Surface roughness prediction and control method for ultra-precision grinding of semiconductor wafer

Abstract

The invention provides a surface roughness prediction and control method for ultra-precision grinding of a semiconductor wafer. The method comprises the following steps: step 1, calculating to obtain a relation model between abrasive particle cutting depth and grinding process parameters when a grinding wheel grinds a wafer; 2, calculating the critical cutting depth of ductile-brittle transition; 3, calculating the cross sectional area of the wafer cut by the abrasive particles; step 4, calculating a key coefficient of the abrasive particle protrusion height distribution function; 5, calculating the influence of the elastic recovery characteristic of the wafer; step 6, calculating an elastic recovery coefficient of the wafer; and step 7, establishing a surface roughness model considering elastic recovery. According to the method, mechanical properties and elastic recovery characteristics of different materials are considered, and the method has universality. According to the method, the grinding process parameters are reversely solved based on the surface roughness model, the grinding process can be formulated according to the specific surface roughness index, and the machining efficiency is improved on the basis of meeting the machining requirement.

Description

Technical Field

[0001] The present invention relates to the technical field of semiconductor wafer processing, and more particularly, to a method for predicting and controlling the surface roughness of ultra-precision grinding of semiconductor wafers. Background Art

[0002] In the manufacturing process of semiconductor wafers, ultra-precision grinding based on the principle of workpiece rotation is one of the common finishing processes. During the grinding process, the surface layer of the wafer will be damaged to varying degrees, and in particular, the control of the subsurface damage depth is crucial. Surface roughness is an important indicator for evaluating the quality of the grinding surface. Accurately predicting and controlling the surface roughness of the wafer after grinding can significantly improve processing efficiency and reduce production costs.

[0003] Currently, the research on the prediction of grinding surface roughness mainly includes two types: one is the empirical fitting model based on experimental data, and the other is the analytical model based on the grinding motion and removal principle. The former requires a large amount of experimental data as support, which is extremely costly and lacks a scientific theoretical basis, resulting in low credibility of the prediction results. The latter has a relatively complete scientific theory as support, but does not consider the mechanical properties of the processed semiconductor wafer, and the calculation of some key parameters is difficult, resulting in insufficient reliability and universality of the model prediction. For example, in "Nanomechanical characterization of RB-SiC ceramics based on nanoindentation and modelling of the ground surface roughness" published by Zhang et al. (pages 6243-6253, volume 46, issue 5, 2020 of the journal Ceramics International), the ductile grinding and brittle grinding modes are divided according to the surface topography of the ground RB-SiC, but this method is only applicable to surface grinding and not applicable to workpiece rotation grinding; in "Prediction of subsurface damage depth of silicon wafers ground by the workpiece rotation method" published by Gao Shang et al. (pages 2077-2087, volume 30, issue 17, 2022 of the journal Optics and Precision Engineering), a prediction model for the surface roughness of silicon wafers is established based on the kinematic principle and material removal mechanism of workpiece rotation grinding. This model considers the random distribution characteristics of the grinding wheel abrasive grains, but the calculation of the key coefficient in the probability density function of the abrasive grain distribution is approximated. Moreover, the above studies do not consider the elastic recovery characteristics of the material in the grinding area after grinding. Due to the lack of solution to the calculation of the key coefficient of abrasive grain distribution and the unclear influence mechanism of elastic recovery on surface roughness, accurately predicting and controlling surface roughness remains a research difficulty. Summary of the Invention

[0004] According to the above-mentioned technical problems, the present invention provides a method for predicting and controlling the surface roughness of ultra-precision grinding of semiconductor wafers. The present invention fully considers the random distribution characteristics of abrasive grains and the elastic recovery characteristics of wafer materials, can accurately predict the surface roughness of the ground semiconductor wafer, and realizes the precise control of the surface roughness by inverse-solving the grinding process parameters. By considering the grinding kinematics principle, material removal mechanism, abrasive grain distribution characteristics and wafer material rebound characteristics, the present invention establishes a more accurate surface roughness prediction model and inverse-solves appropriate grinding process parameters to achieve precise control of the surface roughness.

