A particle isotropic distribution motion simulation method, device, equipment and medium

Abstract

The application discloses a kind of particle isotropic distribution movement simulation method, device, equipment and medium, it is related to plasma etching technical field, to solve the problem that existing etching simulation simulation method cannot accurately simulate the actual etching process of laminated structure, leading to simulation movement deviates from actuality.The method comprises: obtaining the transport parameter of etching process simulation model;According to initial particle concentration and surface reaction probability, the etching rate of target cell is determined;The level set method is used to update the morphology of semiconductor device, and the updated etching process simulation model is obtained;Based on the updated etching process simulation model, the current particle concentration of each cell is calculated using Knudsen diffusion equation, and the corresponding etching rate is determined based on the current particle concentration and the morphology update is continued until the simulation time reaches the preset etching time to end simulation;The simulation precision of the etching process of simulating laminated structure is improved by the particle isotropic distribution movement simulation method provided by the application.

Description

Technical Field

[0001] This invention relates to the field of plasma etching technology, and in particular to a method, apparatus, equipment and medium for simulating the isotropic distribution and motion of particles. Background Technology

[0002] Gate-All-Around FETs (GAAFETs) are key device architectures for 3nm and below technology nodes. Their channels are typically composed of a stacked material formed by alternating layers of silicon and silicon-germanium. In integrated circuit manufacturing, a stacked material refers to a vertically stacked multilayer structure formed by sequentially depositing or growing multiple material layers with different properties on a silicon substrate according to specific process requirements. It is a composite structure composed of multiple different materials stacked in a specific order and thickness. The core concept of stacked materials is to move away from relying on a single material to perform all functions. Instead, based on the specific requirements of each process step, multiple material layers with specific physical, chemical, and optical properties are vertically stacked to overcome problems that cannot be solved by a single material through synergistic effects.

[0003] The GAA Si / SiGe stack structure requires the formation of alternating layers through epitaxial growth techniques, with a mask pattern defined on its surface. Subsequently, isotropic etching is performed, selectively removing the SiGe layer laterally while leaving the Si layer almost unaffected. This process places extremely high demands on the selectivity, uniformity, and morphology control of the etching. During etching, parameters such as the Ge concentration of SiGe, pattern size and density, and chamber process conditions all significantly affect the etching profile. Improper process control can easily lead to problems such as Si layer damage and irregular sidewall morphology, affecting device performance and yield. To improve the device performance and yield of the stack structure, etching simulation is necessary.

[0004] Existing technologies treat the etching morphology as static, decoupling the simulation process from the particle transport process. This makes it impossible to simulate the real-time strongly coupled feedback loop of etching, deformation, and re-diffusion, thus failing to predict key process defects caused by dynamic morphology changes, such as lateral drilling. Furthermore, traditional models use simplified average reaction rate constants, which cannot truly reflect the differences in reaction probabilities between particles and different material surfaces in the stacked structure at the microscopic level. This leads to the simulation motion deviating from reality, and ultimately, the material ratio of the stacked structure predicted based on the simulation results is inaccurate. Summary of the Invention

[0005] The purpose of this invention is to provide a method, apparatus, device, and medium for simulating the isotropic distribution motion of particles, in order to solve the problem that existing etching simulation methods cannot accurately simulate the actual etching process of stacked structures, resulting in the simulated motion deviating from reality.

[0006] To achieve the above objectives, the present invention provides the following technical solution: In a first aspect, the present invention provides a method for simulating the isotropic distribution motion of particles, comprising: The transport parameters of the etching process simulation model are obtained; the etching process simulation model includes a semiconductor device with a stacked structure; the transport parameters include the initial particle concentration of each cell in the simulation area and the surface reaction probability corresponding to different materials; The etching rate of the target cell is determined based on the initial particle concentration and the surface reaction probability; the target cell is the cell in the etching process simulation model that is in contact with each structural boundary. Based on the etching rate, the semiconductor device is updated using the level set method to obtain the updated etching process simulation model. Based on the updated etching process simulation model, the Knudsen diffusion equation is used to calculate the current particle concentration of each cell, and the corresponding etching rate is determined based on the current particle concentration. The morphology is then updated until the simulation time reaches the preset etching time, at which point the simulation ends and the simulation data is output. The simulation data includes at least the morphology data of the semiconductor device at each preset time point and the data on the change of the lateral etching depth of the target etched structure over time.

[0007] Optionally, determining the etching rate of the target cell based on the initial particle concentration and the surface reaction probability includes: Formula used: ; Calculate the etching rate of the target cell corresponding to each structure; in, Etching rate, The reaction rate constant is... The material type is Surface reaction probability, Let be the initial particle concentration of the target cell with coordinates (l, m).

[0008] Optionally, the etching process simulation model is updated once after each time step; based on the etching amount, the semiconductor device is updated using the level set method to obtain the updated etching process simulation model. Based on the initial level set function and the etching rate, the formula is as follows: ; The solution is performed to obtain the target level set function after a time step; the initial level set function is the level set function corresponding to the boundary at the initial moment of the etching process simulation model; Where t is time, The gradient of the level set function. The etching rate is the etch rate along the normal direction of the target cell; The corresponding boundary in the etching process simulation model is moved along the normal direction according to the target level set function to obtain the updated boundary; Boundary conditions are set for the updated boundary to obtain the updated etching process simulation model.

[0009] Optionally, the calculation of the current particle concentration of each cell based on the updated etching process simulation model and the Knudsen diffusion equation includes: Formula used: ; Calculate the current particle concentration in each cell; in, The current particle concentration, This represents the particle concentration at the previous moment. Knudsen diffusion coefficient, For time step.

