Cluster-based multivariate spline model for dopant activation in SiC

Abstract

Ion implantation in SiC damages its crystallinity, resulting in the clustering of inactive dopants. Subsequent annealing repairs the crystal structure and activates the implant. Current models for this process are fully empirical, and a physical understanding is unavailable. To generate a physical model of dopant activation, we study the time-dependent reaction between the as- implanted species, such as dopants, defects, and clusters, described using a set of ODEs. Combining known post-annealing activation ratios and implant conditions (temperature and dose), a global optimizer is applied to find the initial dopant, defect, and cluster concentrations as free parameters. The optimizer systematically tunes these parameters and evaluates the ODEs in each step to get the simulated activation ratio. Its deviation from the empirical model is used as feedback to the optimizer to tune the parameters. The optimizer’s initial concentrations are approximated using multi-variate B-splines.