A modular framework for predictive modeling of microstructural evolution in silicon materials processing

The effect of material defects in silicon, nucleated and grown during crystal growth, on subsequent microelectronic device processing and on device performance is becoming clear. With microdevices increasing in size and complexity and the feature sizes for these devices decreasing, the premium on control of microdefects in crystalline silicon has become critical to commercial success. Traditional approaches to refining electronic materials processing technology, using empirical experimentation to determine the relationship between material properties and material processing conditions, have become impractical as experimental costs rise dramatically and finer control of microdefects is demanded. Mathematical modeling in this area has emerged as an essential resource, allowing quantitative predictions to be made of the response in microdefect distributions to changes in operating conditions. The demand for robust simulation tools that can predict the dynamics of defects in silicon material across a range of different processing stages is now immense. A systematic approach based on multiple model regression to several distinct types of experimental data is developed in this thesis, which is used to create a robust modeling framework for defect and impurity evolution during crystalline silicon processing. The experimental systems investigated are (1) Czochralski single-crystal growth, (2) zinc diffusion, (3) oxide precipitation during wafer thermal annealing, and (4) void formation in crystalline silicon. All these systems are intimately connected at the atomistic level by the thermodynamic and transport properties of single point defects. Several different stochastic global optimization methods are used for model regression of systems (1)–(3) to experimental data, performing the computationally expensive task of minimizing a multi-objective function. The thermophysical parameters determined by this approach are vital input to a new, predictive, continuum model developed for system (4), the central feature of which is a refined mechanistic description of point defect aggregation at the atomic scale, determined from extensive atomistic calculations of cluster thermodynamic and structural properties. This work demonstrates how the microscopic overlap in macroscopically distinct systems can substantially reduce uncertainty in model regression to experimental data, leading to strict bounds on the transport, reaction, and thermodynamic properties of the various species present. The result is, for this first time, a quantitatively coherent modeling framework for several technologically important phenomena related to crystalline silicon processing