Determination method and device for wafer edge polishing removal amount, medium and program product

Abstract

The invention discloses a wafer edge polishing removal amount determination method and device, a medium and a program product, the wafer edge polishing removal amount determination method comprises the steps that edge contour measurement data before polishing and after polishing are acquired, and the measurement data comprise contour point coordinates of multiple angles; based on the assumed n-degree polynomial fitting equation, using a least square algorithm to construct an objective function, and based on the objective function, performing matrix parameter solving to obtain a parameter set of a plurality of polynomial fitting modes; fitting error calculation is carried out according to the parameter set, if a single fitting error or two continuous fitting errors do not meet a preset termination condition, fitting is carried out again after the polynomial number n of the polynomial fitting equation is increased until the single fitting error and the two continuous fitting errors meet the preset termination condition, and if the fitting error does not meet the preset termination condition, fitting is carried out again. If yes, polynomial fitting is completed to obtain a front value curve; determining a tangent point corresponding to each angle on the previous value curve, and calculating a normal equation at each tangent point; solving the intersection point of the normal equation and the polished measurement data to obtain the coordinate of the intersection point corresponding to each tangency point; and the polishing removal amount of each angle is calculated according to the spatial distance between the tangent point coordinates and the corresponding intersection point coordinates.

Description

Technical Field

[0001] The present application relates to the field of semiconductor processing technologies, and particularly to a method and device, medium, and program product for determining the removal amount of wafer edge polishing. Background Art

[0002] During the wafer edge polishing process, accurately calculating the edge polishing removal amount is a key link to ensure the wafer quality. However, in the current edge polishing equipment and methods, there is a lack of a specific calculation method for the edge polishing removal amount. Existing calculation methods mostly target the conventional wafer surface polishing process, while the geometric shape and physical properties of the edge polishing part are significantly different from those of conventional polishing. Directly applying the conventional polishing calculation method will lead to result deviations and cannot meet the requirements of high-precision processing.

[0003] In addition, when actually measuring the edge polishing removal amount, due to the precision limitation of the measuring equipment, the interference of the measuring environment, and the influence of the wafer surface microstructure, the measured data shows a serrated or other irregular state. This irregular data makes it easy to deviate from the true value when calculating the removal amount based on it, thereby affecting the subsequent optimization and control of the polishing process.

[0004] Therefore, how to accurately calculate the edge polishing removal amount by compatibly considering the measurement error is an urgent problem to be solved, which is of great significance for improving the edge polishing precision and quality of semiconductor wafers. Summary of the Invention

[0005] In view of this, the present application provides a method and device, medium, and program product for determining the removal amount of wafer edge polishing to at least partially solve the above technical problems.

[0006] The first aspect of the present application provides a method for determining the removal amount of wafer edge polishing, including: obtaining the edge profile measurement data before and after polishing, where the measurement data includes the profile point coordinates at multiple angles; based on a hypothesized n-degree polynomial fitting equation, using the least squares algorithm to construct an objective function, and solving the matrix parameters based on the objective function to obtain parameter sets for multiple polynomial fitting methods; calculating the fitting error according to the parameter sets, if the single fitting error or the continuous two fitting errors do not meet the preset termination conditions, then increase the polynomial degree n of the polynomial fitting equation and perform fitting again until both the single fitting error and the continuous two fitting errors meet the preset termination conditions, then complete the polynomial fitting to obtain a pre-value curve; determining the tangent points corresponding to each angle on the pre-value curve, and calculating the normal equations at each tangent point; solving the intersection points of the normal equations and the measurement data after polishing to obtain the intersection coordinates corresponding to each tangent point; calculating the polishing removal amount for each angle according to the spatial distance between the tangent point coordinates and the corresponding intersection coordinates.

[0007] Optionally, for the assumed nth-degree polynomial fitting equation, the least squares algorithm is used to construct an objective function, and matrix parameters are solved based on the objective function, including:

[0008] Based on the assumed nth-degree fitting equation: y = θ0 + θ1X + θ2X 2 +…+ θ n X n , let y’ be the true value of the measured data, and the least squares algorithm is used to construct the objective function g:

[0009]

[0010] According to the derivative formula Solve A*θ = B to obtain matrix A, matrix θ, and matrix B.

[0011] Among them,

[0012]

[0013] means summing the nth powers of the x coordinate values of m samples. means summing the products of the nth powers of the x coordinate values of m samples and the corresponding y coordinate values of the samples.

[0014] Optionally, the preset termination conditions include: the range of the single fitting error G is [0.8, 1.6], and the range of the difference between the fitting errors ΔG of two adjacent times is [0, 0.5]. The calculation formula for the fitting error G is:

[0015]

[0016] where yi is the fitting value and y’i is the true measured data.

