Crystallographic and optical properties and band structures of CuInSe2, CuIn3Se5, and CuIn5Se8 phases in Cu-poor Cu2Se–In2Se3 pseudo-binary system

We prepared CuInSe2 and Cu-poor Cu–In–Se (CIS) phases such as CuIn3Se5 and CuIn5Se8 in the composition of (1 − x)Cu2Se–(x)In2Se3 with 0.5 ≤ x ≤ 1.0. The crystal structure of the sample changed from chalcopyrite-type CuInSe2 to hexagonal CuIn5Se8 through stannite-type CuIn3Se5 with increasing x (decreasing Cu/In ratio). The band-gap energies of Cu-poor CIS samples, i.e., CuIn3Se5 (1.17 eV) and CuIn5Se8 (1.22–1.24 eV), are larger than that of chalcopyrite-type CuInSe2 (0.99 eV). The energy levels of the valence band maxima (VBMs) were estimated from the ionization energy by photoemission yield spectroscopy (PYS) measurements. The energy levels of the VBMs of the Cu-poor CIS samples decrease rapidly with decreasing Cu/In ratio. The ionization energy of stannite-type CuIn3Se5 is 0.4 eV larger than that of chalcopyrite-type CuInSe2. The ionization energy of CuIn5Se8 is 0.1–0.3 eV larger than that of CuIn3Se5. These results show that the energy position of the VBM from the vacuum level of Cu-poor CIS phases, such as CuIn3Se5 and CuIn5Se8, is deeper than that of CuInSe2. To understand the electronic structure of Cu-poor CIS compounds, we performed first-principles band structure calculations on stannite-type CuIn5Se8 and a reference compound, tetragonal chalcopyrite-type CuInSe2, using the HSE06 nonlocal screened hybrid density functional. The calculated band-gap energy of tetragonal stannite-type CuIn5Se8 (1.19 eV) is larger than that of chalcopyrite-type CuInSe2 (0.94 eV).


Introduction
CuInSe 2 (CIS), Cu(In,Ga)Se 2 (CIGS), and related compounds have attracted attention as the most promising materials for thin-film photovoltaic devices owing to the suitability of their tunable band-gap energy and their high absorption coefficient for solar radiation. Recently, several research groups have announced more than 20% conversion efficiency for CIGS solar cells. [1][2][3] The Swiss Federal Laboratories for Materials Science and Technology (EMPA) 1) and Zentrum für Sonnenenergie-und Wasserstoff-Forschung Baden-Württemberg (ZSW) 3) groups fabricated high-efficiency CIGS solar cells by the post-deposition of sodium fluoride (NaF) and potassium fluoride (KF) on CIGS films and annealing in a Se atmosphere. After the post-deposition treatment and annealing, a Cu-deficient layer was formed at the surface of the CIGS layer. 4) Figure 1 shows the reported phase diagram for the Cu 2 Se-In 2 Se 3 pseudo-binary system. 5) In this system, tetragonal chalcopyrite-type CuInSe 2 (Cu=In = 1) and some Cu-poor compounds such as tetragonal stannite-type CuIn 3 Se 5 (Cu= In = 0.33) and tetragonal and hexagonal CuIn 5 Se 8 (Cu= In = 0.2) phases have been reported. 6) Most of the CIGS absorbers utilized for high-efficiency solar cells have been prepared by physical vapor deposition as typified by the "three-stage" process. 7,8) In the first stage, an (In,Ga) 2 Se 3 layer is deposited at a relatively low substrate temperature. In the second stage, the phase changes observed in CIGS films during the deposition of Cu and Se on the In-Ga-Se precursor films were as follows: (In,Ga) 2 Se 3 → [Cu(In,Ga) 5 Se 8 ] → Cu(In,Ga) 3 Se 5 → Cu(In,Ga)Se 2 → Cu-rich Cu(In,Ga)Se 2 . Finally, in the third stage, In, Ga, and Se are again deposited and the final composition of the CIGS film is made Cu-deficient [Cu=(In + Ga) < 1]. The CIGS absorber usually exhibits p-type conductivity because of the formation of a Cu-poor CIGS thin film. 9) CuInSe 2 (Cu=In = 1.0) crystallizes in a tetragonal chalcopyrite structure [space group: I 42d (No. 122)]. The crystal structure of chalcopyrite-type CuInSe 2 is shown in Fig. 2(a).
