The kesterite semiconductors Cu₂ZnSnS₄ and Cu₂ZnSnSe₄ and their alloys Cu₂ZnSn(S,Se)₄ have drawn intensive attention as the light-absorber materials in thin film solar cells since 2010.^[1–3] The rapid development of the kesterite solar cells in the past years has been reviewed in a series of review papers or books^[4] as well as in this special issue.

Both Cu₂ZnSnS₄ and Cu₂ZnSnSe₄ belong to the group I₂–II–IV–VI₄ quaternary compound semiconductors. The study on the I₂–II–IV–VI₄ quaternary semiconductors dates back to 1950s, and a series of I₂–II–IV–VI₄ semiconductors have been synthesized by different methods.^[5–8] From the view of theoretical material design, the quaternary I₂–II–IV–VI₄ semiconductors, in which both the anions and cations have tetrahedral coordination, can be designed through a two-step cation mutation (substitution) from the binary II–VI semiconductors in the zincblende or wurtzite structure with tetrahedral coordination,^[1,9–13] as shown schematically in Fig. 1. For example, the zincblende-structured ZnSe mutates into the chalcopyrite-structured CuGaSe₂ through replacing two Zn by one Cu and one Ga, and the chalcopyrite-structured CuGaSe₂ further mutates into the kesterite-structured Cu₂ZnSnSe₄ through replacing two Ga by one Zn and one Sn, giving the mutation from binary compound semiconductors to the quaternary compound semiconductors, . By choosing different component elements, a series of I₂–II–IV–VI₄ quaternary compounds can be derived, as shown in Fig. 1. The mutation derivation of new ternary and quaternary compound semiconductors is possible not only from the II–VI semiconductors such as ZnSe, but also from the III–V semiconductors such as GaN and GaP, with a series of new nitrides and phosphides designed recently.^[11,14,15]

Fig. 1.

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	Fig. 1. (color online) The schematic plot of the cation-mutation from the group IV elemental semiconductors to the group III–V and II–VI binary compound semiconductors, and then to the group II–IV–V2 and I–III–VI2 ternary compound semiconductors and the group I–III-IV2–V4 and I2–II–IV–VI4 quaternary compound semiconductors.[1,9–13]

The application of Cu₂ZnSnS₄ (CZTS) in solar cells dates back to 1988 when Ito and Nakazawa synthesized Cu₂CdSnS₄ and Cu₂ZnSnS₄ thin films, fabricated a CZTS solar cell, and reported a 165 meV open-circuit voltage.^[16] During the 14 years from 1996 to 2009, Katagiri et al. have pioneered the fabrication of Cu₂ZnSnS₄ thin film solar cells with a device structure ZnO:Al/CdS/CZTS/Mo/SLG (similar to that of the Cu(In,Ga)Se₂ solar cells), and increased the energy-conversion efficiency from 0.66% (an open-circuit voltage of 400 mV) in 1996 to 6.7% in 2009.^[3,17] In 1997, Friedlmeieret al. also fabricated a Cu₂ZnSnS₄ solar cell with 2.3% efficiency and a Cu₂ZnSnSe₄ cell with 0.6% efficiency.^[18]

Despite the steady efficiency increase during the period of 1996–2009, Cu₂ZnSnS₄, Cu₂ZnSnSe₄, and also all other I₂–II–IV–VI₄ semiconductors had not attracted special attention in the photovoltaic field, and many fundamental properties (crystal structure, electronic structure, optical properties) of I₂–II–IV–VI₄ had not been well characterized and were even wrong.^[19] Until 2009, Cu₂ZnSnSe₄ was even reported experimentally to crystallize in the stannite structure (rather than the kesterite structure), and its band gap was reported to be around 1.5 eV, which is close to that of Cu₂ZnSnS₄, indicating that it is impossible to tune the band gap through forming Cu₂ZnSn(S,Se)₄ alloys.^[1,9] Using the first-principles calculations, we studied the chemical trends in the crystal structure and electronic band structure of a series of I₂–II–IV–VI₄ semiconductors, showing that the ground-state structure of Cu₂ZnSnSe₄ is the kesterite structure and its band gap is 1.0 eV (0.5 eV smaller than that of Cu₂ZnSnS₄), and thus pointed out the long-standing misunderstanding in the crystal structure^[20] and band gaps of Cu₂ZnSnSe₄ as well as other I₂–II–IV–VI₄ semiconductors.^[1,9]

Since 2010, the Cu₂ZnSnS₄ and Cu₂ZnSnSe₄ systems become a hot topic in the photovoltaic field, especially after the publication of the experimental paper by Mitzi et al. who reported a hydrazine-based deposition of the Cu₂ZnSn(S,Se)₄ (CZTSSe) alloys and a fabrication of a 9.7% efficiency solar cell based on the CZTSSe alloys.^[2] The record efficiency was then increased to 11.1% in 2012,^[21] and to 12.6% in 2013.^[22] In 2010, Ahn et al. also reported their experimental determination of the band gap of Cu₂ZnSnSe₄ at 1.02 eV.^[23] Nowadays the thin film solar cells using Cu₂ZnSnS₄ (with a band gap at 1.5 eV), Cu₂ZnSnSe₄ (with a band gap at 1.0 eV), and their alloys Cu₂ZnSn(S,Se)₄ (with a linearly and continuously tunable band gap from 1.0 eV to 1.5 eV) as the light-absorber layer are called CZTS, CZTSe, and CZTSSe solar cells, respectively, or more generally kesterite solar cells.

