A method for predicting and controlling subsurface damage depth of ultra-precision grinding of semiconductor wafers
By establishing a subsurface damage depth model based on mechanical behavior and grinding parameters, the problem of accurate prediction and control of subsurface damage depth during semiconductor wafer grinding was solved, achieving efficient and low-damage processing results.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- DALIAN UNIV OF TECH
- Filing Date
- 2025-02-25
- Publication Date
- 2026-05-19
AI Technical Summary
Existing technologies struggle to accurately predict and control the subsurface damage depth during semiconductor wafer grinding, especially under different materials and grinding conditions, where the prediction accuracy and applicability of traditional methods are insufficient.
By establishing a subsurface damage depth model based on mechanical behavior and grinding parameters, and combining the characteristics of ductile and brittle grinding, grinding process parameters are calculated, and a suitable grinding process is derived to control the damage depth.
It enables high-precision prediction and control of subsurface damage depth during semiconductor wafer grinding, improving processing efficiency and reducing damage, and is applicable to different material systems.
Smart Images
Figure CN120244708B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of semiconductor wafer processing technology, and more particularly to a method for predicting and controlling subsurface damage depth in ultra-precision grinding of semiconductor wafers. Background Technology
[0002] Grinding is a common finishing process in semiconductor wafer manufacturing. During grinding, the wafer surface and subsurface may suffer varying degrees of damage, with controlling the depth of subsurface damage being particularly crucial. Excessive subsurface damage increases the difficulty and cost of subsequent chemical mechanical polishing (CMP) and can even affect wafer performance. As semiconductor wafers evolve towards larger sizes and higher performance, traditional grinding methods are no longer sufficient to meet the stringent requirements for subsurface damage control. Therefore, the accurate prediction and control of subsurface damage depth during semiconductor wafer grinding has become a current research hotspot.
[0003] Currently, some studies have attempted to predict the subsurface damage depth during semiconductor wafer grinding, but these models neglect the mechanical properties of different materials and their relationship with grinding mechanics. For example, in Li et al.'s "Evaluation of grinding-induced subsurface damage in optical glass bk7" (Journal of Materials Processing Technology, 2016, Vol. 229, pp. 785-794) and Gao Ruizhi et al.'s "Prediction and Experimental Study of Subsurface Damage Depth in Optical Glass" (Journal of Optical Instruments, 2019, Vol. 41, No. 5, pp. 53-58), both assumed that the depth of the transverse crack was equal to the surface roughness R of the grinding surface. z This establishes the relationship between subsurface damage depth and surface roughness R. zNonlinear relationship models have been developed, but this method can only predict the damage depth in brittle domain grinding and is not applicable to ductile domain grinding. In the papers "Influence of strain rate effect on material removal and deformation mechanism based on ductile nanoscratch tests of Lu2O3 single crystal" (Ceramics International, Vol. 44, No. 17, 2018, pp. 21486-21498) by Li et al. and "Ananalytical model to predict the depth of sub-surface damage for grinding of brittle materials" (CIRP Journal of Manufacturing Science and Technology, Vol. 33, 2021, pp. 454-464) by Yin et al., the damage depth is predicted by grinding force. However, the grinding force in their studies is derived from experimental results and does not explore the underlying mechanical principles, resulting in insufficient prediction accuracy and applicability of the model. Because the above studies have not addressed the complex mechanical principles of the grinding process, accurate damage prediction and control methods remain a research challenge. Summary of the Invention
[0004] To address the aforementioned technical problems, this invention provides a method for predicting and controlling subsurface damage depth in ultra-precision grinding of semiconductor wafers. By considering the mechanical behavior, material properties, and grinding parameters during the grinding process, this invention establishes a more accurate subsurface damage prediction model and inversely calculates suitable grinding process parameters to achieve effective control of subsurface damage depth. This invention can accurately predict the subsurface damage depth during semiconductor wafer grinding and achieve precise control of the damage depth by inversely calculating grinding process parameters. This method can simultaneously achieve high-precision subsurface damage depth prediction for both ductile and brittle grinding, and can inversely solve for grinding process parameters based on the mechanical properties of different materials, improving processing efficiency and reducing damage.
