Method for creating a responsive profile of the polishing rate of a workpiece, polishing method, and polishing apparatus.

Abstract

To provide a method capable of accurately acquiring responsiveness of a polishing rate with respect to a change of a pressure with which a workpiece such as a wafer is pushed to a polishing pad.SOLUTION: An estimated polishing rate responsiveness profile indicating distribution of responsiveness of a polishing rate with respect to a pressure change in a first pressure chamber of a polishing head 7 is created using simulation. An actual polishing rate responsiveness profile indicating distribution of responsiveness of a polishing rate with respect to a pressure change in a second pressure chamber is created using a polishing result of a workpiece. The estimated polishing rate responsiveness profile and the actual polishing rate responsiveness profile are combined, thereby creating a hybrid polishing rate responsiveness profile.SELECTED DRAWING: Figure 8

Description

Technical Field

[0001] The present invention relates to a technique for polishing workpieces such as wafers, substrates, and panels used in the manufacture of semiconductor devices, and particularly to a technique for calculating the responsiveness of a polishing rate to changes in the pressure for pressing a workpiece against a polishing pad.

Background Art

[0002] Chemical mechanical polishing (hereinafter referred to as CMP) is a process of polishing a workpiece (for example, a wafer, a substrate, or a panel) by bringing it into sliding contact with a polishing pad while supplying a polishing liquid containing abrasive grains such as silica (SiO2) onto the polishing pad. A polishing apparatus for performing this CMP includes a polishing table that supports a polishing pad having a polishing surface, and a polishing head for pressing the workpiece against the polishing pad.

[0003] The polishing head is configured to press the workpiece against the polishing pad with an elastic membrane that forms a pressure chamber. A pressurized gas is supplied into the pressure chamber, and the pressure of the gas is applied to the workpiece through the elastic membrane. Therefore, the force by which the workpiece is pressed against the polishing pad can be adjusted by the pressure in the pressure chamber.

[0004] The polishing apparatus polishes the workpiece as follows. While rotating the polishing table and the polishing pad integrally, a polishing liquid (typically a slurry) is supplied to the polishing surface of the polishing pad. The polishing head presses the surface of the workpiece against the polishing surface of the polishing pad while rotating the workpiece. The workpiece is brought into sliding contact with the polishing pad in the presence of the polishing liquid. The surface of the workpiece is polished by the chemical action of the polishing liquid and the mechanical action of the abrasive grains contained in the polishing liquid and the polishing pad.

[0005] The thickness of a workpiece gradually decreases with polishing time. The rate at which the thickness of the workpiece decreases is often expressed as the polishing rate. The polishing rate is the amount of surface material of the workpiece that is removed per unit time by polishing, and the amount of reduction is expressed as thickness. The polishing rate is also called the removal rate.

[0006] To optimize the CMP process, it is crucial to understand the responsiveness of the workpiece polishing rate to pressure changes within the polishing head's pressure chamber. Polishing rate responsiveness refers to the change in polishing rate in response to changes in unit pressure within the pressure chamber. Knowing the polishing rate responsiveness allows for polishing the workpiece at the polishing rate necessary to achieve the target profile. [Prior art documents] [Patent Documents]

[0007] [Patent Document 1] Japanese Patent Publication No. 2006-43873 [Overview of the project] [Problems that the invention aims to solve]

[0008] It is known that the polishing rate basically follows Preston's Law, as follows: Polishing rate ∝ Pressing pressure × Relative speed However, the pressing force applied to the workpiece by the elastic membrane of the polishing head is not constant within the pressing surface of the elastic membrane, and it also changes due to various factors such as temperature, polishing pad, and polishing fluid.

[0009] Therefore, the present invention provides a method for accurately obtaining the response of the polishing rate to changes in the pressure applied to a workpiece such as a wafer against a polishing pad. Furthermore, the present invention provides a polishing method for polishing a workpiece using a polishing rate response profile. and polishing equipment To provide. [Means for solving the problem]

[0010] In one embodiment, a method is provided for creating a polishing rate responsiveness profile that shows the distribution of the responsiveness of the polishing rate to pressure changes in the first pressure chamber and the second pressure chamber when a workpiece used in the manufacture of a semiconductor device is pressed against a polishing pad with an elastic film having a first pressure chamber and a second pressure chamber formed on the inside, the method comprising: creating an estimated polishing rate responsiveness profile that shows the distribution of the responsiveness of the polishing rate to pressure changes in the first pressure chamber using simulation; creating an actual polishing rate responsiveness profile that shows the distribution of the responsiveness of the polishing rate to pressure changes in the second pressure chamber using the polishing results of the workpiece; and creating a hybrid polishing rate responsiveness profile by combining the estimated polishing rate responsiveness profile and the actual polishing rate responsiveness profile.

[0011] In one embodiment, the step of creating the estimated polishing rate responsiveness profile includes: calculating by simulation a pressing pressure responsiveness profile showing the distribution of pressing pressure applied from the first workpiece to the polishing pad, which changes in response to a change in the unit pressure in the first pressure chamber; polishing the first workpiece by pressing it against the polishing pad while the first pressure chamber is maintained at a predetermined pressure; creating a polishing rate profile showing the distribution of the polishing rate of the polished first workpiece; and creating the estimated polishing rate responsiveness profile based on the pressing pressure responsiveness profile, the predetermined pressure, and the polishing rate profile. In one embodiment, the step of creating the estimated polishing rate responsiveness profile includes creating a virtual polishing rate profile by multiplying the pressing pressure responsiveness profile by the predetermined pressure and polishing rate coefficient, determining the polishing rate coefficient that minimizes the difference between the polishing rate profile and the virtual polishing rate profile, and creating the estimated polishing rate responsiveness profile by multiplying the pressing pressure responsiveness profile by the determined polishing rate coefficient.

[0012] In one embodiment, the step of calculating the pressing pressure response profile includes the steps of calculating by simulation the distribution of a first pressing pressure when a gas having a first pressure is supplied to the first pressure chamber and the distribution of a second pressing pressure when a gas having a second pressure is supplied to the first pressure chamber, and calculating the pressing pressure that has changed in response to a change in the unit pressure of the gas in the first pressure chamber by dividing the difference between the first pressing pressure and the second pressing pressure at each radial position on the first workpiece by the difference between the first pressure and the second pressure. In one embodiment, the step of creating the actual polishing rate responsiveness profile includes polishing the second workpiece by pressing it against the polishing pad while changing the pressure in the second pressure chamber, calculating a plurality of polishing rates of the second workpiece corresponding to different pressures in the second pressure chamber, and calculating the responsiveness of the polishing rate to changes in the pressure in the second pressure chamber.

[0013] In one embodiment, the steps for creating the estimated polishing rate responsiveness profile and the actual polishing rate responsiveness profile are: polishing the first workpiece by pressing it against the polishing pad while the first pressure chamber is maintained at a predetermined first pressure and the second pressure chamber is maintained at a predetermined second pressure; creating an actual polishing rate profile showing the distribution of the polishing rate of the polished first workpiece; creating a first polishing rate profile based on the first pressure, the first polishing rate coefficient, and the pressing pressure responsiveness profile calculated by simulation; creating a second polishing rate profile based on the second pressure, the second polishing rate coefficient, and a provisional polishing rate responsiveness profile created from the polishing results of the second workpiece; creating a third polishing rate profile by combining the first polishing rate profile and the second polishing rate profile; and minimizing the difference between the actual polishing rate profile and the third polishing rate profile by setting the first polishing rate coefficient and the second polishing rate coefficientThis includes determining the first polishing rate coefficient, multiplying the determined first polishing rate coefficient by the pressing pressure response profile to create the estimated polishing rate response profile, and multiplying the determined second polishing rate coefficient by the provisional polishing rate response profile to create the actual polishing rate response profile. In one embodiment, the step of calculating the pressing pressure response profile includes a step of calculating by simulation the distribution of a first pressing pressure when a gas having a third pressure is supplied to the first pressure chamber and the distribution of a second pressing pressure when a gas having a fourth pressure is supplied to the first pressure chamber, and then calculating the pressing pressure that has changed in response to a change in the unit pressure of the gas in the first pressure chamber by dividing the difference between the first pressing pressure and the second pressing pressure by the difference between the third pressure and the fourth pressure at each radial position on the first workpiece.

