First Principles Calculations of Defect Formation in In ...
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Japanese Journal of Applied Physics 50 (2011) 04DP07 DOI: 10.1143/JJAP.50.04DP07
First Principles Calculations of Defect Formation in In-Free Photovoltaic Semiconductors Cu2 ZnSnS4 and Cu2 ZnSnSe4 Tsuyoshi Maeda, Satoshi Nakamura, and Takahiro Wada Department of Materials Chemistry, Ryukoku University, Otsu 520-2194, Japan Received October 12, 2010; revised December 20, 2010; accepted December 21, 2010; published online April 20, 2011 To quantitatively evaluate the formation energies of Cu, Zn, Sn, and S vacancies in kesterite-type Cu2 ZnSnS4 (CZTS), first-principles pseudopotential calculations using plane-wave basis functions were performed. The formation energies of neutral Cu, Zn, Sn, and S vacancies were calculated as a function of the atomic chemical potentials of constituent elements. We compared the vacancy formation in the In-free photovoltaic semiconductor CZTS with those of Cu2 ZnSnSe4 (CZTSe) and CuInSe2 (CIS). The obtained results were as follows. (1) Under the Cu-poor and Zn-rich condition, the formation energy of the Cu vacancy was generally smaller than those of the Zn, Sn and S vacancies in CZTS, as is the case for CZTSe. (2) The formation energies of Cu, Zn, and Sn vacancies in CZTS were larger than those in CZTSe. On the other hand, the formation energy of the S vacancy is smaller than that of the Se vacancy in CZTSe. (3) Under the Cu-poor and Zn-rich condition, the formation energies of the Cu vacancy in CZTS and CZTSe are much larger than that in CIS. These results indicate that in kesterite-type CZTS and CZTSe, the Cu vacancy is easily formed under Cu-poor, Zn-rich, and S(Se)-rich condition, but it is more difficult than that in CIS. # 2011 The Japan Society of Applied Physics
1. Introduction
Cu(In,Ga)Se2 (CIGS) solar cells are among the most promising materials for thin-film solar cells. Recently, finding a substitute for indium in CIS has also become an important issue because indium and gallium are expensive rare metals. Cu2 ZnSnS4 (CZTS) is anticipated as an indiumfree absorber material. Katagiri et al. reported CZTS-based solar cells with an efficiency of 6.7% fabricated by the sputtering and sulfurization method,1) and that they could fabricate high-efficiency CZTS solar cells under Cu-poor and Zn-rich condition in the CuS–ZnS–SnS system.2) Todorov et al. fabricated Cu2 ZnSn(S,Se)4 (CZTSSe) solar cells with an efficiency of 9.6% by the hybrid coating process.3) Most recently, they have reported CZTSSe solar cells with an efficiency of 6.71% fabricated by the aqueous printing process. For the Cu(I)2 –Zn(II)–IV–VI4 compounds, three types of crystal structure have been reported: kesterite, stannite, and wurtz-stannite types. We studied the phase stability of the kesterite-, stannite-, and wurtz-stannite-type Cu2 ZnSnSe4 (CZTSe) by first-principles calculation.4) The formation enthalpy of kesterite-type CZTSe was smaller than those of stannite- and wurtz-stannite-type CZTSe. Then, we confirmed that CZTSe has a kesterite-type structure by neutron powder diffraction.5) We also reported the electronic structures of CZTS and CZTSe by first principles calculations.6) The valence band maximum (VBM) of kesterite-type CZTSe is the antibonding state of (Cu 3d þ Se 4p), while the conduction band minimum (CBM) is the antibonding state of (Sn 5s þ Se 4p). The electronic structure and stability of CZTS and the other quaternary chalcogenide semiconductors were reported by Chen et al.7,8) Recently, a more accurate electronic structure of Cu2 ZnSnS4 has been calculated with the Heyd–Scuseria–Ernzerhof (HSE) hybrid functional by Paier et al.9) The basic science research group at the National Renewable Energy Laboratory (NREL) has studied the electronic structure and defect formation energy of CuInSe2 (CIS) and related compounds since the 1980s. Recently, Chen et al. calculated the formation energies of defects in CZTS.10)
E-mail address: [email protected]
They reported that Cu vacancy and defect pairs such as (VCu þ ZnCu ), (CuZn þ ZnCu ), and (ZnSn þ SnZn ) are easily formed in the Cu-poor and Zn-rich condition.11) They suggested that the intrinsic p-type conductivity in CZTS was attributable to the CuZn antisite, which had a lower formation energy. Nagoya et al. calculated the formation energies of Cu and Zn vacancies and antisite defects such as CuZn , ZnCu , CuZn , and ZnSn .12) They reported that Cu substitution at the Zn site is the most stable defect. Our group studied the defect formation of CuInSe2 (CIS) and related compounds, and reported that the formation energy of the Cu vacancy is smaller than those of In and Se vacancies in CIS.13) Recently, we have reported the formation energies of Cu, Zn, Sn, and Se vacancies in CZTSe in the pseudo-ternary Cu–(Zn1=2 Sn1=2 )–Se system. In CZTSe, the formation energy of the Cu vacancy is smallest under the Cu-poor and Zn-rich condition. The formation energy of the Zn vacancy is smallest under Zn-poor and Serich condition.14) In this study, we calculate the vacancy formation energies in CZTS and CZTSe in the pseudo-ternary Cu2 S–ZnS–SnS2 and Cu2 Se–ZnSe–SnSe2 systems, respectively, because Katagiri et al. reported that they obtained high-efficiency CZTS solar cells under the Cu-poor and Zn-rich condition.2) We compare the vacancy formation in In-free photovoltaic semiconductors CZTS and CZTSe with that of CIS. 2. Computational Procedure
We performed first-principles calculations within a density functional theory with the generalized gradient approximation (GGA),15) using a plane-wave pseudopotential method. The present calculations were performed using the CASTEP program code.16) Ultrasoft pseudopotentials17) were applied with a plane-wave cutoff energy of 350 eV to obtain a strict solution. The total energies of CZTS and CZTSe in the kesterite phase calculated with a cutoff energy of 350 eV agreed with these with a cutoff energy of 500 eV within 0.01 eV. For the primitive cells of CZTS and CZTSe, a 556 k point mesh generated by the Monkhorst–Pack scheme18) was employed for numerical integrations over the Brillouin zone. Self-consistent total energies were obtained by the density-mixing scheme19) in connection with the conjugate gradient technique.20) Atomic positions were
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optimized by the quasi-Newton method with the latest Broyden–Fletcher–Goldfarb–Shanno scheme.21) First, we optimized lattice parameters a and c, and the u-parameter of the S atom, u(S), through the minimization of total energy. The formation energy of point defects was calculated from the difference in total energy between the perfect crystal and the imperfect crystal with defect. The total energy of the perfect crystal was calculated using the with 16 atoms. Calculations for kesterite-type unit cell (I 4) the imperfect crystal with vacancy were performed using the supercell with 64 atoms, which is 4 times greater than that of the kesterite-type unit cell. Since we used a neutral supercell, the result corresponded to quantities for a neutral vacancy. Since we dealt with an imperfect crystal with an infinitely dilute defect concentration, lattice constants were fixed at the optimized values of the perfect crystal. Atomic arrangements around a vacancy were optimized allowing relaxation of the first- and second-nearest neighbor atoms. The relaxation procedures were truncated when all the residual To forces for the relaxed atoms were less than 0.01 eV/A. calculate the chemical potentials of constituent elements, we also performed calculations of many reference materials, i.e., Cu2 S, Cu2 Se, ZnS, ZnSe, SnS2 , SnSe2 , Cu, Zn, Sn, S, and Se.