The chalcopyrite structure is based on the zincblende structure; the c-axis is almost twice as long as the a-axis of the basic zincblende structure, but the c=a ratio is not equal to 2.0 because CuInSe 2 has two kinds of chemical bonds, i.e., Cu-Se and In-Se. 10,11) Density functional calculations have shown that the formation energy for the Cu vacancy (V Cu ) is small in comparison with other types of vacancies. 12,13) The p-type conductivity of the Cu-poor CIS phase is attributed to the formation of shallow acceptor levels of V Cu . 12) A number of studies on Cu-poor Cu-In-Se (CIS) compounds such as CuIn 3 Se 5 have been carried out since 1993. [14][15][16][17][18]   cells. In the last stage of the three-stage process, small amounts of In, Ga, and Se are added to the CIGS absorber layer and a slightly Cu-poor CIGS surface is formed. 19) Therefore, a thin Cu-poor CIS compound layer including CuIn 3 Se 5 and CuIn 5 Se 8 exists on the surface of a Cu-poor CIS absorber. Schmid et al. 14) first reported that the p-n junction between the p-type CIS and n-type CuIn 3 Se 5 plays an important role in enabling high-efficiency CIS solar cells.
A number of structural studies on Cu-poor CIS compounds have been reported in the last few decades. One of the authors of this paper has also studied CuIn 3 Se 5 and CuIn 5 Se 8 for 20 years. [20][21][22][23] For CuIn 3 Se 5 , three main types of crystal structures have been reported. First, Hönle et al. 24) suggested the structure of the ordered vacancy chalcopyrite (OVC) or the ordered defect chalcopyrite (ODC) with the space group I 42c. Second, Hanada et al. 6) investigated the structure of CuIn 3 Se 5 by a combination of convergent beam transmission electron microscopy (TEM) and Rietveld refinement of the X-ray diffraction. They concluded that CuIn 3 Se 5 has a stannite structure with the space group: I 42m. The space group of the stannite-type I 42m is not a subgroup of the chalcopyrite-type I 42d, and therefore the extinction rule of the X-ray diffraction is different between chalcopyrite-and stannite-type structures. The third structure is the modified stannite-like structure reported by Paszkowicz et al. 25) Paszkowicz's crystal structure model of CuIn 3 Se 5 is also based on the stannite-type structure with the space group I 42m. Their structural model is shown in Fig. 2(b). More information about the difference between these three suggested structures was summarized in our previous paper. 26) Recently, we studied in detail the crystal structure of Cu-poor CIS compounds by X-ray absorption fine structure (XAFS). 26) We concluded that CuIn 3 Se 5 and CuIn 5 Se 8 have a stannite-like structure with V Cu and In Cu defects. However, the optical properties and band diagrams of Cu-poor CIS compounds are still under discussion.
To clarify the optical properties of Cu-poor CIS compounds, we synthesized the (1 − x)Cu 2 Se-(x)In 2 Se 3 (0.5 ≤ x ≤ 1.0) samples. The phases in the obtained powders were identified by X-ray powder diffraction (XRD). The band-gap energies of the Cu-poor CIS samples were determined from the diffuse reflectance spectra of the ultraviolet-visible-near infrared (UV-vis-NIR) spectroscopy. Then, the energy levels of the valence band maxima (VBMs) of the Cu-poor CIS samples were estimated from the ionization energies measured by photoemission yield spectroscopy (PYS). We discuss the band diagrams of CuInSe 2 and Cu-poor CIS compounds such as CuIn 3 Se 5 and CuIn 5 Se 8 , which were estimated from the obtained ionization energy and band-gap energy. Additionally, in order to understand the electronic structure of Cu-poor CIS compounds, we performed firstprinciples band structure calculations on stannite-type CuIn 5 Se 8 and reference compound, tetragonal chalcopyritetype CuInSe 2 , using the HSE06 nonlocal screened hybrid density functional.

Experimental and theoretical procedures
2.1 Preparation of CuInSe 2 , CuIn 3 Se 5 , and CuIn 5 Se 8 samples in Cu 2 Se-In 2 Se 3 pseudo-binary system CIS powder samples on the Cu-poor side of the Cu 2 Se-In 2 Se 3 pseudo-binary system were synthesized by a mechanochemical process and post-heating. 27) Starting materials of elemental powders such as Cu, In, and Se were weighed to give a molar ratio of (1 − x)Cu 2 Se-(x)In 2 Se 3 (x = 0.50, 0.55, 0.60, 0.70, 0.75, 0.80, 0.85, 0.90, 0.95, 1.0). The compositions of these samples are indicated by dots on the horizontal axis in Fig. 1. The chemical compositions of the samples with x = 0.50, 0.75, and 0.83 correspond to CuInSe 2 (Cu= In = 1), CuIn 3 Se 5 (Cu=In = 0.33), and CuIn 5 Se 8 (Cu=In = 0.2), respectively. The elemental powders were placed in a grinding jar made of zirconia along with zirconia balls. The milling was conducted in a planetary ball mill (Fritsch premium line P-7) under a rotational speed of 800 rpm with a milling period of 20 min in a N 2 gas atmosphere. The mixed powders were heated to 550°C at a rate of 20°C=min and annealed at 550°C for 30 min in a N 2 gas atmosphere in a single-zone silica tube furnace.

