Simple bipolar host materials incorporating CN group for highly efficient blue electrophosphorescence with slow efficiency roll-off

Article abstract of DOI:10.1039/c3tc31893a

A group of small-molecular compounds, namely 6-(3-(9H-carbazol-9-yl)phenyl) -9-ethyl-9H-carbazole-3-carbonitrile (m-CzCzCN), 6-(2-(9H-carbazol-9-yl)phenyl)- 9-ethyl-9H-carbazole-3-carbonitrile (o-CzCzCN), 6-(3,5-di(9H-carbazol-9-yl) phenyl)-9-ethyl-9H-carbazole-3-carbonitrile (mCPCzCN), 8-(3-(9H-carbazol-9-yl) phenyl)dibenzo[b,d]furan-2-carbonitrile (m-CzOCN), 8-(3-(9H-carbazol-9-yl) phenyl)dibenzo[b,d]thiophene-2-carbonitrile (m-CzSCN), are designed and synthesized for use as host materials in blue phosphorescent organic light-emitting diodes (PhOLEDs). The p-type carbazole and the n-type cyano-decorated carbazole, dibenzofuran or dibenzothiophene unit are incorporated, to either the meta- or ortho-positions of the phenylene bridge. The bipolar feature was confirmed by theoretical calculation and experimental results of the single-carrier devices. These materials exhibit an excellent performance in their hosted blue phosphorescent OLEDs with iridium(iii)bis(4,6- (difluorophenyl)pyridinato-N,C²′)picolinate (Firpic) as the doped emitter. The ortho-substituted o-CzCzCN realizes higher device efficiencies than the meta-substituted isomer m-CzCzCN, with a maximum external quantum efficiency of 21.0% and a current efficiency of 43.9 cd A^-1. The device hosted by m-CzSCN also exhibits remarkably high efficiencies of 23.3% and 46.1 cd A^-1. Furthermore, these blue PhOLEDs are characterized by a slow efficiency roll-off. Even at a high brightness of 10 000 cd m ^-2, the o-CzCzCN hosted device still retain high efficiencies of 13.6% and 28.5 cd A^-1. This is a systematic study of incorporating the CN group onto carbazole, dibenzofuran and dibenzothiophene, to develop high-triplet-energy bipolar hosts for OLED applications.

Full text of DOI:10.1039/c3tc31893a

Journal of
Materials Chemistry C
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PAPER
Simple bipolar host materials incorporating CN group
for highly efficient blue electrophosphorescence with
slow efficiency roll-off†
Cite this: J. Mater. Chem. C, 2013, 1,
8140
a
a
b
b
*
*
Lijun Deng, Jiuyan Li, Ge-Xia Wang and Li-Zhu Wu
A group of small-molecular compounds, namely 6-(3-(9H-carbazol-9-yl)phenyl)-9-ethyl-9H-carbazole-3-
carbonitrile (m-CzCzCN), 6-(2-(9H-carbazol-9-yl)phenyl)-9-ethyl-9H-carbazole-3-carbonitrile (o-CzCzCN),
6-(3,5-di(9H-carbazol-9-yl)phenyl)-9-ethyl-9H-carbazole-3-carbonitrile (mCPCzCN), 8-(3-(9H-carbazol-9-yl)
phenyl)dibenzo[b,d]furan-2-carbonitrile (m-CzOCN), 8-(3-(9H-carbazol-9-yl)phenyl)dibenzo[b,d]thiophene-
2-carbonitrile (m-CzSCN), are designed and synthesized for use as host materials in blue phosphorescent
organic light-emitting diodes (PhOLEDs). The p-type carbazole and the n-type cyano-decorated carbazole,
dibenzofuran or dibenzothiophene unit are incorporated, to either the meta- or ortho-positions of the
phenylene bridge. The bipolar feature was confirmed by theoretical calculation and experimental results
of the single-carrier devices. These materials exhibit an excellent performance in their hosted blue
2
0
phosphorescent OLEDs with iridium(III)bis(4,6-(difluorophenyl)pyridinato-N,C )picolinate (Firpic) as the
doped emitter. The ortho-substituted o-CzCzCN realizes higher device efficiencies than the meta-
substituted isomer m-CzCzCN, with a maximum external quantum efficiency of 21.0% and a current
efficiency of 43.9 cd Aꢀ1. The device hosted by m-CzSCN also exhibits remarkably high efficiencies of
23.3% and 46.1 cd Aꢀ1. Furthermore, these blue PhOLEDs are characterized by a slow efficiency roll-off.
