Chemical mechanical polishing system and chemical mechanical polishing method of workpiece

Abstract

To provide a chemical mechanical polishing system for polishing workpiece, while calculating an estimated polishing rate of workpiece such as a wafer using a physical model.SOLUTION: A chemical mechanical polishing system is configured to acquire an actual measurement polishing physical amount including an actual measurement polishing rate of first workpiece, and a measured value of a torque generated in a polishing device 1 during or after polishing of the first workpiece, to identify a model parameter of a simulation model using the actual measurement polishing physical amount as a variable for identification, to input a polishing condition for second workpiece to the simulation model, and to thereby calculate an estimated polishing rate of the second workpiece.SELECTED DRAWING: Figure 1

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 to a technique for polishing a workpiece while estimating the polishing rate of the workpiece using a simulation model constructed based on the actual measurement data of chemical mechanical polishing.

Background Art

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

[0003] For the purpose of estimating the film thickness of a wafer and detecting the end point of wafer polishing, simulation techniques for wafer polishing have been developed. As a typical 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 by inputting the polishing conditions of the wafer into the model, an estimated value of the polishing result is output from the model. Such polishing prediction by machine learning is expected as a technique capable of obtaining prediction results close to actual polishing.

Prior Art Documents

Patent Documents

[0004]

Patent Document 1

Patent Document 2

Summary of the Invention

Problems to be Solved by the Invention

[0005] However, a large amount of training data (so-called big data) is required for the work of creating a model by machine learning. In particular, in order to create a model that can output more accurate polishing results, a larger amount of data is required, and as a result, it takes a long time to create the model. Furthermore, since the model itself has a complex configuration, it takes a relatively long time for the model to output the polishing result.

[0006] In addition, a model composed of a neural network is a so-called black box, and it is unknown what structure it has (what weight parameters it has). For this reason, when the actual polishing result is different from the polishing result output from the model, it is impossible to specify the part of the model that should be corrected. To correct the model, additional training data is required, and a long time is required for model correction.

[0007] 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 an estimated polishing rate of the workpiece using a physical model.

Means for Solving the Problems

[0008] In one aspect, a polishing apparatus includes 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 estimated polishing physical quantities including an estimated polishing rate of the workpiece and an estimated torque as an estimated value of the torque generated in the polishing apparatus due to the sliding resistance of the polishing pad. The simulation model includes a polishing rate model for calculating the estimated polishing rate and a polishing torque model for calculating the estimated torque. The storage device stores an identification program for determining model parameters of the simulation model. The arithmetic system acquires measured polishing physical quantities including a measured polishing rate of the first workpiece and a measured value of the torque during or after polishing of the first workpiece, uses the measured polishing physical quantities as variables for identification, identifies the model parameters of the simulation model, and inputs polishing conditions for a second workpiece into the simulation model to calculate an estimated polishing rate of the second workpiece. A chemical mechanical polishing system is provided.

[0009] In one aspect, after the model parameters are identified, the arithmetic system calculates a difference between the reference model parameters and the model parameters by subtracting the model parameters from the predetermined reference model parameters, and updates the simulation model by substituting the difference as corrected model parameters into the simulation model. In one aspect, the arithmetic system calculates a correction amount based on a difference between the estimated polishing physical quantities obtained from polishing of a previous workpiece and the measured polishing physical quantities obtained from polishing of the previous workpiece, which were executed before polishing of the first workpiece, and determines the model parameters for the first workpiece by adding the correction amount to the model parameters obtained from polishing of the previous workpiece.

[0010] In one aspect, there is provided a chemical mechanical polishing method for polishing a workpiece 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 method including: polishing a first workpiece with the polishing apparatus; obtaining measured polishing physical quantities including a measured polishing rate of the first workpiece and a measured value of torque generated in the polishing apparatus due to a sliding resistance of the polishing pad during or after polishing of the first workpiece; identifying model parameters of a simulation model including a polishing rate model for calculating an estimated polishing rate of a workpiece and a polishing torque model for calculating an estimated torque as an estimated value of the torque, by using the measured polishing physical quantities as variables for identification by an arithmetic system including an identification program; and calculating an estimated polishing rate of a second workpiece by inputting polishing conditions for the second workpiece into the simulation model.

[0011] In one aspect, after the model parameters are identified, the chemical mechanical polishing method further includes updating the simulation model by calculating a difference between the reference model parameters and the model parameters by subtracting the model parameters from the predetermined reference model parameters, and substituting the difference as corrected model parameters into the simulation model. In one aspect, determining the model parameters of the simulation model includes calculating a correction amount based on a difference between an estimated polishing physical quantity obtained from polishing of a previous workpiece and a measured polishing physical quantity obtained from polishing of the previous workpiece, which was performed before polishing of the first workpiece, and determining the model parameters for the first workpiece by adding the correction amount to the model parameters obtained from polishing of the previous workpiece.

[0012] In one aspect, a polishing apparatus includes 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 an estimated polishing physical quantity including an estimated polishing rate of the workpiece and an estimated torque as an estimated value of torque generated in the polishing apparatus due to the sliding resistance of the polishing pad. The simulation model includes a polishing rate model for calculating the estimated polishing rate and a polishing torque model for calculating the estimated torque. The storage device stores an identification program for determining model parameters of the simulation model. The arithmetic system uses, as variables for identification, an actually measured polishing rate and an actually measured torque obtained from polishing of a previous workpiece, which were executed before polishing of the workpiece, to identify the model parameters of the simulation model, sets a plurality of estimation sections within the polishing time of the workpiece, obtains an actually measured polishing physical quantity including a measured value of the torque within one of the plurality of estimation sections during polishing of the workpiece, uses the actually measured polishing physical quantity as a variable for identification to identify a part of the model parameters of the simulation model and update the model parameters, updates the simulation model using the updated model parameters, and is configured to calculate an estimated polishing rate of the workpiece within the one estimation section by inputting polishing conditions into the updated simulation model. A chemical mechanical polishing system is provided.

[0013] In one aspect, the arithmetic system is configured to calculate a posteriori estimated torque by applying a Kalman filter to an estimated torque calculated using the polishing torque model in an estimation section before the one estimation section and a measured value of the torque obtained within the one estimation section, and use the actually measured polishing physical quantity including the 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.

[0014] In one aspect, there is provided a chemical mechanical polishing method for polishing a workpiece 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 method including: identifying model parameters of a simulation model using, as variables for identification, an actually measured polishing rate and an actually measured torque obtained from polishing of a previous workpiece, which are executed before polishing of the workpiece; the simulation model including a polishing rate model for calculating an estimated polishing rate of the workpiece and a polishing torque model for calculating an estimated torque as an estimated value of torque generated in the polishing apparatus due to sliding resistance of the polishing pad; setting a plurality of estimation intervals within a polishing time of the workpiece; during polishing of the workpiece, acquiring an actually measured polishing physical quantity including a measured value of the torque within one of the plurality of estimation intervals; using the actually measured polishing 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; and calculating an estimated polishing rate of the workpiece within the one estimation interval by inputting polishing conditions into the updated simulation model.

[0015] In one aspect, the chemical mechanical polishing method further includes calculating a posteriori estimated torque by applying a Kalman filter to an estimated torque calculated using the polishing torque model in an estimation interval before the one estimation interval and a measured value of the torque obtained within the one estimation interval, and updating the simulation model includes identifying a part of the model parameters of the simulation model and updating the model parameters using, as variables for identification, the actually measured polishing physical quantity including the posteriori estimated torque.

[0016] In one aspect, there is provided a chemical mechanical polishing system comprising 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 a computing system having a storage device storing a simulation model that outputs estimated polishing physical quantities including an estimated polishing rate of the workpiece and an estimated torque as an estimated value of torque generated in the polishing apparatus due to sliding resistance of the polishing pad. The simulation model includes a polishing rate model for calculating the estimated polishing rate and a polishing torque model for calculating the estimated torque. The storage device stores an identification program for determining model parameters of the simulation model. The computing system acquires initial measured polishing physical quantities from polishing of a sample using the polishing pad in an initial state, determines initial values of the model parameters using the initial measured polishing physical quantities as variables for identification, calculates an initial Preston coefficient from the initial values of the model parameters, sets a plurality of estimation intervals during a polishing time of the workpiece, inputs polishing conditions into the simulation model to calculate an initial estimated torque, acquires a measured value of the torque within a first estimation interval among the plurality of estimation intervals during polishing of the workpiece, calculates a correction amount by multiplying a difference between the measured value of the torque and the initial estimated torque by a predetermined correction coefficient, determines a corrected Preston coefficient by adding the correction amount to the initial Preston coefficient, updates the polishing rate model by substituting the corrected Preston coefficient into the polishing rate model, and is configured to 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.

[0017] In one aspect, a chemical mechanical polishing method for polishing a workpiece 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, comprising: obtaining an initial measured polishing physical quantity from polishing of a sample using the polishing pad in an initial state, and a polishing rate model for calculating an estimated polishing rate of the workpiece; and an identification program for determining model parameters of a simulation model including a polishing torque model for calculating an estimated torque as an estimated value of the torque generated in the polishing apparatus due to the sliding resistance of the polishing pad, identifying an initial value of the model parameters using the initial measured polishing physical quantity as a variable for identification by an arithmetic system having the identification program, calculating an initial Preston coefficient from the initial value of the model parameters, setting a plurality of estimation sections during the polishing time of the workpiece, inputting polishing conditions into the simulation model to calculate an initial estimated torque, obtaining a measured value of the torque within a first estimation section among the plurality of estimation sections during the polishing of the workpiece, calculating a correction amount by multiplying a difference between the measured value of the torque and the initial estimated torque by a predetermined correction coefficient, determining a corrected Preston coefficient by adding the correction amount to the initial Preston coefficient, updating the polishing rate model by substituting the corrected Preston coefficient into the polishing rate model, and calculating an estimated polishing rate of the workpiece within the second estimation section by inputting polishing conditions for the second estimation section among the plurality of estimation sections into the polishing rate model.

