materials Science
and Engineering, Massachusetts Institute of Technology, 77 Massachusetts Ave,
Cambridge, MA, 02141, USA  Fuhui Shao  Université Paris-Saclay, CNRS,
Laboratoire de Physique des Solides, 91405, Orsay, France  Steffi Y. Woo
Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405,
Orsay, France  Jean-Denis Blazit  Université Paris-Saclay, CNRS, Laboratoire
de Physique des Solides, 91405, Orsay, France  Kenji Watanabe  Research Center
for Functional Materials, National Institute for Materials Science, 1-1
Namiki, Tsukuba 305-0044, Japan  Takashi Taniguchi  International Center for
Materials Nanoarchitectonics, National Institute for Materials Science, 1-1
Namiki, Tsukuba 305-0044, Japan  Alberto Zobelli  Université Paris-Saclay,
CNRS, Laboratoire de Physique des Solides, 91405, Orsay, France  Odile Stéphan
Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405,
Orsay, France  Mathieu Kociak  Université Paris-Saclay, CNRS, Laboratoire de
Physique des Solides, 91405, Orsay, France  Silvija Gradecak-Garaj
<EMAIL_ADDRESS>Department of Materials Science and Engineering,
Massachusetts Institute of Technology, 77 Massachusetts Ave, Cambridge, MA,
02141, USA  Luiz H. G. Tizei<EMAIL_ADDRESS>Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405,
Orsay, France

###### Abstract

Structural, electronic, and chemical nanoscale modifications of transition
metal dichalcogenide monolayers alter their optical properties, including the
generation of single photon emitters. A key missing element for complete
control is a direct spatial correlation of optical response to nanoscale
modifications, due to the large gap in spatial 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 electron spectroscopy,
specifically electron energy loss spectroscopy (EELS) for absorption and
cathodoluminescence (CL) for emission, which were directly correlated to
chemical and structural information. In an h-BN/WS2/h-BN heterostructure, we
observe local modulation of the trion (X-) emission due to tens of nanometer
wide dielectric patches, while the exciton, XA, does not follow the same
modulation. Trion emission also increases in regions where charge accumulation
occurs, close to the carbon film supporting the heterostructures. Finally,
localized exciton emission (L) detection is not correlated to strain
variations above 1 $\%$, suggesting point defects might be involved in their
formations.

Transition metal dichalcogenides (TMDs) of the form MX2 (where M = W, Mo, and
X = S, Se) with the 2H phase are semiconductors with indirect bandgap in bulk,
and direct bandgap in monolayer [1]. Photoluminescence (PL) due to exciton
decay is then brightest for monolayers. Their particular excitonic spin-valley
physics, created by the lack of inversion symmetry, the strong spin-orbit
coupling [2], and the reduced coulomb screening, have recently attracted great
interest. Up to now, spectral changes in PL have not been linked to specific
nanometer structural or chemical modifications in TMD monolayers, despite the
observation of single photon emitters (SPE) in these materials. These SPE are
of particular interest for their temporal stability, narrow spectral
linewidths [3, 4, 5, 6] indicating a low coupling to phonons, and possibility
to create them selectively in space [4, 6], which places them as strong
candidates for applications in quantum optics.

Near band-edge optical resonances of TMD monolayers are governed by excitonic
transitions with Bohr radii in the nanometer range [7]. The two lowest
excitons, namely XA and XB, occur at the $K$ point in reciprocal space and are
split by spin-orbit coupling. Emission spectra of TMD monolayers, such as from
PL spectroscopy, contain excitons (XA) [8], trions that 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,
12, 13]. Some of these have 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) [14, 15, 5]. Nanometer scale modulation of the
dielectric environment of WSe2 through a gated h-BN/graphene heterostructure
creates moiré bands [16]. These bands were attributed to local changes of the
single particle bandgap, but not directly measured. Local measurements of the
absorption of these heterostructures (where WSe2 is buried in layers of h-BN
and graphene) or the identification of the of nanoscale emitters in TMDs
require at least an order of magnitude increase in the spatial resolution in
measurements of the local structure and the chemistry to be coupled with
optical measurements. Electron spectroscopies, such as electron energy loss
spectroscopy (EELS), cathodoluminescence (CL) have the potential to address
the obstacle of measuring the optical properties at deep sub-wavelength scales
[17].

