Method for creating a response profile of a polishing rate of a workpiece, polishing method, and computer-readable recording medium having a program stored thereon

Abstract

The present invention relates to techniques for calculating polishing rate responsiveness with respect to a change in the pressure with which a workpiece used for manufacturing a semiconductor device, such as a wafer, a substrate, or a panel, is pressed against a polishing pad. A method of the present invention comprises: calculating by simulation a pressing-pressure responsiveness profile indicating a distribution of pressing-pressure applied from a workpiece to a polishing pad (2) as the pressing-pressure changes in response to a change of unit pressure in a pressure chamber of a polishing head (7); polishing the workpiece by pressing the workpiece against the polishing pad with the interior of the pressure chamber maintained at a predetermined pressure; creating a polishing rate profile indicating a polishing rate distribution of the workpiece being polished; and creating a polishing rate responsiveness profile on the basis of the pressing-pressure responsiveness profile, the predetermined pressure, and the polishing rate profile.

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 more particularly to a technique for calculating the response of the removal rate to changes in the pressure pressing the workpiece against a polishing pad. [Background technology]

[0002] Chemical mechanical polishing (hereinafter referred to as CMP) is a process in which a workpiece (e.g., a wafer, substrate, or panel) is polished by sliding the workpiece against a polishing pad while supplying a polishing solution containing abrasive grains such as silica (SiO2) onto the polishing pad. A polishing apparatus for performing CMP is equipped with a polishing table that supports a polishing pad with a polishing surface, and a polishing head that presses 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. Pressurized gas is supplied into the pressure chamber, and the gas pressure is applied to the workpiece through the elastic membrane. Therefore, the force with which the workpiece is pressed against the polishing pad can be adjusted by the pressure in the pressure chamber.

[0004] A polishing apparatus polishes a workpiece as follows: A polishing liquid (typically a slurry) is supplied to the polishing surface of the polishing pad while the polishing table and polishing pad are rotated together. 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 the 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 reduced 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 important to understand the responsiveness of the workpiece removal rate to pressure changes in the polishing head's pressure chamber. Removal rate responsiveness refers to the change in removal rate in response to a unit pressure change in the pressure chamber. Knowing the removal rate responsiveness allows the workpiece to be polished at the removal rate required to achieve the target profile. [Prior art documents] [Patent documents]

[0007] [Patent Document 1] Japanese Patent Application Laid-Open No. 2006-43873 Summary of the Invention [Problem to be solved by the invention]

[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 from the elastic membrane of the polishing head is not constant across the pressing surface of the elastic membrane and changes due to various factors such as temperature, polishing pad, and polishing liquid. Conventionally, the polishing rate response is obtained by actually polishing the workpiece while increasing or decreasing the pressure in the pressure chamber using a design of experiments (DOE). However, this method requires a considerable number of workpieces and a long work time, making it a very costly process.

[0009] Therefore, the present invention provides a method for easily obtaining the responsiveness of the removal rate to changes in the pressure pressing a workpiece such as a wafer against a polishing pad. The present invention also provides a polishing method for polishing a workpiece using the removal rate response profile. Furthermore, the present invention also provides a computer-readable recording medium storing a program for causing a computer to create the removal rate response profile. [Means for solving the problem]

[0010] In one aspect, a method for creating a polishing rate response profile showing the distribution of polishing rate response to pressure changes in a pressure chamber when a workpiece used in the manufacture of semiconductor devices is pressed against a polishing pad by an elastic membrane formed inside the pressure chamber is provided, the method comprising: calculating by simulation a pressing pressure response profile showing the distribution of pressing pressure applied from the workpiece to the polishing pad, which changes in response to changes in unit pressure in the pressure chamber; polishing the workpiece by pressing the workpiece against the polishing pad while maintaining a predetermined pressure in the pressure chamber; creating a polishing rate profile showing the distribution of polishing rate of the polished workpiece; and creating the polishing rate response profile based on the pressing pressure response profile, the predetermined pressure, and the polishing rate profile.

[0011] In one embodiment, the step of creating the polishing rate response profile is a step of multiplying the pressing pressure response profile by the predetermined pressure and a polishing rate coefficient to create a virtual polishing rate profile, determining the polishing rate coefficient that minimizes the difference between the polishing rate profile and the virtual polishing rate profile, and multiplying the pressing pressure response profile by the determined polishing rate coefficient to create the polishing rate response profile. In one aspect, the pressure chamber is a plurality of pressure chambers, and the polishing rate coefficient is a plurality of polishing rate coefficients respectively corresponding to the plurality of pressure chambers. In one aspect, the method further includes determining a correction coefficient to eliminate the difference between the polishing rate profile and the virtual polishing rate profile, and the step of multiplying the pressing pressure responsive profile by the determined polishing rate coefficient to create the polishing rate responsive profile is a step of multiplying the pressing pressure responsive profile by the determined polishing rate coefficient and the correction coefficient to create the polishing rate responsive profile.

[0012] In one embodiment, the step of creating the polishing rate response profile is a step of creating a virtual polishing rate profile by adding a polishing rate offset to a value obtained by multiplying the pressing pressure response profile by the predetermined pressure and the polishing rate coefficient, determining the polishing rate coefficient and the polishing rate offset that minimize the difference between the polishing rate profile and the virtual polishing rate profile, and adding the determined polishing rate offset to a value obtained by multiplying the pressing pressure response profile by the determined polishing rate coefficient to create the polishing rate response profile. In one aspect, the pressure chamber is a plurality of pressure chambers, and the polishing rate coefficient is a plurality of polishing rate coefficients respectively corresponding to the plurality of pressure chambers. In one embodiment, the method further includes determining a correction coefficient for eliminating a difference between the polishing rate profile and the virtual polishing rate profile, and the step of creating the polishing rate response profile by multiplying the pressing pressure responsive profile by the determined polishing rate coefficient is a step of creating the polishing rate response profile by adding the determined polishing rate offset to a value obtained by multiplying the pressing pressure responsive profile by the determined polishing rate coefficient and the correction coefficient.