[0010] Optionally, the semiconductor device includes a substrate, a stacked structure formed by alternating layers of silicon and germanium silicide, and a mask layer disposed on the stacked structure; the surface reaction probability of the germanium silicide layer is the highest.

[0011] Optionally, before obtaining the transport parameters of the etching process simulation model, the method further includes: Obtain simulation input parameters; the simulation input parameters include the initial concentration of neutral particles injected at the simulation inlet, the Knudsen diffusion coefficient, and the surface reaction probability of different materials; An initial simulation model is constructed based on the geometric parameters of the semiconductor device; Based on the cellular method, the simulation region of the initial simulation model is discretized into multiple cells; each cell stores the material type, particle concentration, and surface normal vector. The cells are labeled according to their material type; The initial boundaries of each structure are determined based on the cell labels, and boundary conditions are set for the initial boundaries. The model is initialized based on the simulation input parameters to obtain the etching process simulation model.

[0012] Optionally, when the stacked structure is a three-dimensional structure, the simulation data further includes the etching depth of multiple nanochannels; the output simulation data also includes: The etching process simulation model was simulated multiple times using different simulation input parameters to obtain multiple simulation data. Result curves are generated based on multiple simulation data; the result curves include the relationship curve between gas pressure and etching depth, and the relationship curve between etching time and the material selectivity ratio of the target etched structure.

[0013] Compared with existing technologies, the present invention provides a simulation method for isotropic particle distribution motion, comprising: acquiring transport parameters of an etching process simulation model; the etching process simulation model includes a semiconductor device with a stacked structure; determining the etching rate of the target cell based on the initial particle concentration and surface reaction probability; updating the morphology of the semiconductor device using the level set method based on the etching rate to obtain an updated etching process simulation model; calculating the current particle concentration of each cell using the Knudsen diffusion equation based on the updated etching process simulation model, determining the corresponding etching rate based on the current particle concentration, and continuing to update the morphology until the simulation time reaches a preset etching time to end the simulation, and outputting simulation data; the simulation data includes at least the morphology data of the semiconductor device at each preset time point and the data on the change of the lateral etching depth of the target etched structure over time. This invention innovatively couples the cellular method, Knudsen diffusion, and level sets dynamically, enabling closed-loop simulation of the entire diffusion, reaction, and deformation process in isotropic etching at the nanoscale. This method accurately predicts key morphological defects such as lateral drilling and microgrooving, significantly improving the predictive ability for material etching selectivity and uniformity in stacked structures. It provides a quantifiable and scalable simulation tool for the process development of advanced devices such as GAAs, greatly reducing R&D cycle time and cost. Specifically, the interface advancement algorithm of the level set method can update the etching morphology and feed back to influence subsequent particle diffusion paths, achieving true dynamic coupling simulation. The Knudsen diffusion method based on the cellular method, through discretized meshes and random motion simulation, accurately describes the transport behavior of neutral particles in a nanoscale confined space, overcoming the simulation distortion problem of continuous medium models at extreme scales. Simultaneously, by calculating the corresponding etching rate through the surface reaction probabilities of different materials, it can realistically reflect the differences in reaction probabilities between particles and different material surfaces in stacked structures at the microscopic level, improving the accuracy of the simulation.

[0014] Secondly, the present invention also provides a particle isotropic distribution motion simulation device, comprising: The transport parameter acquisition module is used to acquire the transport parameters of the etching process simulation model; the etching process simulation model includes a semiconductor device with a stacked structure; the transport parameters include the initial particle concentration of each cell in the simulation area and the surface reaction probability corresponding to different materials; An etching rate determination module is used to determine the etching rate of the target cell based on the initial particle concentration and the surface reaction probability; the target cell is the cell in the etching process simulation model that is in contact with each structural boundary; The topography update module is used to update the topography of the semiconductor device based on the etching rate using the level set method, so as to obtain the updated etching process simulation model. The particle concentration confirmation and iteration module is used to calculate the current particle concentration of each cell based on the updated etching process simulation model using the Knudsen diffusion equation, and to determine the corresponding etching rate based on the current particle concentration and continue to update the morphology until the simulation time reaches the preset etching time to end the simulation and output simulation data; the simulation data includes at least the morphology data of the semiconductor device at each preset time point and the data on the change of the lateral etching depth of the target etched structure over time.

[0015] Thirdly, the present invention also provides a particle isotropic distribution motion simulation device, comprising: A communication unit / interface is used to acquire transport parameters of an etching process simulation model; the etching process simulation model includes a semiconductor device with semiconductor devices; the transport parameters include the initial particle concentration of each cell in the simulation area and the surface reaction probability corresponding to different materials; A processing unit / processor is used to determine the etching rate of the target cell based on the initial particle concentration and the surface reaction probability; the target cell is the cell in the etching process simulation model that is in contact with each structural boundary; Based on the etching rate, the semiconductor device is updated using the level set method to obtain the updated etching process simulation model. Based on the updated etching process simulation model, the Knudsen diffusion equation is used to calculate the current particle concentration of each cell, and the corresponding etching rate is determined based on the current particle concentration. The morphology is then updated until the simulation time reaches the preset etching time, at which point the simulation ends and the simulation data is output. The simulation data includes at least the morphology data of the semiconductor device at each preset time point and the data on the change of the lateral etching depth of the target etched structure over time.

[0016] Fourthly, the present invention also provides a computer-readable storage medium storing instructions that, when executed by a processor, implement the particle isotropic distribution motion simulation method.