The fundamental crystal structure, electronic structure, and defect properties have been reviewed in a series of papers^[13,24,25] or book chapters.^[4] Here we will introduce the crystal structure and electronic band structure first, and review the theoretical study on the mixed-cation and mixed-anion alloys, alkaline dopants, and grain boundaries in detail, which we believe will be very important for the further optimization of the kesterite solar cell performance.

Since the I₂–II–IV–VI₄ semiconductors can be derived from the binary II–VI semiconductors which usually crystallize in the zincblende or wurtzite structure with the tetrahedral coordination, their crystal structures can also be derived from the zincblende and wurtzite structures, as shown in Fig. 2. By following the electronic octet rule (the eight-electron full-shell state has lower energy), two ternary structures (chalcopyrite and CuAu structures) can be derived from the zincblende structure, and then the quaternary kesterite structure can be derived from the chalcopyrite structure, while the stannite structure and primitive-mixed CuAu structure can be derived from the CuAu structure.^[1,9] Total energy calculations showed clearly that the kesterite structure has lower energy than the other structures for Cu₂ZnSnS₄, Cu₂ZnSnSe₄, Cu₂ZnGeS₄, and other I₂–II–IV–VI₄ semiconductors with small cation-size difference,^[1,9] which can be understood according to the lower Coulomb energy (Madelung energy) and strain energy of the kesterite structure than the other structures.^[26,27]

Fig. 2.

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Fig. 2. (color online) The crystal structure mutation from (a) zinc-blende ZnS to (b) chalcopyrite CuGaS2 and (c) CuAu-like CuGaS2, then to (d) kesterite Cu2ZnSnS4, (e) stannite Cu2ZnSnS4, and (f) PMCA-Cu2ZnSnS4, and the mutation from (g) wurtzite ZnS to (h) wurtzite-chalcopyrite CuGaS2 and (i) wurtzite-CuAu CuGaS2, then to (j) wurtzite-kesterite Cu2ZnSnS4 and (k) wurtzite-stannite Cu2ZnSnS4. Adapted from Refs. [4], [9], and [10].

However, when the cation-size difference is large, both the kesterite and stannite structures may become the lowest-energy structures, e.g., the stannite structure has lower energy than kesterite for Cu₂Cd–IV–S₄, while Ag₂ZnSnS₄ and Ag₂ZnSnSe₄ are still more stable in the kesterite structure. Zhang et al.^[28] have studied a series of Cu-based quaternary semiconductors and proposed that the stannite structure is energetically more stable for systems containing Cd. The calculated lowest-energy structures for a series of I₂–II–IV–VI₄ semiconductors can be found in Ref. [20]. For the lattice constants, no matter the ground state structure is kesterite or stannite, the most stable one always has larger a and smaller .^[9,28]

The crystal structure mutation is also possible for the wurtzite structure. As shown in Figs. 2(g)–2(k), two wurtzite-derived ternary structures (we name them the wurtzite-chalcopyrite and wurtzite-CuAu structures) and two wurtzite-derived quaternary structures (we name them the wurtzite-kesterite and wurtzite-stannite structures) can be derived from the binary wurtzite structure. These wurtzite-derived structures can be corresponding to the zincblende-derived structures, as shown by their names, i.e., when the kesterite structure is more stable than the stannite structure, the wurtzite-kesterite structure is more stable than the wurtzite-stannite structure. Usually the quaternary I₂–II–IV–VI₄ semiconductors with small and very ionic elements tend to have wurtzite-kesterite or wurtzite-stannite as their ground-state structures, e.g., Cu₂CdSiS₄ and Cu₂CdSiSe₄ are more stable in the wurtzite-stannite structure, while Cu₂ZnSiS₄ and Cu₂ZnSiSe₄ are more stable in the kesterite structure. Nakamuraet al.^[29] also showed that Cu₂ZnSiSe₄ is more stable in the kesterite structure, which is consistent with our calculation. However, since the energy difference between the wurtzite-derived and zincblende-derived structures is very small for some I₂–II–IV–VI₄ semiconductors, the real structure of the samples may be sensitive to synthesis kinetics.

Although the ground state structures of Cu₂ZnSnS₄, Cu₂ZnSnSe₄, Cu₂ZnGeS₄, and other I₂–II–IV–VI₄ semiconductors have been determined, the unique partial disorder makes the real structure of the synthesized thin films more complicated for the standard x-ray diffraction characterization. In kesterite structure, the/Cu+Zn/Cu+Sn/Zn+Cu/Sn+Cu/layers are ordered along the (001) direction, as shown in Fig. 3(a), and all the anions satisfy the electronic octet rule. The occupation of Zn and Cu cations in the third layer can be exchanged, changing the order to/Cu+Zn/Cu+Sn/Cu+Zn/Sn+Cu/, which does not violate the octet rule, and the calculated energy of this new structure is slightly higher (by less than 1 meV/atom) than that of the kesterite, and lower than that of the stannite (which is 3 meV/atom higher than that of the kesterite). Since the energy cost for the exchange of Cu and Zn cations in the (001) layers is very small, the Cu and Zn sites in the (001) layers become partially disordered at the growth temperature (which is usually much higher than room temperature), as shown in Fig. 3(b). With the partial disorder in the Cu+Zn (001) layer (disordered Cu and Zn can be considered as one element), the kesterite structure has the same symmetry as the stannite structure. The atomic numbers (form factors) of Cu and Zn are similar, so the partially disordered kesterite structure and the stannite structure cannot be distinguished using the standard x-ray diffraction measurements, explaining why Cu₂ZnSnSe₄ and Cu₂ZnGeSe₄ used to be reported to crystallize in the stannite structure in many experimental papers before 2009. The recent neutron scattering measurements by Schorr et al. and synchrotron radiation x-ray diffraction measurements by Washio et al. both observed the existence of the Cu + Zn partial disorder in Cu₂ZnSnS₄ and Cu₂ZnSnSe₄.^[20,30,31]

Fig. 3.