Crystallographic characterization
The phases in the obtained powders were identified by XRD using Cu-Kα radiation. XRD measurements for Rietveld analysis were performed using an X-ray diffractometer (Rigaku RINT-2400) equipped with a rotating-anode source and a curved graphite monochromator. The diffraction data were collected with a step width of 0.04°(2θ) and a counting time of 4 s for each step over a 2θ range from 5 to 120°. Rietveld refinement was carried out using Reflex Plus in Accelrys Materials Studio's analytical and crystallization software. The crystal structures of CIS samples such as CuInSe 2 , CuIn 3 Se 5 , and CuIn 5 Se 8 were refined on the basis of tetragonal chalcopyrite-type structure [space group: I 42d (No. 122)] and the tetragonal stannite-type structure (Paszkowicz's model 25) ) [space group: I 42m (No. 121)].

Optical characterization and measurement of ionization energy
The optical properties of the CIS samples were characterized by UV-vis-NIR spectroscopy (JASCO V-670DS). Diffuse reflectance measurements were carried out using the CIS powders, which were pulverized for 2 h in an agate mortar. The band-gap energies of the CIS samples were determined from diffuse reflectance spectra. The band-gap energies were calculated from a Tauc plot of the diffuse reference data.
To discuss the band diagrams of the CIS samples, the energy levels of the VBM were estimated from the ionization energies. The ionization energy of the CIS samples was directly measured by PYS (Bunkoukeiki BIP-KV201).

First-principles calculations
We performed first-principles calculations on the basis of the density functional theory (DFT) as implemented in the program code CASTEP 28) in Materials Studio version 7.0 SP2 (Accelrys). Calculations using a plane-wave pseudopotential method were performed using the nonlocal screened hybrid density functional method of Heyd-Scuseria-Ernzerhof (HSE06) 29,30) as an electron exchange and correlation functional because a first-principles calculation based on the DFT using the local density approximation (LDA) 31,32) and the generalized gradient approximation (GGA) 33,34) usually underestimates the band-gap energy. The HSE06 functional provides a more accurate band-gap energy than the LDA and GGA functionals. Since performing a geometric optimization with the HSE06 functional is very timeconsuming, the crystallographic parameters were optimized using the GGA-PBE functional. Ultrasoft pseudopotentials 35) were applied with a plane-wave cutoff energy of 500 eV. The electronic structure calculations with the HSE06 functional were performed using norm-conserving pseudopotentials because CASTEP does not currently support the use of the HSE06 functional for ultrasoft pseudopotentials. Normconserving pseudopotentials with a plane-wave cutoff energy of 1,000 eV were employed for the HSE06 calculations. Selfconsistent total energies were obtained using the densitymixing scheme 36) in connection with the conjugate gradient technique. 37) Atomic positions were optimized by the quasi-Newton method with the latest Broyden-Fletcher-Goldfarb-Shanno scheme. 38) The experimentally reported structure of CuInSe 2 was adopted as the initial model, which was obtained from the Inorganic Crystal Structure Database (ICSD). For CuInSe 2 , the chalcopyrite-type unit cell (space group: I 42d) with the lattice parameters a = 5.776(4) Å, c = 11.611(7) Å, and c=a = 2.01 (ICSD #86872) was employed. For Cu-poor CIS samples, a virtual model of the tetragonal CuIn 5 Se 8 with a stannite-type unit cell was constructed. The initial crystal structure model for the virtual tetragonal CuIn 5 Se 8 was made from the lattice parameters experimentally determined by Rietveld analysis. The crystal structures of tetragonal chalcopyrite-type CuInSe 2 (a), tetragonal stannite-type CuIn 3 Se 5 (Paszkowicz's model 25) ) (b), and virtual tetragonal stannitetype CuIn 5 Se 8 used in the first-principles calculation (c) are shown in Fig. 2. Figure 3(a) shows the XRD patterns of the (1 − x)Cu 2 Se-(x)In 2 Se 3 with 0.5 ≤ x ≤ 1.0 synthesized by mixing the elemental powders with additional heating at 550°C. The XRD pattern of the synthesized sample with x = 0.5 (CuInSe 2 ) is in good agreement with the simulated pattern of chalcopyrite-type CuInSe 2 (ICSD #86872), and there is no peak of a secondary impurity phase. Therefore, we concluded