Modeling method, breakdown test method, system and storage medium of ultra-thin polycrystalline dielectric layer
By generating a three-dimensional grain boundary model using the Thiessen polygon model and distributing defects on the grain boundaries, the problem of discrepancies between the polycrystalline dielectric layer morphology model and the actual morphology is solved, improving the accuracy of leakage current and breakdown time prediction and the modeling efficiency.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-08-19
- Publication Date
- 2026-03-17
AI Technical Summary
In existing technologies, the morphology model of polycrystalline dielectric layers differs greatly from the actual morphology, resulting in large errors in the prediction of leakage current and breakdown time. Furthermore, the modeling is complex and does not take into account the influence of initial defects.
A two-dimensional grain boundary model is generated by using the Thiessen polygon model, and then stretched into a three-dimensional model along the dielectric layer thickness direction. The defect dataset is distributed on the grain boundary, which simplifies the modeling process and improves accuracy.
It reduces the randomness of defect distribution, improves the accuracy of leakage current and breakdown time prediction, and simplifies the modeling process.
Smart Images
Figure CN115497579B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of crystallography in materials science, and in particular to a method for establishing a model of an ultrathin polycrystalline dielectric layer, a breakdown test method, a system, and a storage medium. Background Technology
[0002] During the growth of polycrystalline materials, grain boundaries are generated. The instability of chemical bonds at the grain boundaries can lead to the generation of defects. These defects can induce defect-assisted tunneling, which in turn generates leakage current and exacerbates the failure of dielectric layer materials and devices.
[0003] In related technologies, a morphological model of a polycrystalline dielectric layer is constructed based on molecular dynamics and Monte Carlo methods. Initial defects are randomly distributed throughout the dielectric layer, and the position of new defects is then determined using the standard Monte Carlo method. However, the establishment of this morphological model of the polycrystalline dielectric layer is quite complex and does not consider the existence of initial defects in the polycrystalline material itself, which determine the breakdown site during dielectric breakdown. Therefore, the morphological model of this polycrystalline dielectric layer differs significantly from the actual morphology of the polycrystalline dielectric layer, resulting in high randomness in the three-dimensional positions of defects. Since defect aggregation leads to changes in local current, temperature, and electric field, it causes significant errors in the leakage current and breakdown time predictions calculated based on the morphological model of the polycrystalline dielectric layer. Summary of the Invention
[0004] This invention aims to at least solve one of the technical problems existing in the prior art. To this end, this invention proposes a modeling method, breakdown testing method, system, and storage medium for ultrathin polycrystalline dielectric layers, which enables defects to occur at grain boundaries, more closely resembling the actual morphology of ultrathin polycrystalline dielectric layers. While improving accuracy, it simplifies the grain morphology and defect locations in the thickness direction of ultrathin polycrystalline dielectric layers, thereby improving modeling efficiency.
[0005] In a first aspect, embodiments of the present invention provide a method for establishing a model of an ultrathin polycrystalline dielectric layer, including:
[0006] Obtain the dimensional data and material parameters of the ultrathin polycrystalline dielectric layer, wherein the dimensional data includes the thickness data of the ultrathin polycrystalline dielectric layer;
[0007] Based on the dimensional data and the material parameters, a two-dimensional grain boundary model is generated based on the Thiessen polygon model;
[0008] The thickness data is stretched in the direction of dielectric layer thickness from the two-dimensional grain boundary model to obtain a three-dimensional grain boundary model.
[0009] Obtain the defect dataset and distribute the defect data on the three-dimensional grain boundary of the three-dimensional grain boundary model according to the preset distribution rules, so as to update the three-dimensional grain boundary model.
[0010] According to one or more technical solutions provided in the embodiments of the present invention, at least the following beneficial effects are achieved: acquiring the dimensional data and material parameters of an ultrathin polycrystalline dielectric layer; generating a two-dimensional grain boundary model based on a Thiessen polygon model according to the dimensional data and material parameters; stretching the thickness data of the two-dimensional grain boundaries in the two-dimensional grain boundary model towards the thickness of the dielectric layer to obtain a three-dimensional grain boundary model; acquiring a defect dataset and distributing the defect data on the three-dimensional grain boundaries of the three-dimensional grain boundary model according to a preset distribution rule to update the three-dimensional grain boundary model. This method allows defects to be generated at the grain boundaries, reducing the randomness of defect distribution and more closely reflecting the actual morphology of the ultrathin polycrystalline dielectric layer. While improving the accuracy of calculated leakage current and breakdown time predictions, it simplifies the morphology and defect location of the grains in the thickness direction of the thin polycrystalline dielectric layer, thus improving modeling efficiency.
[0011] According to some embodiments of the first aspect of the present invention, the material parameters include initial defect concentration, polycrystalline grain density, and a minimum preset distance between any two adjacent defects.
