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.

中文翻译：

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掺杂Ca的BiFeO3中小极化子和双极化子导致的空穴陷阱中心的多样性：电致变色的起源

由施加的电压引起的颜色变化引起的电致变色是否是由小的极化子引起的，这一直存在争议。最近，掺钙的着色效率$\mathrm{铋铁}{\mathrm{Ø}}_3$据报道（CBFO）在更宽的能量范围内比常规氧化物更加突出。但是，仅基于氧气空位的解释（${\mathrm{V}}_{\mathrm{Ø}}$已经尝试了不能解释吸收的广泛能量依赖性的）。在这里，我们表明，使用第一性原理的混合函数计算，CBFO中的空穴陷阱中心可以由围绕取代Ca的各种小空穴极化子和双极化子产生。$\mathrm{C}{\mathrm{一种}}_{双}$），并最终在变色方面发挥重要作用。极化子的形成归因于以下事实：最多捕获了两个多余的空穴以增强Bi-O$sp\sigma$键。与实验结果一致的是，在电铸条件下，电致变色现象在电铸中很好地发生。$p$当CBFO分为两个离散区域时相对丰富 ${\mathrm{V}}_{\mathrm{Ø}}$ （$ñ$ 类型）和 $\mathrm{C}{\mathrm{一种}}_{双}$ （$p$类型）。因此，我们建议，识别载流子陷阱极化子的多样性为深入了解电致变色的起源提供了关键线索。