Here, we used transmission electron microscopy techniques including highly
monochromated EELS, CL, high angle annular dark field (HAADF), and diffraction
imaging to correlate sub-10 nanometer optical absorption and luminescence
spectral mapping to structural and chemical mapping. We show that the trion
and other localized (L) light emission energy and intensity can vary on scales
down to tens of nanometers in WS2 monolayers while exciton emission intensity
remains unchanged. In short, three effects are revealed: localized trion
emission intensity increase at constant absorption rate due to either 1)
chemical changes in tens of nanometer patches or 2) to charge accumulation in
a metal-insulator-semiconductor heterostructure combined with near-field
emission enhancement; and 3) the presence of a bright emission, attributed to
L, below the trion energy, highly localized in space. These effects, sketched
in Fig. 1a, are linked to local charge density variations and to near-field
enhancement and not to the generally evoked local strain modification. In
addition, the spatially-constant absorption, coupled to nanoscale-resolved CL,
shows that the trion emission intensity increases due to a locally faster
decay rate.

XA, X-, and the localized emission possibly linked to defects have been
observed with CL in TMD monolayers before [18, 19, 20], utilizing specific
sample heterostructures, but with only hundreds of nanometer spatial
resolution. More importantly, previous reports of EELS measurements on TMD
monolayers did not reach spectral resolution comparable with optical
absorption experiments to allow for facile interpretation [21, 22, 23, 24]. An
alternative technique, scanning tunnelling microscopy induced luminescence
(STM-lum) allows the detection light emission 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 nanoscale equivalent
of PL.

The samples used here are made from WS2 monolayers exfoliated from bulk
material, and encapsulated in h-BN (5 and 25 nm thick on each side). The
heterostructures created are then deposited on a conductive carbon film (ten
of nanometer thick) with 2 $\mu$m-wide holes, itself supported on copper TEM
grids (see the Methods section for details on sample preparation). The
encapsulation offers high CL emission rate due to the increased interaction
volume with the fast electron beam. The high charge-carriers density then
produced enables CL detection [18, 19, 20]. High purity and homogeneity in the
h-BN layers are critical to get spectral line shapes comparable to those using
pure optical means. Four samples were analyzed, with a typical surface area of
150 $\mu m^{2}$.

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 arrays with a spectrum or a diffraction
pattern at each pixel), see Fig. SI3. Energy filtered maps can be produced by
cuts of these datacubes at different energies. Structural information was
retrieved from atomic scale images (Fig. 1a inset) and strain mapping through
diffraction datacubes (Fig. SI2). For more information, see the Methods
section.

Fig. 1b presents the typical optical information that can be collected using
CL and EELS on WS2 monolayers with the samples kept at 150 K. CL and EELS
spectral resolution used were 8 and 26 meV, respectively, for the measurements
presented here.

CL can be directly compared to off-resonance PL [27], where the emission from
XA and X- (X+ occurs only in negatively gated WS2 [10]) is observed for the
WS2 monolayer. An overview of the energies measured for XA and X- CL emission
is plotted as histograms in Fig. 1c-d (more histograms corresponding to the
localized L emission and exciton energies in EELS are shown in Fig. SI11),
where the survey areas are of few $\mu$m each (represented by a different
color). The measurements average around 2.049 eV and 2.011 eV (with full width
at half maxima (FWHM) 13 meV and 19 meV, respectively), showing agreement
between ensemble of CL measurements across a sample with macroscopic optical
measurements (typical variations are of 20 to 30 meV for XA emission and
absportion in regions above 10 $\mu$m2 [14, 8, 28, 29]). Regions with broader
($\sim$15 meV, black histogram in Fig 1c-d) and narrower ($\sim$5 meV, yellow
histogram in the same figure) distributions can also be seen. In fact, of most
interest in our study are the areas with spatial variations of the optical
properties to unveil the origin of these variations.

For atomically thin materials, EELS measures the imaginary part of the
dielectric function [30, 31], and it has been used for exciton mapping in TMDs
[21, 22, 23, 24]. A comparison of the EELS and the optical absorbance
($1-R-T$, where $R$ and $T$ are the optical reflectivity and transmission [8])
spectra of h-BN encapsulated WS2 at 150 K shows a one-to-one match between
features (see Fig. SI1 and the Methods section for a discussion on EELS and
optical absorption). The features seen in the EELS spectrum presented in Fig
1b are exciton peaks. In addition to XA and XB, two others are detected:
X${}_{A}^{*}$, the excited state of XA, and XC which arises from strong
absorption due to band nesting around the $Q$ point [32]. The energy positions
of XA and XB measured in EELS are plotted as histograms in Fig. SI10 and Fig.
SI11, showing the mean value of XA and XB to be 2.101 eV and 2.502 eV (with
FWHM 24 meV and 25 meV, respectively).

