First-principles calculation of the bulk photovoltaic effect in ${\mathrm{KNbO}}_3$ and (K,Ba)(Ni,Nb)${\mathrm{O}}_{3-\delta }$

The connection between noncentrosymmetric materials' structure, electronic structure, and bulk photovoltaic performance remains not well understood. In particular, it is still unclear which photovoltaic (PV) mechanisms are relevant for the recently demonstrated visible-light ferroelectric photovoltaic (K,Ba)(Ni,Nb)${\mathrm{O}}_{3-\delta }$. In this paper, we study the bulk photovoltaic effect (BPVE) of (K,Ba)(Ni,Nb)${\mathrm{O}}_{3-\delta }$ and ${\mathrm{KNbO}}_3$ by calculating the shift current from first principles. The effects of structural phase, lattice distortion, oxygen vacancies, cation arrangement, composition, and strain on BPVE are systematically studied. We find that (K,Ba)(Ni,Nb)${\mathrm{O}}_{3-\delta }$ has a comparable shift current with that of the broadly explored ${\mathrm{BiFeO}}_3$, but for a much lower photon energy. In particular, the Glass coefficient of (K,Ba)(Ni,Nb)${\mathrm{O}}_5$ in a simple layered structure can be as large as 12 times that of ${\mathrm{BiFeO}}_3$. Furthermore, the nature of the wavefunctions dictates the eventual shift current yield, which can be significantly affected and engineered by changing the O vacancy location, cation arrangement, and strain. This is not only helpful for understanding other PV mechanisms that relate to the motion of the photocurrent carriers, but also provides guidelines for the design and optimization of PV materials.

Figure 1

The (a) shift current susceptibility and (b) Glass coefficient of various phases of ${\mathrm{KNbO}}_3$.

Figure 2

The projected densities of states (PDOSs) onto the Nb $d$ orbitals of the (a) tetragonal and (b) rhombohedral ${\mathrm{KNbO}}_3$. The inset shows the corresponding real-space wavefunction distribution around the ${\mathrm{NbO}}_6$ octahedra for the conduction band minimum at the $\Gamma$ point in the Brillouin zone. (Top) View along $z$. (Bottom) View along $x$.

Figure 3

The atomic structure representation of the (K,Ba)(Ni,Nb)${\mathrm{O}}_5$ solid solution with (a) layered and (b) rocksalt cation arrangements. Atoms are drawn with accepted ionic radii. In (a), both the apical and equatorial O vacancies are shown.

Figure 4

The largest tensor element of (a) shift current susceptibility $\left({\sigma }_{zzZ}\right)$ and (b) Glass coefficient $\left(G_{zzZ}\right)$, and the (c) imaginary dielectric constant $\left({\epsilon }_{zz}^{\left(2\right)}\right)$, and (d) shift vector integrated over the Brillouin zone $\left(R_Z\right)$ of the (K,Ba)(Ni,$\mathrm{Nb}){\mathrm{O}}_5$ solid solution with $1\times 1\times 2$ layered and rocksalt cation arrangements. For the $1\times 1\times 2$ layered arrangement, both the apical and equatorial O vacancy sites are included, while for the rocksalt arrangement the vacancy is at the apical site.

Figure 5

The band structure of the $1\times 1\times 2$ layered (K,Ba)(Ni,$\mathrm{Nb}){\mathrm{O}}_5$ solid solution (a) with apical and (b) equatorial O vacancies. The inset shows the real-space wavefunction distribution for the corresponding conduction electronic states at $A$(0.5, 0.5, 0.5) $k$ point in (a) and $\Gamma k$ point in (b). The wavefunction plot in (a) is in view along $x$, while the left and right insets in (b) are in views along $x$ and $z$, respectively. The K and Ba ions are not shown in the wavefunction plot.

Figure 6

The projected densities of states (PDOSs) of the (K,Ba)(Ni,$\mathrm{Nb}){\mathrm{O}}_5$ solid solution with $1\times 1\times 2$ layered and rocksalt cation arrangements. The inset shows the real-space wavefunction distribution (view along $x)$ for the corresponding electronic states as indicated by the red arrow. In both cases, the O vacancy is at the top apical site. In (a), the equatorial O atom nearest to the viewer is hidden in order to show the orbital character of the Ni $3d_{xz/yz}$ orbitals.

