Motivated by experimental results on transport properties of graphene covered by gallium atoms, the density functional theory study of clustering of gallium atoms on graphene (up to a size of 8 atoms) is presented. The paper explains a rapid initial increase of graphene electron doping by individual Ga atoms with Ga coverage, which is continually reduced to zero, when bigger multiple-atom clusters have been formed. According to DFT calculations with and without the van der Waals correction, gallium atoms start to form a three-dimensional cluster from five and three atoms, respectively. The results also explain an easy diffusion of Ga atoms while forming clusters caused by a small diffusion barrier of 0.11 eV. Moreover, the calculations show this barrier can be additionally reduced by the application of an external electric field, which was simulated by the ionization of graphene. This effect offers a unique possibility to control the cluster size in experiments only by applying a gate-voltage to the graphene in a field-effect transistor (FET) geometry and thereby without growth temperature assistance.

中文翻译：

---

石墨烯上镓簇的密度泛函研究：电子掺杂和扩散

受镓原子覆盖的石墨烯传输特性的实验结果的启发，提出了镓原子在石墨烯上（最多 8 个原子的大小）聚集的密度泛函理论研究。该论文解释了由具有 Ga 覆盖率的单个 Ga 原子引起的石墨烯电子掺杂的快速初始增加，当形成更大的多原子簇时，该电子掺杂会不断减少到零。根据有和没有范德华修正的 DFT 计算，镓原子开始分别由五个和三个原子形成三维簇。结果还解释了 Ga 原子在形成簇时容易扩散，这是由 0.11 eV 的小扩散势垒引起的。此外，计算表明，可以通过施加外部电场来额外降低这种势垒，这是通过石墨烯的电离模拟的。这种效应提供了一种独特的可能性来控制实验中的簇大小，只需在场效应晶体管 (FET) 几何结构中向石墨烯施加栅极电压，从而无需生长温度辅助。