# Morphology-induced spectral modification of self-assembled WS2 pyramids

Irina Komen  Sabrya E. van Heijst  Sonia Conesa-Boj  L. Kuipers
<EMAIL_ADDRESS>Kavli Institute of Nanoscience, Department of Quantum
Nanoscience, Delft University of Technology, The Netherlands

###### Abstract

Due to their intriguing optical properties, including stable and chiral
excitons, two-dimensional transition metal dichalcogenides (2D-TMDs) hold the
promise of applications in nanophotonics. Chemical vapor deposition (CVD)
techniques offer a platform to fabricate and design nanostructures with
diverse geometries. However, the more exotic the grown nanogeometry, the less
is known about its optical response. WS2 nanostructures with geometries
ranging from monolayers to hollow pyramids have been created. The hollow
pyramids exhibit a strongly reduced photoluminescence with respect to
horizontally layered tungsten disulphide, facilitating the study of their
clear Raman signal in more detail. Excited resonantly, the hollow pyramids
exhibit a great number of higher-order phononic resonances. In contrast to
monolayers, the spectral features of the optical response of the pyramids are
position dependent. Differences in peak intensity, peak ratio and spectral
peak positions reveal local variations in the atomic arrangement of the hollow
pyramids crater and sides. The position-dependent optical response of hollow
WS2 pyramids is characterized and attributed to growth-induced nanogeometry.
Thereby the first steps are taken towards producing tunable nanophotonic
devices with applications ranging from opto-electronics to non-linear optics.

##  I Introduction

Two-dimensional transition metal dichalcogenites (2D-TMDs) have recently
attracted enormous scientific attention for their distinctive optical
properties. Like graphene, TMDs materials consist of layers held together only
by van der Waals forces. 2D TMDs (e.g. MoS2, WS2, MoSe2, WSe2 etc.) are
atomically thin semiconductors, with a transition from indirect to direct
bandgap in the few-layer limit [1]. Due to their high binding energy,
electron-hole pairs form stable excitons even at room-temperature. A
pseudospin can be attributed to each of the two valleys 2D TMDs possess,
making it possible to address them selectively with circularly polarized light
[2, 3, 4]. The electronic and optical properties of these 2D semiconductors,
for instance the excitons and valley pseudospin, make them an interesting
platform for opto-electronics [5, 6] and valleytronics [7, 8, 9] applications.

One of the ways of creating 2D TMD monolayer samples is by exfoliation from
bulk [9]. An alternative method to produce layered TMDs materials is Chemical
Vapor Deposition (CVD) [10, 11, 12, 13, 14, 15]. While CVD can reproduce
horizontal layers as found in naturally occurring TMDs, adjusting the growth
conditions enables the growth of nanostructures with exciting properties and
applications in nanotechnology, for instance vertical walls, flowers and
pyramids [16]. Under certain CVD growth parameters TMDs materials form
pyramid-like structures [17, 18], having many active adsorption site useful
for applications in hydrogen sensors [19] and water disinfection [20], at the
same time possessing interesting electronic properties like ferromagnetism
[21] and high mobility [22, 23]. Moreover, pyramid-like TMDs structures have
applications in non-linear optics [24, 22, 25], as they exhibit higher non-
linear optical conversion efficiency than monolayers due to the thickness
increase, while demonstrating a much larger non-linear optical response than
multilayer TMDs.

It is interesting to note that only in a limited number of studies in the
literature photoluminescence of these spiral or pyramid like structures is
reported [17, 18, 22, 20]. In some, the non linear optical response is studied
[24, 22, 25]. In most, the TMDs spirals and pyramids are studied using Raman
spectroscopy [23, 17, 18, 22, 24, 21, 20, 19]. However, comparing the measured
optical response of pyramid-like structures of different studies needs to be
done with caution, as the terms spiral flake or pyramid are used for
nanostructures that have different thicknesses, geometry and sizes.

Raman spectroscopy is a powerful tool to study 2D TMDs, as knowledge on the
vibrational modes of the layers provides insights in their structure [26, 27,
28]. Commonly studied are the characteristic vibrational modes of TMDs, the
E${}^{1}_{2g}$ that corresponds to the in-plane displacement of the atoms, and
the A1g that corresponds to the out-of-plane displacement of the chalcogenide
atoms, as well as the longitudinal acoustic phonon LA(M) [28, 27, 29, 30].
Studying the Raman response as a function of temperature [31, 32, 33, 34, 35],
excitation polarization [29, 27, 36] and excitation wavelength [37, 38, 39],
provides information on structural properties like number of layers, strain
and defect density.

It is important to note that the existence of exciton resonances in 2D TMDs
has large implications for its Raman response. Raman features are greatly
enhanced when the excitation is in resonance with an excitonic transition [40,
28, 27, 37, 38, 39]. Resonance Raman spectroscopy on 2D TMDs materials results
in the excitation of higher-order phononic resonances [41], which yields rich
Raman spectra with many more modes than the two mentioned characteristic
modes.

Many questions arise about the nature of the optical response from complex
CVD-grown TMDs pyramid like nanostructures. It is unknown how the nanogeometry
of TMDs pyramids influences its photoluminescence and Raman response and how
it depends on temperature and polarization. For potential applications, this
knowledge is paramount.

Figure 1: Hollow WS2 pyramids
a. SEM image of the hollow WS2 pyramid. The lines along the sides indicate the
single stair steps, whereas the darker region in the middle is the crater.
inset. Schematic representation of the hollow pyramid. b. AFM image of the
hollow WS2 pyramid. The blue line indicates the position of the AFM crosscut
depicted in c, ranging from A the pyramid crater to B the substrate. d. SEM
image of a WS2 monolayer on the same substrate. e. Photoluminescence spectrum
of the WS2 monolayer (black dotted line), and spectra of a pyramid obtained
with a $595\text{\,}\mathrm{n}\mathrm{m}$ excitation (orange) and a
$561\text{\,}\mathrm{n}\mathrm{m}$ excitation (green). When converting the
x-axis to wavenumber $\Delta\nu$ in f, the spectral response on the two
different lasers overlaps nicely, indicating that the collected light
originates from Raman processes rather than photoluminescence.

Here, we study the Raman and photoluminesence response of CVD-grown hollow WS2
pyramids, comparing it to the optical response of WS2 monolayers. Even though
the WS2 monolayers and pyramids are grown on the same substrate and under the
same conditions, their measured optical response is completely different. We
find, surprisingly, that the pyramids exhibit a strongly reduced
photoluminescence (PL) with respect to horizontal layers. The reduced PL
enables us to study the Raman signal of the hollow WS2 pyramids, that contains
both the characteristic Raman peaks of flat layers and a great number of
higher-order phononic resonances. In contrast with the monolayers, the
measured optical response of the hollow WS2 pyramids is non-uniform over the
nanostructures. Annular dark-field (ADF) scanning transmission electron
microscopy (STEM) measurements confirm position-dependent variations in atomic
arrangement.

##  II Results and discussion

###  II.1 Hollow WS2 pyramids

Figure 1a presents an SEM image of a CVD-grown hollow WS2 pyramid (the
substrate is a SiN film on Si, see Methods). The WS2 is crystallized in a
3R-phase (see Fig.8c-d and Section A in the Supplementary Materials.) The
clear lines along the pyramid sides indicate single steps (see Fig.7c and
Fig.8a,b in the Supplementary Materials). The geometry of the darker middle
becomes more clear when examining the AFM image in Fig.1b. The height profile
measured with the AFM along the blue line is presented in Fig.1c. The bottom
of the crater in the middle is roughly $5.6\text{\,}\mathrm{n}\mathrm{m}$ high
with respect to the substrate, whereas the pyramid sides reach a height of
$44\text{\,}\mathrm{n}\mathrm{m}$. The inset of Fig.1a displays a schematic
representation of the hollow pyramid, depicting the stair-like sides in white
and the crater with a bottom of finite thickness in the middle.

