Chemical mechanical polishing system and chemical mechanical polishing method for workpiece

Abstract

The present invention provides a chemical mechanical polishing system and a chemical mechanical polishing method for polishing a workpiece while calculating an estimated polishing rate of the workpiece such as a wafer using a physical model. The chemical mechanical polishing system is configured such that, during or after polishing of a first workpiece, a measured polishing physical quantity including a measured value of a measured torque generated by a polishing device (1) and a measured polishing rate of the first workpiece is acquired, and a model parameter of a simulation model is identified using the measured polishing physical quantity as a variable for identification. A polishing condition for the second workpiece is input to the simulation model, thereby calculating an estimated polishing rate of the second workpiece.

Description

Technical Field

[0001] The present invention relates to chemical mechanical polishing for polishing the surface of workpieces such as wafers, substrates, and panels, and particularly relates to a technique for polishing a workpiece while estimating the polishing rate of the workpiece using a simulation model constructed based on measured data of chemical mechanical polishing. Background Art

[0002] In the manufacture of semiconductor devices, various films are formed on a wafer. After the film formation process, the wafer is polished to remove unnecessary portions and surface irregularities of the film. Chemical mechanical polishing (CMP) is a representative technique for wafer polishing. CMP is performed by supplying a slurry to a polishing surface while slidingly contacting the wafer with the polishing surface. The film forming the surface of the wafer is polished by the combination of the chemical action of the slurry and the mechanical action of abrasive grains contained in the slurry.

[0003] Simulation techniques for wafer polishing have been developed for the purpose of estimating the film thickness of a wafer and detecting the end point of wafer polishing. As a representative technique for polishing simulation, there is machine learning such as deep learning. For example, a model composed of a neural network is created by machine learning, and the polishing conditions of the wafer are input into the model, and thus an estimated value of the polishing result is output from the model. The polishing prediction performed by such machine learning is expected as a technique capable of obtaining a prediction result close to actual polishing.

[0004] Prior Art Documents

[0005] Patent Documents

[0006] Patent Document 1: Japanese Patent Application Laid-Open No. 2012-74574

[0007] Patent Document 2: Japanese Patent Application Laid-Open No. 2021-146493

[0008] Technical Problems to be Solved by the Invention

[0009] However, in the operation of creating a model by machine learning, a large amount of training data (so-called big data) is required. In particular, in order to create a model that can output a more accurate polishing result, a larger amount of data is required, and as a result, it takes a long time to create the model. Moreover, since the model itself has a complex structure, it takes a relatively long time for the model to output the polishing result.

[0010] In addition, the model composed of a neural network is a so-called black box, and it is not clear what kind of structure (what kind of weight parameters) it has. Therefore, when the actual polishing result is different from the polishing result output from the model, it is impossible to determine the part of the model to be corrected. In order to correct the model, additional training data is required, and it takes a long time to correct the model. Summary of the Invention

[0011] The present invention provides a chemical mechanical polishing system and a chemical mechanical polishing method for polishing a workpiece such as a wafer while calculating a presumed polishing rate of the workpiece using a physical model.

[0012] Technical means for solving technical problems

[0013] In one aspect, there is provided a chemical mechanical polishing system including: a polishing device including a polishing table for supporting a polishing pad having a polishing surface, a polishing head for pressing a workpiece against the polishing surface, and a slurry supply nozzle for supplying slurry to the polishing surface; and an arithmetic system having a storage device storing a simulation model that outputs a presumed polishing physical quantity including a presumed polishing rate of the workpiece and a presumed torque that is a presumed value of a torque generated in the polishing device due to a sliding resistance of the polishing pad. The simulation model includes a polishing rate model for calculating the presumed polishing rate and a polishing torque model for calculating the presumed torque. An identification program for determining model parameters of the simulation model is stored in the storage device. The arithmetic system is configured to, during or after polishing of a first workpiece, obtain measured polishing physical quantities including a measured polishing rate of the first workpiece and a measured value of the torque, identify the model parameters of the simulation model using the measured polishing physical quantities as variables for identification, and calculate a presumed polishing rate of a second workpiece by inputting polishing conditions for the second workpiece into the simulation model.

[0014] In one aspect, the arithmetic system is configured to, after identifying the model parameters, subtract the model parameters from predetermined reference model parameters to calculate a difference between the reference model parameters and the model parameters, and update the simulation model by substituting the difference as corrected model parameters into the simulation model.

[0015] In one aspect, the arithmetic system is configured to calculate a correction amount based on a difference between a presumed polishing physical quantity obtained from polishing of a previous workpiece performed before polishing of the first workpiece and a measured polishing physical quantity obtained from polishing of the previous workpiece, and determine the model parameters for the first workpiece by adding the correction amount to the model parameters obtained from polishing of the previous workpiece.

[0016] In one aspect, a chemical mechanical polishing method is provided, in which a workpiece is polished using a polishing apparatus including: a polishing table for supporting a polishing pad having a polishing surface; a polishing head for pressing the workpiece against the polishing surface; and a slurry supply nozzle for supplying slurry to the polishing surface. The chemical mechanical polishing method includes the following: polishing a first workpiece using the polishing apparatus, and obtaining an actual measured polishing physical quantity during or after the polishing of the first workpiece, the actual measured polishing physical quantity including an actual measured polishing rate of the first workpiece and a measured value of torque generated in the polishing apparatus due to the sliding resistance of the polishing pad. Through an arithmetic system, using the actual measured polishing physical quantity as a variable for identification to identify model parameters, the arithmetic system having an identification program for determining the model parameters of a simulation model, the simulation model including a polishing rate model for calculating a predicted polishing rate of the workpiece and a polishing torque model for calculating a predicted torque as a predicted value of the torque. Inputting polishing conditions for a second workpiece into the simulation model, thereby calculating the predicted polishing rate of the second workpiece.

[0017] In one aspect, the chemical mechanical polishing method further includes the following: after identifying the model parameters, subtracting the model parameters from pre-determined reference model parameters, thereby calculating a difference between the reference model parameters and the model parameters, and substituting the difference as the corrected model parameters into the simulation model, thereby updating the simulation model.

[0018] In one aspect, determining the model parameters of the simulation model means calculating a correction amount based on a difference between a predicted polishing physical quantity obtained from polishing of a previous workpiece performed before polishing of the first workpiece and an actual measured polishing physical quantity obtained from polishing of the previous workpiece, and adding the correction amount to the model parameters obtained from polishing of the previous workpiece, thereby determining the model parameters for the first workpiece.

[0019] In one aspect, there is provided a chemical mechanical polishing system including: a polishing apparatus having a polishing table, a polishing head, and a slurry supply nozzle, where the polishing table is configured to support a polishing pad having a polishing surface, the polishing head presses a workpiece against the polishing surface, and the slurry supply nozzle supplies slurry to the polishing surface; and an arithmetic system having a storage device that stores a simulation model which outputs a predicted polishing physical quantity including a predicted polishing rate of the workpiece and a predicted torque which is a predicted value of a torque generated in the polishing apparatus due to a sliding resistance of the polishing pad. The simulation model includes a polishing rate model for calculating the predicted polishing rate and a polishing torque model for calculating the predicted torque. An identification program for determining model parameters of the simulation model is stored in the storage device. The arithmetic system is configured to identify the model parameters of the simulation model using, as variables for identification, the measured polishing rate and the measured torque obtained during polishing of a previous workpiece, which are performed before polishing of the workpiece. During the polishing time of the workpiece, a plurality of prediction intervals are set. During the polishing of the workpiece, measured polishing physical quantities including a measured value of the torque are obtained within one of the plurality of prediction intervals, and the measured polishing physical quantities are used as variables for identification to identify a part of the model parameters of the simulation model and update the model parameters. The simulation model is updated using the updated model parameters, and the predicted polishing rate of the workpiece within the one prediction interval is calculated by inputting polishing conditions into the updated simulation model.

[0020] In one aspect, the arithmetic system is configured to calculate a posteriori predicted torque by applying a Kalman filter to the predicted torque calculated using the polishing torque model in a prediction interval before the one prediction interval and the measured value of the torque obtained within the one prediction interval, and use the measured polishing physical quantities including the posteriori predicted torque as variables for identification to identify a part of the model parameters of the simulation model and update the model parameters.

[0021] In one aspect, a chemical mechanical polishing method is provided, in which a workpiece is polished using a polishing apparatus including: a polishing table for supporting a polishing pad having a polishing surface; a polishing head for pressing the workpiece against the polishing surface; and a slurry supply nozzle for supplying slurry to the polishing surface. In this chemical mechanical polishing method, measured polishing rates and measured torques obtained during polishing of a previous workpiece, which are performed before polishing of the workpiece, are used as variables for identification to identify model parameters of a simulation model. The simulation model includes: a polishing rate model for calculating a predicted polishing rate of the workpiece; and a polishing torque model for calculating a predicted torque that is a predicted value of the torque generated in the polishing apparatus due to the sliding resistance of the polishing pad. During the polishing time of the workpiece, a plurality of prediction intervals are set. During the polishing of the workpiece, measured polishing physical quantities including a measured value of the torque are obtained within one of the plurality of prediction intervals, and the measured polishing physical quantities are used as variables for identification to identify a part of the model parameters of the simulation model and update the model parameters. The simulation model is updated using the updated model parameters, and the predicted polishing rate of the workpiece within the one prediction interval is calculated by inputting polishing conditions into the updated simulation model.

[0022] In one aspect, the chemical mechanical polishing method further includes the following: a posteriori predicted torque is calculated by applying a Kalman filter to the predicted torque calculated using the polishing torque model in a prediction interval before the one prediction interval and the measured value of the torque obtained within the one prediction interval. Updating the simulation model means using the measured polishing physical quantities including the a posteriori predicted torque as variables for identification to identify a part of the model parameters of the simulation model and update the model parameters.

[0023] In one aspect, a chemical mechanical polishing system is provided, comprising: a polishing apparatus including a polishing table, a polishing head, and a slurry supply nozzle, wherein the polishing table is configured to support a polishing pad having a polishing surface, the polishing head presses a workpiece against the polishing surface, and the slurry supply nozzle supplies slurry to the polishing surface; and an arithmetic system having a storage device that stores a simulation model which outputs estimated polishing physical quantities, the estimated polishing physical quantities including an estimated polishing rate of the workpiece and an estimated torque which is an estimated value of a torque generated in the polishing apparatus due to a sliding resistance of the polishing pad, the simulation model including a polishing rate model for calculating the estimated polishing rate and a polishing torque model for calculating the estimated torque, an identification program for determining model parameters of the simulation model is stored in the storage device, the arithmetic system is configured to obtain initial measured polishing physical quantities from polishing of a sample using the polishing pad in an initial state, determine an initial value of the model parameters using the initial measured polishing physical quantities as variables for identification, calculate an initial Preston coefficient based on the initial value of the model parameters, set a plurality of estimation intervals during a polishing time of the workpiece, calculate an initial estimated torque by inputting polishing conditions into the simulation model, during polishing of the workpiece, obtain a measured value of the torque within a first estimation interval among the plurality of estimation intervals, calculate a correction amount by multiplying a difference between the measured value of the torque and the initial estimated torque by a predetermined correction coefficient, determine a corrected Preston coefficient by adding the correction amount to the initial Preston coefficient, update the polishing rate model by substituting the corrected Preston coefficient into the polishing rate model, and calculate an estimated polishing rate of the workpiece within the second estimation interval by inputting polishing conditions for the second estimation interval among the plurality of estimation intervals into the polishing rate model.

[0024] In one embodiment, a chemical mechanical polishing method is provided, wherein a workpiece is polished using a polishing device, the polishing device comprising: a polishing table for supporting a polishing pad having a polishing surface; a polishing head for pressing the workpiece against the polishing surface; and a slurry supply nozzle for supplying slurry to the polishing surface. In the chemical mechanical polishing method, an initial measured polishing physical quantity is obtained from polishing a sample using the polishing pad in an initial state, and an initial value of a model parameter is identified by a computing system using the initial measured polishing physical quantity as a variable for identification. The computing system comprises an identification program for determining the model parameters of a simulation model, the simulation model comprising: a polishing rate model for calculating an estimated polishing rate of the workpiece; and a polishing torque model for calculating a friction force at a position where the friction force at the workpiece is caused by sliding resistance of the polishing pad. The invention relates to an embodiment of the present invention, wherein the present invention is to provide an estimated torque of an estimated value of the torque generated by the grinding device, calculate an initial Preston coefficient based on the initial value of the model parameter, set a plurality of estimation intervals during the grinding time of the workpiece, calculate the initial estimated torque by inputting grinding conditions into the simulation model, obtain a measured value of the torque in a first estimated interval among the plurality of estimation intervals during the grinding of the workpiece, calculate a correction amount by multiplying the difference between the measured value of the torque and the initial estimated torque by a predetermined correction coefficient, determine a corrected Preston coefficient by adding the correction amount to the initial Preston coefficient, update the grinding rate model by substituting the corrected Preston coefficient into the grinding rate model, and calculate an estimated grinding rate of the workpiece in a second estimated interval by inputting grinding conditions for a second estimated interval among the plurality of estimation intervals into the grinding rate model.

