Devices with active van der waals junctions and methods of making same

Abstract

The technology disclosed herein generally concerns novel layered designs of van der Waals (vdW) structure materials incorporating spacer sheets and patterned cavity arrangements, and uses thereof as functional devices.

Description

[0001] DEVICES WITH ACTIVE VAN DER WAALS JUNCTIONS AND METHODS OF MAKING SAME

[0002] STATEMENT REGARDING FUNDING FROM THE EUROPEAN RESEARCH COUNCIE

[0003] The project leading to this application has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grant agreement No. 852925).

[0004] TECHNOEOGICAE FIELD

[0005] The technology disclosed herein generally concerns unique layered designs of van der Waals (vdW) structures and uses thereof in the construction of layered two- dimensional materials.

[0006] BACKGROUND

[0007] Unlike electronic transitions, crystalline structural transitions are challenging to control due to considerable energy barriers associated with breaking solid bonds at ambient conditions away from the melting temperature. Nevertheless, some materials can exhibit practical transitions between amorphous and crystalline orders in response to external stimuli such as optical or electric pulses. Switching the discrete periodic symmetries in these "phase-change" materials directly impacts their collective lattice excitations and numerous subsequent properties. Thus, electric control of structural transitions enables, in principle, rapid switching of intrinsic responses such as light emission, conductivity, and magnetic order in so-called multiferroic devices.

[0008] PUBLICATIONS

[0009] [1] PCT Publication No. WO 2022 / 064505

[0010] [2] PCT Publication No. WO2023 / 248225.

[0011] SUMMARY OF THE INVENTION

[0012] Existing semiconductor technologies rely on patterning of active crystal or shaping gate electrodes to create local active junctions or quantum dots. In contrast to these technologies, the inventors of the technology disclosed herein have designed layered van-der Waals (vdW) structures characterized by active regions within lubricant cavities. These active regions, or junctions, formed as cavities in a thin spacer substance (an interface material or a lubricant layer) are encapsulated by two vdW flakes / layers / sheets, causing the vdW flakes to sag into the cavities and come into contact with each other, generating active junctions at each cavity region. The atomic stacking configuration at the active region between the encapsulating layers can switch between commensurate and incommensurate stackings to determine the device's properties and response. Outside the cavity regions, the interaction of the encapsulating layers with the spacer substance remains incommensurate due to lattice mismatch or interlayer twists and, therefore, are highly lubricant. The encapsulating layers strain, slide, and twist on these lubricant interfaces to rearrange the relative twist angle, strain, and stacking configuration at the active touching points (within the cavities). The cavity dimensions and shapes which can be squeezed down to the nanometer quantum dot limit modify the properties of the junction. These dimensions also set a minimal dislocation length and a corresponding energy barrier for switchable stacking configurations at each junction. The junctions, which are further coupled by elastic and electromagnetic interactions enable cavity arrays with diverse properties, enabling parallel computation schemes.

[0013] Exceptional electric field switching was observed between commensurate, metastable, and periodic stacking configurations of layered materials (so-called vdW polytypes) that break inversion and mirror symmetries. Owing to relatively weak interlayer adhesion and high planar stiffnesses, partial dislocations between domains with opposite structural and polar orientations elongate and slide to expand better-stable configurations of co-aligned polarization Pz. For example, the stacking-fault dislocation strips in polytypes of honeycomb graphene, hexagonal boron nitride ( / z-BN), or transition metal dichalcogenides (TMDs), have been determined to be ~ 30 atoms wide by the Burgers vector in the partial dislocation (one bond length), the potential well energy in the commensurate state (~ one meV per atom), and the planar elastic modulus (~ 1 TPa). The stacking misalignment, extra interlayer separation, and planar strain energy in the boundary set an energy barrier of ~1 eV per nm strip length. Thus, nucleating the boundary strips, an essential step for structural transition, is restricted at room temperature (below the turbostratic transition), even if cutting the structure into small nm-scale islands and applying local external stimuli. The open dangling bonds at the physical edges of the layers tend to zip the layers together and restrict interlayer motions. Indeed, previous electric hysteresis measurements have relied on preexisting dislocation strips in micrometer- size structures. Additional challenges arising in mechanically assembled interfaces are uncontrollable twists and stiff moire networks that tend to freeze the sliding and restrict local switching. Moreover, after removing the external field, the rigid strip network pulls the moire pattern back to its initial dimensions and eliminates hysteretic memory response.

[0014] These super lubricant arrays of polytype (SLAP) islands presented herein bypass challenges of the art and enable highly desired electrical switching of nm-scale single domains. Considering the numerous electronic phases in vdW polytypes reported to date, such as cumulative polarizations, superconductivity, spin, orbital, and topological orders, the established structural switching provides straightforward multiferroic control mechanisms for subsequent electronic phases. By tuning the position of single boundary strips, interlayer twist angles, and topological domain patterns in minute crystalline islands, multi-state responses and enhanced collective properties coupled by inter-island interactions could be obtained.

[0015] Thus, in the most general aspect of the invention, there is provided a van der Waals hetero structure having at least one pair of material sheets, said material sheets being separated by a lubricant layer comprising one or more lubricant-free or cavity regions enabling direct contact between the two material sheets solely at said cavity regions.

[0016] As will be further explained, the van der Waals (vdW) heterostructure of the invention is formed by combining multiple material sheets through vdW bonds. The hetero structure combines the advantages of electronic, optical, thermal, and magnetic properties of different or various 2D materials and presents high-performance functional devices. The heterostructure of the invention is a multilayered device comprising a lubricant layer separating two van-der Waals (vdW) material sheets (preventing interaction between the two material sheets), wherein the lubricant layer having one or more cavity regions enabling or permitting interaction or coupling between the two vdW sheets.

[0017] Thus, the invention provides a device, or a multilayered device, or a heterostructure comprising a lubricant sheet having one or more cavity regions, said lubricant sheet being provided between two van-der Waals (vdW) material sheets, wherein the two vdW material sheets interact or couple with each other (solely) in each of the one or more cavity regions, to define active junctions. Typically, the device has or may be characterized by incommensurate regions where the two vdW sheets are separated by the lubricant sheet; and commensurate regions within each of the one or more cavity regions.

[0018] In another aspect, the invention provides a multilayered device comprising a lubricant layer comprising one or more cavity regions, said lubricant layer being provided between two van-der Waals (vdW) material sheets, the device having incommensurate regions wherein the two vdW sheets are separated by the lubricant layer; and commensurate regions, wherein the two vdW sheets interact or couple through or within at least some or each of the one or more cavity regions.

[0019] Typically, the interaction or coupling between the two vdW sheets occurs solely in the one or more cavity regions. The device is configured for controlling local electronic and structural responses at said regions or junctions

[0020] Further provided is a device comprising or implementing a layered vdW structure comprising a plurality (one or more) of confined cavity junctions, said device being configured for controlling local electronic and structural responses at said junctions.

[0021] As used herein, the term “sheer is interchangeable with the terms ‘layer’ and ‘flake’, each having a meaning as known in the art. Typically, each term encompasses a continuous material film of a specific material or composition. The terms are not to be understood to mean a single ply of the material. The terms encompass single plys, as well as multi-plys of the material. For example, a lubricant sheet may be a sheet or a layer of a lubricant material that is a multilayered material.

[0022] The device architecture disclosed comprises a layer of a solid lubricant sheet that is sandwiched or encapsulated between two 2D material layers, the so-called vdW sheets. The presence of the lubricant sheet between two vdW sheets prevents interaction between the vdW sheets, but for cavities present in the lubricant sheet, where the two vdW sheets deform and sag into the cavities. Sagging into the cavities, enabled by a sliding interaction between the lubricant sheet with a top encapsulating vdW sheet and a bottom encapsulating vdW sheet, bring about direct commensurate (or at times an incommensurate) interaction between the vdW sheets in each of the cavities.

[0023] The vdW interaction is at the center of each of the cavities where the encapsulating vdW layers touch. This tangent or interface defining an interaction between the encapsulating vdW layers can include an interaction between tens to thousands of atoms and forms the device's active interface region. The active interface can typically anneal to a minimal energy point, rearranging to one of two stable configurations (a commensurate state), or multiple domains in case of a relative strain and twist. Once at an energy minimum, the interface can be switched between the two states by applying an external electric field through electrodes or gate electrodes, for example.

[0024] The thickness, and thus the flexibility, of the two sagging vdW sheets can be modified by adding inert layers that will not affect functionality, such as hexagonal boron nitride (hBN) on top of, e.g., the active graphene layer. The parameters of the architecture may be controlled to include such parameters as a tangent contact surface area, an angle of the sag between the layers, a thickness of the spacing cavity, its shape and size, and a (mechanical) thickness of the top and bottom vdW sheets. The architecture removes edge effects because there are no edges (dangling bonds) in the vicinity of the active region.

[0025] Thus, at each of the cavities, the two vdW sheets interact to define a ‘Tangent profile” unique to a particular cavity or a plurality of cavities or an arrangement of cavities along an array of junctions. Each of the cavities or junctions may be independentlymodified to adopt an independent or predesigned tangent profile, such that a tangent profile of the junctions may vary in one or more tangent contact surface area, an angle of the sag between the sheets, a thickness of the cavity, the cavity shape and size, the cavities array symmetry (such as triangular, hexagonal, cubic arrays and others), the cavities spread and separation distance, and a (mechanical) thickness of the top and bottom vdW sheets encapsulating the cavities.

[0026] In some embodiments, in a device of the invention, e.g., a multilayered device comprising a lubricant sheet separating two van-der Waals (vdW) material sheets (preventing interaction between the two material sheets), the lubricant sheet having one or more cavity regions enabling or permitting interaction or coupling between the two vdW sheets, wherein the one or more cavities having a tangent profile defining the interaction or coupling between the two vdW sheets. The one or more cavities may differ in one or more of tangent contact surface area, an angle of the sag between the sheets, a thickness of the cavity, the cavity shape and size, the cavities array symmetry (e.g., triangular, hexagonal, or cubic arrays), the cavities spread and separation distance, and a (mechanical) thickness of the top and bottom vdW sheets encapsulating the cavities.

[0027] The lubricant sheet provided between any two vdW sheets is formed of a layered material with a different lattice constant than the encapsulating vdW layers. In other words, the lubricant sheet, acting as a spacer between any two vdW sheets may be of a material that is same or different than the materials of two vdW sheets, provided that the spacer lattice orientation is twisted relative to that of the encapsulating vdW layers. This mismatch necessarily results in super lubricant properties that permit sheet sliding outside of the cavity regions. The interfaces of the lubricant sheet and the vdW sheets remain incommensurate and support lubricant interfacial motion.

[0028] The lubricant sheet can vary in thickness and may, for example, be of a thickness ranging from sub-nanometer to several nanometers.

[0029] In some cases, therefore, the lubricant sheet may be selected from a layered material such as h-BN, graphene, transition metal dichalcogenides (TMDs), and others. Where the vdW sheets and the lubricant sheet are of the same material, e.g., h-BN, the lattice orientation of the lubricant sheet must be twisted relative to the encapsulating vdW layers.

[0030] In some embodiments, the lubricant sheet is graphene.

[0031] In some embodiments, the lubricant sheet is hexagonal boron-nitride (h-BN), hexagonal aluminium-nitride (h-AIN), hexagonal zinc-oxide (h-ZnO), hexagonal gallium-nitride (li-GaN), transition metal dichalcogenides (TMD) and others.

[0032] In some embodiments, the lubricant sheet is hexagonal boron-nitride (h-BN).

[0033] The transition metal dichalcogenides (TMD) may be selected amongst 2D materials exhibiting unique electrical, mechanical, and optical properties and are therefore of virtually unlimited potential in various fields, including electronic, optoelectronic, sensing, and energy storage applications. Non-limiting examples of these layered materials include M0S2, WS2, MoSe? and WSei.

[0034] Each of the two (or more) vdW material sheets are selected to exhibit strong in- plane covalent or ionic bonding and weak interlayer (van der Waals) interactions. Typically, the two vdW sheets are of the same material and typically further of the same lattice orientation, enabling commensurate interaction therebetween at the tangent interface points. Each of the vdW sheets may be independently selected from h-BN and TMD materials, as defined herein.

[0035] In some configurations, the device comprises a graphene lubricant layer and two vdW encapsulating layers formed of h-BN or a TMD material.

[0036] In some configurations, the device comprises a h-BN lubricant layer and two vdW encapsulating layers formed of h-BN or a TMD material, wherein the lattice orientation of the vdW layers and the lattice orientation of the lubricant layer are twisted one relative to the other.

[0037] Devices or heterostructures of the invention may comprise a plurality (more than one) lubricant sheets, each encapsulated between two vdW sheets, as explained. In some cases, a single vdW sheet may contact two different lubricant layers, wherein the cavity arrangement in each of the lubricant layers is different to permit sagging of the common vdW sheet into cavities formed in either of the adjacent lubricant sheets.

[0038] As used herein, the term "cavity region”, interchangeably used herein with ‘cavity’, refers to a cavity of any structure, shape and size, which may or may not a point cavity or a circular cavity. The term encompasses any region of the cavity in which interaction between two vdW sheets may take place.

[0039] While the shape of each cavity may be substantially circular, this need not always be the case. In some cases, the cavity shape is not circular and can be designed for optimum desired functionality. In some cases, the cavities are spaced-apart individual regions, while in other cases, some or all of the cavities may be interconnected. In some cases, the cavity region is a cavity having an irregular size, which defines a structure connecting two or more cavities. The connectivity between the two or more cavities may itself be a cavity. Generally, the cavities are confined lubricant-free regions.

[0040] A tangent profile, e.g., lubricant layer thickness, cavity density, cavity shapes, dimensions, and distance between the cavities, can be used to control elastic and electromagnetic coupling between the junctions (formed in each cavity) and the overall array response.

[0041] While the atomic stacking configuration of any interacting vdW sheets at the cavities can switch between commensurate and incommensurate stackings to determine the device's properties and response, outside the cavities, the interfaces of the vdW sheets with the lubricant sheet remain incommensurate due to lattice mismatch or interlayer twists and, therefore, are highly lubricant. The encapsulating layers strain, slide, and twist on these lubricant interfaces to rearrange the relative twist angle, strain, and stacking configuration at the active touching points.