Figure 1e presents optical spectra obtained by exciting a WS2 pyramid at the
stair-like side with either a $595\text{\,}\mathrm{n}\mathrm{m}$ laser
(orange) or a $561\text{\,}\mathrm{n}\mathrm{m}$ laser (green). The spectra
contain a similar sequence of peaks, but their spectral position does not
overlap in wavelength. However, these peaks are located at the same relative
frequency distance to the excitation laser, as depicted in Fig.1f. The clear
overlap of the larger peak positions in the spectra from the two different
lasers indicates that the collected light originates from an inelastic Raman
process rather than from photoluminescence.

Figure 1d presents an SEM image of a single horizontal layer (monolayer) WS2
grown on the same substrate (next to hollow pyramids and monolayers, also
fully grown pyramids are present on this substrate, see Supplementary
Materials, Fig.7a, Fig.11 and Fig.12). Comparing in Fig.1e the optical
response of the monolayer (black dotted line) with that of the pyramid, it
becomes apparent that the pyramid exhibits a strongly reduced
photoluminescence with respect to monolayer WS2. A small background under the
Raman modes is visible in the spectrum of the pyramid around the PL wavelength
of $630\text{\,}\mathrm{n}\mathrm{m}$. If this is remnant PL emerging from the
hollow WS2 pyramid, it has an intensity of at most 1% of the WS2 monolayer
(see Supplementary Materials Fig.9). The immense reduction of the
photoluminescence intensity from the hollow pyramids is unexpected. Even
though the pyramid crater is only a few nanometers thin, the pyramid spectra
do not resemble spectra of standard few-layered horizontal WS2 (see
Supplementary Materials Fig.9f). When the WS2 thickness increases from
monolayer to bulk, it transitions from a direct to an indirect bandgap
semiconductor [1]. It is important to note that, in contrast to the hollow
pyramids, the reduced PL from the direct bandgap can be easily measured for
few-layered WS2 [9, 1]. Moreover, the hollow WS2 pyramids do not exhibit any
luminescence at the known wavelength of the indirect bandgap, as would have
been expected from both bulk and few-layer WS2 (see Supplementary Materials
Fig.9f). Therefore we conclude that the increase of the layer number from
monolayer WS2 to the pyramid crater cannot explain the reduction of the PL
intensity. CVD-grown horizontal 2D TMDs flakes exhibit a similar amount of
photoluminescence as exfoliated samples. Hence, the PL intensity reduction by
at least two orders of magnitude of the hollow pyramids cannot merely be
explained as being intrinsic to the CVD growth process, e.g. through an
increase in defect density. Furthermore, the 3R-WS2 nanostructure cannot
explain the PL intensity reductions, as 3R-WS2 exhibits the same
photoluminescence as the naturally occurring 2H-WS2 [42, 43].

We conclude that our hollow WS2 pyramids have a lower quantum efficiency than
WS2 flakes: assuming that the optical absorption of a WS2 monolayer and a
pyramid is the same, the quantum efficiency of these pyramids is at least two
orders of magnitude lower than that of a monolayer WS2. Given the fact that
the pyramids have a thickness of $5\text{\,}\mathrm{n}\mathrm{m}$ \-
$44\text{\,}\mathrm{n}\mathrm{m}$, it is safe to assume that a pyramid
actually absorbs more than a monolayer, therefore the quantum efficiency is
likely to be at least another order of magnitude lower. We attribute the
decrease in the quantum efficiency to the increase in possible non-radiative
loss channels due to the presence of all the edges in the structure of these
pyramids. The increase in non-radiative loss channels due to the edges in the
pyramid structure is therefore the main factor that leads to a severe
quenching of the exciton photoluminescence, without influencing the Raman
modes.

The reduction of the PL enables us to study the Raman response of the hollow
WS2 pyramids in more detail, as many Raman features are usually obscured by
the PL spectrum. The pyramid spectra obtained with the
$595\text{\,}\mathrm{n}\mathrm{m}$ excitation exhibit roughly 10-12 Raman
features, three of which have not been reported before for neither horizontal
WS2 layers nor WS2 nanostructures (see Fig.3). For the
$561\text{\,}\mathrm{n}\mathrm{m}$ excitation, fewer Raman features are
visible in the spectra, and these features have a lower intensity. This can be
attributed to the fact that the $595\text{\,}\mathrm{n}\mathrm{m}$ excitation
light is close to the A-exciton resonance, whereas the
$561\text{\,}\mathrm{n}\mathrm{m}$ is out-of-resonance with both the A- and
B-excitons. Raman modes of TMDs can be greatly enhanced when they are excited
in resonance with an excitonic transition [40, 28, 27, 38, 39].

###  II.2 Structural characterization

Figure 2: ADF-STEM of a hollow WS2 pyramid
Atomic resolution annular dark-field scanning transmission electron microscopy
images taken in a-b the middle region, and c. the side of a hollow WS2
pyramid. Subtle variations in the atomic arrangement can be observed. The
corresponding FFTs, as given as insets in each of the panels, highlight this
feature further. Changes in the Bragg reflections occur between them. One of
which is a reduction of the intensity of one of the Bragg reflections in the
middle region of the hollow pyramid, as marked by the yellow circles in b.

In order to help interpret the studied optical response, we perform a detailed
structural characterization of the hollow WS2 pyramids by means of
Transmission Electron Microscopy measurements. Figure 2 displays annular dark-
field (ADF) scanning transmission electron microscopy (STEM) images taken in
different regions of these WS2 nanostructures. Figures 2a and 2b display
atomic resolution ADF-STEM images of two different locations corresponding to
the middle region of the hollow pyramid, while Fig.2c corresponds to the
pyramid side. By comparing these three images, we can clearly observe
differences in the atomic arrangement. In Figure 2a, the atomic distribution
displays a well defined hexagonal shape, and this symmetry is also highlighted
by the corresponding fast Fourier transform (see inset in Fig.2a). As we can
observe from Fig.2b, the atomic arrangements at this location are somewhat
different from those observed in Fig.2a. This structural variation is also
reflected in the corresponding FFT (inset in Fig.2b), where one of the Bragg
reflections exhibits a reduced intensity (marked with a yellow circles to
facilitate its visualization). Structural variation is also observed in the
side region of the hollow pyramid. The difference in contrast in Fig.2c
corresponds to two stair-like steps in the pyramid side. By comparing their
relative atomic arrangement, we can determine that, while the external step
exhibits a clear hexagonal honeycomb structure, this arrangement is lost in
the subsequent layer. Note also that, as observed from the results obtained in
the middle region of the nanostructures, even across its sides the atomic
arrangement can vary slightly (see also Figure 13 in the Supplementary
Materials).

These subtle variations of the atomic arrangement might be induced by the
local presence of strain, which in turn results into a slight change of the
orientation of the flake. Importantly, the level of structural disorder is
more marked in the middle of the pyramids as compared to the sides (see Figure
13) due to the additional presence of free-standing WS2 flakes arising from
the walls of the hollow pyramid.

Figure 3: Characterization of Raman peaks
a. The optical response of the hollow pyramids (orange) can be fitted by
eleven Lorentzian lineshapes (red) and two Gaussians (grey). The Raman
features are indicated by arrows with their spectral position in cm-1. The
last three features (in blue) have not been reported before. b. Part of the
features can be explained as being multiphonon resonances involving the LA(M)
phonon. The blue line depicts the higher order resonances of $A_{1g}$+n*LA(M).
The red line depicts the higher order resonances of n*LA(M).

