LAUSR

Currently, intercalation of foreign guest atoms into two-dimensional (2D) layered van der Waals materials is an active research area motivated in part by the development of next-generation energy-storage technologies and optoelectronic devices. One such extensively studied 2D material is the graphene-on-SiC system. To realize and control the desired intercalated structures, it is fundamentally important to understand the kinetic process of intercalation. For the intercalation of a guest atom into graphene layers on SiC substrate, a critical kinetic parameter is the energy barrier of a guest atom penetrating the perfect graphene top layer into the gallery under it. However, accurate theoretical calculations for such penetration barriers are unavailable in literature. From our first-principles density functional theory calculations, we obtain the global energy barriers of 3.47 and 1.80 eV for single Dy and H atoms penetrating the graphene top layer on a graphene buffer layer supported by a Si-terminated 6H-SiC(0001) substrate, respectively. For comparison as well as for examining the lateral strain effects, we also obtain the global barriers of 5.05 and 1.50 eV for single Dy and H atoms penetrating freestanding bilayer graphene with a tensile strain of about 8.8% to match our model for supported graphene, as well as the global barriers of 7.21 and 4.18 eV for penetrating unstrained freestanding bilayer graphene, respectively. From corresponding minimum energy paths with multiple energy minima and saddle points, we can also obtain various local energy barriers and the global backward barrier from the graphene gallery back to the top surface.