Even at a high brightness of 10 000 cd mꢀ2, the o-CzCzCN hosted device still retain high efficiencies of
13.6% and 28.5 cd Aꢀ1. This is a systematic study of incorporating the CN group onto carbazole,
dibenzofuran and dibenzothiophene, to develop high-triplet-energy bipolar hosts for OLED applications.
Received 25th September 2013
Accepted 15th October 2013
DOI: 10.1039/c3tc31893a
www.rsc.org/MaterialsC
For the host materials used for blue PhOLEDs, even higher
triplet energies are required to efficiently conne the triplet
Introduction
excitons on the dopant molecules.8,9 In comparison with the
traditional uni-polar host materials,10–12 bipolar hosts that are
typically composed of both p-type and n-type functional groups
have been well proved to lead to much higher device efficiencies
and a slower efficiency roll-off, due to a more balanced charge
transportation.13,14 The appropriate selection of the n-type unit is
critical to construct high-quality bipolar blue host materials. It is
worth noting that the strongly electron-withdrawing cyano group
(CN) should be a good candidate as an n-type unit to form bipolar
molecules in principle.15–17 However, CN-containing compounds
are not so extensively studied as bipolar host materials for
PhOLEDs, to date. Apparently, a systematic study incorporating
CN-decorated structures as the electron-decient moieties for
high triplet energy bipolar host materials is still absent.
In this report, we selected CN-decorated carbazole, diben-
zofuran or dibenzothiophene as the n-type unit, the neat
carbazole as the p-type unit, and the phenylene as the bridge, to
build up a group of novel bipolar host materials (Scheme 1). The
CN-decorated carbazole, dibenzofuran, or dibenzothiophene is
located at the meta-position relative to the p-type carbazole, to
form m-CzCzCN, m-CzOCN, and m-CzSCN. The ortho-linked
Organic light-emitting diodes (OLEDs) have been extensively
studied due to their practical applications as new-generation
at-panel displays and energy-saving lighting sources.1–3 The
phosphorescent OLEDs (PhOLEDs) are advantageous over the
uorescent devices in improving the emission efficiency, by
utilizing both singlet and triplet excitons.4 For the transition-
metal complex phosphors that usually have relatively long
excited-state lifetimes,5 it is necessary to be dispersed at a low
doping level into a host matrix, to suppress the concentration
quenching and triplet–triplet annihilation.6,7 Therefore, the
host materials are as important as the phosphorescent dopant
to determine the overall device performance, since it occupies
the majority of the emitting layer in the OLED.
aState Key Laboratory of Fine Chemicals, School of Chemical Engineering, Dalian
University of Technology,
2 Linggong Road, Dalian 116024, China. E-mail:
jiuyanli@dlut.edu.cn
bKey Laboratory of Photochemical Conversion and Optoelectronic Materials, Technical
Institute of Physics and Chemistry, The Chinese Academy of Sciences, Beijing 100190,
China. E-mail: lzwu@mail.ipc.ac.cn
† Electronic supplementary information (ESI) available: Compounds syntheses
and characterization. See DOI: 10.1039/c3tc31893a
8140 | J. Mater. Chem. C, 2013, 1, 8140–8145
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isomer o-CzCzCN of m-CzCzCN was designed to verify the
inuence of the molecular conguration on the optoelectronic
properties. In order to further verify the inuence of the
increased number of electron-donating carbazoles, the
mCPCzCN was obtained. The blue PhOLEDs containing these
bipolar hosts exhibited excellent performances, characterized
by high efficiency and slow efficiency roll-off. This is a system-
atic study using different CN-decorated aromatic structures as
the n-type unit, to construct high-triplet-energy host materials
for blue PhOLEDs.
Results and discussion
Synthesis and thermal properties
The materials were synthesized according to the procedure in
Scheme 1. First, the substituted carbazole, dibenzofuran, and
dibenzothiophene were brominated at both the para-positions
of the corresponding heteroatom, by NBS (N-bromosuccini-
mide), or bromine. Then, the CN group was introduced through
a Rosenmund–von Braun reaction with CuCN (1.0 equiv.) in
DMF, replacing one of the bromine atoms on the aromatic rings.