###  II.3 Characterization of vibrational modes

In Figure 3a we present a WS2 pyramid spectrum, acquired at the pyramid side,
in which all Raman features are indicated with arrows. Commonly, only three
Raman modes are measured on both horizontal TMDs layers or nanostructures. We
measure 10-12 Raman features, three of which have not been reported previously
(indicated in blue in Fig.3a). The other modes can be attributed following a
limited amount of previous investigations (see also Table 1). In order to
analyze the spectra in more detail, we fit the overall spectrum with a
collection of eleven Lorentzian lineshapes (red) and a background consisting
of two Gaussians (grey) (see Supplementary Materials Section 1 for a
discussion on the background). This way we are able to attribute the new Raman
modes from hollow WS2 pyramids to being multiphonon resonances involving the
LA(M) phonon, adopting the methodology for high frequency Raman features in
MoS2 [41]. The blue line in Fig.3b depicts the higher order resonances of
$A_{1g}$+n*LA(M). The peak $580\text{\,}\mathrm{c}\mathrm{m}^{-1}$ is commonly
attributed to $A_{1g}$+LA(M) [30, 28, 31, 32], and the peak at
$769\text{\,}\mathrm{c}\mathrm{m}^{-1}$ is attributed to $A_{1g}$+2LA(M) by
Molas et al [30]. Thus we attribute the newly observed peak at
$1128\text{\,}\mathrm{c}\mathrm{m}^{-1}$ (n=4) to $A_{1g}$+4LA(M). The red
line in Fig.3b depicts the higher order resonances of n*LA(M). The peak at
$702\text{\,}\mathrm{c}\mathrm{m}^{-1}$ is commonly attributed to 4LA(M) [28,
31], which is twice the first 2LA(M) Raman peak at
$350\text{\,}\mathrm{c}\mathrm{m}^{-1}$. Therefore we attribute the newly
observed small shoulder of the last peak around
$1057\text{\,}\mathrm{c}\mathrm{m}^{-1}$ to 6LA(M). The expected resonance at
3LA(M) (red line in Fig.3b) would spectrally overlap with the first silicon
peak at $520\text{\,}\mathrm{c}\mathrm{m}^{-1}$, as well as the expected
resonance at n=3 (blue line in Fig.3b) would overlap with the second silicon
peak $955\text{\,}\mathrm{c}\mathrm{m}^{-1}$, so these possible features
cannot be distinguished from the substrate response. The expected 5LA(M) (red
line in Fig.3b) would be around $880\text{\,}\mathrm{c}\mathrm{m}^{-1}$, but
is too dim to distinguish very clearly from the background. The peak at
$833\text{\,}\mathrm{c}\mathrm{m}^{-1}$ is 2*$A_{1g}$, and the peak at
$475\text{\,}\mathrm{c}\mathrm{m}^{-1}$ is commonly attributed to LA(M)+2ZA(M)
(see Table 1). We conclude that the observed high-frequency Raman modes are
multiphonon resonances involving the LA(M) phonon, excited because the
$595\text{\,}\mathrm{n}\mathrm{m}$ laser is in resonance with the A-exciton.

The highest frequency Raman modes have not been reported before on horizontal
WS2 layers (indicated in blue in Fig.3a). A possible explanation for not
observing them on monolayers is that investigating Raman modes on horizontal
WS2 layers is experimentally challenging because of the presence of
photoluminescence, that is much brighter than any Raman feature. An intriguing
alternative hypothesis is that the nanogeometry of the hollow pyramid plays a
role in exciting the higher order Raman modes more resonantly, e.g. through a
higher phonon density of states.

position | std (cm-1) | brightness | attributed to | possibly | literature
---|---|---|---|---|---
350 cm-1 | 1.6 | ++ | E${}^{1}_{2g}$ / 2LA(M) |  | [28, 27, 29, 38, 31, 44, 30]
417 cm-1 | 1.5 | ++ | A1g |  | [28, 27, 38, 31, 44, 30]
475 cm-1 | 4.7 | \- - | LA + 2ZA |  | [30]
|  |  | or E”(M) + TA(M) |  | [39]
520 cm-1 | 0.8 | ++ | Si | 3LA(M) | [45, 46, 47]
580 cm-1 | 1.0 | +- | A1g \+ LA(M) |  | [28, 31, 44, 30, 32]
702 cm-1 | 1.4 | + | 4LA(M) | 2E${}^{1}_{2g}$ |  [28, 31, 44] ([30])
769 cm-1 | 1.0 | + | A1g \+ E${}^{1}_{2g}$ | A1g \+ 2LA(M) | [30]
833 cm-1 | 1.2 | + | 2A1g |  | [30]
880 cm-1 |  | \- - |  | 5LA(M) |
958 cm-1 | 3.3 | +- | Si | A1g \+ 3LA(M) | [45, 46, 47]
1057 cm-1 | 1.0 | \- - |  | 6LA(M) |
1128 cm-1 | 4.0 | + |  | A1g \+ 4LA(M) |
Table 1: Overview of the measured Raman features on the hollow pyramid (see
Fig.3) at room-temperature. The first column gives the peak position
determined by fitting, with the statistical standard deviation in the second
column and the brightness in the third. The fourth column indicates known
Raman modes, where the last column gives a few references. The fifth columns
indicates possible explanations, either taken from only one article or being
our hypothesis. Figure 4: Position dependence of intensity and shape of
spectra
a. Intensity map of the first WS2 Raman feature around
$350\text{\,}\mathrm{c}\mathrm{m}^{-1}$, with a step size of around
$1.5\text{\,}\mu\mathrm{m}$. The stars indicate the positions of the spectra
in d-e. Note that the x and y axis in the map are slightly skewed due to
experimental constraints (see Experimental Section). b. Intensity map of the
Si Raman peak at $520\text{\,}\mathrm{c}\mathrm{m}^{-1}$. c. Optical image of
a hollow WS2 pyramid. Note the white colour at the sides, indicating a clear
increase in scattering from the sides with respect to the top. d,e. Pyramid
spectra at $300\text{\,}\mathrm{K}$ and $4\text{\,}\mathrm{K}$. The substrate
spectrum (green) shows the two Si peaks at 520 and
$955\text{\,}\mathrm{c}\mathrm{m}^{-1}$. The spectrum at the hollow part of
the pyramid (red) has an overall higher intensity than at the side (black). f.
Map of the ratio between the first two Raman features in the spectra
(E2g/A1g).

###  II.4 Position dependence of spectral features

The hollow WS2 pyramids contain two distinct regions: the crater in the middle
and the stair-like sides. We find that these regions exhibit a different
spectral response. This is in contrast from the more homogeneous spectral
response for horizontal WS2 flakes (see Supplementary Materials, Fig.11 and
Fig.12). Figure 4a presents an intensity map of the first Raman peak
(E2g,2LA). To create this map, the maximum value of the fitted peak is used
(see Fig.3a). The peak intensity is higher and the peaks are more pronounced
at the pyramid crater than at the stair-like sides. For the other WS2 Raman
peaks, as well as at different temperatures and using different excitation
wavelengths, this intensity distribution looks similar (see Supplementary
Materials Fig.10).

