Wafer deviation correction calibration method based on clustering algorithm
Through multiple calibrations and clustering algorithm screenings, the problem of inaccurate calibration caused by electromagnetic interference in wafer bias correction methods has been solved, improving the accuracy and reliability of automatic wafer bias correction.
Patent Information
- Application Number
- CN202510552810.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-04-29
- Publication Date
- 2026-11-03
AI Technical Summary
Existing wafer alignment methods are susceptible to electromagnetic interference in semiconductor manufacturing, leading to inaccurate calibration results and affecting the accuracy of automatic alignment.
A wafer correction calibration method based on clustering algorithm is adopted. By performing multiple calibrations and using clustering algorithm to filter the calibration results, interference points are eliminated, thereby improving the accuracy of the calibration results.
By using clustering algorithms to select the optimal sensor coordinates, the accuracy of automatic wafer alignment and the reliability of subsequent alignment calculations are improved.
Smart Images
Figure CN123035910A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the fields of intelligent manufacturing, automation control and intelligent robots, specifically a wafer alignment and calibration method based on clustering algorithms. Background Technology
[0002] The semiconductor industry occupies a vital position in modern technology and the global economy, and is hailed as the "food of industry" or the "cornerstone of the information age." Semiconductor manufacturing processes are extremely delicate; the circuits on a wafer may only be a few nanometers or even at the atomic level. Therefore, the accuracy of wafer positioning is paramount during the manufacturing process.
[0003] Currently, the commonly used wafer alignment method mainly involves using a laser sensor to acquire the coordinates of the wafer when the sensor is triggered, calculating the position coordinates of the laser sensor relative to the robot arm's coordinate system, and then calculating the deviation value based on the finger coordinates, the wafer center coordinates, and the angle between the trigger point and the robot arm's coordinate system origin. The calibration process involves calculating the sensor's coordinates relative to the robot arm's coordinate system. The accuracy of the calibration results directly affects the accuracy of automatic alignment.
[0004] In actual working conditions, the main external interference in semiconductor cleanrooms comes from electromagnetic interference that may exist around the complex circuits of large equipment, which can lead to errors in data acquisition. Summary of the Invention
[0005] The purpose of this invention is to provide a wafer alignment calibration method based on a clustering algorithm. By performing multiple calibrations and using a clustering algorithm to filter the calibration results, interference points are eliminated, improving the accuracy of the calibration results and thus enhancing the accuracy of automatic wafer alignment.
[0006] The technical solution adopted by this invention to achieve the above objectives is: a wafer offset calibration method based on clustering algorithm, comprising the following steps:
[0007] 1) Robotic arm calibration data acquisition: Control the robotic arm to perform high-level extension and retraction operations at the workstation, sequentially trigger the sensors, collect the spatial position coordinates of the robotic arm at the four triggers, and determine the candidate coordinate positions of sensor A and sensor B in the robot's basic coordinate system based on geometric symmetry;
[0008] 2) Calibration result screening: By performing two extension and retraction operations with different T-axis joint values, sensor layouts that meet multiple candidate positions are screened out;
[0009] 3) Calculate the deviation distance of the wafer relative to the center of the finger, and select the group with the smallest deviation value as the valid calibration sample;
[0010] 4) Clustering of multiple calibration data sets: Repeat steps 1) to 2) N times to form a dataset, use a clustering algorithm to classify the dataset, remove abnormal calibration points, and output the optimal sensor coordinates;
[0011] 5) Based on the clustered sensor coordinates, generate automatic correction control parameters for the robotic arm to achieve wafer correction calibration.
[0012] In step 1), the sensor position calculation includes:
[0013] 1-1) Based on the coordinates of the robot arm's center at the four trigger points P1 to P4, calculate the coordinates of the midpoints P1 to P4 respectively. 14M P 23M ;
[0014] 1-2) Based on the Pythagorean theorem, calculate the distance d from the sensor to the midpoint. A d B Combined with the direction angle t of the perpendicular bisector 14P t 14N t 23P t 23N Determine the candidate location of sensor A (A P A N ) and candidate locations of sensor B (B P B N ).
