Tight-binding studies of the tendency for boron to cluster in c-Si. II. Interaction of dopants and defects in boron-doped Si

Clusters containing up to five boron atoms were considered as extended defects within a crystalline Si matrix. Tight-binding calculations suggest that a cluster containing two boron atoms occupying substitutional sites is stable, unlike any other small boron cluster that we studied. The formation energy increases when a third and fourth substitutional boron atom is added to the cluster. Estimates of the equilibrium concentration, using tight-binding-derived formation energies and formation entropies from the Stillinger–Weber model, indicate that ${\mathrm{B}}_{\mathrm{2}}$ clusters become important when the boron doping level is ${\text{∼10}}^{18}\hspace{0.17em}{\mathrm{cm}}^{\mathrm{-3}},$ well below the solubility limit. In contrast, the formation energy of defect clusters involving an interstitial $({\mathrm{B}}_{n}I$ clusters, $\text{n=1–5,}$ in their preferred charge states) decreases with increasing cluster size, down to 0.6 eV for ${\mathrm{B}}_{\mathrm{5}}I$ in a −5 charge state. None had formation energies that would lead to stable bound clusters. Several ${\mathrm{B}}_{n}I$ clusters were found to be considerably more stable than isolated Si self-interstitials (by 1–2 eV), the ${\mathrm{B}}_S{\mathrm{B}}_I$ cluster, assumed in some continuum modeling codes to be important, was not a particular interesting defect structure (a formation energy in the −2 charge state, $E_F^{\text{−2}},$ of 2.8 eV). There seemed to be little energetic penalty for creating clusters larger than about ${\mathrm{B}}_{\mathrm{5}}\mathrm{I,}$ in good agreement with Sinno and Brown’s Stillinger–Weber studies of self-interstitial clusters in Si [Mater. Res. Soc. Symp. Proc. 378, 95 (1997)]. Some support was found for the suggestion of Pelaz et al. [Appl. Phys. Lett. 70, 2285 (1997)] that $\mathrm{B}{I}_2$ is a nucleation site for boron clustering. Boron clusters involving a boron interstitial were generally found to be less likely to form than analogous clusters involving a Si self-interstitial. ${\mathrm{B}}_{\mathrm{2}}$ clusters involving vacancies are not energetically favored, confirming the known tendency for boron to diffuse via an interstitial mechanism rather than vacancies. These results suggest that boron clusters could serve as traps, which slow the diffusion of self-interstitials under conditions of interstitial supersaturation in highly doped silicon, consistent with experimental evidence.