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Effect of Ce doping on the magnetic and optical properties of ZnO by the first principle
Accepted Manuscript Review Articles Effect of Ce doping on the magnetic and optical properties of ZnO by the first principle X.F. Jia, Q.Y. Hou, Z.C. Xu, L.F. Qu PII: DOI: Reference:
S0304-8853(18)30463-3 https://doi.org/10.1016/j.jmmm.2018.05.037 MAGMA 63949
To appear in:
Journal of Magnetism and Magnetic Materials
Received Date: Revised Date: Accepted Date:
20 February 2018 1 May 2018 14 May 2018
Please cite this article as: X.F. Jia, Q.Y. Hou, Z.C. Xu, L.F. Qu, Effect of Ce doping on the magnetic and optical properties of ZnO by the first principle, Journal of Magnetism and Magnetic Materials (2018), doi: https://doi.org/ 10.1016/j.jmmm.2018.05.037
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Effect of Ce doping on the magnetic and optical properties of ZnO by the first principle X. F. Jia a, Q. Y. Hou a,b,* , Z. C. Xu a, L. F. Qua a
b
College of Science, Inner Mongolia University of Technology, Hohhot 010051,China
Key Laboratory of Thin Films and Coatings of Inner Mongolia, Hohhot 010051, China * Corresponding author. Email:[email protected]. Abstract
The absorption spectrum and the magnetic mechanism of Ce-doped ZnO are controversial. To address these issues, we investigated the effects of Ce doping on the magnetic and optical properties of ZnO using geometry optimization and energy calculation based on the first-principle generalized gradient approximation +U (GGA+U) method of density functional theory. First, the undoped ZnO and Ce-mono-doped ZnO supercell models were calculated. Within a limited doping amount in range 3.13–6.25 mol%, higher Ce doping amount results were observed in terms of higher doping system volume, higher formation energy, and lower system stability. Compared with the band gap of pure ZnO, the band gap of each doping system narrowed, and the absorption spectrum showed red-shift. High Ce doping amount led to weak narrowing of the band gap and weak red-shift in the absorption spectrum. The ferromagnetism of the mono-doped systems increased with increasing Ce doping concentration and was mainly attributed to the hybrid coupling effect of the Ce-4f, Ce-5d, and O-2p states. Second, four Zn30Ce2O32 supercell models with the same doping concentration and different spatial arrangements were calculated. A
relatively stable antiferromagnetic state was observed when -Ce-O-Ce- was doped along the a-axis bonding of the Ce double-doped ZnO system, whereas favorable ferromagnetic state was found when -Ce-O-Ce- was doped along the deflection of the c-axis. The Curie temperature of doping system can be higher than room temperature. Keywords: First principle; Ce doped ZnO; Room temperature ferromagnetism; Absorption spectrum.
1. Introduction The direct band gap of pure ZnO is 3.40 eV [1], and its exciton binding energy is 60 meV at room temperature
[2]
. Pure ZnO does not only exhibit excellent physical
and chemical properties but is also characterized by its rich raw materials, low cost, and environmental friendliness. Given that pure ZnO can achieve ferromagnetism (FM) at room temperature, ZnO-based diluted magnetic semiconductor (DMS) has attracted considerable attention. Doping different elements into the ZnO crystal can alter and enhance its properties to achieve better performance. Metals (e.g., Cr, Mn, Fe, Cu, Al, Ga, In, and Ag) have been doped into the ZnO crystal to adjust the width of its band gap and form a dilute magnetic semiconductor, which has important applications in high-density non-volatile memory, spin quantum computer, and magnetic sensor fields
[3-8]
.
Compared with transition metal elements, rare-earth (RE) atoms have very special electronic structures. Their valence electrons are located in the 4f orbit, which is surrounded by filled 5s and 5p orbits. Temperature and crystal field have very little impact on the transition of 4f electrons because of the shield effect of the 5s and 5p orbits. Consequently, RE optical transition is very stable even in strong electric fields [9]. The effects of RE doping on the magnetic and optical properties of ZnO
have been investigated, and related studies have yielded interesting results [10–13]. In
transition-metal-doped
oxides,
room-temperature
ferromagnetism
or
antiferromagnetism may be attributed to the precipitation of a magnetic cluster or a secondary magnetic phase. However, these extrinsic magnetic behaviors are undesirable in practical applications. The lack of evidence of excess composite metal oxide (such as CeO2 and Ce2O3) in the Ce-doped ZnO
[14]
ruled out the presence of
any secondary phase. Therefore, Ce is one of the most ideal doping elements, which are used to avoid the effect of secondary phase on the source of ferromagnetism in ZnO dilute magnetic semiconductors. Ce-doped ZnO thin films obtained through various preparation methods have been experimentally evaluated, and excellent magnetic and optoelectronic properties have been observed. In previous studies, the effects of Ce doping on the optical and electrical properties of ZnO were investigated using hydrothermal, sol-gel, and chemical solution
[15-17]
. Compared with undoped ZnO, Ce doping increased the
volume of the ZnO system, narrow band gap, and red-shift of the absorption spectrum. In addition, enhanced ionic behavior in Ce-doped ZnO resulted in a significant increase in dielectric constant, piezoelectric coefficient, and ferroelectric properties. Sharma et al.
[18]
studied the effect of Ce doping on the structural, optical, and
magnetic properties of ZnO by chemical precipitation method. Ce doping leads to a narrow band gap and to the red-shift of the absorption spectrum. Moreover, a study on the
magnetization
of
Ce-doped
ZnO
nanoparticles
exhibited
outstanding
ferromagnetic (FM) property at room temperature. This characteristic may have been
caused by a new coupling mechanism via intra-ion 4f-5d swap over interaction, which is followed by inter-ion 5d-5d coupling mediated through charge carriers. The magnetic and electronic properties of Ce-doped ZnO have been theoretically explored. Zhang et al. [19] predicted the electronic structure and magnetic properties of ZnO doped with RE elements. La doping can lead to a diamagnetic ground state. The doping of La and Ce is more stable than that of Pr, ND, and Eu. The total magnetic moment of Ce-single-doped ZnO is 0.92 B . Hachimi et al.
[20]
predicted the
electronic structure and magnetic properties of ZnO doped with RE elements by electron spin polarization all-electron linearly interpolated plane wave method. The La-doped ZnO was a nonmagnetic system, whereas the Ce, Eu, and other doped ZnO belonged to a magnetic system; the total magnetic moments originated from the RE 4f states spin-polarized states. Tan et al.
[21]
investigated the structural, electronic, and
magnetic properties of RE-metal-doped ZnO through first-principle calculations. The Y-doped ZnO has almost no spin polarization, but Ce-, Eu-, Gd-, and Dy-doped ZnO systems have magnetic properties. The localized f states of RE atoms respond to the introduction of a magnetic moment. Although the magnetic and optical properties of the Ce-doped ZnO system have been demonstrated, the exact systematic mechanism of intrinsic ferromagnetism in a Ce-doped ZnO system remains unclear. The effect of Ce doping on the optical properties of ZnO has been studied using the sol–gel method in a previous study [22], and Ce doping leads to the broadening of ZnO band gap and blue-shift of the absorption spectrum. The blue-shift is contrary to the result from the experimentally
determined absorption spectrum in another study [23]. Experimental study on magnetism showed that the Ce-doped ZnO system is ferromagnetic, and the magnetic properties of Ce-doped system have been predicted to be caused by a new coupling mechanism via intra-ion 4f-5d swap over interaction
[18]
. However, this finding has
not been verified. The result from a theoretical study on the magnetic source of Ce-doped ZnO system is also controversial. In this theoretical study [21], the localized f states of RE atoms respond to the introduction of a magnetic moment, which is inconsistent with the theory of Zener
[24]
RKKY interaction. To validate the
absorption spectrum distribution and the magnetic mechanism of Ce-doped ZnO systems, we examined the effect of Ce doping on the magnetic and optical properties of ZnO systems by performing first-principle generalized gradient approximation +U (GGA+U) calculations. The absorption spectrum is red-shifted for Ce-mono-doped systems, and the double-doped systems possess high Curie temperature and achieve ferromagnetism at above room temperature. Therefore, Ce-double-doped ZnO can be practically used as an unambiguous diluted magnetic semiconductor. 2. Theoretical models and calculation method 2.1 Theoretical models Undoped ZnO has a hexagonal wurtzite structure with a space group P63mc and C64 symmetry. The ZnO cell is composed of two lattices with hexagonal close-packed
structure along the c axis. The lattice constant is a = b = 0.3249 nm, c = 0.5205 nm. An experimental study [25] showed that no phase change occurs in the Ce-doped ZnO structure at a doping concentration of 10 mol%. Therefore, the doping concentration
of all systems used in the present study was in the range of 0–6.25 mol% to ensure the hexagonal wurtzite structure of all doped systems. To investigate the effect of Ce doping on the crystal structure, stability, optical properties, electronic structure, and magnetic properties of ZnO system, we constructed 1×1×1 undoped hexagonal wurtzite ZnO model and 2×2×4, 2×2×3, and 2×2×2 Ce-mono-doped hexagonal wurtzite ZnO models. These models are shown in Figs. 1(a)–(d). No polarity along the a-axis in the ZnO system was observed, but the direction along the c-axis is polar, as reported in the literature [26]. Thus, the different spatial arrangements of Ce-Ce had diverse effects on the magnetic properties of the system. Four kinds of (2×2×4) Zn30Ce2O32 supercells with different spatial arrangements of Ce–Ce were explored to study the effect of Ce doping with the substitution of two Zn atoms by Ce atoms on the magnetic properties of ZnO and evaluate whether the Ce-double-doped ZnO system is ferromagnetic (FM) or antiferromagnetic (AFM) [Figs. 1(e)-(h)]. If all the atoms spin up, the doped system demonstrated ferromagnetism. However, antiferromagnetism was demonstrated when half of the atoms spin up and the other half spin down.
