Computational Characterization of the Dependence of Halide Perovskite Effective Masses on Chemical Composition and Structure

Effective masses are calculated for a large variety of perovskites of the form ABX(3) differing in chemical composition (A= Na, Li, Cs; B = Pb, Sn; X= Cl, Br, I) and crystal structure. In addition, the effects of some defects and dopants are assessed. We show that the effective masses are highly correlated with the energies of the valence-band maximum, conduction-band minimum, and band gap. Using the kp theory for the bottom of the conduction band and a tight-binding model for the top of the valence band, this trend can be rationalized in terms of the orbital overlap between halide and metal (B cation). Most of the compounds studied in this work are good charge-carrier transporters, where the effective masses of the Pb compounds (0 < m(h)(*) < m(e)(*) < 1) are systematically larger than those of the Sn-based compounds (0 < m(h)(*) approximate to m(e)(*) < 0.5). The effective masses show anisotropies depending on the crystal symmetry of the perovskite, whether orthorhombic, tetragonal, or cubic, with the highest anisotropy for the tetragonal phase (ca. 40%). In general, the effective masses of the perovskites remain low for intrinsic or extrinsic defects, apart from some notable exceptions. Whereas some dopants, such as Zn(II), flatten the conduction-band edges (m(e)(*) = 1.7m(0)) and introduce deep defect states, vacancies, more specifically Pb2+ vacancies, make the valence -band edge more shallow (m(h)(*) = 0.9m(0)). From a device-performance point of view, introducing modifications that increase the orbital overlap [e.g., more cubic structures, larger halides, smaller (larger) monovalent cations in cubic (tetragonal/orthorhombic) structures] decreases the band gap and, with it, effective masses of the charge carriers.