[0015] The direction angle t 14P t 14N t 23P t 23N The method for obtaining it is as follows:
[0016] Based on the direction angle t of trigger points P2~P3 and P1~P4 23P t 14N The direction angle t of the perpendicular bisector can be obtained by adding or subtracting π / 2. 23P t 23N and t 14P t 14N ;
[0017] The atan2 function is used to calculate the direction angles of P2P3 and P1P4, and it is defined as a piecewise function:
[0018]
[0019] P 23M B P P 14M A P The direction angle is:
[0020]
[0021] P 23M B N P 14M A N The direction angle is:
[0022]
[0023] Combined with the direction angle t of the perpendicular bisector 14P t 14N t 23P t 23N The candidate locations of sensor A and sensor B are determined.
[0024] Combined with the direction angle t of the perpendicular bisector 14P t 14N t 23P t 23N Determine the candidate locations of sensor A and sensor B, that is:
[0025] The coordinate positions of sensor A and sensor B are:
[0026]
[0027] The two scaling operations are as follows:
[0028] To mitigate the error caused by sensor delay, two sets of data are collected: one for the extended sensor and one for the retracted sensor.
[0029] During the first extension operation, the robot arm's R-value is greater than its actual position; during the retraction operation, the R-value is less than its actual position.
[0030] The second operation adjusts the T-axis joint values. Based on the comparison of the deviation distances of the four trigger points, candidate results that match the sensor layout are selected, namely:
[0031] a. Both sensor A and sensor B are located on the left side (AP+BP);
[0032] b. At the left side of sensor A and the right side of sensor B (AP+BN);
[0033] c. To the right of sensor A and to the left of sensor B (AN+BP);
[0034] d. Both sensor A and sensor B are located on the right side (AN+BN).
[0035] In step 3), the calculation of the deviation distance between the wafer and the center of the finger, and the selection of the group with the smallest deviation value as the valid calibration sample, specifically involves:
[0036] 2-1) Let the theoretical radius of the wafer be r, and the polar coordinates of the robot arm center be (R... i ,T i), i = 1, 2, 3, 4, record the spatial coordinates of the robot's end effector during the four triggers, i.e., the actual coordinates of the robot's center are (x, y). i ,y i ):
[0037]
[0038] The theoretical distances from P1 and P4 to sensor A are equal to the wafer radius r, while the theoretical distances from P2 and P3 to sensor B are equal to the wafer radius r. Sensor B is located on the perpendicular bisector of P2 and P3, and sensor A is located on the perpendicular bisector of P1 and P4. According to geometric symmetry, both sensor A and sensor B have two positions: (AP, AN, BP, BN).
[0039] 2-2) The four trigger points (x) of the second scaling operation i ,y i Calculate the four offset distances of the wafer relative to the center of the finger;
[0040] Four trigger points (x) i ,y i Substitute (x) into the following categories respectively c ,y c ),Right now:
[0041]
[0042] Among them, (x ε ,y ε ) represents the coordinates of the robot's end effector captured when the sensor is triggered, d x d y Determined by the robotic arm model;
[0043] 2-3) will yield (d) x ,d y The trigger point corresponding to the smallest set of solutions is used as the final coordinate position of the sensor.
[0044] In step 4), the clustering algorithm includes:
[0045] 3-1) Initialization: Randomly select 3 initial center points from the calibration dataset, and the Euclidean distance between any two center points must satisfy the following condition:
[0046]
[0047] Where, σ 2 Let d be the global variance of the dataset. 12 ,d 13 ,d 23 The Euclidean distance between any two center points;
[0048] Based on the distance threshold, determine three initial center points that meet the conditions;
[0049] 3-2) Iterative optimization: Calculate the Euclidean distance from each data point to the center point and classify them, then update the center point to the geometric center of the data points within the class;
[0050] 3-3) Termination condition: The iteration stops when the rate of change of the total distance from each data point to its respective center point is less than a preset threshold;
[0051] 3-4) Calculate the amount of data contained in each cluster, retain the cluster with the largest amount of data as the valid calibration result, and discard the rest of the data as outliers.