that single-phase CuInSe 2 can be obtained by a mechanochemical process with additional heating at 550°C.     samples with x = 0.5 and 0.55 can be indexed on the basis of a tetragonal chalcopyrite-type structure. For the Cu-poor CIS samples with 0.60 ≤ x ≤ 0.75, the diffraction peaks can be indexed on the basis of a tetragonal stannite-type structure. For the samples with 0.80 ≤ x ≤ 0.95, the diffraction peaks are identified to be from a mixed CuIn 5 Se 8 phases with the tetragonal and hexagonal 6) structures. This result suggests that the crystal structure of the sample changed from chalcopyrite-type CuInSe 2 to hexagonal CuIn 5 Se 8 through stannite-type CuIn 3 Se 5 with increasing x (decreasing Cu=In ratio). Although there is a region of the mixed phase of a chalcopyrite-type structure and a stannite-type structures in the phase diagram of the Cu 2 Se-In 2 Se 3 system (shown in Fig. 1), we did not clearly observe this mixed phase. The XRD pattern of a stannite-type structure is similar to that of a chalcopyrite structure. Most of the peaks of a chalcopyritetype structure should also be included in the peaks of a stannite-type structure. Therefore, it is difficult to determine the region of existence of the mixed phase. However, both a chalcopyrite-type CuInSe 2 phase with E g of about 1.0 eV and a stannite-type CuIn 3 Se 5 phase with E g of about 1.11 eV are observed in the diffuse reflectance spectra of the (1 − x)Cu 2 Se-(x)In 2 Se 3 powder samples with x = 0.60 and 0.65. These results are discussed in the next section.

Crystal structures of Cu-poor CIS samples
The crystal structures of the CIS samples (0.50 ≤ x ≤ 0.80) were analyzed by Rietveld refinement using XRD data. The crystal structures of the CIS samples such as CuInSe 2 , CuIn 3 Se 5 , and CuIn 5 Se 8 were refined on the basis of the tetragonal chalcopyrite-type structure [space group: I 42m (No. 122)] and stannite-type structure (Paszkowicz's model 25) ) [space group: I 42m (No. 121)]. Figure 4 shows the final profile fitting patterns of (a) chalcopyrite-type CuInSe 2 with x = 0.5 (Cu=In = 1.0) and (b) stannite-type CuIn 3 Se 5 with x = 0.75 (Cu=In = 0.33) determined by Rietveld analysis. The determined crystallographic parameters of chalcopyrite-type CuInSe 2 and stannite-type CuIn 3 Se 5 such as the lattice constants a and c and the atomic coordinates (u-parameter) of the Se atom are summarized in Fig. 4. The refined lattice parameters of chalcopyrite-type CuInSe 2 are a = 5.778(4) Å, c = 11.609(4) Å, c=a = 2.01, and u x (Se) = 0.229. These agree with the reported values of a = 5.776(4) Å, c = 11.611(7) Å, and c=a = 2.01, and u x (Se) = 0.230 (ICSD #86872). The final value of the R factor corresponding to the weighted residual error (R wp ) is 5.02%. The refined lattice parameters of stannite-type CuIn 3 Se 5 are a = 5.740(8) Å, c = 11.49(2) Å, c=a = 2.00, u x (Se) = 0.237, and u z (Se) = 0.116. These agree with Paszkowicz's reported values 25) of a = 5.75812(2) Å, c = 11.53593(7) Å, c=a = 2.00, u x (Se) = 0.2308(3), and u z (Se) = 0.1155 (2). The final value of the R factor is R wp = 6.68%. Figure 5 shows the R wp values obtained by Rietveld refinement of the Cu-poor CIS samples (0.50 ≤ x ≤ 0.85). For the samples with 0.50 ≤ x ≤ 0.55, the R wp values of the chalcopyrite structure (I 42d) are lower than 5%. For the samples with 0.60 ≤ x ≤ 0.80, the R wp values of the stannite structure (I 42m) are lower than 8% and lower than those of the chalcopyrite structure. The R wp values of the samples with x = 0.85 are considerably higher than those of the other samples (0.50 ≤ x ≤ 0.80) because the sample with x = 0.85 comprises mixed CuIn 5 Se 8 phase with the tetragonal and hexagonal structures. The key feature of the Cu 2 Se-In 2 Se 3 pseudo-binary system in Fig. 1 is that CuInSe 2 has a solidsolution region with a chalcopyrite structure on the Cu-poor (Cu=In < 1) side of the Cu 2 Se-In 2 Se 3 system. In the further Cu-poor side of the system, there are tetragonal stannite-type CuIn 3 Se 5 (Cu=In = 0.33) and hexagonal CuIn 5 Se 8 phases.   Chalcopyrite-type I4 -2d Stannite-type I4 -2m Therefore, in the second stage of the "three-stage" process, the crystal structure of the Cu-In-Ga-Se film changes as follows: (In,Ga) 2 Se 3 → [Cu(In,Ga) 5 Se 8 ] (hexagonal) → Cu(In,Ga) 3 Se 5 (tetragonal stannite-type) → Cu(In,Ga)Se 2 (tetragonal chalcopyrite-type).
