Ferroelectricity in HfO₂ from a Coordination Number Perspective

Abstract

Ferroelectricity observed in thin-film HfO 2 , either doped with Si, Al, and so forth or in the Hf 0.5 Zr 0.5 O 2 form, has gained great technical significance. While a trilinear coupling between phonon modes could explain its ferroelectric distortion, from a practical perspective, one may be concerned with a theory that is more straightforward to predict similar ferroelectric candidates through some apparent features of HfO 2 and ZrO 2 . In this work, we propose that the 7 cation coordination number of HfO 2 /ZrO 2 lies at the heart of this ferroelectricity, which stems from the proper ionic radii of Hf/Zr compared with O. Among the numerous compounds with a non-centrosymmetric nature, for example, the mm2 point group, HfO 2 and ZrO 2 are special in that they are close to the border of 7 and 8 cation coordination, such that the 8-coordination tetragonal intermediate phase could greatly reduce the switching barrier. Other 7-coordination candidates, including SrI 2 , TaON, YSBr, and YOF, are also studied in comparison to HfO 2 /ZrO 2 , and six switching paths are analyzed in detail for the Pca2 1 phase. A rule of the preferred switching path in terms of the ionic radii ratio and coordination number has been established. We also show the possible route from the ferroelectric Pca2 1 phase to the monoclinic P2 1 /c phase in HfO 2 , which is relevant to the fatigue phenomenon.

In search of Pca21 phase ferroelectrics

“…The possible reason for this is that Lu 3+ is smaller than Y 3+ , and Fanions may penetrate the z = 0 plane (made of Lu 3+ ) to prefer the external path. It is interesting to note that the preferred path of LuOF corresponds to the larger P S , which is quite unusual among Pca2 1 ferroelectrics [35]. Subsequently, we compare LuOF and YOF with HfO 2 in terms of their theoretical ferroelectric and electronic properties.…”

“…On the other hand, table 2 lists the ten candidate materials that exhibit a finite polarization in their Pca2 1 phase. Among these, YOF has already been reported [35] but is included in our comparison due to its potentially excellent ferroelectric properties. Phonon instability is not observed in any of these ten compounds in their relaxed Pca2 1 phase.…”

“…The ferroelectric distortion in HfO 2 /ZrO 2 has an entirely different manifestation, involving the transition of certain O anions between two equivalent positions [34]. Recently, Yuan et al [35] proposed that the ferroelectricity of hafnia-based ferroelectrics stems from their special cation/anion ionic radius ratio, which points to the seven-coordination (7C) configuration. The so-called 7C theory predicts that HfO 2 and ZrO 2 should not be the only member of this category, and more binary or ternary compounds, such as SrI 2 and YSBr, are listed as potential ferroelectric candidates.…”

“…Important parameters for some known or predicted ferroelectric candidates, from[54] (CaO2, SrO2, Al2O3, Ga2O3),[35] (HfO2 and YOF) and this work (LuOF). All the band gaps were calculated in this work, with the HSE06 hybrid functional or shell GGA-1/2.…”

Hafnia-Based Ferroelectric Memory: Device Physics Strongly Correlated with Materials Chemistry

“…In situations where there is no mechanical strain, it would be even more difficult to induce symmetry breaking. In this case, a specific range of the relative ratio of the radii of cation and anion may be a key factor as Yuan et al recently suggested (Figure b). According to their computational simulation, the coordination number 7 of HfO 2 and ZrO 2 , arising from their characteristic ionic radii ratio value at the boundary between coordination numbers 6 and 8, is critical for the ferroelectricity with a rather strong crystallographic distortion with noncentrosymmetry …”