Subsurface damage quantitative prediction method for silicon carbide lapping and polishing process

Abstract

The application discloses a quantitative prediction method for subsurface damage in a silicon carbide polishing process, which is implemented according to the following steps: S1, calculating the indentation depth of a single abrasive grain according to input parameters; S2, calculating the critical indentation depth of the single abrasive grain, and comparing the critical indentation depth of the single abrasive grain with the indentation depth of the single abrasive grain to determine brittle-plastic transition; and S3, calculating the subsurface damage depth after the corresponding brittle-plastic transition. The application has the beneficial effects that: the application realizes micro contact parameter calculation, automatic brittle-plastic transition determination and mode damage prediction through steps, constructs a unified subsurface damage quantitative prediction framework, completely solves the problem that a macro empirical model based on a Preston equation has poor universality and is difficult to reflect a micro contact mechanism in the prior art, and overcomes the defects that error distribution of a traditional indentation fracture mechanics model is dispersed and a single model has poor cross-working condition applicability.

Description

Technical Field

[0001] This invention relates to a damage prediction model, and more particularly to a method for quantitative prediction of subsurface damage in silicon carbide grinding and polishing processes. Background Technology

[0002] In the semiconductor manufacturing field, silicon carbide wafers are widely used in power devices and radio frequency devices due to their excellent properties such as high hardness and high thermal conductivity. Grinding and polishing, as a key process in wafer fabrication, aims to obtain an ultra-smooth surface; however, subsurface damage, such as microcracks and plastic deformation layers, is inevitably generated during the process. This damage reduces the electrical performance and reliability of the devices. To control these damages, existing technologies employ subsurface damage mechanism prediction methods, primarily based on the Preston equation's removal depth model. This model, by fitting correction coefficients to experimental data, predicts the material removal depth and potential damage layer thickness under given grinding pressure, relative speed, and abrasive characteristics. This guides the setting and optimization of process parameters, helping to reduce defects in processing and improve wafer quality.

[0003] However, existing technologies have significant drawbacks. First, the removal depth model based on the Preston equation is a macroscopic empirical model, and its correction coefficients need to be fitted under specific experimental conditions. It only holds true within the corresponding range of conditions, lacks universality, and is difficult to reflect the microscopic contact and deformation mechanism between the abrasive and the workpiece. Second, some SiC subsurface damage prediction models based on indentation fracture mechanics have relatively dispersed error distributions in engineering applications, with error ranges reaching 12% to 80.7%, which seriously affects the reliability of process parameter optimization. In addition, in actual processing, materials may be in either plastic removal or brittle removal modes, and the damage morphology and mechanism are different in different modes. If a single model is used without determining the removal mode, it is easy to cause applicability bias. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a quantitative prediction method for subsurface damage in the silicon carbide grinding and polishing process, which solves the problems of large prediction errors and poor universality in SiC subsurface damage prediction.

[0005] To achieve the above objectives, the technical solution of this invention is as follows: A method for quantitative prediction of subsurface damage in silicon carbide grinding and polishing processes, implemented according to the following steps: S1, calculates the indentation depth of a single abrasive grain based on the input parameters; S2, calculate the critical indentation depth of a single abrasive grain, and compare the critical indentation depth of a single abrasive grain with the indentation depth of a single abrasive grain to determine the brittle-plastic transition; S3, calculate the subsurface damage depth after the corresponding brittle-plastic transformation.

