Cathodoluminescence of Surface Plasmon Induced Light Emission
Cathodoluminescence Brief Overview
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Transcript of Cathodoluminescence Brief Overview
UNIVERSITY OF ILLINOIS, URBANA CHAMPAIGN
Cathodoluminescence Spectroscopy
by
Anshuman Kumar
Final Report for the requirements of the course
Optical Spectroscopy (PHYS-552)
in the
Department of Physics
December 2010
Abstract
This report discusses some of the basic aspects of Cathodoluminiscence(CL) Spec-
troscopy, with special reference to plasmonics. CL setup offers several advantages. The
multimode imaging capabilities of the electron microscope enable the correlation of op-
tical properties (via cathodoluminescence) with surface morphology (secondary electron
mode) at the nanometre scale. But perhaps most intriguingly, the small beam can probe
a single selected nanostructure.
The report is divided into three chapters and a bibliography. Chapter one discusses a
general overview of CL and provides the mathematical background of the field of a mov-
ing charge in presence of an interface. Chapter two gives some idea of the experimental
setup involved, without going into much detail. Chapter three lists two applications of
CL: one involving a study of plasmon modes in a annular shaped nanoresonator; the
second application deals with probing the gap plasmon modes in a metal-sphere & metal
film configuration. In both these examples, I haven’t delved into the theory of plasmon-
ics itself, but just attempted to highlight how CL gives us a means to probe some of
these resonances, by varying excitation location.
Contents
Abstract i
List of Figures iii
1 Introduction: Overview, History and Mathematical Formulation 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.3 Principles of the technique . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.4 Mathematical Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.4.1 Transition Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.4.2 Surface Plasmons . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2 Experimental Setup 8
3 Examples from Literature 10
3.1 Plasmonic Modes of Annular Nanoresonators Imaged by Spectrally Re-solved Cathodoluminescence[1] . . . . . . . . . . . . . . . . . . . . . . . . 10
3.1.1 Fabrication of Nanoresonators . . . . . . . . . . . . . . . . . . . . . 10
3.1.2 CL measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.2 Gap and Mie Plasmons in Individual Silver Nanospheres near a SilverSurface[2] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.2.1 What we expect? . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.2.2 Fabrication of the nanostructures . . . . . . . . . . . . . . . . . . . 13
3.2.3 CL measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Bibliography 17
ii
List of Figures
1.1 Cherenkov radiation glowing from a spent fuel core of the High FluxIsotope Reactor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Evanescent character of of the electromagnetic field produced by a fastelectron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1 CL setup incorporated in a Scanning Electron Microscope . . . . . . . . . 8
3.1 Panchromatic CL imaging of Ag annular nanoresonators . . . . . . . . . 11
3.2 Spectrally resolved imaging of plasmonic modes in an Ag annular nanores-onator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.3 Excitation of gap and Mie plasmons in supported silver nanospheres . . . 14
3.4 Schematic representation of the charge distribution in gap and Mie plas-mons excited in silver spheres supported on silver for different beam con-figurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.5 Angular and position dependence of the emission from gap and dipoleMie plasmons in supported spheres . . . . . . . . . . . . . . . . . . . . . . 16
iii
Chapter 1
Introduction: Overview, History
and Mathematical Formulation
1.1 Introduction
Cathodoluminescence(CL)[3][4] is basically the emission of photons from a specimen
stimulated using an electron beam. A common example of the CL process is the screen
of a television CRT monitor. Here, the electron beam generated by a cathode ray
tube, impacts a luminiscent material causing it to emit light. Today, CL is used in the
fields of geology, minerology, materials science and fundamental experimental physics.
Usually these are used, in conjunction with a scanning electron microscope, to examine
the internal structure of semiconductors, rocks, ceramics, glass and to study surface
plasmon modes in nanostructures.
This configuration of CL setup offers several advantages. The multimode imaging ca-
pabilities of the electron microscope enable the correlation of optical properties (via
cathodoluminescence) with surface morphology (secondary electron mode) at the nanome-
tre scale. The broad energy range of the electrons can excite wide-bandgap materials,
such as diamond- or gallium-nitride-based structures that are not easily excited by con-
ventional optical means. But perhaps most intriguingly, the small beam can probe a
single selected nanostructure.