Fig.1. Models: (a) pure ZnO; (b) single-doped Zn0.9687Ce0.0313O; (c) single-doped Zn0.9583Ce0.0417O; (d) single-doped Zn0.9375Ce0.0625O; (e)-(h) four configurations of double-doped Zn30Ce2O32.
2.2 Calculation method All density functional theory (DFT) calculations in the present work were performed on CASTEP (MS8.0) code based on the plane–wave pseudopotential method. The first-principle-generalized gradient approximation + U (GGA+U) method
with
the
Perdew–Burke–Ernzerhof
(PBE)
was
used
as
the
exchange-correlation function. Geometric optimization and energy calculations were conducted for all the models, and the electrons were spin polarized in the energy calculation. Geometric optimization was first achieved using the convergence thresholds of 1.0 × 10−5 eV per atom for total energy, 0.3 eV/nm for maximum force, 0.05 GPa for pressure, and 2.0×10−4 nm for maximum displacement. The self-consistent calculations were performed with a total tolerance of less than 1 × 10−6 eV per atom. The k points of the Brillouin zones of Zn0.9687Ce0.0313O, Zn0.9583Ce0.0417O, and Zn0.9375Ce0.0625O supercells were at 4×4×2. Lattice parameters and atomic coordinates were relaxed using the cutoff energy of 370 eV. Valence electron configurations for constructing pseudo-potential were Zn3d104s2, Ce4f15s25p65d16s2,
and O2s22p4. By using atomic orbitals and searching for and attaining the absolute minima of the occupied energies (i.e., the ground state), DFT calculations yielded results consistent with the experimental findings
[27]
. On the basis of DFT, the method of
GGA+U accurately calculated the electronic structures and magnetic properties of the system under the condition of electron spin polarization
[28]
. In this paper, GGA + U
method was used in the calculations. After several attempts, the U values of Zn-3d and O-2p in the undoped ZnO cells were set as 10.00 and 7.00 eV, respectively
[29]
.
The calculated band gap was based on the experimental value of 3.40 eV [30]. The U of Ce-4f was set to 6.00 eV [9], which is consistent with the MS software default value. 3. Results and discussion 3.1 Crystal structure, stability, and formation energy analysis The geometric structures of the Zn1-xCexO (x=0, 0.0313, 0.0417, 0.0625) models are optimized. The resulting equivalent lattice parameters, volumes, total energies, and formation energies are listed in Table 1. The lattice parameter and volume of the doped system increased with the increasing amount of Ce dopant. Mulliken method was used in this study to calculate the orbital charges. In the supercell Zn1-xCexO (x=0, 0.0313, 0.0417, and 0.0625) of the doped systems, the sum of the charge transfer on the f-state orbit and d-state orbit of the Ce atom in the valence-electron configuration Ce4f15s25p65d16s2 approaches +3. The valence of Ce doped in ZnO was +3, and Ce existed in the form of Ce3+. These results were consistent with the experimental results in the literature [31]. Quantum chemical theory states that given that the ionic
radius of Ce3+ (0.103 nm) is remarkably larger than that of Zn2+ (0.074 nm), replacing Zn2+ with Ce3+ can increase the volume of the unit cell. In this study, substitution impurity increased the repulsive interaction of the excess positive charges of the Ce3+ ion. Consequently, increasing the Ce dopant led to increased doped system volume. This result agreed with the experimental results obtained in a previous study [32]. Formation energy is a physical variable that indicates the stability of a doped system and the degree of difficulty of atomic doping. Formation energies are calculated based on the total energy of the optimized Ce–Ce distance crystal structures and chemical potentials of different doping atoms. The impurity formation energy (Ef) is defined as follows [33]:
E f EZnO:Ce EZnO nZn Zn nCe Ce ,
(1)
In Equation (1), EZnO:Ce is the total energy of the Ce-doped system, EZnO is the total energy of the undoped ZnO supercell system with the same size as the doped system, and coefficient nCe is the number of Ce atoms doped in the supercells of ZnO. nZn represents the number of Zn atoms substituted by impurity atoms. Zn and Ce are the chemical potentials of Zn and Ce, respectively, that is, the chemical potentials for the total energy of the atoms used to replace Ce and Zn. Chemical potentials depend on experimental conditions for material preparation. To determine
Zn and O , we must calculate Zn + O = EZnO in ZnO under thermal equilibrium conditions and in o 1 Eo2 , Zn Zn (bulk ) . During the sample preparation, 2
o 1 2 Eo under O-rich and Zn Zn (bulk ) under Zn-rich were calculated. Other 2
chemical potentials can be deduced from the thermal equilibrium relation. For instance, Zn ZnO (bulk ) 1 Eo2 under O-rich, and o EZnO (bulk ) EZn (bulk ) 2
under Zn-rich, where EZnO (bulk ) , EZn (bulk ) , and EO2 are the total energies of block ZnO, Zn, and O molecules, respectively. The calculated results of the formation energy of doped systems under O-rich or Zn-rich condition are shown in Table 1. The formation energy under O-rich condition was smaller than that under Zn-rich condition in the same doped system. Thus, stability was enhanced under O-rich conditions and can be used as a criterion for selecting the experimental conditions for material preparation. The calculated results indicated that increased doping content increased the formation energy of the Ce-doped system and reduced the stability. Table 1. The lattice parameters and formation energies of all systems after geometry optimized. a, c /nm
Model This paper ZnO (Unit cell)
a=0.3289 c=0.5308
Zn0.9687Ce0.0313O
a=0.3315 c=0.5344
Zn0.9583Ce0.0417O
a=0.3328 c=0.5346
Zn0.9375Ce0.0625O
a=0.3338 c=0.5364
Ef /eV
V /nm3
Experiment
O-rich
Zn-rich
0.04973
-
-
0.05083
-5.89
-2.42
0.05125
-4.87
-1.40
0.05170
-3.51
-0.04
[32]
a=3.251 c=5.211[32]
a=0.3264[32] c=0.5222[32]
3.2 Analysis on Degeneration As reported in Ref. [34], the critical doping content for the Mott phase change of a ZnO semiconductor (the doped system is half-metallized, that is, degenerated) should be determined by using the following equation: 1
aH Nc 3 0.2
(2)
where aH is the Bohr radius of undoped ZnO with the value of 2.03 nm[34] and N c is the doping content for the Mott phase change. Substituting the known data in
Equation (2), we obtain N c = 9.56 × 1017 cm−3. In this article, the doping content of supercells Zn0.9687Ce0.0313O, Zn0.9583Ce0.0417O, and Zn0.9375Ce0.0625O were set as N1 ,
N 2 , and N 3 , respectively. The calculated results showed that N1 = 1.23 × 1021 cm-3, N 2 = 1.63 × 1021 cm-3, and N 3 = 2.42 × 1021 cm-3, which were higher than N c . The doping content of the ionized impurity exceeded the critical doping content for the Mott phase change of semiconductor ZnO, which extremely matched the conditions of degeneration. This finding can be further proven in the later density of state and band structure. 3.3 Analysis of the electronic structure of Ce-mono-doped ZnO systems The energy band structures of undoped and doped ZnO along with high symmetry directions in the Brillouin zone were calculated using the GGA+U method, and the results are plotted in Fig. 2. Fermi level (shown by a dashed line in Fig. 2) was set to zero in the energy level, which was determined by MS software performance characteristics. Figs. 3 and 4 show the same. The calculated band gap of the undoped ZnO is 3.40 eV fitted well with the experimental value
[30]
. The band gaps of the
doped systems were 2.98, 3.12, and 3.19 eV. Compared with the undoped ZnO, the band gap of each doped system narrowed. As the amount of Ce dopant in the range of 0-0.0625 mol increased, the narrowing of the band gap weakened, which was consistent with the reported trend [32]. The spatial scale and temperature of the system were the reason that the system band gap was slightly different from that reported in the literature [35], but the trend of change was not affected.
8
8
(a)
(b)
4
4
3.40eV
2.98eV
Energy/eV
0
-4
0
G
F
Q
8
-4
Z G G
F Q
ZG
F Q
Z G
8
(c)
(d)
4
4
3.12eV
3.19eV
0
0
-4
-4
G
FQ
Z G G
Fig. 2. Band structures: (a) ZnO; (b) Zn0.9687Ce0.0313O; (c) Zn0.9583Ce0.0417O; (d) Zn0.9375Ce0.0625O.
The calculated total density of states of undoped ZnO and Zn1-xCexO (x=0, 0.0313, 0.0417, 0.0625) systems is shown in Fig. 3. The positions of valence band maximum of all doped systems were almost unchanged. Thus, the trend of the band gap was mainly determined by the position of the conduction band minimum. Compared with undoped ZnO, the position of the conduction band minimum of each doped system decreased. High molar amount of the Ce dopant led to a weak decrease in the conduction band minimum. This result was consistent with the band structure
analysis. Therefore, the band gap of a doped system mechanism shall be studied using the partial density of states (PDOS). 100 80
ZnO Zn0.9687Ce0.0313O Zn0.9583Ce0.0417O Zn0.9375Ce0.0625O
TDOS(electrons/eV)
60 40 20 0 -20 -40 -60 -80 -100 -10
-5
0
5
10
15
20
25
30
Energy(eV) Fig. 3. Spin total density of states in undoped ZnO and doped systems.