[0006] The beneficial effects of this invention are as follows: By implementing microscopic contact parameter calculation, automatic brittle-plastic transition determination, and sub-mode damage prediction in a step-by-step manner, this invention constructs a unified quantitative prediction framework for subsurface damage. This completely solves the problems of poor universality and difficulty in reflecting microscopic contact mechanisms in existing macroscopic empirical models based on the Preston equation. It also overcomes the shortcomings of traditional indentation fracture mechanics models, such as dispersed error distribution and poor applicability of single models across different working conditions. This method does not rely on a large number of repeated experiments to fit correction coefficients; it can complete the prediction using only known material and process parameters, significantly improving prediction efficiency and reliability. It can provide accurate theoretical basis for optimizing silicon carbide grinding and polishing process parameters and controlling processing quality. As a preferred approach, this prediction method is integrated into the central control system of a CNC grinding and polishing equipment. By collecting the process parameters of the equipment in real time, it automatically completes the calculation of single abrasive grain indentation depth, brittle-plastic transition determination, and subsurface damage depth prediction, and feeds the prediction results back to the equipment execution unit in real time, realizing closed-loop control of the processing process. As another preferred approach, a process parameter optimization platform is built based on this prediction method. By inputting the target subsurface damage depth, the optimal combination of process parameters such as external load and abrasive surface density is derived in reverse, providing process engineers with a basis for rapid process scheme formulation.

[0007] Furthermore, all the input parameters are known parameters, including the total height of the abrasive grains on the surface of the bonded abrasive polishing pad, the hardness of the workpiece material, the Poisson's ratio of the workpiece material, the elastic modulus of the workpiece material, the fracture toughness of the workpiece material, the abrasive apex angle of the abrasive grains participating in the polishing process, the external load, the surface density of the abrasive grains on the surface of the polishing pad, and the equivalent particle size of the abrasive grains.

[0008] This technical solution avoids the drawbacks of traditional models that require extensive experimental fitting and correction of coefficients for different working conditions by limiting all input parameters to directly obtainable known parameters, significantly improving the model's universality and engineering applicability. These parameters cover three core dimensions: grinding pad characteristics, workpiece material mechanical properties, and processing technology, comprehensively reflecting the key factors affecting subsurface damage and ensuring the accuracy of prediction results. Simultaneously, the standardized input parameter system facilitates technical exchange and model reuse between different laboratories and manufacturers, lowering the application threshold of the model. As a preferred approach, a standardized parameter input interface is established, automatically importing the mechanical parameters of the workpiece material and the abrasive characteristics of the grinding pad by connecting to material performance databases and grinding pad product parameter libraries, reducing errors and workload from manual input. As another preferred approach, a parameter verification module is set up to automatically verify the range of input parameters, issuing a warning when the input parameters exceed a reasonable range to avoid distortion of prediction results due to parameter errors.

[0009] Furthermore, if the abrasive grain shape is an octahedral structure, then the equivalent grain size is the diameter of a circle with the same projected area as the abrasive grain.

[0010] This technical solution proposes a clear equivalent particle size definition for octahedral diamond abrasives widely used in industry. It simplifies the complex geometry of polyhedral abrasives into an equivalent circular projection, significantly reducing the complexity of abrasive geometry modeling while ensuring the accuracy of contact mechanics calculations. This avoids the tedious polyhedral contact analysis process and improves computational efficiency. This equivalent method conforms to the basic assumptions of indentation fracture mechanics, accurately reflecting the stress state and deformation behavior when the abrasive contacts the workpiece, laying a reliable foundation for subsequent calculations of single abrasive load and indentation depth. As a preferred approach, abrasive images of the grinding pad surface are acquired using an industrial camera. An edge detection algorithm is used to extract the projected contour of a single abrasive grain, and the area enclosed by the contour is calculated to obtain the diameter of the corresponding equivalent circle. As another preferred approach, a corresponding equivalent particle size calculation model library is established for abrasive grains of different shapes. When using non-octahedral abrasives, the matching calculation model is automatically invoked, achieving universal modeling for multiple types of abrasives.

[0011] Furthermore, step S1 specifically includes: S100, calculate the distance between the workpiece and the bottom polishing pad; S110, calculate the number of effective abrasive grains within the effective area of ​​the workpiece and the grinding pad; S120, the depth of penetration of a single abrasive grain is determined by the number of effective abrasive grains within the effective area of ​​the workpiece and the grinding pad and the distance between the workpiece and the bottom polishing pad.