In a previous study, we synthesized the Cu-based chalcogenide compounds CuSb(S,Se) 2 by a mechanochemical process and post-heating. We confirmed that the actual composition ratio of the synthesized powder measured by energy dispersive X-ray analysis (EDX) was almost consistent with the feed composition in the preparation. 39) In the present study, the regions of existence of the chalcopyriteand stannite-type phases are consistent with those in the Cu 2 Se-In 2 Se 3 pseudo-binary phase diagram (Fig. 1). Therefore, we believe that there is no significant difference between the feed composition in the preparation and the actual composition of the synthesized powder.
The refined lattice parameters a and c are respectively shown in Figs. 6(a) and 6(b), both of which decrease with increasing x (decreasing Cu=In ratio). The c=a ratios of the samples with 0.60 ≤ x ≤ 0.80 (stannite phase) are smaller than those of the samples with x = 0.50 and 0.55 (chalcopyrite phase).      system, the samples with x = 0.60 and 0.65 are the mixed phase of chalcopyrite-and stannite-type structures. Therefore, we considered that the samples with x = 0.60 and 0.65 have two different band-gap energies (i.e., chalcopyrite-and stannite-type). CuInSe 2 is known as a semiconductor and has a direct band gap (Γ-Γ) of 1.04 eV. 37) Additionally, our firstprinciples calculations in this study showed that both tetragonal chalcopyrite-type CuInSe 2 and tetragonal stannite-type CuIn 5 Se 8 have a direct band gap (Γ-Γ). Therefore, the band gaps of the CIS samples were estimated by assuming they were direct transition-type semiconductors.  Fig. 8(c). Figure 9 shows the band-gap energies of (1 − x)Cu 2 Se-(x)In 2 Se 3 with 0.5 ≤ x ≤ 1.0 estimated from the [F(R)hν] 2 vs hν plot of the reflectance spectra. The determined band-gap energies of (1 − x)Cu 2 Se-(x)In 2 Se 3 with x = 0.5 and 0.55 in the tetragonal chalcopyrite phase are 0.99 and 0.98 eV, respectively. The band-gap energy determined from the diffuse reflectance spectra is 0.05 eV smaller than the reported value (1.04 eV). In our previous report on Cu 2 ZnSn(S,Se) 4 (CZTSSe), 40) the band-gap energy determined from the diffuse reflectance spectra of the powder was also about 0.05 eV smaller than that determined from the transmittance spectra of the film. The band-gap energies of

Ionization energy of Cu-poor CIS samples and their band diagram
To apply CIS films to a p-type absorber layer for a thin-film compound solar cell, it is important to know the parameters of the band diagram, such as the depth of the top of the valence band from the vacuum level, which corresponds to the energy levels of the VBM from the vacuum level. A material with a higher energy position of the VBM of around −5 eV can easily become p-type because electrons can be easily removed from the valence bands to form holes.
To discuss the band diagrams of the Cu-poor CIS samples such as CuInSe 2 , CuIn 3 Se 5 , and CuIn 5 Se 8 , energy levels of the VBM from the vacuum level were estimated from the ionization energies. The ionization energies of the Cu-poor CIS samples were directly measured by PYS. The photoelectron yield has the following relationship for semiconductors: 3 , where Y is the photoelectron yield, I s is the photocurrent, A is a constant, hν is the photon energy, and E WF is the difference in energy between the vacuum level and the Fermi level, determined by linear fitting of the I 1=3 s vs hν plot. Before measuring the CIS samples, we calibrated the work function of the Au film (as a standard substance), which corresponds to the Fermi energy level from the vacuum level. The work function of the Au film measured by PYS (4.75 eV) is 0.35 eV smaller than that of the reported value (5.1 eV). 43) Therefore, we corrected the ionization energies of the CIS samples measured by PYS by adding 0.35 eV. Figure 10 shows the photoemission yield spectroscopy spectrum of CuInSe 2 and (1 − x)Cu 2 Se-(x)In 2 Se 3 powders with 0.5 ≤ x ≤ 1.0. The determined ionization energy of CuInSe 2 (x = 0.5) was 5.25 eV. Therefore, the energy level of the VBM from the vacuum level of CuInSe 2 (−5.25 eV) is slightly higher than Jaegermann's value (−5.4 eV). 44) Since the measured sample was analyzed for a composition on the Cu-deficient side of CuInSe 2 , it is considered that a large number of Cu vacancies (V Cu ) are present in the sample. Additionally, some antisite defects of Cu In and In Cu and their complex defects exist in the samples. If V Cu and Cu In are included in the sample, their accepter levels are formed at a slightly higher than the VBM. These defects might have led to underestimation of ionization energy by PYS. However, we recently confirmed that the ionization energy determined by PYS is in good agreement with the value determined by X-ray photoelectron spectroscopy (XPS) with UV photoelectron yield spectroscopy (UVPYS) for BaCuSeF. 45) The ionization energy of BaCuSeF (4.85 eV) determined by PYS was in good agreement with the ionization energy determined by XPS and UVPYS (4.9 eV).
