HAFNIUM-ZIRCONIUM-OXIDE BASED FERROELECTRIC DEVICES: PHASE-FIELD MODELING AND PHYSICAL INSIGHTS

<p dir="ltr">Doped Hafnium Oxide (\ce{HfO2})-based ferroelectric (FE) devices are promising candidates for next-generation logic and memory technologies. Unlike traditional perovskite ferroelectrics, \ce{HfO2} provides key advantages such as CMOS process compatibility, scalability, and robust ferroelectricity. However, FE \ce{HfO2} is inherently polycrystalline and exhibits an anisotropic crystal structure, whose influence on device behavior and performance remains poorly understood. In this thesis, we develop physics-based phase-field models for FE devices that explicitly capture the polycrystalline and anisotropic nature of zirconium-doped hafnium oxide (\ce{Hf_{0.5}Zr_{0.5}O_2} or \ce{HZO}). Using these models, we systematically study how the material properties of ferroelectric \ce{HZO} affect device performance and propose strategies for application-specific optimization.</p><p><br></p><p dir="ltr">A major challenge in integrating \ce{HZO} into scaled technology nodes is its polycrystalline nature. To study its impact, we develop a 3D multi-grain phase-field simulation framework for metal-ferroelectric-insulator-metal (MFIM) capacitors, modeling \ce{HZO} at the lattice scale. The framework generates realistic polycrystalline structures with non-uniform grain shapes and sizes using the grain growth equation. The polarization switching and electrostatic behavior of these polycrystalline FE devices are modeled by self-consistently solving the time-dependent Ginzburg-Landau (TDGL) and Poisson's equations. Analyzing the formation of multi-domain (MD) polarization configurations and switching via domain growth and nucleation, we relate MFIM device characteristics to grain orientations of the polycrystalline \ce{HZO}. Our simulation results reveal that minor hysteresis loops can originate from partial MD switching in individual grains, rather than complete switching of only a few grains. They also show that polycrystallinity induces deterministic cycle-to-cycle variations in the MFIM characteristics due to the presence of multiple closely spaced local minima in the multi-domain polarization energy landscape.</p><p><br></p><p dir="ltr">We find that polycrystallinity-induced device-to-device variations in the remanent polarization depend non-monotonically on the maximum voltage applied to the MFIM capacitors, with maximum variations near the coercive voltage. This behavior arises from the voltage dependence of the domain nucleation and growth mechanisms, and the associated amount of polarization switched per unit voltage. Near the coercive voltage, domain nucleation leads to rapid polarization switching, which amplifies the intrinsic polycrystalline variations between devices, leading to higher device variability. Reducing ferroelectric thickness or increasing insulator thickness increases domain density in the ferroelectric, which suppresses domain nucleation and lowers the maximum polarization switching slope. This decreases the maximum variability across devices. We further extend the framework to capture the dynamics of polarization switching and analyze the influence of voltage pulse amplitude and duration on device variability. Our results reveal that lower-amplitude, longer-duration voltage pulses yield more uniform switching across devices, achieving the target mean polarization state with less variability than higher-amplitude, shorter-duration pulses.</p><p><br></p><p dir="ltr">Simulation models of polycrystalline FE devices differ in how they treat inter-grain interactions. Using our phase-field framework, we systematically study the effects of inter-grain electrostatic and polarization-gradient interactions on device performance and simulation outcomes. We demonstrate that different interaction choices, ranging from fully coupled to decoupled grains, predict fundamentally different domain configurations and switching behaviors: fully coupled grains exhibit continuous, correlated MD switching, while decoupled grains switch independently in a single domain fashion. While the different interaction choices can be calibrated to match experimental characteristics, only the models that include inter-grain electrostatic interactions capture cycle-to-cycle variations, underscoring the importance of these interactions. </p><p><br></p><p dir="ltr">Ferroelectric capacitors exhibit non-linear and hysteretic butterfly-shaped small-signal capacitance voltage ($C$-$V_0$) characteristics, whose physical origins remain poorly understood. To investigate this, we develop a 2D multigrain phase field framework that mirrors experimental methodology and reproduces