Theoretical investigation of halide perovskites for solar cell and optoelectronic applications

The crystal structure of (a) α phase MAPbI₃, (b) partial charge density of the CBM, (c) partial charge density of the VBM, (d) band structure, (e) density of states (DOS) and partial DOS of MAPbI₃. (f) Schematic optical absorption of Si, GaAs, and halide perovskites. Modified with permission from Ref. [17].

The formation energies (a) and the transition energy levels (b) of intrinsic point defects in MAPbI₃ under the condition of different chemical potentials. Defects with much higher formation energies are displayed as dashed lines. Zero in energy is referred to the VBM. Modified with permission from Refs. [17, 23].

Correlations between tolerance factor and crystal structure of perovskite materials. Reprinted with permission from Ref. [44].

(a) Variations of volumes, formation energies (per halogen atom), and band gaps of the mixed halide alloys CsPb(X_{1 – x}Y_x)3 (X, Y = I, Br, Cl) by SQS calculation. The solid lines are fitted by calculated results of SQS at nine different concentrations (fitted points are not shown for clarity). The triangles represent the stable ordered structures at x = 1/3. For band gaps, the available experimental data are given (red cross marks are data from Ref. [71], the red plus marks are data from Ref. [58], and the green star marks are date from Ref. [63]). (b) The contributions of strain energy and Coulomb energy in the alloy. (c) Particularly stable mixed-halide structures for CsPbX₂Y₁ (X, Y = I, Br, Cl; the atomic size of X is larger than Y). Reprinted with permission from Ref. [45].

(a) Four common structures for ABX₃ compounds as denoted. (b) Screening progress. (c) Calculated optical absorption coefficients and conversion efficiencies of six types of perovskites, MAPbI₃, and GaAs. Reprinted with permission from Ref. [46].

(a) Schematic idea of atomic transmutation and candidate $ {A}_{2}{B}_{1}^{+}{B}_{2}^{3+}{X}_{6}^{{\rm{VII}}} $ perovskites for materials screening. (b) Energies of Cs₂AgBiCl₆ with different arrangements of AgCl₆ (in gray) + BiCl₆ (in blue). The energy of the lowest configuration F is set to zero. (c) Materials screening process by considering the properties relevant to photovoltaic performance, such as decomposition enthalpy (Δ H), band gap, effective masses ($ {m}_{{\rm{e}}}^{* } $ , $ {m}_{{\rm{h}}}^{* } $ ), and exciton binding energy (Δ E_b). The red squares mean the materials passing the screening (selected) and the green ones mean not passing (abandoned). The optimal nontoxic $ {A}_{2}{B}_{1}^{+}{B}_{2}^{3+}{X}_{6} $ perovskites satisfying all the criterions are marked with red checks. (d) The Δ H corresponding to different decomposition pathways for selected $ {A}_{2}{B}_{1}^{+}{B}_{2}^{3+}{X}_{6} $ . Reprinted with permission from Ref. [42].

Calculated band structures for (a) CsMgCl₃, (b) Cs₂Mg₂Cl₆, (c) Cs₂NaInCl₆, (d) Cs₂AgInCl₆, (e) Cs₂In⁺In³⁺Cl₆, (f) Cs₂NaBiCl₆, (g) Cs₂AgBiCl₆, and (h) Cs₂InBiCl₆. The s, p, and d orbital components of the bands are represented as red/light blue, green/dark blue, and pink spheres, respectively. All the bands are aligned with respect to the Cs 1s core level. The dashed lines are at the middle of the band gaps. Reprinted with permission from Ref. [82].

(a) The band structures of the ordered and fully disordered Cs₂AgBiBr₆. The red dots represent the band edge states with the spectral weight over 50%. (b) The calculated optical absorption coefficients α (cm⁻¹) of the fully ordered (black), partial disordered (blue), and fully disordered (red) Cs₂AgBiBr₆. (c) The Monte–Carlo simulation of the excess energy and (d) the corresponding averaged atomic correlation functions of pairs up to the mth neighbor (Π_2m) as a function of temperature. Modification with permission from Ref. [83].

The schematic idea to stablize the disordered phase by introducing extra electrons. Modification with permission from Ref. [83].

