R3040 ECS Journal of Solid State Science and Technology, 5 (1) R3040-R3048 (2016)
JSS FOCUS ISSUE ON NOVEL APPLICATIONS OF LUMINESCENT OPTICAL MATERIALS
Luminescent Behavior of the K
2
SiF
6
:Mn
4+
Red Phosphor at High
Fluxes and at the Microscopic Level
Heleen F. Sijbom,
a,b,z
Jonas J. Joos,
a,b
Lisa I. D. J. Martin,
a,b
Koen Van den Eeckhout,
a,b
Dirk Poelman,
a,b,∗
and Philippe F. Smet
a,b,∗,z
a
LumiLab, Department of Solid State Sciences, Ghent University, Ghent, Belgium
b
Center for Nano- and Biophotonics (NB-Photonics), Ghent University, Ghent, Belgium
Phosphor-converted white light-emitting diodes (LEDs) are becoming increasingly popular for general lighting. The non-rare-earth
phosphor K
2
SiF
6
:Mn
4+
, showing promising saturated red d-d-line emission, was investigated. To evaluate the application potential of
this phosphor, the luminescence behavior was studied at high excitation intensities and on the microscopic level. The emission shows
a sublinear behavior at excitation powers exceeding 40 W/cm
2
, caused by ground-state depletion due to the ms range luminescence
lifetime. The thermal properties of the luminescence in K
2
SiF
6
:Mn
4+
were investigated up to 450 K, with thermal quenching only
setting in above 400 K. The luminescence lifetime decreases with increasing temperature, even before thermal quenching sets in,
which is favorable to counteract the sublinear response at high excitation intensity. A second, faster, decay component emerges
above 295 K, which, according to crystal field calculations, is related to a fraction of the Mn
4+
ions incorporated on tetragonally
deformed lattice sites. A combined investigation of structural and luminescence properties in a scanning electron microscope using
energy-dispersive X-ray spectroscopy and cathodoluminescence mappings showed both phosphor degradation at high fluxes and a
preferential location of the light outcoupling at irregularities in the crystal facets. The use of K
2
SiF
6
:Mn
4+
in a remote phosphor
configuration is discussed.
© The Author(s) 2015. Published by ECS. This is an open access article distributed under the terms of the Creative Commons
Attribution 4.0 License (CC BY, http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse of the work in any
medium, provided the original work is properly cited. [DOI: 10.1149/2.0051601jss] All rights reserved.
Manuscript submitted July 15, 2015; revised manuscript received August 6, 2015. Published August 22, 2015. This paper is part of
the JSS Focus Issue on Novel Applications of Luminescent Optical Materials.
Most phosphor-converted white LEDs contain phosphors doped
with rare earths such as divalent europium and trivalent cerium. These
ions feature relatively broad emission bands based on the parity al-
lowed 5d-4f transition. They are often easily excited with blue light
and can show high quantum efficiency, even at elevated temperature.
To improve the color rendering of white LEDs, red phosphors are
added to the traditional blue LED and yellow Y
3
Al
5
O
12
:Ce (YAG:Ce)
phosphor combination. These red phosphors need to be stable and have
a high quantum efficiency. The emission spectrum should both be suf-
ficiently red (>600 nm) and well within the eye sensitivity curve, to
obtain a high luminous efficacy.
1
Sulfide phosphors doped with Eu
2+
,
such as (Ca,Sr)S:Eu
2+
are known for their efficient red emission,
2
but
they lack stability in humid environments and the eye sensitivity is
low for part of their broad emission band.
3
Nitride phosphors doped
with Eu
2+
are often chemically more stable, but their synthesis at
high pressure and temperature is a drawback.
4
Most europium-doped
nitride phosphors show a relatively broad emission band.
5,6
Cost and supply issues of the rare-earth materials pave the way
for transition-metal-doped phosphors.
