Journal of the Korean Physical Society, Vol. 60, No. 8, April 2012, pp. 1253∼1257
Electronic Structures and Optical Properties of CuSCN with Cu Vacancies Wei Ji, Guo-Qing Yue, Fu-Shun Ke, Song Wu, Hai-Bin Zhao, Liang-Yao Chen and Song-You Wang∗ Shanghai Ultra-Precision Optical Manufacturing Engineering Center, Department of Optical Science and Engineering, Fudan University, Shanghai 200433, China
Yu Jia School of Physics and Engineering, Zhengzhou University, Zhengzhou 450052, China (Received 12 October 2011) Based on density functional theory (DFT) within the generalized gradient approximation (GGA) using the CASTEP code, we calculated the formation energy of a Cu vacancy, as well as the band structure and the optical properties of β-CuSCN with Cu vacancies. Removal a Cu atom from the 32-site and the 72-site supercell results in an enlargement of the band-gap and a slight relaxation in the lattice parameter. An accepter level above the valence band maximum is observed in the 32-site supercell with a Cu vacancy, which results in the onset of a small absorption pre-peak at 0.65 eV. PACS numbers: 71.55.Cn, 71.15.Mb, 81.40.Tv Keywords: CuSCN, Vacancy defects, Electronic structure, Optical properties DOI: 10.3938/jkps.60.1253
I. INTRODUCTION As the supplies of fossil fuels have been decreasing, energy conservation and alternative energy sources are expected to be investigated to achieve sustainable development [1]. High-efficiency and low-cost dye-sensitized solar cells are considered as good candidates to exploit solar energy, which is regarded as one of the most important alternative energies [2]. For dye-sensitized solar cells, the main problem is the photodegradation of the dye. However, for dye-sensitized solid-state photovoltaic solar cells, dye photodegradation may be minimum because no electrolytes is employed to transport photogenerated carriers [3,4]. In all-solid-state or heterojunction solar cells, the liquid electrolyte is replaced by a molecular type or p-type semiconductor. This can improve the durability of the cells owing to the volatility and the leachability of the acetonitrile used as the solvent in the liquid electrolyte. CuSCN is one of the most promising wide-band-gap ptype semiconductors for this purpose because of its high chemical stability which is due to the polymeric nature of the solid [5, 6]. CuSCN was first used as the hole transport material in dye-sensitized solar cells in 1994 [7]. ZnO (electron conductor) nano-rod arrays coated with CdSe (absorber) and CuSCN (hole conductor) have been demonstrated as solar cell structures [8]. CuSCN is transparent in the visible light spectral ∗ E-mail:
range with a reasonable hole conductivity and chemical stability [9]. It can be prepared by using simple solutionbased growth methods, cutting the cost of the cells. As a good hole transporting material, CuSCN has been used for photovoltaic devices [10,11]. The band-gap of CuSCN film is 3.6 eV. The conductivity is 10−2 ∼ 10−3 S/cm [12]. A cuprous thiocyanate CuSCN composite film can also be used as the active medium layer for a resistive switching memory [13]. CuSCN exists in two polymorphic forms, α [14] and β [14] , where the β form is commonly available and more stable [14, 16–20]. β-CuSCN has a hexagonal crystal structure in which layers of SCN ions separate the planes of Cu atoms and strong Cu-S bonds three-dimensionally interconnect these layers [14, 17]. Because of this polymeric nature, CuSCN thin films, free of defects and pinholes, can be deposited on a large scale. A stoichiometric excess of SCN induces p-type conductivity in β-CuSCN. The p-type copper thiocyanate (CuSCN) is a transparent solid semiconductor [21], and has been widely used in dye-sensitized [20,22] and other nanostructured [8,23] solar cells. The intrinsic acceptors of CuSCN are associated with the copper deficiency [24,25]. For the native defects and the nature of its electronic states, little knowledge is known. In a previous work, Jaffe et al. [26] studied the band structure, bonding characteristics and the basic native defect configurations of hexagonal β-CuSCN by using first principles and corroborated the results by using experimental measurements of thin CuSCN films. The cal-
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Journal of the Korean Physical Society, Vol. 60, No. 8, April 2012 Table 1. Calculated lattice constants for β-CuSCN. a = b (˚ A) c (˚ A) uS (c) uC (c) This work 3.857 10.979 0.431 0.280 Theory [26] 3.781 10.987 0.430 0.279 Expt. [14] 3.850 10.938 0.433 0.277
uN (c) c/a 0.172 2.847 0.172 2.906 0.176 2.841
Fig. 1. (Color online) Ball and stick model of β-CuSCN.
culated valence band DOS matches well with the valence band of CuSCN measured by using X-ray Photoelectron Spectroscopy (XPS). However, to our knowledge, there are no reported optical data for perfect and Cu-defected β-CuSCN. In this paper, the hexagonal type of CuSCN is considered. The formation energy of a Cu vacancy and the electronic and the optical properties of β-CuSCN with Cu vacancies are calculated.
