Nature of the excited state in lead iodide perovskite materials: Time-dependent charge density response and the role of the monovalent cation

Charge density response is responsible for the excited-state properties of lead iodide perovskites and is related to both the light absorption properties as well as subsequent electronic and lattice relaxation in the system, important for the working conditions of the material in solar cell applications. Here we investigate the nature of the excited state and its relation to pathways for electronic and lattice relaxations by performing time-dependent density-functional theory (TDDFT). Charge density response upon photoexcitation close to the band edge and deeper into the absorption spectra are investigated for three lead perovskite compounds with different $A$-site monovalent cations ${\mathrm{CsPbI}}_3,\mathrm{C}{\mathrm{H}}_2{\left(\mathrm{N}{\mathrm{H}}_2\right)}_2\mathrm{Pb}{\mathrm{I}}_3\left(\mathrm{FAPb}{\mathrm{I}}_3\right)$, and $\mathrm{C}{\mathrm{H}}_3\mathrm{N}{\mathrm{H}}_3\mathrm{Pb}{\mathrm{I}}_3\left(\mathrm{MAPb}{\mathrm{I}}_3\right)$. The carrier cooling mechanism is analyzed and shows that the initial force acting on the nuclei follows the symmetry of the ground-state electronic structure upon photoexcitation with a force parallel to the polarization of the incoming light. This effect is investigated for the three different compounds and shows an initial force for induced ionic movement that depends on both the underlying symmetry of the inorganic lattice as well as on the type and orientation of the organic cation. The excess energy after thermalization under blue-light illumination is large enough for overcoming the activation energy for iodide migration and can thus trigger vacancy formation. Iodide vacancies are seen to be dipole-field compensated by the organic cation, with a shielding of the local field, and thus form an explanation for the defect tolerance found in these systems under photovoltaic operation. A partial charge transfer from the inorganic cage to the monovalent organic cation is predicted with TDDFT calculations for blue- and UV-light illumination with a population of antibinding orbitals in the N–H bond in both ${\mathrm{CH}}_3{\mathrm{NH}}_3$ (MA) and ${\mathrm{CH}}_2{\left({\mathrm{NH}}_2\right)}_2$ (FA), where the implication for this is discussed in terms of the intrinsic photostability of organic cation containing lead perovskites. The results show the importance of a fundamental understanding of the excited-state properties of perovskite material to reveal the underlying mechanism for the defect tolerance and thus high photovoltaic performance when using organic dipolar cations as well as a rationale for using mixed halide perovskites to decrease the halide migration, effect of vacancy formation, and stability issues under blue- and UV-light illumination.

Figure 1

Schematic illustration of bulk lattice structures for (a) ${\mathrm{CsPbI}}_3$, (b) ${\mathrm{FAPbI}}_3$, and (c) ${\mathrm{MAPbI}}_3$ within the $ab$ plane. The gray, purple, blue, brown, cyan, and white spheres denote the lead, iodide, nitrogen, carbon, cesium, and hydrogen, respectively.

Figure 2

Charge density response for the bulk perovskite materials ${\mathrm{CsPbI}}_3$ (a), (d); ${\mathrm{FAPbI}}_3$ (b), (e); and ${\mathrm{MAPbI}}_3$ (c), (f) with different light polarizabilities: along the $z$ axis (d)–(f) and within $ab$ plane (a)–(c) of the perovskite lattice. The excitation wavelength is 430 nm. The gray, purple, blue, brown, cyan, and white spheres are representative of the lead, iodide, nitrogen, carbon, cesium, and hydrogen, respectively. Cyan and yellow electronic clouds are indicative of bounding/antibonding orbitals. The corresponding values for isosurfaces of charge density have been chosen as 0.000 16, 0.000 22, 0.000 65, 0.000 73, 0.0013, and 0.000 42 for (a)–(f), respectively. The black arrow shows the polarizability of the incoming light.

Figure 3

Charge density response for the perovskite materials with an iodine vacancy: Charge density within $ab$ plane (a), (c) and $ac$ plane (b), (d) for $\mathrm{vacancy}\left(V_{\mathrm{I}}\right)$ present at equilateral position (a), (b) and axial position (c), (d). Insets presenting the imbalance of charge for vicinity of vacancy in comparison to a normal lattice site. (e) Charge density profile at ${\mathrm{FAPbI}}_3$ in vicinity of iodine vacancy. (e) Red arrows indicate the differences and imbalance in charge density in presence and absence of vacancy; black circle represents vacancy and gray; purple spheres represent lead and iodine atoms, respectively. The excitation wavelength is 430 nm and the polarization is within the $ab$ plane.

Figure 4

Schematic illustration of electronic dipole moment at excited state and the resulting electric field acting on the ${\mathrm{MA}}^{+}$ cation inside the organic cage. (a) and (b) represent the pristine and iodine vacancy cases, respectively. The polarizability of excitation light is along $c$ axis.

Figure 5

Energy-dependent charge density response for ${\mathrm{FAPbI}}_3$ and ${\mathrm{MAPbI}}_3$ excited with (a) UV (395 nm) and (b) red (720 nm) light. Polarization is within the $ab$ plane.