Figure 7

(a) The Glass coefficient of the (1-$x){\mathrm{KNbO}}_3-x\mathrm{Ba}({\mathrm{Ni}}_{1/2}{\mathrm{Nb}}_{1/2}){\mathrm{O}}_{11/4}$ solid solution with different compositions $(x=2/3$, 1/2, and 1/3). The left and right insets show the real-space wavefunction of the valence band maximum (VBM) of the 1/$3{\mathrm{KNbO}}_3$-2/$3\mathrm{Ba}({\mathrm{Ni}}_{1/2}{\mathrm{Nb}}_{1/2}){\mathrm{O}}_{11/4}$ $\left(\sqrt{2}\times \sqrt{2}\times 3\right)$ and 1/$2{\mathrm{KNbO}}_3$-1/$2\mathrm{Ba}({\mathrm{Ni}}_{1/2}{\mathrm{Nb}}_{1/2}){\mathrm{O}}_{11/4}$ $\left(\sqrt{2}\times \sqrt{2}\times 4\right)$ solid solutions, respectively. The wavefunction in the right inset has an extended nature along the Cartesian $z$ direction, while that in the left inset is only distributed within the $xy$ plane. (b) The calculated absorption spectrum compared with the experimental ellipsometry measurement [35].

Figure 8

The atomic structure representation of the 2/$3{\mathrm{KNbO}}_3$-1/$3\mathrm{Ba}({\mathrm{Ni}}_{1/2}{\mathrm{Nb}}_{1/2}){\mathrm{O}}_{11/4}$ $\left(2\times 2\times 3\right)$ solid solution with (a) two ${\mathrm{Ni}}^{2+}$ ions at the body diagonal positions $\left(B_1\right)$ (b) two ${\mathrm{Ni}}^{2+}$ ions along the Cartesian $z$ direction $\left(B_3\right)$. The atoms are shown with their accepted atomic radii. The ${\mathrm{K}}^{+}$ and ${\mathrm{Ba}}^{2+}$ are omitted for clarity. The Glass coefficients of the 2/$3{\mathrm{KNbO}}_3-1/3\mathrm{Ba}({\mathrm{Ni}}_{1/2}{\mathrm{Nb}}_{1/2}){\mathrm{O}}_{11/4}$ solid solutions with different (c) $A$-site and (d) $B$-site cation arrangements. The $B$-cation arrangement remains the same (with two ${\mathrm{Ni}}^{2+}$ ions distributed along the body diagonal direction) when the $A$-cation arrangement is varied in (c), whereas the $A$-cation arrangement remains the same when the $B$-cation arrangement is varied in (d). “$A_1$,” “$A_2$,” and “$A_3$” correspond to configurations with the four ${\mathrm{Ba}}^{2+}$ cations distributed within 1, 2, and 3 layers, while “$B_1$,” “$B_2$,” and “$B_3$” correspond to the configurations that the two ${\mathrm{Ni}}^{2+}$ cations are distributed along the body-diagonal, face-diagonal, and the Cartesian $z$ directions. “$A_2$” and “$B_1$” are the same structure.

Figure 9

The densities of states (DOSs) of the 2/$3{\mathrm{KNbO}}_3-1/3\mathrm{Ba}({\mathrm{Ni}}_{1/2}{\mathrm{Nb}}_{1/2}){\mathrm{O}}_{11/4}$ solid solutions with (a) the two ${\mathrm{Ni}}^{2+}$ cations aligned along the body-diagonal direction $\left(B_1\right)$ and (b) the two ${\mathrm{Ni}}^{2+}$ cations aligned along the Cartesian $z$ direction $\left(B_3\right)$. The inset shows the real-space wavefunction distribution for the top of the VB state, which shows a great contribution of Ni $3d_{z^2}$ (also some Nb $4d_{z^2})$ orbital character.

Figure 10

The schematic representation of crystal field splitting of the ${\mathrm{Ni}}^{2+}$ $3d$ orbitals under distorted octahedral and square pyramidal crystalline environments. The Ni-O distance along the Cartesian $z$ direction is longer than that in the $xy$ plane.

Figure 11

(a) The Glass coefficient of the ${2/3\mathrm{KNbO}}_3-1/3\mathrm{Ba}\left({\mathrm{Ni}}_{1/2}{\mathrm{Nb}}_{1/2}\right){\mathrm{O}}_{11/4}$ solid solution with different in-plane biaxial compressive strains. (b) The projected density of states (PDOS) of ${2/3\mathrm{KNbO}}_3-1/3\mathrm{Ba}\left({\mathrm{Ni}}_{1/2}{\mathrm{Nb}}_{1/2}\right){\mathrm{O}}_{11/4}$ solid solution under 2% in-plane compressive strain. The inset in (b) shows the real-space wavefunction distribution (side view) for the top of the VB state. The solid solution is with the “$B_1$” arrangement; the two Ni atoms are distributed along the body diagonal positions and the O vacancy is at the apical site of one Ni atom.