Figure 1: Nanoscale optics of WS2 monolayers: (a) Sketch of the main results:
a WS2 monolayer (orange) encapsulated by two h-BN flakes (purple, 20 and 5 nm
thickness) partially supported by a holey carbon film (gray) shows three
emission lines: A excitons (XA, red), trions (X-, cyan) and localized emitters
(L, blue). X- emission intensity increases close to the carbon support edges
and around tens of nanometer residues patches throughout the WS2 monolayer.
The inset shows an atomically resolved image of the WS2 in the heterostructure
(the scale bar is 2 nm). (b) Typical electron energy loss spectra (EELS,
orange) and cathodoluminescence (CL, purple). The XA, XB, XC, and X- peaks are
labeled. The extra absorption between XA and XB is attributed to the 2s
excited state of XA, marked X${}_{A}^{*}$. The difference between XA emission
and absorption maxima is marked as Stokes shift. The curves intensities are
normalized to match the XA maxima. (c) Histogram of the A exciton energy,
measured by Gaussian fitting of the CL XA peak at each position contained in 6
different regions. (d) Histogram of the trion energy, measured by Gaussian
fitting of the same CL data as (c). Each color represents a distinct region of
between 1 and 2 µm2 surface area containing hundreds of pixels, that would be
only few pixels if measured by optical diffraction-limited methods.

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 of tens of nanometers, while the XA
peak intensity is relatively uniform. Fig. 2a and c show an example of this
local intensity change for the X- and the L emission, which can occur for
areas as small as 30x30 nm2. Spectra averaged in such small regions (Fig. 2e)
show varying peak heights. This behavior is not homogeneous across a single
h-BN/WS2/h-BN heterostructure or between different samples, and has been
observed in regions of a few hundred nanometers across. A similar increase in
X- intensity is observed close to edges of the carbon support (which appear as
brighter regions in HAADF images, as in the upper right of Fig. 2b), which is
in direct contact with the thicker (20 nm) h-BN layer (the sample details are
described in the Methods section), but not with the WS2 layer. Indeed,
filtered emission maps at the trion energy (Fig. 2d) have stronger intensities
close to the edge, as observed systematically in other holes of the same
heterostructure (see Fig. SI6) and of different samples. Spectra close to the
edge (cyan curve in Fig. 2f) show stronger trion emission in comparison to
those in the suspended region (red curve in Fig. 2f). At first glance, these
emission modifications could have the same origin. Yet, they occur at
different scales Figs. 3 (tens of nanometers) and 4 (above a hundred
nanometers) further entailing a detail analysis.

Figure 2: Nanoscale emission intensity variations: (a) HAADF image of the area
measured in (c) and (e), (b) HAADF image of the suspended area measured in (d)
and (f). (c) L emitters (left), X- (center) and XA (right) intensity maps,
where small localized spots are seen for L and X-. (d) X- intensity map
showing trion enhancement next to the carbon support edge.(e) CL spectra
corresponding to highlighted regions in (c). (f) CL spectra corresponding to
highlighted regions in (d). The intensity in (e) and (f) was normalized by the
maximum of the cyan spectrum to conserve the intensity changes of all peaks.
The intensity in (c) and (d) was normalized by dividing by the maximum of each
integrated datacube. The shaded regions in (e) and (f) mark where intensities
were integrated for (c) and (d).

In suspended regions where the X- intensity varies locally while XA intensity
remains constant (Fig. 3a-b and Fig. SI4), the typical spatial extension where
enhanced trion emission is observed is of the order of tens of nanometers. As
a function of position across different bright spots, the X- and XA
intensities change independently (Fig. 3b), with no measurable energy shift.
The typical size of these regions brings to mind the possibility of discrete
light emitters, such as individual point defects, as observed in h-BN in the
past [33] using CL. The trion formation and decay probabilities are known to
depend on the local density 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 show intensity
variations, indicating the presence of extra matter either on the
heterostructures’ interfaces or surfaces. Core loss EELS shows that in
addition to the expected chemical species (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 during the
exfoliation of layers.

Blind source separation spectral analysis (see Methods, and Fig. SI5) shows
that a component 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 trion emission occurs in the areas which lack this
residue-related component (marked by dash circles 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 the Methods
section). Their presence do not prevent the excitation transfer from the h-BN
to the monolayer, indicating they are thin (as also suggested by EELS).
h-BN/TMD stacks can be very clean [34], but they contain some thin interface
residue and bubbles. These additional surrounding dielectric patches change
the local electromagnetic environment of the WS2 monolayer.

Figure 3: Trion modification due to local surface patches:  (a) X- intensity
map. The intensity was normalized by the maximum of trion emission. (b)
Spectral profile along the arrow in (a), where intensity modulation of X-
occurs. (c) Residue content extracted using a blind source separation
algorithm on the EELS datacube. The residue is present due to the monolayer
transfer process. (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 not present.

