Storage medium, polishing apparatus, and method for evaluating electrode arrangement design

Abstract

The invention provides an evaluation program for an electrode arrangement design, a polishing apparatus, and an evaluation method for an electrode arrangement design, capable of enabling an operator to appropriately recognize a cross-sectional shape of a wafer during processing. An evaluation program (100) that evaluates the arrangement design of a pair of electrodes for detecting the resonance frequency of a wafer during polishing of the wafer made of a piezoelectric material causes a computer to execute: an electrode orbital calculation process (101) that calculates the orbital of the pair of electrodes on the basis of prescribed information including the arrangement conditions of the pair of electrodes; calculating an electrode track, which is a track of the pair of electrodes when the target wafer is polished for a predetermined time; a repetition interval calculation process (102) for calculating a repetition interval above the target wafer in the electrode track; an effective section calculation process (103) for calculating an effective section in which the pair of electrodes simultaneously face the target wafer in the repetition section; and a ratio calculation process (104) for calculating an effective ratio, which is the ratio of the effective section to the repeating section.

Description

Technical Field

[0001] The present invention relates to a storage medium storing an evaluation program for evaluating a configuration design of electrodes for detecting the resonance frequency of a wafer during polishing, a polishing apparatus for polishing a wafer, and a method for evaluating the configuration design of the electrodes. Background Art

[0002] Conventionally, there has been known a polishing apparatus that measures the thickness of a wafer by an optical method such as a light reflection interference method, generates a shape drawing line showing the cross-sectional shape of the wafer based on the acquired thickness data, and displays it (for example, refer to Patent Document 1).

[0003] In addition, it is known that the resonance frequency of a piezoelectric material such as quartz depends on its thickness dimension. Therefore, there is known a polishing apparatus that, when polishing a wafer made of a piezoelectric material, in order to process it to a specified thickness that can obtain a desired frequency characteristic, sets a pair of electrodes on a stage, applies a specified frequency sweep signal from one electrode, and acquires the frequency sweep signal passing through the wafer via the other electrode, thereby being able to obtain the resonance frequency of the wafer (for example, refer to Patent Documents 2 and 3).

[0004] Prior Art Documents

[0005] Patent Documents

[0006] Patent Document 1: Japanese Patent No. 6605395

[0007] Patent Document 2: Japanese Unexamined Patent Application Publication No. 2002-103221

[0008] Patent Document 3: Japanese Unexamined Patent Application Publication No. 2002-190628 Summary of the Invention

[0009] Problems to be Solved by the Invention

[0010] However, in a polishing apparatus, in the case of measuring the thickness of a wafer by an optical method, the polishing liquid used needs to be permeable. In a polishing environment using a non-permeable polishing liquid, the light that should originally be irradiated onto the wafer is blocked by the polishing liquid, and the purpose of thickness measurement cannot be achieved. In addition, in the method of measuring the thickness of a wafer by an optical method, there are many examples in which the position of the wafer and the position of the thickness measuring device are grasped based on the respective origin (center) positions of the internal gear, sun gear, stage, etc., and a shape drawing line is generated while comparing the irradiation position of the measurement light of the thickness measuring device with the position of the internal gear, etc. in the polishing apparatus. In such a measurement method for grasping position information, in principle, the origin position information of each gear or stage, the setting position information of the wafer, the origin position information of the carrier, etc. are required.

[0011] On the other hand, in the case of a measurement method for obtaining the resonance frequency of a wafer, regardless of whether the grinding fluid is permeable or not, as long as the electrical conductivity from the measuring device to the wafer is ensured to a certain extent, the resonance frequency of the wafer can be measured. Additionally, in the device structure, even without calculating the position information of the wafer, etc., based on the characteristic of the continuity of the resonance frequency data, the information on the cross-sectional shape of the wafer can be theoretically obtained. On the other hand, in a grinding device using a conventional measuring device, a shape drawing line showing the cross-sectional shape of the wafer is not generated based on the resonance frequency data of the wafer. Therefore, it is difficult for the operator of the grinding device to grasp the cross-sectional shape of the wafer during processing.

[0012] Furthermore, if the configuration of the electrodes for detecting the resonance frequency changes, the trajectory of the electrodes during wafer grinding also changes, resulting in variations in the measurement results such as changes in the signal intensity for detecting the resonance frequency or no signal being obtained. Additionally, it may also occur that the electrodes cannot properly pass above the wafer, resulting in no measurement opportunity or fewer measurement opportunities. That is to say, the detection accuracy of the resonance frequency of the wafer varies according to the electrode configuration design, and the generation of the shape drawing line showing the cross-sectional shape of the wafer also changes according to the electrode configuration design. Therefore, in order for the operator to accurately grasp the cross-sectional shape of the wafer during processing, in addition to using a system for measuring the resonance frequency of the wafer, an appropriate design of the electrode configuration is also required.

[0013] The present invention is completed in view of the above problems, and its object is to provide an evaluation program for the electrode configuration design, a grinding device, and an evaluation method for the electrode configuration design that can enable the operator of the grinding machine to appropriately identify the cross-sectional shape of the wafer during processing.

[0014] Means for Solving the Problem

[0015] To achieve the above object, a storage medium of the present invention stores an evaluation program for electrode configuration design, and the evaluation program is used to evaluate the electrode configuration design in a grinding device. In the grinding device, a pair of electrodes are mounted on a stage, and the pair of electrodes are used to detect the resonance frequency of a wafer made of a piezoelectric material during grinding of the wafer. The storage medium is characterized in that, through the evaluation program, a computer is caused to execute the following processes: an electrode orbit calculation process of calculating an electrode orbit based on prescribed information including the configuration conditions of the pair of electrodes, where the electrode orbit is the orbit of the pair of electrodes when grinding an arbitrary wafer for a prescribed time; a repetition interval calculation process of calculating the length of a repetition interval, where the repetition interval is an interval in the electrode orbit that passes above the arbitrary wafer; an effective interval calculation process of calculating the length of an effective interval, where the effective interval is an interval in the repetition interval in which the pair of electrodes face the arbitrary wafer simultaneously; and a ratio calculation process of calculating an effective ratio, where the effective ratio is the ratio of the effective interval to the repetition interval.

[0016] To achieve the above object, a grinding device of the present invention is characterized by including: a grinder that grinds a wafer made of a piezoelectric material through a stage; a first electrode and a second electrode mounted on the stage with their front faces facing the wafer; a frequency calculation unit that applies a prescribed frequency sweep signal from the first electrode to the wafer and calculates the resonance frequency of the wafer based on the frequency sweep signal received by the second electrode; a shape drawing unit that generates a shape drawing line showing the cross-sectional shape of the wafer based on the resonance frequency; and a display that displays the shape drawing line; and the first electrode and the second electrode are arranged at prescribed positions on the stage according to the electrode configuration design evaluated by the evaluation program stored in the storage medium.

[0017] To achieve the above object, an evaluation method for electrode configuration design of the present invention is executed by a computer loaded with an evaluation program for evaluating the electrode configuration design in a grinding device. In the grinding device, a pair of electrodes are mounted on a stage, and the pair of electrodes are used to detect the resonance frequency of a wafer made of a piezoelectric material during grinding of the wafer. The evaluation method is characterized by including the following steps: calculating an electrode orbit based on prescribed information including the configuration conditions of the pair of electrodes, where the electrode orbit is the orbit of the pair of electrodes when grinding an arbitrary wafer for a prescribed time; calculating the length of a repetition interval, where the repetition interval is an interval in the electrode orbit that passes above the arbitrary wafer; calculating the length of an effective interval, where the effective interval is an interval in the repetition interval in which the pair of electrodes face the arbitrary wafer simultaneously; calculating an effective ratio, where the effective ratio is the ratio of the effective interval to the repetition interval; and comparing the effective ratio with a prescribed threshold value to evaluate the electrode configuration design.

