- Email: [email protected]
Theoretical investigations of the effect of vacancies on the geometric and electronic structures of zinc sulfide
Physica B 407 (2012) 3888–3892
Contents lists available at SciVerse ScienceDirect
Physica B journal homepage: www.elsevier.com/locate/physb
Theoretical investigations of the effect of vacancies on the geometric and electronic structures of zinc sulfide Jinhuan Yao a, Yanwei Li a,b,n, Ning Li a, Shiru Le c a
College of Chemistry and Bioengineering, Guilin University of Technology, Guilin, Guangi 541004, PR China GuangXi Key Laboratory of New Energy and Building Energy Saving, Guilin University of Technology, Guilin, Guangxi 541004, PR China c Natural Science Research Center, Academy of Fundamental and Interdisciplinary Sciences, Harbin Institute of Technology, Harbin 150001,PR China b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 14 December 2011 Received in revised form 5 June 2012 Accepted 8 June 2012 Available online 16 June 2012
The effects of S-vacancy and Zn-vacancy on the geometric and electronic structures of zinc blende ZnS are investigated by the first-principles calculation of the plane wave ultrasoft pseudopotential method based on the density functional theory. The results demonstrate that both S-vacancy and Zn-vacancy decrease the cell volume and induce slight deformation of the perfect ZnS. Furthermore, this change of geometric structure caused by Zn-vacancy is more obvious than the one due to the S-vacancy. The formation energy of S-vacancy is higher than that of Zn-vacancy, indicating that Zn-vacancy is easier to form than S-vacancy in ZnS crystal. Electronic structure analysis shows that Zn-vacancy increases the band-gap of ZnS from 2.03 eV to 2.15 eV, while the S-vacancy has almost no effect on the band-gap of ZnS. Bond population analysis shows that Zn-vacancy increases covalence character of the Zn–S bonds around Zn-vacancy, while S-vacancy shows a relatively weak effect on the covalence character of Zn–S bonds. & 2012 Elsevier B.V. All rights reserved.
Keywords: ZnS Vacancy Electronic structure Geometric structure First-principles calculation
1. Introduction Zinc sulfide (ZnS) is an important semiconductor material with exceptional physical and chemical properties and it has a great variety of potential applications including optical coatings, solidstate solar window layers, electrooptic modulators, photoconductors, field effect transistors, optical sensors, photocatalysts, and other light-emitting materials [1–5]. In addition, ZnS is also the main component of sphalerite, which is the most significant zinc source. ZnS has two basic phase structures: the cubic zinc blende and the hexagonal wurtzite. Typically, the stable phase structure at room temperature is the cubic zinc blende [6]. Structural defects, especially vacancies exist very commonly in ZnS crystal due to the variation of temperature and pressure in the process of crystallization of ZnS. S-vacancy and Zn-vacancy exist in ZnS crystal in practice. Vacancy defect will influence the geometric and electronic structures of the crystalline materials and therefore results in the change of physical and chemical properties, such as conductivity, optical and field emission properties [7,8], and reactivity [9]. Therefore, it is of great importance to study the effect of vacancies on the geometric and electronic structures of ZnS at the atomic level for a better understanding of
n Corresponding author at: Guilin University of Technology, Guilin, Guangxi 541004, PR China. Tel.: þ 86 773 5896446; fax: þ 86 773 5896839. E-mail addresses: [email protected] (J. Yao), [email protected], [email protected] (Y. Li).
0921-4526/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.physb.2012.06.016
the structure–properties relationship of the material. However, there are few systematic studies on this issue. First-principles calculations are powerful tools to predict various properties of molecules, small aggregates of atoms, and bulk solids [10–12]. In this work, we studied the effect of vacancies (S-vacancy and Zn-vacancy) on the geometric and electronic structures of zinc sulfide by using first-principles density-functional calculations. In particular, the changes of lattice parameters, band structures, bond orders, and redistributions of Mulliken atomic charges of the ZnS caused by S-vacancy and Zn-vacancy are discussed in detail. The results are helpful to further understanding the nature of the role of vacancy defects in ZnS crystal and provide a wealth of theoretical data giving insights into the geometric and electronic structures of ZnS with and without vacancy.
2. Computational models and methods In this study, the zinc blende ZnS with a space group of F-43 m was adopted. The primitive cell of zinc blende ZnS (Fig. 1(a)) was used to test exchange–correlation functional. The ZnS with Zn-vacancy or S-vacancy was constructed by removing one Zn or S atom from a 32-atom 2 2 1 supercell (Fig. 1(b) and (c)), which corresponds to the defect level of 3.125 at%. The vacancy formation energy (Ef) is defined as follows [13,14]: total Ef ¼ Etotal vacancy þ Evacancyatom Eperfect
ð1Þ
J. Yao et al. / Physica B 407 (2012) 3888–3892
3889
Fig. 1. Computational model: (a) the primitive cell of ZnS, (b) ZnS supercell (2 2 1) with Zn-vacancy, and (c) ZnS supercell (2 2 1) with S-vacancy.
