Characteristics of Low‐Energy Phases of Hafnia and Zirconia from Density Functional Theory Calculations

Abstract

A systematic simulation study of low‐energy phases of HfO2 and ZrO2, including 24‐atomic cells derived from 180° interphases, leads to a new monoclinic Pc phase (mIII) with a monoclinic angle and a polarization of 0.3 C m−2. This opens up a new transition path toward the monoclinic P2 1 /c phase (m) starting from the tetragonal P4 2 /nmc phase (t), with comparable lower‐energy barriers, where the high‐symmetric phases show the largest temperature dependence. The tetragonal P4 2 /nmc phase, the cubic (c) phase, and the less investigated cubic (cII) phase are favored.

Ferroelectric ZrO2 phases from infrared spectroscopy

“…† Additionally, as mentioned in the introduction, first-principles calculations suggest the stability of other polar phases, including the Pc and Pmn2 1 phases. Although these phases have not been observed experimentally yet, the Pc phase was found to have low bulk energy, similar to the o phase in HfO 2 and ZrO 2 , 42 while the Pmn2 1 phase was found to have lower energy than the t phase in HfO 2 , 41,42 and higher energy in ZrO 2 . 42 The IR active phonon modes of these two phases were also calculated and are given in the ESI.…”

“…Although these phases have not been observed experimentally yet, the Pc phase was found to have low bulk energy, similar to the o phase in HfO 2 and ZrO 2 , 42 while the Pmn2 1 phase was found to have lower energy than the t phase in HfO 2 , 41,42 and higher energy in ZrO 2 . 42 The IR active phonon modes of these two phases were also calculated and are given in the ESI. † The simulated IR absorbance of ZrO 2 thin films reveals distinct differences between polar and non-polar phases, in contrast to XRD where most phases, especially the polar ones (Fig.…”

“…38 First-principles calculations have demonstrated other possible ferroelectric phases in HfO 2 and ZrO 2 materials, such as rhombohedral R3, 39 orthorhombic Pmn2 1 , 40,41 and monoclinic Pc. 42 In addition to the ferroelectricity in HfO 2 and ZrO 2 , antiferroelectricity has also been observed in pure ZrO 2 , and ZrO 2 -rich thin films. [43][44][45][46] Most studies in the literature on HfO 2 and ZrO 2 ferroelectric thin films use X-ray Diffraction (XRD) for structure determination.…”

Thickness dependence of the crystallization and phase transition in ZrO 2 thin films

“…For instance, the diluted magnetism could only appear in the t-phase for undoped ZrO 2 thin films [22]. Recently, the ferroelectricity has also been studied in ZrO 2 films [23][24][25]. For instance, Silva et al [23] reported an unprecedented ferroelectric structure in pure ZrO 2 thin films, opening up a new route to ferroelectric devices using Zr-rich HZO.…”

Ferroelectricity in Epitaxial Tetragonal ZrO2Thin Films

“…[22,38,39] This phase is also found to be energetically close to the ground state mphase. [39,40] Additionally, the t-phase has been identified as a potential driver of antiferroelectric behavior in ZrO 2 polycrystalline thin films [41] ; this has been explained as a transition from the nonpolar t-phase to the polar o-phase. [41] This second approach is the most commonly adopted in the literature.…”