JP2024078709A - Method for creating a response profile of the polishing rate of a workpiece and polishing method - Patents.com - Google Patents

Abstract

[Problem] To provide a method capable of accurately acquiring the responsiveness of a polishing rate to changes in pressure pressing a workpiece such as a wafer against a polishing pad. [Solution] This method creates an estimated polishing rate responsiveness profile showing the distribution of the responsiveness of the polishing rate to pressure changes in a first pressure chamber of a polishing head 7 by using a simulation, creates an actual polishing rate responsiveness profile showing the distribution of the responsiveness of the polishing rate to pressure changes in a second pressure chamber by using the polishing results of the workpiece, and creates a hybrid polishing rate responsiveness profile by combining the estimated polishing rate responsiveness profile and the actual polishing rate responsiveness profile. [Selected Figure] Figure 8

Description

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

Chemical mechanical polishing (hereinafter referred to as CMP) is a process in which a workpiece (e.g., _a wafer, a substrate, or a panel) is polished by sliding the workpiece against a polishing pad while supplying a polishing liquid containing abrasive grains such as silica (SiO2) onto the polishing pad. A polishing apparatus for performing CMP includes a polishing table that supports a polishing pad having a polishing surface, and a polishing head that presses the workpiece against the polishing pad.

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.

The 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.

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.

To optimize the CMP process, it is important to understand the responsiveness of the workpiece polishing rate to pressure changes in the pressure chamber of the polishing head. Polishing rate responsiveness refers to the change in polishing rate in response to a change in unit pressure in the pressure chamber. Knowing the polishing rate responsiveness allows the workpiece to be polished at the polishing rate required to achieve the target profile.

JP 2006-43873 A

It is known that the polishing rate basically follows Preston's law as follows.
Polishing rate ∝ pressing pressure × relative velocity However, the pressing force applied to the workpiece from the elastic membrane of the polishing head is not constant within the pressing surface of the elastic membrane, and changes due to various factors such as temperature, polishing pad, and polishing liquid.

Therefore, the present invention provides a method for accurately obtaining the responsiveness of the polishing 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 polishing rate responsiveness profile.

In one aspect, a method is provided for creating a polishing rate response profile showing the distribution of polishing rate response 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 membrane formed inside the first pressure chamber and the second pressure chamber, the method comprising: creating an estimated polishing rate response profile showing the distribution of polishing rate response to pressure changes in the first pressure chamber using a simulation; creating an actual polishing rate response profile showing the distribution of polishing rate response to pressure changes in the second pressure chamber using the polishing results of the workpiece; and combining the estimated polishing rate response profile and the actual polishing rate response profile to create a hybrid polishing rate response profile.

In one aspect, the step of creating the estimated polishing rate response profile includes calculating by simulation a pressing pressure responsive profile indicating a distribution of a pressing pressure applied from a first workpiece to the polishing pad that changes in response to a change in unit pressure in the first pressure chamber, polishing the first workpiece by pressing the first workpiece against the polishing pad while maintaining a predetermined pressure in the first pressure chamber, creating a polishing rate profile indicating a distribution of the polishing rate of the polished first workpiece, and creating the estimated polishing rate response profile based on the pressing pressure responsive profile, the predetermined pressure, and the polishing rate profile.
In one embodiment, the step of creating the estimated polishing rate responsive profile includes multiplying the pressing pressure responsive 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 responsive profile by the determined polishing rate coefficient to create the estimated polishing rate responsive profile.

In one aspect, the step of calculating the pressing pressure responsiveness profile includes a step of calculating by simulation a distribution of a first pressing pressure when gas having a first pressure is supplied into the first pressure chamber and a distribution of a second pressing pressure when gas having a second pressure is supplied into the first pressure chamber, and calculating the pressing pressure that has changed in response to a change in unit pressure of 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 aspect, the step of creating the actual polishing rate response profile includes polishing the second workpiece by pressing the second workpiece against the polishing pad while changing the pressure in the second pressure chamber, calculating multiple 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 pressure in the second pressure chamber.

In one embodiment, the steps of creating the estimated polishing rate response profile and the actual polishing rate response profile include: polishing the first workpiece by pressing the first workpiece against the polishing pad while maintaining a predetermined first pressure in the first pressure chamber and a predetermined second pressure in the second pressure chamber; creating an actual polishing rate profile showing a distribution of the polishing rate of the polished first workpiece; creating a first polishing rate profile based on the first pressure, a first polishing rate coefficient, and a pressing pressure response profile calculated by simulation; and creating a tentative polishing rate profile based on the second pressure, the second polishing rate coefficient, and the polishing result of the second workpiece. the first polishing rate profile and the second polishing rate profile are combined to create a third polishing rate profile; the first polishing rate coefficient and the second polishing rate are determined to minimize a difference between the actual polishing rate profile and the third polishing rate profile; the first polishing rate coefficient and the second polishing rate are determined to minimize a difference between the actual polishing rate profile and the third polishing rate profile; the first polishing rate coefficient is multiplied by the pressing pressure responsiveness profile to create the estimated polishing rate responsiveness profile; and the second polishing rate coefficient is multiplied by the tentative polishing rate responsiveness profile to create the actual polishing rate responsiveness profile.
In one aspect, the step of calculating the pressing pressure responsiveness profile includes a step of calculating by simulation a distribution of a first pressing pressure when gas having a third pressure is supplied into the first pressure chamber and a distribution of a second pressing pressure when gas having a fourth pressure is supplied into the first pressure chamber, and calculating the pressing pressure that has changed in response to a change in unit pressure of 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.

