Three-dimensional contour simulation method and device for semiconductor etching process

Abstract

The invention discloses a three-dimensional contour simulation method and device for a semiconductor etching process, relates to the technical field of semiconductors, and aims to solve the problem that the precision and efficiency of a three-dimensional etching contour simulation method for an etching process in the prior art cannot be considered at the same time. The method comprises the following steps: constructing a three-dimensional simulation domain of a semiconductor structure to be etched and obtaining simulation parameters; dispersing the three-dimensional simulation domain into a plurality of voxels, and performing material type marking on the plurality of voxels to obtain a plurality of types of voxels; the multiple types of voxels at least comprise substrate voxels and mask voxels; based on the simulation parameters, simulating an action process of incident particles and target voxels by adopting a Monte Carlo method; the target voxel is the substrate voxel or the mask voxel; and after the action process of all the incident particles is completed, outputting the three-dimensional contour of the etched semiconductor structure. The method is used for improving the precision and efficiency of the three-dimensional etching contour simulation method of the etching process.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of semiconductor, and in particular to a three-dimensional profile simulation method and device for semiconductor etching process. BACKGROUND

[0002] In semiconductor manufacturing, etching process is a key step to transfer photoresist pattern to material surface, which is mainly divided into dry etching (such as plasma etching RIE, ICP, which realizes anisotropic etching through high-energy ions and active radicals) and wet etching (such as using KOH and other chemical solutions to realize isotropic or anisotropic etching according to material and solution characteristics).

[0003] With the rapid development of semiconductor process nodes below 5nm and three-dimensional integration technology, the requirement of etching process on three-dimensional profile precision is rapidly increasing. However, the coupling effect of ion bombardment, chemical reaction and material surface dynamic evolution in the etching process easily leads to complex morphology deviation such as sidewall roughness and critical dimension narrowing; at the same time, the traditional trial-and-error method is high in optimization cost and long in cycle, and the existing simulation method is either insufficient in precision (such as continuous medium model lacking micro details) or low in computational efficiency, which is difficult to meet the dual requirements of precision and computational time for advanced process.

[0004] A new three-dimensional etching profile simulation method is provided to ensure accurate simulation of complex morphology evolution in etching process (to meet the precision requirement) while controlling the calculation time within an acceptable range, thereby reducing the optimization cost of traditional trial-and-error method, adapting to the advanced etching process requirements of 5nm and three-dimensional integration technology, and solving the problems in cost field. SUMMARY

[0005] The purpose of the present application is to provide a three-dimensional profile simulation method and device for semiconductor etching process, which can improve the precision and efficiency of three-dimensional etching profile simulation method for etching process.

[0006] In order to achieve the above purpose, the present application provides the following technical scheme: In a first aspect, the present application provides a three-dimensional profile simulation method for semiconductor etching process, comprising: constructing a three-dimensional simulation domain of a semiconductor structure to be etched and obtaining simulation parameters; discretizing the three-dimensional simulation domain into a plurality of voxels and marking the plurality of voxels with material types to obtain a plurality of voxels; the plurality of voxels at least include substrate voxels and mask voxels; based on the simulation parameters, simulating the action process of incident particles and target voxels by using Monte Carlo method; the target voxels are the substrate voxels or the mask voxels; outputting the three-dimensional profile of the etched semiconductor structure after all incident particles complete the action process.

[0007] Optionally, the multiple types of voxels further comprise a material-free voxel; and the simulation parameters at least comprise a total number of incident particles, an incident position distribution, and an incident angle distribution; Based on the simulation parameters, a Monte Carlo method is used to simulate the interaction process of the incident particles and the target voxels, comprising: According to the total number of incident particles, in a serial loop, for each incident particle in all incident particles, based on the incident position distribution and the incident angle distribution, the Monte Carlo method is used to randomly generate initial incident parameters and calculate a particle motion trajectory, and the impact position with the target voxel is determined in real time; At the impact position, the action mode is determined based on a preset material reflection probability; the preset material reflection probability matches the material type of the target voxel; If the action mode is reflection, only one reflection simulation is performed, and the reflected particle continues to move until the next etching reaction occurs; If the action mode is etching reaction and etching reaction occurs, the material type of the corresponding target voxel is updated to the material-free voxel; After the interaction process of the current incident particle ends, the next particle is simulated, and all particles are simulated.

[0008] Optionally, the initial incident parameters comprise an initial incident position and an initial incident angle; The motion trajectory is calculated, and the impact position with the target voxel is determined in real time, comprising: Based on the incident angle, the particle motion direction is determined; Based on the particle motion direction, the initial incident position is combined to calculate the particle motion trajectory and update the three-dimensional motion coordinates of the incident particle in real time; By comparing the three-dimensional motion coordinates with the spatial coordinate range of the target voxel, it is determined whether the incident particle enters the spatial region where the target voxel is located to determine the impact position.

[0009] Optionally, at the impact position, the action mode is determined based on a preset material reflection probability, comprising: At the impact position, a first random number is generated; the first random number is greater than or equal to 0 and less than or equal to 1; If the first random number is less than or equal to the preset material reflection probability, it is determined that reflection occurs; If the first random number is greater than the preset material reflection probability, it is determined whether etching reaction occurs; When the reflection occurs, a preset range of voxel domain is selected with the impact position as the center, a least square fitting method is used to perform plane fitting on the surface of the voxel domain, and a fitting plane is obtained; Based on the normal vector of the fitting plane and the incident vector when the particle impacts, a reflection vector of the particle is calculated to determine the reflection direction.

[0010] Optionally, determining whether the etching reaction occurs includes: generating a second random number; the second random number is greater than or equal to 0 and less than or equal to 1; If the second random number reaches the etching reaction probability, it is determined that the etching reaction occurs. If the second random number does not reach the etching reaction probability, the action process of the current incident particle ends, and the next incident particle is simulated.

[0011] Optionally, a preset range of voxel domain is selected with the impact position as the center, a least square fitting method is used to perform plane fitting on the surface of the voxel domain, and a fitting plane is obtained, including: extracting the three-dimensional coordinates of all surface voxels in the voxel domain ; wherein, ; the number of voxels in the preset range of voxel domain; by solving the parameter that minimizes the deviation sum of squares formula: ; the plane equation of the fitting plane: wherein, is the deviation sum of squares.

[0012] Optionally, before obtaining the simulation parameters, the method further includes determining the simulation parameters; determining the simulation parameters includes: determining the incident position distribution as being uniformly distributed on the upper surface of the three-dimensional simulation domain; determining the total number of incident particles according to the size and grid subdivision accuracy of the three-dimensional simulation domain; setting an incident angle distribution; wherein the incident angle distribution follows a cosine distribution or a Gaussian distribution; determining the type of incident particles according to the substrate material and the mask material; setting the boundary condition of the three-dimensional simulation domain as a periodic boundary condition; the periodic boundary condition represents that the incident particle continues to enter the three-dimensional simulation domain from the same position on the opposite side at the same angle after crossing the boundary of the three-dimensional simulation domain.