[0012] This technical solution establishes a complete quantitative mapping chain from macroscopic process parameters to microscopic contact parameters by calculating the workpiece-polishing pad distance, effective abrasive grain number, and single abrasive grain indentation depth step by step. It accurately reveals the microscopic contact behavior and load transfer mechanism between the abrasive grains and the workpiece, solving the core problem that traditional macroscopic models cannot reflect the microscopic machining process. The step-by-step calculation logic is clear, and the physical meaning is explicit. Each step's calculation result has a corresponding physical meaning, facilitating model debugging and verification, and providing a clear entry point for subsequent improvements to different aspects. As a preferred method, iterative calculations are used to simultaneously solve for the workpiece-polishing pad distance and the effective abrasive grain number. By setting a convergence threshold, the results are gradually approximated to the true values, ensuring the accuracy of the calculation results. As another preferred method, the wear characteristics of the abrasive grains are incorporated into the calculation process, updating the total abrasive grain height and equivalent grain size parameters in real time to achieve dynamic prediction of the abrasive grain wear state during machining.

[0013] Furthermore, step S100 specifically includes: S101, the probability density function for calculating the height of abrasive grain protrusion; S102, Calculate the desired protrusion height of the abrasive grain; S103, Calculate the normal load of a single abrasive grain on the workpiece surface; S103, the distance between the workpiece and the bottom polishing pad is obtained by using the probability density function of the abrasive protrusion height, the expected abrasive protrusion height, and the normal load of a single abrasive grain on the workpiece surface.

[0014] This technical solution introduces a probability density function for the abrasive grain protrusion height, fully considering the randomness of the abrasive grain protrusion height in actual processing, making the model more closely resemble real engineering conditions and avoiding calculation errors caused by assuming all abrasive grains have the same height. Based on the definition of hardness, the normal load of a single abrasive grain is derived, establishing a theoretical foundation of microscopic contact mechanics, rather than relying on empirical assumptions, ensuring the physical correctness of the load calculation. By deriving the distance between the workpiece and the polishing pad by simultaneously solving the above parameters, the organic unity of the macroscopic total load and the microscopic single abrasive grain load is achieved. As a preferred approach, a uniform distribution is used to describe the abrasive grain protrusion height, and a correction coefficient is introduced to characterize the abrasive grain detachment conditions in actual engineering, making the model more consistent with actual processing conditions. As another preferred approach, the calculation results of the normal load of a single abrasive grain are verified through finite element simulation, and the formula derived from the hardness definition is slightly modified to further improve the accuracy of the load calculation.

[0015] Furthermore, step S110 specifically includes: S111, calculate the effective contact area between the workpiece and the grinding pad; S112, Calculate the total number of abrasive grains within the effective contact area between the workpiece and the grinding pad; S113 converts the total number of abrasive grains within the effective contact area between the workpiece and the grinding pad into the effective number of abrasive grains.

[0016] This technical solution accurately distinguishes between effective abrasive grains that truly participate in load bearing and cutting and ineffective abrasive grains that do not contact the workpiece by first calculating the total number of abrasive grains and then converting it into the effective number of abrasive grains. This solves the problem of inaccurate load sharing calculations caused by the general use of the total number of abrasive grains in traditional models. The conversion from the total number of abrasive grains to the effective number of abrasive grains is achieved through the abrasive grain participation probability, fully reflecting the influence of abrasive grain height distribution on the effective number of abrasive grains. This makes the calculated effective number of abrasive grains closer to reality, thereby improving the prediction accuracy of single abrasive grain indentation depth and subsurface damage depth. As a preferred method, the effective contact area is calculated based on the actual shape of the workpiece and the contact state of the grinding pad, considering the differences in contact pressure distribution in the workpiece edge area, and the effective number of abrasive grains in the edge area is corrected. As another preferred method, high-speed camera technology is used to capture the contact state between the abrasive grains and the workpiece during processing, and the actual number of abrasive grains participating in cutting is counted to verify and optimize the calculation model for the effective number of abrasive grains.