[0012] According to some embodiments of the first aspect of the present invention, the minimum preset distance between any two adjacent defects includes:
[0013] The minimum preset distance between any two adjacent oxygen vacancies.
[0014] According to some embodiments of the first aspect of the present invention, the defect dataset includes a plurality of initial defects and newly generated defects, wherein distributing the defect data on the three-dimensional grain boundaries of the three-dimensional grain boundary model according to a preset distribution rule to update the three-dimensional grain boundary model includes:
[0015] Based on the minimum preset distance, multiple initial defects are randomly distributed on the three-dimensional grain boundary of the three-dimensional grain boundary model;
[0016] Based on the minimum preset distance, the new defects are distributed on the three-dimensional grain boundaries of the three-dimensional grain boundary model and close to the initial defects.
[0017] According to some embodiments of the first aspect of the present invention, the step of randomly distributing a plurality of the initial defects on the three-dimensional grain boundaries of the three-dimensional grain boundary model according to the minimum preset distance includes:
[0018] Multiple initial defects are randomly distributed on the three-dimensional grain boundary of the three-dimensional grain boundary model, and the distance between any two adjacent initial defects is greater than or equal to the minimum preset distance.
[0019] The step of distributing the new defects on the three-dimensional grain boundaries of the three-dimensional grain boundary model and close to the initial defects according to the minimum preset distance includes:
[0020] The new defects are distributed on the three-dimensional grain boundaries of the three-dimensional grain boundary model, and the distance between them and the adjacent initial defects is greater than or equal to the minimum preset distance.
[0021] Secondly, embodiments of the present invention provide a breakdown test method for an ultrathin polycrystalline dielectric layer, applied to a three-dimensional grain boundary model corresponding to the ultrathin polycrystalline dielectric layer, the breakdown test method comprising:
[0022] Obtain the preset breakdown density, defect-assisted tunneling current density, and direct tunneling current density in the three-dimensional grain boundary model;
[0023] The total leakage current density of the three-dimensional grain boundary model is calculated based on the defect-assisted tunneling current density and the direct tunneling current density.
[0024] Based on the total leakage current density and the preset breakdown density, it is determined whether the three-dimensional grain boundary model has been broken down.
[0025] According to some embodiments of the second aspect of the present invention, obtaining the defect-assisted tunneling current density and the direct tunneling current density of the three-dimensional grain boundary model includes:
[0026] The defect-assisted tunneling current density is calculated based on the coupled three-dimensional master equation and Poisson equation of defect-assisted tunneling.
[0027] The direct tunneling current density was calculated based on the Kawasaki diode equation.
[0028] According to some embodiments of the second aspect of the present invention, determining whether the three-dimensional grain boundary model is broken down based on the total leakage current density and the preset breakdown density includes:
[0029] If the total leakage current density is less than the preset breakdown density, it is determined that the three-dimensional grain boundary model has not been broken down;
[0030] If the total leakage current density is greater than or equal to the preset breakdown density, the three-dimensional grain boundary model is determined to be broken down.
[0031] A modeling system for ultrathin polycrystalline dielectric layers according to a second aspect of the present invention includes: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to perform:
[0032] The modeling method for ultrathin polycrystalline dielectric layers as described in the first aspect above;
[0033] or,
[0034] The breakdown test method for ultrathin polycrystalline dielectric layers as described in the second aspect above.
[0035] According to a fourth aspect of the present invention, a computer-readable storage medium stores computer-executable instructions, the computer-executable instructions being used for:
[0036] The model establishment method for the ultrathin polycrystalline dielectric layer described in the first aspect above shall be implemented;
[0037] or,
[0038] Perform the breakdown test method for the ultrathin polycrystalline dielectric layer described in the second aspect above.
[0039] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description
[0040] The accompanying drawings are provided to further understand the technical solutions of the present invention and constitute a part of the specification. They are used together with the embodiments of the present invention to explain the technical solutions of the present invention and do not constitute a limitation on the technical solutions of the invention.
[0041] Figure 1 This is a schematic flowchart of the method for establishing a model of an ultrathin polycrystalline dielectric layer provided in an embodiment of the present invention;
[0042] Figure 2 This is a schematic diagram of the structure of converting a two-dimensional grain boundary model into a three-dimensional grain boundary model according to an embodiment of the present invention;
[0043] Figure 3 This is a schematic diagram of the structure of the two-dimensional grain boundary model provided in the embodiment of the present invention;
[0044] Figure 4 This is a schematic diagram of the structure of the grain boundary of an actual polycrystalline material provided in one embodiment of the present invention;
[0045] Figure 5 This is a schematic diagram of the structure of a polycrystalline dielectric layer morphology model at different times in a related technology provided by another embodiment of the present invention;
[0046] Figure 6 This is a schematic diagram of the defect dataset distribution provided in an embodiment of the present invention;
[0047] Figure 7 This is a schematic diagram illustrating the specific process of defect dataset distribution provided in this embodiment of the invention;
[0048] Figure 8 This is a schematic flowchart of the breakdown test method for ultrathin polycrystalline dielectric layers provided in this embodiment of the invention;
[0049] Figure 9 This is a schematic diagram of the process for obtaining two leakage current densities provided in an embodiment of the present invention;
[0050] Figure 10 This is a schematic diagram of the process for determining whether an ultrathin polycrystalline dielectric layer has been broken down, provided in an embodiment of the present invention.