The PDOS of undoped ZnO and Zn1-xCexO (x=0, 0.0313, 0.0417, 0.0625) systems are shown in Fig. 4. Given the PDOS of undoped ZnO in Fig. 4(a), the valence band mainly consisted of O-2p and Zn-3d states, with limited contribution from Zn-3p and Zn-4s states. The hybridization of the O-2p and Zn-3d states, which occupied the upper and lower parts of the valence band, formed the bonding states in this energy region. The conduction band of ZnO was mainly composed of Zn-3p, Zn-4s, and O-2p states, with limited contribution from Zn-3d. Hence, the antibonding states in the conduction band of ZnO comprised Zn-4s, Zn-3p, and O-2p. The conduction band minimum was determined by the Zn-4s state. For convenience, an enlarged view is provided below Fig. 4(a), and the following Figs. 4(b)-(d) are similar. In Figs. 4(b)-(d), the impurity level appeared in the conduction band of the doped
systems, mainly because the incorporation of Ce atoms caused the systems to undergo hybrid coupling of Ce-4f and Ce-5d orbits. The conduction band in the doped system mainly involved the hybrid coupling of Zn-4s, O-2p, Zn-3p, Ce-4f, and Ce-5d orbits to form antibonding states. The strength of the antibonding states can be quantitatively analyzed by the number of quantum states of the Zn-4s, O-2p, Zn-3p, Ce-4f, and Ce-5d states in the conduction band in Figs. 4. 1.0
1.0
(a)
(b)
Zn-4s Zn-3p Zn-3d O-2p
0.5
0.5
0.0
0.0
Zn-4s Zn-3p Zn-3d O-2p Ce-4f Ce-5d
0.05 0.10
-0.5
-0.5
0.05
0.00
PDOS(electrons/eV)
0.00
-0.05
-0.05
-1.0
2
-5
4
0
-0.10
6
5
10
15
20
25
1.0
-1.0 -6
-4
-2
0
4
6
4
6
8
10
8
10
1.0
(c)
(d)
Zn-4s Zn-3p Zn-3d O-2p Ce-4f Ce-5d
0.5
Zn-4s Zn-3p Zn-3d O-2p Ce-4f Ce-5d
0.5
0.0
0.0
0.10
0.10
0.05
-0.5
0.05
-0.5 0.00
0.00
-0.05
-0.10
-1.0 -6
2
2
-4
-2
0
-0.05
2
4
6
2
4
6
-0.10
8
-1.0 -6 10
-4
-2
0
2
4
6
2
4
6
Energy(eV) Fig. 4. Spin partial density of states: (a) ZnO; (b) Zn0.9687Ce0.0313O; (c) Zn0.9583Ce0.0417O; (d) Zn0.9375Ce0.0625O.
The enhancement of the antibonding states led to the conduction band to move to a higher energy level, whereas the weakening of these states led to the conduction band to move toward a low energy level. Integral operations for the density of the states of the undoped ZnO cells and Zn1-xCexO (x=0, 0.0313, 0.0417, 0.0625) were performed using Origin 8.0. Then, the superposition operation was performed to obtain the total number of quantum states. Fig. 4(a) shows that integral operations for the Zn-4s, Zn-3p, and O-2p orbits were performed within the energy range of the conduction band to obtain the number of quantum states of each orbit, and then the superposition operation total quantum number was 9. Similarly, Figs. 4 (b)-(d) show that integral operations for the Zn-4s, Zn-3p, O-2p, Ce-4f, and Ce-5d orbits of Zn1-xCexO (x=0, 0.0313, 0.0417, 0.0625) systems were performed within the energy range of the conduction band to obtain the number of quantum states of each orbit. The superposition operation total quantum numbers of the three systems are 5, 7, and 8. Compared with the undoped ZnO, the number of total quantum states within the energy range of the conduction band of all doped systems was smaller than that of the undoped ZnO. Therefore, the conduction band minimum of doped systems moved toward the low energy level. For the Zn1-xCexO (x=0, 0.0313, 0.0417, 0.0625) systems, with increasing Ce dopant, the total number of quantum states within the energy range of the conduction band of the doped system increased; the hybrid coupling strength of the antibonding states was enhanced. The movement of the conduction band minimum of doped systems toward the low energy level was weakened. Compared with the undoped ZnO, the band gaps of the doped systems narrowed; high molar
amount of Ce dopant led to weaker narrowing of band gap. 3.4 Analysis of the absorption spectrum of Ce-mono-doped ZnO systems The optical properties of the medium can be described by the complex dielectric response function
() 1 () i 2 ()
in the linear response range, where
1 () n()2 k ()2 and 2 () 2n()k () , n( ) are the refractive indexes and k ( )
is the extinction coefficient. The real part 1 ( ) and imaginary part 2 ( ) can be calculated on the basis of the Kramers–Kronig dispersion relation. Absorption coefficient ( ) can be obtained if 1 ( ) , 2 ( ) , n( ) , and k ( ) were used to describe the optical properties of the crystal. The concerned equations are expressed as follows:
2 ( )
C
2
V,C
BZ
2 (2 )
1 ( ) 1
2
M CV (k ) ( ECk EVk )d 3 k , 2
3
0
0
(3)
' 2 ( ) d , '2 2
(4) 1
2 2 , （）= 2 （ +（ -1 ） 1 ） 2 ）（
2
(5)
where subscripts C and V represent the conduction and valence bands, respectively. k is the reciprocal lattice vector. BZ is the first Brillouin zone. MCV (k )
2
is the
momentum matrix element. c is a constant. ω is the angular frequency. ECk and
EVk
are the intrinsic energy levels. ' and are the angular frequencies of the initial and final states, respectively. 0 is the polarization response. The above equations provide a theoretical foundation for absorption spectrum analysis. Absorption of radiation by matter is the process in which the energy of a photon is absorbed by matter via electrons or atoms. The calculated absorption spectra of
undoped ZnO and Zn1-xCexO (x=0, 0.0313, 0.0417, 0.0625) supercells are shown in Fig. 5. First, in the range of 50–185 nm of the short UV light region, the absorption spectrum of the undoped ZnO exhibited a strong intrinsic absorption peak near 86 nm. The absorption spectra of all the Ce-doped ZnO showed a characteristic absorption peak near 135 nm because after the Ce-5d state coupling with O-2p. The transition to Zn-4s at the conduction band minimum led to a strong transition absorption peak. Compared with undoped ZnO, the absorption peak of the doping system moved to the long wavelength direction, and the absorption intensity weakened. With increasing Ce doping concentration, the value of the absorption peak gradually increased, and the absorption peak position moved in the short wavelength direction. Second, in the range of 185–420 nm of the long UV light region, the absorption intensity of the doping system was obviously enhanced. A strong absorption peak appeared near 227 nm because of the Ce-4f state Zn-4s transition at the conduction band minimum formed a strong transition absorption peak. In general, compared with undoped ZnO, the absorption spectra of each doped system exhibited a red shift. High molar amount of the Ce dopant in the range of 0–6.25 mol% led to a weak red-shift. The calculated results of the absorption spectra were in accordance with the experimental results in the previous study [23]. In addition to the difference of Ce doping amount, the spatial scale and temperature of the system also differed between this paper and the experiment. Therefore, deviation from the absorption spectrum in the experiment was normal [35, 36]. This finding may be used as a theoretical guide for preparing Ce-doped ZnO optics, which could red-shift in the long UV light region.
In previous experiments [22] and [23], the absorption spectrum distribution of ZnO was investigated in the range of similar Ce doping concentrations, and the experimental results were contradictory. In literature [22], the Ce-doped ZnO system adopted a 200 nm film thickness, which far exceeded the range defined by the nanoscale level (1–100 nm). Thus, the doping system mainly manifested a macroscale effect. However, in a previous study [23], the thickness of Ce-doped ZnO film was about 50 nm, which was at a nanoscale level. Hence, the quantum effect was obvious in the doping system. Therefore, under the same doping amount, the absorption spectrum distributions of their doping systems were contradictory mainly because of the differences in film thickness. In this paper, the lattice constants in the c-axis direction of the Zn0.9722Ce0.0278O, Zn0.9583Ce0.0417O, and Zn0.9583Ce0.0625O supercells were in the range of 1.06–2.12 nm. The quantum effect of the doping system was more significant. The absorption spectral distribution in this paper agreed with previous experimental results [23]. This result was achieved because the doping systems applied similar scales and achieved similar quantum effects. In summary, besides limiting the Ce doping amount, a Ce-doped ZnO photocatalyst with a red-shifted absorption spectrum can be attained by restricting the doping system’s dimensions to a small nanoscale range.
400000 350000
ZnO Zn0.9687Ce0.0313O Zn0.9583Ce0.0417O
-1
Absorption(cm )
300000
Zn0.9375Ce0.0625O
250000 200000 150000 100000 50000 0 0
50
100
150
200
250
300
350
400
Wavelength(nm)
Fig.5. Absorption spectra of the pure and doped ZnO.
