Machine Learning for Classifying Retaining Rings

Abstract

A method for optimizing polishing includes: for each retaining ring of a plurality of retaining rings mounted to a particular carrier head, taking measurements of a bottom surface of each retaining ring mounted to a particular carrier head using a coordinate measuring machine, and collecting respective removal profiles of substrates polished using each retaining ring. A machine learning model is trained based on the measurements of the bottom surfaces of the retaining rings and the respective removal profiles.

Description

[Technical field]

[0001] The present disclosure relates generally to chemical mechanical polishing, and more particularly to classifying retaining rings using machine learning. [Background technology]

[0002] Integrated circuits are typically formed on a substrate (eg, a semiconductor wafer) by successively depositing conductive, semiconductive, or insulating layers on the silicon wafer and successively processing these layers.

[0003] One manufacturing step involves depositing a fill layer over a non-planar surface and planarizing the fill layer. For certain applications, the fill layer is planarized until the top surface of the patterned layer is exposed or until a desired thickness remains above the underlying layer. In addition, planarization can be used to planarize the surface of a substrate for lithography, such as a dielectric layer.

[0004] Chemical mechanical polishing (CMP) is one accepted method of planarization. This method of planarization typically involves mounting a substrate on a carrier head. The exposed surface of the substrate is positioned against a rotating polishing pad. The carrier head exerts a controllable load on the substrate to press the substrate against the polishing pad. In some polishing machines, the carrier head includes a membrane that forms a plurality of separately pressurizable radial concentric chambers, where the pressure in each chamber controls the polishing rate in each corresponding area on the substrate. A polishing fluid, such as a slurry containing abrasive particles, is supplied to the surface of the polishing pad.

[0005] As a separate issue, machine learning has been widely used to aid automation through experience (e.g., historical data), for example, to classify items into various categories. Machine learning can be broadly divided into three categories: supervised learning, which uses input data with known category labels; unsupervised learning, which uses input data without known category labels; and reinforcement learning, which aims to reach a specific goal by navigating and interacting with an environment. Unsupervised learning has been used in marketing (e.g., customer segmentation), biology (e.g., DNA pattern clustering), and finance (e.g., anomaly detection or fraud detection), to name a few.

[0006] Deep learning is a branch of machine learning that typically uses neural networks. A neural network is a machine learning model that uses one or more layers of nonlinear units to predict an output for a received input. Some neural networks include one or more hidden layers in addition to an output layer. The output of each hidden layer is used as the input to the next layer in the network, i.e., the next hidden layer or the output layer. Each layer of the network generates an output from the received input according to the current values ​​of its respective set of parameters. Summary of the Invention

[0007] A method for evaluating polishing includes, for each of a plurality of retaining rings mounted to a particular carrier head, taking measurements of a bottom surface of each of the retaining rings mounted to a particular carrier head using a coordinate measuring machine, the measurements being representative of a characteristic of the bottom surface, an unsupervised learning algorithm is executed to classify each of the plurality of retaining rings into a respective category based on the measurements of the plurality of retaining rings, the classifications produced by the unsupervised learning algorithm are stored, and the classifications are evaluated against the polishing profile measurements to determine parameters that result in profile differences.

[0008] In another aspect, a method for optimizing polishing includes, for each retaining ring of a plurality of retaining rings mounted to a particular carrier head, taking measurements of a bottom surface of each retaining ring mounted to a particular carrier head using a coordinate measuring machine, and collecting respective removal profiles of substrates polished using each retaining ring, A machine learning model is trained based on the measurements of the bottom surfaces of the retaining rings and the respective removal profiles.

[0009] Particular embodiments include, but are not limited to, one or more of the following anticipated advantages.

[0010] Measurements can be taken with high resolution across the bottom surface of the retaining ring, for example as a mesh scan across the entire bottom surface of the retaining ring, which generates sufficient topographical information to allow analysis of the properties of the retaining ring. The analyzed properties of a particular retaining ring can be correlated with one or more polishing profiles of substrates polished using the retaining ring, allowing a determination of one or more parameters related to the retaining ring that cause differences in the polishing profiles.

[0011] Further, polishing profiles can be predicted based on measurements collected by the mesh scan. Specifically, one or more retaining rings can be classified into respective categories of a plurality of categories using an unsupervised machine learning algorithm. Each classified retaining ring can be associated with one or more polishing profiles for a respective substrate polished using the classified retaining ring.