[0051] Figure 11 This is a schematic diagram of the structure of the first, second, and third three-dimensional distribution images provided in the embodiments of the present invention. Detailed Implementation
[0052] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.
[0053] It should be noted that although functional modules are divided in the device schematic diagram and a logical order is shown in the flowchart, in some cases, the steps shown or described may be performed in a different order than the module division in the device or the order in the flowchart. The terms "first," "second," etc., in the specification, claims, and the aforementioned drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence.
[0054] During the growth of polycrystalline materials, grain boundaries are generated. The instability of chemical bonds at the grain boundaries can lead to the generation of defects. These defects can induce defect-assisted tunneling, which in turn generates leakage current and exacerbates the failure of dielectric layer materials and devices.
[0055] In related technologies, a morphological model of a polycrystalline dielectric layer is constructed based on molecular dynamics and Monte Carlo methods. Initial defects are randomly distributed throughout the dielectric layer, and the position of new defects is then determined using the standard Monte Carlo method. However, the establishment of this morphological model of the polycrystalline dielectric layer is quite complex and does not consider the existence of initial defects in the polycrystalline material itself, which determine the breakdown site during dielectric breakdown. Therefore, the morphological model of this polycrystalline dielectric layer differs significantly from the actual morphology of the polycrystalline dielectric layer, resulting in high randomness in the three-dimensional positions of defects. Since defect aggregation leads to changes in local current, temperature, and electric field, it causes significant errors in the leakage current and breakdown time predictions calculated based on the morphological model of the polycrystalline dielectric layer.
[0056] Based on this, embodiments of the present invention provide a modeling method, breakdown testing method, system, and storage medium for ultrathin polycrystalline dielectric layers, which enables defects to occur at grain boundaries, more closely resembling the actual morphology of ultrathin polycrystalline dielectric layers. While improving accuracy, it simplifies the grain morphology and defect location in the thickness direction of ultrathin polycrystalline dielectric layers, thereby improving modeling efficiency.
[0057] The embodiments of the present invention will be further described below with reference to the accompanying drawings.
[0058] The first aspect of this invention specifically provides a method for establishing a model of an ultrathin polycrystalline dielectric layer, such as... Figures 1 to 3 As shown. The modeling method for ultrathin polycrystalline dielectric layers includes, but is not limited to, the following steps:
[0059] Step S100: Obtain the size data and material parameters of the ultrathin polycrystalline dielectric layer, wherein the size data includes the thickness data of the ultrathin polycrystalline dielectric layer;
[0060] It should be noted that the ultrathin polycrystalline dielectric layer is the insulating layer in the metal insulating layer structure. The metal insulating layer structure includes an ultrathin polycrystalline dielectric layer, a first metal layer, and a second metal layer. The ultrathin polycrystalline dielectric layer is formed on the first metal layer, and the second metal layer is formed on the ultrathin polycrystalline dielectric layer. The dimensional data includes the length, width, and thickness of the ultrathin polycrystalline dielectric layer.
[0061] It should be noted that, due to the local atomic environment, chemical bonds break more easily at grain boundaries than within single-crystal grains. For example, using first-principles calculations, McKenna et al. showed that, for polycrystalline chromium dioxide as a dielectric layer, the probability of trap formation at grain boundaries is approximately 87 times higher than that inside the grain. Therefore, for simplicity, we only consider traps at grain boundaries; that is, the generation of initial and new defects only exists at grain boundaries.
[0062] Step S200: Based on the dimensional data and material parameters, generate a two-dimensional grain boundary model based on the Thiessen polygon model;
[0063] It should be noted that the Thiessen polygon is also known as a Voronoi diagram. The main idea of a Voronoi diagram is to divide an n-dimensional space into a collection of countless polyhedra using the proximity principle (e.g., in the case of two dimensions, dividing the space plane into a collection of countless polygons). Each polyhedron is actually generated by a core point within it. The influence domain of each core point is the set of core points closest to that core point, and this influence domain constitutes the corresponding polyhedron. The initial point used to generate the Voronoi diagram is called the generator of the Voronoi diagram. In other words, a Voronoi diagram is a collection of two-dimensional polygons or three-dimensional polyhedra formed by dividing space based on the proximity principle. The distance from any point inside each polygon to its corresponding seed point is shorter than its distance to other seed points. It mainly describes the boundary of the neighborhood or influence region of a point in space. For example, refer to... Figure 3 , is a two-dimensional grain boundary model corresponding to the ultrathin polycrystalline dielectric layer, obtained from the Thiessen polygon model.