[0017] Compared with the prior art, the beneficial effects of the second aspect device-type solution, the third aspect equipment-type solution, and the fourth aspect computer-readable storage medium-type solution provided by the present invention are the same as the beneficial effects of the particle isotropic distribution motion simulation method described in the above technical solutions, and will not be repeated here. Attached Figure Description

[0018] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this invention, illustrate exemplary embodiments of the invention and are used to explain the invention, but do not constitute an undue limitation of the invention. In the drawings: Figure 1A flowchart of a particle isotropic distribution motion simulation method provided by the present invention; Figure 2 This is a schematic diagram of the semiconductor device structure provided by the present invention; Figure 3 A schematic diagram of the structure of a particle isotropic distribution motion simulation device provided by the present invention; Figure 4 This is a schematic diagram of the structure of a particle isotropic distribution motion simulation device provided by the present invention. Detailed Implementation

[0019] To facilitate a clear description of the technical solutions in the embodiments of the present invention, the terms "first" and "second" are used to distinguish identical or similar items with essentially the same function and effect. For example, the first threshold and the second threshold are merely used to distinguish different thresholds and do not limit their order. Those skilled in the art will understand that the terms "first" and "second" do not limit the quantity or execution order, and that the terms "first" and "second" are not necessarily different.

[0020] It should be noted that in this invention, the terms "exemplary" or "for example" are used to indicate examples, illustrations, or descriptions. Any embodiment or design described as "exemplary" or "for example" in this invention should not be construed as being more preferred or advantageous than other embodiments or designs. Specifically, the use of terms such as "exemplary" or "for example" is intended to present the relevant concepts in a concrete manner.

[0021] In this invention, "at least one" refers to one or more, and "more than one" refers to two or more. "And / or" describes the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A alone, A and B simultaneously, or B alone, where A and B can be singular or plural. The character " / " generally indicates that the preceding and following related objects are in an "or" relationship. "At least one of the following" or similar expressions refer to any combination of these items, including any combination of single or plural items. For example, at least one of a, b, or c can represent: a, b, c, a combination of a and b, a combination of a and c, a combination of b and c, or a, b, and c, where a, b, and c can be single or multiple.

[0022] Isotropic etching is a widely used etching method in semiconductor manufacturing, characterized by the same etching rate in all directions, primarily driven by chemical reactions. In GAA Si / SiGe stacked structures, isotropic etching is used to selectively remove the SiGe sacrificial layer to form an inner sidewall cavity structure. This process mainly relies on the diffusion and reaction of neutral free radicals (such as F radicals) on the material surface, without relying on directional physical bombardment. The basic process of isotropic etching is as follows: First, neutral free radicals in the reactive gas enter the nanoscale channel through the mask opening and undergo random motion under the Knudsen diffusion mechanism, forming a spatial concentration gradient. Then, the free radicals react chemically with the exposed SiGe surface, generating volatile products and achieving material removal. As etching progresses, the sidewall morphology changes dynamically, further affecting the diffusion path and local concentration of subsequent particles, forming a strongly coupled feedback loop of "etching-deformation-re-diffusion".

[0023] Current simulation optimization of isotropic etching processes for GAA Si / SiGe stacked structures mainly relies on methods such as hydrodynamic models based on the continuum assumption, static morphology simulation, and averaged reaction rates. These simulation techniques have the following limitations: Distortion in nanoscale particle transport simulation: Existing models struggle to accurately describe the Knudsen diffusion behavior of neutral radicals within extremely confined channels only a few nanometers wide. The continuum assumption fails at this scale, making it impossible to calculate the true particle concentration gradient, leading to inaccurate predictions of etching uniformity. Lack of dynamic morphology coupling: Existing techniques treat the etching morphology as static, decoupling the simulation process from the particle transport process. They cannot simulate the real-time, strongly coupled feedback loop of "etching-deformation-re-diffusion," thus completely failing to predict critical process defects caused by dynamic morphology changes, such as lateral drilling. Multi-material interface reaction selectivity misalignment: Traditional models use simplified average reaction rate constants, which cannot accurately reflect the differences in reaction probabilities between particles and different material surfaces such as Si, SiGe, and masks at the microscopic level. This leads to a significant deviation between the predicted Si / Ge etching selectivity ratio and experimental values, rendering the simulation ineffective for guiding high-selectivity etching processes. These limitations collectively result in the inability to accurately predict and optimize key morphologies for etching the inner sidewall cavities of GAAs, such as lateral etching depth, sidewall fillet morphology, and Si channel layer damage.

[0024] To address the aforementioned issues, this invention provides a method, apparatus, device, and medium for simulating the isotropic distribution and motion of particles. Based on the cellular method for simulating Knudsen diffusion, a level set method is coupled to achieve real-time updates of the etching morphology, ultimately constructing a closed-loop simulation process encompassing diffusion, reaction, and deformation. This improves the fidelity of nanoscale particle transport simulation, achieves real-time coupled simulation of dynamic morphology evolution, and for the first time realizes a nonlinear feedback process in which morphology changes affect diffusion, and diffusion alters the etching morphology, enabling accurate prediction of dynamic defects such as lateral drilling. It ensures the selective simulation accuracy of multi-material interface reactions, significantly improves the prediction accuracy of the silicon and germanium etching selectivity ratio, and provides a quantitative basis for process optimization. The following description, in conjunction with the accompanying drawings, further clarifies the process.

[0025] See Figure 1 The present invention provides a method for simulating the isotropic distribution motion of particles, comprising the following steps: Step 101: Obtain the transport parameters of the etching process simulation model.

[0026] The etching process simulation model includes a semiconductor device with a stacked structure; the transport parameters include the initial particle concentration of each cell in the simulation region and the surface reaction probability corresponding to different materials. The surface reaction probability corresponding to the material being etched is the highest and much higher than that corresponding to other materials, to reflect the selectivity of etching.

