Method for calculating and predicting dielectricity of two-dimensional hafnium oxide based on first principle

Abstract

The invention relates to a method for calculating and predicting the dielectricity of two-dimensional hafnium oxide based on a first principle, and the method specifically comprises the steps: S1, cutting out different surfaces of hafnium oxide through crystal structure modeling software, and adding a vacuum layer in a c direction, so as to obtain a two-dimensional hafnium oxide thin film structure; s2, calculating surface energy of different two-dimensional structures by using density functional theory software, and determining a stable surface configuration with the lowest energy; s3, constructing film structures with different thicknesses along the stable crystal face, calculating static and optical dielectric constant matrixes by using a density functional perturbation theory method, and analyzing the influence of the film thickness on the dielectric constant; s4, lattice constants a and b in the input file are manually adjusted, and the influence of lattice distortion on dielectricity is evaluated; and S5, constructing a structure model of a hafnium oxide and zirconium oxide growth interface, and investigating the influence of interface stress on dielectricity. Compared with the prior art, the device structure of the dynamic random access memory is combined, and a prospective solution is provided for improving the capacitor performance of the dynamic random access memory.

Description

Technical Field

[0001] The present invention relates to the technical field of new materials, and in particular to a method for predicting the dielectric properties of two-dimensional hafnium oxide based on first-principles calculations. Background Art

[0002] As a core component of high-performance artificial intelligence chips and computing-intensive applications, dynamic random access memory (DRAM) needs to have efficient, stable, low-latency and low-power storage characteristics. Among them, the capacitor is one of the key factors affecting the performance of DRAM devices. It is composed of a metal-insulator dielectric-metal (MIM) structure and requires the characteristics of low leakage current density and high capacitance density to ensure the stability and reliability of the device. As the size of DRAM devices shrinks, the effective area and the thickness of the dielectric layer will decrease, and the capacitor will face challenges such as increased leakage and insufficient charge storage. Therefore, increasing the dielectric constant (k) of the dielectric in the capacitor to reduce the equivalent oxide thickness (EOT) has become an important prerequisite for the evolution of DRAM to advanced nodes. Hafnium oxide (HfO2), as a high dielectric constant (high-k) material, has been widely used to improve the performance of capacitors.

[0003] The dielectric constant, also known as the permittivity, is a physical parameter that measures the ability of a material to store charge under an electric field. In the design and application of capacitors, the use of high-k materials can achieve higher capacitance values. However, the ideal high-k dielectric needs to have both a large band gap and a dielectric constant. It is extremely challenging to have both of these physical properties, and a lot of exploration work is required at the material, interface, and device levels. The interface reaction between ZrO2 / Al2O3 / ZrO2 or Al-doped ZrO2 (AZO) and the upper and lower TiN electrodes is small, which effectively supports the nano-scale technology nodes required for DRAM capacitors and demonstrates excellent compatibility and stability. The minimum EOT that can be achieved with this structure is limited to about 0.6-0.7nm. With the continuous miniaturization of DRAM, in order to achieve a more compact capacitor structure design, the new generation of DRAM uses high-k dielectric materials such as HfO2 / ZrO2. This system can significantly reduce the EOT, thereby meeting the needs of smaller sizes.

[0004] HfO2 has a variety of crystalline phase structures, including monoclinic (monoclinic, m), tetragonal (tetragonal, t), cubic (cubic, c), and orthorhombic (orthorhombic, o). At room temperature and pressure, the most stable crystalline phase of HfO2 is the m phase, with a space group of P21 / c and a k value of about 22-26. With the increase of temperature, the m phase can be transformed into the t phase and c phase with higher k values; during the deposition of HfO2 thin films, the o phase has the lowest free energy and is easier to produce during the film formation process. Therefore, the fine control of the crystalline phase structure is an important guarantee for obtaining high k. Despite this, the physical mechanism of HfO2 having a high k value is still unclear, and the technical approach to improving the k value is still in the trial and error stage of experiments. In particular, tetragonal hafnium oxide (t-HfO2) with a space group of P42 / nmc has the highest k value (~70) among all crystalline phases and has attracted much attention. At temperatures between 1800 and 2400°C, t-HfO2 exhibits a tetragonal distorted fluorite structure. However, there are relatively few theoretical studies on this tetragonal structure, and few experimentally obtained fine structures. Factors such as film thickness, stress strain, and surface energy play an important role in enhancing the stability and dielectric properties of t-HfO2, and these mechanisms still need to be further refined and studied.

[0005] The existing technology has the following problems: experimental research on high-k HfO2 materials with high-temperature stable structures is difficult and the trial-and-error cost is high; so far, there has been little theoretical research on the influencing mechanism of the dielectric properties of two-dimensional HfO2, and there are certain difficulties in calculating the dielectric constants of such two-dimensional materials through first-principles calculations. Summary of the invention

[0006] The purpose of the present invention is to provide a method for predicting the dielectric properties of two-dimensional hafnium oxide based on first-principles calculations in order to overcome the defects of the above-mentioned prior art. The purpose of the present invention is to solve the problem of limited dielectric constants of existing two-dimensional materials. By closely combining the device structure of DRAM capacitors, the present invention provides a method for significantly improving the dielectric constant of two-dimensional HfO2 materials by regulating film thickness, lattice distortion and interface stress. This method can provide a theoretical basis and underlying logical support for improving the dielectric constant of dielectric materials in DRAM capacitors, thereby providing a forward-looking solution for improving capacitor performance.

[0007] The purpose of the present invention can be achieved by the following technical solutions:

[0008] The first aspect of the present invention provides a method for predicting the dielectric properties of two-dimensional hafnium oxide based on first-principles calculations. Based on first-principles calculations, the variation trend of the dielectric constant of the two-dimensional material under different film thicknesses, lattice distortions, and interface stresses is obtained, and a method for optimizing the dielectric properties of the material is proposed, comprising the following steps:

[0009] S1, using crystal structure modeling software to cut out different surfaces of the three-dimensional HfO2 crystal, and increase the thickness of the vacuum layer in the c direction to obtain the surface structure of the two-dimensional HfO2 film.