[0052] The method for obtaining the distance threshold includes the following steps:
[0053] The global variance of the dataset is calculated as follows:
[0054]
[0055] Where μ is the mean of the dataset, N is the amount of data, and P is the mean of the dataset. k For the k-th data point;
[0056] The minimum spacing threshold for the initial center point is set to 1.5σ. If the spacing of the randomly selected center point does not reach the threshold, a new center point is selected until the condition is met.
[0057] It also includes a sensor position verification step:
[0058] The clustered sensor coordinates are input into the wafer correction system to perform a simulated correction operation.
[0059] If the wafer center offset correction error exceeds the threshold, the calibration process will be retried.
[0060] A wafer offset correction system based on a clustering algorithm for wafer offset calibration includes:
[0061] The robotic arm module is a vacuum cleanroom robotic arm that uses frictional contact to pick up and place wafers under vacuum conditions;
[0062] The built-in encoder is located in the robotic arm module and is used to provide real-time feedback on joint angles and end-effector position coordinates.
[0063] A sensor array containing two symmetrically distributed sensors, A and B;
[0064] Both sensor A and sensor B are photoelectric sensors or laser displacement sensors, and are respectively installed on both sides of the workstation;
[0065] The control unit stores clustering algorithm modules and correction control logic, which are used to receive data transmitted from the sensor array and the built-in encoder, and to correct the motion trajectory of the robotic arm module.
[0066] The present invention has the following beneficial effects and advantages:
[0067] 1. This invention can obtain relatively accurate sensor coordinate positions through clustering algorithms.
[0068] 2. The accurate calibration results of this invention significantly improve the reliability of subsequent correction calculations. Attached Figure Description
[0069] Figure 1 Flowchart of the wafer polarization calibration method of the present invention;
[0070] Figure 2 This embodiment is a schematic diagram of wafer alignment calibration. Detailed Implementation
[0071] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments.
[0072] like Figure 1 The diagram shows a flowchart of the wafer offset calibration method of the present invention. The present invention is a wafer offset calibration method based on a clustering algorithm. It obtains multiple sets of sensor position coordinates through multiple calibrations, and then uses a clustering algorithm to classify and filter the multiple sets of data, eliminating abnormal position information caused by external factors, thereby improving the accuracy of the calibration results and enhancing the precision of automatic offset correction.
[0073] The present invention specifically includes the following steps:
[0074] 1) Robotic arm calibration data acquisition: Control the robotic arm to perform high-level extension and retraction operations at the workstation, sequentially trigger the sensors, collect the spatial position coordinates of the robotic arm at the four triggers, and determine the candidate coordinate positions of sensor A and sensor B in the robot's basic coordinate system based on geometric symmetry;
[0075] 1-1) Based on the coordinates of the robot arm's center at the four trigger points P1 to P4, calculate the coordinates of the midpoints P1 to P4 respectively. 14M P 23M ;
[0076] 1-2) Based on the Pythagorean theorem, calculate the distance d from the sensor to the midpoint. A d B Combined with the direction angle t of the perpendicular bisector 14P t 14N t 23P t 23N Determine the candidate location of sensor A (A P AN ) and candidate locations of sensor B (B P B N ).
[0077] 2) Calibration result screening: By performing two extension / retraction operations with different T-axis joint values, sensor layouts that meet multiple candidate positions are screened; to address errors caused by sensor delay, two sets of data are collected: one for extension and one for retraction.
[0078] During the first extension operation, the robot arm's R-value is greater than its actual position; during the retraction operation, the R-value is less than its actual position.
[0079] The second operation adjusts the T-axis joint values. Based on the comparison of the deviation distances of the four trigger points, candidate results that match the sensor layout are selected, namely:
[0080] a. Both sensor A and sensor B are located on the left side (AP+BP);
[0081] b. At the left side of sensor A and the right side of sensor B (AP+BN);
[0082] c. To the right of sensor A and to the left of sensor B (AN+BP);
[0083] d. Both sensor A and sensor B are located on the right side (AN+BN).