[0012] The neural network model can be trained by receiving as input the classified retaining ring shape information associated with the polishing profile, and the neural network model can then be used to predict the polishing profile, i.e., by performing inference operations within the trained neural network that receives as input the measured bottom surface profile of the retaining ring.

[0013] It is possible to improve the time to production. Using the described technology, the system can more efficiently detect whether the retaining ring is usable for polishing substrates according to various polishing requirements before or after the break-in process. The system can also efficiently determine whether the break-in of the retaining ring is sufficient, and provide information or guidance for further break-in process to the user based on the classification result.

[0014] The quality control of the polishing process can be improved and throughput can be increased. In particular, defective retaining rings can be identified and replaced. The polishing rate within one or more regions of the substrate being polished can be adjusted based on a predicted polishing profile associated with the retaining ring, thus improving within-wafer uniformity during polishing and ultimately achieving higher throughput.

[0015] Furthermore, the described techniques can be easily scaled up with low computational costs. The system can further adjust or modify the classification and neural network models based on subsequent measured topographical data and polishing profiles, eliminating unnecessary recalculation and reducing computational costs. The stored classification data and neural network models can be accessed and utilized by one or more polishing machines at various locations simultaneously without recalculation, allowing for easy scaling up of systems consisting of multiple polishing machines.

[0016] The details of one or more embodiments of the invention are set forth in the accompanying drawings and the description below. Other features, objects, and advantages will become apparent from the description and drawings, and from the claims. [Brief description of the drawings]

[0017] [Figure 1] 1 shows a schematic cross-sectional view of an example of a polishing apparatus including a retaining ring. [Figure 2A] 1 illustrates a schematic perspective cross-sectional view of an exemplary retaining ring. [Figure 2B] 1 shows an enlarged schematic cross-sectional view of a retaining ring. [Figure 2C] 1 illustrates a schematic bottom view of an exemplary retaining ring. [Diagram 3] 1 illustrates a schematic top view of an exemplary retaining ring as measured using a coordinate measuring machine. [Figure 4] 1 shows schematic top views of various types of mesh scans for measurements. [Diagram 5] FIG. 13 is a flow diagram illustrating an example classification process for retaining rings using a machine learning algorithm. [Figure 6] FIG. 1 is a flow diagram illustrating an exemplary process for training a neural network to predict a polishing profile based on input data. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0018] Like reference numbers and designations in the various drawings indicate like elements.

[0019] Ideally, a substrate being polished would have a substantially uniform polishing rate across the substrate surface. In reality, however, different radial and / or angular regions of the substrate may have different polishing rates. Furthermore, the substrate being polished may initially have radial and / or angular non-uniformities.

[0020] One of the causes of polishing non-uniformity is the variation in the bottom profile of the retaining ring. That is, even slight differences in the bottom profiles of the two retaining rings can result in different polishing rates in the edge region. By correlating the bottom profile of the retaining ring with the polishing profile of the substrate, the polishing performance can be better understood. Furthermore, the polishing process can be adjusted, for example, by changing the pressure applied to the substrate, to improve the polishing rate uniformity in the edge region.

[0021] Conventionally, when checking the bottom surface profile of a retaining ring, only a few measurement points are provided across the bottom surface of the retaining ring. Therefore, the prior art may not provide enough information to analyze the characteristics of the bottom surface of the retaining ring. Techniques such as "ring break-in" have been applied to retaining rings before they are used in integrated circuit manufacturing, but as precision requirements become more stringent, "ring break-in" increases machine downtime and therefore manufacturing costs.

[0022] However, the techniques described herein can increase throughput, reduce manufacturing costs, and improve polishing quality (eg, reduce non-uniformity near the edge of the substrate).

[0023] The bottom surface of the retaining ring can be measured with high precision using a coordinate measurement machine (CMM) to generate a high quality bottom surface profile for further analysis. Each of the multiple retaining rings can be classified into a respective category using an unsupervised machine learning algorithm, and the classification information can be used to derive a parameter related to the difference in the polishing profile.

[0024] A neural network model can be trained that receives as input the classification of each retaining ring and the polishing profile of a substrate using each classified retaining ring. After training, the neural network can generate a prediction of the polishing profile (e.g., edge polishing profile) of a substrate polished using the retaining ring, i.e., by extrapolating the trained neural network with the input of the retaining ring shape information.

