Abstract text (incl. figure legends and references)

Due to the recent discovery of ferroelectricity in doped Hafnium Oxide (HfO₂) film, HfO₂-based materials have significantly attracted lots of attention in the semiconductor industry because of their strong compatibility with Si-based Complementary Metal-Oxide-Semiconductor (CMOS) and thereby their potential for fully integrated ferroelectric devices. The equilibrium phase diagram of bulk HfO₂ consists of non-ferroelectric polymorphs that are the monoclinic (P2₁/c, O phase), tetragonal (P4₂/nmc, T phase), and cubic (Fm-3m, C phase) phases. The ferroelectric HfO₂ is the metastable, orthorhombic phase (Pca2₁), where a unit cell is divided into active cell/inactive cell, in which oxygen atoms can/cannot generate electric dipole. Based on the flat phonon band theory, the inactive cell is predicted to be an inherent spacer between neighboring active cells and therefore inactive cells enable electric dipoles to switch without forming a domain wall [1].The domain-wall-free ferroelectric behavior in HfO₂ has been directly identified by TEM analyses [2,3], but is still challenging due to the polymorphism in doped HfO₂ and pico-metric regime of structural modulation. In this work, we present an atomistic behavior of ferroelectricity in epitaxially grown Yttria-doped HfO₂ (YHO). The crystallographic structure of YHO is quantitatively analyzed by scanning transmission electron microscopy combined with computational techniques via deep machine learning. Furthermore, we apply a 4D-STEM ptychography to visualize the electric field distribution in YHO. Combined experimental results show YHO can hold polarization within a width of to a single unit cell. Boundary cells, inactive cells between the up- and down-polarized cells, are investigated by our first-principle calculation, and our atomistic analysis confirmed that boundary cell possesses the same structure with the inactive cell in bulk YHO, indicative of the absence of the domain wall. This result gives the new insight into the realization of unit cell scale control of ferroelectric materials.

[1] Lee et al., Science 369 (6509), 1343-1347 (2020)

[2] Xu et al., Nature Materials 20, 826–832 (2021)

[3] Kang et al., Science 376 (6594), 731-738 (2022)