II. COMPUTATIONAL METHODS The β-CuSCN crystal is in the hexagonal space group and has a wurtzite (B4) structure. A ball and stick model of β-CuSCN is shown in Fig. 1. The lattice parameters of CuSCN in the β-phase are a = 3.850 ˚ A and c = 10.938 ˚ A. The c/a ratio is 2.841. A new parameter u is used to give the displacement of an anion from the nearest cation along the c axis in units of the lattice constant c, so the three independent anion displacement parameters are uS = 0.433, uC = 0.277, and uN = 0.176 [26]. The calculations were based on density functional theory (DFT) using the CASTEP code [27]. The generalized gradient approximation (GGA) with the Perdew, Burke, and Enzerhof form of the exchange-correlation functional was employed [25,28]. The 8-site CuSCN primitive cell, the 32-site supercell (2 × 2 × 1 of primitive cell) with a Cu vacancy, and the 72-site supercell (3 × 3 × 1 of primitive cell) with a Cu vacancy were calculated. Geometric optimizations for both the perfect structure and the supercells with vacancies were carried out until changes in energy were less than 5 × 10−6 eV/atom, corresponding to forces less than 0.01 eV/˚ A. The energy cutoff is chosen as 320 eV. Integrations in the Brillouin zone are performed using special k-points generated with 4 × 4 × 2 for the 8-site primitive cell. The k-points set are 2 × 2 × 2 and 1 × 1 × 2 for the 32-site and the 72-site supercells with Cu vacancies, respectively.
Fig. 2. Band structure of CuSCN in the hexagonal βphase.
III. RESULTS AND DISCUSSION The copper deficiency in the CuSCN crystal will influence its band structure and optical properties, especially its intrinsic acceptors [24, 25]. Different supercells were built to study how the concentration of Cu vacancies in CuSCN would affect the band structure and the optical properties. A 32-site supercell (2 × 2 × 1 of primitive cell) with a Cu vacancy and a 72-site supercell (3 × 3 × 1 of primitive cell) with a Cu vacancy were built. CuSCN lattices were calculated for comparison. The consistency between this work and previous study ensures reliability.
1. Perfect CuSCN
A ball and stick model of CuSCN is showed in Fig. 1. The optimized lattice parameters are listed in Table 1. The results are in good agreement with previous theoretical work [26] and the experiments [14]. The band structure of CuSCN is shown in Fig. 2. CuSCN in the hexagonal β-phase can be inferred to be an indirect gap semiconductor with a band-gap of 2.03 eV. The conduction band minimum is at the K point, and the valence band maximum is at the Γ point. However, much care is needed in drawing conclusions from the DFTGGA calculations because its band-gaps are severely underestimated. The calculated total density of states (DOS) and partial density of states for CuSCN are plotted in Fig. 3. The vertical line indicates the Fermi level. It can be seen from the total DOS that the valence band is separated
Electronic Structures and Optical Properties of CuSCN with Cu Vacancies – Wei Ji et al.
Fig. 3. (Color online) Total and partial densities of state calculated for CuSCN in the β-phase.
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Fig. 5. Band structures for two defects of CuSCN: (a) 32site CuSCN with a Cu vacancy, and (b) 72-site CuSCN with a Cu vacancy.
a Cu vacancy were chosen to recognize the influence that the Cu vacancy concentration in CuSCN would have on the band structure and the optical properties. The ball and stick models of both considered supercells are shown in Fig. 4. After geometric optimization, the atoms surrounding the Cu vacancy were slightly relaxed. The formation energy of a vacancy can be calculated by using the equation [29] vac (n − 1, V ) + Ec ] − Erel (n, V ), Efvac = [Erel
Fig. 4. (Color online) Two defected structures of CuSCN. The left one is a 32-site supercell with a Cu vacancy, and the right one is a 72-site supercell with a Cu vacancy.
into two parts, the upper valence band (from −3 eV to 0 eV) and the sub-valence band (from −10 eV to −3 eV). The upper valence band is mostly derived from Cu 3d orbitals. The sub valence band is from −10 eV to −3 eV. It mainly arises from N 2p states, S 3p states and C 2p states, and it can be associated with S-C and C≡N covalent bonds. The bands around −8.5 eV are mainly from S 3p and C 2s states, indicating the S-C covalent bond. The next bands centered around −6 eV have predominantly p states of C and N, cyanide triple bond states. The bands near −3.5 eV are from the Cu-S semi-ionic or Cu-N dative bonds. The conduction band mainly shows a C and N 2p character.