[0010] S2, using density functional theory (DFT) calculation software to optimize the surface structure of the two-dimensional HfO2 film obtained in S1 (two-dimensional HfO2 film structure) and perform self-consistent calculations to obtain a stable film structure. By monitoring the energy changes during the optimization process, the surface energies of different surface structures are calculated and compared to determine the stable surface with the lowest energy.

[0011] S3, constructing thin film structures of different thicknesses along the stable surface obtained in S2, obtaining thin film structures of different thicknesses, and using the density functional perturbation theory (DFPT) method to calculate the static and optical dielectric constant matrices, and analyzing the effect of film thickness on the dielectric constant.

[0012] S4, manually adjust the lattice constants a and b in the input file to simulate the lattice distortion in the two-dimensional HfO2 film. Use the DFPT method to calculate the static and optical dielectric constant matrices and evaluate the effect of lattice distortion on dielectric properties.

[0013] S5, using crystal structure modeling software to construct the interface growth structure model of two-dimensional HfO2 and ZrO2 substrate (two-dimensional HfO2 / ZrO2). Continue to use the DFPT method to calculate the static and optical dielectric constant matrices of two-dimensional HfO2 / ZrO2 to examine the effect of interface stress on dielectric properties.

[0014] Furthermore, the S1 includes:

[0015] S1.1, using the three-dimensional HfO2 bulk crystal obtained from the crystal database as the initial structure, the main surfaces of the three-dimensional HfO2 crystal, such as (110), (111) and (001), were cut out using crystal structure modeling software. At the same time, the c direction was increased A vacuum layer is created to eliminate the influence of interlayer interactions and obtain the surface structure of the two-dimensional HfO2 film.

[0016] S1.2, export the structure obtained in S1.1 as a .cif file containing complete information of crystal atomic coordinates, and convert it into the input file format required by the DFT calculation software.

[0017] Furthermore, the main surface includes (001), One or more of (010), (110), (111).

[0018] Further, the S2 includes:

[0019] S2.1, perform calculation tests on the cutoff energy and K point. Calculate and analyze the convergence of the system energy under the changes of these two parameters respectively, so as to determine the optimal values ​​of the two parameters.

[0020] S2.2, DFT calculation software was used to perform structural optimization and energy self-consistent calculation on the thin film structures of two-dimensional HfO2 on different surfaces. The conjugate gradient algorithm was used for structural optimization, and the force convergence criterion was set to the Hellmann-Feynman force of each atom to be less than The energy convergence criterion is 10 -8 eV to ensure a stable film structure.

[0021] S2.3, when the convergence criteria are reached, the next step of electronic structure calculation is performed. At the same time, by monitoring the energy changes during the optimization process, the surface energies of different two-dimensional surface structures are calculated and compared to determine the stable surface configuration with the lowest energy. The surface energy of a two-dimensional system with a stoichiometric ratio and asymmetric configuration σ S The calculation formula is as follows:

[0022]

[0023] Where A represents the surface area, and refers to the energy of the unrelaxed surface and the relaxed surface, N atoms is the number of atoms on the surface, E B Represents the energy of each atom in the bulk.

[0024] S2.4, further first-principles molecular dynamics (AIMD) simulations, phonon spectra and elastic constant calculations were performed on the stable surface of two-dimensional HfO2 to confirm the thermodynamic, kinetic and mechanical stability of the stable surface structure of two-dimensional HfO2.

[0025] Further, the S3 includes:

[0026] S3.1, based on the stable surface obtained in S2, with HfO2 in a stoichiometric ratio of 1:2 as a basic unit (N=1), a two-dimensional HfO2 film structure with different thicknesses (N=1-5) was constructed using crystal structure modeling software. The structure of each system was optimized and the energy was self-consistent to obtain stable structures at different thicknesses.

[0027] S3.2, based on the density functional perturbation theory (DFPT) method implemented in the DFT calculation software, the dielectric constant matrix of film structures with different thicknesses is obtained through linear response theory.

[0028] S3.3, extract the ionic part and the electronic part of the dielectric constant matrix from the output file of the DFT calculation software, and add the two together to obtain the static dielectric constant matrix, where the electronic contribution is the optical dielectric constant matrix.

[0029] S3.4, according to the two-dimensional dielectric constant normalization formula obtained by the equivalent capacitance method, the static dielectric constant matrix and the optical dielectric constant matrix are processed to eliminate the vacuum contribution contained in the dielectric response calculated by the DFPT method, obtain reliable dielectric constant values, and analyze the effect of film thickness on the dielectric properties of HfO2 materials. The two-dimensional dielectric constant normalization formula is as follows:

[0030]

[0031] Among them, ε SC,|| and ε SC,⊥ are the in-plane and out-of-plane dielectric constants of the two-dimensional material (two-dimensional HfO2 thin film structure) directly calculated by DFT software. c is the supercell height including vacuum, and t is the van der Waals effective thickness of the two-dimensional material, which is defined as the distance of the most surface atom plus twice the van der Waals radius of the most surface atom.

[0032] S3.5, calculate the equivalent oxide thickness (EOT) of 2D HfO2 films to evaluate their potential in DRAM applications:

[0033]

[0034] in, They are the dielectric constant of SiO2, the out-of-plane static dielectric constant of two-dimensional HfO2 film and the van der Waals effective thickness of two-dimensional HfO2 film respectively.

[0035] S3.6, calculate and analyze the electronic structure of two-dimensional HfO2 thin films, including energy bands and state density, and analyze the relationship between electronic structure and dielectric constant.

[0036] Further, the S4 includes:

[0037] S4.1, select the two-dimensional HfO2 film structure, and manually adjust the lattice constants a and b in the input file. The range of lattice distortion is set to ±5% with an interval of 1% to simulate the application of in-plane biaxial tensile stress and compressive stress on the material.