[0018] Effect of the Invention

[0019] According to the evaluation program of the electrode configuration conditions of the present invention, the grinding device, and the evaluation method of the electrode configuration conditions, the operator of the grinding machine can appropriately identify the cross-sectional shape of the wafer during processing. Brief Description of the Drawings

[0020] Figure 1 It is an explanatory diagram schematically showing the overall structure of the grinding device of Embodiment 1.

[0021] Figure 2 It is an explanatory diagram showing the positional relationship between the sun gear, the internal gear, and the carrier plate of Embodiment 1.

[0022] Figure 3 It is an explanatory diagram showing the distance between electrodes, the angle between electrodes, and the radial position of the platform.

[0023] Figure 4A It is an explanatory diagram showing the transmission state of the frequency sweep signal when the distance between electrodes is set to an appropriate distance.

[0024] Figure 4B It is an explanatory diagram showing the transmission state of the frequency sweep signal when the distance between electrodes is set shorter than the appropriate distance.

[0025] Figure 4C It is an explanatory diagram showing the transmission state of the frequency sweep signal when the distance between electrodes is set longer than the appropriate distance.

[0026] Figure 5A It is an explanatory diagram showing the change in the relative position of a pair of electrodes with respect to the wafer when the angle between electrodes with respect to the wafer is set to 0°.

[0027] Figure 5B It is an explanatory diagram showing the change in the relative position of a pair of electrodes with respect to the wafer when the angle between electrodes with respect to the wafer is set to 90°.

[0028] Figure 6 It is a diagram showing an example of the shape description line of the wafer, that is, the cross-sectional shape line, generated by the shape description unit of Embodiment 1.

[0029] Figure 7 It is a block diagram showing the evaluation program of the electrode configuration design of Embodiment 1.

[0030] Figure 8 It is a flowchart showing the sequence of the evaluation method of the electrode configuration design of the evaluation program of Embodiment 1.

[0031] Figure 9It is an explanatory diagram showing the electrode track, the repetition interval, and the effective interval.

[0032] Figure 10A It is an explanatory diagram showing the rotation tracks of the first electrode and the second electrode with respect to the center of the platform.

[0033] Figure 10B It is an explanatory diagram showing the rotation tracks of the first electrode and the second electrode with respect to the center of the target wafer.

[0034] Figure 10C It is an explanatory diagram showing the rotation tracks of the first electrode and the second electrode with the positional relationship between the carrier plate and the target wafer fixed.

[0035] Figure 11 It is a table explaining the differences in the shape drawing lines under different effective ratios.

[0036] Explanation of reference numerals

[0037] 1: Grinding device

[0038] 10: Grinder

[0039] 11: Lower platform (platform)

[0040] 12: Upper platform (platform)

[0041] 20: Frequency detector

[0042] 21a: First electrode

[0043] 21b: Second electrode

[0044] 22: Frequency operation unit

[0045] 30: Control unit

[0046] 32: Shape drawing unit

[0047] 33: Display control unit

[0048] 42: Display

[0049] 100: Evaluation program for electrode configuration design

[0050] 101: Electrode track operation process

[0051] 102: Repetition interval operation process

[0052] 103: Effective interval operation process

[0053] 104: Ratio calculation process

[0054] 105: Design evaluation process

[0055] W: Wafer. Detailed implementation manners

[0056] Hereinafter, based on Embodiment 1 shown in the drawings, the detailed implementation manners of the grinding device, the evaluation program of the electrode configuration design, and the evaluation method of the electrode configuration design of the present invention will be described.

[0057] [Grinding device]

[0058] The grinding device 1 of Embodiment 1 is a double-sided grinding device that grinds the front and back surfaces of a thin plate-shaped wafer W made of a piezoelectric material such as crystal or ceramic. In addition, the "piezoelectric material" refers to a crystalline material that can generate an electric current when pressure is applied.

[0059] As Figure 1 shown, the grinding device 1 includes a grinding machine 10, a frequency detector 20, and a control unit 30.

[0060] The grinding machine 10 clamps the wafer W between a lower platform 11 and an upper platform 12 disposed opposite to the lower platform 11, and relatively moves the lower platform 11 and the upper platform 12 with respect to the wafer W in a state where a load is applied to the wafer W, thereby grinding the front and back surfaces of the wafer W simultaneously. In addition, the grinding machine 10 may also be a single-sided grinding device that grinds one surface of the wafer W through the lower platform 11 or the upper platform 12.

[0061] The grinding machine 10 includes an annular disk-shaped lower platform 11 and an upper platform 12 that are concentrically arranged with the axis L1 as the center, a sun gear 13 rotatably disposed at the central portion of the lower platform 11, an internal gear 14 disposed on the outer peripheral side of the lower platform 11, and a disk-shaped carrier plate 15 disposed between the lower platform 11 and the upper platform 12 and formed with a wafer holding hole 15a (refer to Figure 2 ). In addition, a grinding pad 11a is pasted on the upper surface of the lower platform 11, and a grinding pad 12a is pasted on the lower surface of the upper platform 12. Further, a supply hole (not shown) for supplying grinding slurry is provided on the upper platform 12.

[0062] As Figure 2 shown, the carrier plate 15 is formed with gears on its outer periphery and meshes with the sun gear 13 and the internal gear 14. And the carrier plate 15 rotates (revolves) around the axis L1 while rotating on its own axis through the rotation of the sun gear 13 and the internal gear 14.

[0063] The wafer W is disposed inside the wafer holding hole 15a of the carrier plate 15. And, with the wafer W sandwiched between the polishing pad 11a adhered to the rotating lower platen 11 and the polishing pad 12a adhered to the rotating upper platen 12, the carrier plate 15 rotates both around its own axis and around the axis of the upper and lower platens, whereby the lower platen 11 and the upper platen 12 move relative to the wafer W, and the wafer W is polished by the polishing pads 11a and 12a. That is, the surfaces of the polishing pads 11a and 12a become the polishing surfaces for polishing the wafer W.

[0064] In addition, the polishing pads 11a and 12a are used when polishing the wafer W. The polishing pads 11a and 12a may not be used when roughly polishing the wafer W. Here, "rough polishing" means polishing at a relatively high rate using coarse abrasive grains, and "polishing" means polishing at a relatively low rate using fine abrasive grains to improve the surface finish.

[0065] The upper platen 12 is fixed to the rod 16 via the support studs 16a and the mounting members 16b mounted on the upper surface. The rod 16 is extended and retracted in the vertical direction by the fifth drive device H5, and the upper platen 12 moves up and down with the extension and retraction of the rod 16. And, a predetermined load is applied to the wafer W from the upper platen 12 according to the extension and retraction length of the rod 16.

[0066] In addition, a vertically standing first drive shaft 17a is disposed along the axis L1 at the center of the grinding machine 10. The first drive shaft 17a is a rotating shaft rotated by the first drive device H1. A driver 18 is fixed to the upper end portion of the first drive shaft 17a, and the driver 18 rotates integrally with the first drive shaft 17a. Further, a groove portion (not shown) for engaging the hook 12b provided on the upper platen 12 is formed on the outer peripheral surface of the driver 18. When the rod 16 extends and the upper platen 12 moves downward, the hook 12b engages with the groove portion of the driver 18, whereby the driver 18 and the upper platen 12 can rotate integrally.

[0067] The second drive shaft 17b is fixed in a penetrating state in the hole 13a at the central portion of the sun gear 13. The second drive shaft 17b is a hollow tube open at both ends, and the first drive shaft 17a passes through it rotatably. Further, the second drive shaft 17b is rotated by the second drive device H2.

[0068] A third drive shaft 17c is formed at the lower portion of the central portion of the lower platen 11. The third drive shaft 17c is a hollow tube open at both ends, and the first drive shaft 17a and the second drive shaft 17b pass through it rotatably. Further, the third drive shaft 17c is rotated by the third drive device H3.

[0069] In addition, a fourth drive shaft 17d is formed on the internal gear 14. The fourth drive shaft 17d is a hollow tube open at both ends, through which the first drive shaft 17a, the second drive shaft 17b, and the third drive shaft 17c are rotatably inserted. Further, the fourth drive shaft 17d is rotated by a fourth drive device H4.

