Film thickness analysis method, film thickness analysis device, and storage medium

Abstract

This film thickness analysis method includes: acquiring film thickness values at a plurality of measurement points differing from one another along the radial direction of a target film, which is formed on a target substrate to be analyzed by supplying a treatment liquid while rotating the target substrate on the basis of a prescribed liquid treatment condition; and creating an approximation formula for the film thickness distribution of the target film by approximating the film thickness values at the plurality of measurement points relative to one Zernike polynomial. When creating the approximation formula, the approximation formula is created by specifying, among the plurality of coefficients included in the Zernike polynomial, a coefficient relating to the film thickness of the target substrate as a whole and at least one coefficient relating to a concentric curve component.

Description

[Technical field]

[0001] The present disclosure relates to a film thickness analysis method, a film thickness analysis apparatus, and a storage medium. [Background technology]

[0002] Patent Document 1 discloses a configuration for obtaining a measurement value at least at one point during the coating liquid supply process and determining whether or not to eject the coating liquid based on the measurement value, in order to stabilize the film thickness profile of the coating film. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] JP 2003-93959 A Summary of the Invention [Problem to be solved by the invention]

[0004] The present disclosure provides a technique for more appropriately estimating the tendency of film thickness distribution on a substrate. [Means for solving the problem]

[0005] A film thickness analysis method according to one embodiment of the present disclosure includes obtaining film thickness values ​​at a plurality of measurement points different from each other along a radial direction of a target film formed on a target substrate to be analyzed by supplying a processing liquid while rotating the target substrate based on predetermined liquid processing conditions, and creating an approximation equation relating to a film thickness distribution of the target film by approximating the film thickness values ​​at the plurality of measurement points to one Zernike polynomial, in which, in creating the approximation equation, a coefficient relating to the film thickness of the entire substrate and one or more coefficients relating to a concentric curved component are identified from among a plurality of coefficients included in the Zernike polynomial to create the approximation equation. Effect of the Invention

[0006] According to the present disclosure, a technique for more appropriately estimating the tendency of film thickness distribution on a substrate is provided. [Brief description of the drawings]

[0007] [Figure 1] FIG. 1 is a schematic diagram illustrating an example of a substrate processing system. [Diagram 2] FIG. 2 is a schematic diagram showing an example of a coating and developing apparatus. [Diagram 3] FIG. 3 is a schematic diagram showing an example of the liquid processing unit and the measuring section. [Figure 4] FIG. 4 is a schematic diagram showing an example of the irradiation position of light from the measurement unit. [Diagram 5] 5(a) and 5(b) are schematic diagrams for explaining the relationship between film thickness and reflected light. [Figure 6] FIG. 6 is a graph showing an example of the change over time in intensity of reflected light. [Figure 7] FIG. 7 is a block diagram illustrating an example of a functional configuration of the control device. [Figure 8] FIG. 8 is a block diagram illustrating an example of a hardware configuration of the control device. [Figure 9] FIG. 9 is a flowchart showing an example of a film thickness estimation method. [Figure 10] FIG. 10 is a flowchart showing an example of a film thickness distribution estimation method and a process condition correction method. [Figure 11] 11(a) to 11(g) are diagrams showing definitions of calculation matrices and related matrices used for correcting processing conditions. [Figure 12] FIG. 12 is a flowchart showing an example of a method for calculating a calculation matrix used for correcting a processing condition. [Figure 13] 13(a) and 13(b) are diagrams for explaining an example of an outline of correction using a weighting matrix. [Figure 14] FIG. 14 is a flow chart illustrating an example of a method for detecting outliers. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0008] Various exemplary embodiments are described below.

[0009] A film thickness analysis method according to one embodiment of the present disclosure includes obtaining film thickness values ​​at a plurality of measurement points along a radial direction of a target film formed on a target substrate to be analyzed by supplying a processing liquid while rotating the target substrate based on predetermined liquid processing conditions, and creating an approximation equation relating to a film thickness distribution of the target film by approximating the film thickness values ​​at the plurality of measurement points to one Zernike polynomial, wherein in creating the approximation equation, a coefficient relating to the film thickness of the entire substrate and one or more coefficients relating to a concentric curved component are identified from among a plurality of coefficients included in the Zernike polynomial to create the approximation equation.

[0010] According to the above-mentioned film thickness analysis method, the film thickness values ​​at a plurality of measurement points obtained for the target film are approximated to one Zernike polynomial, thereby obtaining an approximation equation relating to the film thickness distribution of the target film. Here, the approximation equation is created by identifying a coefficient relating to the film thickness of the entire target substrate and one or more coefficients relating to the concentric curved component among the plurality of coefficients included in the Zernike polynomial. By adopting such a configuration, an approximation equation that appropriately reflects the characteristics of the coating film formed while rotating the target substrate is obtained. In addition, by creating the approximation equation in this manner, the film thickness distribution of the target film based on the measurement results at a large number of measurement points can be described by one approximation equation. Therefore, it becomes possible to more appropriately estimate the tendency of the film thickness distribution on the substrate.

[0011] In the approximation, the approximation formula may be created using a coefficient matrix that is a matrix that specifies a relationship between each of the measurement points and a plurality of coefficients included in the Zernike polynomial.

[0012] As described above, since the concentric curved components are defined in advance in the Zernike polynomials, it is possible to specify which components of the Zernike polynomials are closely related to the measured values ​​at each point on the substrate. Therefore, as described above, by creating an approximation formula using a coefficient matrix that is a matrix that specifies the relationship between each measurement point and multiple coefficients included in the Zernike polynomials, the approximation formula can be created more simply and appropriately.

[0013] The approximation formula may include four types of terms, 0th order, 2nd order, 4th order, and 6th order, related to the diameter of the target substrate.

[0014] The Zernike polynomial may also include higher-order terms as components described using the diameter of the target substrate. In contrast, by creating an approximation formula that includes the above four types of terms, 0th order, 2nd order, 4th order, and 6th order, it is possible to prevent the coefficients used in the approximation formula from becoming complicated and to prevent overlearning when approximating the film thickness distribution.

[0015] The method may further include obtaining the liquid processing conditions during formation of the target film on the target substrate, and calculating adjustment amounts of the setting values ​​when approximating the film thickness distribution of the target film to a target value by applying an adjustment amount calculation matrix, which is a calculation matrix relating adjustment amounts of setting values ​​included in the liquid processing conditions to changes in a plurality of coefficients included in the created approximation equation, to a coefficient matrix obtained from an approximation equation related to a film thickness distribution of the target film on the target substrate.

[0016] As described above, the adjustment amount calculation matrix, which is a calculation matrix that relates the adjustment amount of the set value included in the liquid processing conditions to the change amount of multiple coefficients included in the created approximation formula, is applied to the coefficient matrix obtained from the approximation formula related to the film thickness distribution of the target film on the target substrate. This calculates the adjustment amount of the set value when the film thickness distribution of the target film approaches the target value. By configuring the system to calculate the adjustment amount of the set value in the processing conditions using the approximation formula related to the film thickness distribution, it becomes possible to calculate the adjustment amount of the set value suitable for overall adjustment of the film thickness distribution on the target substrate by a simpler calculation.

[0017] The liquid processing conditions may include a plurality of set values ​​for processes that are independent of each other.

[0018] When multiple set values ​​in the liquid processing conditions to be adjusted are set values ​​in mutually independent processes, the adjustment amount can be calculated without considering the relationship between different set values ​​in the same process, etc. Therefore, the adjustment amount for the set value to bring the film thickness distribution closer to the target value can be calculated more accurately.

[0019] The one or more coefficients relating to the concentric curvature components in the approximation formula may be coefficients corresponding to multiple order terms in the Zernike polynomial related to the diameter of the target substrate, and in calculating the adjustment amount of the setting value, the coefficients of each term in the Zernike polynomial may be weighted, and the adjustment amount calculation matrix may be applied to a coefficient matrix obtained from the approximation formula.

[0020] When calculating the adjustment amount of the setting value, by weighting the coefficients of each term in the Zernike polynomial, it is possible to calculate the adjustment amount taking into consideration, for example, the importance of coefficients corresponding to multiple order terms related to the diameter of the target substrate in the Zernike polynomial. Therefore, since it is possible to calculate the adjustment amount taking into consideration characteristics such as the importance of multiple order terms in the Zernike polynomial, it is possible to calculate a more appropriate adjustment amount.

[0021] The weighting may be set such that, among the terms of the plurality of kinds of degrees, terms of lower degrees are weighted greater than terms of higher degrees.

[0022] Generally, in Zernike polynomials, lower order terms may be more important than higher order terms, so the above configuration allows a more appropriate adjustment amount to be calculated.

[0023] The weighting may be set based on the variance of each basis function of a plurality of types of order terms related to the diameter of the target substrate.

[0024] With the above configuration, the conditions for calculating the adjustment amount can be adjusted based on the variance of the basis functions, so that a more appropriate adjustment amount can be calculated.

[0025] The one or more coefficients relating to the concentrically curved components in the approximation formula may be coefficients corresponding to multiple types of order terms related to a diameter of the target substrate in the Zernike polynomials, and before creating the approximation formula for the thickness distribution of the target film, the method may further include creating a low-order approximation formula for the thickness distribution of the target film by approximating the film thickness values ​​at the multiple measurement points to low-order Zernike polynomials including only terms with an order related to the diameter of the target substrate that is smaller than that of the Zernike polynomials used in creating the approximation formula, and determining whether or not each of the film thickness values ​​at the multiple measurement points is an abnormal value based on a difference between a film thickness value at a point corresponding to the multiple measurement points included in the low-order approximation formula and the film thickness values ​​at the multiple measurement points.

[0026] With the above configuration, a low-order approximation formula is created using a low-order Zernike polynomial that includes only smaller terms than the Zernike polynomial used in creating the approximation formula, and, for example, a film thickness value that has a large deviation between the low-order approximation formula and the film thickness value can be determined to be an abnormal value. Therefore, when an abnormal value is included in the film thickness values ​​at multiple measurement points, it becomes possible to appropriately identify this.

[0027] In creating the approximation equation, a thickness value at the plurality of measurement points that is different from the thickness value determined to be the abnormal value may be approximated to the Zernike polynomial to create an approximation equation relating to the thickness distribution of the target film.

[0028] By using the above configuration, it is possible to create an approximation equation without using film thickness values ​​that are determined to be abnormal, making it possible to create an approximation equation that more accurately reflects the actual film thickness state of the target film.