[0017] Furthermore, if the indentation depth of a single abrasive grain is less than the critical indentation depth of a single abrasive grain, the material is subjected to plastic removal; if the indentation depth of a single abrasive grain is greater than the critical indentation depth of a single abrasive grain, the material is subjected to brittle removal.

[0018] This technical solution achieves automatic and objective determination of material removal mode by quantitatively comparing the actual indentation depth with the critical indentation depth, replacing the traditional subjective judgment method relying on process experience and avoiding errors caused by human judgment. This determination method relies only on the inherent mechanical parameters of the material, eliminating the need for experimental fitting for different working conditions and exhibiting good versatility. Accurate determination of the removal mode provides a reliable basis for subsequent selection of the corresponding subsurface damage calculation model, fundamentally solving the problem of poor applicability of a single model under different removal modes. As a preferred method, a calculation formula for the critical indentation depth of the brittle-plastic transition is derived based on indentation fracture mechanics theory, incorporating inherent parameters such as material hardness, elastic modulus, and fracture toughness into the calculation to ensure the accuracy of the critical indentation depth. As another preferred method, a transition interval is set in the critical region of the brittle-plastic transition. When the actual indentation depth is within the transition interval, the contributions of both plastic and brittle removal are considered, and a weighted average method is used to calculate the subsurface damage depth.

[0019] Furthermore, the subsurface damage depth is calculated based on different models inputted from plastic removal and brittle removal structures.

[0020] This technical solution addresses two different material removal mechanisms: plastic removal and brittle removal. Corresponding subsurface damage calculation models are constructed for each, accurately reflecting the formation mechanism and evolution of subsurface damage under different modes. Modeling is based on the plastic deformation layer in the plastic removal mode and on crack propagation in the brittle removal mode, achieving accurate prediction of subsurface damage under both modes and significantly reducing prediction errors. The overall prediction error of the model is controlled within 10%, significantly better than traditional models. Simultaneously, a mapping relationship between surface roughness and subsurface damage is established in the brittle removal mode, enabling the indirect characterization of internal invisible damage using measurable surface parameters, reducing the cost and difficulty of damage detection in engineering. As a preferred approach, in the plastic removal mode, the subsurface damage depth is calculated based on the ratio of the contact radius between the abrasive grain and the workpiece to the depth of the plastic zone, and an elastic recovery coefficient is introduced to correct the damage depth after unloading. As another preferred approach, in the brittle removal mode, the propagation depths of the median crack and transverse crack are calculated separately, with the maximum propagation depth of the median crack used as a characterization index of the subsurface damage depth. A quantitative mapping relationship is also established between the maximum surface roughness and the subsurface damage depth. Attached Figure Description

[0021] Figure 1 This is a flowchart illustrating the model of an embodiment of the present invention; Figure 2 This is a schematic diagram of the polishing process of SiC material according to an embodiment of the present invention; Figure 3 This is a schematic diagram of crack propagation on a silicon carbide (SiC) substrate, a third-generation semiconductor material, during the grinding and polishing process according to an embodiment of the present invention. ((a) Schematic diagram of surface plastic deformation and subsurface crack propagation stages during grinding of SiC material; (b) Schematic diagram of surface and subsurface crack propagation during the brittle removal stage of single abrasive grain processing of SiC material; (c) Cross-sectional view of surface and subsurface crack propagation during the brittle removal stage of grinding of SiC material) Detailed Implementation

[0022] An embodiment of the present invention provides a method for quantitative prediction of subsurface damage in silicon carbide grinding and polishing processes, implemented according to the following steps: S1, Calculate the indentation depth of a single abrasive grain based on the input parameters. .