[0014] In one embodiment, a polishing method is provided which involves optimizing the polishing conditions of a workpiece using the hybrid polishing rate response profile created by the above method, and polishing the workpiece by pressing the workpiece against the polishing pad with the elastic film under the optimized polishing conditions. [Effects of the Invention]

[0015] According to the present invention, an accurate polishing rate responsiveness profile can be obtained from a combination of an estimated polishing rate responsiveness profile generated by simulation and an actual polishing rate responsiveness profile obtained by actual polishing. [Brief explanation of the drawing]

[0016] [Figure 1] This is a schematic diagram showing one embodiment of a polishing apparatus. [Figure 2] This is a cross-sectional view showing one embodiment of a polishing head. [Figure 3] This is a flowchart illustrating one embodiment for creating a hybrid polishing rate response profile. [Figure 4]This is a diagram for explaining one embodiment of creating a pressing pressure responsiveness profile. [Figure 5] This is a graph showing an example of a pressing pressure responsiveness profile. [Figure 6] This is a graph showing an example of an estimated polishing rate responsiveness profile calculated by simulation for all pressure chambers. [Figure 7] This is a graph showing an example of an actual polishing rate responsiveness profile for all pressure chambers calculated based on actual polishing. [Figure 8] This is a graph showing an example of a hybrid polishing rate responsiveness profile composed of a combination of an estimated polishing rate responsiveness profile and an actual polishing rate responsiveness profile. [Figure 9] This is a part of a flowchart for explaining another embodiment of creating a hybrid polishing rate responsiveness profile. [Figure 10] This is another part of the above flowchart.

Embodiments for Carrying Out the Invention

[0017] Hereinafter, embodiments of the present invention will be described with reference to the drawings. FIG. 1 is a schematic diagram showing one embodiment of a polishing apparatus. The polishing apparatus is an apparatus for chemically and mechanically polishing a wafer W, which is an example of a workpiece used in the manufacture of semiconductor devices. As shown in FIG. 1, this polishing apparatus includes a polishing table 5 that supports a polishing pad 2 having a polishing surface 2a, a polishing head 7 that presses the wafer W against the polishing surface 2a, a polishing liquid supply nozzle 8 that supplies a polishing liquid (for example, a slurry containing abrasive grains) to the polishing surface 2a, and an arithmetic system 10 that creates a polishing rate responsiveness profile described later.

[0018] The polishing head 7 is configured to hold a wafer W on its lower surface. The wafer W has a film to be polished. In the following embodiments, a wafer is used as an example of a workpiece, but the workpiece is not limited to a wafer and may be a circular substrate, rectangular substrate, panel, etc., as long as it is used in the manufacture of semiconductor devices.

[0019] The computing system 10 consists of at least one computer. The computing system 10 includes a storage device 10a that stores a program for creating a polishing rate responsiveness profile, which will be described later, and a computing device 10b that performs calculations according to the instructions contained in the program. The storage device 10a includes a main memory such as random access memory (RAM) and an auxiliary storage device such as a hard disk drive (HDD) or solid-state drive (SSD). Examples of computing devices 10b include a CPU (central processing unit) and a GPU (graphics processing unit). However, the specific configuration of the computing system 10 is not limited to these examples. The computing system 10 may be located within a polishing module, within a polishing device, within a substrate processing system including multiple polishing modules, within the management system of a factory where the polishing device is located, or outside the factory where the polishing device is located.

[0020] The polishing device further comprises a support shaft 14, a polishing head oscillating arm 16 connected to the upper end of the support shaft 14, and a polishing head shaft 18 rotatably supported at the free end of the polishing head oscillating arm 16. The polishing head 7 is fixed to the lower end of the polishing head shaft 18. A polishing head rotation mechanism (not shown) equipped with an electric motor or the like is arranged inside the polishing head oscillating arm 16. This polishing head rotation mechanism is connected to the polishing head shaft 18 and is configured to rotate the polishing head shaft 18 and the polishing head 7 in the direction indicated by the arrow.

[0021] The polishing head shaft 18 is connected to a polishing head lifting mechanism (including a ball screw mechanism, etc.) not shown. This polishing head lifting mechanism is configured to move the polishing head shaft 18 up and down relative to the polishing head swing arm 16. This up and down movement of the polishing head shaft 18 allows the polishing head 7 to move up and down relative to the polishing head swing arm 16 and the polishing table 5, as indicated by the arrows.

[0022] The polishing apparatus further includes a table rotation motor 21 that rotates the polishing pad 2 and the polishing table 5 around their respective axes. The table rotation motor 21 is located below the polishing table 5, and the polishing table 5 is connected to the table rotation motor 21 via a table axis 5a. The polishing table 5 and the polishing pad 2 are rotated by the table rotation motor 21 around the table axis 5a in the direction indicated by the arrow. The polishing pad 2 is attached to the upper surface of the polishing table 5. The exposed surface of the polishing pad 2 constitutes the polishing surface 2a for polishing the wafer W.

[0023] The wafer W is polished as follows: The wafer W is held in the polishing head 7 with its surface to be polished facing downwards. While the polishing head 7 and the polishing table 5 are rotated, a polishing liquid (for example, a slurry containing abrasive particles) is supplied from a polishing liquid supply nozzle 8 located above the polishing table 5 onto the polishing surface 2a of the polishing pad 2. The polishing pad 2 rotates integrally with the polishing table 5 around its central axis. The polishing head 7 is moved to a predetermined height by a polishing head lifting mechanism (not shown). Furthermore, while the polishing head 7 is maintained at the predetermined height, the wafer W is pressed against the polishing surface 2a of the polishing pad 2. The wafer W rotates integrally with the polishing head 7. With the polishing liquid present on the polishing surface 2a of the polishing pad 2, the wafer W is brought into sliding contact with the polishing surface 2a. The surface of the wafer W is polished by a combination of the chemical action of the polishing liquid and the mechanical action of the abrasive particles contained in the polishing liquid and the polishing pad 2.

[0024] The polishing apparatus includes a film thickness sensor 42 for measuring the film thickness of the wafer W on the polishing surface 2a. The film thickness sensor 42 is configured to generate a polishing index value that directly or indirectly indicates the film thickness of the wafer W. This polishing index value changes according to the film thickness of the wafer W, and thus indicates the film thickness of the wafer W. The polishing index value may be a value that represents the film thickness of the wafer W itself, or it may be a physical quantity or signal value before it is converted to film thickness.

[0025] Examples of film thickness sensors 42 include optical film thickness sensors and eddy current sensors. An optical film thickness sensor is configured to irradiate the surface of a wafer W with light and determine the film thickness of the wafer W from the spectrum of the reflected light from the wafer W. An eddy current sensor is configured to induce eddy currents in a conductive film formed on a wafer W and output a signal value that changes according to the impedance of an electrical circuit including the conductive film and the coil of the eddy current sensor. Known devices can be used for optical film thickness sensors and eddy current sensors.