[0029] A film thickness analysis apparatus according to one embodiment of the present disclosure includes an acquisition unit that acquires film thickness values ​​at multiple different measurement points along a radial direction of a target film formed on a target substrate to be analyzed by supplying a processing liquid while rotating the target substrate based on specified liquid processing conditions, and an approximation equation creation unit that creates an approximation equation relating to a film thickness distribution of the target film by approximating the film thickness values ​​at the multiple measurement points to one Zernike polynomial, and the approximation equation creation unit creates the approximation equation by identifying, from among multiple coefficients included in the Zernike polynomial, a coefficient relating to the film thickness of the entire target substrate and one or more coefficients relating to concentric curved components.

[0030] According to the above-mentioned film thickness analysis device, an approximation equation relating to the film thickness distribution of the target film is obtained by approximating the film thickness values ​​at a plurality of measurement points obtained for the target film to one Zernike polynomial. Here, the approximation equation is created by identifying a coefficient relating to the film thickness of the entire target substrate and one or more coefficients relating to the concentric curved component among the plurality of coefficients included in the Zernike polynomial. This allows an approximation equation that appropriately reflects the characteristics of the coating film formed while rotating the target substrate to be obtained. In addition, by creating an approximation equation in this manner, the film thickness distribution of the coating film based on the measurement results at a large number of measurement points can be described by one approximation equation. Therefore, it becomes possible to more appropriately estimate the tendency of the film thickness distribution on the substrate.

[0031] A storage medium according to one aspect of the present disclosure is a computer-readable storage medium storing a program for causing an apparatus to execute the above-described film thickness analysis method.

[0032] Various exemplary embodiments will now be described in detail with reference to the drawings, in which the same or corresponding parts are designated by the same reference numerals.

[0033] [Substrate processing system] The substrate processing system 1 (substrate processing apparatus) shown in FIG. 1 is a system that forms a photosensitive coating on a workpiece W, exposes the photosensitive coating, and develops the photosensitive coating. The workpiece W to be processed is, for example, a substrate, or a substrate on which a film, circuit, or the like has been formed by performing a predetermined process. One example of the substrate is a silicon wafer. The workpiece W (substrate) may be circular. The workpiece W may also be a glass substrate, a mask substrate, or an FPD (Flat Panel Display), etc. The photosensitive coating is, for example, a resist film.

[0034] 1 and 2, the substrate processing system 1 includes a coating and developing apparatus 2, an exposure apparatus 3, and a control device 100 (control unit). The exposure apparatus 3 is an apparatus that exposes a resist film (photosensitive coating) formed on a workpiece W (substrate). Specifically, the exposure apparatus 3 irradiates an exposure target portion of the resist film with an energy beam by a method such as immersion exposure.

[0035] The coating and developing apparatus 2 applies a resist (chemical solution) to the surface of the workpiece W to form a resist film before the exposure process by the exposure device 3, and develops the resist film after the exposure process. The coating and developing apparatus 2 includes a carrier block 4, a processing block 5, and an interface block 6.

[0036] The carrier block 4 introduces the workpiece W into the coating and developing apparatus 2 and removes the workpiece W from the coating and developing apparatus 2. For example, the carrier block 4 can support multiple carriers C for the workpiece W and has a built-in transport device A1 including a delivery arm. The carrier C accommodates, for example, multiple circular workpieces W. The transport device A1 removes the workpiece W from the carrier C and delivers it to the processing block 5, and receives the workpiece W from the processing block 5 and returns it to the carrier C. The processing block 5 has processing modules 11, 12, 13, and 14.

[0037] The processing module 11 incorporates a liquid processing unit U1, a heat processing unit U2, and a transport device A3 that transports the workpiece W to these units. The processing module 11 forms an underlayer film on the surface of the workpiece W using the liquid processing unit U1 and the heat processing unit U2. An example of the underlayer film is a SOC (Spin On Carbon) film. The liquid processing unit U1 applies a processing liquid for forming the underlayer film onto the workpiece W. The heat processing unit U2 performs various heat treatments associated with the formation of the underlayer film.

[0038] The processing module 12 incorporates a liquid processing unit U1, a heat processing unit U2, and a transport device A3 that transports the workpiece W to these units. The processing module 12 forms a resist film on the underlayer film using the liquid processing unit U1 and the heat processing unit U2. The liquid processing unit U1 applies a processing liquid for forming a resist film onto the underlayer film, thereby forming a film of the processing liquid on the underlayer film (on the surface of the workpiece W). The heat processing unit U2 performs various heat treatments associated with the formation of the resist film.

[0039] The processing module 13 incorporates a liquid processing unit U1, a heat processing unit U2, and a transport device A3 that transports the workpiece W to these units. The processing module 13 forms an upper layer film on the resist film using the liquid processing unit U1 and the heat processing unit U2. The liquid processing unit U1 applies a processing liquid for forming the upper layer film onto the resist film. The heat processing unit U2 performs various heat treatments associated with the formation of the upper layer film.

[0040] The processing module 14 incorporates a liquid processing unit U1, a heat processing unit U2, and a transport device A3 that transports the workpiece W to these units. The processing module 14 uses the liquid processing unit U1 and the heat processing unit U2 to perform development processing of the resist film that has been subjected to exposure processing and heat processing associated with the development processing. The liquid processing unit U1 applies a developer to the surface of the exposed workpiece W, and then washes it away with a rinsing liquid to perform development processing of the resist film. The heat processing unit U2 performs various heat processing associated with the development processing. Specific examples of heat processing include a heat processing before development (PEB: Post Exposure Bake) and a heat processing after development (PB: Post Bake), etc.

[0041] A shelf unit U10 is provided on the carrier block 4 side in the processing block 5. The shelf unit U10 is divided into multiple cells arranged in the vertical direction. A transport device A7 including a lifting arm is provided near the shelf unit U10. The transport device A7 lifts and lowers the workpiece W between the cells of the shelf unit U10.

[0042] A shelf unit U11 is provided on the interface block 6 side in the processing block 5. The shelf unit U11 is partitioned into a plurality of cells arranged in the vertical direction.

[0043] The interface block 6 transfers the workpiece W to and from the exposure apparatus 3. For example, the interface block 6 has a built-in transport device A8 including a transfer arm, and is connected to the exposure apparatus 3. The transport device A8 transfers the workpiece W placed on the shelf unit U11 to the exposure apparatus 3. The transport device A8 receives the workpiece W from the exposure apparatus 3 and returns it to the shelf unit U11.

[0044] The control device 100 controls the coating and developing apparatus 2 to perform coating and developing processes, for example, in the following procedure. First, the control device 100 controls the transfer device A1 to transfer the workpiece W in the carrier C to the shelf unit U10, and controls the transfer device A7 to place the workpiece W in a cell for the processing module 11.

[0045] Next, the control device 100 controls the transport device A3 to transport the workpiece W on the shelf unit U10 to the liquid treatment unit U1 and heat treatment unit U2 in the processing module 11. The control device 100 also controls the liquid treatment unit U1 and heat treatment unit U2 to form an underlayer film on the surface of the workpiece W. Thereafter, the control device 100 controls the transport device A3 to return the workpiece W on which the underlayer film has been formed to the shelf unit U10, and controls the transport device A7 to place the workpiece W in a cell for the processing module 12.

[0046] Next, the control device 100 controls the transport device A3 to transport the workpiece W on the shelf unit U10 to the liquid processing unit U1 and heat processing unit U2 in the processing module 12. The control device 100 also controls the liquid processing unit U1 and heat processing unit U2 to form a resist film on the underlying film of the workpiece W. Thereafter, the control device 100 controls the transport device A3 to return the workpiece W to the shelf unit U10, and controls the transport device A7 to place the workpiece W in a cell for the processing module 13.

[0047] Next, the control device 100 controls the transport device A3 to transport the workpiece W on the shelf unit U10 to each unit in the processing module 13. The control device 100 also controls the liquid processing unit U1 and the heat processing unit U2 to form an upper layer film on the resist film of the workpiece W. Thereafter, the control device 100 controls the transport device A3 to transport the workpiece W to the shelf unit U11.

[0048] Next, the control device 100 controls the transport device A8 to send the workpiece W on the shelf unit U11 to the exposure device 3. Thereafter, the control device 100 controls the transport device A8 to receive the workpiece W that has been subjected to the exposure process from the exposure device 3 and place it in a cell for the processing module 14 in the shelf unit U11.

[0049] Next, the control device 100 controls the transport device A3 to transport the workpiece W on the shelf unit U11 to each unit in the processing module 14, and controls the liquid processing unit U1 and the heat processing unit U2 to perform a developing process on the resist film of the workpiece W. Thereafter, the control device 100 controls the transport device A3 to return the workpiece W to the shelf unit U10, and controls the transport device A7 and the transport device A1 to return the workpiece W into the carrier C. This completes the coating and developing process for one workpiece W. The control device 100 controls the coating and developing apparatus 2 to perform the coating and developing process for each of the subsequent multiple workpieces W in the same manner as described above.

[0050] The specific configuration of the substrate processing apparatus is not limited to the above-described configuration of the substrate processing system 1. The substrate processing apparatus may be any type as long as it includes a liquid processing unit that supplies a processing liquid to a substrate and performs liquid processing, and a control device that can control the liquid processing unit.

[0051] (Liquid processing unit) Next, an example of the liquid processing unit U1 of the processing module 12 will be described with reference to Fig. 3. The liquid processing unit U1 (liquid processing section) supplies a processing liquid to the surface Wa of the workpiece W, and then rotates the workpiece W with the processing liquid supplied onto the surface Wa so that a film of the processing liquid is formed on the surface Wa. Hereinafter, the liquid film of the processing liquid immediately after the processing liquid is supplied and the film before solidification in which evaporation progresses as the workpiece W rotates are collectively referred to as a "coating film AF". As shown in Fig. 3, the liquid processing unit U1 has a spinning holder 30 and a processing liquid supplying section 40.

[0052] The rotating holding unit 30 holds and rotates the workpiece W. The rotating holding unit 30 has, for example, a holding unit 32, a shaft 34, and a rotation drive unit 36. The holding unit 32 (support unit) supports the workpiece W. The holding unit 32 supports, for example, the center of the workpiece W arranged horizontally with the surface Wa facing up, and holds the workpiece W by vacuum suction or the like. The upper surface of the holding unit 32 (the surface supporting the workpiece W) may be formed in a circular shape when viewed from above, and may have a radius of about 1 / 6 to 1 / 2 times the radius of the workpiece W. The rotating drive unit 36 ​​is connected to the lower part of the holding unit 32 via the shaft 34.