[0038] S4.2, calculate the optical and static dielectric constant matrices under different lattice distortions, and use the two-dimensional dielectric constant normalization formula for data processing to evaluate the effect of lattice distortion on the dielectric properties of HfO2 materials.

[0039] S4.3, extract the Born effective charge of each atom inside the two-dimensional HfO2 film structure from the output file of the DFT calculation software, and explain the change of the dielectric constant from the perspective of interatomic charge interaction.

[0040] Further, the S5 includes:

[0041] S5.1, using crystal structure modeling software to construct a heterojunction structure model of the interface growth of two-dimensional HfO2 and ZrO2 substrate (zirconia substrate). The substrate is selected as a ZrO2 structure with the same bulk space group as HfO2 to simulate the induced growth process of the two-dimensional HfO2 film.

[0042] S5.2, calculate the optical and static dielectric constant matrices of the two-dimensional HfO2 / ZrO2 heterojunction structure as the number of HfO2 layers changes, and use the two-dimensional dielectric constant normalization formula for data processing to investigate the effect of interface stress on the dielectric properties of HfO2 materials.

[0043] A second aspect of the present invention provides a storage medium comprising computer executable instructions, which, when executed by a computer processor, is used to perform the above-mentioned method for predicting the dielectric properties of two-dimensional hafnium oxide based on first-principles calculations.

[0044] The storage medium may be an electronic medium, a magnetic medium, an optical medium, an electromagnetic medium, an infrared medium, or a semiconductor system or a propagation medium. The storage medium may also include semiconductor or solid-state memory, magnetic tape, a removable computer disk, a random access memory (RAM), a read-only memory (ROM), a hard disk, and an optical disk. Optical disks may include compact disk-read only memory (CD-ROM), compact disk-read-write (CD-RW), and DVD.

[0045] Compared with the prior art, the present invention has the following technical advantages:

[0046] 1. The present invention provides a method for predicting the dielectric properties of two-dimensional hafnium oxide based on first-principles calculations, which reduces experimental costs. The present invention can predict the dielectric properties of two-dimensional HfO2 materials before actual material synthesis and performance testing, which can guide experiments and thus significantly reduce the trial and error costs in experiments. The method is simple to operate, easy to implement, and effectively reduces material consumption and experimental time, improves material research and development efficiency, and avoids high costs and blindness.

[0047] 2. The present invention provides a method for predicting the dielectric properties of two-dimensional hafnium oxide based on first-principles calculations, which is an advanced calculation scheme. The present invention provides a calculation scheme based on first principles, closely combined with experimental processes, to explore the influence of material thickness, lattice distortion, and interface stress on the dielectric properties of two-dimensional high-k material HfO2 thin film system. This calculation method helps to deeply understand the relationship between the electronic structure and dielectric properties inside the material, and provides a scientific basis for the design of two-dimensional high-k materials.

[0048] 3. The present invention provides a method for predicting the dielectric properties of two-dimensional hafnium oxide based on first-principles calculations to optimize material properties. The present invention provides a new platform for the study of the dielectric properties of two-dimensional materials, helps to optimize the performance of high-performance capacitor materials, and thus accelerates the development and application of new microelectronic devices.

[0049] 4. The present invention provides a method for predicting the dielectric properties of two-dimensional hafnium oxide based on first-principles calculations. The advantages of the present invention are: (1) reducing the cost of experimental trial and error; (2) realizing the first-principles calculation of the dielectric constant of two-dimensional HfO2 materials; (3) providing a method for exploring the influence mechanism of material thickness, lattice distortion, and interface stress on the dielectric properties of thin film systems. The technical effects that can be achieved are: starting from the first principles, calculating and analyzing the dielectric properties of two-dimensional HfO2 materials and their influence mechanisms, finding methods that can improve the dielectric properties of two-dimensional HfO2 and reduce the leakage current density, and providing a feasible research plan for experiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 It is a flow chart of a method for predicting the dielectric properties of two-dimensional t-HfO2 materials based on first-principles calculations in an embodiment of the present invention;

[0051] Figure 2 Schematic diagram of different surface structures of three layers of t-HfO2 in the embodiment. Figure 2 (a) is the bulk material, 2(b) is the (001) surface, Figure 2 (c) surface, Figure 2 (d) is the (010) surface, Figure 2 (e) is the (110) surface, Figure 2 (f) is the (111) surface.

[0052] Figure 3 The VASP software package calculation parameter test of t-HfO2 in the embodiment. Figure 3 (a) is the energy convergence curve of the K-point test. Figure 3 (b) is the energy convergence curve of the cut-off energy test.

[0053] Figure 4The calculation results of the thermodynamic and kinetic stability of the t-HfO2 structure in the embodiment are shown in FIG. Figure 4 (a) The energy evolution over time obtained from the molecular dynamics simulation of monolayer t-HfO2 at T = 1000 K. The inset is the side view and top view of the structure of t-HfO2 after 6ps simulation. Figure 4 (b) is the phonon spectrum result of medium monolayer t-HfO2.

[0054] Figure 5 is the relationship between the dielectric constant of t-HfO2 film and the number of material layers. Figure 5 (a) Schematic diagram of the structure of t-HfO2 films with 1 to 5 layers. The brown balls (large) and red balls (small) represent Hf atoms and O atoms, respectively. Figure 5 (b) and Figure 5 (c) The functional relationship between the two dielectric constants (static (S) and optical (∞)) and the number of layers in the in-plane (||) and out-of-plane (⊥) directions is shown. For the out-of-plane direction, the variation of the EOT value with the number of layers is also analyzed. Figure 5 (d) The band structure and state density diagram of single-layer t-HfO2. Figure 5 (e) shows the negative correlation between the band gap and thickness of t-HfO2 film and the positive correlation curve between the out-of-plane static dielectric constant and thickness.

