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DOE OSTI2024

Spherulite-enhanced macroscopic polarization in molecular ferroelectric films from vacuum deposition

Proton-transfer type molecular ferroelectrics hold significant promise for practical application due to their large spontaneous polarizations, high Curie temperatures, and small switching fields. However, it remains puzzling that preparation of quasi-2D films exhibiting macroscopic ferroelectric behaviors has been reported in only few molecular ferroelectrics. To address this puzzle, we studied the impact of microstructures on the macroscopic ferroelectric properties of 5,6-dichloro-2-methylbenzimidazole (DC-MBI) films grown using the low-temperature deposition followed by the restrained crystallization (LDRC) method. Our findings revealed a competition between dense spherulites and porous microstructures containing randomly oriented nanograins in the as-grown films. Post-growth annealing at moderate temperature promotes the formation of spherulites, leading to macroscopic ferroelectric polarization switching. These results underscore the critical role of microstructure density in determining macroscopic ferroelectric properties, potentially resolving the puzzle for the absence of such behavior in many molecular ferroelectric films. Here, we anticipate that the approach proposed in this study to enhance microstructure density will significantly advance the fabrication of quasi-2D molecular ferroelectric films and unlock their potential in device applications.

36 MATERIALS SCIENCE↗

DOE OSTI2025

From prediction to experimental realization of ferroelectric wurtzite Al1− x Gd x N alloys

AlN-based alloys find widespread application in high-power microelectronics, optoelectronics, and electromechanics. The realization of ferroelectricity in wurtzite AlN-based heterostructural alloys has opened up the possibility of directly integrating ferroelectrics with conventional microelectronics based on tetrahedral semiconductors, such as Si, SiC, and III–Vs, enabling compute-in-memory architectures, high-density data storage, and more. The discovery of AlN-based wurtzite ferroelectrics has been driven to date by chemical intuition and empirical explorations. Here, we demonstrate the computationally-guided discovery and experimental demonstration of new ferroelectric wurtzite Al1−xGdxN alloys. First-principles calculations indicate that the minimum energy pathway for switching changes from a collective to an individual switching process with a lower overall energy barrier, at a rare-earth fraction x with x > 0.10–0.15. Experimentally, ferroelectric switching is observed at room temperature in Al1−xGdxN films with x > 0.12, which strongly supports the switching mechanisms in wurtzite ferroelectrics proposed previously [Lee et al., Sci. Adv. 10, eadl0848 (2024)]. This is also the first demonstration of ferroelectricity in an AlN-based alloy with a magnetic rare-earth element, which could pave the way for additional functionalities such as multiferroicity and opto-ferroelectricity in this exciting class of AlN-based materials.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Giant Nonlinear Optical Response via Coherent Stacking of In-Plane Ferroelectric Layers

Thin ferroelectric materials hold great promise for compact nonvolatile memory and nonlinear optical and optoelectronic devices. Herein, an ultrathin in-plane ferroelectric material that exhibits a giant nonlinear optical effect, group-IV monochalcogenide SnSe, is reported. Nanometer-scale ferroelectric domains with ≈90°/270° twin boundaries or ≈180° domain walls are revealed in physical-vapor-deposited SnSe by lateral piezoresponse force microscopy. Atomic structure characterization reveals both parallel and antiparallel stacking of neighboring van der Waals ferroelectric layers, leading to ferroelectric or antiferroelectric ordering. Ferroelectric domains exhibit giant nonlinear optical activity due to coherent enhancement of second-harmonic fields and the as-resulted second-harmonic generation was observed to be 100 times more intense than monolayer WS 2 . This work demonstrates in-plane ferroelectric ordering and giant nonlinear optical activity in SnSe, which paves the way for applications in on-chip nonlinear optical components and nonvolatile memory devices.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Peptide programming of supramolecular vinylidene fluoride ferroelectric phases