[0013] Optionally, the three-dimensional simulation domain of the semiconductor structure to be etched is constructed, including: constructing a substrate structure based on the size of the substrate; constructing a mask structure above the substrate structure based on a preset mask pattern; determining the height, length and width of a three-dimensional simulation domain based on the substrate structure and the mask structure, and forming the three-dimensional simulation domain comprising the substrate structure and the mask structure.

[0014] Optionally, before the second random number is generated, the method further comprises: determining the etching reaction probability; determining the etching reaction probability comprises: determining an initial value of the etching reaction probability based on the etching selectivity ratio of the substrate and the mask; obtaining the etching reaction probability based on the number of times the impact position is impacted and a preset single probability increment.

[0015] Compared with the prior art, the three-dimensional profile simulation method for the semiconductor etching process provided by the present application firstly constructs a three-dimensional simulation domain comprising a substrate and a mask, combines simulation parameters (lays a foundation for accurate simulation of the etching process, and specifically reproduces the complex structure environment in three-dimensional integration technology; secondly, voxel cubic subdivision is used to discretize the simulation domain, and material marking is used to dynamically track topography evolution, which can not only accurately capture microscopic deviations such as sidewall roughness and critical dimension narrowing (meet the accuracy requirement), but also reduce the processing complexity of complex geometry through structured calculation of voxel grid (optimize the calculation time); thirdly, the Monte Carlo method is used to simulate the interaction process of particles and target voxels, which reproduces the microscopic kinetic randomness through a random model (improves the accuracy), and reasonably controls the particle simulation scale based on the simulation parameters to avoid redundant calculation (controls the calculation time), so as to ensure that the calculation time is controlled within an acceptable range while accurately simulating the three-dimensional etching profile (matches the accuracy requirement of 5nm and three-dimensional integration technology), effectively reduces the dependence on physical experiments, reduces the optimization cost, and meets the dual needs of advanced etching process. In summary, the present method combines the efficient geometric expression of voxel subdivision with the precise microscopic simulation of the Monte Carlo method, which not only realizes high-precision simulation of the three-dimensional etching profile, but also controls the calculation time within an acceptable range, effectively reduces the dependence on physical experiments, reduces the optimization cost, and meets the dual needs of advanced etching process.

[0016] In a second aspect, the present application also provides a three-dimensional profile simulation device for a semiconductor etching process, comprising: a construction module for constructing a three-dimensional simulation domain of a semiconductor structure to be etched and obtaining simulation parameters; a discretization module for discretizing the three-dimensional simulation domain into a plurality of voxels and marking the plurality of voxels with material types to obtain a plurality of voxel types; the plurality of voxel types at least include substrate voxels and mask voxels; a simulation module, configured to simulate, based on the simulation parameters, a process of interaction between the incident particles and a target voxel by using a Monte Carlo method; the target voxel is the substrate voxel or the mask voxel; an output module, configured to output a three-dimensional profile of the etched semiconductor structure after all the incident particles complete the process. BRIEF DESCRIPTION OF DRAWINGS

[0017] The accompanying drawings, which are included to provide a further understanding of the application and are incorporated in and constitute a part of this application, illustrate embodiments of the application and together with the description serve to explain the application. In the drawings: Figure 1 FIG. 1 is a flowchart of a three-dimensional profile simulation method for a semiconductor etching process according to an embodiment of the present application; Figure 2 FIG. 2 is a process diagram of constructing a three-dimensional simulation domain according to an embodiment of the present application; Figure 3 FIG. 3 is a diagram of meshing a three-dimensional simulation domain according to an embodiment of the present application; Figure 4 FIG. 4 is a diagram of setting a distribution of incident positions of particles and boundary conditions of a three-dimensional simulation domain according to an embodiment of the present application; Figure 5 FIG. 5 is a flowchart of a three-dimensional profile simulation method for a semiconductor etching process according to another embodiment of the present application; Figure 6 FIG. 6 is a process diagram of simulating a motion trajectory of an incident particle by using a Monte Carlo method according to an embodiment of the present application; Figure 7 FIG. 7 is a state diagram of fitting a plane to a surface of a substrate around a collision point and calculating a reflection vector of a particle by using a least square method according to an embodiment of the present application; Figure 8 FIG. 8 is a structural diagram of a three-dimensional profile simulation device for a semiconductor etching process according to an embodiment of the present application. DETAILED DESCRIPTION

[0018] In order to clearly describe the technical solutions of the embodiments of the present application, in the embodiments of the present application, the terms of "first", "second", and the like are used to distinguish the same or similar items or elements with basically the same functions and effects. For example, the first threshold and the second threshold are merely used to distinguish different thresholds, and do not limit the order. Those skilled in the art can understand that the terms of "first", "second", and the like do not limit the number and execution order, and the terms of "first", "second", and the like do not necessarily mean different.

[0019] It should be noted that in the present application, the words "exemplary" or "for example" are used to mean serving as an example, instance, or illustration. Any embodiment or design described herein as "exemplary" or "for example" should not be construed as being preferred or advantageous over other embodiments or designs. Rather, the embodied words are used merely to present concepts in a concrete manner.

[0020] In the present application, "at least one" means one or more, and "multiple" means two or more. The association relationship of the associated objects is described, which means that there can be three relationships.

[0021] Referring to Figure 1 The embodiment of the present application provides a three-dimensional profile simulation method for a semiconductor etching process, which can include: Step 100: constructing a three-dimensional simulation domain of a semiconductor structure to be etched and obtaining simulation parameters; For example, constructing a three-dimensional simulation domain of a semiconductor structure to be etched can include: Referring to Figure 2 Based on the size of the substrate, a substrate structure is constructed; wherein the size of the substrate includes the length, width and height of the substrate; Based on the preset mask pattern, a mask structure is constructed above the substrate structure; wherein the preset mask pattern at least includes: period length and opening size.

[0022] Based on the substrate structure and the mask structure, the height, length and width of the three-dimensional simulation domain are determined, and a three-dimensional simulation domain including the substrate structure and the mask structure is formed; Specifically, based on the substrate structure and the mask structure, the height, length and width of the three-dimensional simulation domain are determined, which means that the three-dimensional simulation domain is a whole space that can completely contain the substrate structure and the mask structure, and the size (height, length and width) thereof needs to be set according to the size of the substrate and the mask, and must be greater than the size of the two structures, so as to ensure that the substrate and the mask can be completely contained in the simulation domain.