[0013] In one embodiment, the process of creating the pressing pressure responsiveness profile is a process of creating, by simulation, a first pressing pressure responsiveness profile that shows the distribution of the pressing pressure that changes in response to a change from a first pressure to a second pressure in the pressure chamber, creating, by simulation, a second pressing pressure responsiveness profile that shows the distribution of the pressing pressure that changes in response to a change from a third pressure to a fourth pressure in the pressure chamber, and creating the pressing pressure responsiveness profile based on the first pressing pressure responsiveness profile and the second pressing pressure responsiveness profile.

[0014] In one embodiment, the process of creating the compression pressure responsiveness profile based on the first compression pressure responsiveness profile and the second compression pressure responsiveness profile is a process of creating the compression pressure responsiveness profile by interpolation or extrapolation using the first compression pressure responsiveness profile and the second compression pressure responsiveness profile. In one embodiment, the process of creating the pressing pressure responsiveness profile based on the first pressing pressure responsiveness profile and the second pressing pressure responsiveness profile is a process of inputting the first pressing pressure responsiveness profile and the second pressing pressure responsiveness profile into a model constructed by machine learning and outputting the pressing pressure responsiveness profile from the model.

[0015] In one embodiment, the polishing rate profile is one selected from a plurality of polishing rate profiles created by polishing a plurality of workpieces, and the plurality of polishing rate profiles are obtained by polishing the plurality of workpieces by pressing the plurality of workpieces one by one against the polishing pad while setting different pressures in the pressure chamber for each of the plurality of workpieces, and generating a plurality of polishing rate profiles that indicate the distribution of the polishing rates of the polished plurality of workpieces.

[0016] In one embodiment, the method further includes optimizing polishing conditions for another workpiece using the polishing rate response profile. In one embodiment, the process of optimizing the polishing conditions for the other workpiece is a process of creating a current film thickness profile for the other workpiece while polishing the other workpiece, and determining the pressure in the pressure chamber that minimizes the difference between the current film thickness profile and a target film thickness profile based on the polishing rate response profile. In one embodiment, the process of optimizing the polishing conditions for the other workpiece is a process of creating a pre-polishing film thickness profile and a post-polishing film thickness profile for the workpiece used to generate the polishing rate profile, and determining the pressure in the pressure chamber based on the pre-polishing film thickness profile, the post-polishing film thickness profile, the target film thickness profile, and the polishing rate response profile.

[0017] In one aspect, a polishing method is provided, which includes optimizing polishing conditions for a workpiece using the polishing rate response profile created by the method, and polishing the workpiece by pressing the workpiece against the polishing pad with the elastic membrane under the optimized polishing conditions.

[0018] In one aspect, there is provided a computer-readable recording medium having stored thereon a program for causing a computer to create a polishing rate response profile that indicates the distribution of polishing rate response to pressure changes in a pressure chamber when a workpiece used in the manufacture of semiconductor devices is pressed against a polishing pad by an elastic membrane formed inside the pressure chamber, the program being configured to cause the computer to execute the steps of: calculating by simulation a pressing pressure response profile that indicates the distribution of pressing pressure applied from the workpiece to the polishing pad, which changes in response to changes in unit pressure in the pressure chamber; creating a polishing rate profile that indicates the distribution of polishing rates of the workpiece polished by pressing the workpiece against the polishing pad while the pressure chamber is maintained at a predetermined pressure; and creating the polishing rate response profile based on the pressing pressure response profile, the predetermined pressure, and the polishing rate profile. [Effects of the Invention]

[0019] According to the present invention, the polishing rate response profile can be easily obtained based on the pressing pressure response profile generated by simulation and the polishing rate profile obtained by actual polishing. [Brief explanation of the drawings]

[0020] [Figure 1] FIG. 1 is a schematic diagram illustrating an embodiment of a polishing apparatus. [Figure 2] FIG. 2 is a cross-sectional view showing one embodiment of a polishing head. [Figure 3] 10 is a flowchart illustrating an embodiment for creating a polishing rate response profile. [Figure 4] FIG. 10 illustrates one embodiment for creating a pressure response profile. [Figure 5] 10 is a graph showing an example of a pressing pressure responsiveness profile. [Figure 6]10 is a graph showing an example of a virtual polishing rate profile for each pressure chamber, a virtual polishing rate profile for all pressure chambers, and an actual polishing rate profile. [Figure 7] 10 is a flowchart illustrating an embodiment for updating a correction coefficient. DETAILED DESCRIPTION OF THE INVENTION

[0021] 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 (e.g., a slurry containing abrasive grains) to the polishing surface 2a, and a calculation system 10 that creates a polishing rate response profile, which will be described later.

[0022] 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, a rectangular substrate, a panel, or the like, as long as it is used in the manufacture of semiconductor devices.

[0023] The calculation system 10 is composed of at least one computer. The calculation system 10 includes a storage device 10a storing a program for creating a polishing rate response profile (described later) and a calculation device 10b that executes calculations according to instructions included in the program. The storage device 10a includes a main storage device such as a random access memory (RAM) and an auxiliary storage device such as a hard disk drive (HDD) or a solid state drive (SSD). Examples of the calculation device 10b include a CPU (central processing unit) and a GPU (graphics processing unit). However, the specific configuration of the calculation system 10 is not limited to these examples.

[0024] The polishing apparatus further includes a support shaft 14, a polishing head swing 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 swing 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 and the like is disposed within the polishing head swing 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.

[0025] 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. The 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 shown by the arrows.