(a) Top and side views of bulk orthorhombic CsPbBr₃, CsBr-terminated and PbBr₂-terminated triple-layer (L3) 2D orthorhombic CsPbBr₃, respectively. The structures of the monolayer (L1) and double-layers (L2) are indicated. (b) Formation energies (eV/f.u.) of 2D orthorhombic CsPbBr₃ (top) and orthorhombic MAPbI₃ (bottom). Relaxed AX-terminated slabs (squares) and PbX₂-terminated slabs (triangles) are presented for three different thicknesses, i.e., L1, L2, and L3. The symbols are connected by lines for a better view. The formation energy of bulk APbX₃ is indicated by a horizontal dashed line. Reprinted with permission from Ref. [107].

(a) Representative examples of two classes of structural families for solar cell absorbers of tetrahedral coordination structure and octahedral coordination structure. Spinel structure can be considered as the mixing of tetrahedral and octahedral building blocks but keep high crystal symmetry. (b) The calculated optical absorption spectrum and the spectroscopic limited maximum efficiency (SLME) for 10 spinel compounds MgIn₂Se₄, ZnSc₂Se₄, ZnY₂Se₄, CdSc₂Se₄, CdY₂Se₄, HgAl₂Se₄, HgIn₂S₄, CdIn₂Se₄, HgSc₂S₄, and HgY₂S₄, in comparison to typical solar cell absorbers GaAs and CH₃NH₂PbI₃. Five compounds with inferior performance (MgIn₂Se₄, ZnSc₂Se₄, ZnY₂Se₄, CdSc₂Se₄, and CdY₂Se₄) have been shaded. The orbital character of VBM and CBM for three selected compounds, HgAl₂Se₄, ZnSc₂Se₄, and CH₃NH₂PbI₃. The dipole-allowed intra-atomic transitions are indicated. Reprinted with permission from Ref. [108].

(a) The schematic illustration of DX center in tetragonal semiconductor. The local structures of the host and α⁺, α^–, and DY^– defect states and the calculated defect formation energy of Bi_Pb in (b) Bi-doped MAPbBr₃ and (c) Bi-doped MAPbI₃ as a function of Fermi energy E_F under the anion-rich/Pb-poor condition. The numbers indicate the obtained bond lengths for the full lines or distances for the dotted lines of the broken bonds. (d) The alignment of the band edges of MAPbI₃ and MAPbBr₃ and the relative single electron energy levels of α^– and DY^– states. The red lines represent the stable states, while the grey lines represent the metastable states. The numbers in brackets represent the projected p orbital percentage of (anion/cation). Modification with permission from Refs. [29, 130].

(a) Schematic diagram of energy levels of the Bi-doped MAPbBr₃ crystal in dark. (b) Schematic representation of the emergence of DX-like (DY) defect levels under light illumination. Also shown are the dynamic photocarrier generation and recombination processes that lead to the negative photoconductivity. (c) Negative photoconductivity curve corresponding to the transitions taking place relevant to DY center under light. (d) Schematic plot of formation energies of a shallow donor Bi_Pb (α⁺) and DY center in MAPbBr₃ as functions of the Fermi level (ϵ_f). (e) Atomic configuration of the DY center in Bi-doped MAPbBr₃. (f) The transition of Bi-doped MAPbBr₃ from the metastable α^– state to the stable DY^– state. Modification with permission from Refs. [29, 120].

(a) Schematic illustration of normal band structure for conventional n-type TCOs such as In₂O₃ and inverted band structure for p-type TCs. The black dashed line indicates the position of Fermi level, while the green dotted lines present the doping-limit energy level. (b) Interband (T1) and intraband (T2) optical transitions in p-type TCs. (c) Band structures of CsPbCl₃ calculated by HSE06 and GW+SOC methods. (d) Calculated formation energies for various intrinsic defects, two defect complexes, and three extrinsic defects (K_Pb, Na_Pb, and Ag_Pb) in CsPbCl₃, under both the Pb-rich and Pb-poor conditions. (e) Decomposition energies (Δ H_d) of 27 IMHPs. (f) Band gaps of 10 stable IMHPs, calculated with GW+SOC method. Modification with permission from Ref. [121].