[0023] Step 200: discretizing the three-dimensional simulation domain into a plurality of voxels and marking the plurality of voxels with material types to obtain a plurality of voxel types; the plurality of voxel types at least include substrate voxels and mask voxels; It should be noted that before obtaining the simulation parameters, the three-dimensional profile simulation method for the semiconductor etching process further includes: determining the simulation parameters.

[0024] Determining the simulation parameters includes: (1) setting the grid subdivision precision.

[0025] In the specific implementation of step 200, referring to Figure 3Based on the grid resolution, the three-dimensional simulation domain is discretized into multiple voxels by using the voxel subdivision method, and the multiple voxels are marked with material types to obtain multiple voxels.

[0026] The voxel is a cubic grid unit obtained by subdividing the grid, and the size of the voxel is positively correlated with the grid resolution (for example, when the resolution is 1 nm, the edge length of the voxel is 1 nm; when the resolution is 5 nm, the edge length of the voxel is 5 nm). The higher the resolution, the smaller the size of the voxel, and the more accurate the description of the surface topography details.

[0027] The multiple voxels also include material-free voxels. When the multiple voxels are marked with material types, the following marking can be performed: for example, substrate-1, mask-2, and material-free-0.

[0028] Through the correlation between the size of the voxel and the resolution (for example, 1 nm resolution corresponds to 1 nm voxel), the accurate description of the surface topography details is realized, and it is ensured that the simulation result can reflect the slight deviation such as sidewall roughness, thereby improving the simulation accuracy.

[0029] The voxel cubic subdivision method is particularly suitable for complex structures in three-dimensional integration technology. Through real-time updating of the voxel marking (for example, substrate voxel 1 to material-free voxel 0), the irregular topography evolution such as micro-mask shielding and anisotropic etching direction deviation can be dynamically tracked, and the three-dimensional dynamic changes of the material surface in the etching process are directly reflected.

[0030] (2) Set the etching selectivity ratio of the substrate material and the mask material.

[0031] The etching selectivity ratio indirectly affects the reflection probability and the etching reaction probability through the physical and chemical properties of the materials (such as surface hardness and chemical reactivity): generally, the higher the etching selectivity ratio (that is, the substrate is more easily etched than the mask), the higher the reflection probability of the mask material and the lower the initial etching reaction probability, and the lower the reflection probability of the substrate material and the higher the initial etching reaction probability.

[0032] For example, if the etching selectivity ratio of the substrate and the mask is set to 5:1 (that is, the etching rate of the substrate is 5 times that of the mask), the following can be further set: Reflection probability: the reflection probability of the substrate voxel is 20%, and the reflection probability of the mask voxel is 60% (the mask is more difficult to be penetrated by particles, and the reflection is stronger); Initial etching reaction probability: the initial reaction probability of the substrate voxel is 30%, and the initial reaction probability of the mask voxel is 6% (consistent with the selectivity ratio of 5:1), and the reaction probability of the same voxel is increased by 5% each time it is hit (for example, the reaction probability of the substrate voxel is increased to 35% when it is hit for the second time, and the reaction probability of the mask voxel is increased to 11%).

[0033] By correlating the etching selectivity ratio with the reflection probability and the reaction probability, the different behaviors of different materials in the etching process can be accurately simulated, and the simulation results are consistent with the material loss law in the actual process.

[0034] (3) The incident position distribution of the incident particles is determined to be uniformly distributed on the upper surface of the three-dimensional simulation domain. See Figure 4 .

[0035] Uniform distribution of the incident position ensures the spatial uniformity of the particle incidence, which is consistent with the actual physical characteristics of the particle distribution in plasma etching, and improves the authenticity of the simulation.

[0036] (4) The total number of incident particles is determined according to the size and grid subdivision accuracy of the three-dimensional simulation domain. For example, the total number of incident particles increases by 1000 for every 1000nm³ increase in the volume of the three-dimensional simulation domain and every 1nm increase in the grid subdivision accuracy.

[0037] The number is set according to the size and accuracy of the simulation domain, balancing the simulation efficiency and statistical effectiveness, and ensuring the reliability of the results (such as sufficient number of particles to reduce random errors).

[0038] (5) Set the incident angle distribution; wherein the incident angle distribution follows a cosine distribution (isotropic) or a Gaussian distribution (anisotropic).

[0039] The particle behavior of different etching types (dry / wet) is simulated by a cosine distribution (isotropic) or a Gaussian distribution (anisotropic), which adapts to different process scenarios and enhances the versatility of the method. In actual etching process simulation, isotropic particles following a cosine distribution and anisotropic particles following a Gaussian distribution can be included at the same time, and the two types of particles are mixed at a predetermined ratio (such as 50% each) to reproduce the complex transport characteristics of particles in plasma etching, and improve the simulation accuracy of processes such as dry etching.

[0040] (6) Determine the type of incident particles according to the substrate material and mask material; for example, the types of incident particles that can be selected include but are not limited to halogen plasma such as Cl, F, etc., and can also include a small amount of inert gas and protective gas (oxygen) etc.

[0041] (7) Set the boundary condition of the three-dimensional simulation domain as a periodic boundary condition; the periodic boundary condition represents that when the incident particles cross the boundary of the three-dimensional simulation domain, they continue to enter the three-dimensional simulation domain from the same position on the opposite side at the same angle.

[0042] It should be noted that the same position on the opposite side means that when the particle moves beyond a certain boundary of the three-dimensional simulation domain, its re-entry position in the simulation domain is symmetric to the position of the boundary with respect to the center of the simulation domain. For example: If a particle crosses the right boundary (x=Xmax) of the simulation domain, it will re-enter from the symmetric position of the left boundary (x=Xmin+(Xmax-crossing point x coordinate)); similarly, when crossing the boundary along the y-axis or z-axis, it will re-enter from the symmetric coordinate of the opposite boundary of the corresponding axis, and the motion angle at the time of crossing will remain unchanged. This setting ensures the continuity of particle transport in the simulation domain, avoiding the interference of boundary effects on etching simulation.

[0043] By symmetric entry and exit of particles across the boundary, the interference of boundary effects is avoided, the continuity of particle transport in the simulation domain is ensured, and the overall law of large-scale etching process is truly reflected.

[0044] Figure 4 The process of plasma interacting with the mask and substrate to achieve etching process is demonstrated, and the concepts therein are explained in detail.

[0045] The plasma excitation region is the spatial range where plasma is generated, and the plasma is excited in this region to provide particle sources for subsequent interaction with the mask and substrate.

[0046] The initial mask profile represents the shape and boundary of the mask before the process starts. The mask is used to define the area of process action and protect the part that does not need to be processed.

