Subsurface damage depth prediction and control method for ultra-precision grinding of semiconductor wafer

Abstract

The invention provides a subsurface damage depth prediction and control method for ultra-precision grinding of a semiconductor wafer. The method comprises the following steps that the subsurface damage depth difference of ductile grinding and brittle grinding is analyzed; calculating the critical cutting depth of ductile-brittle transition; establishing the relationship between the subsurface damage depth and the normal force of a single abrasive particle; specifically, on the basis of the relation between the normal force of a single abrasive particle and the plastic radius of a plastic deformation area in ductile grinding and the median crack depth in brittle grinding, the relation between the subsurface damage depth of wafer grinding and the normal force of the single abrasive particle is obtained in combination with ductile-brittle transformation judgment conditions; establishing the relationship between the normal force of a single abrasive particle and the cutting depth of the abrasive particle; establishing the relationship between the abrasive particle cutting depth and the grinding process parameters; and establishing the relationship between the subsurface damage depth and the grinding process parameters. According to the method, the grinding process parameters are reversely solved based on the subsurface damage depth model, the grinding process can be formulated according to specific damage indexes, and the machining efficiency is improved on the basis of meeting the machining requirements.

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 depth of subsurface damage in ultra-precision grinding of semiconductor wafers. Background Art

[0002] In the manufacturing process of semiconductor wafers, grinding is one of the common finishing processes. During the grinding process, the surface and subsurface of the wafer may be damaged to varying degrees, and in particular, the control of the depth of subsurface damage is crucial. Excessive subsurface damage will increase the processing difficulty and cost of subsequent chemical mechanical polishing, and even affect the performance of the wafer. With the development of semiconductor wafers towards larger sizes and higher performance, traditional grinding methods have been difficult to meet the strict requirements for subsurface damage control. Therefore, the accurate prediction and control of the depth of subsurface damage during the grinding process of semiconductor wafers have become a current research hotspot.

[0003] Currently, some studies have attempted to predict the depth of subsurface damage in semiconductor wafer grinding, but these models ignore the mechanical properties of different materials and their interaction with grinding mechanics. For example, in "Evaluation of grinding-induced subsurface damage in optical glass bk7" published by Li et al. (Volume 229, Pages 785 - 794, 2016, Journal of Materials Processing Technology) and "Experimental study and prediction of subsurface damage depth in optical glass" published by Gao Ruizhi et al. (Volume 41, Issue 5, Pages 53 - 58, 2019, Optical Instruments), both assume that the depth of the transverse crack is equal to the grinding surface roughness R z , thereby establishing the relationship between the depth of subsurface damage and the surface roughness R zThe non-linear relationship model, but this method can only predict the damage depth of brittle-domain grinding and is not applicable to ductile-domain grinding; in "Influence of strain rate effect on material removal and deformation mechanism based on ductile nanoscratch tests of Lu2O3 single crystal" published by Li et al. (pages 21486 - 21498, volume 44, issue 17, 2018 of Ceramics International) and "An analytical model to predict the depth of sub-surface damage for grinding of brittle materials" published by Yin et al. (pages 454 - 464, volume 33, 2021 of CIRP Journal of Manufacturing Science and Technology), the damage depth is predicted through grinding force, but the grinding force in their research is obtained by fitting test results and does not explore the underlying mechanical principles, resulting in insufficient prediction accuracy and applicability of the model. Due to the failure to solve the complex mechanical principles in the grinding process in the above research, accurate damage prediction and control methods remain research difficulties. Summary of the Invention

[0004] In view of the above-mentioned technical problems, a method for predicting and controlling the depth of subsurface damage in ultra-precision grinding of semiconductor wafers is provided. By considering the mechanical behavior, material properties, and grinding parameters during the grinding process, the present invention establishes a more accurate subsurface damage prediction model and inversely calculates appropriate grinding process parameters to effectively control the depth of subsurface damage. The present invention can accurately predict the depth of subsurface damage during the grinding process of semiconductor wafers and achieve precise control of the damage depth by reverse-deducing the grinding process parameters. This method can simultaneously achieve high-precision prediction of the depth of subsurface damage in both ductile-domain grinding and brittle-domain grinding, and can inversely solve the grinding process parameters according to the mechanical properties of different materials, improving the processing efficiency and reducing damage.

