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org/JACS Article

Insight into the Heterogeneity of Longitudinal Plasmonic Field in a

Nanocavity Using an Intercalated Two-Dimensional Atomic Crystal
Probe with a ∼7 Å Resolution
Siyu Chen, Shirui Weng, Yuan-hui Xiao, Pan Li, Miao Qin, Guoliang Zhou, Ronglu Dong,
Liangbao Yang,* De-yin Wu, and Zhong-qun Tian*
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ABSTRACT: Quantitative measurement of the plasmonic field

distribution is of great significance for optimizing highly efficient
optical nanodevices. However, the quantitative and precise measure-
ment of the plasmonic field distribution is still an enormous challenge.
In this work, we design a unique nanoruler with a ∼7 Å spatial
resolution, which is based on a two-dimensional atomic crystal where
the intercalated monolayer WS2 is a surface-enhanced Raman
scattering (SERS) probe and four layers of MoS2 are a reference
layer in a nanoparticle-on-mirror (NPoM) structure to quantitatively
and directionally probe the longitudinal plasmonic field distribution at
high permittivity by the quantitative SERS intensity of WS2 located in
different layers. A subnanometer two-dimensional atomic crystal was
used as a spacer layer to overcome the randomness of the molecular
adsorption and Raman vibration direction. Combined with comprehensive theoretical derivation, numerical calculations, and
spectroscopic measurements, it is shown that the longitudinal plasmonic field in an individual nanocavity is heterogeneously
distributed with an unexpectedly large intensity gradient. We analyze the SERS enhancement factor on the horizontal component,
which shows a great attenuation trend in the nanocavity and further provides precise insight into the horizontal component
distribution of the longitudinal plasmonic field. We also provide a direct experimental verification that the longitudinal plasmonic
field decays more slowly in high dielectric constant materials. These precise experimental insights into the plasmonic field using a
two-dimensional atomic crystal itself as a Raman probe may propel understanding of the nanostructure optical response and
applications based on the plasmonic field distribution.

■ INTRODUCTION
The light field and energy are confined to the subwavelength
heterogeneous distribution of the plasmonic field experimen-
tally. Existing plasmonic field instruments, such as near-field
scale due to the strong local constraints of surface plasmon scanning optical microscopy (NSOM) and cathode lumines-
resonance (SPR), resulting in a large enhancement of the cence (CL), have successfully detected the plasmonic field
plasmonic field.1,2 It is therefore of great significance to distribution of Mie resonance at deep subwavelength
understand and quantitatively probe the plasmonic field to scales,13−16 but they do not provide quantitative information
promote the rapid development of these plasmon-enhanced about the enhancement, while surface-enhanced Raman
applications, such as surface-enhanced Raman spectroscopy,2 scattering (SERS), which is strongly related to plasmonic
surface plasmon-enhanced fluorescence,3,4 nonlinear optical field enhancement, provides a unique opportunity to measure
effects,5 photothermal conversion,6 photoacoustic effects,7 the plasmonic field inside nanostructures.
catalysis,6 and photovoltaic conversion.8 To obtain the large At present, the relationship between Raman signals and
enhancement of the plasmonic field, attention has been given plasmonic fields has been utilized in plasmonic nano-
to the nanoparticle-on-mirror (NPoM) structure. The
individual NPoM structure is composed of a single nano-
particle spaced above the film by a spacer.9,10 The light field is Received: March 22, 2022
strictly confined to the nanocavity, forming the ultrasmall Published: June 20, 2022
mode volume V ≃ Rd2/n2g set by the particle radius R, spacer
size d, and refractive index ng.11,12 Although it is clear
theoretically that the plasmonic field in the nanocavity is not
evenly distributed, it is still very challenging to verify the

© 2022 American Chemical Society https://doi.org/10.1021/jacs.2c03081

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Figure 1. (a) Schematic diagram of a plasmonic coupling nanocavity between the ultrasmooth Au film and AuNP, where each layer of the two-
dimensional atomic crystal in the hot spot is subjected to the plasmonic field of the ultrahigh enhancement. (b) Enlarged image of the marked area
(black square) in (a). (c) Schematic diagram of four layers of MoS2 and intercalated monolayer WS2 inside the nanocavity, where the position of
the WS2 probe is shifted by altering its location along with the different layers (longitudinal resolution, ∼0.7 Å). WS2 is the 1st layer on the side
away from the nanocavity and the 5th layer on the side near the top of the nanocavity. W, Mo, and S atoms are represented in red, green, and
yellow, respectively. (d) Atomic force microscopy (AFM) images and (e) the corresponding height profiles of 1- to 5-layer two-dimensional atomic
crystals on the ultrasmooth Au film. Scale bar, 200 nm. (f) Transmission electron microscopy (TEM) image and (g) the corresponding energy-
dispersive spectroscopy (EDS) mapping analysis results of the individual nanocavity, taking WS2 placed in the 3rd layer as an example.