Ferroelectric structures have spontaneous macroscopic polarization that can be inverted using external electric fields and have potential applications including information storage, energy transduction, ultralow-power nanoelectronics and biomedical devices. These functions would benefit from nanoscale control of ferroelectric structure, the ability to switch polarization with lower applied fields (low coercive field) and biocompatibility. Soft ferroelectrics based on poly(vinylidene fluoride) (PVDF) have a thermodynamically unstable ferroelectric phase in the homopolymer, complex semi-crystalline structures, and high coercive fields. Here, in this work, we report on ferroelectric materials formed by water-soluble molecules containing only six VDF repeating units covalently conjugated to a tetrapeptide, with the propensity to assemble into the β-sheet structures that are ubiquitous in proteins. This led to the discovery of ribbon-shaped ferroelectric supramolecular assemblies that are thermodynamically stable with their long axes parallel to both the preferred hydrogen-bonding direction of β-sheets and the bistable polar axes of VDF hexamers. Relative to a commonly used ferroelectric copolymer, the biomolecular assemblies exhibit a coercive field that is two orders of magnitude lower, as the result of supramolecular dynamics, and a similar level of remnant polarization, despite having a peptide content of 49 wt%. Furthermore, the Curie temperature of the assemblies is about 40 °C higher than that of a copolymer containing a similar amount of VDF. This supramolecular system was created using a biologically inspired strategy that is attractive in terms of sustainability and that could lead to new functions for soft ferroelectrics.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Ferroelectricity in a semiconducting all-inorganic halide perovskite

Ferroelectric semiconductors are rare materials with both spontaneous polarizations and visible light absorptions that are promising for designing functional photoferroelectrics, such as optical switches and ferroelectric photovoltaics. The emerging halide perovskites with remarkable semiconducting properties also have the potential of being ferroelectric, yet the evidence of robust ferroelectricity in the typical three-dimensional hybrid halide perovskites has been elusive. Here, we report on the investigation of ferroelectricity in all-inorganic halide perovskites, CsGeX 3 , with bandgaps of 1.6 to 3.3 eV. Their ferroelectricity originates from the lone pair stereochemical activity in Ge (II) that promotes the ion displacement. This gives rise to their spontaneous polarizations of ~10 to 20 μC/cm 2 , evidenced by both ab initio calculations and key experiments including atomic-level ionic displacement vector mapping and ferroelectric hysteresis loop measurement. Furthermore, characteristic ferroelectric domain patterns on the well-defined CsGeBr 3 nanoplates are imaged with both piezo-response force microscopy and nonlinear optical microscopic method.

36 MATERIALS SCIENCE↗

DOE OSTI2020

100th Anniversary of the discovery of Ferroelectricity: How did it impact the Current Day Physics

Ferroelectric phenomenon in materials was identified for the first time about 100 years ago in 1920 (paper presented at the American Physical Society (APS) Meeting in Washington, DC, April 1920), at the University of Minnesota, MN, USA; by then a graduate student Joseph Valasek working under the supervision of Prof. W. F. G. Swann. Before this announcement, some prominent physicists had envisaged and even predicted the possibility of an analogous electrical behavior in some materials to that of the well-established hysteresis behavior of magnetic materials. Debye’s work tried to put the concept of Curie temperature in some solids in 1912 but it Schrodinger in the same year who formalized the term ferroelectricity. The names ferroelectrics, ferroelectricity, etc. are fully symbolic of the hysteresis loop-like behavior originally displayed by the magnetic materials. Later on when the physics of ferroelectrics was formalized, most of the terminology, e.g. Curie constant, Curie temperature, etc. that characterized the hysteresis loop or its related characteristics, was inherited from the magnetic materials. Over the years basic ferroelectricity concepts were significantly developed. The observed ferroelectric hysteresis loop between electric polarization vs applied electric field in the then well-known material, Rochelle salt, was presented at the April meeting of the APS, held at, then known as, the National Bureau of Standards or NBS (currently known as the National Institute for Standards and Technology or NIST). Interestingly, even though Valasek submitted the abstract but it was presented by Swann (and Valasek was not present). It happened to be a unique case of the earlier predictions but it did not catch the attention of many researchers working in the field of electronics. Whatever the reason, there was a little attention paid to this newly identified effect in Rochelle salt in 1920s. In late 1920, Valasek’s paper was submitted to Physical Review and that appeared in April 1921. Both ferroelectricity and ferromagnetism are the observational or experimental characteristics of a special class of materials which were not predicted by any basic theoretical approaches to start with at that time.