[0042] As used herein, the term "commensurate” generally relates to atomic stacking configurations that can be defined as metastable stacking configurations that bring the vdW layers closer, enhancing their electronic interlayer coupling and interlayer friction force. The "incommensurate'' states or regions, defining regions of the device wherein the vdW sheets are separated by the lubricant sheet, typically being outside of the cavity regions, may be defined as atomic stackings that lack the interlayer coupling between the vdW sheets and permit interlayer shifts with substantially lower friction forces.

[0043] In case of slight relative strain or marginal twist between the layers, an alternating domain pattern of polytype configurations may form in each junction (referred to as a moire domain pattern). Tuning the size and number of the domains in the moire pattern further controls the junction properties but is challenging due to the global deformation required. The incommensurate lubricant interfaces outside the cavity enables strain relief and relative twist control in response to external stimuli. Hence, the cavity architecture enables further control of a device's properties through tuning of its moire pattern, which is otherwise challenging. In the case of minute relative strain or shear, the lubricant sliding at the external interfaces enables the spontaneous formation of a uniform domain of single-polytype-configuration in each junction. The single domain can switch controllably to another polytype configuration by nucleating a narrow dislocation strip that slides across the entire junction. The junction dimensions set a minimal dislocation length and a corresponding energy barrier for such uniform switching. The switching dynamics depend on the dislocation mobility, which is sensitive to changes in the dislocation length, its orientation relative to the crystal axes, and the structural purity. Vacancies, atomic mixing, external contaminations, or any other sources of local disorder set practical pinning barriers and prevent switching. In particular, cutting the layers introduces open edge dangling bonds that pin down the dislocation motion and prevent switching. Thus, cavities defining confined junctions may be characterized as having no open bonds or active chemical functionalities in the active encapsulating layers that can pin or arrest the sliding of the sheets. This removes restrictions on the sheets and enables efficient switching between distinct polytype configurations despite the meta-stability of their commensurate interfaces.

[0044] While reduced planar dimensions at the junction enable tuning its switching stability without physically cutting the layers, the planar shape of the cavities is used to capture the boundary dislocation in narrow constrictions and further tune the coercive switching field. The overall array design controls the couplings between the cavities and further tunes the switching dynamics. Electrical contacts to the encapsulating layers may be implemented outside the cavity, bypassing the challenge of shrinking the active region dimensions. The top and bottom sheets, or the multilayer, may be cut outside the cavity into various shapes and used as shared or individual contact channels. Compared to current technologies based on structures made of 3D crystals, devices of the invention implementing cavities for active vdW junctions bring together unmatched properties of layered structures, enabling structural sliding between commensurate / incommensurate interfacial configurations and active junctions squeezed in dimensions down to the ultimate atomic scale.

[0045] Thus, the cavities described herein enable efficient, controlled, and robust switching of structural and electronic states in various moire patterns and stacking configurations of vdW interfaces. The switchable junctions form at the cavities and serve as active electronic, magnetic, optical, non-volatile multi-ferroic components, diodes, transistors, tunnel junctions, ferroelectric tunnel junctions (FTJ), magnetic tunnel junctions, memristors, optical sensor, optical emitters, and optical switches, memory cells. Coupling between the individual cavities enables neuromorphic response and computing beyond Von-Neumann-Architecture.

[0046] The invention therefore further provides a hetero structure device comprising a lubricant layer separating two vdW sheets, the lubricant layer having a plurality of cavity structures permitting interaction between the two vdW sheets, defining switchable active junctions. The switchable active junctions may act as electronic junctions, magnetic junctions, optical junctions, non-volatile multi-ferroic components, diodes, transistors, tunnel junctions, ferroelectric tunnel junctions (FTJ), magnetic tunnel junctions, and others, enabling device configurations as memristor devices, optical sensors, optical emitters, optical switches, and memory cells.

[0047] In some embodiments, at least a number of the cavity regions are connected to each other or to other cavities, thereby enabling neuromorphic computation. The memory , computation, and learning processes rely on the connectivity between the cavity regions.

[0048] Additionally, de vices of the invention may be configured to affect a ‘multiply and accumulate’ function, as further disclosed herein. In addition, devices of the invention may be used for (a) neuromorphic computation where the memory, computation, and learning processes rely on the connectivity matrix between the various cavity regions; or for (b) algebraic operations (e.g. matrix or vector multiplications) where the cavities spatial arrangement and dimensions can be used to implement multiply and accumulate functions. In other words, the cavity regions may be spatially arranged and dimensioned to enable algebraic operations. The novel concept of the invention may be further understood from Fig. 1 which shows typical stacking potentials of vdW interfaces between two layers with similar lattice constants. In the demonstrated example, elemental honeycomb layers such as graphene have been used with two identical atoms in the unit cell of each layer (Fig. 1A) or binary compounds like boron nitride and transition metal dichalcogenides (TMDs) with two distinct atoms. The metastable stacking configurations place half (Fig. IB) or all (Fig. 1C) of the atoms precisely above each other while the other half of the atoms (or none) face the open hexagon center of the opposite layer. Notably, the metastable stacking configurations at the bottom of the stacking potential wells bring the layers closer, enhancing the electronic interlayer coupling. As shown, interlayer shifts of single atomic spacing a-O. lnm along the armchair lattice direction switch the polytype configuration between three cyclic positions marked as AA, AB, and BA in parallel bilayers (Fig. IB) or AA’, AB 1', and AB2' in antiparallel bilayers ( Fig. 1C). Each configuration has distinct crystal structures and orientation, resulting in different properties and electromagnetic responses. Thus, switching by interlayer sliding between incommensurate / 'commensurate stackings and between the commensurate polytype configurations is a pronounced method to control the device response.

[0049] Switching, however, in a controlled, reversible, and efficient manner is challenging. It requires overcoming the energy bander at the shifted intermediate states where the layers are further apart, and the stacking potential is higher. Since the atoms in each monolayer are held tightly together by solid bonds with a large stiffness k~ 0.1-1 TPa, indi vidual atoms cannot jump out of the metastable potential wells. Instead, the shift between polytypes accommodates over a partial dislocation strip that is a few nanometers wide, set by W oc 1 meV the energy barrier height marked in Figs. 1B-C. The properties of the dislocation determine the polytype stability, critical transition temperature Tc, and switching dynamics. In response to thermal fluctuations, external stress, or electromagnetic fields, the boundary strips form and then slide along the structure to swatch between the structural configurations. The mobility of the dislocation strips is further affected by structural defects, open bonds, and external contamination that can pin down the lubricant motion of the incommensurate strip and suppress efficient structural switching. In particular, the physical edges with open bonds in each layer pose a substantial pinning potential that further suppresses boundary strip motion and switching.

[0050] Thus, the lubricant cavity architecture enables a method to control the polytype dimensions down to the nm scale (comparable to W) without physically cutting the encapsulating layers and introducing open edge dangling bonds. It is further disclosed that designing non-circular shapes allows for pinning down partial dislocation to narrow cavity sections and further control of the switching dynamics in different cavity regions. Outside the cavity, the lubricant incommensurate interfaces enable interlayer rotations and deformations towards adjusting the commensurate configuration and moire pattern in the cavity with a relatively small energy cost. The spacing between the cavities and the global array design permits tunning individual junctions' structural stability and switching properties. For a dense pattern of cavities, the overall response becomes sensitive to the interaction between the junctions. These elastic and electromagnetic interactions enable multi-ferroic devices that respond as artificial materials where junctions replace the atoms, and the array geometry controls the inter-junction coupling. Unlike current technologies where the local active junctions or quantum dots form by patterning the active crystal or the shape of the gate electrodes, the active regions in the novel lubricant cavity architecture may be defined by patterning the spacer material only, while the gates and electrodes remain uniform above and under the dots.

[0051] Source and drain electrodes can be attached near (above and under) the active regions. In some embodiments, the electrodes can be made from thin 3D metals. For example, according to some embodiments, the 3D metals can include gold or layered metal, layered semi-metals like graphene, or semiconductors like TMDs. Since the lubricant spacers separate the layers outside the cavity regions, these sections of the device can act as part of the electronic leads to the confined active interfaces of the junctions. This geometrical architecture can minimize the active junction dimensions while maintaining sufficient electrical contacts. This architecture also decouples the contacts and contact areas from the active area, allowing more flexibility in design and higher manufacturability of the device regardless of the switching capabilities.

[0052] In some embodiments, top or bottom gate electrodes, or both, can be positioned above and under the encapsulating layers, and separated by a thin dielectric layer as in standard field effect devices. According to some embodiments, a device or system can include insulating or semiconducting active layers like h-BN and TMDs that form vertical electric polarization at the active junction region. The electric field from the external gates or the source and drain electrodes can control the vdW sliding at the active region, flipping the internal polarization. The tunneling current between the source and drain electrodes depends on the internal polarization, thus enabling non-volatile ferroelectric tunnel junctions (FTJ).

[0053] The invention thus further provides a ferroelectric tunnel junction (FTJ) comprising an architecture according to the invention or a cavity arrangement as disclosed herein. The FTJ may comprise or may be a device as defined herein.

[0054] In some embodiments, the FTJ may be incorporated into a crossbar array or a memory cell. In some embodiments, the FTJ may be incorporated into a neuromorphic computing chip or a synaptic device such as a synaptic memristor or a synaptic transistor.

[0055] In some embodiments, in a device of the invention, the vdW sliding is sensitive to external stimuli such as electric / magnetic fields, current pulses, mechanical stress, etc, applied locally from a nearby electrode or an optical pulse from a nearby light source. Each external stimulus can nucleate and push boundary dislocations to switch between different polytypes and stacking configurations, even if the latter are not polar. The external stimuli can generate a relative strain or twists between the active layers to induce and control the moire pattern in the active interfaces. In case of sizeable relative strain or twists, the active interface is fully incommensurate, the coupling between the layers reduces significantly, and the overall junction response changes. Such switching between commensurate polytypes and incommensurate interfaces is similar to phase change materials that switch between ordered and amorphous atomic configurations and can have several technological applications. The lubricant cavity concept according to some embodiments disclosed herein enables switching between the ordered polytype configurations and switching from each ordered configuration to a non-periodic disordered incommensurate configuration.

[0056] In more complex scenarios, the number of active interfaces can be larger than two, and several polytypes can exist in each cavity. For example, according to some embodiments, tri-layer graphene can be arranged in several orientations: AAA, ABA, ABC, etc. The basic architecture described above is the building block of the device (Fig. 3). Each additional layer on top of the first interface can have an additional spacer cavity on top of the original one, where the sagging of the top layer 2D material in the second cavity extends to the tangent on the bottom of the original cavity. An optional electrode to each layer can be interlaced into the respectable cavity. Thi s can form another interface in the tangent, and many more can be added on top, each with a separate electrode and control.

[0057] Current and voltage bias between the source of one or more cavities and the drain of one or more cavities, some of which may be different cavities, can be applied in order to affect a measured result which is a function of the interfacial atomic arrangement of all participating cavities. This can be used to implement mathematical functions, for example multiple and accumulate, but also other functions, as further disclosed herein.

[0058] Devices of the invention may implement arrangements of cavity regions of same or different cavity sizes (and / or shapes); or a plurality of devices having each a different arrangement of cavity regions. In cases where different or a plurality of devices are utilized, the assembly or array of devices may be operated or used as a single device. In such and other arrangements, devices may be further be utilized in digital to analog conversions. In some applications, energy consumption associated with digital to analog conversion (DAC) is prohibitive. Devices of the invention may implement cavities arranged in groups of powers of X (XB, for example powers of 2“, wherein n is an integer, i.e., zero, 1, 2, 3 and so forth and the groups sizes is thus 1, 2, 4, 8, 16, and so forth, and wherein X may be any integer equal to or greater than 2), wherein the first group is driven by an electrode representing the least significant bit (e.g., 2°, LSB), the second-to-the-last significant bit is connected to the second group, and so on until a full digital ‘word’ is applied. Alternatively, an array of devices, each having a different arrangement of cavities in X“, e.g., 2" groups may be used. In such an arrangement, each group of cavity regions may be associated with an independent input electrode. Each of the groups may be configured to generate a cumulative current in response to applying a digital signal to input electrodes associated with each of the groups, to thereby generate an analog output representing an input digital word. In other words, as a result of applying a digital signal to the input electrodes and reading the cumulative current (or in other electrical arrangements, the cumulati ve voltage) one can get an analog output representing the input digital word. Similarly, devices in sizes of powers of two connected together can achieve similar function. This analog signal can be used to effect high speed modulation or mixed with other such generated signal for high frequency processing (such as software defined radio or other RF applications) or accumulated in the analog domain (e.g. on a capacitor) to affect a ‘multiply and accumulate’ function.

[0059] In some embodiments, such devices, as well as others as disclosed herein, may be used for high speed modulation or for high frequency processing.

[0060] In some embodiments, devices of the invention are configured and operable to change at least one electrical, magnetic or optical property thereof in response to externally stimulating one or more of the cavity regions.

[0061] The invention further provides a device comprising a lubricant sheet comprising an array of cavity regions, said lubricant sheet being provided between two van-der Waals (vdW) material sheets, having incommensurate regions where the two vdW sheets are separated by the lubricant sheet; and commensurate regions within each of the cavities in the cavity regions, where the two vdW sheets interact or couple; wherein the array of cavity regions is arranged in groups of powers of 2 (2s), and wherein each of the groups is configured and operable to generate a cumulative current in response to applying a signal to input electrodes associated with each of the groups, to thereby generate an analog output representing an input digital word.

[0062] Expanding the performance of field effect devices is a key challenge of the ever- growing chip industry at the core of current technologies. A highly desired nonvolatile response in tiny multiferroic transistors is expected by electric field control of atomic movements rather than the typical electronic redistribution. According to the present disclosure, such field effect control of structural transitions was established in commensurate stacking configurations of honeycomb van der Waals (vdW) polytypes by sliding narrow boundary dislocations between oppositely polarized domains. The interfacial ferroelectric response, however, relied on preexisting boundary strips between relatively large micron-scale domains, severely limiting practical implementations.