cavities.17−19 They wisely positioned molecules as Raman independently extract anisotropic field enhancement. In this
probes in gaps of a few nanometers in size to measure the work, we first synthesized high-quality large-scale WS2 and
plasmonic fields. These Raman measurements provide insight MoS2 using an improved CVD method and transferred four
into the limits of plasmonic field enhancement as well as the layers of MoS2 and monolayer WS2 in the individual NPoM
field distribution in the nanocavity. The SERS intensity strictly using the PMMA layer-by-layer transfer method (see Materials
depends on the direction of the probe in the plasmonic field and Methods in the Supporting Information). We then
and the plasmonic field strength.20,21 However, the random- constructed four layers of MoS2 as a reference and intercalated
ness of molecular adsorption, the randomness of molecular monolayer WS2 as a Raman probe in the individual NPoM to
vibration direction, and the change of molecular polarizability measure the longitudinal plasmonic field distribution by the
due to chemical effect change the position of the atoms in the quantitative SERS intensity of WS2 located in different layers
SPR “hot spot”, thus leading to differences in SERS intensity in (Figure 1a−c).
the same plasmonic field strength.20 Therefore, it is of great Using the individual NPoM as a plasmonic enhancement
significance to find a marker that can overcome the system, incident light is effectively confined to the individual
randomness of molecular adsorption and vibration direction nanocavity, exciting an ultrahigh enhancement, which greatly
to probe the real plasmonic field strength and distribution. enhances the lattice vibration of WS2. Two-dimensional
Transition-metal dichalcogenides (TMDs) have recently crystals as a spacer and WS2 as a SERS probe also have
received considerable attention due to their unique optical and outstanding advantages. First, the spatial resolution can reach
flexible manufacturing properties.22−26 The two-dimensional the subnanometer scale due to the monolayer thickness of ∼7
atomic crystal has a clearly defined lattice direction27 and a Å. They are accurately positioned in the SPR hot spot, and the
subnanometer thickness,28 which enables direct direction intercalated WS2 layer can orientate the precise location within
matching between the lattice vibration of the two-dimensional the gap. Second, they also overcome the random movement or
crystal probe and the plasmonic field component, and thus can light damage of molecules acting as probes around the hot
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Figure 2. (a) Atomic displacements of the A1g and E2g modes in the unit cell of WS2. (b) Raman scattering spectra of monolayer WS2 on silica, on
an ultrasmooth Au film before and after annealing, and in NPoM before and after annealing. (c) Raman scattering spectra of monolayer MoS2,
monolayer WS2, and WS2 in the 3rd layer on silica. (d) Experimental intrinsic Raman scattering spectra and (e) first-principles off-resonant Raman
spectra of WS2 are located in different layers. (f) Complex refractive index and (g) normalized dark-field scattering of WS2 are located in different
layers in the individual plasmonic nanocavity.

spot. Third, WS2 is used as a SERS probe because the light agreement with the theoretical calculation in the nanocavity
absorption band of monolayer WS2 (630 nm) is matched with with a high dielectric constant. We also quantitatively,
a 633 nm excitation wavelength to form Raman resonance to directionally, and precisely measure the horizontal component
realize maximum field enhancement. Fourth, the characteristic of the plasmonic field by the horizontal SERS enhancement
peaks of WS2 and MoS2 do not interfere with one another, and factor (SERS EFxy) of E2g. The distribution of the plasmonic
the characteristic peaks of WS2 do not overlap with those of field under different dielectric constants is also obtained by
the four MoS2 layers in the reference layer, so the characteristic replacing AuNPs with AuNP@SiO2 in the individual NPoM.
peaks of WS2 can be clearly identified. Finally, the WS2/Au The details are shown below.