Advantages of the Invention

[0018] The polishing rate model and the polishing torque model, which are physical models included in the simulation model, are virtual chemical mechanical polishing systems that mimic actual polishing apparatuses. The model parameters constituting the simulation model are identified based on the comparison between the actually measured polishing physical quantities (actually measured polishing rate, actually measured mechanical torque, etc.) obtained from the actual polishing apparatus and the estimated polishing physical quantities (estimated polishing rate, estimated mechanical torque, etc.) obtained from the simulation model. More specifically, model parameters for bringing the estimated polishing physical quantities closer to the actually measured polishing physical quantities are determined. Therefore, the simulation model can accurately calculate the estimated polishing rate of the workpiece.

Brief Description of Drawings

[0019]

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Best Mode for Carrying Out the Invention

[0020] Hereinafter, embodiments of the present invention will be described with reference to the drawings. FIG. 1 is a schematic diagram showing one embodiment of a chemical mechanical polishing system. As shown in FIG. 1, the chemical mechanical polishing system includes a polishing apparatus 1 that chemically mechanically polishes a workpiece W. This polishing apparatus 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 an operation control unit 80 that controls the operation of the polishing apparatus 1. The polishing head 7 is configured to be able to hold the workpiece W on its lower surface.

[0021] The polishing apparatus 1 further includes a support shaft 14, a polishing head swing arm 16 connected to the upper end of the support shaft 14 for swinging the polishing head 7, a polishing head shaft 18 rotatably supported at the free end of the polishing head swing arm 16, and a polishing head rotation motor 20 for rotating 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, pulleys, and 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 torque transmission mechanism, and the polishing head 7 rotates together with the polishing head shaft 18. In this way, the polishing head 7 is rotated by the polishing head rotation motor 20 in the direction indicated by the arrow about its axis.

[0022] The polishing apparatus 1 further includes a table rotation motor 21 for rotating 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 are rotated by the table rotation motor 21 about the table shaft 5a in the direction indicated by the arrow. 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 attached 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.

[0023] The polishing head shaft 18 is vertically movable relative to the polishing head swing arm 16 by a lifting mechanism 24, and the vertical movement of the polishing head shaft 18 enables the polishing head 7 to move vertically relative to the polishing head swing arm 16. A rotary joint 25 is attached to the upper end of the polishing head shaft 18.

[0024] The polishing device 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 rotatable about the support shaft 14. The polishing head swing motor 22 swings the polishing head swing arm 16 by a predetermined angle clockwise and counterclockwise about the support shaft 14, so that the polishing head 7 swings on the polishing pad 2 while pressing the workpiece W against the polishing surface 2a of the polishing pad 2.

[0025] In this embodiment, the polishing head swing motor 22 is installed at the upper end of the support shaft 14 and is arranged to swing the polishing head swing arm 16 without rotating the support shaft 14. In one embodiment, the polishing head swing arm 16 may be fixed to the support shaft 14, and the polishing head swing motor 22 may be connected to the support shaft 14 so as to rotate the support shaft 14 together with the polishing head swing arm 16.

[0026] The lifting mechanism 24 for lifting and lowering the polishing head shaft 18 and the polishing head 7 includes a bearing 26 that rotatably supports the polishing head shaft 18, a bridge 28 to which the bearing 26 is fixed, a ball screw mechanism 32 attached to the bridge 28, a support base 29 supported by a support column 30, and a servo motor 38 fixed to the support base 29. The support base 29 that supports the servo motor 38 is connected to the polishing head swing arm 16 via the support column 30.

[0027] The ball screw mechanism 32 includes a screw shaft 32a connected to the servo motor 38 and a nut 32b that engages with the screw shaft 32a. The nut 32b is fixed to the bridge 28. The polishing head shaft 18 is configured to move up and down (vertically) integrally with the bridge 28. Therefore, when the servo motor 38 drives the ball screw mechanism 32, the bridge 28 moves up and down, and thereby the polishing head shaft 18 and the polishing head 7 move up and down.

[0028] 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 onto 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 by a lifting mechanism 24 to a predetermined polishing position. Further, the polishing head 7 presses the workpiece W against the polishing surface 2a of the polishing pad 2 at the above polishing position. With the slurry existing on the polishing surface 2a of the polishing pad 2, the workpiece W is brought into 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.

[0029] The polishing apparatus 1 is provided with a film thickness sensor 49 for measuring 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 crossing 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 operation control unit 80 and the arithmetic system 47. The specific configuration of the film thickness sensor 49 is not particularly limited as long as the film thickness of the workpiece W can be measured. For example, the film thickness sensor 49 is an optical film thickness sensor or an eddy current film thickness sensor.

[0030] The film thickness sensor 49 is a so-called in-situ type film thickness measuring device incorporated in the polishing apparatus 1 for polishing the workpiece W. In one embodiment, instead of the film thickness sensor 49, an ex-situ type film thickness measuring device provided outside the polishing apparatus 1 may be provided. Before and after polishing the workpiece W, the film thickness of the workpiece W is measured by the ex-situ type film thickness measuring device. The measured value of the film thickness is sent to the operation control unit 80 and the arithmetic system 47.

[0031] The polishing device 1 further includes a dresser 50 that dresses the polishing surface 2a of the polishing pad 2, a dresser shaft 51 to which the dresser 50 is connected, an air cylinder 53 as a dresser pressing actuator provided at the upper end of the dresser shaft 51, a dresser swing arm 55 that rotatably supports the dresser shaft 51, and a support shaft 58 to which the dresser swing arm 55 is fixed.

[0032] The lower surface of the dresser 50 constitutes a dressing surface 50a, and this dressing surface 50a is composed of abrasive grains (for example, diamond particles). The air cylinder 53 is disposed on a support base 57 supported by a support column 56, and these support columns 56 are fixed to the dresser swing arm 55. The air cylinder 53 is connected to the dresser 50 via the dresser shaft 51. The air 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 polishing surface 2a of the polishing pad 2 with a predetermined force. Instead of the air cylinder 53, a combination of a servo motor and a ball screw mechanism may be used for the dresser pressing actuator.

[0033] The polishing device 1 further includes a dresser rotation motor 60 that rotates the dresser 50 about its axis. This 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 or the like. 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 50 is rotated by the dresser rotation motor 60 in the direction indicated by the arrow about its axis.

[0034] The grinding device 1 further includes a dresser swing motor 63 that swings the dresser 50 on the polishing surface 2a. This dresser swing motor 63 is connected to the support shaft 58. The dresser swing arm 55 is configured to be rotatable together with the support shaft 58 about the support shaft 58. The dresser swing motor 63 rotates the dresser swing arm 55 clockwise and counterclockwise by a predetermined angle about the support shaft 58, so that the dresser 50 swings in the radial direction of the polishing pad 2 on the polishing pad 2 while pressing its dressing surface 50a against the polishing surface 2a of the polishing pad 2.

[0035] In this 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 so as to rotate the support shaft 58 together with the dresser swing arm 55. In one embodiment, the dresser swing motor 63 may be installed at the upper end of the support shaft 58 and arranged to swing the dresser swing arm 55 without rotating the support shaft 58.

[0036] The dressing of the polishing surface 2a of the polishing pad 2 is performed as follows. During the polishing of the workpiece W, the dresser 50 rotates about the dresser shaft 51, and the dressing surface 50a of the dresser 50 is pressed against the polishing surface 2a by the air cylinder 53. With the slurry present on the polishing surface 2a, the dresser 50 is brought into sliding contact with the polishing surface 2a. While the dresser 50 is in sliding contact with the polishing surface 2a, the dresser swing motor 63 rotates the dresser swing arm 55 clockwise and counterclockwise by a predetermined angle about the support shaft 58 to move the dresser 50 in the radial direction of the polishing pad 2. In this way, the polishing pad 2 is shaved off by the dresser 50, and the polishing surface 2a is dressed (regenerated).

[0037] In this embodiment, the dressing of the polishing surface 2a is performed during the polishing of the workpiece W. However, in one embodiment, the dressing of the polishing surface 2a may be performed after the polishing of the workpiece W. In this case, pure water may be supplied onto the polishing surface 2a instead of the slurry during dressing.

[0038] FIG. 2 is a cross-sectional view of the polishing head 7 shown in FIG. 1. The polishing head 7 includes a carrier 71 fixed to a polishing head shaft 18 and a retainer ring 72 disposed below the carrier 71. A flexible membrane (elastic film) 74 that contacts the workpiece W is held at the lower part of the carrier 71. Four pressure chambers G1, G2, G3, and G4 are formed between the membrane 74 and the carrier 71. The pressure chambers G1, G2, G3, and G4 are formed by the membrane 74 and the carrier 71. The central pressure chamber G1 is circular, and the other pressure chambers G2, G3, and G4 are annular. These pressure chambers G1, G2, G3, and G4 are arranged concentrically. In one embodiment, more than four pressure chambers may be provided, or less than four pressure chambers may be provided.

[0039] Compressed gas such as compressed air is supplied to the pressure chambers G1, G2, G3, and G4 by a gas supply source 77 via 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 membrane 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 membrane 74, pressing the workpiece W against the polishing surface 2a. The internal pressures of the pressure chambers G1, G2, G3, and G4 can be changed independently, whereby the polishing pressures on 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 adjusted independently. The pressure chambers G1, G2, G3, and G4 communicate with a vacuum source (not shown) via the fluid paths F1, F2, F3, and F4.

[0040] An annular rolling diaphragm 76 is disposed between the carrier 71 and the retainer ring 72, and a pressure chamber G5 is formed inside the rolling diaphragm 76. The pressure chamber G5 communicates with the gas supply source 77 via a 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 retainer ring 72 against the polishing surface 2a of the polishing pad 2.

[0041] The peripheral edge of the workpiece W and the lower surface of the membrane 74 (i.e., the workpiece pressing surface) are surrounded by the retainer ring 72. During the polishing of the workpiece W, the retainer ring 72 presses the polishing surface 2a of the polishing pad 2 outside the workpiece W, preventing the workpiece W from popping out of the polishing head 7 during polishing.

[0042] The fluid passages F1, F2, F3, F4, F5 extend from the pressure chambers G1, G2, G3, G4, G5 through the rotary joint 25 to the gas supply source 77. Pressure regulators R1, R2, R3, R4, R5 are respectively attached to the fluid passages F1, F2, F3, F4, F5. The compressed gas from the gas supply source 77 is supplied into the pressure chambers G1 - G5 through the pressure regulators R1 - R5, the rotary joint 25, and the fluid passages F1 - F5.