1.2 History
Although the phenomenon of luminescence was recognized as early as the seventeenth
century, systematic observations and discussio of cathodoluminiscence did not take place
1
Chapter 1. Introduction: Overview, History and Mathematical Formulation 2
until around 1960’s.
Early CL studies were carried out using a CL microscope, which is basically a pet-
rographic microscope to which a cathode gun is attached. Subsequently, the scanning
electron microscope has been utilized to generate high resolution and high magnification
CL images.
CL was mostly employed for determining characteristics of geological materials. How-
ever, with the advent of nanotechnology, CL measurements are now routinely used to
investigate localized surface plasmons excited by electron impact. Here, the photon
emission of a metal nanostructure is induced via a high energy electron beam and col-
lected using a suitable detection pathway. The advantage of this technique is that by
scanning the electron beam over the particle surface, spatial profile of these modes can
be efficiently mapped out by light collection at particular resonance wavelengths . This
technique is also found to work for propogating Surface Plasmon Polaritons.
1.3 Principles of the technique
The main emission processes involved in CL are Cherenkov radiation and transition
radiation. It turns out that each of these processes is coherent with the field generated
by the incoming electron. Besides, although the generation of SPPs can be considered as
an indirect process (2-step), it is still coherent emission. This kind of coherence between
different sources of emission can result in interesting interference phenomenon, which
can be used for easy characterization.
However, there are also incoherent emission channels associated with electron-hole pair
generated which eventually recombine and emit. But in metals, which are the major
focus of this report, electronic relaxation proceeds much faster than radiative recombi-
nation, hence one can safely consider the incoherent contribution to CL to be a minor
contribution only.
Now we provide a brief overview of the emission processes involved.
Cherenkov Radiation
When a charged particle passes through a medium with speed greater than the speed of
light in that medium, it emits Cherenkov Radiation. The basic idea here is that these
charged particlespolarize the molecules of the medium, which return to their ground
state rapidly resulting in an emission of radiation. A classic example of this is the
characteristic ”blue-glow” of nuclear reactors. See for instance, figure 1.1.
Chapter 1. Introduction: Overview, History and Mathematical Formulation 3
Figure 1.1: Cherenkov radiation glowing from a spent fuel core of the High FluxIsotope Reactor[Wikipedia].
However, this emission is not important for metals, since the disruption in the local
electromagnetic field can be restored without emission of a photon.
Transition Radiation
This kind of emission occurs when a charged particle passes through a boundary between
two media of different dielectric constants. It is usually a result of the time dependent
variation of the dipole moment formed by the incident charged particle and its image
charge inside the other dielectric. This radiation can be explained by noting that since
the electric field of the particle is different in each medium, the particle has to get rid
of the difference when it crosses the boundary. This results in a net energy loss of the
particle.
In view of the above two phenomena, if metals are bombarded with an electron beam,
the excitation of bulk or surface plasmons can ocur if the moving charge couples to
the free electrons in the metal. This effect becomes apparent in Electron Energy Loss
Experiments (EELS)
1.4 Mathematical Theory
We know that an electron moving with a constant velocity in free space does not result
in a radiation. However, in the presence of a boundary of another material, it induces
a polarization charge, which together with the original electron can be considered to
be a dipole. In a metal, there are two channels available for the dipole to decay: (a)
transition radiation emission into the far field and (b) generation of surface plasmons.
We look at both these processes in the following subsections[5].
