Molecular dynamics simulations were used to study the structure of calcium silicate intergranular films (IGFs) formed between the basal planes of silicon nitride crystals. A multibody potential was used to describe the interactions between ions. Samples with different film thickness and CaO contents were studied. Epitaxial adsorption of Si and O atoms from the intergranular films onto N and Si, respectively, in the crystal surface was observed. This epitaxial order induced a structural order into the nominally amorphous IGF that decreased as a function of distance from the IGF/crystal interface. A higher concentration of strained siloxane bonds was observed at the IGF/crystal interface in comparison to the amorphous interior of the IGF. While Ca ions were observed to segregate to the IGF/crystal interface in simulations of calcium silicate glass IGFs between alumina crystals, no segregation of calcium to the first adsorbed layer on the nitride was found in these simulations using silicon nitride crystals. Planar alignment of Ca ions parallel to the IGF/crystal interface occurred with either the largest concentrations of CaO or with the thinnest IGFs studied here. This alignment creates localized nonbridging oxygen that would affect the stability of the IGF/crystal system.

We used density-functional theory ͑DFT͒ to resolve interactions between Ag atoms on a compressed Ag͑111͒ surface from the first to the 53rd neighbor distance, a separation range of over 2 nm. We find that these interactions are primarily pairwise and electronic in origin. A spatially resolved plot of the pair interactions reveals that they form concentric rings that alternate between attraction and repulsion. Calculations of the band structure of the strained Ag͑111͒ surface reveal that there is a surface state at the ⌫ point just below the Fermi level, similar to what is observed for unstrained Ag͑111͒. The band structure of the strained Ag͑111͒ surface is consistent with the magnitude and spatial dependence of the oscillatory interactions that we find in the DFT calculations. A comparison between a theory developed to describe adsorbate pair interactions mediated by surface-state electrons and our DFT results indicates that the theory describes the DFT results in an average way at distances beyond the third neighbor-although the DFT results contain angular variations in the interactions not predicted by the theory. At short adsorbate separations, we find that interactions at the firstneighbor and second-neighbor distances are strongly attractive and indicative of direct chemical bonds between the adatoms. The third-neighbor interaction is repulsive and is possibly mediated by bulk electrons. The results of these studies may be useful in the design of metal thin heteroepitaxial films.

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.

As a particularly important p-type dopant, boron exhibits some problematical phenomena during the fabrication of microelectronic devices, especially transient enhanced diffusion (TED) following ion implantation and annealing. TED is due, in large part, to the formation of boron-defect clusters. This article describes a search for particularly stable boron-defect clusters (up to B4I4). A tight-binding method, in conjunction with atomic-scale statics calculations, is used to study boron and boron-defect clusters containing up to four boron atoms and four self-interstitials within a matrix of crystalline silicon. Formation and binding energies are reported for these species. There is a tendency to form a four-atom ring containing two Si self-interstitials and two boron atoms. One guiding principle for the stability of the geometry of the clusters is to maximize the number of unstrained bonds (i.e. with Si-like bond lengths); the higher the extent of unstrained bonds, the lower the formation energy. Symmetry is found to play a smaller role in determining preferred structures.

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