In one aspect, a polishing method is provided in which the hybrid polishing rate response profile created by the above method is used to optimize polishing conditions for a workpiece, and the workpiece is polished by pressing the elastic membrane against the polishing pad under the optimized polishing conditions.

According to the present invention, an accurate polishing rate response profile can be obtained by combining an estimated polishing rate response profile generated by simulation with an actual polishing rate response profile obtained by actual polishing.

FIG. 1 is a schematic diagram illustrating an embodiment of a polishing apparatus. FIG. 2 is a cross-sectional view showing one embodiment of a polishing head. 1 is a flow chart illustrating an embodiment of creating a hybrid polishing rate response profile. FIG. 13 illustrates one embodiment for creating a forcing pressure responsiveness profile. 13 is a graph showing an example of a pressing pressure responsiveness profile. 13 is a graph showing an example of an estimated polishing rate response profile calculated by simulation for all pressure chambers. 11 is a graph showing an example of an actual polishing rate response profile for all pressure chambers calculated based on actual polishing. 1 is a graph showing an example of a hybrid polishing rate response profile formed by combining an estimated polishing rate response profile and an actual polishing rate response profile. 11 is a part of a flowchart for explaining another embodiment of creating a hybrid polishing rate response profile. 4 is another part of the above flowchart.

Hereinafter, an embodiment 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 that chemically and mechanically polishes 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.

The polishing head 7 is configured to hold a wafer W on its underside. The wafer W has a film to be polished. In the following embodiment, 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.

The calculation system 10 is composed of at least one computer. The calculation system 10 includes a storage device 10a in which a program for creating a polishing rate response profile described later is stored, 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) and a solid state drive (SSD). Examples of the calculation device 10b include a CPU (central processing unit) and a GPU (graphic processing unit). However, the specific configuration of the calculation system 10 is not limited to these examples. The calculation system 10 may be disposed in a polishing module, a polishing device, a substrate processing system including multiple polishing modules, a management system of a factory in which the polishing device is disposed, or outside the factory in which the polishing device is disposed.

The polishing device further comprises 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 or 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.

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.

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 disposed below the polishing table 5, and the polishing table 5 is connected to the table rotation motor 21 via the table shaft 5a. The polishing table 5 and the 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 constitutes the polishing surface 2a that polishes the wafer W.

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 the 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). Furthermore, the polishing head 7 is pressed against the polishing surface 2a of the polishing pad 2 while being maintained at the above-mentioned predetermined height. 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.

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 of the wafer W itself, or may be a physical quantity or signal value before being converted into film thickness.

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 reflected light from the wafer W. The eddy current sensor is configured to induce eddy currents in the conductive film formed on the 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 the optical film thickness sensor and eddy current sensor.

The film thickness sensor 42 is installed in the polishing table 5 and rotates together 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 while crossing the wafer W on the polishing surface 2a each time the polishing table 5 rotates once. 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 in the radial direction of the wafer W.

The film thickness sensor 42 is connected to the calculation system 10. The film thickness measurements generated by the film thickness sensor 42 are monitored by the calculation 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 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 measurements. The film thickness profile represents the distribution of film thickness along the radial direction of the wafer W.

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 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 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 of the wafer W.

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.

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, respectively. 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.

The gas transfer line F3 that 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 adsorbed and held by the polishing head 7. In addition, by supplying compressed gas to this pressure chamber C3, the wafer W is released from the polishing head 7.

Between the head body 31 and the retainer ring 32, an annular elastic membrane 36 is disposed, 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 the gas transfer line F5. The 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.

The gas transfer lines F1, F2, F3, F4, and F5 extend via a rotary joint 40 attached to the polishing head shaft 18. Pressure regulators R1, R2, R3, R4, and R5 are provided on the gas transfer lines F1, F2, F3, F4, and F5, which communicate with the pressure chambers C1, C2, C3, C4, and C5, 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.

The pressure regulators R1 to R5 can change the internal pressure of the pressure chambers C1 to C5 independently of each other, thereby independently adjusting the pressing pressure on the four corresponding regions of the wafer W, i.e., the center, inner middle, outer middle, and edge, and the pressing pressure of the retainer ring 32 against the polishing pad 2. The gas transfer lines F1, F2, F3, F4, and F5 are also connected to atmospheric release valves (not shown), respectively, and the pressure chambers C1 to C5 can be opened 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 or more than four pressure chambers.

The pressure regulators R1 to R5 are connected to the calculation system 10. The calculation system 10 receives the measured film thickness of the wafer W from the film thickness sensor 42 (see FIG. 1), determines the target pressure values of the pressure chambers C1 to C5 to achieve the target film thickness profile based on the measured film thickness, 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 the pressure chambers C1 to C5 at the corresponding target pressure values.