Finally, the palladium-catalyzed C–N coupling reaction between
the mono-brominated intermediates with the corresponding
boronic acid produced the target compounds in good yields of
Fig.
1
DSC traces (at the second heating cycle) of o-CzCzCN, mCPCzCN,
m-CzOCN, and m-CzSCN recorded at a heating rate of 10 ꢁC minꢀ1
.
improved morphological stabilities of these materials. No phase
transition was detected for m-CzCzCN before its decomposition.
Photophysical properties
85–90%. The details of the syntheses and characterization are Fig. 2 shows the absorption and uorescence spectra of all the
given in the ESI.† All these compounds have a good solubility in compounds in dilute CH2Cl2 solutions. Interestingly, the
most common organic solvents, so that they could be thoroughly absorption spectra of these compounds are very similar, in
puried by column chromatography and repeated recrystalliza- terms of the spectral prole, which should be because they have
tion, to reach a high purity for OLED applications.
a similar molecular skeleton and possess identical functional
The thermal properties of these compounds were investigated groups, such as the same p-type carbazole and the phenylene
by thermogravimetric analysis (TGA) and differential scanning core. Strong absorption peaks around 290 nm can be assigned
calorimetry (DSC). The TGA thermograms are provided in Fig. S1 to the p–p* transitions of the carbazole moiety and the weak
(in ESI),† the DSC traces are shown in Fig. 1, and all the pertinent absorption peaks at 340 nm could be attributed to the n–p*
data are summarized in Table S1.† All these compounds exhibit transitions of extended conjugation of the carbazole moiety.6
high thermal decomposition temperatures (Td, corresponding to Upon photoexcitation at the absorption maximums at room
a 5% weight loss) in the range 320–437 ꢁC, except m-CzCzCN temperature, these ve compounds show different uorescent
ꢁ
(Td ¼ 186 C), indicating a good thermal stability. Their glass- features in dilute dichloromethane solutions. Both m-CzCzCN
transition temperatures (Tg) range from 98 to 167 ꢁC, which are and o-CzCzCN exhibit a structureless emission, with peaks at
substantially higher than that of mCP (Tg ¼ 65 ꢁC), indicating the 390 and 384 nm, respectively. The small hypochromatic shi of
Scheme 1 Synthesis and molecular structures of m-CzCzCN, o-CzCzCN, mCPCzCN, m-CzOCN and m-CzSCN.
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these compounds implies they possess a similar ability to
capture electrons from external sources. This is reasonable,
since all of them have the same CN group as the most electron-
decient moiety.
Density functional theory (DFT) calculations were performed
for these molecules using B3LYP hybrid functional theory with
Gaussian 03.18 The optimized geometries and the distribution of
the HOMO and LUMO for these molecules are shown in Fig. S4.†
For all these molecules, the HOMO is mainly distributed on the
p-type carbazole ring with a small contribution from the phen-
ylene bridge, while the LUMO is exclusively located on the
CN-decorated aromatic rings. The complete spacial separation of
the HOMO and LUMO indicates the bipolar charge-transporting
property for these molecules. In addition, the larger dihedral
angles in o-CzCzCN, compared to all the other molecules reect
that the steric hindrance of an ortho-linked molecule is signi-
cantly increased over the meta-linked conformation.
Fig. 2 The UV-vis absorption and room-temperature fluorescence spectra of
m-CzCzCN, o-CzCzCN, mCPCzCN, m-CzOCN and m-CzSCN.
6 nm in the uorescence spectrum of o-CzCzCN, relative to its
isomer m-CzCzCN, should be assigned to the rigid molecular
conformation of o-CzCzCN that will lead to a higher excited
state energy. On the contrary, the uorescence spectra for
m-CzOCN and m-CzSCN show well-dened vibronic bands
covering a spectral range from 350 nm to over 450 nm. Their
phosphorescence spectra were measured in a frozen 2-methyl-
tetrahydrofuran matrix at 77 K (Fig. S2†). m-CzSCN shows a
remarkably higher phosphorescence intensity relative to uo-
rescence, in comparison with the other compounds in this
study. This should be because the heavy atom effect of the
sulphur atom is favorable for intersystem crossing from the
singlet to the triplet excited state and nally for a more efficient
phosphorescence emission. The triplet energies were estimated
from the highest-energy vibronic sub-band of the phosphores-
cence spectra.6 All of the compounds show higher triplet energy
levels (2.78–2.89 eV) than that of the widely-used blue phosphor,
Firpic (2.65 eV), implyng they could serve as host materials for
blue phosphors.
