Grinding device and grinding method

Abstract

The present invention provides a polishing apparatus and a polishing method that can obtain a desired film thickness profile. The polishing apparatus includes a polishing unit (14a), a film thickness measurer (8) that measures a film thickness profile of a substrate (W), and a control device (30) that controls at least the operation of the polishing unit and the film thickness measurer. The control device stores in advance a reaction model that is created in consideration of changes in polishing amount among a plurality of monitoring regions of the substrate that are caused by changes in pressure within each pressure chamber (7a to 7h). Further, the control device polishes the substrate using the film thickness measurer to obtain a film thickness profile before polishing of the substrate, and polishes the substrate using an optimal polishing plan that is created based on a difference between the film thickness profile of the substrate before polishing and a target film thickness of the substrate, and the reaction model. The next substrate is polished using a new optimal polishing plan that is created based on a target polishing amount of the next substrate and the reaction model that is corrected using the optimal polishing plan and the film thickness profiles of the previous substrate before and after polishing.

Description

TECHNICAL FIELD

[0001] The present application relates to a polishing apparatus and a polishing method for polishing a substrate such as a wafer, and particularly to a polishing apparatus and a polishing method for polishing a substrate to obtain a desired film thickness profile. Further, the present application relates to a polishing method for polishing a substrate using such a polishing apparatus. BACKGROUND

[0002] In recent years, with the high integration and high density of semiconductor devices, the wiring of the circuit is more and more fine, and the number of layers of the multilayer wiring is also increased. When the fine of the circuit is pursued and the multilayer wiring is implemented, since the surface of the lower layer is uneven, and the step difference is larger, as the number of layers of the wiring increases, the film coverage of the step difference shape is deteriorated when forming a thin film. Therefore, in order to implement the multilayer wiring, the film coverage must be improved, and the planarization process must be performed with an appropriate process. In addition, because of the fine of the photolithography and the shallower depth of focus, it is necessary to planarize the surface of the semiconductor device in such a way that the surface unevenness step difference of the semiconductor device does not exceed the depth of focus.

[0003] Therefore, in the manufacturing process of semiconductor devices, the planarization of the surface of the semiconductor device is becoming more and more important. The most important technology in this surface planarization is chemical mechanical polishing (CMP). The chemical mechanical polishing (hereinafter referred to as CMP) is a technology that supplies a polishing liquid (slurry) containing polishing particles such as silicon dioxide (SiO2) to the polishing surface of a polishing pad, and makes a substrate such as a wafer in sliding contact with the polishing surface to perform polishing.

[0004] The polishing apparatus for performing CMP has a polishing table that supports a polishing pad having a polishing surface, and a polishing head (substrate holding device) for holding a substrate. The polishing of the substrate using such a polishing apparatus is performed as follows. The polishing table is rotated together with the polishing pad, and the slurry is supplied onto the polishing pad. The polishing head rotates the substrate and presses the substrate against the polishing surface of the polishing pad. The surface of the substrate is planarized by the combination of the chemical action of the slurry and the mechanical action of the polishing particles contained in the slurry in the sliding contact of the substrate with the polishing pad in the presence of the slurry.

[0005] In the polishing of the substrate, since the surface of the substrate is in sliding contact with the rotating polishing pad, a frictional force acts on the substrate. Therefore, in the polishing of the substrate, the polishing head has a retaining ring in order to prevent the substrate from being detached from the polishing head. The retaining ring is arranged in such a way as to surround the substrate, and in the polishing of the substrate, the retaining ring rotates and presses the polishing pad on the outside of the substrate.

[0006] PRIOR ART DOCUMENTS

[0007] PATENT LITERATURE

[0008] Patent Literature 1: Japanese Patent Application Publication No. 2015-193068

[0009] Problem to be Solved by the Invention

[0010] In recent years, the demand for more precisely controlling (i.e., increasing in-plane uniformity indicating flatness of a substrate surface) film thickness profile of a substrate has been increasing for various reasons such as changing various initial film thickness profiles with semiconductor components and CMP processes and improving yield.

[0011] Further, the allowable range of the target film thickness is also narrowing. In the past polishing method in which a film thickness detector is used in polishing to obtain a film thickness index value of a substrate and polishing of the substrate is ended in accordance with the film thickness index value, it is difficult to limit the film thickness within the required allowable range. For example, the polishing amount during one cycle of rotation of a polishing table can be larger than the allowable range. At this time, if the polishing endpoint is determined in accordance with the film thickness index value obtained from the film thickness detector disposed on the polishing table, the film thickness after polishing can exceed the allowable range of the target film thickness.

[0012] Further, the film thickness profile before polishing differs among substrates to be polished, or the polishing conditions (e.g., the state of the polishing surface of a polishing pad) differ among polishing apparatuses. Because of these compounded factors, it is difficult to precisely control the film thickness profile to limit the film thickness profile within the required allowable range. SUMMARY

[0013] Therefore, an object of the present application is to provide a polishing apparatus that can obtain a desired film thickness profile. Further, an object of the present application is to provide a polishing method of polishing a substrate using such a polishing apparatus.

[0014] Technical Means for Solving the Technical Problem

[0015] In one embodiment, a polishing apparatus is provided, including: at least one polishing unit including a polishing table for supporting a polishing pad and a substrate holding device for pressing a substrate against the polishing pad; a film thickness measurer for measuring a film thickness profile of the substrate; and a control device for controlling at least the operation of the polishing unit and the film thickness measurer, the substrate holding device including an elastic membrane forming a plurality of pressure chambers for pressing the substrate, a head body on which the elastic membrane is mounted, and a clasp disposed in a manner of surrounding the substrate, the control device having stored in advance a reaction model made in consideration of changes in polishing amount among a plurality of monitoring regions of the substrate caused by changes in pressure within each pressure chamber, the control device acquiring a film thickness profile of the substrate before polishing using the film thickness measurer, and the control device polishing the substrate with an optimal polishing recipe made in accordance with a target polishing amount and the reaction model, the target polishing amount being a difference between the film thickness profile of the substrate before polishing and a target film thickness of the substrate, and the control device polishing a next substrate with a new optimal polishing recipe made in accordance with a target polishing amount of the next substrate and the reaction model corrected using the optimal polishing recipe and the film thickness profiles of the substrate before and after polishing.

[0016] In one embodiment, the optimal polishing recipe is made using an optimization calculation that minimizes an objective function including at least a term of a difference between the target polishing amount and a predicted polishing amount calculated using the reaction model.

[0017] In one embodiment, the objective function further includes a term of a difference between a pressure of the compressed fluid of the optimal polishing recipe and a predetermined reference pressure of the compressed fluid, and / or a term of a difference between a pressure of the compressed fluid of the optimal polishing recipe and a pressure of the compressed fluid of an optimal polishing recipe of a wafer polished before.

[0018] In one embodiment, the optimization calculation is a quadratic programming method.

[0019] In one embodiment, the number of the plurality of monitoring regions is greater than the number of the plurality of pressure chambers.

[0020] In one embodiment, the reaction model is also a reaction model made in consideration of changes in polishing amount among a plurality of monitoring regions of the substrate caused by changes in pressing force of the clasp against the polishing pad, and the optimal polishing recipe further includes the pressing force of the clasp.

[0021] In one embodiment, the film thickness measurer is configured to measure film thickness at a plurality of measurement points respectively provided in the plurality of monitoring regions.

[0022] In one embodiment, the reaction model includes a reaction coefficient that represents an increase in the polishing rate per unit of polishing pressure in each of the plurality of monitoring regions.

[0023] In one embodiment, a plurality of local load applying devices that apply a local load to a portion of the clasp are further provided, and the reaction model is further made in consideration of changes in the amount of polishing that occurs among the plurality of monitoring regions as the local load changes.

[0024] In one embodiment, a polishing apparatus is provided that includes at least one polishing unit including a polishing table for supporting a polishing pad and a substrate holding device for pressing a substrate against the polishing pad, a film thickness measurer for measuring a film thickness profile of the substrate, and a control device for controlling at least the operation of the polishing unit and the film thickness measurer. The substrate holding device includes an elastic membrane that forms a plurality of pressure chambers for pressing the substrate, a head body on which the elastic membrane is mounted, and a clasp that is disposed in a manner surrounding the substrate. The control device stores in advance a film thickness profile before polishing of a plurality of substrates and a reaction model when the plurality of substrates are polished respectively, the reaction model being made in consideration of changes in the amount of polishing that occurs among a plurality of monitoring regions of the substrate as the pressure in each pressure chamber changes. The plurality of film thickness profiles before polishing of the plurality of substrates are classified in advance into a plurality of groups to which film thickness profiles similar to each other belong. The control device acquires the film thickness profile before polishing of the substrate using the film thickness measurer, and determines a group to which the film thickness profile before polishing of the substrate belongs from the plurality of groups. The control device polishes the substrate with an optimal polishing recipe that is made in accordance with a target polishing amount and a reaction model associated with the determined group, and at least includes the pressure of a compressed fluid supplied to the plurality of pressure chambers and the polishing time. The target polishing amount is the difference between the film thickness profile before polishing of the substrate and a target film thickness of the substrate. The control device polishes a next substrate with a new optimal polishing recipe that is made in accordance with a target polishing amount of the next substrate and a reaction model that is corrected using the optimal polishing recipe and the film thickness profiles before and after polishing of the substrate.

[0025] In one embodiment, a polishing apparatus is provided, including: a plurality of polishing units including a polishing table for supporting a polishing pad and a substrate holding device for pressing a substrate against the polishing pad; and a control device for controlling at least the operation of the polishing units, the substrate holding device including: an elastic membrane forming a plurality of pressure chambers for pressing the substrate; a head body for mounting the elastic membrane; and a clasp disposed in a manner surrounding the substrate, the substrate being polished by a plurality of polishing processes including a first polishing and a second polishing performed by a polishing unit different from the polishing unit performing the first polishing, the polishing unit performing the first polishing having a film thickness detector capable of measuring a film thickness profile of the substrate, the control device having stored in advance a second polishing reaction model made in consideration of changes in polishing amounts among a plurality of monitoring regions of the substrate as pressure within each pressure chamber changes, the control device obtaining a film thickness profile of the substrate before the second polishing using the film thickness detector after the first polishing, and performing the second polishing on the substrate with a second polishing optimal solution made in accordance with a target polishing amount and the second polishing reaction model, the second polishing optimal solution including at least a pressure of a compressed fluid supplied to the plurality of pressure chambers and a polishing time, the target polishing amount being a difference between the film thickness profile of the substrate before the second polishing and a target film thickness of the substrate, and the control device performing the second polishing on a next substrate with a new second polishing optimal solution made in accordance with a target polishing amount of the next substrate and the second polishing reaction model corrected using the second polishing optimal solution and the film thickness profiles of the substrate before and after the second polishing.

[0026] In one embodiment, there is provided a polishing apparatus including: a plurality of polishing units including a polishing table for supporting a polishing pad and a substrate holding device for pressing a substrate against the polishing pad; a film thickness measurer for measuring a film thickness profile of the substrate; and a control device for controlling at least the operation of the polishing units and the film thickness measurer, the substrate holding device including: an elastic membrane forming a plurality of pressure chambers for pressing the substrate; a head body to which the elastic membrane is attached; and a clasp disposed so as to surround the substrate, the substrate being polished by a plurality of polishing processes including a first polishing and a second polishing performed by a polishing unit different from the polishing unit performing the first polishing, the polishing unit performing the second polishing having a film thickness detector capable of measuring a film thickness profile of the substrate, the control device having stored in advance a first polishing reaction model made in consideration of changes in polishing amount occurring among a plurality of monitoring regions of the substrate as pressure in each pressure chamber changes, the control device acquiring the film thickness profile of the substrate before the first polishing using the film thickness measurer, and the control device polishing the substrate by a first polishing optimal plan made in accordance with a target polishing amount and the first polishing reaction model, the first polishing optimal plan including at least pressure of a compressed fluid supplied to the plurality of pressure chambers and polishing time, the target polishing amount being a difference between the film thickness profile of the substrate before the first polishing and a target film thickness of the substrate, and the control device, after the first polishing, conveying the substrate to a polishing unit having the film thickness detector, acquiring the film thickness profile of the substrate after the first polishing using the film thickness detector, and polishing a next substrate by a new first polishing optimal plan made in accordance with a target polishing amount of the next substrate and the first polishing reaction model corrected using the first polishing optimal plan and the film thickness profile of the substrate before and after the first polishing.

[0027] In one embodiment, a polishing apparatus is provided, including: a plurality of polishing units including a polishing table for supporting a polishing pad, a substrate holding device for pressing a substrate against the polishing pad, and a film thickness detector capable of measuring a film thickness profile of the substrate; and a control device for controlling at least an operation of the polishing units, the substrate holding device including an elastic membrane forming a plurality of pressure chambers for pressing the substrate, a head body on which the elastic membrane is mounted, and a clasp disposed in a manner of surrounding the substrate, the substrate being polished by a plurality of polishing processes including a first polishing and a second polishing performed by a polishing unit different from that performing the first polishing, the control device having stored in advance a first polishing reaction model and a second polishing reaction model, the first polishing reaction model and the second polishing reaction model being created in consideration of a change in polishing amount between a plurality of monitoring regions of the substrate as a pressure in each pressure chamber changes, the control device transporting the substrate to one of the plurality of polishing units, and acquiring a film thickness profile of the substrate before the first polishing using the film thickness detector, and the control device performing the first polishing on the substrate using a first polishing optimal plan created in accordance with a target polishing amount and the first polishing reaction model, and at least including a pressure of a compressed fluid supplied to the plurality of pressure chambers and a polishing time, the target polishing amount being a difference between the film thickness profile of the substrate before the first polishing and a target film thickness of the substrate, and the control device acquiring a film thickness profile of the substrate before the second polishing using the film thickness detector, and the control device performing the second polishing on the substrate using a second polishing optimal plan created in accordance with a target polishing amount and the second polishing reaction model, and at least including a pressure of a compressed fluid supplied to the plurality of pressure chambers and a polishing time, the target polishing amount being a difference between the film thickness profile of the substrate before the second polishing and a target film thickness of the substrate, and the control device acquiring a film thickness profile of the substrate after the second polishing using the film thickness detector, and the control device performing the first polishing on a next substrate using a new first polishing optimal plan created in accordance with a target polishing amount of the next substrate and the first polishing reaction model corrected using the first polishing optimal plan and the film thickness profiles before and after the first polishing of the substrate, and the control device performing the second polishing on the next substrate using a new second polishing optimal plan created in accordance with a target polishing amount of the next substrate and the second polishing reaction model corrected using the second polishing optimal plan and the film thickness profiles before and after the second polishing of the substrate.

[0028] In one embodiment, a polishing method is provided. A substrate held by a substrate holding device is polished against a polishing pad supported by a polishing table. The substrate holding device has an elastic membrane forming a plurality of pressure chambers for pressing the substrate, a head body on which the elastic membrane is mounted, and a retaining ring disposed in a manner surrounding the substrate. A film thickness profile of the substrate before polishing is obtained using a film thickness profiler. The substrate is polished using an optimal polishing recipe made based on a target polishing amount and a reaction model, and at least a pressure of a pressurized fluid supplied to the plurality of pressure chambers and a polishing time. The target polishing amount is a difference between the film thickness profile of the substrate before polishing and a target film thickness of the substrate. A next substrate is polished using a new optimal polishing recipe made based on a target polishing amount of the next substrate and the reaction model corrected using the optimal polishing recipe and the film thickness profiles of the substrate before and after polishing. The reaction model is made considering changes in polishing amounts among a plurality of monitoring regions of the substrate as pressures of the respective pressure chambers change.

[0029] In one embodiment, the optimal polishing recipe is made using an optimization calculation that minimizes an objective function including at least a term of a difference between the target polishing amount and a predicted polishing amount calculated using the reaction model.

[0030] In one embodiment, the objective function further includes a term of a difference between a pressurized fluid pressure of the optimal polishing recipe and a predetermined reference pressurized fluid pressure, and / or a term of a difference between the pressurized fluid pressure of the optimal polishing recipe and a pressurized fluid pressure of an optimal polishing recipe for a wafer polished before.

[0031] In one embodiment, the optimization calculation is a quadratic programming method.

[0032] In one embodiment, the number of the plurality of monitoring regions is greater than the number of the plurality of pressure chambers.

[0033] In one embodiment, the reaction model is also a reaction model made considering changes in polishing amounts among a plurality of monitoring regions of the substrate as a pressing force of the retaining ring against the polishing pad changes. The optimal polishing recipe further includes the pressing force of the retaining ring.

[0034] In one embodiment, the film thickness profiler measures film thicknesses at a plurality of measurement points respectively provided in the plurality of monitoring regions.

[0035] In one embodiment, the reaction model includes a reaction coefficient representing an increase in a polishing rate per unit polishing pressure in each of the plurality of monitoring regions.

[0036] In one embodiment, the reaction model is further created in consideration of changes in the amount of polishing that occur among the plurality of monitoring regions as the local load applied to a portion of the chuck ring by the plurality of local loads imparted to the device changes.

[0037] In one embodiment, a polishing method is provided in which a substrate held by a substrate holding device is pressed against a polishing pad supported by a polishing table to perform polishing, the substrate holding device having an elastic membrane that forms a plurality of pressure chambers for pressing the substrate, a head body to which the elastic membrane is attached, and a chuck ring that is disposed in a manner surrounding the substrate, wherein a film thickness profile before polishing of a plurality of substrates and a reaction model for polishing the plurality of substrates respectively are stored in advance, the reaction model being created in consideration of changes in the amount of polishing that occur among a plurality of monitoring regions of the substrate as a pressure within each pressure chamber changes, the film thickness profile before polishing of the plurality of substrates is classified into a plurality of groups to which film thickness profiles similar to each other belong in advance, a film thickness profile before polishing of the substrate is obtained, and a group to which the film thickness profile belongs is determined from the plurality of groups, the substrate is polished with an optimal polishing recipe created in accordance with a target polishing amount and the reaction model associated with the determined group, the target polishing amount being a difference between the film thickness profile before polishing of the substrate and a target film thickness of the substrate, and at least a pressure of a compressed fluid supplied to the plurality of pressure chambers and a polishing time, a next substrate is polished with a new optimal polishing recipe created in accordance with a target polishing amount of the next substrate and the reaction model corrected using the optimal polishing recipe and film thickness profiles before and after polishing of the substrate.