Around holes in the carbon support of the sample, the X- to XA ratio also
increases (Fig. 4a-b and Methods). On top of the carbon support the XA
emission increases, with a drastic decrease of the X- to XA ratio. A series of
emission spectra acquired starting from the suspended region up to the hole’s
edge along three different line profiles show the continuous increase in X-
and XA emission. This evolution in emission occurs without observable
modification of the absorption spectra (Fig. 4c-e, right panels). The same
behavior occurs in 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 $\epsilon_{yy}$ component) and these modifications has not been
detected (the bright lines occur due to structural changes including a fold
and the carbon support edge).

In addition to the X- intensity increase, its peak emission energy varies
towards the edge of the support (white curved arrow in Fig. 4d and Fig. SI6):
initially the peak redshifts by about 20 meV over a distance of 200 nm, and as
its intensity increases, the redshift is followed by a final abrupt shift back
to its initial energy, over a distance of 50 nm, and a larger intensity
increase. The energy shifts lead to broader emission X- histograms compared
the XA (orange curves in Fig. 1c-d). Where this effect is observed, the XA
emission and absorption energy do not follow the variations observed for the
X-. However, along with this characteristic shift of the trion, other energy
shifts are observed, which the XA does follow (Fig. 4c and Fig. SI6). These
will be disentangled in the discussion.

Figure 4: Trion and L increase due to charge accumulation in a conductor-
insulator-semiconductor interface: (a) Strain map of $\epsilon_{yy}$
component. The brightest lines correspond to 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 along each
arrow marked in (a) and (b). In both (c) and (d) the trion peak redshifts then
shifs back to its initial energy when approaching the carbon membrane
(represented by a dotted line), as explained in the text. (e) A lower energy
emission, marked by L 35 meV below the XA emission, which does not shift in
energy is observed. It is attributed to localized excitons.

Finally, close to the carbon support edge, one also observes localized
emissions which match the lower-energy transitions referred to as L in
literature [14, 15, 8, 10] (Fig. 4, vertical profiles e in Fig. 4a-b). This
emission can be separated from that of the trion since their energy splittings
to the XA are different: XA \- X- is 35 meV on average while XA \- L is 45
meV. This particular energy splitting is systematically observed for this
localized emission on the edge of the carbon support (observed on 21
measurements of 14 local emitters from two different samples). Its intensity
is usually brighter than that of the trion, with an intensity 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 the L emission is about the same as that
of the X-, respectively 31 and 33 meV, but larger than that of the XA is 17
meV, on average. The appearance of L emission could not be directly linked to
patterns in strain maps.

The ensemble of observations concerning the trion can be explained by making a
hypothesis 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] semiconductors, which controls the density of free
electrons; conversely, chemical doping can also modify this quantity [36].
Unintentional doping in MoS2 has been shown to increase trion emission [37],
while a similar increase in WS2 has been attributed to a larger concentration
of defects [38]. Substrate modification has also demonstrated an effect on the
trion emission intensity in WS2 monolayers [39]. In view of these reported
observations, we attribute the localized trion emission increase described in
Fig. 3 to an augmentation of the local free electron density due to the
absence of the surface contaminants. It has also been observed that strain
(0.6 $\%$ and above) applied to WS2 monolayers [40] could induce trion
intensity modification. Strain maps of regions around holes in the support do
not show a correlation to the trion increase pattern (Fig. SI7). Our strain
measurements are not precise below 1$\%$ for the buried WS2 monolayer (see
Methods), so small deformations cannot be excluded. Finally, XA emission
energy is not modified by the local dielectric patches. It is known that the
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 (to first order).

At first sight, one could invoke a similar interpretation to the increase in
the X-/XA emission ratio close to the carbon support edge, that is, an effect
of the local dielectric environment of the monolayer. However, given the
sample geometry, the carbon support is not in contact with the monolayer, but
separated by 20 nm of h-BN (the lower layer in the heterostructure), a
thickness far larger than the extent of the exciton wavefunction outside the
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 emission from the monolayers (TMD monolayer deposited
directly on TEM grids do not emit light in 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 WS2
heterostructure forms a metal-insulator-semiconductor (MIS) capacitor, as the
WS2 is in contact with the carbon support away from measurement area.
Therefore, free carriers at the center of the suspended region (distant from
the carbon support) have different potential profiles than those in proximity
to the carbon support. This changes the free carrier density at the center of
the hole and around its edges, resulting in the different X-/XA emission
ratio. Rough estimates show that the capacitance created by a 20 nm h-BN
(considering its bulk dielectric function), given the difference in
workfunction between amorphous carbon and WS2, can induce charge densities of
the order of 1x$10^{13}$ cm-2. A $3.2$x$10^{12}$ cm-2 increase in the electron
density in WS2 (achieved by a 40 V gate voltage) has demonstrated an increase
of the X- absorption intensity and a redshift of about 20 meV [9]. This energy
shift matches the magnitude of that observed in Fig. 4c. In short, we
interpret the redshift and higher emission rate as an increase 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 nm when approaching the carbon support; a blueshift of the trion
which is in fact a shift back to its initial energy far from the carbon
membrane. Along with this shift, an intensity increase at distances below 50
nm from the edge of the membrane is clearly visible. This is at first
counterintuitive, as the former MIS capacitor explanation implies a continuous
redshift with intensity increase. This second shift cannot be explained by a
local change of the optical bandgap, since the energy of XA remains constant
or changes marginally, both in absorption and emission (Fig. 4d) across the
whole range. A simple reduction of the charge density would explain the shift
back to initial energy, but not the increase in emission. We attribute this
second shift and increase in intensity to a locally higher density of optical
modes, which increases the decay rate due to the Purcell effect, where both
the X- and XA are modified. A substantial increase in the emission intensity
of molecules has been known to occur in close proximity to metallic structures
[41].