[0027] A laminated structure is a structure composed of at least two different materials. For example, such as... Figure 2 As shown, the semiconductor device is a GAA, comprising a substrate, a stacked structure formed by alternating layers of silicon and germanium silicide, and a mask layer disposed on the stacked structure. The surface reaction probability of the germanium silicide layer is the highest.

[0028] The simulation region of the etching process simulation model is discretized into multiple cells, and the model uses the Knudsen diffusion method for diffusion. In the actual simulation, F free particles are injected from the top opening and move randomly within the confined space formed by the mask and sidewalls. The Knudsen diffusion equation is solved numerically. Due to structural obstructions, such as the initial indentation of the inner sidewall, free particles need to take a more tortuous path to reach the deeper regions. After quantitative time-layer diffusion simulation, the particle concentration at the depths and corners of the structure is significantly lower than that near the opening, forming a spatial concentration gradient.

[0029] Step 102: Determine the etching rate of the target cell based on the initial particle concentration and the surface reaction probability; the target cell is the cell in contact with the boundary of each structure in the etching process simulation model. The target cell is the cell in each structure.

[0030] At the initial moment of the simulation, F free particles, i.e. neutral particles, are injected from the top opening. There are particles only at the top opening of the etching process simulation model, and the initial particle concentration of each cell in the simulation area is 0.

[0031] Step 103: Based on the etching rate, the semiconductor device is updated using the level set method to obtain the updated etching process simulation model.

[0032] Topography updates are performed within the etching process simulation model. After each topography update, the structural boundaries of the semiconductor device change, and the corresponding target cells also change.

[0033] The core of the level set method is to represent the moving interface as the zero isosurface of a higher-dimensional scalar field, and to evolve the scalar field by solving partial differential equations, thus naturally handling topological changes and large deformations.

[0034] Step 104: Based on the updated etching process simulation model, the Knudsen diffusion equation is used to calculate the current particle concentration of each cell, and the corresponding etching rate is determined based on the current particle concentration. The morphology is then updated until the simulation time reaches the preset etching time, at which point the simulation ends and the simulation data is output. The simulation data includes at least the morphology data of the semiconductor device at each preset time point and the data on the change of the lateral etching depth of the target etched structure over time.

[0035] It should be noted that step 102 actually calculates the etching rate of the target cell after particle diffusion over the first time step from the initial moment. Step 103 actually performs the topography update step for the first time step, and step 104 performs simulation calculations for the second and subsequent time steps. Here, the "corresponding etching rate based on the current particle concentration" refers to the etching rate of the target cell in the updated etching process simulation model. The Knudsen diffusion equation simulation calculates the particle concentration of all cells. When calculating the etching rate of the target cell, the initial particle concentration of the target cell at the current time step and the surface reaction probability of the corresponding structure can be used to calculate the etching rate of the target cell at the current time step. Specifically, starting from the second time step, the simulation steps for any time step other than the first time step are as follows: Based on the etching process simulation model updated at the previous time step, the Knudsen diffusion equation is used to calculate the current particle concentration of each cell, and the current etching rate of the target cell corresponding to the current time step is determined based on the current particle concentration and the surface reaction probability. Based on the current etching rate, the morphology of the semiconductor device is updated using the level set method to obtain the updated etching process simulation model corresponding to the current time step.

[0036] The simulation then continues to the next time step until the preset etching time is reached, at which point the simulation ends.

[0037] It should be noted that the current particle concentration calculated each time is the initial particle concentration of the cell at the current time step, and the initial particle concentration of the current time step is the particle concentration of the cell at the end of the previous time step. The current etching rate is the average etching rate of the current time step.

[0038] The target etched structure refers to the actual structure that needs to be etched. The steps for simulation data extraction and recording are as follows: Morphology evolution sequence: The system automatically saves morphology data at preset time points, such as morphology data for every 1000 time steps, thus reconstructing a time-series animation of the entire etching process. The animation clearly shows how the lateral grooves develop from nothing to something, and from shallow to deep. Critical dimension monitoring: The system monitors and records the depth of the germanium silicide layer laterally etched in real time, and plots the relationship curve between etching depth and time. The slope of this curve is the instantaneous etching rate. Simultaneously, it monitors the dimensional changes of adjacent silicon layers to ensure that their losses are within the process tolerance range, such as less than 0.5nm. Data output formats can include: visualization charts, morphology evolution animations, critical dimension change curves over time, and two-dimensional contour maps of the final etched morphology with dimension annotations.

[0039] Figure 1 The aforementioned method innovatively couples the cellular method, Knudsen diffusion, and level sets dynamically, enabling closed-loop simulation of the entire diffusion, reaction, and deformation process in isotropic etching at the nanoscale. This method can accurately predict key morphological defects such as lateral drilling and microgrooving, significantly improving the predictive ability for material etching selectivity and uniformity in stacked structures. It provides a quantifiable and scalable simulation tool for the process development of advanced devices such as GAAs, greatly reducing R&D cycle and cost. Specifically, the interface advancement algorithm of the level set method can update the etching morphology and feed back to influence the subsequent particle diffusion path, achieving true dynamic coupling simulation. The Knudsen diffusion method based on the cellular method, through discretized mesh and random motion simulation, accurately describes the transport behavior of neutral particles in a nanoscale confined space, overcoming the simulation distortion problem of continuous medium models at extreme scales. Simultaneously, by calculating the corresponding etching rate through the surface reaction probabilities of different materials, it can realistically reflect the differences in reaction probabilities between particles and different material surfaces in stacked structures at the microscopic level, improving the accuracy of the simulation.

