From kesterite to stannite photovoltaics: stability and band gaps of the Cu 2 (Zn,Fe)SnS 4 alloy

Kesterite semiconductors, particularly Cu 2 ZnSnS 4 (CZTS), have attracted attention for thin-ﬁlm solar cells. We investigate the incorporation of Fe into CZTS to form the Cu 2 (Zn,Fe)SnS 4 solid-solution for tuning the lattice spacing and band gap. First-principles calculations conﬁrm a phase transition from kesterite (Zn-rich) to stannite (Fe-rich) at Fe/Zn = 0 . 4. The exothermic enthalpy of mixing is consistent with the high solubility of Fe in the lattice. There is a linear band-gap bowing for each phase, which results in a blue-shift of photo-absorption for Fe-rich alloys due to the conﬁnement of the conduction states. We propose compositions optimal for Si tandem cells.


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The first-wave of thin-film solar cell technologies resulted in the success of CdTe and CuInSe 2 devices. Now, there is a focus on finding alternate, earth-abundant absorber materials that could support a terawatt scale photovoltaic industry. 1 Systems of interest include Cu 2 S, Fe 2 S, SnS and the quaternary semiconductor Cu 2 ZnSnS 4 (CZTS). Solar cells based on CZTS have reached 11% light-to-electricity conversion efficiency, making it the leading candidate in the field. 13? ,14 While CZTS itself has many attractive properties for solar cells, further increases in the performance will require optimisation that can be achieved through control of the materials stoichiometry and/or incorporation of extrinsic impurities, such as Fe (to replace Zn) or Se (to replace S). 16,17 The theory of binary (A x B 1−x ) and pseudo-binary (e.g. A x B 1−x X or A x B 1−x XY) semiconductor alloys is well developed. 18,19 Ordering of the binary elements can occur along fundamental crystal planes, e.g. (001), (111) and (201) orientations for the face-centredcubic (fcc) zincblende structure, or they can be distributed in a homogeneous fashion as a disordered alloy. Quaternary semiconductors such as Cu 2 ZnSnS 4 can be viewed as a mixture of their component binary semiconductors (i.e. Cu 2 S, ZnS and SnS 2 ) with specific ordering of the metals. 21 For example, the kesterite and stannite mineral structures can be described by the same 1 × 1 × 2 zincblende superlattice with Cu, Zn and Sn occupying distinct fcc lattice sites (Fig. 1).
Kesterite and stannite are structurally similar but distinct mineral structures: the former is known for Cu 2 ZnSnS 4 and the latter for Cu 2 FeSnS 4 ; 22 although, the energy difference between the two polymorphs is small. For the Cu 2 (Zn,Fe)SnS 4 solid solution, the structural transition from kesterite to stannite is suggested as the Zn:Fe ratio decreases. 23,24 Unfortunately, due to their structural similarity, the complete determination of the transition is challenging. It should also be noted that standard X-ray diffraction can not distinguish between Cu and Zn due to their similar cross-sections; neutron diffraction is a more appropriate characterisation technique, especially for complex cation disorder. 24 In this Letter, we combine a quantum mechanical description of the total energy and electronic structure with a statistical mechanical description of the solid-solution to predict the structural and electronic properties of the Fe/Zn alloy from first-principles. The predictive value of atomistic modelling for this class of materials has been well established, ? and our results provide guidelines for expanding their range of applications.
The Cu 2 Zn 1−x Fe x SnS 4 alloy was modeled using a 2 × 2 × 1 supercell of the conventional 2 tetragonal kesterite/stannite crystal structures. In this 64-atom supercell, Zn/Fe occupy 8 distinct lattice sites. We have calculated x = 0, 0.25, 0.5, 0,75, 1 for kesterite and stannite, which corresponds to 2, 4 and 6 Zn substitutions by Fe. To describe the site occupation, we considered all symmetry inequivalent configurations using the Site Occupation Disorder 27 approach. These were used to construct a statistical representation of the disordered alloy at an equilibrium temperature T, assuming a representative annealing temperature of 750 • C. The total energy and band structures were obtained using density functional theory within the generalized gradient approximation (PBE), 28 as implemented in the plane-wave code VASP. 29,30 The core-valence interaction was treated within the projector-augmented wave scheme. 31 In order to overcome semi-local description of electron exchange and correlation, we employed screened hybrid functional of Heyd, Scuseria, and Ernzerhof (HSE06) 32 The HSE screening parameter was set to 0.2Å −1 . A plane-wave cutoff of 400 eV was used, and the Brillouin-zone sampled at the zone-centre with σ = 0.05 eV (density of states were calculated using a 2 × 2 × 2 k -mesh).