In fact, such enhancement induces shorter exciton and trion lifetimes, leading
directly to higher emission rates. It also explains the shift back in energy,
which is related to the subsequent decrease of the trion population. We note
that this is followed by an increase of XA emission, which is stronger on top
of the carbon support (Fig. 4c, above the white dashed line), where the trion
emission is reduced (Fig. 4d and SI6). We interpret this as a consequence of
the reduction of the XA lifetime, which increases its emission rate and
decreases the trion formation probability. Here, we note that absorption
intensity does not increase, ruling out a larger emission intensity simply due
to a larger excitation rate. That is, at a constant excitation rate, the total
number of exciton and trion formation is fixed, leading to a competition
between their emission intensities.

More specifically, the hypothesis of a trion blueshift due to strain is
excluded because strain would also blueshift the XA emission and absorption
energies, since it would change the WS2 optical bandgap. Notably, in other
regions XA emission and absorption are observed to change locally, as in the
profiles in Fig. 4c and Fig. SI6. These energy shifts are followed by the X-,
but they do not preclude the general behavior demonstrated in Fig. 4d. Strain
mapping (Fig. SI8) along the profiles in the regions where the XA energy (and
X-) varies does not allow one to attribute the energy profiles solely to
strain. Shear and tensile strain and in-plane rotation are observed, but a
one-to-one correspondence between these and the energy variations was not
detected in Fig. SI8 and Fig. SI9.

Finally, we return to the L emission observation. Strain maps of the monolayer
close to the carbon support edges show that it is strained (see Fig. SI9 and
Fig. SI8). The strain pattern is not simply that of a suspended membrane
covering a circular hole, as one might initially expect. Indeed, regions close
to the support edges show they can be under compression, including those where
trion emission is increased. We interpret this as a result of the strain
created during the heterostructure transfer.

This complex strain profile brings to mind the multiple observations of single
photon emitters in TMDs [3, 4, 5, 6], specifically WSe2, which are currently
attributed to the formation of 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 of these
single photon source. We do not observe a one-to-one correspondence of the
appearance of L emission and strain maps. These emitters can be distinguished
from trions based on their 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 exploration at the
nanometer and atomic scales.

In addition to allowing us to validate some hypothesis concerning energy
shifts, the absorption 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 (XA here). In molecular systems this energy
difference occurs due to the interaction with phonons. In semiconductors, in
addition to phonon interaction, other phenomena can intervene, such as doping,
strain, and substrate-related effects. The Stokes shift measured for our
samples is of the order of 40 meV. This is much larger than the smallest
reported values for bare or h-BN encapsulated WS2 monolayer [8, 29]. We
attribute this difference to sample quality (source of WS2 or the
heterostructure preparation), which further motivates future EELS and optical
absorption experiments on the same objects.

The results presented here demonstrate the existence of nanometer scale
localized light emission in relatively structurally homogeneous TMD
monolayers, which can be attributed to variations of the free electron density
in the material caused by surface residue modifying the dielectric environment
locally. Trion mapping on TMDs could also be used as local dielectric sensor,
similar to the suggestion by Xu et. al [16] based on optical reflectivity.
From another perspective, the creation of nanoscale emitters indicate that
dense arrays could be engineered by manipulation of the surface, such as by
way of patterning. Finally, a lack of correlation between L emitters and
strain above 1$\%$ indicates that strain alone is not sufficient for their
generation. Possibly, point defects are necessary to generate them, as
suggested by the detection of single photon emitters in h-BN encapsulated WSe2
placed on dielectric pillars only after 100 keV electron-irradiation [6]. As
such, nanoscale electron microscopy and spectroscopy can offer a way to
generate and characterize atomic-scale defects, and to monitor the change in
optical response in real-time towards better understanding of nanoscale
emitters in TMDs.

