Different roles of carbon and silicon interstitials in the interstitial-mediated boron diffusion in $\mathrm{SiC}$

The interstitial and vacancy mediated boron diffusion in silicon carbide is investigated with an ab initio method. The boron interstitials in $p$-type and $n$-type materials are found to be far more mobile than the boron-vacancy complexes. A kick-out mechanism and an interstitialcy mechanism govern the diffusion in $p$-type/intrinsic and $n$-type material, respectively. A comparison of activation energies demonstrates that the equilibrium diffusion is dominated by the positive hexagonal interstitial for typical experimental conditions. The activation energy and the charge state is in agreement with experimental findings. The analysis of the kick-out reaction demonstrates that silicon and carbon interstitials have different effects on boron acceptors on the silicon and carbon sublattice (${\mathrm{B}}_{\mathrm{Si}}$ and ${\mathrm{B}}_{\mathrm{C}}$). While silicon interstitials mediate the diffusion of both acceptors, carbon interstitials are only relevant for ${\mathrm{B}}_{\mathrm{C}}$. A larger kick-in barrier into silicon sites is found than into carbon sites. This implies a dominant formation of ${\mathrm{B}}_{\mathrm{C}}$ in the extended diffusion tails of boron profiles. The stable boron complexes with carbon or boron interstitials are found that potentially reduce the boron diffusion. This and the characteristics of the kick-out mechanism facilitate an explanation of recent co-implantation experiments.

Figure 1

Boron interstitials: formation energy for $\mathrm{Si}$-rich conditions in $3\mathrm{C}\text{−}\mathrm{SiC}$. Dashed or dash-dotted lines are used to distinguish the formation energy of ${\mathrm{B}}_{sp\mathrm{Si}⟨110⟩}$ and ${\mathrm{B}}_{sp\mathrm{C}⟨100⟩}$ from that of ${\mathrm{B}}_{sp\mathrm{Si}⟨100⟩}$, respectively. Charge states are indicated. The geometry of the most stable boron interstitials and the intermediate sites ${\mathrm{B}}_{sp\mathrm{Si}⟨100⟩}$ and ${\mathrm{B}}_{sp\mathrm{C}⟨100⟩}$ is displayed in Figs. 2a, 2b.

Figure 2

Boron interstitials in $3\mathrm{C}\text{−}\mathrm{SiC}$: geometry of (a) the most stable boron interstitials, (b) the intermediate sites ${\mathrm{B}}_{sp\mathrm{Si}⟨100⟩}$ and ${\mathrm{B}}_{sp\mathrm{C}⟨100⟩}$, and (c) the boron complexes ${\left(\mathrm{BC}\right)}_{\mathrm{Si}}$, ${\mathrm{Si}}_{\mathrm{TC}}{\text{−}\mathrm{B}}_{\mathrm{C}}$, ${\left(\mathrm{BC}\right)}_{\mathrm{Si}}$, and ${\left({\mathrm{B}}_2\right)}_{\mathrm{Si}}$.

Figure 3

Interstitials in $4\mathrm{H}\text{−}\mathrm{SiC}$: geometry of the hexagonal and cubic interstice. The interstitial sites ${\mathrm{B}}_{\mathrm{TC},k}$, ${\mathrm{B}}_{\mathrm{TSi},k}$ and ${\mathrm{B}}_{\mathrm{Hex},b-k}$ in the cubic interstice, and ${\mathrm{B}}_{\mathrm{Hex},h-b}$ and (unstable) ${\mathrm{B}}_{\mathrm{TCSi}}$ in the hexagonal interstice are indicated.

Figure 4

Boron-vacancy complexes: formation energy for $\mathrm{Si}$-rich conditions. The geometry of ${\mathrm{B}}_{\mathrm{Si}}\text{−}{V}_{\mathrm{C}}$ and ${\mathrm{B}}_{\mathrm{C}}\text{−}{V}_{\mathrm{C}}$ is displayed in Figs. 5a, 5d.

Figure 5

Migration of the boron-vacancy complexes. Upper panel: ${\mathrm{B}}_{\mathrm{C}}\text{−}{V}_{\mathrm{C}}$: (a) initial hop of the boron atom, (b) hop of carbon neighbor ${\mathrm{C}}_1$, and (c) hop of carbon neighbor ${\mathrm{C}}_2$. Lower panel: ${\mathrm{B}}_{\mathrm{Si}}\text{−}{V}_{\mathrm{C}}$ (d) concerted exchange of ${\mathrm{B}}_{\mathrm{Si}}$ and $\mathrm{Si}$ and (e) site change of $V_{\mathrm{C}}$ by a second neighbor hop of a $\mathrm{C}$-neighbor.

Figure 6

Chemical potential $\Delta {\mu }_{\mathrm{B}}$ versus boron concentration for $\mathrm{Si}$-rich and $\mathrm{C}$-rich conditions for $3\mathrm{C}\text{−}\mathrm{SiC}$.

Figure 7

Fermi-level ${\mu }_{\mathrm{F}}$ versus boron concentration for $\mathrm{Si}$- and $\mathrm{C}$-rich conditions. The upper panel refers to $3\mathrm{C}\text{−}\mathrm{SiC}$, the lower panel to $4\mathrm{H}\text{−}\mathrm{SiC}$.