A method for controlling the surface shape of a laser crystal wafer by ultra-precision grinding

Abstract

The present application relates to a kind of face shape regulation and control methods of laser crystal wafer ultra-precision grinding, comprising the following steps: according to grinding surface quality, determine the grinding process parameters in preset range;By the contact state of abrasive particle and wafer, determine the grinding force of single abrasive particle in different contact states, on this basis, determine the number of abrasive particle in different contact states, and calculate the total grinding force in grinding process;Calculate the deformation of grinding wheel matrix under the action of grinding force;Analyze the influence of grinding wheel matrix deformation on spindle inclination, obtain the actual grinding surface shape PV value of wafer under this grinding condition;According to the requirement of laser crystal wafer grinding surface shape precision PV value, determine the adjustment amount of spindle inclination, adjust based on existing spindle inclination result;Grinding processing obtains crystal wafer.The present application can obtain surface roughness RMS<2nm and surface / subsurface low-damage surface quality, greatly reduce the processing time and cost of removing damage in polishing stage.

Description

Technical Field

[0001] This invention relates to the field of ultra-precision machining technology for laser crystal wafers in thin-film lasers, and more particularly to a method for controlling the surface shape of ultra-precision grinding of laser crystal wafers. Background Technology

[0002] Thin-plate lasers, due to their extremely thin gain medium, high pump efficiency, and low wavefront distortion, combined with the compact structure of solid-state lasers, have become the future development direction for high-power lasers. Among these components, the gain medium, as the core component of a thin-plate laser, directly affects the laser's performance and service life through the precision of its surface finish. Common gain media (such as YAG, Lu₂O₃, and GGG laser crystal wafers) are characterized by high hardness, brittleness, and strong chemical inertness. Furthermore, the thinness and high aspect ratio of laser crystal wafers make it difficult to guarantee the required surface finish due to warping deformation caused during processing and holding.

[0003] For the processing of laser crystal wafers, a combination of grinding and polishing is mainly used. However, grinding laser crystal wafers with free abrasives results in a low material removal rate, and the large abrasive particles in the grinding slurry can easily cause deep scratches and subsurface damage on the processed surface of the laser crystal wafer, thereby increasing the processing time of the subsequent polishing stage. In addition, it is difficult to guarantee the surface accuracy of laser crystal wafers processed by grinding. To ensure the surface accuracy requirements of the laser crystal wafers, the polishing and shaping stage needs to be extended, leading to increased processing costs.

[0004] Therefore, the stringent precision requirements for laser crystal wafers pose new challenges to ultra-precision machining technology. It is necessary to study new ultra-precision machining methods by combining the material properties and machining requirements of laser crystal wafers. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention provides a method for controlling the surface shape of ultra-precision laser crystal wafers. This invention establishes a predictive model for the surface shape accuracy of crystal wafers under the influence of grinding force and grinding wheel matrix deformation, clarifying the influence of grinding process parameters on the surface shape accuracy of crystal wafers. Based on the surface quality requirements of the grinding process, reasonable grinding process parameters are determined. On this basis, the grinding surface shape accuracy under corresponding grinding conditions is calculated. Then, according to the surface shape accuracy requirements of the ground surface, the adjustment amount of the machine tool spindle tilt angle is calculated and adjusted. Finally, a grinding surface that meets the surface quality and surface shape accuracy requirements is obtained, reducing the processing time and cost of the polishing stage.

[0006] The technical means employed in this invention are as follows:

[0007] A method for controlling the surface shape of laser crystal thin films in ultra-precision grinding includes the following steps:

[0008] Step 1: Determine the grinding process parameters within the preset range based on the surface quality of the ground surface;

[0009] Step 2: By clarifying the contact state between the abrasive grains and the wafer, determine the grinding force of a single abrasive grain under different contact states. Based on this, determine the number of abrasive grains under different contact states and calculate the total grinding force during the grinding process. Calculate the deformation of the grinding wheel matrix under the action of the grinding force. Analyze the influence of the deformation of the grinding wheel matrix on the spindle tilt angle to obtain the actual grinding surface shape PV value of the wafer under this grinding condition.

