A simulation method and application based on the slip ferroelectricity and transformer properties of two-dimensional heterolayer materials

Abstract

This invention provides a simulation method and application based on the slip ferroelectricity and piezoelectricity of two-dimensional heterolayer materials. The simulation method first constructs a g-C3N4 / graphene heterolayer model, forming various stacking configurations such as AA, AB, and BA. Then, based on density functional theory, structural optimization and electronic structure calculations are performed on the constructed heterolayer model. Based on this, the out-of-plane ferroelectric polarization and in-plane piezoelectric coefficient of the heterolayer under different stacking configurations are solved. Finally, combined with charge transfer characteristics and band structure analysis, the microscopic physical mechanism of the coexistence of slip ferroelectricity and piezoelectric properties of the system is elucidated. This invention can provide a theoretical basis for multifunctional two-dimensional materials through this simulation method, and has broad prospects for applications in memory, sensors, and actuators.

Description

Technical Field

[0001] This invention relates to the fields of materials science and computational physics, specifically to a simulation method and application based on the slip ferroelectricity and transformer properties of two-dimensional heterolayer materials. Background Technology

[0002] Ferroelectrics, as a class of dielectric materials with spontaneous ferroelectric polarization and stable polarization state reversal under the influence of an external electric field, have been widely used in non-volatile memories, high dielectric constant dielectric materials, electromechanical integrated actuators, pyroelectric sensors, and microelectromechanical systems (MEMS) due to their unique electric dipole modulation characteristics. They are core functional materials for information storage and intelligent sensing. However, as microelectronic devices continue to develop towards miniaturization, flexibility, and high integration, traditional perovskite ferroelectric structures are constrained by finite size effects, depolarization fields, and charge shielding effects. Ferroelectric polarization tends to decay or even disappear as the film thickness decreases, making it difficult to meet the requirements of next-generation microdevices for low-dimensional, high-efficiency, and stable ferroelectric performance.

[0003] Two-dimensional materials, due to their reduced dimensionality, are more prone to spatial symmetry breaking, providing natural conditions for ferroelectricity. They also possess characteristics such as weak interlayer van der Waals interactions, absence of surface dangling bonds, high chemical stability, and ease of stacking and integration, offering significant advantages in device miniaturization and heterogeneous integration. In recent years, experiments have successfully prepared two-dimensional ferroelectric materials such as CuInP2S6, In2Se3, d¹T-MoTe2, and SnTe. However, overall, there are still problems such as a scarcity of candidate systems and a single control mechanism. Furthermore, the ferroelectricity of most two-dimensional ferroelectric systems is driven by ion displacement, resulting in slow responses to external electric fields and stresses, making it difficult to achieve high-speed, low-energy-consumption, and multi-state control.

[0004] In 2017, Wu Menghao's research group proposed a novel mechanism for glide ferroelectricity. This mechanism breaks the centrosymmetric structure through interlayer relative slip, achieving non-ionic displacement-type ferroelectric polarization and opening a new path for the design of low-dimensional ferroelectric materials. This mechanism has been experimentally verified in various van der Waals bilayer materials, demonstrating advantages such as low barrier, high-speed flipping, and room-temperature stability. The introduction of heterolayer structures further broadens the design space of glide ferroelectric systems, enabling significant performance improvements through interface coupling, charge transfer, and bandgap modulation, bringing new opportunities for the development of multifunctional ferroelectric piezoelectric materials.

[0005] However, current research on slip ferroelectricity in two-dimensional heterolayers still has significant shortcomings: the understanding of the coexistence mechanism of slip ferroelectricity and piezoelectricity is not deep enough, and there is a lack of systematic simulation methods that can accurately characterize the relationship between interlayer stacking, charge distribution, band structure, and polarization / piezoelectric response. It is difficult to quantitatively reveal the intrinsic laws governing slip-induced polarization reversal and piezoelectric coefficient sign reversal, leading to material design relying on trial and error and difficulties in precisely controlling device performance. Therefore, constructing accurate simulation methods for slip ferroelectricity and piezoelectricity in two-dimensional heterolayer materials, and revealing their physical essence, has significant theoretical and applied value for promoting the development of novel low-dimensional ferroelectric piezoelectric materials and high-performance micro / nano devices. Summary of the Invention