36 MATERIALS SCIENCE↗

NASA NTRS2000

Ferroelectric Pump

A ferroelectric pump has one or more variable volume pumping chambers internal to a housing. Each chamber has at least one wall comprising a dome shaped internally prestressed ferroelectric actuator having a curvature and a dome height that varies with an electric voltage applied between an inside and outside surface of the actuator. A pumped medium flows into and out of each pumping chamber in response to displacement of the ferroelectric actuator. The ferroelectric actuator is mounted within each wall and isolates each ferroelectric actuator from the pumped medium, supplies a path for voltage to be applied to each ferroelectric actuator, and provides for positive containment of each ferroelectric actuator while allowing displacement of the entirety of each ferroelectric actuator in response to the applied voltage.

Jalink, Antony, Jr.↗

NASA NTRS2001

Future Development of Dense Ferroelectric Memories for Space Applications

The availability of high density, radiation tolerant, nonvolatile memories is critical for space applications. Ferroelectric memories, when fabricated with radiation hardened complementary metal oxide semiconductors (CMOS), can be manufactured and packaged to provide high density replacements for Flash memory, which is not radiation tolerant. Previous work showed ferroelectric memory cells to be resistant to single event upsets and proton irradiation, and ferroelectric storage capacitors to be resistant to neutron exposure. In addition to radiation hardness, the fast programming times, virtually unlimited endurance, and low voltage, low power operation make ferroelectric memories ideal for space missions. Previously, a commercial double level metal 64-kilobit ferroelectric memory was presented. Although the capabilities of radiation hardened wafer fabrication facilities lag behind those of the most modern commercial wafer fabrication facilities, several paths to achieving radiation tolerant, dense ferroelectric memories are emerging. Both short and long term solutions are presented in this paper. Although worldwide major semiconductor companies are introducing commercial ferroelectric memories, funding limitations must be overcome to proceed with the development of high density, radiation tolerant ferroelectric memories.

Philpy, Stephen C.↗

NASA NTRS2007

Performance Measurement of a Multi-Level/Analog Ferroelectric Memory Device Design

Increasing the memory density and utilizing the unique characteristics of ferroelectric devices is important in making ferroelectric memory devices more desirable to the consumer. This paper describes the characterization of a design that allows multiple levels to be stored in a ferroelectric based memory cell. It can be used to store multiple bits or analog values in a high speed nonvolatile memory. The design utilizes the hysteresis characteristic of ferroelectric transistors to store an analog value in the memory cell. The design also compensates for the decay of the polarization of the ferroelectric material over time. This is done by utilizing a pair of ferroelectric transistors to store the data. One transistor is used a reference to determinethe amount of decay that has occurred since the pair was programmed. The second transistor stores the analog value as a polarization value between zero and saturated. The design allows digital data to be stored as multiple bits in each memory cell. The number of bits per cell that can be stored will vary with the decay rate of the ferroelectric transistors and the repeatability of polarization between transistors. This paper presents measurements of an actual prototype memory cell. This prototype is not a complete implementation of a device, but instead, a prototype of the storage and retrieval portion of an actual device. The performance of this prototype is presented with the projected performance of the overall device. This memory design will be useful because it allows higher memory density, compensates for the environmental and ferroelectric aging processes, allows analog values to be directly stored in memory, compensates for the thermal and radiation environments associated with space operations, and relies only on existing technologies.