[0010] Step 3: Based on the required surface accuracy PV value for laser crystal wafer grinding, and combined with the calculation process in Step 2, determine the adjustment amount of the spindle tilt angle, and make adjustments based on the existing spindle tilt angle results;

[0011] Step 4: Grinding process to obtain crystal wafers.

[0012] Furthermore, step 4 is followed by the following steps:

[0013] Step 5: Use anhydrous ethanol as a cleaning agent to clean the laser crystal wafer after grinding.

[0014] Furthermore, in step 1, the grinding process parameters include the grinding wheel grit size, grinding wheel bond type, grinding wheel speed, workpiece speed, and feed rate.

[0015] Furthermore, in step 2, the formula for calculating the grinding force is:

[0016] F n =N c F nc

[0017] Where F n For the total grinding force, F nc The grinding force of a single abrasive grain, N c This refers to the number of abrasive grains.

[0018] Grinding force F of a single abrasive grain nc =H w S nc-ave H w S represents the hardness of a YAG wafer. nc-ave This represents the normal contact area between the abrasive grains and the workpiece.

[0019] Furthermore, the number of abrasive grains is calculated as follows:

[0020]

[0021] Where, r g Where W is the abrasive grain radius, D is the grinding wheel tooth width, and Z is the grinding wheel diameter. wLet h be the assumed distance between the working surface of the grinding wheel and the surface of the workpiece. pc η is the critical depth from plowing to cutting, k is the porosity of the grinding wheel and the theoretical abrasive shedding rate in actual grinding, and η is the volume fraction of abrasive grains in the grinding wheel.

[0022] r g -Z w pass Calculations show that

[0023] Among them, E w N is the elastic modulus of the workpiece material. t k represents the total number of abrasive grains on the working surface of the grinding wheel. s To calculate the empirical coefficient for the elastic recovery of the workpiece material, H w σ represents the hardness of the workpiece material, and σ is a calculation coefficient that takes into account the change in abrasive depth of cut caused by the deformation of the grinding wheel bond.

[0024] A w The cross-sectional area of ​​the region where the material is removed from the wafer surface is determined by... calculate,

[0025] Where r1 is the radial position on the wafer, n w n is the workpiece rotational speed. s r is the grinding wheel speed. w Let be the radius of the workpiece, and f be the feed speed of the grinding wheel.

[0026] Furthermore, the deformation of the grinding wheel under the action of grinding force is calculated based on the following formula:

[0027] Where ρ is the crystallographic distance of the grinding wheel, w(ρ) is the grinding wheel deformation at the corresponding crystallographic distance, and ν s M is the Poisson's ratio of the grinding wheel matrix, and M is the torque exerted on the edge of the grinding wheel by the grinding force, M = F n (ba), Fn is the calculated grinding force, a is the radius of the flange for mounting the grinding wheel on the machine tool spindle, and b is the radius of the grinding wheel.

[0028] Furthermore, based on the amount of grinding wheel deformation, the change in the grinding wheel tilt angle is calculated as follows:

[0029] R w R is the wafer radius. s Let be the radius of the grinding wheel, and α and β represent the original tilt angles of the spindle, respectively.

[0030] Furthermore, after determining the change in grinding wheel inclination angle, the theoretical grinding surface shape of the wafer is calculated using the following formula:

[0031]

[0032] Where L represents the distance from the center of the grinding wheel to the center of the wafer, and its value is equal to the radius Rs of the grinding wheel; x(t), y(t), z(t) are the coordinates of any point on the contact arc between the grinding wheel and the workpiece as a function of time; ω w Let ω be the angular velocity of the workpiece material. s ω is the angular velocity of the grinding wheel, and t is time.

[0033] To obtain the actual ground surface profile of the wafer, the arc formed by the movement of the grinding wheel and the workpiece contact point is rotated around the Z-axis to obtain the actual ground surface profile of the wafer:

[0034]

[0035] X, Y, and Z are the coordinates of the wafer surface after the contact arc is rotated around the Z-axis, where Z is the contact arc. max and Z min The maximum and minimum coordinates on the rotating surface in the Z-axis direction are given by the value of the wafer, and the difference between them is the PV value.