[0026] The polishing apparatus further includes a table rotation motor 21 that rotates the polishing pad 2 and polishing table 5 around their respective axes. The table rotation motor 21 is disposed below the polishing table 5, and the polishing table 5 is connected to the table rotation motor 21 via a table shaft 5a. The polishing table 5 and polishing pad 2 are rotated by the table rotation motor 21 around the table shaft 5a in the direction indicated by the arrow. The polishing pad 2 is affixed to the upper surface of the polishing table 5. The exposed surface of the polishing pad 2 forms a polishing surface 2a that polishes the wafer W.

[0027] The wafer W is polished as follows. The wafer W is held by the polishing head 7 with its surface to be polished facing downward. While the polishing head 7 and polishing table 5 are rotating, a polishing liquid (e.g., a slurry containing abrasive grains) is supplied onto the polishing surface 2a of the polishing pad 2 from a polishing liquid supply nozzle 8 provided above the polishing table 5. 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). The polishing head 7 is then maintained at the predetermined height and presses the wafer W 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 grains contained in the polishing liquid and the polishing pad 2.

[0028] The polishing apparatus is equipped with a film thickness sensor 42 that measures 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 therefore indicates the film thickness of the wafer W. The polishing index value may be a value that represents the film thickness itself of the wafer W, or may be a physical quantity or signal value before being converted into film thickness.

[0029] Examples of the film thickness sensor 42 include an optical film thickness sensor and an eddy current sensor. The optical film thickness sensor is configured to irradiate the surface of the wafer W with light and determine the film thickness of the wafer W from the spectrum of the light reflected from the wafer W. The eddy current sensor is configured to induce eddy currents in a conductive film formed on the wafer W and output a signal value that varies according to the impedance of an electric circuit including the conductive film and a coil of the eddy current sensor. Known devices can be used for the optical film thickness sensor and eddy current sensor.

[0030] The film thickness sensor 42 is installed inside the polishing table 5 and rotates integrally with the polishing table 5. More specifically, the film thickness sensor 42 is configured to measure film thicknesses at multiple measurement points on the wafer W while crossing the wafer W on the polishing surface 2a each time the polishing table 5 makes one rotation. In this embodiment, the film thickness sensor 42 is arranged to measure film thicknesses at multiple measurement points including the center of the wafer W. Therefore, the multiple measurement points are aligned in the radial direction of the wafer W.

[0031] The film thickness sensor 42 is connected to the calculation system 10. The film thickness measurement values ​​generated by the film thickness sensor 42 are monitored by the calculation system 10. That is, the film thickness measurement values ​​at multiple measurement points on the wafer W are output from the film thickness sensor 42, sent to the calculation system 10, and stored in the storage device 10a. The calculation system 10 creates a film thickness profile of the wafer W based on the film thickness measurement values. The film thickness profile represents the film thickness distribution along the radial direction of the wafer W.

[0032] Next, the polishing head 7 will be described. Fig. 2 is a cross-sectional view showing one embodiment of the polishing head 7. The polishing head 7 includes 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 disposed below the head body 31. The retainer ring 32 is disposed around the elastic membrane 34. The retainer ring 32 is an annular structure that holds the wafer W to prevent the wafer W from jumping out of the polishing head 7 during polishing.

[0033] 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, and the other pressure chambers C2, C3, and C4 are annular. These pressure chambers C1, C2, C3, and C4 are arranged concentrically.

[0034] Gas transfer lines F1, F2, F3, and F4 are connected to the pressure chambers C1, C2, C3, and C4, respectively. One end of the 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 apparatus is installed. Compressed gas, such as compressed air, is supplied to the pressure chambers C1, C2, C3, and C4 through the gas transfer lines F1, F2, F3, and F4. The compressed gas in the 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.

[0035] The gas transfer line F3 communicating 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 film 34 that constitutes the pressure chamber C3, and by creating a vacuum within the pressure chamber C3, the wafer W is attracted and held 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.

[0036] An annular elastic membrane 36 is disposed between the head body 31 and the retaining 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 inside the pressure chamber C5 presses the retaining ring 32 against the polishing pad 2.

[0037] The gas transfer lines F1, F2, F3, F4, and F5 extend via a rotary joint 40 attached to the polishing head shaft 18. The gas transfer lines F1, F2, F3, F4, and F5, which communicate with the pressure chambers C1, C2, C3, C4, and C5, are provided with pressure regulators R1, R2, R3, R4, and R5, respectively. Compressed gas from a compressed gas supply source is supplied independently into the pressure chambers C1 to C5 through the pressure regulators R1 to R5. The pressure regulators R1 to R5 are configured to adjust the pressure of the compressed gas in the pressure chambers C1 to C5.

[0038] The pressure regulators R1 to R5 can independently change the internal pressures of the pressure chambers C1 to C5, thereby independently adjusting the pressures applied to the four corresponding regions of the wafer W, i.e., the center, inner middle, outer middle, and edge regions, and the pressure applied to the retainer ring 32 against the polishing pad 2. The gas transfer lines F1, F2, F3, F4, and F5 are also connected to atmospheric relief valves (not shown), allowing the pressure chambers C1 to C5 to be opened to the atmosphere. In this embodiment, the elastic membrane 34 forms four pressure chambers C1 to C4; however, in another embodiment, the elastic membrane 34 may form fewer or more than four pressure chambers. Only a single pressure chamber may be provided.

[0039] The pressure regulators R1 to R5 are connected to a calculation system 10. The calculation system 10 receives measurements of the film thickness of the wafer W from a film thickness sensor 42 (see FIG. 1), determines target pressure values ​​for the pressure chambers C1 to C5 to achieve a target film thickness profile based on the film thickness measurements, and transmits the target pressure values ​​to the pressure regulators R1 to R5. The pressure regulators R1 to R5 operate to maintain the pressures in the pressure chambers C1 to C5 at the corresponding target pressure values.

[0040] The polishing head 7 can apply independent pressures to multiple regions of the wafer W. For example, the polishing head 7 can press different regions of the surface of the wafer W 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.