Figure 4b presents an intensity map for the silicon peak at
$520\text{\,}\mathrm{c}\mathrm{m}^{-1}$. As expected, there is a constant
intensity for the substrate next to the pyramid. It is interesting to note
that the intensity of this substrate peak also decreases on the pyramid edges.
We hypothesise that light scatters a lot from the stair-like pyramid sides, as
seen from the bright white colour of the sides in the optical image (Fig.4c).
This both reduces the available excitation light to excite Raman modes, and
scattering of the resulting Raman response reduces the detected light,
including the Raman response of the silicon substrate. Figures 4d-e depict
spectra on three different positions: on the hollow pyramid middle (red), on
the substrate (green) and on the pyramid side (black) (indicated by stars in
Fig.4a,b). In both the room temperature spectra in Fig.4d and
$4\text{\,}\mathrm{K}$ spectra in Fig.4e (temperature dependence will be
discussed later), the two silicon peaks at 520 and
$955\text{\,}\mathrm{c}\mathrm{m}^{-1}$ can be clearly distinguished (in
green). The spectrum at the pyramid crater (red) has clearly a higher overall
intensity. In addition to the Raman peaks, there is also a background visible.
Especially at $4\text{\,}\mathrm{K}$, this background signal becomes extremely
high, turning the signal from all the higher frequency Raman modes into mere
shoulders. Based on its spectral position, we attribute this background to
intermediate gap states or defect states (see Supplementary materials Fig.9).
It is interesting to note that this background is significantly higher in the
pyramid crater than on the sides, which might be originated by the presence of
crystallographic defects.

Figure 4f presents a map of the intensity ratio between the first two Raman
peaks (E2g/A1g). Just like the intensity of the individual peaks, this
intensity ratio is also non-uniform over the WS2 pyramid. In the pyramid
crater, the peak ratio is approximately 1.0, whereas on the stair-like sides,
the A1g peak is higher. The difference in peak ratio between the pyramid
crater and sides is also present and much higher for the
$561\text{\,}\mathrm{n}\mathrm{m}$ excitation (see Supplementary Materials
Fig.11). Note that the spectral features of a fully grown pyramid are very
similar to the spectral response from the hollow pyramid sides (see
Supplementary Materials Fig.11). We conclude that both the peak intensity and
the overall shape of the spectra are non-uniform along the WS2 pyramid,
behaving differently at the hollow pyramid crater and the stair-like sides.
This indicates a difference in the atomic arrangement between the two parts of
the pyramid.

Figure 5: Position dependence of spectral position
a. Map at $4\text{\,}\mathrm{K}$ of the spectral position of the first WS2
Raman feature (2LA(M),E2g), with a step size of around
$1.5\text{\,}\mu\mathrm{m}$. The spectral position is fairly homogeneous over
most of the pyramid, except for the edge, where it is blue shifted up to
$320\text{\,}\mathrm{c}\mathrm{m}^{-1}$. The stars indicate the position of
the spectra in b. Three gray lines are drawn as guides to the eye. Comparing
the position of the Si peak of the three spectra with the line at
$520\text{\,}\mathrm{c}\mathrm{m}^{-1}$ indicates that the spectral position
of this peak does not shift. Comparing the position of the first WS2 peak with
the line at $355\text{\,}\mathrm{c}\mathrm{m}^{-1}$ does indicate the large
shift of the spectrum on the pyramid edge (light blue) with respect to the
rest of the nanostructure.

We also find a spatial non-uniformity in the spectral position of the peaks.
Figure 5a depicts the spectral position of the first WS2 Raman peak (E2g,2LA)
as a function of position. This spectral position is fairly uniform over most
of the nanostructure, except for the right edge, where the spectral position
is red shifted significantly up to $320\text{\,}\mathrm{c}\mathrm{m}^{-1}$.
Moreover, a small blue shift of the peak is seen on the left pyramid edge. The
second WS2 Raman peak exhibits a similar spectral shift (not shown), as do
spectra obtained for a $561\text{\,}\mathrm{n}\mathrm{m}$ excitation. This
spectral shift of peaks becomes more evident when comparing the spectra at the
positions of the blue stars (Fig.5b). The second line indicates the position
of the silicon peak at $520\text{\,}\mathrm{c}\mathrm{m}^{-1}$, which is
clearly constant in all three spectra. However, when comparing the line at
$355\text{\,}\mathrm{c}\mathrm{m}^{-1}$ with the position of the first Raman
peak, it is clear that the WS2 peaks in the spectrum are blue shifted.

The spectral position of Raman modes in TMD materials is known to depend on
the number of layers [26, 27, 28, 22, 21]. One might therefore have expected a
gradual spectral shift along the stair-like sides of the pyramid, because of
their gradual increase in WS2 layer thickness. Unfortunately, the diffraction-
limited laser spot of size $450\text{\,}\mathrm{n}\mathrm{m}$ (see Methods) is
much bigger than the width of the individual terraces. Therefore, if the size
of the steps is one or even a few layers, we do not have the resolution to
distinguish thickness-dependent changes in the Raman response of individual
steps. The changes in the Raman response are smallest for low N, where N is
the number of layers. The reported difference in spectral position for
different layer thicknesses is at most $5\text{\,}\mathrm{c}\mathrm{m}^{-1}$
(between a monolayer and a bilayer), much less than the shift of
$30\text{\,}\mathrm{c}\mathrm{m}^{-1}$ that we observe at the edge of this
pyramid. Therefore this spectral shift cannot be explained by a thickness
increase alone.

Figure 6: Temperature dependence of spectral features
a-b. Spectra obtained as a function of temperature with a
$595\text{\,}\mathrm{n}\mathrm{m}$ excitation on the stair-like pyramid sides
(black star in Fig.4) and on the hollow pyramid middle (red star in Fig.4),
respectively. c. Spectra obtained with a $561\text{\,}\mathrm{n}\mathrm{m}$
excitation of the hollow pyramid middle as a function of temperature. The
background visible at higher frequencies overlaps in wavelength with the
background under the $595\text{\,}\mathrm{n}\mathrm{m}$ spectra in Fig.4b (see
Supplementary Materials Fig.9) d. Temperature dependence of the intensity
ratio of the first two Raman features, the fingerprint of WS2 material. The
intensity ratio is presented for spectra upon
$595\text{\,}\mathrm{n}\mathrm{m}$ excitation (circles), spectra at the
pyramid crater (stars) and pyramid sides (diamonds) upon
$561\text{\,}\mathrm{n}\mathrm{m}$ excitation.

The spectral position of Raman modes in TMD materials does not only depend on
the number of layers, it is also known to be influenced by the defect density
[48, 49], strain [50, 51] and pressure [33]. The reported shift due to strain
is 2-$3\text{\,}\mathrm{c}\mathrm{m}^{-1}$ [50, 51] and due to an increased
defect density is 5-$10\text{\,}\mathrm{c}\mathrm{m}^{-1}$ [48, 49]. For both
strain and defects, the A1g peak is much less affected than the E2g peak. The
reported shift due to pressure is up to $40\text{\,}\mathrm{c}\mathrm{m}^{-1}$
for pressures up to $20\text{\,}\mathrm{G}\mathrm{P}\mathrm{a}$ [33]. Since
our measurements were performed in either ambient (room temperature) or vacuum
(low temperature) conditions, we do not expect a spectral shift due to
pressure. It is not unlikely that a large defect density and/or the presence
of strain are present in the hollow pyramids. Interestingly, spectra taken on
fully grown WS2 pyramids with curved edges do exhibit small shifts in the
spectral peak position along the edges with highest curvature, where a higher
stress or strain is expected (see Supplementary Materials Fig.12). Therefore
we assume that the origin of the large spectral shift in the hollow WS2
pyramid in Fig.5 lies in a combination of the mentioned effects of defect
density and strain or stress. Having said that, the previously reported
shifts, even when added, are much lower than the
$30\text{\,}\mathrm{c}\mathrm{m}^{-1}$ that we observe on the edge of the
hollow pyramid, so we cannot exclude unknown other causes related to the
specific nanogeometry of the hollow pyramid.