Table 1 Comparison of the lattice parameters of ZnS calculated with different DFT potentials. Functional
GGA PBE
˚ Cell constant a ¼b ¼c (A) ˚ Zn–S bond length (A)
LDA RPBE
PW91
Experimental value
WC
PBESOL
CA-PZ
5.468
5.526
5.461
5.390
5.384
5.306
5.401 [19]
2.368
2.393
2.365
2.334
2.331
2.298
2.34 [20]
total where Etotal vacancy andEperfect are the total energies of ZnS with and without a vacancy, respectively; and Evacancyatom is the energy of the removed Zn or S species. All calculations were performed using the Cambridge Serial Total Energy Package (CASTEP) based on the density functional theory (DFT) [15]. The core-valence interactions are taken into account by the ultrasoft pseudopotentials [16]. The valence electron configurations considered in this study included Zn 3d104s2 and S 3s23p4. Two different functionals, generalized gradient approximation (GGA) [17] and local density approximation (LDA) [18] were applied to optimize the structure of the perfect bulk ZnS as a test. The convergence criteria for the structure optimization and energy calculation were set as follows: SCF tolerance is 1.0 10 6 eV/atom, energy tolerance is ˚ and 1.0 10 5 eV/atom, maximum force tolerance is 0.03 eV/A, ˚ The kinetic maximum displacement tolerance is 1.0 10 3 A. energy cutoff of 310 eV for the plane wave basis was used throughout the study. A Monkhorst–Pack 5 5 5 sampling was used to evaluate integrals in the reciprocal space. The structural parameters of perfect ZnS calculated by the different DFT functionals as well as the experimental results are listed in Table 1. It can be seen that GGA/WC functional may be expected to produce more reliable predictions of the structures. Therefore the GGA/WC functional was used in all the calculations of ZnS with Zn-vacancy or S-vacancy.
3. Results and discussion 3.1. Effect of vacancies on geometric structure The calculated lattice parameters for the perfect ZnS, the ZnS with Zn-vacancy, and the ZnS with S-vacancy are summarized in Table 2. It can be seen that the presence of both Zn-vacancy and S-vacancy decreases the cell volume of ZnS and results in a slight
Table 2 Effect of Zn-vacancy and S-vacancy on lattice parameters of ZnS. Type of vacancy
˚ Cell constant (A) a
Perfect Zn-vacancy S-vacancy
b
c
Angle (1)
a
b
Volume (A˚ 3)
g
5.390 5.390 5.390 90 90 90 156.576 5.251 5.434 5.405 90.014 89.937 90.067 154.230 5.308 5.308 5.326 90.094 90.091 89.978 150.044
deformation from the perfect cubic structure. In particular, the cell volume of ZnS with S-vacancy decreases by 4.17%, which is much larger than that (1.50%) for ZnS with Zn-vacancy. Since the volume occupied by vacancy S-atom is bigger than that of vacancy Zn-atom, the cell volume decrease due to S-vacancy is more obvious than that due to Zn-vacancy after geometric relaxations. The calculated formation energy of Zn-vacancy is 5.99 eV, which is smaller than that (7.05 eV) of S-vacancy, indicating that the formation of Zn-vacancy is easier than that of S-vacancy in ZnS. 3.2. Effects of vacancies on band structure and density of states The calculated band structures of perfect ZnS, ZnS with Zn-vacancy, and ZnS with S-vacancy are shown in Fig. 2. The value of band-gap was defined as the difference between the conduction band minimum (CBM) and the valence band maximum (VBM) [21]. For perfect ZnS, the calculated band gap is about 2.03 eV, which is close to the other theoretical value of 2.2 eV [22], but much smaller than the experimental value 3.6– 3.8 eV [23]. Our computations, due in part to the use of pseudopotentials and plane waves as opposed to localized orbitals (i.e., Gaussians or exponentials), could not utilize the known method [24] that avoids band gap underestimation. The band-gap of ZnS with Zn-vacancy increases from 2.03 eV to 2.15 eV as compared
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J. Yao et al. / Physica B 407 (2012) 3888–3892
4 2.032 eV
0
Energy (eV)
Energy (eV)
0 -4 -8
4 2.151 eV Energy (eV)
4
-4 -8 -12
-12 G
F
Q
Z
G
2.028 eV
0 -4 -8 -12
G
F
Q
Z
G
G
F
Q
Z
G
Fig. 2. The band structures of (a) perfect ZnS, (b) ZnS with Zn-vacancy, and (c) ZnS with S-vacancy.
s p d
100 50
-4
0
4
8
50
S-atom s p
24
-16
16 8
-12
-8
-4
0
4
8
-12
-8
-4
0
32
4
16 8
-8
-4
0
4
8
100 50
-12
-8
-4
0
4
8
Total 150 100 50 0 -16
-12
-8
-4
0
32
4
8
S-atom s p
24 16 8
-16
-12
-8
-4
0
4
8
200 DOS (states/eV/cell)
150
DOS (states/eV/cell)
Total
50
0 -12
200
200
s p d
100
-16
8
S-atom s p
24
-16
Zn-atom
150
0
0
0
DOS (states/eV/cell)
s p d
100
DOS (states/eV/cell)
-8
DOS (states/eV/cell)
DOS (states/eV/cell)
-12
32
0 -16
Zn-atom
150
0
0
-16
DOS (states/eV/cell)
Zn-atom
150
-16
200
200 DOS (states/eV/cell)
DOS (states/eV/cell)
200
Total 150 100 50 0
-12
-8
Engergy (eV)
-4 0 Engergy (eV)
4
8
-16
-12
-8
-4 0 Engergy (eV)
4
8
Fig. 3. The density of states of (a) perfect ZnS, (b) ZnS with Zn-vacancy, and (c) ZnS with S-vacancy.