[0063] The rapid growth of artificial intelligence (AT) pushes traditional computing architectures to their limits. These limitations are particularly pronounced in data- intensive applications, such as Large Language Models (LLMs), where memory access and efficiency are critical bottlenecks. For example, most of the LLMs’ operation involve matrix-vector-multiplications (MVM), where traditional computing architectures cannot keep pace with the evol ving requirements. The root cause of the bottleneck is the classical GPU-Bus-Memory traffic. As the GPU serially executes the multiple-and-accumulate operations (MAC), a significant traffic is bottlenecked on the bus, causing latency and redundant energy consumption. An alternative approach that bypasses this challenge relies on realizing artificial neural networks (ANN) on dedicated neuromorphic hardware composed of crossbar arrays of non-volatile memory units which directly implement the matrix that needs to be multiplied. While expected to lead to a major boost in energy efficiency and computational throughput, the non-volatile elements at the core of present ANN face practical challenges that limit the learning capabilities and lifetime of such devices. Presently developed crossbar arrays are based on magnetic or resistive random- access memories (MRAMs, RRAMs), phase change memory PCM, Ferroelectric field effect transistors (FeFETs), and ferroelectric tunnel junctions (FTJs) elements that serve as an analog or binary weight of the ANN. Notably these devices are limited in efficiency, speed, heat dissipation, uniformity, durability, and sustainability which restricted their implementation in crossbar arrays to date.

[0064] The ferroelectric tunnel junction (FTJ) device of the invention, as disclosed herein, uses the natural polarization properties of the active regions to achieve a non- volatile control of the tunneling conductance at the crossbars' junctions. Exceeding a threshold switching bias between a top and bottom electrodes in the device stimulates a sub-nanometer sliding motion between the vdW layers that flip the internal polarization and enhance / reduce the tunnelling current at the junction between the electrodes. Since the tunnelling conductance and switching mechanisms of FTJs rely on inert interfaces between single-crystal materials they exhibit significantly lower variability, greater reliability, and improved repeatability compared to the previous non-volatile element that rely on polycrystalline or amorphous materials, which typically suffer from high stochasticity and surface inhomogeneity. These properties are particularly crucial for ANN training and inference, where consistency and precision are essential for robust and efficient operation.

[0065] Thus, the invention further provides a non-volatile resistive memory unit implementing a multilayered assembly as disclosed herein.

[0066] Further provides is a neuromorphic computing system implementing an artificial neural network (.ANN) comprising an array of non-volatile memory units implementing a multilayered assembly as disclosed herein, w'herein the assembly implementing an array of cavities. The array may enable memory, computation, and learning processes.

[0067] The invention also provides a neuromorphic computing platform according to the invention when installed with an artificial intelligent (Al) based tool. Also provided is a neuromorphic computing chip comprising a ferroelectric tunnel junction (FTJ) according to the invention, wherein the FTJ is a synaptic device.

[0068] Also provided is a device according to the invention, wherein the cavity arrangement provides a neuromorphic function.

[0069] Further provided is a crossbar memory array comprising a ferroelectric tunnel junction (FTJ) according to the invention.

[0070] The “crossbar” is generally as known in the art. The crossbar may be a hardware block that has a plurality of inputs, a plurality of outputs and routing, or switching, logic that can selectively couple or connect certain inputs to certain outputs. It is to be noted that various implementations need not be fully connected or otherwise have a particular design. Rather, the crossbar contemplates any type of switching structure with multiple input / output ports that is configured to receive data via one or more ports and selectively convey corresponding data via one or more ports.

[0071] The ANN of the invention provides a groundbreaking fast, energy-efficient and reliable non-volatile resistive memory element that overcomes the limitations of existing technologies, pushing the performance boundaries in all these dimensions and thus paving the way for breakthroughs in Al, high-performance computing, and next-generalion electronics.

[0072] The development of low-power, reliable, and scalable physical ANN hardware remains an ongoing challenge, requiring continued advancements in materials science, device engineering, and circuit-level compensation techniques. Inferencing and learning in ANN imposes distinct requirements on non-volatile devices. The ideal device characteristics for analog synaptic weight storage in neural networks include a large dynamic resistance range with a relatively large low' -resistance state (LRS) value (~1 MQ), high resistance tunability with uniform incremental updates, multiple distinguishable resistance levels, and CMOS-compatible switching voltages. Conductance switching must be optimized to ensure precise MVM operations with specific resistance range to balance power consumption (low conductance) and read speed requirements (high conductance). Endurance is more critical than retention for online learning, where frequent weight updates occur. In contrast, offline training, where weights are updated infrequently via off-chip training, demands robust retention characteristics. To match the biological systems, platforms for ANNs should achieve ultra-high integration density (>1 Terabit per cm2) and low energy consumption (< 10 fJ per operation), yet to date no single device technology has demonstrated all these desired properties simultaneously and there is no feasible path to achieve this with traditional GPU-Bus -Memory architecture .

[0073] Among the existing non-volatile technologies, flash memory, based on charge- trapping or floating-gate field-effect transistors, is widely used in mass storage applications such as solid-state drives (SSDs). Flash memory can store multiple states per cell, making it suitable for adjustable weight storage. NAND flash offers high density, but it restricts read and write operations to the page level and requires block-level erasing. NOR Flash, allows random access but has a significantly lower density than NAND. A major drawback of flash technology in ANN applications is its high programming voltages (> 10 V), leading to increased power and energy consumption. Additionally, its endurance is limited (~10k cycles), and its performance is further constrained by variability and reliability issues due to the stochastic nature of charge trapping and emission, as well as dielectric degradation under high-voltage stress. Emerging memristive technologies, such as RRAM and PCM, are commercialized as standalone memory solutions but still constitute a small fraction of the global NVM market. RRAM uses oxide-based defect formation, whereas PCM utilizes amorphous-crystalline phase transitions in chalcogenides. Their two-terminal structure facilitates high-density crossbar arrays, enabling random access and efficient stacking for increased memory density. State-of-the-art chips targeting inference through in-memory computing have been demonstrated with RRAM and PCM memristors, achieving competitive energy efficiencies exceeding 10 trillion operations per second per watt (TOPS / W) and memory sizes on the order of megabits for MVM tasks. However, these devices also suffer from stochastic variability, cycle-to-cycle and device-to-device, due to defect formation in RRAM and phase nucleation in PCM, making precise weight updates in ANNs challenging. Additional reliability concerns include endurance limitations (~1M cycles), resistance drift, and random telegraph noise, particularly in high-resistance states.

[0074] Unlike any other thin film of polar 3D material, the intrinsic interfacial polarization demonstrated for devices of the invention is robust and uniform down to the two-layers thin limit and accumulates in fixed potential steps with each additional layer and interface. The remarkably low depolarization response at this ultimately thin limit (stemming from the inert nature of van der Waals interfaces) enables less than 5% variability across all devices we measured to date, and tunnelling currents as high as pA per a 10 nm diameter junction. By adding layers into the polar barrier, the ON conductivity and the overall polarization of TFJ are expected to exhibit unprecedented control, reliability and device to device uniformity. Likewise, the sliding switching mechanism, which is fundamentally different from common ferroelectric materials, supports practically unlimited durability, and was experimentally measured to be greater than 1011operations at a fester than 1 nanosecond switching time (limited by test time). The switching is not susceptible to defect formation, disorder, and stochastic domain nucleation, which are unavoidable in 3D materials under high switching pulses. Rather, the single crystalline nature of TFJ remains intact with robust polarization (up to the turbostratic phase transition - above 800 degrees Celsius).

[0075] Markedly, the results show a highly appealing and robust control of the conductance switching field by adjusting the junctions' shape and dimensions. At present, the tiniest junctions with a 30 nm diameter exhibit a switching energy cost of only 0.15 Joules, while this is expected to further reduce to smaller junctions. In terms of integration density, it should be noted that previous memristive elements in crossbar arrays may also reach these appealing dimensions. Yet their passive footprint is much larger as they often require a 1 transistor- 1 -resistor (1T1R) structure to regulate current flow and as an access device (and even 6-transi stars, 6T, in the case of DRAM devices). Conversely, the abrupt internal polarization switching in FTJs enables the highest possible integration density with purely passive crossbars without any additional transistors. The key characteristics of Sliding Ferroelectric Tunnel Junctions (FTJ) of the invention:

[0076] As we can see, the FTJ is the only technology that potentially provides the reliability, uniformity, sustainability and endurance required for physical ANN while operating on a lower voltage (driving lower energy consumption per operation) and at potentially higher speed than competing technologies.

[0077] The invention further contemplates a process for manufacturing a device of the invention, the process comprising encapsulating a lubricant sheet having a patterned array of (go-through) holes or cavities with a pair of van der Waals (vdW) sheets, permitting contact interaction between the pair of vdW sheets solely within cavities of the cavity pattern. The contact interaction within each cavity defines an active junction that can be externally stimulated to modify a property of the device, as disclosed herein.

[0078] Also provided is a process for manufacturing a device of the invention, the process comprising patterning a lubricant sheet, as defined herein, with a hole or a cavity pattern and encapsulating the lubricant sheet with a pair of van der Waals (vdW) sheets, permitting contact interaction between the pair of vdW sheets solely within cavities of the cavity pattern.

[0079] As used herein, the term “encapsulation” refers to placement of a first of the pair of vdW sheets above (on a top surface or face of) the lubricant sheet and placement of a second of the pair of vdW sheets below (on a bottom surface or face of) the lubricant sheet. In some embodiments, the two vdW sheets are the same. In some embodiments, the two vdW sheets are different from the lubricant sheet in composition or lattice orientation.

[0080] In some embodiments, the process further comprises forming a top and a bottom electrode.

[0081] As disclosed herein, the cavities may be patterned to achieve a desired spatial arrangement or cavity density or generally a desired cavity or tangent profile which can determine the functionality and use of a device of the invention. Typically, the cavity pattern is predesigned. The cavity pattern may be designed to provide a digital to analog conversion, to provide a neuromorphic function, to provide a vector product, or provide any other functionable device.

[0082] In some embodiments, the cavity pattern and / or cavity connectivity allows for neuromorphic computation, including memory, computation, and learning processes.

[0083] In some embodiments, the cavity pattern and / or cavity or tangent profile, as defined herein, e.g., cavity dimensions, may be used to implement multiply and accumulate functions. In some embodiments, the holes or cavities are obtained by etching the lubricant sheet. In some cases, etching was achieved by electron-free local anodic oxidation (LAO) lithography. Other methods may also be used.

[0084] The invention further provides a process for modulating an electric, optical, magnetic property of a device of the invention, the process comprising stimulating one or more of the plurality of active junctions (cavities), wherein stimulation may be achievable by application of an electric field, a magnetic field, an optical pulse, a current pulse, a mechanical stress, and others.

[0085] In some embodiments, the stimulus is applied normal to the surface of the device.

[0086] The invention further provides a hardware-implemented method for operating a neural network system for vector matrix multiplication (MVM), the method comprising providing a neural network system comprising a controller, a memory, and an interface connecting the controller to the memory, wherein the controller comprises a processing unit configured to engineer the neural network and the memory comprises a neuromorphic memory device with a crossbar array structure comprising input lines and output lines interconnected at active ferroelectric tunnel junctions serving as a memristive device(s); said active junctions being in a form of a plurality of patterned cavities arrayed in a lubricant sheet encapsulated between two vdW sheets.

[0087] In some embodiments, the memristive device(s) is configured to change states thereof by external stimulation reflecting write signals into one or more of the gate and or bias input lines based on write instructions received from the controller and write vectors generated by the interface, according to the write instructions; and retrieving data from the neuromorphic memory device, by coupling read signals into one or more of the output current lines of the neuromorphic memory device.

[0088] Further provided is a hardware-implemented method for operating a neural network system for vector matrix multiplication (MVM) (see Fig. 22), the method comprising providing a neural network system comprising a controller, a memory, and an interface connecting the controller to the memory, wherein the controller comprises a processing unit configured to engineer the neural network (for example the array of gate electrodes, Vg 1-11) and the memory comprises a neuromorphic memory device with a crossbar array structure comprising input lines and output lines interconnected at active ferroelectric tunnel junctions serving as a memristive device(s) (for example, the greed of bias inputs Vl-5, and the greed of current outputs 11-8); said active junctions being in a form of a plurality of patterned cavities arrayed in a lubricant sheet encapsulated between two vdW sheets, as disclosed herein; the memristive device(s) being configured to change states thereof by external stimulation reflecting write signals into one or more of the gate and or bias input lines based on write instructions received from the controller and write vectors generated by the interface, according to the write instructions; and retrieving data from the neuromorphic memory device, by coupling read signals into one or more of the output current lines of the neuromorphic memory device.

[0089] The invention further provides:

[0090] A multilayered device or a device or a hetero structure comprising a lubricant sheet comprising one or more cavity regions, said lubricant sheet being provided between two van-der Waals (vdW) material sheets, wherein the two vdW material sheets interact or couple in each of the one or more cavity regions, to define active junctions.

[0091] In various configurations of the device of the invention, the device has incommensurate regions where the two vdW sheets are separated by the lubricant sheet; and commensurate regions within each of the one or more cavity regions.

[0092] Also provided is a device or a multilayered device or a heterostructure comprising a lubricant sheet comprising one or more cavity regions, said lubricant sheet being provided between two van-der Waals (vdW) material sheets, having incommensurate regions where the two vdW sheets are separated by the lubricant sheet; and commensurate regions within each of the one or more cavity regions, where the two vdW sheets interact or couple, to define active junctions.

[0093] In various configurations of the device of the invention, the device is configured for controlling local electronic and structural responses at said regions or junctions.

[0094] In various configurations of the device of the invention, in some or in each of the one or more cavity regions the two vdW sheets deform and sag into the cavities, enabling direct commensurate interaction between the vdW sheets in each of the cavities.

[0095] In various configurations of the device of the invention, the one or more cavity regions having each independently a tangent profile defining for each of the one or more cavity regions one or more tangent contact surface area, an angle of the sag between the sheets, a thickness of the cavity, the cavity shape and size, the cavities array symmetry, the cavities spread and separation distance, and a mechanical thickness of the top and bottom vdW sheets encapsulating the cavities. In various configurations of the device of the invention, the lubricant sheet is formed of a layered material with a different lattice constant / structure than the encapsulating vdW layers.

[0096] In various configurations of the device of the invention, the lubricant sheet is of a material that is same as the materials of two vdW sheets, provided that the lubricant sheet having a lattice orientation twisted relative to that of the two vdW layers.

[0097] In various configurations of the device of the invention, the lubricant sheet is selected from h-BN, hexagonal aluminum-nitride (h-AIN), hexagonal zinc-oxide (h- ZnO), hexagonal gallium-nitride (li-GaN), graphene, and transition metal dichalcogen ides (TMD s ) .

[0098] In various configurations of the device of the invention, the lubricant sheet is graphene.

