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Recently Silicon Germanium alloy (Si_1-xGe_x) is showing lots of potentials in device fabrication. Most of the structures containing Si_1-xGe_x that are fabricated at present involve Si/Si_1-xGe_x heterostructure. The fabrication process involves several high temperature anneal steps in either inert, oxidizing or nitriding ambient which results the interdiffusion of Si and Ge through the hetero-interfaces. The interdiffusion causes broadening of Si/Si1_xGex interface and changes the physical position of the heterointerface which can cause degradation of device performance. Several studies have so far been done to quantify the amount of Ge interdiffusion in heterostructures. However no study has yet been performed to model this phenomenon. Modeling the interdiffusion mechanism is important for two reasons: (1) it will facilitate to calibrate the device characteristics taking the effect of interdiffusion mechanism into calculations prior to device fabrication; and (2) to get a better insight of the actual mechanism involved in the interdiffusion process. In this study, attempt has been taken to model interdiffusion of Si and Ge in structures having Si/Si_1-xGe_x hetero-interfaces. Mathematical models are proposed to model the behavior and the models are applied to previously published results where samples were annealing in inert, oxidizing and nitriding ambient at different anneal temperatures for different anneal times. First only the contributions of vacancies in the interdiffusion mechanism are considered. This can successfully model the interdiffusion mechanism for samples annealed in inert and oxidizing ambients at low temperatures (below 1050°C). Next the contributions of interstitials along with vacancy in the interdiffusion mechanism are considered. These are able to successfully model the interdiffusion phenomenon for the samples annealed in oxidizing and nitriding ambients at high temperatures (above 1050°C). The success of the modeling is justified by getting good match between the simulated and the experimental interdiffusion profiles along with good match between the fitting parameters used in the simulations compared with previous reported values. Besides modeling the interdiffusion mechanism, for the first time, a mathematical model is proposed for vacancy injection while nitridation of silicon is done. / Thesis / Master of Applied Science (MASc)

The electronic band structure of a semiconductor is an essential property to determine most of its optical characteristics. The complexity of the energy band structure calculations makes analytical calculations impossible. Any calculation leading to electronic band structures has to utilize numerical methods. In this thesis, two solvers were developed to calculate the energy band structure of 1D Kronig-Penney lattice, 30 diamond lattice-structure and silicon lattice. In this thesis, many of the important methods of calculating the energy band structures were discussed. Through comparisons among different methods, we have determined that Self-Consistent Pseudopotential Method, SCPM, is the most suitable method for calculating the energy band structures when self-sufficiency and accuracy are of special importance. The SCPM is an iterative method which was utilized in this thesis by using efficient numerical methods. Instead of using conventional numerical methods such as Finite Difference Method or Finite Element Method which cause inefficiency, this thesis calculates the energy band structure by utilizing Orthogonal Plane-Wave expansion of the potentials. The 1D electronic band structure solver was developed as a foundation for the implementation of the 30 electronic band structure solver. It uses a minimal number of Fourier coefficients to calculate the energy band structure of the 1D Lattices without compromising accuracy. The 30 electronic band structure solver development needs multiple changes and modifications to the 1D solver. As the 30 solver is essentially made using the 10 solver platform, it is also efficient and needs a minimal number of Fourier coefficients for accurate results. The 30 solver can be used for either Nearly Free Electron Method, NFEM, or SCPM calculations. The NFEM calculations were done on the diamond lattice structure. The results were shown to be the same as the benchmarks of [28, 80]. The silicon lattice energy band structure was also calculated with the 30 solver using SCPM with LOA. The results were in the same range as the four sets of data gathered from three benchmarks [58, 81, 82], showing good agreement. Based on the two comparisons made for the 30 solver, it was shown that it is a reliable and efficient program to calculate energy band structures of the 30 lattices. / Thesis / Master of Applied Science (MASc)