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. Thus, the polishing head 7 can control the film thickness profile of the wafer W to achieve a target film thickness profile.

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 reduced 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.

In the embodiment described below, the calculation system 10 creates a polishing rate responsiveness profile that indicates the distribution of 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. More specifically, the calculation system 10 creates an estimated polishing rate responsiveness profile that indicates the distribution of polishing rate responsiveness to pressure changes in the pressure chambers C1 to C3 using a simulation, creates an actual polishing rate responsiveness profile that indicates the distribution of polishing rate responsiveness to pressure changes in the pressure chamber C4 using the polishing results of the wafer as the workpiece, and creates a hybrid polishing rate responsiveness profile by combining the estimated polishing rate responsiveness profile and the actual polishing rate responsiveness profile.

That is, for the pressure chambers C1 to C3, a polishing rate response profile is created based on a simulation, and for the pressure chamber C4, a polishing rate response profile is created based on an actual polishing result, and a hybrid polishing rate response profile is created as a combination of these polishing rate response profiles. The pressure chamber C4 is the outermost pressure chamber for pressing the edge of the wafer against the polishing pad 2. The relationship between the pressure in the outermost pressure chamber C4 and the polishing rate may differ from the relationship between the pressure in the other pressure chambers C1 to C3 and the polishing rate. In addition, it is difficult to simulate the polishing rate response profile for the outermost pressure chamber C4, and the simulation accuracy may be low. This is because the edge of the wafer pressed by the pressure chamber C4 comes into contact with the retainer ring during polishing of the wafer, and the rotating polishing pad 2 enters under the wafer from the edge of the wafer. Therefore, in this embodiment, for the outermost pressure chamber C4, an actual polishing rate response profile is created based on the actual polishing result.

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

The location of the calculation system 10 for creating the hybrid polishing rate responsiveness profile is not particularly limited. For example, the calculation system 10 may be located away from the polishing module that performs polishing, such as the polishing table 5 and the polishing head 7. The calculation system 10 may be connected to the polishing module via a communication system such as the Internet or a local area network. For example, the calculation system 10 may be composed of a workstation connected to the communication system, or may be composed of a combination of an edge server and a cloud server.

FIG. 3 is a flow chart illustrating one embodiment of creating a hybrid polishing rate response profile.
In step 101, the calculation system 10 calculates a pressing pressure responsiveness profile by simulation, which indicates the distribution of the pressing pressure applied from the wafer W1 to the polishing pad 2, which changes in response to the change in the unit pressure in the pressure chambers C1 to C4. The simulation is performed using a mathematical model of the elastic membrane 34 of the polishing head 7, the polishing pad 2, and the wafer. Therefore, the shape and elasticity of the elastic membrane 34, the elasticity of the polishing pad 2, the rigidity of the wafer W1, and the like are reflected in the simulation result. The simulation used is not particularly limited as long as it can calculate the intended pressing pressure responsiveness profile, but in this embodiment, a simulation based on the finite element method is used. The simulation in this embodiment is performed under conditions in which the wafer W1 and the polishing pad 2 are not rotated, but the simulation may be performed under conditions in which the wafer W1 and the polishing pad 2 are rotated as in actual polishing.

In step 102, the polishing apparatus shown in FIG. 1 actually polishes the wafer W1 by pressing the wafer W1 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 W1 is performed by rotating the polishing table 5 and 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 pressing the surface of the wafer W1 (the surface to be polished) against the polishing surface 2a with the polishing head 7.

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

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

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 the 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 a distribution of the responsiveness of the estimated polishing rate to pressure changes in the pressure chambers C1 to C4 at multiple radial positions (i.e., multiple measurement points of the film thickness) of the wafer W1.

In step 105, the polishing apparatus shown in FIG. 1 polishes the wafer W2 by pressing the wafer W2 against the polishing pad 2 with the polishing head 7 while changing the pressure in the pressure chamber C4 while maintaining the pressure in the pressure chambers C1 to C3 of the polishing head 7 constant. As described above, the polishing of the wafer W2 is performed by rotating the polishing table 5 and the polishing pad 2, rotating the wafer W2 with the polishing head 7, and pressing the surface of the wafer W2 (the 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.

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

In step 106, the calculation system 10 calculates a plurality of polishing rates of the wafer W2 corresponding to different pressures in the pressure chamber C4 from the measured film thickness, and calculates the responsiveness of the polishing rate to changes in the pressure in the pressure chamber C4.
In step 107, the calculation system 10 creates an actual polishing rate response profile from the polishing rate response for the pressure chamber C4 calculated in step 106 above.
In one embodiment, steps 105-107 may occur before steps 101-104.

In step 108, the calculation system 10 creates a hybrid polishing rate responsiveness profile by combining the estimated polishing rate responsiveness profile for the pressure chambers C1 to C3 obtained in step 104 with the actual polishing rate responsiveness profile for the pressure chamber C4 obtained in step 107. In this embodiment, the hybrid polishing rate responsiveness profile is created by replacing the estimated polishing rate responsiveness profile for the pressure chamber C4 obtained in step 104 with the actual polishing rate responsiveness profile for the pressure chamber C4 obtained in step 107. The calculation system 10 can correctly determine the pressures in the pressure chambers C1 to C4 to achieve the target film thickness profile based on the hybrid polishing rate responsiveness profile.