[0017] Optionally, solving the intersection of the normal equation and the polished measurement data to obtain the intersection coordinates corresponding to each tangent point includes: calculating the distances between the coordinates of each contour point in the post-value data and the normal equation to obtain two candidate contour points closest to the normal equation; selecting one from the two candidate contour points to determine the intersection coordinates according to the spatial position relationship between the two candidate contour points and the normal.

[0018] Optionally, selecting one from the two candidate contour points to determine the intersection coordinates according to the spatial position relationship between the two candidate contour points and the normal line includes: if one of the two candidate contour points is on the normal line, determining this point as the intersection point; or, if the two candidate contour points are on both sides of the normal line, calculating the intersection point according to the following intersection coordinate equation: (x1, y1) = ((x3 + x4) / 2, (y4 + y4) / 2), where (x1, y1) are the intersection coordinates, and (x3, y3), (x4, y4) are the coordinates of the two candidate contour points; or, if the two candidate contour points are on the same side of the normal line, determining the candidate contour point closer to the normal line as the intersection point.

[0019] The second aspect of the present application provides an edge polishing method, including: obtaining the wafer edge polishing removal amount and the edge profile measurement data before and after polishing as polishing history data through the above method; controlling the current edge polishing process of the wafer polishing equipment according to the polishing history data.

[0020] Optionally, controlling the current edge polishing process of the wafer polishing equipment according to the polishing history data includes: calculating the polishing removal amount per unit time corresponding to the polishing pressure according to the historical polishing data; calculating the polishing pressure or polishing time of the polishing head at each angle according to the polishing removal amount and the edge profile measurement data of the current wafer before polishing, and controlling the current edge polishing process of the wafer polishing equipment according to the calculation result.

[0021] The third aspect of the present application provides an edge polishing device, including: a wafer workbench for supporting the wafer; a polishing component for polishing the edge portion of the wafer; a sensor for measuring the edge profile measurement data before and after polishing, and a controller for executing the above method.

[0022] The fourth aspect of the present application provides a computer storage medium, on which a computer program is stored, and when the program is executed by a processor, the above method is implemented.

[0023] The fifth aspect of the present application provides a computer program product, including computer instructions, and the computer instructions instruct a computing device to execute the operations corresponding to the above method.

[0024] In the present application, by using the normal line as a reference, the tangent point of the pre-polishing contour curve and the intersection point of the post-polishing contour curve are found, and then the spatial distance between the two is directly calculated to determine the removal amount. This calculation method is not only simple and convenient, avoiding the cumbersome process of complex numerical integration or iterative calculation, but also significantly improves the calculation efficiency, and is particularly suitable for rapid application in the actual production environment.

[0025] Moreover, the calculation method of the present application based on the normal line can ensure that the calculation direction of the removal amount is consistent with the actual acting direction of polishing, thus more accurately reflecting the actual removal amount and effectively avoiding errors caused by inaccurate calculation directions.

[0026] Meanwhile, the present invention processes the measurement data before and after polishing through polynomial fitting, making the measurement values that may originally be serrated or irregular due to measurement noise or equipment precision limitations become smooth and uniform. This not only makes the determination of the tangent point and intersection point more accurate, but also makes the calculated removal amount closer to the true value. In practical applications, this method can effectively reduce calculation deviations caused by measurement errors or data irregularities, thereby improving the control precision and reliability of the polishing process; by accurately calculating the removal amount at each angle, the effect of the polishing process can be better evaluated, and then the polishing parameters can be optimized to ensure the quality and consistency of the wafer edge.

[0027] In addition, this method also realizes directional denoising of the edge profile measurement data through local slope analysis and angle constraint filtering, significantly improving the signal-to-noise ratio while retaining the effective data. Moreover, it innovatively integrates the process physical direction (normal line direction) into the filtering logic, breaking through the limitation of traditional filtering methods of "weakening noise and signal without discrimination", providing a reliable data basis for accurately determining the removal amount. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the drawings in the following description are only some embodiments recorded in the embodiments of the present application. For those of ordinary skill in the art, other drawings can also be obtained based on these drawings.

[0029] Figure 1 The top view of the wafer edge polishing device provided for another embodiment of the present application;

[0030] Figure 2 It is a schematic flow chart of the method for determining the removal amount of wafer edge polishing in an embodiment of the present application;

[0031] Figure 3 It is a schematic diagram of the edge profile of a wafer in an embodiment of the present application;

[0032] Figure 4 It is a schematic diagram of the edge profile measurement data before fitting in an embodiment of the present application;

[0033] Figure 5 It shows a schematic diagram of a front value curve and a back value curve;

[0034] Figure 6It is an exemplary flowchart showing a method for determining the removal amount of wafer edge polishing according to an embodiment of the present application;

[0035] Figure 7 It is a schematic diagram of an electronic device according to an embodiment of the present application. Detailed implementation manners

[0036] In order to enable those skilled in the art to better understand the technical solutions in the embodiments of the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the embodiments of the present application.