In this context, it is interesting to note that we measure an average spectral
position of the first Raman peak on a WS2 monolayer of
$357\text{\,}\mathrm{c}\mathrm{m}^{-1}$, which is higher than the average of
$350\text{\,}\mathrm{c}\mathrm{m}^{-1}$ of this and other WS2 pyramids (see
Supplementary Materials Fig.12). Given that the first WS2 Raman feature is a
combination of the E2g and 2LA(M) phonon, we hypothesise that the first Raman
feature in the monolayer has a larger contribution from the E2g than the same
first feature in the hollow pyramid spectra.

We conclude that the spectral features of the hollow pyramids, namely
intensity, peak ratio and spectral peak position, vary in space over the
nanostructures. This in contrast with the homogeneous distributions of these
spectral features on a WS2 monolayer. Moreover, the spectral position of the
first WS2 Raman feature is different for a WS2 monolayer than for a hollow WS2
pyramid, indicating a larger contribution from the E2g than the 2LA(M) phonon.

###  II.5 Temperature dependence of spectral features

Studying the temperature dependence of spectral features provides insights on
the structural properties of the WS2 pyramids. Figure 6a presents spectra at
four temperatures at the pyramid side (black star in Fig.4a), obtained with a
$595\text{\,}\mathrm{n}\mathrm{m}$ excitation. With decreasing temperature,
the Raman modes become more pronounced. Note for instance the three features
at 702, 769 and $833\text{\,}\mathrm{c}\mathrm{m}^{-1}$. The intensity of both
the Raman features and the background increases with decreasing temperature.
This intensity increase of the background is even more clear in Fig.6b-c, that
present the spectra from the hollow pyramid middle (red star in Fig.4a)
obtained upon either $595\text{\,}\mathrm{n}\mathrm{m}$ or
$561\text{\,}\mathrm{n}\mathrm{m}$ excitation. The background also seems to
exhibit a spectral blue shift as a function of temperature, with its maximum
moving from $635\text{\,}\mathrm{n}\mathrm{m}$ at room temperature to
$620\text{\,}\mathrm{n}\mathrm{m}$ at $4\text{\,}\mathrm{K}$. Based on the
temperature dependence of its spectral position, we attribute this background
to intermediate gap states or defect states rather than excitons, trions or an
indirect bandgap response (see Supplementary Materials Section 3).

Figure 6d presents the temperature dependence of the average intensity ratio
of the first two Raman peaks (E2g/A1g). As shown in Fig.4f, this ratio is not
uniform over the pyramid, but is higher at the hollow pyramid middle than at
the stair-like sides. This non-uniformity is most evident in the spectra
obtained by $561\text{\,}\mathrm{n}\mathrm{m}$ excitation (diamonds in
Fig.6d), as the A1g peak in the spectra from the pyramid sides almost
completely disappears at room temperature (see Supplementary Materials
Fig.11). For a $595\text{\,}\mathrm{n}\mathrm{m}$ excitation, at room
temperature the first Raman peak ($E_{2g}$,2LA(M)) is 1.5x higher than the
second Raman peak ($A_{1g}$) and at $4\text{\,}\mathrm{K}$ this ratio is
exactly inverted (circles in Fig.6d). The peak ratio upon
$561\text{\,}\mathrm{n}\mathrm{m}$ excitation of spectra taken at the pyramid
middle follow a similar temperature-dependent behaviour (stars in Fig.6d).

The temperature-dependent intensity increase of TMDs Raman peaks has been
reported previously for horizontal TMDs layers, and is attributed to an
increase in phonon thermal population [35, 32, 31]. The difference in
intensity ratio between the E2g and A1g for the different excitation
frequencies can be explained by the more resonant
$595\text{\,}\mathrm{n}\mathrm{m}$ laser exciting the Raman peaks differently
than the out-of-resonance $561\text{\,}\mathrm{n}\mathrm{m}$ laser [37, 38].
The strength of the exciton-phonon interaction, and therefore the resonance
condition, is different for the in-plane E2g than the out-of-plane A1g Raman
modes [52, 38]. This explains why the ratio E2g/A1g is higher for a
$561\text{\,}\mathrm{n}\mathrm{m}$ excitation, e.g., out-of-resonance with the
excitonic transition, than for the resonant $595\text{\,}\mathrm{n}\mathrm{m}$
excitation. The Raman intensity ratio also depends on the layer thickness of
the material [27]. However, the main difference in intensity ratio is reported
between a monolayer and a bilayer, whereas we observe different relative Raman
intensities between the few-layer pyramid crater and the thick pyramid edge.
Moreover, the temperature-dependent behaviour of the Raman intensity also
depends on the defect density in the sample [34]. These factors are not
mutually independent, e.g., the WS2 thickness influences the exciton-phonon
interaction, the resonance of the excitation affects the influence of phonons
and defects on the Raman intensity. The temperature dependence of the Raman
peak intensities, excited with two different frequencies, is therefore an
interplay between the phonon thermal population, the resonance conditions for
the different phonon peaks and the defect density in the structure.

It is interesting to note in this context the intensity ratio of the first two
Raman peaks on a WS2 monolayer, excited at $561\text{\,}\mathrm{n}\mathrm{m}$.
This ratio is 1.4 at room temperature, much lower than both the intensity
ratio at the hollow pyramid middle and at the stair-like sides, excited at
$561\text{\,}\mathrm{n}\mathrm{m}$ (see Supplementary Materials Fig.11).
Unexpectedly, this indicates a clear difference in structure and/or thickness
between the WS2 monolayer and hollow pyramid. The large difference in
intensity ratio on the hollow pyramid middle and the stair-like sides suggests
a difference in atomic arrangement, pointing out that nanogeometrical
differences induce spectral modifications.

##  III Conclusions

We have studied the optical response of hollow WS2 pyramids, comparing them
with WS2 monolayers grown on the same substrate. The optical response of these
nanostructures is completely different, as hollow WS2 exhibit a strongly
reduced photoluminescence with respect to WS2 monolayers. This enables us to
study the rich variety of Raman peaks that the pyramids exhibit as a result of
the resonant excitation. Following the hypothesis of a multiphonon excitation
involving the longitudinal acoustic phonon LA(M), we are able to explain the
origin of all 10-12 observed Raman resonances. In contrast with monolayers,
the measured optical response of the pyramids is non-uniform in both
intensity, intensity ratio between peaks, spectral shape and spectral
position. We attribute the spectral differences between the hollow pyramid
middle and the stair-like sides to differences in both nanogeometry and atomic
arrangement. ADF-STEM measurements confirm variations in the atomic
arrangement, where the level of disorder is more marked in the pyramid crater
than on the sides. Next to a positional dependence, we measure the temperature
dependent behaviour of the spectral response of the hollow WS2 pyramids. With
decreasing temperature, the spectra change in intensity and shape. We see
clear differences between spectra obtained with a resonant and out-of-
resonance excitation laser. As the optical response of WS2 monolayers,
exhibiting photoluminescence, is completely different, we therefore deduce to
have fabricated a platform of structures with tunable optical properties. Both
nanostructures offer exciting possibilities, with applications ranging from
opto-electronics to non-linear optics.