[0006] This invention focuses on S-type and T-type tris(triazine) g-C3N4, using first-principles calculations to reveal the origin of interlayer sliding ferroelectricity, the mechanism of piezoelectric property differences, and the multilayer polarization regulation. The study confirms that nonpolar centrosymmetric AA-stacked bilayer g-C3N4 can slide approximately two bond lengths in-plane under an electric field, transforming into a spontaneously polarized AB / BA bistable state. S-type and T-type g-C3N4 exhibit completely opposite piezoelectric responses due to their different in-plane pore structures, with the S-type possessing a negative longitudinal piezoelectric effect. Three-layer S-type g-C3N4 can form various polarity stacking configurations through interlayer sliding, achieving multi-valued polarization output and possessing multi-state storage potential. This material system combines advantages such as being metal-free, low-cost, having clean interfaces, and thermodynamic stability, making it valuable for applications in ferroelectric storage, piezoelectric sensing, and flexible electronics.

[0007] This invention, through the construction of an S / T-type g-C3N4 / graphene heterostructure, and based on density functional theory simulations, reveals the synergistic mechanism of interlayer slip-induced ferroelectric polarization reversal and piezoelectric coefficient sign inversion, providing a theoretical solution for two-dimensional ferroelectric piezoelectric materials and devices. Specifically, it includes the following steps:

[0008] Step 1: Model construction and calculation method determination;

[0009] Step 2: Analysis of the ferroelectric properties of double-layer g-C3N4 stacking;

[0010] Step 3: Elucidation of the differences and mechanisms in piezoelectric properties;

[0011] Step 4: Verification of the potential of three-layer g-C3N4 multi-state polarization and device fabrication.

[0012] Further, in step 1, based on the characteristics of graphite-like carbon nitride crystals, S-type and T-type g-C3N4 monolayer, bilayer, and trilayer supercell structures were constructed respectively, with a 30 Å vacuum layer set to eliminate interlayer interactions. Density functional theory was used for calculations, executed in VASP and DS-PAW software, with the PBE-GGA exchange-correlated functional selected, combined with the DFT-D3 method to correct van der Waals interactions. The plane wave cutoff energy was set to 520 eV. The Brillouin zone was sampled using the Monkhorst-Pack scheme, with a 13×13×1 grid for S-type g-C3N4 and a 9×9×1 grid for T-type; the energy convergence accuracy was set to 10⁻⁻⁶. 7 ~10⁻ 6 The force convergence accuracy was set to 0.001~0.01 eV / Å. The polarization intensity was calculated using the Berry phase method, the ferroelectric switching path was searched using the CI-NEB method, and the structural stability was verified by phonon spectroscopy and first-principles molecular dynamics.

[0013] Step 1 generates three typical stacking configurations: By adjusting the in-plane relative positions between the g-C3N4 layer and the graphene layer, three typical stacking configurations, AA, AB, and BA, are generated. Specifically defined as follows:

[0014] (1) AA stacking: The atoms of the g-C3N4 layer and the graphene layer are completely aligned in the horizontal direction to form a stacked structure with the highest symmetry.

[0015] (2) AB stacking: The carbon atoms of the graphene layer are precisely located at the center of the pores in the g-C3N4 layer.

[0016] (3) BA stacking: It is mirror symmetrical to the AB stacking configuration, with the carbon atoms of the graphene layer located at specific positions on the other side of the pores in the g-C3N4 layer.

[0017] Furthermore, step 1 establishes the basis for structural regulation. The three stacking configurations mentioned above achieve reversible switching through interlayer lateral slip, laying the structural foundation for subsequent research on slip-induced symmetry breaking, ferroelectric polarization reversal, and piezoelectric response changes.

[0018] To optimize the electronic structure calculations, step 2 involved structural relaxation of the bilayer g-C3N4, identifying six stacking configurations: AA, AB, BA, AA', AB', and B'A. AB / BA represents the lowest-energy ferroelectric bistable state, with a point group of C3ᵥ and exhibiting non-centrosymmetric characteristics. The AB and BA states can reversibly flip their polarization directions through in-plane shear displacement, while the nonpolar AA state requires a slip of approximately two bond lengths to transform into a polar state. Calculations showed that the out-of-plane polarization of the bilayer S-type g-C3N4 is approximately 0.27 pC / m, and that of the bilayer T-type is approximately 1.75 pC / m. The ferroelectric switching barriers are 45 meV / cell and 15 meV / cell, respectively, demonstrating potential for low-power switching. The phonon spectrum showed no imaginary frequencies, and molecular dynamics maintained structural integrity, confirming room-temperature kinetic and thermodynamic stability.