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

[0006] A method for predicting and controlling the depth of subsurface damage in ultra-precision grinding of semiconductor wafers, comprising the following steps:

[0007] Step 1: Analyze the difference in the depth of subsurface damage between ductile grinding and brittle grinding;

[0008] Step 2: Calculate the critical cutting depth for the ductile-brittle transition;

[0009] Step 3: Establish the relationship between the subsurface damage depth and the normal force of a single abrasive grain. Specifically, based on the relationship between the normal force of a single abrasive grain and the plastic radius in the plastic deformation zone during ductile grinding and the median crack depth in brittle grinding, and combining with the ductile-brittle transition determination condition, the relationship between the subsurface damage depth of wafer grinding and the normal force of a single abrasive grain is obtained.

[0010] Step 4: Establish the relationship between the normal force of a single abrasive grain and the depth of cut of the abrasive grain.

[0011] Step 5: Establish the relationship between the depth of cut of the abrasive grain and the grinding process parameters.

[0012] Step 6: Combine Step 3, Step 4, and Step 5 to establish the relationship between the subsurface damage depth and the grinding process parameters.

[0013] Furthermore, after Step 6, the following steps are also included:

[0014] Based on the model in Step 6, analyze the influence law of the grinding process parameters on the subsurface damage depth.

[0015] Based on the above influence law, within the range of process parameters allowed for 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.

[0016] Substitute the requirement of the subsurface damage depth index required for actual processing into the model in Step 6, and inversely calculate the maximum feed rate that meets the index requirements.

[0017] Take the above maximum grinding wheel speed, minimum wafer speed, and maximum feed rate as the finally optimized grinding process parameters.

[0018] Furthermore, in Step 1, 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 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, where 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, and at this time, the subsurface damage depth SSD = c.

[0019] The critical condition for the brittle-ductile transition is b = c, which represents the critical state when the median crack initially initiates, and based on this, the critical depth of cut d for the ductile-brittle transition is calculated. c 。

[0020] Furthermore, in Step 3, the relationship between the subsurface damage depth of wafer grinding and the normal force of a single abrasive grain is calculated based on the following formula:

[0021]

[0022] Among them, α b and α kM are both constant coefficients, θ is the semi-cone angle of the abrasive grain, E, H, and K c are respectively the elastic modulus, hardness, and fracture toughness of the wafer, P is the normal force of a single abrasive grain, and d is the depth of cut of the abrasive grain. Use b and c in this formula to establish an equation for calculation to obtain d in step 1 c , and the calculated d at this time is the critical depth of cut d c for ductile-brittle transition.

[0023] Furthermore, in step 4, according to the stress action principle of the wafer during the grinding process, calculate the normal forces on the workpiece under the action of elastic stress and residual stress respectively:

[0024] P e =σ c A c =πH(dtanθ) 2

[0025] P r =σ hyd πb 2 =2κd 2 tanθ

[0026] P = P e +P r =d 2 tanθ(πHtanθ + 2κ)

[0027] Among them, P e and P r are respectively the normal force components under the action of elastic stress and residual stress, σ c is the contact stress between the abrasive grain and the workpiece, A c is the normal projection area of the contact area, σ hyd is the hydrostatic stress, and κ is the bulk modulus of the wafer.

[0028] Furthermore, in step 5, according to the motion principle of the grinding wheel in ultra-precision grinding, considering the mechanical properties of the wafer, the rebound characteristics of the grinding wheel abrasive grains, and the overlapping effect, calculate the relationship model between the depth of cut of the grinding wheel abrasive grains and the grinding process parameters when the grinding wheel grinds the wafer:

[0029]

[0030] Among them, d is the depth of cut of the abrasive grain, r g is the average radius of the grinding wheel abrasive grains, f is the feed speed 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 sCollectively 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 resilience 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 width of the grinding wheel teeth.

[0031] Further, in step 6, combining steps 3, 4, and 5, establish the relationship between the subsurface damage depth and the grinding process parameters:

[0032]

[0033] Further, the material of the semiconductor wafer includes single-crystal silicon, silicon carbide, gallium nitride, gallium arsenide, and aluminum nitride.

[0034] Further, the relationship between the subsurface damage depth and the grinding process parameters described in step 6 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.

[0035] Compared with the prior art, the present invention has the following advantages:

[0036] 1. The present invention establishes a subsurface damage depth model through mechanical and kinematic principles, considering the mechanical properties of the wafer material, so it has universality.