[0064] Step S300: The thickness data of the two-dimensional grain boundary in the two-dimensional grain boundary model is stretched towards the direction of the dielectric layer thickness to obtain the three-dimensional grain boundary model;
[0065] For example, refer to Figure 2 The thickness of the ultrathin polycrystalline dielectric layer is 50 angstroms, L X This indicates the thickness data of an ultrathin polycrystalline dielectric layer. The thickness data is stretched in the direction of the dielectric layer thickness, i.e., towards... Figure 2 The image shows a stretch of 50 angstroms in the X direction from... Figure 2 The two-dimensional grain boundary model shown in the left figure is converted to Figure 2 The three-dimensional grain boundary model shown in the right figure.
[0066] Step S400: Obtain the defect dataset and distribute the defect data on the three-dimensional grain boundary of the three-dimensional grain boundary model according to the preset distribution rules, so as to update the three-dimensional grain boundary model.
[0067] For example, refer to Figure 11 , Figure 11 A three-dimensional grain boundary model of a 50 Å × 200 Å × 200 Å polycrystalline hafnium dioxide dielectric layer is shown. Figures a, b, and c represent the random distribution of the defect dataset at different times. The defect dataset includes multiple initial defects and newly generated defects. The initial defects are distributed along the three-dimensional grain boundaries, while the new defects are distributed along the grain boundaries and close to the initial defect distribution. Figure 11 The upper length boundary and the left and right width boundaries of the grayscale box in the image represent the three-dimensional grain boundaries, and the black dots represent defects.
[0068] It should be noted that grain boundaries refer to the boundaries between crystal particles. The chemical bonds at grain boundaries are unstable, and under the influence of an external electric field, these chemical bonds are more likely to break, generating defects and forming a defect dataset, which often refers to oxygen vacancies.
[0069] In related technologies, refer to Figure 5 The dielectric layer morphology model constructed by Luca Vandelli's team in Italy is based on molecular dynamics and Monte Carlo methods. Initial defects are randomly distributed throughout the dielectric layer, and subsequent defects are located using the standard Monte Carlo method. However, Vandelli et al.'s research neglected the influence of grain boundary characteristics on device failure. Furthermore, the model assumes that the material itself has no defects, and that defects are generated under an applied electric field. This view contradicts the reality of polycrystalline materials, which inherently possess initial defects that determine the breakdown location during dielectric layer breakdown. Additionally, the three-dimensional location of defects in this polycrystalline dielectric layer morphology model exhibits high randomness, and defect aggregation leads to changes in local current, temperature, and electric field, resulting in significant errors in the leakage current and breakdown time predictions calculated based on this model. Based on these factors, refer to... Figure 4 The modeling method for ultrathin polycrystalline dielectric layers provided in this embodiment, which is a grain boundary diagram of actual polycrystalline materials, allows defects to be generated on the grain boundaries, reducing the randomness of the random distribution of defects and more closely resembling the morphology of actual ultrathin polycrystalline dielectric layers. While improving the accuracy of calculations such as leakage current and breakdown time prediction, it simplifies the morphology of grains and defect locations in the thickness direction of thin polycrystalline dielectric layers, thereby improving modeling efficiency.
[0070] It is understandable that the material parameters include the initial defect concentration, polycrystalline grain density, and the minimum preset distance between any two adjacent defects.
[0071] For example, taking polycrystalline chromium dioxide material as an example, the initial defect concentration is 8×10⁻⁶. 24 / m 3 The polycrystalline grain density is 10. 16 / m 2 The minimum distance between any two initial defects in chromium dioxide is 0.36 nm. This minimum distance between any two initial defects is calculated using first-principles calculations. Figure 2 As shown, a three-dimensional grain boundary model of a 50 Å × 200 Å × 200 Å polycrystalline hafnium dioxide dielectric layer is presented, using L... y L represents the length of the ultrathin polycrystalline dielectric layer. Z L represents the width of the ultrathin polycrystalline dielectric layer. XThe value L represents the height, or thickness, of the ultrathin polycrystalline dielectric layer. The lateral dimension in the y-direction is the length of the ultrathin polycrystalline dielectric layer, and the lateral dimension in the z-direction is its width. X The value ranges from 50 to 80 angstroms. Figure 2 L in X =50 angstroms, L y =L Z =200 Angstroms.
[0072] It is understandable that the minimum preset distance between any two adjacent defects is the same as the minimum preset distance between any two adjacent oxygen vacancies.
[0073] It should be noted that for ultrathin polycrystalline dielectric layers, three-dimensional grain boundaries exist, and these three-dimensional grain boundaries are prone to generating oxygen vacancy defects. The defects in the dielectric are mainly oxygen vacancy defects, and the closest distance between two oxygen atom vacancies is limited by the length of the chemical bond. Taking hafnium dioxide as an example, the minimum distance between defects at the grain boundary is 0.36 nm.