[0053] The rotation drive unit 36 ​​is an actuator including a power source such as an electric motor, and rotates the holder 32 around a vertical axis Ax. The rotation of the holder 32 by the rotation drive unit 36 ​​rotates the workpiece W held (supported) by the holder 32. The holder 32 may hold the workpiece W such that a center CP (see FIG. 4) of the workpiece W approximately coincides with the axis Ax.

[0054] The processing liquid supply unit 40 supplies the processing liquid to the surface Wa of the workpiece W. The processing liquid is a solution (resist) for forming a resist film. The processing liquid supply unit 40 has, for example, a nozzle 42, a supply source 44, an opening / closing valve 46, and a nozzle driving unit 48. The nozzle 42 ejects the processing liquid onto the surface Wa of the workpiece W held in the holding unit 32. For example, the nozzle 42 is disposed above the workpiece W (vertically above the center CP of the workpiece W) and ejects the processing liquid downward. The supply source 44 supplies the processing liquid to the nozzle 42.

[0055] The opening / closing valve 46 is provided in the supply path between the nozzle 42 and the supply source 44. The opening / closing valve 46 switches the supply path between an open and closed state. The nozzle driving unit 48 moves the nozzle 42 between a discharge position above the workpiece W and a retracted position away from the discharge position. The discharge position is, for example, a position vertically above the center of rotation of the workpiece W (a position on the axis Ax). The standby position is, for example, set to a position outside the periphery of the workpiece W.

[0056] (Measuring section) The coating and developing apparatus 2 further includes a measuring section 60 for measuring the thickness of the coating film AF of the processing liquid. The measuring section 60 is provided in the liquid processing unit U1. The measuring section 60 rotates the workpiece W after the processing liquid is supplied, and irradiates light onto the rotating workpiece W during the period in which the coating film AF is being formed. The measuring section 60 irradiates light capable of penetrating the coating film AF (processing liquid) on the surface Wa onto the surface Wa of the workpiece W held by the holding section 32, and receives reflected light (reflected by the workpiece W) generated in response to the irradiated light.

[0057] The measurement unit 60 has, for example, light emitting and receiving devices 70A to 70C. The light emitting and receiving devices 70A to 70C respectively irradiate light toward irradiation points P1 to P3 overlapping with the surface Wa of the workpiece W on the holder 32, and receive the reflected light reflected from the irradiation points P1 to P3. The irradiation points P1 to P3 are fixed positions and do not change even if the workpiece W rotates. Each of the light emitting and receiving devices 70A to 70C irradiates laser light as irradiation light toward the surface Wa of the workpiece W. Each of the light emitting and receiving devices 70A to 70C irradiates laser light that can pass through a coating film AF of the processing liquid formed on the surface Wa.

[0058] The laser light emitted from each of the light emitting and receiving devices 70A to 70C may be visible light or infrared light. The wavelength of the laser light may be 500 nm to 1200 nm, 600 nm to 1100 nm, or 780 nm to 1000 nm. The wavelength of the laser light may be set according to the type of the treatment liquid. For example, the wavelength of the laser light is set so as not to promote a reaction in the treatment liquid and to reduce light absorption.

[0059] The frequencies of the laser beams irradiated from the light emitting and receiving devices 70A to 70C may be different from each other. That is, the frequency of the light irradiated from the light emitting and receiving device 70A toward the irradiation point P1 may be different from the frequency of the light irradiated from the light emitting and receiving device 70B (light emitting and receiving device 70C) toward the irradiation point P2 (irradiation point P3). The light source included in each of the light emitting and receiving devices 70A to 70C may be a laser diode or an LED. The beam width of the laser beam may be about several mm to several tens of mm.

[0060] The irradiation points P1 to P3 of the light (laser light) from the light projecting and receiving devices 70A to 70C are set at different positions from each other as shown in FIG. 4. That is, the measurement unit 60 irradiates the laser light toward the irradiation point P1 (point) and irradiation points P2 and P3 (other points) that overlap with the surface Wa of the workpiece W at a position different from the irradiation point P1. The distances between the irradiation point P1 of the light from the light projecting and receiving device 70A, the irradiation point P2 of the light from the light projecting and receiving device 70B, and the irradiation point P3 of the light from the light projecting and receiving device 70C and the center CP of the workpiece W are different from each other. In one example, the distance between the irradiation point P1 and the center CP of the workpiece W is smaller than the distance between the irradiation point P2 and the center CP of the workpiece W. The distance between the irradiation point P2 and the center CP of the workpiece W is smaller than the distance between the irradiation point P3 and the center CP of the workpiece W.

[0061] The irradiation point P1, the irradiation point P2, and the irradiation point P3 may be arranged in a line in this order from the center CP of the workpiece W along the radial direction of the workpiece W. The irradiation point P1, the irradiation point P2, and the irradiation point P3 may be arranged at approximately equal intervals. The irradiation point P1 is located at the center of the front surface Wa of the workpiece W. Specifically, the irradiation point P1 is set so as to overlap with the upper surface of the holding part 32 (the surface that supports the back surface of the workpiece W). The irradiation point P3 located on the outside is located in an area (peripheral area) near the periphery of the workpiece W. As described above, the light emitting and receiving devices 70A to 70C function as a light emitting part that irradiates light toward a predetermined area that overlaps with the front surface Wa of the workpiece W.

[0062] The light emitting / receiving devices 70A to 70C may generate an electrical signal according to the intensity of the received reflected light. Since the laser light can pass through the coating film AF on the surface Wa of the workpiece W, at the irradiated location, it is reflected by the outer surface Fa (upper surface) of the coating film AF and also reflected by the surface Wa of the workpiece W located below the coating film AF, and then emitted through the coating film AF. In the present disclosure, the surface Wa of the workpiece W from which part of the laser light is reflected is the surface of a base material contained in the workpiece W, or the surface of another film that exists below the coating film AF and has already solidified. The other film may be, for example, a film (for example, the above-mentioned underlayer film) that exists directly below the coating film AF.

[0063] The light projecting and receiving device 70A receives light emitted from the irradiation point P1. Specifically, the light projecting and receiving device 70A receives reflected light obtained by combining light emitted through the coating film AF after reflecting off the surface Wa of the workpiece W and light reflected off the outer surface Fa of the coating film AF at the irradiation point P1. At each of the irradiation points P2 and P3, the laser light is also reflected by the outer surface Fa of the coating film AF and the surface Wa located under the coating film AF. That is, the light projecting and receiving devices 70B and 70C also receive light emitted from the irradiation points P2 and P3, respectively, similar to the light projecting and receiving device 70A. More specifically, the light projecting and receiving devices 70B and 70C receive reflected light obtained by combining light emitted through the coating film AF after reflecting off the surface Wa of the workpiece W and light reflected off the outer surface Fa of the coating film AF at the irradiation points P2 and P3, respectively. As described above, the light emitting and receiving devices 70A to 70C also function as a light receiving section that receives reflected light that is a combination of light reflected from the outer surface Fa of the coating film AF of the treatment liquid on the surface Wa and light reflected from the surface Wa.

[0064] Here, the change in the intensity of the reflected light over time will be described with reference to Fig. 5(a) and Fig. 5(b). The reflected light has an intensity according to the thickness of the coating film AF of the processing liquid during the period when the coating film AF of the processing liquid is formed on the surface Wa of the workpiece W. In Fig. 5(a) and Fig. 5(b), the part of any one of the light-emitting and receiving devices that emits the laser light is indicated as "light-emitting part 72", and the part that receives the reflected light is indicated as "light-receiving part 74". Note that Fig. 5(a) and Fig. 5(b) illustrate a case where light is incident on the surface Wa from an oblique direction, unlike Fig. 3.

[0065] As described above, the reflected light accompanying the laser light irradiated toward the surface Wa of the workpiece W contains light L1 and light L2 after passing through the coating film AF of the processing liquid and reflecting off the surface Wa. The light L1 is light that is emitted to the outside through the coating film AF. The light L2 is light that is reflected off the outer surface Fa of the coating film AF without entering the coating film AF. The reflected light received by the light receiving unit 74 is reflected light Lc obtained by combining the light L1 and the light L2. Depending on the thickness of the coating film AF, the phase of the light L2 relative to the light L1 changes, and there are cases where the light L2 strengthens each other or weakens each other. As shown in FIG. 5(a), when the peak portion of the amplitude of the light L1 and the peak portion of the amplitude of the light L2 overlap, the light L1 and the light L2 strengthen each other, and the intensity of the reflected light increases. On the other hand, as shown in FIG. 5(b), when the peak of the amplitude of the light L1 and the valley of the amplitude of the light L2 overlap, the light L1 and the light L2 weaken each other, and the intensity of the reflected light decreases.

[0066] Immediately after the processing liquid is supplied to the surface Wa, a liquid film of the processing liquid is formed. Thereafter, by rotating the workpiece W, solidification (volatilization) of the coating film AF gradually progresses. Therefore, during the period in which the workpiece W is rotated, the thickness of the coating film AF gradually decreases. This causes the phase of the light L2 relative to the light L1 to change, and a state in which they strengthen each other and a state in which they weaken each other are repeated. As a result, a waveform in which peaks and valleys are alternately repeated is obtained as a waveform indicating the time change in the intensity of the reflected light (see FIG. 6). In the substrate processing system 1 of the present disclosure, the thickness (film thickness) of the coating film AF is estimated based on this waveform. The method of estimating the film thickness will be described in detail later.

[0067] Furthermore, in the substrate processing system 1, conditions related to the formation of the coating film AF can be adjusted based on the film thickness estimation result. Specifically, the control device 100 of the substrate processing system 1 adjusts the processing conditions to adjust the film thickness estimation result and the target film thickness. The method of adjusting the processing conditions will be described in detail later.

[0068] (Control device) The control device 100 controls the coating and developing apparatus 2 partially or entirely, thereby causing the coating and developing apparatus 2 to process the workpiece W. As shown in Fig. 7, the control device 100 has, for example, a processing information storage unit 112, a liquid processing control unit 114, and a film thickness adjustment unit 120 as functional configurations (hereinafter referred to as "functional modules"). The processing executed by these functional modules corresponds to the processing executed by the control device 100.