[0038] In one embodiment, a polishing method is provided for polishing a substrate by a plurality of polishing processes performed by a plurality of polishing units including a polishing table for supporting a polishing pad and a substrate holding device for pressing the substrate against the polishing pad, wherein the substrate holding device has an elastic membrane forming a plurality of pressure chambers for pressing the substrate, a head body on which the elastic membrane is mounted, and a clasp disposed in a manner of surrounding the substrate, the plurality of polishing processes includes a first polishing and a second polishing performed by a polishing unit different from the polishing unit performing the first polishing, the polishing unit performing the first polishing has a film thickness detector capable of measuring a film thickness profile of the substrate, a second polishing reaction model is prepared in advance, the second polishing reaction model is made considering a change in polishing amount generated among a plurality of monitoring areas of the substrate with a change in pressure in each pressure chamber, after the first polishing is performed, a film thickness profile of the substrate before the second polishing is obtained using the film thickness detector, the second polishing is performed on the substrate using a second polishing optimal solution, the second polishing optimal solution is made in accordance with a target polishing amount and the second polishing reaction model, and at least includes a pressure of a compressed fluid supplied to the plurality of pressure chambers and a polishing time, the target polishing amount is a difference between the film thickness profile of the substrate before the second polishing and a target film thickness of the substrate, the second polishing is performed on a next substrate using a new second polishing optimal solution, the new second polishing optimal solution is made in accordance with a target polishing amount of the next substrate and the second polishing reaction model corrected using the second polishing optimal solution and the film thickness profiles of the substrate before and after the second polishing.

[0039] In one embodiment, a substrate is polished by a plurality of polishing processes performed by a plurality of polishing units including a polishing table for supporting a polishing pad and a substrate holding device for pressing the substrate against the polishing pad, wherein the substrate holding device has an elastic membrane forming a plurality of pressure chambers for pressing the substrate, a head body on which the elastic membrane is mounted, and a clasp disposed in a manner of surrounding the substrate, the plurality of polishing processes include a first polishing and a second polishing performed by a polishing unit different from the polishing unit performing the first polishing, the polishing unit performing the second polishing has a film thickness detector capable of measuring a film thickness profile of the substrate, a first polishing reaction model is prepared in advance, the first polishing reaction model is made considering a change in polishing amount generated among a plurality of monitoring regions of the substrate as a pressure in each pressure chamber changes, a film thickness profile of the substrate before the first polishing is obtained using a film thickness measurer, the first polishing is performed on the substrate using a first polishing optimum scheme made in accordance with a target polishing amount and the first polishing reaction model, and at least a pressure of a compressed fluid supplied to the plurality of pressure chambers and a polishing time, the target polishing amount is a difference between the film thickness profile of the substrate before the first polishing and a target film thickness of the substrate, after the first polishing is performed, the substrate is transported to the polishing unit having the film thickness detector, a film thickness profile of the substrate after the first polishing is obtained using the film thickness detector, and the first polishing is performed on a next substrate using a new first polishing optimum scheme made in accordance with a target polishing amount of the next substrate and the first polishing reaction model corrected using the first polishing optimum scheme and the film thickness profiles of the substrate before and after the first polishing.

[0040] In one embodiment, a polishing method is provided for polishing a substrate by a plurality of polishing processes performed by a plurality of polishing units including a polishing table for supporting a polishing pad and a substrate holding device for pressing the substrate against the polishing pad, wherein the substrate holding device has an elastic membrane forming a plurality of pressure chambers for pressing the substrate, a head body on which the elastic membrane is mounted, and a clasp disposed in a manner of surrounding the substrate, the plurality of polishing processes include a first polishing and a second polishing performed by a polishing unit different from the polishing unit performing the first polishing, the polishing unit performing the first polishing and the polishing unit performing the second polishing each have a film thickness detector capable of measuring a film thickness profile of the substrate, a first polishing reaction model and a second polishing reaction model are prepared in advance, the first polishing reaction model and the second polishing reaction model are made considering changes in polishing amount between a plurality of monitoring regions of the substrate caused by changes in pressure in each pressure chamber, the substrate is transported to the polishing unit performing the first polishing, a film thickness profile of the substrate before the first polishing is obtained using the film thickness detector, the first polishing is performed on the substrate using a first polishing optimal plan made in accordance with a target polishing amount and the first polishing reaction model, and at least includes pressure of a compressed fluid supplied to the plurality of pressure chambers and polishing time, the target polishing amount is a difference between the film thickness profile of the substrate before the first polishing and a target film thickness of the substrate, a film thickness profile of the substrate before the second polishing is obtained using the film thickness detector, the second polishing is performed on the substrate using a second polishing optimal plan made in accordance with a target polishing amount and the second polishing reaction model, and at least includes pressure of a compressed fluid supplied to the plurality of pressure chambers and polishing time, the target polishing amount is a difference between the film thickness profile of the substrate before the second polishing and a target film thickness of the substrate, a film thickness profile of the substrate after the second polishing is obtained using the film thickness detector, the first polishing is performed on a next substrate using a new first polishing optimal plan made in accordance with a target polishing amount of the next substrate and the first polishing reaction model corrected using the first polishing optimal plan and the film thickness profiles of the substrate before and after the first polishing, and the second polishing is performed on the next substrate using a new second polishing optimal plan made in accordance with a target polishing amount of the next substrate and the second polishing reaction model corrected using the second polishing optimal plan and the film thickness profiles of the substrate before and after the second polishing.

[0041] Effects of the Invention

[0042] When the present application is used, the optimum polishing plan obtained using the reaction model takes into account the variation in polishing amount among the regions of the substrate that occurs as the pressure of each pressure chamber varies. Therefore, the film thickness profile of the substrate can be controlled more precisely. BRIEF DESCRIPTION OF DRAWINGS

[0043] Figure 1 is a plan view showing the overall configuration of a substrate processing apparatus according to an embodiment.

[0044] Figure 2 is a perspective view schematically showing Figure 1 is a perspective view of an example of the polishing unit shown in

[0045] Figure 3 is a cross-sectional view schematically showing an example of the polishing head.

[0046] Figure 4 is a schematic view showing Figure 3 is a schematic view of the pressure adjusting device shown in

[0047] Figure 5 is a flowchart showing a polishing method according to an embodiment.

[0048] Figure 6 (a) of is a schematic view showing an example of a plurality of pressure chambers, Figure 6 (b) of is a schematic view showing an example of a monitoring region of a wafer, Figure 6 (c) of is a schematic view showing another example of a monitoring region of a wafer, Figure 6 (d) of is a schematic view showing still another example of a monitoring region of a wafer, Figure 6 (e) of is a schematic view showing still another example of a monitoring region of a wafer.

[0049] Figure 7 is a conceptual view showing the curve of the polishing rate at each measurement point of a large number of wafers.

[0050] Figure 8 is a conceptual view showing the curve of the reaction coefficient at each measurement point of a wafer.

[0051] Figure 9 is a view showing an example of the matrices C, D, R, X of the reaction model.

[0052] Figure 10 is a view showing an example of the matrices C', X' of the reaction model.

[0053] Figure 11 is a perspective view schematically showing the polishing head according to another embodiment.

[0054] Figure 12 is a longitudinal cross-sectional view schematically showing the state when the clasp presses the polishing surface.

[0055] Figure 13 FIG. 13 is a graph showing the variation in in-plane uniformity in various embodiments when continuously polishing a plurality of wafers using the optimal polishing recipe fabrication method of a plurality of embodiments.

[0056] Figure 14 FIG. 14 is a flowchart showing a polishing method of another embodiment.

[0057] Figure 15 FIG. 15 is a schematic diagram showing a polishing unit of another embodiment.

[0058] Figure 16 FIG. 16 is a flowchart showing a polishing method of yet another embodiment.

[0059] Figure 17 FIG. 17 is a flowchart showing a polishing method of yet another embodiment.

[0060] Figure 18 FIG. 18 is a flowchart showing the first half of a polishing method of yet another embodiment.

[0061] Figure 19 FIG. 19 is a flowchart showing the second half of a polishing method of yet another embodiment.

[0062] Legend

[0063] 2: head body

[0064] 3: clasp

[0065] 4a-4i: flow path

[0066] 5: elastic film

[0067] 5a-5h: peripheral wall

[0068] 6a-6i: fluid line

[0069] 7a-7h: pressure chamber

[0070] 8: film thickness meter

[0071] 10: housing

[0072] 12: load port

[0073] 14a-14d: polishing unit

[0074] 16: first cleaning unit

[0075] 18: second cleaning unit

[0076] 20: drying unit

[0077] 22: first substrate transfer robot

[0078] 24: substrate conveyance device

[0079] 26: second substrate conveyance robot

[0080] 28: third substrate conveyance robot

[0081] 30: control device

[0082] 31: table motor

[0083] 32: compressed fluid supply source

[0084] 33: polishing pad

[0085] 33a: polishing surface

[0086] 34: fixed chamber

[0087] 35: polishing table

[0088] 35a: table shaft

[0089] 36: head shaft

[0090] 37: polishing head

[0091] 38: polishing liquid supply nozzle

[0092] 40: dressing device

[0093] 41: dresser

[0094] 41a: dressing surface

[0095] 42: head arm

[0096] 43: head rotation shaft

[0097] 45: dresser shaft

[0098] 47: air cylinder

[0099] 48: dresser arm

[0100] 49: dresser rotation shaft

[0101] 50: support table

[0102] 51: support column

[0103] 52: film thickness detector

[0104] 54: head rotation motor

[0105] 55: dresser rotation motor

[0106] 65: pressure adjustment device

[0107] 70: arithmetic device

[0108] 71: Rotating Ring

[0109] 81: Stationary Ring

[0110] 83A, 83B: Partial load application device

[0111] 84A, 84B: Pressing components

[0112] 85A, 85B: Network Bridge

[0113] 86A, 86B: Air cylinders

[0114] 87A, 87B: Linear guide rails

[0115] 88A, 88B: Guide rods

[0116] 89A, 89B: Unit base

[0117] 90A: First Actuator

[0118] 90B: Second Actuator

[0119] 101a, 101b: Piston rod

[0120] 103a: Pressing lever

[0121] 103b: Second pressing lever

[0122] 151-159: Atmospheric open pipelines

[0123] D1~Dm: Monitoring area

[0124] L1~L9: Atmospheric opening valves

[0125] R1~R11: Pressure regulators

[0126] Ra~Rh: Predicted grinding amount

[0127] Ra'~Rh': Target grinding amount

[0128] Rac: Actual grinding amount

[0129] Ta~Th: Initial film thickness

[0130] V1~V9: On / off valves

[0131] W: Chip Detailed Implementation

[0132] Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings.

[0133] Figure 1 This is a top view showing the overall configuration of a grinding apparatus according to one embodiment. Figure 1The polishing apparatus is a CMP apparatus that performs polishing of a wafer surface as an example of a substrate, cleans the polished wafer, and dries the cleaned wafer.

[0134] As shown in Figure 1 The polishing apparatus has a substantially rectangular housing 10 and a load port 12 for housing a substrate cassette in which a large number of wafers (substrates) are loaded. The load port 12 is disposed adjacent to the housing 10. The load port 12 can accommodate an open cassette, a SMIF (Standard Manufacturing Interface) pod, or a FOUP (Front Opening Unified Pod). The SMIF and the FOUP are closed containers that house a substrate cassette inside and cover it with a partition wall to maintain an environment independent of the outside.

[0135] Inside the housing 10, there are housed a plurality of (four in this embodiment) polishing units 14a to 14d that polish wafers, a first cleaning unit 16 and a second cleaning unit 18 that clean the polished wafers, and a drying unit 20 that dries the cleaned wafers. The polishing units 14a to 14d are arranged in the length direction of the substrate processing apparatus, and the cleaning units 16 and 18 and the drying unit 20 are also arranged in the length direction of the substrate processing apparatus. Further, the polishing apparatus has a control device 30 that controls the operation of each unit inside the housing 10.

[0136] A first substrate transfer robot 22 is disposed in a region surrounded by the load port 12, the polishing units 14a, and the drying unit 20, and a substrate transfer device 24 is disposed in parallel with the polishing units 14a to 14d. The first substrate transfer robot 22 receives wafers before polishing from the load port 12 and delivers them to the substrate transfer device 24, and receives wafers after drying from the drying unit 20 and delivers them back to the load port 12. The substrate transfer device 24 transfers the substrates received from the first substrate transfer robot 22 and hands over the substrates between the polishing units 14a to 14d.

[0137] Between the first cleaning unit 16 and the second cleaning unit 18, a second substrate transfer robot 26 is disposed that transfers wafers between these cleaning units 16 and 18 and the substrate transfer device 24, and between the second cleaning unit 18 and the drying unit 20, a third substrate transfer robot 28 is disposed that transfers wafers between these units 18 and 20. These first substrate transfer robot 22, the substrate transfer device 24, the second substrate transfer robot 26, and the third substrate transfer robot 28 constitute a substrate transfer unit for handing over wafers between the load port 12, the polishing units 14a to 14d, the cleaning units 16 and 18, and the drying unit 20.

[0138] In this embodiment, a substrate cleaning apparatus that uses a friction roller sponge to clean the substrate on both sides of the wafer in the presence of a chemical solution is used as the first cleaning unit 16, and a substrate cleaning apparatus using a pen-shaped sponge (pen sponge) is used as the second cleaning unit 18. In one embodiment, a substrate cleaning apparatus that uses a friction roller sponge to clean the wafer on both sides of the wafer in the presence of a chemical solution may also be used as the second cleaning unit 18. Furthermore, a spin drying apparatus that holds the wafer, sprays IPA vapor from a moving nozzle to dry the wafer, and further dries the wafer by high-speed rotation is used as the drying unit 20.

[0139] The wafer is polished by at least one of polishing units 14a to 14d. The polished wafer is then cleaned by a first cleaning unit 16 and a second cleaning unit 18, and further dried by a drying unit 20. In one embodiment, the polished substrate may also be cleaned by either the first cleaning unit 16 or the second cleaning unit 18.

[0140] like Figure 1 As shown, the polishing apparatus of this embodiment includes an in-line thickness monitor (ITM) 8 for detecting (measuring) the film thickness profile of a wafer surface (the surface being polished). The type of film thickness monitor 8 is not limited, as long as it can obtain the film thickness profile of the wafer. For example, the film thickness monitor 8 may be a non-contact measurement machine such as an eddy current type or an optical type, or it may be a measurement machine that detects the film thickness profile by non-contactly scanning a detection head above the wafer. Alternatively, the film thickness monitor 8 may be a measurement machine that scans a probe in contact with the wafer surface and detects the surface unevenness distribution of the wafer by monitoring the up-and-down movement of the probe. In either contact or non-contact detection methods, the output of the detection is the film thickness or a signal equivalent to the film thickness. When detecting the film thickness profile of the wafer, the film thickness profile can be associated not only with the radial direction but also with the circumferential direction by using the location of the wafer's grooves or the location of its orientation plane as a reference.

[0141] The film thickness measuring device 8 is connected to the control device 30, which is configured to control the operation of the film thickness measuring device 8. Furthermore, the film thickness measuring device 8 transmits its measured values ​​to the control device 30, which can obtain the film thickness profile of the wafer from the measured values ​​transmitted by the film thickness measuring device 8.

[0142] Figure 2 It is a schematic display Figure 1 A perspective view of an example of the grinding unit 14a shown. Furthermore, because... Figure 1The polishing units 14a to 14d of the polishing apparatus shown have the same configuration as each other, and therefore, the polishing unit 14a will be described below.

[0143] Figure 2 The polishing unit 14a shown is provided with a polishing table 35 on which a polishing pad 33 having a polishing surface 33a is installed, a polishing head 37 that holds a wafer W and presses the wafer W against the polishing pad 33 on the polishing table 35, a polishing liquid supply nozzle 38 for supplying a polishing liquid and a dresser liquid (e.g., pure water) to the polishing pad 33, and a dresser 40 having a dresser 41 for performing dressing of the polishing surface 33a of the polishing pad 33.

[0144] The polishing table 35 is linked to a table motor 31 disposed below it via a table shaft 35a, and is rotated in the direction indicated by the arrow by the table motor 31. The polishing pad 33 is attached to the upper surface of the polishing table 35, and the upper surface of the polishing pad 33 constitutes the polishing surface 33a for polishing the wafer W. The polishing head 37 is linked to the lower end of a head shaft 36. The polishing head 37 is configured to hold the wafer W on its lower surface by vacuum suction. The head shaft 36 is movable up and down by an up-and-down movement mechanism (not shown).

[0145] The head shaft 36 is rotatably supported by a head arm 42, and the head arm 42 is driven by a head rotation motor 54 to be rotatable about a head rotation shaft 43. By driving the head rotation motor 54, the polishing head 37 is moved between a polishing position above the polishing pad 33 and a standby position to the side of the polishing pad 33.

[0146] The dresser 40 is provided with the dresser 41 in sliding contact with the polishing pad 33, a dresser shaft 45 to which the dresser 41 is linked, an air cylinder 47 provided at the upper end of the dresser shaft 45, and a dresser arm 48 that rotatably supports the dresser shaft 45. The lower surface of the dresser 41 constitutes a dresser surface 41a, which is composed of polishing grains (e.g., diamond particles). The air cylinder 47 is disposed on a support table 50 supported by a plurality of support columns 51 fixed to the dresser arm 48.