7
In particular the Mn
4+
ion
is a promising alternative for Eu
2+
as it shows line emission from
parity and spin-forbidden d-d transitions in the red and near-infrared
spectral region. Investigation of the optical properties of the Mn
4+
dopant showed that fluoride hosts are preferred for LED phosphors
over oxide hosts, since only the ionic nature of fluorides results in a
sufficiently small nephelauxetic effect, maintaining the energy of the
emitting
2
E
g
→
4
A
2g
transition within the visible part of the spectrum,
corresponding to red emission with a zero phonon line in the 617–
624 nm range.
8,9
For instance in the oxide phosphors, GdAlO
3
:Mn
4+
,
SrTiO
3
:Mn
4+
and Y
2
Sn
2
O
7
:Mn
4+
the emission is well beyond 650 nm
and thus unsuitable for visible displays or lighting.
10–12
The interest in K
2
SiF
6
:Mn
4+
as a red phosphor started with the
development of a synthesis method by Adachi and Takahashi, etching
Si wafers in HF in the presence of KMnO
4
.
13,14
This ambient wet
chemical synthesis is cost effective compared to standard phosphor
syntheses, which take place at high firing temperatures in controlled
∗
Electrochemical Society Active Member.
z
E-mail: Heleen.Sijbom@UGent.be; Philippe.Smet@UGent.be
atmosphere. The synthesis of K
2
SiF
6
:Mn
4+
was further developed
with etching of crushed quartz schist
15
and silica glasses.
16
Variations
in the synthesis method led to the synthesis of the host lattice K
2
SiF
6
from etching SiO
2
powder with HF in the presence of KF.
17
In the
presence of KMnO
4
,theMn
4+
-doped phosphor precipitates from the
etching solution.
This phosphor has already been subject of detailed investiga-
tions. The electronic structure and mechanical properties of the
host compound were obtained from density functional theory (DFT)
calculations.
18
From DFT, an electronic bandgap around 8 eV was
found. Takahashi and Adachi reported an optical bandgap of 5.6 eV,
obtained from diffuse-reflectance spectroscopy.
9
This is surprisingly
low compared to the DFT value. It is possible that the observed ab-
sorption band, which occurs at the edge of the spectral range of the
used detector, is due to intrinsic defects, rather than fundamental
absorption.
9,18
The multiplet structure originating from the 3d
3
configuration has
been investigated in the framework of crystal field theory
16
and by
coupling single-particle orbitals, obtained from Hartree–Fock–Slater
calculations.
19
Both investigations started from the octahedral sym-
metry of the Si
4+
site of the K
2
SiF
6
host. The vibronic fine structure
of the Mn
4+
emission and excitation spectra has been described in
detail.
9,20
Applications for K
2
SiF
6
:Mn
4+
and other Mn
4+
-doped fluoride
phosphors are found in warm-white LEDs,
21,22
following the in-
clusion of K
2
SiF
6
:Mn
4+
in several patents.
23–26
No prior research
was reported on the influence of a high excitation intensity on the
K
2
SiF
6
:Mn
4+
phosphor. The long, ms range, lifetime of the d-d tran-
sitions in Mn
4+
can cause problems when Mn
4+
-doped materials are
used in high-power LEDs,
27
similartothecaseofMn
2+
.
28
Until now
luminescence-lifetime measurements were only performed for low
and high dopant concentrations
27
in the temperature range of 20–
300 K.
29,30
We performed both luminescence-lifetime and thermal-
quenching measurements up to 450 K, which is important in view of
its application in high-power LEDs. Crystal field calculations were
performed for theoretical support of experimental findings. We com-
bined cathodoluminescence with SEM-EDX mappings to evaluate
the chemical composition, degradation and light output of phosphor
particles at the microscopic level.
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ECS Journal of Solid State Science and Technology, 5 (1) R3040-R3048 (2016) R3041
Figure 1. Two step synthesis of K
2
SiF
6
:Mn
4+
in HF at 0
◦
C. Appearance of
K
2
SiF
6
:Mn
4+
under day light and UV illumination (right).
Experimental
The phosphor particles were synthesized by solution synthesis in
40% HF (Sigma Aldrich), according to the procedure described by
Nguyen.
