Small Signal Capacitance in Ferroelectric HZO: Mechanisms and Physical Insights

TL;DR

This paper uses phase-field simulations to analyze the physical mechanisms behind small signal capacitance in ferroelectric HZO, revealing how domain responses influence capacitance behavior and memory window characteristics.

Contribution

It introduces a simulation framework that closely mimics experimental measurements, providing new insights into domain contributions and thickness effects on ferroelectric capacitance.

Findings

Domain bulk and wall responses both contribute to butterfly capacitance.

Increasing ferroelectric thickness enhances polarization capacitance.

Maximum memory window varies non-monotonically with HZO thickness.

Abstract

This study presents a theoretical investigation of the physical mechanisms governing small signal capacitance in ferroelectrics, focusing on Hafnium Zirconium Oxide. Utilizing a time-dependent Ginzburg Landau formalism-based 2D multi-grain phase-field simulation framework, we simulate the capacitance of metal-ferroelectric-insulator-metal (MFIM) capacitors. Our simulation methodology closely mirrors the experimental procedures for measuring ferroelectric small signal capacitance, and the outcomes replicate the characteristic butterfly capacitance-voltage behavior. We delve into the components of the ferroelectric capacitance associated with the dielectric response and polarization switching, discussing the primary physical mechanisms - domain bulk response and domain wall response - contributing to the butterfly characteristics. We explore their interplay and relative contributions to the capacitance and correlate them to the polarization domain characteristics. Additionally, we investigate the impact of increasing domain density with ferroelectric thickness scaling, demonstrating an enhancement in the polarization capacitance component (in addition to the dielectric component). We further analyze the relative contributions of the domain bulk and domain wall responses across different ferroelectric thicknesses. Lastly, we establish the relation of polarization capacitance components to the capacitive memory window (for memory applications) and reveal a non-monotonic dependence of the maximum memory window on HZO thickness.