Ab initio computational modeling of surface supercells of pseudo-cubic halide perovskites
Hybrid organic-inorganic perovskites (HP) such as methylammonium lead halide (MHP) are an exciting class of semiconductors with compelling advantages for solar cell applications, such as strong absorption and very low cost. HPs also exhibit balanced carrier mobilities, long carrier diffusion lengths, and shallow defect levels, making them even more attractive for photovoltaics and other optoelectronic devices. However, HPs face two significant challenges, which may be related: a lack of material stability as well as anomalous and unpredictable charge carrier transport. The performance of perovskite solar cells can vary wildly and unpredictably depending on their history of exposure to light, heat, mechanical stress, oxygen, or moisture, which raises serious questions about device reliability and the interpretation of experimental data. Furthermore, surfaces and grain boundaries likely play a fundamental role in charge transport, localization, and trapping in polycrystalline HP thin films. Previous work demonstrated polaron formation using hybrid functionals leveraging density functional theory (DFT) when modeling MHP surfaces which may contribute to lattice instability. Hybrid functionals are computationally expensive, creating a hurdle in studying polaronic effects in these materials. Through alternative computational methods known as the Hubbard U correction, polarons were modeled in the bulk, which significantly reduced the need for computational resources. In this work, DFT implemented in the Vienna Ab-initio Simulation (VASP) was used to model several MHP bulk materials and surfaces, including surface termination by different halides (Cl, Br, I) and methylammonium (MA). These calculations used a semi-local exchange functional (PBEsol) and compared the results after implementing the Hubbard U correction ix (PBEsol+U) to verify the feasibility of extending the DFT+U model for modeling halide perovskite surfaces. A non-constant potential was eliminated in the vacuum by implementing dipole corrections. The minimum vacuum size for the MAPbCl, MAPbBr, and MAPbI terminated slabs (both MAX and PbX) was determined to be 28.4 Å, 29.6 Å, and 31.56 Å using 7 monolayers. MA ions reoriented so that the NH3 group was pointing toward the vacuum within the Pb-X lattice using both PBEsol and PBEsol+U functionals in the bulk and all slab supercell models (with the latter functional reducing the amount of reorientation observed). The Pb-halide bond lengths shrank in the bulk as well as for both surface slab terminations after adding a U correction. The bulk band gaps for MAPbCl, MAPbBr, and MAPbI changed from 2.22 eV, 1.84 eV, and 1.52 eV to 2.44 eV, 1.79 eV, and 1.27 eV after including an 8 eV U correction. A smaller U value used for MAPbBr (4 eV) and MAPbI (1 eV) in the bulk resulted in band gaps much closer to experimental values, 1.83 eV and 1.5 eV. MAPbCl experienced octahedral tilting that resulted in a tiny band gap increase while the MAPbBr and MAPbI bandgap shrank due to lattice contractions. The 8 eV U correction changed the bandgap for the MAX terminated slabs from 1.68 eV, 1.39 eV, and 1.27 eV to 1.77 eV, 1.36 eV, and 1.07 eV for MAPbCl, MAPbBr, and MAPbI, respectively. The 8 eV U value also changed the PbX terminated slab bandgaps for MAPbCl, MAPbBr, and MAPbI from 1.31 eV, 1.03 eV, 0.88 eV to 1.35 eV, 0.90 eV, and 0.61 eV, respectively. The smaller bandgaps for the PbX slabs were determined to be due to surface reconstruction caused by dangling bonds on the PbX surfaces. The smaller bandgaps of the PbX slabs suggest the MAX surface would be less prone to radiative recombination occurring. Midgap states were not observed in the bulk nor in either the PbX or MAX surface slabs suggesting defect assisted recombination does not occur in the bulk nor the neutral surface slabs. x The DFT+U method was shown to significantly reduce computational resources for simulating surfaces, however, results show the U value needs to be individually reoptimized for each perovskite compound studied in this work as the U correction changes the physical bond lengths and electronic properties (band gap) of each compound differently in the bulk as well as both PbX and MAX slab supercells.
DFT, VASP, MAPbi, MAPbBr, MAPbCl, halide, perovskite DFT+U
Rodriguez, L. (2023). Ab initio computational modeling of surface supercells of pseudo-cubic halide perovskites (Unpublished thesis). Texas State University, San Marcos, Texas.