[0025] Effects of the Invention

[0026] The grinding rate model and grinding torque model as physical models included in the simulation model are imaginary chemical mechanical polishing systems that imitate actual polishing devices. Model parameters constituting the simulation model are identified based on comparison of measured polishing physical quantities (measured grinding rate, measured mechanical torque, etc.) obtained from the actual polishing device with estimated polishing physical quantities (estimated grinding rate, estimated mechanical torque, etc.) obtained from the simulation model. More specifically, model parameters are determined to make the estimated polishing physical quantities close to the measured polishing physical quantities. Therefore, the simulation model can accurately calculate the estimated grinding rate of the workpiece. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 is a schematic diagram showing one embodiment of a chemical mechanical polishing system.

[0028] Figure 2 yes Figure 1 A cross-sectional view of the grinding head is shown.

[0029] Figure 3 is a flow chart illustrating a method of identifying unknown model parameters of a simulation model.

[0030] Figure 4 It is a schematic diagram showing the velocity vectors on the polishing head, workpiece, and dresser on the polishing pad.

[0031] Figure 5 is a schematic diagram illustrating the pad rotation torque model.

[0032] Figure 6 This is a schematic diagram showing the distribution of the friction coefficient of the workpiece.

[0033] Figure 7 This is a graph showing the relationship between the torque of the polishing pad and the polishing time.

[0034] Figure 8 This is a flowchart for explaining one embodiment of polishing a workpiece using a chemical mechanical polishing system.

[0035] Figure 9 This is a block diagram illustrating one embodiment of the identification of model parameters and the calculation of the estimated polishing rate.

[0036] Figure 10 It is a block diagram for explaining another embodiment of the identification of model parameters and the calculation of the estimated polishing rate.

[0037] Figure 11 This is a block diagram for explaining still another embodiment of the identification of model parameters and the calculation of the estimated polishing rate.

[0038] Figure 12 This is a flowchart for explaining another embodiment of polishing a workpiece using a chemical mechanical polishing system.

[0039] Figure 13 This is a graph showing an example of a plurality of estimated intervals set in the grinding time of one workpiece.

[0040] Figure 14 This is a block diagram illustrating one embodiment of the identification of model parameters and the calculation of the estimated polishing rate.

[0041] Figure 15 This is a block diagram for explaining still another embodiment of polishing a workpiece using a chemical mechanical polishing system.

[0042] Figure 16 This is a block diagram for explaining still another embodiment of polishing a workpiece using a chemical mechanical polishing system.

[0043] Figure 17 It is a reference Figure 16Flowchart of the described embodiment

[0044] Figure 18 is with reference to Figure 16 Flowchart of the described embodiment

[0045] Symbol description

[0046] 1 Polishing device, 2 Polishing pad, 5 Polishing table, 5a Table shaft, 7 Polishing head, 8 Slurry supply nozzle, 14 Support shaft, 16 Polishing head swing arm, 18 Polishing head shaft, 20 Polishing head rotation motor, 21 Table rotation motor, 22 Polishing head swing motor, 24 Lifting mechanism, 25 Rotary joint, 26 Bearing, 28 Bridge part, 29 Support table, 30 Support pillar, 32 Ball screw mechanism, 32a Screw shaft, 32b Nut, 38 Servo motor, 47 Operation system, 47a Storage device, 47b Processing device, 49 Film thickness sensor, 50 Truing device, 50a Truing surface, 51 Truing device shaft, 53 Cylinder, 55 Truing device swing arm, 56 Support pillar, 57 Support table, 58 Support shaft, 60 Truing device rotation motor, 63 Truing device swing motor, 71 Carrier, 72 Retaining ring, 74 Diaphragm (elastic film), 76 Rolling diaphragm, 77 Gas supply source, 80 Motion control unit, W Workpiece, G1, G2, G3, G4, G5 Pressure chambers, F1, F2, F3, F4, F5 Fluid paths, R1, R2, R3, R4, R5 Pressure regulators. Detailed implementation mode

[0047] Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings. Figure 1 is a schematic diagram showing an embodiment of a chemical mechanical polishing system. As Figure 1 shown, the chemical mechanical polishing system includes a polishing device 1 for chemically and mechanically polishing a workpiece W. The polishing device 1 includes: a polishing table 5 that supports a polishing pad 2 having a polishing surface 2a; a polishing head 7 that presses a workpiece W such as a wafer, a substrate, or a panel against the polishing surface 2a; a slurry supply nozzle 8 that supplies a slurry containing abrasive grains to the polishing surface 2a; and a motion control unit 80 that controls the operation of the polishing device 1. The polishing head 7 is configured to be able to hold the workpiece W on its lower surface.

[0048] The polishing apparatus 1 further includes: a support shaft 14; a polishing head swing arm 16 that is connected to the upper end of the support shaft 14 and swings the polishing head 7; a polishing head shaft 18 that is rotatably supported at the free end of the polishing head swing arm 16; and a polishing head rotation motor 20 that rotates the polishing head 7 about its axis. The polishing head rotation motor 20 is disposed within the polishing head swing arm 16 and is connected to the polishing head shaft 18 via a torque transmission mechanism (not shown) composed of a belt and a pulley or the like. The polishing head 7 is connected to the lower end of the polishing head shaft 18. The polishing head rotation motor 20 rotates the polishing head shaft 18 via the above torque transmission mechanism, and the polishing head 7 rotates together with the polishing head shaft 18. In this way, the polishing head 7 rotates about its axis in the direction shown by the arrow by the polishing head rotation motor 20.

[0049] The polishing apparatus 1 further includes a table rotation motor 21 that rotates the polishing pad 2 and the polishing table 5 about their axes. The table rotation motor 21 is disposed below the polishing table 5, and the polishing table 5 is connected to the table rotation motor 21 via a table shaft 5a. The polishing table 5 and the polishing pad 2 rotate about the table shaft 5a in the direction shown by the arrow by the table rotation motor 21. The axes of the polishing pad 2 and the polishing table 5 coincide with the axis of the table shaft 5a. The polishing pad 2 is adhered to the upper surface of the polishing table 5. The upper surface of the polishing pad 2 constitutes a polishing surface 2a for polishing a workpiece W such as a wafer.

[0050] The polishing head shaft 18 can move relatively up and down with respect to the polishing head swing arm 16 by means of a lifting mechanism 24, and by the up and down movement of the polishing head shaft 18, the polishing head 7 can move relatively up and down with respect to the polishing head swing arm 16. A rotary joint 25 is installed at the upper end of the polishing head shaft 18.

[0051] The polishing apparatus 1 further includes a polishing head swing motor 22 that swings the polishing head 7 on the polishing surface 2a. The polishing head swing motor 22 is connected to the polishing head swing arm 16. The polishing head swing arm 16 is configured to be able to swing about the support shaft 14. The polishing head swing motor 22 swings the polishing head swing arm 16 about the support shaft 14 by a predetermined angle in the clockwise and counterclockwise directions, whereby the polishing head 7 presses the workpiece W against the polishing surface 2a of the polishing pad 2 and swings on the polishing pad 2.

[0052] In the present embodiment, the polishing head swing motor 22 is disposed at the upper end of the support shaft 14 and is configured to swing the polishing head swing arm 16 without rotating the support shaft 14. In one embodiment, it may also be that the polishing head swing arm 16 is fixed to the support shaft 14, and the polishing head swing motor 22 is connected to the support shaft 14 in such a way as to rotate the support shaft 14 and the polishing head swing arm 16 together.

[0053] The lifting mechanism 24 for lifting the polishing head shaft 18 and the polishing head 7 includes: a bearing 26 that supports the polishing head shaft 18 so as to be rotatable; a bridge portion 28 to which the bearing 26 is fixed; a ball screw mechanism 32 that is mounted on the bridge portion 28; a support table 29 that is supported by a support column 30; and a servo motor 38 that is fixed to the support table 29. The support table 29 that supports the servo motor 38 is connected to the polishing head swing arm 16 via the support column 30.

[0054] The ball screw mechanism 32 includes a screw shaft 32a connected to the servo motor 38 and a nut 32b that is screwed onto the screw shaft 32a. The nut 32b is fixed to the bridge portion 28. The polishing head shaft 18 moves up and down (vertically) integrally with the bridge portion 28. Therefore, when the servo motor 38 drives the ball screw mechanism 32, the bridge portion 28 moves up and down, whereby the polishing head shaft 18 and the polishing head 7 move up and down.

[0055] The polishing of the workpiece W is performed as follows. While rotating the polishing head 7 and the polishing table 5 respectively, slurry is supplied from a slurry supply nozzle 8 provided above the polishing table 5 to the polishing surface 2a of the polishing pad 2. The polishing pad 2 rotates integrally with the polishing table 5 about its axis. The polishing head 7 is lowered to a prescribed polishing position by the lifting mechanism 24. Moreover, the polishing head 7 presses the workpiece W against the polishing surface 2a of the polishing pad 2 at the above-mentioned polishing position. In a state where slurry is present on the polishing surface 2a of the polishing pad 2, the workpiece W is in sliding contact with the polishing surface 2a of the polishing pad 2. The surface of the workpiece W is polished by a combination of the chemical action of the slurry and the mechanical action of the abrasive grains contained in the slurry.

[0056] The polishing apparatus 1 includes a film thickness sensor 49 that measures the film thickness of the workpiece W on the polishing surface 2a of the polishing pad 2. The film thickness sensor 49 is disposed within the polishing table 5 and rotates integrally with the polishing table 5 and the polishing pad 2. The film thickness sensor 49 is configured to measure the film thickness of the workpiece W while traversing the surface of the workpiece W held by the polishing head 7. The film thickness of the workpiece W measured by the film thickness sensor 49 is sent to the motion control unit 80 and the arithmetic system 47. The specific structure of the film thickness sensor 49 is not particularly limited as long as it can measure the film thickness of the workpiece W. For example, the film thickness sensor 49 is an optical film thickness sensor or an eddy current film thickness sensor.

[0057] The film thickness sensor 49 is a so-called in-situ film thickness measuring device incorporated into the grinding device 1 for grinding the workpiece W. In one embodiment, an ex-situ film thickness measuring device provided outside the grinding device 1 may be provided instead of the film thickness sensor 49. Before and after grinding the workpiece W, the film thickness of the workpiece W is measured by the ex-situ film thickness measuring device. The measured value of the film thickness is sent to the motion control unit 80 and the arithmetic system 47.

[0058] The grinding device 1 further includes: a dresser 50 for dressing the grinding surface 2a of the grinding pad 2, a dresser shaft 51 connecting the dresser 50, a cylinder 53 provided at the upper end of the dresser shaft 51 as a dresser pressing actuator, a dresser swing arm 55 that supports the dresser shaft 51 so as to be rotatable, and a support shaft 58 to which the dresser swing arm 55 is fixed.

[0059] The lower surface of the dresser 50 constitutes a dressing surface 50a, which is composed of abrasive grains (e.g., diamond particles). The cylinder 53 is disposed on a support table 57 supported by columns 56, and these columns 56 are fixed to the dresser swing arm 55. The cylinder 53 is connected to the dresser 50 via the dresser shaft 51. The cylinder 53 is configured to move the dresser shaft 51 and the dresser 50 integrally up and down, and press the dressing surface 50a of the dresser 50 against the grinding surface 2a of the grinding pad 2 with a predetermined force. A combination of a servo motor and a ball screw mechanism may be used as the dresser pressing actuator instead of the cylinder 53.

[0060] The grinding device 1 further includes a dresser rotation motor 60 that rotates the dresser 50 about its axis. The dresser rotation motor 60 is disposed within the dresser swing arm 55 and is connected to the dresser shaft 51 via a torque transmission mechanism (not shown) composed of a belt and pulleys, etc. The dresser 50 is connected to the lower end of the dresser shaft 51. The dresser rotation motor 60 rotates the dresser shaft 51 via the above torque transmission mechanism, and the dresser 50 rotates together with the dresser shaft 51. In this way, the dresser rotation motor 60 rotates the dresser 50 about its axis in the direction shown by the arrow.

[0061] The grinding device 1 further includes a dresser swing motor 63 that swings the dresser 50 on the grinding surface 2a. The dresser swing motor 63 is connected to the support shaft 58. The dresser swing arm 55 is configured to be able to swing about the support shaft 58 together with the support shaft 58. The dresser swing motor 63 swings the dresser swing arm 55 about the support shaft 58 by a predetermined angle in the clockwise and counterclockwise directions, whereby the dresser 50 presses its dressing surface 50a against the grinding surface 2a of the grinding pad 2 and swings on the grinding pad 2 in the radial direction of the grinding pad 2.