[0084] 3) Calculate the deviation distance of the wafer relative to the center of the finger, and select the group with the smallest deviation value as the valid calibration sample;
[0085] 3-1) Let the theoretical radius of the wafer be r, and the polar coordinates of the robot arm center be (R... i ,T i ), i = 1, 2, 3, 4, record the spatial coordinates of the robot's end effector during the four triggers, i.e., the actual coordinates of the robot's center are (x, y). i ,y i ):
[0086]
[0087] The theoretical distances from P1 and P4 to sensor A are equal to the wafer radius r, while the theoretical distances from P2 and P3 to sensor B are equal to the wafer radius r. Sensor B is located on the perpendicular bisector of P2 and P3, and sensor A is located on the perpendicular bisector of P1 and P4. According to geometric symmetry, both sensor A and sensor B have two positions: (AP, AN, BP, BN).
[0088] 3-2) The four trigger points (x) of the second scaling operation i ,y i Calculate the four offset distances of the wafer relative to the center of the finger;
[0089] Four trigger points (x) i ,y i Substitute (x) into the following categories respectively c ,y c ),Right now:
[0090]
[0091] Among them, (x ε ,y ε ) represents the coordinates of the robot's end effector captured when the sensor is triggered, d x d y Determined by the robotic arm model;
[0092] 3-3) will yield (d) x ,d y The trigger point corresponding to the smallest set of solutions is used as the final coordinate position of the sensor.
[0093] 4) Clustering of multiple calibration data sets: Repeat steps 1) to 2) N times to form a dataset, use a clustering algorithm to classify the dataset, remove abnormal calibration points, and output the optimal sensor coordinates;
[0094] 4-1) Initialization: Randomly select 3 initial center points from the calibration dataset, and the Euclidean distance between any pair of center points must satisfy the following condition:
[0095]
[0096] Where, σ 2 Let d be the global variance of the dataset. 12 ,d 13 ,d 23 The Euclidean distance between any two center points;
[0097] Based on the distance threshold, determine three initial center points that meet the conditions;
[0098] The method for obtaining the distance threshold includes the following steps:
[0099] The global variance of the dataset is calculated as follows:
[0100]
[0101] Where μ is the mean of the dataset, N is the amount of data, and P is the mean of the dataset. k For the k-th data point;
[0102] The minimum spacing threshold for the initial center point is set to 1.5σ. If the spacing of the randomly selected center point does not reach the threshold, a new center point is selected until the condition is met.
[0103] 4-2) Iterative optimization: Calculate the Euclidean distance from each data point to the center point and classify them, then update the center point to the geometric center of the data points within the class;
[0104] 4-3) Termination condition: The iteration stops when the rate of change of the total distance from each data point to its respective center point is less than a preset threshold;
[0105] 4-4) Calculate the amount of data contained in each cluster, retain the cluster with the largest amount of data as the valid calibration result, and remove the rest of the data as outliers.
[0106] 5) Based on the clustered sensor coordinates, generate automatic correction control parameters for the robotic arm to achieve wafer correction calibration.
[0107] The present invention also includes a sensor position verification step:
[0108] The clustered sensor coordinates are input into the wafer correction system to perform a simulated correction operation.
[0109] If the wafer center offset correction error exceeds the threshold, the calibration process will be retried.
[0110] Based on the above-mentioned wafer alignment and calibration method based on clustering algorithm, this invention provides a wafer alignment system, comprising:
[0111] The robotic arm module is a vacuum cleanroom robotic arm that uses frictional contact to pick up and place wafers under vacuum conditions;
[0112] The built-in encoder is located in the robotic arm module and is used to provide real-time feedback on joint angles and end-effector position coordinates.
[0113] A sensor array containing two symmetrically distributed sensors, A and B;
[0114] Both sensor A and sensor B are photoelectric sensors or laser displacement sensors, and are installed on both sides of the workstation respectively;
[0115] The control unit stores clustering algorithm modules and correction control logic, which are used to receive data transmitted from the sensor array and the built-in encoder, and to correct the motion trajectory of the robotic arm module.