MacLeod, Todd C.↗

DOE OSTI2026

Proximity Ferroelectricity in Compositionally Graded Structures

Proximity ferroelectricity is a novel paradigm for inducing ferroelectricity in a non-ferroelectric polar material, such as AlN or ZnO that are typically unswitchable with an external field below their dielectric breakdown field. When placed in direct contact with a thin switchable ferroelectric layer (such as Al 1-x Sc x N or Zn 1-x Mg x O), they become a practically switchable ferroelectric. Using the thermodynamic Landau-Ginzburg-Devonshire theory, in this work, we perform the finite element modeling of the polarization switching in the compositionally graded AlN-Al 1-x Sc x N, ZnO-Zn 1-x Mg x O, and MgO-Zn 1-x Mg x O structures sandwiched in both a parallel-plate capacitor geometry as well as in a sharp probe-planar electrode geometry. We reveal that the compositionally graded structure allows the simultaneous switching of spontaneous polarization in the whole system by a coercive field significantly lower than the electric breakdown field of unswitchable polar materials. The physical mechanism is the depolarization electric field determined by the gradient of chemical composition “x”. The field lowers the steepness of the switching barrier in the otherwise unswitchable parts of the compositionally graded AlN-Al 1-x Sc x N and ZnO-Zn 1-x Mg x O structures. In the MgO-like regions of the compositionally graded MgO-Zn 1-x Mg x O structure, a shallow double-well free energy potential emerges. Proximity ferroelectric switching of the compositionally graded structures placed in the probe-electrode geometry occurs due to nanodomain formation under the tip. We predict that a gradient of chemical composition “x” significantly lowers effective coercive fields of the compositionally graded AlN-Al 1-x Sc x N and ZnO-Zn 1-x Mg x O structures compared to the coercive fields of the corresponding multilayers with a uniform chemical composition in each layer. A tip-induced switching further lowers the coercive field, enabling control of ferroelectric domains in otherwise unswitchable compositionally graded structures, which can provide nanoscale domain control for memory, actuation, sensing, and optical applications.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Electrode Elastic Modulus as the Dominant Factor in the Capping Effect in Ferroelectric Hafnium Zirconium Oxide Thin Films

The discovery of ferroelectricity in hafnia based thin films has catalyzed significant research focused on understanding the ferroelectric property origins and means to increase stability of the ferroelectric phase. Prior studies have revealed that biaxial tensile stress via an electrode “capping effect” is a suspected ferroelectric phase stabilization mechanism. This effect is commonly reported to stem from a coefficient of thermal expansion (CTE) incongruency between the hafnia and top electrode. Despite reported correlations between ferroelectric phase fraction and electrode CTE, the thick silicon substrate dominates the mechanics and CTE-related stresses, negating any dominant contribution from an electrode CTE mismatch toward the capping effect. In this work, these discrepancies are reconciled, and the origin of these differences deriving from electrode elastic modulus, not CTE, is demonstrated. Pt/M/TaN/Hf 0.5 Zr 0.5 O 2 /TaN/Si devices, where M is platinum, TaN, iridium, tungsten, and ruthenium, were fabricated. Sin 2 (ψ)-based X-ray diffraction measurements of biaxial stress in the HZO layer reveal a strong correlation between biaxial stress, remanent polarization, and electrode elastic modulus. Conversely, a low correlation exists between the electrode CTE, HZO biaxial stress, and remanent polarization. A higher elastic modulus enhances the resistance to electrode elastic deformation, which intensifies the capping effect during crystallization, and culminates in the tandem restriction of out-of-plane hafnia volume expansion and preferential orientation of the polar c-axis normal to the plane. These behaviors concomitantly increase the ferroelectric phase stability and polarization magnitude. This work provides electrode material selection guidelines toward the development of high-performing ferroelectric hafnia into microelectronic devices, such as nonvolatile memories.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Self–Healing and Stretchable Molecular Ferroelectrics with High Expandability

The interplay between crystal ordering and stretchability is frequently encountered in contemporary materials science, particularly in the case of ferroelectrics. The inherent dilemma arises when these materials need to withstand repetitive mechanical deformations or stretching without sacrificing their crystal integrity, all while retaining their remarkable ferroelectric properties and even exhibiting self-healing capabilities. This complexity further presents a significant challenge in the design and engineering of mechanically rigid molecular ferroelectric crystals, particularly for applications where both precise crystalline structure and mechanical adaptability are crucial. In this study, the humidity-controlled expansion and contraction, dissolution, and recrystallization of a self-assembled molecular ferroelectric-in-hydrogel framework are reported. Self-healing ferroelectric-in-hydrogel networks exhibit a recyclable humidity-tailored ionic conductivity from 2.86 × 10 –6 to 1.36 × 10 –5 S cm –1 , facilitating the stretchable piezoelectric sensing. Additionally, the dynamic bond reforming interactions are observed, leading to the tailoring of Young's modulus from 452 to 170 MPa, maintaining ferroelectricity under a strain of 20% with a piezoelectric coefficient of 15.7 pC N –1 . Upon lattice contraction, the molecular contacts undergo reforming, leading to the restoration of stretchable ferroelectrics/piezoelectrics and paving the way for stretchable bioelectronics for full-body motion monitoring. The capabilities highlighted here open avenues for stretchable and self-healing ferroelectric-in-hydrogel bioelectronic technologies.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Near Room Temperature Solvothermal Growth of Ferroelectric CsPbBr 3 Nanoplatelets with Ultralow Dark Current

