Chemical bonding and diffusion of B dopants in C-predoped Si

We investigate the atomic structure and electronic properties of various defect configurations which consist of B and C atoms in Si predoped with C impurities through first-principles density-functional calculations. In the absence of Si self-interstitials (I’s), substitutional B and C atoms interact repulsively with each other, implying that B-C pairs at neighboring substitutional sites do not behave as a trap for B dopants. For I-B-C complexes, which can be formed in the presence of self-interstitials, we find that a C-B split interstitial, where the B and C atoms share a single lattice site along the [001] axis, is the most stable configuration. For several diffusion pathways, along which the B dopant diffuses from the C-B split-interstitial configuration with the [001] orientation to nearby tetrahedral and hexagonal sites, we find very high migration energies of about 3 eV. Thus, the diffusing B atom can be easily trapped in the neighborhood of C, resulting in the reduction in the B diffusivity. The range of the C trap potential is estimated to be about $7\text{Å}$. We also examine the diffusion of C from the stable C-B split interstitial, leaving the B dopant at a substitutional site, and find the migration energy to be much reduced to 2.16 eV. This result indicates that, as the C atom is dissociated, it acts as a trap for self-interstitials, leading to the reduction in self-interstitials which are available for B diffusion. In this case, the suppression of the B diffusivity is still expected, without degrading the electrical activity of the B dopants.

Figure 1

(Color online) The atomic structures of the (a) ${\text{I-B}}_s{\text{-C}}_s$, (b) ${\text{B}}_i{\text{-C}}_s$, (c) ${\text{C}}_s\text{−}{\left(\text{B-I}\right)}_{split}^{\left[110\right]}$, (d) ${\text{C}}_s\text{−}{\left(\text{B-I}\right)}_{split}^{\left[001\right]}$, (e) ${\left(\text{C-B}\right)}_{split}^{\left[111\right]}$, and (f) ${\left(\text{C-B}\right)}_{split}^{\left[001\right]}$ configurations. Numbers in (a) and (b) denote possible positions of I and ${\text{B}}_i$, respectively. The Si, C, and B atoms are represented by yellow (unlabeled white balls in print), red, and green balls, respectively.

Figure 2

(Color online) (a) Four defect levels of ${\left(\text{C-B}\right)}_{split}^{\left[001\right]}$ are compared with those for ${\left(\text{C-I}\right)}_{split}^{\left[001\right]}$ in pure Si. (b) The isosurfaces of electronic charge densities are plotted for the $\text{C}s$-derived level and the $a_1$, $b_1$, and $b_2$ defect levels of ${\left(\text{C-B}\right)}_{split}^{\left[001\right]}$.

Figure 3

(Color online) (a) Three possible diffusion pathways for the B dopant from ${\left(\text{C-B}\right)}_{split}^{\left[001\right]}$ are labeled 1, 2, and 3, which correspond to the final configurations in which the B atom is positioned at the first-nearest tetrahedral, first- and second-nearest hexagonal sites, respectively. (b) The variations in the energies are plotted for B diffusion along the three diffusion pathways.

Figure 4

The variations in the $a_1$, $b_1$, and $b_2$ defect levels are drawn when B diffuses from the ${\left(\text{C-B}\right)}_{split}^{\left[001\right]}$ configuration into the interstitial B positioned at the first-nearest hexagonal site along the diffusion pathway 1 in Fig. 3a.

Figure 5

(Color online) The C atom, which initially forms the (a) ${\left(\text{C-B}\right)}_{split}^{\left[001\right]}$ configuration, diffuses into the (d) ${\text{B}}_s\text{−}{\left(\text{C-I}\right)}_{split}^{\left[001\right]}$ configuration via the intermediate configurations of (b) ${\text{B}}_s\text{−}{\left(\text{C-I}\right)}_{split}^{\left[010\right]}$ and (c) ${\text{B}}_s\text{−}{\left(\text{C-I}\right)}_{split}^{\left[100\right]}$. (e) The variation in the energy is plotted along the diffusion pathway of the C atom.

Figure 6

(Color online) (a) Inward relaxations of the Si atoms around a substitutional C are drawn as a function of the distance between the C and Si atoms. (b) Numbers denote five different positions of the B dopant, which initially forms an ${\text{I-B}}_s$ pair with the self-interstitial, in the vicinity of the substitutional C. Arrows in different colors denote inward and outward directions of the B diffusion relative to the C atom. Small and large dashed circles represent distances of 4 and $7\text{Å}$, respectively, from the C atom.