[0037] The terms used in the present application are only for the purpose of describing specific embodiments, and are not intended to limit the present application. The singular forms "a", "the" and "said" used in the present application and the appended claims are also intended to include the plural forms unless the context clearly indicates otherwise. It should also be understood that the term "and / or" used herein refers to and includes any or all possible combinations of one or more of the associated listed items.

[0038] It should be understood that although the terms first, second, third, etc. may be used in the present application to describe various information, such information should not be limited to these terms. These terms are only used to distinguish the same type of information from each other. For example, without departing from the scope of the present application, the first information may also be referred to as the second information, and similarly, the second information may also be referred to as the first information. Depending on the context, the word "if" as used herein may be interpreted as "when" or "while" or "in response to a determination".

[0039] The technical solutions in the embodiments of the present application will be clearly and completely described below in conjunction with the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative efforts shall fall within the protection scope of the present application. Without conflict, the following various embodiments and their technical features can be combined with each other.

[0040] In order to illustrate the technical solutions described in the present invention, the following will be described with reference to the accompanying drawings and in conjunction with embodiments.

[0041] In the present application, a wafer is also referred to as a chip, a silicon wafer, a substrate or a base plate (substrate), etc., and their meanings and actual functions are equivalent.

[0042] The solution of this application is mainly used for an edge bevel removal device. Refer to Figure 1 , the device includes a wafer stage (not shown in the figure) for supporting the wafer W and driving the wafer to rotate; a stage moving part (not shown in the figure) for moving the wafer stage in a direction parallel to the surface of the wafer stage; and a plurality of polishing components 11 for polishing the edge part of the wafer. Among them, the polishing component includes a chamfer polishing head and a polishing belt supply part. The chamfer polishing head presses the polishing belt against the chamfer part of the wafer through a contact pad, and during the polishing process, the polishing head can perform vertical reciprocating motion or rotational reciprocating motion around the chamfer part through a swing driving mechanism, and at the same time supply polishing liquid and cooling water to the chamfer part through a nozzle. In addition, the device also includes a sensor assembly for detecting the position of the wafer notch and the radial displacement of the wafer to ensure the accuracy of the polishing process.

[0043] During the edge polishing process of semiconductor wafers, accurately calculating the edge polishing removal amount is one of the key links to ensure the wafer quality. However, in current edge polishing devices and methods, there is no specific method for calculating the edge polishing removal amount. Existing calculation methods mainly target conventional wafer surface polishing processes. Since the geometric shape and physical characteristics during the polishing process of the edge polishing part are significantly different from those of conventional polishing, directly applying the calculation methods of conventional polishing will result in a large deviation between the calculation result and the actual removal amount, which cannot meet the requirements of high-precision processing.

[0044] In addition, when actually measuring the edge polishing removal amount, due to the accuracy limitation of the measuring device, the interference of the measuring environment, and the influence of the microscopic structure of the wafer surface, the measured data often shows a serrated or other irregular state. This irregular measured data makes it easy to deviate from the true value when calculating the removal amount based on these data, thus affecting the optimization and control of subsequent polishing processes. Therefore, how to accurately calculate the edge polishing removal amount while taking into account the errors generated during the measurement process as much as possible is an urgent problem to be solved at present, and it is of great significance for improving the accuracy and quality of semiconductor wafer edge polishing.

[0045] To at least solve some of the above problems, refer to Figure 2 , based on the above chemical mechanical polishing device, an embodiment of the present invention provides a method for determining the edge polishing removal amount of a wafer, including:

[0046] S101. Obtain the edge profile measurement data before and after polishing, and the measurement data includes the profile point coordinates at multiple angles.

[0047] In this embodiment, refer to Figure 3 , the edge profile of the wafer refers to the chamfer profile of the edge of the wafer in the thickness direction.

[0048] The measurement data should include the coordinates of profile points at multiple angles, which can comprehensively reflect the geometric shape of the wafer edge. In addition, there are notch marks for positioning on the outer circumference of the wafer. During measurement, multiple measurement positions determined according to the notch marks on the circumference can be measured, and a set of edge profile measurement data in the thickness direction of the wafer can be obtained for each measurement position.

[0049] A measurement station can be set in the wafer edge polishing equipment. When specifically measuring the edge profile, a high-precision optical measurement device or a contact profilometer in the measurement station can be used to measure the edge profile of the wafer. Of course, the measurement station can be not set, and integrating the high-precision optical measurement device or the contact profilometer into the polishing station is also within the protection scope of this application.

[0050] The sensor can be divided into an upper sensor and a lower sensor, which respectively measure the upper edge and the lower edge of the Wafer. The positions of the upper and lower sensors are generally at the positions of 45 degrees of the upper and lower edges of the wafer, but the positions can be adjusted according to the test situation in the actual process.

