Two-Dimensional Carbon Incorporation into Si(001): C Amount and Structure of $\mathrm{S}\mathrm{i}(001)\mathrm{\text{−}}c(4\times 4)$

The C amount and the structure of the $\mathrm{S}\mathrm{i}(001)\mathrm{\text{−}}c(4\times 4)$ surface is studied using scanning tunneling microscopy (STM) and ab initio calculations. The $c(4\times 4)$ phase is found to contain $1/8$ monolayer C (1 C atom in each primitive unit cell). From the C amount and the symmetry of high-resolution STM images, it is inferred that the C atoms substitute the fourth-layer site below the dimer row. We construct a structure model relying on ab initio energetics and STM simulations. Each C atom induces an on-site dimer vacancy and two adjacent rotated dimers on the same dimer row. The $c(4\times 4)$ phase constitutes the subsurface ${\mathrm{S}\mathrm{i}}_{0.875}{\mathrm{C}}_{0.125}$ $\delta$ layer with two-dimensionally ordered C atoms.

Figure 1

(a) A bird's eye view of the C-induced DV41 defect. (b)–(e) Schematic diagrams of previously proposed models for the $\mathrm{S}\mathrm{i}(001)\mathrm{\text{−}}c(4\times 4)$ phase: (b) missing dimer [16], (c) ad-dimer [8], (d) six-C-cluster [9, 18], and (e) Si-C heterodimer [12] models. Atoms in two surface layers and the fourth-layer C [(b),(e)] are shown. Dashed squares indicate the $\sqrt{8}\times \sqrt{8}\mathrm{\text{−}}R45°$ primitive unit cell.

Figure 2

Filled-state STM images of C-incorporated Si(001) with different C concentrations (${\theta }_{\mathrm{C}}$). (a) ${\theta }_{\mathrm{C}}\simeq 0.06\mathrm{M}\mathrm{L}$, where the $c(4\times 4)$ patches are surrounded by the $2\times n$ phase. The inset shows that the $c(4\times 4)$ phase appears darker than the $2\times n$ phase on the same terrace. (b) ${\theta }_{\mathrm{C}}\simeq 0.11\mathrm{M}\mathrm{L}$, where the $c(4\times 4)$ phase is the majority. (c) ${\theta }_{\mathrm{C}}\simeq 0.12\mathrm{M}\mathrm{L}$, where the whole surface is covered with the $c(4\times 4)$ phase. The inset shows both $\alpha$ and $\beta$ primitive unit cells of the $c(4\times 4)$ phase. (d) A two-terrace image clearly showing that the central features (a bright protrusion in the $\alpha$ cell and a depression in the $\beta$ cell) of upper-terrace $c(4\times 4)$ cells are in registry with every second dimer row on the lower terrace, as pointed out by the arrowheads, indicating the $\times 4$ periodicity.

Figure 3

The fractional area ($S$) occupied by the $c(4\times 4)$ phase at different ${\theta }_{\mathrm{C}}$'s. The symbols ($\times$) are measured data and the thick solid line is the linear fit. Dashed (dotted) lines are hypothetical curves for ${\theta }_{c(4\times 4)}=1/16$ and $1/4$ with ${\theta }_{2\times n}=0.05$ (0.0) ML.

Figure 4

Schematic diagrams of the models based on (a) dv41 and (b) $\mathrm{D}\mathrm{V}41+2\mathrm{R}\mathrm{D}$. (c),(d) STM simulations on the ${\mathrm{R}\mathrm{D}}_{\alpha \beta }$ model are compared with experiments at the sample bias voltage of $-2.5\mathrm{V}$: (c) the filled-state STM image and (d) the line profile along $\overline{\mathtt{A}\mathtt{B}}$ in (c) with the side view of ${\mathrm{R}\mathrm{D}}_{\alpha \beta }$. The dashed squares and rectangle indicate $\sqrt{8}\times \sqrt{8}\mathrm{\text{−}}R45°$ and $2\sqrt{8}\times \sqrt{8}\mathrm{\text{−}}R45°$ primitive unit cells, respectively.