[0069] The processing information storage unit 112 stores processing information related to liquid processing for the workpiece W. The processing information includes various conditions for performing liquid processing. For example, the timing (time) for starting and stopping the ejection of the processing liquid, the rotation speed (number of rotations) of the workpiece W when the processing liquid is ejected, and the like are predefined as setting values ​​for the various conditions. Furthermore, for example, the rotation speed of the workpiece W when forming a coating film AF on the surface Wa after the processing liquid is supplied, and the rotation time of the workpiece W when forming the coating film AF are also predefined as setting values ​​for the various conditions.

[0070] The liquid treatment control unit 114 controls the liquid treatment unit U1 to perform liquid treatment on the workpiece W. The liquid treatment control unit 114 controls the spin holder 30 and the treatment liquid supply unit 40 to perform liquid treatment on the workpiece W in accordance with various conditions defined in the treatment information stored in the treatment information storage unit 112.

[0071] The film thickness adjustment unit 120 has a film thickness estimation function 121 that estimates a film thickness, and a film thickness adjustment function 122 that adjusts the film thickness estimated by the film thickness estimation function 121. The film thickness estimation function 121 is a function that acquires a waveform (hereinafter referred to as a "signal waveform") that indicates a time change in the intensity of reflected light from the workpiece W from the measurement unit 60, and estimates the thickness of the coating film AF on the surface Wa based on the signal waveform. The film thickness adjustment function 122 is a function that adjusts the processing conditions based on the film thickness estimation result to adjust the thickness of the coating film AF to be applied to the workpiece W to be processed next time onwards to a target film thickness.

[0072] The film thickness adjustment unit 120 includes, as functional modules related to the film thickness estimation function 121, for example, a light projection control unit 124, a signal acquisition unit 126, a feature acquisition unit 128, a model information storage unit 130, and a film thickness calculation unit 132, as shown in FIG. 7.

[0073] The light projection control unit 124 controls the light emitting and receiving devices 70A-70C to irradiate light toward an irradiation location overlapping with the surface Wa of the workpiece W during a rotation period in which the rotation holding unit 30 of the liquid processing unit U1 rotates the workpiece W after the supply of the processing liquid. The light projection control unit 124 may start irradiating light from the light emitting and receiving devices 70A-70C before starting to discharge the processing liquid in the liquid processing onto the workpiece W. The light projection control unit 124 stops irradiating light from the light emitting and receiving devices 70A-70C after stopping the rotation for forming the coating film AF.

[0074] The signal acquiring unit 126 acquires, from each light emitting / receiving device, a signal waveform indicating a time change in the intensity of the reflected light received by the corresponding irradiation device during the above rotation period. The signal acquiring unit 126 may acquire the intensity of the reflected light at a predetermined sampling period. The sampling period is set to a degree that allows a change in the interference state between the light L1 reflected from the surface Wa and the light L2 reflected from the outer surface Fa of the coating film AF to be grasped from the signal waveform. The sampling period may be set to about several tens of ms to several hundreds of ms.

[0075] The feature amount acquiring unit 128 acquires a feature amount from a waveform between a predetermined measurement time point within a rotation period and a time point before the measurement time point at which the signal waveform satisfies a predetermined condition, among the signal waveforms acquired by the signal acquiring unit 126. The feature amount is a value acquired from the signal waveform according to a predetermined condition, and correlates with the thickness of the coating film AF. For example, the feature amount acquiring unit 128 acquires a feature amount from the signal waveform for each of the irradiation points P1 to P3.

[0076] The model information storage unit 130 stores a model formula that is constructed in advance to estimate the thickness of the coating film AF. This model formula is constructed so as to indicate the relationship between the feature amount of the signal waveform and the estimated value of the film thickness.

[0077] The film thickness calculation unit 132 calculates the thickness of the coating film AF at the time of measurement based on the feature amount acquired by the feature amount acquisition unit 128. For example, the film thickness calculation unit 132 calculates the thickness of the coating film AF based on the feature amount for each of the irradiation points P1 to P3. The measurement time may be set at any time during the rotation period. The measurement time is set, for example, at the end of the rotation period (the time when the rotation of the workpiece W stops). In this case, the film thickness calculation unit 132 calculates the thickness of the coating film AF at the end of the rotation period. The film thickness calculation unit 132 may calculate the thickness of the coating film AF at the time of measurement by applying a model formula held in the model information storage unit 130.

[0078] The model formula can be created, for example, by the following method. For example, while performing liquid processing on a plurality of test workpieces W by changing the rotation speed in a plurality of stages, a feature value based on a signal waveform and a measured value of the thickness of the coating film AF at the time of measurement are acquired for each stage. Based on the feature value and the measured value of the thickness of the coating film AF for each of the plurality of stages in which the rotation speed is changed, obtained by the above procedure, a model formula showing the relationship between the estimated value of the thickness of the coating film AF and the feature value is generated. The model formula may be created in the coating and developing apparatus 2, or may be created in another coating and developing apparatus 2. The model formula may be prepared for each irradiation location, or one model formula may be prepared for a plurality of irradiation locations.

[0079] 7 as functional modules related to the film thickness adjustment function 122. Specifically, the film thickness adjustment unit 120 includes, for example, a condition acquisition unit 134, a film thickness estimation result acquisition unit 136, a polynomial approximation unit 138, a calculation matrix storage unit 140, a film thickness adjustment condition calculation unit 142, and a calculation matrix creation unit 144.

[0080] The condition acquisition unit 134 acquires from the processing information storage unit 112 the set values ​​of the conditions of a plurality of liquid treatments corresponding to the results of the film thickness estimation. The liquid treatment conditions acquired from the processing information storage unit 112 are conditions that are considered to affect the film thickness of the coating film AF. A representative liquid treatment condition that affects the film thickness is the rotation speed of the workpiece W. Specifically, the rotation speed of the workpiece W when the treatment liquid is supplied to the surface of the workpiece W, the rotation speed of the workpiece W when the treatment liquid is spread on the surface of the workpiece W by centrifugal force, the rotation speed when the treatment liquid after supply is shaken off from the surface of the workpiece W, the rotation speed when the treatment liquid is fixed to the surface of the workpiece W, and the like can be mentioned. These rotation speeds of the workpiece W are known to affect the film thickness. In addition, the residence time of the treatment liquid until it is fixed on the workpiece W, the surrounding environment, and the like may also affect the film thickness. In addition, the liquid treatment conditions actually acquired from the processing information storage unit 112 may be conditions whose values ​​are relatively easy to adjust during the liquid treatment. Examples of such conditions include the number of rotations when the processing liquid is discharged, the reflow time after the processing liquid is discharged, and the number of rotations of the workpiece W when shaking off the processing liquid after the discharge. The type of condition for which the condition acquisition unit 134 acquires the setting value is determined in advance, and it can be said that the acquired condition is the condition to be adjusted (adjustment knob). Note that the multiple adjustment knobs used here may be processing conditions (setting values) in different processes, or may be the same process. Different processes refer to stages in which the operation related to the liquid processing changes, such as "before supplying the processing liquid," "during supplying the processing liquid," "during reflow," and "time to shake off the processing liquid." By selecting processing conditions (setting values) in different processes as multiple adjustment knobs, it becomes unnecessary to consider interactions between the adjustment knobs.

[0081] The film thickness estimation result acquisition unit 136 acquires an estimation result of the thickness of the coating film AF on the target workpiece W. The estimation result is a result calculated by the film thickness calculation unit 132, and the result is used as is.

[0082] The polynomial approximation unit 138 approximates the estimated result of the thickness of the coating film AF to the coefficients of a Zernike polynomial. When correcting the film thickness, the distribution of the film thickness of the coating film AF on the surface of the workpiece W is approximated to a Zernike polynomial, and the adjustment knob to be adjusted to correct the film thickness and the adjustment amount are estimated using this.

[0083] Here, we will briefly explain Zernike polynomials. Zernike polynomials are complex functions on a unit circle with a radius of 1 that are often used in the field of optics (in practice, they are used as real functions), and have polar coordinate arguments (r, θ). In the field of optics, Zernike polynomials are mainly used to analyze the aberration components of lenses, and by decomposing wavefront aberration using Zernike polynomials, it is possible to know the aberration components based on each independent wavefront shape, for example, a mountain shape, a saddle shape, etc.

[0084] In this embodiment, for example, the estimated values ​​of the film thickness at multiple points on the workpiece W are shown in the radial direction of the workpiece, and the estimated values ​​of the film thickness are connected by a smooth curved surface, so that the in-plane distribution of the film thickness on the surface of the workpiece W is captured as a wave surface that undulates up and down. Using Zernike polynomials, the film thickness distribution Z on the surface of the workpiece W is expressed as a wave surface that undulates up and down, and multiple types of in-plane trend components Z i Each in-plane tendency component Z i The magnitude of can be expressed by the Zernike coefficients.

[0085] Each in-plane trend component Z i Specifically, the Zernike coefficients expressing the above are expressed by the following equation using polar coordinate arguments (r, θ): Note that in this disclosure, the Zernike coefficients are described in a hierarchy of notation based on fringes.

[0086] Z1(1) Z2(r cosθ) Z3(r sinθ) Z4(2r 2 -1) Z5(r 2 cos2θ) Z6(r 2 sin2θ) Z7((3r 3 -2r)·cosθ) Z8((3r 3 -2r) sinθ) Z9(6r 4 -6r 2 +1) … Z16(20r 6 -30r 4 +12r 2 +1) …

[0087] In this embodiment, four types of Zernike coefficients are used: coefficients Z1, Z4, Z9, and Z16. Coefficient Z1 corresponds to the average film thickness within the workpiece surface (Z-direction deviation component). Z4, Z9, and Z16 are all concentric curved components, and each indicates a different unevenness. In addition, when the above four types of coefficients are used, the zeroth order term (constant term), the second order (r 2 ), 4th order (r 4 ), and 6th order (r 6 ) terms will be included.

[0088] The estimated thickness of the coating film AF includes the estimated thickness at multiple measurement points along the radial direction. The distribution of the film thickness on the workpiece W surface obtained by the estimated film thickness at each point can be expressed using Zernike polynomials, and can be described by a combination of four feature quantities (Zernike coefficients). When approximating using Zernike polynomials, the least squares method can be used. As a result of the approximation, coefficients Z1, Z4, Z9, and Z16 are obtained. The coefficients Z1, Z4, Z9, and Z16 obtained by the approximation are used for correcting the film thickness, and details will be described later.