[0051] The measurement data before polishing characterizes the profile morphology of the wafer before polishing and is used to construct the pre-value curve; similarly, the measurement data after polishing is used to characterize the profile morphology of the wafer after polishing and can be used to evaluate the effect of the polishing process.

[0052] S102. Based on the assumed nth-degree polynomial fitting equation, use the least squares algorithm to construct an objective function, and solve the matrix parameters based on the objective function to obtain a parameter set of multiple polynomial fitting methods.

[0053] S103. Calculate the fitting error according to the parameter set. If the single fitting error or the continuous two fitting errors do not meet the preset termination conditions, increase the polynomial degree n of the polynomial fitting equation and then perform fitting again until both the single fitting error and the continuous two fitting errors meet the preset termination conditions, then complete the polynomial fitting to obtain the pre-value curve.

[0054] Increasing the polynomial degree n of the polynomial fitting equation means making n = n + 1.

[0055] In this embodiment, since the actually measured edge profile measurement data is often affected by noise and measurement errors, and the profile of the wafer itself may not change smoothly, the edge profile measurement data directly represents a serrated or other irregular state, which will lead to inaccurate calculation results and increase the difficulty of the thickness calculation process.

[0056] Therefore, in this step, the measurement data before polishing is smoothed by the polynomial fitting algorithm.

[0057] Optionally, in this embodiment, for the assumed n-th degree polynomial fitting equation, the least squares algorithm is used to construct an objective function, and matrix parameters are solved based on the objective function, including:

[0058] Based on the assumed n-th degree fitting equation: y = θ0 + θ1X + θ2X 2 +…+ θ n X n , let y’ be the true value of the measured data, and the least squares algorithm is used to construct the objective function g:

[0059]

[0060] According to the derivative formula Solve A*θ = B to obtain matrix A, matrix θ, and matrix B.

[0061] Among them,

[0062]

[0063] means summing the n-th powers of the x coordinate values of m samples, means summing the products of the n-th powers of the x coordinate values of m samples and the corresponding y coordinate values of the samples.

[0064] Through the polynomial equation, the least squares algorithm is used to adaptively fit discrete and irregular data, making the fitted curve smoother and the search for the tangent point more accurate, thereby improving the accuracy of the removal amount calculation. By setting the single fitting error and the continuous two fitting errors as preset termination conditions, it is possible to ensure that the fitted curve is smooth and minimize precision loss.

[0065] Preferably, the preset termination conditions include: the single fitting error G ranges from [0.8, 1.6], and the difference range of the adjacent two fitting errors ΔG is [0, 0.5]. The fitting error G calculation formula is: where yi is the fitted value and y’i is the true measured data. The range value of the single fitting error can minimize precision loss, and the interpolation range of the adjacent two fitting errors can ensure that the fitted curve is smooth and the fitting accuracy is high.

[0066] After the fitting is completed, the parameter set θ obtained by fitting can be substituted into the polynomial fitting equation to obtain the previous value curve.

[0067] See Figure 4 , which shows a graph of the edge profile measurement data before and after polishing. Figure 4 In [], the abscissa corresponds to the wafer thickness direction, the ordinate corresponds to the wafer radial direction, and the units of the abscissa and ordinate in the figure are micrometers μm. Figure 4The curve on the outer and middle sides corresponds to the measured data of the edge contour before polishing, and the curve on the inner side corresponds to the measured data of the edge contour after polishing.

[0068] S104. Determine the tangent points corresponding to each angle on the previous value curve, and calculate the normal equations at each tangent point.

[0069] On the generated smoothed previous value curve, multiple tangent points corresponding to key angles can be determined. The selection of the tangent points needs to cover each important area of the wafer edge, so as to comprehensively evaluate the effect of wafer edge polishing and calculate the polishing removal amount. Specifically, tangent points can be determined at intervals of a certain number of data points. For example, a tangent point is determined at every preset arc length on the previous value curve; tangent points corresponding to fixed normal angles can be selected. For example, points corresponding to normal angles of 0°, 30°, 60°, etc. are selected as tangent points, as long as the important areas of the wafer edge can be covered, which are all within the protection scope of this application.

[0070] Based on the previous value curve, for each tangent point, its corresponding tangent slope can be calculated, and further the normal equation can be obtained.

[0071] Specifically, the slope k1 of two adjacent points in the previous value curve can be calculated in sequence, and the slope k that is closest to being perpendicular to the normal of this angle is determined from multiple slopes k1. The midpoint of the two adjacent points where this slope k is obtained is confirmed as the tangent point. The obtained normal equation is: y - y0 = ((-1) / k) * (x - x0).

[0072] S105. Solve the intersection of the normal equation and the measured data after polishing to obtain the intersection coordinates corresponding to each tangent point.

[0073] In this embodiment, since the measured data after polishing is used to reflect the morphological contour of the wafer edge after polishing, the intersection of the normal equation and the measured data after polishing can be solved to obtain the intersection of the wafer edge after polishing and the normal, and the intersection coordinates are obtained.