heterojunction and WS2/MoS2 heterojunction have little
influence on the Raman signal of WS2 by the PMMA layer-
by-layer transfer method. Based on this unique design, we
realize the quantitative and directional probing of the
■ RESULTS AND DISCUSSION
Design and Construction of a Nanocavity with Four
longitudinal plasmonic field in a nanocavity by measuring the Layers of MoS2 and an Intercalated Monolayer WS2 as
SERS signal of the out-of-plane phonon mode A1g and the in- Spacers. The individual nanocavity is configured by a single
plane phonon mode E2g symmetric lattice vibrations of WS2 Au nanoparticle, an ultrasmooth Au film, and four layers of
located in different layers, respectively. We observe the MoS2 and intercalated monolayer WS2 as spacers (abbreviated
heterogeneity of the plasmonic field distribution on the as AuNP/1L WS2-4L MoS2/Au film), where WS2 is used as a
longitudinal gradient at nearly 9-fold, which is in good SERS probe (WS2 is the 1st layer on the side away from the
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nanocavity (close to the Au film), and the 5th layer on the side ISERS | ( R, )E( )|2 (1)
near the top of the nanocavity) and four layers of MoS2 is used
as the reference layer. SERS signals of WS2 located in different The Raman scattering intensity depends on the plasmonic field
layers are high-precision measured quantitatively to probe the strength E(ω) induced by the incident field with the frequency
distribution law of the longitudinal plasmonic field (Figure 1a− of ωi and the Raman polarizability tensor α⃗ (ωR,ω).20 For
c). monolayer WS2, α⃗ (ωR,ω) can be expressed as29
The NPoM structure is composed of an ultrasmooth Au E E
xx xy 0
film, where atomic force microscopy (AFM) reveals a root-
mean-square (RMS) roughness of ∼0.28 nm (Figure S1a,b), E
( R, )= E E
0
yx yy
five layers of a two-dimensional atomic crystal, and 98.6 ± 4.3
nm AuNP scattered individually on a Au substrate (Figures 0 0 0
S1c,d and S2a,c). It was observed from the AFM topography
image and dark-field scattering image that AuNPs independ- and
ently dispersed on the ultrasmooth Au film covering two- A
xx 0 0
dimensional atomic crystal had good size uniformity, thus
reducing the error of SERS performance (Figure S2e−f). A A
( R, )= 0 yy 0
Taking WS2 placed in the 3rd layer as an example, two-
A
dimensional atomic crystals with different layers are observed 0 0 zz (2)
on the ultrasmooth Au film, as shown in the AFM images
(Figure S3). The measured thickness of the 5-layer two- with αExx = αExy = αEyx = −αEyy for the in-plane phonon
mode E2g
dimensional atomic crystal is 3.46 nm, and the average and αAxx = αAyy for the out-of-plane phonon modeA1g. The
thickness of each layer is 0.7 nm (Figure 1d,e), which is highly vibration directions of phonon mode E2g and A1g are consistent
consistent with the thicknesses of two-dimensional atomic with the horizontal (x, y) and vertical (z) components of the
crystals in other works (monolayer WS2 or MoS2 is plasmonic field, respectively (Figure 2a), and selectively
approximately 0.65 nm).27 Furthermore, the Raman peak enhance the direction and intensity of the plasmonic field.
intensities of MoS2 increase with the thickness (Figure S4). These equations also imply that the Raman intensity of A1g is
The dark-field scattering spectra of the individual nanocavities related to both the horizontal Exy and vertical Ez components
indicate that the layers of two-dimensional atomic crystals of the longitudinal plasmonic field, while the Raman intensity
increase and the resonance wavelength gradually blue-shifts of E2g is only determined by the horizontal component Exy.
