Tight-binding studies of the tendency for boron to cluster in c-Si . I. Development of an improved boron-boron model 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 B 2 clusters become important when the boron doping level is ϳ10 18 cm Ϫ3 , well below the solubility limit. In contrast, the formation energy of defect clusters involving an interstitial ͑B n I clusters, nϭ1 -5, in their preferred charge states͒ decreases with increasing cluster size, down to 0.6 eV for B 5 I in a Ϫ5 charge state. None had formation energies that would lead to stable bound clusters. Several B n I clusters were found to be considerably more stable than isolated Si self-interstitials ͑by 1-2 eV͒, the B S B I cluster, assumed in some continuum modeling codes to be important, was not a particular interesting defect structure ͑a formation energy in the Ϫ2 charge state, E F Ϫ2 , of 2.8 eV͒. There seemed to be little energetic penalty for creating clusters larger than about B 5 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 ͑1997͔͒. Some support was found for the suggestion of Pelaz et al. ͓Appl. Phys. Lett. 70, 2285 ͑1997͔͒ that BI 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. B 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.

Empirical tight-binding (ETB) calculations have been used in extensive searches for new point defect structures in pure silicon as well as silicon doped with boron. In general, these searches, which use a steepest-descents energy minimization from random starting structures, have produced the same set of simple defects in pure silicon (tetrahedral interstitials, split interstitials, and simple vacancies) which have been widely studied. However, a variety of boron interstitials, and several new di-interstitials (with and without boron) have been discovered. Similarities between these defects and defects found in ab initio and classical studies are discussed, as well as the accuracy of the theoretical results in general. A Stillinger–Weber (SW) model for Si–B interactions has been developed in order to obtain vibrational entropies for simple point defects. Using the SW potential, concentration prefactors have been obtained, and traditional Arrhenius plots for concentration have been produced. The theoretical equilibrium concentrations of self-interstitials are consistent with results obtained from Pt and Au In-diffusion experiments, and contrast with oxidation-enhanced diffusion/oxidation-retarded diffusion (OED/ORD)-derived results. The theoretical results for point defect concentrations and binding energies are used to examine the assumptions of several diffusion models.

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Articles you may be interested inCoordination-resolved local bond contraction and electron binding-energy entrapment of Si atomic clusters and solid skinsTight-binding studies of the tendency for boron to cluster in c-Si. II. Interaction of dopants and defects in borondoped SiA tight-binding model for B-B interactions has been developed to study the stability of small boron clusters in crystalline silicon. The model was produced by fitting to the band structure determined by local-density approximation calculations on periodic supercells. This model is able to reproduce, relatively accurately, the cohesive energy of free boron clusters as determined by self-consistent field and configuration-interaction calculations.