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	Fig. 3. (color online) The crystal structures of (a) the kesterite and (b) Cu/Zn partially disordered kesterite Cu2ZnSnS4. Partially disordered means that the Cu/Zn disordered occupation exists only in the (001) CuZn layers, so the symmetry of the crystal lattice is also I-4, equivalent to that of the stannite structure. Adapted from Ref. [4].

It is also interesting to see that the partial disorder in the (001) layers has negligible influence on the electronic structure, so its influence on the electrical properties may be small although the partial disorder may increase the carrier scattering and decrease the mobility. In contrast, the structure change from kesterite to stannite can decrease the band gap by 0.2 eV. The exchange of Cu and Zn in the kesterite structure (formation of a Cu_Zn+Zn_Cu antisite pair in a 128-atom supercell) decreases the band gap by about 0.1 eV and costs a formation energy about 0.2 eV/pair. As we can see, the partial disorder in the (001) layer costs less energy and also induces smaller band gap change than single antisite-pair or the structure change from kesterite to stannite.

Since 2013, the cation mutation has attracted more attention, and Be, Mg, Ca, Sr, and Ba are also considered as the group II cations, whereas Ti, Zr, and Hf are considered as the group IV cations.^[32–36] One important reason for the substitution of elements is to increase the size difference between the cations and thus suppress the formation of caton antisites. Zhong et al.^[33] showed in 2016 that when Zn is replaced by Mg and Ca, leading to Cu₂MgSnS₄ and Cu₂CaSnS₄, respectively, the lowest-energy (ground state) structure changes from kesterite to stannite, which shows the same trend as in the case of Cu₂Cd–IV–S₄ series. In 2017, Chen et al.^[36] calculated the electronic structure of Cu₂BeSnS₄ and predicted a band gap of 1.76 eV, and also showed that Cu₂BeSnS₄ exhibits benign defect properties for the large difference of its atomic size, thus evidently lowering the concentration of the antisite defects. The absorption coefficient is as high as 10⁵ cm⁻¹ according to their calculation. However, the toxic element Be limits the development of practical solar cells.

Interestingly, Cu₂–II–Sn–VI₄ (II = Ba, Sr; VI = S, Se) were proposed as promising light-absorber materials for solar cells and photoelectrochemical water-splitting applications during the last year.^[34,35] For these systems with very large group II cations, the crystal structure is very different from the kesterite or stannite structure, and the lowest-energy structure is usually not those with the tetrahedral coordination. Since the commercialized solar cells are most based on Si, CdTe, and Cu(In,Ga)Se₂ with tetrahedral coordination, it will be interesting to see the photovoltaic semiconductors with non-tetrahedral coordination, such as the perovskite semiconductors.

The electronic structure analysis is helpful for understanding the electrical conductivity of the I₂–II–IV–VI₄ semiconductors and why the band gaps and band edge positions change as the component elements change. The chemical trends in the band gaps of these semiconductors have been summarized in Ref. [37]. Figure 4 shows the calculated band structure, density of states, and band component analysis for the kesterite Cu₂ZnSnS₄. We can see: (i) Cu₂ZnSnS₄ is a direct bandgap semiconductor, (ii) the valence band maximum (VBM) state depends on the orbital hybridization between Cu 3d (t_2g) and S 3p, and the conduction band minimum (CBM) state is composed mainly of Sn 5s and S 3s, 3p, and (iii) the group II cation Zn has little contribution to the band gap (valence and conduction band edges).^[38–41] Similar characteristics exist for the band structure of Cu₂ZnSnSe₄, despite that the band gap is smaller by 0.5 eV and the valence band dispersion is larger than that of Cu₂ZnSnS₄.

Fig. 4.

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	Fig. 4. (color online) The calculated band structure, total and partial density of states, and the schematic plot of the band component for kesterite Cu2ZnSnS4. Adapted from Ref. [24].

Compared to ZnS, the Cu-based chalcogenides, such as Cu₂ZnGeS₄, have much smaller band gaps, because the valence band edge is much higher due to the shallower Cu 3d levels, which can be seen clearly in the calculated band alignment in Fig. 5(a). The valence band edge of CuGaS₂ and Cu₂ZnGeS₄ is about 1.15 eV higher that of ZnS. The band gap of Cu₂ZnGeS₄ is also smaller than that of CuGaS₂ because the conduction band edge is lower due to the lower Ge 4s level than the Ga 4s orbital.

Fig. 5.

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	Fig. 5. (color online) (a) The calculated band alignment of ZnS, CuGaS2, and Cu2ZnGeS4. Adapted from Ref. [9]. (b) The calculated band alignment of binary CdS, ternary CuInSe2 and CuGaSe2, and quaternary Cu2ZnSnS4 and Cu2ZnSnSe4. The red dashed lines near the conduction band show the n-type doping limit. Adapted from Ref. [42].

