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)

В работе проведено исследование структурных, оптических и электронных свойств графитоподобного нитрида углерода (g-C3N4), синтезированных методом пиролиза мочевины при температурах 450–600°С. Метод функционала плотности использован для подтверждения выводов, основанных на экспериментальных данных. Был выполнен анализ литературных данных по g-C3N4, были рассмотрены структурные особенности получаемого материала и их оптическое поглощение. Также приведено описание используемых экспериментальных методов и математическое описание используемого метода моделирования – теории функционала плотности. Структура синтезированных образцов g-C3N4 определена по спектрам рентгеновской дифракции и ИК поглощения. Оптическое поглощение образцов исследованы по спектрам диффузного отражения, преобразованным в соответствии с теорией Кубелки-Мунка, оценка ширины энергетической щели для прямых и непрямых оптических переходов проводилась по методу Тауца. Была установлена линейная зависимость параметров кристаллической решетки и ширины щели от температуры синтеза. Для подтверждения экспериментальных результатов было проведено моделирование возможных структур g-C3N4 методом функционала плотности в пакете Quantum ESPRESSO. Была проведена оптимизация положений атомов для различных модельных структур, рассчитаны ИК спектры и зонные структуры электронных состояний. / In this work we investigated structural, optical and electrical properties of graphitic carbon nitride (g-C3N4) synthesized by thermal treatment of urea at 450– 600°C. Density functional theory calculations were performed to support suggestions based on experimental data. Available research data for g-C3N4 was studied, with interest in structural and absorption properties of the material. Additionally, the experimental methods and theory behind DFT-calculations were described. We determined the structure of g-C3N4 samples based on XRD and IR spectra. Optical absorption was investigated using diffuse reflectance spectra transformed with Kubelka-Munk function. Energy band gap was evaluated with Tauc plot for direct and indirect optical transitions. We show that crystal lattice parameters and band gap linearly depend on the synthesis temperature. To further prove our assumptions based on experimental data we also performed DFT-calculations for g-C3N4 in Quantum ESPRESSO software package. We calculated IR spectra and electronic band structures for models of each sample.