[0005] The technical means employed in this invention are as follows:
[0006] A method for predicting and controlling subsurface damage depth in ultra-precision grinding of semiconductor wafers includes the following steps:
[0007] Step 1: Analyze the differences in subsurface damage depth 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 subsurface damage depth and 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 subsurface damage depth and normal force of a single abrasive grain in wafer grinding 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 abrasive depth of cut and grinding process parameters;
[0012] Step 6: Combining steps 3, 4, and 5, establish the relationship between subsurface damage depth and grinding process parameters.
[0013] Furthermore, step 6 is followed by the following steps:
[0014] Based on the model in step 6, the influence of grinding process parameters on subsurface damage depth is analyzed.
[0015] Based on the above-mentioned influence patterns, within the range of process parameters allowed for stable operation of the grinding machine, the optimal grinding wheel speed and wafer speed should be determined first, namely the maximum grinding wheel speed and the minimum wafer speed.
[0016] Substitute the required subsurface damage depth index for actual processing into the model in step 6, and inversely calculate the maximum feed rate that meets the index requirement.
[0017] The maximum grinding wheel speed, minimum wafer speed, and maximum feed rate mentioned above are used as the final optimized grinding process parameters.
[0018] Furthermore, in step 1, during the ductile grinding stage, the subsurface of the semiconductor wafer only has a plastic deformation zone with radius b, and the subsurface damage depth SSD = b at this time; during the brittle grinding stage, in addition to the plastic deformation zone with radius b, microcracks will also form on the subsurface of the semiconductor wafer, among which the median crack will initiate from below the plastic deformation zone and extend downward, causing the maximum damage depth, i.e., the median crack depth c, and the subsurface damage depth SSD = c at this time;
[0019] The critical condition for the brittle-ductile transition is b = c, which represents the critical state for the initial initiation of a median crack. Based on this, the critical depth d for the brittle-ductile 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] Where, α b and α kM All are constant coefficients, θ is the semi-cone angle of the abrasive grain, and E, H, and K are constants. c These represent 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 abrasive grain depth of cut. Using b and c from this formula, an equation is established to calculate d in step 1. c The d calculated at this point is the critical cutting depth d for the ductile-brittle transition. c .
[0023] Furthermore, in step 4, based on the principle of stress action on the wafer during grinding, the normal force on the workpiece under elastic stress and residual stress is calculated 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 These are the normal force components under elastic stress and residual stress, respectively, σ c It is the contact stress between the abrasive grains and the workpiece, A c It is the normal projected area of the contact region, σ hyd κ is the hydrostatic stress, and κ is the bulk modulus of the wafer.
[0028] Furthermore, in step 5, based on the grinding wheel motion principle of ultra-precision grinding, considering the mechanical properties of the wafer and the springback characteristics and overlap effect of the grinding wheel abrasive grains, a model relating the abrasive grain depth of cut to the grinding process parameters during wafer grinding is calculated:
[0029]
[0030] Where d is the abrasive cutting depth, r g is the average radius of the abrasive grains on the grinding wheel, f is the feed rate of the grinding wheel, and n w It is the workpiece rotational speed, n s These are the grinding wheel rotation speeds, f and n. w and n sThese 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 springback coefficient of the abrasive grain, β is the overlap coefficient of the abrasive grain, η and k are constants characterizing the distribution and concentration of the abrasive grains, D is the diameter of the grinding wheel, and W is the tooth width of the grinding wheel.
[0031] Furthermore, in step 6, combining steps 3, 4, and 5, the relationship between subsurface damage depth and grinding process parameters is established:
[0032]
[0033] Furthermore, the materials used in semiconductor wafers include single-crystal silicon, silicon carbide, gallium nitride, gallium arsenide, and aluminum nitride.
[0034] Furthermore, the relationship between subsurface damage depth and grinding process parameters described in step 6 can be used to predict the subsurface damage depth based on the grinding process parameters, or to inversely calculate and optimize the grinding process parameters to meet the processing requirements based on the subsurface damage depth index.
[0035] Compared with the prior art, the present invention has the following advantages:
[0036] 1. This invention establishes a subsurface damage depth model based on mechanical and kinematic principles, taking into account the mechanical properties of wafer materials, and therefore has universal applicability.
[0037] 2. The subsurface damage depth model established in this invention is entirely based on theoretical derivation and does not require fitting based on experimental data, thus possessing complete theoretical and scientific validity.