[0099] In various configurations of the device of the invention, the lubricant sheet is hexagonal boron-nitride (h-BN).

[0100] In various configurations of the device of the invention, the transition metal dichalcogenide (TMD) is selected amongst M0S2, WS2, MoSer and WSe2.

[0101] In various configurations of the device of the invention, each of the two or more vdW material sheets is independently selected to exhibit strong in-plane covalent or ionic bonding and weak interlayer van der Waals interactions.

[0102] In various configurations of the device of the invention, each of the two or more vdW material sheets having a same lattice orientation, enabling commensurate interaction therebetween at each of the cavity regions.

[0103] In various configurations of the device of the invention, each of the vdW sheets is independently selected from h-BN and TMD materials.

[0104] In various configurations of the device of the invention, the device comprises a graphene lubricant sheet and two same or different vdW sheets formed of h-BN and / or a TMD material.

[0105] In various configurations of the device of the invention, the device comprises a plurality of lubricant sheets, each encapsulated between two vdW sheets.

[0106] In various configurations of the device of the invention, the tangent profile of each one of the one or more cavity regions and a distance between the cavity regions are selected to control elastic and electromagnetic coupling between the cavities and an overall array response. In various configurations of the device of the invention, the device is provided with a bottom electrical contact and a top electrical contact.

[0107] In various configurations of the device of the invention, the device is a hetero structure device comprising a lubricant sheet separating two vdW sheets, the lubricant sheet having a plurality of cavity structures permitting interaction between the two vdW sheets in each structure and defining switchable active junctions, wherein stimulating the switchable active junctions permits modifying device property / function.

[0108] Also provided is a device or a heterostructure device comprising a lubricant sheet separating two vdW sheets, the lubricant sheet having a plurality of cavity structures permitting interaction between the two vdW sheets in each structure and defining switchable active junctions, wherein stimulating the switchable active junctions permits modifying device property / function.

[0109] In various configurations of the device of the invention, the switchable active junctions being configured and operable as electronic junctions, magnetic junctions, optical junctions, non-volatile multi-ferroic components, diodes, transistors, tunnel junctions, ferroelectric tunnel junctions (FTJ), magnetic tunnel junctions, enabling device configurations as memristor devices, optical sensors, optical emitters, optical switches, and me mon cells.

[0110] In various configurations of the device of the invention, at least a number of the cavity regions are connected to enable neuromorphic computation, wherein memory, computation, and learning processes rely on the connectivity between the cavity regions.

[0111] In various configurations of the device of the invention, the cavity regions are spatially arranged and dimensioned to enable algebraic operations.

[0112] In various configurations of the device of the invention, the device implements an arrangement of cavity regions of same or different cavity sizes; or a plurality of devices having each a different arrangement of cavity regions.

[0113] In various configurations of the device of the invention, the arrangement of cavity regions is in groups of powers of 2 (2H).

[0114] In various configurations of the device of the invention, in the arrangement- each group of cavity regions is associated with an independent input electrode.

[0115] In various configurations of the device of the invention, each of the groups is configured to generate a cumulative current in response to applying a digital signal to input electrodes associated with each of the groups, to thereby generate an analog output representing an input digital word.

[0116] In various configurations of the device of the invention, the device is configured and operable for high-speed modulation or for high frequency processing.

[0117] In various configurations of the device of the invention, the device is configured and operable to change at least one electrical, magnetic or optical property thereof in response to externally stimulating one or more of the cavity regions.

[0118] Also provided is a device comprising a lubricant sheet comprising an array of cavity regions, said lubricant sheet being provided between two van-der Waals (vdW) material sheets, having incommensurate regions where the two vdW sheets are separated by the lubricant sheet; and commensurate regions within each of the cavities in the cavity regions, where the two vdW sheets interact or couple; wherein the array of cavity regions is arranged in groups of powers of 2 (2”), and wherein each of the groups is configured and operable to generate a cumulative current in response to applying a signal to input electrodes associated with each of the groups, to thereby generate an analog output representing an input digital word.

[0119] Further provided is a ferroelectric tunnel junction (FTJ) being or comprising a device, or having a cavity arrangement as defined herein.

[0120] In various configurations of the FTJ of the invention, the FTJ is incorporated into a crossbar array or a memory cell.

[0121] In various configurations of the FTJ of the invention, the FTJ is incorporated into a neuromorphic computing chip or a synaptic device.

[0122] In various configurations of the FTJ of the invention, the synaptic device is a synaptic memristor or a synaptic transistor.

[0123] Also provided is a non-volatile resistive memory unit implementing or being a device accoridng to the invention.

[0124] The invention further provides a neuromorphic computing system implementing an artificial neural network (ANN) comprising an array of non-volatile memory units implementing a device accoridng to the invention, wherein the assembly implementing an array of cavity regions enabling memory', computation, and learning processes.

[0125] A neuromorphic computing system is provided that is installed with an artificial intelligent (Al) based tool. A neuromorphic computing chip is disclosed that comprises a ferroelectric tunnel junction (FTJ) according to the invention, wherein the FTJ is a synaptic device.

[0126] The invention further provides a crossbar memory array comprising or implementing a ferroelectric tunnel junction (FTJ) according to the invention.

[0127] The invention further discloses a process for manufacturing a device accoridng to the invention, the process comprising encapsulating a lubricant sheet having a patterned array of (go-through) holes or cavities with a pair of van der Waals (vdW) sheets, permitting contact interaction between the pair of vdW sheets solely within cavities of the cavity pattern.

[0128] Also provided is a process for manufacturing a device accoridng to the invention, the process comprising patterning a lubricant sheet with a hole or a cavity pattern and encapsulating the lubricant sheet with a pair of van der Waals (vdW) sheets, permitting contact interaction between the pair of vdW sheets solely within cavities of the cavity pattern.

[0129] In various configurations of the process of the invention, the process further comprises forming a top and a bottom electrode.

[0130] In various configurations of the process of the invention, the cavity pattern is predesigned to provide a digital to analog conversion, to provide a neuromorphic function, or to provide a vector product.

[0131] In various configurations of the process of the invention, the cavity pattern and / or cavity connectivity is designed for neuromorphic computation.

[0132] In various configurations of the process of the invention, the cavity pattern and / or cavity or tangent profile is designed to implement multiply and accumulate functions.

[0133] In various configurations of the process of the invention, each of the holes or cavities is formed by etching the lubricant sheet.

[0134] Also provided is a process for modulating an electric, optical, magnetic property of a device accoridng to the invention, the process comprising stimulating one or more of the plurality of active junctions (cavities), wherein stimulation is achievable by application of an external stimulus to the device.

[0135] In various configurations of the process of the invention, the external stimulus is an external electric field, an external magnetic field, an external optical pulse, a current pulse, or a mechanical stress. The invention further provides a hardware-implemented method for operating a neural network system for vector matrix multiplication (MVM), the method comprising providing a neural network system comprising a controller, a memory, and an interface connecting the controller to the memory, wherein the controller comprises a processing unit configured to engineer the neural network and the memory comprises a neuromorphic memory device with a crossbar array structure comprising input lines and output lines interconnected at active ferroelectric tunnel junctions serving as a memristive device; said active junctions being in a form of a plurality of patterned cavities arrayed in a lubricant sheet encapsulated between two vdW sheets.

[0136] In various configurations of the process of the invention, the memristive device being configured to change states thereof by external stimulation reflecting write signals into one or more of gate and / or bias input lines based on write instructions received from the controller and write vectors generated by the interface, according to the write instructions; and retrieving data from the neuromorphic memory device, by coupling read signals into one or more of the output current lines of the neuromorphic memory device.

[0137] The invention further provides a hardware-implemented method for operating a neural network system for vector matrix multiplication (MVM), the method comprising providing a neural network system comprising a controller, a memory, and an interface connecting the controller to the memory, wherein the controller comprises a processing unit configured to engineer the neural network and the memory comprises a neuromorphic memory device with a crossbar array structure comprising input lines and output lines interconnected at active ferroelectric tunnel junctions serving as a memristive device; said active junctions being in a form of a plurality of patterned cavities arrayed in a lubricant sheet encapsulated between two vdW sheets; the memristive devices being configured to change states thereof by external stimulation reflecting write signals into one or more of gate and / or bias input lines based on write instructions received from the controller and write vectors generated by the interface, according to the write instructions; and retrieving data from the neuromorphic memory device, by coupling read signals into one or more of the output current lines of the neuromorphic memory device. BRIEF DESCRIPTION OF THE DRAWINGS

[0138] In order to better understand the subject matter that is disclosed herein and to exemplify how it may be carried out in practice, embodiments will now be described, by way of non-limiting example only, with reference to the accompanying drawings, in which:

[0139] Figs. 1A-E. Illustration of typical 2D polytypes made of honeycomb layers and their corresponding binding energies. (A) vdW stack of two honeycomb layers like graphene. The relative shift vector ux= a along the armchair crystal direction moves one of the layers between three cyclic positions (A,B,C) to switch between high-symmetry stacking configurations. (B) The vdW stacking potential (right axis) and interlayer distance Z (left axis) of parallel and antiparallel (C,E) bilayers made of binary honeycomb compounds like boron-nitride. The local potential wells show the metastability of the polytypes. (D) Interlayer separation Z near the partial dislocations. The deformation is confined within a few nanometers from the dislocation center.

[0140] Figs. 2A-E. Illustration of a lubricant cavity junction and device array. (A) A cross-section of a cavity in the lubricant spacer (green polygon), encapsulated by two layered flakes that touch at the center of the cavity to form an active interface. The active junction region (dashed red frame) can switch between incommensurate and commensurate stacking configurations. Top and bottom electrodes (gray graphene, or any other material) are positioned above and under and function as source and drain in a ferroelectric tunnel junction device. The width of the cavity is tuned down to the dislocation width limit W without physically cutting the layers. Top and bottom gates are further implemented in some devices to control the properties of the electrodes as in field effect devices. (B) Top view of a cavity array. The shape of each cavity, the distance to the nearest neighbor cavity, and the symmetries of the cavity array are designed to tune the elastic and electromagnetic coupling between the cavities. (C) Atomic force microscope topography map of a lubricant cavity junction and a height profile. (D) Line- cut showing the spacer's thickness (~3nm in this example). In some implementations, the thickness is as thin as a monolayer (sub -nanometer). The active interface dimensions (~100nm) and the cavity diameter (~600nm) are controlled independently down to a few nm limit. (E) Examples of non-circular cavity designs confining the boundary dislocation to narrow sections in the cavity. Fig. 3. According to some embodiments, an architecture for a multilayer / multi- polytype device wherein each layer has its own cavity stacked on top of the previous cavity.

[0141] Figs. 4A-D. Super-Lubricant Array of vdW Polytypes (SLAP). (A, B) Sideview, and Top view device illustrations. The line cut shows a pair of cavities etched in a bilayer graphene spacer (identical carbon spheres) and encapsulated by two parallel h-BN layers (yellow and blue spheres). Commensurate h-BN interfaces of AB / BA polytype configurations at the cavities are shaded with dark / bright brown color for down / up internal polarizations. Lubricant incommensurate interfaces with the spacer are cyan- shaded. The right-side cavity island shows mixed BA / AB domains separated by a w-wide partial dislocation strip. The dashed-dotted line borders a region of antiparallel AA' and AB 1' polytypes islands marked by dark blue / bright blue colors, respectively. (C) Topographic image of Device 1 with two nm thick parallel h-BN flakes. Note the brighter (one layer thicker) surface below the dashed-dotted line. (D) Corresponding electric surface potential map by Kelvin probe force microscopy (KPFM).

[0142] Figs. 5A-C. Electric field-induced dislocation nucleation and annihilation. (A) AFM topography and surface potential maps of Device 2 before electric field polling. (B) The relative bright domain area (A-p) in the 150 nm cavity marked by a solid line frame in a. as a function of the tip bias during the electric polling scan before imaging. The coercive switching fields are indicated by bright / dark bars. Full hysteresis loop maps of all marked cavities are shown in Figs. 9 and 10. (C) Illustration of intermediate domain structures observed in the experiments (see Fig. 11).

[0143] Figs. 6A-C. Mechanical nucleation and reconfiguration of confined domain patterns. (A) Surface potential maps of Device 3 with functional WSe2 monolayers before and after contact mode scans at a tip force of 300 nN. Black arrows show the orientation of the slow and fast contact scanning axes before the non-contact imaging. (B) Schematic illustration of the cavity topologies observed, including single, two, and multi-domains of twisted moire patterns. (C) Surface potential maps taken after pressure scanning the regions marked in dashed lines. Scanning the fast axes perpendicular to the boundary strip in the forward direction only (straight arrows) does not change the final pattern, while back and forward scanning of the fast axes along the strip (armchair) direction (curved arrows) controls the boundary position accurately and reversibly. Figs. 7A-C. Optical device images. (A,B,C) Optical microscope image of devices 1, 2, and 3 presented in Figs. 4, 5 and 6, respectively. Scale bars indicate 25 pm.

[0144] Figs. 8A-D. Comparison of spacer lithography methods. (A,B) AFM and optical microscope image of local anodic oxidation lithography with cavity diameter down to ~20 nm. (C,D) AFM and optical image of laser pulse lithography.

[0145] Fig. 9. Imaging ferroelectric hysteresis loop for a 150 nm cavity (Device 2, see Fig. 5). Domain pattern imaged by KPFM after bias scans at the voltage and time indicated on each map.

[0146] Figs. 10A-D. Additional ferroelectric hysteresis measurements (Device 2). (A) Topographic and KPFM maps of the cavity array. (B,C,D) Hysteresis loops of the cavities marked in a. with diameters 150, 250, 350 nm respectively. Bright and Dark column stands for the switching to complete up and down polarization.

[0147] Figs. 11A-D. Triangular intermediate transition states (Device 2). (A) Topographic image of a 250 nm cavity. (B,C,D) KPFM image measured before and after applying bias scans as indicated in each map.

[0148] Figs. 12A-C. Determination of threshold pressure for dislocation movement. (A) Topographic AFM image of the measured array. (B) KPFM signals before tip pressing. (C) Successive pressing experiments. Scanning illustration and applied force indicate the contact mode scan parameters before the KPFM image.

[0149] Figs. 13A-D. Imaging sagging of active layers (Device 2). (A,B) Topography and surface potential maps of as-fabricated cavity array. (C,D) Topographic and KPFM maps after AFM contact mode scans at a pressure of 300 nN. Scale bars are 1 pm.