[0147] The dresser arm 48 is driven by a dresser rotation motor 55 and is configured to be rotatable about a dresser rotation shaft 49. The dresser shaft 45 is rotated by driving of a motor not shown, and by the rotation of the dresser shaft 45, the dresser 41 is rotated about the dresser shaft 45 in the direction indicated by the arrow. The air cylinder 47 functions as an actuator that moves the dresser 41 up and down via the dresser shaft 45 and presses the dresser 41 against the polishing surface (surface) 33a of the polishing pad 33 at a specified pressing force.

[0148] Second, with reference to Figure 3 An example of the polishing head 37 provided in the polishing unit 14a will be described. Figure 3 is a cross-sectional view schematically showing an example of the polishing head. As shown in Figure 3 , the polishing head 37 is basically composed of a head body 2 fixed to the lower end of the head shaft 36, a clamping ring 3 directly pressing the polishing surface 33a (see Figure 2 ), and an elastic film (diaphragm) 5 pressing the wafer W against the polishing surface 33a. The clamping ring 3 is disposed in a manner to surround the wafer W and is coupled to the head body 2. The elastic film 5 is attached to the head body 2 in a manner to cover the lower surface of the head body 2.

[0149] The elastic film 5 has a plurality of (eight in the example shown in the drawing) annular peripheral walls 5a, 5b, 5c, 5d, 5e, 5f, 5g, 5h disposed concentrically. A central pressure chamber 7a of circular shape located at the center, an annular edge pressure chamber 7h located at the outermost periphery, and six annular intermediate pressure chambers (first to sixth intermediate pressure chambers) 7b, 7c, 7d, 7e, 7f, 7g located between the central pressure chamber 7a and the edge pressure chamber 7h are formed between the upper surface of the elastic film 5 and the lower surface of the head body 2 by the plurality of peripheral walls 5a to 5h. In the present embodiment, the number of pressure chambers formed in the elastic film 5 is eight, but the number of pressure chambers is not limited to the present embodiment. The number of pressure chambers can be increased or decreased depending on the configuration of the elastic film 5.

[0150] Flow paths 4a, 4b, 4c, 4d, 4e, 4f, 4g, 4h respectively communicating with the pressure chambers 7a to 7h are respectively formed in the head body 2. The flow paths 4a, 4b, 4c, 4d, 4e, 4f, 4g, 4h are connected to the pressure adjusting device 65 via fluid lines 6a, 6b, 6c, 6d, 6e, 6f, 6g, 6h, respectively. The pressure adjusting device 65 is connected to the control device 30, which is configured to control the operation of the pressure adjusting device 65.

[0151] A fixing chamber 34 is formed directly above the clamping ring 3, and the fixing chamber 34 is connected to the pressure adjusting device 65 via a flow path 4i formed in the head body 2 and a fluid line 6i.

[0152] As described above, the polishing head 37 is configured to press the wafer W against the polishing surface 33a by adjusting the pressure of the pressure chambers 7a to 7h. Figure 3When the polishing head 37 is configured as shown, in a state where the wafer W is held by the polishing head 37, by controlling the pressures of the compressed fluids supplied to the respective pressure chambers 7a to 7h, the wafer W can be pressed at different pressures in each of a plurality of areas (Areas) on the elastic membrane 5 in the radial direction of the wafer W. Thus, in the polishing head 37, by adjusting the pressures of the compressed fluids supplied to the respective pressure chambers 7a to 7h formed between the head body 2 and the elastic membrane 5, the pressing force applied to the wafer W can be adjusted for each area of the wafer W. At the same time, by controlling the pressure of the compressed fluid supplied to the fixed chamber 34, the pressing force of the clamping ring 3 against the polishing pad 33 (see Figure 2 ) can be adjusted.

[0153] When the clamping ring 3 presses the polishing pad 33, the shape of the polishing pad 33 changes depending on the pressing force thereof. Thus, the pressing force of the clamping ring 3 against the polishing pad 33 also becomes an important factor that affects the film thickness profile of the polished wafer W.

[0154] The clamping ring 3 is formed of a resin such as an engineering plastic (e.g., PEEK), and the elastic membrane 5 is formed of a rubber material such as ethylene-propylene rubber (EPDM), urethane rubber, or silicone rubber, which has excellent strength and durability.

[0155] Next, the configuration of the pressure adjusting device 65 shown in Figure 4 will be described. Figure 3 The pressure adjusting device 65 shown in Figure 4 is a schematic view. As shown in Figure 3 , the fluid lines 6a to 6i are respectively connected with on-off valves VI, V2, V3, V4, V5, V6, V7, V8, V9 and pressure adjusters Rl, R2, R3, R4, R5, R6, R7, R8, R9. The flow paths 4a to 4i are connected to the fluid supply source 32 via the fluid lines 6a to 6i, respectively. Figure 4 Further, the fluid lines 6a to 6i are connected with atmosphere opening lines 151 to 159. These atmosphere opening lines 151 to 159 are respectively provided with atmosphere opening valves LI to L9.

[0156] The pressure adjusters Rl to R9 have pressure adjusting functions of adjusting the pressures of the compressed fluids supplied from the fluid supply source 32 to the pressure chambers 7a to 7h and the fixed chamber 34. The pressure adjusters Rl to R9, the on-off valves VI to V9, and the atmosphere opening valves LI to L9 are connected to the control device 30, and the operations thereof can be controlled by the control device 30. When the atmosphere opening valves LI to L9 are operated, the respective pressure chambers 7a to 7h, 34 are opened to the atmosphere to become an atmospheric pressure state.

[0157]

[0158] ​Although not shown, a plurality of vacuum lines are connected to the fluid lines 6a to 6i, respectively, and negative pressure is formed in each of the chambers 7a to 7h and 34 through the plurality of vacuum lines. Thus, each of the pressure chambers 7a to 7h and 34 is adjusted to one of a pressurized state, a negative pressure state, and an atmospheric pressure state by the pressure adjusting device 65.

[0159] In a state where the wafer W contacts the lower surface of the elastic film 5, when vacuum is formed in one of the intermediate pressure chambers 7b to 7g (for example, the intermediate pressure chamber 7d), the wafer W is held to the polishing head 37 by vacuum suction. Further, in a state where the wafer W is separated from the polishing pad 33, if compressed fluid is supplied to one of the intermediate pressure chambers 7b to 7g (for example, the intermediate pressure chamber 7d), the wafer W is released from the polishing head 37.

[0160] Next, a polishing method using the polishing apparatus will be described. Figure 5 is a flowchart showing a polishing method according to an embodiment. As shown in Figure 5 , the control device 30 of the polishing apparatus takes out the wafer W from the substrate cassette loaded in the load port 12 (refer to Figure 1 ), carries it to the film thickness meter 8, and acquires a film thickness profile of the wafer W before polishing (refer to step 1 of Figure 5 ).

[0161] Next, the control device 30 creates an optimal polishing recipe based on the film thickness profile of the wafer W before polishing and a reaction model (refer to step 2 of Figure 5 ). The reaction model is stored in the control device 30 in advance. The method of creating the reaction model will be described later.

[0162] Hereinafter, the method of creating the optimal polishing recipe according to an embodiment will be described.

[0163] First, the control device 30 calculates the initial film thickness of each monitoring region of the wafer W corresponding to each pressure chamber 7a to 7h of the elastic film 5 from the film thickness profile of the wafer W before polishing, which is acquired by the film thickness meter 8. Hereinafter, for the convenience of explanation, the monitoring region of the wafer W corresponding to the pressure chamber 7a is denoted as Da, and the initial film thickness of the monitoring region Da is denoted as Ta. Similarly, the monitoring region of the wafer W corresponding to the pressure chamber 7b is denoted as Db, and the initial film thickness of the monitoring region Db is denoted as Tb, the monitoring region of the wafer W corresponding to the pressure chamber 7c is denoted as Dc, and the initial film thickness of the monitoring region Dc is denoted as Tc, the monitoring region of the wafer W corresponding to the pressure chamber 7d is denoted as Dd, and the initial film thickness of the monitoring region Dd is denoted as Td, the monitoring region of the wafer W corresponding to the pressure chamber 7e is denoted as De, and the initial film thickness of the monitoring region De is denoted as Te, the monitoring region of the wafer W corresponding to the pressure chamber 7f is denoted as Df, and the initial film thickness of the monitoring region Df is denoted as Tf, the monitoring region of the wafer W corresponding to the pressure chamber 7g is denoted as Dg, and the initial film thickness of the monitoring region Dg is denoted as Tg, and the monitoring region of the wafer W corresponding to the pressure chamber 7h is denoted as Dh, and the initial film thickness of the monitoring region Dh is denoted as Th.

[0164] The film thickness meter 8 measures the film thickness at a plurality of measurement points in each of the monitoring regions Da to Dh, and transmits the measurement values to the control device 30. The control device 30 determines a representative value of the plurality of film thickness measurement values in each of the monitoring regions Da to Dh as the initial film thickness Ta to Th. The representative value is, for example, an average value of the plurality of measurement values. Next, the control device 30 calculates the difference between the initial film thickness Ta to Th and the target film thickness Tt, and calculates the target polishing amount Ra' to Rh' of each of the monitoring regions Da to Dh.

[0165] Next, the control device 30 calculates the predicted polishing amount Ra to Rh in each of the monitoring regions Da to Dh using a reaction model stored in advance in the control device 30. Further, the control device 30 calculates at least the pressure of the compressed fluid supplied to each of the pressure chambers 7a to 7h and the polishing time by optimization calculation in such a manner that the predicted polishing amount Ra to Rh becomes a value close to the target polishing amount Ra' to Rh' which is approximately calculated.

[0166] The optimization calculation is, for example, a target function shown by the following formula (1). Specifically, in the optimization calculation, the pressure of the compressed fluid supplied to each of the pressure chambers 7a to 7h and the polishing time are calculated in such a manner that the target function including the difference between the predicted polishing amount Ra to Rh and the target polishing amount Ra' to Rh' becomes the minimum.

[0167] Target function = Σ |Predicted polishing amount - Target polishing amount| 2 …(1)

[0168] The objective function shown in Equation (1) takes into account only the polishing amount, but the present embodiment is not limited to this example. For example, as shown in Equation (2) below, the objective function preferably includes: a term of the difference between the calculated optimum compressed fluid pressure and the reference compressed fluid pressure set in advance; and a term of the difference between the calculated optimum compressed fluid pressure and the optimum compressed fluid pressure at the previous wafer polishing.

[0169] Objective function =∑|predicted polishing amount - target polishing amount| 2

[0170] + λ∑|calculated optimum compressed fluid pressure - reference compressed fluid pressure| 2

[0171] + γ∑|calculated optimum compressed fluid pressure - reference compressed fluid pressure of previous wafer| 2 …(2)

[0172] Here, λ and γ are weighting coefficients that determine the weighting of each term, and can be set to any real number of 0 or more. By adding these terms, the large variation in the calculated optimum compressed fluid pressure for each wafer can be suppressed, and stable optimum polishing conditions can be obtained.

[0173] The pressure of the compressed fluid supplied to each pressure chamber 7a to 7h corresponds to the polishing pressure in each monitoring region Da to Dh. In addition, the pressing force of the clamping ring 3 against the polishing pad 33 corresponds to the pressure of the compressed fluid supplied to the stationary chamber 34.

[0174] In the present embodiment, the monitoring region of the film thickness of the wafer W corresponds to each pressure chamber 7a to 7h of the elastic membrane 5, and is divided into regions equal in number to the total number of the pressure chambers of the elastic membrane 5 (see (a) of FIG. 10 and (b) of FIG. 11). Figure 6 Figure 6 However, the monitoring region of the film thickness of the wafer W can be further subdivided. As described above, the film thickness measurer 8 can measure the film thickness at a plurality of measurement points in each monitoring region Da to Dh. Thus, for example, the monitoring region of the film thickness of the wafer W can be divided into monitoring regions D1 to Dm corresponding to each measurement point MP of the film thickness measured by the film thickness measurer 8 (see (a) of FIG. 10 and (c) of FIG. 11). Figure 6 Figure 6 Here, the suffix "m" corresponds to the number of measurement points.

[0175] Further, in other methods of subdividing the monitoring regions, the entire wafer, or each monitoring region Da to Dh, can be divided at equal intervals (for example, at 1 mm intervals), and each divided region can be taken as a new monitoring region D1 to Dn (see (a) of FIG. 10 and (b) of FIG. 11). Figure 6 ​​(d)). Here, "n" is the total number of the subdivided monitoring regions. When the monitoring regions are thus subdivided, there are cases where there is no measurement point of the film thickness measured by the film thickness measurer 8 within each monitoring region. Therefore, the film thickness value at a representative point (for example, the center position of each monitoring region) of each monitoring region is calculated from the measured film thickness value at each measurement point using an interpolation process, and the representative film thickness value (estimated film thickness value) of each monitoring region after the subdivision can be calculated. In this way, by dividing the monitoring regions of the film thickness of the wafer W into regions more than the total number of the pressure chambers of the elastic film 5, the film thickness profile of the wafer W can be controlled more precisely.

[0176] In deciding the monitoring regions of the film thickness of the wafer W, it is not necessary to select only one of the above-described setting methods of the monitoring regions, and a plurality of setting methods can be combined. For example, in the region inside the wafer W (for example, the region corresponding to the pressure chambers 7a to 7f), the monitoring regions of the film thickness of the wafer W can be set to the monitoring regions Da to Df corresponding to the pressure chambers 7a to 7f, and in the region outside the wafer W (for example, the region corresponding to the pressure chambers 7g to 7h), the monitoring regions of the film thickness of the wafer W can be set to the monitoring regions corresponding to each measurement point MP of the film thickness measured by the film thickness measurer 8 (refer to FIG. 6). In this way, the monitoring regions of the film thickness of the wafer W can be set in accordance with the film thickness profile of the wafer W. Figure 6 (a) and Figure 6 (e) of FIG. 6.

[0177] Next, the method of creating the reaction model will be described. The reaction model is created, for example, by experiments. In the experiments, first, the wafer whose film thickness profile is obtained by the film thickness measurer 8 is polished with a polishing recipe that becomes a reference (i.e., a specified polishing pressure and a specified polishing time), and the film thickness profile of the polished wafer is obtained by the film thickness measurer 8. Next, a large number of wafers different from the wafer W polished by the reference polishing recipe are polished while changing the pressure of the compressed fluid supplied to each of the pressure chambers 7a to 7h of the elastic film 5 and the stationary chamber 34 from the pressure of the reference polishing recipe. At this time, the film thickness profiles before and after polishing of the large number of wafers are obtained by the film thickness measurer 8.

[0178] As described above, the film thickness measurer 8 can measure the film thickness at a plurality of measurement points on the wafer W. Therefore, the control device 30 can calculate the polishing rate at each measurement point from the film thickness profiles before and after polishing of the wafer polished by the reference polishing recipe and the large number of wafers. Figure 7 is a conceptual diagram of the polishing rate at each measurement point of the large number of wafers. Figure 7 In FIG. 10, the vertical axis represents the polishing rate, and the horizontal axis represents the position in the radial direction of the wafer.

[0179] Next, the control device 30 calculates the increase in polishing rate per unit polishing pressure (e.g., 1 hPa) from the polishing rates of a large number of wafers at each measurement point. In this specification, the increase in polishing rate per unit polishing pressure is referred to as a "reaction coefficient". Furthermore, the offset amount D is calculated in such a manner that the predicted polishing amount R calculated by substituting the reaction coefficient into the formula (3) described later is equal to the actual polishing amount obtained by polishing according to the polishing plan described above as a reference.

[0180] Further, the reaction coefficient and the offset amount at each monitoring region are determined by interpolating the reaction coefficient and the offset amount calculated at each measurement point. Figure 8 is a conceptual view of the reaction coefficient at each measurement point of the wafer. Figure 8 In, the vertical axis represents the reaction coefficient, and the horizontal axis represents the position in the radial direction of the wafer.

[0181] The reaction coefficient and the offset amount thus calculated are included in the reaction model. The control device 30 creates an optimal polishing plan using the reaction model. Specifically, the control device 30 calculates the predicted polishing amount R from the pressure of the compressed fluid supplied to each pressure chamber 7a to 7h and the polishing time by the following formula (3).

[0182] R = Tp · (C · X + D)... (3)

[0183] The objective function value is further calculated by substituting the predicted polishing amount R calculated into the formula (1) or the formula (2). The control device 30 calculates the pressure of the compressed fluid supplied to each pressure chamber 7a to 7h and the polishing time at which the objective function value becomes the minimum by optimization calculation, thereby creating an optimal polishing plan. Here, since the formula (1) or (2) described above can be expressed as a quadratic equation in X, the optimal polishing plan can be uniquely determined by using the quadratic programming method at the time of optimization calculation. Furthermore, a gradient method such as the steepest descent method or an optimization calculation method such as the Monte-Carlo method can be used.

[0184] In the formula (3), R is a matrix composed of the predicted polishing amounts R1 to Rm of the monitoring regions D1 to Dm of the wafer W, Tp is the polishing time, C is a matrix composed of the reaction coefficients at the monitoring regions of the wafer W, X is a matrix composed of the pressures of the compressed fluid supplied to each pressure chamber 7a to 7h, and D is a matrix composed of the offsets of the monitoring regions D1 to Dm of the wafer W. Here, the suffix "m" corresponds to the number of the monitoring regions of the wafer W.

[0185] R, C, D, and X are as described above. Figure 9The matrix R, C, D shown in the drawing. In the matrix R, C, D, each row corresponds to each monitoring area Dl ~ Dm of the wafer W. The matrix X multiplied by the matrix C corresponds to the pressure of the compressed fluid to be supplied to each pressure chamber 7a ~ 7h of the elastic membrane 5. Therefore, "Pa" in the matrix X is the pressure of the compressed fluid to be supplied to the pressure chamber 7a of the elastic membrane 5, and "Pc" is the pressure of the compressed fluid to be supplied to the pressure chamber 7c of the elastic membrane 5.

