Effect of thickness and surface composition on the stability of polarization in ferroelectric ${\mathrm{Hf}}_{x}{\mathrm{Zr}}_{1\text{\ensuremath{-}}x}{\mathrm{O}}_{2}$ thin films

Effect of thickness and surface composition on the stability of polarization in ferroelectric ${Hf}_{x} {Zr}_{1 − x} O_{2}$ thin films

Adrian Acosta, J. Mark P. Martirez, Norleakvisoth Lim, Jane P. Chang, and Emily A. Carter

Phys. Rev. Materials 7, 124401 – Published 4 December 2023

Abstract

Using density functional theory, we find that tailoring the surface composition provides a route to stabilize the polar phases of the promising ferroelectric material, ${Hf}_{x} {Zr}_{1 − x} O_{2}$ . First, we show that for pure $Hf O_{2}$ , controlling the positively polarized surface to be relatively oxygen rich adequately screens the ferroelectric surface charges and stabilizes the polar orthorhombic phase. We then demonstrate that the ferroelectric polarization, as measured by the structural polar displacements, increases with decreasing thickness, leading to the emergence of a polar rhombohedral-like phase at the ultrathin limit (1.5 unit cells). Our findings extend to the cases of ${Hf}_{0.5} {Zr}_{0.5} O_{2}$ and $Zr O_{2}$ , both of which have surface energy landscapes similar to that of $Hf O_{2}$ . These findings are consistent with and offer insights into the observed absence of a ferroelectric thickness limit in ${Hf}_{x} {Zr}_{1 − x} O_{2}$ -based thin films.

Received 21 March 2022
Revised 10 October 2023
Accepted 2 November 2023

DOI:https://doi.org/10.1103/PhysRevMaterials.7.124401

Physics Subject Headings (PhySH)

Ferroelectricity

Oxides Thin films

Density functional calculations

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Adrian Acosta¹, J. Mark P. Martirez ^1,2, Norleakvisoth Lim¹, Jane P. Chang ^1,*, and Emily A. Carter ^1,2,3,†

¹Department of Chemical and Biomolecular Engineering, University of California, Los Angeles, Los Angeles, California 90095, USA
²Princeton Plasma Physics Laboratory, Princeton, New Jersey 08540, USA
³Department of Mechanical and Aerospace Engineering and the Andlinger Center for Energy and the Environment, Princeton University, Princeton, New Jersey 08544-5263, USA

^*jpchang@ucla.edu
^†eac@princeton.edu

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Vol. 7, Iss. 12 — December 2023