[0074] Specifically, the measured data after polishing can be fitted by the same method to obtain the fitted posterior value curve, and the intersection of the normal equation and the posterior value curve is calculated to obtain the intersection coordinates; or the unfitted measured data after polishing can be used for calculation with the normal to obtain the intersection coordinates; or the intersection coordinates can be obtained by calculating the normal and the fitted discrete values, which are all within the protection scope of this application.

[0075] In the embodiments of the present application, when calculating the intersection coordinates using un-fitted post-polishing measurement data or discrete numerical points, step S104 may include: If one of the two candidate contour points is on the normal line, then determine this point as the intersection point; or, if the two candidate contour points are on both sides of the normal line, calculate the intersection point according to the following intersection coordinate equation: (x1, y1) = ((x3 + x4) / 2, (y4 + y4) / 2), where (x1, y1) are the intersection coordinates, and (x3, y3), (x4, y4) are the coordinates of the two candidate contour points; or, if the two candidate contour points are on the same side of the normal line, determine the candidate contour point closer to the normal line as the intersection point.

[0076] S106. Calculate the polishing removal amount of each angle according to the spatial distance between the tangent point coordinates and the corresponding intersection point coordinates.

[0077] Refer to Figure 5 , which shows a schematic diagram of a pre-value curve and a post-value curve. The abscissa in the figure corresponds to the wafer radial direction, and the ordinate corresponds to the wafer thickness direction. The curve located on the outside in the figure is the pre-value curve, which has a tangent point A and a tangent line q. The curve located on the inside is the post-value curve, which has an intersection point B. The normal line f passes through the tangent point A and the intersection point B.

[0078] The method proposed by the present invention finds the tangent point A of the pre-polishing contour curve and the intersection point B of the post-polishing contour curve with the normal line as the reference, and then directly calculates the spatial distance between the two to determine the removal amount. This calculation method is not only simple and convenient, avoiding the cumbersome process of complex numerical integration or iterative calculation, but also significantly improves the calculation efficiency, and is especially suitable for rapid application in the actual production environment. At the same time, the calculation method with the normal line as the reference can ensure that the calculation direction of the removal amount is consistent with the actual action direction of polishing, so as to more accurately reflect the actual removal amount and effectively avoid errors caused by inaccurate calculation directions.

[0079] In addition, the present invention processes the measurement data before and after polishing through polynomial fitting, making the measurement values that may be serrated or irregular due to measurement noise or equipment precision limitations become smooth and uniform. This not only makes the determination of the tangent point and the intersection point more accurate, but also makes the calculated removal amount closer to the true value. In practical applications, this method can effectively reduce the calculation deviation caused by measurement errors or data irregularities, thereby improving the control accuracy and reliability of the polishing process; by accurately calculating the removal amount of each angle, the effect of the polishing process can be better evaluated, and then the polishing parameters can be optimized to ensure the quality and consistency of the wafer edge.

[0080] Optionally, in this embodiment, during the edge polishing process, the polishing head can perform vertical reciprocating motion or rotational reciprocating motion around the chamfered part through a swing driving mechanism, so as to polish the chamfer on the edge. However, there is often a deviation between the actual contact direction of the polishing tool with the wafer surface (determined by the inclination angle θ of the polishing head) and the theoretical normal direction. This deviation will cause a certain error between the normal direction when calculating the removal amount and the actual acting direction of the polishing head. Therefore, in this embodiment, before performing polynomial fitting on the edge profile measurement data before polishing, it may further include: obtaining the attitude data of the polishing head in the wafer thickness direction during the edge polishing process; determining the inclination angle of each position of the polishing head in the wafer thickness direction according to the attitude data; and performing filtering processing on the edge profile measurement data before polishing according to the inclination angle.

[0081] During the measurement process, there may be data fluctuations due to sensor noise or microscopic fluctuations on the wafer surface. In order to ensure the calculation accuracy of the removal amount and reduce the calculation amount during the fitting process, in this embodiment, by combining the inclination angle of the polishing head during the edge polishing process, data points in the edge profile measurement data that deviate greatly from the polishing angle can be filtered out. This method realizes directional denoising of the edge profile measurement data through local slope analysis and angle constraint filtering, significantly improves the signal-to-noise ratio while retaining valid data, and innovatively integrates the process physical direction (normal direction) into the filtering logic, breaking through the limitation of traditional filtering methods of "weakening noise and signal without distinction", providing a reliable data basis for accurately determining the removal amount.

[0082] Specifically, when performing filtering processing on the edge profile measurement data before polishing according to the inclination angle, the effective direction range can be determined according to the inclination angle, and then the slope of two adjacent or several adjacent edge profile measurement data is calculated. If the vertical vector of the slope is within the effective direction range, the edge profile measurement data is retained; if not, it is filtered out. After filtering through the inclination angle, polynomial fitting can be continued on the edge profile measurement data to obtain a pre-value curve.