[0041] To optimize the polishing process, it is important to understand the responsiveness of the polishing rate of the wafer W to the pressure in the pressure chambers C1 to C4. The polishing rate is the amount of surface material of the wafer W that is reduced per unit time by polishing, and the amount of reduction 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.

[0042] 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 the pressure chambers C1 to C4 when the elastic membrane 34 of the polishing head 7 presses the wafer W against the polishing pad 2.

[0043] FIG. 3 is a flowchart illustrating an embodiment for creating a polishing rate response profile. In step 1, the calculation system 10 calculates, by simulation, a pressing pressure responsiveness profile that indicates the distribution of pressing pressure applied from the wafer W to the polishing pad 2, which changes in response to changes in the unit pressure in the pressure chambers C1 to C4. The simulation is performed using mathematical models of the elastic membrane 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 membrane 34, the elasticity of the polishing pad 2, the rigidity of the wafer W, and the like. The simulation used is not particularly limited as long as it can calculate the intended pressing pressure responsiveness profile. In this embodiment, however, a simulation based on the finite element method is used. The simulation in this embodiment is performed under conditions where the wafer W and polishing pad 2 are not rotated; however, the simulation may also be performed under conditions where the wafer W and polishing pad 2 are rotated, as in actual polishing.

[0044] 1 polishes the wafer W by pressing the wafer W against the polishing pad 2 with the polishing head 7 while maintaining a predetermined pressure inside the pressure chambers C1 to C4 of the polishing head 7. As described above, the polishing of the wafer W is performed by rotating the polishing table 5 and the polishing pad 2 and rotating the wafer W with the polishing head 7, and pressing the surface of the wafer W (surface to be polished) against the polishing surface 2a with the polishing head 7 while the polishing liquid is present on the polishing surface of the polishing pad 2.

[0045] During polishing of the wafer W, the film thickness sensor 42 measures the film thickness at multiple measurement points on the wafer W while moving across the wafer W. In this embodiment, the multiple measurement points are arranged along the radial direction of the wafer W. The measured film thickness values ​​are sent from the film thickness sensor 42 to the calculation system 10. Polishing of the wafer W is terminated when the film thickness of the wafer W reaches a target value. The film thickness sensor 42 continues to measure the film thickness of the wafer W from the start to the end of polishing of the wafer W, and transmits the measured film thickness values ​​to the calculation system 10.

[0046] In step 3, the calculation system 10 creates a polishing rate profile that indicates the distribution of the polishing rate of the polished wafer W. This polishing rate profile represents the polishing rate at each position on the wafer W in the radial direction.

[0047] In step 4, the calculation system 10 creates a polishing rate response profile based on the pressing pressure response profile calculated in step 1, the predetermined pressures in the pressure chambers C1 to C4 set in step 2, and the polishing rate profile calculated in step 3. The polishing rate response profile is a distribution of polishing rate responses to pressure changes in the pressure chambers C1 to C4 at multiple radial positions on the wafer W (i.e., multiple film thickness measurement points). Based on this polishing rate response profile, the calculation system 10 can correctly set the pressures in the pressure chambers C1 to C4 to achieve the target film thickness profile.

[0048] Each of the above steps will be described in detail below. Fig. 4 is a diagram illustrating one embodiment for calculating the pressing pressure responsiveness profile of step 1 shown in Fig. 3. The vertical axis of Fig. 4 represents the pressure (hereinafter referred to as pressing pressure) applied from the wafer W to the polishing surface 2a of the polishing pad 2, and the horizontal axis represents the radial position on the wafer W. The horizontal axis of Fig. 4 represents the case where the radius of the wafer W is 150 mm, but the radius of the wafer W is not limited to the example of Fig. 4.

[0049] First, the distribution of the pressing pressure (denoted by the symbol CP1+) when gas having a first pressure is supplied into the pressure chamber C1 shown in Figure 2 is calculated by simulation. Next, the distribution of the pressing pressure (denoted by the symbol CP1-) when gas having a second pressure is supplied into the same pressure chamber C1 is calculated by simulation. The first pressure and the second pressure are both preset pressures, and the first pressure is higher than the second pressure.

[0050] Similarly, the distribution of the pressing pressure when gas having the first pressure is supplied into pressure chamber C2 (indicated by symbol CP2+), the distribution of the pressing pressure when gas having the second pressure is supplied into pressure chamber C2 (indicated by symbol CP2-), the distribution of the pressing pressure when gas having the first pressure is supplied into pressure chamber C3 (indicated by symbol CP3+), the distribution of the pressing pressure when gas having the second pressure is supplied into pressure chamber C3 (indicated by symbol CP3-), the distribution of the pressing pressure when gas having the first pressure is supplied into pressure chamber C4 (indicated by symbol CP4+), and the distribution of the pressing pressure when gas having the second pressure is supplied into pressure chamber C4 (indicated by symbol CP4-) are calculated by simulation.

[0051] Next, the calculation system 10 calculates the change in the pressing pressure in response to the change in the unit pressure of the gas in the pressure chamber C1 at each radial position on the wafer W by dividing the difference between the pressing pressure CP1+ and the pressing pressure CP1- by the difference between the first pressure and the second pressure. In a similar manner, the calculation system 10 calculates, at each radial position on the wafer W, the change in the pressing pressure in response to a change in the unit pressure of the gas in the pressure chamber C2 by dividing the difference between the pressing pressure CP2+ and the pressing pressure CP2- by the difference between the first pressure and the second pressure; at each radial position on the wafer W, the change in the pressing pressure in response to a change in the unit pressure of the gas in the pressure chamber C3 by dividing the difference between the pressing pressure CP3+ and the pressing pressure CP3- by the difference between the first pressure and the second pressure; and at each radial position on the wafer W, the change in the pressing pressure in response to a change in the unit pressure of the gas in the pressure chamber C4 by dividing the difference between the pressing pressure CP4+ and the pressing pressure CP4- by the difference between the first pressure and the second pressure.