[0186] The former of the two suffixes of the reaction coefficient in the matrix C corresponds to each monitoring area Dl ~ Dm of the wafer W, and the latter corresponds to the pressure of the compressed fluid to be supplied to each pressure chamber 7a ~ 7h. For example, the reaction coefficient C2b is the reaction coefficient to the compressed fluid pressure supplied to the pressure chamber 7b at the monitoring area D2 of the wafer W, and the reaction coefficient C3c is the reaction coefficient to the compressed fluid pressure supplied to the pressure chamber 7c at the monitoring area D3 of the wafer W.

[0187] The control device 30 calculates the pressure Pa ~ Ph of the compressed fluid to be supplied to each pressure chamber 7a ~ 7h of the elastic membrane 5 and the polishing time Tp by the above-described optimization calculation, and uses these pressure Pa ~ Ph of the compressed fluid and the polishing time Tp as the optimum polishing plan. The optimum polishing plan thus calculated can precisely control the film thickness profile of the wafer W because it determines the polishing pressure of each pressure chamber 7a ~ 7h using the plurality of film thickness measurement values at each monitoring area Dl ~ Dm of the wafer W.

[0188] In one embodiment, the optimum polishing plan corresponding to the pressure Pa ~ Ph of the compressed fluid to be supplied to each pressure chamber 7a ~ 7h of the elastic membrane 5 and the polishing time Tp plus the pressure Pi of the compressed fluid to be supplied to the fixed chamber 34 can also be calculated. At this time, instead of the above-described reaction matrix C, a matrix C' composed of reaction coefficients C la ~ Cmh corresponding to the pressure of the compressed fluid supplied to each pressure chamber 7a ~ 7h and reaction coefficients C li ~ Cmi corresponding to the pressure of the compressed fluid supplied to the fixed chamber 34 is used. In addition, instead of the matrix X, a matrix X' composed of the pressure Pa ~ Ph of the compressed fluid to be supplied to each pressure chamber 7a ~ 7h of the elastic membrane 5 and the pressure Pi of the compressed fluid to be supplied to the fixed chamber 34 is used. Figure 10

[0189] ​The reaction coefficients C1a to Cmh and the reaction coefficients C1i to Cmi can be determined as follows. First, in an experiment for determining the reaction coefficients C1a to Cmh, the reaction coefficients C1a to Cmh are calculated by changing the pressure of the compressed fluid supplied to each of the pressure chambers 7a to 7h while the pressure of the compressed fluid supplied to the fixed chamber 34 is fixed to a specified value. Next, in an experiment for determining the reaction coefficients C1i to Cmi, the reaction coefficients C1i to Cmi are obtained by changing the pressure of the compressed fluid supplied to the fixed chamber 34 while the pressure of the compressed fluid supplied to each of the pressure chambers 7a to 7h is fixed to a specified value.

[0190] The optimal polishing plan obtained using the matrix C' of the above reaction model takes into account not only the change in the polishing amount among the monitoring regions D1 to Dm resulting from the change in the pressure of the compressed fluid supplied to each of the pressure chambers 7a to 7h but also the change in the polishing amount among the monitoring regions D1 to Dm resulting from the change in the pressing force of the clamping ring 3 against the polishing pad 33. Therefore, the film thickness profile of the wafer W can be controlled more precisely.

[0191] In one embodiment, the reaction model, i.e., the matrix C (or the matrix C') composed of the reaction coefficients C1a to Cmh and the matrix D (or the matrix D') can also be determined by simulation. At this time, the matrix C (or the matrix C') and the matrix D (or the matrix D') obtained by simulation are also stored in advance in the control device 30.

[0192] Returning to Figure 5 , the control device 30 carries the wafer W to one of the polishing units 14a to 14d and polishes the wafer W in the optimal polishing plan described above (see Step 3 of Figure 5 ). The polishing of the wafer W is performed as follows. As shown in Figure 2 , the polishing head 37 and the polishing table 35 are rotated in the directions indicated by the arrows, and the polishing liquid (slurry) is supplied from the polishing liquid supply nozzles 38 onto the polishing pad 33. In this state, the polishing head 37 presses the wafer W against the polishing surface 33a of the polishing pad 33 to the extent of the polishing time in the optimal polishing plan. The pressure of the compressed fluid supplied to each of the pressure chambers 7a to 7h of the elastic membrane 5 and the fixed chamber 34 is adjusted to the pressure in the optimal polishing plan while the wafer W is pressed against the polishing pad 33. The surface of the wafer W is polished by the mechanical action of the polishing particles contained in the polishing liquid and the chemical action of the polishing liquid. After the polishing is completed, the polishing surface 33a is dressed (adjusted) by the dressing device 40.

[0193] The dressing of the polishing pad 33 is performed as follows. The dresser 41 is rotated with the dresser shaft 45 as the center, and pure water is supplied from the polishing liquid supply nozzle 38 onto the polishing pad 33. In this state, the dresser 41 is pressed against the polishing pad 33 by the air cylinder 47 with the dressing surface 41a thereof in sliding contact with the polishing surface 33a of the polishing pad 33. Further, the dresser arm 48 is rotated with the dresser rotation shaft 49 as the center, and the dresser 41 is rocked in the radial direction of the polishing pad 33. In this way, the polishing surface 33a of the polishing pad 33 is dressed (renewed) by slightly removing the same by the dresser 41.

[0194] Next, the control device 30 carries the polished wafer W to the first cleaning unit 16 and / or the second cleaning unit 18 to perform cleaning, and further carries the cleaned wafer W to the drying unit 20 to dry the same. Further, the control device 30 carries the polished wafer W to the film thickness meter 8 to obtain the film thickness profile of the polished wafer W (see Step 4 of Figure 5 The control device 30 stores the film thickness profiles of the wafer W before and after polishing and the optimum polishing recipe for polishing the wafer W.

[0195] Next, the control device 30 corrects the stored reaction model in order to prepare the optimum polishing recipe for polishing the next wafer W (see Step 5 of Figure 5 The correction of the reaction model is performed as follows.

[0196] The control device 30 calculates the actual polishing amount Rac in each of the monitoring regions D1 to Dm of the wafer W from the film thickness profiles before and after polishing of the wafer W that has been polished. In calculating the actual polishing amount Rac, the control device 30 subtracts the post-polishing film thickness values T1' to Tm' that correspond to the representative values of the plurality of film thickness measurement values of each of the monitoring regions D1 to Dm of the polished wafer W from the above-mentioned initial film thickness values T1 to Tm of each of the monitoring regions D1 to Dm, respectively. The post-polishing film thickness values T1' to Tm' are, for example, the average of the plurality of film thickness measurement values in each of the monitoring regions D1 to Dm, or the film thickness value at the representative point in each of the monitoring regions calculated by interpolation from the post-polishing film thickness measurement values. The control device 30 calculates the actual polishing amounts Rac1 to Racm of each of the monitoring regions D1 to Dm by subtracting the post-polishing film thickness values T1' to Tm' from the initial film thickness values T1 to Tm.

[0197] Next, the control device 30 calculates the correction coefficient K in such a manner that the predicted polishing amount R in the above-mentioned formula (3) and the actual polishing amount Rac satisfy the following formula (4).

[0198] Rac = K • R... (4)

[0199] Here, Rac is a matrix composed of the actual polishing amounts Rac1 to Racm of the respective monitoring regions D1 to Dm, and K is a matrix composed of the correction coefficients corresponding to the respective monitoring regions D1 to Dm.

[0200] Next, the control device 30 multiplies the above-mentioned matrix C and matrix D by K obtained from the equation (4) to calculate a corrected reaction coefficient matrix Cadj and a corrected bias amount matrix Dadj and stores them, as shown in the following equations (5) and (6).

[0201] Cadj = K - C... (5)

[0202] Dadj = K - D... (6)

[0203] Next, the control device 30 carries the next wafer W to the film thickness measurer 8 to obtain the film thickness profile of the next wafer W before polishing (see Step 6 of Figure 5 ).

[0204] Next, the control device 30 uses the corrected predicted polishing amount Radj obtained from the following equation (7) and calculates the pressures of the compressed fluid supplied to the respective pressure chambers 7a to 7h and the fixed chamber 34 and the polishing time by the above-mentioned optimization calculation.

[0205] Radj = Tp - (Cadj - X + Dadj)... (7)

[0206] In the equation (7), Radj is a matrix composed of the predicted polishing amounts of the next wafer W in the respective monitoring regions D1 to Dm, and Tp is the polishing time of the wafer W.

[0207] In the present embodiment, the optimal polishing plan for polishing the next wafer W is made using the reaction model corrected in accordance with the film thickness profiles of the previous wafer W before and after polishing, which are data reflecting the state of the polishing unit (for example, the surface properties of the polishing pad 33) actually polishing the wafer W. Therefore, by making the optimal polishing plan for polishing the next wafer W using the reaction model corrected in accordance with the film thickness profiles of the previous wafer W before and after polishing, the film thickness profile of the next wafer W can be controlled more precisely.

[0208] Next, the control device 30 polishes the next wafer W with the made optimal polishing plan (see Step 8 of Figure 5 ). Next, the control device 30 carries the polished next wafer W to the first cleaning unit 16 and / or the second cleaning unit 18 to clean it, and further carries the cleaned next wafer W to the drying unit 20 to dry it. Further, the control device 30 carries the polished next wafer W to the film thickness measurer 8 to obtain the film thickness profile of the polished wafer W (see Step 9 of Figure 5Step 9).

[0209] Furthermore, the control device 30 repeatedly executes... Figure 5 Steps 5 through 9. That is, before grinding the next wafer W, the control device 30 corrects the reaction model using the film thickness profile of the next wafer W before and after grinding and the optimal grinding scheme. Next, the film thickness profile of the next wafer W before grinding is obtained using the film thickness measuring device 8. Next, an optimal grinding scheme for grinding the next wafer W is created based on the corrected reaction model. Then, the control device 30 grinds the next wafer W using the created optimal grinding scheme, and obtains the film thickness profile of the next wafer W after grinding. In this way, by correcting the reaction model each time wafer W is ground, the film thickness profile of the next wafer W can be controlled more precisely.

[0210] In one embodiment, the control device 30 may also be connected to the computing device 70 located outside the grinding apparatus (see reference). Figure 1 (The dashed line indicates a data transmission / reception connection). At this time, the reaction model is pre-stored in the computing device 70, and the control device 30 transmits the pre-grinding film thickness profile and the target film thickness to the computing device 70. The computing device 70 generates an optimal grinding scheme based on the grinding amount and the reaction model according to the difference between the transmitted film thickness profile and the target film thickness. Next, the computing device 70 transmits the optimal grinding scheme to the control device 30 of the grinding apparatus, and the control device 30 grinds the wafer W according to the received optimal grinding scheme. Furthermore, the control device 30 transmits the post-grinding film thickness profile of the wafer W to the computing device 70, and the computing device 70 stores the pre-grinding and post-grinding film thickness profiles of the wafer W and the optimal grinding scheme used to grind the wafer W. Furthermore, the control device 30 uses the pre-grinding and post-grinding film thickness profiles of the wafer W and the optimal grinding scheme used to grind the wafer W to correct the reaction model.

[0211] When grinding the next wafer W, the control device 30 transmits the film thickness profile of the next wafer W before grinding to the computing device 70. The computing device 70, based on the target grinding amount (the difference between the film thickness profile of the next wafer W before grinding and the target film thickness) and a corrected reaction model, creates an optimal grinding scheme for grinding the next wafer W and transmits it to the control device 30. The control device 30 grinds the next wafer W using the transmitted optimal grinding scheme. Furthermore, the control device 30 transmits the film thickness profile of the next wafer W after grinding to the computing device 70, which stores the film thickness profile of the next wafer W before and after grinding, along with the optimal grinding scheme for grinding the next wafer W. The computing device 70 uses the film thickness profile of the next wafer W before and after grinding, along with the optimal grinding scheme for grinding the next wafer W, to correct the reaction model used when grinding the next wafer W after that.

[0212] Figure 11is a perspective view schematically showing a polishing head of another embodiment. Since the configuration of the present embodiment not particularly mentioned is the same as that of the above-described embodiment, the repeated description thereof is omitted. Further, the following is a description of the polishing head 37 to be described with reference to Figure 11 is mounted on the polishing unit 14a shown in Figure 1 , but the polishing head 37 can be mounted on the polishing units 14b to 14d.

[0213] Figure 11 The polishing head 37 shown in has a head body 2 that presses the wafer W against the polishing pad 33, and a clamping ring 3 that is disposed so as to surround the wafer W. The clamping ring 3 is configured to be movable up and down independently of the head body 2. The clamping ring 3 extends radially outward from the head body 2. During polishing of the wafer W, the clamping ring 3 is in contact with the polishing surface 33a of the polishing pad 33, and presses the polishing pad 33 against the outer side of the wafer W while rotating.

[0214] The polishing head 37 further has a rotating ring 71 in which a plurality of rollers are disposed inside, and a stationary ring 81. The rotating ring 71 is fixed to the upper surface of the clamping ring 3, and is configured to be rotatable together with the clamping ring 3. The stationary ring 81 is disposed on the rotating ring 71. The rotating ring 71 rotates together with the clamping ring 3, but the stationary ring 81 is stationary without rotating.

[0215] The polishing unit 14a has a plurality of local load applying devices that apply a local load to a portion of the clamping ring 3. In the illustrated example, the polishing unit 14a has two local load applying devices, i.e., a first local load applying device 83A and a second local load applying device 83B. The local load applying devices 83A, 83B are disposed above the clamping ring 3. The local load applying devices 83A, 83B are fixed to the head arm 42 (see Figure 2 ). The clamping ring 3 rotates around the axis thereof during polishing, but the local load applying devices 83A, 83B are stationary without rotating integrally with the clamping ring 3. The stationary ring 81 is linked to the local load applying devices 83A, 83B. The first local load applying device 83A is disposed on the upstream side of the clamping ring 3 in the advancing direction of the polishing surface 33a of the polishing pad 33 (the side of the clamping ring 3 through which the polishing surface 33a flows), and the second local load applying device 83B is disposed on the downstream side of the clamping ring 3 in the advancing direction of the polishing surface 33a of the polishing pad 33 (the opposite side of the clamping ring 3 through which the polishing surface 33a flows).

[0216] The plurality of local load imparting devices 83A, 83B are provided with: a plurality of pressing members 84A, 84B that impart a downward local load to the stationary ring 81; a plurality of web bridges 85A, 85B; a plurality of air cylinders 86A, 86B that generate a downward force; a plurality of pressure regulators R10, R11 that regulate the pressure of a compressed fluid within the air cylinders 86A, 86B; a plurality of linear guides 87A, 87B; a plurality of guide rods 88A, 88B; and a plurality of unit bases 89A, 89B.

[0217] Specifically, the first local load imparting device 83A is provided with: a first pressing member 84A, a first web bridge 85A, a first air cylinder 86A, a first pressure regulator R10, a first linear guide 87A, a first guide rod 88A, and a first unit base 89A. The second local load imparting device 83B is provided with: a second pressing member 84B, a second web bridge 85B, a second air cylinder 86B, a second pressure regulator R11, a second linear guide 87B, a second guide rod 88B, and a second unit base 89B.

[0218] The piston rod 101a of the first air cylinder 86A is linked to the first pressing member 84A via the first web bridge 85A, and the end portion of the first pressing member 84A is linked to the stationary ring 81. Thus, the force generated by the first air cylinder 86A is transmitted to the first pressing member 84A, and the first pressing member 84A exerts a local load on a portion of the stationary ring 81. Likewise, the piston rod 101b of the second air cylinder 86B is linked to the second pressing member 84B via the second web bridge 85B, and the end portion of the second pressing member 84B is linked to the stationary ring 81. Thus, the force generated by the second air cylinder 86B is transmitted to the second pressing member 84B, and the second pressing member 84B exerts a local load on a portion of the stationary ring 81.

[0219] In the present embodiment, the combination of the first air cylinder 86A and the first pressure regulator R10 constitutes a first actuator 90A that regulates the local load exerted on the stationary ring 81 from the first pressing member 84A, and the combination of the second air cylinder 86B and the second pressure regulator R11 constitutes a second actuator 90B that regulates the local load exerted on the stationary ring 81 from the second pressing member 84B. In one embodiment, the first actuator 90A and the second actuator 90B can each also be constituted by a combination of a servo motor, a ball screw mechanism, and a motor driver.

[0220] The first pressing member 84A includes two pressing rods 103a, and the second pressing member 84B includes two second pressing rods 103b. The pressing rods 103a and the second pressing rods 103b are linked to the stationary ring 81. The first pressing member 84A is configured to apply a local load to a portion of the upstream side of the stationary ring 81 in the traveling direction of the polishing surface 33a of the polishing pad 33, and the second pressing member 84B is configured to apply a local load to a portion of the downstream side of the stationary ring 81 in the traveling direction of the polishing surface 33a of the polishing pad 33.

[0221] The local load imparting devices 83A, 83B are fixed to the head arm 42 via the unit bases 89A, 89B (refer to Figure 2 ). Therefore, during polishing of the wafer W, the polishing head 37 and the wafer W rotate, and the local load imparting devices 83A, 83B are stationary. Similarly, during polishing of the wafer W, the rotating ring 71 rotates together with the polishing head 37, and the stationary ring 81 is stationary.

[0222] The local load imparting devices 83A, 83B have the same configuration. The following description is about the first local load imparting device 83A, but is also applicable to the second local load imparting device 83B. The first air cylinder 86A and the first linear guide 87A are installed in the first unit base 89A. The piston rod 101a of the first air cylinder 86A and the first guide rod 88A are connected to the first web 85A. The first guide rod 88A is supported by the first linear guide 87A so as to be able to move up and down freely. With the first linear guide 87A, the first web 85A is not tilted and can smoothly move up and down.