[0005] The technical means adopted by the present invention are as follows:

[0006] A method for predicting and controlling the surface roughness of ultra-precision grinding of semiconductor wafers, comprising the following steps:

[0007] Step 1, calculate the relationship model between the abrasive grain depth of cut and the grinding process parameters when the grinding wheel grinds the wafer;

[0008] Step 2, calculate the critical depth of cut for ductile-brittle transition;

[0009] Step 3, calculate the cross-sectional area of the abrasive grain cutting the wafer;

[0010] Step 4, calculate the key coefficient of the abrasive grain protrusion height distribution function;

[0011] Step 5, calculate the influence of the elastic recovery characteristics of the wafer;

[0012] Step 6, calculate the elastic recovery coefficient of the wafer;

[0013] Step 7, establish a surface roughness model considering elastic recovery.

[0014] Furthermore, after step 7, the following steps are further included:

[0015] Based on the model in step 7, analyze the influence law of the grinding process parameters on the surface roughness;

[0016] Based on the above influence law, within the process parameter range allowed by the stable operation of the grinding machine, preferentially determine the optimal grinding wheel speed and wafer speed, that is, the maximum grinding wheel speed and the minimum wafer speed;

[0017] Substitute the surface roughness index requirements required for actual processing into the model in step 7, and inverse-solve the maximum abrasive grain depth of cut that meets the index requirements; substitute the abrasive grain depth of cut into step 1, and on the basis of the selected grinding wheel speed and wafer speed, inverse-solve the maximum feed rate that meets the index requirements.

[0018] Take the above maximum feed rate, grinding wheel speed and wafer speed as the finally optimized grinding process parameters.

[0019] Further, in Step 1, based on the grinding wheel motion principle of ultra-precision grinding, considering the mechanical properties of the wafer, the rebound characteristics and overlapping effect of the grinding wheel grains, a relationship model between the grain depth of cut and the grinding process parameters when the grinding wheel grinds the wafer is calculated:

[0020]

[0021] where d is the grain depth of cut, r g is the average radius of the grinding wheel grains, f is the feed rate of the grinding wheel, n w is the workpiece rotation speed, n s is the grinding wheel rotation speed, f, n w and n s collectively are called grinding process parameters; r1 is the distance from the center on the wafer, θ is the half-cone angle of the grain, φ is the grain rebound coefficient, β is the grain overlapping coefficient, η and k are constants characterizing the grain distribution characteristics and concentration, D is the grinding wheel diameter, and W is the grinding wheel tooth width.

[0022] Further, in Step 2, during the ductile grinding stage, there is only a plastic deformation zone with a radius of b on the subsurface of the semiconductor wafer. At this time, the subsurface damage depth SSD = b; during the brittle grinding stage, in addition to the plastic deformation zone with a radius of b on the subsurface of the semiconductor wafer, microcracks will also be formed. Among them, the median crack initiates from below the plastic deformation zone and propagates downward, causing the maximum damage depth, that is, the median crack depth c. At this time, the subsurface damage depth SSD = c;

[0023] The critical condition for brittle-ductile transition is b = c, which represents the critical state of the initial initiation of the median crack. Based on this, the critical depth of cut d for brittle-ductile transition is calculated c :

[0024]

[0025] where α b and α kM are both constant coefficients, and E, H, κ, K c are the elastic modulus, hardness, bulk modulus, and fracture toughness of the wafer, respectively.

[0026] Further, in Step 3, based on the conical geometric characteristics of the grain, the cross-sectional area A of the grain cutting the wafer is calculated w :

[0027]

[0028] where r g is the grain size.

[0029] Further, in step 4, the protrusion height h of the grinding wheel grains follows the following Rayleigh distribution:

[0030]

[0031] where σ is the Rayleigh distribution coefficient;

[0032] Calculate the mathematical statistics definition of E(h 2 ) in the Rayleigh distribution and the geometric meaning in the cross-sectional area of the grain cutting the wafer, and establish an equation between the two to calculate σ. E(h 2 ) is the mathematical expectation of h 2 :

[0033]

[0034] where A w is the cross-sectional area of the grain cutting the wafer.

[0035] Further, in step 5, the elastic recovery of the wafer after grinding will be manifested in the following three aspects: the residual grain cutting depth d' is less than the grain cutting depth d during grinding, the observed critical ductile-brittle transition cutting depth d c ’ is less than the critical ductile-brittle transition cutting depth d during grinding c , and the Rayleigh distribution parameter σ related to the grain cutting depth also changes. Specifically:

[0036] d' = (1 - λ)d

[0037] d c ' = (1 - λ)d c

[0038]

[0039] where γ is the elastic recovery rate of the wafer after grinding.