[0036] The theoretical surface shape PV1 of the wafer is obtained by substituting the original tilt angles α and β of the spindle into the calculation. Then, the actual surface shape PV2 of the lens is obtained by substituting α' = α - Δα and β' = β - Δβ into the calculation. The change in wafer grinding surface shape accuracy under grinding force is obtained as ΔPV = PV1 - PV2.

[0037] If the target surface accuracy of the wafer is set to PV3, then the spindle tilt angles need to be adjusted to α1 and β1 so that the theoretical grinding surface of the wafer is PV4 = PV3 + ΔPV; finally, the wafer is ground to the target surface accuracy PV.

[0038] Furthermore, the grinding process parameters within the preset range specifically include: a grinding wheel rotation speed range of 500–3000 rpm, a laser crystal wafer rotation speed range of 20–300 rpm, and a grinding wheel axial feed speed range of 1–100 μm / min.

[0039] Furthermore, the abrasive grit size of the grinding wheel is #1500 to #5000.

[0040] Compared with the prior art, the present invention has the following advantages:

[0041] 1. High processing efficiency: Under the premise of given surface quality and surface accuracy, the total processing time for traditional grinding is about 4 hours, while the total processing time for the ultra-precision grinding method described in this invention is up to about 2 hours, which improves the processing efficiency by nearly 100%.

[0042] 2. Good surface / subsurface quality: By using the ultra-precision grinding surface shape accuracy control method described in this invention, a surface roughness RMS < 2nm and low surface / subsurface damage can be obtained. The surface roughness is close to the processing quality of chemical mechanical polishing, which greatly reduces the processing time and cost of removing damage in the polishing stage.

[0043] 3. High surface accuracy: The combined process method described in this invention produces laser crystal wafers with an average surface accuracy (PV) of 150nm, which is far superior to the surface accuracy of traditional grinding processes, greatly reducing the processing time and cost of surface accuracy adjustment during the polishing stage.

[0044] 4. This invention is reasonably designed, has low processing costs, is highly versatile, and is suitable for mass production. Attached Figure Description

[0045] 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.

[0046] Figure 1 This is a flowchart of the laser crystal thin-film surface accuracy control method of the present invention.

[0047] Figure 2 This is a schematic diagram illustrating the principle of ultra-precision grinding of laser crystal wafers according to the present invention.

[0048] Figure 3 This is a schematic diagram of the surface accuracy and surface quality of the laser crystal thin film of the present invention, wherein (a) is the surface accuracy PV, (b) is the surface roughness, and (c) is the subsurface damage.

[0049] Figure 4 This is a schematic diagram of a mass-produced sample of the laser crystal thin film of the present invention (Φ12mm×300um), wherein (a) is a YAG laser crystal thin film; and (b) is a Lu2O3 laser crystal thin film.

[0050] In the figure: 1. Laser crystal wafer; 2. Vacuum chuck stage; 3. Cup-shaped grinding wheel; 4. Axial direction of machine tool spindle; 5. Angle of rotation of grinding wheel spindle around X-axis, represented by α; 6. Angle of rotation of grinding wheel spindle around Y-axis, represented by β. Detailed Implementation

[0051] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0052] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The following description of at least one exemplary embodiment is merely illustrative and is in no way intended to limit the present invention or its application or use. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0053] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0054] Unless otherwise specifically stated, the relative arrangement, numerical expressions, and values ​​of the components and steps described in these embodiments do not limit the scope of the invention. It should also be understood that, for ease of description, the dimensions of the various parts shown in the drawings are not drawn to actual scale. Techniques, methods, and devices known to those skilled in the art may not be discussed in detail, but where appropriate, such techniques, methods, and devices should be considered part of the specification. In all examples shown and discussed herein, any specific values ​​should be interpreted as merely exemplary and not as limitations. Therefore, other examples of exemplary embodiments may have different values. It should be noted that similar reference numerals and letters in the following drawings denote similar items; therefore, once an item is defined in one drawing, it need not be further discussed in subsequent drawings.

[0055] In the description of this invention, it should be understood that the orientation or positional relationship indicated by directional terms such as "front, back, up, down, left, right", "horizontal, vertical, horizontal" and "top, bottom" is generally based on the orientation or positional relationship shown in the accompanying drawings, and is only for the convenience of describing this invention and simplifying the description. Unless otherwise stated, these directional terms do not indicate or imply that the device or element referred to must have a specific orientation or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation on the scope of protection of this invention. The directional terms "inner" and "outer" refer to the inner and outer contours relative to the outline of each component itself.