[0026] The film thickness sensor 42 is installed within the polishing table 5 and rotates integrally with the polishing table 5. More specifically, the film thickness sensor 42 is configured to measure the film thickness at multiple measurement points on the wafer W as it moves across the wafer W on the polishing surface 2a each time the polishing table 5 rotates. In this embodiment, the film thickness sensor 42 is positioned to measure the film thickness at multiple measurement points, including the center of the wafer W. Therefore, the multiple measurement points are aligned radially across the wafer W.

[0027] The film thickness sensor 42 is connected to the arithmetic system 10. The film thickness measurements generated by the film thickness sensor 42 are monitored by the arithmetic system 10. That is, the film thickness measurements at multiple measurement points on the wafer W are output from the film thickness sensor 42, sent to the arithmetic system 10, and stored in the storage device 10a. The arithmetic system 10 creates a film thickness profile of the wafer W based on the film thickness measurements. The film thickness profile represents the distribution of film thickness along the radial direction of the wafer W.

[0028] Next, the polishing head 7 will be described. Figure 2 is a cross-sectional view showing one embodiment of the polishing head 7. The polishing head 7 comprises a head body 31 fixed to the end of the polishing head shaft 18, an elastic membrane 34 attached to the lower part of the head body 31, and a retainer ring 32 positioned below the head body 31. The retainer ring 32 is positioned around the elastic membrane 34. This retainer ring 32 is an annular structure that holds the wafer W to prevent the wafer W from flying out of the polishing head 7 during polishing.

[0029] Four pressure chambers C1, C2, C3, and C4 are provided between the elastic membrane 34 and the head body 31. The pressure chambers C1, C2, C3, and C4 are formed by the elastic membrane 34 and the head body 31. The central pressure chamber C1 is circular, while the other pressure chambers C2, C3, and C4 are annular. These pressure chambers C1, C2, C3, and C4 are arranged concentrically.

[0030] Gas transfer lines F1, F2, F3, and F4 are connected to pressure chambers C1, C2, C3, and C4, respectively. One end of gas transfer lines F1, F2, F3, and F4 is connected to a compressed gas supply source (not shown) provided as a utility in the factory where the polishing equipment is installed. Compressed gas, such as compressed air, is supplied to pressure chambers C1, C2, C3, and C4, respectively, through gas transfer lines F1, F2, F3, and F4. The compressed gas in pressure chambers C1, C2, C3, and C4 presses the wafer W against the polishing surface 2a of the polishing pad 2 via the elastic membrane 34.

[0031] A gas transfer line F3, which communicates with the pressure chamber C3, is connected to a vacuum line (not shown), making it possible to create a vacuum within the pressure chamber C3. An opening is formed in the elastic membrane 34 that constitutes the pressure chamber C3, and by creating a vacuum in the pressure chamber C3, the wafer W is held in place by suction to the polishing head 7. Furthermore, by supplying compressed gas to the pressure chamber C3, the wafer W is released from the polishing head 7.

[0032] An annular elastic membrane 36 is positioned between the head body 31 and the retainer ring 32, and a pressure chamber C5 is formed inside this elastic membrane 36. The pressure chamber C5 is connected to the compressed gas supply source via a gas transfer line F5. Compressed gas is supplied into the pressure chamber C5 through the gas transfer line F5, and the compressed gas in the pressure chamber C5 presses the retainer ring 32 against the polishing pad 2.

[0033] Gas transfer lines F1, F2, F3, F4, and F5 extend via rotary joints 40 attached to the polishing head shaft 18. Pressure regulators R1, R2, R3, R4, and R5 are provided for each of the gas transfer lines F1, F2, F3, F4, and F5 that communicate with the pressure chambers C1, C2, C3, C4, and C5, respectively. Compressed gas from the compressed gas supply source is supplied independently into the pressure chambers C1 to C5 through pressure regulators R1 to R5. Pressure regulators R1 to R5 are configured to regulate the pressure of the compressed gas in the pressure chambers C1 to C5.

[0034] The pressure regulators R1 to R5 can independently change the internal pressure of the pressure chambers C1 to C5, thereby independently adjusting the pressing pressure on the four corresponding regions of the wafer W, namely the central portion, the inner intermediate portion, the outer intermediate portion, and the edge portion, and the pressing pressure of the retainer ring 32 on the polishing pad 2. The gas transfer lines F1, F2, F3, F4, and F5 are also connected to atmospheric release valves (not shown), respectively, making it possible to release the pressure chambers C1 to C5 to the atmosphere. In this embodiment, the elastic membrane 34 forms four pressure chambers C1 to C4, but in one embodiment, the elastic membrane 34 may form fewer than four or more pressure chambers.

[0035] Pressure regulators R1 to R5 are connected to the calculation system 10. The calculation system 10 receives measurement values ​​of the wafer W film thickness from the film thickness sensor 42 (see Figure 1), determines target pressure values ​​for pressure chambers C1 to C5 to achieve the target film thickness profile based on the measurement values, and transmits the target pressure values ​​to the pressure regulators R1 to R5. The pressure regulators R1 to R5 operate to maintain the pressure in pressure chambers C1 to C5 at the corresponding target pressure values.

[0036] The polishing head 7 can apply independent pressure to multiple regions of the wafer W. For example, the polishing head 7 can press different areas of the wafer W surface against the polishing surface 2a of the polishing pad 2 with different pressures. Therefore, the polishing head 7 can control the film thickness profile of the wafer W to achieve a target film thickness profile.

[0037] To optimize the polishing process, it is crucial to understand the responsiveness of the wafer W polishing rate to the pressure in pressure chambers C1-C4. The polishing rate is the amount of surface material removed from wafer W per unit time by polishing, and this amount is expressed as thickness. The polishing rate is also called the removal rate. The responsiveness of the polishing rate refers to the change in the polishing rate in response to a change in the unit pressure in the pressure chamber.

[0038] In the embodiment described below, the calculation system 10 creates a polishing rate responsiveness profile that shows the distribution of the polishing rate responsiveness to pressure changes in pressure chambers C1 to C4 when the wafer W is pressed against the polishing pad 2 with the elastic film 34 of the polishing head 7. More specifically, the calculation system 10 creates an estimated polishing rate responsiveness profile that shows the distribution of the polishing rate responsiveness to pressure changes in pressure chambers C1 to C3 using simulation, and creates an actual polishing rate responsiveness profile that shows the distribution of the polishing rate responsiveness to pressure changes in pressure chamber C4 using the polishing results of a wafer as a workpiece. By combining the estimated polishing rate responsiveness profile and the actual polishing rate responsiveness profile, a hybrid polishing rate responsiveness profile is created.

[0039] Specifically, for pressure chambers C1 to C3, polishing rate responsiveness profiles are created based on simulations, and for pressure chamber C4, a polishing rate responsiveness profile is created based on actual polishing results. A hybrid polishing rate responsiveness profile, which is a combination of these polishing rate responsiveness profiles, is then created. Pressure chamber C4 is the outermost pressure chamber for pressing the wafer edge against the polishing pad 2. The relationship between pressure and polishing rate in the outermost pressure chamber C4 may differ from the relationship between pressure and polishing rate in the other pressure chambers C1 to C3. Furthermore, simulating the polishing rate responsiveness profile for the outermost pressure chamber C4 is difficult, and the simulation accuracy may be low. This is because the wafer edge pressed by pressure chamber C4 comes into contact with the retainer ring during wafer polishing, and the rotating polishing pad 2 enters under the wafer from the wafer edge. Therefore, in this embodiment, for the outermost pressure chamber C4, an actual polishing rate responsiveness profile is created based on actual polishing results.