[0116] Example 1:
[0117] This embodiment first collects the coordinate positions of multiple sensors by repeatedly extending and retracting the sensor. Then, the dataset is processed using a clustering algorithm to categorize the data into three groups: sensor A, sensor B, and calibration failure. The cluster centers of sensors A and B are selected as the actual coordinate positions of sensors A and B, respectively.
[0118] (1) Wafer polarization calibration method
[0119] After setting up the workstation, place the wafer, aligning its center with the center of the finger. Control the robotic arm to perform a high-position extension / retraction operation at the workstation, triggering it four times sequentially. Collect the spatial position of the robotic arm when the sensors are triggered, and calculate the positions of sensor A and sensor B in the robot's basic coordinate system.
[0120] like Figure 2 The diagram shown is a schematic diagram of wafer correction calibration in this embodiment. In this embodiment, the wafer center (which is also the center of the finger) during the four triggers in the movement are P1 to P4 in chronological order.
[0121] The polar coordinates of the robot arm's center are (R i ,T i (i = 1, 2, 3, 4, record the coordinates of the robot's center at the four triggers:)
[0122]
[0123] The theoretical distances from P1 and P4 to sensor A are equal to the wafer radius, while the theoretical distances from P2 and P3 to sensor B are also equal to the wafer radius. Sensor B is located on the perpendicular bisector of P2 and P3, and sensor A is located on the perpendicular bisector of P1 and P4. Due to geometric symmetry, sensors A and B each have two possible positions: (AP, AN, BP, BN). 14M P is the midpoint between P1 and P4. 23M It is the midpoint between P2 and P3.
[0124] According to the Pythagorean theorem, we can obtain:
[0125]
[0126] The orientation angles of P2P3 and P1P4 are:
[0127]
[0128] As can be seen from the figure, P 23M B P P 14M A P The direction angle is:
[0129]
[0130] P 23M B N P 14M A N The direction angle is:
[0131]
[0132] Finally, the coordinate positions of sensors A and B were determined:
[0133]
[0134] (2) Calibration result screening:
[0135] Because of the time delay in the measurement results obtained by the control system from the sensors, the robot's RT coordinates obtained when the sensors are triggered lag behind the actual position. Therefore, the calibration results for the extension and retraction processes differ; the R-value (absolute value) of the former is greater than the actual position, while the R-value (absolute value) of the latter is less than the actual position. Therefore, the calibration process must be performed once for each of the extension and retraction processes. The sensor position can be categorized into four cases:
[0136] Both sensors are on the left side (AP+BP);
[0137] The closer sensors are on the left, and the farther ones are on the right (AP+BN);
[0138] The closer sensors are on the right, and the farther ones are on the left (AN+BP);
[0139] Both sensors are on the right side (AN+BN).
[0140] To differentiate between the above situations, two extension / retraction operations are performed, with different T-axis joint values for the first and second operations. The first extension / retraction calibration calculates all possible scenarios. Then, for the four trigger points of the second movement, the four deviation distances of the wafer relative to the center of the finger are calculated, and the group with the smallest deviation value is selected as the sample set for sensor coordinates. The above process can be repeated 5 to 10 times to obtain the dataset, and then a clustering algorithm is used to remove points that failed calibration or contained interference.
[0141] (3) In this embodiment, the specific steps of the clustering algorithm are as follows:
[0142] 1. Randomly select 3 center points from the dataset, and the differences between these 3 center points should be relatively large.
[0143] 2. For each data point, calculate its distance to each of the three center points, and then classify the data point into the category corresponding to the center point that is closer to it, based on the distance.
[0144] 3. For each type of data point, calculate its midpoint and use this midpoint as the new position of the center point of that type that will be updated.
[0145] 4. Update the centroids, and then repeat the steps of calculating the distance from each data point to the three centroids and classifying the data points. If the sum of the distances between each data point and the centroid of its category no longer changes, then the algorithm can stop running.
[0146] In the above steps, the results of multiple calibrations are filtered and classified using a clustering algorithm to exclude calibration failures and calibration results with interference.