Each of the above steps will now be described in detail.
Fig. 4 is a diagram for explaining an embodiment of calculating the pressing pressure responsiveness profile in step 101 shown in Fig. 3. The vertical axis of Fig. 4 represents the pressure (hereinafter, referred to as pressing pressure) applied from the wafer W1 to the polishing surface 2a of the polishing pad 2, and the horizontal axis represents the radial position on the wafer W1. The horizontal axis of Fig. 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 of Fig. 4.

First, the distribution of the pressing pressure (indicated by the symbol CP1+) when gas with pressure P1 is supplied into the pressure chamber C1 shown in Figure 2 is calculated by simulation. Next, the distribution of the pressing pressure (indicated by the symbol CP1-) when gas with pressure P2 is supplied into the same pressure chamber C1 is calculated by simulation. Both pressure P1 and pressure P2 are preset pressures, and pressure P1 is higher than pressure P2.

In the same manner, the distribution of the pressing pressure when gas having the above pressure P1 is supplied into the pressure chamber C2 (indicated by symbol CP2+), the distribution of the pressing pressure when gas having the above pressure P2 is supplied into the pressure chamber C2 (indicated by symbol CP2-), the distribution of the pressing pressure when gas having the above pressure P1 is supplied into the pressure chamber C3 (indicated by symbol CP3+), the distribution of the pressing pressure when gas having the above pressure P2 is supplied into the pressure chamber C3 (indicated by symbol CP3-), the distribution of the pressing pressure when gas having the above pressure P1 is supplied into the pressure chamber C4 (indicated by symbol CP4+), and the distribution of the pressing pressure when gas having the above pressure P2 is supplied into the pressure chamber C4 (indicated by symbol CP4-) are calculated by simulation.

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 by dividing the difference between the pressing pressure CP1+ and the pressing pressure CP1- by the difference between the pressure P1 and the pressure P2 at each radial position on the wafer W1. In the same manner, the calculation system 10 calculates the pressing pressure that has changed in response to the change in the unit pressure of the gas in the pressure chamber C2 at each radial position on the wafer W1 by dividing the difference between the pressing pressure CP2+ and the pressing pressure CP2- by the difference between the pressure P1 and the pressure P2, calculates the pressing pressure that has changed in response to the change in the unit pressure of the gas in the pressure chamber C3 at each radial position on the wafer W1 by dividing the difference between the pressing pressure CP3+ and the pressing pressure CP3- by the difference between the pressure P1 and the pressure P2, and calculates the pressing pressure that has changed in response to the change in the unit pressure of the gas in the pressure chamber C4 at each radial position on the wafer W1 by dividing the difference between the pressing pressure CP4+ and the pressing pressure CP4- by the difference between the pressure P1 and the pressure P2.

Figure 5 is a graph showing an example of a pressing pressure responsiveness profile. The vertical axis of Figure 5 represents the pressing pressure that has changed 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. Symbol PP1 in Figure 5 represents the distribution of pressing pressure that has changed in response to a change in the unit pressure of the gas in the pressure chamber C1, symbol PP2 represents the distribution of pressing pressure that has changed in response to a change in the unit pressure of the gas in the pressure chamber C2, symbol PP3 represents the distribution of pressing pressure that has changed in response to a change in the unit pressure of the gas in the pressure chamber C3, and symbol PP4 represents the distribution of pressing pressure that has changed in response to a change in the unit pressure of the gas in the pressure chamber C4. In this way, the calculation system 10 creates a pressing pressure responsiveness profile.

As explained with reference to Figure 4, the pressing pressure responsiveness profile is created by running a simulation under conditions where the pressures in the pressure chambers C1 to C4 are preset at pressures P1 and P2. The pressing pressure responsiveness profile may vary depending on the pressure settings in the pressure chambers C1 to C4, and furthermore, during actual polishing of the wafer, the pressure in the pressure chambers C1 to C4 may vary depending on the structure and film thickness of the wafer, etc.

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 pressure P1 to pressure P2 in the pressure chambers C1 to C4, and calculating, through simulation, a second pressing pressure responsiveness profile that indicates the distribution of pressing pressure that changes in response to a change from pressure P3 to pressure P4 in the pressure chambers C1 to C4. Pressures P3 and P4 are different from pressures P1 and P2.

Furthermore, the calculation system 10 may further create a new pressing pressure responsiveness profile by interpolation or extrapolation using the multiple pressing pressure responsiveness profiles calculated by the simulation. In one embodiment, the calculation system 10 may further create a pressing pressure responsiveness profile by inputting the multiple pressing pressure responsiveness profiles created by the simulation into a model constructed by machine learning and outputting a new pressing pressure responsiveness profile from the model. The multiple pressing pressure responsiveness 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 pressing pressure responsiveness profiles to create an estimated polishing rate responsiveness profile in the above step 104.

The above-described embodiment relates to the pressure with which the elastic membrane 34 of the polishing head 7 presses the wafer W1 against the polishing pad 2, but 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 responsiveness profile. That is, the simulation may be performed using a mathematical model of the elastic membrane 34 of the polishing head 7, the polishing pad 2, the retaining ring 32, and the wafer W1.