[0043] The pressure regulators R1, R2, R3, R4, R5 are configured to control the pressure in the pressure chambers G1, G2, G3, G4, G5. The pressure regulators R1, R2, R3, R4, R5 are connected to the operation control unit 80. The operation control unit 80 is connected to the arithmetic system 47. The fluid passages F1, F2, F3, F4, F5 are also connected to an atmosphere release valve (not shown), and it is also possible to release the pressure chambers G1, G2, G3, G4, G5 to the atmosphere.

[0044] The operation control unit 80 is configured to generate the target pressure values for each of the pressure chambers G1 - G5. The operation control unit 80 sends the target pressure values to the pressure regulators R1 - R5, and the pressure regulators R1 - R5 operate so that the pressure in the pressure chambers G1 - G5 matches the corresponding target pressure values. The polishing head 7 having a plurality of pressure chambers G1, G2, G3, G4 can independently press each region on the surface of the workpiece W against the polishing pad 2 based on the progress of polishing, so that the film of the workpiece W can be polished uniformly.

[0045] During the polishing of the workpiece W, the polishing head 7 is maintained at the reference height. The reference height of the polishing head 7 is the overall relative height of the polishing head 7 with respect to the polishing surface 2a of the polishing pad 2. With the polishing head 7 at the reference height, compressed gas is supplied to the pressure chambers G1, G2, G3, G4, G5. The membranes 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.

[0046] Returning to FIG. 1, the chemical mechanical polishing system further includes a computing system 47 having a simulation model for simulating the polishing of the workpiece W and calculating the estimated polishing physical quantities of the workpiece W. The computing system 47 is electrically connected to the polishing apparatus 1. More specifically, the computing system 47 is connected to the operation control unit 80. The simulation model represents a virtual 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, which is a virtual polishing apparatus constructed in the virtual space, constitute a digital twin. A system that utilizes such a digital twin, feeds back the results of the simulation to the real world, and performs optimal control (for example, controls so that the workpiece can be polished more flatly) is called a cyber-physical system.

[0047] When preset polishing conditions are input to the simulation model, the simulation model executes virtual chemical mechanical polishing of the workpiece W using the virtual polishing apparatus and outputs estimated polishing physical quantities such as the estimated polishing rate of the workpiece W. Examples of the polishing conditions include the rotational speed [min -1 or rad / s] of the polishing table 5 and the rotational speed [min -1Or [rad / s], the pressure [Pa] applied from the workpiece W to the polishing surface 2a of the polishing pad 2, the pressure [Pa] applied from the retainer ring 72 to the polishing surface 2a of the polishing pad 2, the relative position between the polishing head 7 and the polishing pad 2, the rotational speed of the dresser 50 [min -1 Or [rad / s], the pressure [Pa] applied from the dresser 50 to the polishing surface 2a of the polishing pad 2, the relative position between the dresser 50 and the polishing pad 2, the position and flow rate of slurry supply, etc. can be mentioned. The polishing rate is defined as the amount of the surface material of the workpiece W removed per unit time, and is also called the material removal rate.

[0048] The arithmetic system 47 includes a storage device 47a in which a program and a simulation model are stored, and a processing device 47b that executes arithmetic operations according to instructions included in the program. The storage device 47a includes a main storage device such as a RAM and an auxiliary storage device 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 configuration of the arithmetic system 47 is not limited to these examples.

[0049] The arithmetic system 47 is composed of at least one computer. The at least one computer may be one server or a plurality of servers. The arithmetic system 47 may be an edge server, or a cloud server connected to a communication network such as the Internet or a local area network, or a fog server installed in the network. The arithmetic system 47 may be a plurality of servers connected by a communication network such as the Internet or a local area network. For example, the arithmetic system 47 may be a combination of an edge server and a cloud server.

[0050] The calculation system 47 and the operation control unit 80 may be integrally configured. The calculation system 47 and the operation control unit 80 may be virtually constructed by one or more computers.

[0051] The simulation model is at least composed of a physical model that outputs an estimated polishing physical quantity. The simulation model is stored in the storage device 47a. The physical model includes at least 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 apparatus 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, similar to the estimated polishing rate. Specific examples of the torque include a polishing head rotation torque for rotating the polishing head 7 and the workpiece W around the axis of the polishing head 7, a polishing pad rotation torque for rotating the polishing pad 2 (or the polishing table 5) around its axis, a dresser rotation torque for rotating the dresser 50 around its axis, a dresser swing torque around the swing axis required for swinging the dresser 50 on the polishing pad 2, and a head swing torque around the swing axis required for swinging the polishing head 7 on the polishing pad 2.

[0052] The simulation model includes a plurality of model parameters. These model parameters include known model parameters determined by polishing conditions (e.g., polishing pressure, rotation speed of the polishing head 7, rotation speed of the polishing pad 2) and unknown model parameters such as the friction coefficient of the workpiece W. Once the unknown model parameters are determined, by inputting the polishing conditions into the simulation model, the estimated polishing physical quantity (estimated polishing rate and estimated values of various torques) of the workpiece W can be output from the simulation model.

[0053] The actually 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 from the measured data. Therefore, the arithmetic system 47 is configured to identify the unknown model parameters of the simulation model by using the actually measured polishing physical quantities obtained by actual polishing as variables for identification. The identification of the unknown model parameters is to approximate the unknown model parameters to the optimum values.

[0054] The program stored in the storage device 47a of the arithmetic system 47 includes an identification program for identifying the unknown model parameters. The arithmetic system 47 operates according to the instructions included in the identification program, and determines the model parameters of the simulation model for approximating the estimated polishing physical quantity of the workpiece to the actually measured polishing physical quantity of the workpiece. The actually measured polishing physical quantity of the workpiece includes the actually measured polishing rate of the workpiece and the measured value of the torque. The estimated polishing physical quantity of the workpiece includes the estimated polishing rate of the workpiece and the estimated value of the torque.

[0055] The grinding device 1 grinds at least one workpiece under predetermined grinding conditions. The calculation system 47 acquires the actually measured grinding physical quantity determined from the grinding of the workpiece and stores the actually measured grinding physical quantity in the storage device 47a. The above-mentioned predetermined grinding conditions may be, for example, the actual grinding conditions of the workpiece or the grinding conditions for pre-set test grinding. The grinding conditions may be dynamically changed during grinding. In this case, it may be possible to improve the identification accuracy and utilize advanced basis functions. The actually measured grinding physical quantity includes 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 the workpiece is being ground. The measured value of the torque may be a value directly indicating the torque, such as the measured value of a torque meter (not shown), or may be a value indirectly indicating the torque, 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 may be a value that indirectly estimates the grinding torque based on the mechanism model of the mechanical structure and the in-process information of the motor current and the acceleration / deceleration physical quantity. 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 respectively predetermined constant speeds. Therefore, when the sliding resistance acting on the grinding head 7, the grinding pad 2, and the dresser 50 increases, the torque current also increases.

[0056] Figure 3 is a flowchart for explaining a method of identifying unknown model parameters of a simulation model. In step 1, the grinding device 1 shown in FIG. 1 grinds at least one workpiece under predetermined grinding conditions. In step 2, the arithmetic system 47 determines the actually measured polishing physical quantities from the actually measured data obtained from the actual polishing of the workpiece. More specifically, the arithmetic system 47 calculates the actually measured polishing rate of the workpiece and further obtains the measured values of various torques generated when the workpiece is being polished. The actually measured polishing rate can be calculated by dividing the difference between the initial film thickness of the workpiece and the film thickness of the polished workpiece by the polishing time. The measured values of various torques are, for example, the torque currents supplied to the polishing head rotation motor 20, the table rotation motor 21, the polishing head oscillation motor 22, the dresser oscillation motor 63, and the dresser rotation motor 60. These actually measured polishing physical quantities are stored in the storage device 47a.

[0057] 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. In step 4, the arithmetic system 47 inputs the polishing conditions of the workpiece into the simulation model and determines the model parameters that bring the estimated polishing physical quantities of the workpiece closer to the actually measured polishing physical quantities obtained in step 2. This step 4 is a process of identifying the unknown model parameters that can bring the estimated polishing physical quantities closer to the actually measured polishing physical quantities. In step 5, the arithmetic system 47 replaces the current model parameters of the simulation model with the model parameters determined in step 4 and updates the simulation model. In step 6, the arithmetic system 47 inputs the polishing conditions used in step 4 into the updated simulation model and updates the estimated polishing physical quantities by outputting the estimated polishing physical quantities from the simulation model.

[0058] In step 7, the arithmetic system 47 calculates the difference between the updated estimated polishing physical quantities and the corresponding actually measured polishing physical quantities. In step 8, the arithmetic system 47 evaluates the above difference. The steps from step 5 to step 8 are steps for evaluating the determined model parameters. If the above difference is equal to or greater than a predetermined threshold value, the arithmetic system 47 repeats steps 4 to 8. If the above difference is less than the threshold value, the arithmetic system 47 ends the operation of determining the model parameters. In one embodiment, the arithmetic system 47 counts the number of times steps 4 to 8 are repeated, and if the number of repetitions is equal to or greater than a predetermined value (or the calculation time for repeating steps 4 to 8 is equal to or greater than a predetermined value), and / or if the above difference is less than the threshold value, the arithmetic system 47 ends the operation of determining the model parameters.

[0059] The arithmetic system 47 determines model parameters for bringing the estimated polishing physical quantity closer to the actually measured polishing physical quantity according to algorithms such as the least squares method, the steepest descent method, and the simplex method included in the identification program stored in the storage device 47a. Constraints can also be given to the range of parameters to be identified according to algorithms such as the constrained least squares method. The simulation model having the model parameters finally determined according to the flowchart shown in FIG. 3 is stored in the storage device 47a.

[0060] Next, the simulation model will be described. As described above, the simulation model includes a polishing rate model for calculating the estimated polishing rate of the workpiece W and a polishing torque model for calculating an estimated value of the torque generated due to the sliding resistance of the polishing pad 2.

[0061] The polishing rate model is expressed as follows, for example, based on Preston's law. Polishing rate MRR = k p p |V|=(β1 W μ + β0) p |V| …(1) Here, k pis the Preston coefficient, p is the pressure of the workpiece W against the polishing pad 2, V is the relative speed between the workpiece W and the polishing pad 2, β1 and β0 are constants that relate the friction coefficient and the Preston coefficient of the workpiece W, W μ is the friction coefficient of the workpiece W.