[0025] Thus, a system incorporating the present technology can detect whether a retaining ring is defective based on the measured bottom surface shape of the retaining ring, and based on the obtained parameters, adjust the polishing process when using the retaining ring and predict the polishing profile of a substrate polished with the retaining ring. The system can improve within-wafer uniformity after polishing and increase polishing throughput.

[0026] 1 shows an example of a polishing apparatus 100. The polishing apparatus 100 includes a rotatable, disk-shaped platen 120 on which a polishing pad 110 is positioned.

[0027] The platen 120 is operable to rotate about an axis 125. For example, a motor 121 can turn a drive shaft 124 to rotate the platen 120. The polishing pad 110 can be removably secured to the platen 120, for example, by an adhesive layer. The polishing pad 110 can be a two-layer polishing pad including an outer polishing layer 112 and a softer backing layer 114.

[0028] The polishing apparatus 100 may include a dispense port 130 for supplying a polishing fluid 132 (such as a polishing slurry) onto the polishing pad 110 .

[0029] The polishing apparatus may also include a polishing pad conditioner to polish the polishing pad 110 and maintain it in a consistent polishing condition.

[0030] The polishing apparatus 100 includes a carrier head 140 operable to hold the substrate 10 against the polishing pad 110. The carrier head 140 can be configured to independently control polishing parameters, such as pressure, for each of a number of zones on the substrate 10.

[0031] Carrier head 140 is suspended from a support structure 150, such as a carousel, and is connected by a drive shaft 152 to a carrier head rotation motor 154, which allows the carrier head to rotate about axis 155. Optionally, carrier head 140 may oscillate laterally, such as on a slider on carousel 150, or may be oscillated by the rotational oscillation of the carousel itself. In operation, the platen rotates about its central axis 125. Each carrier head rotates about its central axis 155 and moves laterally over the top surface of the polishing pad.

[0032] The carrier head 140 may include a housing 144 connectable to the drive shaft 152, a support plate 184 extending above the flexible central membrane 182, an annular pressure control assembly 195 surrounding the flexible central membrane 182, and a retaining ring 142 surrounding the annular pressure control assembly 195 and holding the substrate 10 below the flexible central membrane 182.

[0033] The underside of a flexible central membrane 182 provides a mounting surface for the substrate 10. The flexible central membrane 182 can include one or more flaps secured to a support plate 184 to form one or more pressurizable chambers. The chambers are connected to one or more pressure supplies 181 via respective pressure supply lines 183 to apply different pressures to inner regions of the substrate (e.g., at least 6 mm away from the edge of the substrate) during polishing, thereby enabling the system to adjust the respective polishing rates at different regions within the substrate.

[0034] FIG. 2A illustrates a schematic perspective cross-sectional view of an exemplary retaining ring 142.

[0035] As previously described, the retaining ring 142 is generally an annular ring that is securable to the carrier head 140 of the polishing apparatus 100 .

[0036] 2A, the upper portion 205 of the retaining ring 100 has a cylindrical inner surface 265, a cylindrical outer surface 250, and a top surface 215 that is generally perpendicular to both the inner and outer surfaces. The top surface includes holes 220 for receiving mechanical fasteners (not shown), such as bolts, screws, or other hardware (e.g., screw sheaths or inserts), for securing the retaining ring 142 and carrier head 140 together. Additionally, one or more alignment openings 225 may be disposed in the top surface 215 of the upper portion 205 for properly aligning the retaining ring 142 and carrier head 140.

[0037] The upper portion 205 may be formed from a rigid material or a material with a high tensile modulus, such as a metal, ceramic, or hard plastic. Suitable metals for forming the upper portion include stainless steel, molybdenum, titanium, or aluminum. Additionally, composite materials, such as composite ceramics, may be used.

[0038] The second portion, or lower portion 210, of the retaining ring 142 may be formed from a material that is chemically inert to the CMP process and may be softer than the material of the upper portion 205. The material of the lower portion 210 should be sufficiently compressible and elastic so that the edge of the substrate does not scratch or crack the substrate when it contacts the retaining ring 142. The lower portion 210 should also be durable and highly wear resistant, although it may be acceptable for the lower portion 210 to wear down. For example, the lower portion 130 may be made of a plastic, such as polyphenylene sulfide (PPS), polyethylene terephthalate (PET), polyetheretherketone (PEEK), carbon filled PEEK, polyetherketoneketone (PEKK), polybutylene terephthalate (PBT), polytetrafluoroethylene (PTFE), polybenzimidazole (PBI), polyetherimide (PEI), or a composite material.