[0040] Further, in step 6, based on the contact mechanics principle of the grain cutting the wafer, calculate the elastic recovery coefficient λ of different wafers:

[0041]

[0042] where h is the indentation depth, h r is the residual depth, E r is the contact modulus, σ u is the yield strength of the wafer material, and ε is the indenter shape coefficient.

[0043] Further, in step 7, according to the definition of the roughness Ra and the stage division of grinding ductile-brittle, a surface roughness model considering elastic recovery is finally established:

[0044]

[0045] Furthermore, the material of the semiconductor wafer includes, but is not limited to, single crystal silicon, silicon carbide, gallium nitride, gallium arsenide, and aluminum nitride.

[0046] Furthermore, the surface roughness model described in step 7 uses the abrasive cutting depth as an intermediate variable to establish the relationship between the grinding process parameters and the surface roughness. It can not only predict the subsurface damage depth based on the grinding process parameters, but also inversely calculate and optimize the grinding process parameters that meet the processing requirements according to the subsurface damage depth index.

[0047] Compared with the prior art, the present invention has the following advantages:

[0048] 1. The present invention takes into account the mechanical properties and elastic recovery characteristics of different materials and has universality.

[0049] 2. The surface roughness model established by the present invention is completely based on theoretical derivation and does not require fitting based on experimental data, having complete theoreticality and scientificity.

[0050] 3. The present invention inversely calculates the grinding process parameters based on the surface roughness model and can formulate the grinding process according to specific surface roughness indexes, improving the processing efficiency on the basis of meeting the processing requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0052] Figure 1 It is a schematic diagram of the process for predicting and controlling the grinding surface roughness of the semiconductor material involved in the present invention.

[0053] Figure 2 It is a schematic diagram of the damage distribution characteristics after grinding the semiconductor wafer.

[0054] Figure 3 It is the test verification result of the surface roughness prediction model in the present invention.

[0055] Figure 4 It is the surface roughness effect diagram of the processing of a certain semiconductor wafer after control in the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0056] To enable those skilled in the art to better understand the solution of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0057] It should be noted that the terms "first", "second", etc. in the specification and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged under appropriate circumstances so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "comprising" and "having" and any variations thereof are intended to cover non-exclusive inclusion. For example, a process, method, system, product or device comprising a series of steps or units is not necessarily limited to those steps or units clearly listed, but may include other steps or units not clearly listed or inherent to these processes, methods, products or devices.

[0058] As Figure 1 shown, an embodiment of the present invention discloses a method for predicting and controlling the surface roughness of ultra-precision grinding of semiconductor wafers, which includes the following steps:

[0059] Step 1: Calculate the relationship model between the grain depth of cut and the grinding process parameters when the grinding wheel grinds the wafer;

[0060] Step 2: Calculate the critical depth of cut for ductile-brittle transition;

[0061] Step 3: Calculate the cross-sectional area of the grain cutting the wafer;

[0062] Step 4: Calculate the key coefficient of the grain protrusion height distribution function;

[0063] Step 5: Calculate the influence of the elastic recovery characteristics of the wafer;

[0064] Step 6: Calculate the elastic recovery coefficient of the wafer;

[0065] Step 7: Establish a surface roughness model considering elastic recovery.

[0066] Further, after step 7, the following steps are further included:

[0067] Based on the model in step 7, analyze the influence law of the grinding process parameters on the surface roughness;

[0068] Based on the above influence rules, within the process parameter range allowed for the stable operation of the grinding machine, the optimal grinding wheel speed and wafer speed are preferentially determined, that is, the maximum grinding wheel speed and the minimum wafer speed;

[0069] Substitute the surface roughness index requirements required for actual processing into the model in step 7 to inversely calculate the maximum abrasive grain depth of cut that meets the index requirements; substitute this abrasive grain depth of cut into step 1, and based on the selected grinding wheel speed and wafer speed, inversely calculate the maximum feed rate that meets the index requirements.

[0070] Take the above maximum feed rate, grinding wheel speed, and wafer speed as the finally optimized grinding process parameters.