##  IV Methods

The WS2 hollow pyramids are directly grown on a microchip using chemical
vapour deposition (CVD) techniques. This microchip is composed of a silicon
frame with nine windows over which a continuous silicon nitride (Si3N4) film
is spanned. Preceding the CVD growth procedure[16], tungsten trioxide (WO3) is
deposited onto the microchip. This deposition is achieved by dispersing
$50\text{\,}\mathrm{m}\mathrm{g}$ of WO3 in $1\text{\,}\mathrm{m}\mathrm{L}$
of isopropanol, followed by a deposition by means of a pipette. The subsequent
sulfurization process [16] is carried out in a gradient tube furnace from
Carbolite Gero. The microchip is placed in the middle zone and a crucible
holding $400\text{\,}\mathrm{m}\mathrm{g}$ of sulfur is placed upstream from
it. The middle zone is heated to 750℃, and kept at this reaction temperature
for 1 hour after which the system is naturally cooled down to room
temperature. Sulfurization is carried out under an argon flow of
$150\text{\,}\mathrm{s}\mathrm{c}\mathrm{c}\mathrm{m}$. The zone containing
the sulfur is heated to 220℃.

The optical measurements are performed using a home-built spectroscopy set-up.
We placed the sample in a Montana cryostation S100, using Attocube
ANPxy101/RES piezo scanners to perform the presented raster scans. The small
cross-coupling between the in-plane and out-of-plane piezo scanners causes a
skewing between the x and y axis of the spectral-feature maps depicted in this
work. Comparing the maps with the optical and SEM images of the pyramids, we
can correlate the position of certain spectral features with the position on
the pyramid. The cryostation is cooled down from room temperature to
$200\text{\,}\mathrm{K}$, $100\text{\,}\mathrm{K}$ and $4\text{\,}\mathrm{K}$.
The sample is illuminated through an $0.85\text{\,}\mathrm{N}\mathrm{A}$ Zeiss
100x objective. Two continuous wave lasers are used, one with a wavelength of
$595\text{\,}\mathrm{n}\mathrm{m}$ and a power of
$1.6\text{\,}\mathrm{m}\mathrm{W}\mathrm{/}\mathrm{m}\mathrm{m}^{2}$, and one
with a wavelength of $561\text{\,}\mathrm{n}\mathrm{m}$ and a power of
$3.6\text{\,}\mathrm{m}\mathrm{W}\mathrm{/}\mathrm{m}\mathrm{m}^{2}$. To avoid
the consequences of tight focussing on (circular) polarization, a
$2\text{\,}\mathrm{m}\mathrm{m}$ laser diameter is used, slightly underfilling
the objective in the excitation path. This results in an excitation spot size
of approximately $450\text{\,}\mathrm{n}\mathrm{m}$. A linear (vertical)
polarization is used for the laser light. The sample emission is collected in
reflection through the same objective as in excitation, and projected onto a
CCD camera (Princeton Instruments ProEM 1024BX3) and spectrometer (Princeton
Instruments SP2358) via a 4f lens system. The excitation light is filtered out
using colour filters.

The transmission electron microscopy (TEM) measurements were carried out using
an ARM200F Mono-JEOL microscope with Cs probed corrected. The microscope was
operated at $200\text{\,}\mathrm{k}\mathrm{V}$ both in TEM and STEM modes,
with the monochromator on and a slit of $2\text{\,}\mu\mathrm{m}$ inserted.
For the atomic resolution ADF-STEM measurements, an objective aperture of
$30\text{\,}\mu\mathrm{m}$ and a camera length of
$12\text{\,}\mathrm{c}\mathrm{m}$ were used. The convergence semi-angle was
$23\text{\,}\mathrm{m}\mathrm{r}\mathrm{a}\mathrm{d}$.

##  V Acknowledgements

The authors acknowledge funding from ERC Starting Grant “TESLA” No. 805021.
The authors acknowledge dr Martin Caldarola and dr Filippo Alpeggiani for
their help in the data analysis.

## Supplementary Materials

###  V.1 WS2 hollow pyramid sample

Figure 7: Hollow WS2 pyramid sample
a. Wide-field optical image of a part of the sample, with hollow pyramids
(red), WS2 monolayer flakes (green) and full pyramids (blue). The black
squares are windows in the silicon frame over which a silicon nitride film is
spanned (see Methods). Under these growth conditions, many hollow pyramids
arise size 10 - $25\text{\,}\mu\mathrm{m}$, comparable to the one presented in
this work. b,c. SEM images of the hollow WS2 pyramid studied in the main text.
In b, the black triangle in the middle is the bottom of the pyramid crater.
The top rim of the pyramid can also be distinguished around the triangle of
the pyramid crater. The steps in the stair-like sides can be easily recognized
in c.

Figure 7a presents a wide-field optical image of a part of the sample. Under
these growth conditions both hollow pyramids (red), monolayer flakes (green)
and full pyramids (blue) are created. Note that there are many hollow pyramids
with a comparable size to the one studied in this work
($15\text{\,}\mu\mathrm{m}$). Using the same CVD growing conditions (see
Methods) yields similar samples with the same distribution of pyramid-like
structures.

To provide better insight in the morphology of the hollow WS2 pyramids,
Fig.7b,c depict higher magnification SEM images of the hollow pyramid depicted
in Fig.1a in the main text. The black triangle in the middle of Fig.7b is the
bottom of the pyramid crater. The top rim can also be distinguished around the
crater triangle. The steps of the stair-like sides can clearly be recognized
in Fig.7c.

Figure 8: Morphology and crystal structure of the hollow WS2 pyramids
a-b. Low-magnification ADF-STEM images of a hollow WS2 pyramid. The step-like
nature of the pyramid side is clearly visible by the changes in contrast with
every step. c. Atomic resolution image corresponding to the side of the hollow
pyramid (left panel) and the ADF intensity profile (right panel) acquired
along the black outlines region in the atomic resolution image. d. Schematic
atomic model of the top-view (upper panel) and side-view (lower) of the
crystalline structure associated to the 3R-WS2 phase.

In addition, Transmission Electron Microscopy (TEM) measurements are performed
to gain access to the atomic structure of the hollow pyramids. Figure 8a and
8b display low-magnification annular dark-field (ADF) scanning transmission
electron microscopy (STEM) images of the side of a hollow WS2 pyramid. The
variations in the contrast visualise clearly the step-like nature of the
hollow pyramid side. Figure 8c presents an atomic-resolution ADF-STEM image
corresponding to the side of the pyramid. Each bright spot corresponds to an
atomic column that is composed of alternating tungsten (W) and sulfur (S)
atoms. Using an ADF linescan, extracted from the atomic resolution image
across six lattice points, we confirm that the WS2 within the hollow pyramid
crystallizes in a 3R crystal phase (see Fig.8d).

###  V.2 Spectral background

The hollow pyramid spectra exhibit a number of Raman modes plus a background
(see Fig.3, Fig.6 in the main text). Using the temperature-dependent spectral
position of this background, we can explain its origin. Figure 9 depicts the
spectral response of the hollow pyramid upon a
$595\text{\,}\mathrm{n}\mathrm{m}$ excitation (orange) and a
$561\text{\,}\mathrm{n}\mathrm{m}$ excitation (green), comparing this with the
photoluminescence of a monolayer exciton (black dotted line). The spectral
response of the hollow pyramid to a $595\text{\,}\mathrm{n}\mathrm{m}$
excitation exhibits a background under the higher order Raman modes, whereas
the spectral response of a $561\text{\,}\mathrm{n}\mathrm{m}$ excitation
exhibits a background separated from the Raman modes, that overlap spectrally
(see Fig.9c-d). The spectral position of the photoluminescence peak is
completely different (610 - $630\text{\,}\mathrm{n}\mathrm{m}$ in the
temperature range $4\text{\,}\mathrm{K}$ \- $300\text{\,}\mathrm{K}$). Figure
9e depicts the spectral position of the pyramid background, determined from
the spectra of $561\text{\,}\mathrm{n}\mathrm{m}$ excitation (in green), and
the spectral position of the exciton PL (black dotted line). Both the pyramid
background and the exciton PL peak are blue-shifting with decreasing
temperature, however their spectral position is different from each other. At
room temperature (Fig.9a), the spectral position of the PL peak (at
$630\text{\,}\mathrm{n}\mathrm{m}$) is very close to the background of the
pyramid spectra acquired with a $595\text{\,}\mathrm{n}\mathrm{m}$ excitation
(around $645\text{\,}\mathrm{n}\mathrm{m}$). At $4\text{\,}\mathrm{K}$
(Fig.9d), the PL peak (at $615\text{\,}\mathrm{n}\mathrm{m}$) overlaps roughly
with the first few Raman features of the pyramid spectra acquired with a
$595\text{\,}\mathrm{n}\mathrm{m}$ excitation (around
$620\text{\,}\mathrm{n}\mathrm{m}$). However, at $200\text{\,}\mathrm{K}$ and
especially $100\text{\,}\mathrm{K}$ (Fig.9b,c), the PL peak overlaps neither
with the first Raman features nor the background of the pyramid spectra
acquired with a $595\text{\,}\mathrm{n}\mathrm{m}$ excitation. Therefore we
conclude that the background of the hollow pyramid spectra is not
photoluminescence from the direct bandgap of WS2.