[0223] The air cylinders 86A, 86B are connected to the compressed fluid supply source 32 via gas delivery lines Fl, F2 (refer to Figure 4 ). The pressure regulators R10, R11 are respectively provided in the gas delivery lines Fl, F2, and are disposed in the pressure adjusting device 65 shown in Figure 4 . Compressed fluid from the compressed fluid supply source is supplied to the air cylinders 86A, 86B independently via the pressure regulators R10, R11.

[0224] The pressure regulators R10, R11 can independently adjust the pressure of the compressed fluid in the air cylinders 86A, 86B, and thus the air cylinders 86A, 86B can independently generate force.

[0225] The pressure regulators R10, R11 are electrically connected to the control device 30 shown in Figure 1 . During polishing of the wafer W, the control device 30 issues an instruction to one of the pressure regulators R10, R11 to adjust the pressure of the compressed fluid in the air cylinder 86A or the air cylinder 86B.

[0226] The forces generated by the air cylinders 86A, 86B are transmitted to the bridges 85A, 85B, respectively. The bridges 85A, 85B are connected to the stationary ring 81 via the pressing members 84A, 84B, which transmit the forces of the air cylinders 86A, 86B applied to the bridges 85A, 85B to the stationary ring 81. That is, the first pressing member 84A presses a portion of the stationary ring 81 with a partial load corresponding to the force generated by the first air cylinder 86A, and the second pressing member 84B presses a portion of the stationary ring 81 with a partial load corresponding to the force generated by the second air cylinder 86B.

[0227] The partial load imparting devices 83A, 83B impart a downward partial load to a portion of the chuck ring 3 via the stationary ring 81 and the rotating ring 71, respectively. That is, the downward partial load is transmitted to the chuck ring 3 through the stationary ring 81 and the rotating ring 71.

[0228] The polishing device rotates the rotating ring 71 fixed to the chuck ring 3 together with the chuck ring 3, and polishes the wafer W by applying a partial load to the stationary ring 81 from the first pressing member 84A or the second pressing member 84B. In the polishing of the wafer W, the chuck ring 3 is in contact with the polishing surface 33a of the polishing pad 33, presses the polishing pad 33 on the outer side of the wafer W while rotating, and imparts a downward partial load to a portion of the polishing surface 33a.

[0229] Figure 12 is a longitudinal sectional view schematically showing the state when the chuck ring presses the polishing surface. As Figure 12 shown, when the chuck ring 3 imparts a downward partial load to a portion of the polishing surface 33a, a portion of the polishing surface 33a bulges upward. The polishing surface 33a that bulges upward exerts a partial upward force on the wafer W. In the present specification, this partial upward force is referred to as a partial bounce-up force. In Figure 12 the present specification, only the portion of the polishing surface 33a that bulges is in contact with the wafer W for the sake of explanation, but in actual polishing, the entire lower surface (polished surface) of the wafer W is in contact with the polishing surface 33a. The polishing rate of the portion of the wafer W that receives the partial bounce-up force becomes large. The magnitude of the partial bounce-up force depends on the magnitude of the force with which the chuck ring 3 presses the polishing pad 33, and the polishing rate varies depending on the magnitude of the partial bounce-up force. That is, the larger the partial bounce-up force, the larger the polishing rate. The position at which the partial bounce-up force is generated depends on the position at which the chuck ring 3 imparts the partial load to the polishing surface 33a.

[0230] Therefore, by applying a local load to the stationary ring 81 from the first pressing member 84A or the second pressing member 84B to polish the wafer W, a local reaction force corresponding to each local load is generated, and it is possible to change the polishing rate of the portion of the wafer W to which the local reaction force is applied. For example, when the control device 30 is to increase the local load imparted by the first pressing member 84A, an instruction is issued to the pressure adjuster R10 to increase the pressure of the compressed fluid in the air cylinder 86A. When the local load imparted by the second pressing member 84B is to be increased, an instruction is issued to the pressure adjuster R11 to increase the pressure of the compressed fluid in the air cylinder 86B.

[0231] Thus, the local load imparted to the clasp 3 by the local load imparting devices 83A, 83B (in this embodiment, the pressure of the compressed fluid supplied to the air cylinders 86A, 86B) also becomes an important factor that affects the film thickness profile of the polished wafer W.

[0232] Therefore, in this embodiment, the control device 30 (see Figure 1 ) calculates the above-described reaction model (i.e., the above-described matrix C composed of the reaction coefficients C1a to Cmh and the matrix D composed of the bias values) in consideration of not only the pressures of the compressed fluid supplied to each pressure chamber 7a to 7h and the stationary chamber 34 but also the local load. Further, the control device 30 creates an optimal polishing recipe using the reaction model to which the local load is also added (see step 3 of Figure 5 ).

[0233] The optimal polishing recipe thus obtained takes into account not only the changes in the polishing amounts among the monitoring regions D1 to Dm due to changes in the pressures of the compressed fluid supplied to each pressure chamber 7a to 7h, the changes in the polishing amounts among the monitoring regions D1 to Dm due to changes in the pressing force of the clasp 3 against the polishing pad 33, and the changes in the polishing amounts among the monitoring regions D1 to Dm due to changes in the local load. Therefore, it is possible to more precisely control the film thickness profile of the wafer W.

[0234] Further, the modified reaction model used to calculate the optimal polishing recipe for polishing the next wafer W also takes into account not only the changes in the polishing amounts among the monitoring regions D1 to Dm due to changes in the pressures of the compressed fluid supplied to each pressure chamber 7a to 7h, the changes in the polishing amounts among the monitoring regions D1 to Dm due to changes in the pressing force of the clasp 3 against the polishing pad 33, and the changes in the polishing amounts among the monitoring regions D1 to Dm due to changes in the local load. Therefore, it is also possible to more precisely control the film thickness profile of the next wafer W polished in accordance with the optimal polishing recipe created based on the modified reaction model.

[0235] Figure 13is a graph showing the change in in-plane uniformity in each of the embodiments when a plurality of wafers are continuously polished using the optimum polishing recipe of the plurality of embodiments. Figure 13 In the graph, the vertical axis represents in-plane uniformity, and the horizontal axis represents the serial number of the wafer being polished. Figure 13 The in-plane uniformity shown is represented by the difference between the maximum value and the minimum value of the film thickness measurement values of the polished wafer W.

[0236] Figure 13 In the graph, the dotted line shows the change in in-plane uniformity when the optimum polishing recipe is created and the reaction model is corrected (hereinafter, referred to as Example 1) using a reaction model created by taking into account only the change in the pressure of the compressed fluid supplied to each pressure chamber 7a to 7h. The thick solid line shows the change in in-plane uniformity when the optimum polishing recipe is created and the reaction model is corrected (hereinafter, referred to as Example 2) using a reaction model created by taking into account the change in the pressure of the compressed fluid supplied to each pressure chamber 7a to 7h and the change in the pressure of the compressed fluid supplied to the fixed chamber 34. The thin solid line shows the change in in-plane uniformity when the optimum polishing recipe is created and the reaction model is corrected (hereinafter, referred to as Example 3) using a reaction model created by taking into account the change in the pressure of the compressed fluid supplied to each pressure chamber 7a to 7h, the change in the pressure of the compressed fluid supplied to the fixed chamber 34, and the change in the local load.

[0237] In addition, Figure 13 The double-dot chain line graph in is a graph of the reference example, and is a graph showing the change in in-plane uniformity when a plurality of wafers W are continuously polished using a past polishing pressure adjustment method. The past polishing pressure adjustment method is a method of polishing the next wafer W by changing the pressure of the compressed fluid supplied to each pressure chamber 7a to 7h in such a manner that the difference between the film thickness in each monitoring region Da to Dh and the target film thickness corresponding to each pressure chamber 7a to 7h of the polished wafer W becomes zero. Furthermore, the past polishing pressure adjustment method does not create the above-described reaction model taking into account the change in the polishing amount between the monitoring regions Da to Dh, but rather the pressure of the compressed fluid supplied to each pressure chamber 7a to 7h is made to correspond to the polishing amount of each monitoring region Da to Dh. Thus, the next wafer W is polished with a polishing recipe that does not take into account the change in the polishing amount between the monitoring regions Da to Dh due to the change in the pressure of the compressed fluid supplied to each pressure chamber 7a to 7h.

[0238] From Figure 13 It can be seen that the in-plane uniformity of Examples 1 to 3 is greatly improved compared to the in-plane uniformity of the reference example. Thus, it can be seen that by creating the optimum polishing recipe using the above-described reaction model, correcting the reaction model, and continuously polishing the wafer W, the film thickness profile can be precisely controlled.

[0239] Further, it is known that the in-plane uniformity of Examples 2 and 3 is superior to that of Example 1. Therefore, it is known that by using a reaction model made by taking into account at least the variation of the pressure of the compressed fluid supplied to each of the pressure chambers 7a to 7h and the variation of the pressure of the compressed fluid supplied to the fixed chamber 34, the film thickness profile can be precisely controlled.

[0240] Figure 14 is a flowchart showing another embodiment of the polishing method. Since the steps of the present embodiment that are not particularly described are the same as those of the flowchart shown in Figure 5 , the repeated description thereof is omitted. Figure 14 The polishing method shown in Figure 1 may require a large amount of data processing, and therefore, it is preferable to be performed by a polishing apparatus having a control device 30 connected to an arithmetic device 70 (see the broken line in Figure 14 ). Thus, in the following description, a method of polishing a wafer W using the arithmetic device 70 and the control device 30 is described. However, when the control device 30 has sufficient data processing capacity, the polishing method shown in may be executed by the control device 30 alone without passing through the arithmetic device 70. In this case, "arithmetic device 70" described below is appropriately rewritten as "control device 30".

[0241] Figure 14 As shown in Figure 14 , in the present embodiment, first, a plurality of film thickness profiles before polishing of wafers W and reaction models are collected and stored in a memory (not shown) provided in the arithmetic device 70 (see Step 1 in Figure 14 ). Further, the arithmetic device 70 classifies the plurality of film thickness profiles before polishing into a plurality of groups to which film thickness profiles similar to each other belong (see Step 2 in ). The film thickness profile before polishing of a wafer W and the reaction model are associated with the group to which the wafer W belongs.

[0242] The control device 30 transmits the film thickness profile before and after polishing of a wafer W and the optimum polishing recipe for polishing the wafer W to the arithmetic device 70 each time the polishing of the wafer W is performed. The arithmetic device 70 corrects the reaction model using the film thickness profile before and after polishing and the optimum polishing recipe each time the combination of the film thickness profile before and after polishing and the optimum polishing recipe of the wafer W is sent from the control device 30. Further, the arithmetic device 70 stores the combination of the film thickness profile before polishing of the wafer W and the corrected reaction model in one of the plurality of groups.

[0243] When classifying the film thickness profiles before polishing, for example, a shape coincidence index obtained by calculation can be used. The shape coincidence index is, for example, an absolute average, a square average, an average film thickness difference, a correlation coefficient, or a GOF (Good of Fitting) value. The shape coincidence index is an index of the degree of coincidence (similarity) of the shapes of two film thickness profiles, and when a first film thickness profile is set as T1 to Tm, an average value of T1 to Tm is set as Tave, a second film thickness profile is set as T'1 to T'm, and an average value of T'1 to T'm is set as T'ave, the shape coincidence index can be calculated by one of the following equations (8) to (11), respectively.

[0244] [Equation 1]

[0245]

[0246] [Equation 2]

[0247]

[0248] Average film thickness difference = |Tave - T'ave|... (10)

[0249] [Equation 3]

[0250]

[0251] Further, the GOF is a generally used index showing the degree of coincidence of two profiles. The smaller the values of the absolute average, the square average, and the average film thickness difference, the higher the degree of coincidence of the shapes (the shapes are similar), and the larger the values of the correlation coefficient and the GOF, the higher the degree of coincidence of the shapes.

[0252] The arithmetic device 70 classifies the film thickness profiles using at least one of these shape coincidence indices. Specifically, the arithmetic device 70 previously calculates a representative film thickness profile of each group, calculates the shape coincidence indices of the film thickness profiles before polishing and the representative film thickness profiles of each group, and classifies the above film thickness profiles before polishing into the group having the highest degree of coincidence of the shapes exceeding a predetermined threshold value. The representative film thickness profile of each group can be, for example, an average film thickness profile obtained by averaging the film thickness values at each measurement point of the film thickness profiles classified into each group.

[0253] When there is no group having a degree of coincidence of the shapes exceeding the threshold value, that is, when there is no group to be classified according to the shape coincidence index, the arithmetic device 70 creates a new group. By this operation, a plurality of groups in which the film thickness profiles similar to each other are collected are created.

[0254] In one embodiment, a mechanical learner (no icon) is provided in the arithmetic device 70, and this mechanical learner can also be used to classify the film thickness profile of the wafer W before polishing. At this time, the film thickness profile of the wafer W before polishing is input into the mechanical learner. The mechanical learner outputs the group to which the input film thickness profile belongs. When the mechanical learner determines that there is no group to which the input film thickness profile belongs, the mechanical learner outputs an instruction for the arithmetic device 70 to create a new group.

[0255] Next, the control device 30 takes out the wafer W from the cassette loaded in the loading port 12 (see Figure 1 ), and carries it to the film thickness measurer 8, and acquires the film thickness profile of the wafer W before polishing (see Figure 14 , Step 3). This Step 3 corresponds to Step 1 of Figure 5 . Next, the control device 30 transmits the film thickness profile of the wafer W before polishing to the arithmetic device 70, and the arithmetic device 70 selects the group to which the received film thickness profile (i.e., the wafer after polishing) belongs (see Figure 14 , Step 4).

[0256] When selecting the group, the arithmetic device 70 uses the shape coincidence index described above. Specifically, the arithmetic device 70 calculates the shape coincidence index for each group using the received film thickness profile and the representative film thickness profile of each group, and selects the group having the highest shape coincidence index exceeding the threshold value as the group to which the film thickness profile belongs.

[0257] Next, the arithmetic device 70 creates the optimal polishing recipe using the reaction model of the group to which the film thickness profile belongs (see Figure 14 , Step 5). Since this Step 5 corresponds to Step 2 of Figure 5 , the description of the method of creating the optimal polishing recipe is omitted.

[0258] In Step 4, when there is no group having a shape coincidence index exceeding the threshold value, the arithmetic device 70 selects the group having the threshold value of the highest shape coincidence index, and creates the optimal polishing recipe using the reaction model of this group. Further, the arithmetic device 70 creates a new group to which this film thickness profile belongs.

[0259] Next, the arithmetic device 70 transmits the created optimal polishing recipe to the control device 30, and the control device 30 performs polishing of the wafer W in accordance with the received polishing recipe (see Figure 14 , Step 6).

[0260] Next, the control device 30 carries the wafer W after polishing to the first cleaning unit 16 and / or the second cleaning unit 18 to perform cleaning, and further carries the wafer W after cleaning to the drying unit 20 to perform drying. Further, the control device 30 carries the wafer W after polishing to the film thickness measurer 8, and acquires the film thickness profile of the wafer W after polishing (see Figure 14of Step 7) of FIG. 6. The control device 30 records the film thickness profile of the wafer W before and after polishing and the optimum polishing recipe correction reaction model associated with the group to which the film thickness profile belongs (see Figure 14 of Step 8) of FIG. 6.

[0261] Because Figure 12 the processes of Steps 9 to 12 of FIG. 6 are the same as those of Steps 6 to 9 of FIG. 5, the repeated description is omitted. Figure 5

[0262] When the present embodiment is employed, the optimum polishing model of the first wafer is created using the optimum polishing recipe and reaction model of the group having a film thickness profile similar to that of the first wafer W. Thus, the film thickness profile of the first wafer W can be precisely controlled.

[0263] Figure 15 is a schematic view showing a polishing unit of another embodiment. Because the configuration of the present embodiment not particularly described is the same as that of the embodiment described with reference to Figure 2 , the repeated description is omitted. Figure 15 The illustration of the dressing device 40 (see Figure 2 ) is omitted. The following is a description of the polishing unit 14b shown in Figure 1 . The polishing unit 14b shown in Figure 13 is an example of the polishing unit described with reference to Figure 15 . However, the polishing unit shown in may be disposed in at least one of the polishing units 14a, 14c, and 14d of the polishing device.

[0264] Figure 15 Figure 2 The configuration of the polishing unit 14b shown in is different from that of the polishing unit 14a shown in

[0265] . The polishing unit 14b is provided with a film thickness detector 52 that acquires a film thickness signal varying with the film thickness of the wafer W. The film thickness detector 52 is disposed in the polishing table 35, and acquires the film thickness signal at a plurality of measurement points in each of the plurality of monitoring regions Dl to Dm of the wafer W every time the polishing table 35 rotates once. The film thickness detector 52 is, for example, an optical detector or an eddy current detector.

[0266] With the high integration and high density of semiconductor devices, a wiring formed of a multilayer structure is formed on a wafer W. Thus, when polishing of the wafer W is performed to a desired film exposure with one polishing unit, the polishing time is long, and as a result, wafer defects are caused due to an increase in polishing temperature and accumulation of by-products on a polishing pad, or the like, or the flatness of the wafer surface is reduced. Depending on the type of film of the multilayer structure formed on the wafer W, a plurality of polishing units can also be included to perform a plurality of polishing processes. For example, a metal film of an uppermost layer of the wafer W can be polished with a first polishing unit, and a dielectric film layer formed under the metal film can be polished with a second polishing unit.

[0267] When the plurality of polishing processes are continuously performed, if the film thickness profile after polishing is obtained every time the polishing process is completed Figure 2 by the film thickness measurer 8 shown in FIG. 8, the throughput is reduced. Therefore, in the present embodiment, the film thickness profile of the wafer W before polishing and / or the film thickness profile of the wafer W after polishing are obtained by the film thickness detector 52.

[0268] Figure 16 is a flowchart showing a polishing method according to another embodiment. Since the steps of the present embodiment that are not particularly described are the same as the steps of the flowchart shown in Figure 5 , the repeated description thereof is omitted.