3.5 Analysis of the magnetic properties of Ce-mono-doped ZnO systems The total magnetic moments of the Ce-doped ZnO system were calculated to investigate the magnetic properties of Ce-doped ZnO. The total magnetic moments of Zn1-xCexO (x=0, 0.0313, 0.0417, 0.0625) were 0.965, 1.013, and 1.014 B ( B is Bohr magneton). The magnetic moment of Ce-mono-doped ZnO systems increased with increasing Ce doping concentration, which was consistent with a change trend in the experimental results in a previous study [38] on Eu-doped ZnO at similar concentrations. The intrinsic magnetic moments of Ce atoms were 1.00, 1.02, and 1.03 B . The spin polarized magnetic moments of the unpaired 2p state of O atoms nearest the Ce atom were -0.02, -0.01, and -0.01 B , whereas the spin polarized magnetic moment of the O-2p state next nearest to the Ce atom was almost zero. Thus, the magnetic properties of the doped systems were mainly derived from the
contribution of Ce and O atoms. The magnetic moment of the Ce-doped ZnO system with Ce dopant concentration in the range of 0–6.25 mol% was very close to integer 1, which was an important feature of ferromagnetism for the doped system according to experimental results in the previous study [39]. According to Goodenough–Kanamori rules, FM ordering prevails among Ce ions because the 4f electrons of Ce ions are less than half-filled
[40, 41]
. Therefore, in the present work, doped systems exhibited FM
behavior that would be analyzed in detail in the analysis of the magnetic properties of Ce-double-doped ZnO systems. 3.6 Analysis on the magnetic properties of Ce-double-doped ZnO systems The unipolar structure of ZnO was the reason that different spatial-ordered occupations have a significant effect on the FM or AFM of Ce-doped ZnO systems. For the Ce-double-doped ZnO systems in Figs. 1 (e)-(h), we constructed four different spatial-ordered occupancy models at the same doping concentration. The results of Ce-Ce distance, total energies of AFM and FM, E EAFM EFM , and total magnetic moment are shown in Table 2. We used the energy difference between FM and AFM ordering, E EAFM EFM , as an indicator of magnetic stability. A positive ΔE implies that the system is FM, and a negative ΔE was obtained for AFM [42]. Table 2. Spacing of Ce-Ce, total energies of AFM and FM, difference of total energies, total magnetic moments and formation energy for double-doped Zn30Ce2O32 EFM
EAFM
E
(eV)
(eV)
(meV)
e
-67372.756
-67372.717
39
f
-67385.174
-67385.320
-146
Models
（nm）
Total magnetic moments ( B )
FM
0.3208
AFM
0.3249
Type
dCeCe
Ef /eV O-rich
Zn-rich
2.00413
-5.09
1.85
0
-5.19
1.71
g
-67372.744
-67372.692
52
FM
0.6136
2.00275
-5.37
1.57
h
-67372.725
-67372.657
68
FM
0.8030
2.00183
-5.41
1.53
In Table 2, the smallest Ce–Ce distance is found in the model in Fig. 1(e), and the AFM–FM energy difference was 39 meV, thereby indicating that the system was FM. The total magnetic moment was 2.00413 B . The AFM-FM energy difference in Fig. 1(f) was -146 meV, thereby indicating a favorable antiferromagnetism. The total magnetic moment was 0 B . The results confirmed that magnetic moment quenching occurred in the doped system. The AFM-FM energy difference values in Figs. 1 (g) and (h) are 52 and 68 meV, respectively, with increased Ce–Ce distance. The Ce-double-doped ZnO models display advantageous ferromagnetic coupling. The total magnetic moments of the models in Figs. 1 (g) and (h) are 2.00175 and 2.00283 B , respectively. When the -Ce-O-Ce- for the Ce-double-doped system in Fig. 1 (f) formed a bond along the a-axis, magnetic moment quenching occurred in the doped system. This result may have been caused by the nonpolar structure of ZnO along the a-axis. When the -Ce-O-Ce- for the Ce-double doped system in Figs. 1 (e), (g), and (h) formed a bond along the approaching c-axis, systems showed ferromagnetism and had a certain magnetic moment. The Ce–Ce distance increased, and the magnetic moment of the doped system decreased. When the -Ce-O-Ce- formed a bond along the approaching c-axis, the magnetic moment of the Ce-double-doped ZnO system increased to nearly twice as much as that of the Ce-mono-doped ZnO system under the same doping
amount. The magnetic moment was contributed by the spin magnetic moment and the orbital magnetic moment, in which the contribution of the track magnetic moment to the total magnetic moment was small and almost negligible. The incorporation of two Ce atoms was the reason that the number of spin electrons in the Zn30Ce2O32 system was twice that of the Ce-mono-doped system, thereby resulting in an increase in the total magnetic moment to nearly twice. This result may be used as a guide in the design and preparation of new dilute magnetic semiconductors. The formation energies of Ce-double-doped ZnO systems were calculated using Equation (1) to compare the stability and degree of doping difficulty of Ce-double-doped ZnO systems with different Ce–Ce distances. The results are shown in Table 2. The calculated results indicated that greater Ce-Ce distance led to lower formation energy of the Ce-double-doped ZnO and to higher stability. The formation under O-rich conditions was smaller than that under Zn-rich conditions in the same doped system. From the total energy difference E between AFM and FM, realistic estimations of Curie temperature were achieved by mapping on the classical Heisenberg model in the mean-field approximation
[43]
. The classical Heisenberg
model assumed in our analysis is given by the following:
H ij J ij Si S j
(6)
i j
where Si is the unit vector parallel to the local moment at site i and J ij is the exchange coupling constant between the local moments at sites i and j . We can calculate the total energy difference E H as follows:
E H S 2C 2 J n 0
(7)
n0
where C is the amount of the magnetic ions and n sums over all sites of the cation sublattice. E H was directly identified with the energy difference E and was also calculated from the first principles, because CPA also represented a mean-field theory. Meanwhile, within the mean-field theory of the Heisenberg model, we estimated TC by using the Brillouin function expression, which is known as the molecular field theory. The Brillouin function is expressed as follows:
kBTC
2 2 S C J n0 3 n0
(8)
where k B is the Boltzmann constant. Following (7) and (8), the TC can be obtained from first principles: kBTc 2E
3C
(9)
where TC is the estimated Curie temperature of the DMS. From Equation (9), TC is proportional to E . As reported in the previous study [42], the total energy difference E between AFM and FM is approximately equal to the thermodynamic energy kBT;
thus, the ΔE is about 30 meV at T = 300 K. In this paper, E of the models in Figs. 1 (e), (g), and (h) were 39, 52, and 68 meV, respectively, which were greater than 30 meV. Thus, the Ce-double-doped ZnO achieved ferromagnetism at above room temperature. Curie temperatures of the models in Figs. 1 (e), (g), and (h) were estimated using Equation (9); the approximated temperatures were 390 K, 520 K, and 680 K, respectively. The Ce-double-doped systems possessed high Curie temperature and achieved long-term ferromagnetism above room temperature. This result was consistent with the experimental results, in which the doped system has demonstrated
ferromagnetism at room temperature [44]. This characteristic is essential for the design and preparation of new DMS functional materials. 3.7 Analysis of the magnetic mechanism of Ce-mono-doped ZnO systems The net spin density distribution of Ce-doped ZnO system was calculated to illustrate the magnetic mechanism of Ce mono-doped ZnO system. The blue area in Fig. 6 is the spin net magnetic moment of the models. The net magnetic moments of the doped system were mainly contributed by the spin polarization of Ce and O atoms. Combined with the spin PDOS in Fig. 4, Figs. 4 (b)-(d) show that the spin and unspin PDOS of the Ce-4f, Ce-5d, and O-2p orbits were asymmetric. The asymmetry of spin and unspin PDOS of Ce-4f and Ce-5d orbits induced polarization of the spin electrons of O-2p orbit in the conduction band, which resulted in the asymmetry of the spin and unspin total density of states. The doped systems produced the net magnetic moment and exhibited ferromagnetism. This phenomenon was consistent with the analysis of the magnetic moment. The total magnetic moment was generated by the hybrid coupling between the Ce and O atoms, and the Zn atoms showed almost no effect. The magnetic properties of the doped systems were mainly caused by the hybrid coupling of Ce-4f, Ce-5d, and O-2p orbits. This phenomenon was consistent with the Zener [24] RKKY theory. However, speculation on the magnetic source of Ce-doped ZnO system in the experiment in the previous study [18] was insufficient. In a theoretical study [21], the Ce-4f state was considered as the magnetic source of the Ce-doped ZnO system, because the hybrid coupling between the Ce and O atoms was neglected, thereby resulting in an
insufficient understanding of the magnetic mechanism.
Fig. 6. Net spin density distribution: (a) Zn0.9687Ce0.0313O; (b) Zn0.9583Ce0.0417O; (c) Zn0.9375Ce0.0625O.
4. Conclusion In this study, the magnetic and optical properties of Ce-mono-doped ZnO and the magnetic properties of Ce-double-doped ZnO were investigated via plane-wave super-soft pseudo-potential method based on density functional theory. The following conclusions are drawn: (1) Increased doping content led to higher formation energy of the Ce-doped system and lower stability. In addition, the formation energy under O-rich condition was smaller than under Zn-rich condition in the same doped system. The stability under O-rich condition was enhanced. (2) Compared with the band gap of pure ZnO, the band gap of each doped system became narrow, and the absorption spectrum showed a red-shift. High molar amount of Ce dopant in the range of 0–6.25 mol% led to weak narrowing of
band gap and weak red-shift in absorption spectrum. (3) The magnetism of Ce-mono-doped ZnO was mainly attributed to the hybrid coupling effect of Ce-4f, Ce-5d, and O-2p states. The calculated magnetic moments of mono-doped systems reached 0.965, 1.012, and 1.014 B .The ferromagnetism of mono-doped systems increased with increasing Ce doping concentration. (4) For Ce-double-doped ZnO systems, a relatively stable AFM state was observed when -Ce-O-Ce- was doped along the a-axis bonding of the Ce double-doped ZnO system, whereas a favorable FM state was found when -Ce-O-Ce- was doped along the deflection of the c-axis. The double-doped systems possessed high Curie temperature and achieved ferromagnetism above room temperature. In addition, the magnetic moment of the Ce-double-doped ZnO system increased to nearly twice as much as that of the Ce-mono-doped ZnO system under the same doping amount. Acknowledgment This work was supported by the National Natural Science Foundation of China (Grant Nos. 61366008, 61664007). References [1]
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Highlights
Band structure and density of states were calculated based on DFT with GGA+U.
By increasing the Ce doping amount, absorption spectra exhibit red-shift。
Four possible magnetic coupling configurations for Zn14Ce2O16 are calculated.
the Curie temperature of doping system can reach a temperature higher than room temperature.