Table I. Theoretically and experimentally determined lattice parameters a, c, c=a, and u(S) of kesterite-type Cu2 ZnSnS4 calculated using a conventional GGA functional and ultrasoft-type pseudopotential with cutoff energy of 350 eV. The parameters ux (S), uy (S), and uz (S) are the x-, y-, and z-coordinates of S. The lattice parameters and u-parameters of CZTSe are shown for comparison.
a (A) Cu2 ZnSnS4
Theoretical
c (A)
c=a
ux (S) uy (S) uz (S)
5.465 10.944 2.00 0.240 0.232 0.130
Experimental Cu2 ZnSnSe4 Theoretical
5.434 10.856 2.00 0.244 0.244 0.128 5.729 11.427 1.99 0.246 0.230 0.130
ExperimentalaÞ 5.692 11.340 1.99 0.251 0.245 0.129 a) Experimental lattice parameters were determined by Rietveld refinement from powder X-ray diffraction data.5) Table II. Enthalpy of formation Hf of Cu2 ZnSnS4 and reference compounds (Cu2 S, ZnS, SnS2 , and Cu2 SnS3 ). Enthalpies of formation of their selenides are shown for comparison.
Hf (kJ/mol) Theoretical
Experimental
Error (kJ/mol)
Error (eV)
Cu2 S
—
79:5
—
—
ZnS
155:0
205:2
+50.2
+0.52
SnS2
104:6
153:6
+49.0
+0.51
Cu2 SnS3
178:4
Not reported
—
—
Cu2 ZnSnS4
336:9
Not reported
—
—
Cu2 Se
—
65:3
—
—
3.1 Crystallographic parameters of Cu2 ZnSnS4 and Cu2 ZnSnSe4
ZnSe
141:5
170:3
+28.8
+0.30
SnSe2
106:6
121:3
+14.7
+0.15
Table I shows the theoretically determined lattice parameters a, c, c=a, and u(S) of CZTS calculated using a GGAPBE (PBE: Perdew–Burke-Ernzerhof) functional. The parameters ux (S), uy (S), and uz (S) are the x-, y-, and z-coordinates of element S. Those of CZTSe are shown for ref. 14. The lattice parameters of CZTS calculated with the GGA-PBE functional had satisfactory agreement with their experimental values.5) The calculated c=a ratio of CZTS is 2.00, which means that the theoretical lattice constant c of CZTS is equal to 2a. The calculated x-, y-, and z-coordinates of S, ux (S), uy (S), and uz (S), successfully reproduce their experimental values.
Cu2 SnSe3
169:9
Not reported
—
—
Cu2 ZnSnSe4
312:2
Not reported
—
—
3. Results
3.2 Enthalpies of formation of Cu2 ZnSnS4 , Cu2 ZnSnSe4 , and reference compounds
Table II shows the enthalpies of formation of reference compounds ZnS, SnS2 , Cu2 SnS3 , and CZTS calculated from the following equations:4) Hf ðZnSÞ ¼ Et ðZnSÞ ½Et ðZnÞ þ Et ðSÞ; Hf ðSnS2 Þ ¼ Et ðSnS2 Þ ½Et ðSnÞ þ 2Et ðSÞ; Hf ðCu2 SnS3 Þ
crystal structures of Cu2 S and Cu2 Se, Cu atoms occupy a number of sites. The calculated enthalpies of formation of binary compounds Hf (ZnS) and Hf (SnS2 ) are 155:0 (205:2) and 104:6 (153:6) kJ/mol, respectively (experimental values are in parentheses). The calculated enthalpies of formation of binary compounds Hf (ZnSe) and Hf (SnSe2 ) are 141:5 (170:3) and 106:6 (121:3) kJ/mol, respectively. The calculated enthalpies of formation of these binary compounds were successfully reproduced with an error of about 20–50 kJ/mol (about 0.2–0.5 eV). The calculated enthalpies of formation of ternary and quaternary compounds Hf (Cu2 SnS3 ) and Hf (Cu2 ZnSnS4 ) are 178:4 and 336:9 kJ/mol, respectively. The experimental enthalpies of formation of ternary Cu2 SnS3 and Cu2 SnSe3 and quaternary Cu2 ZnSnS4 and Cu2 ZnSnSe4 have not yet been reported. 3.3 Vacancy formation energies in Cu2 ZnSnS4 and Cu2 ZnSnSe4
¼ Et ðCu2 SnS3 Þ ½2Et ðCuÞ þ Et ðSnÞ þ 3Et ðSÞ; Hf ðCu2 ZnSnS4 Þ
The formation energies of a neutral vacancy in a compound depend on the chemical potentials of constituent elements in the system.13) The formation energies of Cu, Zn, Sn, and S vacancies in CZTS can be respectively presented by
¼ Et ðCu2 ZnSnS4 Þ ½2Et ðCuÞ þ Et ðZnÞ þ Et ðSnÞ þ 4Et ðSÞ; where Hf ðXÞ is the enthalpy of formation of X and Et ðYÞ is the total energy of Y. The enthalpies of formation of two of the reference compounds, Cu2 S and Cu2 Se, are not shown in Table II. We could not calculate the accurate total energy of Cu2 S and Cu2 Se by present first principles calculation because, in the
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EF ðVCu Þ ¼ EV t ½Cu2n1 Znn Snn S4n Et ½Cu2n Znn Snn S4n þ Cu ; EF ðVZn Þ ¼ EV t ½Cu2n Znn1 Snn S4n Et ½Cu2n Znn Snn S4n þ Zn ; # 2011 The Japan Society of Applied Physics
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S
ZnS
Cu2ZnSnS4
Cu2S
SnS2
Cu2ZnSnS4
Cu2S
3 Zn
Cu
Cu2SnS3
4 2
Zn:Sn=1:1 µZn+µSn
1
Sn
ZnS
SnS2
Fig. 1. (Color online) Schematic phase diagram of quaternary Cu–Zn– Sn–S system.
(a)
S EF ðVSn Þ ¼ EV t ½Cu2n Znn Snn1 S4n
Cu2ZnSnS4 (CuInSe2)
Et ½Cu2n Znn Snn S4n þ Sn ; EF ðVS Þ ¼ EV t ½Cu2n Znn Snn S4n1 Et ½Cu2n Znn Snn S4n þ S ; where EV t is the total energy of the supercell with a vacancy and Et is the total energy of the perfect crystal of CZTS. The symbol is the chemical potential of the constituent elements (Cu, Zn, Sn, and S) and n ¼ 8. The chemical potential changes depending on the chemical environment of the system. Figure 1 shows a schematic phase diagram of the quaternary Cu–Zn–Sn–S system. In the quaternary system, the chemical potentials of constituent elements, i.e., Cu , Zn , Sn , and S , can change independently. Therefore, it is very complicated to determine the chemical potential of each element. To calculate the chemical potentials of constituent elements simply, we consider the pseudo-ternary system. In the present study, we calculate the vacancy formation energies in CZTS and CZTSe in the pseudoternary Cu2 S–ZnS–SnS2 and Cu2 Se–ZnSe–SnSe2 systems, respectively, because Katagiri et al. reported that they obtained high-efficiency CZTS solar cells under the Cupoor and Zn-rich condition in the CuS–ZnS–SnS system under constant S atmosphere condition.2) Figure 2(a) shows the schematic phase diagrams of the pseudo-ternary Cu2 S– ZnS–SnS2 system. This pseudo-ternary system is shown in the quaternary Cu–Zn–Sn–S system in Fig. 1. Under the condition in which CZTS coexists with each component, the chemical potentials of Cu, Zn, Sn, and S should be correlated with each other to satisfy the following equation: 2Cu þ Zn þ Zn þ 4S ¼ Cu2 ZnSnS4 ðbulkÞ : Chemical potentials for the bulk substances were obtained as the total energies per unit formula by separate calculations, i.e., X ðbulkÞ ¼ Et ðXÞ. Chemical potentials were calculated from the total energy of the reference materials in the pseudo-ternary phase diagram shown in Figs. 2(a) and 2(b). Four points in the pseudo-ternary Cu2 S–ZnS–SnS2 phase diagram shown in Fig. 2(a) correspond to the vertices of the three-phase regions. For example, at point 1, CZTS is in equilibrium with ZnS and SnS2 (Cu-poor, Zn-rich, and Srich). At point 3, CZTS is in equilibrium with Cu2 SnS3 and
3
ZnS+SnS2 (In2Se3)
2 4 1
Cu2S
5 Cu
Zn+Sn Zn:Sn = 1:1 (b)
Fig. 2. (Color online) Schematic phase diagram of pseudo-ternary Cu2 S– ZnS–SnS2 system (a). Points 1 and 2 correspond to Cu-poor conditions. Points 3 and 4 correspond to Cu-rich conditions. Point 1 corresponds to Cupoor, Zn-rich, and S-rich condition. The pseudo-ternary phase diagram of Cu–(Zn þ Sn[Cu : Zn ¼ 1 : 1])–S system (b) is shown for reference.