Another potential explanation for the background in the pyramid spectra is
emission from the indirect bandgap. Few-layer WS2 samples exhibit a
combination of direct and indirect bandgap emission [1]. Figure 9f compares
the room-temperature spectra of a WS2 trilayer (grey) and five WS2 layers
(blue) (exfoliated on a Si substrate) with a spectrum from the hollow WS2
pyramid. The room-temperature spectral position of the indirect bandgap ranges
from $700\text{\,}\mathrm{n}\mathrm{m}$ for a bilayer to
$850\text{\,}\mathrm{n}\mathrm{m}$ for multilayers [53]. This constitutes a
large spectral separation with the measured spectrum (compare Fig.9a).
Moreover, with decreasing temperature, the indirect bandgap is reported to
exhibit a red shift, i.e., away from the exciton position [54, 55], whereas
the pyramid background exhibits a similar blue shift to the exciton PL (see
Fig.9e).

An alternative explanation would be emission from a charged exciton or trion.
However, the reported spectral position of the trion lies closer to the
exciton than the background in the hollow pyramid spectra [56, 57]. We
conclude that this background originates in intermediate gap states or defect
states, that are reported to be in a range of spectral positions further away
from the exciton PL than the trion [58, 57, 59], but closer than the indirect
bandgap [53, 54, 55].

It is interesting to note that the spectral background from these intermediate
gap states is more present in the pyramid crater than on the pyramid sides. We
propose this might be originated in the higher density of crystallographic
defects.

Figure 9: Comparison pyramid, monolayer and few-layer spectra
a-d. Spectral response of a pyramid upon a $595\text{\,}\mathrm{n}\mathrm{m}$
excitation (orange) and a $561\text{\,}\mathrm{n}\mathrm{m}$ excitation
(green), and the spectral response of a monolayer upon
$595\text{\,}\mathrm{n}\mathrm{m}$ excitation (black dotted line), at
temperatures between room temperature and $4\text{\,}\mathrm{K}$ (the spectra
are re-scaled for easier comparison, see legends). The spectral response of
the monolayer upon a $561\text{\,}\mathrm{n}\mathrm{m}$ excitation (green
dotted line in a) has a lower intensity than to the
$595\text{\,}\mathrm{n}\mathrm{m}$ excitation, but is at the same wavelength.
e. The background under the higher order Raman features in the spectra of the
$595\text{\,}\mathrm{n}\mathrm{m}$ excitation, and the spectral position of
the exciton PL are both blue-shifting with decreasing temperature. f. In
contrast to the spectra of a WS2 trilayer (in grey) and five layers of WS2 (in
blue) (exfoliated on a Si substrate), the spectrum of the WS2 pyramid (in
orange) does not exhibit light from an indirect bandgap at 800 -
$850\text{\,}\mathrm{n}\mathrm{m}$ wavelength. Moreover, although reduced with
respect to the monolayer, the PL from the direct bandgap of the few-layers of
WS2 is clearly distinguishable from the background. g. Comparison of the
spectral response of the hollow pyramid (in orange) and of five layers of WS2
(in blue), acquired at $4\text{\,}\mathrm{K}$ with a
$595\text{\,}\mathrm{e}\mathrm{x}\mathrm{c}\mathrm{i}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}$.
Figure 10: Position dependence of Raman intensity
a-d Intensity map of the Raman features of the hollow WS2 pyramid a. around
$350\text{\,}\mathrm{c}\mathrm{m}^{-1}$ (2LA,E2g), b. around
$417\text{\,}\mathrm{c}\mathrm{m}^{-1}$ (A1g), c. around
$702\text{\,}\mathrm{c}\mathrm{m}^{-1}$ (4LA) and d. around
$833\text{\,}\mathrm{c}\mathrm{m}^{-1}$ (2A1g), taken at room temperature upon
a $561\text{\,}\mathrm{n}\mathrm{m}$ excitation. e-h Intensity map of the
Raman features of the hollow WS2 pyramid e. around
$350\text{\,}\mathrm{c}\mathrm{m}^{-1}$ (2LA,E2g), f. around
$417\text{\,}\mathrm{c}\mathrm{m}^{-1}$ (A1g), g. around
$770\text{\,}\mathrm{c}\mathrm{m}^{-1}$ (A1g+2LA) and h. around
$1120\text{\,}\mathrm{c}\mathrm{m}^{-1}$ (6LA), taken at
$4\text{\,}\mathrm{K}$ upon a $561\text{\,}\mathrm{n}\mathrm{m}$ excitation.
Note that in all cases (compare with Fig.4a,b in the main text) the intensity
of the Raman features from the pyramid crater is significantly higher than the
Raman intensity from the stair-like sides. Figure 11: Position dependence of
peak ratio
a-c Room-temperature map of the ratio between the first two Raman features in
the spectra (E2g/A1g) of a the monolayer, b the hollow pyramid and c a full
WS2 pyramid (compare SEM images) (blue stars indicate the positions of the
spectra in d-f). a. The peak ratio on the monolayer is homogeneous along the
full flake, 1.4 on average (upon a $561\text{\,}\mathrm{n}\mathrm{m}$
excitation). b. The peak ratio on the hollow pyramid (upon a
$561\text{\,}\mathrm{n}\mathrm{m}$ excitation) is much higher along the stair-
like pyramid sides (namely 4-7) than on the pyramid crater (roughly 1.0). c.
The peak ratio on the full pyramid is significantly higher along the upper
side. Note in the presented SEM image that this side of this full WS2 pyramid
is curved, potentially inducing strain. d. Raman spectrum of the WS2
monolayer. e. Spectrum of the side of the WS2 hollow pyramid upon
$561\text{\,}\mathrm{n}\mathrm{m}$ excitation. Note that the A1g feature is
merely a shoulder on the E2g,2LA(M) feature, which explains the high peak
ratio in b. f. Spectrum of the full WS2 pyramid
($595\text{\,}\mathrm{n}\mathrm{m}$ excitation), which is comparable to the
spectra of the hollow WS2 pyramid presented in the main text.