[0056] For ease of description, spatial relative terms such as "above," "over," "on the upper surface of," "above," etc., are used herein to describe the spatial positional relationship of a device or feature as shown in the figures to other devices or features. It should be understood that spatial relative terms are intended to encompass different orientations in use or operation besides the orientation of the device as described in the figures. For example, if the device in the figures is inverted, a device described as "above" or "above" other devices or structures would subsequently be positioned as "below" or "under" other devices or structures. Thus, the exemplary term "above" can include both "above" and "below." The device may also be positioned in other different ways (rotated 90 degrees or in other orientations), and the spatial relative descriptions used herein will be interpreted accordingly.

[0057] Furthermore, it should be noted that the use of terms such as "first" and "second" to define components is merely for the purpose of distinguishing the corresponding components. Unless otherwise stated, the above terms have no special meaning and therefore should not be construed as limiting the scope of protection of this invention.

[0058] like Figure 1 As shown in the figure, this invention discloses a method for controlling the surface shape of ultra-precision grinding of laser crystal wafers, comprising the following steps:

[0059] Step 1: Determine the grinding process parameters within the preset range based on the grinding surface quality; specifically, determine reasonable grinding process parameters based on the wafer surface roughness requirements.

[0060] Step 2: Calculate the grinding force under the corresponding grinding process parameters using a grinding force prediction model to determine the influence of grinding force on the grinding surface deviation. Based on the grinding surface accuracy requirements and the deviation of the surface under the action of grinding force, calculate and determine the adjustment amount of the machine tool spindle tilt angle. Specifically, by clarifying the contact state between the abrasive grain and the wafer, determine the grinding force of a single abrasive grain under different contact states. On this basis, determine the number of abrasive grains under different contact states and calculate the total grinding force during the grinding process. Calculate the deformation of the grinding wheel matrix under the action of grinding force. Analyze the influence of the grinding wheel matrix deformation on the spindle tilt angle to obtain the actual grinding surface PV value of the wafer under the grinding conditions. In this process, verify the accuracy of the theoretical calculation by cross-referencing theoretical calculations with finite element simulations. Obtain the influence law of grinding process parameters on the grinding surface accuracy PV value.

[0061] Step 3: Based on the surface quality requirements of the wafer grinding, the grinding process parameters, and the calculated machine tool spindle tilt angle adjustment amount, adjust the machine tool spindle tilt angle to ensure that the surface quality and surface accuracy of the wafer grinding meet the requirements. Specifically, based on the requirements of the surface accuracy PV value of the laser crystal wafer grinding, and combined with the calculation process in Step 2, determine the adjustment amount of the spindle tilt angle, and adjust it based on the existing spindle tilt angle results.

[0062] Step 4: Grinding process to obtain crystal wafers.

[0063] Furthermore, step 4 is followed by the following steps:

[0064] Step 5: Use anhydrous ethanol as a cleaning agent to clean the laser crystal wafer after grinding.

[0065] Steps 4 and 5 above are specifically as follows: The laser crystal wafer is adsorbed onto the vacuum chuck stage, ensuring the center of the wafer coincides with the center of the stage. During grinding, the grinding wheel and the laser crystal wafer rotate around their respective axes. The grinding wheel feeds along the axial direction of the machine tool spindle to remove material. Deionized water is used as the coolant for grinding. The ground laser crystal wafer is then cleaned using anhydrous ethanol as a cleaning agent to remove residual contaminants and obtain a clean laser crystal wafer surface.

[0066] Furthermore, in step 1, the grinding process parameters include the grinding wheel grit size, grinding wheel bond type, grinding wheel speed, workpiece speed, and feed rate.

[0067] Furthermore, in step 2, the formula for calculating the grinding force is:

[0068] F n =N c F nc

[0069] Where F n For the total grinding force, F nc The grinding force of a single abrasive grain, N c This refers to the number of abrasive grains.

