Dy adsorption on and intercalation under graphene on 6 H -SiC(0001) surface from first-principles calculations

Abstract

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.

Energy barriers for Dy and H penetrating graphene on 6H-SiC(0001) and freestanding bilayer graphene from first-principles calculations

“…2(b) by considering that the graphene can relax and consequently result in significant corrugations, so that the local tensile strain larger than 0.4% is likely available. 38 Thus, we obtain a lower limit of 3.47 eV and an upper limit of 7.21 eV for a Dy atom penetrating any graphene-SiC system. Consider the penetration rate with the Arrhenius forms r dp ¼ e ÀE dp =ðkBTÞ , where % 10 13 /s is the attempt frequency, T is the temperature, and k B is the Boltzmann constant.…”

“…This has motivated us to consider other pathways which might be operative to interpret the experimentally observed intercalation for this system. 38 From the MEP in Fig. 2(a), we also note that there is a barrier E m0!m1 (at s1) from m0 to m1.…”

“…2(c)], the intercalation into the gallery is always energetically more favorable than the adsorption on the top. 38,44 For the graphene-SiC system in Fig. 2(a), we find three saddle points.…”

“…In model 1, a 13 Â 13 graphene overlayer with a small lateral tensile strain of about 0.4% matches the substrate, while a 2 Â 2 graphene overlayer with a relatively larger lateral tensile strain of about 8.8% matches the substrate in model 2. 38 Due to the extreme computational expense for model 1, we only choose model 2, which, in fact, has already been widely used in literature. 9,[39][40][41][42] However, to examine the strain effects and the substrate effects, we also report our results for penetration into unsupported or freestanding bilayer graphene with and without a tensile strain of about 8.8%.…”

“…Results for intercalation through freestanding bilayer graphene are also instructive, given recent experiments for K, Cs, Li, and Pd intercalations in freestanding bilayer graphene. 43 The DFT method used in this work was described previously in detail, 38 and key information is provided in the supplemental material.…”