Pathway to oxide photovoltaics via band-structure engineering of SnO

The prospects of scaling current photovoltaic technologies to terawatt levels remain uncertain. All-oxide photovoltaics could open rapidly scalable manufacturing routes, if only oxide materials with suitable electronic and optical properties were developed. A potential candidate material is tin monoxide (SnO), which has exceptional doping and transport properties among oxides, but suffers from a low adsorption coefficient due to its strongly indirect band gap. Here, we address this shortcoming of SnO by band-structure engineering through isovalent but heterostructural alloying with divalent cations (Mg, Ca, Sr, Zn). Using first-principles calculations, we show that suitable band gaps and optical properties close to that of direct-gap semiconductors are achievable in such SnO based alloys. Due to the defect tolerant electronic structure of SnO, the dispersive band-structure features and comparatively small effective masses are preserved in the alloys. Initial Sn1-xZnxO thin films deposited by sputtering exhibit crystal structure and optical properties in accord with the theoretical predictions, which confirms the feasibility of the alloying approach. Thus, the implications of this work are important not only for terawatt scale photovoltaics, but also for other large-scale energy technologies where defect-tolerant semiconductors with high quality electronic properties are required.

harvesting, and therefore the short circuit current, J SC . An ideal PV absorber material should have the same energy for both the two gaps, together with a sharp onset of optical absorption. Hence tuning the band structure of SnO to bring together its fundamental band gap and optical band gap is technically very attracting.
In this work, we will show the effects of cation-site isoelectronic alloying on reducing the difference of the two band gaps in SnO. Using first-principles calculations, we explored the electronic structure and optical properties of (Sn, M)O alloys with M including Mg, Ca, Sr, and Zn. The cation-site alloying weakens the original Sn-O and Sn-Sn connection, opening the fundamental band gap. Meanwhile, it reduces the symmetry, allowing for optical transition between the valence band conduction bands with a smaller energy separation.
Accompanying these improvement, the good properties of the pristine SnO, such as the light effective masses, have been preserved. We found that cation-site alloying with a composition around 10% is quite promising to tailor SnO as a PV absorber, which makes all-oxide-based solar cell feasible.
We have considered alloying SnO with Mg, Ca, Sr, and Zn, with compositions of 3.125%, 6.25%, 12.5%, and 25%. To model the alloy structures, we employed the special quasirandom structures (SQS) [24,25] as generated with the mcsqs utility as implemented in ATAT. [26] The SQS method allows us to model the fully random alloys with a relatively small supercell, and the 256-atom supercells were chosen which enable the resulting SQSs to have the pair correlation functions agree with the ideal random alloys even beyond the 8th nearest neighbour of the cation sublattice for all compositions considered. To further take into account the nature of random alloying, four different SQSs for each composition were implemented, and the averaged quantities were reported in the following. To facilitate the Brillouin zone sampling during the DFT calculations, we have chosen the supercells with a shape close to a cube.