31
SiO
2
(99.5%, Alfa Aesar) was dissolved in HF at room
temperature. KMnO
4
(98%, Alfa Aesar) was added to this s olution,
such that a dopant concentration of 8% of Mn is obtained. In a separate
solution, KF (99%, Alfa Aesar) was dissolved in HF and 35% H
2
O
2
(Sigma Aldrich) was added. The two solutions were mixed in an ice
bath, where the phosphor particles precipitated. The precipitate was
washed with 20% HF and ethanol and dried at room temperature in
air, resulting in a light-yellow powder (Figure 1).
Powder X-ray diffraction (XRD) patterns were measured on a
Siemens D5000 diffractometer (40 kV, 40 mA) using Cu Kα
1
radi-
ation. Photoluminescence (PL) excitation and emission spectra were
measured using an Edinburgh FS920 fluorescence spectrometer with
a monochromated 450 W Xe arc lamp as excitation source. Low tem-
perature PL measurements were performed using an Oxford Optistat
CF cryostat. An integrating sphere (LabSphere GPS-SL series) was
used to measure the internal and external quantum efficiency of the
phosphor upon LED excitation at 450 nm. For these measurements,
Al
2
O
3
was used as a white reflective standard. SEM-EDX-CL mea-
surements were performed with a Hitachi S-3400 N scanning elec-
tron microscope (SEM), equipped with a Thermo Scientific Noran 7
energy-dispersive X-ray detector (EDX). Furthermore, cathodolumi-
nescence (CL) was collected with an optical fiber and analyzed using
an EMCCD camera (Princeton Instruments ProEM 16002), attached
to a spectrograph (Princeton Instruments Acton SP2358). Thermal-
quenching and s aturation measurements were performed in a home
built set-up using the same EMCCD camera and spectrograph. A blue
445 nm 600 mW laser diode was used as excitation source for the
saturation measurements. Sample temperatures were measured us-
ing a FLIR A35sc thermal infrared (IR) camera. Decay profiles were
collected as a function of temperature using an Oxford Optistat CF
cryostat. A pulsed nitrogen laser with emission at 337 nm was used
as excitation source in combination with an intensified CCD detector
(Andor Instruments DH720) coupled to a 0.5 m monochromator. Sim-
ulations of phosphor combinations for white LEDs were performed
using the NIST-CQS software.
32–34
Computational Method
The electronic structure of Mn
4+
in K
2
SiF
6
was described within
the formalism of crystal field theory (CFT). An effective Hamilto-
nian, accounting for all the relevant interactions concerning the 3d
3
configuration was diagonalized. All terms in the Hamiltonian consist
of an exactly calculable factor containing an angular integral and a
radial integral for which no straightforward analytical expression is
available. Empirical parameters are typically used for the latter. In this
case, the effective Hamiltonian is written as:
35,36
H = E
0
+
k=2,4
f
k
F
k
+
k=2,4
k
q=−k
B
kq
C
kq
+ ζ
nd
A
so
+ αL
(
L + 1
)
[1]
10 20 30 40 50 60 70 80
ICSD #29407
Normalized
intensity
(a.u.)
K
2
SiF
6
K
2
SiF
6
:Mn
4+
2
(a)
(b)
Figure 2. XRD measurement of the red phosphor K
2
SiF
6
:Mn
4+
(b), com-
pared with the reference pattern (ICSD 29407) for K
2
SiF
6
(a).
Herein, the first term contains the spherical symmetric contributions
of all interactions. In practice, the obtained energy spectrum is shifted
to put the lowest eigenvalue at zero. The second term represents
the inter-electronic coulomb repulsion and is traditionally written in
terms of Slater–Condon parameters which transform according to
the irreducible representations (irrep) of the three-dimensional rota-
tion group. In the case of partially filled d and f shells, it is how-
ever more convenient to introduce Racah parameters which transform
properly for the complete Lie group chain that describes the elec-
tron configuration.
37
Two Racah parameters, B and C are required
for nd
N
configurations. The third term is the crystal field potential.
Point symmetry of the defect dictates which crystal field parameters,
B
kq
are nonzero.