Similarly, the valence band edge of Cu₂ZnSnS₄ is about 1 eV higher than that of Cu-free CdS, as shown in Fig. 5(b). Since the band gap of CdS is 2.42 eV and that of Cu₂ZnSnS₄ is 1.5 eV, the conduction band edge of Cu₂ZnSnS₄ is about 0.1 eV higher than that of CdS, giving a type-II band alignment between Cu₂ZnSnS₄ and CdS. The valence band edge of Cu₂ZnSnSe₄ is 0.15 eV higher than that of Cu₂ZnSnS₄, while its conduction band edge is 0.35 eV lower than that of Cu₂ZnSnS₄. As we know, the VBM of quaternary Cu₂ZnSnS₄ and Cu₂ZnSnSe₄ is an antibonding state of the hybridization between Cu d orbitals and anion p orbitals.^[9] It is well known that the Se p level is higher than S p level, but due to that the shorter Cu–S bond makes the p–d hybridization stronger, the valence band offset between Cu₂ZnSnS₄ and Cu₂ZnSnSe₄ is just 0.15 eV. On the other hand, the anion s and Sn s orbitals compose the CBM and the shorter Sn–S bond makes the s–s level repulsion stronger, thus moving the CBM of the Cu₂ZnSnS₄ higher than that of Cu₂ZnSnSe₄. It is obvious that the CBM downshift plays a more important role for the bandgap reduction from Cu₂ZnSnS₄ to Cu₂ZnSnSe₄.

The conduction band edge of Cu₂ZnSnSe₄ is 0.25 eV lower than that of CdS, giving a type-I band alignment between Cu₂ZnSnSe₄ and CdS. The type-I and type-II band alignment difference of Cu₂ZnSnS₄ and Cu₂ZnSnSe₄ relative to CdS has been discussed in Ref. [42]. The experimental measurement of the valence band offset between Cu₂ZnSnSe₄ and CdS is around 0.9–1.2 eV.^[42–48] The 0.3 eV difference may result from the different interfaces, elemental composition ratios, and measurement methods used by different groups. If the valence band offset is only 0.9 eV, the band alignment between Cu₂ZnSnS₄ and CdS becomes type-I. The accurate measurement of the band offset and the influence of the different interfaces, elemental composition ratios, and measurement methods on the results are still interesting topics deserving further study.

Different structures (kesterite, stannite, and PMCA) have the valence band edges close to each other, while the conduction band edge shifts down from kesterite to stannite and PMCA, leading to smaller band gaps of stannite and PMCA. Figure 6 shows the calculated band gaps of Cu₂ZnSiS₄, Cu₂ZnGeS₄, and Cu₂ZnSnS₄, which shows clearly that the kesterite structure always has larger band gap than the stannite structure, and the wurtzite-derived structure always has larger band gap than the corresponding zincblende-derived structure.^[9,10] The larger band gap of the wurtzite structure than the zincblende structure has also been noticed in binary II–VI semiconductors.^[19]

Fig. 6.

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	Fig. 6. (color online) The GGA calculated band gaps of CuZn–IV–S4. Compared to the experimental values, the GGA calculated values have a general underestimation by about 1.4 eV for these semiconductors. Adapted from Ref. [10].

Liu et al.^[49] have studied the electron and hole effective masses of KS and ST structured Cu₂Zn–IV–VI₄. They found that the electron effective masses are rather small and almost isotropic while the hole effective masses show strong anisotropies, and the effective masses of the Se-based compounds are much smaller than those of the S-based compounds. Table 1 shows the electron and hole effective masses calculated from band energy dispersions. For the conduction band, both longitudinal and transverse electron effective masses are rather small and similar. For the valence band, the longitudinal and transverse hole effective masses are calculated from the topmost 3 valence bands. Interestingly, the trend is apparent for all of the chosen quaternary compounds: for the kesterite structure, the 1st VB has a much smaller hole effective mass along the c-axis (longitudinal masses) than the other two VBs. However, the stannite structure has an opposite ordering in the band, which shows that the 3rd VB has the smaller effective mass than the topmost 2 VBs.

Table 1.

Table 1.

Table 1. The point electron effective masses and hole effective masses (mn for , v2, and v3, where v1 is the topmost valence band) calculated from the band-energy dispersions. The longitudinal masses are determined from the dispersions along the (001) direction, while the transverse masses are derived from the dispersions in both the (110) and (100) directions. The values are in unit of the free electron mass . Adapted from Ref. [49]. . Cu2ZnSnS4 Cu2ZnGeS4 Cu2ZnSiS4 Kesterite Stannite Kesterite Stannite Kesterite Stannite 0.18 0.18 0.21 0.22 0.26 0.29 0.19 0.19 0.22 0.21 0.24 0.22 0.22 0.74 0.27 0.67 0.4 0.71 0.74 0.34 0.91 0.41 2.45 0.55 0.65 0.69 0.65 0.63 0.67 0.66 0.34 0.32 0.37 0.38 0.47 0.52 0.66 0.2 0.63 0.25 0.67 0.38 0.3 0.69 0.34 0.83 0.44 1.52 Cu2ZnSnSe4 Cu2ZnGeSe4 Cu2ZnSiSe4 Kesterite Stannite Kesterite Stannite Kesterite Stannite 0.1 0.09 0.11 0.11 0.15 0.16 0.11 0.1 0.12 0.11 0.15 0.14 0.12 0.55 0.13 0.5 0.21 0.52 0.32 0.14 0.38 0.17 0.58 0.27 0.53 0.13 0.51 0.2 0.54 0.39 0.16 0.23 0.18 0.23 0.26 0.32 0.34 0.18 0.39 0.16 0.47 0.21 0.26 0.35 0.29 0.48 0.39 0.81

Table 1. The point electron effective masses and hole effective masses (mn for , v2, and v3, where v1 is the topmost valence band) calculated from the band-energy dispersions. The longitudinal masses are determined from the dispersions along the (001) direction, while the transverse masses are derived from the dispersions in both the (110) and (100) directions. The values are in unit of the free electron mass . Adapted from Ref. [49]. .