The electron affinity, which is the energy level of the conduction band minimum (CBM), of the Cu-poor CIS samples can also be determined by adding the value of the optical band gap (in Fig. 9) to the energy level of the VBM, which was estimated from the ionization energies obtained by PYS measurements. The energy levels of the VBM and CBM of CuInSe 2 from the vacuum level were estimated to be −5.25 and −4.26 eV (electron affinity), respectively.
For samples of the (1 − x)Cu 2 Se-(x)In 2 Se 3 powders with 0.5 ≤ x ≤ 1.0, the detection limit of their photoelectron yield shifts to the higher-energy side with increasing x (decreasing Cu=In ratio). Figure 11 shows the energy levels of the VBM and CBM of the (1 − x)Cu 2 Se-(x)In 2 Se 3 samples from the vacuum level. The ionization energies of CuIn 3 Se 5 and CuIn 5 Se 8 are 5.65 and 5.75-5.95 eV, respectively. The energy level of the VBM of CuIn 3 Se 5 (x = 0.75, Cu=In = 0.33), −5.65 eV, is deeper than that of chalcopyrite-type CuInSe 2 (−5.25 eV), and that of CuIn 5 Se 8 (x = 0.83, Cu= In = 0.2) is around −5.75 to 5.95 eV, which is deeper than that of CuIn 3 Se 5 . The energy levels of the VBMs of the Cu-poor CIS samples significantly decrease with increasing x (decreasing Cu=In ratio). In the region with the mixed chalcopyrite-type and the stannite-type phase, two different band gaps were observed in the diffuse reflectance spectra. On the other hand, two different of VBMs were not observed in the PYS measurement. We could not separate the two VBMs of the two different crystalline phases. By adding the value of the optical band gap (in Fig. 9) to the VBM, the estimated energy levels of the CBM for CuInSe 2 , CuIn 3 Se 5 , and CuIn 5 Se 8 are −4.26, −4.48, and −4.53 to 4.71 eV, respectively. The energy level of the CBM also decreases with increasing x (decreasing Cu=In ratio), but the difference in the energy level of the CBM between CuInSe 2 and CuIn 3 Se 5 (0.22 eV) is smaller than that of the VBM (0.4 eV). The energy levels of the VBMs of the Cupoor CIS samples decrease significantly with decreasing Cu=In ratio.
The results obtained in this paper suggest that the energy level of the VBM of a Cu-poor CIS film can be controlled by the Cu=In ratio. In particular, CuIn 3 Se 5 is expected to be useful for controlling the valence band offset (ΔE v ) of a CIS solar cell. CuIn 3 Se 5 has a tetragonal stannite-type crystal structure, which is similar to the chalcopyrite structure of CuInSe 2 (not similar to hexagonal CuIn 5 Se 8 ). It has a wider band gap than with CuInSe 2 , and the energy levels of the VBMs are deeper below the vacuum level than that of CuInSe 2 . Most recently, Nishimura et al. reported the control of the valence offset at a CdS=Cu(In,Ga)Se 2 interface to reduce the interfacial recombination in CIGS solar cells. 46) Cu(In,Ga) 3 Se 5 layers (5-30 nm) were inserted into the CdS= Cu(In,Ga)Se 2 interface of CIGS solar cells with a flat band profile for the Cu(In,Ga)Se 2 layers with band-gap energies of 1.2 and 1.4 eV. They found that the open-circuit voltage (V OC ) for a CIGS film with a flat band profile was clearly improved from 0.66 to 0.75 V for the band gap of 1.4 eV, although V OC was only increased from 0.63 to 0.64 V for the band gap of 1.2 eV. Then, a Cu(In,Ga) 3 Se 5 layer was applied at the CdS=CIGS interface for a CIGS film with a singlegraded band profile having an average band gap of 1.4 eV. They achieved a conversion efficiency of 14.4% and V OC of 0.72 V when 30-nm-thick Cu(In,Ga) 3 Se 5 was inserted, although the conversion efficiency and V OC were 10.5% and 0.57 V without the Cu(In,Ga) 3 Se 5 layer, respectively. They suggested that the valence band offset ΔE v is important to suppress the interfacial recombination by repelling holes at the CdS=CIGS interface.