Cu2 S (Cu-rich, Zn-poor, and S-rich). Points 1 and 2 correspond to the Cu-poor condition and points 3 and 4 correspond to the Cu-rich condition. In the regions where CZTS (CZTSe) coexists with Cu2 S (Cu2 Se), the chemical potentials of the constituent elements were corrected by an experimental enthalpy of formation of Cu2 S (Cu2 Se). The theoretical formation energies of Cu, Zn, Sn, and S vacancies in CZTS are plotted in Fig. 3(a) at four points as indicated in Fig. 2(a). Those of CZTSe are shown in Fig. 3(b). Under the Cu-poor condition such as point 1, the formation energy of the Cu vacancy is smaller than those of Zn, Sn, and S vacancies, as well as the result of CZTSe. In addition, the formation energy of the Zn vacancy is much smaller than those of the Cu vacancy under the Zn-poor and S-rich condition, such as point 3. The formation energy of the Sn vacancy is larger than those of Cu and Zn vacancies under the Cu-poor, Zn-rich, and S-rich condition (Sn-poor condition) shown in Fig. 2(a). Therefore, the Cu vacancy is easily formed under Cu-poor, Zn-rich, and S-rich condition, but the Zn vacancy is easily formed under the Zn-poor and S-rich condition. The formation energies of Cu, Zn, and Sn vacancies in CZTS are larger than those in CZTSe. On the other hand, the formation energy of the S vacancy is a little smaller than that of the Se vacancy in CZTSe. These results indicate that in
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Formation energy (eV)
2.00 1.50 Cu Zn
1.00
Sn S
0.50 0.00 1
2
3
4
Points in schematic phase diagram Fig. 4. (Color online) Comparison of formation energies of Cu vacancies in Cu2 ZnSnS4 , Cu2 ZnSnSe4 , and CuInSe2 .
(a)
Formation energy (eV)
2.00 Cu
1.50
Table III. Formation energy of Cu, Zn, and Sn vacancies in Cu2 ZnSnS4
Zn
and Cu2 ZnSnSe4 under the Cu-poor, Zn-rich, and S(Se)-rich condition and the displacement (l) of the surrounding S or Se after the formation of the vacancy.
Sn
1.00
Se
Vacancy formation energy (eV)
l after formation of the vacancy (A)
VCu
+0.37
0:016 (0:7%)
VZn
+0.49
0:063 (2:7%)
VSn
+2.98
0:089 (3:6%)
VCu VZn
+0.19 +0.27
0:035 (1:4%) 0:036 (1:4%)
VSn
+2.51
0:096 (3:8%)
VCu
0:81
0:006 (0:3%)
VIn
+0.37
0:114 (5:9%)
0.50 0.00 1
2
3
Cu2 ZnSnS4
4
Points in schematic phase diagram (b)
Cu2 ZnSnSe4
Fig. 3. (Color online) Theoretical formation energies of Cu, Zn, Sn, and
S vacancies in Cu2 ZnSnS4 (a) plotted at four points as shown in Fig. 2(a). Those of Cu, Zn, Sn, and Se vacancies in Cu2 ZnSnSe4 (b) are shown for reference.
kesterite-type CZTS and CZTSe, the Cu vacancy is easily formed under Cu-poor, Zn-rich, and S(Se)-rich condition. CZTS-based solar cells with a high efficiency of 6.7% were fabricated in the Cu-poor, Zn-rich, and S-rich condition.2) Therefore, defect formation under the Cu-poor and Zn-rich condition is very important. Point 1 in Fig. 2(a) corresponds to the Cu-poor, Zn-rich, and S-rich condition. For CZTS and CZTSe, under the Cu-poor, Zn-rich, and S(Se)-rich condition [point 1 in Fig. 2(a)], the formation energy of the Cu vacancy is smallest. Therefore, Cu vacancies in CZTS (CZTSe) are easily formed under the Cu-poor, Zn-rich, and S (Se)-rich condition. 4. Discussion
To investigate the difference in the formation energies of the Cu vacancy among CZTS, CZTSe, and CIS, the formation energies of the Cu vacancy in CZTS and CZTSe are plotted in Fig. 4 as indicated in Fig. 2(b) in comparison with the Cu vacancy in CIS. The pseudo-ternary phase diagram of the Cu–(Zn þ Sn½Zn : Sn ¼ 1 : 1)–S system in Fig. 2(b) corresponds to the ternary diagram of the Cu–In–Se system in our previous calculation of the vacancy formation in CIS.13,22) The formation energies of the Cu vacancy in CZTS and CZTSe are much larger than that of the Cu vacancy in CIS under both Cu-poor and Cu-rich conditions. Therefore, Cu
CuInSe2
vacancies in CZTS and CZTSe are not easily formed in comparison with the Cu vacancy in CIS. The formation energies of the Cu, Zn, and Sn vacancies in CZTS and CZTSe in the Cu-poor and Zn-rich condition are summarized in Table III. Those of Cu and In vacancies in the Cu-poor and In-rich condition in CIS are also shown for reference. The displacement (l) of the surrounding S or Se after the formation of the Cu, Zn, or Sn vacancy is also shown in Table III. In CZTS, the jlj after the formation of the Cu vacancy of is slightly smaller than the jlj after the formation 0.016 A The jlj after the formation of of the Zn vacancy of 0.063 A. the Sn vacancy of 0.089 A is much greater than the jlj after We think that the formation of the Cu vacancy of 0.016 A. the crystal structure of CZTS (CZTSe) is mainly established by the chemical bond of Sn–S (Sn–Se). The formation energy of the Cu vacancy in CZTS is larger than those of the Cu vacancy in CIS. If a Cu vacancy is formed, the displacement of surrounding S atoms in CZTS is slightly larger than that in CIS. Therefore, CIS has a large Cu-poor solid solution area with a chalcopyrite structure in the pseudo binary phase diagram of the Cu2 Se–In2 Se3 system. We consider that CZTS and CZTSe also have an area of solid solution with a kesterite structure in the Cu-poor region but they are smaller than that in CIS.
