Natural Intermediate Band in I2-II-IV-VI4 Quaternary Chalcogenide Semiconductors

An intermediate band in the band gap of semiconductors is fundamental to the development of the intermediate band solar cells, but it is usually produced artificially, which imposes technical challenges on the experimental realization. Here we found that there are natural intermediate bands in the band gaps of the I2-II-IV-VI4 quaternary chalcogenide semiconductors such as Cu2ZnSnS4 and Ag2ZnSnSe4, which had been proposed as promising light-absorber semiconductors in thin film solar cells. By first-principles calculations, we found the lowest conduction band of these I2-II-IV-VI4 semiconductors in the kesterite structure is isolated (a lone band, resulting from the energy separation between Sn 5s and 5p states), which can be viewed as a natural intermediate band. The gap between the intermediate band and higher-energy conduction band can be increased through changing the crystal structure from the zincblende-derived kesterite structure to the wurtzite-derived wurtzite-kesterite structure. In contrast, the intermediate-conduction band gap shrinks when the component element Sn is replaced by Ge (Cu2ZnGeS4), and the gap even disappears (intermediate band disappear) when Sn is replaced by Si (Cu2ZnSiS4). Through tuning the intermediate-conduction and intermediate-valence band gaps, we show that the wurtzite-kesterite structured Ag2ZnSnSe4 may be a potential light-absorber semiconductor in intermediate band solar cells.

The intermediate band solar cells have attracted intensive attention after Luque and Martí showed in 1997 that an energy-conversion efficiency as high as 63.2% can be achieved with a properly located intermediate band 1,2 . The efficiency is much higher than the theoretical efficiency limit at 33.7% of an ideal single-junction solar cell which is known as the Shockley-Queisser limit 3,4 .
In order to obtain a properly located intermediate band in a semiconductor, several methods have been proposed, such as using quantum nanostructures [5][6][7][8][9][10][11] , high concentration of impurities (forming impurity bands) [12][13][14][15][16][17][18] , highly mismatched alloys (HMAs) [19][20][21][22][23][24] and so on 25,26 . However, the experimental realization of these ideas in practical devices is still very challenging technically. The quantum dots (QDs) have received intensive attention as the first practical intermediate band solar cell 1 , but the quantum dots solar cells (QDSC) are often plagued by marginal optical absorption 27 . Till now, the optical absorption of QDs is still much inferior to that of bulk materials 27,28 . The impurity-band method requires a very high concentration of doping, but it is usually challenging to dope such a high concentration of impurity elements into the crystalline semiconductors that can form an impurity band and meanwhile avoid forming impurity complexes and precipitates 29 . Forming intermediate bands in the highly mismatched alloys such as Zn 1−y Mn y Te x O 1−x and GaN x As 1−x−y P y alloys opens up a window to the wide material space for searching possible semiconductors with intermediate bands 22,24 . In 2010, Lee and Wang even found that the highly lattice-mismatched alloys ZnTe 1−x O x with intermediate band states formed as a result of the coupling between the O impurity states can be used for intermediate band solar cells with an efficiency as high as 63% 20 . However, the synthesis or growth of these lattice-mismatched alloys stabilized by the configuration entropy is difficult and the control of the composition uniformity is especially challenging.
If one can design a stable semiconductor with an intermediate band naturally existing in its band gap, the current limit in the development of practical high-efficiency intermediate band solar cells may be overcome. In this paper, we found the I 2 -II-IV-VI 4 series of quaternary chalcogenide semiconductors such as Cu 2 ZnSnS 4 , Cu 2 ZnGeS 4 , Ag 2 ZnSnS 4 and Ag 2 ZnSnSe 4 in the kesterite and wurtzite-kesterite crystal structures have natural intermediate bands according to the band structure calculation. Recently, these I 2 -II-IV-VI 4 semiconductors have been studied both experimentally and theoretically as one of the most promising light-absorber materials to overtake Cu(In,Ga)Se 2 (CIGS) in the commercialized CIGS thin film solar cells, because their component elements possess high abundance and less toxicity [30][31][32][33] . A record efficiency as high as 12.6% have been achieved in thin film solar cells based on their alloys Cu 2 ZnSn(S,Se) 4 31 which are very stable and composition-uniform and can be synthesized using different methods 30 .
Our calculations here showed that their lowest conduction band is an isolated band and can be viewed as a natural intermediate band, which results from the energy separation between the Sn 5s and 5p states. Furthermore, the gap between the intermediate band and higher-energy conduction band and the gap between the intermediate band and valence band can be tuned efficiently through changing the crystal structure or replacing the component elements, indicating that these I 2 -II-IV-VI 4

Results and Discussion
Origin of the Intermediate Band. The crystal structure and electronic structure of the I 2 -II-IV-VI 4 quaternary chalcogenide semiconductors have been intensively studied since 2008, because Cu 2 ZnSnS 4 and Cu 2 ZnSnSe 4 are candidate photovoltaic materials with high efficiency and earth-abundant component elements [34][35][36][37][38] . Five characteristic crystal structures derived from binary zincblende and wurtzite structures have been reported theoretically in literature 37,38 , among them the kesterite (KS) 37 and wurtzite-kesterite (WKS) 38 structures (as shown in Fig. 1) were predicted to have lower energy than other zincblende-and wurtzite-derived structures according to previous calculations 37, 38 .