[0047] The initial substrate profile is the original shape and boundary of the substrate before the process starts. The substrate is the basic carrier of semiconductor devices and other devices, and subsequent processes will act on it.

[0048] The updated mask profile represents the profile of the mask shape change after a period of process action. This change may be caused by the impact of plasma particles, reactions, etc.

[0049] The updated substrate profile reflects the shape change of the substrate after the process action, such as the etching process that removes some areas of the substrate to form a new profile.

[0050] The adherent is a substance formed by the attachment of particles and other substances to the surface of the mask, substrate, etc. during the process, which may affect the subsequent process or the formation of the final structure.

[0051] Anisotropic distribution particles have directionality in their motion or distribution, and the arrows and other identifiers in the figure show that they mainly move in a certain direction (such as the vertical direction). When interacting with the mask and substrate, they will make the etching or deposition process exhibit anisotropy (different effects in different directions).

[0052] Isotropic distribution particles have no obvious directionality in their motion or distribution, and are uniformly distributed in space. When interacting with the mask and substrate, they may make the etching or deposition process consistent in all directions.

[0053] Anisotropic angular distribution, which shows the distribution characteristics of anisotropic particles in angle, that is, the particles mainly move in a certain angle range, further embodying the directionality.

[0054] Isotropic angular distribution, which indicates that isotropic particles are uniformly distributed in angle and have no obvious angle concentration trend.

[0055] Overall, Figure 4 This figure presents the dynamic changes and particle distribution characteristics of the whole process from the initial state (initial mask, substrate profile), through plasma excitation, the interaction of anisotropic and isotropic particles with the mask and substrate, to the final mask and substrate profile update and the formation of attachments on the surface.

[0056] Step 300: Based on the simulation parameters, the Monte Carlo method is used to simulate the interaction process of incident particles with target voxels; the target voxels are substrate voxels or mask voxels; Step 400: When all incident particles complete the interaction process, output the three-dimensional profile of the etched semiconductor structure.

[0057] Specifically, the Monte Carlo method simulates the particle transport process by randomly simulating the incident trajectory of particles (including position and angle distribution); the voxel method dynamically tracks the evolution of the morphology of the substrate and mask during etching by three-dimensional grid subdivision and material marking. The combination of the two can simulate the etching process of different structures: the interaction results of incident particles and target voxels are directly reflected in the update of voxel marking, and finally the etching profile is output through the state change of voxel set.

[0058] Beneficial effect analysis of the embodiment: The application provides a three-dimensional profile simulation method for a semiconductor etching process. First, a three-dimensional simulation domain containing a substrate and a mask is constructed, and simulation parameters are combined to lay a foundation for accurate simulation of the etching process and to reproduce a complex structure environment in three-dimensional integration technology. Second, voxel cubic subdivision is used to discretize the simulation domain, and material markers are used to dynamically track topography evolution, which can accurately capture microscopic deviations such as sidewall roughness and critical dimension narrowing, and can reduce the complexity of complex geometry processing through structured calculation of the voxel grid, thereby optimizing the calculation time. Third, the Monte Carlo method is used to simulate the interaction process of particles and target voxels, and a random model is used to reproduce microscopic dynamics randomness, which improves the accuracy, and the simulation scale of particles is reasonably controlled based on the simulation parameters to avoid redundant calculation, which controls the calculation time, ensures accurate simulation of three-dimensional etching profile, and matches the accuracy requirements of three-dimensional integration technology below 5nm, and effectively reduces the dependence on physical experiments and the optimization cost, thereby meeting the dual requirements of advanced etching processes. In summary, the method combines the efficient geometric expression of voxel subdivision with the accurate microscopic simulation of the Monte Carlo method, which realizes high-precision simulation of three-dimensional etching profile, controls the calculation time within an acceptable range, effectively reduces the dependence on physical experiments and the optimization cost, and meets the dual requirements of advanced etching processes.

[0059] In an optional embodiment, as known from the above embodiment, the multiple types of voxels further include a material-free voxel; and the simulation parameters include a total number of incident particles, an incident position distribution, and an incident angle distribution.

[0060] Referring to Figure 5 , step 300: based on the simulation parameters, the Monte Carlo method is used to simulate the interaction process of incident particles and target voxels, including: Step 310: according to the total number of incident particles, in a serial loop, for each incident particle in all incident particles, based on the incident position distribution and the incident angle distribution, the Monte Carlo method is used to randomly generate initial incident parameters and calculate a particle motion trajectory, and the impact position with the target voxel is determined in real time; wherein the initial incident parameters include an initial incident position and an initial incident angle; Step 310 specifically includes: Based on the incident angle, the particle motion direction is determined; Based on the particle motion direction, the initial incident position is combined to calculate the particle motion trajectory and update the three-dimensional motion coordinates of the incident particle in real time; By comparing the three-dimensional motion coordinates with the spatial coordinate range of the target voxel, it is determined whether the incident particle enters the spatial region where the target voxel is located, so as to determine the impact position. The spatial coordinate range of the target voxel is determined according to the side length of the voxel and the position of the voxel in the three-dimensional simulation domain.

[0061] For example, refer to Figure 6 , Figure 6 The formula is: (1) ; Determine the particle motion trajectory of the incident particle, in the scene of simulating particle incidence by using the Monte Carlo method, represents the displacement of each step of the particle in three-dimensional space, , , are the displacement components of the particle in the x-axis, y-axis and z-axis directions, respectively. According to the displacement of the particle in the three coordinate axis directions, the actual displacement length of the particle can be calculated by formula (1), so as to help determine the motion trajectory of the particle, and then find the incident trajectory and impact point of the particle and other key positions.

[0062] For example, the voxel size of the three-dimensional simulation domain is 1 nm (grid subdivision precision 1 nm), and the initial incidence parameters of a certain incident particle are: Initial incidence position: three-dimensional coordinates (the upper surface of the three-dimensional simulation domain); Incidence angle: 30° along the x-axis in the negative direction of the z-axis (anisotropic, following Gaussian distribution), by simplifying the calculation of the motion direction vector (keeping the integer trend), the motion direction vector is determined as .

[0063] Calculate the particle motion trajectory: The particle moves in the above direction, each step moving 1 nm, and the three-dimensional coordinates are updated in real time as ( is the step number) ; When , the coordinates are updated as: ; When , the coordinates are updated as: ; When , the coordinates are updated as , which falls within the spatial range of a certain substrate voxel (marked as 1) , and the impact position is determined as .