[0038] 3. This invention uses a subsurface damage depth model to inversely calculate grinding process parameters, which can be used to formulate grinding processes based on specific damage indicators, thereby improving processing efficiency while meeting processing requirements. Attached Figure Description
[0039] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0040] Figure 1 This is a schematic diagram of the subsurface damage depth modeling and damage control process for semiconductor materials involved in the present invention.
[0041] Figure 2 This is a schematic diagram showing the damage distribution characteristics of a semiconductor wafer after grinding.
[0042] Figure 3These are the experimental verification results of the subsurface damage depth prediction model in this invention.
[0043] Figure 4 This is a diagram illustrating the subsurface damage effect during the processing of a semiconductor wafer after controlled damage, as described in this invention. Detailed Implementation
[0044] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.
[0045] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention 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 where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.
[0046] like Figure 1 As shown in the figure, this invention discloses a method for predicting and controlling subsurface damage depth in ultra-precision grinding of semiconductor wafers, comprising the following steps:
[0047] Step 1: Analyze the difference in subsurface damage depth between ductile grinding and brittle grinding, such as... Figure 2 As shown;
[0048] Step 2: Calculate the critical cutting depth for the ductile-brittle transition;
[0049] Step 3: Establish the relationship between subsurface damage depth and 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 subsurface damage depth and normal force of a single abrasive grain in wafer grinding is obtained.
[0050] Step 4: Establish the relationship between the normal force of a single abrasive grain and the depth of cut of the abrasive grain;
[0051] Step 5: Establish the relationship between abrasive depth of cut and grinding process parameters;
[0052] Step 6: Combining steps 3, 4, and 5, establish the relationship between subsurface damage depth and grinding process parameters.
[0053] Furthermore, step 6 is followed by the following steps:
[0054] Based on the model in step 6, the influence of grinding process parameters on subsurface damage depth was analyzed. The results showed that the smaller the feed rate, the larger the grinding wheel speed, and the smaller the wafer speed, the smaller the subsurface damage depth.
[0055] Based on the above-mentioned influence patterns, within the range of process parameters allowed for stable operation of the grinding machine, the optimal grinding wheel speed and wafer speed should be determined first, namely the maximum grinding wheel speed and the minimum wafer speed.
[0056] Substitute the required subsurface damage depth index for actual processing into the model in step 6, and inversely calculate the maximum feed rate that meets the index requirement.
[0057] By using the maximum grinding wheel speed, minimum wafer speed, and maximum feed rate as the final optimized grinding process parameters, the fastest material removal rate can be achieved while controlling the damage depth.
[0058] Further, in step 1, the analysis determined that during the ductile grinding stage, the subsurface of the semiconductor wafer only has 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, microcracks will also form on the subsurface of the semiconductor wafer, among which the median crack will initiate from below the plastic deformation zone and extend downward, causing the maximum damage depth, i.e., the median crack depth c, and the subsurface damage depth SSD = c at this time;
[0059] The critical condition for the brittle-ductile transition is b = c, which represents the critical state for the initial initiation of a median crack. Based on this, the critical depth d for the brittle-ductile transition is calculated. c .
[0060] 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:
[0061]
[0062] Where, α b and α kM All are constant coefficients, θ is the semi-cone angle of the abrasive grain, and E, H, and K are constants. c These 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 abrasive grain cutting depth.
[0063] Furthermore, in step 4, based on the principle of stress action on the wafer during grinding, the normal force on the workpiece under elastic stress and residual stress is 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 These are the normal force components under elastic stress and residual stress, respectively, σ c It is the contact stress between the abrasive grains and the workpiece, A c It is the normal projected area of the contact region, σ hyd κ is the hydrostatic stress, and κ is the bulk modulus of the wafer.
[0068] In the figure, 'a' represents the half-width of the groove formed by abrasive cutting of the wafer.
[0069] Furthermore, the above formula can be written as P e =σ c A c =πHa 2 =πH(dtanθ) 2 ,
[0070] Furthermore, in step 5, based on the grinding wheel motion principle of ultra-precision grinding, considering the mechanical properties of the wafer and the springback characteristics and overlap effect of the grinding wheel abrasive grains, a model relating the abrasive grain depth of cut to the grinding process parameters during wafer grinding is calculated:
[0071]
[0072] Where d is the abrasive cutting depth, r g is the average radius of the abrasive grains on the grinding wheel, f is the feed rate of the grinding wheel, and n w It is the workpiece rotational speed, n s These are the grinding wheel rotation speeds, f and n. w and n sThese 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 springback coefficient of the abrasive grain, β is the overlap coefficient of the abrasive grain, η and k are constants characterizing the distribution and concentration of the abrasive grains, D is the diameter of the grinding wheel, and W is the tooth width of the grinding wheel.
