Photovoltage from ferroelectric domain walls in ${\mathrm{BiFeO}}_3$

We calculate the component of the photovoltage in bismuth ferrite that is generated by ferroelectric domain walls, using first-principles methods, in order to compare its magnitude to the experimentally measured photovoltage. We find that excitons at the ferroelectric domain walls form an electric dipole layer resulting in a domain-wall driven photovoltage. This is of the same order of magnitude as the experimentally measured one, but only if the carrier lifetimes and diffusion lengths are larger than previously assumed.

Figure 1

71° domain wall: (a) 280-atom supercell with two domain walls, (b) all three components of the ferroelectric polarization $P$, (c) polarization component $P_s$ perpendicular to the domain wall, and (d) polarization-based electronic potential energy $V_e^{\mathrm{pb}}$ and electronic potential energy $V_e$ directly obtained from DFT (thick black lines), shifted to zero and smoothened [23]. The dashed lines in (d) denote open-circuit conditions.

Figure 2

The same as Fig. 1 for the 109° domain wall.

Figure 3

Smoothened densities of excess electrons and holes for excitons ($X$) at the 71° domain wall before (“instantaneous”) and after (“relaxed”) polaron formation: (a) for an $X$ density of $0.1X$ per 120-atom supercell (a planar $X$ density of $\approx 2.3\times {10}^{13}X/{\mathrm{cm}}^2$) a large polaron forms; (b) for an $X$ density of $1X$ per 120-atom supercell ($\approx 2.3\times {10}^{14}X/{\mathrm{cm}}^2$) a small polaron forms. Gray bars and arrows indicate ferroelectric domains.

Figure 4

Smoothened densities of excess electrons and holes for exciton ($X$) densities in the coexistence region of the large (dashed line) and the small (solid line) $X$ polaron in a 120-atom supercell (SC) with 71° domain walls. (a) For a planar $X$ density $n_X^{\mathrm{DW}}$ of $\approx 1.2\times {10}^{14}X/{\mathrm{cm}}^2$ the small $X$ polaron is stable and the large $X$ polaron is metastable. (b) For a planar $X$ density of $\approx 2.3\times {10}^{12}X/{\mathrm{cm}}^2$ the large $X$ polaron is stable and the small $X$ polaron is metastable. (c) Formation energies of the small (small filled circles) and the large (large empty circles) $X$ polarons. The large $X$ polaron is stable for $X$ densities below $n_X^{\mathrm{crit}}$ and between $n_X^{\mathrm{crit}}$ and $n_X^{\mathrm{met}}$ it is metastable.

Figure 5

Excitonic phase diagram. The solid blue line indicates the critical light intensity as a function of the carrier diffusion length $l_{\mathrm{diff}}$ according to Eq. (6) in the Supplemental Material; the dashed blue line marks the upper boundary of the coexistence region of the small and the large exciton polarons. Orange vertical bars mark the intensity of sunlight and thousandfold concentrated sunlight above the band gap of $\mathrm{Bi}\mathrm{Fe}{\mathrm{O}}_3$, and the gray horizontal bar marks a range of typical domain-wall spacings $d_{\mathrm{DW}}$ found in the experimental literature.

Figure 6

(a) Smoothened potential energy of electrons at the 71° domain wall in the ground state ($V_e^{\mathrm{GS}}$) and in the excited state ($V_e^X$) in a 280-atom supercell with 0.1 excitons. (b) Instantaneous photovoltage profile $V_{\mathrm{photo}}$ [cf. Eq. (1)] for short-circuit (solid line) and open-circuit conditions (dashed line). Green arrows show the magnitude of the domain-wall photovoltage $V_{\mathrm{photo}}^{\mathrm{DW}}$.

Figure 7

Measured photovoltage per domain of $\mathrm{Bi}\mathrm{Fe}{\mathrm{O}}_3$ films with 71° domain walls from Ref. [11] and calculated domain-wall photovoltage of the 71° and the 109° domain walls as a function of the illumination intensity for different photocarrier life times $\tau$ and diffusion lengths $l_{\mathrm{diff}}$: (a) $\tau =75\mu \mathrm{s}$, $l_{\mathrm{diff}}=140\mathrm{nm}$; (b) $\tau =75\mu \mathrm{s}$, $l_{\mathrm{diff}}=10\mathrm{nm}$; (c) $\tau =1\mathrm{ns}$, $l_{\mathrm{diff}}=140\mathrm{nm}$. Solid lines are an extrapolation; dotted lines are a guide to the eye.