Systems analysis applied to modeling dopant activation and TED in rapid thermal annealing

Insufficient dopant activation and excessive transient enhanced diffusion (TED) of boron in silicon has been major inhibitors to forming low-resistivity ultrashallow junctions for CMOS device applications. However, the predictive capability of most simulation-based models is subject to serious doubt. Here we apply several mathematical methods drawn from systems analysis to greatly reduce the magnitudes of these uncertainties and to determine optimal temperature trajectories. We begin by outlining firmly grounded procedures for estimating simulation rate parameters using maximum likelihood estimation together with multivariate statistics to quantify accuracy. We also describe a rigorous parameter sensitivity analysis by the finite difference method to investigate model behavior. These combined approaches not only lead to vast improvements in the ability of simulations to match experiment, but also show that, out of roughly 30 total parameters in the model, only 4 need further serious attention as targets for determination by independent experiments or quantum calculations.