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###  .1 Acknowledgments

This project has been funded in part by the National Agency for Research under
the program of future investment TEMPOS-CHROMATEM (reference no.
ANR-10-EQPX-50) and from the European Union’s Horizon 2020 research and
innovation programme under grant agreement No 823717 (ESTEEM3) and 101017720
(EBEAM). K.W. and T.T. acknowledge support from the Elemental Strategy
Initiative conducted by the MEXT, Japan, Grant Number JPMXP0112101001, JSPS
KAKENHI Grant Number JP20H00354 and the CREST(JPMJCR15F3), JST. This work has
been supported by Region Île-de-France in the framework of DIM SIRTEQ”. We
thank NION, HennyZ, and Attolight for the helpfull interaction on the
adaptation of the CL system to the NION sample chamber on the ChromaTEM
microscope and customization of the liquid nitrogen sample holder. We
acknowledge the joint effort of the STEM team at the LPS-Orsay and, in
particular Marcel Tencé and Xiaoyan Li, concerning instrumental developments.
We thank Ashish Arora and co-authors for kindly providing the optical
absorption data on a WS2 monolayer encapsulated in h-BN. Luiz F. Zagonel is
acknowledged for ideas and discussion on data analysis.

###  .2 Competing interests

MK patented and licensed technologies at the basis of the Attolight Mönch used
in this study, and is a part time consultant at Attolight. All other authors
declare no competing financial interests.

##  I Supplementary information to Nanoscale modification of WS2 trion
emission by its local electromagnetic environment

###  I.1 Methods

Scanning transmission electron microscopy (STEM) imaging, diffraction, CL and
EELS experiments 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] can be generated for high spatial resolution imaging,
diffraction and spectroscopy. High energy and spatial resolution have been
substantially improved over the last ten years due to new monochromator
technologies [43, 21, 44, 45, 46, 47]. The energy resolution of the EELS data
presented here was between 20 and 30 meV (energy width of the primary electron
beam). CL used a Mönch system from Attolight [31], with an energy resolution
of 8 meV (minimum separation between two discernible emission peaks). Combined
EELS-CL experiments have been used in the past to understand optical
extinction and scattering in metallic plasmonic nanoparticles [48], but
required much smaller requirements on the spectral resolution, due to the very
large linewidth of the plasmons. Sample were kept at 150 K using a liquid
nitrogen HennyZ 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 for core-loss and diffraction, 50 ms.

Atomically resolved imaging and spatially resolved EELS chemical maps were
acquired on Nion UltraSTEM 200 operated at 100 keV, with the samples at room
temperature. All images shown are high angle annular dark field (HAADF)
images, in which the intensity is 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 background created by scattering
in the h-BN layers. Diffraction effects play a smaller role in HAADF image
intensity, so imaging with the h-BN slightly off-axis is beneficial to observe
the single WS2 monolayer embedded in 25 nm of h-BN, as demonstrated before for
CeSi clusters in Si matrices [49]. Encapsulation has also ensured a high
stability of the monolayers under 60 keV 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 convergence semi-angle between 3 and 5 mrad and the camera dwell time
was 50 ms. Diffraction mapping analysis was done with the Pyxem [50] and
Hyperspy [51] python libraries. The quantity calculated is the displacement
gradient tensor, corresponding to the difference between the deformed vectors
and a reference, where the reference is a calculated vector with the
reciprocal space length and orientation for unstrained WS2. A right-handed
polar decomposition was used to separate deformation and rotation. The angle
of rotation was then recovered from the rotation matrix. Each deformed vector
was defined with the barycenter of the diffraction spots, and the center of
the direct beam was first aligned with a cross correlation method. The
barycenter method is limited by illumination changes of the diffraction spots
(due to diffraction on the thicker h-BN layers), limiting our current strain
measurements to above 1$\%$.

The CL and EELS datacube spectral fitting was done with the Hyperspy bounded
multifit tool, using gaussian profiles. The Lorentzian profile was also tried
since the EELS exciton peak profiles should be close to lorentzian, but the
results are not displayed here to keep coherence for all curve fits. Most of
the values found in the text are from mean spectra extracted from different
regions of interest in each spectrum-image (these extracted spectra have a
much higher signal to noise ratio). The extracted spectra are fitted with
gaussian profiles, and the uncertainty associated is the standard deviation of
the fit.

####  I.1.1 BSS+PCA analysis description

The blind source separation (BSS) technique consists of the separation of a
mixed signal into individual components. The algorithm used in this paper was
the independent component analysis (ICA) implemented in Hyperspy. In the ICA
algorithm, the individual components are additive, and treated as non-gaussian
and statistically independent. We chose 3 components, the first one contains
the background, the h-BN and the carbon that are correlated together. This
carbon can be from contamination of the sample. The second one contains the
silicon and some carbon, and the third one contains mostly noise.