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The electronic structure and characteristics of chemical bonds in stannite-type CZTSe were described in our previous report.6) In the kesterite-type CZTS, there are three types of chemical bond, i.e., Cu–S, Zn–S, and Sn–S bonds. Cu, Zn, and Sn atoms are tetrahedrally coordinated by four S atoms. The electronic structure of kesterite-type CZTS is similar to that of the stannite-type CZTSe because the local crystal structures of kesterite- and stannite-type phases resemble each other.4) Figures 5(a)–5(c) show schematic molecular orbital diagrams of tetrahedral CuS4 7 (a), ZnS4 6 (b), and SnS4 4 (c) clusters. The atomic orbital energies23,24) of component elements of Cu, Zn, Sn, and S for CZTS are shown in Fig. 5. In Fig. 5(a), the Cu 3d orbitals interact with S 3p, leading to the bonding orbitals of (t2 , e), nonbonding orbitals of (t1 , t2 ), and antibonding orbitals of (t2 , e ). All these orbitals of Cu 3d and S 3p are occupied by electrons. The Cu 4s orbital has a covalent interaction with S 3p, leading to an occupied bonding orbital of a1 and an unoccupied antibonding orbital of a1 . The Cu–S bond is a weak covalent bonding because both bonding and antibonding orbitals of Cu 3d and S 3p are occupied, and the bonding orbital (a1 ) of Cu 4s and S 3p is occupied and the antibonding orbital (a1 ) is unoccupied. In Fig. 5(b), the atomic orbital energy of Zn 3d (17:3 eV) is greatly lower than the energy of S 3p (11:6 eV). Zn 4s (9:4 eV) is much closer to S 3p (11:6 eV). The Zn 4s orbital has a strong interaction with S 3p, leading to an occupied bonding orbital of a1 and an unoccupied antibonding orbital of a1 . The bonding orbital (a1 ) of Zn 4s and S 3p is occupied and the antibonding orbital (a1 ) is unoccupied. In Fig. 5(c), the atomic orbital energy of Sn 5s (14:6 eV) is lower than the energy of S 3p (11:6 eV), and that of Sn 5p (7:0 eV) is higher than that of S 3p. The Sn 5s and 5p orbitals in CZTSe are lower than those of In 5s (12:0 eV) and 5p (5:6 eV) in CIS.22) Therefore, the interaction between Sn 5s and S 3p in CZTS is weaker than that between In 5s and Se 4p in CIS. The interaction between Sn 5p and S 3p in CZTS is stronger than that between In 5p and Se 4p in CIS because the energy of Sn 5p is closer to the energy of S 3p than that of In 5p. The average bond order of Cu–S, Zn–S, and Sn–S is calculated from the schematic molecular orbital diagrams in Figs. 5(a)–5(c). The average bond order is [(electrons in the bonding orbitals)/2 (electrons in antibonding orbitals)/ 2]/4. The average bond order of Cu–S, Zn–S, and Sn–S bonds can be calculated as 1/4, 1/4, and 1, respectively. Thus, the Cu–S bond in the kesterite-type CZTS is a weak covalent bonding as is the case with CIS.22) Therefore, the Cu vacancy can be formed easily in CZTS. The Zn 3d orbitals have a weak interaction with S 3p and localize in the lower level of the valence band. The characteristic of the Zn–S bond is more ionic than the Cu–S bond. The Zn–S bond is a little stronger than the Cu–S bond. Therefore, the formation energy of the Zn vacancy is larger than that of the Cu vacancy. The average bond order of the Sn–S bond is much greater than those of the Cu–S and Zn–S bonds. The Sn–S bond in CZTS is much stronger than the Cu–S and Zn– S bonds. Therefore, the formation energy of the Sn vacancy is much larger than those of the Cu and Zn vacancies.
a1* t2* A1
4s (-8.4eV)
3d (-13.5eV)
e*
t1 t2
T1 T2 T2 E A1 3p (-11.6eV)
E T2
a1
e t2
Cu+
CuS4 7cluster
4(S2-)
(a)
a1*
4s (-9.4eV)
A1
t2 e t1 t2
T1 T2 T2 E A1 3p (-11.6eV)
a1 e
3d (-17.3eV)
E T2
t2
Zn2+
ZnS46cluster
4(S2-)
(b)
t2 * a1* 5p (-7.0eV)
T2
t2
T1 T2 T2 E A1
e t1 5s A1 (-14.6eV)
Sn4+
3p (-11.6eV)
t2 a1 SnS44cluster
4(S2-)
(c) Fig. 5. (Color online) Schematic molecular orbital diagrams of tetrahedral CuS4 7 (a), ZnS4 6 (b), and SnS4 4 (c) clusters. Atomic orbital energies of Cu (3d, 4s), Zn (3d, 4s), Sn (5s, 5p), and S (3s, 3p) are in refs. 23 and 24.
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8) S. Chen, X. G. Gong, A. Walsh, and S. H. Wei: Phys. Rev. B 79 (2009)
Acknowledgments
165211.
This work was supported by the Incorporated Administrative Agency New Energy and Industrial Technology Development Organization (NEDO) under the Ministry of Economy, Trade and Industry (METI). This work was also partially supported by a grant based on the High-Tech Research Center Program for private universities from the Japan Ministry of Education, Culture, Sports, Science and Technology.
9) J. Paier, R. Asahi, A. Nagoya, and G. Kresse: Phys. Rev. B 79 (2009)
115126. 10) S. Chen, X. G. Gong, A. Walsh, and S. H. Wei: Appl. Phys. Lett. 96 (2010)
021902. 11) S. Chen, J. H. Yang, X. G. Gong, A. Walsh, and S. H. Wei: Phys. Rev. B
81 (2010) 245204. 12) A. Nagoya, R. Asahi, R. Wahl, and G. Kresse: Phys. Rev. B 81 (2010)
113202. 13) T. Maeda and T. Wada: J. Phys. Chem. Solids 66 (2005) 1924. 14) T. Maeda, S. Nakamura, and T. Wada: to be published in Thin Solid Films. 15) J. P. Perdew, J. A. Chevary, K. A. Jackson, M. R. Pederson, D. J. Singh,
S. H. Vosko, and C. Fiolhais: Phys. Rev. B 46 (1992) 6671. 16) M. D. Segall, P. L. D. Lindan, M. J. Probert, C. J. Pickard, P. J. Hasnip,
1) H. Katagiri, K. Jimbo, M. Tahara, H. Araki, and K. Oishi: Appl. Phys.
Express 1 (2008) 041201. 2) H. Katagiri, K. Jimbo, M. Tahara, H. Araki, and K. Oishi: Mater. Res. Soc.
17) 18) 19) 20)
Symp. Proc. 1165 (2009) 1165-M04-01. 3) T. K. Todorov, K. B. Reuter, and D. B. Mitzi: Adv. Mater. 22 (2010) E156. 4) T. Maeda, S. Nakamura, and T. Wada: Mater. Res. Symp. Proc. 1165
21)
(2009) 1165-M04-03. 5) T. Maeda, S. Nakamura, H. Kou, T. Wada, K. Inoue, and Y. Yamaguchi:
Tech. Dig. PVSEC-19, 2009, CIG-O-44. 6) S. Nakamura, T. Maeda, and T. Wada: Phys. Status Solidi C 6 (2009) 1261. 7) S. Chen, X. G. Gong, A. Walsh, and S. H. Wei: Appl. Phys. Lett. 94 (2009) 041903.
22) 23) 24)
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S. J. Clark, and M. C. Payne: J. Phys.: Condens. Matter 14 (2002) 2717. D. Vanderbilt: Phys. Rev. B 41 (1990) 7892. H. J. Monkhorst and J. D. Pack: Phys. Rev. B 13 (1976) 5188. G. Kresse and J. Furthmu¨ller: Phys. Rev. B 54 (1996) 11169. M. C. Payne, M. P. Teter, D. C. Allan, T. A. Arias, and J. D. Joannopoulos: Rev. Mod. Phys. 64 (1992) 1045. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery: Numerical Recipes (Cambridge University Press, Cambridge, U.K., 1992) 2nd ed., p. 418. T. Maeda and T. Wada: Phys. Status Solidi C 6 (2009) 1312. J. B. Mann, T. L. Meek, and L. C. Allen: J. Am. Chem. Soc. 122 (2000) 2780. J. B. Mann, T. L. Meek, E. T. Knight, J. F. Capitani, and L. C. Allen: J. Am. Chem. Soc. 122 (2000) 5132.