[0037] 2. The subsurface damage depth model established by the present invention is completely based on theoretical derivation and does not require fitting based on experimental data, having complete theoretical and scientific nature.

[0038] 3. The present invention inversely calculates the grinding process parameters based on the subsurface damage depth model, and can formulate the grinding process according to specific damage indicators, improving the processing efficiency on the basis of meeting the processing requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] 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 following drawings 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.

[0040] Figure 1 It is a schematic diagram of the process for modeling the subsurface damage depth and controlling the damage of semiconductor material grinding involved in the present invention.

[0041] Figure 2 It is a schematic diagram of the damage distribution characteristics after grinding the semiconductor wafer.

[0042] Figure 3This is the test verification result of the subsurface damage depth prediction model in the present invention.

[0043] Figure 4 This is the subsurface damage effect diagram of a semiconductor wafer processed after controlling damage in the present invention. Detailed implementation manners

[0044] In order 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 of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0045] It should be noted that the terms "first", "second", etc. in the description and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects, and do not necessarily need 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 "including" and "having" and any variations thereof are intended to cover non-exclusive inclusion. For example, a process, method, system, product or device that includes a series of steps or units does not necessarily have to be 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.

[0046] As Figure 1 shown, the embodiments of the present invention disclose a method for predicting and controlling the subsurface damage depth of ultra-precision grinding of semiconductor wafers, including the following steps:

[0047] Step 1: Analyze the difference in subsurface damage depth between ductile grinding and brittle grinding, as Figure 2 shown;

[0048] Step 2: Calculate the critical cutting depth of the ductile-brittle transition;

[0049] Step 3: Establish the relationship between the subsurface damage depth and the normal force of a single abrasive grain; specifically, based on the relationship between the normal force of a single abrasive grain and the plastic radius of the plastic deformation zone in ductile grinding and the median crack depth in brittle grinding, and combining the ductile-brittle transition determination condition, obtain the relationship between the subsurface damage depth of wafer grinding and the normal force of a single abrasive grain;

[0050] Step 4: Establish the relationship between the normal force of a single abrasive grain and the cutting depth of the abrasive grain;

[0051] Step 5: Establish the relationship between the cutting depth of the abrasive grain and the grinding process parameters;

[0052] Step 6: Combine steps 3, 4 and 5 to establish the relationship between the subsurface damage depth and the grinding process parameters.

[0053] Furthermore, after step 6, the following steps are also included:

[0054] Based on the model in step 6, the influence of grinding process parameters on subsurface damage depth is analyzed; the results show that the smaller the feed speed, the greater the grinding wheel speed, and the smaller the chip speed, the smaller the subsurface damage depth.

[0055] 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;

[0056] Substitute the subsurface damage depth index required for actual machining into the model in step 6, and inversely calculate the maximum feed rate that meets the index requirement;

[0057] By taking the above-mentioned maximum grinding wheel speed, minimum wafer speed and maximum feed speed as the final optimized grinding process parameters, the fastest material removal rate can be achieved on the basis of controlling the damage depth.

[0058] Further, in step 1, it is analyzed and determined that in 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 at this time is equal to b; in 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, wherein the median crack initiates from below the plastic deformation zone and extends downward, resulting in the maximum damage depth, i.e., the median crack depth c, and the subsurface damage depth SSD at this time is equal to c;

[0059] The critical condition of brittle-ductile transition is b=c, which indicates the critical state of initial initiation of median crack. Based on this, the critical cutting depth d of ductile-brittle transition is calculated. c .

[0060] Further, in step 3, the relationship between the subsurface damage depth of wafer grinding and the normal force of a single abrasive grain is calculated based on the following formula:

[0061]

[0062] Among them, α b and α kM are all constant coefficients, θ is the semi-cone angle of the abrasive grain, E, H, K c are the elastic modulus, hardness and fracture toughness of the wafer, P is the normal force of a single abrasive grain, and d is the cutting depth of the abrasive grain.

[0063] Further, in step 4, according to the stress action principle of the wafer during the grinding process, the normal forces on the workpiece under the action of elastic stress and residual stress are calculated respectively:

[0064] P e =σ c A c =πH(dtanθ) 2

[0065] P r =σ hyd πb 2 =2κd 2 tanθ

[0066] P = P e +P r =d 2 tanθ(πHtanθ + 2κ)

[0067] Among them, P e and P r are the normal force components under the action of elastic stress and residual stress respectively, σ c is the contact stress between the abrasive grain and the workpiece, A c is the normal projection area of the contact region, σ hyd is the hydrostatic stress, and κ is the bulk modulus of the wafer.