[0064] Step 320: Determine the action mode based on the preset material reflection probability at the impact position; the preset material reflection probability matches the material type of the target voxel; Step 320 includes: generating a first random number at the impact position; the first random number is greater than or equal to 0 and less than or equal to 1; if the first random number is less than or equal to the preset material reflection probability, determining that reflection occurs; if the first random number is greater than the preset material reflection probability, determining whether etching reaction occurs; when reflection occurs, selecting a preset range of voxel domains centered on the impact position, using a least squares fitting method to perform plane fitting on the surface of the voxel domains to obtain a fitting plane, see Figure 7 ; based on the normal vector of the fitting plane and the incident vector when the particle impacts, calculating the reflection vector of the particle to determine the reflection direction.

[0065] For example, assuming that the preset reflection probability of the substrate voxel is 20%. The first random number generated is 0.15, and 0.15≤20%, determining that reflection occurs.

[0066] Step 330: if the action mode is reflection, only one reflection simulation is performed, and the particle after reflection continues to move until the next etching reaction occurs; For example, the reflected particle moves along the reflection vector until it impacts another substrate voxel, at which time it no longer reflects and directly undergoes etching reaction.

[0067] Step 340: if the action mode is etching reaction and etching reaction occurs, updating the material type label of the corresponding target voxel to a material-free voxel; For example, after etching reaction occurs, the substrate voxel (label 1) at the original impact position is completely etched and is updated to a material-free voxel (label 0).

[0068] Step 350: after the action process of the current incident particle ends, the next particle is simulated until all particles are simulated.

[0069] For example, after the current particle action ends, the next particle is simulated until all particles are simulated.

[0070] In an optional embodiment, the step 320 of selecting a preset range of voxel domains centered on the impact position and using a least squares fitting method to perform plane fitting on the surface of the voxel domains to obtain a fitting plane includes: selecting a preset range of voxel domains centered on the impact position and using a least squares fitting method to perform plane fitting on the surface of the voxel domains to obtain a fitting plane, including: extracting the three-dimensional coordinates of all surface voxels in the voxel domains ; wherein, ; is the number of voxels in the preset range of voxel domains; By solving the parameters that minimize the sum of squared deviations: (2) ; The plane equation of the fitted plane is obtained; wherein, is the sum of squared deviations.

[0071] For example, the preset range of the voxel domain can be 9x9x9 voxels (such as 9 voxels in the x direction, the y direction and the z direction), which can accurately capture the micro-undulation characteristics of the surface around the impact point; at the same time, the reflection simulation is only performed once, and the particles after reflection continue to move and inevitably have etching reaction with the target voxels, forming a continuous action logic of "reflection-etching".

[0072] It needs to be explained that, in the present application, the plane fitting of the surface of the voxel domain around the impact point based on the least square fitting method is the core step of realizing the accurate calculation of the particle reflection direction, and the complete mathematical derivation and physical implementation process is as follows: Firstly, in the etching simulation, the local area of the particle impacting the substrate surface can be approximated as a plane, and the mathematical form of the plane equation needs to be determined first.

[0073] The general equation of a plane in a three-dimensional space (see Figure 7 ) is: (3) ; Wherein, , and are the components of the plane normal vector, constitute the plane normal vector , is a constant, and , can ensure that the plane is not parallel to the z-axis, which adapts to the scenario of particle incidence in the vertical / tilted direction in etching, and avoids equation without solution.

[0074] In order to simplify the subsequent fitting calculation, the general formula is converted into an explicit form with as the dependent variable. The general equation is transformed to obtain: (4) ; Divide both sides by , and , , , then the general equation of the plane can be expressed as: (5) ; Wherein, , and are the parameters to be fitted. , is the horizontal coordinate of the voxel, is the vertical coordinate of the voxel.

[0075] selecting a preset range of voxel domain centered on the impact position, extracting the three-dimensional coordinates of all surface voxels in the voxel domain ; wherein, ; is the number of voxels in the preset range of voxel domain, and .

[0076] For each surface voxel, the actual z-axis coordinate The deviation of the z-axis coordinate predicted by the plane equation is: .

[0077] The sum of squares of deviations is defined as the sum of squares of deviations of all surface voxels: (6) ; The goal of fitting is to solve , , So that reach the minimum value.

[0078] According to the mathematical principle of finding extreme value of multivariate function, by solving partial derivative of about , , And let the partial derivative be 0, build the equation group: (7) ; Using numerical calculation tools (such as MATLAB, Python's numpy.linalg.solve function) to solve the above equation group, the unique optimal parameters , , , Substitute the optimal solution into equation , the fitted plane of the surface voxels around the impact position can be obtained, which provides the basis for subsequent particle reflection vector calculation.

[0079] Referring to Figure 7 , it should be further pointed out that the plane equation obtained by the above fitting can determine the position and orientation of the plane in three-dimensional space, which provides the plane basis for subsequent vector calculation (such as normal vector, incident vector, reflection vector).

[0080] The normal vector is a vector perpendicular to the fitted plane, for example, for , the direction of its normal vector is determined by the coefficients , , The decision can be generally expressed as and then normalized to obtain a unit normal vector. The calculation process can refer to related technologies, and the embodiments of the present application will not be described again.

[0081] Incident vector The incident vector represents the direction of the particle's motion when it hits the fitting plane, and describes the particle's motion trend at the moment of impact. The incident vector can be calculated based on the initial position and the impact position. The specific calculation method can refer to related technologies, and will not be described again here.

[0082] Reflection vector According to the law of reflection, the reflection vector is symmetric with the incident vector about the normal vector, and its calculation usually follows the formula: (8) ; Wherein, is the incident vector, is the unit normal vector.

[0083] In an optional embodiment, determining whether an etching reaction occurs includes: generating a second random number; the second random number is greater than or equal to 0 and less than or equal to 1; If the second random number reaches the etching reaction probability, it is determined that the etching reaction occurs; If the second random number does not reach the etching reaction probability, the action process of the current incident particle ends, and the next incident particle is simulated.

[0084] In an optional embodiment, before generating the second random number, the method further includes: determining the etching reaction probability; Determining the etching reaction probability includes: Based on the etching selectivity of the substrate and the mask, the initial value of the etching reaction probability is determined; specifically, for the substrate voxel, the initial reaction probability is ; for the mask voxel, the initial reaction probability is , and is equal to the preset etching selectivity; the same voxel is hit once, and its reaction probability is increased by a preset increment (for example, 5%); Based on the number of times the impact position is hit and the preset single probability increment, the etching reaction probability is obtained.

[0085] For example, if the initial reaction probability of the substrate voxel is 30%, and the preset single probability increment is 5%, the reaction probability of the voxel is 30% when it is hit the first time, 35% when it is hit the second time, and 40% when it is hit the third time. In this way, the probability increment simulation accurately reflects the increase in etching activity caused by multiple impacts on the material surface, and accurately reflects the local rate fluctuations caused by factors such as surface roughness and micro-mask shielding.