[0150] Figs. 14A-C. Friction force measurement around the cavity. (A) Friction force calibration curve measured in atomically flat h-BN. (B) Topographic image of cavity in Device 3 measured in 300 nN loading force. (C) Corresponding friction force mapping at 300 nN normal force applied.

[0151] Figs. 15A-F. Optical image of the devices. (A) Two pieces of bilayer graphene (BLG), (B) Monolayer graphene spacer (MLG), (C) Final device, where the red, blue, and yellow dashed rectangles represent the boundaries of the two BLG pieces and the MLG spacer, respectively. (D-F) Another similar device.

[0152] Figs. 16A-I. Friction force imaging. (A,B) Schematic illustration of lateral photodiode signals and the torsional motion of the AFM tip during forward and backward scans. (C) Map of the lateral signal for forward and backward scans. (D) Line-cut along the dashed line in (C). (E) Friction force as a function of the loading force. (F-H) Examples of friction force calibration maps. (I) Corresponding topography map.

[0153] Figs. 17A-F. Comparison of Raman and current maps. (A) Optical image of few- layer exfoliated graphene flakes. (B) 2D Raman map of the four-layer graphene region outlined by the red frame in (A). (C) 2D Raman peaks corresponding to R and B polytype regions. (D) Current map of the regions shown in (B). (E) Current map of the SLAP device. (F) Line-cut along the dashed lines in (D) and (E).

[0154] Figs. 18A-H. Switchable graphitic polytypes in superlubricant arrays. (A) Illustration of a SLAP device and the conductive AFM measurement circuit. A rotationally misaligned monolayer graphene spacer (dark gray) with circular cavities is sandwiched between a pair of parallel bilayer graphene sheets (light gray), placed on a flat hexagonal boron-nitride substrate. (B) Cross-sectional view of two cavities along the red line-cut in (A). Black commensurate spheres within each cavity (shaded in dark and light gray) mark an eight-atom unit cell of Bernal (B) and Rhombohedral (R) polytypes. Lubricant incommensurate interfaces outside the cavities are shaded in light blue. (C) AFM topography image. (D) Imaging current scan measured with low friction force of 6.7 nN (corresponding to 100 nN load on the tip). Dark and bright islands are B and R polytypes, respectively. (E) Imaging scan after performing several high-load switching scans. Red and green frames mark single and double-switching events, respectively. (F- H) Example of another SLAP array. The current map during the switching scan with a 17 nN friction force (350 nN load) is shown in (G). Scale bars mark 400 nm.

[0155] Figs. 19A-J. Island stability versus spacer twist angle. (A) Illustration of a dense dislocation pattern with short, partially commensurate, hexagonal moire wavelength =10 nm between the spacer and the aligned active bilayers. (B) Zoom in current map near the cavity. (C,D) Current maps collected at forward (C) and backward (D) scan direction under a friction force of 19 nN (corresponding to a vertical tip load of 400 nN). In each successive line, the B / R boundary strip in the cavity is shifted before it retracts back spontaneously to its initial middle position. (E) Topography of the measured area. (F,G) Similar current maps obtained under a low friction force of 4.5 nN (corresponding to a 50 nN load), below the threshold coercive force. (H) Illustration of a commensurate and hence triangular moire pattern with the spacer. (I) Current map of a commensurate cavity array. Although the twist between the active bilayers is smaller than with the spacer, it remains finite inside the cavity (see islands with triangles). The red frame outside the cavity marks a large triangle (with no twist between the active layers) containing small triangles due to the twist with the spacer. Here, the commensurate patterns outside the holes stabilize moire patterns within the holes. The yellow frame shows smaller domains outside the cavity with a less commensurate spacer. (J) Topographic image of the area in (I).

[0156] Figs. 20A-F. Boundary strips between remote stacking configurations. (A) Current AFM map optimized to detect partial dislocation between the separated active layers (dark stripes) outside the cavities under a friction force of 19 nN (corresponding loading force of 400 nN). (B) Cross-sectional illustration of the remote stacking at the boundary strip. The unit cells of weakly commensurate Bernal-like (B) and Rhombohedral-like (R) remote configurations across the misaligned spacer are framed in red. (C,D) Zoom-in maps taken before and after R to B switching showing the accompanied motions of remote dislocation. The dashed green lines intersect the bright R islands and then shift to the bottom of the cavity while the islands switch to B polytypes. The yellow circle shows an R island, which is not intersected by any remote dislocation. Instead, a dark circular halo appears around the island. (E,F) Example of remote dislocations which are attracted to the cavity and tend to align with the inter-island axis. The red frame shows a switching event of one individual island separated by 50 nm from another island.

[0157] Figs. 21A-F. Coupled cavities via narrow channels. (A) Topographic image of a lubricant cavity array connected by narrow cavity channels. (B-F) Successive current imaging maps tracing the direct boundary strip motions (colored lines) before and after switching scans (not shown). The orientation and friction force of the switching scans between the low-load imaging scans are indicated by the black wiggling arrow. For example, the low-friction force of 5.5 nN (corresponding loading force of 70 nN) imaging scan in (C) is followed by a switching scan with a 17 nN friction force (350 nN of load) and a slow scan axis oriented from bottom to top, and then panel (C) show the final rearrangements.

[0158] Figs. 22A-B. Illustrations of a super-lubricant sliding ferroelectric tunnel junctions (SFTJs) crossbar array. (A) The SFTJs arrays are made by assembling honeycomb layers of boron and nitrogen atoms (yellow and blue dots) into a two-atom- thick ferroelectric crystal in nanometer- scale diameter islands. The up / down pointing polarization (arrows) control the electric potential difference (gold / blue colors) between a top metal and a bottom graphene electrode and the corresponding on / off tunneling current (red). (B) A Voltage input vector (VI -5) is converted to a current output vector (11-8), depending on the polarization state of the junction at each crossing point of the matrix. Junctions with different / same polarizations (and colors) in the array are separated by an odd / even number of soliton boundary strips (gray lines). The yellow crossbar represents a second set of gate electrodes (Vg 1-11) that allows reconfiguring the position of these superlubricant soliton strips and the long-range elastic coupling between the junctions.

[0159] DETAILED DESCRIPTION OF EMBODIMENTS

[0160] Methods

[0161] Sample preparation: Our vdW cavity arrays include (top to bottom): / z-BN / top functional layer / graphene spacer / bottom functional layer / graphite gate electrode / SiOi substrate assembled using dry polymer stamping method with either monolayers WSe2or few layers / z-BN as the functional layers.

[0162] Device characterization

[0163] In the main text we present data from three selected devices. Device 1, (Fig. 1) with a 4.3 nm thick / z-BN flake used to pick up active 2.3 nm and 2 nm active / z-BN flakes, and a bilayer graphene spacer. In device 2 (Fig. 2) we used 2.5 nm thick / z-BN to pick up trilayer / z-BN (1 nm), monolayer graphene spacer, and trilayer / z-BN. In device 3 (Fig. 3) we used a 4.5 nm / z-BN to pick up monolayer WSe2, graphene spacer and monolayer WSe2. Thicknesses of the Flakes are summarized in the Table below, and an optical microscope image of each device is shown in Figs. 7A-C. .

[0164] Pick-up / z-BN, top layer, graphene spacer, bottom layer are outlined with red, green, blue, and orange lines respectively. Graphene spacer lithography

[0165] The quality of the cavity edges is crucial to minimizing the pinning of dislocation boundary strips. Our best results were obtained using the electrode free local anodic oxidation (LAO) lithography method. Step-by-step procedures are summarized as follows, a. Choose the wrinkle- and tape-residue free graphene monolayer with optical microscope. b. Pt-coated AFM tip (Mikromasch HQ:NSC35 / Pt Tip C) was used to clean 10x 10 pm2lithographic area in advance for removing dirt which is not captured by optical microscopy. Relative humidity (RH) was maintained 60-80 % to boost chemical reaction between tip and graphene with commercial humidifier. c. Tip was retracted from the graphene surface to form water bubbles on the tip edge. 10 VAC, 40 kHz were applied in PFM mode (NX10, Parksystem inc.). d. Using the lithographic option in NX10, predesigned bitmap image was used to make various shapes. 100 nN setpoint was used for each pixel approach. We avoid higher setpoint results in breaking and flipping graphene edge. e. After lithography, any remaining oxidized residue and dirts was removed by cleaning the surface using HQ:CSC38 / A1 BS tip B from MikroMasch. The outer spacer dimensions were cut to ~ 10 X 10 pm2using high-intensity pulsed laser light (1064 nm, in a WITEC alpha300 Apyron confocal microscope setup).

[0166] A typical AFM topography map and an optical microscopy image of a trilayer graphene spacer are shown in Figs. 8A-D. . The cavity diameter is reduced down to ~20 nm which is related to the tip apex dimensions (see AFM map) and remains free of oxidation residues. In contrast, cutting the spacer with high-intensity pulsed laser light resulted in substantial oxidation rings (see bright rings in Fig. 8C) that damaged the device performance. We note that various laser exposure times and beam intensities always resulted in oxidized layers and topographic eruptions at the edges, extending by approximately 1 pm from the center of the heated area. These oxide layers are not visible in optical microscopy (Fig. 8D).

[0167] KPFM: KPFM images were acquired under an inert nitrogen environment using a Park NX10 Hivac system in sideband mode. HQ:NSC35 / Pt tip C with -150 kHz resonant frequency, 5.4 N / m spring constant or N doped diamond tip HQ:DMD-XSC11 tip B with -110 kHz resonant frequency, 6.5 N / m spring constant were used for KPFM measurements. For sideband measurements, the resonant frequency of the tip was calibrated and then set 2.5 kHz away. The tip was excited by 2 VAC with 9 nm - 15 nm setpoints for all measurements.

[0168] Dislocation control by electric fields: To maintain a large contact area between the tip and the surface, we used contact scanning with 160 nN on HQ:NSC35 / Pt tip C (apex radius below 30 nm), 1 Hz scan speed, and pixel sizes under 5 nm at all specified DC voltage. Alternatively, for HQ:DMD-XSC11 tip B, (apex radius 100-250 nm), we used 90 nN. The same scan direction was used in all scans.

[0169] Size dependence of coercive switching fields

[0170] Switching a uniform single-domain cavity into a full oppositely-polarized state involves intermediate domain patterns that govern the system response. To reveal the intermediate state pattern, we imaged the cavity’s surface potential evolution after each increment of the external electric field. Fig. 9 shows a selected set of images for a 150 nm cavity . In this case, we used bias increments of ~0.3 V, corresponding to displacement field steps of 0.06 V / nm, and measured repeatable hysteresis loops for 5 times. The first two maps show a fully-polarized cavity after polling beyond the positive / negative coercive fields (as indicated). Starting with a uniform up (bright) polarization in Fig. 5B in the main text, the following image (1 V, at time ft) shows the first bias in which a boundary wall nucleates and a dark domain covering -1 / 2 of the cavity area appears. This domain pattern remains the same up to a 3 V bias, where the cavity switches to a fully down-polarized state. The following maps show reversible switching along hysteresis loops with a coercive field between -2.1 Vtip and -2.4 Vtip for up-polarization and a coercive field between 2.7 Vtip and 3.0 Vtip for down-polarization.

[0171] Fig. 10 presents hysteresis loop measurements of the three additional cavities marked by dashed frame in Fig. 5A of the main text. The additional 150 nm-size cavity and the 250 nm-size cavities exhibit a switching bias window of 5 V, while the 350 nm- size cavity does not switch completely in a window of 8 V. We could switch up- polarization at —4 V but could not achieve complete down-polarization even at 4.5 V. We note that higher field values were avoided due to finite damage observed (in other cavities). We also note an asymmetry in positive and negative coercive fields in different cavities, while the overall window remains the same. Since the center of the switching window shifts from positive to negative potential in different cavities, and seems to be smaller for cavities that are further separated from neighbors and pining contaminants, we attribute this anisotropy to elastic coupling of the cavity to its environment, rather than vertical electric fields arising by flexoelectric response.

[0172] Intermediate switching states

[0173] Here, a cavity of 250 nm diameter is scanned with a sharp tip (< 30 nm apex diameter) in Fig. 11, allowing better spatial resolution and a more local polling electric field. A biased scan of the single domain map (dark uniform potential, panel b) first opens a 120° triangle domain (bright, panel c), which then extends by 60° to a straight dislocation strip (boundary of dark / bright, panel d). We note that the tip force and bias affect the stability of the intermediate state and that so far we were not able to robustly control the triangular intermediate states. We call for further experiments to establish the intermediate domain pattern as a function of the cavity dimensions, shape, and elastics coupling to adjacent cavities.

[0174] Dislocation control by tip pressing: Dislocation control can be performed by various methods. For example, nm to pm size cantilever were used to apply external stress to control twisted layer in the other works. In this paper, we used commercial HQ:NSC35 / Pt tip C (MikroMasch inc.) with 50 - 600 nN forces, 1 Hz scan speed, and pixel size under 20 nm. The spring constant was calibrated using Sader methods, which is recommended above 100 kHz resonant frequency, and optical lever sensitivity was calibrated using a single-layer graphene on SiOi-

[0175] Threshold force for boundary strip sliding

[0176] To test the threshold pressure for dislocation nucleation and movement, we conducted dragging experiments with unbiased tip. Error! Reference source not found.12 shows the potential maps of cavity arrays after applying increasingly growing forces to a narrow tip of less than 30 nm apex radius. The first map showing any domain wall motion appears after applying a 200 nN force (marked by blue rectangular frames). Note that variations in the cavity matrix potential are extremely sensitive to any deformation in the array. Contact scanning with 200 nN in the opposite direction reverts the domain pattern in a reversible manner, while higher force levels moved the strips in additional cavities and to larger extent (see 250 nN maps). The latter indicates different threshold values in different cavities as naturally expected. Applying forces below the 200 nN threshold value and after doing dragging experiments, did not change the potential pattern as expected (see bottom two maps). We used HQ:NSC35 / Pt - Tip C for these experiments, with typical spring constant value of 5.4 N / m. Assuming that 20 nm tip apex curvature, threshold pressure is approximately 161 MPa.