The ferromagnetism was mainly attributed to the hybrid coupling effect of the Ce-4f, Ce-5d, and O-2p states.
S0304-8853(18)30463-3 https://doi.org/10.1016/j.jmmm.2018.05.037 MAGMA 63949
To appear in:
Journal of Magnetism and Magnetic Materials
Received Date: Revised Date: Accepted Date:
20 February 2018 1 May 2018 14 May 2018
Please cite this article as: X.F. Jia, Q.Y. Hou, Z.C. Xu, L.F. Qu, Effect of Ce doping on the magnetic and optical properties of ZnO by the first principle, Journal of Magnetism and Magnetic Materials (2018), doi: https://doi.org/ 10.1016/j.jmmm.2018.05.037
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Effect of Ce doping on the magnetic and optical properties of ZnO by the first principle X. F. Jia a, Q. Y. Hou a,b,* , Z. C. Xu a, L. F. Qua a
b
College of Science, Inner Mongolia University of Technology, Hohhot 010051,China
Key Laboratory of Thin Films and Coatings of Inner Mongolia, Hohhot 010051, China * Corresponding author. Email:[email protected]. Abstract
The absorption spectrum and the magnetic mechanism of Ce-doped ZnO are controversial. To address these issues, we investigated the effects of Ce doping on the magnetic and optical properties of ZnO using geometry optimization and energy calculation based on the first-principle generalized gradient approximation +U (GGA+U) method of density functional theory. First, the undoped ZnO and Ce-mono-doped ZnO supercell models were calculated. Within a limited doping amount in range 3.13–6.25 mol%, higher Ce doping amount results were observed in terms of higher doping system volume, higher formation energy, and lower system stability. Compared with the band gap of pure ZnO, the band gap of each doping system narrowed, and the absorption spectrum showed red-shift. High Ce doping amount led to weak narrowing of the band gap and weak red-shift in the absorption spectrum. The ferromagnetism of the mono-doped systems increased with increasing Ce doping concentration and was mainly attributed to the hybrid coupling effect of the Ce-4f, Ce-5d, and O-2p states. Second, four Zn30Ce2O32 supercell models with the same doping concentration and different spatial arrangements were calculated. A
relatively stable antiferromagnetic state was observed when -Ce-O-Ce- was doped along the a-axis bonding of the Ce double-doped ZnO system, whereas favorable ferromagnetic state was found when -Ce-O-Ce- was doped along the deflection of the c-axis. The Curie temperature of doping system can be higher than room temperature. Keywords: First principle; Ce doped ZnO; Room temperature ferromagnetism; Absorption spectrum.
1. Introduction The direct band gap of pure ZnO is 3.40 eV [1], and its exciton binding energy is 60 meV at room temperature
[2]
. Pure ZnO does not only exhibit excellent physical
and chemical properties but is also characterized by its rich raw materials, low cost, and environmental friendliness. Given that pure ZnO can achieve ferromagnetism (FM) at room temperature, ZnO-based diluted magnetic semiconductor (DMS) has attracted considerable attention. Doping different elements into the ZnO crystal can alter and enhance its properties to achieve better performance. Metals (e.g., Cr, Mn, Fe, Cu, Al, Ga, In, and Ag) have been doped into the ZnO crystal to adjust the width of its band gap and form a dilute magnetic semiconductor, which has important applications in high-density non-volatile memory, spin quantum computer, and magnetic sensor fields
[3-8]
.
Compared with transition metal elements, rare-earth (RE) atoms have very special electronic structures. Their valence electrons are located in the 4f orbit, which is surrounded by filled 5s and 5p orbits. Temperature and crystal field have very little impact on the transition of 4f electrons because of the shield effect of the 5s and 5p orbits. Consequently, RE optical transition is very stable even in strong electric fields [9]. The effects of RE doping on the magnetic and optical properties of ZnO
have been investigated, and related studies have yielded interesting results [10–13]. In
transition-metal-doped
oxides,
room-temperature
ferromagnetism
or
antiferromagnetism may be attributed to the precipitation of a magnetic cluster or a secondary magnetic phase. However, these extrinsic magnetic behaviors are undesirable in practical applications. The lack of evidence of excess composite metal oxide (such as CeO2 and Ce2O3) in the Ce-doped ZnO
[14]
ruled out the presence of
any secondary phase. Therefore, Ce is one of the most ideal doping elements, which are used to avoid the effect of secondary phase on the source of ferromagnetism in ZnO dilute magnetic semiconductors. Ce-doped ZnO thin films obtained through various preparation methods have been experimentally evaluated, and excellent magnetic and optoelectronic properties have been observed. In previous studies, the effects of Ce doping on the optical and electrical properties of ZnO were investigated using hydrothermal, sol-gel, and chemical solution
[15-17]
. Compared with undoped ZnO, Ce doping increased the
volume of the ZnO system, narrow band gap, and red-shift of the absorption spectrum. In addition, enhanced ionic behavior in Ce-doped ZnO resulted in a significant increase in dielectric constant, piezoelectric coefficient, and ferroelectric properties. Sharma et al.
[18]
studied the effect of Ce doping on the structural, optical, and
magnetic properties of ZnO by chemical precipitation method. Ce doping leads to a narrow band gap and to the red-shift of the absorption spectrum. Moreover, a study on the
magnetization
of
Ce-doped
ZnO
nanoparticles
exhibited
outstanding
ferromagnetic (FM) property at room temperature. This characteristic may have been
caused by a new coupling mechanism via intra-ion 4f-5d swap over interaction, which is followed by inter-ion 5d-5d coupling mediated through charge carriers. The magnetic and electronic properties of Ce-doped ZnO have been theoretically explored. Zhang et al. [19] predicted the electronic structure and magnetic properties of ZnO doped with RE elements. La doping can lead to a diamagnetic ground state. The doping of La and Ce is more stable than that of Pr, ND, and Eu. The total magnetic moment of Ce-single-doped ZnO is 0.92 B . Hachimi et al.
[20]
predicted the
electronic structure and magnetic properties of ZnO doped with RE elements by electron spin polarization all-electron linearly interpolated plane wave method. The La-doped ZnO was a nonmagnetic system, whereas the Ce, Eu, and other doped ZnO belonged to a magnetic system; the total magnetic moments originated from the RE 4f states spin-polarized states. Tan et al.
[21]
investigated the structural, electronic, and
magnetic properties of RE-metal-doped ZnO through first-principle calculations. The Y-doped ZnO has almost no spin polarization, but Ce-, Eu-, Gd-, and Dy-doped ZnO systems have magnetic properties. The localized f states of RE atoms respond to the introduction of a magnetic moment. Although the magnetic and optical properties of the Ce-doped ZnO system have been demonstrated, the exact systematic mechanism of intrinsic ferromagnetism in a Ce-doped ZnO system remains unclear. The effect of Ce doping on the optical properties of ZnO has been studied using the sol–gel method in a previous study [22], and Ce doping leads to the broadening of ZnO band gap and blue-shift of the absorption spectrum. The blue-shift is contrary to the result from the experimentally
determined absorption spectrum in another study [23]. Experimental study on magnetism showed that the Ce-doped ZnO system is ferromagnetic, and the magnetic properties of Ce-doped system have been predicted to be caused by a new coupling mechanism via intra-ion 4f-5d swap over interaction
[18]
. However, this finding has
not been verified. The result from a theoretical study on the magnetic source of Ce-doped ZnO system is also controversial. In this theoretical study [21], the localized f states of RE atoms respond to the introduction of a magnetic moment, which is inconsistent with the theory of Zener
[24]
RKKY interaction. To validate the
absorption spectrum distribution and the magnetic mechanism of Ce-doped ZnO systems, we examined the effect of Ce doping on the magnetic and optical properties of ZnO systems by performing first-principle generalized gradient approximation +U (GGA+U) calculations. The absorption spectrum is red-shifted for Ce-mono-doped systems, and the double-doped systems possess high Curie temperature and achieve ferromagnetism at above room temperature. Therefore, Ce-double-doped ZnO can be practically used as an unambiguous diluted magnetic semiconductor. 2. Theoretical models and calculation method 2.1 Theoretical models Undoped ZnO has a hexagonal wurtzite structure with a space group P63mc and C64 symmetry. The ZnO cell is composed of two lattices with hexagonal close-packed
structure along the c axis. The lattice constant is a = b = 0.3249 nm, c = 0.5205 nm. An experimental study [25] showed that no phase change occurs in the Ce-doped ZnO structure at a doping concentration of 10 mol%. Therefore, the doping concentration
of all systems used in the present study was in the range of 0–6.25 mol% to ensure the hexagonal wurtzite structure of all doped systems. To investigate the effect of Ce doping on the crystal structure, stability, optical properties, electronic structure, and magnetic properties of ZnO system, we constructed 1×1×1 undoped hexagonal wurtzite ZnO model and 2×2×4, 2×2×3, and 2×2×2 Ce-mono-doped hexagonal wurtzite ZnO models. These models are shown in Figs. 1(a)–(d). No polarity along the a-axis in the ZnO system was observed, but the direction along the c-axis is polar, as reported in the literature [26]. Thus, the different spatial arrangements of Ce-Ce had diverse effects on the magnetic properties of the system. Four kinds of (2×2×4) Zn30Ce2O32 supercells with different spatial arrangements of Ce–Ce were explored to study the effect of Ce doping with the substitution of two Zn atoms by Ce atoms on the magnetic properties of ZnO and evaluate whether the Ce-double-doped ZnO system is ferromagnetic (FM) or antiferromagnetic (AFM) [Figs. 1(e)-(h)]. If all the atoms spin up, the doped system demonstrated ferromagnetism. However, antiferromagnetism was demonstrated when half of the atoms spin up and the other half spin down.