Band structure of Cu-poor CIS samples
We performed first-principles band structure calculations on tetragonal CuInSe 2 and CuIn 5 Se 8 to understand the electronic structure of Cu-poor CIS compounds. The structural optimization calculation for a perfect crystal of CuInSe 2 was performed using the chalcopyrite-type unit cell (I 42d) with 16 atoms. The lattice parameters a and c and the internal atomic position (u-parameter) of the Se atom, u(Se), in the chalcopyrite structure were optimized by minimizing the total energy at 0 K. The relaxation procedures were truncated when all the residual forces for the relaxed atoms were less than 0.01 eV=Å. For CuInSe 2 , the chalcopyrite-type unit cell (space group: I 42d) with the lattice parameters a = 5.776(4) Å, c = 11.611(7) Å, and c=a = 2.01 (ICSD #86872) was employed as the initial model.
For Cu-poor CIS samples, a virtual model of tetragonal CuIn 5 Se 8 with the stannite-type unit cell was constructed. The virtual tetragonal CuIn 5 Se 8 includes two Cu vacancies and one In Cu antisite (2V Cu + In Cu ) in the tetragonal unit cell. The defect formation energy and electronic structure of CIS have been theoretically studied in detail by the basic sciences research group of the National Renewable Energy Laboratory (NREL). 12) In 1998, they calculated the formation energies of vacancies (V Cu and V In ), antisite atoms (Cu In and In Cu ), the interstitial atom (Cu i ), and defect pairs such as (2V Cu − + In Cu 2+ ). In 2005, we also reported the formation energies of atomic vacancies (V Cu , V In , and V Se ) and defect pairs of CIS such as (2V Cu − + In Cu 2+ ) and those of CuGaSe 2 (CGS) and CuAlSe 2 (CAS), which were calculated using the different atomic chemical potentials of the constituent elements. 13) In CIS, the formation energies of the Cu vacancy (V Cu ) and defect pair (2V Cu − + In Cu 2+ ) are smaller than those of other types of defects, especially under Cu-poor conditions. In the previous work, the band-gap energy of CIS was considerably underestimated because DFT using the LDA and GGA usually underestimates the band-gap energy. For this reason, the band-gap energy of CIS was corrected to match the experimental value. In this study, the band structures of chalcopyrite CuInSe 2 and virtual tetragonal stannite-type CuIn 5 Se 8 were calculated with the HSE06 functional in order to improve the theoretical band-gap energy.
The initial crystal structure model for the virtual tetragonal stannite-type CuIn 5 Se 8 (I 42m) with 16 atoms was made using the lattice parameters a = 5.735(2) Å, c = 11.49(3) Å, and c=a = 2.00, which were experimentally determined by Rietveld analysis of the XRD data. After the geometric optimization, the band structures of chalcopyrite CuInSe 2 and virtual tetragonal stannite-type CuIn 5 Se 8 [shown in Fig. 2(c)] were calculated with the HSE06 functional. Figures 12(a) and 12(b) show the calculated band structure of chalcopyrite CuInSe 2 (a) and virtual tetragonal stannitetype CuIn 5 Se 8 (b). In the calculated band structures, the VBMs of CuInSe 2 and CuIn 5 Se 8 are set to 0 eV. The band structure of the chalcopyrite-type CuInSe 2 shows that both the VBM and the CBM are located at the Γ-point. Therefore, CuInSe 2 has a direct band gap (Γ-Γ). Both the VBM and CBM of tetragonal stannite-type CuIn 5 Se 8 are also located at the Γ-point, and CuIn 5 Se 8 has a direct band gap (Γ-Γ). The band-gap energy of CuInSe 2 calculated with the HSE06 functional is 0.94 eV. This value is slightly underestimated in comparison with the reported experimental value of   1.04 eV. However, the band-gap energy of CuInSe 2 calculated with the HSE06 functional is considerably improved in comparison with that calculated with the GGA functional of 0.04 eV.