[0019] In step 3 above, in-plane biaxial strain is applied to the double-layer S-type and T-type g-C3N4, the evolution of in-plane polarization with strain is calculated, and the longitudinal piezoelectric coefficient e is extracted. 22 Test results show that S-type g-C3N4 exhibits a negative longitudinal piezoelectric effect (NLP), e 22 ≈-0.15 C / m². T-type g-C3N4 exhibits a positive piezoelectric response, e 22 The piezoelectric properties of the two types of holes are approximately 0.13 C / m², indicating completely opposite characteristics. Microscopic mechanism analysis reveals that this difference is due to the different in-plane hole structures. The S-shaped hole is formed by the superposition of two equilateral triangles with opposite orientations. The charge transfer intensity of the inner triangle is higher than that of the outer triangle, and the net polarization direction is opposite to the direction of the external strain field, thus exhibiting negative piezoelectricity. The T-shaped hole is composed of an outer equilateral triangle and an inner trapezoid, with polarization mainly contributed by the outer triangle, exhibiting positive piezoelectricity. This section presents the first realization of directional control of piezoelectric polarity in the g-C3N4 system, providing a new mechanism for designing complementary, high-sensitivity piezoelectric devices.

[0020] Step 4 further constructs multiple stacking models of three-layer S-type g-C3N4, including typical sequences such as AAA, ABA, AAB, ACA, ABC, ACB, and BAC. Relaxation and energy calculations determine that ABC, ACB, and BAC are stable polar states with a polarization range of 0.49–0.51 pC / m, significantly higher than the bilayer system; ABA, ACA, and AAB are nonpolar states. Reversible transitions between polar states can be achieved through single-layer or bilayer cooperative sliding, with switching barriers all below 50 meV / cell, exhibiting fast, low-power, and rewritable characteristics. Band structure calculations show that the ferroelectric ABC state bandgap is approximately 0.16 eV higher than the paraelectric AAA state, enabling simultaneous polarization and bandgap modulation, suitable for logic-memory fusion devices. The emergence of three-layer multi-polarization states allows a single device to carry multiple bits of information, significantly improving storage density and meeting the development needs of high-density, low-power, and multi-state storage in the post-Moore's Law era.

[0021] The material of this invention is metal-free, low-cost, environmentally friendly, and chemically stable, exhibiting strong compatibility with silicon-based semiconductor processes. It can be widely applied to core devices such as ferroelectric random access memories, ferroelectric field-effect transistors, multi-state memory devices, flexible piezoelectric sensors, and microelectromechanical actuators. The integrated strategy of stacking design, interlayer sliding, and polarization control proposed in this invention provides novel structural degrees of freedom and physical mechanisms for the functional design of two-dimensional van der Waals semiconductors, possessing significant scientific and engineering application value for promoting the development of next-generation low-power, high-density, highly integrated, and multifunctional nanoelectronic devices. Attached Figure Description

[0022] Figure 1 This paper showcases the differences in single-layer structure, double-layer AB stacked ferroelectric configuration, atomic bond lengths, and pore arrangement of S-type and T-type g-C3N4, visually presenting the core structural features of the two types of materials. Among them, (a) shows the structure of graphitic carbon nitride (g-C3N4) of the triazine type (S-type) and tri-triazine type (T-type), with brown spheres representing carbon atoms (C) and silver-gray spheres representing nitrogen atoms (N); (b) shows the top view, side view, and corresponding magnified view of the AB stacked ferroelectric double-layer g-C3N4, showing the two different carbon-nitrogen bond lengths; (c) shows the AB stacked configuration of S-type and T-type g-C3N4, with blue triangles marking the upper pores, reflecting the difference in atomic arrangement inside the pores of the two structures.

[0023] Figure 2 Six typical stacking configurations of bilayer S-type graphitic carbon nitride are fully presented, distinguishing between parallel and antiparallel carbon-nitrogen bond arrangements. Among them, (a)-(c) are configurations with parallel carbon-nitrogen bond arrangements, and (d)-(f) are configurations with antiparallel carbon-nitrogen bond arrangements.