The different hole effective masses for the kesterite and stannite structures result from the opposite crystal filed splitting,^[9,50] and can be understood by their partial charge densities shown in Fig. 7. For the kesterite structure, the p orbitals in sulfur of the 1st VB are parallel to the c-axis, which is the same to those of the 3rd VB in the stannite structure. The remaining two VBs both in kesterite and stannite structures also have the same p orbital configurations.

Fig. 7.

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	Fig. 7. (color online) Partial charge density of the topmost 3 VBs at the Γ point in (a) the Cu–S–Zn plane for the kesterite Cu2ZnGeS4 and (b) the Cu–S plane for the stannite Cu2ZnGeS4. Adapted from Ref. [49].

Since the band gaps of Cu₂ZnSnS₄ and Cu₂ZnSnSe₄ are 1.5 eV and 1.0 eV, respectively, there is a 0.5 eV space for the band gap tuning through forming the S-Se alloys. It is interesting to see that the solar cells based on the mixed-anion Cu₂ZnSn(S,Se)₄ (CZTSSe) alloys have higher efficiency than those based on the pure Cu₂ZnSnS₄ (CZTS) and Cu₂ZnSnSe₄ (CZTSe) compounds,^[2,51] although CZTS has an optimal band gap for single-junction solar cells according to the Shockley–Queisser model.^[52] The physical properties of various alloys based on CZTS have been studied by several groups,^[53–56] which are very important for understanding the better performance of the CZTS-based alloys. In order to simulate the random occupation of S and Se on the anion sites of the CZTSSe alloys, we used the special quasi-random structure (SQS) method^[50,57] to describe the geometrical structure of the CZTSSe alloys. To know the miscibility of the alloys, the alloy formation enthalpy is defined as where and are the total energy of pure CZTS and CZTSe in the kesterite structure (the structure of the alloys is based on the kesterite structure unless otherwise specified), and is the total energy of the alloy Cu₂ZnSn(S_1−xSe_x)₄.

At the same time, for most alloys, the alloy formation enthalpy obeys a quadratic function of the composition x where Ω is the interaction parameter that describes the alloy solubility.

The bandgap dependence of the conventional semiconductor alloys on the composition x follows the function where b is the bowing parameter and is the bandgap.

From Fig. 8, the interaction parameter Ω of CZTSSe is 26 meV/atom by fitting the enthalpy of composition x, which is much smaller than that of Cu(In_xGa_1−x)Se₂ (CIGS) alloys,^[58] so the problem of phase separation and inhomogeneity of CZTSSe can be avoided. The miscibility temperature of the CZTSSe alloy was predicted to be lower than 300 K by applying the mean-field theory to the free energy of the solid solution, indicating that the CZTSSe alloy is stable at the room temperature.

Fig. 8.

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	Fig. 8. (color online) The calculated enthalpy of formation for Cu2ZnSn(S1 −xSex)4 alloys as a function of composition x. Adapted from Ref. [42].

In Fig. 9, the bowing parameter of CZTSSe is 0.10 eV, which is close to that of CuIn(S_1−xSe_x)₂ (0.04 eV)^[58] and CuGa(S_1−xSe_x)₂ (0.07 eV) alloys.^[9] The bandgap of the CZTSSe alloys is nearly a linear function of the composition x, and the value decreases as x increases from 0 to 1, with the CBM level shifting down by 0.35 eV while the VBM level shifting up by 0.15 eV. According to the doping limit rule,^[59] the CZTSSe alloys with high Se concentration can be more easily type-inverted to n-type because of the lower CBM as shown in Fig. 5(b). The easier type-inversion may be one reason for why the solar cells based on the CZTSSe alloys with high Se composition have a higher efficiency.^[42,60]

Fig. 9.

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	Fig. 9. (color online) The calculated bandgaps of the Cu2ZnSn(S1−xSex)4 alloys using the (a) GGA functional and (b) HSE functional, respectively. Adapted from Ref. [42].

Besides the mix-anion alloys, several theoretical groups also studied the mixed-cation alloys, including (Cu,Li)₂ZnSnS₄,^[61] Cu₂(Zn,Fe)SnS₄(CZFSS),^[62] Cu₂(Zn,Cd)SnS₄,^[63] Cu₂Zn(Sn,Si)S₄,^[64] Cu₂Zn(Sn,Ge)Se₄,^[64] and (Cu,Ag)₂ZnSn(S,Se)₄.^[60] Shu et al. studied the properties of the Cu₂Zn(Sn,Si)S₄ and Cu₂Zn(Sn,Ge)S₄ alloys.^[64] They found that the Cu₂ZnSn_1−xGe_xSe₄ alloys are highly miscible and their band gap increases from 1.0 eV to 1.5 eV with composition x increasing from 0 to 1, while the Cu₂ZnSn_{1 −x}Si_xSe₄ alloys are much less miscible and span a bandgap range from 1.0 eV to 2.4 eV. The bowing parameter of the Cu₂Zn(Sn,Ge)S₄ alloy is much smaller than that of Cu₂Zn(Sn,Si)S₄, because the size and chemical differences between Sn and Si are larger. Shen et al. investigated the electronic and optical properties of Cu₂ZnGe(Se_xS_{1 −x})₄ alloy and found that the gap size may range from 1.52 eV to 2.25 eV, which will provide potential applications as solid state lighting^[65] and water splitting photocatalyst. Shibuya et al. found that Fe can be easily mixed into CZTS.^[62] It is interesting to see that the structure of Cu₂Zn_1−xFe_xSnS₄ alloys changes from kesterite to stannite at x = 0.4, which may result in a small discontinuity of the bandgap. The CZFTS alloys with high Fe concentrations may be used in the Si-based tandem solar cells. Other groups^[61,63] tuned the bandgap from 1.55 eV to 1.09 eV through Cu₂(Zn,Cd)SnS₄, and from 1.5 eV to 1.9 eV through (Cu,Li)₂ZnSnS₄. These alloys are also good candidates for tandem solar cells.

