Date: 3 February 2025

Dataset Title: Electric-field-induced domain walls in wurtzite ferroelectrics

Dataset Contact: Zetian Mi ztmi@umich.edu

Dataset Creators:
Name: Zetian Mi
Email: ztmi@umich.edu
Institution: University of Michigan, Department of Electrical Engineering and Computer Science
Name: Danhao Wang
Email: danhaow@umich.edu
Institution: University of Michigan, Department of Electrical Engineering and Computer Science
Name: Ding Wang
Email: dinwan@umich.edu
Institution: University of Michigan, Department of Electrical Engineering and Computer Science

Dataset details:
Fig. 2. d, In-plane distance map of a vertical domain wall (VDW) in ScGaN. f, Dumbbell angle map for VDW in ScGaN. h, Intensity profile of the selected region in dDPC-STEM image of the VDW structure. j, Projected polarization vector distribution across the VDW. l, Electronic density of states of the VDW structure and bulk ScGaN. 
Fig. 3. d, Out-of-plane distance map of an horizontal domain wall (HDW) in ScGaN. f, Dumbbell angle map for HDW in ScGaN. h, Intensity profile of the selected area in dDPC-STEM image of the HDW structure. j, Projected polarization vector distribution across the HDW. l, Electronic density of states of the HDW structure in ScGaN.
Fig. 4. d-g, Atomic force microscopy (AFM), piezo-response force microscopy (PFM) phase and conductive AFM (CAFM) measurements over four regions with different electrical poling conditions. h-k, Current line profiles across the electrode regions poled by different conditions measured at -10 V via conductive AFM.

Description:
Wurtzite ferroelectrics possess transformative potential for next-generation microelectronics. A comprehensive understanding of their ferroelectric properties and domain energetics is crucial for tailoring their ferroelectric characteristics and exploiting their functional properties in practical devices. Despite burgeoning interest, the exact configurations, and electronic structures of domain walls in wurtzite ferroelectrics remain elusive. In this work, we elucidate the atomic configurations and electronic properties of electric-field-induced domain walls in ferroelectric ScGaN. By combining transmission electron microscopy and theoretical calculations, a novel charged domain wall with a buckled two-dimensional hexagonal phase is revealed. Density functional theory calculations confirm that such domain wall structures further give rise to unprecedented mid-gap states within the forbidden band. Quantitative analysis unveils a universal charge-compensation mechanism stabilizing antipolar domain walls in ferroelectric materials, wherein the polarization discontinuity at the 180º domain wall is compensated by the unbonded valence electrons. Furthermore, the reconfigurable conductivity of these domain walls is experimentally demonstrated, showcasing their potential for ultra-scaled device applications. Our findings represent a pivotal advancement in understanding the structural and electronic properties of wurtzite ferroelectric domain walls and lay the groundwork for fundamental physics studies and device applications.