(Figure S5b). These results demonstrate that five layers of two- By comparing the Raman spectra of monolayer WS2 on
dimensional atomic crystals have been successfully transferred silica, an ultrasmooth Au film, and in NPoM (Figure 2b), A1g
onto the substrate. Transmission electron microscopy (TEM) and E2g of monolayer WS2 is enhanced by approximately 80-
cross-sectional imaging was further performed to characterize and 85-fold in NPoM, respectively, which also proves the
the individual nanocavities. A small amount of loosely covered ultrahigh field enhancement that could be formed under the
AuNP surfactants cleaned by ethanol is almost invisible to ultrasmall mode volume in the nanocavity. The transmittance
of monolayer MoS2 or WS2 is greater than 95%, and the
TEM. The TEM (Figure 1f) and energy-dispersive spectros-
excitation wavelength of 633 nm can reduce the light
copy (EDS) element mapping analysis (Figure 1g) clearly
absorption and scattering of two-dimensional atomic crys-
show the sandwich structure of the nanocavity. The EDS
tals.30,31 The light absorption band of monolayer WS2 is 630
element mapping distribution also clearly indicates that
nm, while that of monolayer MoS2 is 681 nm. With an increase
monolayer WS2 and four layers of MoS2 have been successfully
in the number of layers, the light absorption band is red-
transferred to the nanocavity, where AuNP (Au element is shifted.32 The excitation wavelength of 633 nm is used to
shown in yellow) and the ultrasmooth Au film (Au element is resonate with the light absorption band of monolayer WS2
shown in yellow) locate at the top and bottom of two- (Figure S7), and then WS2 forms Raman resonance at an
dimensional atomic crystals, respectively (Mo element is excitation wavelength of 633 nm. Therefore, the Raman signal
shown in green and W element is shown in red). The gap of monolayer WS2 is more than 10-fold higher than that of
between AuNPs and the ultrasmooth Au film is approximately monolayer MoS2 on the same substrate (Figure 2b,c). The
3.55 nm. This is essentially consistent with the results obtained plasmonic resonance of NPoM is approximately 674.6 nm
by AFM. In the experiment of PMMA layer-by-layer (Figures 2g and S5a), which is in energy close to 633 nm and
transferred multilayer two-dimensional atomic crystal, each Raman scattering wavelengths, so the excitation wavelength of
sample was transferred five times (Figure S6f), and Raman 633 nm can provide a higher SERS sensitivity. The
spectra were collected once for each transfer layer (Figure characteristic peaks of WS2 are mainly 351.7 and 419.6
S6a−e). When WS2 is located in the 1st layer, the Raman cm−1, while those of MoS2 are 384.1 and 406.1 cm−1. Their
signal of WS2 appears in the Raman spectrum of the 5th characteristic peaks are not disturbed by one another. The
transfer (Figure S6a) and so on. These results ensure that WS2 formation of the WS2/MoS2 heterojunction increases the
can be accurately placed at different positions in the nanocavity Raman signal of WS2. The characteristic peak intensity of the
by the PMMA layer-by-layer transfer method to probe the four layers of MoS2 is still far less than that of monolayer WS2
longitudinal plasmonic field distribution with a high spatial (Figure 2c). Hence, WS2 can be an optimal probe compared
resolution. with MoS2.
WS2 as an Optimal SERS Probe: Higher Spatial For two-dimensional materials placed on different substrates,
Resolution, Directional Phonon Vibration, Stronger there will also be interface strain, charge transfer, and other
Raman Signal, and High Stability. The enhanced Raman effects.33 Some researches show that the interface strain effect
scattering intensity ISERS can be expressed as will cause a large Raman shift and Raman peak splits,34,35 so
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Figure 3. (a) Schematic theoretical derivation of the plasmonic field strength in the AuNP/1L WS2-4L MoS2/Au film. (b) xy plane was taken from
z = 1 nm and (c) the xz plane of the plasmonic field distribution at 633 nm in a nanocavity. (d) Enlarged view of (c). (e) Fraction of SERS EFxy as
a function of integral radius in the gap region of the AuNP/1L WS2-4L MoS2/Au film. (f) Simulated SERS EFxy as a function of WS2 located in
different layers.

the strain effect can be excluded, and charge transfer will cause SERS substrates due to chemical effects like graphene.38
a small Raman shift.33 Interestingly, the Raman peaks of Chemical effects caused a slight Raman shift of WS2 and MoS2
monolayer WS2 and MoS2 are enhanced in NPoM, but the in 4L MoS2/1L WS2 heterojunction (see the blue arrow in
Raman shift remains unchanged (Figures 2b and S8a), that is Figure S8b). Considering the influence of the SERS signal due
to say, the charge transfer between Au and the two- to the chemical effect of WS2/MoS2 heterojunction, we further
dimensional atomic crystal caused by the weak interlayer calculate that there is essentially no difference between the off-
interaction between them is not sufficient to cause a Raman resonant Raman spectra of WS2 located in different layers via
shift through the PMMA layer-by-layer transfer method, which first-principles calculations29 (Figure S9 and Supporting
indicates that the larger enhancement of the two-dimensional Information Note 1). In contrast, in the experiment, WS2 is
atomic crystal may come from electromagnetic enhancement exposed to the air in the 1st layer. Environmental changes may
to a large extent rather than chemical enhancement. To lead to slight differences in the Raman spectra, which are not
confirm this view, monolayer WS2 and MoS2 on the sufficient to cause adverse effects on the experiment (Figure
ultrasmooth Au film and NPoM are annealed, and it is 2d,e). In addition, we also confirm that the interaction between
determined that the vibration peaks of phonon mode E2g and Au and two-dimensional materials is weak, not affecting the
A1g are red-shifted by 1−2 wavenumbers, which also indicates experiment without stronger chemical effects very much.
