Reduced Moment-Based Models for Oxygen Precipitates and Dislocation Loops in Silicon

Abstract

The demand for ever smaller, higher-performance integrated circuits and more efficient, cost-effective solar cells continues to push the frontiers of process technology. Fabrication of silicon devices requires extremely precise control of impurities and crystallographic defects. Failure to do so not only reduces performance, efficiency, and yield, it threatens the very survival of commercial enterprises in today's fiercely competitive and price-sensitive global market. The presence of oxygen in silicon is an unavoidable consequence of the Czochralski process, which remains the most popular method for large-scale production of single-crystal silicon. Oxygen precipitates that form during thermal processing cause distortion of the surrounding silicon lattice and can lead to the formation of dislocation loops. Localized deformation caused by both of these defects introduces potential wells that trap diffusing impurities such as metal atoms, which is highly desirable if done far away from sensitive device regions. Unfortunately, dislocations also reduce the mechanical strength of silicon, which can cause wafer warpage and breakage. Engineers must negotiate this and other complex tradeoffs when designing fabrication processes. Accomplishing this in a complex, modern process involving a large number of thermal steps is impossible without the aid of computational models. In this dissertation, new models for oxygen precipitation and dislocation loop evolution are described. An oxygen model using kinetic rate equations to evolve the complete precipitate size distribution was developed first. This was then used to create a reduced model tracking only the moments of the size distribution. The moment-based model was found to run significantly faster than its full counterpart while accurately capturing the evolution of oxygen precipitates. The reduced model was fitted to experimental data and a sensitivity analysis was performed to assess the robustness of the results. Source code for both models is included. A moment-based model for dislocation loop formation from {311} defects in ion-implanted silicon was also developed and validated against experimental data. <italic>Ab initio</italic> density functional theory calculations of stacking faults and edge dislocations were performed to extract energies and elastic properties. This allowed the effect of applied stress on the evolution of {311} defects and dislocation loops to be investigated.