[0040] based on Figure 1 In addition to the method described herein, this specification also provides some specific implementation methods of this method, which will be described below.

[0041] As an optional approach, an etching process simulation model needs to be constructed before step 101, which can be achieved through steps 11-16: Step 11: Obtain simulation input parameters; the simulation input parameters include the initial concentration of neutral particles injected at the simulation inlet, the Knudsen diffusion coefficient, and the surface reaction probability of different materials.

[0042] Step 12: Construct an initial simulation model based on the geometric parameters of the semiconductor device.

[0043] Set parameters such as height, width, and length; configure the mask structure above the substrate; and define the material properties of each layer.

[0044] Step 13: Based on the cellular method, the simulation region of the initial simulation model is discretized into multiple cells; each cell stores the material type, particle concentration, and surface normal vector.

[0045] Step 14: Label the cell according to its material type.

[0046] For example, the cell of the silicon layer is labeled as 1, the cell of the germanium silicide layer is labeled as 2, the mask layer is labeled as 3, and the absence of material is labeled as 0, etc.

[0047] Step 15: Determine the initial boundaries of each structure based on the cell labels, and set boundary conditions for the initial boundaries.

[0048] The contact surfaces between cells marked 0 and cells marked with other numbers are defined as initial boundaries. For example, the contact surface between a cell marked 0 and a cell marked 1 is the initial boundary of the silicon layer, the contact surface between a cell marked 0 and a cell marked 2 is the initial boundary of germanium silicide, and the contact surface between a cell marked 0 and a cell marked 3 is the initial boundary of the mask layer. Contact surfaces between different markers of 0 are also defined as boundaries; for example, the contact surface between 0 and 1 is the initial boundary of the silicon layer.

[0049] Boundary conditions can be Neumann or Robin. If mass exchange occurs at the initial boundary, the boundary conditions of that initial boundary are set to Robin; if no particles flow into or out of the initial boundary, the boundary conditions are set to Neumann. The Neumann boundary condition specifies the normal component of the gas molecule concentration gradient at the boundary. The Robin boundary condition specifies the linear relationship between the gas molecule concentration and its gradient at the boundary.

[0050] Step 16: Complete the model initialization based on the simulation input parameters to obtain the etching process simulation model.

[0051] Specifically, injecting neutral particles into the model completed in step 15 completes the model initialization.

[0052] As an optional approach, step 102 can be implemented based on the following steps: Formula (1) is used: (1); Calculate the etching rate of the target cell corresponding to each structure; in, Etching rate, The reaction rate constant is... The material type is Surface reaction probability, Let be the initial particle concentration of the target cell with coordinates (l, m).

[0053] When calculating the etching rate of the target cell corresponding to the remaining time steps, the particle concentration of the cell at the end of the previous time step can be used as the initial particle concentration of the cell in the current time step. The initial particle concentration of the target cell is substituted into formula (1) to calculate the etching rate of the target cell in the current time step.

[0054] As an optional approach, the etching process simulation model is updated once after each time step; step 103 can be implemented based on steps 31-33. Step 31: Apply formula (2) based on the initial level set function and the etching rate: (2); The solution is performed to obtain the target level set function after one time step. Where t is time, The gradient of the level set function. The etching rate is the normal direction of the target cell. The initial level set function is the level set function corresponding to the boundary at the initial moment of the etching process simulation model. In the actual calculation, the value of the initial level set function is substituted into formula (2), and the substituted formula is solved to obtain the target level set function after a time step, that is, a series of... value. A level set function representing a zero isosurface is used to define its boundary. For example, >0 indicates the interior of the germanium silicide layer. <0 indicates the outer space of the germanium silicide layer, i.e. the area that has been etched.

[0055] Step 103 is executed to update the morphology of the etching process simulation model at each time step.

[0056] Step 32: Move the corresponding boundary in the etching process simulation model along the normal direction according to the target level set function to obtain the updated boundary; Step 33: Set boundary conditions for the updated boundary to obtain the updated etching process simulation model.

[0057] At the start of the next time step, the updated boundary conditions of the etching process simulation model are used as the new boundary conditions for the particle diffusion equation. The diffusion field of neutral particles is solved in the new geometric space. Since the morphology has changed, the particle concentration field will adjust accordingly. For example, the bottom of a depression, which previously had a low concentration, will have a high concentration due to the open space. This process is repeated, forming a dynamic coupled simulation of diffusion, reaction, and morphology updating. The innovative value of this invention lies in that it is no longer a simple geometric etching process, but a precise prediction of morphology evolution based on physics and coupled in real time with the upstream particle transport process.

[0058] As an optional approach, step 104, "calculating the current particle concentration of each cell using the Knudsen diffusion equation based on the updated etching process simulation model," can be implemented using the following steps: Formula (3) is used: (3); Calculate the current particle concentration in each cell; in, The current particle concentration is the particle concentration at the beginning of the current time step. Here, represents the particle concentration at the previous time step, and represents the particle concentration at the end of the previous time step. This is the Knudsen diffusion coefficient, which changes with variations in the model's morphology. For time step.

[0059] As an optional approach, when the stacked structure is a three-dimensional structure, the simulation data further includes the etching depth of multiple nanochannels; the output simulation data also includes: The etching process simulation model was simulated multiple times using different simulation input parameters to obtain multiple simulation data. Result curves are generated based on multiple simulation data; the result curves include the relationship curve between gas pressure and etching depth, and the relationship curve between etching time and the material selectivity ratio of the target etched structure.

