Highly Polarizable Semiconductors and Universal Origin of Ferroelectricity in Materials with a Litharge-Type Structural Unit

Abstract

We discover that a large family of [Pb$_2$F$_2$]- and [Bi$_2$O$_2$]-based mixed-anion materials with a litharge-type structural unit are highly polarizable layered semiconductors on the edge of ferroelectricity. First-principles calculations demonstrate that in this family of materials, compounds as diverse as PbFBr, BiOCl, BiCuOSe, Bi$_2$OS$_2$, and Bi$_5$O$_4$S$_3$Cl exhibit static dielectric constants an order of magnitude higher than typical semiconductors. Additionally, they undergo a ferroelectric transition when subjected to a few percent of tensile strain. The ferroelectric transitions of these materials are found to have a universal origin in the strong cross-bandgap hybridization of the cation $p$ orbitals, enabled by the cation 6s$^2$ lone-pair electrons and the litharge-type structure of the [Pb$_2$F$_2$] and [Bi$_2$O$_2$] layers, as demonstrated by the strain-induced ferroelectric transition in the archetypal litharge $α$-PbO. These results establish materials with a litharge-type structural unit as a large and versatile family of highly polarizable layered semiconductors in proximity to ferroelectricity, offering vast opportunities for multifunctional materials design.

Figures (3)

• Figure 1: [Pb$_2$F$_2$]- and [Bi$_2$O$_2$]-based highly polarizable layered semiconductors and their ferroelectric instability. (a) Ball-stick representation of the atomistic structures of PbFX (X=Cl/Br), BiOX (X=Cl/Br/I), Bi$_2$O$_2$X (X=Se/CN$_2$/[CuSe]$_2$), Bi$_2$OS$_2$, and Bi$_5$O$_4$S$_3$Cl. In PbFX, the black, grey and green spheres represent Pb, F, and X atoms, respectively. In other Bi-based compounds, the Bi and O atoms are represented by purple and red spheres, respectively. (b) Side and top views of a Pb$_2$O$_2$ layer in $\alpha$-PbO, which has the same two-dimensional (2D) litharge-like structure as Pb$_2$F$_2$ and Bi$_2$O$_2$ layers. The Pb and O atoms are represented by grey and red spheres. (c) The electronic bandgap of the materials calculated by density functional theory (DFT) with hybrid functional in the Heyd-Scuseria-Enzerhof (HSE) form. The bandgap of BaTiO$_3$ is also shown for comparison. (d) Calculated static dielectric constant of the compounds and their critical in-plane biaxial strain for inducing ferroelectric instability. The size and color of the markers correspond to the electric polarization when the applied in-plane biaxial strain is 2% beyond the critical strain. The inset illustrates the directions of atomic displacements corresponding to the strain-induced ferroelectric transition in BiOCl.
• Figure 2: Origin of the high dielectric polarizability of [Pb$_2$F$_2$]- and [Bi$_2$O$_2$]-based layered semiconductors. (a) Calculated phonon spectrum of BiOCl. A low-frequency ($\sim$10 meV) polar transverse optical (TO) phonon mode at the $\Gamma$ point is indicated. (b) The side and top views of the atomic displacement pattern corresponding to the polar TO mode. (c) The frequency of the polar TO mode and (d) the in-plane static dielectric constant ($\epsilon_0$) of BiOCl as a function of in-plane biaxial strain. (e) The mode effective charge versus the vibrational frequency of the lowest-energy polar TO phonon mode in different [Pb$_2$F$_2$]- and [Bi$_2$O$_2$]-based materials. The size and color of the markers indicate the contribution of the polar TO mode to the static dielectric constant. The inset provides a stereo view of the atomic displacement pattern corresponding to the TO mode, within the [Bi$_2$O$_2$] or [Pb$_2$F$_2$] layers.
• Figure 3: Strain-induced ferroelectricity in archetypal litharge $\alpha$-PbO and its fundamental origin. (a) The top and side views of the atomistic structure of $\alpha$-PbO in the paraelectric (PE) and ferroelectric (FE) phase. Pb and O atoms are represented by black and red spheres, respectively. (b) Calculated projected density of states (PDOS) of monolayer $\alpha$-PbO, showing the cross-bandgap hybridization of the Pb $p$ orbitals. The energy zero corresponds to the valence band maximum (VBM). (c) Molecular orbital diagram of $\alpha$-PbO in the revised lone-pair model. The upper right corner illustrates the calculated electron localization function near a Pb atom of monolayer $\alpha$-PbO. Orange and blue represent high and low electron localization, respectively. (d) Crystal orbital Hamilton population (COHP) of monolayer $\alpha$-PbO. The horizontal axis corresponds to $-$COHP. (e) DFT-calculated electronic band structure of monolayer $\alpha$-PbO. The atomic orbital characters of the bands are indicated using different colors. (f) Strain-dependent energy levels of the electronic states at the M point in the Brillouin zone. These states are indicated using the same symbols (number in circle) in (e). The vertical line at 13 % of biaxial strain corresponds to the critical strain of ferroelectric transition, and the energy-level evolution of the PE and FE phases after the critical strain are represented using solid and dashed lines, respectively. (g,h) The integrated PDOS of Pb $p$ orbitals and (g) integrated $-$COHP of monolayer $\alpha$-PbO (h) as a functional of biaxial strain. The upper limit of integration corresponds to the VBM. After the critical point, the evolutions of integrated PDOS and integrated $-$COHP in both the PE and FE phases are shown.