Disclosure of Invention
In view of the above problems, an object of the present invention is to provide a wafer grinding method and a wafer grinding system, which can solve the above problems at least partially to improve the uniformity of surface shape compensation, grinding speed, and grinding accuracy of a wafer.
According to an aspect of the present application, there is provided a wafer grinding method including the steps of: a surface shape feature detection step of selecting a plurality of measurement points on a surface to be ground of a wafer and measuring the thickness of the wafer at each measurement point, wherein the plurality of measurement points include a start measurement point, a final measurement point and an intermediate measurement point between the start measurement point and the final measurement point; a surface shape feature identification step of acquiring a fullness of the surface shape feature of the surface to be ground based on each thickness measured in the surface shape feature detection step, the fullness being a maximum value in a vertical distance between an intermediate measurement point and a convex-concave line, the convex-concave line being a straight line connecting the initial measurement point and the final measurement point; a pose adjustment grinding step of adjusting a relative spatial positional relationship between a wafer table on which the wafer is placed and a grinding tool for performing a grinding operation based on the saturation obtained in the surface shape feature recognition step, thereby performing a compensatory grinding operation on the surface to be ground by the grinding tool.
Preferably, the surface shape feature identification step further includes calculating a vertical distance between the intermediate measurement point and the convex-concave degree line by the following formula:
wherein i is a positive integer, r
iIs the distance, T (r), from the ith intermediate measurement point to the starting measurement point
i) Is to be r
iThickness, t, calculated by substituting the equation of the convex-concave curve
iMeasured thickness at the ith intermediate measurement point,
wherein T is
RIs the measured thickness, T, at the final measurement point
0And R is the measured thickness at the initial measuring point, and the distance between the final measuring point and the initial measuring point, wherein the convex-concave degree line equation is as follows: t (r) = kr
i+ b, wherein k, r
iThe parameters are defined as above, b is the measured thickness at the starting measurement point, i.e. b = T
0。
Preferably, a horizontal axis passing through a center point of the wafer table in a plan view may be defined as an x-axis, and a vertical axis passing through the center point of the wafer table in a plan view may be defined as a y-axis, and the relative spatial positional relationship between the wafer table and the grinding tool may be adjusted by rotating the wafer table about the x-axis and the y-axis, respectively.
Preferably, the actual angle that the wafer stage needs to rotate around the x-axis can be expressed as αtWorking the waferThe actual angle that the stage needs to rotate around the y-axis is denoted as βtDetermining alpha based on a predetermined convexity mapping table and a fullness mapping tabletAnd betatThe convexity mapping table reflects a series of predetermined angles alphaiWith a series of predetermined convexities δi,1The fullness mapping table reflects a series of predetermined angles betaiWith a series of predetermined degrees of fullness δi,2Wherein i is a positive integer.
Preferably, α can be further accurately calculated by the following mathematical formulatAnd betat:
Wherein, delta1Representing the actual concavity, δ, obtained in the surface-form feature identification stepi,1Representing a smaller than actual concavity δ in the concavity mapping table1Predetermined concavity, δi+1,1Represents the sum delta in the convexity and concavity mapping tablei,1Adjacent and greater than the actual concavity delta1And the three satisfy the relation deltai,1<δ1<δi+1,1,αiRepresents the sum delta in the convexity and concavity mapping tablei,1Corresponding to a predetermined angle, αi+1Represents the sum delta in the convexity and concavity mapping tablei+1,1Corresponding to a predetermined angle when there is an actual concavity δ in the concavity map1Equal predetermined concavity and convexity δi,1When is αt=-αi(ii) a And is
Wherein, delta2Representing the actual degree of fullness, δ, obtained in said face shape feature identification stepi,2Indicating that the fullness mapping table is smaller than the actual fullness delta2Predetermined fullness, δi+1,2Represents the sum delta in the fullness mapi,2Adjacent and greater than the actual degree of fullness δ2And the three satisfy the relation deltai,2<δ2<δi+1,2,βiRepresents the sum delta in the fullness mapi,2Corresponding to a predetermined angle, betai+1Represents the sum delta in the fullness mapi+1,2Corresponding preset angle, when the plumpness mapping table has delta from the actual plumpness2Equal predetermined fullness δi,2When is betat=-βi。
According to another aspect of the present application, there is provided a wafer grinding system, comprising: a wafer stage for placing a wafer; a grinding tool for grinding the wafer; a thickness detection device for detecting a thickness of the wafer, configured to measure the thickness of the wafer at each measurement point based on a plurality of measurement points selected on a surface to be ground of the wafer; a surface shape feature recognition device configured to determine a degree of fullness of a surface to be ground of the wafer according to the wafer grinding method; a pose adjusting mechanism configured to adjust a spatial positional relationship of the wafer stage with respect to the grinding tool based on the plumpness determined by the surface shape feature recognition device, thereby performing a compensatory grinding operation on a plumpness surface shape by the grinding tool.