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Japanese Journal of Applied Physics 50 (2011) 04DP07 DOI: 10.1143/JJAP.50.04DP07
First Principles Calculations of Defect Formation in In-Free Photovoltaic Semiconductors Cu2 ZnSnS4 and Cu2 ZnSnSe4 Tsuyoshi Maeda, Satoshi Nakamura, and Takahiro Wada Department of Materials Chemistry, Ryukoku University, Otsu 520-2194, Japan Received October 12, 2010; revised December 20, 2010; accepted December 21, 2010; published online April 20, 2011 To quantitatively evaluate the formation energies of Cu, Zn, Sn, and S vacancies in kesterite-type Cu2 ZnSnS4 (CZTS), first-principles pseudopotential calculations using plane-wave basis functions were performed. The formation energies of neutral Cu, Zn, Sn, and S vacancies were calculated as a function of the atomic chemical potentials of constituent elements. We compared the vacancy formation in the In-free photovoltaic semiconductor CZTS with those of Cu2 ZnSnSe4 (CZTSe) and CuInSe2 (CIS). The obtained results were as follows. (1) Under the Cu-poor and Zn-rich condition, the formation energy of the Cu vacancy was generally smaller than those of the Zn, Sn and S vacancies in CZTS, as is the case for CZTSe. (2) The formation energies of Cu, Zn, and Sn vacancies in CZTS were larger than those in CZTSe. On the other hand, the formation energy of the S vacancy is smaller than that of the Se vacancy in CZTSe. (3) Under the Cu-poor and Zn-rich condition, the formation energies of the Cu vacancy in CZTS and CZTSe are much larger than that in CIS. These results indicate that in kesterite-type CZTS and CZTSe, the Cu vacancy is easily formed under Cu-poor, Zn-rich, and S(Se)-rich condition, but it is more difficult than that in CIS. # 2011 The Japan Society of Applied Physics
1. Introduction
Cu(In,Ga)Se2 (CIGS) solar cells are among the most promising materials for thin-film solar cells. Recently, finding a substitute for indium in CIS has also become an important issue because indium and gallium are expensive rare metals. Cu2 ZnSnS4 (CZTS) is anticipated as an indiumfree absorber material. Katagiri et al. reported CZTS-based solar cells with an efficiency of 6.7% fabricated by the sputtering and sulfurization method,1) and that they could fabricate high-efficiency CZTS solar cells under Cu-poor and Zn-rich condition in the CuS–ZnS–SnS system.2) Todorov et al. fabricated Cu2 ZnSn(S,Se)4 (CZTSSe) solar cells with an efficiency of 9.6% by the hybrid coating process.3) Most recently, they have reported CZTSSe solar cells with an efficiency of 6.71% fabricated by the aqueous printing process. For the Cu(I)2 –Zn(II)–IV–VI4 compounds, three types of crystal structure have been reported: kesterite, stannite, and wurtz-stannite types. We studied the phase stability of the kesterite-, stannite-, and wurtz-stannite-type Cu2 ZnSnSe4 (CZTSe) by first-principles calculation.4) The formation enthalpy of kesterite-type CZTSe was smaller than those of stannite- and wurtz-stannite-type CZTSe. Then, we confirmed that CZTSe has a kesterite-type structure by neutron powder diffraction.5) We also reported the electronic structures of CZTS and CZTSe by first principles calculations.6) The valence band maximum (VBM) of kesterite-type CZTSe is the antibonding state of (Cu 3d þ Se 4p), while the conduction band minimum (CBM) is the antibonding state of (Sn 5s þ Se 4p). The electronic structure and stability of CZTS and the other quaternary chalcogenide semiconductors were reported by Chen et al.7,8) Recently, a more accurate electronic structure of Cu2 ZnSnS4 has been calculated with the Heyd–Scuseria–Ernzerhof (HSE) hybrid functional by Paier et al.9) The basic science research group at the National Renewable Energy Laboratory (NREL) has studied the electronic structure and defect formation energy of CuInSe2 (CIS) and related compounds since the 1980s. Recently, Chen et al. calculated the formation energies of defects in CZTS.10)
E-mail address: [email protected]
They reported that Cu vacancy and defect pairs such as (VCu þ ZnCu ), (CuZn þ ZnCu ), and (ZnSn þ SnZn ) are easily formed in the Cu-poor and Zn-rich condition.11) They suggested that the intrinsic p-type conductivity in CZTS was attributable to the CuZn antisite, which had a lower formation energy. Nagoya et al. calculated the formation energies of Cu and Zn vacancies and antisite defects such as CuZn , ZnCu , CuZn , and ZnSn .12) They reported that Cu substitution at the Zn site is the most stable defect. Our group studied the defect formation of CuInSe2 (CIS) and related compounds, and reported that the formation energy of the Cu vacancy is smaller than those of In and Se vacancies in CIS.13) Recently, we have reported the formation energies of Cu, Zn, Sn, and Se vacancies in CZTSe in the pseudo-ternary Cu–(Zn1=2 Sn1=2 )–Se system. In CZTSe, the formation energy of the Cu vacancy is smallest under the Cu-poor and Zn-rich condition. The formation energy of the Zn vacancy is smallest under Zn-poor and Serich condition.14) In this study, we calculate the vacancy formation energies in CZTS and CZTSe in the pseudo-ternary Cu2 S–ZnS–SnS2 and Cu2 Se–ZnSe–SnSe2 systems, respectively, because Katagiri et al. reported that they obtained high-efficiency CZTS solar cells under the Cu-poor and Zn-rich condition.2) We compare the vacancy formation in In-free photovoltaic semiconductors CZTS and CZTSe with that of CIS. 2. Computational Procedure
We performed first-principles calculations within a density functional theory with the generalized gradient approximation (GGA),15) using a plane-wave pseudopotential method. The present calculations were performed using the CASTEP program code.16) Ultrasoft pseudopotentials17) were applied with a plane-wave cutoff energy of 350 eV to obtain a strict solution. The total energies of CZTS and CZTSe in the kesterite phase calculated with a cutoff energy of 350 eV agreed with these with a cutoff energy of 500 eV within 0.01 eV. For the primitive cells of CZTS and CZTSe, a 556 k point mesh generated by the Monkhorst–Pack scheme18) was employed for numerical integrations over the Brillouin zone. Self-consistent total energies were obtained by the density-mixing scheme19) in connection with the conjugate gradient technique.20) Atomic positions were
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optimized by the quasi-Newton method with the latest Broyden–Fletcher–Goldfarb–Shanno scheme.21) First, we optimized lattice parameters a and c, and the u-parameter of the S atom, u(S), through the minimization of total energy. The formation energy of point defects was calculated from the difference in total energy between the perfect crystal and the imperfect crystal with defect. The total energy of the perfect crystal was calculated using the with 16 atoms. Calculations for kesterite-type unit cell (I 4) the imperfect crystal with vacancy were performed using the supercell with 64 atoms, which is 4 times greater than that of the kesterite-type unit cell. Since we used a neutral supercell, the result corresponded to quantities for a neutral vacancy. Since we dealt with an imperfect crystal with an infinitely dilute defect concentration, lattice constants were fixed at the optimized values of the perfect crystal. Atomic arrangements around a vacancy were optimized allowing relaxation of the first- and second-nearest neighbor atoms. The relaxation procedures were truncated when all the residual To forces for the relaxed atoms were less than 0.01 eV/A. calculate the chemical potentials of constituent elements, we also performed calculations of many reference materials, i.e., Cu2 S, Cu2 Se, ZnS, ZnSe, SnS2 , SnSe2 , Cu, Zn, Sn, S, and Se.