[0083] See Figure 6 , through a specific implementation manner, the solution of the present application is exemplarily described. As Figure 6 shown, the method includes:

[0084] S201. Obtain the edge profile measurement data before and after polishing, remove duplicates after sorting according to the profile coordinates in the radial direction, and obtain the edge profile measurement data before and after polishing to be processed.

[0085] S202. Adaptively fit the edge profile measurement data before polishing according to polynomial fitting to obtain fitting parameters.

[0086] Polynomial equation hypothesis: Input the sample data M (i.e., the edge profile measurement data) and the polynomial degree N, and assume the fitting equation (1).

[0087] y = θ0 + θ1X + θ2X 2 + … + θ n X n (1)

[0088] Objective function: Let y’ be the true value, and use the least squares method to construct the objective function (2).

[0089]

[0090] After that, perform matrix parametric equation calculation: According to the derivative formula Obtain matrix A, matrix θ, matrix B, and obtain equation (3).

[0091] A * θ = B (3)

[0092] Among them,

[0093]

[0094] means summing up the nth powers of the x - coordinate values of m samples, means summing up the products of the nth powers of the x - coordinate values of m samples and the corresponding y - coordinate values of the samples.

[0095] Due to the large amount of parameters, the inverse matrix cannot be directly used for solution. In this patent, the LU matrix decomposition method can be used to solve for θ, reducing precision loss.

[0096] Calculate the fitting error according to the following formula (4). If the single - fitting error G ranges from [0.8, 1.6], and the difference between adjacent two - fitting errors ΔG ranges from [0, 0.5], then the fitting is completed. If not, update n: n = n + 1 to increase the polynomial degree of the polynomial fitting equation, and jump to the polynomial equation hypothesis step to continue execution.

[0097]

[0098] Where yi is the fitting value and y’i is the true measurement data.

[0099] S203. Reconstruct the edge profile measurement data before polishing according to the fitting parameters to obtain the previous - value curve.

[0100] S204. Through the Loss system, calculate the tangent points corresponding to each angle based on the previous - value curve, the intersection points of the previous - value tangent normal and the subsequent - value, and calculate the distance between the tangent points and the intersection points as the removal amount.

[0101] The Loss system, i.e., the removal amount calculation system. When calculating through the Loss system, first perform the calculation of the intersection point of the posterior value. According to the point-line (assuming the straight line is: Ax + By + C = 0) distance formula (8) in the posterior value data, calculate the distance from the point to the normal line in turn, and find the two points (x3, y3) and (x4, y4) that are closest to the normal line distance.

[0102] d = (|Ax_1 + By_1 + C|) / √(A^2 + B^2) (8)

[0103] Perform intersection point judgment and determine the intersection point from the two points:

[0104] 1. If one of the two candidate contour points is on the normal line, determine this point as the intersection point.

[0105] 2. If the two candidate contour points are on both sides of the normal line, calculate the intersection point according to the following intersection point coordinate equation: (x1, y1) = ((x3 + x4) / 2, (y4 + y4) / 2), where (x1, y1) is the intersection point coordinate, and (x3, y3), (x4, y4) are the coordinates of the two candidate contour points.

[0106] 3. If the two candidate contour points are on the same side of the normal line, determine the candidate contour point that is closer to the normal line distance as the intersection point.

[0107] After determining the intersection point, the removal amount can be calculated: Calculate the distance between the tangent point and the intersection point according to the two-point distance formula to obtain the Loss amount (removal amount) of this angle.

[0108] Another embodiment of the present application also provides an edge polishing method, including: Through the above method, obtain the wafer edge polishing removal amount and the edge profile measurement data before and after polishing as polishing history data; According to the polishing history data, control the current edge polishing process of the wafer polishing equipment.

[0109] Specifically, according to the historical polishing data, calculate the polishing removal amount per unit time corresponding to the polishing pressure, and in combination with the edge profile measurement data before the current wafer polishing, calculate the polishing pressure or polishing time of the polishing head at each angle, and control the current edge polishing process of the wafer polishing equipment according to the calculation results.

[0110] Specifically, it is possible to control the polishing time and / or polishing pressure of the polishing head at the corresponding polishing angle, which are all within the protection scope of the present application.

[0111] In this embodiment, an electronic device 600 is provided, such as Figure 7As shown, the electronic device 600 may include: a processor 601, a communications interface 602, a memory 603, and a communication bus 604. Among them:

[0112] The processor 601, the communications interface 602, and the memory 603 communicate with each other through the communication bus 604.

[0113] The communications interface 602 is used to communicate with other electronic devices or servers.

[0114] The processor 601 is used to execute the program 605, and specifically can execute the relevant steps in the foregoing method for determining the wafer edge polishing removal amount or the edge polishing method embodiment.

