There are a number of existing models for estimating the charge states of defects in silicon. In order of increasing complexity, these are (a) the Fermi-Dirac distribution, (b) the Shockley-Last model, (c) the Shockley-Read-Hall model, and (d) the Sah-Shockley model. In this work, we demonstrate their consistency with the general occupancy ratio α, and show that this parameter can be universally applied to predict the charge states of both monovalent and multivalent deep levels, under either thermal equilibrium or steady-state conditions with carrier injection. The capture cross section ratio is shown to play an important role in determining the charge state under non-equilibrium conditions. The application of the general occupancy ratio is compared with the quasi-Fermi levels, which are sometimes used to predict the charge states in the literature, and the conditions where the latter can be a good approximation are identified. The general approach is then applied to the prediction of the temperature- and injection level-dependent charge states for the technologically important case of multivalent monatomic hydrogen, and several other key monovalent deep levels including Fe, Cr, and the boron-oxygen complex in silicon solar cells. For the case of hydrogen, we adapt the model of Herring et al., which describes the charge states of hydrogen in thermal equilibrium, and generalize it for non-equilibrium conditions via the inclusion of the general occupancy ratio, while retaining the pre-factors which make the model more complete. Based on these results, the impact of temperature and injection on the hydrogenation of the key monovalent defects, and other pairing reactions, are discussed, demonstrating that the presented model provides a rigorous methodology for understanding the impact of charge states.

It is known that the interstitial iron concentration in silicon is reduced after annealing silicon wafers coated with plasma-enhanced chemical vapour deposited (PECVD) silicon nitride films. The underlying mechanism for the significant iron reduction has remained unclear and is investigated in this work. Secondary ion mass spectrometry (SIMS) depth profiling of iron is performed on annealed iron-contaminated single-crystalline silicon wafers passivated with PECVD silicon nitride films. SIMS measurements reveal a high concentration of iron uniformly distributed in the annealed silicon nitride films. This accumulation of iron in the silicon nitride film matches the interstitial iron loss in the silicon bulk. This finding conclusively shows that the interstitial iron is gettered by the silicon nitride films during annealing over a wide temperature range from 250 °C to 900 °C, via a segregation gettering effect. Further experimental evidence is presented to support this finding. Deep-level transient spectroscopy analysis shows that no new electrically active defects are formed in the silicon bulk after annealing iron-containing silicon with silicon nitride films, confirming that the interstitial iron loss is not due to a change in the chemical structure of iron related defects in the silicon bulk. In addition, once the annealed silicon nitride films are removed, subsequent high temperature processes do not result in any reappearance of iron. Finally, the experimentally measured iron decay kinetics are shown to agree with a model of iron diffusion to the surface gettering sites, indicating a diffusion-limited iron gettering process for temperatures below 700 °C. The gettering process is found to become reaction-limited at higher temperatures.

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Effective hydrogenation of interstitial iron in boron-doped multicrystalline silicon wafers is reported. The multicrystalline silicon wafers were annealed with plasma-enhanced chemical vapour deposited silicon nitride films, at temperatures of 400 C-900 C and for times from minutes to hours. At low temperatures where a combined effect of hydrogenation and precipitation of dissolved Fe is expected, results show that the hydrogenation process dominates the effect of precipitation. The concentrations of dissolved interstitial iron reduce by more than 90% after a 30-min anneal at temperatures between 600 and 900 C. The most effective reduction occurs at 700 C, where 99% of the initial dissolved iron is hydrogenated after 30 min. The results show that the observed reductions in interstitial Fe concentrations are not caused by the internal gettering of Fe at structural defects or by an enhanced diffusivity of Fe due to the presence of hydrogen. The hydrogenation process is conjectured to be the pairing of positively charged iron with negatively charged hydrogen, forming less recombination active Fe-H complexes in silicon. V

Injection-dependent lifetime spectroscopy of both n-and p-type, Cr-doped silicon wafers with different doping levels is used to determine the defect parameters of Cr i and CrB pairs, by simultaneously fitting the measured lifetimes with the Shockley-Read-Hall model. A combined analysis of the two defects with the lifetime data measured on both n-and p-type samples enables a significant tightening of the uncertainty ranges of the parameters. The capture cross section ratios k ¼ r n /r p of Cr i and CrB are determined as 3.2 (À0.6, þ0) and 5.8 (À3.4, þ0.6), respectively. Courtesy of a direct experimental comparison of the recombination activity of chromium in n-and p-type silicon, and as also suggested by modelling results, we conclude that chromium has a greater negative impact on carrier lifetimes in p-type silicon than n-type silicon with similar doping levels. V

A set of governing equations and boundary conditions are derived which describe the static deformation of a laminated anisotropic cylindrical shell. The theory includes both transverse shear deformation and transverse normal strain, as well as expansional strains. The validity of the theory is assessed by comparing solutions obtained from the shell theory to results obtained from exact theory of elasticity. Reasonably good agreement is observed and both shear deformation and transverse normal strain are shown to be of importance for shells having a relatively small radius-to-thickness ratio.

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