[0052] FIG. 5 is a graph showing an example of a pressing pressure responsiveness profile. The vertical axis of FIG. 5 represents the pressing pressure that changes in response to a change in the unit pressure of the gas in the pressure chamber, and the horizontal axis represents the radial position on the wafer W. In FIG. 5, symbol PP1 represents the distribution of the pressing 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 the pressing 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 the pressing 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 the pressing pressure that changes in response to a change in the unit pressure of the gas in pressure chamber C4. In this manner, the computing system 10 creates the pressing pressure responsiveness profile.

[0053] 4, the pressing pressure responsiveness profile is created by running a simulation under conditions where the pressure chambers C1 to C4 are set to the first and second pressures, which are preset values. The pressing pressure responsiveness profile may vary depending on the pressure settings in the pressure chambers C1 to C4, and furthermore, during actual wafer polishing, the pressure in the pressure chambers C1 to C4 may vary depending on the wafer structure, film thickness, etc.

[0054] Therefore, in one embodiment, the calculation system 10 executes a simulation multiple times with the pressure in the pressure chambers C1 to C4 set to multiple different values, and further calculates (creates) a pressing pressure responsiveness profile. For example, the calculation system 10 creates multiple pressure responsiveness profiles by calculating, through simulation, a first pressing pressure responsiveness profile that indicates the distribution of pressing pressure that changes in response to a change from a first pressure to a second pressure in the pressure chambers C1 to C4, and by simulating a second pressing pressure responsiveness profile that indicates the distribution of pressing pressure that changes in response to a change from a third pressure to a fourth pressure in the pressure chambers C1 to C4. The third pressure and the fourth pressure are different from the first pressure and the second pressure.

[0055] Furthermore, the computing system 10 may further generate a new pressing pressure response profile by interpolation or extrapolation using the multiple pressing pressure response profiles calculated by simulation. In one embodiment, the computing system 10 may further generate a pressing pressure response profile by inputting the multiple pressing pressure response profiles generated by simulation into a model constructed by machine learning and outputting a new pressing pressure response profile from the model. The multiple pressing pressure response profiles generated in this manner are stored in the storage device 10a of the computing system 10. The computing system 10 generates the polishing rate response profile in step 4 above using one of the multiple pressing pressure response profiles.

[0056] Although the above-described embodiment relates to the pressure with which the elastic membrane 34 of the polishing head 7 presses the wafer W against the polishing pad 2, the pressure with which the retaining ring 32 of the polishing head 7 presses the polishing pad 2 may also be included in the pressing pressure response profile. That is, the simulation may be performed using mathematical models of the elastic membrane 34 of the polishing head 7, the polishing pad 2, the retaining ring 32, and the wafer W.

[0057] Next, step 2 will be described in detail. In step 2, the wafer W is actually polished. The polishing apparatus shown in FIG. 1 polishes the wafer W by pressing the wafer W against the polishing pad 2 using the polishing head 7 while maintaining a predetermined pressure within the pressure chambers C1 to C4 of the polishing head 7. The pressures within 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 equal to or less than the first pressure used in step 1 and equal to or greater than the second pressure. The predetermined pressures SP1, SP2, SP3, and SP4 may be different from one another, or any or all of them may be the same. The polishing of the wafer W is continued at least until the film thickness of the wafer W reaches a target value. The film thickness sensor 42 continues to measure the film thickness of the wafer W from the start to the end of polishing and transmits the measured film thickness to the calculation system 10.

[0058] Next, the above step 3 will be described in detail. In this step 3, the calculation system 10 calculates the polishing rate at the 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 the wafer W by the polishing time of the wafer W. The initial film thickness is the film thickness before polishing of the wafer W, and the final film thickness is the film thickness at the end of polishing of the wafer W. The calculation system 10 creates a polishing rate profile by assigning the calculated polishing rates to the multiple measurement points.

[0059] In actual wafer polishing, the pressures set in the pressure chambers C1 to C4 may vary depending on the wafer structure, film thickness, and the like. Therefore, in one embodiment, multiple polishing rate profiles may be created by polishing multiple wafers with different pressures set in the 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 the pressure chambers C1 to C4 for each wafer. The calculation system 10 generates multiple polishing rate profiles that indicate the distribution of the polishing rates of the polished wafers. The multiple polishing rate profiles created in this manner are stored in the storage device 10a of the calculation system 10. The calculation system 10 uses one of the multiple polishing rate profiles to create the polishing rate response profile in step 4 above.

[0060] Next, the above step 4 will be described in detail. In this step 4, the calculation system 10 uses the following formula stored in its storage device 10a.

number

[0061] The calculation system 10 calculates a virtual polishing rate profile by multiplying the pressing pressure responsiveness profile by a candidate for the 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 the above formula (1). A known algorithm such as an optimization method can be applied as an algorithm for determining the polishing rate coefficient F(n) that minimizes the above formula (1).

[0062] The polishing rate coefficient F(n) is the polishing rate coefficient for the n-th pressure chamber, but the same polishing rate coefficient F(n) may be used for all pressure chambers C1 to C4. Alternatively, multiple polishing rate coefficients F(n) corresponding to the multiple pressure chambers C1 to C4 may be used. The latter method can further minimize the difference between the actual polishing rate profile and the virtual polishing rate profile shown in the above formula (1) compared to the former method.

[0063] The calculation system 10 further multiplies the pressing pressure responsiveness profile by the determined polishing rate coefficient F(n) to calculate (create) the polishing rate responsiveness profile expressed by equation (2).