[0062] The Preston coefficient k p is proportional to the friction coefficient of the workpiece W W Assuming it is proportional to μ and represented by a linear first-order function, the above equation (1) is set. In other words, the material removal rate MRR of the workpiece W is assumed to be correlated with the friction coefficient W μ of the workpiece W.

[0063] In the above equation (1), the constants β1, β0, and the friction coefficient W μ are unknown model parameters, while on the other hand, the pressure p and the relative speed 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, that is, the estimated material removal rate, can be obtained from the above equation (1).

[0064] 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 for the polishing apparatus 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.

[0065] The polishing torque model includes at least a head rotation torque model that calculates an estimated value of the polishing head rotation torque for rotating the polishing head 7 and the workpiece W on the polishing pad 2 about the axis of the polishing head 7 (which coincides with the axis of the polishing head shaft 18), and a pad rotation torque model that calculates an estimated value of the polishing pad rotation torque for rotating the polishing pad 2 about its axis (which coincides with the axis of the table shaft 5a).

[0066] During the polishing of the workpiece W, while the polishing head 7 and the workpiece W are rotating, 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 an estimated value of the torque required to rotate the polishing head 7 about its axis at a predetermined speed while resisting 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.

[0067] In the present embodiment, the dressing of the polishing surface 2a of the polishing pad 2 is performed during the polishing of the workpiece W. Therefore, during the polishing of the workpiece W, the retainer ring 72 of the polishing head 7, the workpiece W, and the dresser 50 come into contact with the polishing pad 2. As a result, the polishing pad rotation torque depends on the friction of the retainer ring 72, the workpiece W, and the dresser 50 against the polishing pad 2. The pad rotation torque model is a physical model for calculating an estimated value of the torque required to rotate the polishing pad 2 (i.e., the polishing table 5) at a predetermined speed while resisting the friction between the retainer ring 72 and the polishing pad 2, the friction between the workpiece W and the polishing pad 2, and the friction between the dresser 50 and the polishing pad 2.

[0068] FIG. 4 is a schematic diagram showing the velocity vectors on the polishing head 7, the workpiece W, and the dresser 50 on the polishing pad 2. Each symbol shown in FIG. 4 is defined as follows. Velocity vector in the rotational direction of the polishing pad 2 at point A1 on the workpiece W or the retainer ring 72: V PH Position vector from the center C1 of the polishing pad 2 to point A1: rPH Position vector from the center C2 of the polishing head 7 to point A1: r Hr Velocity vector in the rotational direction of the polishing head 7 at point A1: V Hr Velocity vector in the rocking direction of the polishing head 7 at point A1: V Ho Resultant velocity vector of the polishing head 7 at point A1: V H = V Hr + V Ho Rocking axis of the polishing head 7: OH (coincides with the axis of the support shaft 14) Position vector from the rocking axis OH of the polishing head 7 to point A1: r Ho

[0069] Velocity vector in the rotational direction of the polishing pad 2 at point A2 on the dresser 50: V PD Position vector from the center C1 of the polishing pad 2 to point A2: r PD Position vector from the center C3 of the dresser 50 to point A2: r Dr Velocity vector in the rotational direction of the dresser 50 at point A2: V Dr Velocity vector in the rocking direction of the dresser 50 at point A2: V Do Resultant velocity vector of the dresser 50 at point A2: V D = V Dr + V Do Rocking axis of the dresser 50: OD (coincides with the axis of the support shaft 58) Position vector from the rocking axis OD of the dresser 50 to point A2: r Do

[0070] Relative velocity vector of the polishing head 7 with respect to the polishing pad 2 at point A1: V PH-H = V H - V PH Relative velocity vector V PH-H Unit vector of: uV PH-H = VPH-H / |V PH-H | Relative velocity vector of the polishing pad 2 with respect to the polishing head 7 at point A1: V H-PH =V PH -V H Relative velocity vector V H-PH Unit vector of: uV H-PH =V H-PH / |V H-PH | Relative velocity vector of the dresser 50 with respect to the polishing pad 2 at point A2: V PD-D =V D -V PD Relative velocity vector V PD-D Unit vector of: uV PD-D =V PD-D / |V PD-D | Relative velocity vector of the polishing pad 2 with respect to the dresser 50 at point A2: V D-PD =V PD -V D Relative velocity vector V D-PD Unit vector of: uV D-PD =V D-PD / |V D-PD |

[0071] Next, the pad rotation torque model will be described with reference to FIG. 5. Microscopic area ds of the workpiece W W and the sliding resistance dF acting between the polishing pad 2 PW (representing a vector) is obtained as follows. Sliding resistance dF PW = W μ W p ds W uV PH-H …(2) Here, W μ is the friction coefficient of the workpiece W, W p is the pressure of the workpiece W against the polishing pad 2, ds W is the microscopic area of the workpiece W, uV PH-H is the unit vector of the relative velocity vector of the polishing head 7 with respect to the polishing pad 2.

[0072] The minute area ds of the retainer ring 72 R and the sliding resistance dF acting between the polishing pad 2 PR (representing a vector) is obtained as follows. The sliding resistance dF PR = R μ R p ds R uV PH-H …(3) Here,[[]] R μ is the friction coefficient of the retainer ring 72, R p is the pressure of the retainer ring 72 against the polishing pad 2, ds R is the minute area of the retainer ring 72, uV PH-H is the unit vector of the relative velocity vector of the polishing head 7 against the polishing pad 2.

[0073] The minute area ds of the dresser 50 D and the sliding resistance dF acting between the polishing pad 2 PD (representing a vector) is obtained as follows. The sliding resistance dF PD = D μ D p ds D uV PD-D …(4) Here,[[]] D μ is the friction coefficient of the dresser 50, D p is the pressure of the dresser 50 against 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 against the polishing pad 2.

[0074] The minute torque acting on the center C1 of the polishing pad 2 due to the sliding resistance at 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 is as follows. The minute torque dN PW =r PH ×dFPW …(5) dN PR =r PH ×dF PR …(6) dN PD =r PD ×dF PD …(7) Here, the symbol × represents the cross product of vectors.

[0075] The position of the micro-area ds of the workpiece W W the position of the micro-area ds of the retainer ring 72 R and the position of the micro-area ds of the dresser 50 D are each represented by polar coordinates (ri, θj), then the pad rotation torque model for calculating the estimated value of the polishing pad rotation torque is given as follows. 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)

[0076] When dressing of the polishing surface 2a of the polishing pad 2 is not performed during polishing of the workpiece W, in the above formula (8), the term of Σ i Σ j dN PD becomes 0.

[0077] Next, the head rotation torque model for calculating the estimated value of the polishing head rotation torque will be described. 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 |. The workpiece W has the same rotational speed as the polishing head 7 [min -1Assuming rotation at [[]], the differential area ds of the workpiece W W and the differential area ds of the retainer ring 72 R The sliding resistance acting on them is expressed as follows. Sliding resistance dF HW = W μ W p ds W uV H-PH …(9) dF HR = R μ R p ds R uV H-PH …(10)

[0078] The differential area ds of the workpiece W W and the differential area ds of the retainer ring 72 R The differential torque acting on the center C2 of the polishing head 7 due to the sliding resistance at them is as follows. Differential torque dN HrW =r Hr ×dF HW …(11) dN HrR =r Hr ×dF HR …(12) Here, r Hr is the position vector from the center C2 of the polishing head 7 to the differential area ds of the workpiece W W and also the position vector from the center C2 of the polishing head 7 to the differential area ds of the retainer ring 72 R and to the differential area ds of the retainer ring 72.

[0079] The position of the differential area ds of the workpiece W W and the position of the differential area ds of the retainer ring 72 R are each expressed in polar coordinates (ri, θj), then the head rotation torque model for calculating the estimated value of the polishing head rotation torque is given as follows. Polishing head rotation torque H r N = Σ i Σ j dN HrW +Σ i Σ j dNHrR …(13)

[0080] In this embodiment, dressing of the polishing surface 2a of the polishing pad 2 is performed during polishing of the workpiece W. Therefore, as shown in the above formula (8), the pad rotation torque model includes the torque caused by the sliding resistance of the dresser 50. The polishing torque model further includes a dresser rotation torque model that calculates an estimated value of the dresser rotation torque for rotating the dresser 50 on the polishing pad 2 about its axis, in addition to the head rotation torque model and the pad rotation torque model. The dresser rotation torque model is a physical model for calculating an estimated value of the torque required to rotate the dresser 50 at a predetermined speed while resisting the friction between the dresser 50 and the polishing pad 2.

[0081] 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. Sliding resistance dF D = D μ D p ds D uV D-PD …(14) Micro torque dN rD =r Dr ×dF D …(15) Dresser rotation torque D r N=Σ i Σ j dN rD …(16) Here, D μ is the friction coefficient of the dresser 50, D p is the pressure of the dresser 50 against 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 to the micro area ds D of the dresser 50.

[0082] During 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 an estimated value of the dresser swing torque around the swing axis OD of the dresser 50 required for this swinging of the dresser 50. The dresser swing torque model is represented by the following equation (18). Micro torque dN oD =r Do ×dF D …(17) Dresser swing torque D o N = Σ i Σ j dN oD …(18) Here, r Do is the position vector from the swing axis OD (see FIG. 4) of the dresser 50 to the micro area ds of the dresser 50 D to.

[0083] In the present embodiment, during 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 an estimated value of the polishing head swing torque around the swing axis OH of the polishing head 7 required for this swinging of the polishing head 7. The head swing torque model is represented by the following equation (21). Micro torque dN HoW =r Ho ×dF HW …(19) dN HoR =r Ho ×dF HR …(20) Polishing head swing torque H o N = Σ i Σ j dN HoW +Σ i Σ j dN HoR …(21) Here, r Ho is the micro area ds of the workpiece W from the swing axis OH (see FIG. 4) of the polishing head 7 wThe position vector to, and the minute area ds of the retainer ring 72 from the swing axis center OH R is the position vector to.

[0084] 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).

[0085] The friction coefficients included in the above formulas (1), (8), (13), (16), (18), and (21) that constitute the simulation model W μ, R μ, D μ are unknown model parameters. These unknown model parameters are identified by the identification process described later.

