Atomistic-to-Continuum Modeling of Defect-Related Phenomena in Silicon Crystals

Abstract

Continuum process modeling of point defect and impurity aggregation during silicon crystal growth and wafer annealing has led to significant contributions toward understanding and improvement of industrial processes. Key inputs to these models are thermophysical properties of point defects and their clusters, which may be strong functions of temperature and cluster size. In this paper, a theoretical framework is presented for probing the high-thermodynamic properties of vacancy and self-interstitial clusters in crystalline silicon at elevated temperature. In particular, configurational and vibrational entropy are shown to be significant in both types of defect clusters. In both cases, configurational entropy leads to the existence of a wide distribution of possible cluster configurations that collectively lowers the free energy of formation relative to the energetic ground state configuration. Moreover, certain self-interstitial cluster sizes are additionally stabilized by configurations that possess anomalously high vibrational entropy.