[0040] However, the pressure chamber from which the actual polishing rate responsiveness profile is created based on the actual polishing results is not limited to pressure chamber C4, but may be any of pressure chambers C1 to C4. In one embodiment, estimated polishing rate responsiveness profiles may be created by simulation for pressure chambers C2 to C4, and the actual polishing rate responsiveness profile may be created for the central pressure chamber C1 based on the actual polishing results. In another embodiment, estimated polishing rate responsiveness profiles may be created by simulation for pressure chambers C1 and C2, and the actual polishing rate responsiveness profiles may be created for pressure chambers C3 and C4 based on the actual polishing results. Even if there are three or fewer pressure chambers, or five or more, the pressure chamber from which the actual polishing rate responsiveness profile is created is not limited to the outermost pressure chamber, but may be any of the multiple pressure chambers.

[0041] The location of the computing system 10 for creating the hybrid polishing rate responsiveness profile is not particularly limited. For example, the computing system 10 may be located away from the polishing modules that perform polishing, such as the polishing table 5 and polishing head 7. The computing system 10 may be connected to the polishing modules by a communication system such as the Internet or a local area network. For example, the computing system 10 may consist of a workstation connected to the communication system, or it may consist of a combination of an edge server and a cloud server.

[0042] Figure 3 is a flowchart illustrating one embodiment for creating a hybrid polishing rate responsiveness profile. In step 101, the calculation system 10 calculates a pressure response profile by simulation, which shows the distribution of the pressing pressure applied from the wafer W1 to the polishing pad 2, as it changes in response to a change in the unit pressure in the pressure chambers C1 to C4. The simulation is performed using mathematical models of the elastic film 34 of the polishing head 7, the polishing pad 2, and the wafer. Therefore, the simulation results reflect the shape and elasticity of the elastic film 34, the elasticity of the polishing pad 2, the stiffness of the wafer W1, etc. The simulation used is not particularly limited as long as it can calculate the intended pressure response profile, but in this embodiment, a simulation based on the finite element method is used. The simulation in this embodiment is performed under conditions where the wafer W1 and the polishing pad 2 are not rotated, but the simulation may be performed under conditions where the wafer W1 and the polishing pad 2 are rotated, just like in actual polishing.

[0043] In step 102, the polishing apparatus shown in Figure 1 actually polishes the wafer W1 by pressing it against the polishing pad 2 with the polishing head 7 while maintaining a predetermined pressure in the pressure chambers C1 to C4 of the polishing head 7. As described above, the polishing of the wafer W1 is performed by rotating the polishing table 5 and the polishing pad 2, and rotating the wafer W1 with the polishing head 7, while the polishing liquid is present on the polishing surface of the polishing pad 2, and the surface of the wafer W1 (the surface to be polished) is pressed against the polishing surface 2a with the polishing head 7.

[0044] During the polishing of wafer W1, the film thickness sensor 42 measures the film thickness at multiple measurement points on wafer W1 as it moves across the wafer W1. In this embodiment, the multiple measurement points are aligned along the radial direction of wafer W1. The measured film thickness is sent from the film thickness sensor 42 to the calculation system 10. Polishing of wafer W1 is terminated when the film thickness of wafer W1 reaches a target value. The film thickness sensor 42 continues to measure the film thickness of wafer W1 from the start to the end of polishing and transmits the measured film thickness to the calculation system 10. Step 102 may be performed before step 101.

[0045] In step 103, the computing system 10 creates a polishing rate profile that shows the distribution of polishing rates on the polished wafer W1. This polishing rate profile represents the polishing rate at each radial position on the wafer W1.

[0046] In step 104, the calculation system 10 creates an estimated polishing rate responsiveness profile based on the pressing pressure responsiveness profile calculated in step 101, the predetermined pressures in pressure chambers C1 to C4 set in step 102, and the polishing rate profile calculated in step 103. The estimated polishing rate responsiveness profile is the distribution of the responsiveness of the estimated polishing rate to pressure changes in pressure chambers C1 to C4 at multiple radial positions (i.e., multiple measurement points of film thickness) of the wafer W1.

[0047] In step 105, the polishing apparatus shown in Figure 1 maintains a constant pressure in pressure chambers C1 to C3 of the polishing head 7, while changing the pressure in pressure chamber C4, and polishes the wafer W2 by pressing it against the polishing pad 2 with the polishing head 7. As described above, the polishing of the wafer W2 is performed by rotating the polishing table 5 and the polishing pad 2, and rotating the wafer W2 with the polishing head 7, while the polishing liquid is present on the polishing surface of the polishing pad 2, and the surface of the wafer W2 (the surface to be polished) is pressed against the polishing surface 2a with the polishing head 7.

[0048] During the polishing of wafer W2, the film thickness sensor 42 measures the film thickness at multiple measurement points on wafer W2 as it moves across the wafer W2. In this embodiment, the multiple measurement points are aligned along the radial direction of wafer W2. The measured film thickness is sent from the film thickness sensor 42 to the calculation system 10. Polishing of wafer W2 is terminated when the film thickness of wafer W2 reaches a target value. The film thickness sensor 42 continues to measure the film thickness of wafer W2 from the start to the end of polishing and transmits the measured film thickness to the calculation system 10.

[0049] In step 106, the calculation system 10 calculates multiple polishing rates for the wafer W2 corresponding to different pressures in the pressure chamber C4 from the film thickness measurements and calculates the responsiveness of the polishing rate to changes in pressure in the pressure chamber C4. In step 107, the calculation system 10 creates an actual polishing rate responsiveness profile from the polishing rate responsiveness for pressure chamber C4 calculated in step 106. In one embodiment, steps 105-107 may be performed before steps 101-104.

[0050] In step 108, the calculation system 10 combines the estimated polishing rate responsiveness profiles for pressure chambers C1 to C3 obtained in step 104 with the actual polishing rate responsiveness profile for pressure chamber C4 obtained in step 107 to create a hybrid polishing rate responsiveness profile. In this embodiment, the estimated polishing rate responsiveness profile for pressure chamber C4 obtained in step 104 is replaced with the actual polishing rate responsiveness profile for pressure chamber C4 obtained in step 107 to create the hybrid polishing rate responsiveness profile. Based on the hybrid polishing rate responsiveness profile, the calculation system 10 can correctly determine the pressures in pressure chambers C1 to C4 required to achieve the target film thickness profile.

[0051] The following details each of the steps mentioned above. Figure 4 illustrates one embodiment for calculating the pressing pressure response profile in step 101 shown in Figure 3. The vertical axis in Figure 4 represents the pressure applied from the wafer W1 to the polishing surface 2a of the polishing pad 2 (hereinafter referred to as pressing pressure), and the horizontal axis represents the radial position on the wafer W1. The horizontal axis in Figure 4 shows the case where the radius of the wafer W1 is 150 mm, but the radius of the wafer W1 is not limited to the example in Figure 4.

[0052] First, the distribution of the compressed pressure (indicated by the symbol CP1+) when a gas with pressure P1 is supplied into pressure chamber C1, as shown in Figure 2, is calculated by simulation. Next, the distribution of the compressed pressure (indicated by the symbol CP1-) when a gas with pressure P2 is supplied into the same pressure chamber C1 is calculated by simulation. Both pressures P1 and P2 are pre-set pressures, and pressure P1 is higher than pressure P2.