Electroluminescence properties
To further verify the bipolar character of these CN-decorated
compounds, single carrier devices were fabricated using
m-CzCzCN and o-CzCzCN, as examples. The famous blue
phosphorescent host material mCP was also studied in the same
way, for comparison. The hole-only devices have the structure of
ITO/PEDOT:PSS (40 nm)/TAPC (5 nm)/host (100 nm)/TAPC
(5 nm)/Al (100 nm), and the electron-only devices have the
structure of ITO/TmPyPB (5 nm)/host (100 nm)/TmPyPB (5 nm)/
LiF (1 nm)/Al (100 nm). The chemical structures and energy level
diagram of these materials and devices are shown in Fig. S5.†19
The higher current density over the whole detected voltage range
in the m-CzCzCN and o-CzCzCN based hole-only devices, over
mCP (Fig. 3a) implies that attaching carbazole through its
3-position to the phenylene core in the m-CzCzCN and
o-CzCzCN molecules may be favorable for a more rapid hole
transportation. In the electron-only devices, the current density
of the m-CzCzCN and o-CzCzCN devices far exceeds that of mCP
(Fig. 3b). Considering that the electron barrier in the mCP device
is more favorable for an efficient electron injection, the superior
Electrochemical properties and theoretical calculations
The electrochemical behavior of all the compounds was studied current density in the m-CzCzCN and o-CzCzCN devices should
by cyclic voltammetry measurements in deoxygenated CH2Cl2 benet from their improved electron transporting ability. We
solutions, containing 0.1 M tetra(n-butyl)ammonium hexa- assigned the improved electron transportation to the contribu-
uorophosphate (n-Bu4NPF6) as the supporting electrolyte. The tion of the strongly electron-withdrawing CN groups. In both the
cyclic voltammograms are shown in Fig. S3.† In the anodic scan, hole-only and electron-only devices, m-CzCzCN always exhibited
all these ve compounds underwent a similar oxidation a higher current than its isomer o-CzCzCN. This should be
processes, which should be because of the oxidation of their because the twisted molecular conformation and the disordered
onset
ox
common p-type carbazole moiety. The onset potentials (E
)
packing in the o-CzCzCN bulky layer restrains the charge
of the rst oxidation wave for these compounds are quite transportation to some extent. The dramatically increased
close to each other, in the range 1.22 to 1.26 V, relative to a electron current observed in the electron-only devices of these
saturated calomel electrode (SCE), and which were used to CN-containing materials and the signicant high current
determine the HOMO energy levels, according to the equation density in their hole-only devices conrmed their bipolar
onset
EHOMO ¼ ꢀe(E
+ 4.4), as ca. ꢀ5.62 eV to ꢀ5.66 eV, respec- charge-transporting characteristics.
ox
tively. No reduction signal was detected for all these compounds
These materials were evaluated by fabricating blue devices
during the cathodic scan to ꢀ2.0 V. The LUMO energy levels of (A–E) with the simple structure of ITO/PEDOT:PSS (40 nm)/
the ve compounds were calculated by subtracting the optical TAPC (20 nm)/host: 8 wt% Firpic (30 nm)/TmPyPB (40 nm)/LiF
band gap6 from the HOMO energy, and found to be ꢀ2.19 eV to (1 nm)/Al (100 nm). For comparison, a mCP-hosted blue device
ꢀ2.37 eV. The small difference in the LUMO energy levels for (F) was also fabricated and tested. All these devices emitted
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Fig. 4 (a) The current density–voltage–brightness characteristics and (b) the
plots of the current efficiency versus brightness for the blue devices A (m-CzCzCN),
B (o-CzCzCN), and C (mCPCzCN).