CsPbBr 3 exhibits outstanding optoelectronic properties and thermal stability, making it a coveted material for detectors, light-emitting diodes, and solar cells. Despite observations of ferroelectricity in CsPbBr 3 quantum dots, synthesizing bulk ferroelectric CsPbBr 3 crystals has remained elusive, hindering its potential in next-generation optoelectronic devices like optical switches and ferroelectric photovoltaics. Here, a breakthrough is reported: a novel solvothermal technique enabling the growth of ferroelectric CsPbBr 3 nanoplatelets with lateral dimensions in the tens of micrometers. This represents a significant step toward achieving large-area ferroelectric CsPbBr 3 crystals. Unlike traditional methods, this approach allows for growth and crystallization of CsPbBr 3 in alcohol solutions by enhancing precursor solubility. Further this study confirms the ferroelectric nature of these nanoplatelets using second harmonic generation, electrical characterizations, and piezoresponse force microscopy. This work paves the way for utilizing ferroelectric CsPbBr 3 in novel optoelectronic devices, significantly expanding the potential of this material and opening doors for further exploration in this exciting field.

25 ENERGY STORAGE↗

DOE OSTI2026

Phase Synergy Enables Low‐Power Ferroelectric Switching in HfO 2 Epitaxial Films

HfO 2 -based ferroelectric materials have emerged as leading candidates for next-generation non-volatile memory technologies, owing to their nanoscale robust ferroelectricity and complementary metal–oxide–semiconductor (CMOS) compatibility. However, challenges and debates persist in advancing and comprehensively understanding their ferroelectric behavior. In particular, conventional approaches typically regard non-ferroelectric phases as detrimental and primarily focus on suppressing their formation, yet overlooking their potentially synergistic contributions—particularly those of the tetragonal (T) phase. Here, we unambiguously clarify the beneficial role of the T-phase and introduce a phase-boundary engineering strategy that deliberately harnesses it to enhance ferroelectricity in HfO 2 films. By stabilizing optimal coherent boundaries between ferroelectric orthorhombic (O) and T phases in epitaxial La-doped HfO 2 films, we achieve significant improvements in ferroelectric properties—doubling the remanent polarization (P r ∼ 30 µC/cm 2 ) and substantially reducing the coercive field (E c ∼ 3 MV/cm) by 30% compared to low-La doped samples without such boundaries. Atomic-scale electron microscopy reveals the structural nature of the atomically sharp, coherent O–T boundaries. Combined with deep-learning enhanced molecular dynamics simulations, our results unravel that these boundaries facilitate intermediate polarization states that lower the switching energy barrier. Consequently, phase coexistence shifts from an inherent drawback to a tunable design element, offering a broadly applicable route to ultra-low-power HfO 2 -based nanoelectronics.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Chapter 3 - Harvesting Thermal Energy with Ferroelectric Materials

Thermal energy is considered the ubiquitous form of energy as all other forms of energy ultimately degrade to thermal energy. Thermal to electrical energy conversion is currently an important method for electricity generation. The traditional power cycles, however, become technically and economically unviable when heat source temperature reduces below 100 °C. Thermal energy harvesting has been proposed as a viable alternative for low-grade thermal to electrical energy conversion. Thermal energy harvesting is a method of generating electricity using temperature-induced variations in material properties. It is particularly useful when the heat sources are available free-of-cost, either in the form of natural heat or waste heat. While there are several thermal energy harvesting techniques, pyroelectricity is the most promising as it can be used in situations where spatial thermal gradients are difficult to establish or the temperature of the heat source is changing. Despite the fact that the pyroelectric effect in ferroelectric materials has been known for past several decades, thermal energy harvesting using ferroelectric materials has not been much explored in the literature. In this chapter, we would explore various aspects of thermal energy harvesting using ferroelectric materials. We have first established the physics behind ferroelectricity, then provided a detailed description on ferroelectric thermal energy harvesting, discussed various ferroelectric thermodynamic cycles and devices proposed in the literature, and finally described various other emerging applications of ferroelectricity.