Next, the above step 102 will be described in detail. In this step 102, the wafer W1 is actually polished. In the polishing apparatus shown in FIG. 1, the wafer W1 is pressed against the polishing pad 2 by the polishing head 7 while the pressure chambers C1 to C4 of the polishing head 7 are maintained at a predetermined pressure, and the wafer W1 is polished. 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 equal to or lower than the pressure P1 used in the above step 101 and equal to or higher than 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. The polishing of the wafer W1 is performed at least until the film thickness of the wafer W1 reaches a target value. The film thickness sensor 42 continues to measure the film thickness of the wafer W1 from the start to the end of polishing of the wafer W1, and transmits the measured film thickness to the calculation system 10.

Next, step 103 will be described 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 of the wafer W1 corresponding to the pressure chambers C1, C2, C3, and C4 by the polishing time of the wafer W1. The initial film thickness is the film thickness of the wafer W1 before polishing, and the final film thickness is the film thickness of the 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 the pressure chambers C1, C2, C3, and C4.

In actual polishing of a wafer, the set pressure in the pressure chambers C1 to C4 may vary depending on the structure and film thickness of the wafer. 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 against the polishing pad 2 one by one 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 multiple 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 an estimated polishing rate response profile in the next step 104.

Resp(n,r)=F(n)*P(n,r) （２）
ここで、ｒはウェーハＷ１上の半径方向の位置、ｒａはウェーハＷ１の半径、Ｒａｔｅ（ｒ）は半径位置ｒでの研磨レート（実測値）、ｎは圧力室の番号、ｎｔは圧力室の数（本実施形態ではｎｔ＝４）、ＡＰ（ｎ）はウェーハＷ１を実際に研磨したときのｎ番目の圧力室内の気体の圧力、Ｆ（ｎ）はｎ番目の圧力室に関する研磨レート係数、Ｐ（ｎ，ｒ）はｎ番目の圧力室に関する半径位置ｒでの押し付け圧力の応答性、Ｒｅｓｐ（ｎ，ｒ）はｎ番目の圧力室に関する半径位置ｒでの研磨レート応答性を表す。 Next, a detailed description will be given of step 104. In step 104, the computing system 10 uses the following formula stored in the storage device 10a.

Resp(n,r)=F(n)*P(n,r) (2)
Here, r is the radial position on the wafer W1, ra is the radius of the wafer W1, Rate(r) is the polishing rate (actual measured value) at the radial position r, n is the pressure chamber number, nt is the number of pressure chambers (nt=4 in this embodiment), AP(n) is the gas pressure in the nth pressure chamber when the wafer W1 is actually polished, F(n) is the polishing rate coefficient for the nth pressure chamber, P(n,r) is the responsiveness of the pressing pressure at the radial position r for the nth pressure chamber, and Resp(n,r) is the polishing rate responsiveness at the radial position r for the nth pressure chamber.

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) to calculate a virtual polishing rate profile, 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 publicly 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).

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 the 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 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.

The calculation system 10 further multiplies the pressing pressure responsiveness profile by the determined polishing rate coefficient F(n) to calculate (create) an estimated polishing rate responsiveness profile represented by equation (2).

Next, the above step 105 will be described in detail. In this step 105, the wafer W2 is actually polished. The polishing apparatus shown in FIG. 1 polishes the wafer W2 by pressing the wafer W2 against the polishing pad 2 with the polishing head 7 while changing the pressure in the pressure chamber C4 while maintaining the pressure in the pressure chambers C1 to C3 of the polishing head 7 constant. For example, in a state in which the pressure in the pressure chamber C4 of the polishing head 7 is maintained at a predetermined pressure TP1, the polishing head 7 presses the wafer W2 against the polishing pad 2 to polish the wafer W2 for a predetermined first polishing time, and then, in a state in which the pressure in the pressure chamber C4 of the polishing head 7 is maintained at a predetermined pressure TP2, the polishing head 7 presses the wafer W2 against the polishing pad 2 to polish the wafer W2 for a predetermined second polishing time. The pressure TP2 is different from the pressure TP1. The pressures in the pressure chambers C1 to C3 are 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 during at least the first polishing time and the second polishing time, and transmits the measured film thickness values to the calculation system 10.

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

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

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

As can be seen from a comparison between Figures 6 and 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 is significantly different 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.

According to the above-described embodiment, as shown in FIG. 8, an accurate hybrid polishing rate responsiveness profile can be obtained by combining the estimated polishing rate responsiveness profiles ER1, ER2, and ER3 generated by simulation with the actual polishing rate responsiveness profile RR4 obtained by actual polishing.

Furthermore, by using the simulation, the number of wafers (workpieces) and the working time required to obtain the polishing rate responsiveness 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 can be one or more, 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.

The hybrid polishing rate responsive 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 the film thickness measurement value obtained from the film thickness sensor 42 (see FIG. 1) during the polishing of the other wafer, and determines the pressure in the 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 responsive 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 used to generate the polishing rate profile, and determines the pressure 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 hybrid polishing rate responsive profile.