[0086] The friction coefficient of the workpiece W W μ can vary depending on the distribution of abrasive grains contained in the slurry supplied onto the polishing pad 2. The friction coefficient of the workpiece W W The distribution of μ can be obtained by calculation. That is, by defining a basis function representing the friction coefficient of the workpiece W and performing simultaneous identification calculations of the torque and the polishing rate, the distribution of the friction coefficient W μ of the workpiece W as shown in FIG. 6 can be obtained.

[0087] Assuming that the polishing efficiency represented by the number of active abrasive grains on the workpiece W is proportional to the friction coefficient W μ of the workpiece W, the distribution of the friction coefficient W μ can be replaced with the distribution of active abrasive grains. Here, the active abrasive grains are 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 shown in FIG. 6, the friction coefficient Wμ is large on the same pad radius where slurry is supplied to the workpiece W and becomes smaller as the radial position moves away. This is because during the polishing of the workpiece W, the slurry containing abrasive grains is supplied from the slurry supply nozzle 8 (see Fig. 1) onto the polishing pad 2 and scatters outward due to the influence of centrifugal force as it moves toward the outer peripheral side. As can be seen from Fig. 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.

[0088] Coefficient of friction at the position of any radius r and angle θ in the plane of the workpiece W W μ is given by the following equation.

Equation

[0089] The above equation (22) is a physical model representing the distribution of the coefficient of friction W μ of the workpiece W. In this embodiment, the simulation model further includes the physical model represented by equation (22) in addition to the physical models represented by the above equations (1), (8), (13), (16), (18), and (21). For equation (22), W μ1 and W μ0 are unknown model parameters.

[0090] Next, the influence of the deterioration of the polishing pad 2 over time on the friction coefficient will be described. FIG. 7 is a graph showing the relationship between the torque of the polishing pad 2 and the polishing time. While actually polishing the workpiece W, the torque required to rotate the polishing pad 2 at a constant speed gradually decreases as shown by the dotted line in FIG. 7. Possible causes include 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, and the like.

[0091] On the other hand, the torque of the polishing pad 2 calculated by the physical model represented by the above formula (8) is constant regardless of the polishing time as shown by the dashed-dotted line in FIG. 7. 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 as the polishing time elapses. In the present embodiment, the deterioration of the polishing pad 2 is represented as an initial rapid decrease and a subsequent gradual decrease in the friction coefficient of the workpiece W.

[0092] The mathematical model function f p1 (t) representing the initial decrease in the friction coefficient of the workpiece W is as follows. f p1 (t) = W μ i [(1 - α1)exp[-(t - t0) / T] + α1] …(23) In formula (23), t is the polishing time, t0 is the start time of polishing, and T is the time constant. The mathematical model function f p2 (t) representing the gradual decrease in the friction coefficient of the workpiece W is as follows. f p2 (t) = α2(t - t0) + 1 …(24) Using the product f p (t)=f p1 (t)f p2 (t) of the above mathematical model functions, the friction coefficient W μ of the workpiece W is obtained by the following formula. W μ= W μi f p (t) …(25)

[0093] The above-mentioned mathematical model is a fitting function f for reducing the friction coefficient of the workpiece W over the polishing time p (t). This fitting function f p (t) is a function with the polishing time t as a variable. In the above formula, α1, α2, and T are unknown model parameters.

[0094] As described above, the simulation model of this 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 one mathematical model representing the decrease in the friction coefficient of the workpiece W. Such a simulation model can calculate an estimated torque that changes in the same way as the actual torque, as shown by the solid line in FIG. 7.

[0095] Next, a method for identifying (determining) the above-mentioned unknown model parameters R μ,[[]END]] D μ,[[]END]] W μ1,[[]END]] 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 polishing physical quantities obtained by actual polishing as variables for identification. The arithmetic system 47 operates according to the instructions included in the identification program stored in the storage device 47a, and uses algorithms such as the least squares method, the steepest descent method, and the simplex method to determine the model parameters that bring the estimated polishing physical quantities closer to the actually measured polishing physical quantities.

[0096] As described below, in this embodiment, the arithmetic system 47 uses the least squares method to calculate the model parameters W μ1,[[]END]] W μ0,[[]END]] R μ,[[]END]] DIt is configured to determine μ and determine the model parameters β1, β0, α1, α2, and T using the simplex method. However, the present invention is not limited to this embodiment, and other algorithms such as the steepest descent method may be used to determine the above unknown model parameters. Alternatively, only the least squares method may be used to determine the above unknown model parameters.

[0097] In one embodiment, the integrated calculation model using the least squares method is as follows. In the following equations, 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.

Equation

[0098] The measured polishing physical quantity obtained from the actual polishing of the workpiece is input to the left side of the above formula (26). The unknown model parameters are obtained as follows using the least squares method. That is, expand formula (26), extract the terms of the parameter X to be identified, and create the formula Y = AX. Furthermore, using the pseudo-inverse matrix A * of the matrix A, the parameter X is identified by the least squares method from the formula X = A * Y. By repeating this, all unknown parameters can be identified.

[0099] The left side of formula (26) is the measured data Yexp obtained from actual polishing, and the right side is the estimated data Ysim obtained from the simulation model. The right side Ysim is the multiplication AX of the matrix A on the left side that can be calculated only from the input polishing conditions and the vector X of the unknown parameters regarding friction on the right side. Using the least squares method and using the pseudo-inverse matrix A * of the known matrix A, the unknown parameter X = A * Yexp can be obtained.

[0100] In one embodiment, the error function model using the simplex method is as follows.

Number

[0101] The arithmetic system 47 operates according to the identification program and identifies the above-described unknown model parameters. The arithmetic system 47 replaces the current model parameters of the simulation model with the determined model parameters. The arithmetic system 47 inputs the polishing conditions of the workpiece into the simulation model including the determined model parameters, and calculates the estimated polishing physical quantity.

[0102] Furthermore, the arithmetic system 47 calculates the difference between the measured polishing physical quantity and the estimated polishing physical quantity, and determines whether this difference is smaller than a predetermined threshold value. If the difference is greater than or equal to the threshold value, the arithmetic system 47 executes the above-described identification again using the measured polishing physical quantity of another workpiece. If the difference is smaller than the threshold value, the arithmetic system 47 calculates the estimated polishing physical quantity of another workpiece using the simulation model including the determined model parameters. That is, the arithmetic system 47 can input the polishing conditions of a workpiece (for example, a wafer) that has not been polished yet into the simulation model, and accurately calculate the estimated polishing rate of that workpiece using the simulation model.

[0103] The arithmetic system 47 transmits the estimated polishing rate to the operation control unit 80 shown in FIG. 1. The operation control unit 80 can predict the polishing end point of the workpiece being polished based on the estimated polishing rate. Further, during the polishing of the workpiece, the operation control unit 80 may create a distribution of the estimated polishing rate on the workpiece, and control the polishing pressure (the pressure applied from the polishing head 7 to the workpiece) on the workpiece being polished based on the distribution of the estimated polishing rate.

[0104] Next, an embodiment of polishing a workpiece using the above-described chemical mechanical polishing system will be described. The chemical mechanical polishing system described below acquires measured polishing physical quantities (measured values of the measured polishing rate and torque of the workpiece) during or after polishing of the workpiece, calculates an estimated polishing rate for the next workpiece, and is configured to determine polishing conditions for the next workpiece based on the estimated polishing rate.

[0105] FIG. 8 is a flowchart for explaining an embodiment of polishing a workpiece using a chemical mechanical polishing system. In step 101, the arithmetic system 47 determines a 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 the film thickness sensor 49 shown in FIG. 1. The target film thickness is input in advance to the arithmetic system 47 before polishing of the workpiece starts.

[0106] In step 102, the polishing apparatus 1 chemically mechanically polishes the workpiece Wi. In step 103, the arithmetic system 47 acquires measured polishing physical quantities (measured values of the measured polishing rate and torque of the workpiece Wi) during or after polishing of the workpiece Wi. In one embodiment, the measured polishing physical quantities include 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 polishing rate of the workpiece Wi during polishing of the workpiece Wi.

[0107] In step 104, the arithmetic system 47 identifies unknown model parameters of the polishing rate model and the polishing torque model using the measured polishing physical quantities obtained from the polishing of the workpiece Wi as variables for identification. Specifically, the arithmetic 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.

[0108] In step 105, the arithmetic system 47 updates the polishing rate model and the polishing torque model by substituting the model parameters determined in 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), and (21). 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 stored in advance in the storage device 47a of the arithmetic system 47.

[0109] 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.

[0110] In step 106, the arithmetic system 47 calculates the estimated polishing rate of the next workpiece Wi+1 to be polished using the polishing rate model represented by the following formula (1)'. Estimated polishing rate MRR = k p p |V| = (β1 W μ + β0) p i+1 |V i+1 | …(1)' Here, k p is the Preston coefficient, p i+1 is the polishing pressure of the next workpiece Wi+1 to the polishing pad 2, V i+1 is the relative speed between the workpiece Wi+1 and the polishing pad 2, β1 and β0 are constants relating the friction coefficient and the Preston coefficient of the workpiece, W μ is the friction coefficient of the workpiece Wi. β1, β0 and W μ are the model parameters determined in step 104, and the above formula (1)' is the polishing rate model updated in step 105.

[0111] In step 107, the arithmetic system 47 determines the polishing time or the polishing pressure p as the polishing condition for the workpiece Wi+1 to be polished next. i+1 In one embodiment, the polishing time for the workpiece Wi+1 to be polished next is determined by the arithmetic system 47 as follows. That is, the arithmetic system 47 calculates the polishing amount of the workpiece Wi from the measured polishing rate and the polishing time of the workpiece Wi, then calculates the difference between the target polishing amount of the workpiece Wi+1 to be polished next and the polishing amount of the workpiece Wi, and calculates the polishing time for the next workpiece Wi+1 based on the calculated difference and the measured polishing rate of the workpiece Wi. In other embodiments, the arithmetic system 47 may calculate the polishing time for the next workpiece Wi+1 based on the measured polishing rate of the workpiece Wi and the target polishing amount of the workpiece Wi+1 to be polished next.