The first-principles calculations were performed the projector augmented wave (PAW) method [27] as implemented in the VASP code. [28][29][30] The SQSs were fully relaxed with the GGA in the standard Perdew-Burke-Ernzerhof(PBE) formalism, [31] with a 2 × 2 × 2 Monkhost-Pack k-mesh, [32] during which an on-site Coulomb correction, U = 6 eV, was applied on the Zn-3d states. With the relaxed SQSs, the modified Becke-Johnson local density approximation (MBJ-LDA) [33] was utilized to calculate the electronic structure, as well as the optical absorption spectrum. MBJ-LDA is a potential-based meta-GGA functional, which uses the modified Becke-Johnson exchange potential together with the LDA correlation. With the MBJ-LDA functional, one can obtain the band gaps close to highlevel GW methods at a computational cost comparable to standard DFT calculations. [34][35][36] A 3 × 3 × 3 Monkhost-Pack k-mesh was employed for the MBJ-LDA calculations. Based on the electronic structure and optical absorption spectrum [37] results from MBJ-LDA, we can assess the theoretical efficiency for these alloys to be used as PV absorbers. Instead of the well-known Shockley-Queisser (SQ) limit, [38] we calculated the so-called Spectroscopic Limited Maximum Efficiency (SLME). [39] Compared to the ideal SQ limit, which only takes the band gap as the single material-related parameter, the SLME also includes the finite absorbance of a film with a certain thickness, which is very important for SnO-based alloys due to the indirect-gap nature and the slow absorption onset.     While no defect-like state within the band gap was identified from the DOS plots, the renormalization near the band edges raises a concern whether the charge carrier effective masses becomes significant heavier than the pristine SnO. To explore the effects of isoelectronic alloying on the carrier mobility, we calculated the DOS effective mass, m e DOS and m h DOS , as tabulated in Table I. The DOS effective mass is a suitable quantity to describe the mobility for the large low-symmetry supercell calculations here. [9] The hole DOS effective mass is defined by the relation [8] and similarly, for the electron DOS effective mass, Here, D(E) denotes the DOS, N v (T ) and N c (T ) are the temperature-dependent effective density of states for the valence and conduction band, respectively. For a single parabolic Here the temperature T = 900 K was chosen which gives more reliable results due to the finite k-mesh used for the large supercell. As shown in Table I  where the calculated optical absorption coefficient becomes larger than 10 3 cm −1 . Fig. 3, we compared the fundamental band gap, E g , and optical band gap, E O g , obtained from the MBJ-LDA calculations, for all the alloy systems considered in this study.
During this calculation, the phonon-assistant indirect absorption, and the excitonic effect, were not taken into account, which can usually enhance noticeably the optical absorption near the absorption edge. [37] For convenience, we define the optical band gap, E O g , as the energy at which the optical absorption coefficient, α, becomes larger than a threshold value for which a value of 10 3 cm −1 was chosen in this study. To put this definition into the context,  To see how alloying actually modifies the band structure, we plotted the "effective band structure" for the Sn 120 Zn 8 O 128 , and Sn 112 Zn 16 O 128 alloys, as shown in Fig. 4. [43] In these plots, we show with a color scale the spectral function A( k; E): where k ( K) denotes Bloch wave vectors of SnO primitive cell and the SQS supercell, Ψ i, K is the eigenstate of the supercell with the eigenvalue of ǫ i , and the spectral weight | Ψ i K | k | 2 describes the projection of the supercell eigenstate onto the basis of the Bloch states in the reciprocal space of the primitive cell. [43] Carefully choosing the K vectors, we can unfold the dispersion, ǫ i ( K), of the SQS supercell along the high-symmetry k-points, i.e., the so-called effective band structure. The unfolding has been performed using the BandUP code.
To have a more straight-forward understanding the effects of tuning the shape of the band structure by alloying on the performance of SnO as a PV absorber, we calculated the SLME assuming a thickness of 2 µm, as shown in Fig. 5. Since the band gaps, optical absorption spectra, and hence the SLME, are very similar for all the alloy systems, we only shown the average value in the figure. First, we found that even the smallest alloying composition considered here enhance the efficiency from zero to 11%. Second, the SLME curve becomes quite flat after 10% of alloying, which suggest that we have quite a large optimal area to prepare the SnO-based alloys for PV absorber. To highlight the importance of the detailed shape of band structure, and hence the optical absorption spectrum, we also compared the SLME with the SQ limit, the latter of which simply assume the absorption spectrum with a step-function. Not surprising, the SLME is always smaller than the SQ limit. We also calculated the SLME for Cu 2 SnZnS 4 (CZTS) based on GW calculation, and found that the performance of SnO-based alloys is actually comparable with the CZTS device.
In summary, we performed first-principles calculations of the energetics, and effects of tuning the shape of the band structure of SnO by isoelectroic alloying. We found that alloying with Mg, Zn, Ca, and Sr with a composition around 10% is quite promising to significantly improve the prospect of the bi-polar SnO as a photovoltaic absorber.