[0070] Furthermore, a pair of electrode holes are formed in the upper platform 12. Each electrode hole penetrates the upper platform 12 and the polishing pad 12a, and a pair of electrodes (a first electrode 21a and a second electrode 21b) of the frequency detector 20 are respectively inserted therein.

[0071] As Figure 1 shown, the frequency detector 20 includes a pair of electrodes (a first electrode 21a and a second electrode 21b) and a frequency calculation unit 22, and detects the resonance frequency of the wafer W during the polishing process by the frequency scanning method.

[0072] In addition, herein, the "frequency scanning method" refers to a method for detecting the resonance frequency of the wafer W performed in the following order. That is, first, during the polishing process of the wafer W, a circuit is formed between a pair of electrodes (a first electrode 21a and a second electrode 21b) mounted on the upper platform 12, the wafer W, and the lower platform 11, and a frequency scanning signal is applied to the wafer W via the first electrode 21a. And, a response signal is obtained based on the signal received through the second electrode 21b. Herein, when the frequency of the applied frequency scanning signal changes (scans) within an appropriate range, if the frequency approaches the natural vibration frequency of the wafer W, a resonance phenomenon occurs and the impedance decreases. Herein, the signal intensity of the response signal varies according to the impedance. Therefore, the signal intensity of the obtained response signal is calculated, and the frequency of the frequency scanning signal when a change in the signal intensity above a specified level is observed (when the influence of the impedance decrease phenomenon is confirmed) is detected as the resonance frequency (natural vibration frequency) of the wafer W at the position of the midpoint O3 of the pair of electrodes (a first electrode 21a and a second electrode 21b) (refer to Figure 3 ).

[0073] The first electrode 21a is composed of a cylindrical metal member whose circumferential surface is covered with an insulating coating, is inserted into one of the electrode holes, and is mounted on the upper platform 12. The front end surface of the first electrode 21a exposed from the insulating coating faces the wafer W and is electrically connected to the frequency calculation unit 22. The first electrode 21a applies a frequency scanning signal output from the frequency calculation unit 22 to the wafer W.

[0074] The second electrode 21b is composed of a cylindrical metal member whose circumferential surface is covered with an insulating coating, is inserted into the other electrode hole, and is mounted on the upper platform 12. The front end surface of the second electrode 21b that is exposed from the insulating coating faces the wafer W and is electrically connected to the frequency calculation unit 22. The second electrode 21b receives the frequency sweep signal output from the first electrode 21a. In addition, the structures of the first electrode 21a and the second electrode 21b are not limited to the above structures. Any electrodes that can appropriately apply and receive the frequency sweep signal between the first electrode 21a and the second electrode 21b can be used.

[0075] Moreover, the positions where the first electrode 21a and the second electrode 21b are arranged are defined by arrangement conditions, which include the distance condition between the first electrode 21a and the second electrode 21b (hereinafter referred to as "inter-electrode distance ID"), the angular condition between the first electrode 21a and the second electrode 21b with respect to each other (hereinafter referred to as "inter-electrode angle θ"), and the position condition of the midpoint O3 between the first electrode 21a and the second electrode 21b with respect to the center (axis L1) of the upper platform 12 (hereinafter referred to as "platform radial position").

[0076] In addition, as Figure 3 shown, the inter-electrode distance ID is the distance between the center O1 of the first electrode 21a and the center O2 of the second electrode 21b. Additionally, as Figure 3 shown, the inter-electrode angle θ is the angle formed by the straight line α connecting the center O1 of the first electrode 21a and the center O2 of the second electrode 21b and the tangent line β drawn in the circumferential direction r concentric with the upper platform 12 passing through the center O1 of the first electrode 21a. Moreover, the midpoint O3 is the central position between the center O1 of the first electrode 21a and the center O2 of the second electrode 21b on the straight line α. And the platform radial position is the position of the midpoint O3 on the straight line γ connecting the center (axis L1) of the upper platform 12 and the midpoint O3. Regarding the platform radial position, taking the inner peripheral end 12x of the upper platform 12 as 0%, and the outer peripheral end 12y of the upper platform 12 as 100%, it is represented by a value that is smaller the closer it is to the inner peripheral end 12x and larger the closer it is to the outer peripheral end 12y.

[0077] Furthermore, as will be described later, the grinding apparatus 1 of Embodiment 1 generates a shape drawing line showing the cross-sectional shape of the wafer W based on the resonance frequency of the wafer W. When generating the shape drawing line, if the grinding apparatus 1 of Embodiment 1 appropriately detects the resonance frequency of the wafer W, a clearer shape drawing line can be generated. Therefore, in order to improve the generation accuracy of the shape drawing line, it is necessary to appropriately detect the resonance frequency of the wafer W by the frequency detector 20. In this regard, it is known that in the electrode arrangement design, by changing the inter-electrode distance ID, the inter-electrode angle θ, and the platform radial position respectively, the detection accuracy of the resonance frequency of the wafer W changes, and the generation accuracy of the shape drawing line fluctuates.

[0078] That is, the distance ID between the electrodes, the angle θ between the electrodes, and the radial position of the stage are all parameters that cause variations in the generation accuracy of the shape drawing line of the wafer W. The reasons why each parameter causes variations in the generation accuracy of the shape drawing line of the wafer W are as follows.

[0079] As Figure 4A shown, when the distance ID between the electrodes is set to an appropriate distance, the frequency sweep signal (shown by a dotted line) output from the first electrode 21a passes through the wafer W and is received by the second electrode 21b. Therefore, when the distance ID between the electrodes is set to an appropriate distance, the frequency detector 20 can obtain a stable response signal and can appropriately detect the resonance frequency. Therefore, a clear shape drawing line can be generated.

[0080] On the other hand, when the distance between the first electrode 21a and the second electrode 21b is small enough, it is speculated that the resistance becomes smaller when the frequency sweep signal is directly input from the first electrode 21a to the second electrode 21b via the polishing slurry (without passing through the wafer W) compared to being received by the second electrode 21b through the wafer W. Therefore, as Figure 4B shown, when the distance ID between the electrodes is set shorter than the appropriate distance (the electrodes are too close to each other), the proportion of the frequency sweep signal short-circuiting without passing through the wafer W increases. In this case, compared with the case where the distance ID between the electrodes is set to an appropriate distance, sometimes the peak value of the response signal becomes smaller, or the response signal becomes unstable. As a result, the frequency detector 20 cannot appropriately detect the resonance frequency, and the generated shape drawing line is likely to become disordered.

[0081] In addition, before the frequency sweep signal is output from the first electrode 21a and received by the second electrode 21b, it sometimes passes through not only the wafer W but also the polishing slurry or the carrier plate 15. However, the presence of the polishing slurry or the carrier plate 15 is the main cause of the resistance of the signal transmission. Therefore, as Figure 4C shown, when the distance ID between the electrodes is set longer than the appropriate distance (the electrodes are too far from each other), the resistance of the intermediate path of the frequency sweep signal output from the first electrode 21a to being received by the second electrode 21b increases, or the transmission path of the frequency sweep signal becomes disordered. Therefore, unevenness is likely to occur in the response signal. Further, it is difficult for the first electrode 21a and the second electrode 21b to face the wafer W simultaneously. As a result, compared with the case where the distance ID between the electrodes is set to an appropriate distance, the peak value of the response signal becomes smaller, the frequency detector 20 cannot appropriately detect the resonance frequency, and unevenness is likely to occur in the generation accuracy of the shape drawing line.

[0082] Thus, the detection accuracy of the resonance frequency of the frequency detector 20 varies according to the distance ID between the electrodes. As a result, the generation accuracy of the shape drawing line of the wafer W fluctuates. Therefore, the distance ID between the electrodes can be said to be a parameter that causes fluctuations in the generation accuracy of the shape drawing line of the wafer W. In addition, the appropriate distance of the distance ID between the electrodes is independent of the platform size, preferably 1 mm to 500 mm, more preferably the distance ID between the electrodes is 6 mm to 150 mm, and further preferably the distance ID between the electrodes is 10 mm to 30 mm.