[0086] For example, if the first random number is 0.3 (> 20%), it is determined that the etching reaction occurs. If the second random number generated is 0.3 (≤ 35%), it is determined that the etching reaction occurs.

[0087] Technical effect analysis of the embodiment: 1) Realize the cross-scale coupling of microcosmic dynamics and macroscopic morphology.

[0088] Step 310 simulates the particle trajectory (micro-ion transport) by the Monte Carlo method, and judges the impact position by the voxel coordinates, to associate the micro-particle behavior with the macro-voxel grid; in step 320, the randomness calculation of the reflection probability and the reaction probability (such as the first and second random numbers) accurately reproduces the micro-randomness of the surface reaction, realizing the cross-scale coupling simulation. At the same time, the structured calculation of the voxel grid is coordinated with the particle transport simulation, ensuring the coherence and coupling of the micro-particle transport process and the macro-voxel morphology update (such as the voxel label changing from 1 to 0), providing core support for the accuracy of the cross-scale simulation.

[0089] 2) Realize the dynamic expression of complex geometry.

[0090] Step 310 supports the dynamic positioning of any complex geometry structure by judging the impact through the voxel space coordinates; step 340 reflects the morphology evolution in the etching process (such as the voxel retention in the mask shielding area and the voxel disappearance in the etching area) in real time by updating the voxel label (1→0), meeting the demand of dynamic expression of complex geometry, while the structured feature of the voxel grid reduces the processing complexity of complex geometry and optimizes the calculation time.

[0091] 3) Realize the dynamic evolution of surface morphology.

[0092] In step 320, the etching reaction probability increases with the number of impacts (such as 30%→35%), simulating the local rate fluctuation caused by surface roughness; the random number generation of the Monte Carlo method (reflection and reaction judgment) combined with the voxel label update accurately describes the dynamic changes of the morphology caused by factors such as micro-masks and roughness, replacing the traditional trial-and-error method and improving the simulation accuracy. At the same time, by reasonably controlling the simulation scale through the simulation parameters (such as the grid subdivision precision and the particle number), the redundant calculation is avoided, the calculation process of the macro-contour output is simplified through the voxel label update rule (such as the label being 0 after complete etching), and the calculation time is shortened, ensuring that the calculation time is controlled within an acceptable range while meeting the precision requirements of 5nm and three-dimensional integration technology, effectively reducing the dependence on physical experiments and reducing the optimization cost.

[0093] In addition, the plane equation obtained by least squares fitting of the surface voxel coordinates around the impact point, for example, a 9x9x9 voxel domain, can truly reflect the local surface macro trend, avoid the reflection error caused by simplifying the surface as an ideal plane, and make the particle reflection direction calculation more in line with the actual physical scene; based on the fitting plane normal vector combined with the incident vector to calculate the reflection vector, it can accurately ensure the physical law of "the incident angle is equal to the reflection angle", reflect the influence of surface micro relief on the reflection direction, and further improve the physical reality of the reflection simulation and the overall simulation accuracy.

[0094] It should be noted that in order to simulate the three-dimensional process in the etching process, the prior art often uses a physics-based model (continuous medium model, empirical and data-driven model (regression model) and empirical and data-driven model (machine learning method).

[0095] Physics-based model (continuous medium model): This kind of model describes the plasma behavior by means of fluid equations and reaction-diffusion equations, although it can grasp the overall trend from a macroscopic perspective, but at the microscopic level, it regards fluid as a continuous medium, ignoring the molecular structure and physical and chemical phenomena at the microscopic scale, resulting in the inability to capture microscopic details such as ion transport and surface reaction randomness in plasma. For example, when describing the interaction between particles and substrate surface, it is difficult to accurately simulate the random motion trajectory of particles and local etching inhibition and other phenomena.

[0096] Empirical and data-driven model (regression model): Regression model relies on experimental data to fit etching rate equation, and its poor generalization ability is mainly because it highly depends on data under specific experimental conditions. Different experimental equipment, process parameters and material properties will cause differences in data. Once the application scenario changes, the model based on the original data fitting will be difficult to accurately reflect the etching rate under the new situation, and cannot be effectively extended to other similar but not completely identical etching processes.

[0097] Empirical and data-driven model (machine learning method): Machine learning methods such as CNN-LSTM hybrid model, although have advantages in handling complex pattern recognition and prediction, but it has a very high requirement for data volume. In the field of etching process, it is often costly and time-consuming to obtain a large amount of high-quality experimental data. If the data is scarce, the model will be difficult to learn enough features and rules, resulting in inaccurate prediction results.

[0098] Unlike the three main models used in the prior art, the embodiment of the present application solves the problem of insufficient micro details by combining Monte Carlo and voxel methods: the Monte Carlo method can simulate the random motion of particles and accurately track the trajectory of particles in three-dimensional space, including ion transport, surface reaction randomness and other micro processes. The voxel method divides the three-dimensional substrate structure into a voxel grid with material properties, so that the interaction position of particles with different materials can be accurately marked at the micro level, and the micro changes of the etching process are reflected by updating the state of each voxel, thereby effectively solving the problem of insufficient micro details of the continuous medium model.

[0099] The embodiment of the present application solves the problem of poor generalization ability: the three-dimensional profile simulation method in the embodiment of the present application is based on physical principles. By setting general physical parameters (such as material etching selectivity, particle species, etc.) and model structures (such as three-dimensional substrate models, particle incidence condition settings, etc.), it can adapt to different etching process scenarios. It does not depend on specific experimental data fitting, but simulates from the physical process of etching, so it has better generalization ability and can be applied in different semiconductor three-dimensional integration technology etching processes.

[0100] The embodiment of the present application solves the problem of large data requirements: the simulation method in the embodiment of the present application does not need a large amount of experimental data to train the model. It simulates the etching profile by setting physical parameters and simulating physical processes. Only basic parameters such as material properties and etching process conditions need to be determined to carry out simulation. Compared with machine learning methods, it greatly reduces the dependence on data volume and avoids the problem of inaccurate model caused by data scarcity.

[0101] In addition, the embodiment of the present application can be fitted and verified with actual etching experimental data (such as critical dimension, sidewall roughness measurement value), and the simulation parameters (such as etching selectivity, particle reflection probability) can be optimized, so that the calibrated model can output personalized process parameter optimization suggestions (such as incident particle species ratio, angle distribution type) for specific experimental equipment, providing theoretical guidance and parameter adjustment basis for etching process research and development.

[0102] The three-dimensional profile simulation device for semiconductor etching process provided by the present application will be described below. The three-dimensional profile simulation device for semiconductor etching process described below can be referred to each other corresponding to the three-dimensional profile simulation method for semiconductor etching process described above.