###  V.3 Spectral features of pyramids, monolayer and few-layer WS2

Figure 10 presents maps of the intensity of different Raman features in
spectra from the hollow WS2 pyramid, taken at room temperature (Fig.10a-d) and
at $4\text{\,}\mathrm{K}$ (Fig.10e-h) upon a
$561\text{\,}\mathrm{n}\mathrm{m}$ excitation. Note that for all the Raman
features the intensity from the pyramid crater is higher than from the pyramid
sides, as was the case for the Raman features depicted in Fig.4a,b in the main
text ($595\text{\,}\mathrm{n}\mathrm{m}$ excitation,
$200\text{\,}\mathrm{K}$). We conclude that the intensity distribution of the
Raman features is independent of temperature or excitation frequency. As
alluded to in the main text, we hypothesise that light scatters from the
stair-like pyramid sides and thus reduces the available excitation light to
excite any Raman modes, or that scattering of the resulting Raman response
reduces the amount of light detected.

Figure 9g depicts a comparison between the spectral response of the pyramid
(in orange) and five layers of exfoliated WS2 (in blue) at
$4\text{\,}\mathrm{K}$ and upon a $595\text{\,}\mathrm{n}\mathrm{m}$
excitation. The spectral response of the few-layer WS2 exhibits a combination
of Raman modes and PL from the excitonic resonance. Due to the high PL
intensity, the higher-order Raman modes are much less clear in the few-layer
WS2 than in the pyramid spectrum. In both spectra, the A1g mode has a higher
intensity than the E2g mode. The ratio of E2g/A1g is 0.60 for few-layer WS2,
whereas it is on average 0.79 for the pyramid spectra (see Fig.6b in the main
text).

Figure 11a-c present room-temperature maps of the ratio between the first two
Raman peaks in the spectra (E2g/A1g) of respectively the WS2 monolayer, the
hollow pyramid and a full WS2 pyramid (compare the presented SEM images). In
contrast with the position dependent peak ratio of the hollow pyramids, the
peak ratio on the monolayer is homogeneous along the full flake (see Fig.11a).
This ratio is around 1.4, as can be observed in the Raman spectrum in Fig.11d.
The Raman peak ratio of the hollow pyramids upon
$561\text{\,}\mathrm{n}\mathrm{m}$ excitation is much higher on the pyramid
sides than in the pyramid crater (see Fig.11b). This difference in ratio was
already apparent upon $595\text{\,}\mathrm{n}\mathrm{m}$ excitation, as
presented in Fig.4f in the main text, but the contrast between the pyramid
sides and crater is much larger upon $561\text{\,}\mathrm{n}\mathrm{m}$
excitation. The Raman peak ratio at the pyramid sides is as high as 4-7 times,
as the A1g feature is reduced to merely a shoulder on the E2g,2LA(M) feature.
This becomes apparent in the spectrum in Fig.11e. The SEM image under Fig.11c
depicts a full WS2 pyramid grown on the same substrate. This pyramid exhibits
a clear curvature. Interestingly, the Raman peak ratio of the spectra from
this pyramid (upon a $595\text{\,}\mathrm{n}\mathrm{m}$ excitation) exhibit a
difference on the side with the largest curvature, potentially induced by
strain. Figure 11f presents a spectrum of the full WS2 pyramid, which is
similar to the spectra of the hollow WS2 pyramid in the main text. We conclude
that the Raman peak ratio provides information on differences in the atomic
structure between different nanostructures, as well information on differences
in both atomic structure and strain or stress within the same nanostructure.

Figure 12: Position dependence of spectral position
a-b Room temperature map of the first WS2 Raman feature around 350cm-1 on a
the monolayer and b a full WS2 pyramid (compare SEM images). Comparing a and b
and Fig.5 in the main text, it becomes apparent that the Raman peak position
on the monolayer is significantly different than on the pyramids. c depicts
the average spectral position of the first Raman peak on all measured pyramids
and the monolayer. Note that the bar does not indicate errors, but rather the
spread of the peak position along the pyramids. The first Raman feature on the
monolayer is around $357\text{\,}\mathrm{c}\mathrm{m}^{-1}$, whereas on all
measured pyramids, it is around $350\text{\,}\mathrm{c}\mathrm{m}^{-1}$, and
around $348\text{\,}\mathrm{c}\mathrm{m}^{-1}$ on five layers of WS2. Possibly
this Raman peak has a larger contribution from the E2g than the 2LA(M) phonon
in the monolayer than in the pyramid spectra.

Another position-dependent spectral feature alluded to in the main text is the
spectral position of the Raman peaks. Figure 12 presents a map of the spectral
position of the first Raman peak on the WS2 monolayer and the full WS2 pyramid
respectively. The peak position is fairly homogeneous along both
nanostructures compared to the hollow pyramid (Fig.5a in the main text).
Figure 12c depicts the average spectral position of the first Raman peak, as
measured on different WS2 pyramids and the monolayer (the bar does not
indicate errors, but rather the spread of the peak position along the
pyramids). The peak position on the monolayer is around
$357\text{\,}\mathrm{c}\mathrm{m}^{-1}$, which is significantly different than
the peak position of around $350\text{\,}\mathrm{c}\mathrm{m}^{-1}$ on all the
pyramid structures and $348\text{\,}\mathrm{c}\mathrm{m}^{-1}$ for five layers
of exfoliated WS2. We hypothesise that this first Raman peak has a larger
contribution from the E2g than the 2LA(M) phonon in the monolayer than in the
pyramid spectra. In conclusion, the different nanogeometry of the WS2 pyramids
induces spectral changes with respect to monolayer WS2.

###  V.4 Structural characterisation

Figure 13: ADF-STEM of a hollow WS2 pyramid
a. Atomic resolution ADF-STEM image taken at the side of a hollow WS2 pyramid.
inset FFTs are taken within two visual different areas of this given region,
highlighting a clear difference between the two areas. b-d. Low-magnification
ADF images of the same hollow pyramid. The characteristic morphology of the
hollow pyramids can clearly be observed, and is also extracted from the line
profile over the white line given within b (see inset). Each of these images
show free-standing flakes which arise from the walls of the hollow pyramid.
The free-standing flake shown in d suggest a growth mechanism where layer-by-
layer stacking and screw-dislocation-driven growth mechanisms co-exist. inset
A schematic visualises this co-existence. Here a free-standing flake initiates
its growing from a central nucleation point via layer-by-layer growth (blue),
after which a separate nucleation event occurs leading to a screw-dislocation-
driven growth (green) on top.

Figure 13 displays additional results obtained in the structural
characterization measurements by means of Transmission Electron Microscopy
(TEM). Figure 13a presents a high-resolution ADF-STEM image taken at the side
of a hollow WS2 pyramid. Within Figure 2 of the main text it could already be
observed that the atomic arrangements present in the sides of the WS2 pyramid
and the middle are not the same. Figure 13a depicts how even within a given
region the atomic arrangement can vary. This is highlighted by the differences
in the FFTs taken in the lower left corner (marked by the green rectangle in
Fig.13a) and the top right corner (marked by the blue rectangle in Fig.13b) of
this given region. Where the FFT in the blue area shows two nicely arranged
hexagonal patterns, e.g., an inner and an outer hexagon, the green area
presents one hexagon. These subtle variations of the atomic arrangement might
be induced by the local presence of strain, which in turn results into a
slight change of the orientation of the flake.

Figures 13b to 13d depict low-magnification ADF images of the hollow WS2
pyramid. Within Fig.13b the hollow nature of the pyramid can clearly be
observed, and illustrated even clearer in the line profile taken along the
white line given in Fig.13b. In addition, Fig.13b-d depict how free-standing
WS2 flakes seem to arise from the walls of the hollow pyramid. These increase
the level of structural disorder in the middle of the pyramids as compared to
the sides. The standing flake depicted in the low-magnification ADF image of
Fig.13d highlights the possible growth mechanism leading to the hollow WS2
pyramids. In this figure it can be observed that both layer-by-layer stacking
and screw-dislocation-driven growth mechanisms contribute to the overall
growth mechanism of the hollow WS2 pyramids.

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