[0055] Figure 6 is the effect of in-plane biaxial strain on the dielectric constant of a single-layer t-HfO2 film. Figure 6 (a) and Figure 6 (b) Schematic diagrams of applying in-plane biaxial tension and compression strain to a single layer of t-HfO2 in the embodiment. Figure 6 (c) and Figure 6 (d) Shows the changes in the in-plane and out-of-plane dielectric constants of monolayer t-HfO2 under biaxial strain, with the strain range from -5% to +5% and an increment of 1%.

[0056] Figure 7 The effect of in-plane biaxial strain on the interatomic charge interaction in a single-layer t-HfO2 film in the embodiment (described by Born Effective Charges). Figure 7 (a) and Figure 7 (b) The in-plane and out-of-plane Born effective charges of a monolayer t-HfO2 film as a function of in-plane strain from -5% to +5%. Due to the symmetry of the surface, O1 and O2 atoms have the same Born effective charge.

[0057] Figure 8 : The effect of interface stress on the dielectric constant of t-HfO2 film in the embodiment. Figure 8 (a) and Figure 8(b) Side view (rotated 90° clockwise for ease of illustration) and top view of the two-dimensional HfO2 / ZrO2 heterostructure, where the t-HfO2 layer changes from 1 to 5 layers. Figure 8 (c) and Figure 8 (d) The functional relationship between the in-plane and out-of-plane dielectric constants of the system and the number of t-HfO2 layers under the action of interface stress. DETAILED DESCRIPTION

[0058] The present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments. Component models, material names, connection structures, control methods, algorithms and other features not clearly described in this technical solution are all considered to be common technical features disclosed in the prior art.

[0059] The present invention relates to a method for predicting the dielectric properties of two-dimensional hafnium oxide based on first-principles calculations, and the specific steps include: S1, using crystal structure modeling software to cut out different surfaces of hafnium oxide, and adding a vacuum layer in the c direction to obtain a two-dimensional hafnium oxide film structure; S2, using density functional theory software to calculate the surface energy of different two-dimensional structures, and determine the stable surface configuration with the lowest energy; S3, constructing film structures of different thicknesses along stable crystal planes, using density functional perturbation theory methods to calculate static and optical dielectric constant matrices, and analyzing the influence of film thickness on dielectric constants; S4, manually adjusting lattice constants a and b in input files, and evaluating the influence of lattice distortion on dielectric properties; S5, constructing a structural model of the growth interface of hafnium oxide and zirconium oxide, and examining the influence of interface stress on dielectric properties. The present invention combines the device structure of dynamic random access memory to provide a forward-looking solution for improving its capacitor performance.

[0060] During specific implementation, the technical solution adopted by the present invention is:

[0061] Based on first-principles calculations, the variation trend of the dielectric constant of two-dimensional materials under different film thicknesses, lattice distortions, and interface stresses is obtained, and a method for optimizing the dielectric properties of materials is proposed, including the following steps:

[0062] S1, using crystal structure modeling software to cut out different surfaces of the three-dimensional HfO2 crystal, and increase the thickness of the vacuum layer in the c direction to obtain the surface structure of the two-dimensional HfO2 film.

[0063] The S1 includes:

[0064] S1.1, using the three-dimensional HfO2 bulk crystal obtained from the crystal database as the initial structure, the main surfaces of the three-dimensional HfO2 crystal, such as (110), (111) and (001), were cut out using crystal structure modeling software. At the same time, the c direction was increased A vacuum layer is formed to eliminate the influence of interlayer interaction.

[0065] S1.2, export the obtained structure as a .cif file containing complete information of crystal atomic coordinates, and convert it into the input file format required by the DFT calculation software.

[0066] S2, using density functional theory (DFT) calculation software to optimize the structure of the two-dimensional HfO2 film obtained in S1 and perform self-consistent calculations to obtain a stable film structure. By monitoring the energy changes during the optimization process, the surface energies of different surface structures are calculated and compared to determine the stable surface configuration with the lowest energy.

[0067] The S2 includes:

[0068] S2.1, perform calculation tests on the cutoff energy and K point. Calculate and analyze the convergence of the system energy under the changes of these two parameters respectively, so as to determine the optimal values ​​of the two parameters.

[0069] S2.2, DFT calculation software was used to perform structural optimization and energy self-consistent calculation on the thin film structures of two-dimensional HfO2 on different surfaces. The conjugate gradient algorithm was used for structural optimization, and the force convergence criterion was set to the Hellmann-Feynman force of each atom to be less than The energy convergence criterion is 10 -8 eV to ensure a stable film structure.

[0070] S2.3, when the convergence criteria are reached, the next step of electronic structure calculation is performed. At the same time, by monitoring the energy changes during the optimization process, the surface energies of different two-dimensional surface structures are calculated and compared to determine the stable surface configuration with the lowest energy. The surface energy of a two-dimensional system with a stoichiometric ratio and asymmetric configuration σ S The calculation formula is as follows:

[0071]

[0072] Where A represents the surface area, and refers to the energy of the unrelaxed surface and the relaxed surface, N atoms is the number of atoms on the surface, E B Represents the energy of each atom in the bulk.

[0073] S2.4, first-principles molecular dynamics (AIMD) simulations, phonon spectra and elastic constant calculations were further performed on the stable surface of two-dimensional HfO2 to confirm the thermodynamic, kinetic and mechanical stability of the structure.

[0074] S3, thin film structures of different thicknesses are constructed along the stable surface, and the static and optical dielectric constant matrices are calculated using the density functional perturbation theory (DFPT) method to analyze the effect of film thickness on the dielectric constant.

[0075] The S3 includes:

[0076] S3.1, based on the stable surface obtained in S2, with HfO2 in a stoichiometric ratio of 1:2 as a basic unit (N=1), a two-dimensional HfO2 film structure with different thicknesses (N=1-5) was constructed using crystal structure modeling software. The structure of each system was optimized and the energy was self-consistent to obtain stable structures at different thicknesses.