Chapter 1. Introduction: Overview, History and Mathematical Formulation 4
1.4.1 Transition Radiation
Consider an electron moving with a velocity v along the z axis. This electron is incident
from the lower half space of z < 0, which is considered vacuum (ε1 = 1) and corsses the
inrface with the upper half consisting of a dielectric of permittivity given by (ε1 = ε)
at time t=0. The electromagnetic fields are expected to satisfy Maxwell’s Equations (’j’
identifies the medium 1,2):
∇ ·H = 0 (1.1)
∇×E = −1
c
∂H
∂t(1.2)
∇ · εjE = 4πρ (1.3)
∇×H = −εjc
∂E
∂t+
4π
cj (1.4)
The charge and current densities associated with the moving electron can be written as:
ρ(z, t) = −eδ(z − vt) (1.5)
j(z, t) = −evδ(z − vt) (1.6)
To solve these equations, we use the method of fourier transforms:
H(r, t) =1
(2π)4
∫dωe−iωt
∫d3qH(q, z, ω)eiq·r (1.7)
The fourier transforms of the sources are found to be:
ρ(k, ω) = − e
(2π)δ(ω − k · v) (1.8)
j(k, ω) = vρ(k, ω) (1.9)
Chapter 1. Introduction: Overview, History and Mathematical Formulation 5
The next task is to to decompose the fields H into a a bulk component and an induced
component near interfaces. The solution for the bulk part is relatively straight-forward
and one gets:
Hbulkj (Q, z, ω) =
4πieQ
ceiωz/v
t
k2j − q2(1.10)
where t = z × Q and Q is the in plane momentum vector.
Performing an inverse fourier transform of the above equation over momentum, we
obtain:
Hbulkj (r, ω) = −2eω
vcγeiωz/vK1(
ωρ
γv)φ (1.11)
where ρ is the perpendicular distance form the electron trajectory, γ is the lorentz
contraction factor, φ is the azimuthal angle and K1 is the modified Bessel function
of second kind. From this equation, one can see that the moving electron acts as a
broadband source of ”electromagnetic field”. However, due to the nature of the Bessel
function, the field decays away from the electron trajectory. I have attached a figure1.2
from a paper which uses different variables for these quantities but shows the ideas well.
Figure 1.2: Evanescent character of of the electromagnetic field produced by a fastelectron[3]
Chapter 1. Introduction: Overview, History and Mathematical Formulation 6
There are some important observations related to this bulk field. The field diverges
at the location of the electron trajectory. Hence it means that the resolution of the
experiments is only limited by the size of the beam spot. However we must also consider
the response of teh material as delocalized, which reduces the actual resolution.
Next, we turn our attention to the induced field, which is evaluated to be
Hindj (Q, z, ω) = 2πekjsje
ikzj |z|αj t (1.12)
where kzj =√k2j −Q2, s1 = −1 and s2 = 1 and αj ’s are the boundary coefficients
calculated using appropriate boundary conditions on parellel components of the electric
and magnetic fields. The actual expressions are:
α1(Q) =2Qi/c
kz1ε2 + kz2ε1[−ω/vε2 + kz2ε1
q2 − k21− −ω/vε1 + kz2ε1
q2 − k22] (1.13)
α2(Q) =2Qi/c
kz1ε2 + kz2ε1[ω/vε2 + kz1ε2
q2 − k21− −ω/vε1 + kz1ε2
q2 − k22] (1.14)
Using the above two expressions, we get the expression for the induced field as
Hindj (r, ω) = −iφesj
∫ ∞0
QdQαjeikzj |z|J1(QR) (1.15)
where J1 is the first order Bessel function.
Since in experiments, we observe the CL signal in the far field, far away from the actual
impact point of the electron, it is clear that the field detected there cannot arise from
the evanescent bulk fields. Hence it is the induced fields that we observe.
1.4.2 Surface Plasmons
An electron incident on a metal surface also excites SPPs. The results of the previous
section can be used to derive the plasmon generation rate. The wave-vector condition
describing SPPs is given by:
kz1ε2 + kz2ε1 = 0 (1.16)
Using a Taylor expansion around the plasmon wave-vector, Qp one gets:
Hindj (ω) = πeQpAje
−ikzj |z|H11 (QpR)φ (1.17)
Chapter 1. Introduction: Overview, History and Mathematical Formulation 7
where H11 is the first Hankel function and Aj = αj(Q−Qp)
Chapter 2
Experimental Setup
As discussed in the previous chapter, CL measurements rely on the detection of radia-
tion emitted when a sample is bombarded by an electron beam. In order to carry out
spectroscopy, the emitted radiation has to be spectrally resolved. On the other hand,
for imaging, one requires spatial resolution of the position from which the emission orig-
inates. However, as proved in the previous section, the spatial resolution of the CL is
determined by the excitation source and not detection.