2. CuSCN with Defects
As the p-type character of CuSCN is clearly associated with the Cu deficiency [26], the simpler point defects that occur in CuSCN should be considered. A 32-site supercell (2 × 2 × 1 of primitive cell) with a Cu vacancy and a 72-site supercell (3 × 3 × 1 of primitive cell) with
(1)
where n is the total number of atoms in a perfect lattice vac and V represent the total chosen for calculation. Erel energy and the equilibrium volume of the lattice with an vacancy, respectively. Erel and V are the energy and the equilibrium volume of a perfect lattice, respectively. The crystal lattice achieves the equilibrium volume when the total energy is at minimum. Ec is the energy of an isolated Cu atom. With Eq. (1), the formation energy of a Cu vacancy can be calculated as follows: the total energy of a 32site supercell is −16399.965 eV, that of a 32-site with a Cu vacancy is −15052.606 eV, the energy of an isolated Cu atom is −1342.912 eV, and the calculated formation energy is 4.447 eV. In the same way, the formation energy of a 72-site supercell with a Cu vacancy can be derived. The calculated value of the 72-site supercell with a Cu vacancy is 5.123 eV, so the structure with vacancies in a concentration like that of a 32-site with a Cu vacancy is more stable. The band structures of β-CuSCN with Cu vacancies are calculated, as shown in Fig. 5. It can be seen that the 32-site CuSCN supercell with a Cu vacancy is still an indirect-gap semiconductor. The band gap is 2.205 eV, which is clearly broader than that of the perfect supercell as shown in Fig. 2. The band gap of the 72-site CuSCN supercell is 2.044 eV and transforms into a direct gap. The conduction band has moved upward compared to that of perfect CuSCN. However, the major difference
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Journal of the Korean Physical Society, Vol. 60, No. 8, April 2012
Fig. 8. (Color online) Optical absorption spectra for three models of CuSCN. Fig. 6. (Color online) (a) Calculated total and partial densities of states of a 32-site CuSCN supercell in the β-phase with a Cu vacancy. The smearing width is 0.2 eV. (b) Enlarged total DOS around the Fermi level of a 32-site CuSCN supercell in the β-phase with a Cu vacancy. The smearing width is 0.01 eV.
site supercell with a Cu vacancy is ionic as the S atoms are coordinated tetrahedrally to three copper atoms in mixed ionic-covalent bonding. The existence of the Cu vacancy greatly influences the bonding between S and Cu atoms.
3. Optical Properties
Fig. 7. (Color online) Total and partial densities of states calculated for a 72-site CuSCN supercell in the β-phase with a Cu vacancy.
between the models is that the accepter levels come out above the Fermi level in 32-site CuSCN, which can be seen more clearly in Fig. 6(b). To make the accepter level clearer, we plot the total DOS for different smearing widths in Fig. 6. In the 32-site supercell with a Cu vacancy, two accepter levels are observed, one at about 0.02 eV and the other at 0.09 eV. This result is in agreement with that of a previous calculation . However, in the 72-site supercell with a Cu vacancy, the accepter level is not observed (see Fig. 7) as the concentration of the Cu vacancy is decreased. Which is more similar to a perfect supercell with no vacancy. Both of the conduction bands move upward in these two supercells, resulting in band-gap broadening. Besides, the electron states of Cu atoms are more localized. The 3s states of S atoms are more concentrated at higher energy than they are in a supercell without vacancy. Predominantly the S atom in the 32-
The existence of the Cu vacancy also influences the optical absorption of CuSCN. The absorption spectra at different concentrations of Cu vacancy are given in Fig. 8. The absorption for crystal CuSCN begins to increase obviously at about 2.0 eV. For the 32-site or the 72-site supercell with a Cu vacancy, the value is 2.2 eV, which can be associated with the bang gap’s broadening, as discussed above. However, interestingly a pre-peak is found at 0.65 eV in the infrared spectrum of the 32-site superecll with a Cu vacancy. As discussed in the previous section, excitations from the localized states above the valence bands to the conduction bands may account for the enhanced optical absorption in the infrared region. No absorption peaks are observed in the 72-site supercell with a Cu vacancy at energies before 2.0 eV.
IV. CONCLUSION The electronic structures and the optical properties of β-CuSCN with Cu defects at different concentrations were studied based on the DFT within the generalized gradient approximation. For a 32-site supercell with a Cu vacancy, the calculated formation energy is 4.447 eV, and the formation energy of the 72-site supercell with a Cu vacancy is 5.123 eV, indicating that the structure with a higher concentration of Cu vacancies is more stable. The results of the band structure calculation show that CuSCN is an indirect-gap semiconductor with a band-gap of 2.03 eV. Removal of a Cu atom from the 32-site supercell results in two accepter levels above the Fermi level. The conduction band moves upward, and
Electronic Structures and Optical Properties of CuSCN with Cu Vacancies – Wei Ji et al.
the band-gap is broadened. The absorption spectrum for crystal CuSCN begins to increase at about 2.0 eV. For the 32-site or the 72-site supercell with a Cu vacancy, the onset is at about 2.2 eV. A small absorption peak is observed at 0.65 eV for a 32-site superecll with a Cu vacancy, which should be associated with the accepter level observed in its band structure.
ACKNOWLEDGMENTS This work was partially supported by the National Basic Research Program of China (Nos. 2010CB933703 and 2012CB934303) and by the Natural Science Foundation of China (Grant No. 10974029).
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