Previous experimental observations motivate clarification of configuration stabilities and kinetic processes for intercalation of guest atoms into a layered van der Waals material such as a graphene-SiC system. From our first-principles density functional theory (DFT) calculations, we analyze Dy adsorption and intercalation for graphene on a 6H-SiC(0001) surface, where the system includes two single-atom-thick graphene layers: the top-layer graphene (TLG) and the underling buffer-layer graphene (BLG) above the terminal Si layer. Our chemical potential analysis shows that intercalation of a single Dy atom into the gallery between TLG and BLG is more favorable than adsorption on TLG but that intercalation into the gallery underneath BLG is highly unfavorable. We obtain diffusion barriers of ∼0.45 and 0.54 eV for a Dy atom diffusing on and under TLG, respectively. We find that the direct penetration of a Dy atom from the graphene top into the gallery under TLG is almost inhibited below a temperature of ∼1400 K due to a large global barrier of at least ∼3.5 eV. Instead, we find that a single Dy atom on TLG can easily intercalate by crossing a TLG step (e.g., a zigzag step presaturated by a Dy chain or a reconstructed zigzag step zz57). We also perform DFT calculations for different Dy coverages to demonstrate how the favorability of Dy intercalation, as well as the corresponding interlayer spacings, depend on the coverage. Consequently, we can provide general insight and guidance for extensively studied systems involving intercalation of foreign atoms into graphene on a SiC substrate.

中文翻译：

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从第一性原理计算得出的 6H-SiC(0001) 表面石墨烯上的 Dy 吸附和嵌入

先前的实验观察促进了对客体原子嵌入层状范德华材料（如石墨烯-碳化硅系统）的构型稳定性和动力学过程的澄清。根据我们的第一性原理密度泛函理论 (DFT) 计算，我们分析了石墨烯在 6 H上的 Dy 吸附和嵌入-SiC(0001) 表面，其中系统包括两个单原子厚的石墨烯层：顶层石墨烯 (TLG) 和位于终端 Si 层上方的底层缓冲层石墨烯 (BLG)。我们的化学势分析表明，单个 Dy 原子嵌入 TLG 和 BLG 之间的通道比在 TLG 上吸附更有利，但嵌入 BLG 下方的通道是非常不利的。对于在 TLG 之上和之下扩散的 Dy 原子，我们分别获得了 0.45 和 0.54 eV 的扩散势垒。我们发现 Dy 原子从石墨烯顶部直接渗透到 TLG 下的画廊中，由于至少约 3.5 eV 的大全局势垒，在约 1400 K 的温度以下几乎被抑制。相反，我们发现 TLG 上的单个 Dy 原子可以通过跨越 TLG 步骤轻松插入（例如，由 Dy 链预饱和的锯齿形台阶或重建的锯齿形台阶 zz57)。我们还对不同的 Dy 覆盖率进行了 DFT 计算，以证明 Dy 插层的有利性以及相应的层间距如何取决于覆盖率。因此，我们可以为广泛研究的系统提供一般的见解和指导，这些系统涉及将外来原子嵌入 SiC 衬底上的石墨烯中。