[0062] In the present embodiment, the dresser swing arm 55 is fixed to the support shaft 58, and the dresser swing motor 63 is connected to the support shaft 58 in such a manner that the support shaft 58 and the dresser swing arm 55 rotate together. In one embodiment, the dresser swing motor 63 may be provided at the upper end of the support shaft 58 and configured to swing the dresser swing arm 55 without rotating the support shaft 58.

[0063] The dressing of the grinding surface 2a of the grinding pad 2 is performed as follows. During the grinding of the workpiece W, the dresser 50 rotates about the dresser shaft 51 and presses the dressing surface 50a of the dresser 50 against the grinding surface 2a by the cylinder 53. With the slurry present on the grinding surface 2a, the dresser 50 is in sliding contact with the grinding surface 2a. During the period when the dresser 50 is in sliding contact with the grinding surface 2a, the dresser swing motor 63 swings the dresser swing arm 55 about the support shaft 58 in the clockwise and counterclockwise directions by a predetermined angle, so that the dresser 50 moves in the radial direction of the grinding pad 2. In this way, the grinding pad 2 is shaved by the dresser 50, and thus the grinding surface 2a is dressed (regenerated).

[0064] In the present embodiment, the dressing of the grinding surface 2a is performed during the grinding of the workpiece W, but in one embodiment, the dressing of the grinding surface 2a may also be performed after the grinding of the workpiece W. In this case, pure water may be supplied to the grinding surface 2a instead of the slurry during dressing.

[0065] Figure 2 Yes Figure 1 is a cross-sectional view of the grinding head 7 shown. The grinding head 7 includes a carrier 71 fixed to the grinding head shaft 18 and a retaining ring 72 disposed below the carrier 71. A soft diaphragm (elastic film) 74 that abuts against the workpiece W is held at the lower part of the carrier 71. Four pressure chambers G1, G2, G3, G4 are formed between the diaphragm 74 and the carrier 71. The pressure chambers G1, G2, G3, G4 are formed by the diaphragm 74 and the carrier 71. The central pressure chamber G1 is circular, and the other pressure chambers G2, G3, G4 are annular. These pressure chambers G1, G2, G3, G4 are arranged concentrically. In one embodiment, more than four pressure chambers may be provided, or less than four pressure chambers may be provided.

[0066] Compressed gas such as compressed air is supplied to the pressure chambers G1, G2, G3, and G4 through the gas supply source 77 and via the fluid paths F1, F2, F3, and F4 respectively. The workpiece W is pressed against the polishing surface 2a of the polishing pad 2 by the diaphragm 74. More specifically, the pressure of the compressed gas in the pressure chambers G1, G2, G3, and G4 acts on the workpiece W via the diaphragm 74, and the workpiece W is pressed against the polishing surface 2a. The internal pressures of the pressure chambers G1, G2, G3, and G4 can be independently changed, whereby the polishing pressures for the corresponding four regions of the workpiece W, namely the central portion, the inner intermediate portion, the outer intermediate portion, and the peripheral portion, can be independently adjusted. The pressure chambers G1, G2, G3, and G4 are communicated with a vacuum source (not shown) via the fluid paths F1, F2, F3, and F4.

[0067] A ring-shaped rolling diaphragm 76 is disposed between the carrier 71 and the retaining ring 72, and a pressure chamber G5 is formed inside the rolling diaphragm 76. The pressure chamber G5 is communicated with the gas supply source 77 via the fluid path F5. The gas supply source 77 supplies compressed gas into the pressure chamber G5, and the compressed gas in the pressure chamber G5 presses the retaining ring 72 against the polishing surface 2a of the polishing pad 2.

[0068] The peripheral end portion of the workpiece W and the lower surface of the diaphragm 74 (i.e., the workpiece pressing surface) are surrounded by the retaining ring 72. During the polishing of the workpiece W, the retaining ring 72 presses the polishing surface 2a of the polishing pad 2 outside the workpiece W to prevent the workpiece W from flying out of the polishing head 7 during polishing.

[0069] The fluid paths F1, F2, F3, F4, and F5 extend from the pressure chambers G1, G2, G3, G4, and G5 to the gas supply source 77 via the rotary joint 25. Pressure regulators R1, R2, R3, R4, and R5 are respectively installed in the fluid paths F1, F2, F3, F4, and F5. The compressed gas from the gas supply source 77 is supplied into the pressure chambers G1 to G5 through the pressure regulators R1 to R5, the rotary joint 25, and the fluid paths F1 to F5.

[0070] The pressure regulators R1, R2, R3, R4, and R5 are configured to control the pressures in the pressure chambers G1, G2, G3, G4, and G5. The pressure regulators R1, R2, R3, R4, and R5 are connected to the operation control unit 80. The operation control unit 80 is connected to the arithmetic system 47. The fluid paths F1, F2, F3, F4, and F5 are also connected to an atmosphere opening valve (not shown), so that the pressure chambers G1, G2, G3, G4, and G5 can also be opened to the atmosphere.

[0071] The operation control unit 80 is configured to generate target pressure values for the respective pressure chambers G1 to G5. The operation control unit 80 sends the target pressure values to the pressure regulators R1 to R5, and the pressure regulators R1 to R5 operate so that the pressures in the pressure chambers G1 to G5 coincide with the corresponding target pressure values. The polishing head 7 having a plurality of pressure chambers G1, G2, G3, G4 can independently press the respective regions on the surface of the workpiece W against the polishing pad 2 based on the progress of polishing, and thus can polish the film of the workpiece W uniformly.

[0072] During the polishing of the workpiece W, the polishing head 7 is maintained at a reference height. The reference height of the polishing head 7 is the relative height of the entire polishing head 7 with respect to the polishing surface 2a of the polishing pad 2. In a state where the polishing head 7 is at the reference height, compressed gas is supplied to the pressure chambers G1, G2, G3, G4, G5. The diaphragms 74 forming the pressure chambers G1, G2, G3, G4 press the workpiece W against the polishing surface 2a of the polishing pad 2, and the rolling diaphragm 76 forming the pressure chamber G5 presses the retainer ring 72 against the polishing surface 2a of the polishing pad 2.

[0073] Return to Figure 1 The chemical mechanical polishing system further includes an arithmetic system 47, and the arithmetic system 47 includes a simulation model for simulating the polishing of the workpiece W and calculating the estimated polishing physical quantities of the workpiece W. The arithmetic system 47 is electrically connected to the polishing apparatus 1. More specifically, the arithmetic system 47 is connected to the operation control unit 80. The simulation model represents a hypothetical polishing apparatus that mimics the above-described polishing apparatus 1 including the polishing table 5, the polishing head 7, and the dresser 50. The actual polishing apparatus 1 and the simulation model as a hypothetical polishing apparatus constructed in a hypothetical space form a digital twin. A system that feeds back the results of the simulation to the real world and performs optimal control (for example, controls in such a way that the workpiece can be polished more flatly) using such a digital twin is called a cyber-physical system.

[0074] When preset polishing conditions are input to the simulation model, the simulation model performs hypothetical chemical mechanical polishing of the workpiece W using the hypothetical polishing apparatus and outputs estimated polishing physical quantities such as the estimated polishing rate of the workpiece W. As an example of the polishing conditions, the rotational speed of the polishing table 5 [min -1 or rad / s], the rotational speed of the polishing head 7 [min -1 or rad / s], the pressure applied from the workpiece W to the polishing surface 2a of the polishing pad 2 [Pa], the pressure applied from the retainer ring 72 to the polishing surface 2a of the polishing pad 2 [Pa], the relative position between the polishing head 7 and the polishing pad 2, the rotational speed of the dresser 50 [min -1or rad / s], the pressure [Pa] applied from the dresser 50 to the polishing surface 2a of the polishing pad 2, the relative position of the dresser 50 and the polishing pad 2, the position and flow rate of slurry supply, etc. The polishing rate is defined as the amount of surface material of the workpiece W removed per unit time and is also referred to as the material removal rate.

[0075] The operation system 47 includes a storage device 47a that stores programs and simulation models, and a processing device 47b that performs operations according to commands included in the programs. The storage device 47a includes a main storage device such as a RAM and auxiliary storage devices such as a hard disk drive (HDD) and a solid state drive (SSD). Examples of the processing device 47b include a CPU (central processing unit) and a GPU (graphics processing unit). However, the specific structure of the operation system 47 is not limited to these examples.

[0076] The operation system 47 is composed of at least one computer. The at least one computer may be one server or multiple servers. The operation system 47 may be an edge server, a cloud server connected to a communication network such as the Internet or a local area network, or a fog server provided in the network. The operation system 47 may also be multiple servers connected through a communication network such as the Internet or a local area network. For example, the operation system 47 may be a combination of an edge server and a cloud server.

[0077] The operation system 47 and the motion control unit 80 may also be integrally formed. The operation system 47 and the motion control unit 80 may also be virtually constructed by one or more computers.

[0078] The simulation model is at least composed of a physical model that outputs estimated polishing physical quantities. The simulation model is stored in the storage device 47a. The physical model at least includes a polishing rate model and a polishing torque model. The polishing rate model is a physical model for calculating an estimated polishing rate, which is an example of the estimated polishing physical quantity. The polishing torque model is a physical model for calculating an estimated value of the torque required for each mechanical element of the polishing device 1 due to the sliding resistance of the polishing pad 2. The estimated value of the torque is also an example of the estimated polishing physical quantity like the estimated polishing rate. As a specific example of the torque, there can be mentioned a polishing head rotation torque that rotates the polishing head 7 and the workpiece W around the axis of the polishing head 7, a polishing pad rotation torque that rotates the polishing pad 2 (or the polishing table 5) around its axis, a dresser rotation torque that rotates the dresser 50 around its axis, a dresser swing torque around the swing axis required to swing the dresser 50 on the polishing pad 2, and a head swing torque around the swing axis required to swing the polishing head 7 on the polishing pad 2.

[0079] The simulation model includes multiple model parameters. These model parameters include known model parameters determined by polishing conditions (such as polishing pressure, rotational speed of the polishing head 7, rotational speed of the polishing pad 2) and unknown model parameters such as the friction coefficient of the workpiece W. If the unknown model parameters are determined, then by inputting the polishing conditions into the simulation model, the estimated polishing physical quantities (estimated polishing rate and estimated values of various torques) of the workpiece W can be output from the simulation model.

[0080] The measured polishing physical quantities including the actual polishing rate of the workpiece W and the measured values of various torques required during the polishing of the workpiece W can be obtained based on the measured data. Therefore, the operation system 47 is configured to identify the unknown model parameters of the simulation model using the measured polishing physical quantities obtained through actual polishing as variables for identification. The identification of the unknown model parameters is to make the unknown model parameters approach the optimal values.

[0081] The program stored in the storage device 47a of the operation system 47 includes an identification program for identifying the unknown model parameters. The operation system 47 operates according to the commands included in the identification program and determines the model parameters of the simulation model for making the estimated polishing physical quantities of the workpiece approach the measured polishing physical quantities of the workpiece. The measured polishing physical quantities of the workpiece include the measured polishing rate of the workpiece and the measured values of the torque. The estimated polishing physical quantities of the workpiece include the estimated polishing rate of the workpiece and the estimated values of the torque.

[0082] The grinding device 1 grinds at least one workpiece under specified grinding conditions. The arithmetic system 47 acquires the actually measured grinding physical quantities determined according to the grinding of the workpiece, and stores the actually measured grinding physical quantities in the storage device 47a. The above-mentioned specified grinding conditions can be, for example, the actual grinding conditions of the workpiece, or the grinding conditions for pre-set test grinding. It is also possible to dynamically change the grinding conditions during grinding. In this case, sometimes the identification accuracy can be improved and high-degree basis functions can be utilized. The actually measured grinding physical quantities include the actually measured grinding rate of the workpiece, and the measured values of the torques of the grinding head 7, the grinding pad 2 (grinding table 5), and the dresser 50 when grinding the workpiece. The measured value of the torque can be a value directly representing the torque, such as the measured value of a torque measuring instrument (not shown), or it can also be an indirectly represented torque value, such as the torque current value supplied to the grinding head rotation motor 20, the table rotation motor 21, and the dresser rotation motor 60, or the torque estimated value calculated using the torque current. In one example, the measured value of the torque can also be a value obtained by indirectly estimating the grinding torque based on the mechanism model of the mechanical structure and the process information of the motor current and acceleration / deceleration physical quantities. The grinding head rotation motor 20, the table rotation motor 21, and the dresser rotation motor 60 are controlled to rotate the grinding head 7, the grinding table 5, and the dresser 50 at a predetermined constant speed, respectively. Therefore, when the sliding resistance acting on the grinding head 7, the grinding pad 2, and the dresser 50 becomes larger, the torque current also becomes larger.

[0083] Figure 3 It is a flowchart for explaining a method for identifying unknown model parameters of a simulation model.

[0084] In step 1, Figure 1 The grinding device 1 shown grinds at least one workpiece under specified grinding conditions.