A schematic of the CL setup incorporated in a Scanning Electron Microscope is shown
in figure 2.1.
Figure 2.1: CL setup incorporated in a Scanning Electron Microscope.
For excitation, a focussed electron beam of a SEM is used. The accelerating voltage
of the beam is tunable between 1-30keV. Beam current is a function of aperture size
and voltage, and can be varied between several pA to tens of nA. Beam currents in the
range of tens of nA provide an electron impact rate which is significantly slower than the
electron relaxation processes in most noble metals important for plasmonics. Hence is it
8
Chapter 2. Experimental Setup 9
safe to consider single electron excitations. We can also accurately position the electron
beam to an accuracy of tens of nanometres over the sample.
The emitted light is detected using a parabolic mirror which is placed a few millimetres
above the sample in such a way that it’s focal point coincides iwth the sample. The
size of this focus is usually in tens of microns. The mirror is arranged to as to have
a large acceptance angle. The light collected from the focal point is reflected as a
parellel beam through a holllow waveguide tube and focussed onto the entrance slits of
a monochromator.
Chapter 3
Examples from Literature
In this chapter, we briefly discuss two examples, from recent literature, of the application
of cathodoluminescence.
3.1 Plasmonic Modes of Annular Nanoresonators Imaged
by Spectrally Resolved Cathodoluminescence[1]
In this study, the authors excite plasmonic modes in engineered annular nanoresonators
on Ag and Au surfaces, using a highly localized electron beam source and use spectrally
resolved CL imaging to probe the plasmon field intensity as a function of excitation
position. The details of the experiment are given below.
3.1.1 Fabrication of Nanoresonators
Nanoresonators are fabricated on Ag surface. The Ag structures were prepared by
evaporation on a quartz substrate and Focussed Ion Beam was used to patter the annular
rings. Each annular resonator has a central plateau and five concentric rings separated
by grooves 50nm deep with varying grating ring period and center diameter.
3.1.2 CL measurement
CL measurements were performed using a field emission SEM operating at 30keV, which
used a usual mirror based detection system. The electron beam spot size was 5nm (which
is also the limit of spatial resolution). To get spectrally resolved images, the emitted
light, after passing through the mirror, is sent to grating monochromator, which is set to
10
Chapter 3. Examples from Literature 11
a specific wavelength, each time. Secondary electron and CL images are simultaneously
recorded. In order to get panchromatic images, the emitted light is directly focussed on
the broadband PMT detection system.
Figure 3.1 shows the panchromatic CL images of nano-resonators in Ag with 315nm
grating period and three different center diameters. These images represent the radiation
collected from the entire resonator as a function of the electron beam excitation position
on the structure. Bright regions correspond to greater emitted photon intensity. From
this figure, it is clear that the high intensity is observed for excitation near at the edges of
the center and of the concentric rings (The locally increased emission inside the grooves
is attributed to scattering from roughness in the polycrystalline Ag film). The CL profile
clearly shows peaks in emission when the electron beam dwells near an edge. An overall
decay in emission intensity is observed as the electron beam moves outward from the
center. Thus, we see that a higher emitted photon intensity is obtained for electron
beam excitation in the center of the structure, indicating that more efficient excitation
and/or more efficient outcoupling occurs in this region. This effect was justified using
simulations, the description of which is not within the scope of the present paper.
Figure 3.1: Panchromatic CL imaging of Ag annular nanoresonators with 315 nmperiod and center sizes of (a) 620 nm, (b) 1.07 m, and (c) 1.70 m. (d) SEM imagetaken concurrently with panchromatic CL image of structure in (c). (e) Line profilesfrom regions indicated by the dashed line in (c) and (d) illustrating strong emissionwhen the electron beam is positioned at an edge and decreasing intensity as the beam
moves outward from the center[1].
