Methodological Issues in First-Principle Calculations of CH₃NH₃PbI₃ Perovskite Surfaces: Quantum Confinement and Thermal Motion

Abstract

Characterization and control of surfaces and interfaces are critical for photovoltaic and photocatalytic applications. In this work, we propose CH 3 NH 3 PbI 3 (MAPI) perovskite slab models whose energy levels, free of quantum confinement, explicitly consider the spin−orbit coupling and thermal motion. We detail methodological tools based on the density functional theory that allow achieving these models at an affordable computational cost, and analytical corrections are proposed to correct these effects in other systems. The electronic state energies with respect to the vacuum of the static MAPI surface models, terminated in PbI 2 and MAI atomic layers, are in agreement with the experimental data. The PbI 2 -terminated slab has in-gap surface states, which are independent of the thickness of the slab and also of the orientation of the cation on the surface. The surface states are not useful for alignments in photovoltaic devices, while they could be useful for photocatalytic reactions. The energy levels calculated for the MAIterminated surface coincide with the widely used values to estimate the MAPI alignment with the charge transport materials, i.e., −5.4 and −3.9 eV for valence band maximum and conduction band minimum, respectively. Our study offers these slab models to provide guidelines for optimal interface engineering.

Atomic scale model and electronic structure of Cu$_2$O/CH$_3$NH$_3$PbI$_3$ interfaces in perovskite solar cells

“…. For a MAPI-invacuum slab that has the same thickness as our models, 12 the confinement energy shift is 0.24 eV. A MAPI slab free of quantum confinement would be at least three times thicker, which is computationally not affordable.…”

“…For an explicit calculation of an interface between two materials, E (m) V (m =Cu 2 O, MAPI) can be identified with the highest occupied energy level the wavefunction of which is delocalized over the central part of the region occupied by material m. The values E (m) V computed in this way depend on the width of the m-material slab, in some cases displaying the quantum confinement effect. 3,12 Hence, E (m) V should be computed for sufficiently wide slabs, which generally contain such a high number of atoms that prevents DFT calculations. However, the VBM alignment across the interface can be determined by means of a twostep procedure.…”

“…6,[9][10][11] This variation is reproduced in calculation for MAPI(001) surfaces with different terminations. 11,12 Cu 2 O, a low cost p-type semiconductor with relatively high hole mobility, and a nominal ionization potential of 5.37 eV, has been proposed 7,13 as HTL in PSC. Experimental PSC with CuO, Cu 2 O or CuO x as HTL have been reported, [14][15][16][17][18][19][20][21][22] with a maximum PCE of 17 %, as well as improved stability with respect to control solar cells, using spiro-MeOTAD.…”

DensityTool: A post-processing tool for space- and spin-resolved density of states from VASP

“…Particularly, we used (2 ˆ2q ˆ6 slabs of (001) MAIand PbI 2 (unpolarized )-terminated surfaces of MAPI, see Ref. [16] for slab nomenclature. Electronic structure was calculated with the HSE06 hybrid functional [17,18] and spin-orbit coupling was included.…”

“…For more calculation details see the supporting information in Ref. [16]. The atomic structure for both slabs is shown on top of Fig.…”