[0083] In addition, in the frequency detector 20, the response signal can be acquired more stably when the response signal is acquired in a state where both the first electrode 21a and the second electrode 21b face the wafer W simultaneously than when the response signal is acquired in a state where only one of the first electrode 21a or the second electrode 21b faces the wafer W.

[0084] In this regard, as the wafer W is polished, when the wafer W moves relative to the first electrode 21a and the second electrode 21b, when the relative movement of the wafer W with respect to the first electrode 21a and the second electrode 21b is along the circumferential direction r concentric with the upper platform 12, when the wafer W is incident at an inter-electrode angle θ of 0°, as Figure 5A shown, it takes time from the moment the first electrode 21a faces the wafer W until it becomes a state where both the first electrode 21a and the second electrode 21b face the wafer W. Therefore, the time during which the pair of electrodes (the first electrode 21a, the second electrode 21b) face the wafer W simultaneously is short, and it is easy for the acquisition of the response signal to become unstable.

[0085] On the other hand, when the relative movement of the wafer W with respect to the first electrode 21a and the second electrode 21b is along the circumferential direction r concentric with the upper platform 12, when the wafer W is incident at an inter-electrode angle θ of 90°, as Figure 5B shown, both the first electrode 21a and the second electrode 21b almost simultaneously start to face the wafer W, and at almost the same moment, both the first electrode 21a and the second electrode 21b completely face the wafer W. Therefore, the time during which the pair of electrodes (the first electrode 21a, the second electrode 21b) face the wafer W can be extended, and the response signal can be stably acquired. That is, when the first electrode 21a and the second electrode 21b are incident relative to the wafer W, it is preferable that the two electrodes (the first electrode 21a and the second electrode 21b) start to face the wafer W as simultaneously as possible.

[0086] Thus, according to the relative movement trajectory of the wafer W with respect to the first electrode 21a and the second electrode 21b and the angle θ between the electrodes, the time required from the start of the relative movement with respect to the wafer W from at least one of the first electrode 21a or the second electrode 21b until the state where both the first electrode 21a and the second electrode 21b face the wafer W completely is different, and the stability of the response signal acquisition also changes. Therefore, the inter-electrode angle θ can be said to be a parameter that causes fluctuations in the generation accuracy of the shape drawing line of the wafer W. In addition, the appropriate numerical range of the inter-electrode angle θ may vary according to conditions such as the inter-electrode distance ID or the platform radial position.

[0087] Furthermore, the more the number of acquisitions of the response signal in the frequency detector 20, the higher the generation accuracy of the shape drawing line. However, the carrier plate 15 rotates around the axis L1 while rotating (revolving) itself, and the wafer W performs a planetary motion centered on the axis L1. Therefore, if the platform radial position is different, the trajectories of the first electrode 21a and the second electrode 21b with respect to the wafer W change, and the number of acquisitions of the response signal of the frequency detector 20 fluctuates. Here, when the platform radial position is set to a position close to the inner peripheral end 12x or the outer peripheral end 12y of the upper platform 12, there is a tendency for the number of acquisitions of the response signal to decrease. Therefore, the platform radial position can be said to be a parameter that causes fluctuations in the generation accuracy of the shape drawing line of the wafer W. And from the viewpoint of the acquisition frequency of these response signals, the platform radial position is preferably set in the range of 10% to 80%, and more preferably set in the range of 20% to 45% or 55% to 80%.

[0088] In addition, in the polishing apparatus 1 of the first embodiment, the first electrode 21a and the second electrode 21b are arranged at specified positions on the upper platform 12 according to the electrode arrangement design evaluated and determined to be effective for the generation of the shape drawing line of the wafer W according to the following electrode arrangement design evaluation procedure 100.

[0089] As Figure 1 shown, the frequency operation unit 22 includes a frequency scanning unit 23, a signal detection unit 24, and a data processing unit 25.

[0090] The frequency scanning unit 23 generates a frequency scanning signal whose frequency varies (scans) within a preset specified frequency range and outputs it.

[0091] The signal detection unit 24 acquires a response signal that varies according to the impedance between the second electrode 21b and the lower platform 11 based on the frequency scanning signal received by the second electrode 21b. The response signal is input to the data processing unit 25.

[0092] The data processing unit 25 calculates the resonance frequency of the wafer W based on the signal strength of the response signal input from the signal detection unit 24 and the frequency of the frequency sweep signal when the response signal is obtained. That is, the data processing unit 25 continuously monitors the signal strength while the frequency of the frequency sweep signal changes within a specified frequency range. And the frequency at which a change in the signal strength accompanied by a resonance phenomenon is observed is set as the resonance frequency at the position facing the midpoint O3 between the first electrode 21a and the second electrode 21b of the wafer W. The data of the resonance frequency is input to the control unit 30.

[0093] Moreover, whenever the frequency of the frequency sweep signal changes within the specified frequency range, the data processing unit 25 calculates the resonance frequency. That is, the resonance frequency data is continuously obtained at the time interval of the change in the frequency of the frequency sweep signal. In addition, when the maximum value of the signal strength obtained during the period when the frequency of the frequency sweep signal changes within the specified frequency range does not satisfy the specified value, the data processing unit 25 does not calculate the resonance frequency. Because in this case, it is presumed that the midpoint O3 between the first electrode 21a and the second electrode 21b does not face the wafer W.

[0094] The control unit 30 is composed of a CPU (Central Processing Unit), etc., as Figure 1 shown, and includes a device control unit 31, a shape drawing unit 32, a display control unit 33, a memory 34, etc. In addition, an input device 41 that can be operated by the operator of the grinding device 1 and a display 42 that can be visually observed by the operator are connected to the control unit 30.

[0095] Based on the processing target or various conditions of the wafer W input by the operator via the input device 41, the program stored in the memory 34, the cross-sectional shape information of the wafer W calculated by the shape drawing unit 32, etc., the device control unit 31 outputs control instructions to the first drive device H1 to the fifth drive device H5 to control the operation of the grinding machine 10.

[0096] The shape drawing unit 32 utilizes the fact that the resonance frequency (natural vibration frequency) of the wafer W varies according to the thickness of the wafer W, and calculates the cross-sectional shape of the wafer W based on the data of the resonance frequency of the wafer W detected by the frequency detector 20, and generates a cross-sectional shape line T1 as Figure 6 shown. The cross-sectional shape line T1 is a shape drawing line showing the cross-sectional shape of the wafer W, and is periodically generated at a specified time interval during the grinding process of the wafer W.

[0097] In addition, during the polishing of the wafer W, the shape depiction unit 32 generates a cross-sectional shape line T1 without obtaining the position information of the wafer W. Here, as long as an appropriate resonance frequency is continuously obtained sufficiently when the first electrode 21a and the second electrode 21b pass above the wafer, the cross-sectional shape line T1 is output. In addition, the shape depiction unit 32 can instantaneously convert the resonance frequency data input from the frequency detector 20 into the thickness data of the wafer W, and display the cross-sectional shape line T1 obtained by depicting the obtained thickness data at equal intervals on the screen as the shape depiction line of the wafer W. At this time, the starting point and the ending point of the continuous thickness data of the wafer W can be used as the values of the outer peripheral ends of the cross-sectional shape of the wafer W, respectively.

[0098] In addition, in the shape depiction line generated based on the data of the resonance frequency obtained at a position deviated from the vicinity of the center of the wafer W, the appropriateness as the shape depiction line showing the cross-sectional shape of the wafer W is lacking. Therefore, the shape depiction unit 32 of the first embodiment does not use the data of the resonance frequency obtained at a position deviated from the vicinity of the center of the wafer W for the generation of the shape depiction line. As a result, the shape depiction unit 32 can generate a shape depiction line with higher accuracy.