[0089] The calculation matrix storage unit 140 stores a calculation matrix used to adjust the thickness of the coating film AF. Two types of calculation matrices are stored in the calculation matrix storage unit 140. The first calculation matrix is ​​a calculation matrix related to the relationship between the amount of change in each coefficient obtained by the Zernike polynomials described below and the amount of adjustment of the adjustment knob required to realize the change in each term. The second calculation matrix is ​​a calculation matrix related to the relationship between the amount of adjustment of the adjustment knob and the amount of change in film thickness due to the knob adjustment. These will be described later.

[0090] Film thickness adjustment condition calculation unit 142 calculates correction conditions for forming a coating film AF of a predetermined film thickness and an expected film thickness based on the correction, based on the set values ​​of the liquid processing conditions acquired by condition acquisition unit 134 and the film thickness estimation result acquired by film thickness estimation result acquisition unit 136. Two types of calculation matrices stored in calculation matrix storage unit 140 are used to calculate the correction conditions and the expected film thickness based on the correction. Details relating to the calculation of the correction conditions and the expected film thickness based on the correction will be described later.

[0091] The calculation matrix creation unit 144 has a function of creating a first calculation matrix and a second calculation matrix. For example, the calculation matrix is ​​created by changing the adjustment knob in multiple steps for multiple test workpieces W to perform liquid processing and obtain the thickness of the coating film AF. Then, the calculation matrix creation unit 144 creates the above-mentioned two types of calculation matrices based on the amount of change in the adjustment knob and the measured thickness of the coating film AF. Details of the creation of the calculation matrix will also be described later.

[0092] The control device 100 is composed of one or more control computers. For example, the control device 100 has a circuit 150 shown in FIG. 8. The circuit 150 has one or more processors 152, a memory 154, a storage 156, an input / output port 158, and a timer 162. The storage 156 has a computer-readable storage medium such as a hard disk. The storage medium stores a program for causing the control device 100 to execute a substrate processing method and a film thickness estimation method, which will be described later. The storage medium may be a removable medium such as a non-volatile semiconductor memory, a magnetic disk, or an optical disk.

[0093] The memory 154 temporarily stores the programs loaded from the storage medium of the storage 156 and the results of calculations by the processor 152. The processor 152 configures the above-mentioned functional modules by executing the above-mentioned programs in cooperation with the memory 154. The input / output port 158 ​​inputs and outputs electrical signals between the spin holder 30, the processing liquid supply unit 40, the measurement unit 60, etc., in accordance with instructions from the processor 152. The timer 162 measures the elapsed time, for example, by counting reference pulses at a constant cycle.

[0094] When the control device 100 is composed of a plurality of control computers, each functional module may be realized by an individual control computer. The control device 100 may be composed of a control computer including a functional module for performing liquid processing by the liquid processing unit U1, and a control computer including a functional module (film thickness adjustment unit 120) for estimating the thickness of the coating film AF. Alternatively, each of these functional modules may be realized by a combination of two or more control computers. In these cases, the multiple control computers may be connected to each other so as to be able to communicate with each other and execute a substrate processing method and a film thickness estimation method to be described later in cooperation with each other. Note that the hardware configuration of the control device 100 is not necessarily limited to one in which each functional module is configured by a program. For example, each functional module of the control device 100 may be configured by a dedicated logic circuit or an ASIC (Application Specific Integrated Circuit) that integrates the dedicated logic circuit.

[0095] [Coating film thickness estimation process] Next, as an example of a substrate processing method, an example of a process related to liquid processing executed by the control device 100 and a process related to estimating the thickness of the coating film AF will be described. In the control device 100, a process for performing liquid processing by the liquid processing unit U1 and a process for estimating the thickness of the coating film AF (a film thickness estimation method) are performed in parallel. In the following, a case will be illustrated in which the end point of the rotation period after the end of the supply of the processing liquid is set as the measurement time point (hereinafter referred to as "measurement time point MT") for estimating the film thickness.

[0096] 9 is a flow chart showing an example of the above-mentioned process executed by control device 100 for estimating the liquid treatment and film thickness. Control device 100 executes step S11 upon receiving a command from a higher-level controller. In step S11, for example, liquid treatment control unit 114 controls spin holding unit 30 to start rotating workpiece W. After workpiece W starts rotating, liquid treatment control unit 114 controls spin holding unit 30 to rotate workpiece W at a set rotation speed value for discharging the treatment liquid.

[0097] Next, the control device 100 executes steps S12 and S13. In step S12, for example, the film thickness adjusting unit 120 waits until a predetermined measurement start time. The measurement start time is, for example, a time determined based on the time when a command is received from a higher-level controller. In step S13, for example, the film thickness adjusting unit 120 controls the measuring unit 60 to start measuring the intensity of reflected light. In one example, the light projection control unit 124 controls the light projecting and receiving devices 70A to 70C to start irradiating the laser light toward the irradiation points P1 to P3, respectively. Then, the signal acquiring unit 126 starts acquiring the intensity of reflected light associated with the irradiation of the laser light from each of the light projecting and receiving devices 70A to 70C. In the subsequent processing, the irradiation of the laser light and the acquisition of the intensity of the reflected light are continued.

[0098] Next, control device 100 executes steps S14 and S15. In step S14, for example, liquid processing control unit 114 waits until a predetermined discharge start time. The discharge start time is, for example, a time that is determined based on the time point at which a command is received from a higher-level controller. In step S15, for example, liquid processing control unit 114 controls processing liquid supply unit 40 to start discharging the processing liquid.

[0099] Next, control device 100 executes steps S16, S17, and S18. In step S16, for example, liquid processing control unit 114 waits until a predetermined discharge time has elapsed from the discharge start time of the processing liquid. In step S17, for example, liquid processing control unit 114 controls processing liquid supply unit 40 to stop discharging the processing liquid. In step S18, for example, liquid processing control unit 114 controls spin holder 30 to adjust the rotation speed of workpiece W so that workpiece W rotates at the set value of the rotation speed after the supply of the processing liquid. The set value of the rotation speed is determined in the processing information stored in processing information storage unit 112.

[0100] Next, control device 100 executes steps S19 and S20. In step S19, for example, liquid processing control unit 114 waits until a predetermined drying time has elapsed from the time when discharge of the processing liquid was stopped. In step S20, for example, liquid processing control unit 114 controls rotation holder 30 to stop rotation of workpiece W. By executing steps S19 and S20 described above, workpiece W to which the processing liquid has been supplied rotates for a predetermined drying time, and a coating film AF of the processing liquid is formed on surface Wa of workpiece W during rotation. The period during which workpiece W is rotated for this drying time corresponds to the rotation period during which workpiece W is rotated after supply of the processing liquid.

[0101] Next, the control device 100 executes step S21. In step S21, for example, the film thickness adjusting unit 120 controls the measuring unit 60 to stop measuring the intensity of the reflected wave. In one example, the light projection control unit 124 controls the light projecting and receiving devices 70A-70C to stop irradiating the irradiation points P1-P3 with the laser light, respectively. Then, the signal acquiring unit 126 stops acquiring the intensity of the reflected light associated with the irradiation of the laser light. By executing the above processes up to step S21, a signal waveform (time change in the intensity of the reflected wave) as shown in FIG. 6 is acquired for each of the irradiation points P1-P3.

[0102] In the graph of the signal waveform shown in FIG. 6, the timing when the command to start processing is received from the upper controller is indicated by "0", and the timing when the discharge of the processing liquid is stopped (the timing when the drying time starts) is indicated by "t1". Furthermore, in FIG. 6, the measurement time point corresponding to the timing when the drying time ends is indicated by "MT". As shown in FIG. 6, after time t1, a signal waveform in which peaks and valleys are repeated is obtained according to the time change in the interference state between the light L1 reflected from the surface Wa and the light L2 reflected from the outer surface Fa of the coating film AF. In FIG. 6, the apex of the peak is depicted by a black circle, and the lowest point of the valley is depicted by a white circle. Note that the signal waveform before time t1 is omitted.

[0103] After executing step S21, the control device 100 executes step S22. In step S22, for example, the film thickness calculation unit 132 calculates the thickness of the coating film AF at the measurement time MT. Specifically, the thickness of the coating film AF at the measurement time MT is calculated based on the waveform between the measurement time MT and the time before the measurement time MT when the signal waveform satisfies a predetermined condition among the signal waveforms obtained up to the execution of step S21. More specifically, the feature amount acquisition unit 128 acquires a feature amount from the waveform between the measurement time MT and the time before the measurement time MT when the signal waveform satisfies a predetermined condition among the above signal waveforms. Then, the film thickness calculation unit 132 calculates the thickness of the coating film AF at the measurement time MT based on the above feature amount.

[0104] The feature value obtained from a portion of the signal waveform is, for example, the time of the nth extreme point (n is an integer equal to or greater than 1) that appears counting from the measurement time MT. That is, the feature value acquisition unit 128 acquires, as a feature value, the time of the nth extreme point of the waveform from the waveform between the measurement time MT and the time point at which the signal waveform satisfies the condition for becoming the nth extreme point counting backward from the measurement time MT. In the present disclosure, the extreme point collectively refers to the apex (maximum point) of a peak portion and the lowest point (minimum point) of a valley portion.

[0105] In the signal waveform graph illustrated in Fig. 6, the time of the tenth extreme point counting from the measurement time MT (the apex of the fifth peak counting from the measurement time MT) is acquired as feature value F1. Note that in the signal waveform graph in Fig. 6, the ninth extreme point counting from the measurement time MT is the lowest point of the fifth valley counting from the measurement time MT. Feature value F1 corresponds to the time between the reference timing of the liquid treatment (for example, the timing when a command to start treatment is received from the above-mentioned upper controller) and the nth extreme point counting from the measurement time MT.

[0106] The film thickness calculation unit 132 uses the correlation between the feature amount F1 and the thickness of the coating film AF to calculate the thickness of the coating film AF at the measurement time point MT based on the feature amount F1. A method for calculating the thickness of the coating film AF using the correlation will be described later. For example, the film thickness calculation unit 132 calculates the thickness of the coating film AF at each irradiation position based on the signal waveform for each of the irradiation points P1 to P3.

