Modeling and control of transient enhanced diffusion of boron in silicon

Forming ultrashallow junctions in Si-based microelectronic logic devices is becoming increasingly critical as device dimensions continue to shrink. Transient enhanced diffusion (TED) occurs during the post-implant annealing process which often leads to a significant increase in the junction depth and greatly impedes the formation of such ultrashallow junctions. Much interest has been directed towards the modeling of TED to reduce the costs and time of process development.; A comprehensive TED model is developed using reaction-diffusion equations, which consist of coupled continuity or mass balance equations and Poisson's equation for the electric field. Determination of the activation energies in TED kinetic parameters has proven difficult with many contradicting experimental and computational estimates reported in the literature. To resolve the disagreement in the published values, maximum likelihood estimation is applied to give prior estimates of the most likely values for the parameters as well as their accuracies. A systematic approach to model parameter identification using parameter sensitivity and maximum a posteriori estimation is then employed combining the maximum likelihood parameter estimates and their uncertainties in conjunction with after-anneal boron secondary ion mass spectroscopy profiles to obtain accurate TED energetics.; Reducing the junction depth using rapid thermal annealing with high heating rates comes at a cost of increasing sheet resistance. A model-based optimization is formulated to design the optimal annealing temperature program that gives the minimum junction depth while maintaining satisfactory sheet resistance. Comparison of different parameterizations of the optimal trajectories shows that linear profiles give the best combination of minimizing junction depth and sheet resistance. Worst-case robustness analysis of the optimal control trajectory motivates improvements in feedback control instrumentation and strategies for these processes.