[0085] In step 2, the arithmetic system 47 determines the actually measured grinding physical quantities according to the actually measured data obtained from the actual grinding of the workpiece. More specifically, the arithmetic system 47 calculates the actually measured grinding rate of the workpiece, and further acquires the measured values of various torques generated when grinding the workpiece. The actually measured grinding rate can be calculated by dividing the difference between the initial film thickness of the workpiece and the film thickness of the ground workpiece by the grinding time. The measured values of various torques are, for example, the torque currents supplied to the grinding head rotation motor 20, the table rotation motor 21, the grinding head swing motor 22, the dresser swing motor 63, and the dresser rotation motor 60. These actually measured grinding physical quantities are stored in the storage device 47a.

[0086] In step 3, the arithmetic system 47 inputs the initial values of the unknown model parameters stored in the storage device 47a into the simulation model.

[0087] In step 4, the operation system 47 inputs the grinding conditions of the workpiece into the simulation model and determines the model parameters that make the estimated grinding physical quantity of the workpiece close to the measured grinding physical quantity obtained in step 2. This step 4 is a process of identifying unknown model parameters that can make the estimated grinding physical quantity close to the measured grinding physical quantity.

[0088] In step 5, the operation system 47 replaces the current model parameters of the simulation model with the model parameters determined in step 4, thereby updating the simulation model.

[0089] In step 6, the operation system 47 inputs the grinding conditions used in step 4 into the updated simulation model, and outputs the estimated grinding physical quantity from the simulation model, thereby updating the estimated grinding physical quantity.

[0090] In step 7, the operation system 47 calculates the difference between the updated estimated grinding physical quantity and the corresponding measured grinding physical quantity.

[0091] In step 8, the operation system 47 evaluates the above difference. The processes from step 5 to step 8 are processes for evaluating the determined model parameters. When the above difference is greater than or equal to a specified threshold value, the operation system 47 repeats steps 4 to 8. When the above difference is less than the threshold value, the operation system 47 ends the determination operation of the model parameters. In one embodiment, the operation system 47 counts the number of times of repeating steps 4 to 8, and when the number of repetitions is greater than or equal to a specified value (or the calculation time of repeating steps 4 to 8 is greater than or equal to a specified value) and / or when the above difference is less than the threshold value, the operation system 47 ends the determination operation of the model parameters.

[0092] The operation system 47 determines the model parameters for making the estimated grinding physical quantity close to the measured grinding physical quantity according to algorithms such as the least squares method, the gradient descent method, and the simplex method included in the identification program stored in the storage device 47a. Constraints can also be imposed on the range of the parameters to be identified according to algorithms such as the least squares method with constraints. Having Figure 3 The simulation model with the model parameters finally determined according to the shown flowchart is stored in the storage device 47a.

[0093] Next, the simulation model will be described. As described above, the simulation model includes a grinding rate model for calculating the estimated grinding rate of the workpiece W and a grinding torque model for calculating the estimated value of the torque generated by the sliding resistance of the grinding pad 2.

[0094] The grinding rate model is expressed as follows based on Preston's law, for example:

[0095] Grinding rate MRR = k p p|V|=(β1 Wμ + β0)p|V|…(1)

[0096] Here, kp is the Preston coefficient, p is the pressure of the workpiece W against the polishing pad 2, V is the relative velocity between the workpiece W and the polishing pad 2, β1 and β0 are constants that relate the friction coefficient of the workpiece W to the Preston coefficient, W and μ is the friction coefficient of the workpiece W.

[0097] The Preston coefficient k p is proportional to the friction coefficient of the workpiece W W μ, and the above equation (1) is set assuming a linear first-order function. In other words, it is assumed that the material removal rate MRR of the workpiece W is related to the friction coefficient W μ of the workpiece W.

[0098] In the above equation (1), the constants β1, β0, and the friction coefficient W μ are unknown model parameters. On the other hand, the pressure p and the relative velocity V are known model parameters given by the polishing conditions. Therefore, if the constants β1, β0, and the friction coefficient W μ are known, the estimated value of the material removal rate, i.e., the estimated material removal rate, can be obtained from the above equation (1).

[0099] Next, the polishing torque model will be described. The polishing torque model is a physical model for calculating the estimated value of the mechanical torque required by the polishing device during the polishing of the workpiece W. During the polishing of the workpiece W, several sliding resistances act on the polishing surface 2a of the polishing pad 2. One is the sliding resistance generated between the polishing head 7 (including the workpiece W) and the polishing pad 2, and the other is the sliding resistance generated between the dresser 50 and the polishing pad 2. Depending on these sliding resistances, the torque required to rotate the polishing head 1, the polishing pad 2, and the dresser 50 at their respective set speeds changes.

[0100] The polishing torque model at least includes: a head rotation torque model that calculates the estimated value of the head rotation torque for rotating the polishing head 7 and the workpiece W on the polishing pad 2 around the axis of the polishing head 7 (coinciding with the axis of the polishing head shaft 18); and a pad rotation torque model that calculates the estimated value of the pad rotation torque for rotating the polishing pad 2 around its axis (coinciding with the axis of the table shaft 5a).

[0101] During the polishing of the workpiece W, while rotating the polishing head 7 and the workpiece W, the workpiece W and the retainer ring 72 are pressed against the polishing pad 2. The head rotation torque model is a physical model for calculating the estimated value of the torque required to rotate the polishing head 7 around its axis at a specified speed while overcoming both the friction between the retainer ring 72 and the polishing pad 2 and the friction between the workpiece W and the polishing pad 2.

[0102] In the present embodiment, dressing of the grinding surface 2a of the grinding pad 2 is performed during grinding of the workpiece W. Therefore, during grinding of the workpiece W, the holding ring 72 of the grinding head 7, the workpiece W, and the dresser 50 are in contact with the grinding pad 2. As a result, the grinding pad rotational torque depends on the friction of the holding ring 72, the workpiece W, and the dresser 50 against the grinding pad 2. The pad rotational torque model is a physical model for calculating an estimated value of the torque required to rotate the grinding pad 2 (i.e., the grinding table 5) at a specified speed while overcoming the friction between the holding ring 72 and the grinding pad 2, the friction between the workpiece W and the grinding pad 2, and the friction between the dresser 50 and the grinding pad 2.

[0103] Figure 4 is a schematic diagram showing the velocity vectors on the grinding head 7, the workpiece W, and the dresser 50 on the grinding pad 2.

[0104] Figure 4 Each symbol shown is defined as follows:

[0105] Velocity vector in the rotational direction of the grinding pad 2 at point A1 on the workpiece W or the holding ring 72: V PH

[0106] Position vector from the center C1 of the grinding pad 2 toward point A1: r PH

[0107] Position vector from the center C2 of the grinding head 7 toward point A1: r Hr

[0108] Velocity vector in the rotational direction of the grinding head 7 at point A1: V Hr

[0109] Velocity vector in the oscillating direction of the grinding head 7 at point A1: V Ho

[0110] Resultant velocity vector of the grinding head 7 at point A1: V H = V Hr + V Ho

[0111] Oscillation axis of the grinding head 7: OH (coincides with the axis of the support shaft 14)

[0112] Position vector from the oscillation axis OH of the grinding head 7 toward point A1: r Ho

[0113] Velocity vector in the rotational direction of the grinding pad 2 at point A2 on the dresser 50: V PD

[0114] Position vector from the center C1 of the grinding pad 2 toward point A2: r PD

[0115] Position vector from the center C3 of the dresser 50 towards the point A2: r Dr

[0116] Velocity vector in the rotational direction of the dresser 50 at the point A2: V Dr

[0117] Velocity vector in the oscillating direction of the dresser 50 at the point A2: V Do

[0118] Resultant velocity vector of the dresser 50 at the point A2: V D = V Dr + V Do

[0119] Oscillation axis of the dresser 50: OD (coincides with the axis of the support shaft 58)

[0120] Position vector from the oscillation axis OD of the dresser 50 towards the point A2: r Do

[0121] Relative velocity vector of the lapping head 7 with respect to the lapping pad 2 at the point A1: V PH-H = V H - V PH

[0122] Unit vector of the relative velocity vector V PH-H : uV PH-H = V PH-H / |V PH-H |

[0123] Relative velocity vector of the lapping pad 2 with respect to the lapping head 7 at the point A1: V H-PH = V PH - V H

[0124] Unit vector of the relative velocity vector VH-PH: uV H-PH = V H-PH / |V H-PH |

[0125] Relative velocity vector of the dresser 50 with respect to the lapping pad 2 at the point A2: V PD-D = V D - V PD

[0126] Unit vector of the relative velocity vector V PD-D : uV PD-D = V PD-D / |V PD-D |

[0127] Relative velocity vector of the lapping pad 2 with respect to the dresser 50 at the point A2: V D-PD = VPD -V D

[0128] Relative velocity vector V D-PD Unit vector of: uV D-PD = V D-PD / |V D-PD |

[0129] Next, with reference to Figure 5 , the pad rotation torque model will be described.

[0130] The sliding resistance dF W acting on the small area ds PW of the workpiece W and the polishing pad 2 (indicating a vector) is obtained as follows:

[0131] Sliding resistance dF PW = W μ W pds W uV PH-H …(2)

[0132] Herein, W μ is the friction coefficient of the workpiece W, W p is the pressure of the workpiece W on the polishing pad 2, ds W is the small area of the workpiece W, and uV PH-H is the unit vector of the relative velocity vector of the polishing head 7 with respect to the polishing pad 2.

[0133] The sliding resistance dF R acting on the small area ds PR of the holding ring 72 and the polishing pad 2 (indicating a vector) is obtained as follows:

[0134] Sliding resistance dF PR = R μ R pds R uV PH-H …(3)

[0135] Herein, R μ is the friction coefficient of the holding ring 72, R p is the pressure of the holding ring 72 on the polishing pad 2, ds R is the small area of the holding ring 72, and uV PH-H is the unit vector of the relative velocity vector of the polishing head 7 with respect to the polishing pad 2.

[0136] The sliding resistance dF D acting on the small area ds PD (indicating a vector) is obtained as follows:

[0137] Sliding resistance dFPD = D μ D pds D uV PD-D …(4)

[0138] Herein, D μ is the coefficient of friction of the dresser 50, D p is the pressure of the dresser 50 on the polishing pad 2, ds D is the minute area of the dresser 50, uV PD-D is the unit vector of the relative velocity vector of the dresser 50 with respect to the polishing pad 2.

[0139] Due to the minute area ds of the workpiece W W , the minute area ds of the retainer ring 72 R and the minute area ds of the dresser 50 D , the minute torque acting on the center C1 of the polishing pad 2 due to the sliding resistance is as follows:

[0140] The minute torque dN PW = r PH × dF PW …(5)

[0141] dN PR = r PH × dF PR …(6)

[0142] dN PD = r PD × dF PD …(7)

[0143] Herein, the symbol × represents the outer product of vectors.

[0144] If the positions of the minute area ds of the workpiece W W , the minute area ds of the retainer ring 72 R , and the minute area ds of the dresser 50 D are represented by polar coordinates (ri, θj) respectively, then the pad rotation torque model for calculating the estimated value of the polishing pad rotation torque is given as follows:

[0145] Polishing pad rotation torque P N = Σ i Σ j dN PW + Σ i Σ j dN PR + Σ i Σ j dN PD …(8)

[0146] When the dressing of the polishing surface 2a of the polishing pad 2 is not performed during the polishing of the workpiece W, in the above formula (8), Σ i Σ j dN PD The item of is 0.

[0147] Next, the head rotation torque model for calculating the estimated value of the rotation torque of the polishing head will be described.

[0148] The relative velocity vector of the polishing pad 2 with respect to the polishing head 7 is V H-PH =V PH -V H , and the unit vector of the relative velocity vector V H-PH is uV H-PH =V H-PH / |V H-PH |.

[0149] If it is assumed that the workpiece W rotates at the same rotational speed [min -1 as the polishing head 7, then the sliding resistance acting on the small area ds W of the workpiece W and the small area ds R of the retaining ring 72 is as follows:

[0150] Sliding resistance dF HW = W μ W p ds W uV H-PH …(9)

[0151] dF HR = R μ R p ds R uV H-PH …(10)

[0152] Due to the sliding resistance at the small area ds W of the workpiece W and the small area ds R of the retaining ring 72, the small torque acting on the center C2 of the polishing head 7 is as follows:

[0153] Small torque dN HrW =r Hr ×dF HW …(11)

[0154] dN HrR =r Hr ×dF HR …(12)

[0155] Here, r Hr is from the center C2 of the polishing head 7 towards the small area ds of the workpiece W WThe position vector is also from the center C2 of the grinding head 7 towards the minute area ds of the holding ring 72 R of the position vector.