The linear band-gap bowing coefficients (b) were obtained from the relation: where E g is the calculated band gap of the alloy at composition x. The mixing enthalpy (∆H) with respect to the parent quaternary compounds was calculated from the total energies (E ): The lattice constants and band gaps (E Γ−Γ g ) of CZTS and CFTS, in both the kesterite and stannite structures, are summarized in Table I The lattice constants of st-CFTS are a = 5.489Å and c = 10.760Å, which are also within 1% of the experimentally reported values. 24 We calculated the band gap of st-CFTS to be 1.8 eV; note this is a quasiparticle gap, which excludes on-site excitations associated with  For all of the magnetic configurations considered, the calculated local magnetic moment of Fe is about 3.5 µ B , confirming the high-spin state. As expected, antiferromagnetic ordering is lowest in energy for st-CFTS; however, we found stripe-AFM and checkerboard-AFM to be stable for stannite and kesterite, respectively. The energy difference between alternative configurations is small, consistent with the low Néel temperature. The magnetic configuration shows no strong influence on the crystal structure or electronic properties. Indeed, the average band gap of spin-up and spin-down for the FM configurations gives almost the same value as the AFM states. For the alloy we therefore assume a FM structure and compute the band gap averaged over both spin channels.
The energy difference between the kesterite and stannite polymorphs for the alloy is shown in Fig. 2. Stannite structure becomes more stable than kesterite in the range of x > 0.4. The associated evolution of the tetragonal distortion parameter is plotted in Fig. 3 The predicted mixing enthalpy is negative (exothermic) for both kesterite and stannite ( Fig. 4), implying that alloy formation is a thermodynamically favourable process. Similar behaviour is seen in I-III-V semiconductor alloys. 45 The stable mixing is consistent with the fact that the natural minerals of kesterite and stannite occur in alloy form, 22 where the equilibrium Fe composition frequently exceeds 25 %. At x = 0.50 and 0.75 kesterite has lower mixing enthalpy than stannite, which manifests as a slight deviation from linear behavior in that region (Fig. 2).
The band gap dependence on composition is illustrated in Fig. 5. Both kesterite and stannite have small quadratic bowing coefficients, suggesting that the alloy is 'well-behaved' in both phases. The band gap increases as the Fe ratio increases: contributions of Zn s orbitals to the delocalised conduction band are replaced by the more localised Fe d orbitals, which results both in a decrease in band width and a spacial confinement of the electronic wavefunction. While linear behaviour is observed for the kesterite and stannite structures, separately, there will be a transition between them at ca. x = 0.4, which may result in a small discontinuity experimentally. The flat region could be useful to search for quaternary materials with optimal photovoltaic band gaps, where previously Si and Ge replacements have been of interest. 33,46,47 It has been suggested that organic or dye-sensitised absorbers could make an inexpensive top layer on Si to form a more efficient tandem cell. 48 Moving to two-junction photovoltaics increases the limiting efficiency considerably. The ease of incorporation of Fe in CZTS allows for the selective tuning of the band gap and the lattice parameters. For Si, which has an indirect band gap of 1.12 eV at 300 K, the optimal band gap for a top layer is between 1.70 and 1.76 eV, 49 giving a theoretical efficiency of 37 %. 50 The Fe/Zn alloy enters the optimal band gap region around x = 0.8 where stannite is thermodynamically stable (2).
The predicted lattice mismatch at this composition is less than 1%, thus the fabrication of a robust heterostructure should be possible.