Fig.1. Models: (a) pure ZnO; (b) single-doped Zn0.9687Ce0.0313O; (c) single-doped Zn0.9583Ce0.0417O; (d) single-doped Zn0.9375Ce0.0625O; (e)-(h) four configurations of double-doped Zn30Ce2O32.
2.2 Calculation method All density functional theory (DFT) calculations in the present work were performed on CASTEP (MS8.0) code based on the plane–wave pseudopotential method. The first-principle-generalized gradient approximation + U (GGA+U) method
with
the
Perdew–Burke–Ernzerhof
(PBE)
was
used
as
the
exchange-correlation function. Geometric optimization and energy calculations were conducted for all the models, and the electrons were spin polarized in the energy calculation. Geometric optimization was first achieved using the convergence thresholds of 1.0 × 10−5 eV per atom for total energy, 0.3 eV/nm for maximum force, 0.05 GPa for pressure, and 2.0×10−4 nm for maximum displacement. The self-consistent calculations were performed with a total tolerance of less than 1 × 10−6 eV per atom. The k points of the Brillouin zones of Zn0.9687Ce0.0313O, Zn0.9583Ce0.0417O, and Zn0.9375Ce0.0625O supercells were at 4×4×2. Lattice parameters and atomic coordinates were relaxed using the cutoff energy of 370 eV. Valence electron configurations for constructing pseudo-potential were Zn3d104s2, Ce4f15s25p65d16s2,
and O2s22p4. By using atomic orbitals and searching for and attaining the absolute minima of the occupied energies (i.e., the ground state), DFT calculations yielded results consistent with the experimental findings
[27]
. On the basis of DFT, the method of
GGA+U accurately calculated the electronic structures and magnetic properties of the system under the condition of electron spin polarization
[28]
. In this paper, GGA + U
method was used in the calculations. After several attempts, the U values of Zn-3d and O-2p in the undoped ZnO cells were set as 10.00 and 7.00 eV, respectively
[29]
.
The calculated band gap was based on the experimental value of 3.40 eV [30]. The U of Ce-4f was set to 6.00 eV [9], which is consistent with the MS software default value. 3. Results and discussion 3.1 Crystal structure, stability, and formation energy analysis The geometric structures of the Zn1-xCexO (x=0, 0.0313, 0.0417, 0.0625) models are optimized. The resulting equivalent lattice parameters, volumes, total energies, and formation energies are listed in Table 1. The lattice parameter and volume of the doped system increased with the increasing amount of Ce dopant. Mulliken method was used in this study to calculate the orbital charges. In the supercell Zn1-xCexO (x=0, 0.0313, 0.0417, and 0.0625) of the doped systems, the sum of the charge transfer on the f-state orbit and d-state orbit of the Ce atom in the valence-electron configuration Ce4f15s25p65d16s2 approaches +3. The valence of Ce doped in ZnO was +3, and Ce existed in the form of Ce3+. These results were consistent with the experimental results in the literature [31]. Quantum chemical theory states that given that the ionic
radius of Ce3+ (0.103 nm) is remarkably larger than that of Zn2+ (0.074 nm), replacing Zn2+ with Ce3+ can increase the volume of the unit cell. In this study, substitution impurity increased the repulsive interaction of the excess positive charges of the Ce3+ ion. Consequently, increasing the Ce dopant led to increased doped system volume. This result agreed with the experimental results obtained in a previous study [32]. Formation energy is a physical variable that indicates the stability of a doped system and the degree of difficulty of atomic doping. Formation energies are calculated based on the total energy of the optimized Ce–Ce distance crystal structures and chemical potentials of different doping atoms. The impurity formation energy (Ef) is defined as follows [33]:
E f EZnO:Ce EZnO nZn Zn nCe Ce ,
(1)
In Equation (1), EZnO:Ce is the total energy of the Ce-doped system, EZnO is the total energy of the undoped ZnO supercell system with the same size as the doped system, and coefficient nCe is the number of Ce atoms doped in the supercells of ZnO. nZn represents the number of Zn atoms substituted by impurity atoms. Zn and Ce are the chemical potentials of Zn and Ce, respectively, that is, the chemical potentials for the total energy of the atoms used to replace Ce and Zn. Chemical potentials depend on experimental conditions for material preparation. To determine
Zn and O , we must calculate Zn + O = EZnO in ZnO under thermal equilibrium conditions and in o 1 Eo2 , Zn Zn (bulk ) . During the sample preparation, 2
o 1 2 Eo under O-rich and Zn Zn (bulk ) under Zn-rich were calculated. Other 2
chemical potentials can be deduced from the thermal equilibrium relation. For instance, Zn ZnO (bulk ) 1 Eo2 under O-rich, and o EZnO (bulk ) EZn (bulk ) 2
under Zn-rich, where EZnO (bulk ) , EZn (bulk ) , and EO2 are the total energies of block ZnO, Zn, and O molecules, respectively. The calculated results of the formation energy of doped systems under O-rich or Zn-rich condition are shown in Table 1. The formation energy under O-rich condition was smaller than that under Zn-rich condition in the same doped system. Thus, stability was enhanced under O-rich conditions and can be used as a criterion for selecting the experimental conditions for material preparation. The calculated results indicated that increased doping content increased the formation energy of the Ce-doped system and reduced the stability. Table 1. The lattice parameters and formation energies of all systems after geometry optimized. a, c /nm
Model This paper ZnO (Unit cell)
a=0.3289 c=0.5308
Zn0.9687Ce0.0313O
a=0.3315 c=0.5344
Zn0.9583Ce0.0417O
a=0.3328 c=0.5346
Zn0.9375Ce0.0625O
a=0.3338 c=0.5364
Ef /eV
V /nm3
Experiment
O-rich
Zn-rich
0.04973
-
-
0.05083
-5.89
-2.42
0.05125
-4.87
-1.40
0.05170
-3.51
-0.04
[32]
a=3.251 c=5.211[32]
a=0.3264[32] c=0.5222[32]
3.2 Analysis on Degeneration As reported in Ref. [34], the critical doping content for the Mott phase change of a ZnO semiconductor (the doped system is half-metallized, that is, degenerated) should be determined by using the following equation: 1
aH Nc 3 0.2
(2)
where aH is the Bohr radius of undoped ZnO with the value of 2.03 nm[34] and N c is the doping content for the Mott phase change. Substituting the known data in
Equation (2), we obtain N c = 9.56 × 1017 cm−3. In this article, the doping content of supercells Zn0.9687Ce0.0313O, Zn0.9583Ce0.0417O, and Zn0.9375Ce0.0625O were set as N1 ,
N 2 , and N 3 , respectively. The calculated results showed that N1 = 1.23 × 1021 cm-3, N 2 = 1.63 × 1021 cm-3, and N 3 = 2.42 × 1021 cm-3, which were higher than N c . The doping content of the ionized impurity exceeded the critical doping content for the Mott phase change of semiconductor ZnO, which extremely matched the conditions of degeneration. This finding can be further proven in the later density of state and band structure. 3.3 Analysis of the electronic structure of Ce-mono-doped ZnO systems The energy band structures of undoped and doped ZnO along with high symmetry directions in the Brillouin zone were calculated using the GGA+U method, and the results are plotted in Fig. 2. Fermi level (shown by a dashed line in Fig. 2) was set to zero in the energy level, which was determined by MS software performance characteristics. Figs. 3 and 4 show the same. The calculated band gap of the undoped ZnO is 3.40 eV fitted well with the experimental value
[30]
. The band gaps of the
doped systems were 2.98, 3.12, and 3.19 eV. Compared with the undoped ZnO, the band gap of each doped system narrowed. As the amount of Ce dopant in the range of 0-0.0625 mol increased, the narrowing of the band gap weakened, which was consistent with the reported trend [32]. The spatial scale and temperature of the system were the reason that the system band gap was slightly different from that reported in the literature [35], but the trend of change was not affected.
8
8
(a)
(b)
4
4
3.40eV
2.98eV
Energy/eV
0
-4
0
G
F
Q
8
-4
Z G G
F Q
ZG
F Q
Z G
8
(c)
(d)
4
4
3.12eV
3.19eV
0
0
-4
-4
G
FQ
Z G G
Fig. 2. Band structures: (a) ZnO; (b) Zn0.9687Ce0.0313O; (c) Zn0.9583Ce0.0417O; (d) Zn0.9375Ce0.0625O.
The calculated total density of states of undoped ZnO and Zn1-xCexO (x=0, 0.0313, 0.0417, 0.0625) systems is shown in Fig. 3. The positions of valence band maximum of all doped systems were almost unchanged. Thus, the trend of the band gap was mainly determined by the position of the conduction band minimum. Compared with undoped ZnO, the position of the conduction band minimum of each doped system decreased. High molar amount of the Ce dopant led to a weak decrease in the conduction band minimum. This result was consistent with the band structure
analysis. Therefore, the band gap of a doped system mechanism shall be studied using the partial density of states (PDOS). 100 80
ZnO Zn0.9687Ce0.0313O Zn0.9583Ce0.0417O Zn0.9375Ce0.0625O
TDOS(electrons/eV)
60 40 20 0 -20 -40 -60 -80 -100 -10
-5
0
5
10
15
20
25
30
Energy(eV) Fig. 3. Spin total density of states in undoped ZnO and doped systems.