[0077] S3.2, based on the density functional perturbation theory (DFPT) method implemented in the DFT calculation software, the dielectric constant matrix of film structures with different thicknesses is obtained through linear response theory.

[0078] S3.3, extract the ionic part and the electronic part of the dielectric constant matrix from the output file of the DFT calculation software, and add the two together to obtain the static dielectric constant matrix. The electronic part of the dielectric constant matrix is ​​the optical dielectric constant matrix.

[0079] S3.4, according to the two-dimensional dielectric constant normalization formula obtained by the equivalent capacitance method, the above dielectric constant matrix is ​​processed to eliminate the vacuum contribution contained in the dielectric response calculated by the DFPT method, obtain a reliable dielectric constant value, and analyze the effect of film thickness on the dielectric properties of HfO2 material. The two-dimensional dielectric constant normalization formula is as follows:

[0080]

[0081] Among them, ε SC,|| and ε SC,⊥ are the in-plane and out-of-plane dielectric constants of the two-dimensional material directly calculated by the DFT software, c is the height of the supercell including the vacuum, and t is the van der Waals effective thickness of the two-dimensional material, which is defined as the distance of the most surface atom plus twice the van der Waals radius of the most surface atom.

[0082] S3.5, calculate the equivalent oxide thickness (EOT) of 2D HfO2 films to evaluate their potential in DRAM applications:

[0083]

[0084] in, They are the dielectric constant of SiO2 (3.9), the out-of-plane static dielectric constant of the two-dimensional HfO2 film, and the van der Waals effective thickness of the two-dimensional HfO2 film.

[0085] S3.6, calculate and analyze the electronic structure of the material, including energy bands and state density, and analyze the relationship between it and the dielectric constant.

[0086] S4, manually adjust the lattice constants a and b in the input file to simulate the lattice distortion in the material. Use the DFPT method to calculate the static and optical dielectric constant matrices and evaluate the effect of lattice distortion on dielectric properties.

[0087] The S4 includes:

[0088] S4.1, select the two-dimensional HfO2 film structure, and manually adjust the lattice constants a and b in the input file. The range of lattice distortion is set to ±5% with an interval of 1% to simulate the application of in-plane biaxial tensile stress and compressive stress on the material.

[0089] S4.2, calculate the optical and static dielectric constant matrices under different lattice distortions, and use the two-dimensional dielectric constant normalization formula for data processing to evaluate the effect of lattice distortion on the dielectric properties of HfO2 materials.

[0090] S4.3, extract the Born effective charge of each atom inside the material from the output file of the DFT calculation software, and explain the change in the dielectric constant from the perspective of interatomic charge interaction.

[0091] S5, using crystal structure modeling software to build a two-dimensional HfO2 and ZrO2 substrate interface growth structure model. Continue to use the DFPT method to calculate its static and optical dielectric constant matrix to examine the effect of interface stress on dielectric properties.

[0092] The S5 includes:

[0093] S5.1, using crystal structure modeling software to construct a two-dimensional heterojunction structure model of the interface growth of HfO2 and ZrO2 substrate. The substrate is selected as a ZrO2 structure with the same bulk space group as HfO2 to simulate the induced growth process of the material.

[0094] S5.2, calculate the optical and static dielectric constant matrices of the two-dimensional HfO2 / ZrO2 heterojunction structure as the number of HfO2 layers changes, and use the two-dimensional dielectric constant normalization formula for data processing to investigate the effect of interface stress on the dielectric properties of HfO2 materials.

[0095] It should be noted that the first principle calculation means used are different, and the specific implementation steps and parameter settings may also be different. An optional method is provided in this embodiment: relying on the DFT software package Vienna Ab-initioSimulation Package (VASP), the energy, optimal structure and dielectric properties of the calculation system are calculated. Similarly, the two-dimensional HfO2 structure obtained by other means does not affect the final calculation results. The crystal database selected in this embodiment is Materials Project, the crystal modeling software is Materials Studio (MS), and the visualization software VESTA is used to convert the input file format of the VASP software package.

[0096] Example

[0097] In this embodiment, a method for predicting the dielectric properties of two-dimensional t-HfO2 materials based on first-principles calculations is provided. Figure 1 As shown, the following steps are included:

[0098] S1, using MS software to cut different surfaces of the three-dimensional t-HfO2 crystal and increase the thickness of the vacuum layer in the c direction to obtain the surface structure of the two-dimensional HfO2 film.

[0099] S1.1, retrieve and obtain the crystal structure file of the three-dimensional t-HfO2 block with the standard space group number 137 (P42 / nmc) from the Materials Project crystal database, such as Figure 2 (a) is shown. Then, the MS software is used to cut the main surfaces of the three-dimensional t-HfO2, including (001), (010), (110), (111). At the same time, increase the The vacuum layer is used to eliminate the influence of the interlayer interaction. The surface structures are as follows: Figure 2 (b)- Figure 2 (f) as shown.

[0100] S1.2, export the obtained structure as a standard .cif file containing complete information of crystal atomic coordinates, and use VESTA software to convert the .cif format structure file into .vasp format as the structure input file POSCAR calculated by VSAP.

[0101] S2, using the VASP software package to perform structural optimization and self-consistent calculation on the two-dimensional HfO2 film structure obtained in S1 to obtain a stable film structure. By monitoring the energy changes during the optimization process, the surface energies of different two-dimensional structures are calculated and compared to determine the stable surface configuration with the lowest energy.

[0102] S2.1, cutoff energy and K point (KPOINTS) test for t-HfO2 system. Set the range of cutoff energy parameter (ENCUT) in VASP input file INCAR to 400 to 900, increase it by 50, select Monkhorst-Pack method to sample K points, and change the K point density in KPOINTS file from 1×1×1 to 20×20×1, with an interval of 1. The energy convergence curves of the system under the two parameter changes are calculated as follows: Figure 3 The convergence criterion is: taking the asymptotic convergence line as a reference, the relative energy fluctuation is less than 10 -3 Parameters within the eV range are tolerable parameters. The optimal cutoff energy value is ENCUT = 800, and the value of KPOINTS is greater than 5 × 5 × 1. Taking into account both the amount of calculation and the accuracy, the K point density is selected as 7 × 7 × 1.