to the perfect ZnS, while the band-gap of ZnS with S-vacancy is almost identical to that of the perfect ZnS. To obtain further information about the bond nature of the ZnS with and without vacancy, the electronic density of states (DOS) and partial DOS (PDOS) are calculated and displayed in Fig. 3. For perfect ZnS, the valence bands extend down to about 13.5 eV below the Fermi level. The entire valence bands can be divided into upper and lower parts. The lower valence band at about 12.2 eV consists of the S 3s state. The upper valence band at about 6.0 eV is contributed by the Zn 3d state and S 3p state. The other parts of the valence band mainly consist of the S 3p state. The conduction bands consist of the S 3p and Zn 4s contributions. The ZnS with Zn-vacancy shows DOS very similar to that of the perfect ZnS, suggesting that the presence of Znvacancy has almost no effect on the total DOS of ZnS. For ZnS with S-vacancy, the valence bands are almost the same as those of the
perfect ZnS. The conduction bands are split as compared to the case in the perfect ZnS. The reason was that the inhomogeneous distribution of charge over ZnS with S-vacancy system led to the conduction levels of partial atoms shift. 3.3. Mulliken atomic population analysis The electronic structure of ZnS with and without vacancy can be further analyzed by examining the charge transfer and bond order. The Mulliken atomic charge and overlap population are useful in evaluating the nature of bonds in a compound [25,26]. The results of Mulliken atomic population analysis of atoms around vacancies are listed in Table 3 (the atoms’ serial number is indexed in Fig. 1(b) and (c)). As shown in Table 3, for the perfect ZnS, Zn atoms act as electron donor, which mainly loses 4s state electrons. The valence electron configuration of Zn-atom changes
J. Yao et al. / Physica B 407 (2012) 3888–3892
Table 3 Mulliken atomic population analysis of atoms around Zn-vacancy and S-vacancy (the corresponding serial number of atoms for Mulliken atomic population analysis are shown in Fig. 1). Vacancy
Species Serial number of atoms
s
p
d
F
Total
Charge (e)
Perfect
S Zn S S Zn Zn Zn Zn S S S Zn Zn Zn
1.81 0.57 1.84 1.84 0.58 0.56 0.66 0.58 1.81 1.82 1.81 0.64 0.63 0.62
4.64 1.00 4.53 4.53 1.01 1.02 1.05 1.01 4.62 4.61 4.61 1.10 1.09 1.07
0.00 9.98 0.00 0.00 9.97 9.97 9.97 9.97 0.00 0.00 0.00 9.98 9.98 9.98
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
6.45 11.55 6.38 6.37 11.55 11.54 11.68 11.56 6.43 6.42 6.43 11.71 11.70 11.67
0.45 0.45 0.38 0.37 0.45 0.46 0.32 0.44 0.43 0.42 0.43 0.29 0.30 0.33
Zn-vacancy
S-vacancy
1 1 2, 5 3, 8 3, 14 4, 7 5, 12 6, 10 1, 4, 8, 12 2, 3 7, 10 4 6, 11 13
Table 4 Mulliken atomic population analysis of atoms around Zn-vacancy and S-vacancy. Type of vacancy perfect
Zn-vacancy
S-vacancy
from Zn 3d104s2 to Zn 3p1.003d9.984s0.57 after structure optimization. S atoms act as electron acceptor, whose 3p state gains electrons and loses partial electrons of 3s state. The valence electron configuration of S-atom changes from S 3s23p4 to S 3s1.813p4.64. However, Zn-vacancy makes the S atoms around Zn-vacancy lose 3p electrons and gain 3s electrons. The Mulliken atomic charges of S atoms around Zn-vacancy decreases from 0.45e to 0.38e due to the lack of electrons donated by the Zn atom when it is present. Moreover, the decrease of the Mulliken atomic charges of S atoms around Zn-vacancy leads to the decrease of the attractive power for partial Zn atoms attached with them so that the charges of Zn 5 and Zn 12 decrease from 0.45e to 0.32e. The S-vacancy makes 3s state of Zn atoms around S-vacancy lose fewer electrons than in the case of the perfect ZnS. The Mulliken atomic charges of Zn atoms (Zn 4, Zn 6, Zn 11, and Zn 13) around S-vacancy decreased from 0.45e to 0.29e, 0.30e, 0.30e and 0.33e, respectively. In addition, the S-vacancy also results in a decrease of the charges of S atoms attached to Zn atoms around the S-vacancy. The overlap population can be used to assess the covalent or ionic nature of a bond. A high value of the bond population indicates a covalent bond, while