Domain distributions in tetragonal ferroelectric thin films probed by optical second harmonic generation

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Domain distributions in tetragonal ferroelectric thin films probed by optical second harmonic generation

Gabriele De Luca and Manfred Fiebig

Phys. Rev. Research 5, 043055 – Published 17 October 2023

Abstract

Controlling the domain arrangement in a ferroelectric material is the key to accessing its functional properties. However, when a ferroelectric thin film is inserted into a multilayer device architecture, conventional characterization techniques provide limited access to the buried distribution of polar states. Here we show that a combination of nondestructive remote probing by nonlinear optics and symmetry analysis allows the unique distinction of the polar orientations coexisting in tetragonal ferroelectric films. We quantify the volumetric ratio between in-plane and out-of-plane polarized domains, and we further illustrate that our approach incorporates the strain-induced changes to the nonlinear susceptibility tensor. We perform the experiment on $Pb ({Zr}_{0.2} {Ti}_{0.8}) O_{3}$ thin films, but the generality of the approach permits its extension to other ferroelectric materials.

Received 23 November 2022
Revised 11 July 2023
Accepted 3 August 2023

DOI:https://doi.org/10.1103/PhysRevResearch.5.043055

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Ferroelectric domains

Ferroelectrics Thin films

Optical second-harmonic generation

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Gabriele De Luca ^1,2,* and Manfred Fiebig ^1,†

¹Department of Materials, ETH Zurich, Vladimir-Prelog-Weg 4, 8093 Zurich, Switzerland
²Institut de Ciència de Materials de Barcelona (ICMAB-CSIC), 08193 Bellaterra (Barcelona), Spain

^*gdeluca@icmab.es
^†manfred.fiebig@mat.ethz.ch

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Vol. 5, Iss. 4 — October - December 2023

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Images

Figure 1
Schematic of the transmission geometry used to collect the SHG data. The laboratory and global reference systems are depicted in the top-left part of the figure. The local reference system of each domain pair is shown in the right part of the figure. The sample-rotation axis along $y = y^{'}$ is parallel to ${[010]}_{PZT}$ . By rotating the sample by an angle τ, we project both the ${[001]}_{PZT}$ and ${[100]}_{PZT}$ onto the $x^{'}$ axis. The possible tetragonal ferroelectric domains in the sample are indicated in yellow in the figure, with the white arrows indicating the polarization orientation. For simplicity, $c^{-}$ domains are not considered. The polarization angles of the incoming ( $0^{\circ}$ , $45^{\circ}$ , $90^{\circ}$ , $135^{\circ}$ ; in red, at frequency ω) and outgoing light ( $0^{\circ}$ , $90^{\circ}$ ; in blue, at frequency 2ω) determine the $α_{in}^{ω}$ / $α_{out}^{2 ω}$ configuration. These angles are defined to be $0^{\circ}$ when the polarization is parallel to the $y^{'}$ axis.
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Figure 2
Strain-engineered domain distribution. (a) A PZT film of 15 nm grown on (110)-oriented DSO exhibits a single-domain configuration with its $c$ axis oriented out of plane. The coordinate systems indicate the epitaxial relation between PZT and DSO. (b) A PZT film of 75 nm results in a $a − c$ domain configuration. The in-plane $a$ domains are predominantly oriented along ${[001]}_{DSO}$ as documented by the PFM analysis shown in Ref. [43]. We disregard the most general case with the coexistence of substantial fractions of $a_{1} − a_{2} − c$ domains as this is not experimentally observed.
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Figure 3
SHG intensity for different polarization configurations for the single- $c$ -domain PZT film, using the labeling introduced in Fig. 1, is shown as a function of the sample-rotation angle $τ$ . The data are grouped such that the $α_{in}^{ω} / 0^{\circ}$ and $α_{in}^{ω} / 90^{\circ}$ configurations are shown in the left and right column, respectively. The top (bottom) row is characterized by $α_{in}^{ω} = 0^{\circ}$ , $90^{\circ}$ ( $α_{in}^{ω} = 45^{\circ}$ , $135^{\circ}$ ). Data are normalized to the $90^{\circ} / 90^{\circ}$ configuration at $τ = 20^{\circ}$ . The dashed lines indicate the instrumental background. Continuous lines correspond to the fit model of Eqs. (4-5) and (4-6) with all data fitted with one set of parameters (Table 1). Note that all eight fit lines vanish for $τ = 0^{\circ}$ and are symmetric for $\pm τ$ , as required by the symmetry of the model.
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Figure 4
SHG intensity for different polarization configurations for the multidomain PZT film, using the labeling introduced in Fig. 1, is shown as a function of the sample-rotation angle $τ$ . The data are grouped such that the $α_{in}^{ω}$ / $0^{\circ}$ and $α_{in}^{ω}$ / $90^{\circ}$ configurations are shown in the left and right column, respectively. The top (bottom) row is characterized by $α_{in}^{ω} = 0^{\circ}$ , $90^{\circ}$ ( $α_{in}^{ω} = 45^{\circ}$ , $135^{\circ}$ ). Data are normalized to the $90^{\circ} / 90^{\circ}$ configuration at $τ = 20^{\circ}$ . The dashed lines indicate the instrumental background. Continuous lines correspond to the fit model of Eqs. (4-5) and (4-6) with all data fitted with one set of parameters (Table 1). The multidomain sample is characterized by a small but nonzero signal for the 0 °/0 ° configuration (top-left panel), which certifies the presence of $a_{2}$ domains as detailed in the main text. Data acquisition of the small SHG signals obtained in the $α_{in}^{ω}$ / $0^{\circ}$ configurations is dominated by systematic variations due to a background-signal drift occurring as a function of measurement time. Note that the $45^{\circ}$ / $α_{out}^{2 ω}$ and $135^{\circ}$ / $α_{out}^{2 ω}$ configurations (bottom row) are no longer symmetric for $\pm τ$ , as expected by the breaking of the model symmetry induced by the presence of $a_{2}$ domains.
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