[0147] In summary, in conjunction with Embodiment 1, this invention introduces a wafer offset calibration method based on a clustering algorithm. This method classifies the results of multiple automatic calibrations using a clustering algorithm. Data deemed unlikely to be sensor coordinates is removed, and the cluster centers determined to be likely sensor coordinates are used as the calibration results. This method effectively improves the accuracy of the calibration results, thereby enhancing the accuracy of automatic offset correction.
[0148] Those skilled in the art will understand that the above description is merely a preferred embodiment of the present invention, and the features described in the various embodiments and / or claims of this disclosure can be combined or combined in various ways, even if such combinations or combinations are not explicitly described in this disclosure. This is not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.
[0149] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention. Clearly, those skilled in the art can make various alterations and modifications to the invention without departing from its spirit and scope. Thus, if these modifications and modifications of the invention fall within the scope of the claims and their equivalents, the invention is also intended to include these modifications and modifications.
Claims
1. A wafer offset calibration method based on clustering algorithm, characterized in that, Includes the following steps: 1) Robotic arm calibration data acquisition: Control the robotic arm to perform high-level extension and retraction operations at the workstation, sequentially trigger the sensors, collect the spatial position coordinates of the robotic arm at the four triggers, and determine the candidate coordinate positions of sensor A and sensor B in the robot's basic coordinate system based on geometric symmetry; 2) Calibration result screening: By performing two extension and retraction operations with different T-axis joint values, sensor layouts that meet multiple candidate positions are screened out; 3) Calculate the deviation distance of the wafer relative to the center of the finger, and select the group with the smallest deviation value as the valid calibration sample; 4) Clustering of multiple calibration data sets: Repeat steps 1) to 2) N times to form a dataset, use a clustering algorithm to classify the dataset, remove abnormal calibration points, and output the optimal sensor coordinates; 5) Based on the clustered sensor coordinates, generate automatic correction control parameters for the robotic arm to achieve wafer correction calibration.
2. The wafer offset correction and calibration method based on clustering algorithm according to claim 1, characterized in that, In step 1), the sensor position calculation includes: 1-1) Based on the coordinates of the robot arm's center at the four trigger points P1 to P4, calculate the coordinates of the midpoints P1 to P4 respectively. 14M P 23M ; 1-2) Based on the Pythagorean theorem, calculate the distance d from the sensor to the midpoint. A d B Combined with the direction angle t of the perpendicular bisector 14P t 14N t 23P t 23N Determine the candidate location of sensor A (A P A N ) and candidate locations of sensor B (B P B N ).
3. The wafer offset calibration method based on clustering algorithm according to claim 2, characterized in that, The direction angle t 14P t 14N t 23P t 23N The method for obtaining it is as follows: Based on the direction angle t of trigger points P2~P3 and P1~P4 23P t 14N The direction angle t of the perpendicular bisector can be obtained by adding or subtracting π / 2. 23P t 23N and t 14P t 14N ; The atan2 function is used to calculate the direction angles of P2P3 and P1P4, and it is defined as a piecewise function: P 23M B P P 14M A P The direction angle is: P 23M B N P 14M A N The direction angle is: Combined with the direction angle t of the perpendicular bisector 14P t 14N t 23P t 23N The candidate locations of sensor A and sensor B are determined.
4. A wafer offset calibration method based on a clustering algorithm according to claim 2 or 3, characterized in that, Combined with the direction angle t of the perpendicular bisector 14P t 14N t 23P t 23N Determine the candidate locations of sensor A and sensor B, that is: The coordinate positions of sensor A and sensor B are:
5. The wafer offset calibration method based on clustering algorithm according to claim 1, characterized in that, In step 2), the two expansion and contraction operations are specifically as follows: To mitigate the error caused by sensor delay, two sets of data are collected: one for the extended sensor and one for the retracted sensor. During the first extension operation, the robot arm's R-value is greater than its actual position; during the retraction operation, the R-value is less than its actual position. The second operation adjusts the T-axis joint values. Based on the comparison of the deviation distances of the four trigger points, candidate results that match the sensor layout are selected, namely: a. Both sensor A and sensor B are located on the left side (AP+BP); b. At the left side of sensor A and the right side of sensor B (AP+BN); c. To the right of sensor A and to the left of sensor B (AN+BP); d. Both sensor A and sensor B are located on the right side (AN+BN).