[0023] These input parameters are all known parameters, specifically including the total height of the abrasive grains on the surface of the bonded abrasive polishing pad. Hardness of workpiece material Poisson's ratio of the workpiece material Elastic modulus of workpiece material Fracture toughness of workpiece material The abrasive tip angle involved in the polishing process External load Equivalent particle size of abrasive grains .

[0024] Diamond abrasive grains are assumed to have an octahedral structure, and the concept of equivalent grain size is introduced. The equivalent grain size of diamond abrasive grains... Defined as: the diameter of a circle whose projected area is the same as the projected area of ​​the abrasive grain within a certain field of view.

[0025] Calculating the indentation depth of a single abrasive grain Since the protrusion height of the abrasive grains on the surface of the bonded abrasive polishing pad has a certain degree of randomness, the following assumptions are made regarding it.

[0026] Theoretically, when the protrusion height of the abrasive grains on the surface of the bonded abrasive polishing pad exceeds the total height of the abrasive grains on the surface of the bonded abrasive polishing pad... At half the depth, abrasive grains will detach. However, in practical engineering applications, this condition can be appropriately relaxed; that is, the protrusion height of abrasive grains on the surface of the bonded abrasive polishing pad is allowed to be slightly greater than their embedding depth in the matrix. To characterize this practical condition, a coefficient is introduced. Its value ranges from 1.0 to 1.1, and it is assumed that the protrusion height of the abrasive grains on the surface of the bonded abrasive polishing pad is... It follows a uniform distribution as shown in formula (1). In this embodiment, It is a probability density function of the protrusion height of abrasive grains on the surface of a bonded abrasive polishing pad, with coefficients... Taking 1.05 as the constant, the desired protrusion height of the abrasive grains can be calculated according to formula (2) based on the uniform distribution. .

[0027] External load during grinding The force is transmitted to the workpiece surface through abrasive grains. The effect of abrasive grains on the workpiece can be simplified as the mechanical behavior of a large-scale indenter acting on a hard and brittle material. Therefore, according to the definition of hardness, the normal load of a single abrasive grain acting on the workpiece surface is... It can be represented as.

[0028] The microscopic contact state between the grinding pad, abrasive grains and workpiece is as follows: Figure 2 As shown, the protrusion height of a single abrasive grain Rather than the depth of indentation The relationship between them can be represented as follows.

[0029] The effective abrasive grains on the grinding pad and the workpiece under external load The interaction is only greater than the convexity. Effective abrasive particles can participate in load bearing and act on the workpiece. The external load is the total number of effective abrasive grains on the polishing pad. It can be viewed as a normal load acting on the workpiece surface by a single abrasive grain. The sum of .

[0030] Substituting formulas (1)-(3) into formula (4), considering the geometric dimensions of the diamond abrasive grains and the distance between the workpiece and the bottom polishing pad... It can be represented as.

[0031] According to formulas (3) and (5), the penetration depth of the abrasive grains on the workpiece surface can be determined. It is closely related to a variety of parameters, mainly including abrasive grain size. External load Hardness of workpiece material And the abrasive tip angles involved in the polishing process Factors such as these.

[0032] Effective number of abrasive particles This usually refers to the number of abrasive grains that actually participate in bearing and cutting at a certain moment, which is to say, the number of abrasive grains that meet the requirements. The number of abrasive grains. According to the probability density function shown in formula (1), the probability of abrasive grain participation can be expressed as:

[0033] The total number of abrasive particles in the contact area Convert to effective abrasive grain count .

[0034] in The surface density of the abrasive particles on the grinding pad. The effective contact area between the workpiece and the grinding pad. Let be the surface area of ​​the workpiece (wafer), that is, the surface area of ​​the circular wafer. Then, by combining formulas (7) and (8), we can obtain .

[0035] S2, calculate the critical indentation depth of a single abrasive grain, and compare the critical indentation depth of a single abrasive grain with the indentation depth of a single abrasive grain to determine the brittle-plastic transition.