[0060] The above series of result curves can help determine the optimal process gas pressure window. The relationship curve between etching time and the material selectivity of the target etched structure is used to determine the optimal etching termination time point to maximize the selectivity.

[0061] The embodiments of the present invention can divide functional modules according to the above method examples. For example, each function can be divided into its own functional module, or two or more functions can be integrated into one processing module. The integrated module can be implemented in hardware or as a software functional module. It should be noted that the module division in the embodiments of the present invention is illustrative and only represents one logical functional division; other division methods may be used in actual implementation.

[0062] When dividing each function into modules according to its corresponding function. Figure 3 A schematic diagram of the structure of a particle isotropic distribution motion simulation device provided by the present invention is shown. Figure 3 As shown, the device includes: The transport parameter acquisition module 301 is used to acquire the transport parameters of the etching process simulation model; the etching process simulation model includes a semiconductor device with a stacked structure; the transport parameters include the initial particle concentration of each cell in the simulation area and the surface reaction probability corresponding to different materials; The etching rate determination module 302 is used to determine the etching rate of the target cell based on the initial particle concentration and the surface reaction probability; the target cell is the cell in the etching process simulation model that is in contact with the boundaries of each structure. The topography update module 303 is used to update the topography of the semiconductor device based on the etching rate using the level set method, so as to obtain the updated etching process simulation model. The particle concentration confirmation and iteration module 304 is used to calculate the current particle concentration of each cell based on the updated etching process simulation model using the Knudsen diffusion equation, and determine the corresponding etching rate based on the current particle concentration and continue to update the morphology until the simulation time reaches the preset etching time to end the simulation and output simulation data; the simulation data includes at least the morphology data of the semiconductor device at each preset time point and the data of the change of the lateral etching depth of the target etched structure over time.

[0063] Optionally, the etching rate determination module 302 can be specifically used for: Formula used: ; Calculate the etching rate of the target cell corresponding to each structure; in, Etching rate, The reaction rate constant is... The material type is Surface reaction probability, Let be the initial particle concentration of the target cell with coordinates (l, m).

[0064] Optionally, the etching process simulation model is updated once after each time step; the topography update module 303 may specifically include: The target level set function determination unit is used to determine the formula based on the initial level set function and the etching rate: ; The solution is performed to obtain the target level set function after a time step; the initial level set function is the level set function corresponding to the boundary at the initial moment of the etching process simulation model; Where t is time, The gradient of the level set function. The etching rate is the etch rate along the normal direction of the target cell; A boundary movement unit is used to move the corresponding boundary in the etching process simulation model along the normal direction according to the target level set function to obtain the updated boundary; The boundary condition setting unit is used to set boundary conditions for the updated boundary to obtain the updated etching process simulation model.

[0065] Optionally, the particle concentration confirmation and iteration module 304 can be specifically used for: Formula used: ; Calculate the current particle concentration in each cell; in, The current particle concentration, This represents the particle concentration at the previous moment. Knudsen diffusion coefficient, For time step.

[0066] Optionally, the semiconductor device includes a substrate, a stacked structure formed by alternating layers of silicon and germanium silicide, and a mask layer disposed on the stacked structure; the surface reaction probability of the germanium silicide layer is the highest.

[0067] Optionally, the device also includes an etching simulation model building module, which may specifically include: The simulation input parameter acquisition unit is used to acquire simulation input parameters, including the initial concentration of neutral particles injected at the simulation inlet, the Knudsen diffusion coefficient, and the surface reaction probability of different materials. The initial simulation model building unit is used to build an initial simulation model based on the geometric parameters of semiconductor devices; A cell partitioning unit is used to discretize the simulation region of the initial simulation model into multiple cells based on the cell method; the cell stores the material type, particle concentration, and surface normal vector. A marking unit is used to mark the cell according to the material type of the cell; An initial boundary determination unit is used to determine the initial boundaries of each structure based on the cell markings, and to set boundary conditions for the initial boundaries. The model initialization unit is used to complete the model initialization based on the simulation input parameters to obtain the etching process simulation model.

[0068] Optionally, when the stacked structure is a three-dimensional structure, the simulation data further includes the etching depth of multiple nanochannels; the device further includes: The multiple simulation module is used to perform multiple simulations on the etching process simulation model using different simulation input parameters to obtain multiple simulation data. The result curve generation module is used to generate result curves based on multiple simulation data; the result curves include the relationship curve between gas pressure and etching depth, and the relationship curve between etching time and the material selectivity ratio of the target etched structure.

[0069] The above mainly describes the solutions provided by the embodiments of the present invention from the perspective of the interaction between various modules. It is understood that, in order to achieve the above functions, it includes corresponding hardware structures and / or software modules for executing each function. Those skilled in the art should readily recognize that, in conjunction with the units and algorithm steps of the various examples described in the embodiments disclosed herein, the present invention can be implemented in hardware or a combination of hardware and computer software. Whether a function is executed in hardware or by computer software driving hardware depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of the present invention.

[0070] When using the corresponding integrated unit Figure 4 This diagram illustrates the structure of a particle isotropic distribution motion simulation device provided by the present invention. Figure 4 As shown, the device includes: A communication unit / interface is used to acquire transport parameters of an etching process simulation model; the etching process simulation model includes a semiconductor device with a stacked structure; the transport parameters include the initial particle concentration of each cell in the simulation area and the surface reaction probability corresponding to different materials; A processing unit / processor is used to determine the etching rate of the target cell based on the initial particle concentration and the surface reaction probability; the target cell is the cell in the etching process simulation model that is in contact with each structural boundary; Based on the etching rate, the semiconductor device is updated using the level set method to obtain the updated etching process simulation model. Based on the updated etching process simulation model, the Knudsen diffusion equation is used to calculate the current particle concentration of each cell, and the corresponding etching rate is determined based on the current particle concentration. The morphology is then updated until the simulation time reaches the preset etching time, at which point the simulation ends and the simulation data is output. The simulation data includes at least the morphology data of the semiconductor device at each preset time point and the data on the change of the lateral etching depth of the target etched structure over time.