a low value indicates an ionic interaction. Table 4 compares the bond population of atoms around vacancies and related bond lengths. The overlap population of 0.52 for the Zn–S bonds in perfect ZnS indicates that the Zn–S bonds have a covalent character. Compared with perfect ZnS, the Zn-vacancy results in the increase of populations of Zn–S bonds around Zn-vacancy and the decrease of Zn–S bond lengths. This suggests that the Zn-vacancy enhances the covalent character of Zn–S bonds around it. In contrast, the S-vacancy shows much less effect on the bond populations of S–Zn bonds around S-vacancy and therefore the S-vacancy has no obvious effect on the covalent character of S–Zn bonds around S-vacancy. But the bond lengths of Zn–S bonds around S-vacancy increase clearly. 3.4. Electron density and electron density difference analysis In order to further investigate the influence of Zn-vacancy and S-vacancy on charge distribution and electronic interaction, the charge density difference contour plots of ZnS with and without vacancy are presented in Fig. 4. The presence of vacancies affects the charge distribution of atoms around the vacancy in the supercell. As shown in Fig. 4, the charges of S atoms around Znvacancy are lower than those of S atoms located in the other positions and the charges of Zn atoms around S-vacancy are lower
3891
Bond
Population
˚ Length (A)
S–Zn S 2–Zn 4 S 2–Zn 10 S 2–Zn 12 S 3–Zn 3 S 3–Zn 4 S 3–Zn 5 S 5–Zn 5 S 5–Zn 6 S 5–Zn 7 S 8–Zn 7 S 8–Zn 12 S 8–Zn 14 S 1–Zn 4 S 2–Zn 4 S 3–Zn 4 S 2–Zn 6 S 4–Zn 6 S 7–Zn 6 S 3–Zn 11 S 8–Zn 11 S 10–Zn 11 S 7–Zn 13 S 10–Zn 13 S 12–Zn 13
0.52 0.58 0.60 0.66 0.60 0.57 0.65 0.66 0.60 0.58 0.58 0.65 0.60 0.56 0.49 0.49 0.51 0.58 0.50 0.51 0.58 0.50 0.53 0.53 0.59
2.3348 2.3042 2.2844 2.2784 2.2853 2.3073 2.2818 2.2780 2.2840 2.3050 2.3070 2.2808 2.28580 2.37841 2.38206 2.38222 2.35904 2.36238 2.37024 2.35905 2.36244 2.37016 2.34436 2.34441 2.34175
S Zn
Zn
Zn
S
S Zn
Zn
S-vacancy Zn
Zn
S
Zn-vacancy
S Zn
S
S
Zn
Zn
S Zn
Fig. 4. The charge density difference contour plots of (a) perfect ZnS, (b) ZnS with Zn-vacancy, and (c) ZnS with S-vacancy.
than those of Zn atoms located in the other positions. In addition, the strength of the Zn–S bonds neighboring Zn-vacancy increases. These results are coincided with the Mulliken atomic population analysis. Fig. 5 shows the charge density counter plots of ZnS with and without vacancy. It can be seen from Fig. 5 that the electronic interaction between Zn-atom and its neighboring S-atom is completely isotopic for the perfect ZnS. However, the charge density of Zn–S bonds neighboring Zn-vacancy is higher than that of the other Zn–S bonds, suggesting that the covalent character of the Zn–S bonds neighboring Zn-vacancy is strengthened. But the charge density of Zn–S bonds neighboring S-vacancy has no
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J. Yao et al. / Physica B 407 (2012) 3888–3892
S
S Zn
S
Zn
Zn
S
S Zn
Zn
Zn
S Zn-Vacancy
density of states of ZnS. For ZnS with S-vacancy, the valence bands are almost the same as those of the perfect ZnS, while the conduction bands are split compared to the perfect ZnS. However, the presence of Zn-vacancy enlarges the band-gap of ZnS, while S-vacancy has almost no effect on the band-gap. The overlap population and electron density analysis show that Zn–S bonds in perfect ZnS have a covalent character. Compared with the perfect ZnS, the Zn-vacancy intensifies the covalent feature of the Zn–S bonds around Zn-vacancy. In contrast, the S-vacancy shows no obvious effect on the covalent character of S–Zn bonds around S-vacancy.
Zn Acknowledgments
S-vacancy
S Zn
Zn
Zn
This work was financially supported by the Guangxi Natural Science Foundation of China (Nos. 0991247 and 2012jjAA20053) and by the Scientific Research Fund of Guangxi Education Department of China (Nos. 201106LX250 and 201010LX174).
S Zn
References
Fig. 5. The charge density contour plots of (a) perfect ZnS, (b) ZnS with Zn-vacancy, and (c) ZnS with S-vacancy.
obvious change. The results are also in good agreement with the Mulliken atomic population analysis.