[0115] Specifically, the program 605 may include program code, and the program code includes computer operation instructions.

[0116] The processor 601 may be a CPU, or a specific integrated circuit ASIC (Application Specific Integrated Circuit), or is configured as one or more integrated circuits. One or more processors included in the intelligent device may be of the same type of processor, such as one or more CPUs; or may be of different types of processors, such as one or more CPUs and one or more ASICs.

[0117] The memory 603 is used to store the program 605. The memory 603 may include high-speed RAM memory, and may also include non-volatile memory, such as at least one disk memory.

[0118] The program 605 is specifically used to cause the processor 601 to execute the method for determining the wafer edge polishing removal amount or the edge polishing method in the foregoing embodiments.

[0119] In this embodiment, a computer-readable storage medium is provided, storing instructions for causing a machine to execute the method for determining the wafer edge polishing removal amount or the edge polishing method as described herein. Specifically, a system or device equipped with a storage medium may be provided, on which software program code for implementing the functions of any one of the foregoing embodiments is stored, and causing the computer (or CPU or MPU) of the system or device to read and execute the program code stored in the storage medium.

[0120] In this case, the program code read from the storage medium itself can implement the functions in the foregoing method embodiments. Therefore, the program code and the storage medium storing the program code constitute a part of this application.

[0121] Examples of storage media for providing program code include floppy disks, hard disks, magneto-optical disks, optical disks (such as CD-ROM, CD-R, CD-RW, DVD-ROM, DVD-RAM, DVD-RW, DVD+RW), magnetic tapes, non-volatile memory cards, and ROMs. Optionally, the program code can be downloaded from a server computer via a communication network.

[0122] In this embodiment, a computer program product is provided, including computer instructions that direct a computing device to perform the operations corresponding to the above method embodiments.

[0123] It should be noted that, according to the needs of implementation, each component / step described in the embodiments of the present application can be split into more components / steps, or two or more components / steps or partial operations of components / steps can be combined into new components / steps to achieve the purpose of the embodiments of the present application.

[0124] The above method according to the embodiments of the present application can be implemented in hardware, firmware, or be implemented as software or computer code that can be stored in a recording medium (such as a CD ROM, RAM, floppy disk, hard disk, or magneto-optical disk), or be implemented as computer code originally stored in a remote recording medium or a non-transitory machine-readable medium and downloaded via a network and to be stored in a local recording medium, so that the method described herein can be stored in such software processing on a recording medium using a general-purpose computer, a dedicated processor, or programmable or dedicated hardware (such as an ASIC or FPGA). It can be understood that a computer, a processor, a microprocessor controller, or programmable hardware includes a storage component (such as RAM, ROM, flash memory, etc.) that can store or receive software or computer code, and when the software or computer code is accessed and executed by the computer, the processor, or the hardware, the method described herein is implemented. In addition, when a general-purpose computer accesses the code for implementing the method shown herein, the execution of the code converts the general-purpose computer into a dedicated computer for executing the method shown herein.

[0125] Although the present application has been shown and described with respect to one or more implementations, those skilled in the art will envision equivalent variations and modifications based on reading and understanding this specification and the drawings. The present application includes all such modifications and changes, and is limited only by the scope of the appended claims. In particular, with respect to the various functions performed by the above components, the terms used to describe such components are intended to correspond to any component that performs the specified function of the component (e.g., it is functionally equivalent), unless otherwise indicated, even if structurally different from the disclosed structure that performs the functions in the exemplary implementations of this specification shown herein.

[0126] That is, the above are only embodiments of the present application, and thus do not limit the patent scope of the present application. Any equivalent structural or equivalent process transformation made by using the content of the specification and drawings of the present application, such as the mutual combination of technical features between embodiments, or directly or indirectly applied in other related technical fields, shall similarly be included in the patent protection scope of the present application.

[0127] In addition, the terms "first" and "second" are only used for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly specifying the quantity of the indicated technical features. Thus, features defined with "first" and "second" may explicitly or implicitly include one or more features. In the description of the present application, "a plurality" means two or more unless otherwise specifically defined.

[0128] The above description is given to enable any person skilled in the art to implement and use the present application. In the above description, various details are listed for the purpose of explanation. It should be understood that those of ordinary skill in the art can recognize that the present application can also be implemented without using these specific details. In other embodiments, well-known processes will not be elaborated in detail to avoid obscuring the description of the present application with unnecessary details. Therefore, the present application is not intended to be limited to the disclosed embodiments, but rather to be in line with the broadest scope consistent with the principles and features disclosed in the present application.

[0129] It should be noted that on the premise of no conflict, the various embodiments described in the present application and / or the technical features in the various embodiments can be arbitrarily combined with each other, and the technical solutions obtained after combination should also fall within the protection scope of the present application.