Fig. 3 Current density versus voltage characteristics for (a) the hole-only and (b)
electron-only devices of m-CzCzCN, o-CzCzCN and mCP.
blue electroluminescence (EL) from the doped Firpic, as
Inspiringly, an excellent performance was also realized in the
shown by the EL spectra in Fig. S6.† The CIE coordinates of m-CzOCN based device D and m-CzSCN-based device E (Fig. S8†
device E are evidently shied in comparison with other and Table 1). The device D achieved the maximum efficiencies
devices, which is probably caused by the different photo- hc of 36.8 cd Aꢀ1, hP of 21.9 lm Wꢀ1 and hext of 15.3%. An even
luminescent behavior of the m-CzSCN host. The current better performance was achieved in device E, with a maximum
density–voltage–brightness (J–V–B) characteristics and effi- hc of 46.1 cd Aꢀ1, hP of 23.4 lm Wꢀ1, and hext of 23.3%, which are
ciency curves of the device A (m-CzCzCN), device B (o-CzCzCN) the highest values among all the blue PhOLEDs in the present
and device C (mCPCzCN) are shown in Fig. 4 and Fig. S7.† The study. At the same time, a slow efficiency roll-off was observed
o-CzCzCN based device, B, withstood a higher driving voltage for device E, with the efficiency still being as high as 23.2% and
and exhibited a maximum brightness of 24 300 cd mꢀ2 at 15 V, 11.6% at the brightness of 1000 and 10 000 cd mꢀ2, respectively.
being much higher than the maximum values of 12 530 and
Hong,19 Ma,20 Wong16 individually reported the high
9184 cd mꢀ2 at 12 V for devices A and C, respectively. It is efficiencies of 46 cd Aꢀ1, 49.4 cd Aꢀ1, and 58.7 cd Aꢀ1 for Firpic-
obvious that the o-CzCzCN-based device B realized much based blue PhOLEDs in recent years, which are typical data for
higher efficiencies than devices A and C, with a maximum blue PhOLEDs, so far. It is unambiguous that the efficiencies of
current efficiency hc of 43.9 cd Aꢀ1 (at 6 V and 50 cd mꢀ2), a our present blue devices, especially those with o-CzCzCN and
maximum power efficiency hP of 23 lm Wꢀ1 and a maximum m-CzSCN as hosts, are close to the best data reported, so far.
forward-viewing external quantum efficiency hext of 21%. In More importantly, our devices are characterized by a remark-
addition, all these blue devices exhibited a slow efficiency roll- ably slow efficiency roll-off, which is really a valuable merit,
off. For example, at a brightness of 1000 cd mꢀ2, the o-CzCzCN- especially when the practical application under high voltage or
based device B exhibited efficiencies hc of 37.7 cd Aꢀ1 and hext high brightness is concerned. In addition, the outstanding
of 18%, which are reduced by only 14% relative to the performance of o-CzCzCN should benet from its twisted
maximum values. Even at an extremely high brightness of molecular structure, which not only further facilitates charge
10 000 cd mꢀ2, the efficiencies reamained as high as hc of 28.5 balance, but also alleviates the triplet–triplet annihilation of the
cd Aꢀ1 and hext of 13.6%, still being much higher than the doped phosphor at a high current range. It should be noted that
maximum hc of 23.8 cd Aꢀ1 and hext of 11.7% for the mCP our excellent performance was obtained from such a traditional
hosted device F.
and much more simple device in comparison with the literature
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Table 1 Electroluminescence characteristics of the devices A–Fa
hp,max
(lm Wꢀ1
)
Device
Host
Von (V)
Lmax (cd mꢀ2
)
hc (cd Aꢀ1
b
)
hextb (%)
CIEc (x, y)
A
B
C
D
E
F
m-CzCzCN
o-CzCzCN
m-CPCzCN
m-CzOCN
m-CzSCN
mCP
3.9
4.8
4.0
3.6
4.0
4.8
12 530 (12)
24 300 (15)
9184 (12)
12 080 (12)
14 730 (12)
23 280 (13)
33.4, 27.6, 15.3
43.9, 37.7, 28.5
19.3, 19.1, NAd
36.8, 36.3, 17.7
46.1, 45.8, 23.0
23.8, 22.8, 18.0
21.0
23.0
10.5
21.9
23.4
12.4
16.4, 13.5, 7.5
21.0, 18.0, 13.6
9.2, 9.1, NAd
15.3, 15.1, 7.4
23.3, 23.2, 11.6
11.7, 11.2, 8.8
0.14, 0.35
0.15, 0.35
0.16, 0.40
0.16, 0.38
0.17, 0.43
0.14, 0.32
a
Abbreviation: Von: turn-on voltage; Lmax: maximum brightness; hc: current efficiency; hp,max: maximum power efficiency; hext: external quantum
b
efficiency; CIE (x, y): Commission International de I'Eclairage coordinates. Order of measured value: maximum, then values at 1000 and
10 000 cd mꢀ2
.