Not only the component-uniform mixed-anion and mixed-cation alloys, but also the component-graded (Cu,Ag)₂ZnSn(S,Se)₄ have been proposed to improve the photovoltaic performance of kesterite solar cells. The efficiency increase of kesterite solar cells stopped after the latest record efficiency was reported in 2013, and it is believed that there is a bottleneck to the further improvement of the open-circuit voltage ( and thus the efficiency. Yuan et al. proposed that one key origin of this bottleneck is that the Cu_Zn antisite defects can form very easily in Cu₂ZnSnS₄ (also in Cu₂ZnSnSe₄), making the material always p-type and cannot be doped easily to n-type under equilibrium condition, which pins the Fermi energy at the p–n junction and thus limits the .^[60] They found that the easy formation of the antistie acceptor defects results from the high valence band (Cu 3d states) of the Cu₂ZnSnS₄, rather than the previously believed small size difference. However, their formation can be largely suppressed through replacing Cu by Ag (group I) to form Ag₂ZnSnS₄, which has a much lower valence band (due to the low Ag 4d states). This defect disparity opens up a possibility to overcome the limit of the Cu₂ZnSnS₄ and Cu₂ZnSnSe₄ solar cells. However, several high-concentration donor defects in Ag₂ZnSnS₄ and Ag₂ZnSnSe₄ have deep levels in the band gap and are thus possible recombination centers, so the efficiency of solar cells based on the pure Ag₂ZnSnS₄ and Ag₂ZnSnSe₄ will still be limited.^[60]

To combine the advantages of Ag₂ZnSnS₄ and Cu₂ZnSnS₄, they proposed that the component-graded (Cu,Ag)₂ZnSnS₄ and (Cu,Ag)₂ZnSnSe₄ alloys can be ideal absorber layer materials if the Ag component is low in the interior of the absorber layer (thus less recombination-center defects) but high near the p–n junction interface (thus less -limiting defects).^[60] The component-graded (Cu,Ag)₂ZnSnSe₄ absorber layers have great potential to increase the and thus improve the solar cell efficiency. This strategy for overcoming the limit has be demonstrated recently by the interesting experimental work of Guchhait et al. who developed a new solution processable method for the Ag incorporation and observed an increase in open-circuit voltage by 50 mV and an accompanying rise in device efficiency from 4.9% to 7.2%.^[66] More recently, Qi et al. demonstrated a significant increase in by appropriately adjusting the Ag gradient in a double-graded (Cu,Ag)₂ZnSn(S,Se)₄ alloy, and an unexpected conversion efficiency of 11.2%, which is the highest efficiency achieved to date for the component-graded (Cu,Ag)₂ZnSn(S,Se)₄ alloy solar cells,^[67] supporting a new aspect that synthesis of a component-graded (Cu,Ag)₂ZnSn(S,Se)₄ absorber has great potential for future research.^[67]

The beneficial effect of alkali-metal dopants on Cu(In,Ga)Se₂ thin film solar cells has been investigated for several decades. The alkali-metal can be doped into the lattice of Cu(In,Ga)Se₂, compensating the donors or promoting the acceptor carrier concentration in the absorber layer,^[68–71] and can also increase the grain size and passivate the grain boundaries (GB) which act as the recombination centers in the thin films.^[68]

Inspired by the prominent effect of alkali-doped Cu(In,Ga)Se₂ devices, it is expected that the alkali metals will also have beneficial effects on CZTS and CZTSe based solar cells because of the similar crystal and device structures. Using the first-principles calculations, Maeda et al. studied the doping effect of Li, Na, and K in CZTS and CZTSe.^[72] Their results show that alkali metal is prone to occupy the Zn site first, then the Cu site, followed by the Sn site and the interstitial site. The substitution defect of alkali metal on the Zn site will be the primary p-type defect in CZTS and CZTSe. However, in the study of Xiao et al.,^[73] Na_Cu has the lowest formation energy, but Na_Cu is an isovalent substitution which cannot produce carriers and increase the hole concentration. Whereas, the formation energy of Na_Zn is a little higher than that of Na_Cu, which will contribute to the electrical conductivity of the CZTS absorber layer. The difference of the two studies results from the different chemical potentials considered in their calculations. In 2016, Yuan et al. proposed a new picture on why the isovalent Na_Cu substitution can increase the hole carrier concentration based on the Na diffusion in the lattice,^[70] which opens a new view on the role of sodium in promoting the hole concentration from the electronic point of view.

