Complex oxides are a class of materials that have recently emerged as potential candidates for electronic applications owing to their interesting electronic properties. The goal of this dissertation is to develop a fundamental understanding of these electronic properties using a combination of first-principles approaches based on density functional theory (DFT), and Schrödinger-Poisson (SP) simulations.

The formation of a high-density (3.3x10¹⁴ cm^-2) two-dimensional electron gas (2DEG) at polar/nonpolar complex oxide interfaces, such as the LaAlO₃/SrTiO₃ (LAO/STO) and GdTiO₃/SrTiO₃ (GTO/STO) interfaces, has raised tremendous interest in complex oxides. However, the mechanism responsible for the 2DEG formation has not yet been agreed upon due to various aspects of experimental observations conflicting with the proposed models. We resolve these conflicts with a consistent model based on polar discontinuities, and explain the role played by surface terminations and surface charging. The study of surface charging using DFT calculations is difficult due to the condition of maintaining charge neutrality. We overcome this complication by developing a rigorous and general methodology for computing the energetics of charged surfaces for semiconductors and insulators.

The developed methodology addresses a common problem in surface science: the exchange of charges between a reservoir and a surface.

Another challenge in the modeling of the high-density 2DEG at interfaces is the correct incorporation of the electric-field dependence of the static dielectric permittivity in materials such as STO, which is due to its incipient ferroelectric nature. So far, a field-dependent dielectric response has not been implemented in any of the commercially available SP solvers. We develop a methodology, in conjunction with the SP solver nextnano³, to account for this field dependence selfconsistently with the resulting band bending in the 2DEG.

Confinement of the high-density 2DEG requires a sufficiently large conduction-band offset at the interface. Confinement is particularly challenging in complex oxides such as BaSnO₃ (BSO) that have a low density of states (DOS). Using SP simulations of BSO heterostructures with possible barrier materials (including STO, LaInO₃, and KTaO₃) we quantitatively study 2DEG confinement in BSO. The results of the simulations serve as a guide to engineering barriers for BSO-based heterostructures.

Finally, carrier mobility is another important component determining the performance of electronic devices. The mobility of electrons in many complex oxides, including STO, tends to be low (~10 cm²V^-1s^-1) at room temperature. Recent experimental demonstrations of high electron mobility (300 cm²V^-1s^-1) in BSO have, therefore, come as a surprise to the complex oxide community. Using accurate first-principles calculations, we study longitudinal-optical-phonon (LO-phonon) and ionized impurity scattering mechanisms in BSO. Our analysis reveals that the low DOS in BSO is the reason behind BSO's high mobility in comparison to STO and other complex oxides, which have a high DOS. The insights gained from the study provide a recipe for identifying or designing high-mobility complex oxides.

Overall, four different aspects of complex oxides were addressed by the accomplishments in this dissertation: (1) developing a rigorous and general methodology for surface charging in thin films, which is a common scenario in surface science; (2) correct implementation of a field-dependent dielectric permittivity in an SP solver; (3) assessing the carrier confinement in the high-density 2DEG within BSO, which has a low DOS; and (4) understanding the impact of LO-phonon and ionized impurity scattering mechanisms on carrier mobility in complex oxides.