[0064] The second method of step 4 above will now be described. As indicated by Preston's law, it is known that the polishing rate tends to be proportional to the pressing pressure. In one embodiment, however, the polishing rate can be expressed as follows, including a polishing rate offset that is independent of pressure: Polishing rate = pressing pressure x polishing rate responsiveness + polishing rate offset By using polishing data of multiple (two or more) wafers polished in advance, it is possible to derive both the optimum polishing rate response and the optimum polishing rate offset. Here, it is preferable to obtain the polishing data of the multiple wafers at different pressing pressures.

[0065] In this second method of step 4, the computing system 10 uses the following formula stored in its storage device 10a:

number

[0066] In this second method as well, the number of wafers required to obtain the polishing rate profile in step 2 can be set to be smaller than the total number of pressure chambers C1 to C4 of the polishing head .

[0067] The calculation system 10 multiplies the pressing pressure responsiveness profile by candidates for the polishing rate coefficient F(n) and a predetermined pressure AP(n), and further adds candidates for the polishing rate offset Offset(r) to calculate a virtual polishing rate profile, thereby determining the polishing rate coefficient F(n) and the polishing rate offset Offset(r) that minimize the difference (absolute value) between the actual polishing rate profile and the virtual polishing rate profile, as shown in the above formula (1'). A known algorithm such as an optimization method can be applied as the algorithm for determining the polishing rate coefficient F(n) and the polishing rate offset Offset(r) that minimize the above formula (1').

[0068] The polishing rate coefficient F(n) is the polishing rate coefficient for the n-th pressure chamber, but the same polishing rate coefficient F(n) may be used for all pressure chambers C1 to C4. Alternatively, multiple polishing rate coefficients F(n) corresponding to the multiple pressure chambers C1 to C4 may be used. The latter method can further minimize the difference between the actual polishing rate profile and the virtual polishing rate profile shown in the above formula (1') compared to the former method.

[0069] The calculation system 10 further multiplies the pressing pressure responsiveness profile by the determined polishing rate coefficient F(n) and adds the determined polishing rate offset Offset(r) to the value obtained, thereby calculating (creating) the polishing rate responsiveness profile expressed by equation (2').

[0070] Instead of the above formula (1'), the following formula (1") may be used.

number

[0071] 6 is a graph showing an example of a virtual polishing rate profile for each pressure chamber, a virtual polishing rate profile for all pressure chambers C1 to C4, and an actual polishing rate profile. The vertical axis of FIG. 6 represents the polishing rate, and the horizontal axis represents the radial position of the wafer. In FIG. 6, symbol RC1 represents the virtual polishing rate profile for pressure chamber C1, symbol RC2 represents the virtual polishing rate profile for pressure chamber C2, symbol RC3 represents the virtual polishing rate profile for pressure chamber C3, and symbol RC4 represents the virtual polishing rate profile for pressure chamber C4. The virtual polishing rate profile for all pressure chambers C1 to C4 is the sum of the virtual polishing rate profiles RC1, RC2, RC3, and RC4.

[0072] As shown in FIG. 6, the difference between the virtual polishing rate profile and the actual polishing rate profile is very small. Therefore, the calculation system 10 can create a profile of the polishing rate responsiveness per unit pressure in the pressure chambers C1 to C4 using the above formula (2) or (2'). In particular, according to this embodiment, the polishing rate responsiveness profile can be easily obtained based on the pressing pressure responsiveness profile generated by simulation and the polishing rate profile obtained by actual polishing. Furthermore, the number of wafers (workpieces) and the operation time required to obtain the polishing rate responsiveness can be reduced. Specifically, the number of wafers actually polished in step 2 can be reduced. The number of wafers actually polished in step 2 may be one or more, but the number of wafers required to obtain the polishing rate profile in step 2 can be less than the total number of pressure chambers C1 to C4 of the polishing head 7.

[0073] Furthermore, the polishing rate response profile obtained as described above can be used to optimize the polishing conditions for another wafer to be polished next. In one embodiment, the calculation system 10 creates a current film thickness profile for the other wafer from film thickness measurements obtained from the film thickness sensor 42 (see FIG. 1) during polishing of the other wafer, and determines the pressures in the pressure chambers C1 to C4 that minimize the difference between the current film thickness profile and the target film thickness profile based on the polishing rate response profile. In another embodiment, the calculation system 10 creates a film thickness profile before polishing and a film thickness profile after polishing for the wafer W used to generate the polishing rate profile, and determines the pressures in the pressure chambers C1 to C4 based on the film thickness profile before polishing, the film thickness profile after polishing, the target film thickness profile, and the polishing rate response profile.

[0074] As described above, the polishing rate response profile obtained by calculation is close to the response profile of the actual polishing rate, but the polishing rate may vary slightly depending on the polishing liquid (e.g., slurry) present on the polishing pad 2 and the temperature of the polishing surface 2a of the polishing pad 2. Therefore, in one embodiment, a correction coefficient, which will be described below, is further used to improve the accuracy of the polishing rate response profile.

[0075] The correction coefficient is a coefficient for eliminating the difference between the actual polishing rate profile and the virtual polishing rate profile. After calculating the polishing rate coefficient F(n) that minimizes the above formula (1), the calculation system 10 calculates the correction coefficient G(r) that satisfies the following formula:

number

[0076] Furthermore, the calculation system 10 creates the polishing rate response profile using the following equation (4) instead of the above equation (2). Resp(n,r)=G(r)*F(n)*P(n,r) (4) The calculation system 10 multiplies the pressing pressure responsiveness profile by the determined polishing rate coefficient F(n) and correction coefficient G(r) to calculate the polishing rate responsiveness profile expressed by the above formula (4).

[0077] In one embodiment, the calculation system 10 may calculate the polishing rate coefficient F(n) and the polishing rate offset Offset(r) that minimize the above equation (1') or (1"), and then calculate a correction coefficient G(r) for eliminating the difference between the actual polishing rate profile and the virtual polishing rate profile, and may calculate (create) the polishing rate response profile by multiplying the pressing pressure responsiveness profile by the determined polishing rate coefficient F(n) and the correction coefficient G(r) and adding the determined polishing rate offset Offset(r) to the obtained value.