4. Conclusions The geometric and electronic structures of ZnS with and without a vacancy were calculated using the DFT method within GGA/WC scheme. The results suggest that both Zn-vacancy and S-vacancy result in the decrease of cell volume of ZnS, especially for S-vacancy. The formation energy of Zn-vacancy is lower than that of S-vacancy, suggesting that Zn-vacancy is easier to form than S-vacancy. Compared to the perfect ZnS, the band-gap of ZnS with Zn-vacancy increases from 2.03 eV to 2.15 eV, while the band-gap of ZnS with S-vacancy is almost identical to that of the perfect ZnS. The presence of vacancies has almost no effect on the distribution of density of states of ZnS. For the perfect ZnS, the lower valence band located at about 12.2 eV consists of the S 3s state. The upper valence band located at about 6.0 eV is contributed by the Zn 3d state and S 3p state. The valence bands close to the Fermi level are mainly contributed by the S 3p state. The conduction bands consist of the S 3p state and Zn 4s state. The presence of Zn-vacancy has almost no effect on the total
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Contents lists available at SciVerse ScienceDirect
Physica B journal homepage: www.elsevier.com/locate/physb
Theoretical investigations of the effect of vacancies on the geometric and electronic structures of zinc sulfide Jinhuan Yao a, Yanwei Li a,b,n, Ning Li a, Shiru Le c a
College of Chemistry and Bioengineering, Guilin University of Technology, Guilin, Guangi 541004, PR China GuangXi Key Laboratory of New Energy and Building Energy Saving, Guilin University of Technology, Guilin, Guangxi 541004, PR China c Natural Science Research Center, Academy of Fundamental and Interdisciplinary Sciences, Harbin Institute of Technology, Harbin 150001,PR China b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 14 December 2011 Received in revised form 5 June 2012 Accepted 8 June 2012 Available online 16 June 2012
The effects of S-vacancy and Zn-vacancy on the geometric and electronic structures of zinc blende ZnS are investigated by the first-principles calculation of the plane wave ultrasoft pseudopotential method based on the density functional theory. The results demonstrate that both S-vacancy and Zn-vacancy decrease the cell volume and induce slight deformation of the perfect ZnS. Furthermore, this change of geometric structure caused by Zn-vacancy is more obvious than the one due to the S-vacancy. The formation energy of S-vacancy is higher than that of Zn-vacancy, indicating that Zn-vacancy is easier to form than S-vacancy in ZnS crystal. Electronic structure analysis shows that Zn-vacancy increases the band-gap of ZnS from 2.03 eV to 2.15 eV, while the S-vacancy has almost no effect on the band-gap of ZnS. Bond population analysis shows that Zn-vacancy increases covalence character of the Zn–S bonds around Zn-vacancy, while S-vacancy shows a relatively weak effect on the covalence character of Zn–S bonds. & 2012 Elsevier B.V. All rights reserved.
Keywords: ZnS Vacancy Electronic structure Geometric structure First-principles calculation
1. Introduction Zinc sulfide (ZnS) is an important semiconductor material with exceptional physical and chemical properties and it has a great variety of potential applications including optical coatings, solidstate solar window layers, electrooptic modulators, photoconductors, field effect transistors, optical sensors, photocatalysts, and other light-emitting materials [1–5]. In addition, ZnS is also the main component of sphalerite, which is the most significant zinc source. ZnS has two basic phase structures: the cubic zinc blende and the hexagonal wurtzite. Typically, the stable phase structure at room temperature is the cubic zinc blende [6]. Structural defects, especially vacancies exist very commonly in ZnS crystal due to the variation of temperature and pressure in the process of crystallization of ZnS. S-vacancy and Zn-vacancy exist in ZnS crystal in practice. Vacancy defect will influence the geometric and electronic structures of the crystalline materials and therefore results in the change of physical and chemical properties, such as conductivity, optical and field emission properties [7,8], and reactivity [9]. Therefore, it is of great importance to study the effect of vacancies on the geometric and electronic structures of ZnS at the atomic level for a better understanding of
n Corresponding author at: Guilin University of Technology, Guilin, Guangxi 541004, PR China. Tel.: þ 86 773 5896446; fax: þ 86 773 5896839. E-mail addresses: [email protected] (J. Yao), [email protected], [email protected] (Y. Li).
0921-4526/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.physb.2012.06.016
the structure–properties relationship of the material. However, there are few systematic studies on this issue. First-principles calculations are powerful tools to predict various properties of molecules, small aggregates of atoms, and bulk solids [10–12]. In this work, we studied the effect of vacancies (S-vacancy and Zn-vacancy) on the geometric and electronic structures of zinc sulfide by using first-principles density-functional calculations. In particular, the changes of lattice parameters, band structures, bond orders, and redistributions of Mulliken atomic charges of the ZnS caused by S-vacancy and Zn-vacancy are discussed in detail. The results are helpful to further understanding the nature of the role of vacancy defects in ZnS crystal and provide a wealth of theoretical data giving insights into the geometric and electronic structures of ZnS with and without vacancy.
2. Computational models and methods In this study, the zinc blende ZnS with a space group of F-43 m was adopted. The primitive cell of zinc blende ZnS (Fig. 1(a)) was used to test exchange–correlation functional. The ZnS with Zn-vacancy or S-vacancy was constructed by removing one Zn or S atom from a 32-atom 2 2 1 supercell (Fig. 1(b) and (c)), which corresponds to the defect level of 3.125 at%. The vacancy formation energy (Ef) is defined as follows [13,14]: total Ef ¼ Etotal vacancy þ Evacancyatom Eperfect
ð1Þ
J. Yao et al. / Physica B 407 (2012) 3888–3892
3889
Fig. 1. Computational model: (a) the primitive cell of ZnS, (b) ZnS supercell (2 2 1) with Zn-vacancy, and (c) ZnS supercell (2 2 1) with S-vacancy.
