Crystal Systems and Lattice Parameters of CH₃NH₃Pb(I_1-Br)₃ Determined Using Single Crystals: Validity of Vegard's Law

Metal halide perovskites are promising materials for light absorbers in solar cell applications. Use of the Br/I system enables us to control band gap energy and improves the efficiency of solar cells. Precise knowledge of lattice parameters and band gap energies as functions of compositions are crucially important for developing the devices using those materials. In this study, we have determined lattice parameters and band gap energies of CH₃NH₃Pb(I_1-Br)₃, one of the most intensively studied mix-halide perovskites, as functions of Br content x. We measured accurate Br contents and lattice parameters of CH₃NH₃Pb(I_1-Br)₃ (0 ≤ x ≤ 1) using single-crystalline samples by X-ray photoelectron spectroscopy (XPS) and X-ray diffraction (XRD) measurements, respectively. The CH₃NH₃Pb(I_1-Br)₃ crystal system is tetragonal for x ≤ 0.06 and cubic for x ≥ 0.08 at 300 K. Lattice parameters of CH₃NH₃Pb(I_1-Br)₃ strictly follow Vegard's law; i.e., they are linearly dependent on x. We give linear expressions of x of lattice parameters for the tetragonal and cubic phases of CH₃NH₃Pb(I_1-Br)₃ at 300 K. We have shown that these expressions can be used for determining the Br contents of CH₃NH₃Pb(I_1-Br)₃ polycrystalline thin-film samples based on XRD measurements and, in addition, demonstrated that XPS measurements on polycrystalline samples may be erroneous because of impure ingredients in the samples. Furthermore, we determined band gap energies of CH₃NH₃Pb(I_1-Br)₃ (0 ≤ x ≤ 1) at room temperature using absorption spectra of polycrystalline thin films taking account of excitonic effects.