[0039] The lower portion may also have a cylindrical inner surface 235, a cylindrical outer surface 230, and a bottom surface 255. The bottom surface 255 of the retaining ring 142 is initially planar, but after break-in or use, the bottom surface 255 of the lower portion typically has a non-planar profile. In certain embodiments, the radial profile of the bottom surface 255 may include a curved section, a frustoconical section, or a flat section. Although it would be advantageous for the radial profile of the bottom surface 255 of the retaining ring 100 to substantially match a nominal profile to allow for wafer-to-wafer uniformity, this may not be possible due to variations during manufacturing or break-in, or different wear patterns during polishing.

[0040] 2B shows a schematic cross-sectional view of the retaining ring 142 with the distortion of the bottom surface 255 greatly exaggerated for clarity. In reality, each retaining ring may have a bottom surface profile that differs slightly from the nominal profile, which may cause undesirable non-uniformity across the edge region of the substrate being polished, or wafer-to-wafer variation.

[0041] 2C shows a schematic bottom view of an exemplary retaining ring 142. Characteristics of the bottom profile of the retaining ring include the height distribution of the bottom surface 255 (or equivalently, the thickness distribution of the lower portion 210), and the flatness of the bottom surface 255 (i.e., the variation in the height or thickness of the bottom surface 255), and the circularity of the retaining ring, as previously described.

[0042] As shown in FIG. 2C, the retaining ring has an inner diameter 260 and an outer diameter 280. If the ring were perfectly round, the width of the retaining ring would be determined by taking the difference between the inner and outer diameters. In reality, however, the retaining ring 142 may have different curvatures at different angular locations of both the inner and outer boundaries, resulting in imperfect circularity. For example, the curvatures of the outer boundaries at locations 290A, 290B, 290C, and 290D may differ from one another. As another example, the curvatures of the inner boundaries at locations 291A and 291B may be substantially the same.

[0043] 3 shows a schematic top view of an exemplary retaining ring 142 being measured using a coordinate measuring machine 300. The retaining ring 142 is positioned with its bottom surface facing up.

[0044] To measure the bottom surface of the retaining ring, the retaining ring is mounted on the carrier head and a coordinate measurement machine (CMM) 300 measures the bottom surface of the retaining ring. The system is capable of measuring the bottom of the retaining ring.

[0045] The CMM 300 may include a sensor 310 configured to measure the vertical position of each of a plurality of points on the bottom surface of the retaining ring. The sensor 310 may be any suitable sensor, such as a laser sensor, a contact probe, etc. In some embodiments, the sensor 310 may provide a height or thickness coordinate (Z-coordinate) measurement at each measurement point on the bottom surface of the retaining ring.

[0046] CMM 300 can include actuators 350 and 355 to which a sensor 310 can be attached, which can move around to obtain height information of the bottom surface of the retaining ring. For example, sensor 310 is attached to actuator 355. Each of the two actuators can move in uncorrelated directions (e.g., non-parallel directions), which allows sensor 310 to be moved to cover the entire XY plane. For example, actuator 355 can move along rail 360 in the X direction, and actuator 350 can move along another rail 370 in the Y direction orthogonal to the X direction.

[0047] The CMM 300 may also include a controller 390 including control lines 380a, 380b for controlling the actuators 350, 355 respectively, and a data or control line 380c for controlling the operation of the sensor and receiving the resulting height information (Z coordinate) of the measurement area.

[0048] 4A and 4B are schematic diagrams of different types of mesh grids. Measurements can be distributed in radial meshes 410, as shown in FIG. 4A, or in rectangular meshes 420, as shown in FIG. 4B. Each mesh can be of any suitable size based on the respective measurement density. The CMM 300 can measure areas in millimeters to centimeters. For example, each radial mesh in FIG. 4A can have an edge, end edge, of about 1 mm in size. The CMM 300 can generate 1,000 to 10,000 measurements across the bottom surface of the retaining ring. For example, the total number of meshes in FIG. 4B is about 3000.

[0049] FIG. 5 is a flow diagram illustrating an example classification process 500 for retaining rings using, for example, machine learning algorithms.

[0050] The CMM 300 takes measurements of the bottom surface of each retaining ring. Each measurement represents the vertical height or thickness at the location of the measurement (502). As described above, each retaining ring is mounted on a corresponding carrier head prior to taking the measurements. In some embodiments, the system takes measurements of one or more retaining rings that have previously been run-in.