[0078] The polishing rate can also vary depending on changes over time in consumables such as the polishing pad 2 and the retainer ring 32 of the polishing head 7. For example, after each wafer polishing, the polishing surface 2a of the polishing pad 2 is usually slightly scraped away by a dresser to regenerate the polishing surface 2a. This operation is called dressing of the polishing pad 2. As the dressing of the polishing pad 2 is repeated, the thickness of the polishing pad 2 gradually decreases, which can affect the wafer polishing rate.

[0079] Therefore, the above-mentioned correction coefficient G(r) may be updated when a predetermined update condition is satisfied. An embodiment of updating the correction coefficient G(r) will be described below with reference to the flowchart shown in Fig. 7. Steps 1 to 4 shown in Fig. 7 are the same as steps 1 to 4 shown in Fig. 3, and therefore, redundant description thereof will be omitted.

[0080] In step 5, the polishing conditions for the next wafer are optimized. For example, the calculation system 10 creates a film thickness profile before polishing the wafer W in step 2 and a film thickness profile after polishing in step 2, and determines the pressures in the pressure chambers C1 to C4 based on the film thickness profile before polishing, the film thickness profile after polishing, the target film thickness profile, and the polishing rate response profile.

[0081] In step 6, the next wafer is polished under the optimized polishing conditions using the polishing apparatus shown in Figure 1, and the calculation system 10 creates a new polishing rate profile. The optimization of the polishing conditions in step 5 may be performed while the next wafer is being polished in step 6. For example, the calculation system 10 creates a current film thickness profile for the next wafer from the film thickness measurements obtained from the film thickness sensor 42 (see Figure 1) while the next wafer is being polished, and determines the pressures in the pressure chambers C1 to C4 that minimize the difference between the current film thickness profile and the target film thickness profile based on the polishing rate response profile.

[0082] In step 7, the calculation system 10 determines whether or not the update condition for the polishing rate coefficient is satisfied. Examples of the update condition for the polishing rate coefficient include the following. The number of polished wafers has reached the specified number (the specified number can be one). The polishing pad 2, retainer ring 32, and other consumable parts have reached the specified usage time. The difference between the predicted film thickness profile and the actual film thickness profile exceeds the allowable value (the predicted film thickness profile can be created from the initial film thickness profile, the polishing rate response profile, the pressure in the pressure chambers C1 to C4, and the polishing time).

[0083] If the update conditions for the polishing rate coefficient are satisfied, in step 8, the calculation system 10 creates a new polishing rate responsive profile based on the pressing pressure responsive profile calculated in step 1, the pressures in the pressure chambers C1 to C4 optimized in step 5, and the new polishing rate profile calculated in step 6, and updates the polishing rate responsive profile by replacing the existing polishing rate responsive profile with the new polishing rate responsive profile.

[0084] If the update conditions for the polishing rate coefficients are not met in step 8 above, the operation flow returns to step 5, the polishing conditions for the next wafer are optimized, and then the wafer after that is polished.

[0085] According to this embodiment, the calculation system 10 can create a polishing rate response profile that reflects the changes over time of consumable members such as the polishing pad 2 and the retaining ring 32.

[0086] The computing system 10 operates in accordance with instructions included in a program electrically stored in the storage device 10a, and executes the operations of each of the above-described embodiments. For example, the computing system 10 calculates, by simulation, a pressing pressure responsiveness profile that indicates the distribution of the pressing pressure applied from the workpiece to the polishing pad 2, which changes in response to a change in the unit pressure in the pressure chamber, creates a polishing rate profile that indicates the distribution of the polishing rate of the workpiece polished by pressing the workpiece against the polishing pad 2 while the pressure chamber is maintained at a predetermined pressure, and creates the polishing rate responsiveness profile based on the pressing pressure responsiveness profile, the predetermined pressure, and the polishing rate profile.

[0087] A program for causing the computing system 10 to perform the operations of each of the above-described embodiments is recorded on a computer-readable recording medium, which is a non-transitory tangible object, and is provided to the computing system 10 via the recording medium. Alternatively, the program may be input to the computing system 10 via a communication network such as the Internet or a local area network.

[0088] The above-described embodiments have been described for the purpose of enabling a person of ordinary skill in the art to practice the present invention. Various modifications of the above-described embodiments would be obvious to a person skilled in the art, and the technical concept of the present invention may be applied to other embodiments. Therefore, the present invention is not limited to the described embodiments, but is to be interpreted in the broadest scope in accordance with the technical concept defined by the claims. [Industrial Applicability]

[0089] The present invention can be used in a technique for calculating the response of the removal rate to changes in the pressure pressing a workpiece, such as a wafer, substrate, or panel, used in the manufacture of semiconductor devices against a polishing pad. [Explanation of symbols]

[0090] 2 polishing pads 2a Polished surface 5 Polishing table 5a Table axis 7 Polishing Head 8 Polishing liquid supply nozzle 10. Computing Systems 10a storage device 10b Arithmetic unit 14 Spindle 16 Polishing head swing arm 18 Polished head shaft 21 Table rotation motor 31 Head body 32 Retainer ring 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 lines R1,R2,R3,R4,R5 Pressure regulator

Claims

1. A method for creating a polishing rate response profile showing a distribution of polishing rate response to a pressure change in a pressure chamber when a workpiece used in manufacturing a semiconductor device is pressed against a polishing pad by an elastic membrane formed inside the pressure chamber, comprising: calculating, by simulation, a pressure response profile that indicates a distribution of pressure applied from the workpiece to the polishing pad, the distribution changing in response to a change in unit pressure in the pressure chamber; While the pressure chamber is maintained at a predetermined pressure, the workpiece is pressed against the polishing pad to polish the workpiece; creating a polishing rate profile showing a distribution of polishing rates of the polished workpiece; multiplying the pressing pressure response profile by the predetermined pressure and a polishing rate coefficient to generate a virtual polishing rate profile; determining the polishing rate coefficient that minimizes the difference between the polishing rate profile and the virtual polishing rate profile; The method multiplying the pressing pressure response profile by the determined polishing rate coefficient to create the polishing rate response profile.

