Variability in Ferroelectric Hf_0.5Zr_0.5O₂: Physical Insights and Implications for Memory Applications

Ferroelectric (FE) hafnium-zirconium-oxide (Hf<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0.5</inf> Zr<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0.5</inf> O<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> or HZO) is a promising candidate for next-generation electronics [1]. However, device-to-device variations in HZO remain a key challenge [1, 2]. Addressing this issue requires analyzing the interplay between polycrystallinity, multi-domain (MD) polarization switching and other HZO attributes [1, 2]. HZO exhibits an anisotropic crystal structure [3, 4], with alternating polar-spacer layers (APSL) in one lateral direction and continuous polar layers (CPL) in the other (Fig. 1a). This anisotropy affects polarization (P) domain formation [3] and leads to direction-dependent MD switching [4], which, in turn, affects variability in HZO. This work presents the physical insights into the mechanisms governing variability in HZO accounting for such unique attributes. We begin with first-principles simulations to provide atomic-scale insights. These findings are utilized to study metal-ferroelectric-insulator-metal (MFIM) capacitors using 3D phase-field simulations and analyze variability across different ferroelectric thicknesses ($T_{F E}$) and set voltages ($V_{S E T}$). Finally, we present how these variability trends affect the trade-offs between distinguishability of binary states and energy consumption for the SET operation in FE memories.