[0156] If the minute area ds of the workpiece W is represented by polar coordinates (ri, θj) respectively W of the position and the minute area ds of the holding ring 72 R of the position, then the head rotation torque model for calculating the estimated value of the grinding head rotation torque is given as follows:

[0157] The grinding pad rotation torque H r N = Σ i Σ j dN HrW +Σ i Σ j dN HrR …(13)

[0158] In the present embodiment, dressing of the grinding surface 2a of the grinding pad 2 is performed during grinding of the workpiece W. Therefore, as shown in the above formula (8), the pad rotation torque model includes the torque due to the sliding resistance of the dresser 50. The grinding torque model includes, in addition to the head rotation torque model and the pad rotation torque model, a dresser rotation torque model that calculates the estimated value of the dresser rotation torque for rotating the dresser 50 on the grinding pad 2 about its axis. The dresser rotation torque model is a physical model for calculating the estimated value of the torque required to rotate the dresser 50 at a specified speed while overcoming the friction between the dresser 50 and the grinding pad 2.

[0159] The dresser rotation torque model for calculating the estimated value of the dresser rotation torque is given as follows in the same manner as the head rotation torque model:

[0160] The sliding resistance dF D = D μ D p ds D uV D-PD …(14)

[0161] The minute torque dN rD = r Dr × dF D …(15)

[0162] The dresser rotation torque D r N = Σ i Σ j dN rD …(16)

[0163] Herein, Dμ is the coefficient of friction of the dresser 50, D p is the pressure of the dresser 50 on the polishing pad 2, uV D-PD is the unit vector of the relative velocity vector of the polishing pad 2 with respect to the dresser 50, r Dr is the position vector from the center C3 of the dresser 50 towards the minute area dsD of the dresser 50.

[0164] In the dressing of the polishing pad 2, the dresser 50 swings on the polishing pad 2 in its radial direction. The polishing torque model further includes a dresser swing torque model that calculates the estimated value of the dresser swing torque required for the swinging of the dresser 50 around the swing axis OD.

[0165] The dresser swing torque model is expressed by the following formula (18):

[0166] Minute torque dN oD = r Do × dF D …(17)

[0167] Dresser swing torque D o N = Σ i Σ j dN oD …(18)

[0168] Here, r Do is the position vector from the swing axis OD of the dresser 50 (refer to Figure 4 ) towards the minute area ds D of the dresser 50.

[0169] In the present embodiment, during the polishing of the workpiece W, the polishing head 7 swings on the polishing pad 2. The polishing torque model further includes a head swing torque model that calculates the estimated value of the head swing torque required for the swinging of the polishing head 7 around the swing axis OH.

[0170] The head swing torque model is expressed by the following formula (21):

[0171] Minute torque dN HoW = r Ho × dF HW …(19)

[0172] dN HoR = r Ho × dF HR …(20)

[0173] Head swing torque H o N = Σ i Σj dN HoW +Σ i Σ j dN HoR …(21)

[0174] Here, r Ho is the position vector from the swing axis OH of the polishing head 7 (refer to Figure 4 ) to the minute area ds of the workpiece W W and the position vector from the swing axis OH to the minute area ds R of the holding ring 72.

[0175] In the present embodiment, the polishing torque model includes the above formulas (8), (13), (16), (18), and (21). When the dressing of the polishing pad 2 is not performed during the polishing of the workpiece W, the polishing torque model does not include the dresser rotation torque model shown in formula (16) and the dresser swing torque model shown in formula (18).

[0176] The friction coefficients W μ, R μ, D μ included in the above formulas (1), (8), (13), (16), (18), and (21) constituting the simulation model are unknown model parameters. These unknown model parameters are identified through the identification process described later.

[0177] The friction coefficient of the workpiece W W μ can vary depending on the distribution of abrasive grains contained in the slurry supplied to the polishing pad 2. The distribution of the friction coefficient W μ of the workpiece W can be obtained by calculation. That is, by defining a basis function representing the friction coefficient of the workpiece W and simultaneously identifying the calculated torque and the polishing rate, the distribution of the friction coefficient Figure 6 shown as W μ of the workpiece W can be obtained.

[0178] If it is assumed that the polishing efficiency represented by the number of abrasive grains acting on the workpiece W is proportional to the friction coefficient W μ of the workpiece W, the distribution of the friction coefficient W μ of the workpiece W can be replaced with the distribution of the acting abrasive grains. Here, the acting abrasive grains refer to the abrasive grains contained in the slurry that come into contact with the workpiece W and move relatively, contributing to the material removal of the workpiece W. As Figure 6 shown, the friction coefficient W μ is larger at the same pad radius where the slurry is supplied to the workpiece W, and the friction coefficient W μ becomes smaller as the position is farther from the radius position. This is because, during the polishing of the workpiece W, the slurry containing abrasive grains is supplied from the slurry supply nozzle 8 (refer to Figure 1) is supplied onto the polishing pad 2, and as it moves more toward the outer peripheral side, it scatters more outward due to the influence of centrifugal force. As is known from Figure 1 the slurry supply nozzle 8 is located on the upstream side of the polishing head 7 in the rotation direction of the polishing pad 2.

[0179] The coefficient of friction at an arbitrary radius r and angle θ position within the plane of the workpiece W W μ is given by the following formula:

[0180] Mathematical formula 1

[0181] w μ (r, θ) = (|R pad | - |R sur |) w μ1 + w μ0 (22)

[0182] wherein, R pad is the position vector at the position of radius r and angle θ, and R sur is the position vector of the slurry supply position. Each vector starts from the center of rotation of the polishing pad. W μ1 and W μ0 are constants that correlate the coefficient of friction with the difference between the rotational radius at the position within the workpiece plane and the rotational radius of the slurry supply position. That is, the radius difference and the coefficient of friction are modeled as a linear first-order function.

[0183] The above formula (22) is a physical model representing the distribution of the coefficient of friction W μ of the workpiece W. In the present embodiment, the simulation model includes, in addition to the physical models shown in the above formulas (1), (8), (13), (16), (18), (21), the physical model shown in formula (22). The W μ1 and W μ0 in formula (22) are unknown model parameters.

[0184] Next, the influence of the deterioration of the polishing pad 2 over time on the coefficient of friction will be described. Figure 7 is a graph showing the relationship between the torque of the polishing pad 2 and the polishing time. During the actual polishing of the workpiece W, the torque required to rotate the polishing pad 2 at a constant speed gradually decreases as shown by the dashed line in Figure 7 . As reasons for consideration, changes in the surface roughness of the polishing pad 2, changes in the viscoelasticity of the polishing pad 2, changes in the thickness of the polishing pad 2, changes in the temperature of the polishing pad 2, etc. can be cited.

[0185] In contrast, the torque of the polishing pad 2 calculated using the physical model shown in the above formula (8) is as shown in Figure 7As shown by the single-dot dash line, it is constant regardless of the polishing time. Therefore, in order to reflect the actual torque change of the polishing pad 2 in the simulation model, the simulation model further includes a mathematical model that represents the deterioration of the polishing pad 2 over time. In the present embodiment, the deterioration of the polishing pad 2 is represented by an initial sharp decrease and subsequent slow decrease in the friction coefficient of the workpiece W.

[0186] The mathematical model function f p1 (t) representing the initial decrease in the friction coefficient of the workpiece W is as follows:

[0187] f p1 (t) = W μ i [(1 - α1)exp[-(t - t0) / T] + α1]…(23)

[0188] In Equation (23), t is the polishing time, t0 is the start time of polishing, and T is the time constant.

[0189] The mathematical model function f p2 (t) representing the slow decrease in the friction coefficient of the workpiece W is as follows:

[0190] f p2 (t) = α2(t - t0) + 1…(24)

[0191] Using the product of the above mathematical model functions f p (t) = f p1 (t)f p2 (t), the friction coefficient W μ of the workpiece W is obtained by the following equation:

[0192] W μ = W μ i f p (t)…(25)

[0193] The above mathematical model includes a fitting function f p (t) for reducing the friction coefficient of the workpiece W over time. This fitting function f p (t) is a function with the polishing time t as a variable. In the above equations, α1, α2, and T are unknown model parameters.

[0194] As described above, the simulation model of the present embodiment includes a physical model for calculating the estimated polishing rate of the workpiece W and the estimated torque of the polishing apparatus 1, and a mathematical model representing the decrease in the friction coefficient of the workpiece W. Such a simulation model, as Figure 7 shown by the solid line, can calculate an estimated torque that changes in the same manner as the actual torque.

[0195] Next, the method for identifying (determining) the above-mentioned unknown model parameters R μ, D μ, W μ1, W μ0, β1, β0, α1, α2, T will be described. The arithmetic system 47 is configured to identify the unknown model parameters of the simulation model using the actually measured grinding physical quantities obtained through actual grinding as variables for identification. The arithmetic system 47 operates according to the commands included in the identification program stored in the storage device 47a, and uses algorithms such as the least squares method, the gradient descent method, and the simplex method to determine the model parameters that make the estimated grinding physical quantity close to the actually measured grinding physical quantity.

[0196] As described below, in the present embodiment, the arithmetic system 47 is configured to use the least squares method to determine the model parameters W μ1, W μ0, R μ, D μ, and uses the simplex method to determine the model parameters β1, β0, α1, α2, T. However, the present invention is not limited to this embodiment, and other algorithms such as the gradient descent method can also be used to determine the above-mentioned unknown model parameters. Alternatively, only the least squares method can be used to determine the above-mentioned unknown model parameters.

[0197] In one embodiment, the comprehensive calculation model using the least squares method is as follows. In the following formulas, the superscript letter P represents the polishing pad 2, the superscript letter H represents the polishing head 7, the superscript letter D represents the dresser 50, the subscript letter r represents rotation, and the subscript letter o represents oscillation.

[0198] Mathematical formula 2

[0199]

[0200] The actually measured grinding physical quantity obtained from the actual grinding of the workpiece is input to the left side of the above formula (26). The unknown model parameters are obtained using the least squares method as follows. That is, the formula (26) is expanded, the terms of the parameter X to be identified are extracted, and the formula Y = AX is created. Further, according to the formula X = A ＊ using the pseudo-inverse matrix A of the matrix A ＊ Y, the parameter X is identified by the least squares method. By repeating this process, all unknown parameters can be identified.

[0201] The left side of Equation (26) is the measured data Yexp obtained from actual grinding, and the right side is the estimated data Ysim obtained from the simulation model. The right side Ysim is the multiplication operation AX of the matrix A on the left side that can be calculated only by using the input grinding conditions and the vector X of unknown parameters regarding friction. By using the least squares method and the pseudo-inverse matrix A of the known matrix A ＊ , the unknown parameter X = A ＊ Yexp can be obtained.

[0202] In one embodiment, the error function model using the simplex method is as follows:

[0203] Mathematical formula 3

[0204]

[0205] In the above Equation (27), the values with superscript exp represent the measured values of torque and grinding rate, and the values with superscript sim are the estimated values obtained from the simulation model. w1, w2, w3, w4 are the weights for the estimated errors of each physical quantity.

[0206] The operation system 47 operates according to the identification program to identify the above-mentioned unknown model parameters. The operation system 47 replaces the current model parameters of the simulation model with the determined model parameters. The operation system 47 inputs the grinding conditions of the workpiece into the simulation model including the determined model parameters and calculates the estimated grinding physical quantities.

[0207] Furthermore, the operation system 47 calculates the difference between the measured grinding physical quantity and the estimated grinding physical quantity, and determines whether the difference is less than a specified threshold. If the difference is above the threshold, the operation system 47 performs the above-mentioned identification again using the measured grinding physical quantities of other workpieces. If the difference is less than the threshold, the operation system 47 uses the simulation model including the determined model parameters to calculate the estimated grinding physical quantities of other workpieces. That is, the operation system 47 can input the grinding conditions of a workpiece (such as a wafer) that has not been ground into the simulation model and accurately calculate the estimated grinding rate of the workpiece using the simulation model.

[0208] The operation system 47 sends the estimated grinding rate to Figure 1 the motion control unit 80 shown. The motion control unit 80 can predict the grinding end point of the workpiece being ground based on the estimated grinding rate. Moreover, the motion control unit 80 can also generate the distribution of the estimated grinding rate on the workpiece during the grinding of the workpiece and control the grinding pressure (the pressure applied to the workpiece from the grinding head 7) for the workpiece being ground based on the distribution of the estimated grinding rate.

[0209] Next, an embodiment of polishing a workpiece using the above chemical mechanical polishing system will be described. The chemical mechanical polishing system described below is configured to obtain measured polishing physical quantities (measured polishing rates and torque measurement values of the workpiece) during or after polishing the workpiece, calculate the estimated polishing rate of the next workpiece, and determine the polishing conditions for the next workpiece based on the estimated polishing rate.

[0210] Figure 8 It is a flowchart for explaining an embodiment of polishing a workpiece using a chemical mechanical polishing system.

[0211] In step 101, the operation system 47 determines the target polishing amount. The target polishing amount is the difference between the initial film thickness and the target film thickness of the workpiece. In one example, the initial film thickness is measured by Figure 1 the film thickness sensor 49 shown. The target film thickness is pre-input to the operation system 47 before the start of polishing the workpiece.

[0212] In step 102, the polishing device 1 performs chemical mechanical polishing on the workpiece Wi.