[0073] Furthermore, in step 6, combining steps 3, 4, and 5, the relationship between subsurface damage depth and grinding process parameters is established:
[0074]
[0075] Furthermore, the materials of semiconductor wafers include, but are not limited to, single-crystal silicon, silicon carbide, gallium nitride, gallium arsenide, and aluminum nitride.
[0076] Furthermore, the normal force under the residual stress described in step 4 is obtained using a purely theoretical derivation method.
[0077] Furthermore, step 6 directly establishes a relationship between the subsurface damage depth and the grinding process parameters based on pure theoretical derivation.
[0078] Furthermore, the relationship between the subsurface damage depth and grinding process parameters mentioned in step 6 can be used to predict the subsurface damage depth based on the grinding process parameters, or to inversely calculate and optimize the grinding process parameters that meet the processing requirements based on the subsurface damage depth index.
[0079] Grinding verification experiments were conducted using four different grit sizes of grinding wheels: 325#, 600#, 1500#, and 5000#. The wheel feed rate was set at 10-30 μm / min, the wheel speed at 2399 r / min, and the wafer speed at 110 r / min. Based on step 5, the abrasive depth of cut was calculated to be 0-400 nm. The model was verified through grinding experiments. Figure 3 As shown; based on this model, a grinding process parameter optimization problem is created. By analyzing the influence of feed rate, grinding wheel speed, and wafer speed on subsurface damage depth, it is clear that the smaller the feed rate, the larger the grinding wheel speed, and the smaller the wafer speed, the smaller the subsurface damage depth. According to the allowable range of grinding machine process parameters, the optimal grinding wheel speed of 3000 r / min (machine tool stable operating range 1000~3000 r / min) and wafer speed of 100 r / min (machine tool stable operating range 100~600 r / min) are selected first. Combined with the target subsurface damage depth requirement, the corresponding maximum feed rate of 6 μm / min is calculated inversely. Finally, the optimized grinding process parameters are output. Using this optimized process, a low-damage wafer that meets the requirements is processed, such as... Figure 4 As shown. The above steps, through systematic modeling of mechanics and kinematics, theoretically achieve the optimized design of grinding process parameters, effectively controlling the subsurface damage depth while improving processing efficiency, demonstrating universality and theoretical scientific validity.
[0080] This method establishes a predictive model for subsurface damage by considering various factors such as grinding force, grinding conditions, material elastic modulus, hardness, and fracture toughness, and verifies its accuracy using experimental data. Based on this predictive model, after determining the target index for the subsurface damage depth during grinding, the subsurface damage depth is precisely controlled during grinding by back-calculating process parameters. Experimental results show that the method of this invention has high predictive accuracy in different material systems and can effectively control the damage depth of wafers after grinding by adjusting process parameters, providing a reliable theoretical basis and technical support for efficient and low-damage processing of semiconductor wafers.
[0081] The sequence numbers of the above embodiments of the present invention are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.
[0082] In the above embodiments of the present invention, the descriptions of each embodiment have different focuses. For parts not described in detail in a certain embodiment, please refer to the relevant descriptions of other embodiments.
[0083] In the several embodiments provided in this application, it should be understood that the disclosed technical content can be implemented in other ways. The device embodiments described above are merely illustrative; for example, the division of units can be a logical functional division, and in actual implementation, there may be other division methods. For instance, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the displayed or discussed mutual coupling, direct coupling, or communication connection may be through some interfaces; the indirect coupling or communication connection between units or modules may be electrical or other forms.
[0084] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.
[0085] Furthermore, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.
[0086] If the integrated unit is implemented as 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 the 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 cause a computer device (which may be a personal computer, server, or 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 capable of storing program code, such as USB flash drives, read-only memory (ROM), random access memory (RAM), portable hard drives, magnetic disks, or optical disks.
[0087] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.