[0051] The controller 390 can receive the measurements and convert them into characteristics of the bottom surface at the measured locations, such as overall flatness of the bottom surface, ring taper, roundness, and average inner or outer diameter for each retaining ring.

[0052] In some embodiments, the controller 390 can determine the circularity by generating data representative of a level of symmetry of the bottom surface of the retaining ring relative to the axis of rotation. For example, the level of symmetry can include data representative of a curvature distribution at the boundary of the retaining ring. Thus, the system can measure and determine the circularity of the retaining ring by determining an asymmetric curvature distribution based on the measured curvature data.

[0053] To analyze the flatness, roundness, and ring taper wear of the retaining ring, the system first generalizes a spatial mapping of the retaining ring based on measurements in a Cartesian coordinate frame. The system then processes the spatial mapping utilizing appropriate numerical techniques to generate a consistent mapping across various measurements of various retaining rings. More specifically, each measurement data includes a respective reference plane and a respective reference center point, and each measurement data represents height information of each measurement point relative to the respective reference plane and reference center point. The system can use various techniques to normalize each measurement data. For example, the system can generate a shared center for each measurement data using numerical techniques such as "best fit plane" or "smallest enclosed circle" to normalize the measurement data for spatial mapping. As another example, the system can use one or more data filters to cull out outlying data to improve the integrity of each measurement.

[0054] After the above data processing, the system stores the processed data representative of one or more characteristics of the bottom surface profile of the retaining ring for analysis.

[0055] The system then performs an unsupervised learning algorithm to classify each of the plurality of retaining rings into a respective category based on the measurements of the plurality of retaining rings (504). To classify each of the plurality of retaining rings, the system first generates one or more characteristics from the data stored in step 502. The one or more characteristics may be of any suitable type that represents one or more features of the measurement data representing the bottom surface profile. For example, the characteristics of the measurement data representing the bottom surface may be averaged overall thickness, thickness variation in an angular direction, a radial direction, or both (i.e., flatness), circularity of an inner boundary, an outer boundary, or both, or a level of symmetry. Each feature type has a respective feature map for analysis.

[0056] The system can use any suitable unsupervised learning algorithm for classification. In one of the preferred embodiments, the system utilizes K-means. In particular, it can assume a number of categories for the measured retaining rings (e.g., a scalar value K for K-means), assume cluster centers for each category in a particular feature map, and assign each retaining ring to the closest category (i.e., the retaining ring is assigned to the category that has the closest cluster center to the characteristic type of the retaining ring in the particular feature map). The system can generalize the global error (e.g., squared Euclidean distance) for assigning each retaining ring to each category, and minimize the global error by adjusting the assignments. The system can also update each cluster center of the category after each adjustment of the assignment based on the respective characteristics of the retaining rings assigned to each category.

[0057] The system can determine the number of categories. To do so, the system can first select a number of category candidates for the K-means algorithm and obtain a respective candidate error (i.e., a respective minimized global error) for assigning the holding ring to one of the number of category candidates (i.e., various K). For example, the system can perform classification on two categories (i.e., K=2), three categories (i.e., K=3), and ten categories (i.e., K=10) and obtain a respective minimized global error. The system can select one of the number of category candidates based on a minimum candidate error as the number of categories for the K-means algorithm to classify the holding ring. For example, the system can set K to be the number of categories with the minimum candidate error. As another example, the system can set K to be the number of categories with the second smallest candidate error with the smallest cost in computation time.

[0058] The system stores 506 the classifications generated by the unsupervised learning algorithm. For example, the system stores the determined number of categories K, the cluster centers for each category in each feature map, and the classification tag for each retaining ring. In some embodiments, the system can store the category with the most retaining rings assigned as the reference category.

[0059] The classifications may then be evaluated against the polishing profile measurements to determine the parameters that cause the profile differences (508). For example, a user may have the system graph various performance index values ​​against various ring characteristics. For example, edge uniformity may be graphed as a function of inner edge roundness shape to determine whether and how the inner edge shape affects the polishing profile.

[0060] The system can be used to adjust retaining rings that do not fall into one or more pre-set categories. For example, the system can store data indicating that certain categories produce acceptable results when polished. A sample ring is then measured by the CMM system and subjected to a classification algorithm. If the sample ring does not fall into the indicated category, corrective action can be taken. For example, the retaining ring can be subjected to further "break-in" for a period of time and measurements of this "break-in" bottom surface can be taken. The above process can be repeated until the retaining ring is classified as acceptable.