[0071] The processing unit can be a processor or controller, such as a Central Processing Unit (CPU), a general-purpose processor, a Digital Signal Processor (DSP), an Application-Specific Integrated Circuit (ASIC), a Field-Programmable Gate Array (FPGA), or other programmable logic devices, transistor logic devices, hardware components, or any combination thereof. It can implement or execute the various exemplary logic blocks, modules, and circuits described in conjunction with the disclosure of this invention. The processor can also be a combination that implements computing functions, such as a combination of one or more microprocessors, a combination of a DSP and a microprocessor, etc. The communication module can be a transceiver, transceiver circuitry, or communication interface, etc. The storage module can be a memory.

[0072] like Figure 4 As shown, the processor described above can be a general-purpose central processing unit (CPU), a microprocessor, an application-specific integrated circuit (ASIC), or one or more integrated circuits used to control the execution of the program of the present invention. The communication interface described above can be one or more. The communication interface can use any transceiver-like device for communicating with other devices or communication networks.

[0073] like Figure 4 As shown, the terminal device described above may also include a communication line. The communication line may include a path for transmitting information between the components described above.

[0074] Optional, such as Figure 4 As shown, the terminal device may further include a memory. The memory stores computer execution instructions for implementing the present invention, and the execution is controlled by a processor. The processor executes the computer execution instructions stored in the memory, thereby implementing the method provided in the embodiments of the present invention.

[0075] like Figure 4As shown, the memory can be read-only memory (ROM) or other types of static storage devices capable of storing static information and instructions, random access memory (RAM) or other types of dynamic storage devices capable of storing information and instructions, or electrically erasable programmable read-only memory (EEPROM), compact disc read-only memory (CD-ROM) or other optical disc storage, optical disc storage (including compressed optical discs, laser discs, optical discs, digital universal optical discs, Blu-ray discs, etc.), magnetic disk storage media or other magnetic storage devices, or any other medium capable of carrying or storing desired program code in the form of instructions or data structures and accessible by a computer, but not limited to these. The memory can exist independently and be connected to the processor via communication lines. The memory can also be integrated with the processor.

[0076] Optionally, the computer execution instructions in the embodiments of the present invention may also be referred to as application code, and the embodiments of the present invention do not specifically limit this.

[0077] In a specific implementation, as one example, such as Figure 4 As shown, a processor may include one or more CPUs, such as Figure 4 CPU0 and CPU1 in the CPU.

[0078] In a specific implementation, as one example, such as Figure 4 As shown, the terminal device may include multiple processors, such as Figure 4 The processors in the system. Each of these processors can be a single-core processor or a multi-core processor.

[0079] On the one hand, a computer-readable storage medium is provided, in which instructions are stored, which, when executed, implement a simulation method for isotropic particle distribution motion.

[0080] In the above embodiments, implementation can be achieved entirely or partially through software, hardware, firmware, or any combination thereof. When implemented using software, it can be implemented entirely or partially in the form of a computer program product. The computer program product includes one or more computer programs or instructions. When the computer program or instructions are loaded and executed on a computer, the processes or functions described in the embodiments of the present invention are performed entirely or partially. The computer can be a general-purpose computer, a special-purpose computer, a computer network, a terminal, a user equipment, or other programmable device. The computer program or instructions can be stored in a computer-readable storage medium or transferred from one computer-readable storage medium to another. For example, the computer program or instructions can be transferred from one website, computer, server, or data center to another website, computer, server, or data center via wired or wireless means. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium, such as a floppy disk, hard disk, or magnetic tape; it can also be an optical medium, such as a digital video disc (DVD); or it can be a semiconductor medium, such as a solid-state drive (SSD).

[0081] Although the invention has been described herein in conjunction with various embodiments, those skilled in the art will understand and implement other variations of the disclosed embodiments by reviewing the accompanying drawings, the disclosure, and the appended claims in carrying out the claimed invention. In the claims, the word "comprising" does not exclude other components or steps, and "a" or "an" does not exclude a plurality. A single processor or other unit can implement several functions listed in the claims. While different dependent claims may recite certain measures, this does not mean that these measures cannot be combined to produce good results.

[0082] Although the invention has been described in conjunction with specific features and embodiments, it is obvious that various modifications and combinations can be made therein without departing from the spirit and scope of the invention. Accordingly, this specification and drawings are merely exemplary descriptions of the invention as defined by the appended claims, and are considered to cover any and all modifications, variations, combinations, or equivalents within the scope of the invention. Clearly, those skilled in the art can make various alterations and modifications to the invention without departing from its spirit and scope. Thus, if such modifications and modifications of the invention fall within the scope of the claims and their equivalents, the invention is also intended to include such modifications and modifications.

Claims

1. A method for simulating the isotropic distribution motion of particles, characterized in that, include: Obtain the transport parameters of the etching process simulation model; The etching process simulation model includes a semiconductor device with a stacked structure; the transport parameters include the initial particle concentration of each cell in the simulation region and the surface reaction probability corresponding to different materials; The etching rate of the target cell is determined based on the initial particle concentration and the surface reaction probability; the target cell is the cell in the etching process simulation model that is in contact with each structural boundary. Based on the etching rate, the semiconductor device is updated using the level set method to obtain the updated etching process simulation model. Based on the updated etching process simulation model, the Knudsen diffusion equation is used to calculate the current particle concentration of each cell, and the corresponding etching rate is determined based on the current particle concentration. The morphology is then updated until the simulation time reaches the preset etching time, at which point the simulation ends and the simulation data is output. The simulation data includes at least the morphology data of the semiconductor device at each preset time point and the data on the change of the lateral etching depth of the target etched structure over time.