[0024] Figure 3 The ferroelectric switching paths and energy barriers of bilayer S-type and T-type g-C3N4 are shown, and the polarization reversal process of the AB / BA polarity states is demonstrated. The NEB method was used to calculate the ferroelectric switching paths and energy barriers of bilayer S-type and T-type g-C3N4 along [1]. The illustration of the ferroelectric switching path in the direction of 0 shows the transition between polar states AB and BA, with opposite polarization directions;

[0025] Figure 4 The effects of interlayer spacing and in-plane biaxial strain on the ferropolarization and electric dipole moment of g-C3N4 were revealed. (a) shows the influence of interlayer spacing on ferropolarization and electric dipole moment, and (b) shows the relationship between the in-plane electric dipole moment in the y-direction and biaxial strain.

[0026] Figure 5The polarity and nonpolarity distribution and energy stability of three-layer g-C3N4 are shown in two stacking configurations. The different stacking orders of three-layer g-C3N4 are shown in (a) AA+1 type and (b) A+2 or (c) B+2 type. The symbol P represents the polarization direction, and NP and X indicate that the configuration is nonpolar and energy-unfavorable, respectively.

[0027] Figure 6 This study demonstrates the path and intermediate structure of polarity transitions in three-layer g-C3N4 through interlayer sliding. The antipolar steady-state structures of A-CB and A-BC in the sliding three-layer g-C3N4 system are investigated, and the reversible ferroelectric switching path between configurations is revealed. Detailed Implementation

[0028] To better illustrate the technical content of this invention, the following calculations of the g-C3N4 / graphene heterobilayer structure are performed using first-principles density functional theory. All simulations are completed using the VASP software package, and the specific implementation steps and parameters are as follows.

[0029] Example 1: Construction and Performance Calculation of a Double-Layer S-Type g-C3N4 Sliding Ferroelectric Material

[0030] A bilayer supercell model of S-type g-C3N4 was constructed using Device Studio software, and six stacking structures, namely AA, AB, BA, AA', AB', and B'A, were established simultaneously. A 30 Å vacuum layer was set along the z-axis to eliminate interlayer interactions caused by periodic boundary conditions. The initial coordinates of C and N atoms were set according to the inherent structure of g-C3N4 crystal to keep the atomic arrangement in the monolayer plane unchanged.

[0031] Based on density functional theory, the entire calculation process was performed in VASP software. The PAW pseudopotential was used to describe the electron-nuclear interaction, the exchange-correlation functional was selected as PBE-GGA, the Grimme DFT-D3 method was introduced to correct the interlayer van der Waals interaction, the plane wave cutoff energy was set to 520 eV, the Monkhorst-Pack scheme was used for k-point sampling in the Brillouin zone, the grid density was set to 13×13×1, and the energy convergence accuracy was set to 1×10⁻. 7 eV, with the atomic force convergence accuracy set to 0.001 eV / Å, the ferroelectric switching path was calculated using the CI-NEB method, and the out-of-plane polarization intensity of the system was calculated using the Berry phase method.

[0032] Complete relaxation was applied to the six stacked structures to obtain the stable states of each configuration. Calculations show that the AB / BA stacked configuration is the lowest-energy ground-state structure with an interlayer spacing of 3.36 Å and a point group of C3ᵥ. The AA stacked configuration has an interlayer spacing of 3.63 Å and a point group of D. 3h Its relative energy is 0.102 eV / cell higher than that of the AB / BA state; specific parameters are detailed in Table 1. Phonon spectrum calculations verified that the system has no imaginary frequencies. First-principles molecular dynamics simulations showed that the ferroelectric phase structure remains intact at room temperature, demonstrating that the bilayer S-type g-C3N4 ferroelectric phase possesses excellent kinetic and thermodynamic stability.

[0033] The nonpolar AA stacked state can be transformed into a polar AB / BA stacked state by sliding approximately two bond lengths along the in-plane CN bond direction under the drive of an external electric field. The polarization directions of the AB and BA polar states can be reversibly reversed through in-plane shear displacement. Calculations show that the out-of-plane polarization of the bilayer S-type g-C3N4 is approximately 0.27 pC / m, and the switching barrier from nonpolar to polar states is approximately 45 meV / cell, fully meeting the application requirements for low-power ferroelectric switching. Differential charge density analysis results indicate that interlayer asymmetric charge transfer is the direct cause of ferroelectric polarization in this system.