36
Alternative parameterizations can be found in lit-
erature (see further). The fourth term, which is often neglected in
the case of 3d transition-metal ions, represents spin–orbit interaction.
The l ast term, first introduced by Trees and Racah, corrects for the
effect of two-body configuration interactions. Herein, L signifies the
total orbital angular momentum of the electronic state. It has been
shown that the inclusion of this additional term in Eq. 1 improves the
correspondence between calculated and experimental spectra.
38–40
The crystal field calculations were performed using an in-house
developed Python program.
41
A Russel–Saunders basis,
2S+1
L
J(M
J
)
,
was used for this purpose. In the case of a d
3
configuration, the basis
is 120 dimensional.
Results and Discussion
Structure.— All the reflections in the measured X-ray diffraction
(XRD) pattern in Figure 2 can be assigned to the standard pattern of
K
2
SiF
6
(cubic space group Fm3m). Although Mn
4+
doping induces a
larger ion (53 pm) in the lattice site of Si
4+
(40 pm),
42
no significant
shift of the reflections caused by the doping is observed.
The cubic crystal structure is also clear from the scanning electron
microscope (SEM) picture in Figure 3, where cubic and octahedral
particles with a diameter of 2–10 μm can be seen. Truncation of cu-
bic particles leads to truncated cubes, cuboctahedrons and octahedral
crystals. This truncation can be beneficial for the luminescence output
of the particles, as will be explained later. Energy-dispersive X-ray
(EDX) analysis shows a homogeneous elemental distribution of K,
Si, F and Mn. No clusters of Mn are observed, so the doping is ho-
mogeneous over the particles within the detection limit and spatial
resolution of EDX. The dopant concentration is 1.5 ± 0.3% of the
amount of Si, as found from EDX analysis. Since the Mn concentra-
tion is 8% of the Si concentration in the precursor solutions, it seems
that only a limited fraction of Mn is incorporated in the phosphor
crystals during the synthesis.
Luminescence.— The room-temperature photoluminescence spec-
tra (Figure 4a) show narrow emission bands due to the
2
E
g
→
4
A
2g
spin-forbidden transitions in Mn
4+
.
8
Its line emission at 630 nm is per-
ceived as saturated red and the eye sensitivity is still quite high in this
wavelength range, which is beneficial for lighting applications. Two
broad excitation bands are present corresponding to the
4
A
2g
→
4
T
2g
and
4
A
2g
→
4
T
1g
spin-allowed transitions.
8
The main excitation band
is centered around 455 nm, which is ideal for blue-LED excitation at
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R3042 ECS Journal of Solid State Science and Technology, 5 (1) R3040-R3048 (2016)
Figure 3. Low-vacuum scanning electron microscopy image from backscat-
tered electron detection (a) and energy-dispersive X-ray mappings of
K
2
SiF
6
:Mn
4+
(b–e).
Figure 4. Photoluminescence excitation (upon monitoring emission at 630
nm) and emission (upon monitoring excitation at 455 nm) spectra of
K
2
SiF
6
:Mn
4+
measured at room temperature (a) and at 10 K (b).
Figure 5. SEM picture (a), cathodoluminescence mapping (b), and F Kα EDX
mapping of K
2
SiF
6
:Mn
4+
particles (c).
450–460 nm. No excitation bands are present at wavelengths above
500 nm, which prevents reabsorption of yellow and green phosphor
emission in a phosphor-converted white LED.
Additionally, the PL spectra were measured at 10 K (Figure 4b).
The vibronic fine structure is clearly visible in the case of the
2
E
g
→
4
A
2g
and
4
A
2g
→
4
T
2g
transitions. For the
2
E
g
→
4
A
2g
transition,
the zero phonon line (ZPL) is located at 620.5 nm. The location of the
ZPL is hard to determine in case of the
4
A
2g
→
4
T
2g
transition because
in addition to the occurrence of the different phonon-assisted transi-
tions, the
4
T
2g
electronic energy level is expected to be split due to
low-symmetry crystal field components and the spin–orbit interaction
(see further).
