Free Energies, Structures, and Diffusion of Point Defects and Hydrogen-Point Defect Complexes in Silicon.

The nearly complete lack of reliable data on the thermodynamic and kinetic properties of point defects in silicon has forced workers in the semiconductor industry to use empirical, process-specific data for point defect populations, diffusivities, and so on, that can vary by orders of magnitude between their use in one process versus another. A primary aim of this project was to investigate phenomena at the atomic level in silicon, using empirical potentials, in hope of reconciling some of these disparities. In the literature, the results of atomistic simulations of defects in silicon, including those employing density functional methods, are incomplete. I address two of the weaknesses in previous efforts: the neglect of entropic contributions to defect energetics at high temperatures, and of the effects of hydrogen, which is a highly mobile and reactive species in the silicon crystal lattice. I particularly stress the calculation of free energy in our atomistic computer simulations, rather than internal energy or enthalpy. To date, there is very little published work on free energy calculations, even though knowledge of the entropy is essential for understanding systems at elevated temperatures. Furthermore, the few articles that address these issues typically use methods that are inadequate for point defect calculations, even within the constraints of a particular model. This is due, in part, to the stringent demands of accurate techniques for free energy estimation, which are often impossible to meet even with the use of empirical potentials. However, by using a carefully optimized coding of the Tersoff potential energy function for silicon, I have been able to perform sequences of simulations involving hundreds of silicon atoms under selected conditions of temperature, pressure, etc., to compute free energies of point defect formation and migration via thermodynamic integration. In order to extend these simulations to include hydrogen, I devised a framework to generalize the Tersoff potential to include multiple atom types that, unlike previous models, avoids haphazardly pasting new interactions onto old functional forms. These studies to date do not allow us to distinguish the different behavior of different charge states of the defects.