[0036] Material removal modes for hard and brittle materials mainly include two types: plastic removal and brittle removal. Different removal modes correspond to different material removal mechanisms, resulting in different cross-sectional morphologies of the machined surface. In the plastic removal mode, the cross-sectional shape of the undeformed chip can usually be approximated as triangular. However, in the brittle removal mode, due to the initiation and propagation of cracks, the material removal process is more complex and requires further analysis. During the machining of hard and brittle materials, when the abrasive grain indentation depth exceeds the critical indentation depth... At this point, the material removal mode will change from plastic removal to brittle removal, and the critical indentation depth corresponding to the brittle-plastic transition is... It can be represented as.

[0037] when When the material is removed plastically; when At this time, the material undergoes brittle removal. Furthermore, when a sharp indenter is pressed into the surface of a brittle material, a near-hemispherical plastic deformation zone forms in the near-surface region, exhibiting two basic deformation and fracture modes: (i) when the indentation depth is less than the critical indentation depth... When the material exhibits only a subcritical crack-free yield zone; (ii) when the indentation depth is greater than the critical indentation depth Under stress, macroscopic cracks such as radial cracks, mid-range cracks, and transverse cracks will form within the plastic deformation zone. In actual processing, these two deformation and fracture modes often coexist and interact.

[0038] S3, calculate the subsurface damage depth after the corresponding brittle-plastic transformation.

[0039] When plastic contact dominates, the average contact pressure is on the same order of magnitude as hardness. Using hardness as a definition, the contact projected area can be inversely calculated. Assuming the contact projected area is circular, the contact radius between the abrasive grain and the workpiece surface is... With the applied load on a single abrasive grain The relationship between them can be represented as follows.

[0040] In the absence of cracks, subsurface damage is dominated by the deformed layer formed by plastic deformation or densification. Extensive research on indentation and abrasion in hard and brittle materials shows that the depth of the plastic zone is on the same order of magnitude as the contact radius, and the size of the plastic zone (radius or characteristic depth) is related to the contact radius. There is a proportional relationship; the proportionality coefficient is related to the material's yield behavior and hardening. Subsurface damage depth. It can be represented as.

[0041] in For calibration coefficients, The elastic recovery coefficient is the coefficient of elasticity of the workpiece material. Based on the material properties of SiC, the elastic recovery coefficient is... This can be considered as 0.363.

[0042] When brittle contact dominates, the median crack depth generated during the processing of hard and brittle materials... Horizontal crack depth and abrasive indentation depth The relationship between them can be represented as follows.

[0043] in and These are coefficients related to the physical parameters of the workpiece material and the abrasive tip angle, which can be expressed as follows:

[0044] When the shear stress in the contact area exceeds the material's fracture strength limit, the material undergoes plastic flow removal similar to that of metallic materials, exhibiting a ductile removal mode in brittle materials. Conversely, in the brittle removal mode, transverse cracks propagate continuously towards the free surface of the workpiece, and the material is removed through brittle fracture. Therefore, the cross-sectional profile of the machined surface will be determined by the abrasive indentation depth. The corresponding morphology changes from the depth of the transverse crack. The dominant morphology. Maximum height of surface roughness parameter. Defined as the sum of the maximum peak height and maximum valley depth on the surface within the sampling length (ISO 4287-1997). Therefore, the maximum height of the surface roughness parameter is... It can be represented as.

[0045] Subsurface damage is mainly caused by the initiation and propagation of median cracks, and its damage depth... The maximum propagation depth of the median crack is usually used as a characterization index.

[0046] Combining the above formulas, the abrasive indentation depth can be eliminated. Therefore, subsurface damage depth and the maximum height of the roughness of the machined surface The relationship between them can be calculated using the following formula.

[0047] The above embodiments are merely one preferred embodiment of the present invention. Ordinary variations and substitutions made by those skilled in the art within the scope of the technical solution of the present invention are all included within the protection scope of the present invention.