[0070] Grinding force F of a single abrasive grain nc =H w S nc-ave H w S represents the hardness of a YAG wafer. nc-ave This represents the normal contact area between the abrasive grains and the workpiece.

[0071] Furthermore, the number of abrasive grains is calculated as follows:

[0072]

[0073] Where, r gWhere W is the abrasive grain radius, D is the grinding wheel tooth width, and Z is the grinding wheel diameter. w Let h be the assumed distance between the working surface of the grinding wheel and the surface of the workpiece. pc The critical depth from plowing to cutting is approximately 0.01rg, k is the porosity of the grinding wheel and the theoretical abrasive grain shedding rate in actual grinding, and η is the volume fraction of abrasive grains in the grinding wheel.

[0074] r g -Z w pass Calculations show that

[0075] Among them, E w N is the elastic modulus of the workpiece material. t k represents the total number of abrasive grains on the working surface of the grinding wheel. s The empirical coefficient for calculating the elastic recovery of the workpiece material depends on the mechanical properties of the workpiece material, H. w σ represents the hardness of the workpiece material, and σ is a calculation coefficient that takes into account the change in abrasive depth of cut caused by the deformation of the grinding wheel bond.

[0076] A w The cross-sectional area of ​​the region where the material is removed from the wafer surface is determined by... calculate,

[0077] Where r1 is the radial position on the wafer, n w n is the workpiece rotational speed. s r is the grinding wheel speed. w Let be the radius of the workpiece, and f be the feed speed of the grinding wheel.

[0078] Furthermore, the deformation of the grinding wheel under the action of grinding force is calculated based on the following formula:

[0079] Where ρ is the crystallographic distance of the grinding wheel, w(ρ) is the grinding wheel deformation at the corresponding crystallographic distance, and ν s M is the Poisson's ratio of the grinding wheel matrix, and M is the torque exerted on the edge of the grinding wheel by the grinding force, M = F n (ba), Fn is the calculated grinding force, a is the radius of the flange for mounting the grinding wheel on the machine tool spindle, and b is the radius of the grinding wheel.

[0080] Furthermore, based on the amount of grinding wheel deformation, the change in the grinding wheel tilt angle is calculated as follows:

[0081] R w R is the wafer radius. s Let be the radius of the grinding wheel, and α and β represent the original tilt angles of the spindle, respectively.

[0082] Furthermore, after determining the change in grinding wheel inclination angle, the theoretical grinding surface shape of the wafer is calculated using the following formula:

[0083]

[0084]

[0085] Where L represents the distance from the center of the grinding wheel to the center of the wafer, and its value is equal to the radius Rs of the grinding wheel; x(t), y(t), z(t) are the coordinates of any point on the contact arc between the grinding wheel and the workpiece as a function of time; ω w Let ω be the angular velocity of the workpiece material. s ω is the angular velocity of the grinding wheel, and t is time.

[0086] To obtain the actual ground surface profile of the wafer, the arc formed by the movement of the grinding wheel and the workpiece contact point is rotated around the Z-axis to obtain the actual ground surface profile of the wafer:

[0087]

[0088] X, Y, and Z are the coordinates of the wafer surface after the contact arc is rotated around the Z-axis, where Z is the contact arc. max and Z min The maximum and minimum coordinates on the rotating surface in the Z-axis direction are given by the value of the wafer, and the difference between them is the PV value.

[0089] The theoretical surface shape PV1 of the wafer is obtained by substituting the original tilt angles α and β of the spindle into the calculation. Then, the actual surface shape PV2 of the lens is obtained by substituting α' = α - Δα and β' = β - Δβ into the calculation. The change in wafer grinding surface shape accuracy under grinding force is obtained as ΔPV = PV1 - PV2.

[0090] If the target surface accuracy of the wafer is set to PV3, then the spindle tilt angles need to be adjusted to α1 and β1 so that the theoretical grinding surface of the wafer is PV4 = PV3 + ΔPV; finally, the wafer is ground to the target surface accuracy PV.

[0091] Furthermore, the grinding process parameters within the preset range specifically include: a grinding wheel rotation speed range of 500–3000 rpm, a laser crystal wafer rotation speed range of 20–300 rpm, and a grinding wheel axial feed speed range of 1–100 μm / min.