[0107] This completes the series of processes for performing liquid treatment and film thickness estimation on one workpiece W. The control device 100 may also sequentially execute a similar series of processes on multiple subsequent workpieces W. In this case, the control device 100 may repeatedly execute the series of processes so that the above-mentioned various processing conditions (timing, rotation speed, drying time, etc.) are constant between the multiple workpieces W.

[0108] Before executing the above series of processes on the workpiece W, a model formula for estimating the thickness of the coating film AF is constructed. The model formula is formed by changing the rotation speed of the test workpiece WT in multiple stages to form the coating film AF, and for each stage, the characteristic amount is acquired and the thickness of the coating film AF is measured. As a result, a model formula showing the relationship between the characteristic amount and the estimated value of the thickness of the coating film AF is constructed. The range for changing the rotation speed of the test workpiece WT (the difference between the maximum rotation speed and the minimum rotation speed) is, for example, 80 rpm to 300 rpm, and the change width per time is 5 rpm to 50 rpm, but can be changed depending on the formation conditions of the coating film AF, etc.

[0109] [Coating film thickness correction processing method (film thickness analysis method)] Next, as an example of a substrate processing method, an example of a process (film thickness analysis method) for adjusting the thickness of the coating film AF executed by the control device 100 will be described. This process is performed in a film thickness adjustment function 122 of the film thickness adjustment unit 120 after a process for estimating film thickness is performed in a film thickness estimation function 121 of the film thickness adjustment unit 120 of the control device 100. In the following description, a case where a film thickness analysis is performed on a workpiece W on which a coating film AF is formed will be described. This workpiece W corresponds to a substrate (target substrate) that is the subject of the process.

[0110] FIG. 10 is a flow chart showing an example of the above-mentioned process executed by the control device 100 for estimating the liquid treatment and the film thickness. The control device 100 executes step S31 by receiving a command from a higher-level controller. In step S31, for example, the condition acquisition unit 134 acquires information on the treatment conditions when the liquid treatment of the workpiece W was performed. At this time, the condition acquisition unit 134 acquires the set value of the liquid treatment condition for the result of the film thickness estimation from the treatment information storage unit 112. Here, the parameter related to the liquid treatment condition acquired by the condition acquisition unit 134 is a parameter whose set value is changed when adjusting the film thickness. In the following embodiment, such a parameter may be referred to as an adjustment knob or simply a knob. Also, in step S31, the film thickness estimation result acquisition unit 136 acquires the estimated result of the film thickness of the workpiece W. As the estimated result of the film thickness at this time, the calculation result of the coating film AF by the film thickness calculation unit 132 is used as it is. Therefore, the estimated result of the film thickness can also be said to be the measurement result of the film thickness of the coating film AF. As a result of the above procedure, the set value of the liquid treatment condition and the information related to the film thickness of the coating film AF as a result of the liquid treatment are prepared for the specific workpiece W. In addition, the current setting value of the liquid processing condition (knob) is current Let us assume that.

[0111] Next, the control device 100 executes step S32. In step S32, for example, the polynomial approximation unit 138 derives the coefficients Z1, Z4, Z9, and Z16 of each term by approximating the film thickness estimation result of the workpiece W acquired by the film thickness estimation result acquisition unit 136 with a Zernike polynomial. In this process, each term is calculated by approximation using the least squares method.

[0112] The method of deriving the four coefficients Z1, Z4, Z9, and Z16 will be described in detail. First, as a preparation, the coefficient matrix Z, which is an auxiliary matrix used to specify the contribution to the Zernike polynomial for each point where the film thickness was measured, and its inverse matrix Z inv This can be obtained by transforming the positions of each measurement point in the XY space into the Zernike space defined by the above coefficients.

[0113] The matrix F, which indicates the approximate film thickness after approximating the film thickness distribution of the estimated result (also called the measurement result) with the Zernike approximation, is, for example, the estimated result in the XY space F XYcurrent Then, it can be described using the following equation (1). F=F XYcurrent Z inv …(1)

[0114] By using this formula (1), the Zernike coefficients Z1, Z4, Z9, and Z16 can be derived.

[0115] Next, the control device 100 executes steps S33 and S34. In step S33, for example, the film thickness adjustment condition calculation unit 142 calculates ΔF, which specifies the coefficient to be corrected and the amount of correction, by comparing the coefficient derived in the polynomial approximation unit 138 with a coefficient corresponding to the target film thickness distribution. In step S34, the film thickness adjustment condition calculation unit 142 calculates ΔP, which is the knob adjustment amount, based on ΔF. adj. Calculate.

[0116] The coating film AF is required to be formed evenly on the surface of the workpiece W. Therefore, the target film thickness is required to have a predetermined value regardless of the location in the workpiece W. Therefore, the target film thickness distribution has a predetermined value for coefficient Z1, and Z4, Z9, and Z16 should be zero. Therefore, the correction target film thickness ΔF for the target film thickness in the Zernike space can be calculated by taking the difference between F and Z1.

[0117] If the knob values ​​can be adjusted so that the film thickness can be corrected to correspond to the film thickness to be corrected ΔF in the Zernike space, the film thickness should reach the target value. If a calculation matrix that specifies the relationship between the knob adjustment amount and the correction amount ΔF in the Zernike space is stored in advance, it becomes possible to specify the adjustment amount of each knob if the film thickness to be corrected ΔF is known.

[0118] Therefore, the calculation matrix M for calculating the adjustment amount from the correction target film thickness ΔF is stored as a first calculation matrix, and the adjustment amount of the knob can be calculated by applying this to the correction target film thickness ΔF.

[0119] The model for calculating the knob adjustment amount and the elements included in the model will be described with reference to FIG. 11. FIG. 11(a) shows the knob adjustment amount ΔP adj. In addition, Fig. 11(b), Fig. 11(c), and Fig. 11(d) show the models used to calculate the adjustment amount ΔP adj. The adjustment amount ΔP included in the model to calculate adj. , the correction target film thickness ΔF, and the adjustment amount calculation matrix (first calculation matrix) M.

[0120] As shown in FIG. 11(a), the adjustment amount ΔP adj. is calculated by multiplying the correction target film thickness ΔF by the adjustment amount calculation matrix M. Here, the correction target film thickness ΔF is a coefficient element related to the difference between the actual film thickness and the target film thickness in the state of approximation to the Zernike polynomial as described above. The adjustment amount calculation matrix M is a calculation matrix that relates the knob adjustment amount to the film thickness change amount, and is a calculation matrix used when deriving the knob adjustment amount required to realize the film thickness change amount. As an example, when there are three types of knobs (knob 1 to knob 3) and four coefficients are used in the approximation using the Zernike polynomial, the adjustment amount calculation matrix M is calculated as a matrix of 4 rows x 3 columns. A calculation method of the adjustment amount calculation matrix M will be described later. The adjustment amount calculation matrix M is prepared in advance and stored in the calculation matrix storage unit 140 of the control device 100.

[0121] Next, the control device 100 executes steps S35 and S36. In step S35, for example, the film thickness adjustment condition calculation unit 142 calculates the adjustment amount ΔP adj. , the correction possibility component ΔF in Zernike space by adjusting the knob. adj. Furthermore, in step S35, the thickness of the coating film AF formed under the processing conditions based on the adjusted knob is predicted.

[0122] The model for calculating the correctable component and the elements included in the model will be described with reference to FIG. 11. FIG. 11(e) shows the correctable component ΔF adj. 11(f) and 11(g) show the model used to calculate the correction possibility component ΔF adj. , and the definition of the correction possibility component calculation matrix (second calculation matrix) N.

[0123] As described above, in step S34, the knob adjustment amount ΔP adj. is calculated. The correctable component ΔF adj. is a calculation of the degree to which the coefficients of each term in the Zernike polynomial are corrected as a result of adjusting the knob. Specifically, as shown in FIG. 11(e), the correction possibility component ΔF adj. is the knob adjustment amount ΔP adj. and the correction possibility component calculation matrix N. The correction possibility component calculation matrix N is a calculation matrix that relates the knob adjustment amount and the film thickness change amount, and is a calculation matrix used when estimating the film thickness change amount from the knob adjustment amount when the knob adjustment amount is determined. The adjustment amount calculation matrix M and the correction possibility component calculation matrix N correspond to each other as described above, and the relationship can be such that the pseudo inverse matrix of the adjustment amount calculation matrix M is the correction possibility component calculation matrix N. As an example, when there are three types of knobs (knobs 1 to 3) and four coefficients are used in the approximation using the Zernike polynomials, the correction possibility component calculation matrix N is obtained as a matrix of 3 rows x 4 columns. A calculation method of the correction possibility component calculation matrix N will be described later. The correction possibility component calculation matrix N is prepared in advance and stored in the calculation matrix storage unit 140 of the control device 100.

[0124] A calculation matrix N for calculating the degree to which the coefficients in the Zernike polynomials can be corrected from the knob adjustment amount is stored as a second calculation matrix, and this is used as the knob adjustment amount ΔP adj. By applying to the Zernike polynomials, the correction possibility component ΔF adj. can be calculated.

[0125] In addition, the adjustment amount of the above knob ΔP adj.When this is obtained, the adjusted knob P next In addition, the correction possibility component ΔF adj. Once this is obtained, the correction possibility component ΔF adj. The predicted film thickness F after adjusting the knob from XYnext can be calculated.

[0126] Adjusted knob P next Currently, Nobu P current The knob adjustment amount ΔP calculated using the above procedure adj. This reflects the current -ΔP adj. On the other hand, the expected film thickness F XYnext is the thickness estimation result F XYcurrent For the correction possibility component ΔF adj. However, the correction possibility component ΔF adj. is a coefficient in the Zernike polynomial, so first, the correction possibility component ΔF adj. The correctable component ΔF in XY space XYadj. Convert to the correctable component ΔF XYadj. For example, ΔF adj. and the coefficient matrix Z.

[0127] Furthermore, the expected film thickness F XYnext is the thickness estimation result F XYcurrent and the correction possibility component ΔF XYadj. It is calculated by the following formula (2). F XYnext =F XYcurrent -ΔF XYadj. …(2)

[0128] As a result of the above, the film thickness estimation result F XYcurrent Then, a prediction of what the film thickness will be after adjusting the knob can be calculated.