The internal quantum efficiency (IQE), defined as the ratio between
the number of emitted and absorbed photons, is 42%. About 25% of
the incident photons at 450 nm are absorbed by the phosphor, which
limits the external quantum efficiency. Further improvement of the
IQE is realistic, since values of 74%
43
and 80%
21
have been reported
earlier.
The SEM picture in Figure 5a shows the representative particles
selected for CL and EDX mappings. The CL mapping in Figure 5b
shows a preferential location of the light output on certain edges of the
cubic particle. Rotating the particle with respect to the light-collecting
optical fiber leads to essentially the same spatial emission pattern. The
light outcoupling is maximal at the lower crystal edge, while excitation
with the electron beam in the center of the top surface leads to lower
CL emission intensity, independent of the location of the optical fiber.
At the lower-right corner, the cube is truncated forming an octahedral
crystal face, as is more clearly seen in the fluorine Kα EDX mapping
in Figure 5c. As the low-energy F Kα X-rays have a short attenuation
length in the K
2
SiF
6
lattice, geometrical aspects influence the relative
number of detected X-rays.
For these symmetrically shaped particles, it can be expected that
total internal reflection plays an important role in the light outcoupling
behavior,
44
especially when the particles are measured in vacuum
or air, leading to a significant difference in refractive index at the
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ECS Journal of Solid State Science and Technology, 5 (1) R3040-R3048 (2016) R3043
Figure 6. Integrated emission intensity of K
2
SiF
6
:Mn
4+
as a function of tem-
perature.
faces of the crystals. The longer optical-path length will lower the
final quantum efficiency as defects other than Mn
4+
, which can be
unintentionally present, might reabsorb the light and non-radiatively
dissipate the energy. When K
2
SiF
6
(refractive index of 1.34
18
)is
embedded in epoxy or silicone binder material, the outcoupling from
the phosphor particles will be improved.
Thermal properties.— Both the luminescent emission intensity
and the luminescent lifetime were measured as a function of tem-
perature. From the thermal-quenching measurements up to 450 K
(Figure 6) the characteristic temperature T
1/2,
for which the emis-
sion intensity is halved compared to the intensity at low temperature,
is determined at 430 K. The emission intensity remains stable until
400 K, which is within the 400–450 K operating temperature of LED
chips.
1
At 450 K, the emission intensity is lowered to 16% of the
initial emission intensity. To increase the performance of the phos-
phor in high-power LEDs with elevated operating temperatures, a
remote-phosphor approach can be used. By separating the phosphor
layer from the LED chip, the operating temperature of the phosphor
can be lowered due to the lower excitation flux. The thermal design
should be such that the Stokes losses from the conversion process,
which amount to 30% of the incident blue photon flux, are adequately
removed from the remote phosphor plate.
45
Heat treatment of the phosphor powder at 473 K in air left the lumi-
nescent properties intact, while heat treatment at 673 K caused a color
change of the powder from light-yellow to brown and almost entirely
destroyed the luminescence, with a remaining quantum efficiency of
less than 1%. In SEM, some particles are still intact, but on other
particles, structural changes from cubic crystals to amorphous shapes
are detected. This is in agreement with the decomposition starting at
638 K as reported in literature.
17
Figure 7. Decay profile measurements (dots) and fit (lines) of the lumines-
cence intensity of K
2
SiF
6
:Mn
4+
at 450 K (a), 295 K (b) and 220 K (c).
Figure 8. Decay times (a–c) (boxes) and fraction of decay component (d)
(bars, the full line is a guide to the eye) as a function of temperature of
K
2
SiF
6
:Mn
4+
. With increasing temperature a second, faster decay component
(c) emerges. The effective decay time (b) (open boxes) is calculated as a
weighted average of the two components (a) and (c).
The luminescent-lifetime measurements in Figure 7 show a mono-
exponential decay at 220 K with a decay time τ = 10.5 ms. With
increasing temperature (in the 295–450 K range), a bi-exponential
decay is required since a second, faster decay component emerges.