[0103] S2.2, use the VASP software package to perform structural optimization and self-consistent calculations on the thin film structures of two-dimensional HfO2 on different surfaces. In addition to the convergence parameters determined in the above step S2.1, the structure optimization uses the conjugate gradient algorithm, i.e., IBRION=2. At the same time, the positions of atoms and the constants of the unit cell are optimized, and the parameters are set to ISIF=3; the convergence criterion of the force is set to the Hellmann-Feynman force of each atom is less than The energy convergence criterion is 10 -8 eV to ensure a stable film structure.

[0104] S2.3, when the convergence standard is reached, the next step of electronic structure calculation is carried out, and the energy changes during the optimization process are monitored at the same time. According to the energy output, the surface energy after optimization is statistically calculated. Unoptimized surface energy and the energy E of each atom in the bulk B , substitute into the following formula to calculate the surface energy σ of the two-dimensional surface structure S :

[0105]

[0106] The calculated results of the surface energy are shown in Table 1. It can be seen that the (001) surface has the lowest surface energy and is therefore the most stable surface configuration.

[0107] Table 1 Calculation results of surface energy of different surfaces of t-HfO2

[0108]

[0109]

[0110] S2.4, first-principles molecular dynamics simulation (AIMD), phonon spectrum and elastic constant calculation were further performed on the monolayer t-HfO2 (001) surface to confirm the thermodynamic, kinetic and mechanical stability of the two-dimensional structure.

[0111] AIMD simulations were performed in a canonical ensemble (NVT) with a target temperature of 1000 K. The simulation results are shown in Figure 4 As shown in (a). With the increase of simulation steps, the total energy fluctuates periodically, and the energy fluctuation range gradually stabilizes. At the same time, the final structure remains within the key area, and the geometric structure does not disperse, proving the thermodynamic stability of the structure.

[0112] The calculation of the phonon spectrum is based on the density functional perturbation theory, and a 4×4×1 supercell monolayer t-HfO2 film structure is selected. The results are as follows: Figure 4 As shown in (b), there is no obvious imaginary frequency, indicating the surface structure is dynamically stable.

[0113] The elastic constants are calculated using the energy-strain method, which calculates the total energy change of the system in the strain range of -2% to 2% (in increments of 0.5%), and fits and obtains the elastic stiffness tensor C of the system. ij The elastic stiffness tensor of a single layer is calculated as: C 11 =47.63, C 22 =37.62, C 66 =38.10. Meets the mechanical stability criteria of the tetragonal lattice: C 11 >0,C 66 >0,C 11 >|C 12 |, so the structure is mechanically stable.

[0114] S3, based on the t-HfO2 stable surface determined in S2, the two-dimensional t-HfO2 film structures with different thicknesses under the surface were constructed using MS software. The density functional perturbation theory (DFPT) method was used to calculate the static and optical dielectric constant matrices of these film structures, and the effect of film thickness on the dielectric constant was analyzed.

[0115] S3.1, based on the stable (001) surface obtained above, use MS software to construct two-dimensional HfO2 thin film structures of different thicknesses. Take HfO2 as a basic unit (N=1), and construct thin film structures with N=1 to 5. And optimize each system to obtain free energy and stable structure of different thicknesses, such as Figure 5 (a) shown.

[0116] S3.2, using the density functional perturbation theory (DFPT) method implemented in the VASP software package, adding input parameters: LEPSILON = TRUE, IBRION = 8, to calculate the change in electron density caused by the external perturbation electric field. The dielectric constant matrix of these film structures is obtained by linear response theory.

[0117] S3.3, extract the ionic part and the electronic part of the dielectric constant matrix from the VASP output file OUTCAR, and add the two together to obtain the static dielectric constant matrix. The electronic part of the dielectric constant matrix is ​​the optical dielectric constant matrix.

[0118] S3.4, according to the two-dimensional dielectric constant normalization formula obtained by the equivalent capacitance method, the above dielectric constant matrix is ​​processed to eliminate the uncertainty of the results caused by the influence of the vacuum layer during the calculation process, and a reliable dielectric constant value is obtained. Here, the van der Waals thickness of the two-dimensional material is selected as the distance between the most surface oxygen atoms plus the van der Waals radius of the oxygen atoms twice as much.

[0119]

[0120] The change of the dielectric constant of t-HfO2 film with the number of layers obtained by using the formula is as follows Figure 5 (b) and Figure 5 (c) As shown in Figure 2, it can be seen that both the static dielectric constant and the optical dielectric constant increase with the increase in the number of layers.

[0121] S3.5, calculate the EOT of 2D t-HfO2 thin films to evaluate their potential for DRAM applications:

[0122]

[0123] The EOT calculation results are as follows: Figure 5 As shown in (c), the two-dimensional t-HfO2 has a smaller EOT due to its atomic-level thickness.

[0124] S3.6, calculate and analyze the electronic structure of the material, including energy bands and state density, and analyze the relationship between them and the dielectric constant. In the energy band calculation, the K-point path of the reciprocal space is selected as Γ→X→M→Γ, and the K-point density of the state density calculation is selected as 21×21×21 to ensure the reliability of the band gap calculation results. The energy band and state density of the single layer t-HfO2 are as follows Figure 5 (d) The negative correlation between the band gap and thickness of the t-HfO2 film and the positive correlation between the out-of-plane static dielectric constant and thickness are shown in the curves Figure 5 (e) as shown.

[0125] S4, manually adjust the lattice constants a and b in the VASP input file POSCAR to simulate the lattice distortion in the material. The static and optical dielectric constant matrices are calculated using the density functional perturbation theory method to evaluate the effect of lattice distortion on dielectric properties.