[0053] Similarly, the distribution of the compressive pressure when a gas with the above pressure P1 is supplied to pressure chamber C2 (indicated by symbol CP2+), the distribution of the compressive pressure when a gas with the above pressure P2 is supplied to pressure chamber C2 (indicated by symbol CP2-), the distribution of the compressive pressure when a gas with the above pressure P1 is supplied to pressure chamber C3 (indicated by symbol CP3+), the distribution of the compressive pressure when a gas with the above pressure P2 is supplied to pressure chamber C3 (indicated by symbol CP3-), the distribution of the compressive pressure when a gas with the above pressure P1 is supplied to pressure chamber C4 (indicated by symbol CP4+), and the distribution of the compressive pressure when a gas with the above pressure P2 is supplied to pressure chamber C4 (indicated by symbol CP4-) are calculated by simulation.

[0054] Next, the calculation system 10 calculates the pressure that has changed in response to the change in the unit pressure of the gas in the pressure chamber C1 by dividing the difference between the pressing pressure CP1+ and the pressing pressure CP1- at each radial position on the wafer W1 by the difference between the pressure P1 and the pressure P2. Similarly, the calculation system 10 calculates the pressure that has changed in response to the change in the unit pressure of the gas in pressure chamber C2 by dividing the difference between the pressing pressure CP2+ and the pressing pressure CP2- at each radial position on the wafer W1 by the difference between the pressures P1 and P2; calculates the pressure that has changed in response to the change in the unit pressure of the gas in pressure chamber C3 by dividing the difference between the pressing pressure CP3+ and the pressing pressure CP3- at each radial position on the wafer W1 by the difference between the pressures P1 and P2; and calculates the pressure that has changed in response to the change in the unit pressure of the gas in pressure chamber C4 by dividing the difference between the pressing pressure CP4+ and the pressing pressure CP4- at each radial position on the wafer W1 by the difference between the pressures P1 and P2.

[0055] Figure 5 is a graph showing an example of a compression pressure responsiveness profile. In Figure 5, the vertical axis represents the compression pressure that changes in response to a change in the unit pressure in the pressure chamber, and the horizontal axis represents the radial position on the wafer W1. In Figure 5, symbol PP1 represents the distribution of compression pressure that changes in response to a change in the unit pressure of the gas in pressure chamber C1, symbol PP2 represents the distribution of compression pressure that changes in response to a change in the unit pressure of the gas in pressure chamber C2, symbol PP3 represents the distribution of compression pressure that changes in response to a change in the unit pressure of the gas in pressure chamber C3, and symbol PP4 represents the distribution of compression pressure that changes in response to a change in the unit pressure of the gas in pressure chamber C4. In this way, the calculation system 10 creates a compression pressure responsiveness profile.

[0056] As explained with reference to Figure 4, the pressure response profile is created by running a simulation under conditions where the pressures in pressure chambers C1 to C4 are set to preset values ​​of pressure P1 and pressure P2. The pressure response profile may change depending on the pressure settings in pressure chambers C1 to C4, and furthermore, the pressure in pressure chambers C1 to C4 may also change during actual wafer polishing depending on the wafer structure and film thickness.

[0057] Therefore, in one embodiment, the calculation system 10 performs simulations multiple times with the pressures in pressure chambers C1 to C4 set to multiple different values, and further calculates (creates) a pressure response profile. For example, the calculation system 10 calculates a first pressure response profile by simulation that shows the distribution of pressure that changes in response to the change from pressure P1 to pressure P2 in pressure chambers C1 to C4, and then calculates a second pressure response profile by simulation that shows the distribution of pressure that changes in response to the change from pressure P3 to pressure P4 in pressure chambers C1 to C4, thereby creating multiple pressure response profiles. Pressures P3 and P4 are different from pressures P1 and P2.

[0058] Furthermore, the calculation system 10 may create new pressure response profiles by interpolation or extrapolation using multiple pressure response profiles calculated by simulation. In one embodiment, the calculation system 10 may create further pressure response profiles by inputting multiple pressure response profiles created by simulation into a model constructed by machine learning and outputting new pressure response profiles from the model. Multiple pressure response profiles thus created are stored in the memory device 10a of the calculation system 10. The calculation system 10 uses one of the multiple pressure response profiles to create an estimated polishing rate response profile in step 104 above.

[0059] The embodiments described above relate to the pressure applied by the elastic film 34 of the polishing head 7 to press the wafer W1 against the polishing pad 2, but the pressure applied by the retainer ring 32 of the polishing head 7 to press the polishing pad 2 may also be included in the pressure response profile. That is, the simulation may be performed using mathematical models of the elastic film 34 of the polishing head 7, the polishing pad 2, the retainer ring 32, and the wafer W1.

[0060] Next, step 102 will be described in detail. In step 102, the wafer W1 is actually polished. The polishing apparatus shown in Figure 1 polishes the wafer W1 by pressing it against the polishing pad 2 with the polishing head 7 while the pressure chambers C1 to C4 of the polishing head 7 are maintained at a predetermined pressure. The pressures in the pressure chambers C1, C2, C3, and C4 of the polishing head 7 are set to predetermined pressures SP1, SP2, SP3, and SP4, respectively. In one example, the predetermined pressures SP1, SP2, SP3, and SP4 are less than or equal to the pressure P1 used in step 101, and greater than or equal to the pressure P2. The predetermined pressures SP1, SP2, SP3, and SP4 may be different from each other, or any two or all of them may be the same. Polishing of the wafer W1 is carried out at least until the film thickness of the wafer W1 reaches the target value. The film thickness sensor 42 continuously measures the film thickness of wafer W1 from the start to the end of polishing, and transmits the measured film thickness to the calculation system 10.

[0061] Next, step 103 described above will be explained in detail. In step 103, the calculation system 10 calculates multiple polishing rates at multiple measurement points by dividing the difference between the initial film thickness and the final film thickness at each of the multiple measurement points on wafer W1 corresponding to pressure chambers C1, C2, C3, and C4 by the polishing time of wafer W1. The initial film thickness is the film thickness of wafer W1 before polishing, and the final film thickness is the film thickness of wafer W1 at the end of polishing. The calculation system 10 creates a polishing rate profile by assigning the calculated multiple polishing rates to the multiple measurement points corresponding to pressure chambers C1, C2, C3, and C4.

[0062] In actual wafer polishing, the set pressures in pressure chambers C1 to C4 can vary depending on the wafer structure and film thickness. Therefore, in one embodiment, multiple polishing rate profiles may be created by polishing multiple wafers with different pressures set in pressure chambers C1 to C4. More specifically, multiple wafers are polished by pressing them one by one against the polishing pad 2 with different pressures set in pressure chambers C1 to C4 for each wafer. The computing system 10 generates multiple polishing rate profiles that show the distribution of polishing rates for the multiple polished wafers. The multiple polishing rate profiles thus created are stored in the storage device 10a of the computing system 10. The computing system 10 uses one of the multiple polishing rate profiles to create an estimated polishing rate responsiveness profile in the next step 104.