The time constant of the slow component (Figure 8a), decreases with
increasing temperature, reaching τ = 8.1 ms at room temperature and
τ = 4.9 ms at 450 K. This behavior is consistent with the drop in the
overall decay time from 15 to 7 ms in the 20–300 K temperature range
that was reported earlier.
30
Our results show that the drop in decay
time continues further with increasing temperature, although thermal
quenching only starts above 400 K.
The second, faster component (Figure 8c), has a decay time be-
tween 0.63 and 1.0 ms in the 295–450 K range. The fraction of the
total emission assigned to the fast component increases from 2–3% in
the 295–320 K temperature range to 15% at 345 K and 24% at 450 K
(Figure 8d). An effective decay time (Figure 8b) is calculated as a
weighted average of the two decay components.
The largest fraction of the emission, 76% at 450 K, takes place
following the slower, spin-forbidden
2
E
g
→
4
A
2g
transition and no
extra peaks are observed in the emission spectrum with increasing
temperature.
From the particular shape of the decay curves, it is plausible to
assume that a certain minority of the Mn
4+
centers show different
emission dynamics, provided that sufficient thermal energy is avail-
able. This energy allows the defect center to be thermally excited
to an electronic eigenstate, characterized by a slightly higher total
energy and a higher probability for radiative decay. In the case of
perfectly-octahedral MnF
2−
6
defect clusters, the degeneracy of the
emitting
2
E
g
level is maintained, even with the inclusion of spin–
orbit coupling. In that case, the emitting level transforms according to
the four-dimensional irreducible representation G (irrep) of the double
group O
∗
h
. This is visualized in the modified Tanabe–Sugano diagram,
displayed in Figure 9a. Therefore, the question is what the origin is of
such a faster-decaying, higher-lying multiplet. In the following, it is
examined through crystal field theory whether this can be the result of
a small deformation of the octahedral complex, for example by nearby
lattice defects or other Mn
4+
ions.
Geometry of Mn
4+
defects.— Two straightforward ways exist to
lower the octahedral symmetry, either tetragonally by prolonging or
shortening the body diagonal along a fourfold rotation axis or trig-
onally by altering the length of the body diagonal along a threefold
rotation axis. Consequently, one ends up with respective point symme-
tries D
4h
and D
3d
.InFigures9b and 9c, the effect of the deformation
on the multiplets is given as a function of the Ballhausen 10Ds and
10Dσ parameters, quantifying the deformations.
46
In both cases, it is
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R3044 ECS Journal of Solid State Science and Technology, 5 (1) R3040-R3048 (2016)
Figure 9. Tanabe–Sugano diagram of a d
3
configuration, originating from exact diagonalization of the effective Hamiltonian (Eq. 1) in octahedral symmetry and
with the inclusion of spin–orbit coupling (ζ
3d
= 47 meV) (a). The effect of tetrahedral deformation of the octahedral Mn
4+
defect (O
h
→D
4h
) on the multiplet
energies for a constant 10Dq = 30.2B and Dt = 0 (b). The effect of trigonal deformation of the octahedral Mn
4+
defect (O
h
→D
3d
) on the multiplet energies for a
constant 10Dq = 30.2B and Dτ = 0 (c). The color of the lines represent the amount of spin quartet (S = 3/2) or doublet (S = 1/2) character of the eigenstate.
assumed that the cubic ratios of the crystal field parameters in octa-
hedral symmetry are maintained during the deformation. The exact
definition of the Ballhausen parameters and their relation with the
conventional Wybourne parameters B
kq
is provided in the Appendix.
In the case of a tetragonal deformation, the emitting
2
E
g
multiplet
splits into two singlets, transforming as the
2
A
1g
and
2
B
1g
irreps of
D
4h
, corresponding with the Kramers doublets E
1/2g
and E
5/2g
.The
ground-state multiplet
4
A
2g
of O
h
corresponds with the
4
B
1g
irrep
of D
4h
. Due to the spin–orbit interaction, this level is split in two
Kramers doublets, E
1/2g
and E
5/2g
. If the selection rules for electric
dipole transitions in D
4h
symmetry are considered, every transition is
forbidden due to the presence of an inversion center and Laporte’s
rule. If this parity selection rule is relaxed, or with other words, after
a further descent of symmetry toward C
4v
, one finds that the B
1
→B
1
transition is electric-dipole allowed in this reduced symmetry, that is
the direct product B
1
⊗ A
1
⊗ B
1
transforms according to the totally
symmetric representation A
1
in C
4v
symmetry. In this case, the z
component of the electric dipole moment has symmetry label A
1
.
