Theoretical investigation of octahedral tilting and bandgap non-linearity in monolayer Ruddlesden-Popper A₂Pb_1-xGe_xI₄ perovskites

2D Ruddlesden-Popper (RP) perovskites (R-NH₃)₂A_n−1B_nX_3n+1 with tailorable photovoltaic features of low toxicity, reduced dimensionality, and defect tolerance hold promise to overcome the main constraints of perovskite solar cells (PSCs). A systematic investigation of the structural and electronic properties of pure and mixed (R-NH₃)₂Pb_1−xGe_xI₄ systems was performed with and without spin-orbit coupling (SOC), by using density functional theory (DFT). The organic spacer cations (R-NH₃⁺)₂ of methylammonium (MA-CH₃NH₃⁺) and Phenylethyl ammonium (PEA-C₆H₅[CH₂]₂NH₃⁺) with x = 0.0, 0.25, 0.50, 0.75, 1.0, resulted in the compositionally modified 32-permutations by systematically substituting the inorganic cations. Short-range ordering has categorized all studied compositions of (R-NH₃)₂Pb_0.50Ge_0.50I₄ into column and battenberg schemes depending on the Ge defect site. The competing effects of octahedral tilting and lattice distortion with bandgap bowing and SOC, across Pb-Ge compositional systems, provide a systematic strategy to tune bandgaps. By controlling the cations' composition, these mixed 2D-perovskites outlined the strategy to achieve the desired bandgap and band positions. A rational design approach of low dimensional perovskites was adopted to tune the electronic properties through the spacer and inorganic cation engineering. Our findings expose the scope of monolayer-based systems as an ideal choice of absorber for the bottom sub-cell in all-perovskites 2D-3D tandem solar cell, harvesting light from visible (2.4 eV) up to infrared (1.2 eV) in the solar spectrum with features of defect tolerance, quantum and dielectric confinement, low bandgap, low effective masses, and high mobility.