[0063] Next, step 104 described above will be explained in detail. In step 104, the arithmetic system 10 uses the following expression stored in its storage device 10a.

number

[0064] The calculation system 10 calculates a virtual polishing rate profile by multiplying the pressing pressure response profile by a candidate polishing rate coefficient F(n) and a predetermined pressure AP(n), and determines the polishing rate coefficient F(n) that minimizes the difference (absolute value) between the actual polishing rate profile and the virtual polishing rate profile, as shown in equation (1) above. A known algorithm such as an optimization method can be applied to find the polishing rate coefficient F(n) that minimizes equation (1) above.

[0065] The polishing rate coefficient F(n) is the polishing rate coefficient for the nth pressure chamber, but the same polishing rate coefficient F(n) may be used for pressure chambers C1 to C4. Alternatively, multiple polishing rate coefficients F(n) corresponding to multiple pressure chambers C1 to C4 may be used. The latter method can minimize the difference between the actual polishing rate profile and the virtual polishing rate profile shown in equation (1) above, compared to the former method.

[0066] The calculation system 10 further calculates (creates) an estimated polishing rate responsiveness profile represented by equation (2) by multiplying the pressing pressure responsiveness profile by the determined polishing rate coefficient F(n).

[0067] Next, step 105 described above will be explained in detail. In this step 105, the wafer W2 is actually polished. The polishing apparatus shown in Figure 1 polishes the wafer W2 by pressing it against the polishing pad 2 with the polishing head 7 while changing the pressure in pressure chamber C4, while maintaining a constant pressure in pressure chambers C1 to C3 of the polishing head 7. For example, with the pressure in pressure chamber C4 of the polishing head 7 maintained at a predetermined pressure TP1, the polishing head 7 presses the wafer W2 against the polishing pad 2 and polishes the wafer W2 for a predetermined first polishing time. Then, with the pressure in pressure chamber C4 of the polishing head 7 maintained at a predetermined pressure TP2, the polishing head 7 presses the wafer W2 against the polishing pad 2 and polishes the wafer W2 for a predetermined second polishing time. Pressure TP2 is different from pressure TP1. The pressure in pressure chambers C1 to C3 is constant. The film thickness sensor 42 continues to measure the film thickness at multiple measurement points on the wafer W2 corresponding to the pressure chamber C4 for at least the duration of the first polishing time and the second polishing time, and transmits the measured film thickness to the calculation system 10.

[0068] Next, step 106 described above will be explained in detail. In step 106, the calculation system 10 calculates multiple first polishing rates at multiple measurement points when polishing at pressure TP1, and multiple second polishing rates at multiple measurement points when polishing at pressure TP2, from the measured film thickness, the first polishing time, and the second polishing time. Furthermore, the calculation system 10 determines (calculates) the responsiveness of the polishing rate to changes in pressure within pressure chamber C4 by dividing the difference between the first polishing rate and the second polishing rate at each measurement point corresponding to pressure chamber C4 by the difference between pressure TP1 and pressure TP2. The calculation system 10 creates an actual polishing rate responsiveness profile by assigning the calculated polishing rate responsiveness to multiple measurement points corresponding to pressure chamber C4.

[0069] Figure 6 is a graph showing an example of the estimated polishing rate response profile calculated by simulation for all pressure chambers C1 to C4, and Figure 7 is a graph showing an example of the actual polishing rate response profile for all pressure chambers C1 to C4 calculated based on actual polishing. In Figures 6 and 7, the vertical axis represents the polishing rate that changed in response to the change in unit pressure in each pressure chamber, and the horizontal axis represents the radial position of the wafer.

[0070] In Figure 6, symbol ER1 represents the estimated polishing rate responsiveness profile for pressure chamber C1, symbol ER2 represents the estimated polishing rate responsiveness profile for pressure chamber C2, symbol ER3 represents the estimated polishing rate responsiveness profile for pressure chamber C3, and symbol ER4 represents the estimated polishing rate responsiveness profile for pressure chamber C4. In Figure 7, symbol RR1 represents the actual polishing rate responsiveness profile for pressure chamber C1, symbol RR2 represents the actual polishing rate responsiveness profile for pressure chamber C2, symbol RR3 represents the actual polishing rate responsiveness profile for pressure chamber C3, and symbol RR4 represents the actual polishing rate responsiveness profile for pressure chamber C4.

[0071] As can be seen from the comparison between Figure 6 and Figure 7, the estimated polishing rate response profiles ER1, ER2, and ER3 are similar to the actual polishing rate response profiles RR1, RR2, and RR3, but the estimated polishing rate response profile ER4 differs significantly from the actual polishing rate response profile RR4. Therefore, if estimated polishing rate response profiles are created by simulation for all pressure chambers C1 to CP4, the intended film thickness profile may not be achieved.

[0072] According to the embodiment described above, as shown in Figure 8, an accurate hybrid polishing rate responsive profile can be obtained from a combination of the estimated polishing rate responsive profiles ER1, ER2, and ER3 generated by simulation and the actual polishing rate responsive profile RR4 obtained by actual polishing.

[0073] Furthermore, by using simulation, the number of wafers (workpieces) and the working time required to obtain the polishing rate response can be reduced. Specifically, the number of wafers actually polished in step 102 can be reduced. The number of wafers actually polished in step 102 may be one or multiple, but the number of wafers required to obtain the polishing rate profile in step 102 can be less than the number of pressure chambers C1 to C3 of the polishing head 7.

[0074] The hybrid polishing rate responsiveness profile obtained as described above can be used to optimize the polishing conditions of other wafers to be polished next. In one embodiment, the calculation system 10 creates a current film thickness profile of the other wafer from film thickness measurements obtained from the film thickness sensor 42 (see Figure 1) during the polishing of the other wafer, and determines the pressure in pressure chambers C1 to C4 to minimize the difference between the current film thickness profile and the target film thickness profile, based on the hybrid polishing rate responsiveness profile. In another embodiment, the calculation system 10 creates a pre-polishing film thickness profile and a post-polishing film thickness profile of the wafer used to generate the polishing rate profile, and determines the pressure in pressure chambers C1 to C4 based on the pre-polishing film thickness profile, the post-polishing film thickness profile, the target film thickness profile, and the hybrid polishing rate responsiveness profile.

[0075] Next, other embodiments for creating hybrid polishing rate response profiles will be described. Details of these embodiments that are not specifically described are the same as those of the embodiments described above, so redundant descriptions will be omitted.

[0076] Similar to the embodiments described above, the calculation system 10 creates an estimated polishing rate responsiveness profile using simulation, which shows the distribution of the polishing rate responsiveness to pressure changes in pressure chambers C1 to C3. It also creates an actual polishing rate responsiveness profile using the polishing results of a wafer as a workpiece, which shows the distribution of the polishing rate responsiveness to pressure changes in pressure chamber C4. By combining the estimated polishing rate responsiveness profile and the actual polishing rate responsiveness profile, the calculation system 10 creates a hybrid polishing rate responsiveness profile.

[0077] Figure 9 is a flowchart illustrating an embodiment for creating a hybrid polishing rate responsiveness profile. In step 201, the wafer W3 is polished by pressing it against the polishing pad 2 with the polishing head 7 while the pressure chambers C1, C2, C3, and C4 of the polishing head 7 are maintained at predetermined pressures UP1, UP2, UP3, and UP4, respectively. The predetermined pressures UP1, UP2, UP3, and UP4 may be different from each other, or any two or all of them may be the same. As described above, the polishing of the wafer W3 is performed by rotating the polishing table 5 and the polishing pad 2, and rotating the wafer W3 with the polishing head 7, while the polishing liquid is present on the polishing surface of the polishing pad 2, and the surface of the wafer W3 (the surface to be polished) is pressed against the polishing surface 2a with the polishing head 7.