The PDOS of undoped ZnO and Zn1-xCexO (x=0, 0.0313, 0.0417, 0.0625) systems are shown in Fig. 4. Given the PDOS of undoped ZnO in Fig. 4(a), the valence band mainly consisted of O-2p and Zn-3d states, with limited contribution from Zn-3p and Zn-4s states. The hybridization of the O-2p and Zn-3d states, which occupied the upper and lower parts of the valence band, formed the bonding states in this energy region. The conduction band of ZnO was mainly composed of Zn-3p, Zn-4s, and O-2p states, with limited contribution from Zn-3d. Hence, the antibonding states in the conduction band of ZnO comprised Zn-4s, Zn-3p, and O-2p. The conduction band minimum was determined by the Zn-4s state. For convenience, an enlarged view is provided below Fig. 4(a), and the following Figs. 4(b)-(d) are similar. In Figs. 4(b)-(d), the impurity level appeared in the conduction band of the doped
systems, mainly because the incorporation of Ce atoms caused the systems to undergo hybrid coupling of Ce-4f and Ce-5d orbits. The conduction band in the doped system mainly involved the hybrid coupling of Zn-4s, O-2p, Zn-3p, Ce-4f, and Ce-5d orbits to form antibonding states. The strength of the antibonding states can be quantitatively analyzed by the number of quantum states of the Zn-4s, O-2p, Zn-3p, Ce-4f, and Ce-5d states in the conduction band in Figs. 4. 1.0
1.0
(a)
(b)
Zn-4s Zn-3p Zn-3d O-2p
0.5
0.5
0.0
0.0
Zn-4s Zn-3p Zn-3d O-2p Ce-4f Ce-5d
0.05 0.10
-0.5
-0.5
0.05
0.00
PDOS(electrons/eV)
0.00
-0.05
-0.05
-1.0
2
-5
4
0
-0.10
6
5
10
15
20
25
1.0
-1.0 -6
-4
-2
0
4
6
4
6
8
10
8
10
1.0
(c)
(d)
Zn-4s Zn-3p Zn-3d O-2p Ce-4f Ce-5d
0.5
Zn-4s Zn-3p Zn-3d O-2p Ce-4f Ce-5d
0.5
0.0
0.0
0.10
0.10
0.05
-0.5
0.05
-0.5 0.00
0.00
-0.05
-0.10
-1.0 -6
2
2
-4
-2
0
-0.05
2
4
6
2
4
6
-0.10
8
-1.0 -6 10
-4
-2
0
2
4
6
2
4
6
Energy(eV) Fig. 4. Spin partial density of states: (a) ZnO; (b) Zn0.9687Ce0.0313O; (c) Zn0.9583Ce0.0417O; (d) Zn0.9375Ce0.0625O.
The enhancement of the antibonding states led to the conduction band to move to a higher energy level, whereas the weakening of these states led to the conduction band to move toward a low energy level. Integral operations for the density of the states of the undoped ZnO cells and Zn1-xCexO (x=0, 0.0313, 0.0417, 0.0625) were performed using Origin 8.0. Then, the superposition operation was performed to obtain the total number of quantum states. Fig. 4(a) shows that integral operations for the Zn-4s, Zn-3p, and O-2p orbits were performed within the energy range of the conduction band to obtain the number of quantum states of each orbit, and then the superposition operation total quantum number was 9. Similarly, Figs. 4 (b)-(d) show that integral operations for the Zn-4s, Zn-3p, O-2p, Ce-4f, and Ce-5d orbits of Zn1-xCexO (x=0, 0.0313, 0.0417, 0.0625) systems were performed within the energy range of the conduction band to obtain the number of quantum states of each orbit. The superposition operation total quantum numbers of the three systems are 5, 7, and 8. Compared with the undoped ZnO, the number of total quantum states within the energy range of the conduction band of all doped systems was smaller than that of the undoped ZnO. Therefore, the conduction band minimum of doped systems moved toward the low energy level. For the Zn1-xCexO (x=0, 0.0313, 0.0417, 0.0625) systems, with increasing Ce dopant, the total number of quantum states within the energy range of the conduction band of the doped system increased; the hybrid coupling strength of the antibonding states was enhanced. The movement of the conduction band minimum of doped systems toward the low energy level was weakened. Compared with the undoped ZnO, the band gaps of the doped systems narrowed; high molar
amount of Ce dopant led to weaker narrowing of band gap. 3.4 Analysis of the absorption spectrum of Ce-mono-doped ZnO systems The optical properties of the medium can be described by the complex dielectric response function
() 1 () i 2 ()
in the linear response range, where
1 () n()2 k ()2 and 2 () 2n()k () , n( ) are the refractive indexes and k ( )
is the extinction coefficient. The real part 1 ( ) and imaginary part 2 ( ) can be calculated on the basis of the Kramers–Kronig dispersion relation. Absorption coefficient ( ) can be obtained if 1 ( ) , 2 ( ) , n( ) , and k ( ) were used to describe the optical properties of the crystal. The concerned equations are expressed as follows:
2 ( )
C
2
V,C
BZ
2 (2 )
1 ( ) 1
2
M CV (k ) ( ECk EVk )d 3 k , 2
3
0
0
(3)
' 2 ( ) d , '2 2
(4) 1
2 2 , （）= 2 （ +（ -1 ） 1 ） 2 ）（
2
(5)
where subscripts C and V represent the conduction and valence bands, respectively. k is the reciprocal lattice vector. BZ is the first Brillouin zone. MCV (k )
2
is the
momentum matrix element. c is a constant. ω is the angular frequency. ECk and
EVk
are the intrinsic energy levels. ' and are the angular frequencies of the initial and final states, respectively. 0 is the polarization response. The above equations provide a theoretical foundation for absorption spectrum analysis. Absorption of radiation by matter is the process in which the energy of a photon is absorbed by matter via electrons or atoms. The calculated absorption spectra of
undoped ZnO and Zn1-xCexO (x=0, 0.0313, 0.0417, 0.0625) supercells are shown in Fig. 5. First, in the range of 50–185 nm of the short UV light region, the absorption spectrum of the undoped ZnO exhibited a strong intrinsic absorption peak near 86 nm. The absorption spectra of all the Ce-doped ZnO showed a characteristic absorption peak near 135 nm because after the Ce-5d state coupling with O-2p. The transition to Zn-4s at the conduction band minimum led to a strong transition absorption peak. Compared with undoped ZnO, the absorption peak of the doping system moved to the long wavelength direction, and the absorption intensity weakened. With increasing Ce doping concentration, the value of the absorption peak gradually increased, and the absorption peak position moved in the short wavelength direction. Second, in the range of 185–420 nm of the long UV light region, the absorption intensity of the doping system was obviously enhanced. A strong absorption peak appeared near 227 nm because of the Ce-4f state Zn-4s transition at the conduction band minimum formed a strong transition absorption peak. In general, compared with undoped ZnO, the absorption spectra of each doped system exhibited a red shift. High molar amount of the Ce dopant in the range of 0–6.25 mol% led to a weak red-shift. The calculated results of the absorption spectra were in accordance with the experimental results in the previous study [23]. In addition to the difference of Ce doping amount, the spatial scale and temperature of the system also differed between this paper and the experiment. Therefore, deviation from the absorption spectrum in the experiment was normal [35, 36]. This finding may be used as a theoretical guide for preparing Ce-doped ZnO optics, which could red-shift in the long UV light region.
In previous experiments [22] and [23], the absorption spectrum distribution of ZnO was investigated in the range of similar Ce doping concentrations, and the experimental results were contradictory. In literature [22], the Ce-doped ZnO system adopted a 200 nm film thickness, which far exceeded the range defined by the nanoscale level (1–100 nm). Thus, the doping system mainly manifested a macroscale effect. However, in a previous study [23], the thickness of Ce-doped ZnO film was about 50 nm, which was at a nanoscale level. Hence, the quantum effect was obvious in the doping system. Therefore, under the same doping amount, the absorption spectrum distributions of their doping systems were contradictory mainly because of the differences in film thickness. In this paper, the lattice constants in the c-axis direction of the Zn0.9722Ce0.0278O, Zn0.9583Ce0.0417O, and Zn0.9583Ce0.0625O supercells were in the range of 1.06–2.12 nm. The quantum effect of the doping system was more significant. The absorption spectral distribution in this paper agreed with previous experimental results [23]. This result was achieved because the doping systems applied similar scales and achieved similar quantum effects. In summary, besides limiting the Ce doping amount, a Ce-doped ZnO photocatalyst with a red-shifted absorption spectrum can be attained by restricting the doping system’s dimensions to a small nanoscale range.
400000 350000
ZnO Zn0.9687Ce0.0313O Zn0.9583Ce0.0417O
-1
Absorption(cm )
300000
Zn0.9375Ce0.0625O
250000 200000 150000 100000 50000 0 0
50
100
150
200
250
300
350
400
Wavelength(nm)
Fig.5. Absorption spectra of the pure and doped ZnO.