[0112] In one embodiment, the polishing pressure pi+1 for the workpiece Wi+1 to be polished next is determined by the arithmetic system 47 as follows. That is, the arithmetic system 47 calculates the response rate of the polishing rate per unit polishing pressure (polishing rate / polishing pressure) from the polishing pressure data when polishing the workpiece Wi and the measured polishing rate of the workpiece Wi, and calculates the polishing pressure pi+1 for the next workpiece Wi+1 based on the calculated response rate, the target polishing amount of the workpiece Wi+1 to be polished next, and the polishing time of the workpiece Wi. The polishing time or the polishing pressure p determined in the above step 107 i+1 is applied to the polishing of the next workpiece Wi+1 and is used as the polishing condition for polishing the workpiece Wi+1.

[0113] Steps 102 to 107 may be repeated each time one workpiece is polished, or may be repeated each time a plurality of workpieces are polished. For example, steps 102 to 107 are repeated each time a predetermined number of workpieces are polished.

[0114] FIG. 9 is a block diagram for explaining an embodiment of identification of model parameters and calculation of an estimated polishing rate. The arithmetic system 47 acquires an actually measured polishing physical quantity Ni including a measured torque value and an actually measured polishing rate during or after polishing of the workpiece Wi, and inputs the actually measured polishing physical quantity Ni into identification formulas (26) and (27) as variables for identification. The arithmetic system 47 operates according to an identification program, and identifies (determines) model parameters Xi ( R μ, D μ, W μ1, W μ0, β1, β0, α1, α2, T) using the identification formulas (26) and (27).

[0115] The arithmetic system 47 substitutes the model parameters Xi into a polishing rate model and a polishing torque model, and updates the polishing rate model and the polishing torque model. The arithmetic system 47 inputs polishing conditions for the next workpiece Wi+1 (for example, the pressure of the polishing head 7 against 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 against the polishing pad 2, etc.) into the polishing rate model and the polishing torque model, and calculates an estimated polishing rate and an estimated torque for the next workpiece Wi+1.

[0116] FIG. 10 is a block diagram for explaining another embodiment of identification of model parameters and calculation of an estimated polishing rate. The basic steps of this embodiment are the same as those of the embodiment shown in FIG. 9, but this embodiment is different in that the identified (determined) model parameters Xi are corrected using a predetermined reference model parameter X0.

[0117] The reference model parameter X0 is identified in the same manner as the model parameter Xi before the polishing of the workpiece using the polishing apparatus 1 is started. In one embodiment, the reference model parameter X0 is identified (determined) using the measured polishing physical quantities including the measured values of the polishing rate and torque obtained when polishing a sample with the polishing apparatus 1 in an initial state that has not yet been used for polishing the workpiece. The reference model parameter X0 is stored in the storage device 47a of the arithmetic system 47.

[0118] As shown in FIG. 10, the arithmetic system 47 determines the model parameter Xi using the measured polishing physical quantity Ni including the measured values of the polishing rate and torque obtained from the polishing of the workpiece Wi, subtracts the model parameter Xi from the reference model parameter X0 to calculate the difference Xi' between the reference model parameter X0 and the model parameter Xi, and substitutes the calculated difference Xi' into the polishing rate model and the polishing torque model as the corrected model parameters to update the polishing rate model and the polishing torque model. The arithmetic system 47 inputs the polishing conditions for the next workpiece Wi+1 into the polishing rate model and the polishing torque model, and calculates the estimated polishing rate and the estimated torque of the next workpiece Wi+1.

[0119] According to the present embodiment, the possible noise included in the model parameter Xi can be removed by correction.

[0120] FIG. 11 is a block diagram for explaining still another embodiment of identification of model parameters and calculation of an estimated polishing rate. The basic steps of this embodiment are the same as those of the embodiment shown in FIG. 9. However, in this embodiment, the arithmetic system 47 calculates a correction amount Z based on the difference between an estimated polishing physical quantity Nsim (including an estimated polishing rate and an estimated torque) obtained from polishing of the previous workpiece Wi-1 and an actually measured polishing physical quantity Ni-1 (including measured values of an actually measured polishing rate and torque) obtained from polishing of the previous workpiece Wi-1, and determines a model parameter Xi for the current workpiece Wi by adding the correction amount Z to the model parameter Xi-1 obtained from polishing of the previous workpiece Wi-1.

[0121] The estimated polishing physical quantity Nsim includes an estimated polishing rate and an estimated torque obtained by inputting polishing conditions to a polishing rate model and a polishing torque model updated based on the polishing result of the previous workpiece Wi-1.

[0122] The correction amount Z is determined as follows. The processing system 47 inputs the difference between the estimated polishing physical quantity Nsim obtained from polishing of the previous workpiece Wi-1 and the actually measured polishing physical quantity Ni-1 obtained from polishing of the previous workpiece Wi-1 as variables for identification into the identification formulas (26) and (27), and calculates the correction amount Z using the identification formulas (26) and (27) according to the identification program.

[0123] The arithmetic system 47 determines the model parameter Xi for the current workpiece Wi by adding the correction amount Z to the model parameter Xi-1 obtained from 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 arithmetic system 47 calculates an estimated polishing rate and an estimated torque for the next workpiece Wi+1 by inputting polishing conditions to the updated polishing rate model and polishing torque model.

[0124] FIG. 12 is a flowchart for explaining another embodiment of polishing a workpiece using a chemical mechanical polishing system. In this embodiment, before polishing the workpiece W, the measured polishing rate and the measured torque obtained from the polishing of the previous workpiece Wi-1 are used as variables for identification to identify the model parameters of the simulation model. A plurality of estimation intervals are set within the polishing time of the workpiece W. During the polishing of the workpiece W, the measured polishing physical quantity including the measured value of the torque within one of the plurality of estimation intervals is obtained. Using the measured polishing physical quantity as a variable for identification, a part of the model parameters of the simulation model is identified to update the model parameters. By inputting the polishing conditions into the simulation model, the estimated polishing rate of the workpiece within the one estimation interval is calculated.

[0125] In step 201, before polishing the workpiece W, the polishing apparatus 1 performs chemical mechanical polishing of the workpiece Wi-1. In step 202, the calculation system 47 uses the measured polishing rate and the measured torque obtained from 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. In step 203, the calculation 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 FIG. 1. The target film thickness is input in advance to the calculation system 47 before the polishing of the workpiece W starts.

[0126] In step 204, the calculation system 47 sets a plurality of estimation intervals L1 to L M within the polishing time of the workpiece W. FIG. 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 within the polishing time from the initial film thickness to the target film thickness of the workpiece to be polished. The plurality of estimation intervals L1 to L M are consecutive time intervals during the polishing of one workpiece.

[0127] In step 205, the polishing apparatus 1 starts chemical mechanical polishing of the workpiece W. In step 206, the arithmetic system 47 acquires measured polishing physical quantities including the measured value of torque in the current estimated section Li during the polishing of the workpiece W. In one embodiment, the measured polishing physical quantities include 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, and the measured value of the dresser swing torque during the polishing of the workpiece W.

[0128] In step 207, the arithmetic system 47 uses the measured polishing physical quantities including the measured value of torque obtained from the polishing of the workpiece W as variables for identification, identifies some 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 some of the unknown model parameters R μ, D μ, W μ1, W μ0, β1, β0, α1, α2, T.

[0129] In step 208, the arithmetic system 47 updates the polishing rate model and the polishing torque model by substituting 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). 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 stored in advance in the storage device 47a of the arithmetic system 47.

[0130] Equation (1) is a polishing rate model for calculating the polishing rate of the workpiece, Equation (8) is a pad rotation torque model for calculating the estimated value of the polishing pad rotation torque, Equation (13) is a head rotation torque model for calculating the estimated value of the polishing head rotation torque, Equation (18) is a dresser oscillation torque model for calculating the estimated value of the dresser oscillation torque, and Equation (21) is a head oscillation torque model for calculating the estimated value of the polishing head oscillation torque.

[0131] In step 209, the arithmetic system 47 calculates the estimated polishing rate of the workpiece W in the current estimation interval Li using the polishing rate model updated in step 208 above. In step 210, the arithmetic system 47 determines the polishing time or polishing pressure p i+1 for the workpiece W in the next estimation interval Li+1. In one embodiment, the polishing time of the workpiece W in the next estimation interval Li+1 is determined by the arithmetic system 47 as follows. That is, the arithmetic system 47 calculates the polishing amount of the workpiece W in the estimation interval Li from the estimated polishing rate and polishing time of the workpiece W in the estimation interval Li, calculates the difference between the target polishing amount of the workpiece W in the next estimation interval Li+1 and the polishing amount in the estimation interval Li, and calculates the polishing time in the next estimation interval Li+1 based on the calculated difference and the estimated polishing rate of the workpiece W in the estimation interval Li. In other embodiments, the arithmetic system 47 may calculate the polishing time in the next estimation interval Li+1 based on the estimated polishing rate of the workpiece W in the estimation interval Li and the target polishing amount of the workpiece W in the next estimation interval Li+1.

[0132] In one embodiment, the polishing pressure pi+1 for the workpiece W in the next estimation section Li+1 is determined by the arithmetic system 47 as follows. That is, the arithmetic system 47 calculates the response rate of the polishing rate per unit polishing pressure (polishing rate / polishing pressure) from the polishing pressure data when polishing the workpiece W in the estimation section Li and the estimated polishing rate of the workpiece W in the estimation section Li, and based on the calculated response rate, the target polishing amount of the workpiece W in the next estimation section Li+1, and the polishing time in the estimation section Li, calculates the polishing pressure pi+1 for the workpiece W in the next estimation section Li+1. The polishing time or polishing pressure p determined in step 210 above i+1 is applied to the polishing of the workpiece W in the next estimation section Li+1 and is used as the polishing condition for polishing the workpiece W.

[0133] Steps 206 to 209 may be executed only once when the workpiece W is polished in the first estimation section L1, or may be repeated every time one or more estimation sections have elapsed.

[0134] FIG. 14 is a block diagram for explaining one embodiment of the identification of model parameters and the calculation of the estimated polishing rate. The measured value of torque, which is the actually measured polishing physical quantity Ni obtained in a certain estimation section Li during the polishing of the workpiece W, is input into the identification formulas (26) and (27) as variables for identification. 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 estimation section Li. Further, the arithmetic system 47 updates the model parameter Xref by replacing the model parameter Xref identified from the polishing result of the previous workpiece Wi-1 with the model parameter Xi.

