We present a first-principles computational study of cation–Se $\Sigma$3 (112) grain boundaries in CuGaSe${}_2$. We discuss the structure of these grain boundaries, as well as the effect of native defects and Na impurities on their electronic properties. The formation energies show that the defects will tend to form preferentially at the grain boundaries, rather than in the grain interiors. We find that in Ga-rich growth conditions Cu vacancies as well as Ga at Cu and Cu at Ga antisites are mainly responsible for having the equilibrium Fermi level pinned toward the middle of the gap, resulting in carrier depletion. The Na at Cu impurity in its +1 charge state contributes to this. In Ga-poor growth conditions, on the other hand, the formation energies of Cu vacancies and Ga at Cu antisites are comparatively too high for any significant influence on carrier density or on the equilibrium Fermi level position. Thus, under these conditions, the Cu at Ga antisites give rise to a $p$-type grain boundary. Also, their formation energy is lower than the formation energy of Na at Cu impurities. Thus, the latter will fail to act as a hole barrier preventing recombination at the grain boundary, in contrast to what occurs in CuInSe${}_2$ grain boundaries. We also discuss the effect of the defects on the electronic properties of bulk CuGaSe${}_2$, which we assume reflect the properties of the grain interiors.

我们提出阳离子-硒的第一性原理计算研究 $\Sigma$CuGaSe中的3（112）晶界${}_{\mathrm{2个}}$。我们讨论了这些晶界的结构，以及天然缺陷和Na杂质对其电子性能的影响。形成能表明，缺陷将倾向于优先在晶界而不是在晶粒内部形成。我们发现，在富Ga的生长条件下，Cu空位以及Cu处的Ga和Ga反位处的Cu都是造成平衡费米能级固定在间隙中间的原因，从而导致载流子耗尽。处于+1电荷状态的Cu杂质处的Na对此做出了贡献。另一方面，在Ga贫乏的生长条件下，Cu空位和Ga反位处的Ga的形成能相对较高，对载流子密度或平衡费米能级位置没有任何重大影响。因此，在这些条件下，$p$型晶界。而且，它们的形成能比Na在Cu杂质处的形成能低。因此，与CuInSe中发生的情况相反，后者将不能充当防止在晶界发生复合的空穴阻挡层${}_{\mathrm{2个}}$晶界。我们还将讨论缺陷对块状CuGaSe电子性能的影响${}_{\mathrm{2个}}$，我们假设它反映了谷物内部的特性。