[0092] As a preferred embodiment, the grinding wheel rotation speed range is 1199 rpm to 2399 rpm, the laser crystal wafer rotation speed range is 60 rpm to 240 rpm, and the grinding wheel axial feed speed range is 5 μm / min to 20 μm / min.

[0093] Furthermore, the abrasive grit size of the grinding wheel is #1500 to #5000. In the specific processing, a cup-shaped grinding wheel is used, with abrasive grit sizes of #1500, #2000, #3000, #4000, and #5000.

[0094] The bonding agent for cup-shaped grinding wheels can be a resin bond or a ceramic bond.

[0095] like Figure 2 As shown, in this embodiment, the self-rotating ultra-precision grinding device includes a vacuum chuck stage 2 and a cup-shaped grinding wheel 3. The laser crystal wafer 1 is adsorbed onto the vacuum chuck stage 2, ensuring that the center of the wafer 1 coincides with the center of the stage 2. The cup-shaped grinding wheel is mounted on the high-precision spindle during grinding. The cup-shaped grinding wheel 3 and the laser crystal wafer 1 rotate around their respective axes, while the cup-shaped grinding wheel 3 feeds along the axial direction 4 of the machine tool spindle to remove material. Deionized water is used to remove heat and chips generated during the grinding process. The angle between the grinding wheel spindle and the stage spindle is adjustable, including tilt angles 5 and 6. Tilt angle 5 is the angle of rotation of the grinding wheel spindle around the X-axis (α in the formula), and tilt angle 6 is the angle of rotation of the grinding wheel spindle around the Y-axis (β in the formula). The surface shape accuracy PV of the wafer grinding can be controlled by adjusting tilt angles 5 and 6.

[0096] In this embodiment, the wafer being processed is a Ф12mm YAG wafer, and a #3000 ceramic bond grinding wheel is used to grind the wafer. The required surface roughness RMS after wafer processing is <2nm. Based on this, the grinding wheel speed is determined to be 2000rpm, the wafer speed to be 90rpm, and the axial feed speed of the grinding wheel to be 5μm / min.

[0097] Compared to traditional grinding processes, the ultra-precision grinding of laser crystal wafers described in this invention utilizes an optical microscope and a plane interferometer to inspect the surface of the laser crystal wafer. The surface roughness RMS < 2 nm, the surface / subsurface damage is extremely low, and the surface profile accuracy PV is approximately 150 nm (1 / 10λ@632.8 nm). The final results are as follows: Figure 3 , Figure 4 As shown in (a). Furthermore, the same experiment was performed on Lu2O3 wafers, as shown in [the diagram]. Figure 4 As shown in (b).

[0098] 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 controlling the surface shape in ultra-precision grinding of laser crystal wafers, characterized in that, Includes the following steps: Step 1: Determine the grinding process parameters within the preset range based on the surface quality of the ground surface; Step 2: By clarifying the contact state between the abrasive grains and the wafer, determine the grinding force of a single abrasive grain under different contact states. Based on this, determine the number of abrasive grains under different contact states and calculate the total grinding force during the grinding process. Calculate the deformation of the grinding wheel matrix under grinding force; analyze the influence of the grinding wheel matrix deformation on the spindle tilt angle, and obtain the actual grinding surface shape PV value of the wafer under this grinding condition. Step 3: Based on the required surface accuracy PV value for laser crystal wafer grinding, and combined with the calculation process in Step 2, determine the adjustment amount of the spindle tilt angle, and make adjustments based on the existing spindle tilt angle results; Step 4: Grinding process to obtain crystal wafers; The number of abrasive grains is calculated as follows: ， in, r g Where is the abrasive grain radius. W For the width of the grinding wheel teeth, D The diameter of the grinding wheel. Z w Let be the assumed distance between the working surface of the grinding wheel and the surface of the workpiece. h pc This refers to the critical depth at which the plow reaches the cutting state. k This represents the porosity of the grinding wheel in actual grinding and the theoretical abrasive grain shedding rate. η This represents the volume fraction of abrasive grains in the grinding wheel. r g - Z w pass Calculations show that in, E w The elastic modulus of the workpiece material. N t This refers to the total number of abrasive grains on the working surface of the grinding wheel. k s To calculate the empirical coefficient for the elastic recovery of the workpiece material, H w The hardness of the workpiece material, σ The calculation coefficients are used to account for the changes in abrasive depth of cut caused by the deformation of the grinding wheel bond; A w The cross-sectional area of ​​the region where the material is removed from the wafer surface is determined by... calculate, in, r 1 represents the radial position on the wafer. n w For the workpiece rotation speed, n s The rotational speed of the grinding wheel. r w Let be the radius of the workpiece. f This represents the feed speed of the grinding wheel.