The band structures of kesterite structured Cu 2 ZnSnS 4 have been calculated in the earlier studies 36,37,39 , which all showed that its lowest conduction band is isolated from the higher-energy conduction bands, i.e., the lowest conduction band is a lone band between the highest valence band and higher-energy conduction bands. Although this is clearly shown in the figures of the calculated band structure, the lone band did not attract special attention and most of the previous studies on Cu 2 ZnSnS 4 and Cu 2 ZnSnSe 4 are focused on their application as light absorber material in single-junction thin film solar cells.
In fact, this lone band can be considered as a natural intermediate band if it really has no connection with any other higher-energy conduction bands. To check whether the band is really isolated from other conduction bands, we performed the band structure calculations for both the kesterite and wurtzite-kesterite structured Cu 2 ZnSnS 4 using the PBE functional. The calculated band structure and density of states of kesterite structured Cu 2 ZnSnS 4 are shown in Fig. 2(a-b). Obviously, the lowest conduction band is really isolated from the higher-energy conduction bands in the whole Brillouin zone, and the lone band produces an isolated peak in the density of states.
To understand why the lone band is isolated from other higher-energy conduction bands, we calculated the partial density of states projected on the s, p, d orbitals of Cu, Zn, Sn and S, as shown in Fig. 2(b). The lone band is composed mainly of the Sn 5s orbital and S 3s and 3p orbitals, whereas the higher-energy conduction bands are composed mainly of the Sn 5p orbital and S 3s and 3p orbitals. The higher-energy conduction bands from I and II atoms (Such as Cu and Zn in Fig. 2) is negligible compared with IV and VI atoms (such as Sn and S in Fig. 2), so we will not discuss the influence of I and II atoms here. As we know, Sn takes the +4 charged state in Cu 2 ZnSnS 4 , so its 5s and 5p orbitals are unoccupied (with the electrons given to S) and contribute to the unoccupied conduction band states. Furthermore, the 5s and 5p states of Sn have hybridization with the lower-energy S 3s and 3p states, so the conduction bands are composed mainly of the anti-bonding states of the hybridization between Sn 5s, 5p and S 3s, 3p states. Since the Sn 5s states has lower energy than Sn 5p states, the lowest-energy conduction band is composed mainly of the antibonding state of the Sn 5s + S 3s, 3p hybridization, and the other higher-energy conduction bands are composed mainly of the antibonding states of the Sn 5p + S 3s, 3p hybridization. According to the band component analysis, we can understand the separation between the lowest-energy and higher-energy conduction bands.
The analysis based on the calculated density of states is also supported by the plotted wave-function (shown in Fig. 3  structured Cu 2 ZnSnS 4 . Obviously, the IBM state wave-function in Fig. 3(b) is localized on Sn (5s orbital) and S (3s orbital), and meanwhile there is no wave-function between the bonded Sn and S, indicating that the state is the antibonding state of the Sn -5s and S-3s hybridization. The HE-CBM state in Fig. 3(c) is also localized mainly on Sn (more like 5p states) and S (more like 3p states), and there is no wave-function between the bonded Sn and S either, indicating that the state is the antibonding state of the Sn-5p and S-3p hybridization. In contrast, the VBM state is localized mainly on Cu (Cu 3d states) and S (3p state), and it is the anti-bonding state of the Cu-S p-d hybridization.
Tuning the Intermediate-Conduction Band Gap. Since the gap between the intermediate band  Fig. 2(c,d) the calculated band structure and density of states of the wurtzite-kesterite structured Cu 2 ZnSnS 4 is shown. Obviously, there is also an intermediate band, and the gap between the intermediate band and the higher-energy conduction band is as large as 0.8 eV, larger than that for the kesterite structure. Therefore, it is possible to tune the gap through controlling the crystal structure of Cu 2 ZnSnS 4 . It should be noted that the intermediate band of the wurtzite-kesterite structured Cu 2 ZnSnS 4 is actually composed of two bands, while that of the kesterite structured Cu 2 ZnSnS 4 has only one band. This is due to the larger primitive cell of the wurtzite-kesterite structure which has two Sn atoms (therefore two lone bands composed of the two Sn 5s orbitals), than that of the kesterite structure which has only one Sn atom.