[0269] As shown in Figure 16 , the control device 30 first takes out the wafer W from the substrate cassette loaded in the load port 12 (refer to Figure 1 ), and carries it to the first polishing unit (for example, the polishing unit 14b) having the film thickness detector 52, and the first polishing unit polishes the wafer W according to the specified polishing recipe (refer to Step 1 of Figure 16 ). In the first polishing of the wafer W, the control device 30 monitors the film thickness of the wafer W obtained from the measurement value of the film thickness detector 52, and stops the first polishing when the film thickness reaches the specified threshold value (that is, when the thickness of the film of the uppermost layer of the wafer W reaches the specified target value).

[0270] When the first polishing of the wafer W is completed, the control device 30 supplies pure water to the polishing pad 33 on the polishing table 35, and simultaneously performs water polishing of the wafer W, and the film thickness profile of the wafer W after the first polishing is obtained by the film thickness detector 52 when the water polishing is performed (refer to Step 2 of Figure 16 ). In the water polishing, the wafer W is not substantially polished. Since the polishing liquid, polishing debris, by-products, and the like on the polishing pad 33 can be removed by the water polishing, the correct film thickness profile can be obtained even after the first polishing of the wafer W. The film thickness detector 52 functions as a film thickness measurer that obtains the film thickness profile of the wafer W before the second polishing required to make the optimum polishing recipe for the second polishing of the wafer W.

[0271] Next, the control device 30 transports the wafer W after the first polishing to a second polishing unit (for example, the polishing unit 14a) other than the first polishing unit in order to perform the second polishing of the wafer W (see step 3 of FIG. 6). At this time, the control device 30 creates a second polishing optimum plan for the wafer W based on the film thickness profile of the wafer W before the second polishing (i.e., the film thickness profile of the wafer W after the first polishing obtained by the film thickness detector 52) and the reaction model described above (see step 4 of FIG. 6). The method of creating the second polishing optimum plan is performed in the same manner as the step 2 of FIG. 5. Figure 16 Figure 16 Figure 5

[0272] Next, the control device 30 performs the second polishing of the wafer W in the second polishing unit to which the wafer W is transported in step 3 according to the second polishing optimum plan (see step 5 of FIG. 6). Next, the control device 30 transports the wafer W after the second polishing to the first cleaning unit 16 and / or the second cleaning unit 18 to perform cleaning, and further transports the wafer W after the cleaning to the drying unit 20 to dry the wafer W. Further, the control device 30 transports the wafer W after the second polishing to the film thickness measurer 8 (see step 6 of FIG. 6), and obtains the film thickness profile of the wafer W after the second polishing (see step 6 of FIG. 6). Figure 16 Figure 1 Figure 16

[0273] Next, the control device 30 transports the next wafer W to the first polishing unit, and performs the first polishing of the next wafer W (see step 7 of FIG. 6). After the first polishing of the next wafer W is completed, the control device 30 performs the water polishing of the next wafer W, and obtains the film thickness profile of the next wafer W after the first polishing by the film thickness detector 52 (see step 8 of FIG. 6). Figure 16 Figure 16

[0274] Next, the control device 30 transports the next wafer W after the first polishing to the second polishing unit in order to perform the second polishing of the next wafer W (see step 9 of FIG. 6). At this time, the control device 30 corrects the second polishing reaction model in order to create a second polishing optimum plan for the second polishing of the next wafer W (see step 9 of FIG. 6). As described in step 5 of FIG. 5, the correction of the second polishing reaction model of the next wafer W is performed based on the second polishing optimum plan of the next wafer W and the film thickness profiles before and after the second polishing. Figure 16 Figure 16 Figure 5

[0275] ​​​​​​​​​​​Specifically, the control device 30 has calculated the actual polishing amount Rac of the second polishing of the wafer W at each of the monitoring regions D1 to Dm of the wafer W from the film thickness profiles before and after the second polishing of the first-polished and second-polished wafers W, and calculated the correction coefficient K in such a manner that the predicted polishing amount R in the above formula (3) and the actual polishing amount Rac satisfy the above formula (4). Next, the control device 30 multiplies K obtained from formula (4) by the above matrix C and matrix D, and calculates and stores the reaction coefficient matrix Cadj and the corrected bias amount matrix Dadj corrected by the above formulas (5) and (6).

[0276] Next, the control device 30 calculates the second-polishing optimum plan for the next wafer W including at least the pressures of the compressed fluid supplied to each of the pressure chambers 7a to 7h and the stationary chamber 34 and the polishing time, by the above optimization calculation from the calculated Cadj, Dadj, and the target polishing amount R' of the second polishing of the next wafer W.

[0277] Next, the control device 30 polishes the next wafer W with the calculated second-polishing optimum plan (see step 12 of Figure 16 ). Next, the control device 30 conveys the second-polished next wafer W to the first cleaning unit 16 and / or the second cleaning unit 18 to clean it, and further conveys the cleaned next wafer W to the drying unit 20 to dry it. Further, the control device 30 conveys the second-polished next wafer W to the film thickness meter 8 to obtain the film thickness profile of the second-polished wafer W (see step 13 of Figure 16 ).

[0278] Further, the control device 30 repeatedly performs steps 7 to 13 of Figure 16 . That is, the control device 30 obtains the film thickness profile before the second polishing of the next wafer W using the film thickness detector 52 of the first polishing unit before the second polishing unit polishes the next wafer W. Further, the control device 30 corrects the second-polishing reaction model for polishing the next wafer W in accordance with the film thickness profiles before and after the second polishing of the next wafer W. Next, the control device 30 creates the second-polishing optimum plan for the next wafer W in accordance with the corrected reaction model. Next, the control device 30 polishes the next wafer W with the second-polishing optimum plan calculated in accordance with the corrected reaction model to obtain the film thickness profile of the second-polished next wafer W. In this way, each time the wafer W is polished, the second-polishing reaction model is corrected, and the wafer W is polished with the second-polishing optimum plan calculated in accordance with the corrected reaction model, so that the film thickness profile of the wafer W can be controlled more precisely.

[0279] With the present embodiment, even if a plurality of polishing processes are required, the throughput can be suppressed from decreasing, and the film thickness profile of the wafer W can be controlled precisely.

[0280] Figure 17 is a flowchart showing a polishing method of another embodiment. Since the steps of this embodiment not particularly mentioned are the same as those of the flowchart shown in Figure 16 , the repeated explanation thereof is omitted.

[0281] In the polishing method shown in the flowchart of Figure 17 , the control device 30 first takes out the wafer W from the cassette loaded in the loading port 12 (refer to Figure 1 ) and carries it to the film thickness measurer 8, and acquires the film thickness profile of the wafer W before the first polishing (refer to step 1 of Figure 17 ).

[0282] Next, the control device 30 creates the first polishing optimum plan for the wafer W based on the film thickness profile of the wafer W before the first polishing and the reaction model described above (refer to step 2 of Figure 17 ). The method of creating this first polishing optimum plan is performed in the same way as in step 2 of Figure 5 described above. Next, the control device 30 polishes the wafer W by the first polishing optimum plan (refer to step 3 of Figure 17 ), and carries the wafer W to the second polishing unit (for example, the polishing unit 14b) having the film thickness detector 52 (refer to step 4 of Figure 17 ).

[0283] Next, the control device 30 performs the water polishing described above before the second polishing, and acquires the film thickness profile of the wafer W after the first polishing by the film thickness detector 52 (refer to step 5 of Figure 17 ). Next, the control device 30 polishes the wafer W by the second polishing unit and according to the designated polishing plan (refer to step 6 of Figure 17 ). Next, the control device 30 carries the wafer W after the second polishing to the first cleaning unit 16 and / or the second cleaning unit 18 to clean it, and further carries the cleaned wafer W to the drying unit 20 to dry it.

[0284] Next, the control device 30 carries the next wafer W to the film thickness measurer 8, and acquires the film thickness profile of the next wafer W before the first polishing (refer to step 7 of Figure 17 ). Next, the control device 30 corrects the first polishing reaction model based on the first polishing optimum plan for the wafer W and the film thickness profiles before and after the first polishing (refer to step 8 of Figure 17 ). Next, the control device 30 creates the optimum polishing plan for the first polishing of the next wafer W using the corrected first polishing reaction model (refer to step 9 of Figure 17 ).

[0285] Next, the control device 30 performs the first grinding on the next wafer W using the optimal grinding scheme (see reference). Figure 17 Step 10), and then transfer the next wafer W after the first grinding to the second grinding unit (see step 10). Figure 17 Step 11). The second polishing unit obtains the film thickness profile of the next wafer W after the first polishing in water polishing using the film thickness detector 52 (refer to...). Figure 17 Step 12), then, the second grinding of the next wafer W is performed (refer to step 12). Figure 17 Step 13).

[0286] Furthermore, the control device 30 repeatedly performs... Figure 17 Steps 7 to 13. That is, the first grinding reaction model is corrected using the first optimal grinding scheme for the next wafer W and the film thickness profile before and after the first grinding. Before performing the first grinding on the next wafer W with the first grinding unit, the film thickness profile of the next wafer W before the first grinding is obtained using the film thickness measuring device 8. Further, the control device 30 creates a first optimal grinding scheme for grinding the next wafer W based on the corrected first grinding reaction model and the film thickness profile of the next wafer W before the first grinding. Then, the control device 30 performs the first grinding on the next wafer W using the created first optimal grinding scheme, and obtains the film thickness profile of the next wafer W after the first grinding. In this way, each time wafer W is ground, by correcting the first grinding reaction model and performing grinding with the first optimal grinding scheme calculated based on it, the film thickness profile of the next wafer W can be controlled more precisely.

[0287] Even when multiple polishing processes are required, this embodiment can still suppress the reduction in throughput and precisely control the film thickness profile of the wafer W.

[0288] Figure 18 This is the first half of a flowchart showing another embodiment of a grinding method. Figure 19 This is the latter half of a flowchart showing another embodiment of a grinding method. Because the steps of this embodiment, unless otherwise specified, are similar to... Figure 16 and Figure 17 The steps in the flowchart shown are the same, so repeated explanations are omitted. Figure 18 and Figure 19 In the grinding method shown in the flowchart, the first grinding and the second grinding are performed by a grinding unit equipped with a film thickness detector 52. Therefore, the film thickness measuring device 8 (see reference) can be omitted from the grinding apparatus. Figure 1 ).

[0289] like Figure 18 As shown, the control device 30 first loads from the loading port 12 (see reference). Figure 1) and carried to the first polishing unit having the film thickness detector 52 to perform water polishing and obtain the film thickness profile of the wafer W before the first polishing by the film thickness detector 52 (see step 3 of FIG. 8). Figure 18

[0290] Next, the control device 30 creates the first polishing optimum plan for the wafer W based on the film thickness profile before the first polishing and the above-mentioned first polishing reaction model (see step 2 of FIG. 8). The method of creating the first polishing optimum plan is performed in the same manner as the step 2 of FIG. 6. The control device 30 polishes the wafer W according to the first polishing optimum plan after the water polishing is finished (see step 3 of FIG. 8). Figure 18 Figure 5 Figure 18

[0291] Next, the control device 30 starts the water polishing again after the first polishing is finished and obtains the film thickness profile of the wafer W after the first polishing in the water polishing (see step 4 of FIG. 8). The film thickness profile obtained after the first polishing corresponds to the film thickness profile before the second polishing. Therefore, the control device 30 creates the second polishing optimum plan for the wafer W based on the film thickness profile obtained in the step 4 and the above-mentioned second polishing reaction model (see step 5 of FIG. 8) and polishes the wafer W according to the second polishing optimum plan (see step 6 of FIG. 8). Figure 18 Figure 18 Figure 18

[0292] When the second polishing is finished, the control device 30 starts the water polishing and obtains the film thickness profile of the wafer W after the second polishing in the water polishing (see step 7 of FIG. 8). Next, the control device 30 carries the next wafer W after the second polishing to the first cleaning unit 16 and / or the second cleaning unit 18 to clean and further carries the next wafer W after the cleaning to the drying unit 20 to dry. Figure 18

[0293] Next, the control device 30 carries the next wafer W to the polishing unit and obtains the film thickness profile of the next wafer W before the first polishing using the film thickness detector 52 (see step 8 of FIG. 8). Further, the control device 30 corrects the first polishing reaction model using the first polishing optimum plan for the wafer W and the film thickness profiles before and after the first polishing (see step 9 of FIG. 8) and creates the first polishing optimum plan for the first polishing of the next wafer W (see step 10 of FIG. 8). The creation of the first polishing optimum plan for the next wafer W is performed based on the corrected first polishing reaction model and the target polishing amount of the first polishing of the wafer W. Figure 19 Figure 19 Figure 19

[0294] ​​​​​​​​​​​Next, the control device 30 performs the first polishing on the next wafer W with the corrected first polishing optimum plan (see step 15 of FIG. 4). After the second polishing, the control device 30 starts the water polishing, and obtains the film thickness profile of the next wafer W after the second polishing using the film thickness detector 52 in the water polishing (see step 16 of FIG. 4). Further, the control device 30 repeatedly performs steps 8 to 16 of FIG. 4. Figure 19 Next, the control device 30 performs the first polishing on the next wafer W with the corrected first polishing optimum plan (see step 15 of FIG. 4). After the second polishing, the control device 30 starts the water polishing, and obtains the film thickness profile of the next wafer W after the second polishing using the film thickness detector 52 in the water polishing (see step 16 of FIG. 4). Further, the control device 30 repeatedly performs steps 8 to 16 of FIG. 4. Figure 19

[0295] Next, the control device 30 performs the first polishing on the next wafer W with the corrected first polishing optimum plan (see step 15 of FIG. 4). After the second polishing, the control device 30 starts the water polishing, and obtains the film thickness profile of the next wafer W after the second polishing using the film thickness detector 52 in the water polishing (see step 16 of FIG. 4). Further, the control device 30 repeatedly performs steps 8 to 16 of FIG. 4. Figure 19 Next, the control device 30 performs the first polishing on the next wafer W with the corrected first polishing optimum plan (see step 15 of FIG. 4). After the second polishing, the control device 30 starts the water polishing, and obtains the film thickness profile of the next wafer W after the second polishing using the film thickness detector 52 in the water polishing (see step 16 of FIG. 4). Further, the control device 30 repeatedly performs steps 8 to 16 of FIG. 4. Figure 19 Next, the control device 30 performs the first polishing on the next wafer W with the corrected first polishing optimum plan (see step 15 of FIG. 4). After the second polishing, the control device 30 starts the water polishing, and obtains the film thickness profile of the next wafer W after the second polishing using the film thickness detector 52 in the water polishing (see step 16 of FIG. 4). Further, the control device 30 repeatedly performs steps 8 to 16 of FIG. 4. Figure 19 Next, the control device 30 performs the first polishing on the next wafer W with the corrected first polishing optimum plan (see step 15 of FIG. 4). After the second polishing, the control device 30 starts the water polishing, and obtains the film thickness profile of the next wafer W after the second polishing using the film thickness detector 52 in the water polishing (see step 16 of FIG. 4). Further, the control device 30 repeatedly performs steps 8 to 16 of FIG. 4. Figure 19 Next, the control device 30 performs the first polishing on the next wafer W with the corrected first polishing optimum plan (see step 15 of FIG. 4). After the second polishing, the control device 30 starts the water polishing, and obtains the film thickness profile of the next wafer W after the second polishing using the film thickness detector 52 in the water polishing (see step 16 of FIG. 4). Further, the control device 30 repeatedly performs steps 8 to 16 of FIG. 4. Figure 19 Next, the control device 30 performs the first polishing on the next wafer W with the corrected first polishing optimum plan (see step 15 of FIG. 4). After the second polishing, the control device 30 starts the water polishing, and obtains the film thickness profile of the next wafer W after the second polishing using the film thickness detector 52 in the water polishing (see step 16 of FIG. 4). Further, the control device 30 repeatedly performs steps 8 to 16 of FIG. 4.

[0296] Next, the control device 30 performs the first polishing on the next wafer W with the corrected first polishing optimum plan (see step 15 of FIG. 4). After the second polishing, the control device 30 starts the water polishing, and obtains the film thickness profile of the next wafer W after the second polishing using the film thickness detector 52 in the water polishing (see step 16 of FIG. 4). Further, the control device 30 repeatedly performs steps 8 to 16 of FIG. 4. Figure 1 Next, the control device 30 performs the first polishing on the next wafer W with the corrected first polishing optimum plan (see step 15 of FIG. 4). After the second polishing, the control device 30 starts the water polishing, and obtains the film thickness profile of the next wafer W after the second polishing using the film thickness detector 52 in the water polishing (see step 16 of FIG. 4). Further, the control device 30 repeatedly performs steps 8 to 16 of FIG. 4.