The theoretically calculated band-gap energy of virtual tetragonal stannite-type CuIn 5 Se 8 (1.19 eV) is larger than that of chalcopyrite-type CuInSe 2 (0.94 eV). Both the theoretical and experimental direct band gaps of stannite-type CuIn 5 Se 8 are wider than those of chalcopyrite-type CuInSe 2 . The difference in the theoretical band-gap energy between the chalcopyrite-type CuInSe 2 and stannite-type CuIn 5 Se 8 is 0.25 eV. This theoretical prediction agrees with our experimental band-gap energy. We conclude that the band gaps of CuIn 3 Se 5 and CuIn 5 Se 8 with a tetragonal stannite-type structure are widened by lowering the orbital of the valence band. The orbital of the VBM for the chalcopyrite-type CuInSe 2 is widely dispersed from 0 eV (VBM = 0 eV) to −0.95 eV, while that for the stannite-type CuIn 5 Se 8 is dispersed from 0 to −0.45 eV. The top of the valence band of the stannite-type CuIn 5 Se 8 is flat in comparison with that of the chalcopyrite-type CuInSe 2 . For the virtual stannite-type CuIn 5 Se 8 , two V Cu and one In Cu are included in the unit cell. With decreasing Cu=In ratio, the concentration of Cu atom in the unit cell decreases and Cu atoms in the chalcopyrite CuInSe 2 are gradually replaced by Cu vacancies and In antisites. On average, the Se atoms of stannite-type CuIn 5 Se 8 are coordinated by 1=2 Cu atom, two In atoms and 1=2 In Cu atom, and one V Cu . The calculated bond length of Cu-Se in the virtual stannite-type CuIn 5 Se 8 (2.452 Å) is longer than that in the chalcopyrite-type CuInSe 2 (2.429 Å). Therefore, the dispersion of the antibonding orbital of Cu 3d + Se 4p at the top of the valence band becomes flat and the energy level of the VBM becomes lower. NREL's group 12) provided an explanation that the increase in the band gap of CuIn 5 Se 8 is caused by reduced Se 4p-Cu 3d interband repulsion due to the diminished Cu d character caused by Cu vacancies.
The bond length of In Cu -Se (2.625 Å) in the virtual stannite-type CuIn 5 Se 8 is shorter than that of In-Se in the chalcopyrite-type CuInSe 2 (2.645 Å). However, the bond lengths between the second-nearest-neighbor In atom (In 2nd ) of the In Cu antisite and the surrounding Se atoms are affected by formation of In Cu and V Cu . There are two different bond lengths for In 2nd -Se (2.627 and 2.705 Å). The bond length of 2.705 Å is much longer than that in the chalcopyritetype CuInSe 2 (2.645 Å). The orbital of the CBM for the chalcopyrite-type CuInSe 2 is dispersed from VBM + 0.94 eV to VBM + 3.00 eV, while those for the stannite-type CuIn 5 Se 8 disperse from VBM + 1.19 eV to VBM + 3.00 eV. The dispersion of the antibonding orbital of In 5s + Se 4p at the CBM is also flat. Thus, the energy level of the CBM also decreases with decreasing Cu=In ratio.

Conclusions
To clarify the detailed crystallographic and optical properties of Cu-poor CIS compounds, we synthesized Cu-poor CIS samples such as CuInSe 2 , CuIn 3 Se 5 , and CuIn 5 Se 8 in the composition of (1 − x)Cu 2 Se-(x)In 2 Se 3 with 0.5 ≤ x ≤ 1.0 by a mechanochemical process and post-heating. XRD data showed that the crystal structure of the sample changed from a tetragonal chalcopyrite-type (x = 0.5 and 0.55) to tetragonal stannite-type (0.60 ≤ x ≤ 0.75) with increasing x (decreasing Cu=In ratio). For the samples with 0.80 ≤ x ≤ 0.95, the diffraction peaks were identified to be those of a mixed phase of the tetragonal and hexagonal structures. The band-gap energies of the Cu-poor CIS samples increase in a stepwise manner with increasing x (decreasing Cu=In ratio). The bandgap energies of the Cu-poor CIS samples, i.e., CuIn 3 Se 5 (1.17 eV) and CuIn 5 Se 8 (1.22-1.24 eV), were larger than that of chalcopyrite-type CuInSe 2 (0.99 eV). The difference between the experimental and theoretical band-gap energy for the chalcopyrite-type CuInSe 2 and stannite-type CuIn 5 Se 8 was about 0.25 eV. We considered that the samples with x = 0.60 and 0.65 are a mixed phase of chalcopyrite-and stannite-type structures because of the two-step shape of their diffuse reflectance spectra. The energy levels of the VBM from the vacuum level were estimated from the ionization energies by PYS measurements. The energy level of the VBM of stannite-type CuIn 3 Se 5 (−5.65 eV) is deeper than that of chalcopyrite-type CuInSe 2 (−5.25 eV). The energy levels of the VBMs of the Cu-poor CIS samples decrease significantly with decreasing Cu=In ratio. From the results of first-principles calculation, the band-gap energy of tetragonal stannite-type CuIn 5 Se 8 (1.19 eV) calculated with the HSE06 functional is larger than that of chalcopyrite-type CuInSe 2 (a)