[0135] The calculation system 47 substitutes the updated model parameter Xref into the polishing rate model and the polishing torque model, and updates the polishing rate model and the polishing torque model. The calculation system 47 inputs polishing conditions (for example, the pressure of the polishing head 7 against 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 against the polishing pad 2, etc.) into the polishing rate model and the polishing torque model, and calculates the estimated polishing rate and the estimated torque in the current estimation interval Li.

[0136] FIG. 15 is a block diagram for explaining still another embodiment of polishing a workpiece using a chemical mechanical polishing system. Details of this embodiment not specifically described are the same as those of the embodiment described with reference to FIGS. 12 and 13, and thus the overlapping description is omitted.

[0137] In this embodiment, the calculation system 47 applies a Kalman filter to the estimated torque calculated using the polishing torque model in an estimation interval before the current estimation interval Li and the measured value of the torque obtained within the estimation interval Li to calculate a posteriori estimated torque, and uses the actually measured polishing physical quantity including the posteriori estimated torque as a variable for identification to identify a part of the model parameters of the simulation model, update the model parameters, update the simulation model using the updated model parameters, and input the polishing conditions into the updated simulation model to calculate the estimated polishing rate of the workpiece W within the estimation interval Li.

[0138] The calculation system 47 is configured to calculate the estimated torque Dsim(i) in the current estimation interval Li from the polishing of the workpiece W in the previous estimation interval, obtain the measured value Dobs(i) of the torque in the current estimation interval Li, and apply a Kalman filter to the estimated torque Dsim(i) and the measured value Dobs(i) of the torque to calculate the posteriori estimated torque Dpos(i) in the current estimation interval Li.

[0139] More specifically, as shown in FIG. 15, the arithmetic system 47 first identifies the model parameters Xref of the polishing rate model and the polishing torque model using the initial measured data Ni-1 including the actually measured polishing rate and the actually measured torque obtained from the polishing of the previous workpiece Wi-1. That is, the arithmetic system 47 inputs the initial measured data Ni-1 into the identification formulas (26) and (27), and identifies the model parameters Xref according to the identification program.

[0140] The arithmetic system 47 substitutes the model parameters Xref into the polishing rate model and the polishing torque model, and updates the polishing rate model and the polishing torque model. The arithmetic system 47 inputs the polishing conditions (for example, the pressure of the polishing head 7 against 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 against the polishing pad 2, etc.) into the updated polishing torque model, and calculates the estimated torque Dsim(1) in the first estimation section L1.

[0141] After the estimation section L1, the arithmetic system 47 repeats the following operation using the Kalman filter. That is, in the estimation section Li (i is a natural number of 2 or more), the arithmetic system 47 applies the Kalman filter to the estimated torque Dsim(i) calculated in the previous estimation section Li-1 and the measured value Dobs(i) of the torque obtained in the estimation section Li, and calculates the a posteriori estimated torque Dpos(i) in the estimation section Li. Dpos(i)=Dsim(i)+K(Dobs(i)-Dsim(i)) (28) K is a predetermined Kalman gain.

[0142] The calculation system 47 uses the measured polishing physical quantity including the post - estimated torque Dpos(i) as a variable for identification, identifies some of the model parameters of the polishing rate model and the polishing torque model to update the model parameters, updates the polishing rate model and the polishing torque model using the updated model parameters, and inputs the polishing conditions into the updated polishing rate model and polishing torque model to calculate the estimated polishing rate MRRsim(i) of the workpiece W within the estimation interval Li and the estimated torque Dsim(i + 1) in the next estimation interval Li+1.

[0143] In the estimation interval Li+1, the calculation system 47 applies a Kalman filter to the estimated torque Dsim(i + 1) calculated in the estimation interval Li and the measured value Dobs(i + 1) of the torque obtained in the estimation interval Li+1 to calculate the post - estimated torque Dpos(i + 1) in the estimation interval Li+1. Further, the calculation system 47 uses the measured polishing physical quantity including the post - estimated torque Dpos(i + 1) to identify some of the model parameters of the polishing rate model and the polishing torque model to update the model parameters, updates the polishing rate model and the polishing torque model using the updated model parameters, and inputs the polishing conditions into the updated polishing rate model and polishing torque model to calculate the estimated polishing rate MRRsim(i + 1) of the workpiece W within the estimation interval Li+1 and the estimated torque Dsim(i + 2) in the next estimation interval Li+2. Hereinafter, the same operation is repeated until the film thickness of the workpiece W reaches the target film thickness. As shown in FIG. 15, the estimated torque calculated in the previous estimation interval is used in the next estimation interval.

[0144] Similar to the embodiment described with reference to FIG. 12, after the estimated polishing rate is calculated in each estimation interval, the calculation system 47 determines the polishing time or polishing pressure in the next estimation interval.

[0145] FIG. 16 is a block diagram for explaining yet another embodiment of polishing a workpiece using a chemical mechanical polishing system. In this embodiment, the arithmetic system 47 is configured to correct the Preston coefficient in an estimation section and calculate an estimated polishing rate using the corrected Preston coefficient.

[0146] As shown in FIG. 16, first, a sample is polished by the polishing apparatus 1 using the polishing pad 2 in an initial state. The polishing pad 2 in the initial state is a polishing pad that has been subjected to a running-in process and has not yet been used for polishing the workpiece. During or after the sample polishing using the polishing pad 2 in the initial state, the arithmetic system 47 acquires an initial actually measured polishing physical quantity Nini. In one embodiment, the initial actually measured polishing physical quantity Nini includes measured values of the polishing pad rotation torque, the polishing head rotation torque, the polishing head swing torque, the dresser swing torque, and the actually measured polishing rate of the sample during sample polishing.

[0147] The arithmetic system 47 identifies initial values Xini of model parameters of the polishing rate model and the polishing torque model by executing an identification program using the initial actually measured polishing physical quantity Nini as a variable for identification. Specifically, the arithmetic system 47 uses the above identification formulas (26) and (27) to identify the initial values Xini of the model parameters R μ, D μ, W μ1, W μ0, β1, β0, α1, α2, T.

[0148] The calculation system 47 updates the polishing torque model by substituting the initial value Xini of the model parameters into the polishing torque models represented by the above equations (8), (13), (18), and (21). The calculation system 47 inputs polishing conditions (such as the pressure of the polishing head 7 against 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 against the polishing pad 2, etc.) into the polishing torque model, and calculates the initial estimated torque TTsim(ini). In one embodiment, the polishing conditions input into the polishing torque model are the polishing conditions in the estimation section Li. In one embodiment, the initial estimated torque TTsim(ini) is the initial estimated torque of the polishing pad 2.

[0149] During the polishing of the workpiece W, the calculation system 47 acquires the measured value TTi of the torque in the estimation section Li. 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 calculation 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 to determine the correction amount Zi. The correction coefficient kob is a predetermined numerical value. The correction amount Zi is represented by the following equation. Zi = (TTi - TTsim(ini)) * kob (29)

[0150] The calculation system 47 calculates the initial Preston coefficient k p 0 from the initial value Xini of the model parameters. More specifically, the calculation 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 calculation system 47 adds the correction amount Zi to the initial Preston coefficient k p 0 to correct 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 equation. k p = k p 0 + Zi = k p 0 + (TTi - TTsim(ini)) * kob(30)

[0151] The calculation 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 stored in advance in the storage device 47a of the calculation system 47.

[0152] The calculation system 47 inputs the polishing conditions (such as the pressure of the polishing head 7 against 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 against 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.

[0153] In one embodiment, the acquisition of the measured torque value TTi described above, the calculation of the correction amount Zi, the calculation of the corrected Preston coefficient k p the calculation of, the update of the polishing rate model, and the calculation of the estimated polishing rate in the next estimation interval may be executed in each estimation interval.

[0154] Similar to the embodiment described with reference to FIG. 12, after the estimated polishing rate is calculated in the estimation interval, the calculation system 47 determines the polishing time or polishing pressure in the next estimation interval.

[0155] FIGS. 17 and 18 are flowcharts of the embodiment described with reference to FIG. 16. In step 301, the polishing apparatus 1 performs chemical mechanical polishing of a sample using the polishing pad 2 in the initial state. In step 302, the calculation system 47 acquires the initial actually measured polishing physical quantity Nini during or after the polishing of the sample. In step 303, the arithmetic system 47 uses the initial actually measured polishing physical quantity Nini as a variable for identification, operates according to the identification program, and determines the initial value Xini of the model parameter.

[0156] In step 304, the arithmetic system 47 updates the polishing torque model by substituting the initial value Xini of the model parameter into the polishing torque model. In step 305, the arithmetic system 47 calculates the initial Preston coefficient k p 0 from the initial value Xini of the model parameter (k p 0 = β1 W μ + β0). In step 306, the arithmetic system 47 sets a plurality of estimation intervals within the polishing time of the workpiece W. In step 307, the polishing apparatus 1 starts the chemical mechanical polishing of the workpiece W. In step 308, the arithmetic system 47 calculates the initial estimated torque TTsim(ini) by inputting the polishing conditions in the estimation interval Li into the updated polishing torque model.

[0157] In step 309, during the polishing of the workpiece W, the arithmetic system 47 acquires the measured value TTi of the torque within the estimation interval Li. In one embodiment, the measured value TTi of the torque is the measured value of the torque of the polishing pad 2 (i.e., the measured value of the torque of the polishing table 5). In step 310, the arithmetic system 47 calculates the 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. 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 .

[0158] In step 312, the arithmetic system 47 updates the polishing rate model by substituting the corrected Preston coefficient k p into the polishing rate model. In step 313, the arithmetic system 47 calculates the estimated polishing rate of the workpiece W within the estimated section Li+1 by inputting the polishing conditions for the next estimated section Li+1 into the updated polishing rate model.

[0159] In step 314, the arithmetic system 47 determines the polishing time or polishing pressure for the workpiece W in the next estimated section Li+1. In one embodiment, the polishing time of the workpiece W in the next estimated section Li+1 is determined by the arithmetic system 47 as follows. That is, the arithmetic system 47 calculates the polishing amount of the workpiece W in the estimated section Li from the estimated polishing rate and polishing time of the workpiece W in the estimated section Li, calculates the difference between the target polishing amount of the workpiece W in the next estimated section Li+1 and the polishing amount in the estimated section Li, and calculates the polishing time in the next estimated section Li+1 based on the calculated difference and the estimated polishing rate of the workpiece W in the estimated section Li. In other embodiments, the arithmetic system 47 may calculate the polishing time in the next estimated section Li+1 based on the estimated polishing rate of the workpiece W in the estimated section Li and the target polishing amount of the workpiece W in the next estimated section Li+1.