[0297] The above-described embodiments are described for the purpose of enabling those having ordinary knowledge in the technical field to which the present application pertains to carry out the present application. Various modifications of the above-described embodiments can be made by those skilled in the art, and the technical idea of the present application can be applied to another embodiment. Therefore, the present application is not limited to the described embodiments, but is construed in the broadest scope defined by the claimed scope.​

Claims

1. A grinding apparatus, characterized in that, have: At least one polishing unit, the polishing unit comprising a polishing table and a substrate holding device, the polishing table being used to support a polishing pad, and the substrate holding device being used to press a substrate onto the polishing pad; A film thickness measuring device that measures the film thickness profile of the substrate; and A control device, which controls at least the operation of the grinding unit and the film thickness measuring device, The substrate holding device includes: An elastic membrane that forms multiple pressure chambers for pressing the substrate; Head body, the head body for mounting the elastic membrane; and A retaining ring, configured to surround the substrate. The control device has a pre-stored reaction model that takes into account the changes in the amount of abrasion between multiple monitoring areas of the substrate caused by pressure changes in each pressure chamber. The reaction model calculates the predicted amount of abrasion in each monitoring area. When the matrix consisting of the predicted grinding amount of each monitored area of ​​the substrate is represented by R, the grinding time of the substrate is represented by Tp, the matrix consisting of the reaction coefficient of each monitored area of ​​the substrate is represented by C, the matrix consisting of the pressure of the compressed fluid supplied to each pressure chamber is represented by X, and the matrix consisting of the deviation of each monitored area of ​​the substrate is represented by D, the reaction model is represented by the formula R=Tp•(C•X+D). The reaction coefficient is the increase in grinding rate per unit grinding pressure. The deviation is calculated in such a way that the predicted grinding amount is equal to the actual grinding amount obtained by grinding with a reference grinding scheme performed under a specified grinding pressure and a specified grinding time. The control device uses the film thickness measuring device to obtain the film thickness profile of the substrate before grinding. Furthermore, the control device grinds the substrate using an optimal grinding scheme, which is formulated based on a target grinding amount and the reaction model, and includes at least the pressure of the compressed fluid supplied to the plurality of pressure chambers and the grinding time. The target grinding amount is the difference between the film thickness profile of the substrate before grinding and the target film thickness of the substrate. Furthermore, the control device grinds the next substrate using a new optimal grinding scheme. This new optimal grinding scheme is based on a reaction model modified using the target grinding amount of the next substrate and the film thickness profile of the substrate before and after grinding to ensure that the predicted grinding amount matches the actual grinding amount. It also includes at least the pressure of the compressed fluid supplied to the plurality of pressure chambers and the grinding time. The reaction model was modified as follows: The actual grinding amount in each monitoring area of ​​the substrate is calculated based on the film thickness profile before and after grinding. When the actual grinding amount is expressed as Rac, the correction coefficient K is calculated such that the predicted grinding amount and the actual grinding amount satisfy Rac=K•R. The correction factor is multiplied by a matrix C consisting of the reaction coefficients of each monitoring area of ​​the substrate and a matrix D consisting of the deviations of each monitoring area of ​​the substrate.

2. The grinding apparatus as claimed in claim 1, characterized in that, The optimal grinding scheme is generated using optimization calculations that minimize an objective function, which includes at least a term representing the difference between the target grinding amount and the predicted grinding amount calculated using the reaction model.

3. The grinding apparatus as claimed in claim 2, characterized in that, The objective function further includes: a term representing the difference between the compressed fluid pressure of the optimal polishing scheme and a preset reference compressed fluid pressure, and / or a term representing the difference between the compressed fluid pressure of the optimal polishing scheme and the compressed fluid pressure of the optimal polishing scheme of the previously polished wafer.

4. The grinding apparatus as claimed in claim 2 or 3, characterized in that, The optimization calculation is performed using the quadratic programming method.

5. The grinding apparatus as claimed in claim 2 or 3, characterized in that, The number of the multiple monitoring areas is greater than the number of the multiple pressure chambers.

6. The grinding apparatus as claimed in claim 1, characterized in that, The reaction model is designed to account for the changes in the amount of abrasion that occurs between multiple monitoring areas of the substrate as the pressure applied by the retaining ring to the abrasion pad changes. The optimal grinding scheme also includes the pressing force of the buckle.

7. The grinding apparatus as claimed in claim 2 or 3, characterized in that, The film thickness measuring device is configured to measure the film thickness at multiple measuring points located in the multiple monitoring areas.

8. The grinding apparatus as claimed in claim 2 or 3, characterized in that, The reaction model includes a reaction coefficient that represents the increase in the grinding rate per unit grinding pressure in each of the plurality of monitoring areas.

9. The grinding apparatus as claimed in claim 2 or 3, characterized in that, It also includes multiple local load-applying devices that apply a local load to a portion of the buckle. The reaction model is further designed to account for the changes in abrasion volume between the multiple monitoring areas as the local load changes.

10. A grinding apparatus, characterized in that, have: At least one polishing unit, the polishing unit comprising a polishing table and a substrate holding device, the polishing table being used to support a polishing pad, and the substrate holding device being used to press a substrate onto the polishing pad; A film thickness measuring device that measures the film thickness profile of the substrate; and A control device, which controls at least the operation of the grinding unit and the film thickness measuring device, The substrate holding device includes: An elastic membrane that forms multiple pressure chambers for pressing the substrate; Head body, the head body for mounting the elastic membrane; and A retaining ring, configured to surround the substrate. The control device pre-stores the film thickness profiles of multiple substrates before polishing and the reaction models for polishing the multiple substrates respectively. The reaction models are constructed considering the changes in polishing amount between multiple monitoring areas of the substrates due to pressure changes in each pressure chamber. The reaction models calculate the predicted polishing amount in each monitoring area. When the matrix consisting of the predicted grinding amount of each monitored area of ​​the substrate is represented by R, the grinding time of the substrate is represented by Tp, the matrix consisting of the reaction coefficient of each monitored area of ​​the substrate is represented by C, the matrix consisting of the pressure of the compressed fluid supplied to each pressure chamber is represented by X, and the matrix consisting of the deviation of each monitored area of ​​the substrate is represented by D, the reaction model is represented by the formula R=Tp•(C•X+D). The reaction coefficient is the increase in grinding rate per unit grinding pressure. The deviation is calculated in such a way that the predicted grinding amount is equal to the actual grinding amount obtained by grinding with a reference grinding scheme performed under a specified grinding pressure and a specified grinding time. The film thickness profiles of the multiple substrates before polishing are pre-classified into multiple groups belonging to film thickness profiles that are similar to each other. The control device uses the film thickness measuring device to obtain the film thickness profile of the substrate before grinding. Furthermore, the control device determines from the plurality of groups the group to which the film thickness profile of the substrate before polishing belongs. Furthermore, the control device grinds the substrate using an optimal grinding scheme, which is formulated based on a target grinding amount and a reaction model associated with the determined set, and includes at least the pressure of the compressed fluid supplied to the plurality of pressure chambers and the grinding time. The target grinding amount is the difference between the film thickness profile of the substrate before grinding and the target film thickness of the substrate. Furthermore, the control device grinds the next substrate using a new optimal grinding scheme. This new optimal grinding scheme is based on a reaction model modified using the target grinding amount of the next substrate and the film thickness profile of the substrate before and after grinding to ensure that the predicted grinding amount matches the actual grinding amount. It also includes at least the pressure of the compressed fluid supplied to the plurality of pressure chambers and the grinding time. The reaction model was modified as follows: The actual grinding amount in each monitoring area of ​​the substrate is calculated based on the film thickness profile before and after grinding. When the actual grinding amount is expressed as Rac, the correction coefficient K is calculated such that the predicted grinding amount and the actual grinding amount satisfy Rac=K•R. The correction factor is multiplied by a matrix C consisting of the reaction coefficients of each monitoring area of ​​the substrate and a matrix D consisting of the deviations of each monitoring area of ​​the substrate.

11. A grinding apparatus, characterized in that, have: Multiple polishing units, each polishing unit including a polishing table and a substrate holding device, the polishing table for supporting a polishing pad, and the substrate holding device for pressing a substrate onto the polishing pad; and A control device, which at least controls the operation of the grinding unit, The substrate holding device includes: An elastic membrane that forms multiple pressure chambers for pressing the substrate; Head body, the head body for mounting the elastic membrane; and A retaining ring, configured to surround the substrate. The substrate is a substrate that has been polished through multiple polishing processes, including a first polishing and a second polishing performed by a polishing unit different from the polishing unit that performed the first polishing. The polishing unit performing the first polishing has a film thickness detector capable of measuring the film thickness profile of the substrate. The control device pre-stores a second polishing reaction model, which takes into account the changes in polishing amount between multiple monitoring areas of the substrate caused by pressure changes in each pressure chamber. The second polishing reaction model calculates the predicted polishing amount for the second polishing in each monitoring area. When the matrix consisting of the predicted grinding amount of each monitored area of ​​the substrate is represented by R, the grinding time of the substrate is represented by Tp, the matrix consisting of the reaction coefficient of each monitored area of ​​the substrate is represented by C, the matrix consisting of the pressure of the compressed fluid supplied to each pressure chamber is represented by X, and the matrix consisting of the deviation of each monitored area of ​​the substrate is represented by D, the second grinding reaction model is represented by the formula R=Tp•(C•X+D). The reaction coefficient is the increase in grinding rate per unit grinding pressure. The deviation is calculated in such a way that the predicted grinding amount is equal to the actual grinding amount obtained by grinding with a reference grinding scheme performed under a specified grinding pressure and a specified grinding time. After the control device performs the first grinding, it uses the film thickness detector to obtain the film thickness profile of the substrate before the second grinding. Furthermore, the control device performs a second polishing on the substrate using a second optimal polishing scheme. This second optimal polishing scheme is based on the target polishing amount of the second polishing and the second polishing reaction model, and includes at least the pressure of the compressed fluid supplied to the plurality of pressure chambers and the polishing time. The target polishing amount of the second polishing is the difference between the film thickness profile of the substrate before the second polishing and the target film thickness of the substrate for the second polishing. Furthermore, the control device performs a second polishing on the next substrate using a new second polishing optimal scheme. This new second polishing optimal scheme is based on a second polishing reaction model that is modified using the second polishing optimal scheme and the film thickness profile of the substrate before and after the second polishing to make the predicted polishing amount consistent with the actual polishing amount. It also includes at least the pressure of the compressed fluid supplied to the plurality of pressure chambers and the polishing time. The second grinding reaction model was modified as follows: The actual grinding amount in each monitoring area of ​​the substrate is calculated based on the film thickness profile before and after the second grinding of the substrate. When the actual grinding amount is expressed as Rac, the correction coefficient K is calculated such that the predicted grinding amount and the actual grinding amount satisfy Rac=K•R. The correction factor is multiplied by a matrix C consisting of the reaction coefficients of each monitoring area of ​​the substrate and a matrix D consisting of the deviations of each monitoring area of ​​the substrate.

12. A grinding apparatus, characterized in that, have: Multiple polishing units, each polishing unit including a polishing table and a substrate holding device, the polishing table being used to support a polishing pad and the substrate holding device being used to press a substrate onto the polishing pad; A film thickness measuring device that measures the film thickness profile of the substrate; and A control device, which controls at least the operation of the grinding unit and the film thickness measuring device, The substrate holding device includes: An elastic membrane that forms multiple pressure chambers for pressing the substrate; Head body, the head body for mounting the elastic membrane; and A retaining ring, configured to surround the substrate. The substrate is a substrate that has been polished through multiple polishing processes, including a first polishing and a second polishing performed by a polishing unit different from the polishing unit that performed the first polishing. The polishing unit performing the second polishing has a film thickness detector capable of measuring the film thickness profile of the substrate. The control device pre-stores a first polishing reaction model, which takes into account the changes in polishing amount between multiple monitoring areas of the substrate caused by pressure changes in each pressure chamber. The first polishing reaction model calculates the predicted polishing amount for the first polishing in each monitoring area. When the matrix consisting of the predicted grinding amount of each monitored area of ​​the substrate is represented by R, the grinding time of the substrate is represented by Tp, the matrix consisting of the reaction coefficient of each monitored area of ​​the substrate is represented by C, the matrix consisting of the pressure of the compressed fluid supplied to each pressure chamber is represented by X, and the matrix consisting of the deviation of each monitored area of ​​the substrate is represented by D, the first grinding reaction model is represented by the formula R=Tp•(C•X+D). The reaction coefficient is the increase in grinding rate per unit grinding pressure. The deviation is calculated in such a way that the predicted grinding amount is equal to the actual grinding amount obtained by grinding with a reference grinding scheme performed under a specified grinding pressure and a specified grinding time. The control device uses the film thickness measuring device to obtain the film thickness profile of the substrate before the first polishing. Furthermore, the control device performs a first polishing on the substrate using a first optimal polishing scheme. This first optimal polishing scheme is formulated based on the target polishing amount of the first polishing and the first polishing reaction model, and includes at least the pressure of the compressed fluid supplied to the plurality of pressure chambers and the polishing time. The target polishing amount of the first polishing is the difference between the film thickness profile of the substrate before the first polishing and the target film thickness of the substrate in the first polishing. After performing the first grinding, the control device transports the substrate to a grinding unit equipped with the film thickness detector, and uses the film thickness detector to obtain the film thickness profile of the substrate after the first grinding. Furthermore, the control device performs a first polishing on the next substrate using a new first polishing optimal scheme. This new first polishing optimal scheme is based on a first polishing reaction model that is modified using the first polishing optimal scheme and the film thickness profile of the substrate before and after the first polishing to make the predicted polishing amount of the first polishing consistent with the actual polishing amount. It also includes at least the pressure of the compressed fluid supplied to the plurality of pressure chambers and the polishing time. The first grinding reaction model was modified as follows: The actual grinding amount in each monitoring area of ​​the substrate is calculated based on the film thickness profile before and after the first grinding of the substrate. When the actual grinding amount is expressed as Rac, the correction coefficient K is calculated such that the predicted grinding amount and the actual grinding amount satisfy Rac=K•R. The correction factor is multiplied by a matrix C consisting of the reaction coefficients of each monitoring area of ​​the substrate and a matrix D consisting of the deviations of each monitoring area of ​​the substrate.

13. A grinding apparatus, characterized in that, have: Multiple polishing units, each polishing unit including a polishing table, a substrate holding device and a film thickness detector, wherein the polishing table is used to support the polishing pad, the substrate holding device is used to press the substrate onto the polishing pad, and the film thickness detector is capable of measuring the film thickness profile of the substrate. and A control device, which at least controls the operation of the grinding unit, The substrate holding device is equipped with: An elastic membrane that forms multiple pressure chambers for pressing the substrate; Head body, the head body for mounting the elastic membrane; and A retaining ring, configured to surround the substrate. The substrate is a substrate that has been polished through multiple polishing processes, including a first polishing and a second polishing performed by a polishing unit different from the polishing unit that performed the first polishing. The control device pre-stores a first grinding reaction model and a second grinding reaction model. These models are designed to account for the changes in grinding amount between multiple monitoring areas of the substrate caused by pressure variations in each pressure chamber. The first and second grinding reaction models respectively calculate the predicted grinding amount for the first grinding and the predicted grinding amount for the second grinding in each monitoring area. When the matrix consisting of the predicted grinding amount of each monitored area of ​​the substrate is represented as R, the grinding time of the substrate is represented as Tp, the matrix consisting of the reaction coefficient of each monitored area of ​​the substrate is represented as C, the matrix consisting of the pressure of the compressed fluid supplied to each pressure chamber is represented as X, and the matrix consisting of the deviation of each monitored area of ​​the substrate is represented as D, the first grinding reaction model and the second grinding reaction model are respectively represented by the formula R=Tp•(C•X+D). The reaction coefficient is the increase in grinding rate per unit grinding pressure. The deviation is calculated in such a way that the predicted grinding amount is equal to the actual grinding amount obtained by grinding with a reference grinding scheme performed under a specified grinding pressure and a specified grinding time. The control device transports the substrate to one of the plurality of polishing units and uses the film thickness detector to obtain the film thickness profile of the substrate before the first polishing. Furthermore, the control device performs a first polishing on the substrate using a first optimal polishing scheme. This first optimal polishing scheme is formulated based on the target polishing amount of the first polishing and the first polishing reaction model, and includes at least the pressure of the compressed fluid supplied to the plurality of pressure chambers and the polishing time. The target polishing amount of the first polishing is the difference between the film thickness profile of the substrate before the first polishing and the target film thickness of the substrate in the first polishing. Furthermore, the control device uses the film thickness detector to obtain the film thickness profile of the substrate before the second polishing. Furthermore, the control device performs a second polishing on the substrate using a second optimal polishing scheme. This second optimal polishing scheme is formulated based on the target polishing amount of the second polishing and the second polishing reaction model, and includes at least the pressure of the compressed fluid supplied to the plurality of pressure chambers and the polishing time. The target polishing amount of the second polishing is the difference between the film thickness profile of the substrate before the second polishing and the target film thickness of the substrate for the second polishing. Furthermore, the control device uses the film thickness detector to obtain the film thickness profile of the substrate after the second polishing. Furthermore, the control device performs a first polishing on the next substrate using a new first polishing optimal scheme. This new first polishing optimal scheme is based on a first polishing reaction model that is modified using the first polishing optimal scheme and the film thickness profile of the substrate before and after the first polishing to make the predicted polishing amount of the first polishing consistent with the actual polishing amount. It also includes at least the pressure of the compressed fluid supplied to the plurality of pressure chambers and the polishing time. Furthermore, the control device performs a second polishing on the next substrate using a new second polishing optimal scheme. This new second polishing optimal scheme is based on a second polishing reaction model that is modified using the second polishing optimal scheme and the film thickness profile of the substrate before and after the second polishing to make the predicted polishing amount consistent with the actual polishing amount. It also includes at least the pressure of the compressed fluid supplied to the plurality of pressure chambers and the polishing time. The first grinding reaction model was modified as follows: The actual grinding amount in each monitoring area of ​​the substrate is calculated based on the film thickness profile before and after the first grinding of the substrate. When the actual grinding amount is expressed as Rac, the correction coefficient K is calculated such that the predicted grinding amount and the actual grinding amount satisfy Rac=K•R. The correction factor is multiplied by a matrix C consisting of the response coefficients of each monitoring area of ​​the substrate and a matrix D consisting of the deviations of each monitoring area of ​​the substrate. The second grinding reaction model was modified as follows: The actual grinding amount in each monitoring area of ​​the substrate is calculated based on the film thickness profile before and after the second grinding of the substrate. When the actual grinding amount is expressed as Rac, the correction coefficient K is calculated such that the predicted grinding amount and the actual grinding amount satisfy Rac=K•R. The correction factor is multiplied by a matrix C consisting of the reaction coefficients of each monitoring area of ​​the substrate and a matrix D consisting of the deviations of each monitoring area of ​​the substrate.