[0074] Reference Figure 6 It is understood that the defect dataset includes multiple initial defects and newly generated defects. In step S400, the defect data is distributed on the three-dimensional grain boundaries of the three-dimensional grain boundary model according to a preset distribution rule to update the three-dimensional grain boundary model, including but not limited to the following steps:
[0075] Step S410: Based on the minimum preset distance, randomly distribute multiple initial defects on the three-dimensional grain boundary of the three-dimensional grain boundary model;
[0076] Step S420: Based on the minimum preset distance, distribute the new defects on the three-dimensional grain boundary of the three-dimensional grain boundary model and close to the initial defects.
[0077] It should be noted that the new defects are generated after simulating the applied voltage on the three-dimensional grain boundary model. The formula for calculating the rate of new defect generation is as follows:
[0078] G F (x,y,z)=G0exp(-E A -b|F ox (x,y,z)| / k B T(x,y,z)),
[0079] Among them, G F G0 represents the rate at which new defects are generated, and E represents the vibrational rate of chemical bonds. A The value represents the activation energy, b represents a parameter related to the polarization of chemical bonds, T represents the temperature of the three-dimensional grain boundary model, and k represents the activation energy. B F represents the Boltzmann constant.ox This represents the electric field distribution after applying an external voltage to a three-dimensional grain boundary model. Both temperature and electric field distribution affect the local chemical bond breaking rate in the three-dimensional grain boundary model.
[0080] Reference Figure 7 It is understood that step S410 includes, but is not limited to, the following steps:
[0081] Step S411: Randomly distribute multiple initial defects on the three-dimensional grain boundary of the three-dimensional grain boundary model, and the distance between any two adjacent initial defects is greater than or equal to the minimum preset distance.
[0082] Reference Figure 7 It is understood that step S420 includes, but is not limited to, the following steps:
[0083] Step S421: Distribute the new defects on the three-dimensional grain boundaries of the three-dimensional grain boundary model, and the distance between the new defects and the adjacent initial defects is greater than or equal to the minimum preset distance.
[0084] In related technologies, Shen Mande combined Monte Carlo and Thiessen polygon models to simulate grain boundaries of polycrystalline materials. In this study, the morphology of polycrystalline metal materials was constructed by combining the Thiessen polygon and Monte Carlo methods. A linked list structure was also introduced into the model program, significantly improving model construction efficiency. However, this study was not applied to polycrystalline dielectric layer models, nor did it investigate the defect distribution of polycrystalline materials on the Thiessen polygon model. Based on the above, the model building method for ultrathin polycrystalline dielectric layers provided in this invention is applied to ultrathin polycrystalline dielectric layers and provides the distribution diagrams of initial and new defects on the three-dimensional grain boundary model of the ultrathin polycrystalline dielectric layer at different times.
[0085] Furthermore, the defect dataset is specifically a second defect dataset, and the three-dimensional grain boundary model is verified by the following steps:
[0086] Step S810: Before applying voltage to the ultrathin polycrystalline dielectric layer, obtain a first three-dimensional distribution image of the initial defect dataset randomly distributed on the three-dimensional grain boundary;
[0087] Step S820: Apply an external voltage to the ultrathin polycrystalline dielectric layer to obtain a second three-dimensional distribution image of the random distribution of the first defect dataset before the ultrathin polycrystalline dielectric layer is broken down, and a third three-dimensional distribution image of the random distribution of the second defect dataset when the ultrathin polycrystalline dielectric layer is broken down; wherein, the first defect dataset includes the initial defect dataset and new defects generated before the ultrathin polycrystalline dielectric layer is broken down, and the second defect dataset includes the initial defect dataset, the first defect dataset, and new defects generated when the ultrathin polycrystalline dielectric layer is broken down;
[0088] Step S830: Based on the first three-dimensional distribution image, the second three-dimensional distribution image, and the third three-dimensional distribution image, determine whether the three-dimensional grain boundary model has passed verification.
[0089] For example, refer to Figure 11 Figure a shows the first three-dimensional distribution image, Figure b shows the second three-dimensional distribution image, and Figure c shows the third three-dimensional distribution image. The initial defects are distributed on the three-dimensional grain boundaries. The new defects generated in the first defect dataset are distributed on the three-dimensional grain boundaries and close to the initial defect distribution. The new defects generated in the second defect dataset are distributed on the three-dimensional grain boundaries and close to the second defect dataset distribution.
[0090] Further, step S830 includes, but is not limited to, the following steps:
[0091] Step S831: Obtain the preset defect distribution rate of the three-dimensional grain boundary;
[0092] Step S832: If the defect distribution rate of the initial defect dataset, the first defect dataset, and the second defect dataset on the three-dimensional grain boundary is greater than or equal to the preset defect distribution rate, the three-dimensional grain boundary model is deemed to be qualified.