3.5 Analysis of the magnetic properties of Ce-mono-doped ZnO systems The total magnetic moments of the Ce-doped ZnO system were calculated to investigate the magnetic properties of Ce-doped ZnO. The total magnetic moments of Zn1-xCexO (x=0, 0.0313, 0.0417, 0.0625) were 0.965, 1.013, and 1.014 B ( B is Bohr magneton). The magnetic moment of Ce-mono-doped ZnO systems increased with increasing Ce doping concentration, which was consistent with a change trend in the experimental results in a previous study [38] on Eu-doped ZnO at similar concentrations. The intrinsic magnetic moments of Ce atoms were 1.00, 1.02, and 1.03 B . The spin polarized magnetic moments of the unpaired 2p state of O atoms nearest the Ce atom were -0.02, -0.01, and -0.01 B , whereas the spin polarized magnetic moment of the O-2p state next nearest to the Ce atom was almost zero. Thus, the magnetic properties of the doped systems were mainly derived from the
contribution of Ce and O atoms. The magnetic moment of the Ce-doped ZnO system with Ce dopant concentration in the range of 0–6.25 mol% was very close to integer 1, which was an important feature of ferromagnetism for the doped system according to experimental results in the previous study [39]. According to Goodenough–Kanamori rules, FM ordering prevails among Ce ions because the 4f electrons of Ce ions are less than half-filled
[40, 41]
. Therefore, in the present work, doped systems exhibited FM
behavior that would be analyzed in detail in the analysis of the magnetic properties of Ce-double-doped ZnO systems. 3.6 Analysis on the magnetic properties of Ce-double-doped ZnO systems The unipolar structure of ZnO was the reason that different spatial-ordered occupations have a significant effect on the FM or AFM of Ce-doped ZnO systems. For the Ce-double-doped ZnO systems in Figs. 1 (e)-(h), we constructed four different spatial-ordered occupancy models at the same doping concentration. The results of Ce-Ce distance, total energies of AFM and FM, E EAFM EFM , and total magnetic moment are shown in Table 2. We used the energy difference between FM and AFM ordering, E EAFM EFM , as an indicator of magnetic stability. A positive ΔE implies that the system is FM, and a negative ΔE was obtained for AFM [42]. Table 2. Spacing of Ce-Ce, total energies of AFM and FM, difference of total energies, total magnetic moments and formation energy for double-doped Zn30Ce2O32 EFM
EAFM
E
(eV)
(eV)
(meV)
e
-67372.756
-67372.717
39
f
-67385.174
-67385.320
-146
Models
（nm）
Total magnetic moments ( B )
FM
0.3208
AFM
0.3249
Type
dCeCe
Ef /eV O-rich
Zn-rich
2.00413
-5.09
1.85
0
-5.19
1.71
g
-67372.744
-67372.692
52
FM
0.6136
2.00275
-5.37
1.57
h
-67372.725
-67372.657
68
FM
0.8030
2.00183
-5.41
1.53
In Table 2, the smallest Ce–Ce distance is found in the model in Fig. 1(e), and the AFM–FM energy difference was 39 meV, thereby indicating that the system was FM. The total magnetic moment was 2.00413 B . The AFM-FM energy difference in Fig. 1(f) was -146 meV, thereby indicating a favorable antiferromagnetism. The total magnetic moment was 0 B . The results confirmed that magnetic moment quenching occurred in the doped system. The AFM-FM energy difference values in Figs. 1 (g) and (h) are 52 and 68 meV, respectively, with increased Ce–Ce distance. The Ce-double-doped ZnO models display advantageous ferromagnetic coupling. The total magnetic moments of the models in Figs. 1 (g) and (h) are 2.00175 and 2.00283 B , respectively. When the -Ce-O-Ce- for the Ce-double-doped system in Fig. 1 (f) formed a bond along the a-axis, magnetic moment quenching occurred in the doped system. This result may have been caused by the nonpolar structure of ZnO along the a-axis. When the -Ce-O-Ce- for the Ce-double doped system in Figs. 1 (e), (g), and (h) formed a bond along the approaching c-axis, systems showed ferromagnetism and had a certain magnetic moment. The Ce–Ce distance increased, and the magnetic moment of the doped system decreased. When the -Ce-O-Ce- formed a bond along the approaching c-axis, the magnetic moment of the Ce-double-doped ZnO system increased to nearly twice as much as that of the Ce-mono-doped ZnO system under the same doping
amount. The magnetic moment was contributed by the spin magnetic moment and the orbital magnetic moment, in which the contribution of the track magnetic moment to the total magnetic moment was small and almost negligible. The incorporation of two Ce atoms was the reason that the number of spin electrons in the Zn30Ce2O32 system was twice that of the Ce-mono-doped system, thereby resulting in an increase in the total magnetic moment to nearly twice. This result may be used as a guide in the design and preparation of new dilute magnetic semiconductors. The formation energies of Ce-double-doped ZnO systems were calculated using Equation (1) to compare the stability and degree of doping difficulty of Ce-double-doped ZnO systems with different Ce–Ce distances. The results are shown in Table 2. The calculated results indicated that greater Ce-Ce distance led to lower formation energy of the Ce-double-doped ZnO and to higher stability. The formation under O-rich conditions was smaller than that under Zn-rich conditions in the same doped system. From the total energy difference E between AFM and FM, realistic estimations of Curie temperature were achieved by mapping on the classical Heisenberg model in the mean-field approximation
[43]
. The classical Heisenberg
model assumed in our analysis is given by the following:
H ij J ij Si S j
(6)
i j
where Si is the unit vector parallel to the local moment at site i and J ij is the exchange coupling constant between the local moments at sites i and j . We can calculate the total energy difference E H as follows:
E H S 2C 2 J n 0
(7)
n0
where C is the amount of the magnetic ions and n sums over all sites of the cation sublattice. E H was directly identified with the energy difference E and was also calculated from the first principles, because CPA also represented a mean-field theory. Meanwhile, within the mean-field theory of the Heisenberg model, we estimated TC by using the Brillouin function expression, which is known as the molecular field theory. The Brillouin function is expressed as follows:
kBTC
2 2 S C J n0 3 n0
(8)
where k B is the Boltzmann constant. Following (7) and (8), the TC can be obtained from first principles: kBTc 2E
3C
(9)
where TC is the estimated Curie temperature of the DMS. From Equation (9), TC is proportional to E . As reported in the previous study [42], the total energy difference E between AFM and FM is approximately equal to the thermodynamic energy kBT;
thus, the ΔE is about 30 meV at T = 300 K. In this paper, E of the models in Figs. 1 (e), (g), and (h) were 39, 52, and 68 meV, respectively, which were greater than 30 meV. Thus, the Ce-double-doped ZnO achieved ferromagnetism at above room temperature. Curie temperatures of the models in Figs. 1 (e), (g), and (h) were estimated using Equation (9); the approximated temperatures were 390 K, 520 K, and 680 K, respectively. The Ce-double-doped systems possessed high Curie temperature and achieved long-term ferromagnetism above room temperature. This result was consistent with the experimental results, in which the doped system has demonstrated
ferromagnetism at room temperature [44]. This characteristic is essential for the design and preparation of new DMS functional materials. 3.7 Analysis of the magnetic mechanism of Ce-mono-doped ZnO systems The net spin density distribution of Ce-doped ZnO system was calculated to illustrate the magnetic mechanism of Ce mono-doped ZnO system. The blue area in Fig. 6 is the spin net magnetic moment of the models. The net magnetic moments of the doped system were mainly contributed by the spin polarization of Ce and O atoms. Combined with the spin PDOS in Fig. 4, Figs. 4 (b)-(d) show that the spin and unspin PDOS of the Ce-4f, Ce-5d, and O-2p orbits were asymmetric. The asymmetry of spin and unspin PDOS of Ce-4f and Ce-5d orbits induced polarization of the spin electrons of O-2p orbit in the conduction band, which resulted in the asymmetry of the spin and unspin total density of states. The doped systems produced the net magnetic moment and exhibited ferromagnetism. This phenomenon was consistent with the analysis of the magnetic moment. The total magnetic moment was generated by the hybrid coupling between the Ce and O atoms, and the Zn atoms showed almost no effect. The magnetic properties of the doped systems were mainly caused by the hybrid coupling of Ce-4f, Ce-5d, and O-2p orbits. This phenomenon was consistent with the Zener [24] RKKY theory. However, speculation on the magnetic source of Ce-doped ZnO system in the experiment in the previous study [18] was insufficient. In a theoretical study [21], the Ce-4f state was considered as the magnetic source of the Ce-doped ZnO system, because the hybrid coupling between the Ce and O atoms was neglected, thereby resulting in an
insufficient understanding of the magnetic mechanism.
Fig. 6. Net spin density distribution: (a) Zn0.9687Ce0.0313O; (b) Zn0.9583Ce0.0417O; (c) Zn0.9375Ce0.0625O.
4. Conclusion In this study, the magnetic and optical properties of Ce-mono-doped ZnO and the magnetic properties of Ce-double-doped ZnO were investigated via plane-wave super-soft pseudo-potential method based on density functional theory. The following conclusions are drawn: (1) Increased doping content led to higher formation energy of the Ce-doped system and lower stability. In addition, the formation energy under O-rich condition was smaller than under Zn-rich condition in the same doped system. The stability under O-rich condition was enhanced. (2) Compared with the band gap of pure ZnO, the band gap of each doped system became narrow, and the absorption spectrum showed a red-shift. High molar amount of Ce dopant in the range of 0–6.25 mol% led to weak narrowing of
band gap and weak red-shift in absorption spectrum. (3) The magnetism of Ce-mono-doped ZnO was mainly attributed to the hybrid coupling effect of Ce-4f, Ce-5d, and O-2p states. The calculated magnetic moments of mono-doped systems reached 0.965, 1.012, and 1.014 B .The ferromagnetism of mono-doped systems increased with increasing Ce doping concentration. (4) For Ce-double-doped ZnO systems, a relatively stable AFM state was observed when -Ce-O-Ce- was doped along the a-axis bonding of the Ce double-doped ZnO system, whereas a favorable FM state was found when -Ce-O-Ce- was doped along the deflection of the c-axis. The double-doped systems possessed high Curie temperature and achieved ferromagnetism above room temperature. In addition, the magnetic moment of the Ce-double-doped ZnO system increased to nearly twice as much as that of the Ce-mono-doped ZnO system under the same doping amount. Acknowledgment This work was supported by the National Natural Science Foundation of China (Grant Nos. 61366008, 61664007). References [1]
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Highlights
Band structure and density of states were calculated based on DFT with GGA+U.
By increasing the Ce doping amount, absorption spectra exhibit red-shift。
Four possible magnetic coupling configurations for Zn14Ce2O16 are calculated.
the Curie temperature of doping system can reach a temperature higher than room temperature.
The ferromagnetism was mainly attributed to the hybrid coupling effect of the Ce-4f, Ce-5d, and O-2p states.