[0213] In step 103, the operation system 47 obtains measured polishing physical quantities (measured polishing rates and torque measurement values of the workpiece Wi) during or after polishing the workpiece Wi. In one embodiment, the measured polishing physical quantities include the measured value of the polishing pad rotation torque during polishing of the workpiece Wi, the measured value of the polishing head rotation torque, the measured value of the polishing head swing torque, the measured value of the dresser swing torque, and the measured polishing rate of the workpiece Wi.

[0214] In step 104, the operation system 47 uses the measured polishing physical quantities obtained from the polishing of the workpiece Wi as variables for identification to identify the unknown model parameters of the polishing rate model and the polishing torque model. Specifically, the operation system 47 uses the above identification formulas (26), (27) to identify (determine) the unknown model parameters R μ, D μ, W μ1, W μ0, β1, β0, α1, α2, T.

[0215] In step 105, the operation system 47 substitutes the model parameters determined in the above step 104 into the polishing rate model represented by the above formula (1) and the polishing torque models represented by the above formulas (8), (13), (18), (21), thereby updating the polishing rate model and the polishing torque model. The polishing rate model represented by the above formula (1) and the polishing torque models represented by the above formulas (8), (13), (18), (21) are pre-stored in the storage device 47a of the operation system 47.

[0216] Equation (1) is a grinding rate model for calculating the grinding rate of a workpiece, Equation (8) is a pad rotation torque model for calculating the estimated value of the grinding pad rotation torque, Equation (13) is a head rotation torque model for calculating the estimated value of the grinding head rotation torque, Equation (18) is a dresser swing torque model for calculating the estimated value of the dresser swing torque, and Equation (21) is a head swing torque model for calculating the estimated value of the grinding head swing torque.

[0217] In step 106, the operation system 47 calculates the estimated grinding rate of the next workpiece Wi+1 to be ground using the grinding rate model represented by the following Equation (1)'.

[0218] Estimated grinding rate MRR = k p p|V|=(β1 W μ + β0)p i+1 |V i+1 |…(1)'

[0219] Here, k p is the Preston coefficient, P i+1 is the grinding pressure of the next workpiece Wi+1 to be ground against the grinding pad 2, V i+1 is the relative velocity between the workpiece Wi+1 and the grinding pad 2, β1 and β0 are constants that relate the friction coefficient of the workpiece to the Preston coefficient, W μ is the friction coefficient of the workpiece Wi. β1, β0, and W μ are model parameters determined in the above step 104, and the above Equation (1)' is the updated grinding rate model in the above step 105.

[0220] In step 107, the operation system 47 determines the grinding time or the grinding pressure p i+1 as the grinding condition for the next workpiece Wi+1 to be ground. In one embodiment, the grinding time for the next workpiece Wi+1 to be ground is determined by the operation system 47 as follows. That is, the operation system 47 calculates the grinding amount of the workpiece Wi based on the measured grinding rate and grinding time of the workpiece Wi, calculates the difference between the target grinding amount of the next workpiece Wi+1 to be ground and the grinding amount of the workpiece Wi, and calculates the grinding time for the next workpiece Wi+1 based on the calculated difference and the measured grinding rate of the workpiece Wi. In other embodiments, the operation system 47 may also calculate the grinding time for the next workpiece Wi+1 based on the measured grinding rate of the workpiece Wi and the target grinding amount of the next workpiece Wi+1 to be ground.

[0221] In one embodiment, the grinding pressure p for the next workpiece Wi+1 to be ground i+1It is determined by the operation system 47 as follows. That is, the operation system 47 calculates the response rate (grinding rate / grinding pressure) of the grinding rate per unit grinding pressure based on the grinding pressure data when grinding the workpiece Wi and the measured grinding rate of the workpiece Wi, and calculates the grinding pressure p for the next workpiece Wi+1 based on the calculated response rate, the target grinding amount of the workpiece Wi+1 to be ground next, and the grinding time of the workpiece Wi. i+1 .

[0222] The grinding time or the grinding pressure p determined in the above step 107 i+1 is applicable to the grinding of the next workpiece Wi+1 and is used for the grinding conditions for grinding the workpiece Wi+1.

[0223] Steps 102 to 107 can be repeated each time one workpiece is ground, or can also be repeated each time multiple workpieces are ground. For example, steps 102 to 107 are repeated each time a preset number of workpieces are ground.

[0224] Figure 9 is a block diagram illustrating an embodiment of the identification of model parameters and the calculation of the estimated grinding rate. The operation system 47 obtains the measured grinding physical quantity Ni including the measured value of torque and the measured grinding rate during or after the grinding of the workpiece Wi, and inputs the measured grinding physical quantity Ni as a variable for identification into the identification formulas (26), (27). The operation system 47 operates according to the identification program and uses the identification formulas (26), (27) to identify (determine) the model parameters Xi ( R μ, D μ, W μ1, W μ0, β1, β0, α1, α2, T).

[0225] The operation system 47 substitutes the model parameters Xi into the grinding rate model and the grinding torque model, and updates the grinding rate model and the grinding torque model. The operation system 47 inputs the grinding conditions for the next workpiece Wi+1 (such as the pressure of the grinding head 7 on the grinding pad 2, the rotation speed of the grinding head 7, the rotation speed of the grinding pad 2, the rotation speed of the dresser 50, the pressure of the dresser 50 on the grinding pad 2, etc.) into the grinding rate model and the grinding torque model, and calculates the estimated grinding rate and the estimated torque of the next workpiece Wi+1.

[0226] Figure 10 is a block diagram illustrating another embodiment of the identification of model parameters and the calculation of the estimated grinding rate. The basic process of this embodiment is the same as that of Figure 9 the embodiment shown, but the difference of this embodiment is that the pre-determined reference model parameters X0 are used to correct the identified (determined) model parameters Xi.

[0227] The reference model parameter X0 is identified in the same manner as the model parameter Xi before the grinding of the workpiece using the grinding device 1 starts. In one embodiment, the reference model parameter X0 is identified (determined) using measured grinding physical quantities, which include measured grinding rates and torque measurement values obtained when grinding a sample using the grinding device 1 in an initial state that has not yet been used for grinding the workpiece. The reference model parameter X0 is stored in the storage device 47a of the arithmetic system 47.

[0228] As Figure 10 shown, the arithmetic system 47 uses the measured grinding physical quantity Ni, which includes measured grinding rates and torque measurement values obtained from the grinding of the workpiece Wi, to determine the model parameter Xi, subtracts the model parameter Xi from the reference model parameter X0, thereby calculating the difference Xi' between the reference model parameter X0 and the model parameter Xi, and substitutes the calculated difference Xi' as the corrected model parameter into the grinding rate model and the grinding torque model, thereby updating the grinding rate model and the grinding torque model. The arithmetic system 47 inputs the grinding conditions for the next workpiece Wi+1 into the grinding rate model and the grinding torque model, and calculates the estimated grinding rate and the estimated torque for the next workpiece Wi+1.

[0229] According to this embodiment, it is possible to remove the noise that may be included in the model parameter Xi through correction.

[0230] Figure 11 is a block diagram illustrating another embodiment of the identification of the model parameter and the calculation of the estimated grinding rate. The basic process of this embodiment is the same as that of the Figure 9 embodiment shown, but in this embodiment, the arithmetic system 47 is configured to calculate a correction amount Z based on the difference between the estimated grinding physical quantity Nsim (including the estimated grinding rate and the estimated torque) obtained from the grinding of the previous workpiece Wi-1 and the measured grinding physical quantity Ni-1 (including the measured grinding rate and the torque measurement value) obtained from the grinding of the previous workpiece Wi-1, and add the correction amount Z to the model parameter Xi-1 obtained from the grinding of the previous workpiece Wi-1, thereby determining the model parameter Xi for the current workpiece Wi.

[0231] The estimated grinding physical quantity Nsim includes the estimated grinding rate and the estimated torque obtained by inputting the grinding conditions into the grinding rate model and the grinding torque model updated based on the grinding results of the previous workpiece Wi-1.

[0232] The correction amount Z is determined in the following manner. The processing system 47 inputs the difference between the estimated grinding physical quantity Nsim obtained from the grinding of the previous workpiece Wi-1 and the measured grinding physical quantity Ni-1 obtained from the grinding of the previous workpiece Wi-1 as a variable for identification into the identification formulas (26), (27), and calculates the correction amount Z using the identification formulas (26), (27) according to the identification program.

[0233] The operation system 47 determines the model parameter Xi for the current workpiece Wi by adding a correction amount Z to the model parameter Xi-1 obtained from the polishing of the previous workpiece Wi-1, substitutes the model parameter Xi into the polishing rate model and the polishing torque model, and updates the polishing rate model and the polishing torque model. The operation system 47 calculates the estimated polishing rate and the estimated torque for the next workpiece Wi+1 by inputting the polishing conditions into the updated polishing rate model and the polishing torque model.

[0234] Figure 12 It is a flowchart for explaining another embodiment of polishing a workpiece using a chemical mechanical polishing system. In this embodiment, the measured polishing rate and the measured torque obtained in the polishing of the previous workpiece Wi-1, which is performed before the polishing of the workpiece W, are used as variables for identification to identify the model parameters of the simulation model. A plurality of estimation intervals are set during the polishing time of the workpiece W, and the measured polishing physical quantity including the measured value of the torque within one of the plurality of estimation intervals is obtained during the polishing of the workpiece W. The measured polishing physical quantity is used as a variable for identification to identify a part of the model parameters of the simulation model and update the model parameters, and the polishing conditions are input into the simulation model, thereby calculating the estimated polishing rate of the workpiece within the above one estimation interval.

[0235] In step 201, before polishing the workpiece W, the polishing device 1 performs chemical mechanical polishing of the workpiece Wi-1.

[0236] In step 202, the operation system 47 uses the measured polishing rate and the measured torque obtained in the polishing of the previous workpiece Wi-1 as variables for identification to identify the model parameters Xref of the polishing rate model and the polishing torque model.

[0237] In step 203, the operation system 47 determines the target polishing amount of the workpiece W. The target polishing amount is the difference between the initial film thickness and the target film thickness of the workpiece W. In one example, the initial film thickness is measured by the film thickness sensor 49 shown in Figure 1 . The target film thickness is pre-input into the operation system 47 before the start of the polishing of the workpiece W.

[0238] In step 204, the operation system 47 sets a plurality of estimation intervals L1 to L during the polishing time of the workpiece W M . Figure 13 is a graph showing an example of the plurality of estimation intervals L1 to L M . The plurality of estimation intervals L1 to L M are set during the polishing time from the initial film thickness of the workpiece to be polished to the target film thickness. The plurality of estimation intervals L1 to L M are consecutive time intervals during the polishing of one workpiece.

[0239] In step 205, the polishing apparatus 1 starts chemical mechanical polishing of the workpiece W.

[0240] In step 206, the arithmetic system 47 obtains measured polishing physical quantities including measured values of torque in the current estimation section Li during polishing of the workpiece W. In one embodiment, the measured polishing physical quantities include measured values of the polishing pad rotation torque, the polishing head rotation torque, the polishing head swing torque, and the dresser swing torque during polishing of the workpiece W.

[0241] In step 207, the arithmetic system 47 uses the measured polishing physical quantities including measured values of torque obtained from polishing of the workpiece W as variables for identification to identify a part of the model parameters of the polishing rate model and the polishing torque model, and updates the model parameter Xref. Specifically, the arithmetic system 47 uses the above identification formulas (26) and (27) to identify unknown model parameters R μ, D μ, W μ1, W a part of μ0, β1, β0, α1, α2, T.

[0242] In step 208, the arithmetic system 47 substitutes the model parameter Xref updated in the above step 207 into the polishing rate model represented by the above formula (1) and the polishing torque models represented by the above formulas (8), (13), (18), and (21), thereby updating the polishing rate model and the polishing torque model. The polishing rate model represented by the above formula (1) and the polishing torque models represented by the above formulas (8), (13), (18), and (21) are pre-stored in the storage device 47a of the arithmetic system 47.

[0243] Formula (1) is a polishing rate model for calculating the polishing rate of the workpiece, formula (8) is a pad rotation torque model for calculating the estimated value of the polishing pad rotation torque, formula (13) is a head rotation torque model for calculating the estimated value of the polishing head rotation torque, formula (18) is a dresser swing torque model for calculating the estimated value of the dresser swing torque, and formula (21) is a head swing torque model for calculating the estimated value of the polishing head swing torque.

[0244] In step 209, the arithmetic system 47 uses the polishing rate model updated in the above step 208 to calculate the estimated polishing rate of the workpiece W in the current estimation section Li.