Next, another embodiment for creating a hybrid polishing rate response profile will be described. Details of this embodiment that are not specifically described are the same as those of the above-mentioned embodiment, so duplicate descriptions will be omitted.

As in the above-described embodiment, the calculation system 10 uses simulation to create an estimated polishing rate responsiveness profile that indicates the distribution of polishing rate responsiveness to pressure changes in pressure chambers C1 to C3, creates an actual polishing rate responsiveness profile that indicates the distribution of polishing rate responsiveness to pressure changes in pressure chamber C4 using the polishing results of a wafer as 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.

FIG. 9 is a flow chart illustrating an embodiment for creating a hybrid polishing rate response profile.
In step 201, the wafer W3 is polished by pressing the wafer W3 against the polishing pad 2 by 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 one another, or any two or all of them may be the same. As described above, the wafer W3 is polished by pressing the surface (polished surface) of the wafer W3 against the polishing surface 2a by the polishing head 7 while rotating the polishing table 5 and the polishing pad 2 and rotating the wafer W3 by the polishing head 7, with the polishing liquid present on the polishing surface of the polishing pad 2.

During polishing of wafer W3, film thickness sensor 42 measures the film thickness at multiple measurement points on wafer W3 while traversing wafer W3. In this embodiment, the multiple measurement points are aligned along the radial direction of wafer W3. The film thickness measurement values are sent from film thickness sensor 42 to calculation system 10. Polishing of wafer W3 is terminated when the film thickness of wafer W3 reaches a target value. Film thickness sensor 42 continues to measure the film thickness of wafer W3 from the start to the end of polishing of wafer W3, and transmits the film thickness measurement values to calculation system 10.

In step 202, the calculation system 10 creates an actual polishing rate profile that indicates 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. This step 202 is performed in the same manner as step 103 described above, so a duplicated explanation will be omitted.

In step 203, the calculation system 10 calculates, by simulation, a pressing pressure responsiveness profile that indicates the distribution of the pressing pressure applied from the wafer W3 to the polishing pad 2, which changes in response to changes in the unit pressure in the pressure chambers C1 to C3. This simulation is performed in the same manner as the simulation of step 101 described in the above embodiment, so a duplicated description will be omitted. In one embodiment, step 203 may be performed before step 201.

ここで、ｒはウェーハＷ３上の半径方向の位置、ｎは圧力室の番号、ｎｔは圧力室の数（本実施形態ではｎｔ＝３）、ＡＰ（ｎ）はウェーハＷ３を実際に研磨したときのｎ番目の圧力室内の気体の圧力（すなわち圧力ＵＰ１，ＵＰ２，ＵＰ３）、Ｆ（ｎ）はｎ番目の圧力室に関する第１研磨レート係数、Ｐsim（ｎ，ｒ）はｎ番目の圧力室に関する半径位置ｒでの押し付け圧力の応答性を表す。 In step 204, the calculation system 10 creates a first polishing rate profile based on the pressures UP1, UP2, and UP3 in the pressure chambers C1 to C3 set in step 201, the pressing pressure responsiveness profile calculated in step 203, and the first polishing rate coefficient. The first polishing rate profile is a distribution of the polishing rates of the wafer W3 for the pressure chambers C1 to C3. The first polishing rate profile is expressed as follows:

Here, r is the radial position on the wafer W3, n is the pressure chamber number, nt is the number of pressure chambers (nt=3 in this embodiment), AP(n) is the gas pressure in the nth pressure chamber when the wafer W3 is actually polished (i.e., pressures UP1, UP2, UP3), F(n) is the first polishing rate coefficient for the nth pressure chamber, and Psim(n,r) is the responsiveness of the pressing pressure at the radial position r for the nth pressure chamber.

In step 205, the polishing apparatus shown in FIG. 1 polishes the wafer W4 by pressing the wafer W4 against the polishing pad 2 with the polishing head 7 while changing the pressure in the pressure chamber C4 while maintaining the pressure in the pressure chambers C1 to C3 of the polishing head 7 constant. As described above, the polishing of the wafer W4 is performed by rotating the polishing table 5 and the polishing pad 2, rotating the wafer W4 with the polishing head 7, and pressing the surface of the wafer W4 (the 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. This step 205 is performed in the same manner as the above-mentioned step 105, so a duplicated explanation will be omitted.

During polishing of wafer W4, film thickness sensor 42 measures the film thickness at multiple measurement points on wafer W4 while traversing wafer W4. In this embodiment, the multiple measurement points are aligned along the radial direction of wafer W4. The film thickness measurement values are sent from film thickness sensor 42 to calculation system 10. Polishing of wafer W4 is terminated when the film thickness of wafer W4 reaches a target value. Film thickness sensor 42 continues to measure the film thickness of wafer W4 from the start to the end of polishing of wafer W4, and transmits the film thickness measurement values to calculation system 10.

In step 206, the calculation system 10 calculates a plurality of polishing rates of the wafer W4 corresponding to different pressures in the pressure chamber C4 from the measured film thickness, and calculates the responsiveness of the polishing rate to the change in pressure in the pressure chamber C4.
In step 207, the calculation system 10 creates a provisional polishing rate response profile from the polishing rate response for the pressure chamber C4 determined in step 206. Steps 206 and 207 are performed in the same manner as steps 106 and 107 described above, and therefore a duplicated description thereof will be omitted.