Preferably, the posture adjustment mechanism is further configured to adjust a spatial positional relationship of the wafer stage with respect to the grinding tool according to the wafer grinding method described above.
According to the method and the device, the convexity and the fullness of the surface characteristic can be simply determined by measuring the thickness of the wafer, and the spatial position relation of the wafer workbench relative to the grinding tool is adjusted according to the convexity and the fullness, so that the surface characteristic is systematically analyzed and identified, the spatial position relation of the wafer workbench relative to the grinding tool can be avoided being determined by depending on the operation experience of equipment operators, and the efficiency and the precision of the wafer grinding operation can be improved.
In addition, according to this application, can accurately calculate the actually required rotation angle of wafer workstation with mathematical formula based on convex-concave degree and plumpness parameter to can control the spatial position relation of wafer workstation for the finish grinding emery wheel more accurately, thereby further improve the precision of wafer grinding operation.
Detailed Description
The present application will be described in further detail with reference to the following drawings and examples. It is to be understood that the specific embodiments described herein are merely illustrative of the relevant invention and not restrictive of the invention. It should be noted that, for convenience of description, only the portions related to the present invention are shown in the drawings. It should be noted that the embodiments and features of the embodiments in the present application may be combined with each other without conflict.
Further, it is also noted that terms used herein such as front, back, up, down, left, right, top, bottom, front, back, horizontal, vertical, and the like, to denote orientation, are used merely for convenience of description to facilitate understanding of relative positions or orientations, and are not intended to limit the orientation of any device or structure.
The present application will be described in detail below with reference to the embodiments with reference to the attached drawings. Finally, the term "wafer" is sometimes referred to in the industry as "substrate", and both terms are equivalent.
Fig. 1 illustrates a perspective view of a portion of a wafer grinding system in accordance with an embodiment of the present application. The wafer grinding system comprises a rotary worktable 111, and a driving device, a supporting shaft system and other structures are arranged in the rotary worktable. Three wafer tables 112 are provided on the wheel table 111. The three wafer tables 112 may be structurally and functionally identical. The wafer stage 112 carries a wafer thereon. In the following description, a wafer will be explained as an example of a wafer.
Also shown in fig. 1 is a rough grinding section 113 that includes a rough grinding wheel, a rough grinding spindle, and a rough grinding feed mechanism. The rough grinding wheel is arranged at the end part of the rough grinding main shaft and is driven to rotate by the rough grinding main shaft. The rough grinding main shaft is connected with the rough grinding feeding system to move up and down, so that axial plunge grinding is realized, and the wafer can reach the thickness required by the rough grinding process.
Also shown in fig. 1 is a refining section 115 comprising a refining wheel, a refining spindle and a refining feed mechanism. The fine grinding wheel is arranged at the end part of the fine grinding main shaft and is driven to rotate by the fine grinding main shaft. The fine grinding main shaft is connected with the fine grinding feeding system to move up and down, so that the axial plunge grinding is realized, and the wafer can reach the thickness required by the fine grinding process.