the butterfly $C$-$V_0$ response. Separating the total capacitance into dielectric and polarization components, we find that the dielectric contribution exhibits an inverted butterfly shape, while the polarization capacitance follows the butterfly shape. Our analysis identifies three primary mechanisms driving polarization capacitance in MFIM stacks: (1) domain bulk response, (2) wide domain wall response at the FE-DE interface, and (3) domain wall vicinity response. Their relative contributions depend on the domain density of the FE film, which is determined by the applied bias voltage and the MFIM stack configuration. Exploring the ferroelectric thickness scaling reveals that in thicker films with lower domain density, domain bulk capacitance dominates. And as FE thickness scales down, domain density increases, enhancing the dielectric and polarization capacitances, with domain wall contribution becoming dominant. This transition in the dominant capacitance component produces a non-monotonic dependence of the capacitive memory window on ferroelectric thickness. In metal-ferroelectric-metal (MFM) stacks, the absence of a dielectric layer weakens depolarization fields, reducing the domain density and making the domain bulk component dominant. </p><p><br></p><p dir="ltr">We next examine the anisotropic crystal structure of the polar orthorhombic phase of \ce{HZO}, which features continuous polar layers (CPL) and alternating polar spacer layers (APSL) along orthogonal in-plane directions. To capture this anisotropy, we develop a 3D anisotropic multi-grain phase-field framework for MFIM capacitors at both lattice and sub-lattice levels. The simulation results reiterate the first principles findings that spacer layers enforce the formation of unit-cell-wide domains along the APSL direction at the device level. They also show the direction-dependent polarization switching: with domain growth dominating along the CPL direction, while the polarization switches layer-by-layer along the APSL direction. We correlate this behavior to device-to-device variability and evaluate its implications for non-volatile memory, highlighting the trade-offs between memory window, write energy, and read error probability as ferroelectric thickness decreases.</p><p><br></p><p dir="ltr">We then extend the 3D anisotropic multi-grain phase-field framework to ferroelectric field effect transistors (FEFETs) by self-consistently solving Poisson's equation, TDGL equation, and semiconductor charge transport via drift-diffusion. Our analysis uncovers the influence of anisotropic domain structure and direction-dependent polarization switching of \ce{HZO} on the FEFET characteristics. In particular, we show that the orientation of APSL and CPL directions relative to the FET channel plays a crucial role in device behavior. Typically, in FEFETs, polarization switching of the FE layer initiates near the source and drain regions where the electric field is strongest. When APSL aligns with the channel length, spacer layers suppress domain growth along the channel length, limiting polarization change between set and reset states. As a result, FEFETs with this configuration exhibit a low threshold voltage modulation and a narrow memory window. In contrast, when APSL is oriented along the channel width or CPL aligns with channel length, domains grow unhindered along the channel, producing a larger polarization change. These devices exhibit stronger threshold voltage modulation and a broader memory window compared to the earlier case, making them attractive for multi-state memory applications. Importantly, this analysis shows that FEFET behavior depends not only on the out-of-plane polar axis but also on the in-plane orientation of the FE layer, which can play a significant role in device variability.</p><p><br></p><p><br></p><p dir="ltr">Finally, we propose that anisotropic polarization switching and domain confinement along the APSL direction in \ce{HZO} lead to a weaker scaling of coercive field ($E_C$) with ferroelectric thickness ($d$). Experiments show that $E_C$ increases as $d$ decreases, but at a slower rate than predicted by the Janovec-Kay-Dunn (JKD) theory ($E_C \propto d^{-2/3}$) for perovskites. To explain this behavior, we model the unit-cell-wide domains as a half-prolate elliptical cylinder geometry and analytically derive the associated nucleation and growth energetics. Considering the energy favorability of polarization switching, we arrive at a revised scaling law for FE \ce{HfO2}: $E_c\propto d^{-1/2}$. This modified exponent of $1/2$ aligns more closely with experimental results across a broad range of atomic layer deposition (ALD)-grown ferroelectric \ce{HfO2} films.</p>