[0071] Furthermore, in step 1, according to the grinding wheel motion principle of ultra-precision grinding, considering the mechanical properties of the wafer, the rebound characteristics and overlapping effect of the grinding wheel abrasive grains, a relationship model between the abrasive grain depth of cut when the grinding wheel grinds the wafer and the grinding process parameters is calculated:

[0072]

[0073] where d is the abrasive grain depth of cut, r g is the average radius of the grinding wheel abrasive grains, f is the feed rate of the grinding wheel, n w is the workpiece speed, n s is the grinding wheel speed, f, n w and n s are collectively referred to as grinding process parameters; r1 is the distance from the center on the wafer, θ is the half-cone angle of the abrasive grain, φ is the rebound coefficient of the abrasive grain, β is the overlapping coefficient of the abrasive grain, η and k are constants characterizing the abrasive grain distribution characteristics and concentration, D is the grinding wheel diameter, and W is the grinding wheel tooth width.

[0074] Furthermore, as Figure 2 shown, in step 2, during the ductile grinding stage, there is only a plastic deformation zone with a radius of b on the subsurface of the semiconductor wafer, and the subsurface damage depth SSD = b at this time; during the brittle grinding stage, in addition to the plastic deformation zone with a radius of b on the subsurface of the semiconductor wafer, microcracks will also be formed. Among them, the median crack initiates from below the plastic deformation zone and propagates downward, causing the maximum damage depth, that is, the median crack depth c. At this time, the subsurface damage depth SSD = c;

[0075] The critical condition for brittle-ductile transition is b = c, which represents the critical state of the initial initiation of the median crack. Based on this, the critical depth of cut d c for brittle-ductile transition is calculated as follows:

[0076]

[0077] where α b and α kMThey are all constant coefficients, E, H, κ, K c are the elastic modulus, hardness, bulk modulus and fracture toughness of the wafer, respectively.

[0078] By establishing the relationship between the radius of the plastic deformation zone and the median crack depth, the critical cutting depth of the ductile-brittle transition is calculated, providing a theoretical basis for the critical point between ductile machining and brittle machining.

[0079] Furthermore, in step 3, based on the conical geometric characteristics of the abrasive grains, the cross-sectional area A of the abrasive grains cutting the wafer is calculated w :

[0080]

[0081] Furthermore, in step 4, the protrusion height h of the grinding wheel abrasive grains follows the following Rayleigh distribution:

[0082]

[0083] where σ is the Rayleigh distribution coefficient;

[0084] Calculate the mathematical statistics definition of E(h 2 ) in the Rayleigh distribution and its geometric meaning in the cross-sectional area of the abrasive grains cutting the wafer, and establish an equation between the two to calculate σ:

[0085]

[0086] Based on the above formula, accurately describe the abrasive grain distribution characteristics.

[0087] Furthermore, in step 5, the elastic recovery of the wafer after grinding will be manifested in the following three aspects: the residual abrasive grain cutting depth d' is less than the abrasive grain cutting depth d during grinding, and the observed critical cutting depth d c ' of the ductile-brittle transition is less than the critical cutting depth d of the ductile-brittle transition during grinding c , and the Rayleigh distribution parameter σ, which is related to the abrasive grain cutting depth, also changes. Specifically:

[0088] d'=(1 - λ)d

[0089] d c '=(1 - λ)d c

[0090]

[0091] Furthermore, in step 6, based on the contact mechanics principle of the abrasive grains cutting the wafer, calculate the elastic recovery coefficient λ of different wafers:

[0092]

[0093] where h is the indentation depth, and h r is the residual depth, E r is the contact modulus, σ u is the yield strength of the wafer material, and ε is the indenter shape factor.

[0094] Considering the influence of wafer elastic recovery on the residual abrasive cutting depth, the critical cutting depth of ductile-brittle transition, and the Rayleigh distribution parameter, the elastic recovery coefficient of different wafer materials is calculated through contact mechanics theory, a surface roughness model containing elastic recovery characteristics is constructed, and the accuracy of the model is verified through experiments, as Figure 3 shown.

[0095] Furthermore, in step 7, according to the definition of roughness Ra and the stage division of grinding ductility-brittle, a surface roughness model considering elastic recovery is finally established:

[0096]

[0097] Furthermore, the materials of the semiconductor wafer include single crystal silicon, silicon carbide, gallium nitride, gallium arsenide, and aluminum nitride.

[0098] The exact solution of the Rayleigh distribution coefficient described in step 4 obtained through pure theoretical derivation method not only satisfies the mathematical definition of this coefficient but also conforms to the physical meaning of actual processing.

