Quantitative Modeling of Oxygen Precipitation in Silicon

The vast majority of modern microelectronic devices are fabricated on single-crystal silicon wafers, which are produced predominantly by the Czochralski (CZ) melt-growth process. Important metrics that ultimately influence the quality of the silicon wafers include the concentration of impurities and the distribution of lattice defects (collectively known as microdefects). This thesis provides a multiscale quantitative modeling framework for describing physics of microdefects formation in silicon crystals, with particular emphasis on oxide precipitates. Among the most prevalent microdefects found in silicon crystals are nanoscale voids and oxide precipitates. Oxide precipitates, in particular, are critically important because they provide gettering sites for highly detrimental metallic atoms introduced during wafer processing and also enhance the mechanical strength of large-diameter wafers during high-temperature annealing. On the other hand, like any other crystalline defect species, they are undesirable in the surface region of the wafer where microelectronic devices are fabricated. Although much progress has been made with regards to oxide precipitate prediction and optimization, it has been surprisingly difficult to generate a robust, quantitative model that can accurately predict the distribution and density of precipitates over a wide range of crystal growth and wafer annealing conditions. In the first part of this thesis, a process scale model for oxide precipitation is presented. The model combines continuum mass transport balances, continuum thermodynamic and mechanical principles, and information from detailed atomic-scale simulations to describe the complex physics of coupled vacancy aggregation and oxide precipitation in silicon crystals. Results for various processing situations are shown and comparisons are made to experimental data demonstrating the predictive capability of the model. In the second part of this thesis, atomistic simulations are performed to study the stress field and strain energy of oblate spheroidal precipitates in silicon crystals as a function of precipitate shape and size. Although the stress field of a precipitate in silicon crystals may be studied within a continuum mechanics framework, atomic scale modeling does not require the idealized mechanical properties (and precipitate shapes) assumed in continuum models and therefore provides additional valuable insight. The atomistic simulations are based on a Tersoff empirical potential framework for silicon, germanium and oxygen. Stress distributions and stress energies are computed for coherent germanium precipitates and for incoherent, amorphous silicon dioxide precipitates in a crystalline silicon matrix. The impacts of precipitate size and shape are considered in detail, and for the case of oxide precipitates, special emphasis is placed on the role of interfacial relaxation. Whenever possible, the atomistic simulation results are compared with analytical solutions