Clusters which contained up to five B atoms were considered to be extended defects within a crystalline matrix. Tight-binding calculations suggested that a cluster which contained two B atoms that occupied substitutional sites was stable; unlike any other small B cluster that was studied here. The formation energy increased when a third and fourth substitutional B atom was added to the cluster. Estimates of the equilibrium concentration, using tight-binding-deduced formation energies and entropies (Stillinger-Weber model), indicated that B2 clusters became important when the B doping level was about 1018/cm3; well below the solubility limit. On the other hand, the formation energy of defect clusters which involved an interstitial decreased with increasing cluster size; down to 0.6eV for B5I in a -5 charge state. None had formation energies that would lead to stable bound clusters. Several clusters were found to be considerably more stable (by 1 to 2eV) than isolated Si self-interstitials. The BsBi cluster, which was sometimes assumed to be important, was not considered here to be a particularly interesting defect structure; with a formation energy (-2 charge state) of 2.8eV. There seemed to be little energetic penalty for creating clusters that were larger than about B5I; in good agreement with previous studies of self-interstitial clusters in Si. Some support was found for the concept that BI2 was a nucleation site for B clustering. Clusters which involved a B interstitial were generally found to be less likely to form than were analogous clusters which involved a Si self-interstitial. Moreover, B2 clusters which involved vacancies were not energetically favored; thus confirming the known tendency of B to diffuse via an interstitial mechanism rather than via vacancies. The results suggested that B clusters could serve as traps, and slow the diffusion of self-interstitials under conditions of interstitial supersaturation in highly-doped silicon.

Tight-Binding Studies of the Tendency for Boron to Cluster in c-Si – II. W.Luo, P.B.Rasband, P.Clancy, B.W.Roberts: Journal of Applied Physics, 1998, 84[5], 2476-86