[0099] The elastic recovery coefficient described in step 5 has an impact on the observed values of the abrasive cutting depth, the critical cutting depth of ductile-brittle transition, and the Rayleigh distribution coefficient.

[0100] Furthermore, the surface roughness model described in step 7 takes the abrasive cutting depth as an intermediate variable to establish the relationship between grinding process parameters and surface roughness. It can not only predict the subsurface damage depth based on grinding process parameters but also inversely calculate and optimize the grinding process parameters that meet the processing requirements according to the subsurface damage depth index.

[0101] Based on the surface roughness model established from step 1 to step 7, the influence rules of grinding process parameters (feed rate, grinding wheel speed, wafer speed) on surface roughness are analyzed. The results show that the following rules are satisfied: the smaller the feed rate, the larger the grinding wheel speed, and the smaller the wafer speed, the smaller the surface roughness.

[0102] Analyze the influence rules of grinding process parameters on surface roughness, and substitute the requirements of the actual processed surface roughness index into the surface roughness model to inversely calculate the optimal grinding process parameters that meet the processing requirements, maximizing the processing efficiency while ensuring the processing quality; finally, use the feed rate, grinding wheel speed, and wafer speed based on the optimization results as the final grinding process parameters, thereby achieving precise control of surface roughness, and the final processing effect is as Figure 4As shown in the figure. The method of the present invention takes into account both the mechanical properties and elastic recovery characteristics of the wafer, making it have good adaptability and universality. At the same time, a complete prediction model is established through theoretical derivation, avoiding the limitations of experimental data fitting and effectively optimizing the processing efficiency.

[0103] In the above embodiments of the present invention, the descriptions of each embodiment have their own emphases. For the parts not detailed in a certain embodiment, reference can be made to the relevant descriptions of other embodiments.

[0104] In the several embodiments provided by the present application, it should be understood that the disclosed technical content can be implemented in other ways. Among them, the device embodiments described above are only illustrative. For example, the division of the units can be a logical function division. In actual implementation, there can be other division methods. For example, multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the displayed or discussed coupling or direct coupling or communication connection between each other can be through some interfaces. The indirect coupling or communication connection of units or modules can be in an electrical or other form.

[0105] The units described as separate components may or may not be physically separated. The components displayed as units may or may not be physical units, that is, they can be located in one place or distributed to multiple units. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0106] In addition, in each embodiment of the present invention, the functional units can be integrated in a processing unit, or each unit can exist physically alone, or two or more units can be integrated in one unit. The above integrated units can be implemented in the form of hardware or in the form of software functional units.

[0107] If the above integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of this technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to enable a computer device (which can be a personal computer, a server or a network device, etc.) to execute all or part of the steps of the methods described in each embodiment of the present invention. And the foregoing storage medium includes: USB flash drives, read-only memories (ROM, Read-Only Memory), random access memories (RAM, Random Access Memory), mobile hard disks, magnetic disks or optical disks and other various media that can store program codes.

[0108] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for predicting and controlling the surface roughness of ultra-precision grinding of semiconductor wafers, characterized in that The following steps are involved: Step 1, calculating and obtaining the relationship model between the abrasive cutting depth and the grinding process parameters when the grinding wheel grinds the wafer; Step 2, calculate the critical cutting depth of ductile-brittle transition; Step 3, calculating the cross-sectional area of ​​the abrasive-cut wafer; Step 4, calculating the key coefficient of the wear particle protrusion height distribution function; Step 5, calculating the influence of the elastic recovery characteristics of the wafer; Step 6, calculating the elastic recovery coefficient of the wafer; Step 7: Establish a surface roughness model considering elastic recovery.

2. The surface roughness prediction and control method for ultra-precision grinding of semiconductor wafers according to claim 1, characterized in that, After step 7, the following steps are also included: Based on the model in step 7, analyze the influence of grinding process parameters on surface roughness; Based on the above influence rules, within the process parameter range allowed for stable operation of the grinder, the optimal grinding wheel speed and wafer speed are preferentially determined, i.e., the maximum grinding wheel speed and the minimum wafer speed; The surface roughness index required for actual processing is brought into the model of step 7 to inversely calculate the maximum abrasive cutting depth that meets the index requirements; the abrasive cutting depth is brought into step 1, and on the basis of the selected grinding wheel speed and chip speed, the maximum feed speed that meets the index requirements is inversely calculated; the above-mentioned maximum feed speed, grinding wheel speed, and chip speed are used as the final optimized grinding process parameters.