that strong heterojunctions are formed between Au and the Therefore, we consider that the chemical effect of WS2 located
two-dimensional atomic crystal after annealing36,37 (Figures 2b in different layers is constant. We also compared the resonance
and S7a). wavenumber and the complex refractive index of WS2, when
For the explanation of whether there is a chemical effect WS2 located in different layers are unchanged (Figure 2f,g).
between MoS2/WS2 heterojunction, we compared the Raman These results all confirmed that the SERS intensity of WS2 in
scattering spectra of 1L WS2, 4L MoS2, and 4L MoS2/1L WS2 the nanocavity can be used as a measure of the plasmonic field
on silica. We observed that the Raman signals of the strength. In conclusion, the SERS intensity of WS2 can
characteristic peaks (351 and 419 cm−1) of WS2 in 4L accurately, quantitatively, and directionally probe the longi-
MoS2/1L WS2 heterojunction were significantly enhanced tudinal plasmonic field distribution in the individual nano-
(Figure S8b). This is because MoS2 and WS2 can be used as cavities.
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Figure 4. (a) SERS spectra of WS2 layer-by-layer in various positions of the AuNP/1L WS2-4L MoS2/Au film. The black dotted box shows the
characteristic peak of MoS2, which is not obvious because its intensity is much lower than that of WS2. (b) SERS intensity of A1g (red line) and E2g
(green line) as a function of WS2 located in different layers in the experiment. (c) SERS intensities of A1g as a function of WS2 probe position (red
point). For WS2 located in the 1st to 5th layers, z = 0.35, 1.05, 1.75, 2.45, and 3.15 nm, respectively. Theoretical fitting of the longitudinal
plasmonic field strength (blue line). The square of the normalized plasmonic field amplitude in the nanocavity (black point), simulated via FEM,
shows the AuNP antenna’s contributions and the ultrasmooth Au film substrate. (d) Experimental and numerical SERS EFxy of E2g layer-by-layer in
various positions of the individual nanocavity.

Theoretical Derivation and Numerical Simulation of nanoantenna, respectively, λ is the wavelength of the incident
Longitudinal Plasmonic Field Distribution in a Nano- light, εm is the dielectric constant of the metal, εd is the
cavity. The plasmonic field strength decreases exponentially dielectric constant of the spacer, d is the gap of the spacer, and
along the z-axis away from the interface. The plasmonic field at z is the distance to the ultrasmooth gold film with the unit in Å
the metal interface can be expressed as39 (Figure 3a). If AuNP is replaced by AuNP@SiO2, then the
dielectric constant in the spacer is different. The theoretical
E(x , z) = E0 eikxx k z |z |
(3) derivation of the plasmonic field amplitude in the nanocavity is
In the vertical z-direction, when the electric field amplitude in somewhat different from that of AuNPs. The detailed
the dielectric decays to 1/e, the distance between the electric derivation process is shown in Supporting Information Note 2.