Through changing the component element in Cu 2 ZnSnS 4 , the gap between the intermediate band and higher-energy bands can also be tuned. Since the intermediate band is related to the element Sn, we expect that the gap can be tuned efficiently through replacing Sn by Ge or Si. As shown in Fig. 2(e), there is also an intermediate band in the calculated band structure of wurtzite-kesterite Cu 2 ZnGeS 4 , however, the gap between the intermediate band and higher-energy bands is only 0.7 eV, smaller than that of the wurtzite-kesterite Cu 2 ZnSnS 4 . That means the gap shrinks as the group IV element becomes smaller. Following this trend, the gap should become even smaller if we replace Ge by Si. Interestingly, the calculated band structure of Cu 2 ZnSiS 4 in Fig. 2(f) shows that the intermediate band disappears, i.e., there is no gap between the intermediate band and higher-energy conduction band, and the lone band disappears. The shrinking of this intermediate-conduction band gap from Sn to Ge to Si should result from the stronger hybridization between Si and S than that between Ge and S (also between Sn and S), which make the s band and p bands merge after hybridizing with the S 3s and 3p bands strongly.
Since the intermediate-conduction band gap increases as the crystal structure is changed into the wurtzite-kesterite structure, and decreases as the component element Sn is replaced by Ge and Si, we will focus on the wurtzite-kesterite structure in the following discussion because a larger intermediate-conduction band gap is required for higher photovoltaic efficiency according to the theoretical model proposed by Luque 40,41 . However, it is still unknown how the Ag substitution of Cu influences the intermediate band, which will be discussed below.
In Fig. 4(a) we plot the calculated band structure of the kesterite-structured Ag 2 ZnSnS 4 . To avoid the serious band gap underestimation of the PBE functional, here the HSE06 hybrid functional is used to calculate the band structure (based on the crystal structure relaxed using PBE functional, which underestimates the band gap of  Fig. 4(b), which is higher than the optimal value according to the best performance model proposed by Luque and Martí 1,2 . Then, we should decrease this band gap. According to the discussion in the above section, the intermediate-conduction band gap may be decreased through changing the crystal structure from the kesterite structure to wurtzite-kesterite structure. In Fig. 5 It should be noted that the width of the intermediate band in Fig. 5 is about 1.2 eV, which is quite large and differ significantly from the infinitesimal bandwidth required by the model of Luque and Martí 1,2 . In 2008, Levy and Honsberg had considered both the positive effect of the finite band width (the recombination through the intermediate band can be suppressed) and the negative effect (the optical absorption is decreased), and showed that the optimal width of the intermediate band should be roughly equal to or lower than 825 meV 43 . Based on their study, we can find that the width of 1.2 eV of the intermediate band in wurtzite-kesterite structured Ag 2 ZnSnSe 4 largely exceeds the optimal width. Therefore, the efficiency of the intermediate band solar cells based on the wurtzite-kesterite structured Ag 2 ZnSnSe 4 may be limited to a low value by the finite band width which is similar to the case shown in Fig. 3 of their paper 43 . This may be an important problem in the development of practical solar cells. One possible way to solve this problem is to investigate other I 2 -II-IV-VI 4 quaternary semiconductors and search for those with narrow intermediate band. On the other hand, although it is shown that the proper n-type doping and filling of the intermediate band is possible in Ag 2 ZnSnSe 4 , however, it is so far unknown which element is the optimal dopant that can have good solubility in this compound semiconductors and meanwhile produce high concentration of electron carriers filling the intermediate band. These problems deserve further study in the development of practical intermediate band solar cells based on the I 2 -II-IV-VI 4 semiconductors.

Conclusions
Using the density functional theory calculations, we found that the I 2 -II-IV-VI 4  Calculation Methods. All the total energy and band structure calculations were performed using the density functional theory methods as implemented in the Vienna Ab initio simulation package (VASP) code 44 . For the exchange-correlation potential, we used the generalized gradient approximation (GGA) 45 of Perdew-Burke-Ernzerhof (known as PBE) 46 to relax the crystal structures and calculate the band structure of Cu 2 ZnSnS 4 , Cu 2 ZnGeS 4 , and Cu 2 ZnSiS 4 . Since PBE is known to underestimate the s-p band gap of semiconductors significantly, which affects our investigation on the intermediate-valence band gap (which is a s-p band gap), the Heyd-Scuseria-Ernzerhof (HSE06) hybrid functional 47,48 is also used to calculate the band structure. In Fig. 2 the band structures are calculated using the PBE functional for a series of high-symmetry k-points, from which we can know the shape of the band structure and determine the k-points where the band gaps open. In Fig. 4 and Fig. 5 the band structures are calculated using the computationally heavier HSE06 functional, so we consider only three representative high-symmetry k-points, from which we can determine the band gap size accurately.
The cutoff of the kinetic energy for the plane-wave basis wave functions is chosen to be 400 eV for all the calculations. For the Brillouin zone integration, we used the 4 × 4 × 4 Monkhorst-Pack k-point meshes 49 for the wurtzite-kesterite structure and equivalent k-point meshes for the kesterite structure. All the lattice parameters and atomic positions were fully relaxed until the quantum mechanical force on each atom is smaller than 0.01 eV/Å. Convergence test calculations showed that the larger energy cutoff, denser k-point meshes and smaller force criterion changes the calculated band gap by less than 0.01 eV.