[0034] Interlayer spacing (Å) 3.63 3.36 3.24 3.46 3.42 Point group <![CDATA[D 3h ]]> <![CDATA[C 3v ]]> <![CDATA[D 3d ]]> <![CDATA[D 3d ]]> <![CDATA[D 3d ]]> ΔE (eV / unit cell) 0.102 0.000 0.014 0.029 0.029

[0035] Table 1. Optimized interlayer spacing, point group, and relative energy for six stacking configurations of bilayer S-type g-C3N4.

[0036] Example 2: Calculation of the sliding ferroelectric and piezoelectric properties of double-layer T-type g-C3N4

[0037] A two-layer computational model of tris(triazine) g-C3N4 was constructed, with overall computational parameters set consistent with those in Example 1. A 9×9×1 grid was used for sampling the k-points in the Brillouin zone, and the energy convergence accuracy was set to 1×10⁻⁻⁻⁶. 6 eV, the atomic force convergence accuracy is set to 0.01 eV / Å.

[0038] After complete structural relaxation, the AB / BA stack configuration is the ground-state ferroelectric phase of the system, with an out-of-plane polarization of approximately 1.75 pC / m and a ferroelectric switching barrier as low as 15 meV / cell. The structural dynamics and thermodynamic stability are consistent with those of the S-type g-C3N4 system.

[0039] By applying in-plane biaxial strain to the bilayer system, the evolution of the electric dipole moment in the y-direction with strain is calculated, and the longitudinal piezoelectric coefficient e is extracted. 22 Calculation results show that the longitudinal piezoelectric coefficient e of T-type g-C3N4 is... 22≈0.13C / m², exhibiting a positive piezoelectric effect; the longitudinal piezoelectric coefficient e of S-type g-C3N4 22 It has a piezoelectric effect of approximately -0.15 C / m², exhibiting a negative longitudinal piezoelectric effect. The two types of piezoelectric response characteristics differ significantly, primarily due to their different in-plane hole structure configurations. The S-type is composed of two sets of superimposed reverse triangular holes, while the T-type is composed of an outer triangular hole and an inner trapezoidal hole.

[0040] Example 3: Construction and polarization regulation of a three-layer S-type g-C3N4 multistate ferroelectric material

[0041] Based on the double-layer S-type g-C3N4 constructed in Example 1, an additional layer was added to construct various stacked supercell structures such as AAA, ABA, AAB, ACA, ABC, ACB, and BAC. Among them, the core calculation parameters such as vacuum layer thickness, plane wave cutoff energy, exchange correlation functional, and k-point sampling grid are completely consistent with those in Example 1, ensuring the accuracy and comparability of the calculation results.

[0042] Complete structural relaxation and energy calculations were performed on all the aforementioned three-layer stacked supercell models. The results show that the ABC, ACB, and BAC stacking configurations are stable polar states with out-of-plane polarization ranging from 0.49 to 0.51 pC / m, while the ABA, ACA, and AAB stacking configurations are non-polar states with no spontaneous polarization. Reversible switching of polarization directions can be achieved between the polar states through single-layer or double-layer cooperative sliding, and the potential barriers for all switching processes are below 50 meV / cell, exhibiting characteristics of fast, low-power, and rewritable operation.

[0043] Comparison of the electronic structures of the paraelectric AAA and ferroelectric ABC states revealed that the band gap of the ferroelectric ABC state is 0.16 eV higher than that of the paraelectric AAA state. Simultaneously, the atomic displacement deviation resulting from the interlayer sliding process is approximately 0.22 Å, enabling simultaneous control of the system's polarization characteristics and band gap width. This characteristic makes this three-layer S-type g-C3N4 material suitable for the fabrication and application of multi-state memory devices and integrated logic / memory devices.