[0129] [Calculation method of adjustment amount calculation matrix M and correction possibility component calculation matrix N] An example of a method for calculating the adjustment amount calculation matrix M and the correction possibility component calculation matrix N used in the process for adjusting the thickness of the coating film AF (see FIG. 10) executed by the control device 100 will be described with reference to FIG. 12. This process is performed in the calculation matrix creation unit 144 of the control device 100. FIG. 12 is a flowchart showing an example of the above-mentioned process executed by the control device 100. The series of processes shown in FIG. 12 is performed before performing liquid processing on the workpiece W that requires film thickness estimation and correction, or at any timing such as when it is determined that the adjustment amount calculation matrix M and the correction possibility component calculation matrix N need to be modified.

[0130] First, the control device 100 executes step S41. In step S41, for example, the calculation matrix creation unit 144 prepares an experimental condition table necessary for creating a calculation matrix (model). As described above, the calculation matrices M and N are matrices related to the relationship of how the film thickness changes when the knob, which is a condition of the liquid processing, is changed. Therefore, in order to create the calculation matrices M and N, experimental data is required to understand how the film thickness changes when the knob that can be adjusted is changed within an expected range. Therefore, in step S41, experimental conditions necessary for creating the model are identified. It is considered that information necessary for the calculation matrices M and N can be collected by forming the coating film AF on the workpiece W under various conditions using more workpieces W and evaluating the change in film thickness. However, considering the work efficiency for preparing the calculation matrices M and N, it is desirable to cover the expected conditions with a relatively limited number of experiments. Therefore, a known experimental design method or the like may be used to select appropriate experimental conditions and prepare an experimental condition table. This experimental condition table can be used as a matrix related to the conditions when calculating the calculation matrices M and N.

[0131] Next, the control device 100 executes step S42. In step S42, for example, liquid processing is performed on the workpiece W based on the experimental condition table created in the computation matrix creation unit 144, and the film thickness after the liquid processing is measured (estimated). The method of measuring (estimating) the liquid processing conditions and film thickness at this time is the same as the method described in the above embodiment. That is, liquid processing is performed on the workpiece W under the control of the liquid processing control unit 114 based on the liquid processing conditions created in the computation matrix creation unit 144. In addition, the film thickness of the workpiece W after the liquid processing is estimated under the control of the film thickness estimation function 121. As a result, experimental results corresponding to the experimental table are obtained.

[0132] Next, the control device 100 executes step S43. In step S43, for example, an adjustment amount calculation matrix M and a correction possibility component calculation matrix N are calculated from the experimental design table prepared in step S41 and the film thickness measurement result (experimental result) obtained in step S42. When the distribution of film thickness obtained from the experimental result is approximated by Zernike polynomials in the same manner as the above-mentioned method, four coefficients corresponding to each experimental result are obtained. That is, a result matrix F of the number of experimental conditions (rows) × 4 (columns) is obtained from the experimental result. On the other hand, a condition matrix P of the number of experimental conditions (rows) × adjustment knob (columns) is obtained as a condition table. Note that the condition matrix P can be removed by adding one column to absorb the intercept, making it the number of experimental conditions (rows) × (adjustment knob + 1) (columns).

[0133] Calculate the matrix product of the above condition matrix P and the transpose of the condition matrix P, and then multiply the inverse of that matrix by the condition matrix P (P T ·P) -1 P is calculated, a matrix is ​​obtained between this and the result matrix F, and processing is performed to slice the intercept. By performing this series of processing, a matrix is ​​obtained that specifies the degree to which each knob contributes to each of the Zernike coefficients. This matrix corresponds to the correctable component calculation matrix N. Furthermore, by finding the pseudo-inverse matrix of the correctable component calculation matrix N, the adjustment amount calculation matrix M is obtained. By the above procedure, the adjustment amount calculation matrix M and the correctable component calculation matrix N are obtained.

[0134] In this way, to calculate the adjustment amount calculation matrix M and the correction possibility component calculation matrix N, it is necessary to prepare multiple experimental results in which the liquid processing conditions (knob settings) are associated with the results of the liquid processing under those conditions (film thickness estimation results). Also, as described above, based on the result matrix F and the condition matrix P, the correction possibility component calculation matrix N and the adjustment amount calculation matrix M are obtained as matrices that can associate these. Since the correction possibility component calculation matrix N and the adjustment amount calculation matrix M change depending on the liquid processing conditions, they can be prepared each time conditions such as the type of target workpiece W, the type of coating film AF to be applied to the workpiece W, and the target film thickness of the coating film AF change.

[0135] [Adjustment amount ΔP adj. Regarding the correction of By the above procedure, the knob adjustment amount ΔP adj. Based on the adjusted knob P next The correction possibility component ΔF can be calculated. adj. Once this is obtained, the correction possibility component ΔF adj. The predicted film thickness F after adjusting the knob from XYnext Here, the knob adjustment amount ΔP adj. A method for calculating under more optimal conditions will be described below. This procedure can be carried out as a modified example of carrying out the above-mentioned step S34 (see FIG. 10).

[0136] As mentioned above, the knob adjustment amount ΔP adj. It has been explained that the above can be written as the matrix product of the correction target film thickness ΔF and the adjustment amount calculation matrix M, ΔF·M. The adjustment amount calculation matrix M is a pseudo-inverse matrix with respect to the correction possible component calculation matrix N. In other words, the adjustment amount calculation matrix M can be expressed as the matrix product of the transposed matrix of the correction possible component calculation matrix N, and the inverse matrix of the matrix product of the correction possible component calculation matrix N and its transposed matrix. In other words, the adjustment amount ΔP adj. can be written as the following equation (3). ΔP adj. = ΔF N T (N N T ) -1 …(3)

[0137] The above formula (3) is the same as the solution used when identifying an approximate straight line using the unweighted least squares method for discrete data. As described above, approximation using the least squares method is performed to calculate the coefficients of each term Z1, Z4, Z9, and Z16 in the Zernike polynomial. FIG. 13(a) shows a schematic image of approximation of coefficients using the least squares method. Here, approximation of three coefficients (Z4, Z9, and Z16 in the above embodiment) related to the concentric curved component is shown. As shown in FIG. 13(a), approximation of coefficients using the least squares method is performed by approximating the target value of the film thickness to be corrected ΔF and the adjustment amount of the knob ΔP adj. The aim is to adjust ΔP so that the film thickness after correction when ΔP is applied is small. At this time, ΔP is adjusted so that the sum of squares of the residuals of the coefficients of each term is small. adj. is required.

[0138] However, in the approximation using the least squares method shown in this formula (3), each coefficient is treated equally, so as shown in FIG. 13(a), the relationship between each term (Z4, Z9, Z16) is not taken into consideration at all, and the value that minimizes the sum of squares is obtained. However, in reality, when approximating the thickness distribution of the target film using Zernike polynomials, the components described with a smaller order among the coefficients of each term are more important in the approximation than the components described with a higher order. This is related to the variance of the basis function of each term in the Zernike polynomials (the above-mentioned formula in which each term is described with the radius r and θ of the workpiece W) at the infinite point. The basis function of each term has different variances depending on the description when using the order of the radius r or θ. Therefore, it is better to set the coefficient of each term so that the residual with the correction target film thickness ΔF is small in the components with large variance, i.e., the components described with a smaller order, so that the variance of the correction target film thickness ΔF with respect to the target value of the approximation formula as a whole can be reduced. Also, as a result, the adjustment amount ΔP adj. The in-plane uniformity of the film thickness after correction is optimized using

[0139] Therefore, when performing approximation using the least squares method, it is possible to adjust the sum of squares of the residuals of each term according to its importance by weighting the coefficient of each term according to its importance. Specifically, by applying a weighting matrix W to formula (3), formula (3) is changed to the following formula (4). ΔP adj. = ΔF W N T (N W N T ) -1 …(4)

[0140] As shown in FIG. 13(b), the weighting matrix W can be expressed as the following formula (5) using coefficients W1, W2, and W3.

[0141]

number

[0142] By inputting the numbers indicating the weights of each term (Z4, Z9, Z16) into the coefficients W1, W2, and W3, which are the components of the matrix, the above formula (4) becomes a formula corresponding to the solution of the weighted least squares method. Therefore, by solving this formula (4), the adjustment amount ΔP adj. As described above, the components described with a smaller degree are considered to be more important in the approximation than the components described with a higher degree, and the relationship W1>W2>W3 is set. In this case, as shown in FIG. 13(b), assuming that the residual in Z4 is the smallest, followed by Z9 and Z16 in that order, ΔP is calculated so that the sum of squares of these components becomes small. adj. As an example, if the coefficients W1, W2, and W3 related to the weights of the terms (Z4, Z9, and Z16) are set to values ​​corresponding to the variance of the basis function of each term, the variance of the basis function of each term is taken into consideration, and thus the variance of the basis function of each term is more optimal. For example, the values ​​corresponding to the variance of the basis function are 1 / 3, 1 / 5, and 1 / 7 for Z4, Z9, and Z16, respectively.

[0143] In this way, when calculating the coefficients of each term (here, Z4, Z9, and Z16) in the Zernike polynomial by approximation using the least squares method, a more appropriate approximation result that reflects the characteristics of each term can be obtained by weighting each term taking into account its importance before calculation.

[0144] In addition, the adjustment amount ΔP is calculated by approximating the weighting matrix W. adj. , the correction possibility component ΔF in Zernike space by adjusting the knob is calculated. adj. The variance of the correction possible component can be calculated as shown in the following formula (6). adj. , the adjustment amount calculation matrix M, and the weighting matrix W can be written as follows: Dispersion of the correctable component [nm 2 ]=-(ΔP adj. N) W (ΔP adj. N) T …(6)

[0145] The correction possibility component ΔF calculated by the above formula (6) adj. The variance of, for example, the adjustment amount ΔP adj. For example, a threshold value is set in advance, and the calculated correction possibility component ΔF can be used to determine whether or not to perform correction. adj. If the variance of is smaller than the threshold, the adjustment amount ΔP adj. It is also possible to determine not to perform correction using such a correction possibility component ΔF adj. The evaluation using the variance of can be performed, for example, after executing the above-mentioned step S35 (see FIG. 10).

[0146] [Screening of abnormal data] Next, the selection of data used when approximating the film thickness distribution with Zernike polynomials in the above-mentioned procedure will be described. In the above-mentioned procedure, in step S31, the film thickness estimation result acquisition unit 136 acquires the film thickness estimation result (measurement result) of the workpiece W. In step S32, the polynomial approximation unit 138 uses this result to approximate the film thickness estimation result of the workpiece W acquired by the film thickness estimation result acquisition unit 136 with Zernike polynomials, thereby deriving the coefficients Z1, Z4, Z9, and Z16 of each term. However, the above description is based on the premise that all the film thickness measurement results acquired in step S31 are used. Therefore, for example, even if an abnormal value is included in the film thickness measurement result, it is not assumed that the data indicating the abnormal value will be removed.