[0078] During the polishing of wafer W3, the film thickness sensor 42 measures the film thickness at multiple measurement points on wafer W3 as it moves across the wafer W3. In this embodiment, the multiple measurement points are aligned along the radial direction of wafer W3. The measured film thickness is sent from the film thickness sensor 42 to the calculation system 10. Polishing of wafer W3 is terminated when the film thickness of wafer W3 reaches a target value. The film thickness sensor 42 continues to measure the film thickness of wafer W3 from the start to the end of polishing and transmits the measured film thickness to the calculation system 10.

[0079] In step 202, the computing system 10 creates an actual polishing rate profile showing the distribution of the polishing rate of the polished wafer W3. This polishing rate profile represents the polishing rate at each radial position on the wafer W3. Step 202 is performed in the same manner as step 103 described above, so a redundant explanation is omitted.

[0080] In step 203, the calculation system 10 calculates a pressure response profile by simulation, which shows the distribution of the pressing pressure applied from the wafer W3 to the polishing pad 2, as it changes in response to the change in the unit pressure in the pressure chambers C1 to C3. This simulation is performed in the same manner as the simulation in step 101 described in the embodiments described above, so a redundant explanation is omitted. In one embodiment, step 203 may be performed before step 201.

[0081] In step 204, the calculation system 10 creates a first polishing rate profile based on the pressures UP1, UP2, and UP3 in pressure chambers C1 to C3 set in step 201, the pressing pressure response profile calculated in step 203, and the first polishing rate coefficient. The first polishing rate profile is the distribution of the polishing rate of wafer W3 for pressure chambers C1 to C3. The first polishing rate profile is expressed as follows.

number

[0082] In step 205, the polishing apparatus shown in Figure 1 maintains a constant pressure in pressure chambers C1 to C3 of the polishing head 7, while changing the pressure in pressure chamber C4, and polishes the wafer W4 by pressing it against the polishing pad 2 with the polishing head 7. As described above, the polishing of the wafer W4 is performed by rotating the polishing table 5 and the polishing pad 2, and rotating the wafer W4 with the polishing head 7, while the polishing liquid is present on the polishing surface of the polishing pad 2, and the surface of the wafer W4 (the surface to be polished) is pressed against the polishing surface 2a with the polishing head 7. Step 205 is performed in the same manner as step 105 described above, so a redundant explanation will be omitted.

[0083] During the polishing of the wafer W4, the film thickness sensor 42 measures the film thickness at multiple measurement points on the wafer W4 as it moves across the wafer W4. In this embodiment, the multiple measurement points are arranged along the radial direction of the wafer W4. The measured film thickness is sent from the film thickness sensor 42 to the calculation system 10. Polishing of the wafer W4 is terminated when the film thickness of the wafer W4 reaches a target value. The film thickness sensor 42 continues to measure the film thickness of the wafer W4 from the start to the end of polishing and transmits the measured film thickness to the calculation system 10.

[0084] In step 206, the calculation system 10 calculates multiple polishing rates for the wafer W4 corresponding to different pressures in the pressure chamber C4 from the film thickness measurements and calculates the responsiveness of the polishing rate to changes in pressure in the pressure chamber C4. In step 207, the calculation system 10 creates a provisional polishing rate responsiveness profile from the polishing rate responsiveness for pressure chamber C4 determined in step 206. Steps 206 and 207 are performed in the same manner as steps 106 and 107 described above, so a redundant explanation is omitted.

[0085] In step 208, the calculation system 10 creates a second polishing rate profile based on the pressure UP4 in the pressure chamber C4 set in step 201, the provisional polishing rate response profile for the pressure chamber C4 created in step 207, and the second polishing rate coefficient. The second polishing rate profile is the distribution of the polishing rate of the wafer W4 for the pressure chamber C4. The second polishing rate profile is expressed as follows:

number

[0086] In step 209, the calculation system 10 combines the first polishing rate profile and the second polishing rate profile to create a third polishing rate profile. The third polishing rate profile is represented as follows:

number

[0087] In step 210, the calculation system 10 determines the first polishing rate coefficient F(n) and the second polishing rate coefficient F(m) that minimize the difference (absolute value) between the actual polishing rate profile created in step 202 and the third polishing rate profile created in step 209. The difference between the actual polishing rate profile and the third polishing rate profile is expressed as follows.

number

[0088] In step 211, the calculation system 10 multiplies the determined first polishing rate coefficient F(n) by the pressure response profile Psim(n,r) to create an estimated polishing rate response profile, and multiplies the determined second polishing rate coefficient F(m) by the provisional polishing rate response profile Rreal(m,r) to create an actual polishing rate response profile. In step 212, the calculation system 10 combines the estimated polishing rate responsiveness profile and the actual polishing rate responsiveness profile created in step 210 to create a hybrid polishing rate responsiveness profile.

[0089] Steps 211 and 212 described above can be expressed by the following formula. Resp(l,r)=F(n)*Psim(n,r)+F(m)*Rreal(m,r) (7) Here, Resp(l,r) represents the polishing rate response at radial position r with respect to the l-th pressure chamber. The calculation system 10 stores the above equations (1) to (7) in its memory device 10a.

[0090] According to the embodiment described above, an accurate hybrid polishing rate responsiveness profile can be obtained from a combination of an estimated polishing rate responsiveness profile generated by simulation and an actual polishing rate responsiveness profile obtained by actual polishing. Furthermore, by using simulation, the number of wafers (workpieces) and working time required to obtain the polishing rate responsiveness can be reduced.

[0091] The hybrid polishing rate responsiveness profile obtained as described above can be used to optimize the polishing conditions of other wafers to be polished next. In one embodiment, the calculation system 10 creates a current film thickness profile of the other wafer from film thickness measurements obtained from the film thickness sensor 42 (see Figure 1) during the polishing of the other wafer, and determines the pressure in pressure chambers C1 to C4 to minimize the difference between the current film thickness profile and the target film thickness profile, based on the hybrid polishing rate responsiveness profile. In another embodiment, the calculation system 10 creates a pre-polishing film thickness profile and a post-polishing film thickness profile of the wafer used to generate the polishing rate profile, and determines the pressure in pressure chambers C1 to C4 based on the pre-polishing film thickness profile, the post-polishing film thickness profile, the target film thickness profile, and the hybrid polishing rate responsiveness profile.

[0092] In the embodiment described with reference to the flowchart in Figure 3, the step of determining the polishing rate coefficients to bring the simulation results for pressure chambers C1 to C3 closer to the actual polishing results is performed independently of the step of calculating the actual polishing rate responsiveness profile for pressure chamber C4. In contrast, in the embodiment described with reference to the flowcharts in Figures 9 and 10, the steps of determining the first and second polishing rate coefficients for pressure chambers C1 to C4 are performed according to substantially the same operations as the step of calculating the estimated polishing rate responsiveness profile for pressure chambers C1 to C3 and the step of calculating the actual polishing rate responsiveness profile for pressure chamber C4. Actual polishing results have shown that the embodiment described with reference to the flowcharts in Figures 9 and 10 can create a polishing rate responsiveness profile with higher accuracy than the embodiment described with reference to the flowchart in Figure 3.

[0093] In the embodiments described so far, hybrid polishing rate response profiles are obtained for four pressure chambers C1 to C4, but hybrid polishing rate response profiles for three or fewer pressure chambers, or five or more pressure chambers, can be obtained in the same manner.