[0103] As Figure 8 shown, the embodiment of the present application also provides a three-dimensional profile simulation device for semiconductor etching process, which is used to implement the three-dimensional profile simulation method for semiconductor etching process in any of the above embodiments. The three-dimensional profile simulation device for semiconductor etching process can include: The constructing module 810 is configured to construct a three-dimensional simulation domain of a semiconductor structure to be etched and acquire simulation parameters; The discretizing module 820 is configured to discretize the three-dimensional simulation domain into a plurality of voxels and mark the plurality of voxels with material types, to obtain multi-class voxels; the multi-class voxels at least include substrate voxels and mask voxels; The simulating module 830 is configured to simulate, based on the simulation parameters, a process of interaction between incident particles and target voxels by using a Monte Carlo method; the target voxels are substrate voxels or mask voxels; The outputting module 840 is configured to output a three-dimensional profile of the semiconductor structure after etching when all the incident particles complete the process of interaction.

[0104] Optionally, the multi-class voxels further include material-free voxels; the simulation parameters at least include a total number of incident particles, an incident position distribution and an incident angle distribution; the simulating module 830 is specifically configured to, according to the total number of incident particles, in a serial loop, for each incident particle in all the incident particles, generate initial incident parameters and calculate a particle motion trajectory by using the Monte Carlo method based on the incident position distribution and the incident angle distribution, and judge an impact position with the target voxels in real time; At the impact position, judge an interaction mode based on a preset material reflection probability; the preset material reflection probability matches a material type of the target voxels; If the interaction mode is reflection, only one reflection simulation is performed, and the particle after reflection continues to move until the next etching reaction occurs; If the interaction mode is etching reaction and the etching reaction occurs, the material type of the corresponding target voxels is updated to a material-free voxel; After the process of interaction of the current incident particle ends, the next particle is simulated, and the simulation of all the particles is completed.

[0105] Optionally, the initial incident parameters include an initial incident position and an initial incident angle; the simulating module 830 is specifically configured to determine a particle motion direction based on the incident angle; Based on the particle motion direction, the particle motion trajectory is calculated and the three-dimensional motion coordinates of the incident particle are updated in real time by combining the initial incident position; The three-dimensional motion coordinates are compared with a spatial coordinate range of the target voxels to determine whether the incident particle enters a spatial region where the target voxels are located, so as to determine the impact position.

[0106] Optionally, the simulating module 830 is specifically configured to generate a first random number at the impact position; the first random number is greater than or equal to 0 and less than or equal to 1; If the first random number is less than or equal to the preset material reflection probability, it is determined that reflection occurs; If the first random number is greater than the preset material reflection probability, it is determined whether etching reaction occurs; When the reflection occurs, a preset range of voxel domain is selected with the impact position as the center, a least square fitting method is used to perform plane fitting on the surface of the voxel domain, and a fitting plane is obtained; Based on the normal vector of the fitting plane and the incident vector when the particle impacts, a reflection vector of the particle is calculated to determine the reflection direction.

[0107] Optionally, the simulation module 830 is specifically configured to: generate a second random number; the second random number is greater than or equal to 0 and less than or equal to 1; If the second random number reaches the etching reaction probability, it is determined that the etching reaction occurs; If the second random number does not reach the etching reaction probability, the action process of the current incident particle ends, and the next incident particle is simulated.

[0108] Optionally, the simulation module 830 is specifically configured to: extract the three-dimensional coordinates of all surface voxels in the voxel domain ; wherein, ; is the number of voxels in the preset range of voxel domain; By solving the parameter that minimizes the deviation square sum formula: ; The plane equation of the fitting plane is obtained; wherein, is the deviation square sum.

[0109] Optionally, the three-dimensional profile simulation device for semiconductor etching process can also include a first determination module. The first determination module is configured to determine the simulation parameters before obtaining the simulation parameters.

[0110] The first determination module is specifically configured to: determine the incident position distribution as uniformly distributed on the upper surface of the three-dimensional simulation domain; According to the size and grid subdivision accuracy of the three-dimensional simulation domain, the total number of incident particles is determined; Set the incident angle distribution; wherein, the incident angle distribution follows a cosine distribution or a Gaussian distribution; According to the substrate material and the mask material, the type of incident particle is determined; The boundary condition of the three-dimensional simulation domain is set to a periodic boundary condition; the periodic boundary condition represents that the incident particle continues to enter the three-dimensional simulation domain from the same position on the opposite side at the same angle after crossing the boundary of the three-dimensional simulation domain.

[0111] The construction module 810 is specifically configured to: construct the substrate structure based on the size of the substrate; Above the substrate structure, a mask structure is constructed based on a preset mask pattern; Based on the substrate structure and the mask structure, a height, a length and a width of a three-dimensional simulation domain are determined, and the three-dimensional simulation domain including the substrate structure and the mask structure is formed.

[0112] Optionally, the three-dimensional profile simulation device for a semiconductor etching process can further include a second determination module configured to determine an etching reaction probability before generating the second random number.

[0113] The second determination module is specifically configured to determine an initial value of the etching reaction probability based on an etching selection ratio of the substrate and the mask. The etching reaction probability is obtained based on the number of times the impact position is impacted and a preset single probability increment.

[0114] The embodiments of the present application also provide an electronic device, which can include a processor, a communication interface, a memory and a communication bus, wherein the processor, the communication interface and the memory complete mutual communication through the communication bus. The memory stores a computer program which can be run by the processor; and the processor can execute the three-dimensional profile simulation method for a semiconductor etching process in any of the above embodiments when running the computer program.

[0115] In addition, the logic instructions in the memory described above can be implemented in the form of a software functional unit and sold or used as an independent product, and can be stored in a computer readable storage medium. Based on such understanding, the technical solutions of the present application essentially or the part that contributes to the prior art or part of the technical solutions can be embodied in the form of a software product, and the computer software product is stored in a storage medium, including a plurality of instructions to make a computer device (which can be a personal computer, a server, or a network device, etc.) execute all or part of the steps of the embodiments of the present application. The foregoing storage medium includes: a U disk, a mobile hard disk, a read-only memory, a random access memory, a magnetic disk or an optical disk, and various program codes that can be stored in the medium.

[0116] Although the present application has been described in connection with various embodiments thereof, it will be understood that the application is capable of further modifications and that this application is intended to cover any and all such variations, using the scope of the application, which is defined by the following claims, properly construed. In the claims, the term "including" does not exclude other components or steps. The indefinite articles "a" or "an" do not exclude a plurality. A single processor or other unit can fulfil the functions of several items recited in the claims. The terms "first", "second" and the like in the description do not necessarily imply that there are only two. The terms "including", "containing", "comprising" and similar terms are not to be construed as implying a quantitative or qualifying relation. The mention of specific embodiments does not prejudice the application's generality and the application's scope, which extends to all functional equivalents that operate like the embodiments but are not claimed. Accordingly, the description and drawings are to be regarded as illustrative in nature and are not to be considered as limiting the scope of the application as defined in the claims. Obviously, many modifications and variations of the present application are possible in light of the above teachings. It is, therefore, to be understood that within the scope of the claims and their equivalents, the application can be practiced otherwise than as specifically described.