[0061] The system can predict the post-polishing profile of a substrate using the classified retaining ring. To do so, the system can collect multiple polishing profiles using retaining rings in a particular category and generate an average polishing profile as the predicted post-polishing profile of a substrate polished using the retaining ring classified in that category.

[0062] 6 is a flow diagram illustrating an example process 600 for training a neural network to predict a polishing profile based on input data. Process 600 may be performed by one or more computers located at one or more locations. Alternatively, process 600 may be stored as instructions in one or more computers. When executed, the instructions may cause one or more components of a polishing apparatus, one or more components of a CMM, or one or more computers to perform the process. For example, at least some steps of the process may be performed by a controller 190 as shown in FIG. 1.

[0063] Similarly, a measurement of the bottom surface of each retaining ring is taken using a coordinate measuring machine, as described for step 502 of FIG. 5. The measurement represents a characteristic of the bottom surface (602). The characteristic of the bottom surface may be a surface height or a surface thickness. More specifically, the system may generate a unique mapping for each retaining ring and store the measurement data in memory. In some embodiments, the system takes measurements on one or more retaining rings that have previously been "run in."

[0064] The system then collects (604) removal profiles for each of the substrates polished using each of the retaining rings and trains (606) a machine learning model based on the measurements of the bottom surface of the retaining rings and the respective removal profiles.

[0065] The machine learning model includes a convolutional neural network model that can be trained using training examples that include training inputs, such as input bottom surface profiles of each retaining ring, polishing profiles of substrates polished using each retaining ring, and training labels for each polishing profile.

[0066] In some embodiments, the system can assign a label to each polishing profile. For example, the system can assign a first label (e.g., "edge fast") to a plurality of polishing profiles each having a faster edge removal rate compared to a reference profile, and assign a label "edge slow" to a plurality of polishing profiles each having a slower edge removal rate compared to a reference profile.

[0067] The system can train the neural network model by minimizing the global misclassification error based on the training examples. During training, the system updates the weights of each layer of the neural network by backpropagation to minimize the global error.

[0068] After training the neural network, the system can predict the removal profile of the substrate using the trained neural network. More specifically, the system can measure the bottom surface profile of the retaining ring or provide stored data representing the measured bottom surface profile of the retaining ring to the trained neural network and perform an inference operation using the trained neural network with the trained weights to generate a prediction of the polishing profile using the retaining ring. Alternatively or additionally, the system can predict a label of the predicted polishing profile using the trained neural network.

[0069] The system can continue to train the neural network with incoming measurements, so that the weights of the neural network can be updated based on newer measurement data. The system can store the trained neural network with updated weights in the memory of one or more computers in one or more locations. The trained neural network can be accessed by one or more computers or computing units to speed up inference calculations.

[0070] As used herein, the term substrate may include, for example, a production substrate (e.g., including multiple memory or processor dies), a test substrate, a bare substrate, and a gating substrate. The substrate may be at various stages of integrated circuit manufacturing, for example, the substrate may be a bare wafer, or the substrate may include one or more deposited and / or patterned layers. The term substrate may include circular plates and rectangular slabs.

[0071] The polishing apparatus and method described above can be applied in various polishing systems. Either or both of the polishing pad and the carrier head can move to provide relative motion between the polishing surface and the substrate. For example, the platen can orbit rather than rotate. The polishing pad can be a circular (or some other shape) pad fixed to the platen. Some aspects of the endpoint detection system can be applicable to linear polishing systems, for example, where the polishing pad is a linearly moving continuous belt or reel-to-reel belt. The polishing layer can be a standard abrasive material (e.g., polyurethane with or without fillers), a soft material, or a fixed-abrasive material. Although the relative positioning terms are used, it should be understood that the polishing surface and the substrate can be held in a vertical orientation or in some other orientation.

[0072] Control of the various systems and processes described herein, or portions thereof, may be implemented in a computer program product that includes instructions stored on one or more non-transitory computer-readable storage media and executable on one or more processing devices. The systems described herein, or portions thereof, may be implemented as an apparatus, method, or electronic system that may include one or more processing devices and memory storing executable instructions for performing the steps described herein.