Meanwhile, calculations on the transition energy levels of Na dopants on different sites revealed that Na_Zn is a shallow acceptor. Although Na_Sn introduces two transition energy levels, one of which is close to the middle of the band gap, the formation energy of Na_Sn is so high that its detrimental effect as recombination center can be ignored.

Experimentally, Heish et al. investigated the efficiency enhancement via alkali metal doping on CZTSSe. They found that small alkali metals are suitable for increasing the carrier concentration because they are easy to substitute the lattice atom in CZTSSe, while the larger alkali metals are favorable for increasing the grain size because of the low melting point of binary selenides, which will suppress the non-radiative recombination caused by the GBs, since less GBs are produced in the absorber layer.^[74]

The benign effect of alkali metal on the increase of the carrier concentration in CZTSSe has also been proved by several previous studies,^[75–77] where one order of increment of the carrier concentration was obtained by doping sodium into CZTS.^[75] It seems that the alkali metal has the similarly beneficial effect as that in CIS. The enhancement of the mobility of the hole carriers was also observed by Nagaoka et al.^[77] Moreover, Zhao et al. calculated the effective mass of holes in the CZTS with Na impurity, and found that effective mass of hole in Na-doped CZTS is lighter, implying that Na benefits the hole mobility in CZTS.

Based on the observation of Prabhakar et al.,^[75] Na impurity in CZTS enhances the (112) texture of the film. Also, potassium was shown to enhance the (112) preferred orientation,^[78] which indicates that the alkali metal improves the crystallinity of the film. The improvement of the grain size was also observed after introducing Li,^[74,79] Na,^{[74,75,77,79,80]} K,^[74,80] Rb,^[74,79] and Cs.^[74] It is worth noting that the grain size reaches its maximum at 1% K doping and decreases as the K doping concentration continues rising as reported in the study of Tong et al.^[78] Based on the aforementioned studies, the effect of the alkali metal on the grain size cannot be drew out, but a detailed investigation of the sodium concentration in CZTS grains has pointed out that the electronic passivation of the GB requires less sodium than that required for producing large grains.^[81] This means that the size of the grain becomes not critical to the solar cell performance as long as the GB is electronically passivated.

Based on the discussions above, it is clear that alkali metal also plays a beneficial role in CZTS, but it is still not clear whether the influence mechanism in CZTS is similar to that in Cu(In,Ga)Se₂. Further investigation on the effect of alkali metal in CZTS and CZTSe is necessary.

Besides the point defects, the grain boundaries of the CZTS and CZTSe thin films are also important for their photovoltaic performance. Usually the polycrystalline semiconductors exhibit a poorer performance in comparison with their monocrystalline counterparts, because there are usually dangling bonds, wrong bonds, and wrong bonding angles on the grain boundaries, which may introduce deep levels in the band gap and act as non-radiative recombination centers in the system. Fig. 10

Fig. 10.

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	Fig. 10. (color online) Schematic plot of the p–n junction interface between the n-type CdS buffer layer and p-type absorber layer: Cu2ZnSn(S,Se)4 with high concentration of CuZn antisite defects limiting (top) and component-graded (Cu1−xAgx)2ZnSn(S,Se)4 alloys free of -limiting CuZn defects (bottom). Adapted from Ref. [60].

The lack of experimental observations on the structures of grain boundaries in CZTS caused the difficulty in obtaining the exact atomic structure of the grain boundaries, however, the theoretical model of the grain boundaries in CZTS can be adopted from those in CdTe which had been observed via the high-resolution transmission electron microscopy (HRTEM).^[82] Considering the ordered substitution of Cu, Zn, and Sn for the cation ions, CZTS has 4 different grain boundaries as shown in Fig. 11, where the GB-I type and GB-III type are anion-core prototype GB structures, and the GB-II type and GB-IV type are cation-core prototype GB structures. As some atoms on these boundaries are not tetrahedrally coordinated, some wrong bonds and dangling bonds are produced, which are the typical feature of polycrystalline semiconductors.

Fig. 11.

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	Fig. 11. (color online) The 4 relaxed atomic structures of Cu2ZnSnSe4 GBs. The grain boundary (114) plane is indicated by the dashed line. Adapted from Ref. [83].

Several groups have investigated the feature of these GBs in CZTS. Li et al. calculated the density of states of the GB structures in Fig. 11,^[83] showing that the wrong bonded atoms on the boundaries of CZTS will introduce deep levels in the bandgap of the bulk crystal. Although structural relaxation will remove these deep levels to a certain extent, it is still not as effective as those in CIS. Yin et al. calculated the band structure and the density of states of the CZTSe Σ3 (114) GB (the GB-III in Fig. 11) and concluded that the wrong bonds at GB will introduce deep levels, which will cause the Shockley–Read–Hall (SRH) recombination centers in the band gap and be detrimental to and in CZTS.^[92] This is different from the case of CIS whose structure is also derived from that of CdTe, i.e., the grain boundary of CIS presents some intrinsic beneficial effects, such as creating a hole barrier and promoting the hole-electron separation, large relaxation in GB moves the defect states into the valence band.^[92,92] These effects made polycrystalline CIS exhibit better performance in comparison with its crystalline counterparts, however, this feature is not inherited by CZTS.

Experimentally, Kim et al. found that the highest efficiency samples of CZTS exhibit downward potential bending at GB area and upward bending at the inter-grains, while the poorer efficiency samples exhibit an opposite behavior,^[87] which shows that the quality of the GB strongly affects the property of the CZTS devices.