Measured at 8 V. NA ¼ not obtained.
c
d
cases.6,10,11 It is reasonable to expect a further performance calomel electrode (SCE) reference electrode were used. All the
improvement, by device structure optimization.
measurements were made at room temperature on samples
dissolved in dichloromethane, deoxygenated with argon, and
with 0.1 M [Bu4N]PF6 as the electrolyte. Density functional theory
(DFT) calculations using B3LYP functional were performed. The
basis set used for the C, H, N atoms was 6-31G. There are no
imaginary frequencies for both the optimized structures. All
these calculations were performed with Gaussian 03.
Conclusion
In conclusion, a group of CN-substituted aromatic rings were
used as n-type units to construct a new series of high-triplet-
energy bipolar host materials for PhOLEDs. The complete spatial
separation of the HOMO and LUMO and the single carrier
devices study combine to conrm their bipolar nature. The blue
PhOLEDs utilizing these bipolar hosts are characterized by high
efficiencies and a slow efficiency roll-off, even obtained with a
simple device structure and other commercial materials. The
maximum efficiencies of 43.9 cd Aꢀ1 (hext of 21.0%) and 46.1 cd
Aꢀ1 (hext of 23.3%) realized in the o-CzCzCN and m-CzSCN
hosted devices are among the highest data ever reported for
Firpic based blue PhOLEDs. Even at a high brightness of 10 000
cd mꢀ2, the o-CzCzCN hosted device retained a high efficiency of
28.5 cd Aꢀ1. We have demonstrated that the CN-substituted
groups are promising n-type units to construct bipolar host
materials for applications in high-performance PhOLEDs.
OLED fabrication and measurements
The pre-cleaned ITO glass substrates, with a sheet resistance of
30 U per square, were treated by UV–ozone for 20 min. A 40 nm
thick PEDOT:PSS lm wasꢁ rst deposited on the ITO glass
substrate and baked at 120 C for 30 min in air. Subsequently,
the substrate was transferred into a vacuum chamber to deposit
the organic layers with a base pressure less than 10ꢀ6 Torr
(1 Torr ¼ 133.32 Pa). Finally, the device fabrication was
completed through the thermal deposition of LiF (1 nm) and
then capping with Al metal (100 nm) as a cathode. The emitting
area of each pixel was determined by overlapping of the two
electrodes as 9 mm2. The EL spectra, CIE coordinates and J–V–B
curves of the devices were measured with a PR705 photometer
Experimental
General information
and
a source-measure-unit Keithley 236, under ambient
conditions at room temperature. The forwarding viewing
external quantum efficiency (hext) was calculated by using the
current efficiency, EL spectra and human photopic sensitivity.
The 1H NMR and 13C NMR spectra were recorded on a 400 MHz
and 100 MHz Varian Unity Inova spectrophotometer. The mass
spectra obtained taken on HP1100LC/MSD MS spectrometer.
The infrared (IR) spectra were measured on a Thermo Fisher
Scientic Nicolet 6700 FT-IR spectrometer. The uorescence and
UV-vis absorption spectra measurements were performed on a
Perkin-Elmer LS55 spectrometer and a Perkin-Elmer Lambda 35
spectrophotometer, respectively. The phosphorescence spectra
were measured on an Edinburgh FLS920 Spectrometer at 77 K in
2-MeTHF. Thermogravimetric analyses (TGA) and differential
scanning calorimetry (DSC) measurements were carried out
using Perkin-Elmer thermogravimeter (Model TGꢀA17) and a
Netzsch DSC 201, at a heating rate of 10 ꢁC min under a
nitrogen atmosphere, respectively. The electrochemical
measurements were carried out by using a conventional three-
electrode conguration and an electrochemical workstation
(BAS100B, USA) at a scan rate of 100 mV sꢀ1. A glass carbon
working electrode, a Pt-wire counter electrode, and a saturated
Acknowledgements
We thank the National Natural Science Foundation of China
(21072026, 21274016, 21374013, and 21090343) and the
Fundamental Research Funds for the Central Universities
(DUT12ZD211 and DUT13LK06) for nancial support.
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