Initial Stages of Ti Growth on Diamond (100) Surfaces: From Single Adatom Diffusion to Quantum Wire Formation

Using first-principles total energy calculations within density functional theory, we investigate the energetics, kinetics, and transport properties of Ti on clean and hydrogen-terminated diamond $(100)\mathrm{\text{−}}2\times 1$ surfaces at increasing Ti coverages. On a clean surface, an isolated Ti adatom prefers to adsorb on top of a C-C dimer row, and also diffuses faster along the dimer row direction. As the Ti coverage increases, the preferred adsorption site converts from an atop site to a site located between the dimer rows. Passivation of the surface at the monohydride coverage not only greatly enhances the Ti mobility, but also weakens the diffusion isotropy. Based on these energetic and kinetic characteristics, we propose a viable approach to fabricate ideal Ti quantum wires on hydrogen-terminated diamond substrates.

Figure 1

(a) Schematic top view of the $\mathrm{C}(100)\mathrm{\text{−}}2\times 1$ surface showing the four different adsorption sites for a Ti adatom: the pedestal site ($P$), the hollow site ($H$), the bridge site ($B$), and the cave site ($C$). Carbon atoms in the top three layers are shown, with the largest balls representing atoms in the topmost layer. (b) The diffusion barriers for a Ti adatom on $\mathrm{C}(100)\mathrm{\text{−}}2\times 1$ along different diffusion pathways (in units of eV).

Figure 2

Side view of the Ti atom chain at half monolayer coverage, with the Ti atoms occupying the $P$ (a) and the $H$ sites (b), respectively. The larger balls are the Ti atoms, and the smaller ones are the carbon atoms. (c),(d) The surface band structures corresponding to the atomic configurations (a),(b), respectively. The high-symmetry points of the surface Brillouin zone are given at ${\Gamma }_{2\times 1}(0,0)$, $Y_{2\times 1}(0,\frac{\sqrt{2}}{2})$, $M_{2\times 1}(\frac{\sqrt{2}}{4},\frac{\sqrt{2}}{2})$, and $X_{2\times 1}(\frac{\sqrt{2}}{4},0)$ (the units are $\frac{2\pi }{a}$, with $a$ being the lattice constant). The Fermi level is at zero energy.

Figure 3

(a) Top view of the four different adsorption sites for a Ti adatom on the hydrogen passivated $\mathrm{C}(100)\mathrm{\text{−}}2\times 1$ surface. (b) Side view of the Ti adatom diffusion pathway from a H-passivated region to the H-depleted region. (c) Diffusion barriers for a Ti adatom on the H-passivated $\mathrm{C}(100)\mathrm{\text{−}}2\times 1$ surface along different diffusion pathways. (d) The diffusion barriers for the processes shown in (b). All the energies are in eV.

Figure 4

(a) Side view of a Ti quantum wire formed on the lithographically treated H-passivated $\mathrm{C}(100)\mathrm{\text{−}}2\times 1$ surface, and (b) the corresponding band structure. The high-symmetry points of the surface Brillouin zone are at ${\Gamma }_{4\times 1}(0,0)$, $Y_{4\times 1}(0,\frac{\sqrt{2}}{2})$, $M_{4\times 1}(\frac{\sqrt{2}}{8},\frac{\sqrt{2}}{2})$, and $X_{4\times 1}(\frac{\sqrt{2}}{8},0)$ (in units of $\frac{2\pi }{a}$, with $a$ being the lattice constant). The Fermi level is at zero energy. (c) Side view of a H-passivated $\mathrm{C}(100)\mathrm{\text{−}}2\times 1$ surface, and (d) the corresponding band structure.