3. The surface roughness prediction and control method for ultra-precision grinding of semiconductor wafers according to claim 1, wherein In step 1, according to the grinding wheel motion principle of ultra-precision grinding, the mechanical properties of the wafer, the rebound characteristics of the grinding wheel abrasive grains and the overlapping effect are considered, and the relationship model between the abrasive grain cutting depth and the grinding process parameters when the grinding wheel grinds the wafer is calculated: Among them, d is the cutting depth of the abrasive grain, r g is the average radius of the grinding wheel abrasive grain, f is the feed rate of the grinding wheel, n w is the rotational speed of the workpiece, n s is the rotational speed of the grinding wheel, f, n w and n s are collectively referred to as grinding process parameters; r1 is the distance from the center on the wafer, θ is the semi-cone angle of the abrasive grain, φ is the rebound coefficient of the abrasive grain, β is the overlap coefficient of the abrasive grains, η and k are constants characterizing the distribution characteristics and concentration of the abrasive grains, D is the diameter of the grinding wheel, and W is the tooth width of the grinding wheel.

4. The surface roughness prediction and control method for ultra-precision grinding of semiconductor wafers according to claim 3, characterized in that In step 2, during the ductile grinding stage, the subsurface of the semiconductor wafer has only a plastic deformation zone with a radius of b, and the subsurface damage depth SSD=b at this time; during the brittle grinding stage, in addition to the plastic deformation zone with a radius of b, the subsurface of the semiconductor wafer will also form microcracks, among which the median crack initiates from below the plastic deformation zone and extends downward, resulting in the maximum damage depth, that is, the median crack depth c, and the subsurface damage depth SSD=c at this time; The critical condition for brittle-ductile transition is b = c, which represents the critical state of the initial initiation of median cracks. Based on this, the critical cutting depth d for brittle-ductile transition is calculated. c : where α b and α kM are both constant coefficients, and E, H, κ, K c are the elastic modulus, hardness, bulk modulus, and fracture toughness of the wafer, respectively.

5. The surface roughness prediction and control method for ultra-precision grinding of semiconductor wafers according to claim 4, characterized in that: In step 3, calculate the cross-sectional area A of the abrasive grain cutting the wafer based on the conical geometric feature of the abrasive grain w :

6. The surface roughness prediction and control method for ultra-precision grinding of semiconductor wafers according to claim 5, characterized in that In step 4, the protrusion height h of the grinding wheel abrasive grains obeys the following Rayleigh distribution: Where σ is the Rayleigh distribution coefficient; Calculate E(h 2 ) in the mathematical statistics definition of the Rayleigh distribution and the geometric meaning in the cross-sectional area of abrasive grains cutting wafers, and establish an equation between the two to calculate σ:

7. The method for predicting and controlling the surface roughness of ultra-precision grinding of semiconductor wafers according to claim 6, characterized in that, In Step 5, the elastic recovery of the wafer after grinding is manifested in the following three aspects: the residual abrasive depth of cut d' is less than the abrasive depth of cut d during grinding, and the observed critical depth of cut d c ’ for ductile-brittle transition is less than the critical depth of cut d for ductile-brittle transition during grinding c , and the Rayleigh distribution parameter σ, which is related to the abrasive depth of cut, also changes. Specifically: d'=(1-λ)d d c d' = (1 - λ)d c 8. The surface roughness prediction and control method for ultra-precision grinding of semiconductor wafers according to claim 7, characterized in that In step 6, based on the contact mechanics principle of abrasive-cut wafers, the elastic recovery coefficient λ of different wafers is calculated: Among them, h is the indentation depth, h r is the residual depth, E r is the contact modulus, σ u is the yield strength of the wafer material, and ε is the indenter shape factor.

9. The surface roughness prediction and control method for ultra-precision grinding of semiconductor wafers according to claim 8, characterized in that, In step 7, based on the definition of roughness Ra and the stage division of grinding ductility-brittleness, a surface roughness model considering elastic recovery was finally established:

10. The surface roughness prediction and control method for ultra-precision grinding of semiconductor wafers according to claim 1, characterized in that The materials of the semiconductor wafer include but are not limited to single crystal silicon, silicon carbide, gallium nitride, gallium arsenide, and aluminum nitride.

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