# Effects of Adding Alkali Metals and Organic Cations to Cu-Based Perovskite Solar Cells
## 2 Computational Conditions and Experimental Methods  
The electronic structures of the perovskite crystals were single-point-calculated with crystallographic structural data obtained from X-ray diffraction. The ab initio quantum calculations were performed using the Vanderbilt ultrasoft pseudo-potentials, scalar relativistic generalized gradient approximations and the Perdew-Burke-Erzzerhof exchange correlation functional and density functional theory without consideration of spin-orbital coupling effect (Quantum Espresso Software Ver. 5. 2. 1, Quantum ESPRESSO Foundation, Cambridge, UK). The basis functions were used properly according to the cases of itinerant and localized electron system. Plane-wave basis set cut offs for the wave functions and charge density were set at 25 and 225 Rydberg. The perovskite crystals were constructed with a crystal system of \(P\overline{m}3\overline{m}\). Uniform \(k\)-point grid (4 \(\times\) 4 \(\times\) 4) in the Brillouin zone was used to calculate the electronic structure and partial density of state. The ABX\({}_{3}\) (A = Na\({}^{+}\), K\({}^{+}\), Rb\({}^{+}\), Cs\({}^{+}\), MA\({}^{+}\), or EA\({}^{+}\), B = Pb\({}^{2+}\) or Cu\({}^{2+}\), X = I\({}^{-}\), Br\({}^{-}\), or Cl\({}^{-}\)) perovskite crystals were formed as a cubic system with a 1 \(\times\) 1 \(\times\) 1 single cell. The cation of MA\({}^{+}\), EA\({}^{+}\), Na\({}^{+}\), K\({}^{+}\), Rb\({}^{+}\), or Cs\({}^{+}\) was set in the center position of the unit cell (1 \(\times\) 1 \(\times\) 1). The cation of Pb\({}^{2+}\) or Cu\({}^{2+}\) ion was set at the position of \(\Gamma\) (0, 0, 0). As the Cu-incorporated perovskite crystal modelling with 2 \(\times\) 2 \(\times\) 2 supercells, parts of the Pb atom at the B-sites were substituted with Cu ion for one-atom substitution at the center of the cubic structure. The Cu-incorporated ABX\({}_{3}\) (A = MA\({}^{+}\), EA\({}^{+}\), or Na\({}^{+}\), X = I\({}^{-}\) or Br\({}^{-}\)) perovskite crystals were constructed with the 2 \(\times\) 2 \(\times\) 2 supercells, and were used for the band calculation. The band structures, effective mass and band gap were analyzed for the Brillouin zone of the lattice of the perovskite crystals along the direction of wave vector. Path for ABX\({}_{3}\) perovskite crystal were set as follows, \(\Gamma\) (0, 0, 0) \(\rightarrow\) X (0, 12, 0) \(\rightarrow\) M (1/2, 1/2, 0) \(\rightarrow\)\(\Gamma\)\(\rightarrow\) R (1/2, 1/2, 1/2) \(\rightarrow\) X, M \(\rightarrow\) R. The Fermi energy was set at zero. The density of states (DOS) and partial density of states (pDOS) were calculated to make clear the energy level for each orbital near the valence band (VB) and conduction band (CB). Structural optimization was performed for the structural models containing the alkali metals. The cut-off energy of the planar wave function was set to 80 eV for the structural optimization and it was set to 25 eV for the other calculations. A 4 \(\times\) 4 \(\times\) 4 \(k\)-point mesh was used for calculations of all structures [46; 47; 48]. F-doped tin oxide (FTO) substrates were cleaned in an ultrasonic bath with acetone and methanol and dried under nitrogen gas. The TiO\({}_{2}\) (0.15 and 0.30 M) precursor solutions were prepared from titanium diisopropoxide bis(acetyl acetonate) (Sigma-Aldrich, Tokyo, Japan, 0.055 and 0.11 mL) with 1-butanol (1 mL). The 0.15 M TiO\({}_{2}\) precursor solution was spin-coated on the FTO substrate at 3000 rpm for 30 s, and the coated substrate was then annealed at 125 \({}^{\circ}\)C for 5 min. The 0.30 M TiO\({}_{2}\) precursor solution was spin-coated on the TiO\({}_{2}\) layer at 3000 rpm for 30 s, and the resulting substrate was annealed at 125 \({}^{\circ}\)C for 5 min. The process to form the 0.30 M precursor layer was performed twice. Then, the FTO substrate was sintered at 550 \({}^{\circ}\)C for 30 min to form a compact TiO\({}_{2}\) layer.