DIRECT ENERGY CONVERSION,MATERIALS SCIENCE,OTHER I↗

DOE OSTI2020

Microscopic Manipulation of Ferroelectric Domains in SnSe Monolayers at Room Temperature

Two-dimensional (2D) van der Waals ferroelectrics provide an unprecedented architectural freedom for the creation of artificial multiferroics and nonvolatile electronic devices based on vertical and coplanar heterojunctions of 2D ferroic materials. Nevertheless, controlled microscopic manipulation of ferroelectric domains is still rare in monolayer-thick 2D ferroelectrics with in-plane polarization. Here we report the discovery of robust ferroelectricity with a critical temperature close to 400 K in SnSe monolayer plates grown on graphene and the demonstration of controlled room-temperature ferroelectric domain manipulation by applying appropriate bias voltage pulses to the tip of a scanning tunneling microscope (STM). This study shows that STM is a powerful tool for detecting and manipulating the microscopic domain structures in 2D ferroelectric monolayers, which are difficult for conventional approaches such as piezoresponse force microscopy, thus facilitating the hunt for other 2D ferroelectric monolayers with in-plane polarization with important technological applications.

2D ferroelectric↗

DOE OSTI2023

Influence of the Ozone Dose Time during Atomic Layer Deposition on the Ferroelectric and Pyroelectric Properties of 45 nm-Thick ZrO 2 Films

Over a decade ago, ferroelectricity was discovered in doped HfO 2 thin films. The HfO 2 -based thin films have attracted much attention due to their remarkable scalability and CMOS compatibility. Other than the HfO 2 -based thin films, the undoped ZrO 2 thin films are understudied despite their commonly reported antiferroelectric behavior. However, being of the same fluorite structure as HfO 2 -based thin films, the undoped ZrO 2 also displayed considerable ferroelectricity as demonstrated in recent studies. Here, 45 nm-thick polycrystalline undoped ZrO 2 films are synthesized using atomic layer deposition with different ozone dose times. The ZrO 2 films are crystallized after atomic layer deposition at 350 °C without anneals. In general, the longer ozone dose time causes a lower in-plane tensile stress and oxygen vacancy content, which help facilitate an irreversible non-polar tetragonal to polar orthorhombic phase transition with electric-field cycling. However, the lower in-plane tensile stress and oxygen vacancy content also stabilize the monoclinic phase so that a long ozone dose time (>17.5 s) reduces the ferroelectric behavior. After wake-up cycles, the ZrO 2 thin film with an ozone dose time of 17.5 s exhibits a remanent polarization of 6 μC·cm –2 and a pyroelectric coefficient of -35 μC·K –1 ·m –2 . Moreover, the wake-up behavior is consistent between the ferroelectric and pyroelectric response. As essential factors in optimizing the growth of fluorite-structure thin films for ferroelectric applications, the in-plane tensile stress and oxygen vacancy content significantly influence the ferroelectric and pyroelectric properties. Additionally, the low thermal budget for processing ferroelectric ZrO 2 thin films is valuable for semiconductor back-end-of-line processes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Direct observation of nanoscale dynamics of ferroelectric degradation

Failure of polarization reversal, i.e., ferroelectric degradation, induced by cyclic electric loadings in ferroelectric materials, has been a long-standing challenge that negatively impacts the application of ferroelectrics in devices where reliability is critical. It is generally believed that space charges or injected charges dominate the ferroelectric degradation. However, the physics behind the phenomenon remains unclear. Here, using in-situ biasing transmission electron microscopy, we discover change of charge distribution in thin ferroelectrics during cyclic electric loadings. Charge accumulation at domain walls is the main reason of the formation of c domains, which are less responsive to the applied electric field. The rapid growth of the frozen c domains leads to the ferroelectric degradation. This finding gives insights into the nature of ferroelectric degradation in nanodevices, and reveals the role of the injected charges in polarization reversal.

42 ENGINEERING↗