Curvature-Controlled Polarization in Adaptive Ferroelectric Membranes

Abstract

This study explores the ferroelectric domain structure and mechanical properties of PbTiO₃-based membranes, which develop a well-ordered and crystallographic-oriented ripple pattern upon release from their growth substrate. The ferrolectric domain structure of the PbTiO₃ layer is examined at various length scales using optical second harmonic generation, piezoresponse force microscopy, and scanning transmission electron microscopy. These methods reveal the presence of purely in-plane domains organized into superdomains at the crest of the ripples, while an in-plane/out-of-plane domain structure is observed in the flat regions separating the ripples, in agreement with phase-field simulations. The mechanical properties of the membranes are assessed using contact resonance force microscopy, which identifies a distinct mechanical behavior at the ripples compared to the flat regions. This study shows that the physical properties of the ferroelectric layer in membranes can be locally controlled within an ordered array of ripples with well-defined geometric characteristics.

Keywords: ferroelectric domains; ferroelectrics; flexible electronics; oxide membranes; strain.

Figure 1

Schematic of the fabrication process for the PbTiO₃/SrRuO₃ membrane. From left to right: the as‐grown PbTiO₃/SrRuO₃/SrTiO₃/Sr₃Al₂O₆/SrTiO₃(001) heterostructure displayed with the AFM topography image showing a flat surface with an RMS roughness of ≈0.4 nm. The lift‐off procedure, where the Sr₃Al₂O₆ sacrificial layer dissolves in deionized water, leaving the membrane attached to a PDMS support. Finally, the membrane is transferred onto a Nb:SrTiO₃(001)‐oriented target substrate. The overlaid 3D AFM topography image clearly reveals the formed ripple pattern. (The AFM topography images are also provided in Figure S1a,b, Supporting Information.)

Figure 2

Ferroelectric symmetry evolution on the PbTiO₃/SrRuO₃ ripples. a) Optical second harmonic generation (SHG) microscopy experiment. b–d) 2D SHG intensity distributions on the PbTiO₃/SrRuO₃ membrane. e,f) Polarization‐angle dependence of SHG intensity as a function of position, crossing a ripple oriented along the [010] _pc axis (e) and a ripple oriented along the [100] _pc axis (f). g–i) Schematic description of the ferroelectric polarization states on g) flat region, h) [010] _pc ‐oriented ripple, and i) [100] _pc ‐oriented ripple. The red arrows and dots represent the polarization axis of each single domain. The blue arrows in (h) and (i) indicate the tangential direction to the ripple curvature.

Figure 3

Classification of the ripples by height and FWHM, and lateral piezoresponse force microscopy analysis of the ripple pattern at different scales. a) 3D AFM topography image of the ripples over a 15×15 µm² area. Just below, the 2D scatter plot classifies the ripples based on their height and FWHM. b,c) Corresponding PFM amplitude and phase signals of the area shown in (a). d,e) PFM amplitude and phase signals of the region highlighted by the red dashed box in (b). f,g) PFM amplitude and phase signals of a “secondary” ripple with height and FWHM of 7 nm and 300 nm, respectively. A purely in‐plane a domain configuration is observed at the ripple, while an a/c domain structure is seen elsewhere. h,i) PFM amplitude and phase signal of a “primary” ripple with height ⩾ 100 nm and FWHM ⩾ 1.5 µm, showing the presence of a ₁ and a ₂ domains organized in superdomains. The schematic on the left shows the possible in‐plane domain configuration within the superdomains.

Figure 4

STEM cross‐sectional study of a “primary” ripple (height > 100 nm, FWHM > 1µm). a) STEM‐HAADF image at low magnification showing the ripple. Image series were acquired and aligned in the highlighted regions, marked in different colors. b) HAADF image and corresponding tetragonality analysis from a flat region far from the ripple, revealing an a/c domain structure (for c domain: z/y >1, for a domain: z/y ⩽1). c) HAADF image and tetragonality analysis from a region highlighted in green, also showing an a/c domain structure. d) HAADF image and tetragonality analysis (z/y >1) from the slope of the ripple, indicating a pure c domain structure (region highlighted in blue). e) HAADF image and tetragonality analysis (z/y <1) from the summit of the ripple, revealing a pure a domain structure (region highlighted in red). Scale bars in panels (b)–(e): 4 nm.

Figure 5

Domain structure naturally developed in a phase‐field simulation of a thin film of PbTiO₃ subjected to an imposed curvature profile. a) Overall view of the simulated system revealing both top and side views of the resulting domain structure as well as the imposed z‐shift of the bottom part of the film (for clarity the shift is enhanced by a factor of 10). b) Top view of the same domain structure. The color scale represents the strain ratio (1+e _zz )/(1+e _xx ) labeled as z/x tetragonality, the arrows in (b) are proportional to the in‐plane polarization. The simulation box contains 256 × 256 × 8 individual points with a spacing of 0.4 nm.

Figure 6

Mechanical properties of the PbTiO₃ ripple structures. Contact‐resonance frequency image of a 40 nm‐high ripple, revealing the mechanical stiffness distribution, with softer regions visible in both the ripple and flat areas.