[0068] In the figure, a is the half-width of the groove formed by the abrasive grain cutting the wafer.

[0069] Further, the above formula can be written as P e =σ c A c =πHa 2 =πH(dtanθ) 2 ,

[0070] Further, in step 5, according to the motion principle of the grinding wheel in ultra-precision grinding, considering the mechanical properties of the wafer, the springback characteristics and overlapping effect of the grinding wheel abrasive grains, a relationship model between the abrasive grain cutting depth and the grinding process parameters when the grinding wheel grinds the wafer is calculated:

[0071]

[0072] Among them, d is the abrasive grain cutting depth, r g is the average radius of the grinding wheel abrasive grains, f is the feed speed of the grinding wheel, n w is the workpiece rotation speed, n s is the grinding wheel rotation speed, f, n w and n sThey 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 resilience coefficient of the abrasive grain, β is the overlapping 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 width of the grinding wheel teeth.

[0073] Further, in step 6, combining steps 3, 4, and 5, establish the relationship between the subsurface damage depth and the grinding process parameters:

[0074]

[0075] Further, the material of the semiconductor wafer includes but is not limited to single crystal silicon, silicon carbide, gallium nitride, gallium arsenide, and aluminum nitride.

[0076] Further, the normal force under the residual stress described in step 4 is obtained by a pure theoretical derivation method.

[0077] Further, step 6 directly establishes a relationship between the subsurface damage depth and the grinding process parameters based on pure theoretical derivation.

[0078] Further, the relationship between the subsurface damage depth and the grinding process parameters described in step 6 can not only predict the subsurface damage depth according to 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.

[0079] Carry out grinding verification tests using 4 different grit grinding wheels such as 325#, 600#, 1500#, and 5000#. In the test, set the grinding wheel feed speed at 10 - 30 μm / min, the grinding wheel rotation speed at 2399 r / min, and the wafer rotation speed at 110 r / min. Calculate the cutting depth of the abrasive grains at 0 - 400 nm based on step 5, and verify this model through the grinding test, as Figure 3 shown; based on this model, create an optimization problem for the grinding process parameters. By analyzing the influence of the feed speed, grinding wheel rotation speed, and wafer rotation speed on the subsurface damage depth, it is clear that the smaller the feed speed, the larger the grinding wheel rotation speed, and the smaller the wafer rotation speed, the smaller the subsurface damage depth; according to the allowable range of the grinding machine process parameters, preferentially select the optimal grinding wheel rotation speed of 3000 r / min (the stable operating range of the machine tool is 1000 - 3000 r / min) and the wafer rotation speed of 100 r / min (the stable operating range of the machine tool is 100 - 600 r / min), and combined with the required target subsurface damage depth, inversely calculate the corresponding maximum feed speed of 6 μm / min. Finally, output the optimized grinding process parameters, and use this optimized process to process low-damage wafers that meet the requirements, as Figure 4 shown. The above steps realize the optimized design of the grinding process parameters theoretically through systematic modeling of mechanics and kinematics, can effectively control the subsurface damage depth, and improve the processing efficiency at the same time, with universality and theoretical scientificity.

[0080] By considering various factors such as grinding force, grinding conditions, elastic modulus, hardness, fracture toughness of the material, etc., a prediction model of subsurface damage is established, and its accuracy is verified by combining experimental data. According to this prediction model, after determining the target index of the subsurface damage depth in grinding, the process parameters are inversely deduced to accurately control the subsurface damage depth during the grinding process. The experimental results show that the method of the present invention has high prediction accuracy under different material systems, and can effectively control the damage depth of the wafer after grinding by adjusting the process parameters, providing a reliable theoretical basis and technical support for the efficient and low-damage processing of semiconductor wafers.

[0081] The serial numbers of the above embodiments of the present invention are only for description and do not represent the advantages and disadvantages of the embodiments.

[0082] 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 may be made to the relevant descriptions of other embodiments.

[0083] 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 the units or modules can be in an electrical or other form.

[0084] 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.

[0085] In addition, the functional units in each embodiment of the present invention 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.

[0086] When the 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 such an understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes: various media such as USB flash drives, read-only memories (ROMs), random access memories (RAMs), mobile hard disks, magnetic disks, or optical discs that can store program codes.

