A reduced moment-based model for precipitation kinetics and application to dopant activation in silicon

Abstract

A moment-based model for the time evolution of extended defect size distributions is introduced as a computationally efficient method for the quantitative modeling of precipitation processes. Because the model accounts for how the size distribution of aggregates changes with time, it is able to account for thermal history effects that are missed by simpler models. However, by considering only the lowest moments of the distribution rather than the full distribution itself, the model can be practically applied to nonhomogeneous systems for which it is impractical to include the full distribution at every point in space. The model is tested by implementing it in a process simulator and applying it to the simultaneous diffusion and activation/deactivation of dopants in silicon. Under the conditions compared, we find that the reduced model is nearly equivalent to a previously studied model [S. T. Dunham, J. Electrochem. Soc. 142, 2823 (1995)] maintains the full size distribution and is thus much more computationally intensive. Because the reduced model is derived directly from the more complete model using an energy-minimizing closure assumption, all parameters retain a physical interpretation and the model can be readily extended to a large range of systems.