field and the interface is called the skin depth, which can also After the theoretical analysis, the plasmonic field distribution
be called the penetration depth δm, δm = 1/|kz|40 follows the classical electromagnetic field theory, and the
electromagnetic field distribution in the individual nanocavity
2 2
m 2 m is numerically calculated using the finite element method
kz = k 0 = (FEM). As the monolayer two-dimensional atomic crystal is
m + d m + d (4)
only ∼0.7 nm, the minimum mesh is set at 0.2 nm to ensure
Therefore, the longitudinal plasmonic field distribution at the the accuracy of the numerical calculation. Here, we ignore the
metal interface of eq 3 can be expressed as effect of the plasmonic field on the refractive index, assuming
2
that the refractive index is the same in the gap.41 The complex
2 / / m+ d |z|
E(0, z) = E0 e m
(5) refractive index of two-dimensional atomic crystals is measured
using ellipsometry (see details in Figure S9 and ellipsometric
The plasmonic field in the nanocavity can be regarded as a measurements in the Supporting Information). The plasmonic
vector superposition of two electromagnetic fields from the field is mainly concentrated in the region directly below the
metal surface and the nanoantenna.19 Therefore, when the nanoparticle and rapidly attenuates outside the nanocavity
dielectric constant of the spacer layer in the nanocavity is εd, region (Figure 3b). From the xz plane in Figure 3c, the
then the amplitude of the longitudinal plasmonic field in the plasmonic field distribution can be observed to mainly
nanocavity formed by the AuNP/1L WS2-4L MoS2/Au film concentrate in the nanogap between AuNP and the ultra-
can be expressed as smooth Au film. The distribution of the plasmonic field in the
2 / 2
/ m + d |z| 2 / 2
/ m+ d |d z| nanocavity is heterogeneous (Figure 3d). This is due to the
E(0, z) = EA e m
+ EB e m
asymmetry of the noble metal nanostructures, that is to say,
(6) AuNP and the ultrasmooth Au film may affect the maximum
where EA and EB represent the maximum amplitudes of the amplitude of the plasmonic field (see eq 6), and the
plasmonic field generated by the metal surface and the attenuation lengths of the electric field in the medium are
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Figure 5. (a) SERS spectra of WS2 layer-by-layer in various positions of the AuNP@SiO2/1L WS2-4L MoS2/Au film. The black dotted box shows
the characteristic peak of MoS2, which is not obvious because its intensity is much lower than that of WS2. (b) SERS intensities of A1g (red line)
and E2g (green line) as a function of WS2 in different layers in the experiment. (c) SERS intensities of A1g as a function of WS2 probe position (red
point). For WS2 located in the 1st to 5th layers, z = 2.35, 3.05, 3.75, 4.45, and 5.15 nm, respectively. Theoretical fitting of the longitudinal
plasmonic field strength (blue line). The square of the normalized plasmonic field amplitude in the nanocavity (black point), simulated via FEM,
shows the AuNP antenna’s contributions and the ultrasmooth Au film substrate. (d) Experimental and numerical SERS EFxy of E2g layer-by-layer in
various positions of the individual nanocavity.

different. And it follows the classical electromagnetic field signal intensity fluctuation comes from the difference in the
model (CEM) because the nanogap is ∼3.5 nm42,43 and plasmonic field, we measured the SERS spectrum of WS2 at the
conforms to eq 6. The SERS intensity of E2g is only 3rd layer over time, which showed high stability and
contributed by Exy. To further analyze the dependence of the repeatability, with only a 3.7% intensity fluctuation within
E2g SERS intensity on the horizontal component of the 150 min (Figure S11a). The dark-field spectra were invariable
longitudinal plasmonic field, theoretical calculations and before and 150 min after exposure (Figure S11b). This is due
experiments were performed. We defined the SERS enhance- to the high light damage threshold of the two-dimensional
ment factor on the horizontal component as SERS EFxy. The atomic crystal and its strict lattice arrangement in the hot spot.
experimental and numerical definition details of SERS EFxy are The two-dimensional atomic crystal overcomes random
given in Supporting Information Note 3. Note that in the motion or light damage that may occur around hot spots
calculations, we used 200 nm as an actual integral radius in the different from molecules acting as probes.44,45 The SERS
denominator of Supporting Information Note 3 eq S5. Figure intensities of A1g first decreased and then increased as WS2 was
3e shows the calculated fraction of SERS EFxy as a function of positioned from the 1st layer to the 5th layer (Figure 4b). The
integral radius Rxy at the xy plane taken from z = 1 nm of the highest and lowest intensities of WS2 are in the 1st layer and
AuNP/1L WS2-4L MoS2/Au film. We can see that the fraction
3rd layer, respectively, and the maximum intensity gradient is
saturates rapidly with an increasing integral radius. Here, we
8.37 (the ratio of ISERS1st to ISERS3rd of A1g), indicating that the
determine Rxy when the fraction of the horizontal SERS
plasmonic field strength is heterogeneous with an unexpectedly
enhancement factor reaches 99%. The insets in Figure 3e show
the effective horizontal electric field distribution profiles for large gradient in the longitudinal direction of the nanocavity.
