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

Abstract

Effective masses are calculated for a large variety of perovskites of
\nthe form ABX
\n3
\ndiffering in chemical composition (A= Na, Li, Cs; B = Pb, Sn; X=
\nCl, Br, I) and crystal structure. In addition, the effects of some defects and dopants
\nare assessed. We show that the effective masses are highly correlated with the
\nenergies of the valence-band maximum, conduction-band minimum, and band gap.
\nUsing the
\nk
\n·
\np
\ntheory for the bottom of the conduction band and a tight-binding
\nmodel for the top of the valence band, this trend can be rationalized in terms of the
\norbital overlap between halide and metal (B cation). Most of the compounds
\nstudied in this work are good charge-carrier transporters, where the effective masses
\nof the Pb compounds (0 <
\nm
\nh
\n*
\n<
\nm
\ne
\n*
\n< 1) are systematically larger than those of the
\nSn-based compounds (0 <
\nm
\nh
\n*
\n≈
\nm
\ne
\n*
\n< 0.5). The effective masses show anisotropies depending on the crystal symmetry of the
\nperovskite, whether orthorhombic, tetragonal, or cubic, with the highest anisotropy for the tetragonal phase (ca. 40%). In general,
\nthe effective masses of the perovskites remain low for intrinsic or extrinsic defects, apart from some notable exceptions. Whereas
\nsome dopants, such as Zn(II),
\nflatten the conduction-band edges (
\nm
\ne
\n*
\n= 1.7
\nm
\n0
\n) and introduce deep defect states, vacancies, more
\nspecifically Pb
\n2+
\nvacancies, make the valence-band edge more shallow (
\nm
\nh
\n*
\n= 0.9
\nm
\n0
\n). From a device-performance point of view,
\nintroducing modifications that increase the orbital overlap [e.g., more cubic structures, larger halides, smaller (larger) monovalent
\ncations in cubic (tetragonal/orthorhombic) structures] decreases the band gap and, with it, effective masses of the charge carriers.