[0177] Sagging of active layers in pristine cavities

[0178] Occasionally, the stamping process resulted in commensurate layers sagging and the appearance of clear polar polytypes only in part of the array. In Fig. 13, for example, the topography and surface potential maps show that cavities from the top part of the array are commensurate and polar (see darker cavity color in topography and bright / dark potential domains). Conversely, the bottom part of the array remains non-polar and exhibits flat topography of suspended cavity membranes or pockets of aggregated contaminations (bright topography regions). In this case, we scanned the array in contact mode with a finite pressure of 300 nN, pushing the active layers to dwell into the vdW adhesion and to push away the self-cleaning contamination pockets. Imaging the array after the several pressured scans confirms clean and commensurate cavities everywhere (see Fig. 13C,D). Hence, we note that the surface potential signal is sensitive to the vertical adhesion and the planar interlayer motion.

[0179] Effect of shear / friction force around the cavity

[0180] A few hundred MPa shear force is known to switching graphene polytypes. To understand detailed impact of mechanical switching of dislocations inside the cavities, it is essential to compare the shear forces applied at the edges and within the cavity. The friction force induces tortional movement of the tip which is reflected in difference between forward and backward lateral photodiode signals (V). We calibrated conversion factor (nN / V) of lateral force by SiOi substrate where the friction coefficient is known as 0.08. Our estimated / z-BN friction coefficient is 0.055 derived from the conversion factor which is also reported in AFM friction experiment on / z-BN.

[0181] Friction to normal load conversion curve measured on atomically flat / z-BN flakes is presented in Fig. 14A. A topographic and friction force maps are shown in panel b,c respectively taken around a cavity at a 300 nN loading force. The brighter signal in c indicates that the lateral friction forces are higher at the edge of cavity, reaching ~30 nN compared ~15 nN in the flat regions. Both values are much below the values reported in previous experiments of mechanical domain nucleation in uniform crystalline flakes (with loading forces exceeding pN). Sliding polytypes in lubricant cavities

[0182] According to certain embodiments, the presently disclosed SLAP devices 1) Squeeze the active commensurate interface into small cavities without physically cutting the functional layers and introducing open edge bonds. 2) Use lattice mismatched or considerably twisted layered spacers to support super-lubricant dynamics between the active cavities.

[0183] Since interfaces of lattices mismatch / twisted layers by more than 2% / a few degrees are not commensurate, the "not-active" inter-cavity regions can facilitate exceptionally high sliding lubricity with record low -10-5 friction coefficients. Via this super lubricant medium, the stress field can spread to reduce the elastic deformation and mediate long-range elastic interactions, which are typically restricted by any pinning barrier. For example, the pining potential wells in the commensurate stacking state (that prevents super lubricity) confine the interlayer shifts within the boundary dislocations

[0184] 1 strip only. Here, the elastic energy cost - ~k — ( fc~150 N / m the shear stiffness, a~ 0.14 nm the bond length) is competing with the misalignment energy - wEsp(with

[0185] CL I k

[0186] Esvthe pinning energy per unit area -ImeV / atom) to set a strip width w = - - 7

[0187] 2 / Esp nm in graphene and h-BN strips. However, on the super lubricant interfaces with orders of magnitude lower friction and pining potentials, the strain relaxation length can substantially exceed w to lower the elastic deformation energy and spread the inter-cavity interactions beyond the present few nm-scale interactions between adjacent dislocation strips. Notably, the dislocation networks and the topological constraints associated with local atomic relaxations and global interlayer twists are eliminated outside the cavities. Rather, boundary dislocations may nucleate / annihilate independently in each isolated island with an energy budget determined only by the cavity's dimensions and the remaining pinning potentials. Altogether, the SLAP concept provides freedom to design the shape and geometry of each cavity down to the nm scale while simultaneously controlling their mutual elastic and electronic interactions by designing the symmetry and spread of the array.

[0188] Fig. 4 illustrates cross-sectional and top views of the conceptual array using a graphene spacer and functional h-BN flakes. Circular cavities were etched into a graphene bilayer (BLG, see the identical carbon spheres in Fig. 4A) using the electrode-free local anodic oxidation (LAO) method (see methods). Then, the BLG was encapsulated with h- BN layers (blue and yellow spheres, respectively) that sag to touch at the cavity position, forming a parallel and commensurate AB or BA interfaces (dark / bright brown shaded). These stable polytype configurations break inversion and mirror symmetry (see rectangular frames with a line-cut illustration of a unit cell along the armchair direction), inducing vertical polarization at this active interface. Outside the cavity, on the other hand, the h-BN / graphene interfaces were incommensurate owing to lattice mismatch and finite twist angle (blue-shaded interfaces). Fig. 4B shows a top view of a cavity array design with various cavity diameters and inter-cavity spaces. Outside the blue-shaded spacer (top right side), triangular domains of AB and BA configuration form, with opposite structural orientations and internal polarizations Pz (noted by bright / dark colors). Islands of non-polar AA' and AB 1' polytypes that preserve inversion symmetry (see framed illustrations) appear in regions of antiparallel functional layers as expected for an extra (rotated) interfacial layer (framed in a dashed-dotted black line).

[0189] Detecting polytypes by imaging interfacial ferroelectricity

[0190] To monitor the cavity polytypes, as a ferroelectric-case study, flakes of h-BN or WSe2were used as the functional encapsulating crystals (see Device 1-3 details in the Table above, Fig. 7). A parallel commensurate stacking of these binary compounds spreads the electrons unequally between the top and bottom layers, inducing interfacial- confined polarization Pz which is resilient to nearby interfaces configurations. Conversely, Pz nullifies for interfacial twists beyond a few degrees that decouple the functional layers. Notably, each interfacial shift by a single inter-atomic distance switches the untwisted AB stacking to BA and vice versa, which is equivalent to switching the interface and Pz upside down (see rectangular frames in Fig. 4A). Hence, monitoring Pz is an exceptional sensor for minute interfacial shear motions. Opposite Pz orientation in adjacent AB / BA domains modifies the electric surface potential by AV-240, 120 mV for h-BN and WSe2, respectively, allowing us to distinguish each polytype configuration deterministically. Figure 1c presents an atomic force microscope (AFM) topography map of the device structure illustrated in Figs. 4A-B. Straight borders were cut, designed 300, 200, 100, and 20 nm cavity diameters in the graphene spacer, and used 2 nm thick functional h-BN flakes (see darker circles, and further details in Fig. 8).

[0191] The surface potential map, measured by Kelvin Probe Force Microscopy (KPFM, see methods), is presented in Fig. 4D. Outside the spacer, at the top and right sides of the map, bright / dark domains differing by 240 mV potential steps confirm the formation of polar AB and BA interfaces. Notably, the same bright / dark circles at the cavity's location reveal uniform single-domain polytypes embedded in uniform spacer potential. A similar response is observed in Device 2 with a monolayer graphene spacer (Fig. 5, Fig. 7, 9-13) and Device 3 with a trilayer graphene spacer and WSe2 monolayers as the functional flakes (Fig. 6, Fig. 7). It is noted that all cavities above the dashed dark line in Fig. 4D appear either bright or dark. Conversely, below this line, the potential at the cavities and outside the spacer is measured to be the average potential as expected for non-polar antiparallel interfaces. The topography map in this section confirms an additional h-BN layer in the bottom flake (7 / 6, 7 / 5 layers in the top / bottom flake below / above the dashed line, respectively) and the formation of mirror symmetric AA' or AB1' interfaces (as in the naturally grown 2H flakes, see framed illustration in Fig. 4B). Altogether, the topography and potential maps confirm commensurate interface formations in pristine cavity arrays spanning many pm regions, released from external contaminations, even at the circular edges of the spacer.

[0192] Boundary strip nucleation and annihilation for ferroelectric Switching

[0193] To explore the cavities switching dynamics, external displacement fields were applied between the AFM tip and a bottom graphite electrode using bias contact scanning mode (methods). A set of poling and then imaging maps were taken above representative cavities with different diameters (Fig. 5A). Fig. 5B shows surface potential maps of a 150 nm wide cavity after increasing / decreasing the poling bias by 0.3V steps, corresponding to electric displacement field steps of 0.05 V / nm. Notably, a new dislocation strip nucleates at ~ ±0.3 V / nm and then slides at a coercive field Ec ~ ±0.6 V / nm to entirely switch the cavity between uniform single-domains of up / down polarization. While previously observing smaller coercive fields of ~ 0.3 V / nm, it is noted that other experiments could only slide preexisting dislocation strips without nucleating new strips up to breakdown displacement fields as high as 1.5 V / nm.

[0194] To analyze the hysteresis loop and the intermediate polarization states, the disclosers plotted the relative coverage of up (bright) domains, A^ / A^ ± A ). A complete set of maps is shown in Fig. 9 and was repeated over five switching cycles. The hysteresis loops of three additional cavities marked in dashed frames in Fig. 5A are presented in Fig. 10. While the 150 and 250 nm cavities show similar hysteresis windows, the disclosers could only switch the 350 nm cavity partially under electric displacements as high as 1 V / nm (before the sample is damaged). In all cavities, the center of the hysteresis loop shifts to positive or negative potentials with no apparent sign preference. A preferred bias shift is expected for vertical electric fields from the asymmetric tip / graphite electrodes or flexoelectric fields (due to pressure gradients from the tip curvature). Therefore, the random shifts are attributed to elastic coupling with adjacent cavities and remote pinning by nearby contaminants. The disclosers also found strip elongations aligning with the smaller width axes of the oval-shaped cavities (see the two bottom left cavities in Fig. 5A). Such tendency to shrink the strip length and to snap many cavities into single domains (see Fig. 4B) testifies that releasing the strain to the lubricant interfaces is energetically favorable. Occasionally, the disclosers found intermediate triangular domains snapping into 120- or 180-degree head angles rather than straight boundary strips (see the Illustration in Fig. 5C and Fig. 11). Such a configurable intermediate domain pattern appearing at confined ferroelectric islands is raising interest for topological texture applications such as, for example, in oxide nanoplates.

[0195] Mechanical switching and interlayer twists

[0196] External stress fields may also nucleate and reconfigure domain patterns in confined ferroelectric structures. 3D ferroelectrics are known to switch under local stress gradients owing to a flexoelectric response. Beyond the flexoelectric stimuli, switching of layered polytypes is expected even under planar stress fields orthogonal to the internal polarization. For example, contact AFM scanning is known to manipulate the dislocation strips between non-polar polytypes like Bernal and rhombohedral graphene trilayers. The latter strips at the top / bottom interface were found to follow the tip position for vertical forces of about 40 pN. However, controlled domain nucleation remains limited even for intensive mechanical stimulus, especially if the structural dislocation is buried much below the surface. Nucleating dislocations in twisted interfaces is an even greater challenge due to the rigid moire network and topologically defined number of alternating domains for a given global twist angle. Once the planar relaxation clicks the layers into commensurate domains, the external stress impact becomes irreversible.

[0197] To assess the mechanical switching dynamics, the disclosers scanned the arrays in AFM contact mode while applying vertical pressures of 50 to 250 nN and keeping the slow axis scan direction parallel to the underlining armchair direction (see methods). The disclosers found a threshold pressure for domain nucleation and motion of ~ 200 nN, corresponding to ~161MPa (Fig. 12). Fig. 6A presents three surface potential maps of Device 3 measured before and after applying a vertical pressure of 300 nN at times - tl, t2, t3. Notably, the domain patterns modify between the scans in nearly all cavities. The red / blue rectangles mark relatively large cavities in which triangular domains are tuned to a single / double domain pattern and back, respectively, as illustrated in Fig. 6B. Note that the strip dislocations in this device are buried ~15 layers below the surface. In some cases of a single dislocation strip between two domains (Fig. 6C), the disclosers could accurately push and reposition the strip within the cavity.

[0198] Here, a unidirectional scanning of the fast axes perpendicular to the strip axes does not change the domain pattern (see straight arrows scan illustration and unaltered potential map). In contrast, the strip precisely follows the end of the scanning pattern position for fast axis with both back and forward scanning along the strip (3rd, 4th images in Fig. 6C). The experiments show substantially lower threshold stress compared to other experiments (reported as ~ 40 pN), allowing sensitive mechanical manipulations of the domain pattern and twist angle.

[0199] Conclusion

[0200] The measured switching responses of the polytype islands imply device concepts that were previously out of reach. Note that any interlayer shift by one atomic spacing switches the cavity color in the potential map, making the array an exceptionally sensitive strain detector. The polarization is also extremely sensitive to twists and out-of-plane motions, appearing only once the layers perfectly sag (Fig. 13). Robust formation of single domain polytypes under finite global twist and electric field switching enable multiferroic devices with coercive fields that depend on the cavity dimensions and the elastic coupling to adjacent cavities in the array. Similar responses are expected in other binary compounds hosting additional electronic order, including magnetism, that couples to the structural phase and provides a rich multiferroic response. While the semi-metallic graphene spacer assists with imaging the surface potential in these experiments, switching it to an insulating substance (like twisted h-BN) and covering the system with a conducting electrode (like graphene) is straightforward. In this case, each cavity acts as a multiferroic tunneling transistor as thin as two atomic layers. Shaping the cavities into non-circular shapes or tuning the symmetry and dimensions of the array are versatile tools to control multi- switching and collective phase transitions. It allows to further control the domain patterns and the number and geometry of the boundary strips that cross each island. A similar switching response is expected in polar and non-polar polytypes of graphitic multilayers that exhibit rich correlated states at low temperatures. Here, the disclosure envisions dense arrays of polytype islands, further interacting by extended quasi-particles that may propagate in the functional layers between the cavities. The ability to design, stabilize, switch, and couple nm-scale islands of distinct periodic crystals should mark a valuable engineering milestone in layered vdW crystals.

[0201] Exemplary device assembly

[0202] The device structure comprised of (from top to bottom) a bi-layer graphene (BLG) / misaligned monolayer graphene (MLG) spacer with a cavity array / aligned BLG / 50 nm thick hBN / 90nm SiO2 / 0.5 mm Si substrate, fabricated using a dry polymer stamping method. A large BLG was initially etched into two parts using high-intensity pulsed laser light (1064 nm, WITEC alpha300 Apyron, Fig. 15A,D). In a separate step, a cavity array was etched into a MLG spacer using electrode-free local anodic oxidation (LAO) lithography (Figs. 15B,E)-

[0203] We assembled the device using a Polyvinyl alcohol (PVA)-coated polydimethylsiloxane (PDMS) stamp to pick up the hBN, the first BLG, the MLG spacer, and the second BLG. To flip the structure and place the active BLG at the top, facing the tip of the AFM, we use a second PDMS stamp coated with PMMA (Polymethyl methacrylate). Then we bring the stacked layers from the PDMS-PVA stamp into contact with the PMMA stamp and inject water into the gap to dissolve the PVA coating, facilitating the transfer. Finally, we drop the entire stack onto a Si / Si O2 substrate at 150°C. After fabrication, we design electrical contact pads (Cr / Au) using electron beam lithography.