Table I. Theoretically and experimentally determined lattice parameters a, c, c=a, and u(S) of kesterite-type Cu2 ZnSnS4 calculated using a conventional GGA functional and ultrasoft-type pseudopotential with cutoff energy of 350 eV. The parameters ux (S), uy (S), and uz (S) are the x-, y-, and z-coordinates of S. The lattice parameters and u-parameters of CZTSe are shown for comparison.
a (A) Cu2 ZnSnS4
Theoretical
c (A)
c=a
ux (S) uy (S) uz (S)
5.465 10.944 2.00 0.240 0.232 0.130
Experimental Cu2 ZnSnSe4 Theoretical
5.434 10.856 2.00 0.244 0.244 0.128 5.729 11.427 1.99 0.246 0.230 0.130
ExperimentalaÞ 5.692 11.340 1.99 0.251 0.245 0.129 a) Experimental lattice parameters were determined by Rietveld refinement from powder X-ray diffraction data.5) Table II. Enthalpy of formation Hf of Cu2 ZnSnS4 and reference compounds (Cu2 S, ZnS, SnS2 , and Cu2 SnS3 ). Enthalpies of formation of their selenides are shown for comparison.
Hf (kJ/mol) Theoretical
Experimental
Error (kJ/mol)
Error (eV)
Cu2 S
—
79:5
—
—
ZnS
155:0
205:2
+50.2
+0.52
SnS2
104:6
153:6
+49.0
+0.51
Cu2 SnS3
178:4
Not reported
—
—
Cu2 ZnSnS4
336:9
Not reported
—
—
Cu2 Se
—
65:3
—
—
3.1 Crystallographic parameters of Cu2 ZnSnS4 and Cu2 ZnSnSe4
ZnSe
141:5
170:3
+28.8
+0.30
SnSe2
106:6
121:3
+14.7
+0.15
Table I shows the theoretically determined lattice parameters a, c, c=a, and u(S) of CZTS calculated using a GGAPBE (PBE: Perdew–Burke-Ernzerhof) functional. The parameters ux (S), uy (S), and uz (S) are the x-, y-, and z-coordinates of element S. Those of CZTSe are shown for ref. 14. The lattice parameters of CZTS calculated with the GGA-PBE functional had satisfactory agreement with their experimental values.5) The calculated c=a ratio of CZTS is 2.00, which means that the theoretical lattice constant c of CZTS is equal to 2a. The calculated x-, y-, and z-coordinates of S, ux (S), uy (S), and uz (S), successfully reproduce their experimental values.
Cu2 SnSe3
169:9
Not reported
—
—
Cu2 ZnSnSe4
312:2
Not reported
—
—
3. Results
3.2 Enthalpies of formation of Cu2 ZnSnS4 , Cu2 ZnSnSe4 , and reference compounds
Table II shows the enthalpies of formation of reference compounds ZnS, SnS2 , Cu2 SnS3 , and CZTS calculated from the following equations:4) Hf ðZnSÞ ¼ Et ðZnSÞ ½Et ðZnÞ þ Et ðSÞ; Hf ðSnS2 Þ ¼ Et ðSnS2 Þ ½Et ðSnÞ þ 2Et ðSÞ; Hf ðCu2 SnS3 Þ
crystal structures of Cu2 S and Cu2 Se, Cu atoms occupy a number of sites. The calculated enthalpies of formation of binary compounds Hf (ZnS) and Hf (SnS2 ) are 155:0 (205:2) and 104:6 (153:6) kJ/mol, respectively (experimental values are in parentheses). The calculated enthalpies of formation of binary compounds Hf (ZnSe) and Hf (SnSe2 ) are 141:5 (170:3) and 106:6 (121:3) kJ/mol, respectively. The calculated enthalpies of formation of these binary compounds were successfully reproduced with an error of about 20–50 kJ/mol (about 0.2–0.5 eV). The calculated enthalpies of formation of ternary and quaternary compounds Hf (Cu2 SnS3 ) and Hf (Cu2 ZnSnS4 ) are 178:4 and 336:9 kJ/mol, respectively. The experimental enthalpies of formation of ternary Cu2 SnS3 and Cu2 SnSe3 and quaternary Cu2 ZnSnS4 and Cu2 ZnSnSe4 have not yet been reported. 3.3 Vacancy formation energies in Cu2 ZnSnS4 and Cu2 ZnSnSe4
¼ Et ðCu2 SnS3 Þ ½2Et ðCuÞ þ Et ðSnÞ þ 3Et ðSÞ; Hf ðCu2 ZnSnS4 Þ
The formation energies of a neutral vacancy in a compound depend on the chemical potentials of constituent elements in the system.13) The formation energies of Cu, Zn, Sn, and S vacancies in CZTS can be respectively presented by
¼ Et ðCu2 ZnSnS4 Þ ½2Et ðCuÞ þ Et ðZnÞ þ Et ðSnÞ þ 4Et ðSÞ; where Hf ðXÞ is the enthalpy of formation of X and Et ðYÞ is the total energy of Y. The enthalpies of formation of two of the reference compounds, Cu2 S and Cu2 Se, are not shown in Table II. We could not calculate the accurate total energy of Cu2 S and Cu2 Se by present first principles calculation because, in the
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EF ðVCu Þ ¼ EV t ½Cu2n1 Znn Snn S4n Et ½Cu2n Znn Snn S4n þ Cu ; EF ðVZn Þ ¼ EV t ½Cu2n Znn1 Snn S4n Et ½Cu2n Znn Snn S4n þ Zn ; # 2011 The Japan Society of Applied Physics
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S
ZnS
Cu2ZnSnS4
Cu2S
SnS2
Cu2ZnSnS4
Cu2S
3 Zn
Cu
Cu2SnS3
4 2
Zn:Sn=1:1 µZn+µSn
1
Sn
ZnS
SnS2
Fig. 1. (Color online) Schematic phase diagram of quaternary Cu–Zn– Sn–S system.
(a)
S EF ðVSn Þ ¼ EV t ½Cu2n Znn Snn1 S4n
Cu2ZnSnS4 (CuInSe2)
Et ½Cu2n Znn Snn S4n þ Sn ; EF ðVS Þ ¼ EV t ½Cu2n Znn Snn S4n1 Et ½Cu2n Znn Snn S4n þ S ; where EV t is the total energy of the supercell with a vacancy and Et is the total energy of the perfect crystal of CZTS. The symbol is the chemical potential of the constituent elements (Cu, Zn, Sn, and S) and n ¼ 8. The chemical potential changes depending on the chemical environment of the system. Figure 1 shows a schematic phase diagram of the quaternary Cu–Zn–Sn–S system. In the quaternary system, the chemical potentials of constituent elements, i.e., Cu , Zn , Sn , and S , can change independently. Therefore, it is very complicated to determine the chemical potential of each element. To calculate the chemical potentials of constituent elements simply, we consider the pseudo-ternary system. In the present study, we calculate the vacancy formation energies in CZTS and CZTSe in the pseudoternary Cu2 S–ZnS–SnS2 and Cu2 Se–ZnSe–SnSe2 systems, respectively, because Katagiri et al. reported that they obtained high-efficiency CZTS solar cells under the Cupoor and Zn-rich condition in the CuS–ZnS–SnS system under constant S atmosphere condition.2) Figure 2(a) shows the schematic phase diagrams of the pseudo-ternary Cu2 S– ZnS–SnS2 system. This pseudo-ternary system is shown in the quaternary Cu–Zn–Sn–S system in Fig. 1. Under the condition in which CZTS coexists with each component, the chemical potentials of Cu, Zn, Sn, and S should be correlated with each other to satisfy the following equation: 2Cu þ Zn þ Zn þ 4S ¼ Cu2 ZnSnS4 ðbulkÞ : Chemical potentials for the bulk substances were obtained as the total energies per unit formula by separate calculations, i.e., X ðbulkÞ ¼ Et ðXÞ. Chemical potentials were calculated from the total energy of the reference materials in the pseudo-ternary phase diagram shown in Figs. 2(a) and 2(b). Four points in the pseudo-ternary Cu2 S–ZnS–SnS2 phase diagram shown in Fig. 2(a) correspond to the vertices of the three-phase regions. For example, at point 1, CZTS is in equilibrium with ZnS and SnS2 (Cu-poor, Zn-rich, and Srich). At point 3, CZTS is in equilibrium with Cu2 SnS3 and
3
ZnS+SnS2 (In2Se3)
2 4 1
Cu2S
5 Cu
Zn+Sn Zn:Sn = 1:1 (b)
Fig. 2. (Color online) Schematic phase diagram of pseudo-ternary Cu2 S– ZnS–SnS2 system (a). Points 1 and 2 correspond to Cu-poor conditions. Points 3 and 4 correspond to Cu-rich conditions. Point 1 corresponds to Cupoor, Zn-rich, and S-rich condition. The pseudo-ternary phase diagram of Cu–(Zn þ Sn[Cu : Zn ¼ 1 : 1])–S system (b) is shown for reference.