Table 1 Comparison of the lattice parameters of ZnS calculated with different DFT potentials. Functional
GGA PBE
˚ Cell constant a ¼b ¼c (A) ˚ Zn–S bond length (A)
LDA RPBE
PW91
Experimental value
WC
PBESOL
CA-PZ
5.468
5.526
5.461
5.390
5.384
5.306
5.401 [19]
2.368
2.393
2.365
2.334
2.331
2.298
2.34 [20]
total where Etotal vacancy andEperfect are the total energies of ZnS with and without a vacancy, respectively; and Evacancyatom is the energy of the removed Zn or S species. All calculations were performed using the Cambridge Serial Total Energy Package (CASTEP) based on the density functional theory (DFT) [15]. The core-valence interactions are taken into account by the ultrasoft pseudopotentials [16]. The valence electron configurations considered in this study included Zn 3d104s2 and S 3s23p4. Two different functionals, generalized gradient approximation (GGA) [17] and local density approximation (LDA) [18] were applied to optimize the structure of the perfect bulk ZnS as a test. The convergence criteria for the structure optimization and energy calculation were set as follows: SCF tolerance is 1.0 10 6 eV/atom, energy tolerance is ˚ and 1.0 10 5 eV/atom, maximum force tolerance is 0.03 eV/A, ˚ The kinetic maximum displacement tolerance is 1.0 10 3 A. energy cutoff of 310 eV for the plane wave basis was used throughout the study. A Monkhorst–Pack 5 5 5 sampling was used to evaluate integrals in the reciprocal space. The structural parameters of perfect ZnS calculated by the different DFT functionals as well as the experimental results are listed in Table 1. It can be seen that GGA/WC functional may be expected to produce more reliable predictions of the structures. Therefore the GGA/WC functional was used in all the calculations of ZnS with Zn-vacancy or S-vacancy.
3. Results and discussion 3.1. Effect of vacancies on geometric structure The calculated lattice parameters for the perfect ZnS, the ZnS with Zn-vacancy, and the ZnS with S-vacancy are summarized in Table 2. It can be seen that the presence of both Zn-vacancy and S-vacancy decreases the cell volume of ZnS and results in a slight
Table 2 Effect of Zn-vacancy and S-vacancy on lattice parameters of ZnS. Type of vacancy
˚ Cell constant (A) a
Perfect Zn-vacancy S-vacancy
b
c
Angle (1)
a
b
Volume (A˚ 3)
g
5.390 5.390 5.390 90 90 90 156.576 5.251 5.434 5.405 90.014 89.937 90.067 154.230 5.308 5.308 5.326 90.094 90.091 89.978 150.044
deformation from the perfect cubic structure. In particular, the cell volume of ZnS with S-vacancy decreases by 4.17%, which is much larger than that (1.50%) for ZnS with Zn-vacancy. Since the volume occupied by vacancy S-atom is bigger than that of vacancy Zn-atom, the cell volume decrease due to S-vacancy is more obvious than that due to Zn-vacancy after geometric relaxations. The calculated formation energy of Zn-vacancy is 5.99 eV, which is smaller than that (7.05 eV) of S-vacancy, indicating that the formation of Zn-vacancy is easier than that of S-vacancy in ZnS. 3.2. Effects of vacancies on band structure and density of states The calculated band structures of perfect ZnS, ZnS with Zn-vacancy, and ZnS with S-vacancy are shown in Fig. 2. The value of band-gap was defined as the difference between the conduction band minimum (CBM) and the valence band maximum (VBM) [21]. For perfect ZnS, the calculated band gap is about 2.03 eV, which is close to the other theoretical value of 2.2 eV [22], but much smaller than the experimental value 3.6– 3.8 eV [23]. Our computations, due in part to the use of pseudopotentials and plane waves as opposed to localized orbitals (i.e., Gaussians or exponentials), could not utilize the known method [24] that avoids band gap underestimation. The band-gap of ZnS with Zn-vacancy increases from 2.03 eV to 2.15 eV as compared
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4 2.032 eV
0
Energy (eV)
Energy (eV)
0 -4 -8
4 2.151 eV Energy (eV)
4
-4 -8 -12
-12 G
F
Q
Z
G
2.028 eV
0 -4 -8 -12
G
F
Q
Z
G
G
F
Q
Z
G
Fig. 2. The band structures of (a) perfect ZnS, (b) ZnS with Zn-vacancy, and (c) ZnS with S-vacancy.
s p d
100 50
-4
0
4
8
50
S-atom s p
24
-16
16 8
-12
-8
-4
0
4
8
-12
-8
-4
0
32
4
16 8
-8
-4
0
4
8
100 50
-12
-8
-4
0
4
8
Total 150 100 50 0 -16
-12
-8
-4
0
32
4
8
S-atom s p
24 16 8
-16
-12
-8
-4
0
4
8
200 DOS (states/eV/cell)
150
DOS (states/eV/cell)
Total
50
0 -12
200
200
s p d
100
-16
8
S-atom s p
24
-16
Zn-atom
150
0
0
0
DOS (states/eV/cell)
s p d
100
DOS (states/eV/cell)
-8
DOS (states/eV/cell)
DOS (states/eV/cell)
-12
32
0 -16
Zn-atom
150
0
0
-16
DOS (states/eV/cell)
Zn-atom
150
-16
200
200 DOS (states/eV/cell)
DOS (states/eV/cell)
200
Total 150 100 50 0
-12
-8
Engergy (eV)
-4 0 Engergy (eV)
4
8
-16
-12
-8
-4 0 Engergy (eV)
4
8
Fig. 3. The density of states of (a) perfect ZnS, (b) ZnS with Zn-vacancy, and (c) ZnS with S-vacancy.