[0204] Conducting Atomic Force Microscopy (C-AFM) Measurements

[0205] The current maps presented in this work were captured using a Park NX10 Hivac in C-AFM mode under an N2 atmosphere. A HQ:NSC35 / Pt tip with a spring constant of 5.4 N / m and a resonant frequency of -150 kHz was used for all measurements. Prior to current mapping, the sample surface was thoroughly cleaned by performing multiple scans in contact mode with a loading force of 350 nN. This process removes any residual contaminations and confirms that all cavity arrays are properly sagged. Following the tip cleaning, a fresh AFM tip is utilized for the current imaging. To avoid saturation of the tip current due to low resistance in several specific devices, we add a series resistor (1-10 MQ) into the measurement circuit. Friction Force Imaging

[0206] We record the lateral photodiode signals during both forward and backward scans, as illustrated in Fig. 16A,B to measure the friction force. Friction force induces torsional motion in the AFM tip (Fig. 16B), which manifests as a difference between the forward and backward lateral photodiode signals (measured in volts), as shown in Fig. 16C,D. We generate a friction force map by calculating this difference, which reflects the torsional motion of the AFM tip. To convert the potential shift into a friction force, we use a SiO2 substrate (with a known friction coefficient of 0.08) and a known conversion factor (nN / V) for lateral force. Fig. 16E shows a plot of the friction force as a function of the loading force, as we deduce from dedicated friction force maps (see examples in Figs. 16F-H).

[0207] Identifying Bernal (B) and Rhombohedral (R) Polytypes

[0208] To confirm the B / R stacking order within each cavity, we conducted 2D Raman mapping and current mapping on naturally exfoliated tetra-layer graphene samples. Fig. 17A shows an optical image example of a typical flake. Panel (B) shows a Raman map of the red-framed area, which is constructed by measuring the reflection spectrum at each pixel and assigning intensities based on the integrated light intensity at the filtered spectrum range shown by the gray bar in panel C. The spectra taken within the domains (using a green laser), confirm the presence of B and R polytypes in the measured regions.

[0209] The corresponding current map of the same regions is displayed in Fig. 17D. R regions exhibit higher current compared to the B regions as in the case of the SLAP devices (see E-F). We note that the R domains tend to shrink during the cleaning process using contact mode scanning. We observed the same Raman / current correspondence in five different samples.

[0210] Force microscopy experiments of super-lubricant arrays of polytypes devices, were conducted, where Bernal-stacked single-crystal islands of graphene reversibly transition into rhombohedral polytypes under friction forces as low as 6 nanoNewtons — corresponding to a switching energy below one femtojoule. As shown, these remarkably efficient structural transitions occur through the effective nucleation and spontaneous sliding of a stacking boundary strip across the island. Specifically, we reveal exceptionally long-range stress relaxations at the incommensurate superlubricant regions between the islands, facilitating structural dynamics at minimal energy cost. By interconnecting islands with narrow cavity channels, we demonstrate configurable elastic coupling, paving the way for novel electrically-controlled SlideTronic applications.

[0211] The transformation of one crystalline material into another with desirable properties has long been a scientific challenge. Historically, alchemists attempted to transmute copper into gold, unaware that such a feat requires a nuclear reaction. In comparison, graphite and diamond — both composed entirely of carbon atoms — differ only in their atomic arrangement. Converting graphite into diamond, however, demands extreme temperatures and pressures to break and reform covalent bonds, rendering the process impractical. A more achievable goal lies in switching between distinct polytype configurations within layered crystals like graphite by shifting carbon planes within relatively weak van der Waals (vdW) stacking arrangements.

[0212] Indeed, recent studies have demonstrated room-temperature sliding transitions in vdW polytypes, driven by feasible electric fields, in materials such as transition metal dichalcogenides (TMDs) and boron nitride (BN). These artificially stacked materials exhibit interfacial ferroelectricity, cumulative polarizations, and planar conductivity, which are attractive for non-volatile technologies. Extending the stacking order control to graphitic polytypes offers further potential despite relatively modest changes in their structural-dependent electronic bands and intrinsic electric polarizations. Instead, the semi-metallic nature of graphitic polytypes enables novel multiferroic mechanisms like electrically controlled infra-red response, orbital magnetizations, unconventional superconductivity, and anomalous fractional quantum Hall.

[0213] Practical nonvolatile technologies, however, demand GHz switching frequencies, Tera of devices per square centimeter, and a femtojoules energy cost per operation. Up until recently, these requirements posed a major challenge due to the underlying polytypes’ switching mechanism. Surface potential measurements on BN showed that rather than a rigid motion of the entire layer, switching is facilitated by sliding narrow boundary strips between adjacent structural configurations. The boundary strips slide to expand polar domains that co-align with the external electric field expand at the expense of domains with opposite polarization. More specifically, the energy cost associated with nucleating, deforming, pinning, and sliding the ~ 10 nm wide strips dictates the structural dynamics. Nucleating a strip loop that encloses a new domain requires an abrupt stimulus like a current pulse, while pushing a strip from the edge that crosses the entire sample requires a substantial mechanical force. Alternatively, one can slightly twisting the layers to from multi-domain devices and avoid the nucleation energy penalty. In this moire pattern case, however, the strips’ network becomes rigid as the domain dimensions shrink and the non-volatile response vanishes.

[0214] To address these challenges, we have recently introduced a super-lubricant array of polytypes (SLAP) device concept. SLAP devices exhibit pure electrical nucleation of boundary strips and efficient structural transitions in uniform nanometer- scale islands. The idea is to reduce the boundary strips' energy cost by confining the islands’ diameter without physically cutting the active layers. Instead, we puncture cavities with predesigned dimensions into incommensurate spacers, allowing the active layers to touch and form commensurate polytypes within the holes only. The SLAP design eliminates the formation of structural pining barriers by edge-dangling atoms that tend to zip the active layers together and prevent interlayer motions. Furthermore, the minute friction with the incommensurate twisted spacer outside the cavity should enable long-range and low-energy cost elastic relaxations of the interlayer shifts that accompany switching events.

[0215] These experiments, however, relied on the surface potential response of polar polytypes only, prohibiting the detection of strain relaxation properties at the lubricant surfaces that dominate the elastic coupling between adjacent islands. Here we report electric current measurements of non-polar graphitic SLAP devices with islands diameters as small as 30 nm, revealing elastic inter-island interactions over tens of nanometers and a coupled switching response. Moreover, we introduce a new concept to control the elastic coupling by interconnecting the islands. The configurable, long-range, elastic coupling extends to the non-volatile polar SLAP devices. Such a coupled switching response is appealing for neuromorphic technologies and was unavailable in any other non-volatile technology to date.

[0216] Imaging SLAP Devices

[0217] As a model graphitic SLAP system, we use a pair of aligned bilayer graphene to encapsulate a twisted monolayer spacer (see Fig. 15A, Fig. 18). The spacer layer is patterned with circular cavities with 30 to 500 nm diameters arranged in rectangular arrays with 30 to 1000 nm separations. The cross-sectional illustration in Fig. 18B shows cavities with commensurate tetra-layers of Bernal (B) and rhombohedral (R) polytypes. Conversely, the bilayers outside the cavities are incommensurate and face a misaligned super lubricant surface (Fig. 18B). Fig. 18C shows an atomic force microscope (AFM) topography map of a typical sample with dark circles corresponding to a height drop of 0.33 nm, the thickness of the monolayer spacer.

[0218] Panels d-h present the electric current between the AFM tip and a metallic gold (Au) lead connected to the active layers (see the electric circuit illustration in panel a). These current imaging maps are measured at a typical 5 mV sample bias (with ~5 M circuit resistance) and a vertical load force of 100 nN. Notably, all observed cavities divide into bright islands representing higher currents, corresponding to the R polytype, and dark islands with ~5 nA suppression of the current, corresponding to B polytypes. We confirm this correspondence by measuring - 500 cavities in 20 arrays assembled on five samples and comparing the current signals with our previous Raman and surface potential measurements (see Fig. 17). We note that the precise circuit resistance fluctuates during the scan due to occasional attachments of surface contaminants to the tip apex. Nevertheless, islands of the R polytype remain brighter than B islands, allowing us to determine the local configuration. Fig. 18D,E show imaging scans with relatively low -100 nN vertical load forces taken before and after a switching scan of the surface with a higher tip load of 300 nN. This load value corresponds to a vertical pressure of 240 MPa, and a lateral friction force of 15 nN, as measured from the tips' torque displacements (see Fig. 16). Remarkably, - 15% of the islands switch from R to B or vice versa (marked in red frames) without any apparent boundary dislocation within the islands.

[0219] Switching Dynamics

[0220] To monitor the polytypes’ switching dynamics inside the islands, we measured the current before, during, and after the high-load scans. Apparently, each switching event occurs at specific tip positions during the scan, once a boundary dislocation nucleates and then propagates spontaneously to switch the island entirely. For example, the red frames in the high-load scan, Fig. 15G, show sharp color switching within the islands (during a single line scan), while previous and following low-load imaging scans show uniform islands (panels F-H). The same response is observed if we stop the scan immediately after detecting a current jump and then take a low-load imaging scan. Occasionally, we observe two successive switching events within the same cavity, resulting in the same polytype at the following imaging scan. Such spontaneous boundary strip propagation and annihilation testify to a low energy barrier for sliding, as enabled by the SLAP concept.

[0221] Conversely, samples containing aligned spacers show restrained strip dynamics due to stiff dislocation networks between the functional layers and the commensurate spacer. Fig. 16 presents the twist-dependent evolution from low barrier switching dynamics into rigid domain patterns by reducing the spacer twist to less than a few degrees. For example, a twist of 9=1.4° between the spacer and the active layers (corresponding to a =10 nm moire wavelength, Fig. 16A,B) permits temporary motions of the strip in the island during each line scan (Fig. 16C,D). However, between the scans, or under low loading forces, the strip slides back to its initial position (see Fig. 16F,G). Reducing 9 further suppresses the switching dynamics and results in rather complicated domain pattern that also depend on the misalignment angle 9active between the active layers.

[0222] Fig. 19 presents another device with marginal twist angles in the range 9.1° < 9 < 1° at different sections of the array, corresponding to moire wavelengths 150 > k > 15 nm. In addition, the active layers are twisted by 9.91° < 9active < 9.2° imposing a second moire as detected within each cavity. To depict the structural stability, we compare the domain dimensions inside and outside the cavities. For example, the triangles in the cavity marked in red frame (panel i) show a ~ 199 nm length (9active -9.14°), while outside the cavity, the active layers create a larger triangle with - 259 nm (9active -9.96°) which is divided into smaller triangles with k - 50 nm (9-9.3°) by the twisted spacer. This tendency to push active dislocations from the Penta-layers medium into the tetra-layers cavity is reversed at the region marked in yellow. Here the cavity also shows a - 199 nm length (9active -9.14°), but the active layers outside the cavity create relatively smaller triangles with k - 50 nm (9active -9.3°) which are divided into tiny domains with - 15 nm by the 9 - 1° twisted spacer. It means that boundary strips between the active bilayers tend to move out of the cavity owing to higher misalignment and lubricity of the spacer in this region. Overall, the spacer misalignment provides another knob to design the structural lubricity, mechanical stability, and switching dynamics of SLAP devices. Aligned spacers cause larger commensurate pinning that limits the strain relaxation length, reduces the dislocation motion, and freezes the switch dynamics.

[0223] Imaging Long-Range Stress Relaxation

[0224] To monitor the interlayer shifts outside the cavities that accompany each switching event within the islands, we focus on SLAP devices with thin monolayer graphene spacers. Notably, current maps with a relatively high tip load of 400 nN reveal moire patterns between the top and bottom bilayers across the misaligned spacer, see Fig. 20A. These "remote" moire patterns are formed due to planar structural relaxations between the active bilayers despite the incommensurate spacer, see the cross-sectional stacking illustration in panel b. Apparently, the residual interactions between the aligned bilayers expand bright domains of enhanced current over dark domains that squeeze into relatively narrow boundary strips. These better-stable bright domains correspond to remote B stacking, while the dark strips correspond to remote R stacking and additional intermediate configurations. We draw this conclusion from the hexagonal shape of this remote moire pattern at the bottom of the map, where the center of the hexagon reveals the better-stable remote- stacking configuration. Conversely, marginally twisted successive layers show triangular moire patterns with equivalent domain dimensions that prevent polytype distinction (as in Fig. 19). Triangular patterns appear for a small energy difference between the two metastable polytypes of a given interface, which is insufficient to elongate the boundary strips and expand the area of the more stable polytype. Apparently, the hexagonal pattern in Fig. 20A means that strip elongations in the case of remotely commensurate layers have lower energy costs. To identify the better stable remote polytype, we note that dark remote boundary strips (with lower current) intersect R islands while switching to B islands is accompanied by shifting these dark strips out of the island. For example, panels C-F show intersecting and shifted strips (marked in dashed green lines) and a corresponding switching from R to B islands. This fascinating interplay of expensive strips between successive layers inside the islands that continue as relatively cheap remote dislocations outside the cavities determines the reach moire patterns observed in Fig. 19-20.

[0225] Markedly, the width of remote stacking boundaries is Wr~ 60+15 nm, much wider than the Ws~ 7 nm wide boundary strips of successive layer. These W values determine the elastic stress relaxation length and play a dominant factor in the stability and switching dynamics of the system, setting the energy cost associated with nucleating and elongating a strip. Overall, W is determined by the energy gain of the commensurate stacking potential, the planar stiffness of the layers, and the Burgers shift at the boundary between the structural phases. On the one hand, narrow W reduces the number of atoms at the intermediate misaligned stacking configuration and the corresponding adhesion energy loss by oc EintW / a, with Eintthe misalignment energy cost per atomic area, and a = 0.142 nm the bond length. On the other hand, the elastic energy loss due to planar strains within each layer grows as oc a2 / l / F (here a is also the Burgers shift vector). The sum of these two terms is minimized for I / I « 7 nm 38^40 for successive lay Jers with Eint~2meV / atom. EY and v are Young's modulus and Poisson's ratio, respectively. E '

[0226] Hence, the ratio — = -l— — « 75 reveals Eremote int« 0.015 meV per atom, and s ^remote int an overall remote strip energy cost of about 100 meV per nm length, ten times smaller than for successive dislocations. This relatively low energy cost enables easier elongations, deformations, and sliding of remote dislocations and subsequent switching of the polytype islands. Thicker spacers that completely mute the residual coupling between the layers, should result in even cheaper rearrangements and longer stress relaxations at the lubricant medium between the cavities.