####  I.1.2 Sample preparation for electron spectroscopy and microscopy

h-BN/WS2/h-BN heterostructures were fabricated by using modified dry transfer
method [52] then transferred to a TEM grid. WS2 was purchased from
2DSemiconductors and high quality h-BN synthesized by high pressure-high
temperature method [53] was used. All constituted layers were first exfoliated
onto a SiO2/Si substrate using the scotch-tape method [1]. A PDMS
(polydimethylsiloxane) mask spin-coated by 15 $\%$ PPC (polypropylene
carbonate) is used for polymer stamp. PDMS is made by using the 20:1 ratio of
Sylgard 184 pro-polymer to curing agent and kept at ambient conditions for
overnight. To enhance adhesion between PDMS and PPC, PDMS mask was treated by
oxygen plasma (18 W) for 5 min, before the spin-coating of PPC at 3000 rpm
followed by heat treatment at 160 ∘C for 10 minutes. This polymer stamp was
mounted to the micromanipulator upside down. A brief description of the
procedures are described below.

  1. 1.

Pick-up exfoliated h-BN crystal from SiO2/Si substrate by contacting polymer
stamp to the target crystal at 50 ∘C for 1 minute and lifting the stamp.

  2. 2.

Repeat step 1 to pick-up the monolayer WS2 crystal and bottom h-BN layer
subsequently.

  3. 3.

Drop-down the stack (h-BN/WS2/h-BN) on a new SiO2/Si substrate by contact at
higher temperature (120 ∘C) for 10 minutes.

  4. 4.

Clean the PPC residue on the surface with acetone and IPA.

  5. 5.

Anneal the heterostructure to enhance the interlayer coupling between
constituent layers at 250 120 ∘C) for 6 hours in Ar environment.

  6. 6.

Spin-coat with polymethylmethacrylate (PMMA, 495K, Microchem) over the
heterostructure at 3000 rpm followed by a heat treatment at 180 ∘C for 5
minutes.

  7. 7.

Etch SiO2/Si substrate by immerse the sample into KOH solution (1M) overnight.

  8. 8.

Transfer the sample to TEM grid (C-flat holey carbon grid with 2 $\mu$m hole
diameter)

  9. 9.

Remove PMMA residue by cleaning with acetone and IPA.

###  I.2 EELS and optical absorption comparison

The electromagnetic response properties of materials are usually described by
its dielectric function
$\epsilon(\omega)=\epsilon_{1}(\omega)+i*\epsilon_{2}(\omega)$. However
optical measurements, usually give access to the complex refractive index,
$\tilde{n}(\omega)=n(\omega)+i*\kappa(\omega)$. These two quantities are
linked by the relation $\tilde{n}^{2}(\omega)=\epsilon(\omega)$, which also
links their real and imaginary parts by

$\epsilon_{1}(\omega)=n^{2}(\omega)-\kappa^{2}(\omega)\epsilon_{2}(\omega)=2n(\omega)\kappa(\omega),$
(1)

$\kappa$ is the extinction coefficient, which is linked absorption
coefficient, $\alpha$, by

$\alpha=\frac{4\pi\kappa}{\lambda},$ (2)

with $\lambda$ the wavelength of light. These two quantities, $\kappa$ and
$\alpha$, are linked to the decrease of the total intensity being transmitted
through a medium.

A large part of optical absorption measurements are made from reflectivity,
which gives access to reflectance, R:

$R=\frac{\tilde{n}-1}{\tilde{n}+1}=\frac{(n-1)^{2}+\kappa^{2}}{(n+1)^{2}+\kappa^{2}},$
(3)

from which $\epsilon_{1}(\omega)$ and $\epsilon_{2}(\omega)$ can be calculated
using the Kramers-Kronig relation and a model taking 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 absorbance spectrum $A(\lambda)=1-R-T$ 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 $\epsilon(\omega)$ measures
$Im{\\{-1/\epsilon(\omega)\\}}$. Therefore, in general, Kramers-Kronig
transformation is required to retrieve $\epsilon_{1}(\omega)$ and
$\epsilon_{2}(\omega)$. However, for atomically thin objects it can be proven
that $Im{\\{\epsilon(\omega)\\}=\epsilon_{2}(\omega)}$ is true. In this case,
a direct comparison of $\epsilon_{2}(\omega)$ measured by EELS for atomically
thin layers and the calculated value from optical reflectivity is justified.
Being a direct measure of $\epsilon_{2}(\omega)$, one can compare the line
shapes of EELS with those in optical absorbance spectra (Fig. SI1). However, a
comparison of exact energy positions requires one to take into account the
dispersion of the real 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). But part of it can also come from the dispersion of
$\epsilon_{1}(\omega)$. Nevertheless, we do not exclude fine differences
between the quantities measured in EELS and optical absorption, in the tens of
meV range. The fact that EELS for atomically thin structures measures
$Im{\\{\epsilon(\omega)\\}}$ has only been demonstrated at higher energies,
with poorer energy precision (at 15 eV with 300 meV precision for single wall
carbon nanotubes [54]).