NPoM corresponding to the E2g peak and A1g peak. Figure 3f Our experimental large gradient of the longitudinal plasmonic
shows the SERS EFxy distribution trend at different positions in field strength also basically agrees with that obtained by Prof.
the clearance calculated by eq S6 in Supporting Information Li et al.19 Figure 4c shows that the SERS intensities of A1g are
Note 3. It can be seen that SERS EFxy at different positions in consistent with the amplitude square of the longitudinal
the clearance has a large intensity gradient. plasmonic field. Theoretical fitting is conducted for the SERS
Quantitative and Directional Analyses of the Longi- intensity of A1g through eqs 1, 6, and ISERS (0,z) ∝ (7.241e
0.871z
+
0.871(3.500−z) 2
tudinal Plasmonic Field Distribution in a Nanocavity. 2.974e ) , where kz is 0.871/nm. The same
SERS spectra of WS2 located in different layers in the exponential depends on the medium in which the electro-
nanocavity are shown in Figure 4a. Through a previous magnetic field decays, while the coefficient is different. This
analysis, we appropriately selected the Raman peak of A1g of asymmetry is due to the different geometries of the metal
WS2 as a measure of the plasmonic field strength. The SERS surface and the nanoantennas. The experimental values,
intensity of A1g is different at different layers. To prove that the theoretical fitting, and numerical calculation all show good
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SERS
consistency, so WS2 can be used to accurately probe the Information Note 2 eq S3, I(0,z) ∝ (−19.420e0.157z +
0.157(3.500−z) 2
longitudinal plasmonic field distribution. 65.520e ) , where kz is 0.157/nm. The numerical
Figure 4b also shows that the intensity distribution of E2g is and experimental SERS EFxy values are also essentially
the same as that of A1g, but lower than that of A1g. We further consistent (Figure 5d). Therefore, we quantitatively and
calculated the SERS EFxy of E2g for WS2 located in different directionally analyzed the longitudinal plasmonic field
layers both experimentally and numerically (details in distributions under different dielectric constants by replacing
Supporting Information Note 3). SERS EFxy of E2g for WS2 AuNPs with AuNP@2 nm SiO2.
in the 1st layer is as high as 0.93 × 105. The strong dependence
of the SERS signal on theoretical electromagnetic intensity can
be observed because the EM mechanism plays a dominant role
■ CONCLUSIONS
In summary, we designed a unique nanoruler based on a two-
(Figure 4c). The numerical SERS EFxy is essentially consistent dimensional atomic crystal that intercalated monolayer WS2 as
with the experimental SERS EFxy (Figure 4d). However, there a SERS probe and four layers of MoS2 as a reference layer to
was still a relative error between experimental and theoretical quantitatively and directionally probe the longitudinal
SERS EF. The difference between experimental and theoretical plasmonic field distribution in a nanocavity at a high
SERS EF is understandable because it is impossible to permittivity using the quantitative SERS intensity of WS2
guarantee that all parameters used in the simulation are located in different layers with a ∼7 Å spatial resolution. We
exactly the same as real samples. First, the gap size used for selected WS2 an optimal SERS probe because of its high spatial
each simulation differs somewhat from that of the correspond- resolution, directional phonon vibration, high Raman signal,
ing actual NPoM sample (see Figures S1a,b and S2 in the high stability, constant chemical effect, and the change of SERS
Supporting Information). This is because the surface rough- intensity mainly from the plasmonic field distribution.
ness of the gold film, the local morphology of AuNPs, and the Combining comprehensive theoretical derivation, numerical
size of AuNPs fluctuate around 98 nm, resulting in different calculations, and experiments, such as TEM cross-sectional
clearance sizes in different regions (see Figures S1c,d and S2 in imaging and dark-field scattering spectra, these results reveal
the Supporting Information). To avoid this effect, we collected that the plasmonic field strength is heterogeneous in the
100 NPoMs data for WS2 at a certain layer and drew error bars. longitudinal direction of the high dielectric constant nano-
Second, the existing 5-layer two-dimensional anisotropic cavity and show an unexpectedly large gradient with 8.37 and
dielectric response model may be too ideal to accurately 5.62 of the out-of-plane phonon mode A1g SERS intensity in
describe the dielectric properties at optical frequency.41 In the AuNP/1L WS2-4L MoS2/Au film and the AuNP@SiO2/1L
addition, there were also chemical effects caused by WS2 WS2-4L MoS2/Au film. Distinctively different from many
placed in different locations, and the effective area of previous studies, we first performed a rigorous correlation
theoretical SERS enhancement (πRxy2) was smaller than SERS EFxy and revealed SERS EFxy of the in-plane phonon
experimental factors. Despite these factors, these results mode E2g, as WS2 located in different layers quantitatively
indicate that the SERS intensity of E2g can quantitatively and showed a great attenuation precision. By comparing the
qualitatively probe the horizontal component distribution of AuNP/1L WS2-4L MoS2/Au film system with the AuNP@
the longitudinal plasmonic field. Therefore, we can conclude SiO2/1L WS2-4L MoS2/Au film system, the plasmonic field
that since the WS2 probe is located in different layers, the attenuates more slowly in a high dielectric medium than in a
longitudinal plasmonic field strength is heterogeneous with an low dielectric medium. This work has deepened our under-
unexpectedly large gradient in nanocavity. These quantitative standing of the plasmonic field in the individual nanocavity
analyses match well with the prediction of the classical both quantitatively and directionally and can improve the
Maxwell’s descriptions, suggesting that SERS EFxy predicts the application of plasmonic nanodevices in sub-nanospace or the
horizontal component orientation of the plasmonic field. optical control assembly of high-precision nanostructures,
According to eq 3, the plasmonic field distribution is also which is of great significance for optimizing linear and
related to the surrounding dielectric environment, so AuNPs nonlinear light−matter interactions.