The wafer table 112 is rotatable about the axis of the wheel table 111 so that the wafers are rotated between the loading and unloading station, the rough grinding station, and the finish grinding station. The rough grinding station and the accurate grinding station operate simultaneously to grind. After both rough grinding and finish grinding, the wheel-rotating worktable 111 can rotate, so that the wafer after rough grinding is rotated to a finish grinding station, the wafer after finish grinding is rotated to a loading and unloading station, and the newly loaded wafer is rotated to a rough grinding station.
Also shown in fig. 1 are contact thickness detection device 131 and non-contact thickness detection device 132. As shown in fig. 1, a non-contact thickness detection device 132 may be used to perform thickness measurements on wafers on the wafer tables of the rough grinding station and the finish grinding station. Of course, the contact thickness detecting device 131 or other types of thickness detecting devices may be used to measure the thickness, or a combination of various thickness detecting devices may be used to measure the thickness, depending on the actual situation.
Figure 2 shows a detailed view of the refining station of an embodiment of the present application. As shown in fig. 2, the refining section 115 includes a refining spindle 115a and a refining wheel 115 b. The non-contact thickness detecting device 132 includes a turn table 141, a swing arm bracket 142, and a thickness sensor 143. The thickness sensor 143 is connected to a control module 152 by an optical fiber 151.
Fig. 3 is a schematic diagram illustrating a thickness measurement performed by the non-contact thickness detection device 132 according to an embodiment of the present application. As shown in fig. 3, the thickness sensor 143 is mounted on the swing arm bracket 142. The thickness sensor 143 is driven by the turntable 141 to perform a rotational motion with a radius of a distance between the thickness sensor 143 and the center of the turntable 141, forming a circular arc-shaped scanning path, thereby detecting the thickness at a plurality of measurement points. The plurality of measurement points may include a start measurement point, a final measurement point, and intervening measurement points therebetween. Preferably, the scan path may scan from a radially inner portion of the wafer 116 to a radially outer portion of the wafer 116. Preferably, the center point of the wafer 116 may be used as the starting measurement point, and a point on the edge of the wafer 116 may be used as the final measurement point. When the thickness is measured, the number of points to be measured can be selected according to the process requirements. For example, one can start at the initial measurement point, measure every 3-5mm, and end at the final measurement point. In this case, preferably, 30 to 50 points may be selected for detection. The number of measurement points can be selected to accurately depict the surface shape characteristics and reduce the number of measurement points as much as possible so as to improve the efficiency.
Fig. 4a and 4b show an attitude adjusting mechanism 170 according to an embodiment of the present application, which may be disposed below the wafer table 112 and configured to adjust a spatial positional relationship of the wafer table 112 with respect to the grindstone 115b according to a condition so that the grindstone 115b performs a grinding operation on a wafer as required. In an embodiment, the posture adjustment mechanism 170 may include a three-point support type structure including three support points 170A, 170B, 170C arranged uniformly around the wafer stage 112, one of the support points 170C may be fixed, and the other two support points 170A, 170B may be provided with a drive system so as to be movable to adjust the spatial positional relationship of the wafer stage 112 with respect to the lapping wheel 115B in both directions. In an embodiment, the two supporting points 170A and 170B may be driven by a screw nut, a piezoelectric device, or the like, so as to realize sub-micron precision motion, thereby realizing precise control of the pose of the wafer stage.
A wafer grinding method according to an embodiment of the present application will be described below.
According to one embodiment, the wafer grinding method of the present application first includes a surface profile feature detection step. In this step, the thickness measurement may be performed by various types of thickness detection devices. During measurement, a plurality of measurement points can be selected according to the process requirements. The plurality of measurement points may include a start measurement point, a final measurement point, and intervening measurement points therebetween. Preferably, the starting measurement point may be selected to be within 20mm from the center of the wafer, and the final measurement point may be selected to be within 20mm from the edge of the wafer. Particularly preferably, the center point of the wafer may be selected as the initial measurement point, and the edge point of the wafer may be selected as the final measurement point. Then, the thickness at each measurement point was measured by a thickness detection device.