Claims

1. A three-dimensional contour simulation method for semiconductor etching processes, characterized in that, include: Construct a three-dimensional simulation domain for the semiconductor structure to be etched and obtain simulation parameters; The three-dimensional simulation domain is discretized into multiple voxels, and the multiple voxels are labeled with material types to obtain multiple types of voxels; the multiple types of voxels include at least substrate voxels and mask voxels; Based on the simulation parameters, the Monte Carlo method is used to simulate the interaction process between the incident particle and the target voxel; The target voxel is either the substrate voxel or the mask voxel; After all the incident particles have completed their interaction, the three-dimensional contour of the etched semiconductor structure is output.

2. The three-dimensional contour simulation method for semiconductor etching processes according to claim 1, characterized in that, The multiple types of voxels also include material-free voxels; the simulation parameters include at least the total number of incident particles, the distribution of incident positions, and the distribution of incident angles. Based on the simulation parameters, the Monte Carlo method is used to simulate the interaction process between the incident particle and the target voxel, including: According to the total number of incident particles, a serial loop is used to randomly generate initial incident parameters and calculate the particle trajectory for each incident particle based on the incident position distribution and the incident angle distribution, using the Monte Carlo method, and to determine the collision position with the target voxel in real time. At the impact location, the action mode is determined based on a preset material reflection probability; the preset material reflection probability matches the material type of the target voxel. If the mode of action is reflection, only one reflection simulation is performed, and the reflected particles continue to move until the next etching reaction occurs. If the action mode is an etching reaction and an etching reaction occurs, the material type label of the corresponding target voxel is updated to the material-free voxel; After the current incident particle's action process ends, the simulation continues with the next particle until all particles have been simulated.

3. The three-dimensional contour simulation method for semiconductor etching processes according to claim 2, characterized in that, The initial incident parameters include the initial incident position and the initial incident angle; Calculate the motion trajectory and determine the impact position with the target voxel in real time, including: Based on the incident angle, the direction of particle motion is determined; Based on the particle's motion direction and the initial incident position, the particle's trajectory is calculated and the three-dimensional motion coordinates of the incident particle are updated in real time. By comparing the three-dimensional motion coordinates with the spatial coordinate range of the target voxel, it is determined whether the incident particle has entered the spatial region where the target voxel is located, thereby determining the impact position.

4. The three-dimensional contour simulation method for semiconductor etching processes according to claim 2, characterized in that, At the impact location, the action mode is determined based on a preset material reflection probability, including: At the impact location, a first random number is generated; the first random number is greater than or equal to 0 and less than or equal to 1. If the first random number is less than or equal to the preset material reflection probability, then reflection is determined to have occurred; If the first random number is greater than the preset material reflection probability, then determine whether an etching reaction has occurred; When reflection occurs, a voxel domain within a preset range is selected with the impact location as the center, and the surface of the voxel domain is fitted using the least squares fitting method to obtain the fitting plane. Based on the normal vector of the fitted plane and the incident vector at the time of particle impact, the reflection vector of the particle is calculated to determine the reflection direction.

5. The three-dimensional contour simulation method for semiconductor etching processes according to claim 4, characterized in that, Determining whether an etching reaction has occurred includes: Generate a second random number; the second random number is greater than or equal to 0 and less than or equal to 1. If the second random number reaches the etching reaction probability, then it is determined that an etching reaction has occurred; If the second random number does not reach the etching reaction probability, the current incident particle's action process ends, and the simulation continues for the next incident particle.

6. The three-dimensional contour simulation method for semiconductor etching processes according to claim 4, characterized in that, A voxel domain within a preset range is selected centered on the impact location. A least-squares fitting method is used to perform planar fitting on the surface of the voxel domain to obtain a fitting plane, including: Extract the three-dimensional coordinates of all surface voxels within the voxel domain. ;in, ; The number of voxels within a preset range of voxel domains; By solving the formula for the sum of squared deviations: ； Minimizing the parameters yields the plane equation of the fitted plane; where, Let be the sum of squares of the deviations.

7. The three-dimensional contour simulation method for semiconductor etching processes according to claim 4, characterized in that, Before obtaining the simulation parameters, the method further includes: determining the simulation parameters; Determining the simulation parameters includes: The incident position distribution is determined to be uniformly distributed on the upper surface of the three-dimensional simulation domain; The total number of incident particles is determined based on the size of the three-dimensional simulation domain and the mesh generation accuracy. The incident angle distribution is set; wherein the incident angle distribution follows a cosine distribution or a Gaussian distribution; The type of incident particles is determined based on the substrate material and mask material; The boundary conditions of the three-dimensional simulation domain are set as periodic boundary conditions; the periodic boundary conditions indicate that after the incident particle crosses the boundary of the three-dimensional simulation domain, it continues to re-enter the three-dimensional simulation domain from the same position on the opposite side at the same angle.

8. The three-dimensional contour simulation method for semiconductor etching processes according to claim 1, characterized in that, Constructing a three-dimensional simulation domain for the semiconductor structure to be etched includes: Based on the substrate dimensions, construct the substrate structure; A mask structure is constructed above the substrate structure based on a preset mask pattern; Based on the substrate structure and the mask structure, the height, length, and width of the three-dimensional simulation domain are determined to form the three-dimensional simulation domain including the substrate structure and the mask structure.

9. The three-dimensional contour simulation method for semiconductor etching processes according to claim 5, characterized in that, Before generating the second random number, the method further includes: determining the etching reaction probability; Determining the etching reaction probability includes: The initial value of the etching reaction probability is determined based on the etching selectivity ratio of the substrate and the mask. The etching reaction probability is obtained based on the number of times the impact location is hit and the preset single probability increment.

10. A three-dimensional contour simulation device for semiconductor etching processes, characterized in that, include: The building module is used to construct a three-dimensional simulation domain for the semiconductor structure to be etched and to obtain simulation parameters. A discretization module is used to discretize the three-dimensional simulation domain into multiple voxels and label the multiple voxels with material types to obtain multiple types of voxels; the multiple types of voxels include at least substrate voxels and mask voxels; The simulation module is used to simulate the interaction process between the incident particle and the target voxel using the Monte Carlo method based on the simulation parameters. The target voxel is either the substrate voxel or the mask voxel; The output module is used to output the three-dimensional contour of the etched semiconductor structure after all incident particles have completed their interaction process.

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