Diffusion of the Diboron Pair in Silicon

We propose a novel mechanism for the diffusion of a diboron pair in Si, based on first principles density functional theory. We find a reaction pathway along which the boron pair diffuses from one lowest energy configuration of $[\text{B}‐\text{B}{]}_s‐⟨001⟩$ to an equivalent structure at an adjacent equivalent site through three local minimum states denoted as $[\text{B}‐\text{B}{]}_s‐⟨111⟩$, ${\text{B}}_s‐\text{B}{}_i$, and ${\text{B}}_s‐\text{B}{}_s‐{\text{Si}}_i$. The activation energy for the diffusion is estimated to be 1.81 eV in the generalized gradient approximation. A kinetic model suggests that the diboron diffusion plays an important role in determining diffusion profiles during ultrashallow junction processing (which requires high boron-dopant concentration as well as high annealing temperature).

Figure 1

The pathway for boron dimer diffusion in Si.

Figure 2

Energetics (DFT/GGA in eV) along the reaction pathway for boron dimer diffusion in Si. LDA results are in parentheses.

Figure 3

Structures for minima along the reaction pathway for boron dimer diffusion in Si. (a) $[\text{B}‐\text{B}{]}_s‐⟨001⟩$, (b) $[\text{B}‐\text{B}{]}_s‐⟨111⟩$, (c) ${\text{B}}_s‐\text{B}{}_i$, (d) ${\text{B}}_s‐\text{B}{}_s‐{\text{Si}}_i$.

Figure 4

Normalized concentrations (with respect to ${\text{C}}_{{\mathrm{B}}_s‐{\mathrm{B}}_i}$ and ${\text{C}}_{{\mathrm{B}}_s‐{\mathrm{S}\mathrm{i}}_i}$ at ${\text{C}}_{{\mathrm{B}}_{\mathrm{t}\mathrm{o}\mathrm{t}}}={10}^{18}{\text{cm}}^{-3}$) of ${\text{B}}_s‐\text{B}{}_i$ and ${\text{B}}_s‐\text{Si}{}_i$ as a function of the total B concentration $({\text{C}}_{{\mathrm{B}}_{\mathrm{t}\mathrm{o}\mathrm{t}}\mathrm{}})$. The inset shows the concentration ratio between ${\text{B}}_s‐\text{B}{}_i$ and ${\text{B}}_s‐\text{Si}{}_i$. In this calculation, the concentration of single Si interstitials and the temperature are kept at $1\times {10}^{14}{\text{cm}}^{-3}$ and $1000°\text{C}$, respectively.