[0130] It should be understood that the specific examples in the embodiments of the present application are only to help those skilled in the art better understand the embodiments of the present application, rather than limiting the scope of the embodiments of the present application. Those skilled in the art can make various improvements and deformations based on the above embodiments, and these improvements or deformations all fall within the protection scope of the present application.

[0131] As described above, these are only the specific implementation manners of the present application, but the protection scope of the present application is not limited thereto. Any person skilled in the art can easily think of changes or substitutions within the technical scope disclosed in the present application, and all should be covered by the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claimed rights.

Claims

1. A method for determining the removal amount of wafer edge polishing, characterized in that, Comprising: Obtaining edge profile measurement data before and after polishing, the measurement data including contour point coordinates at multiple angles; Based on a hypothesized nth-degree polynomial fitting equation, using the least squares algorithm to construct an objective function, and solving matrix parameters based on the objective function to obtain parameter sets for multiple polynomial fitting methods; Calculating the fitting error according to the parameter sets. If the single fitting error or the consecutive two fitting errors do not meet the preset termination conditions, then increase the polynomial degree n of the polynomial fitting equation and perform fitting again until both the single fitting error and the consecutive two fitting errors meet the preset termination conditions, then complete the polynomial fitting to obtain the pre-value curve; Determining the tangent points corresponding to each angle on the pre-value curve, and calculating the normal equations at each tangent point; Solving for the intersection points between the normal equations and the measurement data after polishing to obtain the intersection coordinates corresponding to each tangent point; Calculating the polishing removal amount for each angle according to the spatial distance between the tangent point coordinates and the corresponding intersection coordinates.

2. The method according to claim 1, characterized in that, The step of, based on a hypothesized nth-degree polynomial fitting equation, using the least squares algorithm to construct an objective function, and solving matrix parameters based on the objective function, includes: Hypothesis-based nth-degree fitting equation: y = θ0 + θ1X + θ2X 2 +…+ θ n X n , let y’ be the true value of the measured data, and use the least squares algorithm to construct the objective function g: According to the derivative formula Solve A*θ = B to obtain matrix A, matrix θ, and matrix B Wherein, Denotes the sum of the nth powers of the x - coordinate values of m samples. Denotes the sum of the products of the nth powers of the x - coordinate values of m samples and the corresponding y - coordinate values of the samples.

3. The method according to claim 1, characterized in that, The preset termination conditions include: the single fitting error G ranges from [0.8, 1.6], and the difference between the consecutive two fitting errors ΔG ranges from [0, 0.5]. The fitting error G calculation formula is: Where yi is the fitting value and y’i is the true measurement data.

4. The method according to claim 1, characterized in that, The step of solving for the intersection points between the normal equations and the measurement data after polishing to obtain the intersection coordinates corresponding to each tangent point includes: Calculating the distances between the coordinates of each contour point in the post-value data and the normal equation to obtain the two candidate contour points closest to the normal equation; According to the spatial position relationship between the two candidate contour points and the normal, selecting one from the two candidate contour points to determine the intersection coordinates.

5. The method according to claim 4, wherein The step of, according to the spatial position relationship between the two candidate contour points and the normal, selecting one from the two candidate contour points to determine the intersection coordinates, includes: If one of the two candidate contour points is on the normal, then determine this point as the intersection point; Or, if the two candidate contour points are on both sides of the normal, then calculate the intersection point according to the following intersection coordinate equation: (x1, y1) = ((x3 + x4) / 2, (y4 + y4) / 2), where (x1, y1) are the intersection coordinates, and (x3, y3), (x4, y4) are the coordinates of the two candidate contour points; Or, if the two candidate contour points are on the same side of the normal, then determine the candidate contour point closer to the normal as the intersection point.

6. An edge polishing method, characterized in that, Comprising: Obtaining the wafer edge polishing removal amount and the edge profile measurement data before and after polishing through the method according to any one of claims 1-5 as polishing history data; Controlling the current edge polishing process of the wafer polishing equipment according to the polishing history data.

7. The method according to claim 6, wherein Controlling the current edge polishing process of the wafer polishing equipment according to the polishing history data includes: Calculating the polishing removal amount per unit time corresponding to the polishing pressure according to the historical polishing data; Based on the polishing removal amount and the edge profile measurement data before the current wafer polishing, the polishing pressure or polishing time at each angle of the polishing head is calculated, and the current edge polishing process of the wafer polishing equipment is controlled according to the calculation results.

8. An edge polishing device, characterized in that, Including: A wafer stage for supporting the wafer; A polishing component for polishing the edge portion of the wafer; a sensor for measuring the edge profile measurement data before and after polishing, and a controller for executing the method according to any one of claims 1-8.

9. A computer storage medium, characterized in that, A computer program is stored thereon, and when the program is executed by a processor, it implements the method according to any one of claims 1-7.

10. A computer program product, characterized in that, Including computer instructions, the computer instructions direct the computing device to perform operations corresponding to the method according to any one of claims 1-7.

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