[0094] The arithmetic system 10 operates according to instructions contained in a program electrically stored in the memory device 10a, and performs the operations of each embodiment described above. Specifically, the arithmetic system 10 creates an estimated polishing rate responsiveness profile showing the distribution of the polishing rate responsiveness to pressure changes in a first pressure chamber (e.g., pressure chamber CP1) using simulation, creates an actual polishing rate responsiveness profile showing the distribution of the polishing rate responsiveness to pressure changes in a second pressure chamber (e.g., pressure chamber CP4) using the polishing results of a workpiece, and creates a hybrid polishing rate responsiveness profile by combining the estimated polishing rate responsiveness profile and the actual polishing rate responsiveness profile.

[0095] The program for causing the arithmetic system 10 to perform the operations of each embodiment described above is recorded on a computer-readable recording medium, which is a non-temporary tangible object, and provided to the arithmetic system 10 via the recording medium. Alternatively, the program may be input to the arithmetic system 10 via a communication network such as the Internet or a local area network.

[0096] The embodiments described above are intended to enable persons with ordinary skill in the art to implement the present invention. Various modifications of the above embodiments can be made naturally by those skilled in the art, and the technical idea of ​​the present invention can be applied to other embodiments as well. Therefore, the present invention is not limited to the embodiments described, but is to be interpreted in the broadest sense according to the technical idea defined by the claims. [Explanation of Symbols]

[0097] 2 polishing pads 2a Polished surface 5 Polishing Table 5a Table axis 7 Polishing head 8. Polishing fluid supply nozzle 10 Computational Systems 10a storage device 10b Arithmetic unit 14 Spindle 16. Polishing head oscillating arm 18 Polished Head Shaft 21 Table Rotation Motor 31 Head body 32 Retainer Rings 34,36 Elastic membrane 40 Rotary Joint 42 Film Thickness Sensor C1,C2,C3,C4,C5 Pressure chamber F1, F2, F3, F4, F5 Gas Transfer Line R1, R2, R3, R4, R5 Pressure Regulators

Claims

1. A method for creating a polishing rate response profile that shows the distribution of the response of the polishing rate to pressure changes in the first and second pressure chambers when a workpiece used in the manufacture of a semiconductor device is pressed against a polishing pad with an elastic film having a first pressure chamber and a second pressure chamber formed inside, An estimated polishing rate responsiveness profile showing the distribution of the polishing rate responsiveness to pressure changes in the first pressure chamber was created using simulation. A real polishing rate response profile showing the distribution of the polishing rate response to pressure changes in the second pressure chamber is created using the polishing results of the workpiece. A method for creating a hybrid polishing rate responsive profile by combining the estimated polishing rate responsive profile and the actual polishing rate responsive profile.

2. The process of creating the estimated polishing rate response profile is as follows: A pressure response profile, which shows the distribution of the pressure applied from the first workpiece to the polishing pad, is calculated by simulation in response to a change in the unit pressure in the first pressure chamber. With the first pressure chamber maintained at a predetermined pressure, the first workpiece is pressed against the polishing pad to polish the first workpiece. A polishing rate profile is created that shows the distribution of the polishing rate of the polished first workpiece. The method according to claim 1, comprising creating an estimated polishing rate responsive profile based on the pressing pressure responsive profile, the predetermined pressure, and the polishing rate profile.

3. The process of creating the estimated polishing rate response profile is as follows: A virtual polishing rate profile is created by multiplying the aforementioned pressing pressure response profile by the predetermined pressure and polishing rate coefficient. The polishing rate coefficient that minimizes the difference between the polishing rate profile and the virtual polishing rate profile is determined. The method according to claim 2, comprising multiplying the pressing pressure response profile by the determined polishing rate coefficient to create the estimated polishing rate response profile.

4. The process of calculating the aforementioned compression pressure response profile is as follows: The distribution of the first pressing pressure when a gas with a first pressure is supplied to the first pressure chamber, and the distribution of the second pressing pressure when a gas with a second pressure is supplied to the first pressure chamber are calculated by simulation. The method according to claim 2, further comprising the step of calculating the pressure that has changed in response to a change in the unit pressure of the gas in the first pressure chamber by dividing the difference between the first and second pressing pressures at each radial position on the first workpiece by the difference between the first and second pressures.

5. The process of creating the actual polishing rate response profile is as follows: While changing the pressure in the second pressure chamber, the second workpiece is pressed against the polishing pad to polish the second workpiece. Multiple polishing rates for the second workpiece corresponding to different pressures in the second pressure chamber are calculated. The method according to claim 2, comprising calculating the responsiveness of the polishing rate to a change in pressure in the second pressure chamber.

6. The steps for creating the estimated polishing rate response profile and the actual polishing rate response profile are as follows: With the first pressure chamber maintained at a predetermined first pressure and the second pressure chamber maintained at a predetermined second pressure, the first workpiece is pressed against the polishing pad to polish the first workpiece. A real polishing rate profile is created showing the distribution of the polishing rate of the polished first workpiece. Based on the first pressure, the first polishing rate coefficient, and the pressing pressure response profile calculated by simulation, a first polishing rate profile is created. A second polishing rate profile is created based on the second pressure, the second polishing rate coefficient, and a provisional polishing rate response profile created from the polishing results of the second workpiece. A third polishing rate profile is created by combining the first polishing rate profile and the second polishing rate profile. The first and second polishing rate coefficients are determined to minimize the difference between the actual polishing rate profile and the third polishing rate profile. The determined first polishing rate coefficient is multiplied by the pressing pressure response profile to create the estimated polishing rate response profile. The method according to claim 1, comprising multiplying the provisional polishing rate responsiveness profile by the determined second polishing rate coefficient to create the actual polishing rate responsiveness profile.

7. The process of calculating the aforementioned compression pressure response profile is as follows: The distribution of the first pressing pressure when a gas with a third pressure is supplied to the first pressure chamber, and the distribution of the second pressing pressure when a gas with a fourth pressure is supplied to the first pressure chamber are calculated by simulation. The method according to claim 6, further comprising the step of calculating the pressure that has changed in response to a change in the unit pressure of the gas in the first pressure chamber by dividing the difference between the first pressing pressure and the second pressing pressure at each radial position on the first workpiece by the difference between the third pressure and the fourth pressure.

8. The polishing conditions of the workpiece are optimized using the hybrid polishing rate response profile created by the method according to any one of claims 1 to 7. A polishing method comprising polishing the workpiece by pressing the workpiece against the polishing pad with the elastic film under the optimized polishing conditions described above.

9. A polishing apparatus for polishing a workpiece, A polishing table that supports a polishing pad having a polishing surface, A polishing head that presses the workpiece against the polishing surface, The system comprises a storage device that stores a program and a arithmetic unit that performs calculations according to instructions contained in the program, The polishing head has an elastic membrane with a first pressure chamber and a second pressure chamber formed on its inside. The calculation system is configured to create a polishing rate response profile that shows the distribution of the response of the polishing rate to pressure changes in the first pressure chamber and the second pressure chamber when the workpiece is pressed against the polishing pad with the elastic membrane, The aforementioned computing system is at the same An estimated polishing rate responsiveness profile showing the distribution of the polishing rate responsiveness to pressure changes in the first pressure chamber was created using simulation. A real polishing rate response profile showing the distribution of the polishing rate response to pressure changes in the second pressure chamber is created using the polishing results of the workpiece. A polishing apparatus configured to create a hybrid polishing rate responsive profile by combining the estimated polishing rate responsive profile and the actual polishing rate responsive profile.

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