[0126] S4.1, select a single-layer two-dimensional HfO2 film structure, and manually adjust the lattice constants a and b in the POSCAR file. The range of lattice distortion is set to ±5% and the interval is 1% to simulate the in-plane biaxial tensile stress and compressive stress applied to the material. The schematic diagram is shown in Figure 6 (a) and Figure 6 (b) as shown.

[0127] S4.2, select a single-layer t-HfO2 film, calculate the optical and static dielectric constant matrices under different lattice distortions, and use the two-dimensional dielectric constant normalization formula for data processing to evaluate the effect of lattice distortion on the dielectric properties of HfO2 materials. Under biaxial strain from -5% to +5%, the changes in the in-plane and out-of-plane dielectric constants of the single-layer t-HfO2 are as follows: Figure 6 (c) and Figure 6 (d) In general, tensile strain can effectively increase the static dielectric constant of the material both in-plane and out-of-plane.

[0128] S4.3, extract the Born effective charge of each atom inside the material from the VASP output file OUTCAR, and explain the change of the dielectric constant from the perspective of the interaction between atomic charges. Figure 7 (a) and Figure 7 (b) shows the in-plane and out-of-plane Born effective charges of the monolayer t-HfO2 film as a function of the in-plane strain from -5% to +5%. It can be seen that the effective charges of Hf atoms and O atoms change under strain, thereby inducing the formation of local dipoles, which is the main reason for the increase in the dielectric constant.

[0129] S5, use MS software to construct a two-dimensional HfO2 and ZrO2 substrate interface growth structure model. Continue to use density functional perturbation theory method to calculate the static and optical dielectric constant matrix and examine the effect of interface stress on dielectric properties.

[0130] S5.1, use MS software to construct a heterojunction model of the interface growth of HfO2 and ZrO2 substrate. The ZrO2 substrate is selected to have the same space group as HfO2 to simulate the induced growth process of the material. t-HfO2 thin film structures with N=1~5 are constructed on three layers of t-ZrO2, and each system is optimized to obtain the corresponding stable structure. The side view and top view of the two-dimensional HfO2 / ZrO2 structure are shown in Figure 1. Figure 8 (a) and Figure 8 (b) as shown.

[0131] S5.2, calculate the optical and static dielectric constant matrices of the two-dimensional HfO2 / ZrO2 heterojunction structure as the number of HfO2 layers changes, and use the two-dimensional dielectric constant normalization formula for data processing to investigate the effect of interface stress on the dielectric properties of HfO2 materials. The variation trend of the in-plane and out-of-plane dielectric constants of the system and the number of t-HfO2 layers under the action of interface stress is shown in Figure 8 (c) and Figure 8 (d) As shown. It can be seen that under the action of the ZrO2 substrate, the out-of-plane dielectric constant of HfO2 can maintain an increasing trend. Further EOT calculations show that this structure also has a smaller EOT, which provides important guidance for optimizing the practical application of dielectric materials in capacitors.

[0132] The above is an explanation of the method embodiments of the present invention in conjunction with the accompanying drawings, but the present invention is not limited to the above embodiments, and various changes can be made according to the purpose of the invention of the present invention. Any parameter changes or calculation simplifications made according to the principle of the technical solution of the present invention, as long as they meet the purpose of the invention of the present invention and do not deviate from the principle and concept of the present invention of a method for predicting the dielectric properties of two-dimensional hafnium oxide based on first principles calculation, belong to the protection scope of the present invention.

[0133] The above description of the embodiments is to facilitate the understanding and use of the invention by those skilled in the art. It is obvious that those skilled in the art can easily make various modifications to these embodiments and apply the general principles described herein to other embodiments without creative work. Therefore, the present invention is not limited to the above embodiments, and improvements and modifications made by those skilled in the art based on the disclosure of the present invention without departing from the scope of the present invention should be within the scope of protection of the present invention.

Claims

1. A method for predicting the dielectric properties of two-dimensional hafnium oxide based on first-principles calculations, characterized in that: The following steps are involved: S1, using crystal structure modeling software to cut out different surfaces of the three-dimensional HfO2 crystal, and increasing the thickness of the vacuum layer in the c direction to obtain the surface structure of the two-dimensional HfO2 film; S2, using density functional theory calculation software to perform structural optimization and self-consistent calculation on the surface structure of the two-dimensional HfO2 film obtained in S1 to obtain a stable film structure, by monitoring the energy changes during the optimization process, calculating and comparing the surface energies of different surface structures, and determining the stable surface configuration with the lowest energy, that is, the stable surface; S3, constructing thin film structures of different thicknesses along the stable surface obtained in S2, obtaining thin film structures of different thicknesses, and using density functional perturbation theory method to calculate static dielectric constant matrix and optical dielectric constant matrix, analyzing the influence of film thickness on dielectric constant; S4, adjust the lattice constants a and b in the input file, simulate the lattice distortion of the two-dimensional HfO2 film, use the density functional perturbation theory method to calculate the static dielectric constant matrix and the optical dielectric constant matrix, and evaluate the effect of lattice distortion on dielectric properties; S5, use crystal structure modeling software to construct a two-dimensional interface growth structure model of HfO2 and ZrO2 substrate, continue to use density functional perturbation theory method to calculate the static dielectric constant matrix and optical dielectric constant matrix, and examine the effect of interface stress on dielectric properties.

2. The method for predicting the dielectric properties of two-dimensional hafnium oxide based on first-principles calculations according to claim 1, characterized in that: S1 includes: S1.1, using the three-dimensional HfO2 bulk crystal obtained from the crystal database as the initial structure, the main surface of the three-dimensional HfO2 crystal was cut out using the crystal structure modeling software, and at the same time, the c direction was increased. The vacuum layer is used to obtain the surface structure of the two-dimensional HfO2 film; S1.2, export the surface structure obtained in S1.1 into a .cif file containing complete information of crystal atomic coordinates, and convert the .cif file into the input file format required by the density functional theory calculation software.