The degree of convexity δ of a surface feature can be determined by a number of methods based on the measured thickness of each measurement point1And degree of fullness δ2. The following will describe the method for determining the concavity δ according to the present application1And degree of fullness δ2An embodiment of (1).
FIG. 5 illustrates a schematic diagram of a profile feature of an embodiment of the present application. As shown in fig. 5, in order to describe the surface shape characteristics of the wafer after grinding, the surface shape of the wafer after grinding can be decomposed into a "convexity" (see upper left part in fig. 5) and a "saturation surface shape" (see lower left part in fig. 5). The actual profile can be formed by superimposing these two profiles, see the right half of fig. 5. To is coming toConvenient for surface profile feature analysis, respectively using the degree of concavity and convexity delta1And degree of fullness delta2To characterize both the "asperity profile" and the "plumpness profile".
FIGS. 6-8 illustrate the degree of concavity delta of a surface feature1And degree of fullness δ2The definition and calculation method of (1). As shown in fig. 6, the r-axis represents the distance between each measurement point and the starting measurement point, and the t-axis represents the measured thickness of the wafer. According to the invention, the degree of convexity delta1Can be defined as the difference between the thickness at the final measurement point and the thickness at the starting measurement point. In the example of fig. 6, the initial measurement point is the center point C of the upper surface of the wafer, and the final measurement point is an edge point a of the wafer. At this time, the degree of unevenness δ1I.e. the difference between the thickness of the center point C and the thickness of the edge point a of the wafer. That is, the degree of concavity and convexity δ at this time1Is the distance from the center point C of the upper surface of the wafer to the reference thickness line. The position of the reference thickness line is determined by the thickness value of the edge point A of the wafer, and the reference thickness line is parallel to the r axis. The concavity and convexity δ at a position where the center point C of the upper surface of the wafer is above the reference thickness line1Is positive (i.e. delta)1> 0) or otherwise negative (i.e., δ)1< 0). For example, two portions a and b in fig. 7 show the case of positive convexo-concave characteristics, and two portions c and d in fig. 7 show the case of negative convexo-concave characteristics.
In addition, the degree of fullness δ2Can be defined as the maximum in the vertical distance between the intervening measurement point and the convex-concave curve, which is the straight line connecting the starting measurement point and the final measurement point. In the example of fig. 6, the initial measurement point is the center point C of the upper surface of the wafer and the final measurement point is one edge point a of the wafer with multiple intervening measurement points therebetween. Of course, in an extreme example, it is also possible to select only one intermediate measurement point, for example at half the wafer radius. At this time, the maximum value of the vertical distances between the intermediate measurement point and the convex-concave curve is the vertical distance between the intermediate measurement point and the convex-concave curve itself. In this example, the line of roughness is a straight line connecting the center point C and the edge point of the wafer, and the saturation δ2I.e., contour points to asperities on the upper surface of the waferMaximum distance of the degree line. When the point corresponding to the maximum distance is above the line of concavity and convexity, the degree of fullness δ2Is positive (i.e. delta)2> 0) or otherwise negative (i.e., δ)2< 0). For example, the two parts b and d in fig. 7 show the case of the positive double-satiation feature, and the two parts a and c in fig. 7 show the negative double-satiation feature.
As described above, in the case where the initial measurement point is the center point C of the wafer and the final measurement point is the edge point a of the wafer, the
roughness δ 1 may be expressed as a difference between the thickness of the center point C and the thickness of the edge point a. At this time, the process of the present invention,
wherein T is
RMeasured thickness at edge point A, T
0Is the measured thickness at the center point C and R is the radius of the edge point.