[0099] Here, the shape depiction unit 32 of the first embodiment does not obtain the position information of the wafer W. Therefore, in order not to use the data of the resonance frequency obtained at a position deviated from the vicinity of the center of the wafer W for the generation of the shape depiction line, specifically, when the shape depiction unit 32 continuously inputs the resonance frequency data a specified number of times (for example, 5 to 20 times, etc., which can be arbitrarily set) or more from the frequency detector 20, the shape depiction line is generated based on the resonance frequency data. And when the resonance frequency data is not continuously input a specified number of times or more, it is presumed that the data is obtained when the midpoint O3 of the first electrode 21a and the second electrode 21b passes through the end of the wafer W, and the shape depiction unit 32 does not generate the shape depiction line of the wafer W. As a result, the shape depiction unit 32 can exclude the data of the resonance frequency obtained at a position deviated from the vicinity of the center of the wafer W from the generation of the shape depiction line. This is one of the methods to improve the reliability of the shape depiction line.

[0100] The display control unit 33 controls the display content displayed on the display 42. The display control unit 33 quickly displays the shape depiction line (cross-sectional shape line T1) of the wafer W generated by the shape depiction unit 32 on the display 42 each time it is generated. That is, every time a new shape depiction line of the wafer W is generated, the display 42 switches to display the new shape depiction line. Thereby, the operator of the polishing apparatus 1 can visually confirm the shape depiction line of the wafer W displayed on the display 42 and can grasp (in real time) the cross-sectional shape of the wafer W that changes moment by moment during the polishing process almost simultaneously with the polishing operation of the wafer W, so as to be able to identify the trend of the shape change.

[0101] [Evaluation Procedure for Electrode Configuration Design]

[0102] The evaluation procedure 100 for the electrode configuration design of Example 1 is loaded into an arbitrary computer (personal computer, notebook or tablet computer, smart phone, cloud server, non-cloud server device, etc.). Further, the evaluation procedure 100 for the electrode configuration design of Example 1 is used when designing the electrode configuration in the grinding apparatus 1 or the like, and causes the computer to execute a plurality of processes described later, and evaluates the electrode configuration design in the grinding apparatus 1 or the like. In the grinding apparatus 1, a pair of electrodes (first electrode 21a and second electrode 21b) are mounted on the upper table 12, and the pair of electrodes are used to detect the resonance frequency of the wafer W during the grinding of the wafer W, and the wafer W is made of a piezoelectric material.

[0103] That is, as Figure 7 shown, the evaluation procedure 100 for the electrode configuration design of Example 1 causes the computer to sequentially execute an electrode track calculation process 101, a repetition interval calculation process 102, an effective interval calculation process 103, a ratio calculation process 104, and a design evaluation process 105.

[0104] The electrode track calculation process 101 is a process of calculating an electrode track EO (see Figure 3 ) of a midpoint O3 of a pair of electrodes (first electrode 21a and second electrode 21b) (see Figure 9 ) when grinding an arbitrary wafer W for a specified time based on specified information including the configuration conditions of the pair of electrodes (first electrode 21a and second electrode 21b).

[0105] In addition, the configuration conditions of the pair of electrodes (first electrode 21a and second electrode 21b) used when calculating the electrode track EO in the electrode track calculation process 101 include at least an inter-electrode distance ID, an inter-electrode angle θ, and a platform radial position. The specified information other than the configuration conditions includes, for example, device data of the grinding apparatus 1 or the like, grinding conditions, information of the wafer W to be ground, and the like.

[0106] The repetition interval calculation process 102 is a process of calculating a length of a repetition interval S OV (see Figure 9 ) which is an interval passing above an arbitrary wafer W within a specified time period in the electrode track EO calculated by the electrode track calculation process 101.

[0107] The effective interval calculation process 103 is a process of calculating an effective interval S OV in the repetition interval S VA (see Figure 9Processing of the length of ().

[0108] The ratio calculation process 104 calculates the effective interval S VA Occupying the repetition interval S OV The process of calculating the ratio, that is, the effective ratio ER

[0109] The design evaluation process 105 is a process of comparing the effective ratio ER calculated by the ratio calculation process 104 with a preset specified threshold value to evaluate the electrode configuration design in the polishing device 1. In addition, in the design evaluation process 105, the evaluation result of the electrode configuration design can be displayed on a display device of a computer or a display device separately provided from the computer, etc.

[0110] [Evaluation method of electrode configuration design]

[0111] The evaluation order of the evaluation method of the electrode configuration design in the evaluation program 100 of Example 1 is shown in Figure 8 The flowchart shown. In addition, Figure 8 The evaluation method shown is executed by a computer loaded with the evaluation program 100 of the electrode configuration design when designing the electrode configuration in the polishing device 1 etc.

[0112] Hereinafter, based on Figure 8 The flowchart shown will explain the evaluation method of the electrode configuration design of Example 1

[0113] In step S1, the computer reads the specified information required to calculate the orbits of the polishing wafer W and a pair of electrodes (the first electrode 21a, the second electrode 21b) during polishing, and proceeds to step S2. Here, the information read by the computer is at least information related to the device data of the polishing device 1 for polishing the wafer W, information related to the polishing conditions of the wafer W polished by the polishing device 1, information related to the wafer W polished by the polishing device 1, and information related to the configuration conditions of a pair of electrodes (the first electrode 21a, the second electrode 21b) installed on the polishing device 1. Each piece of information can be appropriately input by the operator of the computer or read from the memory loaded in the computer

[0114] In addition, the device data refers to, for example, the respective diameter sizes (sizes) of the lower platen 11, the upper platen 12, the sun gear 13, the internal gear 14, the carrier plate 15 in the polishing device 1, etc., or the respective number of teeth of the sun gear 13, the internal gear 14, the carrier plate 15, etc. In addition, the polishing conditions refer to, for example, the respective rotation speeds of the lower platen 11, the upper platen 12, the sun gear 13, the internal gear 14. In addition, the wafer information refers to, for example, the size or shape of the polished wafer W, the configuration position information of the wafer W in the carrier plate 15, etc. The polishing conditions or wafer information can be standard information determined according to the polishing device 1 etc.

[0115] Further, the arrangement conditions of a pair of electrodes (the first electrode 21a and the second electrode 21b) differ according to the electrode arrangement design in the polishing apparatus 1, and at least include the inter-electrode distance ID, the inter-electrode angle θ, and the platform radial position.

[0116] In step S2, after the reading of the specified information in step S1, the computer calculates the electrode orbit EO (refer to Figure 9 ) and proceeds to step S3. Here, the "electrode orbit EO" refers to the orbit of the midpoint O3 when polishing an arbitrary wafer W (hereinafter referred to as "target wafer W′") at an arbitrary position on the lower platform 11 for a preset specified time (for example, 250 seconds to 350 seconds). The electrode orbit EO is calculated, for example, in the following order.

[0117] First, the computer calculates the rotation orbit of the target wafer W′ ( Figures 10A to 10C shown by diagonal lines therein) based on the center (axis L1) of the upper platform 12. In addition, the "rotation orbit of the target wafer W′" is the orbit of the center of the target wafer W′ when polishing the target wafer W′ for the specified time.

[0118] Xwafer = C radius × cos(C revolution × i × UT × π / 180) + W position × cos(C rotation × i × UT × π / 180) ··· (1)

[0119] Ywafer = C radius × sin(C revolution × i × UT × π / 180) + W position × sin(C rotation × i × UT × π / 180) ··· (2)

[0120] where, Xwafer: the X coordinate of the target wafer W′ at the center of the upper platform,

[0121] Ywafer: the Y coordinate of the target wafer W′ at the center of the upper platform,

[0122] C radius: the radius of the center orbit during the polishing of the carrier 15,

[0123] C revolution: the revolution speed [rpm] of the carrier 15,

[0124] C rotation: the rotation speed [rpm] of the carrier 15,

[0125] W position: the distance between the center of the carrier 15 and the center of the target wafer W′,

[0126] i: an arbitrary integer,

[0127] UT: an arbitrary time unit [msec].