[0093] Step S833: If the distribution rate of the initial defect dataset, and / or the first defect dataset, and / or the second defect dataset on the three-dimensional grain boundary is less than the preset defect distribution rate, the three-dimensional grain boundary model verification is determined to be unqualified.
[0094] For example, such as Figure 11 As shown, the initial defects are distributed on the three-dimensional grain boundaries. New defects generated in the second defect dataset are also distributed on the three-dimensional grain boundaries and close to the initial defect distribution. Similarly, new defects generated in the third defect dataset are also distributed on the three-dimensional grain boundaries and close to the second defect dataset distribution, indicating that the three-dimensional grain boundary model has been successfully validated. Furthermore, the new defects occur near the initial defects, and the number of defects increases over time, consistent with the defect-assisted tunneling mechanism.
[0095] It should be noted that if the distribution rate of the initial defect dataset on the 3D grain boundary is less than the preset defect distribution rate, and / or the distribution rate of the first defect dataset on the 3D grain boundary is less than the preset defect distribution rate, and / or the distribution rate of the second defect dataset on the 3D grain boundary is less than the preset defect distribution rate, the 3D grain boundary model verification is determined to be unqualified. In this embodiment, the preset defect distribution rate is a percentage set before verification.
[0096] Secondly, embodiments of the present invention also provide a breakdown test method for an ultrathin polycrystalline dielectric layer, referring to... Figure 8 This method is applied to the three-dimensional grain boundary model corresponding to ultrathin polycrystalline dielectric layers. The breakdown test method for ultrathin polycrystalline dielectric layers includes, but is not limited to, the following steps:
[0097] Step S500: Obtain the preset breakdown density, defect-assisted tunneling current density, and direct tunneling current density in the three-dimensional grain boundary model;
[0098] Step S600: Calculate the total leakage current density of the three-dimensional grain boundary model based on the defect-assisted tunneling current density and the direct tunneling current density.
[0099] Step S700: Determine whether the three-dimensional grain boundary model is broken down based on the total leakage current density and the preset breakdown density.
[0100] It should be noted that the formula for calculating the total leakage current density is as follows:
[0101] J = J DT +J TAT ,
[0102] Where J represents the total leakage current density, J DT J represents the direct tunneling current density. TAT This represents the defect-assisted tunneling current density.
[0103] It should be noted that for ultrathin polycrystalline dielectric layers, grain boundaries exist, and these grain boundaries are prone to generating oxygen vacancy defects. These defects can easily lead to defect-assisted tunneling. Defect-assisted tunneling refers to the generation of atomic defects within the dielectric, which in turn generate defect states. These defects can trap or emit electrons, generating defect currents. The electron trapping / emission process releases energy in the form of phonons, causing a local temperature increase near the defect, which makes it easier to generate new defects, increasing leakage current, forming positive feedback, and ultimately leading to the failure of the ultrathin polycrystalline dielectric layer and breakdown. Therefore, by constructing the three-dimensional grain boundary model provided in this embodiment, which is closer to reality, the accuracy of calculations such as leakage current and breakdown time prediction is improved.
[0104] It should be noted that the process for obtaining the 3D grain boundary model corresponding to the ultrathin polycrystalline dielectric layer is as follows: Obtain the dimensional data and material parameters of the ultrathin polycrystalline dielectric layer; generate a 2D grain boundary model based on the Thiessen polygon model according to the dimensional data and material parameters; stretch the 2D grain boundaries in the 2D grain boundary model towards the thickness direction of the dielectric layer to obtain the 3D grain boundary model corresponding to the ultrathin polycrystalline dielectric layer; obtain the defect dataset and distribute the defect data on the 3D grain boundaries of the 3D grain boundary model according to a preset distribution rule to update the 3D grain boundary model. This method allows defects to be generated at the grain boundaries, reducing the randomness of defect distribution and more closely reflecting the actual morphology of the ultrathin polycrystalline dielectric layer. While improving the accuracy of calculations such as leakage current and breakdown time prediction, it also simplifies the morphology of the grains and defect locations in the thickness direction of the thin polycrystalline dielectric layer, thus improving modeling efficiency.
[0105] Reference Figure 9 It is understood that obtaining the defect-assisted tunneling current density and direct tunneling current density of the three-dimensional grain boundary model in step S500 includes, but is not limited to, the following steps:
[0106] Step S510: Based on the coupled three-dimensional master equation and Poisson equation of defect-assisted tunneling, the defect-assisted tunneling current density is calculated.
[0107] Step S520: Calculate the direct tunneling current density according to the Kawasaki diode equation.
[0108] It should be noted that the coupling of the three-dimensional master equation and the Poisson equation is as follows:
[0109]
[0110] Among them, J TAT L represents the defect-assisted tunneling current density. x This represents the thickness data of the ultrathin polycrystalline dielectric layer, indicating that L... y L represents the length of the ultrathin polycrystalline dielectric layer. z p represents the width of the ultrathin polycrystalline dielectric layer. j Let x represent the probability that a defect is occupied by a charge, i represent the first defect, j represent the second defect, and x represent the probability that a defect is occupied by a charge. i The x-axis coordinate of the first defect is represented by x. j The x-axis coordinate of the second defect is represented by e, which represents the unit charge, and w. i,j This represents the transition rate of electrons between the first defect and the second defect.