In the example of fig. 8, since the convex-concave curve is a straight line connecting the center point C and the edge point a of the wafer, the convex-concave curve can be described by a convex-concave curve equation: t (r) = kr + b, where k and b can be calculated from the radius and thickness corresponding to the center point C and the edge point a. For example, k may be represented as
And b is the measured thickness at the center point, i.e. b = T
0. From this convexity and concavity line equation, the thickness t (r) at the corresponding point where the intervening measurement point vertically corresponds to the convexity and concavity line can be calculated.
In the example of fig. 8, δ is due to the fullness2Defined as the maximum distance from the profile point (i.e., each intermediate measurement point) on the upper surface of the wafer to the convex-concave degree line, and thus the saturation δ can be obtained by calculating the distance from each intermediate measurement point to the convex-concave degree line and then taking the maximum value thereof2. For example, the thickness of several points detected by the thickness detecting means can be used as (r)i,ti) To describe the various intervening measurement points, where riIs the distance from the ith intermediate measurement point to the starting measurement point, tiIs the measured thickness at the ith intervening measurement point. In this case, each point (r) can be calculatedi,ti) Distance d to the line of roughness (point-to-line distance) and finding the maximum value to obtain the degree of fullness δ2。
In one embodiment, each intervening measurement point (r)
i,t
i) The distance d to the convex-concave degree line can be calculated by the following formula:
wherein r is
iDistance, T (r), from the ith intermediate measurement point to the starting measurement point
i) Is to be r
iCalculated thickness, t, calculated by substituting into the equation of the convex-concave curve
iMeasured thickness at the ith intermediate measurement point,
wherein T is
RFor measured thickness at the final measurement point, T
0Is the measured thickness at the starting measurement point, and R is the distance between the final measurement point and the starting measurement point. After calculating each intermediate measuring point (r)
i,t
i) Distance d (r) to the line of roughness
i) Then, the fullness δ can be calculated
2=max(d(r
i))。
According to one embodiment, by analyzing the distribution law of the saturation characteristics, it is found that the point, which is typically at a half-wafer radius position, is the largest distance from the convex-concave curve. Thus, in one embodiment, the corresponding surface saturation may be calculated from the thickness measurements at one-half the wafer radius. Thus, in this embodiment, the thickness at half the wafer radius can be used to determine whether the saturation is positive or negative. For example, the positive or negative can be judged by the following formula:
wherein t is
0.5RIs the measured thickness value corresponding to the measuring point at half radius, T (r)
0.5R) To substitute half the radius into the calculated value of the convex-concave curve equation. Therefore, the positive or negative can be judged by comparing the thickness measured value of one-half radius with the calculated value obtained by substituting the convex-concave curve equation, for example,if P is larger than 0, the upper surface of the wafer at the half radius is convex relative to the convex-concave degree line, and the plumpness is judged to be positive; if P is less than 0, the upper surface of the wafer at the half radius is concave relative to the convex-concave degree line, and the plumpness is judged to be negative.
In one embodiment, the relief δ in which the surface features are obtained1And degree of fullness δ2Thereafter, the posture of the wafer table 112 with respect to the finish grinding wheel 115b can be adjusted based on these parameters. This attitude is also the spatial positional relationship of the wafer table 112 with respect to the grindstone 115 b. And performing compensatory grinding processing on the upper surface of the wafer by adjusting the spatial position relation. For example, the spatial positional relationship thereof with respect to the finish grinding wheel 115b may be adjusted by adjusting the spatial angle of the wafer table 112 with respect to the longitudinal axis of the finish grinding spindle 115a or the finish grinding wheel 115 b. Of course, this is merely an example, and according to another embodiment, the spatial positional relationship with respect to the wafer table 112 may be adjusted by adjusting the spatial angle of the grindstone 115b with reference to the wafer table 112.
