Accurate bandgaps of photovoltaic kesterites from first-principles DFT+U

Abstract

Streamlined prediction of the electronic properties of photoactive materials warrants a Density Functional Theory (DFT) based approach that (i) yields reliable bandgaps, (ii) is free of empirically tuned parameters, and (iii) exhibits low computational overhead. Here we show that for Cu2ZnSnS4 and Cu2ZnGeS4 kesterite photovoltaic materials, all three of these demands are met by the DFT plus Hubbard U technique (DFT+U) with corrective parameters evaluated via minimum-tracking linear response. The predicted bandgaps are found to even marginally outperform those from the self-consistent GW approach. Key to this method's success is the application of Hubbard U corrections to all atomic subspaces that dominate the conduction and valence band edges, as opposed to the conventional approach of correcting 3d and 4f atomic states. Intriguingly, the inclusion of Hund's J corrections via the extended DFT+U+J functional significantly worsens these results. This under performance can be ameliorated through the use of the Burgess-Linscott-O'Regan (BLOR) flat-plane based Hubbard U plus Hund's J functional, with bandgap predictions in close agreement with the conventional DFT+U method. The DFT+U method is also used to predict defect-induced changes to the bandgap and associated formation energies, in 1,728-atom supercells.

Figures (7)

• Figure 1: CZGS demonstrating the general crystal structure of a quaternary chalcogenide X$_2$Zn Y S$_4$ in the kesterite phase, space group $I\bar{4}$. The principle transition metal X=Cu is shown in gray, Zn is blue, Y=Sn,Ge in green, and S in yellow.
• Figure 2: Projected density of states (PDOS) of CZGS evaluated at the PBE (top), PBE+$U$$_{\rm eff}$ (middle), and PBE+BLOR (bottom) levels with a Gaussian broadening of 0.1 eV. The energy values are reported with respect to the mid-gap energy of the bare PBE calculation ($E_\perp$) to readily identify the effect of the Hubbard corrections on the valence and conduction bands.
• Figure 3: The predicted bandgap of CZGS using the PBE XC functional with Hubbard corrections applied to an increasing number of atomic subspaces. The element labels refer to the atomic subspaces to which Hubbard corrections were applied, namely Cu-3d, S-3p and Ge-4s.
• Figure 4: Bandgaps of (top) CZTS and (bottom) CZGS evaluated at the PBE, PBE+$U_{\rm eff}$ and PBE+$U$+$J$ level with Hubbard corrections applied to the Cu $3d$, S $3p$, Sn $5s$, and Ge $4s$ atomic subspaces. A variety of bandgap predictions from the literature are also presented khadka2014structuralbottiBandStructuresCu2ZnSnS42011khadkaStudyStructuralOptical2013m.quennetFirstPrinciplesCalculationsn.dilshodDFTStudyStructure2022paier$textCu_2textZnSnS_4$PotentialPhotovoltaic2009parkStabilityElectronicProperties2018wexlerExchangecorrelationFunctionalChallenges2020zhangComparativeStudyStructural2011zhangStructuralPropertiesQuasiparticle2012chenElectronicStructureStability2009korbel2015optical, these were evaluated using a Local Density Approximation (LDA) ceperleyGroundStateElectron1980 (dark pink bar)); semi-local approximations (PBE perdewGeneralizedGradientApproximation1996, PBEsol perdewRestoringDensityGradientExpansion2008, and PW91 Burke1998—light pink bars); a meta-generalized gradient approximation, both with and without dispersion corrections (SCAN sunStronglyConstrainedAppropriately2015 and SCAN+rVV10 sabatiniNonlocalVanWaals2013—dark gray bars); hybrid functionals (PBE0 perdewRationaleMixingExact1996, HSE03 heydHybridFunctionalsBased2003, and HSE06 krukauInfluenceExchangeScreening2006—green bars); the DFT+$U$ method dudarevElectronenergylossSpectraStructural1998 (PBE+$U$ and SCAN+$U$—dark blue bars); and both the perturbative and fully self-consistent GW approximation (light blue bars) hybertsenElectronCorrelationSemiconductors1986brunevalEffectSelfconsistencyQuasiparticles2006. Experimental values from UV-Vis absorption spectroscopy are also provided khadkaStudyStructuralOptical2013khadka2014structural. Bandgaps calculated as part of the current work are bolded and have yellow bars.
• Figure 5: PDOS of CZTS evaluated at the PBE (top), PBE+$U$$_{\rm eff}$ (middle), and PBE+BLOR (bottom) levels with a Gaussian broadening of 0.1 eV. The energy values are reported with respect to the mid-gap energy of the bare PBE calculation ($E_\perp$) to readily identify the effect of the Hubbard corrections on the valence and conduction bands.