3. The method for predicting the dielectric properties of two-dimensional hafnium oxide based on first-principles calculations according to claim 2, characterized in that: The main surface includes (001), One or more of (010), (110), (111).

4. The method for predicting the dielectric properties of two-dimensional hafnium oxide based on first-principles calculations according to claim 1, characterized in that S2 include: S2.1, perform calculation tests on cutoff energy and K point, calculate and analyze the convergence of system energy under the change of cutoff energy parameter and K point density parameter, so as to determine the optimal values ​​of the two parameters; S2.2, density functional theory calculation software was used to perform structural optimization and energy self-consistent calculation on the surface structure of different surfaces of two-dimensional HfO2 thin films. The conjugate gradient algorithm was used for structural optimization, and the force convergence criterion was set to the Hellmann-Feynman force of each atom to be less than The energy convergence criterion is 10 -8 eV to ensure a stable film structure; S2.3, when the convergence criterion is reached, the next step of electronic structure calculation is carried out. At the same time, by monitoring the energy changes during the optimization process, the surface energies of different two-dimensional surface structures are calculated and compared to determine the stable surface configuration with the lowest energy; S2.4, first-principles molecular dynamics simulations, phonon spectra and elastic constant calculations were further performed on the stable surface of two-dimensional HfO2 to confirm the thermodynamic, kinetic and mechanical stability of the stable surface structure.

5. The method for predicting the dielectric properties of two-dimensional hafnium oxide based on first-principles calculations according to claim 4, characterized in that: Surface energy σ S The calculation formula is as follows: Where A represents the surface area, and refers to the energy of the unrelaxed surface and the relaxed surface, N atoms is the number of atoms on the surface, E B represents the energy of each atom in the bulk; The σ S is the surface energy of a two-dimensional system with a stoichiometric ratio and asymmetric configuration.

6. The method for predicting the dielectric properties of two-dimensional hafnium oxide based on first-principles calculations according to claim 1, characterized in that S3 include: S3.1, based on the stable surface obtained in S2, using HfO2 with a stoichiometric ratio of 1:2 as a basic unit, using crystal structure modeling software to construct two-dimensional HfO2 thin film structures of different thicknesses, and performing structural optimization and energy self-consistency on each system to obtain stable structures at different thicknesses; S3.2, based on the density functional perturbation theory method implemented in the density functional theory calculation software, the dielectric constant matrix of the film structure with different thicknesses is obtained through the linear response theory; S3.3, extract the ionic part and the electronic part of the dielectric constant matrix from the output file of the density functional theory calculation software, and add the two together to obtain the static dielectric constant matrix. The electronic part of the dielectric constant matrix is ​​the optical dielectric constant matrix. S3.4, according to the two-dimensional dielectric constant normalization formula obtained by the equivalent capacitance method, the static dielectric constant matrix and the optical dielectric constant matrix are processed to eliminate the vacuum contribution contained in the dielectric response calculated by the density functional perturbation theory method, obtain reliable dielectric constant values, and analyze the effect of film thickness on the dielectric properties of HfO2 materials; S3.5, calculate the equivalent oxide thickness of the two-dimensional HfO2 thin film structure to evaluate its potential in DRAM applications; S3.6, calculate and analyze the electronic structure of two-dimensional HfO2 thin films, including energy bands and state density, and analyze the relationship between them and the dielectric constant.

7. The method for predicting the dielectric properties of two-dimensional hafnium oxide based on first-principles calculations according to claim 6, characterized in that: In S3.4, the normalized formula for the two-dimensional dielectric constant is as follows: Among them, ε SC,|| and ε SC,⊥ are the in-plane and out-of-plane dielectric constants of the two-dimensional HfO2 film directly calculated by the density functional theory software, c is the supercell height including the vacuum, and t is the van der Waals effective thickness of the two-dimensional HfO2 film, which is defined as the distance of the most surface atom plus twice the van der Waals radius of the most surface atom.

8. The method for predicting the dielectric properties of two-dimensional hafnium oxide based on first-principles calculations according to claim 6, characterized in that: In S3.5, the formula for calculating the equivalent oxide thickness EOT of the two-dimensional HfO2 film is as follows: in, They are the dielectric constant of SiO2, the out-of-plane static dielectric constant of two-dimensional HfO2 film and the van der Waals effective thickness of two-dimensional HfO2 film respectively.

9. The method for predicting the dielectric properties of two-dimensional hafnium oxide based on first-principles calculations according to claim 1, characterized in that S4 include: S4.1, select the two-dimensional HfO2 film structure, adjust the lattice constants a and b in the input file, and set the range of lattice distortion to ±5% with an interval of 1% to simulate the application of in-plane biaxial tensile stress and compressive stress on the two-dimensional HfO2 film; S4.2, calculate the optical dielectric constant matrix and static dielectric constant matrix of two-dimensional HfO2 films under different lattice distortions, and use the two-dimensional dielectric constant normalization formula for data processing to evaluate the effect of lattice distortion on the dielectric properties of two-dimensional HfO2 materials; S4.3, extract the Born effective charge of each atom inside the two-dimensional HfO2 film structure from the output file of the density functional theory calculation software, and explain the change of the dielectric constant from the perspective of interatomic charge interaction.

10. The method for predicting the dielectric properties of two-dimensional hafnium oxide based on first-principles calculations according to claim 1, characterized in that S5 include: S5.1, using crystal structure modeling software to construct a heterojunction structure model of the interface growth of the stable two-dimensional HfO2 film and the ZrO2 substrate obtained in step S2, wherein the substrate is selected to be a ZrO2 structure having the same bulk space group as HfO2, so as to simulate the induced growth process of the two-dimensional HfO2 film; S5.2, calculate the optical dielectric constant matrix and static dielectric constant matrix of the two-dimensional HfO2 / ZrO2 heterojunction structure as the number of HfO2 layers changes, and use the two-dimensional dielectric constant normalization formula for data processing to examine the effect of interface stress on the dielectric properties of HfO2 materials.

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