According to the embodiment of the application, the convex-concave degree and the saturation degree parameters of the surface feature can be simply determined by measuring the thickness of the wafer, and the spatial position relation of the wafer workbench relative to the fine grinding wheel is adjusted according to the convex-concave degree and the saturation degree parameters, so that the surface feature is analyzed and identified systematically, the spatial position relation can be prevented from being adjusted depending on the operation experience of an operator, and the efficiency and the precision of the wafer grinding operation are improved.
A preferred embodiment for adjusting the spatial positional relationship of the wafer table 112 with respect to the grindstone 115b by more accurate quantitative calculation will be described below.
As shown in fig. 9 to 10, the spatial positional relationship of the axis of the wafer table 112 with respect to the axis of the refining spindle 115a is described by the angle α, β with reference to the axis of the refining spindle 115 a. As shown in fig. 9, the x, y, and z axes are perpendicular two by two, and the α and β angles describe the angular changes (i.e., rotation angles) of the axis of wafer stage 112 about the x and y axes, respectively. Fig. 10 is a plan view showing the positional relationship of the wafer table 112 and the refining spindle 115a, in which the x-axis is a horizontal axis in the horizontal plane and the y-axis is a vertical axis in the horizontal plane, and in this case, the α angle and the β angle indicate the rotation angles of the wafer table 112 about the x-axis and the y-axis, respectively. In addition, the angle α and the angle β have positive and negative directions, which can be determined according to the right-hand law. For example, if the thumb of the right hand points to the positive direction of the x-axis, the direction of the rest of the four-finger fist is positive for the angle α, and vice versa. Similarly, if the thumb of the right hand points to the positive direction of the y-axis, the direction of the rest of the four fingers to make a fist is the positive direction of the angle β, otherwise, the direction is the negative direction. In the process of equipment debugging and surface shape compensation grinding, the angle adjustment of the wafer workbench 112 around the x axis and the y axis can be realized through a precise adjusting mechanism.
Examples of how the angles α, β take on values are described below. According to an embodiment of the application, a series of predetermined angles alpha, beta and a series of predetermined convexities delta, respectively, may be selected
1And degree of fullness δ
2Correspondingly, the mapping relationship of each corresponding value is made into a convexity mapping table and a fullness mapping table, see fig. 11a and 11b, where α
iDegree of roughness delta
i,1Corresponds, beta
iAnd degree of fullness delta
i,2Correspondingly, i is a positive integer. According to one embodiment, α can range from-0.1 ° to α ≦ 0.1 °, and β can range from-0.1 ° to β ≦ 0.1 °. Alpha is alpha
iIs increased by
The value of (b) may be any one selected from 0.0001 to 0.001 DEG, and beta
iIs increased by
The value of (b) may be any one selected from 0.0001 to 0.001 °.
The following description will be made with specific numerical values. For example, α can be adjusted according to process control accuracy requirementsiThe value range of the alpha is determined to be less than or equal to alpha of minus 0.05 degreesiNot more than 0.05 DEG, and alphaiIs increased by 0.001 deg., thus obtaining alpha1Is-0.05 DEG and alpha2Is-0.049 DEG and alpha3Is-0.048 degree, … and alpha51Is 0 degree,…、α101Is 0.05 deg. In an embodiment, the asperity values corresponding to the range of α values may be obtained from process experiments and/or simulation results with the α angle set to the range of specific values. For example with α1Projection and depression degree delta corresponding to = -0.05 degree1,1= 55.4 μm, and α2Projection and depression degree delta corresponding to = -0.049 DEG2,1= -54.3 μm, etc., and specific corresponding numerical values may be referred to fig. 12.