Cu2 S (Cu-rich, Zn-poor, and S-rich). Points 1 and 2 correspond to the Cu-poor condition and points 3 and 4 correspond to the Cu-rich condition. In the regions where CZTS (CZTSe) coexists with Cu2 S (Cu2 Se), the chemical potentials of the constituent elements were corrected by an experimental enthalpy of formation of Cu2 S (Cu2 Se). The theoretical formation energies of Cu, Zn, Sn, and S vacancies in CZTS are plotted in Fig. 3(a) at four points as indicated in Fig. 2(a). Those of CZTSe are shown in Fig. 3(b). Under the Cu-poor condition such as point 1, the formation energy of the Cu vacancy is smaller than those of Zn, Sn, and S vacancies, as well as the result of CZTSe. In addition, the formation energy of the Zn vacancy is much smaller than those of the Cu vacancy under the Zn-poor and S-rich condition, such as point 3. The formation energy of the Sn vacancy is larger than those of Cu and Zn vacancies under the Cu-poor, Zn-rich, and S-rich condition (Sn-poor condition) shown in Fig. 2(a). Therefore, the Cu vacancy is easily formed under Cu-poor, Zn-rich, and S-rich condition, but the Zn vacancy is easily formed under the Zn-poor and S-rich condition. The formation energies of Cu, Zn, and Sn vacancies in CZTS are larger than those in CZTSe. On the other hand, the formation energy of the S vacancy is a little smaller than that of the Se vacancy in CZTSe. These results indicate that in
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Formation energy (eV)
2.00 1.50 Cu Zn
1.00
Sn S
0.50 0.00 1
2
3
4
Points in schematic phase diagram Fig. 4. (Color online) Comparison of formation energies of Cu vacancies in Cu2 ZnSnS4 , Cu2 ZnSnSe4 , and CuInSe2 .
(a)
Formation energy (eV)
2.00 Cu
1.50
Table III. Formation energy of Cu, Zn, and Sn vacancies in Cu2 ZnSnS4
Zn
and Cu2 ZnSnSe4 under the Cu-poor, Zn-rich, and S(Se)-rich condition and the displacement (l) of the surrounding S or Se after the formation of the vacancy.
Sn
1.00
Se
Vacancy formation energy (eV)
l after formation of the vacancy (A)
VCu
+0.37
0:016 (0:7%)
VZn
+0.49
0:063 (2:7%)
VSn
+2.98
0:089 (3:6%)
VCu VZn
+0.19 +0.27
0:035 (1:4%) 0:036 (1:4%)
VSn
+2.51
0:096 (3:8%)
VCu
0:81
0:006 (0:3%)
VIn
+0.37
0:114 (5:9%)
0.50 0.00 1
2
3
Cu2 ZnSnS4
4
Points in schematic phase diagram (b)
Cu2 ZnSnSe4
Fig. 3. (Color online) Theoretical formation energies of Cu, Zn, Sn, and
S vacancies in Cu2 ZnSnS4 (a) plotted at four points as shown in Fig. 2(a). Those of Cu, Zn, Sn, and Se vacancies in Cu2 ZnSnSe4 (b) are shown for reference.
kesterite-type CZTS and CZTSe, the Cu vacancy is easily formed under Cu-poor, Zn-rich, and S(Se)-rich condition. CZTS-based solar cells with a high efficiency of 6.7% were fabricated in the Cu-poor, Zn-rich, and S-rich condition.2) Therefore, defect formation under the Cu-poor and Zn-rich condition is very important. Point 1 in Fig. 2(a) corresponds to the Cu-poor, Zn-rich, and S-rich condition. For CZTS and CZTSe, under the Cu-poor, Zn-rich, and S(Se)-rich condition [point 1 in Fig. 2(a)], the formation energy of the Cu vacancy is smallest. Therefore, Cu vacancies in CZTS (CZTSe) are easily formed under the Cu-poor, Zn-rich, and S (Se)-rich condition. 4. Discussion
To investigate the difference in the formation energies of the Cu vacancy among CZTS, CZTSe, and CIS, the formation energies of the Cu vacancy in CZTS and CZTSe are plotted in Fig. 4 as indicated in Fig. 2(b) in comparison with the Cu vacancy in CIS. The pseudo-ternary phase diagram of the Cu–(Zn þ Sn½Zn : Sn ¼ 1 : 1)–S system in Fig. 2(b) corresponds to the ternary diagram of the Cu–In–Se system in our previous calculation of the vacancy formation in CIS.13,22) The formation energies of the Cu vacancy in CZTS and CZTSe are much larger than that of the Cu vacancy in CIS under both Cu-poor and Cu-rich conditions. Therefore, Cu
CuInSe2
vacancies in CZTS and CZTSe are not easily formed in comparison with the Cu vacancy in CIS. The formation energies of the Cu, Zn, and Sn vacancies in CZTS and CZTSe in the Cu-poor and Zn-rich condition are summarized in Table III. Those of Cu and In vacancies in the Cu-poor and In-rich condition in CIS are also shown for reference. The displacement (l) of the surrounding S or Se after the formation of the Cu, Zn, or Sn vacancy is also shown in Table III. In CZTS, the jlj after the formation of the Cu vacancy of is slightly smaller than the jlj after the formation 0.016 A The jlj after the formation of of the Zn vacancy of 0.063 A. the Sn vacancy of 0.089 A is much greater than the jlj after We think that the formation of the Cu vacancy of 0.016 A. the crystal structure of CZTS (CZTSe) is mainly established by the chemical bond of Sn–S (Sn–Se). The formation energy of the Cu vacancy in CZTS is larger than those of the Cu vacancy in CIS. If a Cu vacancy is formed, the displacement of surrounding S atoms in CZTS is slightly larger than that in CIS. Therefore, CIS has a large Cu-poor solid solution area with a chalcopyrite structure in the pseudo binary phase diagram of the Cu2 Se–In2 Se3 system. We consider that CZTS and CZTSe also have an area of solid solution with a kesterite structure in the Cu-poor region but they are smaller than that in CIS.
