Formation and transport properties of defects in boron-doped silicon studied through tight-binding bond models

The formation and transport properties of point defects in boron-doped silicon have been studied at the atomic level. Robust continuum models of boron diffusion require a knowledge of equilibrium concentrations and diffusivities of self-interstitials, vacancies, boron-defect pairs, and small boron clusters that cannot easily be obtained experimentally. Such thermodynamic and transport properties can, however, be estimated through statistical mechanical and Transition State theories, provided energies and vibrational entropies of point defect formation and migration are known. These energies and entropies have been determined in this work using an empirical quantum mechanical model called Tight Binding (ETB) to describe Si-Si, Si-B, and B-B bonding. Classical models (via the Stillinger-Weber potential) are used to estimate entropies. Defects were identified using "scramble-relaxation" computer runs in which starting positions of atoms were randomly varied and then relaxed to yield stable defect structures. The ETB results for formation energies are generally consistent with LDA ab initio results, to within approximately 0.3eV. C{dollar}rmsb{lcub}EQ{rcub}{dollar}(I) values determined via the ETB model agree with Au, Pt, and Zn in-diffusion-derived estimates, and contrast with those obtained through modeling of OED and stacking-fault experiments. The negative-U behavior of vacancies and boron interstitials is reproduced by the ETB model, and the correct charge states (0 and {dollar}-{dollar}1 for V, and +1 for B{dollar}rmsb{lcub}S{rcub}{dollar}I and B{dollar}rmsb{lcub}i{rcub}{dollar}) are obtained. Several new di-interstitial clusters, with and without boron, have been obtained which have formation energies 1-2eV/atom lower than isolated interstitials. Although the accuracy limits of the ETB and Stillinger-Weber models make it impossible to determine whether interstitials or vacancies dominate in the mediation of boron transport at equilibrium, it is concluded that, because the migration energy of B{dollar}rmsb{lcub}i{rcub}{dollar} in a direct-interstitial mechanism is very low (0.15eV), boron should have a high effective diffusion coefficient in cases where boron interstitials are super-saturated (e.g., for OED and TED). The ETB model predicts that B{dollar}rmsb{lcub}n{rcub}{dollar} (n from 1 to 4) substitutional clusters decrease in stability with increasing n, but that the inclusion of an interstitial (B{dollar}rmsb{lcub}n{rcub}{dollar}I) makes larger clusters increasingly more stable. This may help explain how boron precipitates nucleate in highly-doped silicon.