14. A polishing method comprising pressing a substrate held in a substrate holding device against a polishing pad supported by a polishing table for polishing, the substrate holding device comprising: an elastic membrane forming a plurality of pressure chambers for pressing the substrate; a head body for mounting the elastic membrane; and a retaining ring configured to surround the substrate, the polishing method being characterized in that... The film thickness profile of the substrate before polishing was obtained using a film thickness measuring instrument. The substrate is polished using an optimal polishing scheme based on a target polishing amount and a reaction model. This optimal polishing scheme includes at least the pressure of the compressed fluid supplied to the plurality of pressure chambers and the polishing time. The target polishing amount is the difference between the film thickness profile of the substrate before polishing and the target film thickness of the substrate. The reaction model calculates the predicted polishing amount for each of the plurality of monitoring areas of the substrate. The next substrate is polished using a new optimal polishing scheme. This new optimal polishing scheme is based on a reaction model that is modified using the target polishing amount of the next substrate and the film thickness profile of the substrate before and after polishing to make the predicted polishing amount consistent with the actual polishing amount. It includes at least the pressure of the compressed fluid supplied to the plurality of pressure chambers and the polishing time. The reaction model is constructed considering the variation in abrasion amount between multiple monitoring areas of the substrate as the pressure in each pressure chamber changes. The matrix representing the predicted abrasion amount of each monitoring area of ​​the substrate is R, the abrasion time of the substrate is Tp, the matrix representing the reaction coefficients of each monitoring area of ​​the substrate is C, the matrix representing the pressure of the compressed fluid supplied to each pressure chamber is X, and the matrix representing the deviation of each monitoring area of ​​the substrate is D. The reaction model is represented by the formula R = Tp•(C•X+D). The reaction coefficient is the increase in grinding rate per unit grinding pressure. The deviation is calculated in such a way that the predicted grinding amount is equal to the actual grinding amount obtained by grinding with a reference grinding scheme performed under a specified grinding pressure and a specified grinding time. The reaction model was modified as follows: The actual grinding amount in each monitoring area of ​​the substrate is calculated based on the film thickness profile before and after grinding. When the actual grinding amount is expressed as Rac, the correction coefficient K is calculated such that the predicted grinding amount and the actual grinding amount satisfy Rac=K•R. The correction factor is multiplied by a matrix C consisting of the reaction coefficients of each monitoring area of ​​the substrate and a matrix D consisting of the deviations of each monitoring area of ​​the substrate.

15. The grinding method as described in claim 14, characterized in that, The optimal grinding scheme is generated using optimization calculations that minimize an objective function, which includes at least a term representing the difference between the target grinding amount and the predicted grinding amount calculated using the reaction model.

16. The grinding method as described in claim 15, characterized in that, The objective function further includes: a term representing the difference between the compressed fluid pressure of the optimal polishing scheme and a preset reference compressed fluid pressure, and / or a term representing the difference between the compressed fluid pressure of the optimal polishing scheme and the compressed fluid pressure of the optimal polishing scheme of the previously polished wafer.

17. The grinding method as described in claim 15 or 16, characterized in that, The optimization calculation is performed using the quadratic programming method.

18. The grinding method as claimed in claim 15 or 16, characterized in that, The number of the multiple monitoring areas is greater than the number of the multiple pressure chambers.

19. The grinding method as described in claim 14, characterized in that, The reaction model is designed to account for the changes in the amount of abrasion that occurs between multiple monitoring areas of the substrate as the pressure applied by the retaining ring to the abrasion pad changes. The optimal grinding scheme also includes the pressing force of the buckle.

20. The grinding method as described in claim 15 or 16, characterized in that, The film thickness measuring device measures the film thickness at multiple measuring points located in the multiple monitoring areas.

21. The grinding method as described in claim 15 or 16, characterized in that, The reaction model includes a reaction coefficient that represents the increase in the grinding rate per unit grinding pressure in each of the plurality of monitoring areas.

22. The grinding method as described in claim 15 or 16, characterized in that, The reaction model is further designed to account for the variation in the amount of abrasion that occurs between the multiple monitoring areas as the local load applied to a portion of the buckle by multiple local load-applying devices changes.

23. A polishing method comprising pressing a substrate held in a substrate holding device against a polishing pad supported by a polishing table for polishing, the substrate holding device comprising: an elastic membrane forming a plurality of pressure chambers for pressing the substrate; a head body for mounting the elastic membrane; and a retaining ring configured to surround the substrate, the polishing method being characterized in that... The film thickness profiles of multiple substrates before polishing and the reaction models for polishing each substrate are pre-stored. These reaction models take into account the changes in polishing amount between multiple monitoring areas of the substrate due to pressure variations in each pressure chamber. The reaction models calculate the predicted polishing amount for each monitoring area of ​​the substrate. The film thickness profiles of the multiple substrates before polishing are pre-classified into multiple groups belonging to film thickness profiles that are similar to each other. Obtain the film thickness profile of the substrate before polishing, and determine the group to which the film thickness profile belongs from the plurality of groups. The substrate is polished using an optimal polishing scheme based on a target polishing amount and a reaction model associated with the determined set of pressure chambers. This optimal polishing scheme includes at least the pressure of the compressed fluid supplied to the plurality of pressure chambers and the polishing time. The target polishing amount is the difference between the film thickness profile of the substrate before polishing and the target film thickness of the substrate. The next substrate is polished using a new optimal polishing scheme. This new optimal polishing scheme is based on a reaction model that is modified using the target polishing amount of the next substrate and the film thickness profile of the substrate before and after polishing to make the predicted polishing amount consistent with the actual polishing amount. The scheme includes at least the pressure of the compressed fluid supplied to the plurality of pressure chambers and the polishing time. The reaction model is constructed considering the variation in abrasion amount between multiple monitoring areas of the substrate as the pressure in each pressure chamber changes. The matrix representing the predicted abrasion amount of each monitoring area of ​​the substrate is R, the abrasion time of the substrate is Tp, the matrix representing the reaction coefficients of each monitoring area of ​​the substrate is C, the matrix representing the pressure of the compressed fluid supplied to each pressure chamber is X, and the matrix representing the deviation of each monitoring area of ​​the substrate is D. The reaction model is represented by the formula R = Tp•(C•X+D). The reaction coefficient is the increase in grinding rate per unit grinding pressure. The deviation is calculated in such a way that the predicted grinding amount is equal to the actual grinding amount obtained by grinding with a reference grinding scheme performed under a specified grinding pressure and a specified grinding time. The reaction model was modified as follows: The actual grinding amount in each monitoring area of ​​the substrate is calculated based on the film thickness profile before and after grinding. When the actual grinding amount is expressed as Rac, the correction coefficient K is calculated such that the predicted grinding amount and the actual grinding amount satisfy Rac=K•R. The correction factor is multiplied by a matrix C consisting of the reaction coefficients of each monitoring area of ​​the substrate and a matrix D consisting of the deviations of each monitoring area of ​​the substrate.

24. A polishing method for polishing a substrate by means of multiple polishing steps performed by a plurality of polishing units, said plurality of polishing units comprising a polishing table and a substrate holding device, the polishing table for supporting a polishing pad and the substrate holding device for pressing the substrate against the polishing pad, the polishing method being characterized in that... The substrate holding device includes: An elastic membrane that forms multiple pressure chambers for pressing the substrate; Head body, the head body for mounting the elastic membrane; and A retaining ring, configured to surround the substrate. The plurality of grinding processes include a first grinding and a second grinding, wherein the second grinding is performed in a different grinding unit than the grinding unit that performs the first grinding. The polishing unit performing the first polishing has a film thickness detector capable of measuring the film thickness profile of the substrate. A second polishing reaction model is prepared in advance. This second polishing reaction model is constructed to take into account the changes in polishing amount between multiple monitoring areas of the substrate due to pressure changes in each pressure chamber. The second polishing reaction model calculates the predicted polishing amount of the second polishing in each monitoring area. After the first polishing process, the film thickness profile of the substrate before the second polishing is obtained using the film thickness detector. The substrate is subjected to a second polishing process using a second optimal polishing scheme. This second optimal polishing scheme is based on the target polishing amount of the second polishing and the second polishing reaction model, and includes at least the pressure of the compressed fluid supplied to the plurality of pressure chambers and the polishing time. The target polishing amount of the second polishing is the difference between the film thickness profile of the substrate before the second polishing and the target film thickness of the substrate for the second polishing. A new second polishing optimal scheme is used to perform a second polishing on the next substrate. This new second polishing optimal scheme is based on a second polishing reaction model that is modified using the second polishing optimal scheme and the film thickness profile of the substrate before and after the second polishing to make the predicted polishing amount of the second polishing consistent with the actual polishing amount. The scheme includes at least the pressure of the compressed fluid supplied to the plurality of pressure chambers and the polishing time. The second polishing reaction model is constructed considering the variation in polishing amount between multiple monitoring areas of the substrate due to pressure changes in each pressure chamber. When R is represented by the matrix of predicted polishing amounts in each monitoring area of ​​the substrate, Tp is represented by the polishing time of the substrate, C is represented by the matrix of reaction coefficients in each monitoring area of ​​the substrate, X is represented by the matrix of pressures of the compressed fluid supplied to each pressure chamber, and D is represented by the matrix of deviations in each monitoring area of ​​the substrate, the second polishing reaction model is represented by the formula R = Tp•(C•X+D). The reaction coefficient is the increase in grinding rate per unit grinding pressure. The deviation is calculated in such a way that the predicted grinding amount is equal to the actual grinding amount obtained by grinding with a reference grinding scheme performed under a specified grinding pressure and a specified grinding time. The second grinding reaction model was modified as follows: The actual grinding amount in each monitoring area of ​​the substrate is calculated based on the film thickness profile before and after the second grinding of the substrate. When the actual grinding amount is expressed as Rac, the correction coefficient K is calculated such that the predicted grinding amount and the actual grinding amount satisfy Rac=K•R. The correction factor is multiplied by a matrix C consisting of the reaction coefficients of each monitoring area of ​​the substrate and a matrix D consisting of the deviations of each monitoring area of ​​the substrate.

25. A polishing method for polishing a substrate by means of multiple polishing steps performed by a plurality of polishing units, said plurality of polishing units comprising a polishing table and a substrate holding device, the polishing table for supporting a polishing pad and the substrate holding device for pressing the substrate against the polishing pad, the polishing method being characterized in that... The substrate holding device includes: An elastic membrane that forms multiple pressure chambers for pressing the substrate; Head body, the head body for mounting the elastic membrane; and A retaining ring, configured to surround the substrate. The plurality of grinding processes include a first grinding and a second grinding, wherein the second grinding is performed in a different grinding unit than the grinding unit that performs the first grinding. The polishing unit performing the second polishing has a film thickness detector capable of measuring the film thickness profile of the substrate. A first polishing reaction model is prepared in advance. This first polishing reaction model is constructed to take into account the changes in polishing amount between multiple monitoring areas of the substrate due to pressure changes in each pressure chamber. The first polishing reaction model calculates the predicted polishing amount of the first polishing in each monitoring area. The film thickness profile of the substrate before the first polishing was obtained using a film thickness measuring instrument. The substrate is subjected to a first polishing process using a first optimal polishing scheme. This first optimal polishing scheme is formulated based on the target polishing amount and the first polishing reaction model, and includes at least the pressure of the compressed fluid supplied to the plurality of pressure chambers and the polishing time. The target polishing amount is the difference between the film thickness profile of the substrate before the first polishing and the target film thickness of the substrate in the first polishing. After the first polishing process, the substrate is transferred to a polishing unit equipped with the film thickness detector. The film thickness profile of the first polished substrate is obtained using the film thickness detector. A new first polishing optimal scheme is used to perform a first polishing on the next substrate. This new first polishing optimal scheme is based on a first polishing reaction model that is modified using the first polishing optimal scheme and the film thickness profile of the substrate before and after the first polishing to make the predicted polishing amount of the first polishing consistent with the actual polishing amount. The scheme includes at least the pressure of the compressed fluid supplied to the plurality of pressure chambers and the polishing time. The first grinding reaction model is constructed considering the variation in grinding amount between multiple monitoring areas of the substrate due to pressure changes in each pressure chamber. When R is represented by the matrix of predicted grinding amounts in each monitoring area of ​​the substrate, Tp is represented by the grinding time of the substrate, C is represented by the matrix of reaction coefficients in each monitoring area of ​​the substrate, X is represented by the matrix of pressures of the compressed fluid supplied to each pressure chamber, and D is represented by the matrix of deviations in each monitoring area of ​​the substrate, the first grinding reaction model is represented by the formula R = Tp•(C•X+D). The reaction coefficient is the increase in grinding rate per unit grinding pressure. The deviation is calculated in such a way that the predicted grinding amount is equal to the actual grinding amount obtained by grinding with a reference grinding scheme performed under a specified grinding pressure and a specified grinding time. The first grinding reaction model was modified as follows: The actual grinding amount in each monitoring area of ​​the substrate is calculated based on the film thickness profile before and after the first grinding of the substrate. When the actual grinding amount is expressed as Rac, the correction coefficient K is calculated such that the predicted grinding amount and the actual grinding amount satisfy Rac=K•R. The correction factor is multiplied by a matrix C consisting of the reaction coefficients of each monitoring area of ​​the substrate and a matrix D consisting of the deviations of each monitoring area of ​​the substrate.

26. A polishing method for polishing a substrate by means of multiple polishing steps performed by a plurality of polishing units, said plurality of polishing units comprising a polishing table and a substrate holding device, the polishing table for supporting a polishing pad and the substrate holding device for pressing the substrate against the polishing pad, characterized in that... The substrate holding device includes: An elastic membrane that forms multiple pressure chambers for pressing the substrate; Head body, the head body for mounting the elastic membrane; and A retaining ring, configured to surround the substrate. The plurality of grinding processes include a first grinding and a second grinding, wherein the second grinding is performed in a different grinding unit than the grinding unit that performs the first grinding. The polishing unit performing the first polishing and the polishing unit performing the second polishing each have a film thickness detector capable of measuring the film thickness profile of the substrate. A first grinding reaction model and a second grinding reaction model are prepared in advance. These models are designed to account for the changes in grinding amount between multiple monitoring areas of the substrate caused by pressure variations in each pressure chamber. The first and second grinding reaction models respectively calculate the predicted grinding amount for the first grinding and the predicted grinding amount for the second grinding in each monitoring area. The substrate is transported to the polishing unit for the first polishing process, and the film thickness profile of the substrate before the first polishing is obtained using the film thickness detector. The substrate is subjected to a first polishing process using a first optimal polishing scheme. This first optimal polishing scheme is formulated based on the target polishing amount and the first polishing reaction model, and includes at least the pressure of the compressed fluid supplied to the plurality of pressure chambers and the polishing time. The target polishing amount is the difference between the film thickness profile of the substrate before the first polishing and the target film thickness of the substrate in the first polishing. The film thickness profile of the substrate before the second polishing is obtained using the film thickness detector. The substrate is subjected to a second polishing process using a second optimal polishing scheme. This second optimal polishing scheme is based on the target polishing amount of the second polishing and the second polishing reaction model, and includes at least the pressure of the compressed fluid supplied to the plurality of pressure chambers and the polishing time. The target polishing amount of the second polishing is the difference between the film thickness profile of the substrate before the second polishing and the target film thickness of the substrate for the second polishing. The film thickness profile of the substrate after the second polishing is obtained using the film thickness detector. A new first polishing optimal scheme is used to perform a first polishing on the next substrate. This new first polishing optimal scheme is based on a first polishing reaction model that is modified using the first polishing optimal scheme and the film thickness profile of the substrate before and after the first polishing to make the predicted polishing amount of the first polishing consistent with the actual polishing amount. The scheme includes at least the pressure of the compressed fluid supplied to the plurality of pressure chambers and the polishing time. A new second polishing optimal scheme is used to perform a second polishing on the next substrate. This new second polishing optimal scheme is based on a second polishing reaction model that is modified using the second polishing optimal scheme and the film thickness profile of the substrate before and after the second polishing to make the predicted polishing amount of the second polishing consistent with the actual polishing amount. The scheme includes at least the pressure of the compressed fluid supplied to the plurality of pressure chambers and the polishing time. The first and second grinding reaction models are respectively constructed considering the changes in grinding amount between multiple monitoring areas of the substrate due to pressure changes in each pressure chamber. When the matrix composed of the predicted grinding amount of each monitoring area of ​​the substrate is represented by R, the grinding time of the substrate is represented by Tp, the matrix composed of the reaction coefficients of each monitoring area of ​​the substrate is represented by C, the matrix composed of the pressure of the compressed fluid supplied to each pressure chamber is represented by X, and the matrix composed of the deviation of each monitoring area of ​​the substrate is represented by D, the first and second grinding reaction models are respectively represented by the formula R = Tp•(C•X+D). The reaction coefficient is the increase in grinding rate per unit grinding pressure. The deviation is calculated in such a way that the predicted grinding amount is equal to the actual grinding amount obtained by grinding with a reference grinding scheme performed under a specified grinding pressure and a specified grinding time. The first grinding reaction model was modified as follows: The actual grinding amount in each monitoring area of ​​the substrate is calculated based on the film thickness profile before and after the first grinding of the substrate. When the actual grinding amount is expressed as Rac, the correction coefficient K is calculated such that the predicted grinding amount and the actual grinding amount satisfy Rac=K•R. The correction factor is multiplied by a matrix C consisting of the response coefficients of each monitoring area of ​​the substrate and a matrix D consisting of the deviations of each monitoring area of ​​the substrate. The second grinding reaction model was modified as follows: The actual grinding amount in each monitoring area of ​​the substrate is calculated based on the film thickness profile before and after the second grinding of the substrate. When the actual grinding amount is expressed as Rac, the correction coefficient K is calculated such that the predicted grinding amount and the actual grinding amount satisfy Rac=K•R. The correction factor is multiplied by a matrix C consisting of the reaction coefficients of each monitoring area of ​​the substrate and a matrix D consisting of the deviations of each monitoring area of ​​the substrate.

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