[0227] Finally, we note the dark ring (~ Wrwide) at each cavity's edge that appears even in isolated cavities (see the yellow frames in Fig. 20C for example). These circular strips of remote incommensurate regions appear because the top bilayers stretch while sagging into the cavity. These long-range stress relaxations that substantially exceed Wsand provide a novel elastic interaction mechanism between adjacent islands (unlike the few nm scale relaxations in the commensurate spacers between the cavities, see Fig. 19). We also note that the remote boundary strips tend to align with the cavity pattern and merge with the circular stretch at the cavities' edge to further reduce the overall elastic energy (see Fig. 20E,F).

[0228] Designing Inter- Island Coupling

[0229] To further lower the coercive friction forces required for switching, and enhance the coupled island response, we implement an additional design concept. Here, islands are linked by narrow channels that capture boundary dislocations and orient them perpendicular to the channel axis. These direct strips are then pushed to switch the island efficiently and deterministically (Fig. 21). The narrow constrictions minimize the length and energy cost of the dislocation strips between successive layers while rearranging the less expensive remote dislocation pattern. Fig. 21A shows a typical topography map of 20 nm wide channels that link 150 nm wide cavities (see the dark regions with no spacer). Panels b-f show current maps of the same region with boundary dislocations that appear only in the channels and always in transversal channel direction (marked in red, green, and orange lines). Although not directly detected under these imaging conditions, each direct boundary strip must proceed as a remote boundary into the lubricant medium. To switch the polytype deterministically, we place the tip outside the nearby strip and scan the slow axis towards the cavity. Fig. 21C, for example, was imaged after placing the tip below the red boundary in panel (b) and pushing it up as sketched by the wiggling black line. For scanning loads exceeding ~ 300 nN, the direct (and remote) dislocations slide to cross the two bottom islands and switch the B polytype to R (from dark to bright cavities). We note that pushing dislocations along the channels without crossing the island requires much lower loading forces below 70 nN (corresponding to a 6 nN friction force), as shown in panel (d), which is taken after the pushing scan sketched in (c). The maps in panels (d) and (e) complete a demonstration of four individually controlled islands by pushing the successive boundaries in all directions. Within the channel, the dislocations can either attract each other as in panel (e) (orange and green lines) or stay apart (panel c, green and red), with each local narrowing of the channel serving as a stabilizing pinning potential and a sliding barrier. We emphasize that the full sliding dynamics include reorientation and motion of remote dislocations outside the islands. For example, the circular island in panel (c), which is not connected by any channel, was also switched after the scan sketched in panel (b).

[0230] A super-lubricant sliding ferroelectric tunnel junctions (SFTJs) crossbar array is depicted in Fig. 22. As demonstrated, a plurality of SFTJs arrays are made by assembling honeycomb layers of boron and nitrogen atoms into a two-atom-thick ferroelectric crystal in nanometer-scale diameter islands. The up / down pointing polarization (arrows) control the electric potential difference between a top metal and a bottom graphene electrode and the corresponding on / off tunneling current.

[0231] A Voltage input vector (Vl-5) is converted to a current output vector (11-8), depending on the polarization state of the junction at each crossing point of the matrix. Junctions with different / same polarizations in the array are separated by an odd / even number of soliton boundary strips. The crossbar represents a second set of gate electrodes (Vg 1-11) that allows reconfiguring the position of these superlubricant soliton strips and the long-range elastic coupling between the junctions.

Claims

CLAIMS:

1. A multilayered device comprising a lubricant sheet comprising one or more cavity regions, said lubricant sheet being provided between two van-der Waals (vdW) material sheets, wherein the two vdW material sheets interact or couple in each of the one or more cavity regions, to define active junctions.

2. The device accoridng to claim 1, wherein the device having incommensurate regions where the two vdW sheets are separated by the lubricant sheet; and commensurate regions within each of the one or more ca vity regions.

3. A multilayered device comprising a lubricant sheet comprising one or more cavity regions, said lubricant sheet being provided between two van-der Waals (vdW) material sheets, the device having incommensurate regions where the two vdW sheets are separated by the lubricant sheet; and commensurate regions within each of the one or more cavity regions, where the two vdW sheets interact or couple, to define active junctions.

4. The device accoridng to any one of claims 1 to 3, wherein the device is configured for controlling local electronic and structural responses at said regions or junctions.

5. The device according to any one of the preceding claims, wherein in each of the one or more cavity regions the two vdW sheets deform and sag into the cavities, enabling direct commensurate interaction between the vdW sheets in each of the cavities.

6. The device accoridng to any one of the preceding claims, wherein the one or more cavity regions having each independently a tangent profile defining for each of the one or more cavity regions one or more tangent contact surface area, an angle of the sag between the sheets, a thickness of the cavity, the cavity shape and size, the cavities array symmetry, the cavities spread and separation distance, and a mechanical thickness of the top and bottom vdW sheets encapsulating the cavities.

7. The device accoridng to any one of the preceding claims, wherein the lubricant sheet is formed of a layered material with a different lattice constant / structure than the encapsulating vdW layers.

8. The device accoridng to claim 7, wherein the lubricant sheet is of a material that is same as the materials of two vdW sheets, provided that the lubricant sheet having a lattice orientation twisted relative to that of the two vdW layers.

9. The device accoridng to any one of the preceding claims, wherein the lubricant sheet is selected from h-BN, hexagonal aluminum-nitride (h-AIN), hexagonal zinc -oxide(h-ZnO), hexagonal gallium-nitride (h-GaN), graphene, and transition metal dichalcogenides (TMDs ).

10. The device accoridng to claim 9, wherein the lubricant sheet is graphene.

11. the device accoridng to claim 9, wherein the lubricant sheet is hexagonal boron- nitride (h-BN).

12. The device accoridng to claim 9, wherein the transition metal dichalcogenide (TMD) is selected amongst M0S2, WS2, MoSe2 and WSe2.

13. The device accoridng to any one of the preceding claims wherein each of the two or more vdW material sheets is independently selected to exhibit strong in-plane covalent or ionic bonding and weak interlayer van der Waals interactions.

14. The device accoridng to any one of the preceding claims, wherein each of the two or more vdW material sheets having a same lattice orientation, enabling commensurate interaction therebetween at each of the cavity regions.

15. The device accoridng to any one of the preceding claims, wherein each of the vdW sheets is independently selected from h-BN and TMD materials.

16. The device accoridng to any one of the preceding claims, wherein the device compri ses a graphene lubricant sheet and two same or different vdW sheets formed of h- BN and / or a TMD material.

17. The device accoridng to any one of the preceding claims, comprising a plurality of lubricant sheets, each encapsulated between two vdW sheets.

18. The device accoridng to any one of the preceding claims, wherein the tangent profile of each one of the one or more cavity regions and a distance between the cavity regions are selected to control elastic and electromagnetic coupling between the cavities and an overall array response.

19. The device accoridng to any one of the preceding claims, provided with a bottom electrical contact and a top electrical contact.

20. The device accoridng to any one of the preceding claims, being a hetero structure device comprising a lubricant sheet separating two vdW sheets, the lubricant sheet having a plurality of cavity structures permitting interaction between the two vdW sheets in each structure and defining switchable active junctions, wherein stimulating the switchable active junctions permits modifying device property / function.

21. A heterostructure device comprising a lubricant sheet separating two vdW sheets, the lubricant sheet having a plurality of cavity structures permitting interaction betweenthe two vdW sheets in each structure and defining switchable active junctions, wherein stimulating the switchable active junctions permits modifying device property / function.

22. The device accoridng to claim 20 or 21, wherein the switchable active junctions being configured and operable as electronic junctions, magnetic junctions, optical junctions, non-volatile multi-ferroic components, diodes, transistors, tunnel junctions, ferroelectric tunnel junctions (FTJ), magnetic tunnel junctions, enabling device configurations as memristor devices, optical sensors, optical emitters, optical switches, and memory cells.

23. The device accoridng to any one of the preceding claims, wherein at least a number of the cavity regions are connected to enable neuromorphic computation, wherein memory, computation, and learning processes rely on the connectivity between the cavity regions.

24. The device according to any one of claims 1 to 22, wherein the cavity regions are spatially arranged and dimensioned to enable algebraic operations.

25. The device accoridng to any one of claims 1 to 22, implementing an arrangement of cavity regions of same or different cavity sizes; or a plurality of devices having each a different arrangement of cavity regions.

26. The device accoridng to claim 25, wherein the arrangement of cavity regions is in groups of powers of 2 (2H).

27. The device accoridng to claim 25, wherein in the arrangement- each group of cavity regions is associated with an independent input electrode.

28. The device accoridng to any one of claims 25 to 27, wherein each of the groups is configured to generate a cumulative current in response to applying a digital signal to input electrodes associated with each of the groups, to thereby generate an analog output representing an input digital word.

29. The device accoridng to claim 28, for high-speed modulation or for high frequency processing.

30. The de vice accoridng to any one of the preceding claims, configured and operable to change at least one electrical, magnetic or optical property thereof in response to externally stimulating one or more of the cavity regions.

31. A device comprising a lubricant sheet comprising an array of cavity regions, said lubricant sheet being provided between two van-der Waals (vdW) material sheets, having incommensurate regions where the two vdW sheets are separated by the lubricant sheet;and commensurate regions within each of the cavities in the cavity regions, where the two vdW sheets interact or couple; wherein the array of cavity regions is arranged in groups of powers of 2 (2n), and wherein each of the groups is configured and operable to generate a cumulative current in response to applying a signal to input electrodes associated with each of the groups, to thereby generate an analog output representing an input digital word.

32. A ferroelectric tunnel junction (FTJ) being or comprising a device according to any one of claims 1 to 30, or having a ca vity arrangement as defined in any one of claims 1 to 30.

33. The FTJ accoridng to claim 32, incorporated into a crossbar array or a memory cell.

34. The FTJ accoridng to claim 32, incorporated into a neuromorphic computing chip or a synaptic device.

35. The FTJ accoridng to claim 34, wherein the synaptic device is a synaptic memristor or a synaptic transistor.

36. A non-volatile resistive memory unit implementing or being a device accoridng to any one of claims 1 to 30.

37. A neuromorphic computing system implementing an artificial neural network (ANN) comprising an array of non-volatile memory units implementing a device accoridng to any one of claims 1 to 30, wherein the assembly implementing an array of cavity regions enabling memory, computation, and learning processes.

38. A neuromorphic computing system accoridng to claim 37, installed with an artificial intelligent (Al) based tool.

39. A neuromorphic computing chip comprising a ferroelectric tunnel junction (FTJ) according to any one of claims 31 to 35, wherein the FTJ is a synaptic device.

40. A crossbar memory array comprising or implementing a ferroelectric tunnel junction (FTJ) according to any one of claims 31 to 35.

41. A process for manufacturing a device accoridng to any one of claims 1 to 30, the process comprising encapsulating a lubricant sheet having a patterned array of (go- through) holes or cavities with a pair of van der Waals (vdW) sheets, permitting contact interaction between the pair of vdW sheets solely within cavities of the cavity pattern.

42. A process for manufacturing a device accoridng to any one of claims 1 to 30, the process comprising patterning a lubricant sheet with a hole or a cavity pattern andencapsulating the lubricant sheet with a pair of van der Waals (vdW) sheets, permitting contact interaction between the pair of vdW sheets solely within cavities of the cavity pattern.

43. The process accoridng to claim 41 or 42, further comprising forming a top and a bottom electrode.

44. The process accoridng to claim 41 or 42, wherein the cavity pattern is predesigned to provide a digital to analog conversion, to provide a neuromorphic function, or to provide a vector product.

45. The process according to any one of claims 41 to 43, wherein the cavity pattern and / or cavity connectivity is designed for neuromorphic computation.

46. The process according to any one of claims 41 to 44, wherein the cavity pattern and / or cavity or tangent profile is designed to implement multiply and accumulate functions.

47. The process according to any one of claims 41 to 44, wherein each of the holes or cavities is formed by etching the lubricant sheet.

48. A process for modulating an electric, optical, magnetic property of a device accoridng to any one of claims 1 to 30, the process comprising stimulating one or more of the plurality of active junctions (cavities), wherein stimulation is achievable by application of an external stimulus to the device.

49. The process accoridng to claim 48, wherein the external stimulus is an external electric field, an external magnetic field, an external optical pulse, a current pulse, or a mechanical stress.

50. A hardware-implemented method for operating a neural network system for vector matrix multiplication (MVM), the method comprising providing a neural network system comprising a controller, a memory, and an interface connecting the controller to the memory, wherein the controller comprises a processing unit configured to engineer the neural network and the memory comprises a neuromorphic memory device with a crossbar array structure comprising input lines and output lines interconnected at active ferroelectric tunnel junctions serving as a memristive device; said active junctions being in a form of a plurality of patterned cavities arrayed in a lubricant sheet encapsulated between two vdW sheets.

51. The method accoridng to claim 50, wherein the memristive device being configured to change states thereof by external stimulation reflecting write signals intoone or more of gate and / or bias input lines based on write instructions received from the controller and write vectors generated by the interface, according to the write instructions; and retrieving data from the neuromorphic memory device, by coupling read signals into one or more of the output current lines of the neuromorphic memory device.

52. The hardware-implemented method accoridng to claim 50, for operating a neural network system for vector matrix multiplication (MVM), the method comprising providing a neural network system comprising a controller, a memory, and an interface connecting the controller to the memory, wherein the controller comprises a processing unit configured to engineer the neural network and the memory comprises a neuromorphic memory device with a crossbar array structure comprising input lines and output lines interconnected at active ferroelectric tunnel junctions serving as a memristive device; said active junctions being in a form of a plurality of patterned cavities arrayed in a lubricant sheet encapsulated between two vdW sheets; the memristive devices being configured to change states thereof by external stimulation reflecting write signals into one or more of gate and / or bias input lines based on write instructions received from the controller and write vectors generated by the interface, according to the write instructions; and retrieving data from the neuromorphic memory device, by coupling read signals into one or more of the output current lines of the neuromorphic memory device.

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