[0160] In one embodiment, the polishing pressure pi+1 for the workpiece W in the next estimated section Li+1 is determined by the arithmetic system 47 as follows. That is, the arithmetic system 47 calculates the response rate of the polishing rate per unit polishing pressure (polishing rate / polishing pressure) from the polishing pressure data when polishing the workpiece W in the estimated section Li and the estimated polishing rate of the workpiece W in the estimated section Li, and calculates the polishing pressure pi+1 for the workpiece W in the next estimated section Li+1 based on the calculated response rate, the target polishing amount of the workpiece W in the next estimated section Li+1, and the polishing time in the estimated section Li. The polishing time or polishing pressure determined in step 313 above is applied to the polishing of the workpiece W in the next estimated section Li+1 and used as the polishing conditions for polishing the workpiece W.

[0161] The above-described embodiments are described for the purpose of enabling those with ordinary knowledge in the technical field to which the present invention pertains to practice the present invention. Various modifications of the above embodiments are naturally possible for 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 construed in the broadest scope in accordance with the technical idea defined by the claims.

Explanation of Signs

[0162] 1 Polishing apparatus 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 29 Support base 30 Support column 32 Ball screw mechanism 32a Screw shaft 32b Nut 38 Servo motor 47 Calculation system 47a Storage device 47b Processing device 49 Film thickness sensor 50 Dressing tool 50a Dressing surface 51 Dressing tool shaft 53 Air cylinder 55 Dressing tool swing arm 56 Support column 57 Support base 58 Support shaft 60 Dresser Rotation Motor 63 Dresser Oscillation Motor 71 Carrier 72 Retainer Ring 74 Membrane (Elastic Membrane) 76 Rolling Diaphragm 77 Gas Supply Source 80 Operation 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

Claims

1. A polishing apparatus 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 an estimated polishing physical quantity including an estimated polishing rate of the workpiece and an estimated torque as an estimated value of torque generated in the polishing apparatus due to the sliding resistance of the polishing pad. The simulation model includes a polishing rate model for calculating the estimated polishing rate and a polishing torque model for calculating the estimated torque. The storage device stores an identification program for determining model parameters of the simulation model. The arithmetic system acquires an actual measured polishing physical quantity including an actual measured polishing rate of the first workpiece and a measured value of the torque during or after polishing of the first workpiece, identifies the model parameters of the simulation model using the actual measured polishing physical quantity as a variable for identification, and is configured to calculate an estimated polishing rate of the second workpiece by inputting polishing conditions for the second workpiece into the simulation model. A chemical mechanical polishing system.

2. The arithmetic system after the model parameters are identified, calculates a difference between the reference model parameters and the model parameters by subtracting the model parameters from the predetermined reference model parameters, and updates the simulation model by substituting the difference as corrected model parameters into the simulation model. The chemical mechanical polishing system according to claim 1.

3. The arithmetic system calculates a correction amount based on a difference between an estimated polishing physical quantity obtained from polishing of a previous workpiece and an actual measured polishing physical quantity obtained from polishing of the previous workpiece, which is executed before polishing of the first workpiece, and is configured to determine the model parameters for the first workpiece by adding the correction amount to the model parameters obtained from polishing of the previous workpiece. The chemical mechanical polishing system according to claim 1.

4. A chemical mechanical polishing method for polishing a workpiece 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, comprising: polishing a first workpiece with the polishing apparatus; acquiring measured polishing physical quantities including a measured polishing rate of the first workpiece and a measured value of torque generated in the polishing apparatus due to sliding resistance of the polishing pad during or after polishing of the first workpiece; identifying the model parameters of a simulation model including a polishing rate model for calculating an estimated polishing rate of a workpiece and a polishing torque model for calculating an estimated torque as an estimated value of the torque by using the measured polishing physical quantities as variables for identification by an arithmetic system having an identification program for determining the model parameters; calculating an estimated polishing rate of a second workpiece by inputting polishing conditions for the second workpiece into the simulation model.

5. After the model parameters are identified, calculating a difference between the reference model parameters and the model parameters by subtracting the model parameters from the predetermined reference model parameters; The chemical mechanical polishing method according to claim 4, further comprising updating the simulation model by substituting the difference as corrected model parameters into the simulation model.

6. Determining the model parameters of the simulation model comprises: calculating a correction amount based on a difference between an estimated polishing physical quantity obtained from polishing of a previous workpiece and a measured polishing physical quantity obtained from polishing of the previous workpiece, the calculation being performed before polishing of the first workpiece; The chemical mechanical polishing method according to claim 4, wherein the model parameters for the first workpiece are determined by adding the correction amount to the model parameters obtained from polishing of the previous workpiece.

7. A polishing apparatus 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; An arithmetic system having a storage device storing a simulation model that outputs an estimated polishing physical quantity including an estimated polishing rate of the workpiece and an estimated torque as an estimated value of the torque generated in the polishing apparatus due to the sliding resistance of the polishing pad. The simulation model includes a polishing rate model for calculating the estimated polishing rate and a polishing torque model for calculating the estimated torque. The storage device stores an identification program for determining model parameters of the simulation model. The arithmetic system uses the measured polishing rate and measured torque obtained from the polishing of the previous workpiece, which were executed before the polishing of the workpiece, as variables for identification, and identifies the model parameters of the simulation model. sets a plurality of estimation sections within the polishing time of the workpiece. During the polishing of the workpiece, an actually measured polishing physical quantity including a measured value of the torque within one of the plurality of estimation sections is acquired. uses the actually measured polishing physical quantity as a variable for identification, identifies a part of the model parameters of the simulation model, and updates the model parameters. updates the simulation model using the updated model parameters. A chemical mechanical polishing system configured to calculate an estimated polishing rate of the workpiece within the one estimation section by inputting polishing conditions into the updated simulation model.

8. The arithmetic system applies a Kalman filter to the estimated torque calculated using the polishing torque model in an estimation section before the one estimation section and the measured value of the torque obtained within the one estimation section to calculate a posteriori estimated torque. The chemical mechanical polishing system according to claim 7, wherein a part of the model parameters of the simulation model is identified and the model parameters are updated using the actually measured polishing physical quantity including the posteriori estimated torque as a variable for identification.

9. A chemical mechanical polishing method for polishing a workpiece 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. Before polishing the workpiece, the measured polishing rate and measured torque obtained from the polishing of the previous workpiece are used as variables for identification to identify the model parameters of the simulation model. The simulation model includes a polishing rate model for calculating the estimated polishing rate of the workpiece and a polishing torque model for calculating the estimated torque as an estimated value of the torque generated in the polishing apparatus due to the sliding resistance of the polishing pad. A plurality of estimation sections are set within the polishing time of the workpiece. During the polishing of the workpiece, an actually measured polishing physical quantity including a measured value of the torque within one of the plurality of estimation sections is acquired. Using the actually measured polishing physical quantity as a variable for identification, a part of the model parameters of the simulation model is identified to update the model parameters. The simulation model is updated using the updated model parameters. A chemical mechanical polishing method for calculating the estimated polishing rate of the workpiece within the one estimation section by inputting polishing conditions into the updated simulation model.

10. Further including calculating an a posteriori estimated torque by applying a Kalman filter to the estimated torque calculated using the polishing torque model in an estimation section before the one estimation section and the measured value of the torque obtained within the one estimation section. The updating of the simulation model is to identify a part of the model parameters of the simulation model to update the model parameters by using the actually measured polishing physical quantity including the a posteriori estimated torque as a variable for identification, according to the chemical mechanical polishing method described in Claim 9.

11. A polishing apparatus 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 an estimated polishing physical quantity including the estimated polishing rate of the workpiece and an estimated torque as an estimated value of the torque generated in the polishing apparatus due to the sliding resistance of the polishing pad. The simulation model includes a polishing rate model for calculating the estimated polishing rate and a polishing torque model for calculating the estimated torque. The memory device stores an identification program for determining model parameters of the simulation model, The arithmetic system, obtains initial actually measured polishing physical quantities from polishing of a sample using the polishing pad in an initial state, uses the initial actually measured polishing physical quantities as variables for identification to determine initial values of the model parameters, calculates an initial Preston coefficient from the initial values of the model parameters, sets a plurality of estimation intervals within the polishing time of the workpiece, inputs polishing conditions into the simulation model to calculate an initial estimated torque, during polishing of the workpiece, obtains a measured value of the torque within a first estimation interval among the plurality of estimation intervals, calculates a correction amount by multiplying a difference between the measured value of the torque and the initial estimated torque by a predetermined correction coefficient, determines a corrected Preston coefficient by adding the correction amount to the initial Preston, updates the polishing rate model by substituting the corrected Preston coefficient into the polishing rate model, configured to calculate an estimated polishing rate of the workpiece within a second estimation interval by inputting polishing conditions for the second estimation interval among the plurality of estimation intervals into the polishing rate model, a chemical mechanical polishing system.

12. A chemical mechanical polishing method for polishing a workpiece 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, obtains initial actually measured polishing physical quantities from polishing of a sample using the polishing pad in an initial state, an arithmetic system having an identification program for determining model parameters of a simulation model including a polishing rate model for calculating an estimated polishing rate of the workpiece and an estimated torque as an estimated value of torque generated in the polishing apparatus due to sliding resistance of the polishing pad, uses the initial actually measured polishing physical quantities as variables for identification to identify initial values of the model parameters, calculates an initial Preston coefficient from the initial values of the model parameters, sets a plurality of estimation intervals within the polishing time of the workpiece, inputs polishing conditions into the simulation model to calculate an initial estimated torque, During polishing of the workpiece, obtain a measured value of the torque within a first estimated section among the plurality of estimated sections, 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, update the polishing rate model by substituting the corrected Preston coefficient into the polishing rate model, a chemical mechanical polishing method for calculating an estimated polishing rate of the workpiece within a second estimated section by inputting polishing conditions for a second estimated section among the plurality of estimated sections into the polishing rate model.

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