The A
1
→B
1
transition remains symmetry forbidden at the electric
dipole level as A
1
⊗ A
1
⊗ B
1
, for polarization along the z axis, and
A
1
⊗ E ⊗ B
1
, for polarizations perpendicular to the z axis, do not
contain A
1
in their reduction. If the B
1
multiplet has a slightly higher
energy than the A
1
multiplet, the particular decay behavior can be
explained. This corresponds with negative Ds values. If the crystal
field is parameterized in terms of a point-charge model, negative
Ds and Dt values signify a shortening of the body diagonal of the
coordination polyhedron. Tetragonal deformation can be expected
in the K
2
SiF
6
crystal from a nearby fluorine vacancy or interstitial
atom. Interstitials might occupy the octahedral voids in the crystal
structure (Wyckoff site 4b) and are indeed expected to compress the
coordination polyhedron in the direction of the fourfold rotation axis.
In the case of a trigonal deformation, the
2
E
g
multiplet does not
split due to symmetry breaking, but rather transforms as the irrep
2
E
g
of D
3d
. However, unlike the octahedral case, this multiplet splits in
two Kramers doublets, E
1/2g
and E
3/2g
due to spin–orbit interaction.
In the case of positive 10Dσ values, the higher-lying Kramers dou-
blet features a slightly higher S = 3/2 content than the lower-lying
one, ensuring a faster decay due to a relaxation of the spin selec-
tion rule. However, the weak spin–orbit interaction for 3d ions mixes
spin multiplicity only in a limited way. Typically 0.2–0.5% of quartet
character is present in the relevant eigenstates. This is also clear from
Figure 9. Only where energy levels are sufficiently close to interact,
substantial spin mixing is visible. For this reason, it is more likely that
the observed decay behavior originates from tetragonal deformation
rather than from trigonal deformation. Electron paramagnetic reso-
nance (EPR) offers an experimental way to distinct one case from the
other. Trigonal deformation is induced when two Mn
4+
ions are in-
corporated on neighboring Si
4+
sites in the crystal or from an adjacent
potassium vacancy.
From symmetry arguments, it is most likely that the observed
decay dynamics originate from a tetragonal compression of the coor-
dination polyhedron. For this reason, the crystal-field Hamiltonian for
D
4h
symmetry was fit to the experimental low-temperature photolu-
minescence spectrum. Racah, spin–orbit and Trees parameters were
kept fixed at literature values that were obtained for similar Mn
4+
systems.
14,47,48
The crystal field 10Dq and 10Ds values were varied
in order to reproduce the experimental transition energies as good as
possible. The location of the ZPLs of the
4
A
2g
→
4
T
2g
and
4
A
2g
→
4
T
1g
transitions were assigned to the low energy side of the respective ex-
citation bands. The crystal field splitting between the
2
B
1g
and
2
A
1g
multiplets was estimated in the order of kT ≈ 250 cm
−1
from the
activation temperature of the fast decay component. The fixed and
optimized parameters are summarized in Table I, the optimized en-
ergies are tabulated in Table II. The root-mean-square deviation of
the fit is 270 cm
−1
, which is reasonable given the limited number of
experimentally available energies.
Saturation behavior.— Previous reports claim no light-induced
degradation in K
2
SiF
6
:Mn
4+
,
49
but at high laser power, both saturation
and degradation of the phosphor occur. In Figure 10, the measured
emission intensity is plotted as a function of excitation power. The
Table I. Parameters used in the crystal field calculation.
Parameter Value (cm
−1
) Reference
B 770 14
C 3470 14
ζ
3d
380 47
α 91 47,48
10Dq 21791
10Ds −1118
10Dt 0
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