[0073] The classification and training of the machine learning models described herein can be implemented in digital electrical circuitry, tangibly embodied computer software or firmware, computer hardware, including the structures disclosed herein and structural equivalents thereof, or one or more combinations thereof. Embodiments of the subject matter described herein can be implemented as one or more computer programs, i.e., as one or more modules of computer program instructions recorded on a tangible, non-transitory storage medium for execution by or for controlling the operation of a data processing apparatus. The computer storage medium can be a machine-readable storage device, a machine-readable storage substrate, a random access memory device, or a serial access memory device, or one or more combinations thereof. Alternatively or additionally, the program instructions can be encoded on an artificially generated propagated signal, e.g., a machine-generated electrical, optical, or electromagnetic signal, which is generated to encode information for transmission to a suitable receiving device for execution by the data processing apparatus.

[0074] A computer program (also referred to as a program, software, software application, app, module, software module, script, or code) can be written in any form of programming language, including compiled, interpreted, declarative, or procedural languages, and can be deployed in any form, such as a stand-alone program or as a module, component, subroutine, or other unit suitable for use in a computing environment. A program can correspond to a file in a file system, but need not correspond to such a file. A program can be stored in part of a file that holds other programs or data, for example, one or more scripts can be stored in a markup language document, in a single file dedicated to the program, or in multiple cooperating files, for example, in a file that stores one or more modules, subprograms, or code portions. A computer program can be deployed to be executed on one computer located at one site, or on multiple computers distributed across multiple sites and interconnected by a data communication network.

[0075] The processes and logic flows described herein may be performed by one or more programmable computers executing one or more computer programs to perform functions by operating on input data and generating output. The processes and logic flows may also be performed by special purpose logic circuitry, such as an FPGA or an ASIC, or a combination of special purpose logic circuitry and one or more programmed computers.

[0076] A computer suitable for running a computer program may be based on a general-purpose or special-purpose microprocessor, or both, or any other type of central processing unit. Typically, the central processing unit receives instructions and data from a read-only memory, or a random access memory, or both. The essential elements of a computer are a central processing unit for performing or executing instructions, and one or more memory devices for storing instructions and data. The central processing unit and memory may be supplemented by, or incorporated in, special purpose logic circuitry. Typically, a computer may also include, or be operatively connected to, one or more mass storage devices for storing data, such as magnetic disks, magneto-optical disks, or optical disks, for receiving data, or for transmitting data, or for both transmitting and receiving data. However, a computer need not have such devices.

[0077] Computer-readable media suitable for storing computer program instructions and data include all forms of non-volatile memory, media, and memory devices, including, for example, semiconductor memory devices (e.g., EPROM, EEPROM, and flash memory devices), magnetic disks (e.g., internal hard disks or removable disks), magneto-optical disks, and CD-ROM and DVD-ROM disks.

[0078] A data processing apparatus for implementing machine learning models may also include application-specific hardware accelerator units, for example for handling the common and computationally intensive parts of machine learning training or production, i.e., inference, workloads.

[0079] The machine learning models can be implemented and deployed using a machine learning framework, such as the TensorFlow framework, the Microsoft Cognitive Toolkit framework, the Apache Singa framework, the Apache MXNet framework, etc.

[0080] An embodiment of the subject matter described herein may be implemented in a computing system that includes a back-end component, e.g., a data server, or a middleware component, e.g., an application server, or a front-end component, e.g., a client computer having a graphical user interface, web browser, or app through which a user can interact with an embodiment of the subject matter described herein, or any combination of one or more such back-end, middleware, or front-end components. The components of the system may be interconnected by any form or medium of digital data communication, e.g., by a communications network. Examples of communications networks include local area networks (LANs) and wide area networks (WANs), e.g., the Internet.

[0081] A computing system may include clients and servers. Clients and servers are usually remote from each other and typically interact through a communication network. The relationship of client and server arises by virtue of computer programs running on the respective computers having a client-server relationship to each other. In some embodiments, a server may send, for example, HTML pages to a user device to display data to and receive user input from a user interacting with the device acting as a client. Data generated at the user device, for example a result of a user interaction, may be received at the server from the device.

[0082] Although the specification contains numerous specific implementation details, these should not be construed as limiting the scope of any invention or what may be claimed, but rather as descriptions of features that may be specific to certain embodiments of a particular invention. Certain features described herein in the context of separate embodiments may also be combined and implemented in one embodiment. Conversely, various features described in the context of one embodiment may also be implemented in multiple embodiments separately or in any suitable subcombination. Furthermore, although features may be described above as acting in a particular combination and may be claimed as such, one or more features from a claimed combination may, in some cases, be excluded from the combination, and the claimed combination may be directed to a subcombination or a variation of the subcombination.