[0128] Next, the computer calculates the rotation orbits RO1 of the first electrode 21a and the second electrode 21b with respect to the center (axis L1) of the above platform 12 based on the following formulas (3) and (4) (refer to Figure 10A ). In addition, although the rotation orbits of the first electrode 21a and the second electrode 21b are calculated separately, in Figures 10A to 10C , each rotation orbit is shown repeatedly. Also, the "rotation orbit of the first electrode 21a" is the orbit of the center O1 of the first electrode 21a when the target wafer W' is polished for a specified time. The "rotation orbit of the second electrode 21b" is the orbit of the center O2 of the second electrode 21b when the target wafer W' is polished for a specified time.

[0129] X electrode = D radius × cos(U rotation × i × UT × π / 180) ··· (3)

[0130] Y electrode = D radius × sin(U rotation × i × UT × π / 180) ··· (4)

[0131] Among them, X electrode: the X coordinate of the first electrode 21a or the second electrode 21b at the center of the upper platform,

[0132] Y electrode: the Y coordinate of the first electrode 21a or the second electrode 21b at the center of the upper platform,

[0133] D radius: the radius of the central orbit during the polishing of the first electrode 21a or the second electrode 21b, U rotation: the rotation speed [rpm] of the upper platform 12.

[0134] Next, the computer converts the rotation orbits RO1 of the first electrode 21a and the second electrode 21b with respect to the center (axis L1) of the above platform 12 into orbits RO2 on the coordinates with respect to the center W' of the target wafer W' based on the following formulas (5) and (6) (refer to O ). Figure 10B )

[0135] X electrode 2 = X electrode - Xwafer ··· (5)

[0136] Y electrode 2 = Y electrode - Ywafer ··· (6)

[0137] Among them, X electrode 2: the X coordinate of the first electrode 21a or the second electrode 21b at the center of the target wafer W',

[0138] Y electrode 2: the Y coordinate of the first electrode 21a or the second electrode 21b at the center of the target wafer W'.

[0139] Further, the computer calculates the cancellation of the rotation of the carrier 15 based on the following formulas (7) and (8), and shows the rotation orbits RO3 of the first electrode 21a and the second electrode 21b while fixing the positional relationship between the carrier 15 holding the target wafer W' and the target wafer W' (refer to Figure 10C ).

[0140] X electrode 3 = X electrode 2 × cos(-C rotation × i × UT × π / 180) - Y electrode 2 × sin(-C rotation × i × UT × π / 180) ··· (7)

[0141] Y electrode 3 = X electrode 2 × sin(-C rotation × i × UT × π / 180) + Y electrode 2 × cos(-C rotation × i × UT × π / 180) ··· (8)

[0142] Among them, X electrode 3: the X coordinate of the first electrode 21a or the second electrode 21b at the center of the target wafer W' when the positional relationship between the carrier 15 and the wafer W is fixed,

[0143] Y electrode 3: the Y coordinate of the first electrode 21a or the second electrode 21b at the center of the target wafer W' when the positional relationship between the carrier 15 and the wafer W is fixed.

[0144] Further, the computer obtains the orbit of the midpoint O3, that is, the "electrode orbit EO", as the orbit of the central position between the rotation orbit RO3 of the first electrode 21a and the rotation orbit RO3 of the second electrode 21b.

[0145] In step S3, after the calculation of the electrode orbit EO in step S2, the computer determines whether the calculated electrode orbit EO passes above a reference region set on the target wafer W' ( Figure 9 the inner region of the circle A shown by the dotted line in the figure). And when the computer determines that it is yes (passes above the reference region), it proceeds to step S4, and when it determines that it is no (does not pass above the reference region), it ends.

[0146] Here, the "reference region" refers to a similar shape whose center coincides with the target wafer W', and its radius is a region of a specified magnification (0.5 times to 0.7 times) of the radius of the target wafer W'. In addition, when the electrode orbit EO does not pass above the reference region, since the resonance frequency data is only obtained at a position deviated from the vicinity of the center of the wafer W, a shape drawing line with good accuracy cannot be obtained. The size of the reference region can be set arbitrarily.

[0147] In step S4, after determining in step S3 that the electrode orbit EO passes above the reference region, the computer extracts the repeating interval S from the electrode orbit EO calculated in step S2 OV (refer to Figure 9), and proceed to step S5. Here, "repetition interval S" OV " refers to the interval that passes above the target wafer W' during a preset specified time (e.g., 250 seconds to 350 seconds) in the electrode orbit EO calculated in step S2.

[0148] In step S5, after the extraction of the repetition interval S in step S4 OV , the computer calculates the length of the repetition interval S extracted in step S4 OV , and proceeds to step S6. In addition, as Figure 9 shown, in the case where multiple repetition intervals S OV are extracted, the length is calculated for each repetition interval S OV .

[0149] In step S6, after the calculation of the repetition interval S in step S5 OV , the computer extracts the valid interval S VA (refer to Figure 9 ) and proceeds to step S7. Here, "valid interval S VA " refers to the interval in the repetition interval S OV extracted in step S4 where a pair of electrodes (first electrode 21a, second electrode 21b) face the target wafer W' simultaneously. In addition, as Figure 9 shown, in the case where multiple repetition intervals S OV are extracted, the valid interval S OV is extracted for each repetition interval S VA . In addition, the valid interval S VA is the interval where the following formulas (9) and (10) hold simultaneously.

[0150] First distance ≤ radius of the target wafer W'... (9)

[0151] Second distance ≤ radius of the target wafer W'... (10)

[0152] Among them, the first distance: the distance from the center O1 of the first electrode 21a to the center W' of the target wafer W' O ;

[0153] The second distance: the distance from the center O2 of the second electrode 21b to the center W' of the target wafer W' O .

[0154] In step S7, after the extraction of the valid interval SVA in step S6, the computer calculates the length of the extracted valid interval S VA and proceeds to step S8. In addition, as Figure 9 shown, in the case where multiple valid intervals S VAIn the case of each valid interval S VA Operation length.

[0155] In step S8, after the operation of the valid interval S in step S7 VA the computer calculates the effective ratio ER and proceeds to step S9. Here, the "effective ratio ER" means the ratio of the length of the valid interval S VA to the length of the repetition interval S OV The effective ratio ER is calculated by the following formula (11). In addition, as Figure 9 shown, in the case where multiple repetition intervals S OV are extracted, for each repetition interval S OV the effective ratio ER is calculated, and the average value of the calculated multiple effective ratios ER is taken as the final effective ratio ER.

[0156] Effective ratio ER [%] = valid interval S VA ÷ repetition interval S OV × 100 ··· (11)

[0157] In step S9, after the calculation of the effective ratio ER in step S8, the computer compares the effective ratio ER calculated in step S8 with a preset specified threshold value, evaluates the electrode configuration design of a pair of electrodes (first electrode 21a, second electrode 21b) in the polishing apparatus 1, and proceeds to the end. In addition, the evaluation result of the electrode configuration design evaluated in step S9 can be displayed on a display device provided in the computer, a display device connected to the computer by wire or wirelessly, etc.

[0158] Here, the threshold value compared with the effective ratio ER is set to an arbitrary value. For example, based on the effective region set within a specified range from the center of the wafer W, it is set to a value of 90% to 85%.

[0159] Hereinafter, the operation of the polishing apparatus 1 of Example 1 will be described.

[0160] In the polishing apparatus 1 of Example 1, in order to improve the processing accuracy of the wafer W or appropriately perform the setting management of the polishing conditions, it is desired that the operator appropriately grasp the state or shape of the wafer W during the polishing process in real time (almost simultaneously with the polishing operation of the polishing apparatus 1 on the wafer W).

[0161] In this regard, the grinding device 1 of Embodiment 1 includes: a grinding machine 10 that grinds a wafer W made of a piezoelectric material by means of platforms (lower platform 11 and upper platform 12); a first electrode 21a and a second electrode 21b that are installed at predetermined positions on the upper platform 12 and whose front ends face the wafer W; a frequency calculation unit 22 that applies a predetermined frequency sweep signal to the wafer from the first electrode 21a and calculates the resonance frequency of the wafer W based on the frequency sweep signal received by the second electrode 21b; a shape drawing unit 32 that generates a shape drawing line showing the cross-sectional shape of the wafer W based on the resonance frequency; and a display 42 that displays the shape drawing line.