are replaced by AuNP@2 nm SiO2 in NPoM (Figures S12 and
S2b,d), and the gap layer thickness of the nanocavity increases
from 3.5 to 5.5 nm. We observed that the SERS intensity in the
■
*
ASSOCIATED CONTENT
sı Supporting Information
AuNP@SiO2/1L WS2-4L MoS2/Au film weakened relative to
The Supporting Information is available free of charge at
the AuNP/1L WS2-4L MoS2/Au film (Figure 5a,b), which was
https://pubs.acs.org/doi/10.1021/jacs.2c03081.
due to the weakening of the plasmonic field strength in the
nanocavity after the gap of the spacer layer increased (Figure Additional experimental details; first-principles off-
S13). Interestingly, the distribution of the longitudinal resonance Raman spectra simulation; theoretical deriva-
plasmonic field changes, with the strongest A1g and E2g tion of the longitudinal plasmonic field distribution in
intensities in the 5th layer and the weakest in the 1st layer, the AuNP@SiO2/1L WS2-4L MoS2/Au film system;
where the intensity ratio of A1g is 5.62. This may be because experimental and numerical calculations of SERS EFxy
the complex refractive index of the 5-layer two-dimensional (including Notes 1−3); AFM characterizations of the
atomic crystal is 3.58 + 0.22i (obtained from Figure 2f), while ultrasmooth Au film and AuNPs on the ultrasmooth Au
the refractive index of SiO2 is 1.48.46 The larger the dielectric film; characterization of size uniformity of AuNP and
constant is, the slower the plasmonic field attenuation is. AuNP@SiO2; AFM characterizations of different layers
Therefore, the plasmonic field near the nanoantenna in the of two-dimensional atomic crystals on the ultrasmooth
SiO2 medium has a great attenuation, and the minimum value Au film; Raman scattering spectra of different layers of
of the field strength moves from the metal surface to the MoS2 on silica; dark-field scattering spectroscopy in
nanoantenna (Figure 5c). Theoretical fitting is performed for NPoM; Raman scattering spectra of WS2 located in 1st,
the SERS intensity of A1g through eq 1 and Supporting 2nd, 3rd, 4th, and 5th layer in the process of transfer,
13181 https://doi.org/10.1021/jacs.2c03081
J. Am. Chem. Soc. 2022, 144, 13174−13183
Journal of the American Chemical Society pubs.acs.org/JACS Article

Notes
respectively; absorption spectrum of monolayer WS2 and
The authors declare no competing financial interest.
monolayer MoS2; Raman scattering spectra of mono-
layer MoS2 on different substrates and WS2/MoS2
heterojunction; schematic of first-principles off-reso-
nance Raman spectra simulation; schematic of ellipso-
■ ACKNOWLEDGMENTS
The authors thank Prof. Jian-feng Li, Xiamen University, for
metric measurements; stability test of the AuNP/1L helpful discussions. This work was supported by the Research
WS2-4L MoS2/Au film; TEM image of AuNP@SiO2; Instrument and Equipment Development Project of the
and schematic diagrams of the theoretical derivation and Chinese Academy of Sciences (YJKYYQ20200022), the
FEM calculation of the AuNP@SiO2/1L WS2-4L MoS2/ National Science Foundation of China (Nos. 21974142 and
Au film (including Figures S1−S13) (PDF) 22032004), and the Nature Science Research Project of Anhui
Province (No. 1908085QB65). The authors greatly thank
these grants.
■ AUTHOR INFORMATION
Corresponding Authors ■ REFERENCES
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