to the perfect ZnS, while the band-gap of ZnS with S-vacancy is almost identical to that of the perfect ZnS. To obtain further information about the bond nature of the ZnS with and without vacancy, the electronic density of states (DOS) and partial DOS (PDOS) are calculated and displayed in Fig. 3. For perfect ZnS, the valence bands extend down to about 13.5 eV below the Fermi level. The entire valence bands can be divided into upper and lower parts. The lower valence band at about 12.2 eV consists of the S 3s state. The upper valence band at about 6.0 eV is contributed by the Zn 3d state and S 3p state. The other parts of the valence band mainly consist of the S 3p state. The conduction bands consist of the S 3p and Zn 4s contributions. The ZnS with Zn-vacancy shows DOS very similar to that of the perfect ZnS, suggesting that the presence of Znvacancy has almost no effect on the total DOS of ZnS. For ZnS with S-vacancy, the valence bands are almost the same as those of the
perfect ZnS. The conduction bands are split as compared to the case in the perfect ZnS. The reason was that the inhomogeneous distribution of charge over ZnS with S-vacancy system led to the conduction levels of partial atoms shift. 3.3. Mulliken atomic population analysis The electronic structure of ZnS with and without vacancy can be further analyzed by examining the charge transfer and bond order. The Mulliken atomic charge and overlap population are useful in evaluating the nature of bonds in a compound [25,26]. The results of Mulliken atomic population analysis of atoms around vacancies are listed in Table 3 (the atoms’ serial number is indexed in Fig. 1(b) and (c)). As shown in Table 3, for the perfect ZnS, Zn atoms act as electron donor, which mainly loses 4s state electrons. The valence electron configuration of Zn-atom changes
J. Yao et al. / Physica B 407 (2012) 3888–3892
Table 3 Mulliken atomic population analysis of atoms around Zn-vacancy and S-vacancy (the corresponding serial number of atoms for Mulliken atomic population analysis are shown in Fig. 1). Vacancy
Species Serial number of atoms
s
p
d
F
Total
Charge (e)
Perfect
S Zn S S Zn Zn Zn Zn S S S Zn Zn Zn
1.81 0.57 1.84 1.84 0.58 0.56 0.66 0.58 1.81 1.82 1.81 0.64 0.63 0.62
4.64 1.00 4.53 4.53 1.01 1.02 1.05 1.01 4.62 4.61 4.61 1.10 1.09 1.07
0.00 9.98 0.00 0.00 9.97 9.97 9.97 9.97 0.00 0.00 0.00 9.98 9.98 9.98
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
6.45 11.55 6.38 6.37 11.55 11.54 11.68 11.56 6.43 6.42 6.43 11.71 11.70 11.67
0.45 0.45 0.38 0.37 0.45 0.46 0.32 0.44 0.43 0.42 0.43 0.29 0.30 0.33
Zn-vacancy
S-vacancy
1 1 2, 5 3, 8 3, 14 4, 7 5, 12 6, 10 1, 4, 8, 12 2, 3 7, 10 4 6, 11 13
Table 4 Mulliken atomic population analysis of atoms around Zn-vacancy and S-vacancy. Type of vacancy perfect
Zn-vacancy
S-vacancy
from Zn 3d104s2 to Zn 3p1.003d9.984s0.57 after structure optimization. S atoms act as electron acceptor, whose 3p state gains electrons and loses partial electrons of 3s state. The valence electron configuration of S-atom changes from S 3s23p4 to S 3s1.813p4.64. However, Zn-vacancy makes the S atoms around Zn-vacancy lose 3p electrons and gain 3s electrons. The Mulliken atomic charges of S atoms around Zn-vacancy decreases from 0.45e to 0.38e due to the lack of electrons donated by the Zn atom when it is present. Moreover, the decrease of the Mulliken atomic charges of S atoms around Zn-vacancy leads to the decrease of the attractive power for partial Zn atoms attached with them so that the charges of Zn 5 and Zn 12 decrease from 0.45e to 0.32e. The S-vacancy makes 3s state of Zn atoms around S-vacancy lose fewer electrons than in the case of the perfect ZnS. The Mulliken atomic charges of Zn atoms (Zn 4, Zn 6, Zn 11, and Zn 13) around S-vacancy decreased from 0.45e to 0.29e, 0.30e, 0.30e and 0.33e, respectively. In addition, the S-vacancy also results in a decrease of the charges of S atoms attached to Zn atoms around the S-vacancy. The overlap population can be used to assess the covalent or ionic nature of a bond. A high value of the bond population indicates a covalent bond, while a low value indicates an ionic interaction. Table 4 compares the bond population of atoms around vacancies and related bond lengths. The overlap population of 0.52 for the Zn–S bonds in perfect ZnS indicates that the Zn–S bonds have a covalent character. Compared with perfect ZnS, the Zn-vacancy results in the increase of populations of Zn–S bonds around Zn-vacancy and the decrease of Zn–S bond lengths. This suggests that the Zn-vacancy enhances the covalent character of Zn–S bonds around it. In contrast, the S-vacancy shows much less effect on the bond populations of S–Zn bonds around S-vacancy and therefore the S-vacancy has no obvious effect on the covalent character of S–Zn bonds around S-vacancy. But the bond lengths of Zn–S bonds around S-vacancy increase clearly. 