Carbon doping is used to obtain semi-insulating GaN crystals. If the carbon doping concentration exceeds $5*10^{17}$ $cm^{-3}$, the carbon atoms increasingly form triatomic clusters. The tri-carbon defect structure is unambiguously proven by the isotope effect on the defects' local vibrational modes (LVMs) originally found in samples containing carbon of natural isotopic composition $(~99 $%$ ^{12}C, ~1$%$ ^{13}C)$ at $1679$ $cm^{-1}$ and $1718$ $cm^{-1}$. Number, spectral positions, and intensities of the LVMs for samples enriched with the $^{13}C$ isotope (~99 % and ~50 %) are consistently interpreted on the basis of the harmonic oscillator model taking into account the probability of possible isotope combinations. Including the polarization dependence of the LVM absorption, we show that the tri-carbon defects form a triatomic molecule-like structure in two crystallographically different configurations: a basal configuration with the carbon bonds near the basal plane and an axial configuration with one of the carbon bonds along the c-axis. Finally, the disappearance of the LVMs under additional below-bandgap illumination is interpreted as defect recharging, i.e. the tri-carbon defects possess at least one charge state transition level within the bandgap and contribute to optical absorption as well as to the electrical charge balance.

中文翻译：

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GaN 的碳掺杂：形成电活性三碳缺陷的证明

碳掺杂用于获得半绝缘 GaN 晶体。如果碳掺杂浓度超过$5*10^{17}$$cm^{-3}$，碳原子会越来越多地形成三原子团簇。三碳缺陷结构通过同位素对缺陷局部振动模式 (LVM) 的影响得到明确证明，这些缺陷的局部振动模式 (LVM) 最初是在含有天然同位素组成的碳的样品中发现的 $(~99 $%$ ^{12}C, ~1$% $ ^{13}C)$ 为 $1679$$cm^{-1}$ 和 $1718$$cm^{-1}$。富含 $^{13}C$ 同位素（~99% 和~50%）的样品的 LVM 的数量、光谱位置和强度均基于谐振子模型一致解释，同时考虑到可能出现的概率同位素组合。包括 LVM 吸收的极化依赖性，我们表明，三碳缺陷以两种晶体学不同的构型形成三原子分子状结构：碳键位于基面附近的基础构型和具有沿 c 轴的碳键之一的轴向构型。最后，在额外的低于带隙照明下 LVM 的消失被解释为缺陷再充电，即三碳缺陷在带隙内具有至少一个电荷态跃迁能级，有助于光吸收以及电荷平衡。