[0111] The equation for the Kawasaki diode is:
[0112]
[0113]
[0114] Among them, J DT E represents the direct tunneling current density. F,L E represents the Fermi level of the left electrode. F,R The Fermi level of the right electrode is indicated, TM represents the transmission coefficient obtained using the WKB method, T represents the temperature of the three-dimensional grain boundary model, and kJ / m² is the kJ / m² value. B Represents the Boltzmann constant. The effective mass of the metal electrode is represented by , e represents the amount of charge per unit, and E represents the amount of charge.
[0115] Reference Figure 10 It is understood that step S700 includes, but is not limited to, the following steps:
[0116] Step S610: If the total leakage current density is less than the preset breakdown density, it is determined that the three-dimensional grain boundary model has not been broken down.
[0117] Step S620: If the total leakage current density is greater than or equal to the preset breakdown density, it is determined that the three-dimensional grain boundary model has been broken down.
[0118] It should be noted that after stretching the thickness data of the two-dimensional grain boundary in the two-dimensional grain boundary model towards the direction of dielectric layer thickness to obtain the three-dimensional grain boundary model corresponding to the ultrathin polycrystalline dielectric layer, the initial defects are randomly distributed on the three-dimensional grain boundary. Then, the total leakage current density is calculated. If the total leakage current density is less than the preset breakdown density, it means that the ultrathin polycrystalline dielectric layer has not broken down, and new defects continue to be generated on the three-dimensional grain boundary and close to the initial defects. If the total leakage current density is greater than or equal to the preset breakdown density, it means that the ultrathin polycrystalline dielectric layer has been broken down.
[0119] In addition, a second aspect of the present invention provides a modeling system for an ultrathin polycrystalline dielectric layer, the modeling system comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor.
[0120] The processor and memory can be connected via a bus or other means.
[0121] Memory, as a non-transitory computer-readable storage medium, can be used to store non-transitory software programs and non-transitory computer-executable programs. Furthermore, memory may include high-speed random access memory, and may also include non-transitory memory, such as at least one disk storage device, flash memory device, or other non-transitory solid-state storage device. In some embodiments, memory may optionally include memory remotely located relative to the processor, and these remote memories can be connected to the processor via a network. Examples of such networks include, but are not limited to, the Internet, intranets, local area networks, mobile communication networks, and combinations thereof.
[0122] The non-transient software program and instructions required to implement the model building method for the ultrathin polycrystalline dielectric layer of the first aspect embodiment described above are stored in memory. When executed by a processor, the model building method for the ultrathin polycrystalline dielectric layer in the above embodiment is executed, for example, the method described above is executed. Figure 1 Method steps S100 to S400 in the text Figure 6 Method steps S410 to S420 in the text Figure 7 The method steps S411 to S422.
[0123] The non-transient software program and instructions required to implement the breakdown test method for the ultrathin polycrystalline dielectric layer in the second aspect embodiment described above are stored in memory. When executed by a processor, the breakdown test method for the ultrathin polycrystalline dielectric layer in the above embodiment is executed, for example, the method described above is executed. Figure 8 Method steps S500 to S700, Figure 9 Method steps S510 to S520 in the text Figure 10 Method steps S610 to S620.
[0124] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate; that is, they may fall into one place or be distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs.
[0125] Furthermore, embodiments of the present invention also provide a computer-readable storage medium storing computer-executable instructions that are executed by a processor or controller, for example, by a processor in the above-described device embodiments. These instructions cause the processor to execute the model building method or breakdown test method for the ultrathin polycrystalline dielectric layer described above, for example, to perform the above-described... Figure 1 Method steps S100 to S400 in the text Figure 6 Method steps S410 to S420 in the text Figure 7 Method steps S411 to S422, Figure 8 Method steps S500 to S700, Figure 9 Method steps S510 to S520 in the text Figure 10 Method steps S610 to S620.
[0126] It will be understood by those skilled in the art that all or some of the steps and systems in the methods disclosed above can be implemented as software, firmware, hardware, and suitable combinations thereof. Some or all of the physical components can be implemented as software executed by a processor, such as a central processing unit, digital signal processor, or microprocessor, or as hardware, or as an integrated circuit, such as an application-specific integrated circuit. Such software can be distributed on a computer-readable medium, which can include computer storage media (or non-transitory media) and communication media (or transient media). As is known to those skilled in the art, the term computer storage media includes volatile and non-volatile, removable and non-removable media implemented in any method or technology for storing information (such as computer-readable instructions, data structures, program modules, or other data). Computer storage media includes, but is not limited to, RAM, ROM, EEPROM, flash memory or other memory technologies, CD-ROM, digital versatile disc (DVD) or other optical disc storage, magnetic cartridges, magnetic tape, disk storage or other magnetic storage devices, or any other medium that can be used to store desired information and is accessible to a computer. Furthermore, as is known to those skilled in the art, communication media typically contain computer-readable instructions, data structures, program modules, or other data in modulated data signals such as carrier waves or other transmission mechanisms, and may include any information delivery medium.