Methodology:
Sample preparation
The ScGaN/GaN heterostructure was grown on 2-inch n-GaN/sapphire templates using a Veeco GENxplor MBE system equipped with a radio frequency (RF) plasma-assisted nitrogen source for supplying active nitrogen (N*, 99.9999 %), dual filament SUMO cells for providing gallium (Ga, 99.99999 %), and a high-temperature Knudsen effusion cell for providing scandium (Sc, 99.999 %). The GaN layer was highly Si-doped with a carrier concentration of ~ 2E19 cm-3, serving as the bottom electrode. The ScGaN layer was grown under N-rich conditions. A nominal Sc content of 0.31 was measured by energy dispersive X-ray spectroscopy (EDX) analysis performed in a scanning electron microscope (SEM, Hitachi SU8000) using a separate sample grown on AlN substrate under the same growth conditions. The VDWs and HDWs were created by a positive triangular pulse (+28 V, pulse width: 1 s), and erased by a negative triangular pulse (-35 V, pulse width: 1 s), applied to the top electrode. Domain walls are formed within the same device but in different regions, naturally determined by the electric field distribution and the relative position of antipolar domains. HDWs are typically found beneath the switched regions, parallel to the ScGaN/GaN interface, while VDWs are primarily located near the electrode edge.
Microstructure imaging
STEM imaging was carried out using a Thermo Fisher Scientific Spectra 300 probe-corrected STEM equipped with a Dual-X EDS system and operated at 300 kV. High-angle annular dark-field (HAADF) images were captured with a collection angle of 62–200 mrad at a beam convergence angle of 22 mrad. The cross-sectional TEM specimen was prepared using an in-situ focused ion beam (FIB) lift-out method employing a Thermo Fisher Helios 600 Xe plasma FIB/SEM system. Initially, the sample was cut using a high current at 30 kV for the lift-out process. Subsequently, to remove the damage induced by the high energy beam, a final thinning process was performed using a 5 kV beam at 10 pA. The specimen's thickness was carefully monitored by observing the secondary electron image in the SEM at 5 kV. This process continued until the sample appeared bright in the image, indicating that it had been thinned to an approximate thickness of ~100 nm. The central position associated with each atomic column was localized by using a two-dimensional Gaussian fitting procedure. The interplanar spacings used in the in-plane and out-of-plane distance mapping are the distances between equivalent atomic positions across successive planes. A band pass filter was adopted to enhance the visibility of the DPC-STEM images. The projected polarization vector maps are calculated based on the extracted atom positions following the procedure detailed in Calderon et al.’s work. Charge maps are calculated using the DPC-STEM images obtained through a quadrant segmented detector. 
DFT calculations
Density functional theory (DFT) calculations were performed using the Vienna ab initio simulation package (VASP). The generalized gradient approximation (GGA) for the exchange-correlation functional and projector augmented wave (PAW) potentials was employed. ScGaN alloys with a 31.25% Sc composition were modeled by special quasirandom structures (SQS) generated by the Alloy Theoretic Automated Toolkit (ATAT) . The VDWs were modeled by constructing a 4×16×2 supercell (in total 512 atoms) that includes one VDW at the center.  To model the horizontal domain wall, a 448-atom structure consisting of two polar wurtzite slabs with opposite polarities surrounded by vacuum was constructed,  with a vacuum size larger than 15 Å. A hexagonal planar ScGaN layer was positioned between the N-polar and M-polar regions as the initial setup to mimic the antipolar interface after switching via a layered-hexagonal intermediate, which also eliminates any influence of subjectively predefined structures on the final domain wall configuration. The atoms within the slabs were then allowed to fully relax vertically with in-plane lattice constant set to that of bulk ScGaN. The atomic structures were relaxed until all interatomic forces were reduced below 0.01 eV Å-1, and the electronic energy convergence criterion was set to 10^-5 eV. The dangling bonds at the N-terminated outer surfaces were passivated with pseudohydrogen atoms with a charge of 3/4. The software VESTA was employed for visualization.
Electrical characterization
Ti/Au (20 nm/120 nm) top electrodes were deposited in an electron-beam evaporator and defined via a photolithography and lift-off process. For piezo-response force microscopy (PFM) measurements, to remove the metal electrodes, Ti/Al (20 nm/120 nm) instead of Ti/Au metal stacks were used. The ferroelectric properties, including P-V and J-V loops, pulse transients, and Positive-Up-Negative-Down (PUND) measurements were conducted using a Radiant Precision Premier II ferroelectric tester driven from the top electrode. A Keithley 2400 SMU was used to set the polarity before TEM characterization.
Characterization of conductive domain walls
50 nm ScGaN was grown under the same conditions as above to explore the conductive domain walls. The thickness was reduced to 50 nm to enhance the conductivity contrast. To avoid possible chemical contamination or etching damage to the surface, a 120 nm Au metal stack was patterned via e-beam deposition and lithography and exfoliated after electrical poling using a dry transfer method. Triangular pulses with a period of 1s were used to pole the devices. A switching voltage of 20 V was extracted, which was used as reference for selecting the poling voltages in Fig. 4. The PFM and c-AFM measurements were carried out using a Bruker ICON SPM. For PFM, the tip frequency was 15 kHz and VAC was 10 V applied to the sample. For c-AFM, SCM-PIT conductive tips were used under contact mode-based tunneling AFM (TUNA). During measurements, the tip frequency was 2.5 kHz and sample bias was -10 V. The electric field distribution was modeled using Silvaco TCAD.