Hierarchical multiscale modeling of solid state diffusion

Silicon germanium alloys are gaining technological popularity in high frequency, low power applications. Typical concentrations of Ge in SiGe alloys in device structures are orders of magnitude larger than typical dopant concentrations. Therefore, the effect of alloy composition on phenomena like diffusion becomes important. This work focuses on the theoretical issues to understand the microscopic mechanism of self-diffusion as a function of alloy composition; it addresses these issues:; Simulating macroscopic diffusion. Current computational capacities preclude a wholly first principles molecular dynamics simulation of macroscopic diffusion. However, a technique to simulate macroscopic diffusion ab initio is invaluable. This work presents a framework to perform such a simulation using a hierarchical multiscale modeling technique: first principles calculations performed to develop a database of environment dependent energy barriers for microscopic processes; these values then being used to simulate macroscopic diffusion using the kinetic Monte Carlo technique. This framework has been used to demonstrate macroscopic diffusion in multilayer structures and has been applied to study the effect of composition on vacancy mediated diffusion in SiGe alloys.; Obtaining point defect energetics. The prevalent models (local density approximation, generalized gradient approximation) used to perform total energy calculations in SiGe systems underestimate the activation energy for self-diffusion. This work investigates the LDA+U model to calculate point defect energetics in Si. This model is shown to give better agreement between theoretical activation energies and experimental observations.; Relating Mmacroscopic activation energy to microscopic barriers. Diffusion of impurities in crystalline materials involves a sequence of several processes, which are repeated in varying combinations a multiple number of times. The concept of "activation energy" has been borrowed from chemical reactions where the reactants form activated complexes before decomposing into products. While ideas like the smallest rate being the rate determining step and hence the overall activation energy may be applicable to simple chemical reactions, such ideas are too simplistic to describe solid state diffusion. This work presents an approach to relate macroscopic activation energy to activation energies of microscopic processes. This approach has been applied to the diffusion of impurities in a diamond structure by a vacancy mechanism.