Fluorite structured ferroelectric materials have garnered significant attention in recent years for their extreme scalability and latent potential for various emerging neuromorphic computing applications. This dissertation presents a comprehensive investigation into the ferroelectric properties of Hafnium-Zirconium Oxide (HZO) and Zirconium Oxide (ZrO₂) capacitors, focusing on their polarization characteristics, scaling effects, and dynamic behavior under applied electric fields. Firstly, we delve into the optimization of ferroelectric polarization in HZO capacitors through rapid thermal annealing (RTA) at varying temperatures. The study reveals a direct correlation between RTA temperature and remnant polarization (2P_r), with capacitors annealed at exhibiting a record-high 2P_r of approximately at a frequency of . Furthermore, these HZO capacitors demonstrate exceptional endurance and retention characteristics, showcasing their potential for neuromorphic computing applications. Later, the focus shifts to the impact of lateral dimension scaling on the ferroelectric properties of HZO capacitors. Through meticulous fabrication techniques and innovative measurement setups, capacitors ranging from to are characterized, revealing diminishing ferroelectric polarization charge with decreasing lateral dimensions. Despite the challenges posed by miniaturization, successful characterization of HZO capacitors as small as is achieved, offering valuable insights for nanoelectronics applications. Lastly, we investigate the field-induced ferroelectric behavior of ZrO₂ capacitors using dynamic charge-voltage (Q-V) measurements and a compact nonlinear dynamical model based on the Landau-Ginzburg-Devonshire theory. The study elucidates the underlying physics of ZrO₂ capacitors, providing insights into the hysteresis loop, their energy storage and dissipation mechanisms. The developed model accurately simulates the nonlinear responses and frequency-dependent dynamical resistance of ZrO₂ capacitors, paving the way for their potential utilization as oscillators and amplifiers. Overall, this dissertation contributes to the advancement of ferroelectric materials research by elucidating the factors influencing polarization characteristics, scaling effects, and dynamic behavior in HZO and ZrO₂ capacitors. The findings presented herein offer valuable insights for the design and optimization of ferroelectric-based electronic devices, ranging from memory applications to neuromorphic computing and beyond.