Also, for example, β can be adjusted according to process control accuracy requirementsiThe value range of the alpha-beta is determined to be less than or equal to-0.05 DEGiNot more than 0.05 DEG, and betaiIs increased by 0.001 deg., thus obtaining beta1Is-0.05 degree and beta2Is-0.049 degree, … and beta51Is 0 degree, … and beta101Is 0.05 deg. In an embodiment, the saturation values corresponding to the range of β values may be obtained from process experiments and/or simulation results with the β angle set to the range of specific values. E.g. beta1Saturation delta of = -0.05 DEG1,2=10.51 μm, and β2Plumpness delta corresponding to = -0.049 DEG2,2=10.30 μm, and the like, and specific corresponding numerical values may be referred to fig. 13.
According to one embodiment, a plurality of different-precision convex-concave degree mapping tables and plumpness degree mapping tables can be prepared in advance by selecting alpha and beta values with different subdivision degrees and increments thereof according to the precision requirement of process control. That is, a series of predetermined angles α are reflected by the concavity mapping tableiWith a series of predetermined convexities δi,1And reflecting a series of predetermined angles beta through the fullness mapping tableiWith a series of predetermined degrees of fullness δi,2Wherein i is a positive integer.
It should be noted here that although the above describes the concavity map and the saturation map in the form of tables, the concavity map and the saturation map do not necessarily have to be in the form of tables as long as the predetermined angle α can be reflectedi、βiRespectively with a predetermined concavity and convexity delta1Predetermined saturation δ2In a one-to-one relationshipIn this regard, the convexity and fullness maps may take any form.
According to a preferred embodiment, the actual angle α of the wafer stage required to rotate around the x-axis can be calculated by the following calculation formula according to the pre-established convexity and concavity mapping tablest:
Wherein, delta1Representing the actual concavity, δ, obtained in the surface-form feature identification stepi,1Representing a smaller than actual concavity δ in the concavity mapping table1Predetermined concavity, δi+1,1Represents the sum delta in the convexity and concavity mapping tablei,1Adjacent and greater than the actual concavity delta1And the three satisfy the relation deltai,1<δ1<δi+1,1,αiRepresents the sum delta in the convexity and concavity mapping tablei,1Corresponding to a predetermined angle, αi+1Represents the sum delta in the convexity and concavity mapping tablei+1,1The corresponding predetermined angle is set to correspond to the predetermined angle,
in particular, when there is a difference δ from the actual concavity in the convexity mapping table1Equal predetermined concavity and convexity δi,1When is αt=-αi。
Further, the actual angle β that the wafer stage needs to rotate around the y-axis can be calculated by the following formulat:
Wherein, delta2Representing the actual degree of fullness, δ, obtained in said face shape feature identification stepi,2Indicating that the fullness mapping table is smaller than the actual fullness delta2Predetermined fullness, δi+1,2Represents the sum delta in the fullness mapi,2Adjacent and greater than the actual degree of fullness δ2Is not required to be sufficient for the predetermined degree of fullness,and the three satisfy the relation deltai,2<δ2<δi+1,2,βiRepresents the sum delta in the fullness mapi,2Corresponding to a predetermined angle, betai+1Represents the sum delta in the fullness mapi+1,2The corresponding predetermined angle is set to correspond to the predetermined angle,
in particular, when the fullness map contains delta from the actual fullness2Equal predetermined fullness δi,2When is betat=-βi。
According to the embodiment of the application, the actual rotation angle alpha required by the wafer workbench can be accurately calculated by a mathematical formula based on the parameters of the convex-concave degree and the saturation degreet、βtTherefore, the spatial position relation of the wafer workbench relative to the fine grinding wheel can be more accurately controlled, and the compensation grinding operation can be more accurately carried out on the surface of the wafer, so that the grinding precision of the wafer is further improved.
The above description is only a preferred embodiment of the application and is illustrative of the principles of the technology employed. It will be appreciated by a person skilled in the art that the scope of the invention as referred to in the present application is not limited to the embodiments with a specific combination of the above-mentioned features, but also covers other embodiments with any combination of the above-mentioned features or their equivalents without departing from the inventive concept. For example, the above features may be replaced with (but not limited to) features having similar functions disclosed in the present application.