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

Abstract

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.

First-Principles Modeling of Boron Clustering in Silicon

“…As pointed out before [16], it is not clear in advance which final atomic arrangement the different clusters will assume in the global-minimum structure. In order to decrease the threat of finding a high-energy local instead of the global minimum, we started for each cluster from many different initial configurations that were structurally relaxed (including previously predicted ones from Refs.…”

“…In order to decrease the threat of finding a high-energy local instead of the global minimum, we started for each cluster from many different initial configurations that were structurally relaxed (including previously predicted ones from Refs. [10,11,16]. Further details will be published elsewhere [22].…”

“…However, fitting a large number of parameters in inverse modeling can be subject to ambiguities and furthermore does not help to identify the structure of the clusters. The second approach, atomistic calculations, especially within density-functional theory (DFT) [9][10][11][12][13][14][15], can in principle overcome these limitations; however, the problems to find global instead of local minima [16] and the possibly considerable error bars for miscoordinated defects [17] also require a cautious use of this approach. Until recently, only one set of BIC reaction barriers from first-principles [18] for B n I m (n 4) clusters had been available, where the influence of the different charge states had been neglected.…”

Mechanisms of boron diffusion in silicon and germanium

“…80 Several studies approached the phenomenon of B-I clustering in crystalline Si from a theoretical point of view, calculating the formation energy and structure of each plausible B-I cluster, the energetically favored B:Si stoichiometry, the possible pathways for BIC growth and dissolution and the interactions with I-type defects. [81][82][83][84][85][86][87][88][89] Most calculations provide such properties for small sized BICs (typically less than 10 atoms) and for a fixed structure or composition, while it cannot be excluded that an ensemble of different BICs size occurs in facts. Here, a major focus will be given on the experimental results on BIC sizes and dissolution barriers, which can be implemented for a viable simulation of the B diffusion process.…”

Formation, nature, and stability of the arsenic-silicon-oxygen alloy for plasma doping of non-planar silicon structures

“…[12][13][14][15] While dopant aggregation has been found to be mediated by point-like defects, 13,14 defect formation and defect-dopant interaction have been rather well studied in bulk Si; for instance, Hwang and co-workers proposed routes for defect-mediated As clustering in Si using first-principles calculations. 15 However, little is known about the formation and structure of the ternary dopant-Si-O alloy despite its importance for a better understanding of the self-limiting processes in plasma doping.…”