Chapter 3. Examples from Literature 12
Another study that they carried out was to experimentally probe the plasmonic modes,
as shown in figure 3.2. At = 350 nm, which is very close to the Ag surface plasmon
resonance, nearly uniform emission occurs for excitation anywhere in the structure. Near
resonance, surface plasmon propagation lengths are very short and thus no resonator
modes can build up. Several different modes are observed at longer wavelengths, as
illustrated in (c) part of Figure 3.2. At = 700 nm, CL data show bright emission for
excitation near the edges of the center plateau, but uniform emission from the rest of
the structure. In figure 3.2, the first subscript ’s’ of Ms,n describes the symmetry of the
mode: s=0 means that the field profile has a node at the centre of the plateau and s=1
stands for an antinode. Numerical methods like FDTD and BEM, given in the figure,
are common in the parlance of plasmonics people and the interested reader is requested
to read the relevant references provided to figure out the meanings of these terms.
Figure 3.2: Spectrally resolved imaging of plasmonic modes in an Ag annular nanores-onator with 620 nm center diameter and 315 nm grating period. (a) Spectrally resolvedCL images at the indicated wavelengths (b) SEM image of nanoresonator indicatingthe scan region for the CL images in (a). (c) Line profiles of modes M0,0,M1,0, andM0,1
from finite element (FDTD) simulated time-averaged electric field intensity, probabil-ity of CL emission from BEM simulations, and spectrally resolved CL images at the
indicated wavelengths. The corresponding surface topography is shown in gray[1].
In summary, the above application demonstrates high-resolution spectrally resolved CL
imaging as a powerful tool to reveal plasmonic modes in Ag annular nanoresonators.
Such a study of plasmonic modes excitation via excitation at precise (highly resolved)
excitation regions on the nanostructure, is a novelty of the CL method.
Chapter 3. Examples from Literature 13
3.2 Gap andMie Plasmons in Individual Silver Nanospheres
near a Silver Surface[2]
In this study, CL is used to study the plasmons confined in the gap between silver
nanospheres and silver planar surfaces using angle and space resolved CL. Plasmons
in individual nanoparticles are excited by an electron beam, giving rise to light emis-
sion that is analyzed as a function of photon-energy, emission direction, and position
of the beam spot. The gap plasmons obtained by bringing a nanoparticle close to a
metal surface have been recently used to produce controlled 1010 enhancement factors
in surface-enhanced Raman scattering (SERS). However, gap plasmons are extremely
sensitive to the distance between metals, and therefore their analysis requires studying
individual structures. In view of what we discussed above, CL seems to be the obvious
choice for such a study.
3.2.1 What we expect?
The gap is a region of huge induced-charge pileup, so it has a large influence on the
plasmons of the nanoparticles. The emergence of a gap mode with m = 0 azimuthal
symmetry relative to the rotational axis of the particle-surface system results in the
aforesaid large pileup of induced charge near the gap, which is compensated by opposite
charges distributed over the rest of the particle. But the sphere can also support Mie
modes that are almost unperturbed with respect to the isolated particle, and in particu-
lar, the sphere dipole parallel to the surface remains rather unaffected by the interaction
with the substrate. We want to use CL to study these properties.
3.2.2 Fabrication of the nanostructures
Silver particles of size 50-600nm were obtained by evaporating silver in Ar atmosphere.
The silver film is deposited on either evaporated silver films or TEM carbon films.
3.2.3 CL measurement
Unlike the previous case, here angle resolved spectral CL is measured. In order to do
this, a TEM is used and ellipsoidal and parabolic mirrors are used for light collection.
A CCD camera provides an image of the mirror. The emission angle can be found out
from the position in the mirror image. Here the beam energy is 200keV and the beam
size is about 10nm.