Claims
1. A method for predicting and controlling subsurface damage depth in ultra-precision grinding of semiconductor wafers, characterized in that, Includes the following steps: Step 1: Analyze the differences in subsurface damage depth between ductile grinding and brittle grinding; Step 2: Calculate the critical cutting depth for the ductile-brittle transition; Step 3: Establish the relationship between subsurface damage depth and 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 subsurface damage depth and normal force of a single abrasive grain in wafer grinding is obtained. Step 4: Establish the relationship between the normal force of a single abrasive grain and the depth of cut of the abrasive grain; Step 5: Establish the relationship between abrasive depth of cut and grinding process parameters; Step 6: Combining steps 3, 4, and 5, establish the relationship between subsurface damage depth and grinding process parameters; Step 6 is followed by the following steps: Based on the model in step 6, the influence of grinding process parameters on subsurface damage depth is analyzed. Based on the above-mentioned influence patterns, within the range of process parameters allowed for stable operation of the grinding machine, the optimal grinding wheel speed and wafer speed should be determined first, namely the maximum grinding wheel speed and the minimum wafer speed. Substitute the required subsurface damage depth index for actual processing into the model in step 6, and inversely calculate the maximum feed rate that meets the index requirement. The maximum grinding wheel speed, minimum wafer speed, and maximum feed rate mentioned above are used as the final optimized grinding process parameters; 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: in, α b and α kM All are constant coefficients. θ It is the semi-cone angle of the abrasive grain. E , H , K c These are the elastic modulus, hardness, and fracture toughness of the wafer. P It is the normal force of a single abrasive grain. d For abrasive cutting depth, d c The critical cutting depth for the brittle-delay transition; In step 4, based on the principle of stress action on the wafer during grinding, the normal force on the workpiece under elastic stress and residual stress is calculated respectively: in, P e and P r These are the normal force components under elastic stress and residual stress, respectively. σ c It is the contact stress between the abrasive grains and the workpiece. A c It is the normal projected area of the contact region. σ hyd It is hydrostatic stress. κ It is the bulk modulus of the wafer; In step 5, based on the grinding wheel motion principle of ultra-precision grinding, considering the mechanical properties of the wafer and the springback characteristics and overlap effect of the grinding wheel abrasive grains, a model relating the abrasive grain depth of cut to the grinding process parameters is calculated: in, d It is the depth of cut of abrasive grains. r g It is the average radius of the abrasive grains in the grinding wheel. f It is the feed rate of the grinding wheel. n w It is the workpiece rotation speed. n s It is the grinding wheel speed. f , n w and n s Collectively referred to as grinding process parameters; r 1 is the distance from the center of the chip. θ It is the semi-cone angle of the abrasive grain. φ It is the resilience coefficient of the abrasive grains. β It is the overlap coefficient of the abrasive particles. η and k It is a constant characterizing the distribution and concentration of abrasive particles. D It is the diameter of the grinding wheel. W It refers to the width of the grinding wheel teeth.
2. The method for predicting and controlling subsurface damage depth in ultra-precision grinding of semiconductor wafers according to claim 1, characterized in that, In step 1, during the ductile grinding stage, the subsurface of the semiconductor wafer has only a plastic deformation zone with radius b, and the subsurface damage depth SSD = b. During the brittle grinding stage, in addition to the plastic deformation zone with radius b, microcracks will also form on the subsurface of the semiconductor wafer. Among them, the median crack will initiate from below the plastic deformation zone and extend downward, causing the maximum damage depth, i.e., the median crack depth c, and the subsurface damage depth SSD = c. The critical condition for the brittle-ductile transition is b = c This represents the critical state for the initial initiation of a median crack, from which the critical depth for the ductile-brittle transition can be calculated. d c .
3. The method for predicting and controlling subsurface damage depth in ultra-precision grinding of semiconductor wafers according to claim 2, characterized in that, In step 6, combining steps 3, 4, and 5, the relationship between subsurface damage depth and grinding process parameters is established: 。 4. The method for predicting and controlling subsurface damage depth in ultra-precision grinding of semiconductor wafers according to claim 1, characterized in that, Semiconductor wafers are made of materials including single-crystal silicon, silicon carbide, gallium nitride, gallium arsenide, and aluminum nitride.
5. The method for predicting and controlling subsurface damage depth in ultra-precision grinding of semiconductor wafers according to claim 1, characterized in that, The relationship between subsurface damage depth and grinding process parameters described in step 6 can both predict the subsurface damage depth based on the grinding process parameters and optimize the grinding process parameters that meet the processing requirements by back-summing based on the subsurface damage depth index.