Multiscale Modeling and Simulations of Defect Clusters in Crystalline Silicon

As the device dimension in semiconductor silicon transistors reach sub-20nm, it significantly enhances the tolerance limits on the size and concentration of defects in the underlying crystalline silicon wafer. Understanding the evolution of defect clusters is critical for controlling the defect density and size distribution within crystalline silicon. The objective of this thesis is to develop the computational methodology that quantitatively describes the evolution of defect clusters in crystalline solids at an atomistic level, and provide a mechanistic understanding of underlying physics behind the defect aggregation process. In first part of the thesis we develop a novel computational method for probing the thermodynamics of defects in solids. We use this to estimate the configurational entropy of vacancy clusters which is shown to substantially alter the thermodynamic properties of vacancy clusters in crystals at high temperature. The modified thermodynamic properties of vacancy clusters at high temperature are found to explain a longstanding discrepancy between simulation predictions and experimental measurements of vacancy aggregation dynamics in silicon. In the next part, a comprehensive atomistic study of self-interstitial aggregation in crystalline silicon is presented. The effects of temperature and pressure on the aggregation process are studied in detail and found to generate a variety of qualitatively different interstitial cluster morphologies and growth behavior. A detailed thermodynamic analysis of various cluster configurations shows that both vibrational and configurational entropies are potentially important in setting the properties of small silicon interstitial clusters. The results suggest that a competition between formation energy and entropy of small clusters could be linked to the selection process between various self-interstitial precipitate morphologies observed in ion-implanted crystalline silicon. Finally in the last section, we investigate the effect of carbon on self-interstitial aggregation. The presence of carbon in the silicon dramatically reduces cluster coalescence, with almost no direct effect on the single self-interstitials. This suggests that suppression of transient enhanced diffusion of boron (in presence of carbon), could be due to the direct interaction between carbon atoms and self-interstitial clusters

Role of configurational entropy in the thermodynamics of clusters of point defects in crystalline solids

The internal configurational entropy of point defect clusters in crystalline silicon is studied in detail by analyzing their potential energy landscapes. Both on-lattice and off-lattice calculation approaches are employed to demonstrate the importance of off-lattice configurational states that arise due to a large number of inherent structures (local minima) in the energy landscape generated by the interatomic potential function. The resulting cluster configurational entropy of formation is shown to exhibit behavior that is qualitatively similar to that observed in supercooled liquids and amorphous solids and substantially alters the thermodynamic properties of point defect clusters in crystals at high temperature. This behavior is shown to be independent of interatomic potential and cluster type, and suggests that defects in crystals at high temperature should be generally described by a quasicontinuous collection of nondegenerate states rather than as a single ground state structure. The modified thermodynamic properties of vacancy clusters at high temperature are found to explain a longstanding discrepancy between simulation predictions and experimental measurements of vacancy aggregation dynamics in silicon

On-lattice kinetic Monte Carlo simulations of point defect aggregation in entropically influenced crystalline systems

An on-lattice kinetic Monte Carlo model of vacancy aggregation in crystalline silicon is parametrized using direct regression to evolution data from nonequilibrium molecular dynamics simulations. The approach bypasses the need to manually compute an energy barrier for each possible transition and leads to an excellent, robust representation of the molecular dynamics data. We show that the resulting lattice kinetic Monte Carlo model correctly captures the behavior of the real, continuous space system by properly accounting for continuous space entropic effects, which are often neglected in lattice-based models of atomistic processes. These contributions are particularly important at the high temperatures relevant to many steps in semiconductor materials processing