ここで、ｒはウェーハＷ４上の半径方向の位置、ｍは圧力室の番号（本実施形態ではｍ＝４）、ＡＰ（ｍ）はウェーハＷ４を実際に研磨したときのｍ番目の圧力室内の気体の圧力（本実施形態では圧力ＵＰ４）、Ｆ（ｍ）はｍ番目の圧力室に関する第２研磨レート係数、Ｒreal（ｍ，ｒ）はｍ番目の圧力室に関する半径位置ｒでの暫定的な研磨レート応答性プロファイルを表す。
一実施形態では、ステップ２０５～２０８は、ステップ２０１～２０４の前に行われてもよい。 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 a distribution of the polishing rate of the wafer W4 for the pressure chamber C4. The second polishing rate profile is expressed as follows:

Here, r represents the radial position on the wafer W4, m represents the number of the pressure chamber (m=4 in this embodiment), AP(m) represents the gas pressure in the m-th pressure chamber when the wafer W4 is actually polished (pressure UP4 in this embodiment), F(m) represents the second polishing rate coefficient for the m-th pressure chamber, and Rreal(m, r) represents the provisional polishing rate responsiveness profile at the radial position r for the m-th pressure chamber.
In one embodiment, steps 205-208 may be performed before steps 201-204.

In step 209, the computing system 10 creates a third polishing rate profile by combining the first polishing rate profile and the second polishing rate profile. The third polishing rate profile is expressed as follows.

ここで、ｒはウェーハ上の半径方向の位置、ｒａはウェーハの半径、Ｒａｔｅ（ｒ）はステップ２０２で算定された、半径位置ｒでの研磨レート（実測値）を表す。
上記式（６）を最小とする第１研磨レート係数Ｆ（ｎ）および第２研磨レート係数Ｆ（ｍ）を求めるアルゴリズムは、最適化法などの公知のアルゴリズムが適用できる。 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.

Here, r represents the radial position on the wafer, ra represents the radius of the wafer, and Rate(r) represents the polishing rate (actual measured value) at the radial position r calculated in step 202.
As an algorithm for determining the first polishing rate coefficient F(n) and the second polishing rate coefficient F(m) that minimize the above formula (6), a known algorithm such as an optimization method can be applied.

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

The above steps 211 and 212 are expressed by the following equations.
Resp(l,r)=F(n)*Psim(n,r)+F(m)*Rreal(m,r) (7)
Here, Resp(l, r) represents the polishing rate response at the radial position r for the lth pressure chamber. The calculation system 10 stores the above formulas (1) to (7) in its storage device 10a.

According to the above-described embodiment, an accurate hybrid polishing rate responsiveness profile can be obtained by combining an estimated polishing rate responsiveness profile generated by simulation with an actual polishing rate responsiveness profile obtained by actual polishing. Furthermore, by using simulation, the number of wafers (workpieces) and the work time required to obtain the polishing rate responsiveness can be reduced.

The hybrid polishing rate responsive 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 the film thickness measurement value obtained from the film thickness sensor 42 (see FIG. 1) during the polishing of the other wafer, and determines the pressure in the 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 responsive 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 used to generate the polishing rate profile, and determines the pressure 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 hybrid polishing rate responsive profile.

In the embodiment described with reference to the flowchart of FIG. 3, the process of determining the polishing rate coefficient for approximating the simulation results for the pressure chambers C1 to C3 to the results of actual polishing is performed independently of the process of calculating the actual polishing rate response profile for the pressure chamber C4. In contrast, in the embodiment described with reference to the flowcharts of FIG. 9 and FIG. 10, the process of determining the first polishing rate coefficient and the second polishing rate coefficient for the pressure chambers C1 to C4 is performed according to substantially the same operation as the process of calculating the estimated polishing rate response profile for the pressure chambers C1 to C3 and the process of calculating the actual polishing rate response profile for the pressure chamber C4. It has been found from actual polishing results that the embodiment described with reference to the flowcharts of FIG. 9 and FIG. 10 can create a polishing rate response profile with higher accuracy than the embodiment described with reference to the flowchart of FIG. 3.

In the embodiment described so far, a hybrid polishing rate responsiveness profile is obtained for four pressure chambers C1 to C4, but a hybrid polishing rate responsiveness profile can be obtained in the same manner for three or less, or five or more pressure chambers.

The calculation system 10 operates according to instructions included in a program electrically stored in the storage device 10a, and executes the operations of each of the above-mentioned embodiments. Specifically, the calculation system 10 creates an estimated polishing rate responsiveness profile showing the distribution of polishing rate responsiveness to pressure changes in a first pressure chamber (e.g., pressure chamber CP1) using a simulation, creates an actual polishing rate responsiveness profile showing the distribution of polishing rate responsiveness to pressure changes in a second pressure chamber (e.g., pressure chamber CP4) using the polishing results of the workpiece, and creates a hybrid polishing rate responsiveness profile by combining the estimated polishing rate responsiveness profile and the actual polishing rate responsiveness profile.