[0127] The above is a detailed description of the preferred embodiments of the present invention. However, the present invention is not limited to the above embodiments. Those skilled in the art can make various equivalent modifications or substitutions without departing from the spirit of the present invention. All such equivalent modifications or substitutions are included within the scope defined by the claims of the present invention.
Claims
1. A method for establishing a model of an ultrathin polycrystalline dielectric layer, characterized in that, The method comprises the following steps: acquiring size data and material parameters of an ultra-thin polycrystalline dielectric layer, wherein the size data comprises thickness data of the ultra-thin polycrystalline dielectric layer; generating a two-dimensional grain boundary model based on a Voronoi polygon model according to the size data and the material parameters; stretching the thickness data in the direction of the dielectric layer thickness to obtain a three-dimensional grain boundary model; acquiring a defect data set and distributing the defect data on the three-dimensional grain boundaries of the three-dimensional grain boundary model according to a preset distribution rule to update the three-dimensional grain boundary model; the material parameters comprise an initial defect concentration, a polycrystalline grain density and a minimum preset distance between any two adjacent defects; the minimum preset distance between any two adjacent defects is a minimum preset distance between any two adjacent oxygen vacancies; the defect data set comprises a plurality of initial defects and generated new defects; the distribution of the defect data on the three-dimensional grain boundaries of the three-dimensional grain boundary model according to the preset distribution rule to update the three-dimensional grain boundary model comprises: randomly distributing a plurality of the initial defects on the three-dimensional grain boundaries of the three-dimensional grain boundary model according to the minimum preset distance; distributing the new defects on the three-dimensional grain boundaries of the three-dimensional grain boundary model and close to the initial defects according to the minimum preset distance.
2. The method of claim 1, wherein the model is established by using a software program. the randomly distributing a plurality of the initial defects on the three-dimensional grain boundaries of the three-dimensional grain boundary model according to the minimum preset distance comprises: randomly distributing a plurality of the initial defects on the three-dimensional grain boundaries of the three-dimensional grain boundary model, and the distance between any two adjacent initial defects is greater than or equal to the minimum preset distance; the distributing the new defects on the three-dimensional grain boundaries of the three-dimensional grain boundary model and close to the initial defects according to the minimum preset distance comprises: distributing the new defects on the three-dimensional grain boundaries of the three-dimensional grain boundary model and the distance between the new defects and adjacent initial defects is greater than or equal to the minimum preset distance.
3. A breakdown test method for an ultra-thin polycrystalline dielectric layer, applied to the three-dimensional grain boundary model obtained by the model establishment method for the ultra-thin polycrystalline dielectric layer according to claim 1, the breakdown test method comprising: acquiring a preset breakdown density, a defect-assisted tunneling current density and a direct tunneling current density in the three-dimensional grain boundary model; calculating a total leakage current density of the three-dimensional grain boundary model according to the defect-assisted tunneling current density and the direct tunneling current density; judging whether the three-dimensional grain boundary model is broken down according to the total leakage current density and the preset breakdown density.
4. The method of breakdown testing of ultra-thin polycrystalline dielectric layers according to claim 3, wherein, the acquiring the defect-assisted tunneling current density and the direct tunneling current density of the three-dimensional grain boundary model comprises: calculating the defect-assisted tunneling current density according to a coupled three-dimensional master equation and a Poisson equation of defect-assisted tunneling; calculating the direct tunneling current density according to a Kawazoe diode equation.
5. The method of breakdown testing of ultra-thin polycrystalline dielectric layers according to claim 3, wherein, The method comprises the following steps: If the total leakage current density is less than the preset breakdown density, it is determined that the three-dimensional grain boundary model is not broken down; If the total leakage current density is greater than or equal to the preset breakdown density, it is determined that the three-dimensional grain boundary model is broken down.
6. A model building system for ultra-thin polycrystalline dielectric layers, characterized by The method comprises the following steps: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement: The method for establishing a model of an ultrathin polycrystalline dielectric layer according to any one of claims 1 to 2; Or, The breakdown test method for an ultrathin polycrystalline dielectric layer according to any one of claims 3 to 5.
7. A computer-readable storage medium, characterized in that: The computer readable storage medium stores computer executable instructions for: The method for establishing a model of an ultrathin polycrystalline dielectric layer according to any one of claims 1 to 2; Or, The breakdown test method for an ultrathin polycrystalline dielectric layer according to any one of claims 3 to 5.
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