Claims

1. A simulation method based on the slip ferroelectricity and transformer properties of two-dimensional heterolayer materials, characterized in that: (1) Construct a g-C3N4 / graphene heterolayer model and generate three stacking configurations: AA, AB, and BA. (2) Density functional theory was used to optimize the structure and calculate the electronic structure of the constructed g-C3N4 / graphene heterolayer model; (3) Calculate the out-of-plane ferroelectric polarization and in-plane piezoelectric coefficient of the heterostructure under different stacking configurations; (4) The mechanism of coexistence of slip ferroelectricity and piezoelectricity is revealed through charge transfer and band structure analysis.

2. The simulation method based on the slip ferroelectricity and transformer properties of two-dimensional heterolayer materials according to claim 1, characterized in that: In step (1), the g-C3N4 / graphene heterolayer model includes two systems: S-type g-C3N4 / graphene (Sg-C3N4 / graphene) and T-type g-C3N4 / graphene (Tg-C3N4 / graphene). Sg-C3N4 uses s-triazine as its structural unit, while Tg-C3N4 uses tri-s-triazine (heptaazine ring) as its structural unit. The graphene layer is a single-layer sp² hybrid carbon honeycomb structure. The heterolayers are stacked through van der Waals forces, and the interlayer spacing is controlled to be 3.2~3.5 Å.

3. The simulation method based on the slip ferroelectricity and transformer properties of two-dimensional heterolayer materials according to claim 1, characterized in that: In step (1), the three stacking configurations are defined as follows: AA stacking is a stacking configuration in which the atoms of the g-C3N4 layer and the graphene layer are completely aligned; AB stacking is a stacking configuration in which the carbon atoms of the graphene layer are precisely aligned with the center of the pores in the g-C3N4 layer; BA stacking is a symmetrical stacking configuration with the opposite sliding direction to AB stacking. The three configurations can be reversibly switched through the relative lateral sliding between the layers. The sliding energy barrier is lower than 0.1 eV / cell, which meets the requirements for reversible control at room temperature.

4. The simulation method based on the slip ferroelectricity and transformer properties of two-dimensional heterolayer materials according to claim 1, characterized in that: In the aforementioned density functional theory calculations, the PBE exchange-correlation functional and ultrasoft pseudopotential are used to describe the interaction between electrons and ions, in order to accurately describe the weak interlayer interactions and electron-ion interactions.

5. The simulation method according to claim 1, characterized in that: In step (3), the out-of-plane ferroelectric polarization is determined by calculating the dipole moment using the Berry phase method. The Tg-C3N4 / graphene heterolayer has stable out-of-plane ferroelectric polarization under AB / BA stacking, with opposite polarization directions, and can achieve 180° reversible flipping through interlayer slip.

6. The simulation method according to claim 1, characterized in that: In step (3), the in-plane piezoelectric coefficient e 22 The e-strain of the Tg-C3N4 / graphene heterolayer under AB / BA and AA stacking conditions was calculated by applying a certain in-plane strain to the heterolayer. 22 With the piezoelectric sign reversed, the piezoelectric coefficient can be reversibly reversed, exhibiting significant voltage-changing characteristics. Sg-C3N4 / graphene heterolayers do not possess piezoelectric sign reversal properties, retaining only slip ferroelectricity.

7. The simulation method according to claim 1, characterized in that: In step (4), the charge transfer analysis quantifies the amount of electron transfer between g-C3N4 and graphene layers under different stacking conditions, the differential charge density intuitively displays the charge redistribution between layers, and the band structure characterizes the control effect of stacking on band gap and orbital hybridization. Among them, the Tg-C3N4 / graphene heterolayer has a smaller band gap and stronger orbital hybridization, providing an electronic structure basis for voltage transformation.

8. The simulation method according to claim 1, characterized in that: The aforementioned piezoelectricity specifically refers to achieving an in-plane piezoelectric coefficient e by controlling the stacking configuration through interlayer slip. 22 The sign can be reversed, which is different from the unidirectional piezoelectric response of traditional piezoelectric materials and can be used for precise control of bidirectional piezoelectric response.

9. An application of the simulation method based on the slip ferroelectricity and transformer properties of two-dimensional heterolayer materials as described in any one of claims 1 to 8, characterized in that: It is applied to the design of two-dimensional heterolayer materials, multi-state non-volatile memory, high-sensitivity piezoelectric sensors, piezoelectric actuators and electromechanical integrated devices. Through simulation methods, it realizes the synergistic control of ferroelectric and piezoelectric properties, providing theoretical support for device performance optimization.

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