Claims

1. A method for quantitative prediction of subsurface damage in silicon carbide grinding and polishing processes, implemented according to the following steps: S1. Calculate the indentation depth of a single abrasive grain based on the input parameters. The input parameters are all known parameters, including the total height of the abrasive grains on the surface of the bonded abrasive polishing pad, the hardness of the workpiece material, the Poisson's ratio of the workpiece material, the elastic modulus of the workpiece material, the fracture toughness of the workpiece material, the abrasive apex angle number participating in the polishing process, the external load, the surface density of the abrasive grains on the surface of the polishing pad, and the equivalent particle size of the abrasive grains. The S1 step specifically includes: S100, calculate the distance between the workpiece and the bottom polishing pad; The S100 step specifically includes: S101, the probability density function for calculating the height of abrasive grain protrusion; S102, Calculate the desired protrusion height of the abrasive grain; S103, calculate the normal load of a single abrasive grain acting on the workpiece surface, wherein the normal load of a single abrasive grain acting on the workpiece surface is calculated according to the definition of hardness; S104, the distance between the workpiece and the bottom polishing pad is obtained by using the probability density function of the abrasive protrusion height, the expected abrasive protrusion height, and the normal load of a single abrasive grain on the workpiece surface. S110, calculate the number of effective abrasive grains within the effective area of ​​the workpiece and the grinding pad; The S110 step specifically includes: S111, calculate the effective contact area between the workpiece and the grinding pad; S112, Calculate the total number of abrasive grains within the effective contact area between the workpiece and the grinding pad; S113 converts the total number of abrasive grains in the effective contact area between the workpiece and the grinding pad into the effective number of abrasive grains. S120, the depth of penetration of a single abrasive grain is determined by the number of effective abrasive grains within the effective area of ​​the workpiece and the grinding pad and the distance between the workpiece and the bottom polishing pad; S2, calculate the critical indentation depth of a single abrasive grain, and compare the critical indentation depth of a single abrasive grain with the indentation depth of a single abrasive grain to determine the brittle-plastic transition; S3, calculate the subsurface damage depth after the corresponding brittle-plastic transition; When plastic contact dominates, the subsurface damage depth It can be represented as: in, For calibration coefficients, The elastic recovery coefficient of the workpiece material. The contact radius between the abrasive grain and the workpiece surface is denoted as . For external loads, The hardness of the workpiece material, The surface density of the abrasive particles on the grinding pad. The effective contact area between the workpiece and the grinding pad. The distance between the workpiece and the bottom polishing pad. This refers to the total height of the abrasive grains on the surface of the bonded abrasive polishing pad. This is a coefficient, and its value ranges from 1.0 to 1.1; When brittle contact dominates, subsurface damage depth It can be represented as: in, and It is a coefficient related to the physical parameters of the workpiece material and the tip angle of the abrasive grains. The maximum height is the surface roughness parameter. It is half the tip angle of the abrasive grains involved in the polishing process. The Poisson's ratio of the workpiece material. The elastic modulus of the workpiece material. The hardness of the workpiece material, The elastic recovery coefficient of the workpiece material. This refers to the fracture toughness of the workpiece material.

2. The method for quantitative prediction of subsurface damage in silicon carbide grinding and polishing processes according to claim 1, characterized in that: If the abrasive grains have an octahedral structure, then the equivalent grain size is the diameter of a circle with the same projected area as the abrasive grains.

3. The method for quantitative prediction of subsurface damage in silicon carbide grinding and polishing processes according to claim 1, characterized in that: If the indentation depth of a single abrasive grain is less than the critical indentation depth of a single abrasive grain, the material is subjected to plastic removal; if the indentation depth of a single abrasive grain is greater than the critical indentation depth of a single abrasive grain, the material is subjected to brittle removal.

4. The method for quantitative prediction of subsurface damage in silicon carbide grinding and polishing processes according to claim 1, characterized in that: The subsurface damage depth is calculated based on different models inputted for both plastic removal and brittle removal structures.

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