[0245] In step 210, the arithmetic system 47 determines the polishing time or the polishing pressure p for the workpiece W in the next estimation section Li+1 i+1。In one embodiment, the grinding time of the workpiece W in the next estimated interval Li+1 is determined by the arithmetic system 47 as follows. That is, the arithmetic system 47 calculates the grinding amount of the workpiece W in the estimated interval Li based on the estimated grinding rate and the grinding time of the workpiece W in the estimated interval Li, calculates the difference between the target grinding amount of the workpiece W in the next estimated interval Li+1 and the grinding amount in the estimated interval Li, and calculates the grinding time in the next estimated interval Li+1 based on the calculated difference and the estimated grinding rate of the workpiece W in the estimated interval Li. In other embodiments, the arithmetic system 47 may also calculate the grinding time in the next estimated interval Li+1 based on the estimated grinding rate of the workpiece W in the estimated interval Li and the target grinding amount of the workpiece W in the next estimated interval Li+1.

[0246] In one embodiment, the grinding pressure p for the workpiece W in the next estimated interval Li+1 i+1 is determined by the arithmetic system 47 as follows. That is, the arithmetic system 47 calculates the response rate (grinding rate / grinding pressure) of the grinding rate per unit grinding pressure based on the grinding pressure data when the workpiece W is ground in the estimated interval Li and the estimated grinding rate of the workpiece W in the estimated interval Li, and calculates the grinding pressure p for the workpiece W in the next estimated interval Li+1 based on the calculated response rate, the target grinding amount of the workpiece W in the next estimated interval Li+1, and the grinding time in the estimated interval Li. i+1 。

[0247] The grinding time or the grinding pressure p determined in the above step 210 i+1 is applied to the grinding of the workpiece W in the next estimated interval Li+1 and is used as the grinding condition for grinding the workpiece W.

[0248] Steps 206 to 209 may be executed only once when the workpiece W is ground in the first estimated interval L1, or may be repeated every time one or more estimated intervals have passed.

[0249] Figure 14 is a block diagram illustrating an embodiment of the identification of model parameters and the calculation of the estimated grinding rate. The measured value of the torque as the measured grinding physical quantity Ni obtained in a certain estimated interval Li during the grinding of the workpiece W is input as a variable for identification into the identification formulas (26) and (27). The arithmetic system 47 operates according to the identification program, identifies a part of the model parameters using the identification formulas (26) and (27), and obtains the model parameter Xi corresponding to the estimated interval Li. Further, the arithmetic system 47 replaces the model parameter Xref identified based on the grinding result of the previous workpiece Wi-1 with the model parameter Xi, thereby updating the model parameter Xref.

[0250] The operation system 47 substitutes the updated model parameter Xref into the grinding rate model and the grinding torque model to update the grinding rate model and the grinding torque model. The operation system 47 inputs the grinding conditions (such as the pressure of the grinding head 7 on the polishing pad 2, the rotation speed of the grinding head 7, the rotation speed of the polishing pad 2, the rotation speed of the dresser 50, the pressure of the dresser 50 on the polishing pad 2, etc.) into the grinding rate model and the grinding torque model, and calculates the estimated grinding rate and the estimated torque in the current estimated interval Li.

[0251] Figure 15 It is a block diagram for explaining another embodiment of grinding a workpiece using a chemical mechanical polishing system. Details of this embodiment not specifically described are the same as those of the embodiment referred to Figure 12 and Figure 13 the described embodiment, so the repeated description thereof is omitted.

[0252] In this embodiment, the operation system 47 is configured to calculate the a posteriori estimated torque by applying a Kalman filter to the estimated torque calculated using the grinding torque model in the estimated interval before the current estimated interval Li and the measured value of the torque obtained within the estimated interval Li, use the measured grinding physical quantity including the a posteriori estimated torque as a variable for identification to identify a part of the model parameters of the simulation model and update the model parameters, update the simulation model using the updated model parameters, and input the grinding conditions into the updated simulation model, thereby calculating the estimated grinding rate of the workpiece W within the estimated interval Li.

[0253] The operation system 47 is configured to calculate the estimated torque Dsim(i) in the current estimated interval Li based on the grinding of the workpiece W in the previous estimated interval, obtain the measured value Dobs(i) of the torque in the current estimated interval Li, apply a Kalman filter to the estimated torque Dsim(i) and the measured value Dobs(i) of the torque, and calculate the a posteriori estimated torque Dpos(i) in the current estimated interval Li.

[0254] More specifically, as Figure 15 shown, the operation system 47 first uses the initial measured data Ni-1 including the measured grinding rate and the measured torque obtained in the grinding of the previous workpiece Wi-1 to identify the model parameters Xref of the grinding rate model and the grinding torque model. That is, the operation system 47 inputs the initial measured data Ni-1 into the identification formulas (26), (27), and identifies the model parameters Xref according to the identification program.

[0255] The operation system 47 substitutes the model parameter Xref into the grinding rate model and the grinding torque model, and updates the grinding rate model and the grinding torque model. The operation system 47 inputs the grinding conditions (such as the pressure of the grinding head 7 on the polishing pad 2, the rotation speed of the grinding head 7, the rotation speed of the polishing pad 2, the rotation speed of the dresser 50, the pressure of the dresser 50 on the polishing pad 2, etc.) into the updated grinding torque model, and calculates the estimated torque Dsim(1) in the initial estimated interval L1.

[0256] After the estimated interval L1, the operation system 47 repeats the following operation using the Kalman filter. That is, in the estimated interval Li (i is a natural number of 2 or more), the operation system 47 applies the Kalman filter to the estimated torque Dsim(i) calculated in the previous estimated interval Li-1 and the measured value Dobs(i) of the torque obtained in the estimated interval Li, to calculate the a posteriori estimated torque Dpos(i) in the estimated interval Li.

[0257] Dpos(i) = Dsim(i) + K(Dobs(i) - Dsim(i)) (28)

[0258] K is a pre-determined Kalman gain.

[0259] The operation system 47 uses the measured grinding physical quantities including the a posteriori estimated torque Dpos(i) as variables for identification, to identify and update a part of the model parameters of the grinding rate model and the grinding torque model, updates the grinding rate model and the grinding torque model using the updated model parameters, inputs the grinding conditions into the updated grinding rate model and the grinding torque model, thereby calculating the estimated grinding rate MRRsim(i) of the workpiece W in the estimated interval Li and the estimated torque Dsim(i+1) in the next estimated interval Li+1.

[0260] In the estimated interval Li+1, the operation system 47 applies the Kalman filter to the estimated torque Dsim(i+1) calculated in the estimated interval Li and the measured value Dobs(i+1) of the torque obtained in the estimated interval Li+1, to calculate the a posteriori estimated torque Dpos(i+1) in the estimated interval Li+1. Further, the operation system 47 uses the measured grinding physical quantities including the a posteriori estimated torque Dpos(i+1) to identify and update a part of the model parameters of the grinding rate model and the grinding torque model, updates the grinding rate model and the grinding torque model using the updated model parameters, inputs the grinding conditions into the updated grinding rate model and the grinding torque model, thereby calculating the estimated grinding rate MRRsim(i+1) of the workpiece W in the estimated interval Li+1 and the estimated torque Dsim(i+2) in the next estimated interval Li+2. Hereinafter, the same operation is repeated until the film thickness of the workpiece W reaches the target film thickness. As Figure 15As shown, the estimated torque calculated in the previous estimation interval is used in the next estimation interval.

[0261] Similar to the Figure 12 embodiment described above, after the operation system 47 calculates the estimated grinding rate in each estimation interval, it determines the grinding time or grinding pressure in the next estimation interval.

[0262] Figure 16 is a block diagram for explaining another embodiment of grinding a workpiece using a chemical mechanical polishing system. In this embodiment, the operation system 47 is configured to correct the Preston coefficient in the estimation interval and use the corrected Preston coefficient to calculate the estimated grinding rate.

[0263] As Figure 16 shown, first, the sample is polished using the polishing pad 2 in the initial state by the polishing device 1. The polishing pad 2 in the initial state refers to the polishing pad that has undergone the adaptation process and has not been used for polishing the workpiece yet. During or after the sample polishing using the polishing pad 2 in the initial state, the operation system 47 obtains the initial measured polishing physical quantity Nini. In one embodiment, the initial measured polishing physical quantity Nini includes the measured value of the polishing pad rotation torque, the measured value of the polishing head rotation torque, the measured value of the polishing head swing torque, the measured value of the dresser swing torque, and the measured actual polishing rate of the sample during sample polishing.

[0264] The operation system 47 executes an identification program that uses the initial measured polishing physical quantity Nini as a variable for identification to identify the initial values Xini of the model parameters of the polishing rate model and the polishing torque model. Specifically, the operation system 47 uses the above-mentioned identification formulas (26) and (27) to identify the model parameters R μ, D μ, W μ1, W the initial values Xini of μ0, β1, β0, α1, α2, and T.

[0265] The operation system 47 updates the polishing torque model by substituting the initial values Xini of the model parameters into the polishing torque model represented by the above formulas (8), (13), (18), and (21). The operation system 47 inputs the polishing conditions (the pressure of the polishing head 7 on the polishing pad 2, the rotation speed of the polishing head 7, the rotation speed of the polishing pad 2, the rotation speed of the dresser 50, the pressure of the dresser 50 on the polishing pad 2, etc.) into the polishing torque model to calculate the initial estimated torque TTsim(ini). In one embodiment, the polishing conditions input to the polishing torque model are the polishing conditions in the estimation interval Li. In one embodiment, the initial estimated torque TTsim(ini) is the initial estimated torque of the polishing pad 2.

[0266] The operation system 47 obtains the measured value TTi of the torque in the estimation interval Li during the polishing of the workpiece W. In one embodiment, the measured value TTi of the torque is the measured value of the polishing pad rotation torque during the polishing of the workpiece W. The operation system 47 calculates the difference (TTi - TTsim(ini)) between the measured value TTi of the torque and the initial estimated torque TTsim(ini), and further multiplies the calculated difference by the correction coefficient kob, thereby determining the correction amount Zi. The correction coefficient kob is a predetermined value. The correction amount Zi is represented by the following formula:

[0267] Zi = (TTi - TTsim(ini)) * kob (29)

[0268] The operation system 47 calculates the initial Preston coefficient k p 0 according to the initial value Xini of the model parameters. More specifically, the operation system 47 uses β1, β0, W μ included in the initial value Xini of the model parameters to determine the initial Preston coefficient k p 0 (k p 0 = β1 W μ + β0). The operation system 47 corrects the initial Preston coefficient kp0 by adding the correction amount Zi to the initial Preston coefficient k p 0, and determines the corrected Preston coefficient k p . The corrected Preston coefficient k p is represented by the following formula:

[0269] k p = k p 0 + Zi

[0270] = k p 0 + (TTi - TTsim(ini)) * kob (30)

[0271] The operation system 47 updates the polishing rate model by substituting the corrected Preston coefficient k p into the polishing rate model represented by the above formula (1). The polishing rate model represented by the above formula (1) is pre-stored in the storage device 47a of the operation system 47.

[0272] The operation system 47 inputs the polishing conditions (the pressure of the polishing head 7 on the polishing pad 2, the rotation speed of the polishing head 7, the rotation speed of the polishing pad 2, the rotation speed of the dresser 50, the pressure of the dresser 50 on the polishing pad 2, etc.) in the next estimation interval Li+1 into the updated polishing rate model, and calculates the estimated polishing rate in the next estimation interval Li+1.

[0273] In one embodiment, the acquisition of the measured torque value TTi, the calculation of the correction amount Zi, the calculation of the corrected Preston coefficient k p the calculation of the updated grinding rate model, and the calculation of the estimated grinding rate in the next estimation interval can also be performed in each estimation interval.

[0274] Similar to the embodiment described with reference to Figure 12 After calculating the estimated grinding rate in the estimation interval, the operation system 47 determines the grinding time or grinding pressure in the next estimation interval.

[0275] Figure 17 and Figure 18 are the flowcharts of the embodiments described with reference to Figure 16 the embodiments described above.

[0276] In step 301, the grinding device 1 performs chemical mechanical polishing of a sample using the polishing pad 2 in the initial state.

[0277] In step 302, the operation system 47 acquires the initial measured grinding physical quantity Nini during or after the grinding of the sample.

[0278] In step 303, the operation system 47 uses the initial measured grinding physical quantity Nini as a variable for identification, and operates according to the identification program to determine the initial value Xini of the model parameters.

[0279] In step 304, the operation system 47 updates the grinding torque model by substituting the initial value Xini of the model parameters into the grinding torque model.

[0280] In step 305, the operation system 47 calculates the initial Preston coefficient k according to the initial value Xini of the model parameters p 0(k p 0 = β1 W μ + β0).

[0281] In step 306, the operation system 47 sets a plurality of estimation intervals during the grinding time of the workpiece W.

[0282] In step 307, the grinding device 1 starts chemical mechanical polishing of the workpiece W.

[0283] In step 308, the operation system 47 calculates the initial estimated torque TTsim(ini) by inputting the grinding conditions in the estimation interval Li into the updated grinding torque model.

[0284] In step 309, the arithmetic system 47 obtains a measured value TTi of the torque within the estimated interval Li during the grinding of the workpiece W. In one embodiment, the measured value TTi of the torque is the measured value of the torque of the grinding pad 2 (i.e., the measured value of the torque of the grinding table 5).