6. The wafer offset calibration method based on clustering algorithm according to claim 1, characterized in that, In step 3), the calculation of the deviation distance between the wafer and the center of the finger, and the selection of the group with the smallest deviation value as the valid calibration sample, specifically involves: 2-1) Let the theoretical radius of the wafer be r, and the polar coordinates of the robot arm center be (R... i ,T i ), i = 1, 2, 3, 4, record the spatial coordinates of the robot's end effector during the four triggers, i.e., the actual coordinates of the robot's center are (x, y). i ,y i ): The theoretical distances from P1 and P4 to sensor A are equal to the wafer radius r, while the theoretical distances from P2 and P3 to sensor B are equal to the wafer radius r. Sensor B is located on the perpendicular bisector of P2 and P3, and sensor A is located on the perpendicular bisector of P1 and P4. According to geometric symmetry, both sensor A and sensor B have two positions: (AP, AN, BP, BN). 2-2) The four trigger points (x) of the second scaling operation i ,y i Calculate the four offset distances of the wafer relative to the center of the finger; Four trigger points (x) i ,y i Substitute (x) into the following categories respectively c ,y c ),Right now: Among them, (x ε ,y ε ) represents the coordinates of the robot's end effector captured when the sensor is triggered, d x d y Determined by the robotic arm model; 2-3) will yield (d) x ,d y The trigger point corresponding to the smallest set of solutions is used as the final coordinate position of the sensor.
7. The wafer offset calibration method based on clustering algorithm according to claim 1, characterized in that, In step 4), the clustering algorithm includes: 3-1) Initialization: Randomly select 3 initial center points from the calibration dataset, and the Euclidean distance between any two center points must satisfy the following condition: Where, σ 2 Let d be the global variance of the dataset. 12 ,d 13 ,d 23 The Euclidean distance between any two center points; Based on the distance threshold, determine three initial center points that meet the conditions; 3-2) Iterative optimization: Calculate the Euclidean distance from each data point to the center point and classify them, then update the center point to the geometric center of the data points within the class; 3-3) Termination condition: The iteration stops when the rate of change of the total distance from each data point to its respective center point is less than a preset threshold; 3-4) Calculate the amount of data contained in each cluster, retain the cluster with the largest amount of data as the valid calibration result, and discard the rest of the data as outliers.
8. The wafer offset calibration method based on clustering algorithm according to claim 7, characterized in that, The distance threshold is obtained as follows: The global variance of the dataset is calculated as follows: Where μ is the mean of the dataset, N is the amount of data, and P is the mean of the dataset. k For the k-th data point; The minimum spacing threshold for the initial center point is set to 1.5σ. If the spacing of the randomly selected center point does not reach the threshold, a new center point is selected until the condition is met.
9. The wafer offset calibration method based on clustering algorithm according to claim 1, characterized in that, It also includes a sensor position verification step: The clustered sensor coordinates are input into the wafer correction system to perform a simulated correction operation. If the wafer center offset correction error exceeds the threshold, the calibration process will be retried.
10. A wafer alignment system based on a clustering algorithm for wafer alignment and calibration, as described in claim 1, characterized in that, include: The robotic arm module is a vacuum cleanroom robotic arm that uses frictional contact to pick up and place wafers under vacuum conditions; The built-in encoder is located in the robotic arm module and is used to provide real-time feedback on joint angles and end-effector position coordinates. A sensor array containing two symmetrically distributed sensors, A and B; Both sensor A and sensor B are photoelectric sensors or laser displacement sensors, and are respectively installed on both sides of the workstation; The control unit stores clustering algorithm modules and correction control logic, which are used to receive data transmitted from the sensor array and the built-in encoder, and to correct the motion trajectory of the robotic arm module.