Chapter 3. Examples from Literature 14
Our main experimental results are summarized in Figure 3.3. A collection of CL spectra
from individual spheres are shown in Figure 3.3(a)(c) for different particle sizes. Figure
3.3(a),(b) corresponds to the emission recorded when the electron beam is passing nearly
grazing with respect to the particle surface, as shown in the upper insets. The spectra
are displays a number of maxima, the position of which is nearly insensitive to the
substrate, as deduced from the fact that their energies are almost the same when the
particles are deposited on either a carbon film or a silver substrate.
Figure 3.3: Excitation of gap and Mie plasmons in supported silver nanospheres. Mieplasmons are resolved in the cathodoluminescence emission when the spheres are excitedby a grazing electron beam, as observed in the spectra measured for particles of differentsize deposited on either (a) a 10 nm carbon film or (b) an optically thick silver surface.Gap plasmons are observed at lower energies in silver particles deposited on silver whenthe beam spot is close to the center of the spheres, as shown in (c). The size-dependentmeasured energies of both multipolar Mie plasmons (extracted from (a) and (b)) andgap plasmons (taken from (c)) are represented in (d) (symbols) and compared to thecalculated cathodolulminescence intensity from self-standing particles under grazingincidence (background density plot). The size-dependence of the gap plasmon obtainedfrom a simple analytical model and from full numerical simulations is shown as pink andyellow solid curves, respectively. The emission is collected over the upper hemisphere(backward emission) in all cases. The arrows in (ac) indicate the position of dipole
(red), quadrupole (green), hexapole (blue), and gap (black) plasmons[2].
From the plots, one can infer that the interaction between Mie modes and the substrate
is weak for grazing trajectories( since, as aforesaid, the position of maxima are nearly
independent of substrate). The only significant effect of the substrate is a small red
Chapter 3. Examples from Literature 15
shift of the modes with a silver substrate as compared to the modes observed with
a thin carbon film, which seems to originate in the attractive interaction with image
charges.
However, we have an interesting observation when the beam spot is positioned at the
center of the particles which are deposited on the silver substrate, there is a new peak
which appears at low energies. This new mode disappears in case of carbon film sub-
strate. This is attributed to the gap mode, it being highly sensitive to the substrate.
Remarkably, the substrate plays a dominant role in this case, even though the external
excitation produced by the electron is initially located far from the gap region (actually,
the electron is likely to undergo strong collisions with silver atoms for diameters above
100 nm).
A physical picture of what is happening is presented via simulations in figure 3.4.
Figure 3.4: Schematic representation of the charge distribution in gap and Mie plas-mons excited in silver spheres supported on silver for different beam configurations(lower part), alongside the calculated electric near-field intensity component corre-
sponding to the frequencies of these modes for 140 nm particles (upper part)[2].
In order to confirm this picture, we can look at the angular distribution of emitted light
as shown in figure 3.5. The dipole picture clearly explains figure 3.5 in view of the model
of fig 3.4.
In conclusion, using the power of high spatial resolution offered by CL imaging, we could
study the Mie and Gap plasmons in this configuration. The present study demonstrates
that spectral CL provides the necessary power for a more detailed investigation of the gap
Chapter 3. Examples from Literature 16
Figure 3.5: Angular and position dependence of the emission from gap and dipoleMie plasmons in supported spheres. A dipole Mie plasmon is observed at 2.5 eV in (a)and (b), which show the measured light intensity as a function of emission angle andenergy for an 140 nm silver sphere supported on a carbon film and a silver substrate, re-spectively, and excited by a grazing electron beam and a central trajectory, respectively(see insets of Figure 1a,c). An additional gap plasmon feature is observed at 1.4 eV in(b). The beam-position dependence of the emission with the silver substrate is shownin (c). The angular patterns of emission for dipole and gap plasmons are represented in(d) (symbols), as compared to the calculated emission from both a dipole placed rightat a silver planar substrate and oriented normal to it (red curved) and a dipole parallel
to the substrate at a distance of 70 nm (i.e., the sphere radius; blue curve)[2].
mode as a function of spacing, which should be of great importance for understanding
the mechanisms involved in ultrasensitive analysis based on plasmon confinement.
Bibliography
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http://pubs.acs.org/doi/abs/10.1021/nl071789f.
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