[0285] In step 310, the arithmetic system 47 calculates a correction amount Zi by multiplying the difference between the measured value TTi of the torque and the initial estimated torque TTsim(ini) by a predetermined correction coefficient kob.

[0286] In step 311, the arithmetic system 47 adds the correction amount Zi to the initial Preston k p 0 to determine the corrected Preston coefficient k p .

[0287] In step 312, the arithmetic system 47 updates the grinding rate model by substituting the corrected Preston coefficient k p into the grinding rate model.

[0288] In step 313, the arithmetic system 47 calculates the estimated grinding rate of the workpiece W within the next estimated interval Li+1 by inputting the grinding conditions for the next estimated interval Li+1 into the updated grinding rate model.

[0289] In step 314, the arithmetic system 47 determines the grinding time or grinding pressure for the workpiece W in the next estimated interval Li+1. In one embodiment, the grinding time of the workpiece W in the next estimated interval Li+1 is determined by the arithmetic system 47 as follows. That is, the arithmetic system 47 calculates the grinding amount of the workpiece W in the estimated interval Li based on the estimated grinding rate and grinding time of the workpiece W in the estimated interval Li, calculates the difference between the target grinding amount of the workpiece W in the next estimated interval Li+1 and the grinding amount in the estimated interval Li, and calculates the grinding time in the next estimated interval Li+1 based on the calculated difference and the estimated grinding rate of the workpiece W in the estimated interval Li. In other embodiments, the arithmetic system 47 may also calculate the grinding time in the next estimated interval Li+1 based on the estimated grinding rate of the workpiece W in the estimated interval Li and the target grinding amount of the workpiece W in the next estimated interval Li+1.

[0290] In one embodiment, the grinding pressure p for the workpiece W in the next estimated interval Li+1 i+1It is determined by the arithmetic system 47 as follows. That is, the arithmetic system 47 calculates the response rate (grinding rate / grinding pressure) of the grinding rate per unit grinding pressure based on the grinding pressure data when the workpiece W is ground in the estimation section Li and the estimated grinding rate of the workpiece W in the estimation section Li, and calculates the grinding pressure p for the workpiece W in the next estimation section Li+1 based on the calculated response rate, the target grinding amount of the workpiece W in the next estimation section Li+1, and the grinding time in the estimation section Li. i+1 .

[0291] The grinding time or grinding pressure determined in the above step 313 is applied to the grinding of the workpiece W in the next estimation section Li+1 and is used as the grinding condition for grinding the workpiece W.

[0292] The above-described embodiments are described for the purpose of enabling a person having ordinary knowledge in the technical field to which the present invention pertains to implement the present invention. Various modifications of the above-described embodiments can be naturally made by those skilled in the art, and the technical idea of the present invention can also be applied to other embodiments. Therefore, the present invention is not limited to the described embodiments, but is interpreted to cover the broadest scope that follows the technical idea defined by the scope of the claims.

Claims

1. A chemical mechanical polishing system, characterized in that: have: A polishing device, comprising a polishing table, a polishing head, and a slurry supply nozzle, wherein the polishing table is used to support a polishing pad having a polishing surface, the polishing head presses a workpiece against the polishing surface, and the slurry supply nozzle supplies slurry to the polishing surface; as well as a computing system having a storage device storing a simulation model, the simulation model outputting an estimated grinding physical quantity including an estimated grinding rate of the workpiece and an estimated torque as an estimated value of a torque generated in the grinding device due to a sliding resistance of the grinding pad, The simulation model includes a grinding rate model for calculating the estimated grinding rate and a grinding torque model for calculating the estimated torque. The storage device stores an identification program for determining model parameters of the simulation model. The operation system is composed of: During or after grinding the first workpiece, obtaining a measured grinding physical quantity, the measured grinding physical quantity including a measured grinding rate of the first workpiece and a measured value of the torque, using the measured grinding physical quantity as a variable for identification to identify model parameters of the simulation model, An estimated grinding rate of the second workpiece is calculated by inputting grinding conditions for the second workpiece into the simulation model.

2. The chemical mechanical polishing system according to claim 1, characterized in that: The operation system is composed of: After the model parameters are identified, the model parameters are subtracted from predetermined reference model parameters, thereby calculating the difference between the reference model parameters and the model parameters, The simulation model is updated by substituting the difference as a corrected model parameter into the simulation model.

3. The chemical mechanical polishing system according to claim 1, characterized in that: The operation system is composed of: calculating a correction amount based on a difference between an estimated grinding physical quantity obtained from grinding of a previous workpiece performed before grinding of the first workpiece and an actually measured grinding physical quantity obtained from grinding of the previous workpiece, The model parameters for the first workpiece are determined by adding the correction amount to the model parameters obtained from grinding of the previous workpiece.

4. A chemical mechanical polishing method, wherein a workpiece is polished using a polishing device, wherein the polishing device comprises: a polishing table for supporting a polishing pad having a polishing surface; a polishing head for pressing the workpiece against the polishing surface; and a slurry supply nozzle for supplying slurry to the polishing surface, wherein: The chemical mechanical polishing method comprises the following contents: grinding the first workpiece using the grinding device, During or after the polishing of the first workpiece, a measured polishing physical quantity is obtained, the measured polishing physical quantity including a measured polishing rate of the first workpiece and a measured value of a torque generated in the polishing device due to a sliding resistance of the polishing pad, identifying model parameters by using the measured grinding physical quantity as a variable for identification through a computing system, the computing system having an identification program for determining the model parameters of a simulation model, the simulation model including a grinding rate model for calculating an estimated grinding rate of a workpiece and a grinding torque model for calculating an estimated torque as an estimated value of the torque, The grinding conditions for the second workpiece are input to the simulation model, thereby calculating an estimated grinding rate of the second workpiece.

5. The chemical mechanical polishing method according to claim 4, characterized in that: The chemical mechanical polishing method also includes the following: After the model parameters are identified, the model parameters are subtracted from predetermined reference model parameters, thereby calculating the difference between the reference model parameters and the model parameters, The difference is substituted into the simulation model as a corrected model parameter, thereby updating the simulation model.

6. The chemical mechanical polishing method according to claim 4, characterized in that: The model parameters that determine the simulation model are: calculating a correction amount based on a difference between an estimated grinding physical quantity obtained from grinding of a previous workpiece performed before grinding of the first workpiece and an actually measured grinding physical quantity obtained from grinding of the previous workpiece, The model parameters for the first workpiece are determined by adding the correction amount to the model parameters obtained from grinding of the previous workpiece.

7. A chemical mechanical polishing system, characterized in that: have: A polishing device, comprising a polishing table, a polishing head, and a slurry supply nozzle, wherein the polishing table is used to support a polishing pad having a polishing surface, the polishing head presses a workpiece against the polishing surface, and the slurry supply nozzle supplies slurry to the polishing surface; as well as a computing system having a storage device storing a simulation model, the simulation model outputting an estimated grinding physical quantity including an estimated grinding rate of the workpiece and an estimated torque as an estimated value of a torque generated in the grinding device due to a sliding resistance of the grinding pad, The simulation model includes a grinding rate model for calculating the estimated grinding rate and a grinding torque model for calculating the estimated torque. The storage device stores an identification program for determining model parameters of the simulation model. The operation system is composed of: identifying model parameters of the simulation model using a measured grinding rate and a measured torque obtained in a previous grinding of the workpiece performed before the grinding of the workpiece as variables for identification, A plurality of estimated intervals are set within the grinding time of the workpiece, During the grinding of the workpiece, an actually measured grinding physical quantity including a measured value of the torque is obtained in one of the plurality of estimated intervals. using the measured grinding physical quantity as a variable for identification to identify a part of the model parameters of the simulation model and update the model parameters, updating the simulation model using the updated model parameters, An estimated polishing rate of the workpiece in the one estimation interval is calculated by inputting polishing conditions into the updated simulation model.

8. The chemical mechanical polishing system according to claim 7, characterized in that: The operation system is composed of: calculating a post-estimation torque by applying a Kalman filter to an estimated torque calculated using the grinding torque model in an estimation interval before the one estimation interval and a measured value of the torque obtained in the one estimation interval, Using the actually measured grinding physical quantity including the post-estimation torque as a variable for identification, a part of the model parameters of the simulation model is identified and the model parameters are updated.

9. A chemical mechanical polishing method, wherein a workpiece is polished using a polishing device, the polishing device comprising: a polishing table for supporting a polishing pad having a polishing surface; a polishing head for pressing the workpiece against the polishing surface; and a slurry supply nozzle for supplying slurry to the polishing surface, wherein: identifying model parameters of a simulation model using a measured grinding rate and a measured torque obtained in a previous grinding of the workpiece performed before the grinding of the workpiece as variables for identification, the simulation model comprising: a grinding rate model that calculates an estimated grinding rate of the workpiece; and a grinding torque model that calculates an estimated torque that is an estimated value of a torque generated in the grinding device due to a sliding resistance of the grinding pad, A plurality of estimated intervals are set within the grinding time of the workpiece, During the grinding of the workpiece, an actually measured grinding physical quantity including a measured value of the torque is obtained in one of the plurality of estimated intervals. using the measured grinding physical quantity as a variable for identification to identify a part of the model parameters of the simulation model and update the model parameters, updating the simulation model using the updated model parameters, An estimated polishing rate of the workpiece in the one estimation interval is calculated by inputting polishing conditions into the updated simulation model.

10. The chemical mechanical polishing method according to claim 9, characterized in that: The method further includes: calculating a post-estimation torque by applying a Kalman filter to an estimated torque calculated using the grinding torque model in an estimation interval before the one estimation interval and a measured value of the torque obtained in the one estimation interval, Updating the simulation model means identifying a part of model parameters of the simulation model using the actually measured grinding physical quantity including the post-estimation torque as a variable for identification and updating the model parameters.

11. A chemical mechanical polishing system, characterized in that: have: A polishing device comprising a polishing table, a polishing head, and a slurry supply nozzle, wherein the polishing table is used to support a polishing pad having a polishing surface, the polishing head presses a workpiece against the polishing surface, and the slurry supply nozzle supplies slurry to the polishing surface; and a computing system having a storage device storing a simulation model, the simulation model outputting an estimated grinding physical quantity including an estimated grinding rate of the workpiece and an estimated torque as an estimated value of a torque generated in the grinding device due to a sliding resistance of the grinding pad, The simulation model includes a grinding rate model for calculating the estimated grinding rate and a grinding torque model for calculating the estimated torque. The storage device stores an identification program for determining model parameters of the simulation model. The operation system is composed of: obtaining an initial measured polishing physical quantity from polishing of a sample using the polishing pad in an initial state, using the initial measured grinding physical quantity as a variable for identification to determine the initial value of the model parameter, Calculate the initial Preston coefficients based on the initial values ​​of the model parameters, A plurality of estimated intervals are set within the grinding time of the workpiece, By inputting the grinding conditions into the simulation model to calculate the initial estimated torque, During the grinding of the workpiece, a measured value of the torque in a first estimated interval among the plurality of estimated intervals is obtained; The correction amount is calculated by multiplying the difference between the measured value of the torque and the initial estimated torque by a predetermined correction coefficient, The corrected Preston coefficient is determined by adding the correction amount to the initial Preston coefficient. The grinding rate model is updated by substituting the corrected Preston coefficient into the grinding rate model, An estimated polishing rate of the workpiece in a second estimated interval is calculated by inputting polishing conditions for a second estimated interval among the plurality of estimated intervals into the polishing rate model.

12. A chemical mechanical polishing method, wherein a workpiece is polished using a polishing device, wherein the polishing device comprises: a polishing table for supporting a polishing pad having a polishing surface; a polishing head for pressing the workpiece against the polishing surface; and a slurry supply nozzle for supplying slurry to the polishing surface, wherein: obtaining an initial measured polishing physical quantity from polishing of a sample using the polishing pad in an initial state, The initial values ​​of the model parameters are identified by a computing system using the initial measured grinding physical quantity as a variable for identification, the computing system having an identification program for determining the model parameters of a simulation model, the simulation model comprising: a grinding rate model for calculating an estimated grinding rate of the workpiece; and a grinding torque model for calculating an estimated torque as an estimated value of the torque generated in the grinding device due to the sliding resistance of the grinding pad, Calculate the initial Preston coefficients based on the initial values ​​of the model parameters, A plurality of estimated intervals are set within the grinding time of the workpiece, By inputting the grinding conditions into the simulation model to calculate the initial estimated torque, During the grinding of the workpiece, a measured value of the torque in a first estimated interval among the plurality of estimated intervals is obtained; The correction amount is calculated by multiplying the difference between the measured value of the torque and the initial estimated torque by a predetermined correction coefficient, The corrected Preston coefficient is determined by adding the correction amount to the initial Preston coefficient. The grinding rate model is updated by substituting the corrected Preston coefficient into the grinding rate model, An estimated polishing rate of the workpiece in a second estimated interval is calculated by inputting polishing conditions for a second estimated interval among the plurality of estimated intervals into the polishing rate model.

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