[0162] Accordingly, the grinding device 1 of Embodiment 1 can detect the resonance frequency of the wafer W by the frequency sweep method during the grinding of the wafer W, generate a shape drawing line showing the cross-sectional shape of the wafer W based on the detected resonance frequency, and display it on the display 42. Here, when generating the shape drawing line based on the resonance frequency, the grinding device 1 does not need to know the position information of the wafer W and the like. That is, the grinding device 1 of Embodiment 1 can generate a shape drawing line showing the cross-sectional shape of the wafer W by instantaneously converting the continuously input resonance frequency data into thickness data of the wafer W and plotting it.

[0163] Accordingly, compared with a case where, for example, the thickness of the wafer W is measured by an optical method and a shape drawing line is generated, the grinding device 1 of Embodiment 1 can shorten the time required to generate the shape drawing line and generate and display the shape drawing line in a manner almost simultaneous (real-time) with the grinding operation of the wafer W. And by the operator visually observing the shape drawing line displayed on the display 42, the operator can identify the cross-sectional shape of the wafer W during grinding almost in real time. Therefore, the grinding device 1 of Embodiment 1 enables the operator to appropriately grasp the cross-sectional shape of the wafer W during processing.

[0164] Moreover, by the operator appropriately grasping the cross-sectional shape of the wafer during processing, the operator can accurately adjust the grinding conditions or grinding time, etc., and can obtain the desired wafer W.

[0165] In addition, when detecting the resonance frequency of the wafer W by the frequency sweep method, if the grinding device 1 cannot sufficiently obtain data on the resonance frequency of the wafer W, the shape drawing line becomes unclear, or there are unevennesses in the generation accuracy of the shape drawing line, and thus an appropriate shape drawing line cannot be generated. And as a result, sometimes the operator cannot appropriately grasp the cross-sectional shape of the wafer W during processing.

[0166] That is, in order to generate clear shape description lines or suppress unevenness in the generation accuracy of shape description lines, it is necessary to continuously and highly accurately detect the resonance frequency of the wafer W at a prescribed interval by the frequency detector 20. However, depending on the arrangement conditions of a pair of electrodes (the first electrode 21a and the second electrode 21b), the resonance frequency cannot be continuously detected. As a result, there is a problem that appropriate shape description lines cannot be generated.

[0167] Furthermore, the arrangement positions of a pair of electrodes (the first electrode 21a and the second electrode 21b) are actually restricted due to the design in the manufacture of the grinding machine 10. That is, in order to prevent interference between a pair of electrodes (the first electrode 21a and the second electrode 21b) and components other than the electrodes provided on the upper table 12 or suppress deterioration of maintainability, the arrangement positions of the first electrode 21a and the second electrode 21b are restricted. Therefore, it is desirable that the arrangement design of the first electrode 21a and the second electrode 21b is a design aimed at obtaining the best shape description lines of the wafer W even under various restrictions.

[0168] In response to this, in the grinding apparatus 1 of the first embodiment, when designing the electrode arrangement, evaluation is performed by the evaluation program 100 for the electrode arrangement design of the first embodiment. That is, in the grinding apparatus 1 of the first embodiment, a pair of electrodes (the first electrode 21a and the second electrode 21b) are arranged at a prescribed position on the upper table 12 according to the electrode arrangement design evaluated by the evaluation program 100 of the first embodiment. And in the first embodiment, the arrangement positions of the first electrode 21a and the second electrode 21b are determined according to the electrode arrangement design determined to be effective for the generation of the shape description lines of the wafer W by the evaluation program 100.

[0169] Thereby, in the grinding apparatus 1 of the first embodiment, it is possible to perform manufacturing after previously confirming whether appropriate shape description lines of the wafer W can be obtained during grinding with an arbitrarily designed electrode arrangement. Then, by arranging the first electrode 21a and the second electrode 21b according to the arrangement design evaluated as being able to obtain appropriate shape description lines, the grinding apparatus 1 of the first embodiment can generate and display appropriate shape description lines of the wafer W during grinding, and can enable an operator to appropriately grasp the wafer shape.

[0170] Hereinafter, the operation of the evaluation program 100 and the evaluation method for the electrode arrangement design of the first embodiment will be described.

[0171] As described above, a pair of electrodes (first electrode 21a, second electrode 21b) are mounted on the upper platform 12 of the polishing apparatus 1 of Embodiment 1. The pair of electrodes are used to detect the resonance frequency of the wafer W during polishing of the wafer W. The wafer W is made of a piezoelectric material. In the polishing apparatus 1 of Embodiment 1, according to the positions where the pair of electrodes (first electrode 21a, second electrode 21b) are arranged, the calculation accuracy of the resonance frequency of the wafer W changes, and the generation accuracy of the shape drawing line showing the cross-sectional shape of the wafer W changes accordingly. Therefore, when designing and manufacturing the polishing apparatus 1, it is required to evaluate the effectiveness of the electrode arrangement designed arbitrarily on the generation accuracy of the shape drawing line, and to determine whether the designed electrode arrangement is suitable for the generation of the shape drawing line.

[0172] In this regard, the evaluation program 100 for the electrode arrangement design of Embodiment 1 is loaded into an arbitrary computer and used when designing the electrode arrangement in the polishing apparatus 1 of Embodiment 1 and the like.

[0173] That is, the evaluation program 100 for the electrode arrangement design of Embodiment 1 causes the computer to execute the following processes: an electrode trajectory calculation process 101 that calculates an electrode trajectory EO based on prescribed information including the arrangement conditions of a pair of electrodes (first electrode 21a, second electrode 21b), where the electrode trajectory EO is the trajectory of the midpoint O3 of the pair of electrodes 21a, 21b when polishing an arbitrary target wafer W' for a prescribed time; a repetition interval calculation process 102 that calculates the length of a repetition interval S OV where the repetition interval S OV is the interval that passes above the target wafer W' during a prescribed time period in the electrode trajectory EO; an effective interval calculation process 103 that calculates the length of an effective interval S VA where the effective interval S VA is the interval in the repetition interval SOV where the pair of electrodes 21a, 21b face the target wafer W' simultaneously; and a ratio calculation process 104 that calculates an effective ratio ER, where the effective ratio ER is the ratio of the effective interval S VA to the repetition interval S OV .

[0174] Thus, based on the effective ratio ER output from the computer, the designer of the polishing apparatus 1 and the like can confirm whether the electrode arrangement design arbitrarily designed is effective for the generation accuracy of the shape drawing line generated during polishing before actually manufacturing the polishing apparatus 1 and the like. That is, it can be confirmed whether it is an electrode arrangement design that can obtain an appropriate shape drawing line. And the designer of the polishing apparatus 1 and the like designs and manufactures the polishing apparatus 1 and the like according to the electrode arrangement whose effectiveness for the generation accuracy of the shape drawing line of the wafer W has been confirmed, so that an appropriate shape drawing line can be generated during polishing. As a result, the operator of the polishing apparatus 1 and the like can appropriately grasp the cross-sectional shape of the wafer W during processing.

[0175] In addition, the evaluation program 100 of Example 1 causes a computer to execute a design evaluation process 105, that is, to compare the effective ratio ER with a specified threshold value and evaluate the electrode configuration design.

[0176] Therefore, the evaluation program 100 of Example 1 can mechanically evaluate the electrode configuration design by a computer. Thus, for example, it is possible to prevent the evaluation result of the electrode configuration design from changing or becoming ambiguous due to the subjectivity of the designer of the grinding device 1 or the like, and it is possible to stably perform the evaluation based on a certain criterion.

[0177] Figure 11 Differences in the shape drawing lines of the wafer W in the case of different effective ratios ER are illustrated.