3.4. Electron density and electron density difference analysis In order to further investigate the influence of Zn-vacancy and S-vacancy on charge distribution and electronic interaction, the charge density difference contour plots of ZnS with and without vacancy are presented in Fig. 4. The presence of vacancies affects the charge distribution of atoms around the vacancy in the supercell. As shown in Fig. 4, the charges of S atoms around Znvacancy are lower than those of S atoms located in the other positions and the charges of Zn atoms around S-vacancy are lower
3891
Bond
Population
˚ Length (A)
S–Zn S 2–Zn 4 S 2–Zn 10 S 2–Zn 12 S 3–Zn 3 S 3–Zn 4 S 3–Zn 5 S 5–Zn 5 S 5–Zn 6 S 5–Zn 7 S 8–Zn 7 S 8–Zn 12 S 8–Zn 14 S 1–Zn 4 S 2–Zn 4 S 3–Zn 4 S 2–Zn 6 S 4–Zn 6 S 7–Zn 6 S 3–Zn 11 S 8–Zn 11 S 10–Zn 11 S 7–Zn 13 S 10–Zn 13 S 12–Zn 13
0.52 0.58 0.60 0.66 0.60 0.57 0.65 0.66 0.60 0.58 0.58 0.65 0.60 0.56 0.49 0.49 0.51 0.58 0.50 0.51 0.58 0.50 0.53 0.53 0.59
2.3348 2.3042 2.2844 2.2784 2.2853 2.3073 2.2818 2.2780 2.2840 2.3050 2.3070 2.2808 2.28580 2.37841 2.38206 2.38222 2.35904 2.36238 2.37024 2.35905 2.36244 2.37016 2.34436 2.34441 2.34175
S Zn
Zn
Zn
S
S Zn
Zn
S-vacancy Zn
Zn
S
Zn-vacancy
S Zn
S
S
Zn
Zn
S Zn
Fig. 4. The charge density difference contour plots of (a) perfect ZnS, (b) ZnS with Zn-vacancy, and (c) ZnS with S-vacancy.
than those of Zn atoms located in the other positions. In addition, the strength of the Zn–S bonds neighboring Zn-vacancy increases. These results are coincided with the Mulliken atomic population analysis. Fig. 5 shows the charge density counter plots of ZnS with and without vacancy. It can be seen from Fig. 5 that the electronic interaction between Zn-atom and its neighboring S-atom is completely isotopic for the perfect ZnS. However, the charge density of Zn–S bonds neighboring Zn-vacancy is higher than that of the other Zn–S bonds, suggesting that the covalent character of the Zn–S bonds neighboring Zn-vacancy is strengthened. But the charge density of Zn–S bonds neighboring S-vacancy has no
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J. Yao et al. / Physica B 407 (2012) 3888–3892
S
S Zn
S
Zn
Zn
S
S Zn
Zn
Zn
S Zn-Vacancy
density of states of ZnS. For ZnS with S-vacancy, the valence bands are almost the same as those of the perfect ZnS, while the conduction bands are split compared to the perfect ZnS. However, the presence of Zn-vacancy enlarges the band-gap of ZnS, while S-vacancy has almost no effect on the band-gap. The overlap population and electron density analysis show that Zn–S bonds in perfect ZnS have a covalent character. Compared with the perfect ZnS, the Zn-vacancy intensifies the covalent feature of the Zn–S bonds around Zn-vacancy. In contrast, the S-vacancy shows no obvious effect on the covalent character of S–Zn bonds around S-vacancy.
Zn Acknowledgments
S-vacancy
S Zn
Zn
Zn
This work was financially supported by the Guangxi Natural Science Foundation of China (Nos. 0991247 and 2012jjAA20053) and by the Scientific Research Fund of Guangxi Education Department of China (Nos. 201106LX250 and 201010LX174).
S Zn
References
Fig. 5. The charge density contour plots of (a) perfect ZnS, (b) ZnS with Zn-vacancy, and (c) ZnS with S-vacancy.
obvious change. The results are also in good agreement with the Mulliken atomic population analysis.
4. Conclusions The geometric and electronic structures of ZnS with and without a vacancy were calculated using the DFT method within GGA/WC scheme. The results suggest that both Zn-vacancy and S-vacancy result in the decrease of cell volume of ZnS, especially for S-vacancy. The formation energy of Zn-vacancy is lower than that of S-vacancy, suggesting that Zn-vacancy is easier to form than S-vacancy. Compared to the perfect ZnS, the band-gap of ZnS with Zn-vacancy increases from 2.03 eV to 2.15 eV, while the band-gap of ZnS with S-vacancy is almost identical to that of the perfect ZnS. The presence of vacancies has almost no effect on the distribution of density of states of ZnS. For the perfect ZnS, the lower valence band located at about 12.2 eV consists of the S 3s state. The upper valence band located at about 6.0 eV is contributed by the Zn 3d state and S 3p state. The valence bands close to the Fermi level are mainly contributed by the S 3p state. The conduction bands consist of the S 3p state and Zn 4s state. The presence of Zn-vacancy has almost no effect on the total
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