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Figure 1
(a) Profile views (after ionic relaxation) of the 11-Hf-half-layer-thick $Hf O_{2}$ supercell slabs constructed with symmetric (1.0-O/1.0-O) or asymmetric (P+:1.5-O/P−:1.0-O) surface terminations. Green spheres are Hf; red spheres are O. Plane-averaged electrostatic potential (top panel) and plane-averaged electron density ( $ρ_{plane − avg}$ , bottom panel) are shown for (b) symmetrically and (c) asymmetrically terminated slabs along the direction of the surface normal, before and after ionic relaxation. The $z$ coordinate starts from the middle of the vacuum (set to $z = 0 Å$ ) through the oxide from the P− surface [ $z \sim 5 Å$ , bottom of slabs in (a)] to the P+ surface [ $z \sim 33 Å$ , top of slabs in (a)] and back to the middle of the vacuum ( $z = 43.52 Å$ ). The plane-averaged potentials and electron densities $(ρ_{plane - avg})$ are plotted from $z = 2.5$ to $37.5 Å$ to ensure small details remain visible in the composite figure. The potentials in the top panels are referenced to the Fermi level (set to 0), depicted with the dashed horizontal orange line. (d) Interlayer spacing from one Hf half layer to the next for asymmetrically terminated slabs along the direction of the surface normal. The $N th$ Hf half layer begins at the P− surface and ends at the P+ surface [as labeled in (a)]. Dashed purple line shows the bulk value for reference. (e) Intralayer spacing between O planes within each O half layer for asymmetrically terminated slabs along the direction of the surface normal. Each O half layer partitions into two O planes of two O atoms each and we use the distance of the average $z$ coordinate of the two O in each plane. Illustration of the measure for this displacement is shown via dashed lines for $N = 1$ and $N = 2$ in (a). The $N th$ O half layer begins at the P− surface and ends at the P+ surface [as labeled in (a)]. Dashed purple line shows the bulk value for reference.
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Figure 2
(a) Average value of the polar displacements of O [as defined in Fig. 1] for asymmetrically terminated orthorhombic $Hf O_{2}$ slabs with varying thickness (the layer-by-layer displacement profiles, as was plotted for the case of 11 Hf half layers in Fig. 1, are shown in Fig. S4 in the SM [53]). Inset figures show the 11- and seven-Hf-half-layer-thick slabs (green spheres are Hf; red spheres are O) and the dashed purple line provides a comparison to the bulk polar displacement. At three Hf layers (labeled “critical thickness”) the asymmetric $Hf O_{2}$ structure [shown in bottom panel (c)] deviates significantly from the bulk orthorhombic phase. Consequently, we do not plot its average O displacement. In its place, we plot the average polar displacement for the symmetric slab [top panel (c)]. (b) Net electrostatic potential as a function of total slab thickness for symmetrically and asymmetrically terminated orthorhombic $Hf O_{2}$ slabs, before (dark cyan) and after (pink) ionic relaxation. (c) Optimized structures for the symmetric (top panel) and asymmetric (bottom panel) $Hf O_{2}$ slabs at a thickness of three Hf half layers.
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Figure 3
(a) Profile views of the relaxed structures for orthorhombic ${Hf}_{0.5} {Zr}_{0.5} O_{2}$ supercell slabs. The compositions of the outermost layers in terms of atoms per formula unit (p.f.u.) of the surface are labeled for the top and bottom layer above each structure (see Sec. 3a and Fig. S1 [53] for the explanation of the nomenclature). The middle three Hf/Zr and two O half layers for all slabs are fixed to their bulklike arrangement with the polarization direction normal to the surface as labeled. The fainter atoms are farther away from the viewer. Plots of the surface energy as a function of (b) temperature from 100 to 1100 K at 1 bar $O_{2}$ and (c) pressure from $10^{- 12}$ to $10^{2}$ bar at 900 K corresponding to the slabs in (a).
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Figure 4
(a) Profile views of the relaxed structures for orthorhombic $Zr O_{2}$ supercell slabs. The composition of the outermost layers in terms of atoms p.f.u. of the surface is labeled for the top and bottom layer above each structure (see Sec. 3 3a and Fig. S1 [53] for the explanation of the nomenclature). The middle three Zr and two O half layers for all slabs are fixed to their bulklike arrangement with the polarization direction normal to the surface as labeled. The fainter atoms are farther away from the viewer. Plots of the surface energy as a function of (b) temperature from 100 to 1100 K at 1 bar $O_{2}$ and (c) pressure from $10^{- 12}$ to $10^{2}$ bar at 900 K corresponding to the slabs in (a).
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Figure 5
(a) Average value of the polar displacements of O [see Fig. 1 for definition] for ${Hf}_{0.5} {Zr}_{0.5} O_{2}$ . Dashed purple line provides a comparison to the bulk polar displacement. Inset figures show profile view of 11- and seven-layer-thick slabs (green spheres are Hf, dark cyan spheres are Zr, and red spheres are O). At three layers (labeled “critical thickness”) the asymmetric ${Hf}_{0.5} {Zr}_{0.5} O_{2}$ structure [shown in bottom panel (b)] deviates significantly from the bulk orthorhombic phase. Thus, as for the case of $Hf O_{2}$ , we do not plot its average O displacement. In its place, the average polar displacement is plotted for the symmetric slab [top panel (b)]. (b) Three-layer optimized structures for the symmetric (top panel) and asymmetric (bottom panel) ${Hf}_{0.5} {Zr}_{0.5} O_{2}$ slab structures.
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Figure 6
(a) Average value of the polar displacements of O [see Fig. 1 for definition] for $Zr O_{2}$ . Dashed purple line provides a comparison to the bulk polar displacement. Inset figures show profile view of 11- and seven-layer-thick slabs (green spheres are Zr and red spheres are O). (b) Three-layer optimized structures for the symmetric (top panel) and asymmetric (bottom panel) $Zr O_{2}$ slab structures.
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Effect of thickness and surface composition on the stability of polarization in ferroelectric HfxZr1−xO2 thin films

Adrian Acosta, J. Mark P. Martirez, Norleakvisoth Lim, Jane P. Chang, and Emily A. Carter

Phys. Rev. Materials 7, 124401 – Published 4 December 2023

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Effect of thickness and surface composition on the stability of polarization in ferroelectric ${Hf}_{x} {Zr}_{1 − x} O_{2}$ thin films