[0178] The trial production device 1 is a grinding device configured with a first electrode 21a and a second electrode 21b according to an electrode configuration design with an effective ratio ER of 90.6%. And when grinding the target wafer W' using the trial production device 1, the electrode track EO (repetition section S OV ) and the effective section S VA (shown by a thick line) of the track prediction diagram is as Figure 11 shown. Further, the shape drawing line prediction diagram in this case is the Figure 11 prediction diagram 1001 shown. If the prediction diagram 1001 is compared with the wafer cross-sectional shape drawing line 1003 measured on the table after actually grinding the target wafer W', they become substantially the same shape, and it is speculated that the trial production device 1 can appropriately grasp the wafer cross-sectional shape during grinding. Therefore, it can be known that the electrode configuration design in the trial production device 1 is effective for the shape drawing line of the wafer W.

[0179] In contrast, the trial production device 2 is a grinding device configured with a first electrode 21a and a second electrode 21b according to an electrode configuration design with an effective ratio ER of 51.5%. And when grinding the target wafer W' using the trial production device 2, the electrode track EO (repetition section S OV ) and the effective section S VA (shown by a thick line) of the track prediction diagram is as Figure 11 shown. Further, the shape drawing line prediction diagram in this case is the Figure 11 prediction diagram 1002 shown. If the prediction diagram 1002 is compared with the wafer cross-sectional shape drawing line 1003 measured on the table after actually grinding the target wafer W', they become completely different shapes, and it is speculated that it is difficult for the trial production device 2 to appropriately grasp the wafer cross-sectional shape during grinding. Therefore, it can be known that the electrode configuration design in the trial production device 2 is ineffective for the shape drawing line of the wafer W.

[0180] Thus, when designing the polishing device 1 etc., by evaluating the configuration design of a pair of electrodes (first electrode 21a, second electrode 21b) using the electrode configuration design evaluation program 100 of Example 1, the polishing device 1 etc. that can appropriately generate shape drawing lines of the wafer W can be manufactured.

[0181] The above describes the evaluation procedure of the electrode configuration conditions, the grinding device, and the evaluation method of the electrode configuration conditions of the present invention based on Example 1, but the specific structure is not limited to this example, and design changes or additions are allowed as long as they do not deviate from the main purpose of the invention of each claim.

[0182] In the evaluation program 100 of the first embodiment, an example is shown in which a computer is caused to execute the design evaluation process 105 of comparing the effective ratio ER with a predetermined threshold value set in advance and evaluating the electrode arrangement design in the polishing device 1. However, the evaluation program 100 does not necessarily need to cause the computer to execute the design evaluation process 105. For example, in the ratio calculation process 104, the calculated effective ratio ER may be displayed on a display device included in the computer or a display device provided separately from the computer, and the designer of the polishing device 1 may visually check it. In this case, the designer can judge the effectiveness of the electrode arrangement design based on the effective ratio ER.

[0183] In the evaluation program 100 of the first embodiment, a plurality of repetitive sections S are extracted. OV Or valid interval S VA In the case of OV Or valid interval S VA Example of length calculation. However, the repeated interval S OV For example, multiple repetition intervals S may be OV The total value is valid in the interval S VA It can also be multiple valid intervals S VA The totaled value.

[0184] In addition, in Example 1, an example is shown in which the electrode track EO is a track of the midpoint O3 between a pair of electrodes (the first electrode 21a and the second electrode 21b). However, since the electrode track EO can be a track that shows the movement of a pair of electrodes (the first electrode 21a and the second electrode 21b), it is not limited to the track of the midpoint O3. For example, any track of the first electrode 21a or the second electrode 21b can be set as the "electrode track EO", and a track at any position between the first electrode 21a and the second electrode 21b can also be set as the "electrode track EO".

[0185] In addition, in the polishing apparatus 1 of Embodiment 1, an example is shown in which the resonance frequency data is converted into the thickness data of the wafer W, and the shape drawing line of the wafer W is generated by drawing the converted thickness data. However, the generation of the shape drawing line is not limited thereto. For example, the shape drawing unit 32 may also use, as the shape drawing line, an approximate curve obtained by averaging a plurality of sectional shape lines T1 generated by drawing the thickness data during a predetermined time period.

[0186] In addition, in the polishing apparatus 1 of Embodiment 1, an example is shown in which the first electrode 21a and the second electrode 21b are mounted on the upper table 12. However, the first electrode 21a and the second electrode 21b may also be mounted on the lower table 11, or may be provided on both the lower table 11 and the upper table 12.

[0187] In addition, in the polishing apparatus 1 of Embodiment 1, an example is shown in which a disk-shaped wafer W is polished. However, the shape of the wafer W is not limited to a disk shape, and may be, for example, a rectangular shape or the like.

Claims

1. A storage medium storing an evaluation program for evaluating an electrode configuration design in a grinding device, wherein a pair of electrodes is mounted on a platform and is used to detect a resonant frequency of a wafer made of a piezoelectric material during grinding of the wafer, wherein the storage medium is characterized in that the evaluation program causes a computer to execute the following processing: An electrode trajectory calculation process of calculating an electrode trajectory based on predetermined information including a configuration condition of the pair of electrodes, the electrode trajectory being a trajectory of the pair of electrodes when an arbitrary wafer is polished for a predetermined time; Repeating section calculation processing, calculating the length of the repeating section, the repeating section is a section of the electrode track passing above the arbitrary wafer; An effective interval calculation process is performed to calculate the length of the effective interval, wherein the effective interval is an interval in which the pair of electrodes simultaneously face the arbitrary wafer in the repetitive interval; as well as The ratio calculation process calculates the effective ratio, where the effective ratio is the ratio of the effective interval to the repeated interval.

2. The storage medium according to claim 1, characterized in that The evaluation program causes the computer to execute a design evaluation process for comparing the effective ratio with a predetermined threshold value and evaluating the electrode arrangement design.

3. A grinding device, characterized in that: have: A grinder that grinds wafers made of piezoelectric materials through a platform; A first electrode and a second electrode are mounted on the platform with their front ends facing the wafer; a frequency calculation unit that applies a predetermined frequency sweep signal from the first electrode to the wafer, and calculates a resonance frequency of the wafer based on the frequency sweep signal received by the second electrode; a shape drawing unit that generates a shape drawing line showing a cross-sectional shape of the wafer based on the resonance frequency; as well as a display, displaying the shape depiction line; The first electrode and the second electrode are arranged at predetermined positions on the platform according to the electrode arrangement design evaluated by the evaluation program stored in the storage medium according to claim 1 or 2.

4. The grinding device according to claim 3, characterized in that: The inter-electrode distance is set to 1 mm to 500 mm, and the inter-electrode distance is the distance between the center of the first electrode and the center of the second electrode.

5. The grinding device according to claim 3, characterized in that: When the radial position of the platform is set to a range of 10% to 80% with the inner end of the platform as 0% and the outer end of the platform as 100%, the radial position of the platform is the position of the midpoint on the straight line connecting the center of the platform and the midpoints of the centers of the first electrode and the second electrode.

6. An evaluation method, executed by a computer loaded with an evaluation program for evaluating an electrode configuration design in a polishing device, wherein a pair of electrodes are mounted on a platform, the pair of electrodes being used to detect a resonant frequency of a wafer made of a piezoelectric material during polishing of the wafer, the evaluation method being characterized in that: The following steps are involved: calculating an electrode trajectory based on predetermined information including arrangement conditions of the pair of electrodes, the electrode trajectory being a trajectory of the pair of electrodes when an arbitrary wafer is polished for a predetermined time; Calculating the length of a repetitive section, wherein the repetitive section is a section of the electrode track passing above the arbitrary wafer; Calculating the length of an effective interval, wherein the effective interval is an interval in which the pair of electrodes simultaneously face the arbitrary wafer in the repetitive interval; Calculating an effective ratio, where the effective ratio is the ratio of the effective interval to the repeated interval; as well as The effective ratio is compared with a predetermined threshold value to evaluate the electrode configuration design.

Images