Diversity of hole-trap centers due to small polarons and bipolarons in Ca-doped $\mathrm{BiFe}{\mathrm{O}}_3$: Origin of electrochromism

It has long been controversial whether or not electrochromism with the color change due to applied voltage is caused by small polarons. Recently, the coloration efficiency of Ca-doped $\mathrm{BiFe}{\mathrm{O}}_3$ (CBFO) was reported to be more prominent over a wider energy range than that of a conventional oxide. However, only an interpretation based on oxygen vacancy (${\mathrm{V}}_{\mathrm{O}}$), which cannot account for the wide energy dependence of absorption, has been attempted. Here, we show that using first-principles hybrid-functional calculations, hole-trap centers in CBFO can be produced by a variety of small hole polarons and bipolarons around substitutional Ca ($\mathrm{C}{\mathrm{a}}_{\mathrm{Bi}}$) and ultimately play a significant role of color change. The polaron formation is attributed to the fact that up to two excess holes are trapped to enhance the Bi–O $sp\sigma$ bond. It is consistent with the experimental results that under the electroforming condition, electrochromism occurs well in the $p$-type region when CBFO is separated into two discrete regions relatively rich in ${\mathrm{V}}_{\mathrm{O}}$ ($n$ type) and $\mathrm{C}{\mathrm{a}}_{\mathrm{Bi}}$ ($p$ type). We, therefore, propose that identifying the diversity of the carrier-trap polarons provides a crucial clue to a deeper understanding of the origin of electrochromism.

Figure 1

(a) Atomic structures of three kinds of $\mathrm{BiFe}{\mathrm{O}}_3$: $\mathrm{BiFe}{\mathrm{O}}_3$ without defects or impurities, $\mathrm{BiFe}{\mathrm{O}}_3$ with oxygen vacancy (${\mathrm{V}}_{\mathrm{O}}$), and $\mathrm{BiFe}{\mathrm{O}}_3$ with substitutional calcium at bismuth ($\mathrm{C}{\mathrm{a}}_{\mathrm{Bi}}$). (b) Stabilized phase diagram of $\mathrm{BiFe}{\mathrm{O}}_3$ corresponding to the experimental synthesis conditions of $\mathrm{\Delta }{\mu }_{\mathrm{O}}$ (yellow area). Dotted line is the boundary of $\mathrm{\Delta }{\mu }_{\mathrm{O}}$ and a red point is a representative growing condition of Ca-doped $\mathrm{BiFe}{\mathrm{O}}_3$. (c) Formation energies of ${\mathrm{V}}_{\mathrm{O}}$ and $\mathrm{C}{\mathrm{a}}_{\mathrm{Bi}}$ as a function of the Fermi level ($E_{\mathrm{F}}$) under oxygen partial pressure at $700{}^{\circ }\mathrm{C}$ and 0.05 Torr. For each system, the most stable charge state at given $E_{\mathrm{F}}$ is shown. The self-consistently calculated Fermi level is plotted in a (black) dotted line.

Figure 2

Partial density of states (pDOS) of the charged $\mathrm{C}{\mathrm{a}}_{\mathrm{Bi}}$ defects calculated in the (a) $1-$, (b) 0, and (c) $1+$ charge states. The red and green lines indicate O-$2p$ and Bi-$6s$ states. Charge density plots corresponding to the localized electronic levels of ${\alpha }^{*}$ (from small hole polaron) and ${\beta }^{*}$ (from small hole bipolaron), respectively. The energy levels were aligned with respect to the valence band maximum. $h$ represents the hole carrier. The dotted line indicates the calculated Fermi energy $\left(E_{\mathrm{F}}\right)$.

Figure 3

(a) Crystal orbital Hamilton population and (b) the molecular orbital energy-level diagram for small hole polaron formation mechanism from $\mathrm{C}{{\mathrm{a}}_{\mathrm{Bi}}}^{1-}$ to $\mathrm{C}{{\mathrm{a}}_{\mathrm{Bi}}}^0$, (c), (d) for bipolaron formation from $\mathrm{C}{{\mathrm{a}}_{\mathrm{Bi}}}^{1-}$ to $\mathrm{C}{{\mathrm{a}}_{\mathrm{Bi}}}^{1+}$.

Figure 4

Total absorption coefficients of (a) pristine $\mathrm{BiFe}{\mathrm{O}}_3$, $\mathrm{V}{\mathrm{o}}^0$, $\mathrm{V}{\mathrm{o}}^{1+}$, and $\mathrm{V}{\mathrm{o}}^{2+}$ and (b) $\mathrm{C}{{\mathrm{a}}_{\mathrm{Bi}}}^{1-}$, $\mathrm{C}{{\mathrm{a}}_{\mathrm{Bi}}}^0$ (small hole polaron), and $\mathrm{C}{{\mathrm{a}}_{\mathrm{Bi}}}^{1+}$ (small hole bipolaron). Bottom: the difference of absorption coefficients of Vo and $\mathrm{C}{\mathrm{a}}_{\mathrm{Bi}}$ to pristine $\mathrm{BiFe}{\mathrm{O}}_3$.

Figure 5

Schematic diagram of oxygen vacancy distribution and optical transitions before (a), (b) and after application of an electric field (c), (d). Positively charged oxygen vacancies move towards the negative electrode and create an $n$-type region, and the residual region becomes $p$-type region.