###  I.3 Supplemental figures

Figure SI1: EELS and optical absorption comparison: EELS (orange) spectrum of
a WS2 monolayer encapsulated with h-BN. A comparison to optical absorption
(purple), from Arora et al. [8], shows a near perfect one to one
correspondence, with the XA, XB and XC excitons shown. The extra absorption
between XA and XB is attributed to the 2s excited state of XA.  Figure SI2:
Atomically resolved HAADF image and diffraction of a WS2 monolayer:  (a)
Atomically resolved image of a WS2 monolayer encapsulated in h-BN. The h-BN
layer is barely visible 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 come from
diffraction on the two h-BN crystals. Figure SI3: Scheme of the experiment: as
described in the main text the microscope used for spectroscopic measurements
is equipped with an electron monochromator and light collection system, 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 shift at a given
position, or variations of the chemical composition. Figure SI4: XA intensity
maps from main text: (a) XA intensity from same area as Fig. 2d, (b) XA
intensity from same area as Fig. 3b, (c) XA intensity from same area as Fig.
4b. All maps have been normalized by the maximum of XA emission in the
spectral integrating range. Figure 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. Figure 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, showing an
increase in X- emission close to the hole edges. (c, d, g, h, k, l) Spectra
from selected profiles in 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 (represented by a
dotted line the in the spectra), the others show a less typical behaviour.
Figure SI7: Strain from same area as Fig. 3: (a) MADF image, (b),
$\epsilon_{xx}$ component of the strain tensor, (c) $\epsilon_{yy}$ component
of the strain tensor, (d) rotation angle extracted from the rotation matrix
with polar decomposition. $\epsilon_{xy}$ corresponding to shear strain is not
displayed and shows similar features as the rotation. The strain measurements
below 1$\%$ show artefacts from the change in illumination in the diffraction
spots. These maps illustrate that the diffraction measurements show only small
variations that do not explain the trion localization by itself.  Figure SI8:
Strain close to the carbon support in Fig. 4: (a) MADF image, (b),
$\epsilon_{xx}$ component of the strain tensor, (c) $\epsilon_{yy}$ component
of the strain tensor, (d) rotation angle extracted from the rotation matrix
with polar decomposition. $\epsilon_{xy}$ corresponding to shear strain is not
displayed and shows similar features as the rotation. The strain measurements
below 1$\%$ show artefacts from the change in illumination in the diffraction
spots. These maps illustrate that the diffraction measurements show only small
variations that do not explain the trion localisation by itself.  Figure SI9:
Strain close to the carbon support in Fig. 2b: (a) MADF image, (b),
$\epsilon_{xx}$ component of the strain tensor, (c) $\epsilon_{yy}$ component
of the strain tensor, (d) rotation angle extracted from the rotation matrix
with polar decomposition. $\epsilon_{xy}$ corresponding to shear strain is not
displayed and shows similar features as the rotation. The strain measurements
below 1$\%$ show artifacts from the change in illumination in the diffraction
spots. These maps illustrate that the diffraction measurements show only small
variations that do not explain the trion localisation by itself.  Figure SI10:
Histogram of measured energies and energies differences in different regions:
(a) XA energy measured in EELS, (b) XA energy measured in CL, (c) XB energy
measured in EELS, (d) X- energy measured in CL, (e) Stokes shift
(corresponding to XA,EELS \- XA,CL energy), (f) Spin-orbit splitting
(corresponding to $X_{B}$ \- XA energy), (g) charging energy (corresponding to
XA \- X- energy). The energies are extracted from Gaussian fit of each pixel
of each datacube. The 12 datacubes were measured on the same day, on different
areas of the same sample. The areas are of few µm2 each. The colorcode refers
to the different areas measured on the same heterostructure within holes in
the amorphous carbon film. Figure SI11: Histogram of absorption and emission
energies across all samples: Each value of the histogram is the mean value of
a measured datacube, each containing tens to hundreds of pixels. For EELS 40
datacubes are taken into account, for XA-CL and X--CL 62 and for L-CL 21. The
area covered by each datacube vary from tens of nanometers to few µm2. (a) XA
energy measured in EELS, (b) XA energy measured in CL, (c) XB energy measured
in EELS, (d) X- energy measured in CL. (e) L energy measured in CL. The
dataset from which L is extracted is different than that of (b) and (c), to
measure the L emission specifically.