Since the intrinsic GB of CZTS is detrimental, an important issue of the GB in CZTS is whether it can be passivated or not. Using DFT calculation, Yin et al. found the segregation of Zn_Sn, O_Se, and Na_i has the beneficial effect of eliminating the deep defect states in the band gap and creating a hole barrier at GB.^[84] Liu et al. found that Na not only can passivate the deep level in the band gap, but also prefers to segregate at the GBs of CZTS because it has negative formation energies in the system.^[88] These calculation studies pointed out the potential passivation method that can be applied on CZTS to ensure the improvement of GB in CZTS.

The effect of sodium in the GB of CZTS was studied by Gerson experimentally, who demonstrated that the CZTS samples without sodium treatment contain non-radiative recombination center defects, and these deep-level defects can be effectively passivated by the addition of sodium.^[81] Sodium prefers to locate on the surface and GBs of CZTS and it can help to produce large grains, and a small amount of sodium is sufficient to passivate GBs effectively.

The number of component elements increased steadily in the 60-year development of photovoltaic semiconductors, i.e., from silicon in 1950s, to GaAs and CdTe in 1960s, CuInSe₂ in 1970s, Cu(In,Ga)Se₂ in 1980s, Cu₂ZnSnS₄ in 1990s, and more recently Cu₂ZnSn(S,Se)₄ and CH₃NH₃PbI₃. The increased number of elements in Cu₂ZnSnS₄ and Cu₂ZnSnSe₄ and their alloys Cu₂ZnSn(S,Se)₄ relative to binary II–VI or III–V semiconductors results in the increased structural and chemical freedom for tuning the material properties. We reviewed how these group I₂–II–IV–VI₄ semiconductors can be derived from the binary II–VI semiconductors through element-mutation, i.e., from II–VI (ZnS) to I–III–VI₂ (CuGaS₂) and then to I₂–II–IV–VI₄ (Cu₂ZnSnS₄). Following the mutation, we can determine the crystal structures of the I₂–II–IV–VI₄ semiconductors and reveal the chemical trends in their electronic band structure, which makes the band structure engineering possible. The band gaps of I₂–II–IV–VI₄ compounds can be tuned from negative (metal or topological insulator^[89]) to more than 4 eV (wide-gap semiconductor). Furthermore, the increased structural freedom enhances the miscibility (component-uniformity) of the Cu₂ZnSn(S,Se)₄ and Cu₂Zn(Sn,Ge)Se₄ alloys, so their band gaps can be tuned continuously and also linearly as a function of the alloy composition.

The easy formation of Cu_Zn antisite defect and related defect complexes was believed to be one critical factor limiting the open-circuit voltage and efficiency of kesterite solar cells. In order to suppress the formation of these defects, the mixed-cation (Ag,Cu)₂ZnSn(S,Se)₄ and Cu₂(Zn,Cd)Sn(S,Se)₄ alloys were proposed as alternative light-absorber layers and are now under intensive study. The recent experimental breakthrough on the component-graded (Ag,Cu)₂ZnSn(S,Se)₄ alloy solar cells may point out a possible direction or method for breaking the 12.6% efficiency record.

The increased structural and chemical freedom also causes the dramatic increase of possible point defects in the lattice of Cu₂ZnSn(S,Se)₄ thin films, which can significantly influence the optical and electrical properties and thus the photovoltaic performance. A series of point defects have been predicted since 2010.^[24,90–92] After that various defect levels have been experimentally observed using different characterization techniques, and compared with the calculated defect levels. Although the ionization levels of the dominant defects such as Cu_Zn and V_Cu have been experimentally well confirmed, other defect levels have not well determined. A careful and systematical characterization of the defect levels in Cu₂ZnSnS₄ and Cu₂ZnSnSe₄ and their alloys Cu₂ZnSn(S,Se)₄ with different chemical composition ratios and different growth techniques will be very useful for the knowledge-based defect optimization. Although the defect properties are not reviewed here, the importance of the defect optimization cannot be neglected.

Besides the intrinsic defects, extrinsic elements may be doped into these quaternary semiconductors intentionally or unintentionally. Whether the real thin films can work as ideal light-absorber layers depends also on the behavior of the possible extrinsic dopants. Here we reviewed the study on the alkaline dopants which may exist in both the grain interiors and on the grain boundaries. Many opinions that were proposed for understanding the alkaline dopants and grain boundaries in Cu(In,Ga)Se₂ solar cells have been borrowed in the study of the alkaline dopants and grain boundaries in Cu₂ZnSnS₄, Cu₂ZnSnSe₄, and Cu₂ZnSn(S,Se)₄. However, obvious differences in these properties have been found between Cu(In,Ga)Se₂ and Cu₂ZnSn(S,Se)₄. More careful, accurate, and systematical studies on the alkaline dopants and grain boundaries in the kesterite solar cells are still necessary and fundamental to the search for new strategies for the performance optimization.

The interfaces between the kesterite Cu₂ZnSnS₄, Cu₂ZnSnSe₄, and Cu₂ZnSn(S,Se)₄ and CdS are currently not well-studied, because the microstructure near the interfaces can be very complicated and also depend on the specific fabrication methods and conditions. It is not clear whether the interfaces between the kesterite absorber layer and CdS are similar to those between the chalcopyrite absorber layer and CdS, so it is still an open question whether the kesterite solar cells should inherit the device structure from the chalcopyrite thin film solar cells. Systematical simulation and characterization of these interfaces are of fundamental importance to the future development of high-efficiency kesterite solar cells.