2. The method for simulating the isotropic distribution motion of particles according to claim 1, characterized in that, The step of determining the etching rate of the target cell based on the initial particle concentration and the surface reaction probability includes: Formula used: ； Calculate the etching rate of the target cell corresponding to each structure; in, Etching rate, The reaction rate constant is... The material type is Surface reaction probability, Let be the initial particle concentration of the target cell with coordinates (l, m).

3. The method for simulating the isotropic distribution motion of particles according to claim 2, characterized in that, After each time step, the etching process simulation model is updated once; based on the etching amount, the semiconductor device is updated using the level set method to obtain the updated etching process simulation model. Based on the initial level set function and the etching rate, the formula is as follows: ； The solution is performed to obtain the target level set function after a time step; the initial level set function is the level set function corresponding to the boundary at the initial moment of the etching process simulation model; Where t is time, The gradient of the level set function. The etching rate is the etch rate along the normal direction of the target cell; The corresponding boundary in the etching process simulation model is moved along the normal direction according to the target level set function to obtain the updated boundary; Boundary conditions are set for the updated boundary to obtain the updated etching process simulation model.

4. The method for simulating the isotropic distribution motion of particles according to claim 1, characterized in that, The simulation model based on the updated etching process uses the Knudsen diffusion equation to calculate the current particle concentration of each cell, including: Formula used: ； Calculate the current particle concentration in each cell; in, The current particle concentration, This represents the particle concentration at the previous moment. Knudsen diffusion coefficient, For time step.

5. The particle isotropic distribution motion simulation method according to claim 1, characterized in that, The semiconductor device includes a substrate, a stacked structure formed by alternating layers of silicon and germanium silicide, and a mask layer disposed on the stacked structure; the surface reaction probability of the germanium silicide layer is the highest.

6. The method for simulating the isotropic distribution motion of particles according to claim 1, characterized in that, Before obtaining the transport parameters of the etching process simulation model, the following steps are also included: Obtain simulation input parameters; the simulation input parameters include the initial concentration of neutral particles injected at the simulation inlet, the Knudsen diffusion coefficient, and the surface reaction probability of different materials; An initial simulation model is constructed based on the geometric parameters of the semiconductor device; Based on the cellular method, the simulation region of the initial simulation model is discretized into multiple cells; each cell stores the material type, particle concentration, and surface normal vector. The cells are labeled according to their material type; The initial boundaries of each structure are determined based on the cell labels, and boundary conditions are set for the initial boundaries. The model is initialized based on the simulation input parameters to obtain the etching process simulation model.

7. The particle isotropic distribution motion simulation method according to claim 6, characterized in that, When the stacked structure is a three-dimensional structure, the simulation data also includes the etching depth of multiple nanochannels; The output simulation data is followed by: The etching process simulation model was simulated multiple times using different simulation input parameters to obtain multiple simulation data. Result curves are generated based on multiple simulation data; the result curves include the relationship curve between gas pressure and etching depth, and the relationship curve between etching time and the material selectivity ratio of the target etched structure.

8. A particle isotropic distribution motion simulation device, characterized in that, include: The transport parameter acquisition module is used to acquire the transport parameters of the etching process simulation model; The etching process simulation model includes a semiconductor device with a stacked structure; The transport parameters include the initial particle concentration of each cell in the simulation area and the surface reaction probability corresponding to different materials; An etching rate determination module is used to determine the etching rate of the target cell based on the initial particle concentration and the surface reaction probability; the target cell is the cell in the etching process simulation model that is in contact with each structural boundary; The topography update module is used to update the topography of the semiconductor device based on the etching rate using the level set method, so as to obtain the updated etching process simulation model. The particle concentration confirmation and iteration module is used to calculate the current particle concentration of each cell based on the updated etching process simulation model using the Knudsen diffusion equation, and to determine the corresponding etching rate based on the current particle concentration and continue to update the morphology until the simulation time reaches the preset etching time to end the simulation and output simulation data; the simulation data includes at least the morphology data of the semiconductor device at each preset time point and the data on the change of the lateral etching depth of the target etched structure over time.

9. A particle isotropic distribution motion simulation device, characterized in that, include: Communication unit / communication interface, used to acquire transport parameters of the etching process simulation model; The etching process simulation model includes a semiconductor device with a stacked structure; the transport parameters include the initial particle concentration of each cell in the simulation region and the surface reaction probability corresponding to different materials; A processing unit / processor is used to determine the etching rate of the target cell based on the initial particle concentration and the surface reaction probability; the target cell is the cell in the etching process simulation model that is in contact with each structural boundary; Based on the etching rate, the semiconductor device is updated using the level set method to obtain the updated etching process simulation model. Based on the updated etching process simulation model, the Knudsen diffusion equation is used to calculate the current particle concentration of each cell, and the corresponding etching rate is determined based on the current particle concentration. The morphology is then updated until the simulation time reaches the preset etching time, at which point the simulation ends and the simulation data is output. The simulation data includes at least the morphology data of the semiconductor device at each preset time point and the data on the change of the lateral etching depth of the target etched structure over time.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores instructions that, when executed by a processor, implement the particle isotropic distribution motion simulation method according to any one of claims 1-7.

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