[0083] Particular embodiments of the present invention have been described.

[0084] Other embodiments are within the scope of the following claims.

Claims

1. 1. A method for evaluating abrasion, comprising: For each retaining ring of a plurality of retaining rings mounted to a particular carrier head, taking measurements of a bottom surface of each retaining ring mounted to the particular carrier head using a coordinate measuring machine, the measurements representing characteristics of the bottom surface, the measurements including a circularity of each retaining ring by determining an asymmetric curvature distribution; executing an unsupervised learning algorithm to classify each of the plurality of retaining rings into a respective category based on the measurements of the plurality of retaining rings; storing the classification generated by the unsupervised learning algorithm; evaluating the classification against polishing profile measurements to determine parameters that cause profile differences; A method comprising:

2. taking a measurement of the bottom surface of each of the retaining rings; The method of claim 1 , comprising taking multiple measurements across the bottom surface at different widths and angular positions.

3. taking multiple measurements across the bottom surface; dividing the bottom surface of the retaining ring into a plurality of regions of the retaining ring; For each of the plurality of regions, measuring a position on a plane of the region and an average thickness of the region; The method of claim 2 , comprising:

4. The method of claim 1 , wherein the characteristic of the bottom surface is a surface height or a ring layer thickness.

5. The method of claim 1 , wherein the unsupervised learning algorithm comprises a K-means algorithm.

6. and determining a number of categories for the classification using the K-means algorithm, the determining a number of categories for the classification comprising: For each of the multiple possible categories, selecting a number of candidates that represents the total number of categories; determining respective candidate errors for classifying the plurality of retaining rings into the candidate number of categories using the K-means algorithm; selecting one of the candidate numbers as the number of categories based on a minimum candidate error; The method of claim 5 , comprising:

7. determining a category of retaining rings having the most retaining rings among all categories; Setting the determined category as a reference category; adjusting a retaining ring not classified as the reference category according to the classification; The method of claim 1 further comprising:

8. The method of claim 1 , further comprising predicting a post-polishing profile of a substrate polished using a classified retaining ring based on the classification of the classified retaining ring.

9. The method of claim 1 , wherein the plurality of retaining rings includes one or more retaining rings that have been broken in.

10. 1. A method for optimizing polishing, comprising: For each retaining ring of the plurality of retaining rings mounted on the particular carrier head, taking measurements of a bottom surface of each of the retaining rings mounted to the particular carrier head using a coordinate measuring machine, the measurements representing characteristics of the bottom surface, the measurements including a circularity of the each of the retaining rings by determining an asymmetric curvature distribution; collecting removal profiles for each of the substrates polished using the respective retaining rings; training a machine learning model based on the measurements of the bottom surfaces of the retaining rings and the respective removal profiles; A method comprising:

11. Measuring the bottom surface of a particular retaining ring; inputting the measurements into the trained machine learning model to generate a predicted removal profile; The method of claim 10, comprising:

12. The method of claim 10 , wherein the characteristic of the bottom surface is a surface height or a ring layer thickness.

13. collecting removal profiles of each of the substrates polished using each of the retaining rings; The method of claim 10 , further comprising determining a respective removal profile label for each of the removal profiles for training.

14. 14. The method of claim 13, wherein the respective removal profile labels include a first label representing a faster removal rate at an edge region of the substrate and a second label representing a slower removal rate at an edge region of the substrate.

15. The method of claim 10 , wherein the machine learning model comprises a convolutional neural network.

16. A non-transitory computer readable medium having a computer program recorded thereon, the computer program comprising instructions for causing one or more computers to: receiving a plurality of measurements representative of a profile of a bottom surface of the retaining ring prior to polishing the substrate; providing the plurality of measurements to a trained machine learning model to generate a predicted removal profile for the substrate; generating adjusted polishing parameters in response to the predicted removal profile to improve polishing uniformity of the substrate; and and causing the polishing system to polish the substrate using the adjusted polishing parameters; the plurality of measurements includes a circularity of the retaining ring obtained by determining an asymmetric curvature distribution; A non-transitory computer-readable medium.

17. The computer-readable medium of claim 16 , wherein the polishing parameters include a pressure on the substrate.

18. The computer-readable medium of claim 16 , wherein the machine learning model comprises a neural network.

19. The computer readable medium of claim 16 , wherein the profile is a surface height or layer thickness profile.

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