Adsorption and diffusion of an alkali-metal adatom on transition-metal dichalcogenides

Employing total-energy density-functional theory calculations the adsorption energies, the diffusion pathways, and the barriers for a Li adatom on stepped ${\mathrm{TiSe}}_2$ surfaces with full relaxation of the atomic environment were studied. The minimum-energy paths for Li diffusion on a ${\mathrm{TiSe}}_2$ (0001) surface and across the $\left(10\overline{1}0\right)$ and $\left(\overline{1}2\overline{1}1\right)$ steps have been calculated. At the $\left(\overline{1}2\overline{1}1\right)$ step edge an Ehrlich-Schwoebel barrier of $0.31\mathrm{eV}$ was obtained, which is additional to the diffusion barrier of $0.25\mathrm{eV}$ on the flat surface. The energies for subsequent diffusion within the van der Waals gap have been calculated, too.

Figure 1

(a) Sphere model of the (0001) ${\mathrm{TiSe}}_2$ surface with $\left(10\overline{1}0\right)$ and $\left(\overline{1}2\overline{1}1\right)$ steps. (b) Top view of ${\mathrm{TiSe}}_2$ (0001) surface with the $\left[10\overline{1}0\right]$ and $\left[\overline{1}2\overline{1}0\right]$ directions indicated.

Figure 2

(a) Schematic illustration of the diffusion path minimum energy of Li across a ${\mathrm{TiSe}}_2$ $\left(10\overline{1}0\right)$ step. Points labeled by $s_i$ and $g_i$ are on the surface and in the van der Waals gap, respectively; $g_5$ would be hidden by full Se sphere here plotted only as dashed circumference. (b) Top view of the sites presented in (a) on the $\left(0001\right)$ surface and the $\left(10\overline{1}0\right)$ step.

Figure 3

Geometry of the (0001) surface with an (a) $\left(10\overline{1}0\right)$ and (b) $\left(\overline{1}2\overline{1}1\right)$ step in the absence of Li. Some atoms are numbered to facilitate the description of their relaxation in the text. The arrows show the components (not scaled) of the relaxation.

Figure 4

(a) Total energy of a Li adatom diffusing on the (0001) surface and $\left(10\overline{1}0\right)$ step corresponding to the diffusion path represented in Fig. 3. The solid line corresponds to the diffusion on the surface and at the step, the broken line to the diffusion into the gap, and the gray line that away from the step on the lower terrace. (b) Contour plot of the energy of Li adatom diffusing at the height of the van der Waals gap; positions of first- (third-)plane Se atoms of second sandwich indicated by empty (full) circles. (c) The diffusion path with minimum energy along the step. The path is shown in (b) as the solid white line joining the numbered sites.

Figure 5

(a) Schematic illustration of the diffusion path with minimum energy of Li across a ${\mathrm{TiSe}}_2$ $\left(\overline{1}2\overline{1}1\right)$ step. Points labeled by $s_i$ and $g_i$ are on the surface and in the van der Waals gap, respectively. (b) Top view of the sites presented in (a) on the (0001) surface and $\left(\overline{1}2\overline{1}1\right)$ step.

Figure 6

(a) Total energy of a Li adatom diffusing on the (0001) surface and $\left(\overline{1}2\overline{1}1\right)$ step corresponding to the diffusion path represented in Fig. 5. The solid line corresponds to the diffusion on the surface and at the step, the broken line to the diffusion into the gap, and the gray line to that away from the step on the second terrace. (b) Contour plot of the energy of Li adatom diffusing at the height of the van der Waals gap; positions of first- (third-)plane Se atoms of second sandwich indicated by empty (full) circles.