2. The surface shape control method according to claim 1, characterized in that, Step 4 is followed by the following steps: Step 5: Use anhydrous ethanol as a cleaning agent to clean the laser crystal wafer after grinding.

3. The surface shape control method according to claim 1, characterized in that, In step 1, the grinding process parameters include wheel grit size, wheel bond type, wheel speed, workpiece speed, and feed rate.

4. The surface shape control method according to claim 1, characterized in that, In step 2, the formula for calculating the grinding force is: in F n The total grinding force, F nc The grinding force of a single abrasive grain. N c This refers to the number of abrasive grains. Grinding force of a single abrasive grain , H w The hardness of the YAG wafer. S nc-ave This represents the normal contact area between the abrasive grains and the workpiece.

5. The surface shape control method according to claim 1, characterized in that, The deformation of the grinding wheel under grinding force is calculated using the following formula: ， in, ρ The crystal orientation distance of the grinding wheel. w ( ρ () represents the grinding wheel deformation amount corresponding to the crystal orientation distance. ν s Let be the Poisson's ratio of the grinding wheel matrix, and M be the torque exerted on the edge of the grinding wheel by the grinding force. , F n To calculate the grinding force, a The radius of the flange for mounting the grinding wheel on the machine tool spindle. b Where is the radius of the grinding wheel.

6. The surface shape control method according to claim 1, characterized in that, Based on the deformation of the grinding wheel, the change in the grinding wheel tilt angle is calculated as follows: ， in, R w For the wafer radius, R s Where is the radius of the grinding wheel. α and β These represent the original tilt angles of the principal shaft.

7. The surface shape control method according to claim 1, characterized in that, After determining the change in grinding wheel inclination angle, the theoretical grinding surface shape of the wafer is calculated using the following formula: Where L represents the distance from the center of the grinding wheel to the center of the wafer, and its value is equal to the radius Rs of the grinding wheel; x(t), y(t), z(t) are the coordinates of any point on the contact arc between the grinding wheel and the workpiece as time changes. ω w The angular velocity of the workpiece material. ω s Let be the angular velocity of the grinding wheel. t For time; To obtain the actual ground surface profile of the wafer, the arc formed by the movement of the grinding wheel and the workpiece contact point is rotated around the Z-axis to obtain the actual ground surface profile of the wafer: X , Y , Z Let be the coordinates of the wafer surface after the contact arc is rotated about the Z-axis. Z max and Z min The maximum and minimum coordinates on the rotating surface in the Z-axis direction are given by the value of the wafer, and the difference between them is the PV value. By adjusting the original spindle tilt angle α and β Substitute the values ​​into the calculation to obtain the theoretical surface shape PV1 of the wafer, and then... α '= α-Δα and β ' =β- Δβ Substituting the values ​​into the calculation, we obtain the actual surface shape PV2 of the lens, and then obtain the change in the surface shape accuracy of the wafer under the action of grinding force. Δ PV=PV 1 -PV 2; If the target surface accuracy of the wafer is set to PV3, then the spindle tilt angle needs to be adjusted to... α 1 and β 1. Make the theoretical grinding surface shape of the wafer as follows: PV 4= PV 3+ ΔPV Finally, the wafer is ground to the target surface shape accuracy PV.

8. The surface shape control method according to claim 1, characterized in that, The grinding process parameters within the preset range specifically include: grinding wheel speed range of 500 ~ 3000 rpm, laser crystal wafer rotation speed range of 20 ~ 300 rpm, and grinding wheel axial feed speed range of 1 ~ 100 μm / min.

9. The surface shape control method according to claim 1, characterized in that, The abrasive grit size of the grinding wheel is #1500~#5000.

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