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The electronic structure and characteristics of chemical bonds in stannite-type CZTSe were described in our previous report.6) In the kesterite-type CZTS, there are three types of chemical bond, i.e., Cu–S, Zn–S, and Sn–S bonds. Cu, Zn, and Sn atoms are tetrahedrally coordinated by four S atoms. The electronic structure of kesterite-type CZTS is similar to that of the stannite-type CZTSe because the local crystal structures of kesterite- and stannite-type phases resemble each other.4) Figures 5(a)–5(c) show schematic molecular orbital diagrams of tetrahedral CuS4 7 (a), ZnS4 6 (b), and SnS4 4 (c) clusters. The atomic orbital energies23,24) of component elements of Cu, Zn, Sn, and S for CZTS are shown in Fig. 5. In Fig. 5(a), the Cu 3d orbitals interact with S 3p, leading to the bonding orbitals of (t2 , e), nonbonding orbitals of (t1 , t2 ), and antibonding orbitals of (t2 , e ). All these orbitals of Cu 3d and S 3p are occupied by electrons. The Cu 4s orbital has a covalent interaction with S 3p, leading to an occupied bonding orbital of a1 and an unoccupied antibonding orbital of a1 . The Cu–S bond is a weak covalent bonding because both bonding and antibonding orbitals of Cu 3d and S 3p are occupied, and the bonding orbital (a1 ) of Cu 4s and S 3p is occupied and the antibonding orbital (a1 ) is unoccupied. In Fig. 5(b), the atomic orbital energy of Zn 3d (17:3 eV) is greatly lower than the energy of S 3p (11:6 eV). Zn 4s (9:4 eV) is much closer to S 3p (11:6 eV). The Zn 4s orbital has a strong interaction with S 3p, leading to an occupied bonding orbital of a1 and an unoccupied antibonding orbital of a1 . The bonding orbital (a1 ) of Zn 4s and S 3p is occupied and the antibonding orbital (a1 ) is unoccupied. In Fig. 5(c), the atomic orbital energy of Sn 5s (14:6 eV) is lower than the energy of S 3p (11:6 eV), and that of Sn 5p (7:0 eV) is higher than that of S 3p. The Sn 5s and 5p orbitals in CZTSe are lower than those of In 5s (12:0 eV) and 5p (5:6 eV) in CIS.22) Therefore, the interaction between Sn 5s and S 3p in CZTS is weaker than that between In 5s and Se 4p in CIS. The interaction between Sn 5p and S 3p in CZTS is stronger than that between In 5p and Se 4p in CIS because the energy of Sn 5p is closer to the energy of S 3p than that of In 5p. The average bond order of Cu–S, Zn–S, and Sn–S is calculated from the schematic molecular orbital diagrams in Figs. 5(a)–5(c). The average bond order is [(electrons in the bonding orbitals)/2 (electrons in antibonding orbitals)/ 2]/4. The average bond order of Cu–S, Zn–S, and Sn–S bonds can be calculated as 1/4, 1/4, and 1, respectively. Thus, the Cu–S bond in the kesterite-type CZTS is a weak covalent bonding as is the case with CIS.22) Therefore, the Cu vacancy can be formed easily in CZTS. The Zn 3d orbitals have a weak interaction with S 3p and localize in the lower level of the valence band. The characteristic of the Zn–S bond is more ionic than the Cu–S bond. The Zn–S bond is a little stronger than the Cu–S bond. Therefore, the formation energy of the Zn vacancy is larger than that of the Cu vacancy. The average bond order of the Sn–S bond is much greater than those of the Cu–S and Zn–S bonds. The Sn–S bond in CZTS is much stronger than the Cu–S and Zn– S bonds. Therefore, the formation energy of the Sn vacancy is much larger than those of the Cu and Zn vacancies.
a1* t2* A1
4s (-8.4eV)
3d (-13.5eV)
e*
t1 t2
T1 T2 T2 E A1 3p (-11.6eV)
E T2
a1
e t2
Cu+
CuS4 7cluster
4(S2-)
(a)
a1*
4s (-9.4eV)
A1
t2 e t1 t2
T1 T2 T2 E A1 3p (-11.6eV)
a1 e
3d (-17.3eV)
E T2
t2
Zn2+
ZnS46cluster
4(S2-)
(b)
t2 * a1* 5p (-7.0eV)
T2
t2
T1 T2 T2 E A1
e t1 5s A1 (-14.6eV)
Sn4+
3p (-11.6eV)
t2 a1 SnS44cluster
4(S2-)
(c) Fig. 5. (Color online) Schematic molecular orbital diagrams of tetrahedral CuS4 7 (a), ZnS4 6 (b), and SnS4 4 (c) clusters. Atomic orbital energies of Cu (3d, 4s), Zn (3d, 4s), Sn (5s, 5p), and S (3s, 3p) are in refs. 23 and 24.
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8) S. Chen, X. G. Gong, A. Walsh, and S. H. Wei: Phys. Rev. B 79 (2009)
Acknowledgments
165211.
This work was supported by the Incorporated Administrative Agency New Energy and Industrial Technology Development Organization (NEDO) under the Ministry of Economy, Trade and Industry (METI). This work was also partially supported by a grant based on the High-Tech Research Center Program for private universities from the Japan Ministry of Education, Culture, Sports, Science and Technology.
9) J. Paier, R. Asahi, A. Nagoya, and G. Kresse: Phys. Rev. B 79 (2009)
115126. 10) S. Chen, X. G. Gong, A. Walsh, and S. H. Wei: Appl. Phys. Lett. 96 (2010)
021902. 11) S. Chen, J. H. Yang, X. G. Gong, A. Walsh, and S. H. Wei: Phys. Rev. B
81 (2010) 245204. 12) A. Nagoya, R. Asahi, R. Wahl, and G. Kresse: Phys. Rev. B 81 (2010)
113202. 13) T. Maeda and T. Wada: J. Phys. Chem. Solids 66 (2005) 1924. 14) T. Maeda, S. Nakamura, and T. Wada: to be published in Thin Solid Films. 15) J. P. Perdew, J. A. Chevary, K. A. Jackson, M. R. Pederson, D. J. Singh,
S. H. Vosko, and C. Fiolhais: Phys. Rev. B 46 (1992) 6671. 16) M. D. Segall, P. L. D. Lindan, M. J. Probert, C. J. Pickard, P. J. Hasnip,
1) H. Katagiri, K. Jimbo, M. Tahara, H. Araki, and K. Oishi: Appl. Phys.
Express 1 (2008) 041201. 2) H. Katagiri, K. Jimbo, M. Tahara, H. Araki, and K. Oishi: Mater. Res. Soc.
17) 18) 19) 20)
Symp. Proc. 1165 (2009) 1165-M04-01. 3) T. K. Todorov, K. B. Reuter, and D. B. Mitzi: Adv. Mater. 22 (2010) E156. 4) T. Maeda, S. Nakamura, and T. Wada: Mater. Res. Symp. Proc. 1165
21)
(2009) 1165-M04-03. 5) T. Maeda, S. Nakamura, H. Kou, T. Wada, K. Inoue, and Y. Yamaguchi:
Tech. Dig. PVSEC-19, 2009, CIG-O-44. 6) S. Nakamura, T. Maeda, and T. Wada: Phys. Status Solidi C 6 (2009) 1261. 7) S. Chen, X. G. Gong, A. Walsh, and S. H. Wei: Appl. Phys. Lett. 94 (2009) 041903.
22) 23) 24)
04DP07-6
S. J. Clark, and M. C. Payne: J. Phys.: Condens. Matter 14 (2002) 2717. D. Vanderbilt: Phys. Rev. B 41 (1990) 7892. H. J. Monkhorst and J. D. Pack: Phys. Rev. B 13 (1976) 5188. G. Kresse and J. Furthmu¨ller: Phys. Rev. B 54 (1996) 11169. M. C. Payne, M. P. Teter, D. C. Allan, T. A. Arias, and J. D. Joannopoulos: Rev. Mod. Phys. 64 (1992) 1045. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery: Numerical Recipes (Cambridge University Press, Cambridge, U.K., 1992) 2nd ed., p. 418. T. Maeda and T. Wada: Phys. Status Solidi C 6 (2009) 1312. J. B. Mann, T. L. Meek, and L. C. Allen: J. Am. Chem. Soc. 122 (2000) 2780. J. B. Mann, T. L. Meek, E. T. Knight, J. F. Capitani, and L. C. Allen: J. Am. Chem. Soc. 122 (2000) 5132.
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