2. 2. The method according to claim 1, wherein the pressure chamber comprises a plurality of pressure chambers, and the polishing rate coefficient comprises a plurality of polishing rate coefficients respectively corresponding to the plurality of pressure chambers.

3. The method further includes determining a correction factor to eliminate a difference between the polishing rate profile and the virtual polishing rate profile; 2. The method according to claim 1, wherein the step of multiplying the pressing pressure responsive profile by the determined polishing rate coefficient to create the polishing rate response profile is a step of multiplying the pressing pressure responsive profile by the determined polishing rate coefficient and the correction coefficient to create the polishing rate response profile.

4. The step of creating the polishing rate response profile includes: a polishing rate offset is added to a value obtained by multiplying the pressing pressure response profile by the predetermined pressure and the polishing rate coefficient to create a virtual polishing rate profile; determining the polishing rate coefficient and the polishing rate offset that minimize a difference between the polishing rate profile and the virtual polishing rate profile; 2. The method according to claim 1, further comprising the step of: multiplying the pressing pressure response profile by the determined polishing rate coefficient, and adding the determined polishing rate offset to the resulting value to create the polishing rate response profile.

5. 5. The method according to claim 4, wherein the pressure chamber comprises a plurality of pressure chambers, and the polishing rate coefficient comprises a plurality of polishing rate coefficients respectively corresponding to the plurality of pressure chambers.

6. The method further includes determining a correction factor to eliminate a difference between the polishing rate profile and the virtual polishing rate profile; 5. The method according to claim 4, wherein the step of creating the polishing rate response profile by multiplying the pressing pressure responsive profile by the determined polishing rate coefficient is a step of creating the polishing rate response profile by adding the determined polishing rate offset to a value obtained by multiplying the pressing pressure responsive profile by the determined polishing rate coefficient and the correction coefficient.

7. The step of creating the pressing pressure response profile includes: creating a first pressing pressure response profile by simulation, the first pressing pressure response profile indicating a distribution of the pressing pressure that changes in response to a change from a first pressure to a second pressure in the pressure chamber; creating a second pressing pressure response profile by simulation, the second pressing pressure response profile indicating a distribution of the pressing pressure that changes in response to a change from the third pressure to a fourth pressure in the pressure chamber; The method of claim 1 , further comprising creating the compression pressure responsive profile based on the first compression pressure responsive profile and the second compression pressure responsive profile.

8. 8. The method of claim 7, wherein the step of creating the pressing pressure response profile based on the first pressing pressure response profile and the second pressing pressure response profile is a step of creating the pressing pressure response profile by interpolation or extrapolation using the first pressing pressure response profile and the second pressing pressure response profile.

9. The method according to claim 7, wherein the step of creating the compression pressure responsive profile based on the first compression pressure responsive profile and the second compression pressure responsive profile is a step of inputting the first compression pressure responsive profile and the second compression pressure responsive profile into a model constructed by machine learning and outputting the compression pressure responsive profile from the model.

10. the polishing rate profile is one selected from a plurality of polishing rate profiles generated by polishing a plurality of workpieces; The plurality of polishing rate profiles include: a pressure chamber for setting a different pressure for each of the plurality of workpieces, and pressing the plurality of workpieces against the polishing pad one by one to polish the plurality of workpieces; The method of claim 1 , wherein the polishing rate profile is obtained by generating a plurality of polishing rate profiles that indicate a distribution of polishing rates of the polished plurality of workpieces.

11. The method of claim 1 , further comprising optimizing polishing conditions for other workpieces using the polishing rate response profile.

12. The step of optimizing the polishing conditions of the other workpiece includes: creating a current film thickness profile of the other workpiece while polishing the other workpiece; 12. The method according to claim 11, further comprising determining the pressure in the pressure chamber for minimizing the difference between the current film thickness profile and the target film thickness profile based on the polishing rate response profile.

13. The step of optimizing the polishing conditions of the other workpiece includes: creating a film thickness profile before polishing and a film thickness profile after polishing of the workpiece used to generate the polishing rate profile; The method according to claim 11 , further comprising determining a pressure in the pressure chamber based on the pre-polishing film thickness profile, the post-polishing film thickness profile, a target film thickness profile, and the polishing rate response profile.

14. Optimizing polishing conditions for a workpiece using the polishing rate response profile created by the method according to any one of claims 1 to 13; a polishing method in which the workpiece is polished by pressing the workpiece against the polishing pad with the elastic membrane under the optimized polishing conditions.

15. A computer-readable recording medium storing a program for causing a computer to create a polishing rate response profile showing a distribution of polishing rate response to pressure changes in a pressure chamber when a workpiece used in manufacturing a semiconductor device is pressed against a polishing pad by an elastic membrane formed inside the pressure chamber, the program comprising: The program calculating, by simulation, a pressure response profile that indicates a distribution of pressure applied from the workpiece to the polishing pad, the distribution changing in response to a change in unit pressure in the pressure chamber; a polishing rate profile indicating a distribution of the polishing rate of the workpiece polished by pressing the workpiece against the polishing pad while maintaining a predetermined pressure in the pressure chamber; multiplying the pressing pressure response profile by the predetermined pressure and a polishing rate coefficient to generate a virtual polishing rate profile; determining the polishing rate coefficient that minimizes the difference between the polishing rate profile and the virtual polishing rate profile; A computer-readable storage medium configured to cause the computer to perform the step of multiplying the pressing pressure response profile by the determined polishing rate coefficient to create the polishing rate response profile.

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