[0087] 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 various embodiments of the present invention.

Claims

1. A method for predicting and controlling the subsurface damage depth in ultra-precision grinding of semiconductor wafers, characterized in that, The steps include: Step 1: Analyze the difference in subsurface damage depth between ductile grinding and brittle grinding; Step 2, calculate the critical cutting depth of ductile-brittle transition; Step 3, establishing the relationship between the subsurface damage depth and the normal force of a single abrasive grain; specifically, based on the relationship between the normal force of a single abrasive grain and the plastic radius of the plastic deformation zone in ductile grinding and the median crack depth in brittle grinding, combined with the ductile-brittle transition judgment condition, the relationship between the subsurface damage depth of wafer grinding and the normal force of a single abrasive grain is obtained; Step 4, establishing the relationship between the normal force of a single abrasive grain and the cutting depth of the abrasive grain; Step 5, establishing the relationship between the abrasive cutting depth and the grinding process parameters; Step 6: Combine steps 3, 4 and 5 to establish the relationship between the subsurface damage depth and the grinding process parameters.

2. The method for predicting and controlling the subsurface damage depth of ultra-precision grinding of semiconductor wafers according to claim 1, characterized in that, After step 6, the following steps are also included: Based on the model in step 6, the influence of grinding process parameters on subsurface damage depth is analyzed; 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; Substitute the subsurface damage depth index required for actual machining into the model in step 6, and inversely calculate the maximum feed rate that meets the index requirement; The above-mentioned maximum grinding wheel speed, minimum wafer speed and maximum feed speed are taken as the final optimized grinding process parameters.

3. The method for predicting and controlling the subsurface damage depth of ultra-precision grinding of semiconductor wafers according to claim 1, wherein, In step 1, 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 the brittle-ductile transition is b = c, which represents the critical state of the initial initiation of the median crack. Based on this, the critical cutting depth d for the ductile-brittle transition is calculated c .

4. The method for predicting and controlling the subsurface damage depth in ultra-precision grinding of semiconductor wafers according to claim 1, characterized in that, In step 3, the relationship between the subsurface damage depth of wafer grinding and the normal force of a single abrasive grain is calculated based on the following formula: where α b and α kM are both constant coefficients, θ is the semi-cone angle of the abrasive grain, E, H, K c are the elastic modulus, hardness and fracture toughness of the wafer respectively, P is the normal force of a single abrasive grain, and d is the depth of cut of the abrasive grain.

5. The method for predicting and controlling the subsurface damage depth of ultra-precision grinding of semiconductor wafers according to claim 1, wherein In step 4, according to the stress action principle of the wafer during the grinding process, the normal force on the workpiece under the action of elastic stress and residual stress is calculated respectively: P e = σ c A c = πH(d tan θ) 2 P r = σ hyd πb 2 = 2κd 2 tanθ P = P e + P r = d 2 tanθ(πHtanθ + 2κ) where, P e and P r are the normal force components under elastic stress and residual stress respectively, σ c is the contact stress between the abrasive grain and the workpiece, A c is the normal projection area of the contact region, σ hyd is the hydrostatic stress, and κ is the bulk modulus of the wafer.

6. The method for predicting and controlling the subsurface damage depth in ultra-precision grinding of semiconductor wafers according to claim 1, wherein, In step 5, 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 workpiece rotational speed, n s is the grinding wheel rotational 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 resilience 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 grinding wheel diameter, and W is the grinding wheel tooth width.

7. The method for predicting and controlling the subsurface damage depth of ultra-precision grinding of semiconductor wafers according to claim 1, wherein In step 6, combining steps 3, 4, and 5, the relationship between subsurface damage depth and grinding process parameters is established:

8. The method for predicting and controlling the subsurface damage depth in ultra-precision grinding of semiconductor wafers according to claim 1, wherein The materials of the semiconductor wafer include but are not limited to single crystal silicon, silicon carbide, gallium nitride, gallium arsenide, and aluminum nitride.

9. The method for predicting and controlling the subsurface damage depth of ultra-precision grinding of semiconductor wafers according to claim 1, characterized in that, The relationship between the subsurface damage depth and the grinding process parameters described in step 6 can be used to predict the subsurface damage depth based on the grinding process parameters, and can also be used to inversely calculate and optimize the grinding process parameters that meet the processing requirements based on the subsurface damage depth index.

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