Prominent Size Effects without a Depolarization Field Observed in Ultrathin Ferroelectric Oxide Membranes

Haoying Sun, Jiahui Gu, Yongqiang Li, Tula R. Paudel, Di Liu, Jierong Wang, Yipeng Zang, Chengyi Gu, Jiangfeng Yang, Wenjie Sun, Zhengbin Gu, Evgeny Y. Tsymbal, Junming Liu, Houbing Huang, Di Wu, and Yuefeng Nie

Phys. Rev. Lett. 130, 126801 – Published 21 March 2023

Abstract

The increasing miniaturization of electronics requires a better understanding of material properties at the nanoscale. Many studies have shown that there is a ferroelectric size limit in oxides, below which the ferroelectricity will be strongly suppressed due to the depolarization field, and whether such a limit still exists in the absence of the depolarization field remains unclear. Here, by applying uniaxial strain, we obtain pure in-plane polarized ferroelectricity in ultrathin ${SrTiO}_{3}$ membranes, providing a clean system with high tunability to explore ferroelectric size effects especially the thickness-dependent ferroelectric instability with no depolarization field. Surprisingly, the domain size, ferroelectric transition temperature, and critical strain for room-temperature ferroelectricity all exhibit significant thickness dependence. These results indicate that the stability of ferroelectricity is suppressed (enhanced) by increasing the surface or bulk ratio (strain), which can be explained by considering the thickness-dependent dipole-dipole interactions within the transverse Ising model. Our study provides new insights into ferroelectric size effects and sheds light on the applications of ferroelectric thin films in nanoelectronics.

Received 26 January 2022
Revised 28 June 2022
Accepted 2 February 2023

DOI:https://doi.org/10.1103/PhysRevLett.130.126801

Physics Subject Headings (PhySH)

Dielectric properties Ferroelectricity Piezoelectricity

Ultrathin films

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Haoying Sun ^1,2, Jiahui Gu^1,2, Yongqiang Li ^3,4, Tula R. Paudel ^5,6, Di Liu ⁷, Jierong Wang ^1,2, Yipeng Zang^1,2,8, Chengyi Gu^1,2, Jiangfeng Yang^1,2, Wenjie Sun ^1,2, Zhengbin Gu^1,2, Evgeny Y. Tsymbal ^5,9, Junming Liu³, Houbing Huang⁷, Di Wu^1,2,*, and Yuefeng Nie ^1,2,†

¹National Laboratory of Solid State Microstructures, Jiangsu Key Laboratory of Artificial Functional Materials, College of Engineering and Applied Sciences, Nanjing University, Nanjing 210093, China
²Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
³National Laboratory of Solid State Microstructures and Department of Physics, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
⁴State Key Laboratory of Laser Interaction with Matter, Northwest Institute of Nuclear Technology, Xi’an, Shaanxi 710024, China
⁵Department of Physics and Astronomy, University of Nebraska–Lincoln, Lincoln, Nebraska 68583, USA
⁶Department of Physics, South Dakota School of Mines and Technology, Rapid City, South Dakota 57701, USA
⁷Advanced Research Institute of Multidisciplinary Science, Beijing Institute of Technology, Beijing 100081, China
⁸School of Materials Science and Engineering, Anhui University, Hefei 230601, China
⁹Nebraska Center for Materials and Nanoscience, University of Nebraska–Lincoln, Lincoln, Nebraska 68588, USA

^*diwu@nju.edu.cn
^†ynie@nju.edu.cn

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Vol. 130, Iss. 12 — 24 March 2023

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Images

Figure 1
Thickness-dependent domain structures under a fixed strain of 1.8%. (a) Schematic of the device for strain engineering. The STO membranes are attached to a polymer substrate (PEN) using epoxy. The cantilever is placed with its arm perpendicular to the stretching direction to detect the in-plane polarization along the [100] direction. (b) High-resolution XRD $2 θ - ω$ scans for 10–20 u.c. thick $STO / epoxy / PEN$ samples. Asterisks denote the PEN diffraction peaks; the vertical dotted line marks the position of the STO (002) diffraction peak. (c) LPFM height, amplitude, and phase images (from top to bottom) for STO membranes with various thicknesses. Red arrows denote the polarization orientations. The scale bars are 400 nm.
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Figure 2
Quantitative analysis and phase-field simulations. Average domain sizes along the [010] (a) and the [100] (b) directions illustrating strong dependence on the film thickness. Insets display the corresponding positions of five linecuts to count the number of domains for meaningful statistics. (c) Average domain area as a function of film thickness. Insets: Two types of domain configurations. (d) Phase-field simulations of domain patterns from 15 and 5 u.c. STO membranes with a strain of 1.8%, respectively. Domain wall (DW); error bars represent the standard deviations.
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Figure 3
Thickness-dependent $T_{c}$ of strained STO membranes. (a) Dielectric characterizations revealing strain-tunable $T_{c}$ in a 15 u.c. $STO / epoxy / PEN$ sample. Considering the relatively broader peaks of the measured curves, the first derivative of capacitance was used to extract the peak positions (black arrows). (b) Optical image of coplanar interdigital electrodes deposited on the surface of the 15 u.c. STO membrane. (c) The extracted $T_{c}$ values of 10–20 u.c. STO as a function of uniaxial strain. Error bars include the uncertainty of peak positions extracted from multiple measurements (vertical) and errors in measuring strain (horizontal). (d) Normalized average deviation ( $V_{adev}$ ) of amplitude intensity vs uniaxial strain revealing domain formation at room temperature. Curves for various thicknesses are offset for clarity. The vertical dashed lines indicate the position of critical strain for room-temperature ferroelectricity. (e) Thickness-dependent critical strain for stretched STO membranes. Error bars come from the measurement error of strain.
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Figure 4
The origin of the ferroelectric size effects. (a) Schematic illustration of the dipole-dipole interaction in a transverse Ising model considering nearest-neighbor interactions. $J_{s}$ is the surface dipole-dipole interaction strength, while $J$ is the bulk dipole-dipole interaction strength. The green triangle and orange box represent the nearest-neighbor interactions at the surface and in the bulk, respectively. (b) Summarized phase diagram of STO membranes unveiling how ferroelectricity (domain area and $T_{c}$ ) evolves with film thickness and uniaxial strain. Solid lines represent the experimental results, while the green dashed line is the simulated data obtained from the transverse Ising model (see Fig. S10). Different scales are used in the strain axis for clarification.
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