The program for causing the computing system 10 to execute the operations of each of the above-described embodiments is recorded on a computer-readable recording medium, which is a non-transient 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.

The above-described embodiments have been described for the purpose of enabling a person having ordinary knowledge in the technical field to which the present invention pertains to practice the present invention. Various modifications of the above-described embodiments would naturally be possible for a person skilled in the art, and the technical concept of the present invention may also 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 scope of the claims.

2 Polishing pad 2a Polishing surface 5 Polishing table 5a Table shaft 7 Polishing head 8 Polishing liquid supply nozzle 10 Calculation system 10a Storage device 10b Calculation device 14 Support shaft 16 Polishing head swing arm 18 Polishing head shaft 21 Table rotation motor 31 Head body 32 Retainer rings 34, 36 Elastic film 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 regulator

Claims (8)

A method for creating a polishing rate response profile showing a distribution of polishing rate response to pressure changes in a first pressure chamber and a second pressure chamber when a workpiece used in manufacturing a semiconductor device is pressed against a polishing pad by an elastic membrane formed inside the first pressure chamber and the second pressure chamber, comprising:
creating an estimated polishing rate responsiveness profile, which indicates a distribution of polishing rate responsiveness to pressure changes in the first pressure chamber, by using a simulation;
creating an actual polishing rate response profile indicating a distribution of polishing rate response to pressure changes in the second pressure chamber using a polishing result of the workpiece;
The method further comprises combining the estimated polishing rate response profile and the actual polishing rate response profile to create a hybrid polishing rate response profile. The step of creating the estimated polishing rate response profile includes:
calculating, by simulation, a pressing pressure response profile indicative of a distribution of pressing pressure applied to the polishing pad from the first workpiece that changes in response to a change in unit pressure in the first pressure chamber;
While the inside of the first pressure chamber is maintained at a predetermined pressure, the first workpiece is pressed against the polishing pad to polish the first workpiece;
creating a polishing rate profile showing a distribution of polishing rates of the polished first workpiece;
The method of claim 1 , further comprising generating the estimated polishing rate response profile based on the applied pressure response profile, the predetermined pressure, and the polishing rate profile. The step of creating the estimated polishing rate response profile includes:
multiplying the pressing pressure responsive profile by the predetermined pressure and a polishing rate coefficient to generate a virtual polishing rate profile;
determining the polishing rate coefficient that minimizes a difference between the polishing rate profile and the virtual polishing rate profile;
The method of claim 2 , further comprising multiplying the forcing pressure responsive profile by the determined polishing rate factor to create the estimated polishing rate responsive profile. The step of calculating the imposition pressure responsive profile comprises:
calculating, by simulation, a distribution of a first pressing pressure when a gas having a first pressure is supplied into the first pressure chamber, and a distribution of a second pressing pressure when a gas having a second pressure is supplied into the first pressure chamber;
3. The method of claim 2, further comprising calculating a change in pressing pressure in response to a change in unit pressure of gas in the first pressure chamber by dividing a difference between the first pressing pressure and the second pressing pressure by a difference between the first pressure and the second pressure at each radial position on the first workpiece. The step of creating an actual polishing rate response profile includes:
While changing the pressure in the second pressure chamber, the second workpiece is pressed against the polishing pad to polish the second workpiece;
determining a plurality of polishing rates of the second workpiece corresponding to different pressures in the second pressure chamber;
The method of claim 2 , further comprising calculating a responsiveness of the polishing rate to changes in pressure within the second pressure chamber. The step of creating the estimated polishing rate response profile and the actual polishing rate response profile includes:
a first workpiece is pressed against the polishing pad to polish the first workpiece 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 a distribution of the polishing rate of the polished first workpiece;
creating a first polishing rate profile based on the first pressure, a first polishing rate coefficient, and a 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 response profile created from the polishing result of the second workpiece;
creating a third polishing rate profile by combining the first polishing rate profile and the second polishing rate profile;
determining the first polishing rate coefficient and the second polishing rate coefficient that minimize a difference between the actual polishing rate profile and the third polishing rate profile;
multiplying the pressing pressure responsiveness profile by the determined first polishing rate coefficient to generate the estimated polishing rate responsiveness profile;
2. The method of claim 1, further comprising multiplying the provisional polishing rate response profile by the determined second polishing rate coefficient to generate the actual polishing rate response profile. The step of calculating the imposition pressure responsive profile comprises:
calculating, by simulation, a distribution of a first pressing pressure when a gas having a third pressure is supplied into the first pressure chamber, and a distribution of a second pressing pressure when a gas having a fourth pressure is supplied into the first pressure chamber;
7. The method of claim 6, further comprising calculating a change in pressing pressure in response to a change in unit pressure of gas in the first pressure chamber at each radial position on the first workpiece by dividing a difference between the first pressing pressure and the second pressing pressure by a difference between the third pressure and the fourth pressure. 8. Optimizing polishing conditions for a workpiece using the hybrid polishing-rate response profile created by the method of any one of claims 1 to 7;
a polishing method comprising: pressing the workpiece against the polishing pad with the elastic membrane under the optimized polishing conditions to polish the workpiece.

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