[0147] Therefore, before performing the approximation using the Zernike polynomials, a process may be performed to remove data including abnormal values ​​from the film thickness measurement results obtained in step S31. Below, a procedure for removing film thickness values ​​determined to be abnormal values ​​from the film thickness measurement results will be described with reference to Fig. 14. This procedure may be performed after performing the above-mentioned step S31 (see Fig. 10).

[0148] First, the control device 100 executes step S51. In step S51, for example, the polynomial approximation unit 138 of the control device 100 derives the coefficients of each term by approximating the measurement result (estimated result) of the film thickness of the workpiece W acquired by the film thickness estimation result acquisition unit 136 with a Zernike polynomial. In this way, the Zernike polynomial is also used when removing abnormal values. However, at this stage, only terms whose basis functions are described at a lower order are used compared to the terms of the Zernike polynomial used in step S32. That is, the film thickness measurement result is approximated using a low-order Zernike polynomial including only lower-order terms. As an example, when the coefficients of the Zernike polynomial used in step S32 are the above-mentioned Z1, Z4, Z9, and Z16, an approximation formula may be created in step S41 by calculating the three coefficients Z1, Z4, and Z9 excluding Z16 as an approximation using the low-order Zernike polynomial. This approximation formula is called a low-order approximation formula because it is an approximation formula based on the low-order Zernike polynomial. In this way, by performing approximation using only low-order terms in the Zernike polynomials to create a low-order approximation equation, a simple approximation curve using all data can be created.

[0149] Next, the control device 100 executes step S52. In step S52, for example, the polynomial approximation unit 138 of the control device 100 calculates the difference (for example, its absolute value) between the approximation curve based on the approximation equation reflecting the coefficients calculated in step S51 and the numerical values ​​of the film thickness measurement results at each point used to create the approximation curve. More accurately, the difference is calculated between the film thickness value at a point corresponding to the multiple measurement points in the low-order approximation equation and the actual film thickness value at the multiple measurement points. This determines the degree of deviation between the measured film thickness (estimated value) at each point and the approximation curve.

[0150] Next, the control device 100 executes step S53. In step S53, for example, the polynomial approximation unit 138 of the control device 100 judges whether or not the difference between the film thickness value corresponding to the measurement point on the approximation curve calculated in step S52 and the film thickness value of the measurement result of the film thickness at each point exceeds a preset threshold value. If any of the measurement results exceeds the threshold value, the polynomial approximation unit 138 judges that the film thickness value at the point is an abnormal value and outputs an error result. The threshold value is a value set to identify an abnormal value at a point determined to be appropriately separated from the approximation curve, and for example, 3% of the median value (film thickness value) of each point included in the approximation curve may be set as the threshold value of the difference. The threshold value is not limited to a value calculated based on the median value of the approximation curve, and a value different from the value calculated from the approximation curve may be used.

[0151] The error result is a notification indicating that there is a point (measurement result) where the difference exceeds the threshold, and includes information identifying the point (measurement result) where the difference exceeds the threshold. When an error result is output from the polynomial approximation unit 138, the control device 100 may be configured to notify, for example, an operator of the coating and developing apparatus 2 that an error result is included. When an error result is output from the polynomial approximation unit 138, the control device 100 may perform processing such as stopping processing related to the workpiece W, which is the target substrate, or canceling processing related to the workpiece W and subsequent works. How the control device 100 operates when an error result is output may be set in advance, for example, by an administrator of the coating and developing apparatus 2.

[0152] Next, the control device 100 executes step S55. In step S55, for example, the control device 100 performs subsequent processing using the abnormal value determined to be an error, that is, the film thickness value other than the measurement result (film thickness value) of the point where the difference exceeds the threshold value. As an example, the polynomial approximation unit 138 may perform processing related to step S32 using the result of the presence or absence of an error in the above-mentioned step S54 and, if an error exists, the measurement result (film thickness value) other than the point where the difference exceeds the threshold value (measurement result). As a result, the approximation of the film thickness distribution in step S32 does not include information related to the point where the difference exceeds the threshold value (measurement result). Also, in subsequent processing, that is, processing after step S33, calculations are performed using the coefficients of each term in the Zernike polynomial calculated under conditions that do not include information related to the point where the difference exceeds the threshold value (measurement result). Note that, when an abnormal value determined to be an error exists, the control device 100 may stop the operation of the coating and developing apparatus 2 without performing subsequent processing. In this way, step S55 is a processing that is performed arbitrarily.

[0153] In this way, before executing step S32 in which the film thickness distribution is approximated by the Zernike polynomial (the coefficients of each term are calculated), an approximation is performed using only the terms of lower orders in the Zernike polynomial, and the result is used to identify abnormal values. In this case, since the abnormal values ​​are prevented from being used in the approximation using the Zernike polynomial in the subsequent stage, the approximation formula becomes more appropriate, and it becomes possible to more appropriately estimate the tendency of the film thickness distribution on the substrate. In addition, if the measurement result includes an abnormal value, it is possible to take measures such as stopping the coating and developing apparatus 2 in consideration of the possibility that some abnormality has occurred in the coating and developing apparatus 2. Therefore, it becomes possible to more appropriately adjust the film thickness distribution in the surface of the workpiece W to a desired state.

[0154] [Effect] According to the above-mentioned film thickness analysis method and film thickness analysis device, the film thickness values ​​at a plurality of measurement points obtained for the coating film AF, which is the target film, are approximated to one Zernike polynomial, thereby obtaining an approximation equation relating to the film thickness distribution of the coating film AF. Here, the approximation equation is created by identifying a coefficient relating to the film thickness of the entire workpiece W, which is the target substrate, and one or more coefficients relating to the concentric curved component, among the plurality of coefficients included in the Zernike polynomial. As a result, an approximation equation that appropriately reflects the characteristics of the coating film AF formed while rotating the workpiece FW is obtained. In addition, by creating an approximation equation in this method, the film thickness distribution of the coating film based on the measurement results at a large number of measurement points can be described by one approximation equation. Therefore, it becomes possible to more appropriately estimate the tendency of the film thickness distribution on the substrate.

[0155] When the coating film AF is formed on the workpiece W, it is important from the viewpoint of process control to properly grasp the film thickness distribution. However, since it is not easy to measure the film thickness formed on the workpiece W, the process control has often been performed indirectly, for example, by using the processing conditions when forming the processing film. However, since the film thickness of the coating film AF also affects the performance of the product obtained from the workpiece W, it is required to grasp it more accurately. In response to this, by using the above-mentioned method, it becomes possible to describe the film thickness distribution of the coating film AF on the surface of the workpiece W by an approximation formula. In addition, in consideration of the fact that the coating film AF is formed by supplying the processing liquid while rotating the workpiece W, a configuration is adopted in which a coefficient of 1 or more relating to the concentric curved component is used from the Zernike polynomial. By adopting such a configuration, an approximation formula that properly grasps the tendency of the film thickness distribution can be obtained while using fewer coefficients.

[0156] In addition, as described above, since the concentric curved components are defined in advance in the Zernike polynomials, it is possible to specify which components of the Zernike polynomials are closely related to the measured values ​​at each point on the substrate. Therefore, as described in the above embodiment, the approximate formula can be created more simply and appropriately by creating the approximate formula using a coefficient matrix, which is a matrix that specifies the relationship between each measurement point and multiple coefficients included in the Zernike polynomials.

[0157] The approximation formula may also include four types of terms, 0th, 2nd, 4th, and 6th orders, related to the diameter (r) of the workpiece W. The Zernike polynomials may also include higher-order terms as components described using the diameter of the target substrate. By creating an approximation formula so as to include the above four types of terms, 0th, 2nd, 4th, and 6th orders (selecting coefficients to be used from the Zernike polynomials), it is possible to prevent the coefficients used in the approximation formula from becoming complicated. Furthermore, by configuring the approximation formula to include the above four types of terms, it is possible to prevent overlearning when approximating the film thickness distribution, compared to when higher-order terms are included.

[0158] In the above embodiment, the current condition of the adjustment knob related to the liquid processing condition when forming the coating film AF on the workpiece W is acquired. In addition, an adjustment amount calculation matrix M, which is a calculation matrix that relates the adjustment amount of the set value included in the liquid processing condition and the change amount of multiple coefficients included in the created approximation formula, is applied to the coefficient matrix obtained from the approximation formula. This makes it possible to calculate the adjustment amount of the set value when bringing the film thickness distribution of the workpiece W closer to the target value. By configuring the system to calculate the adjustment amount of the set value in the processing condition using the approximation formula related to the film thickness distribution, it becomes possible to calculate the adjustment amount of the set value suitable for overall adjustment of the film thickness distribution on the target substrate by a simpler calculation.

[0159] The liquid processing conditions may include multiple set values ​​for mutually independent processes. When multiple set values ​​in the liquid processing conditions to be adjusted are set values ​​for mutually independent processes, it is considered that the adjustment amount can be calculated in a state where the relationship between different set values ​​in the same process is eliminated. Therefore, the adjustment amount of the set value for bringing the film thickness distribution closer to the target value can be calculated more accurately.

[0160] The liquid processing conditions may include set values ​​for three types of liquid processing conditions, and three coefficients (Z4, Z9, and Z16 in the above embodiment) may be used as coefficients for the concentrically curved components. When there are three types of liquid processing set values ​​and the same number of three coefficients are used as coefficients for the concentrically curved components in the approximation formula, the adjustment amount for adjusting the film thickness distribution for the three types of set values ​​can be properly calculated. Note that when there are few coefficients for the concentrically curved components compared to the types of set values, the set values ​​may not be properly calculated.

[0161] Furthermore, one or more coefficients related to the concentric curved component in the approximation formula may be coefficients corresponding to multiple order terms related to the diameter of the target substrate in the Zernike polynomial. In this case, in calculating the adjustment amount of the set value, the adjustment amount calculation matrix M may be applied to the coefficient matrix obtained from the approximation formula after weighting the coefficient of each term in the Zernike polynomial. In the above example, weighting is performed on three coefficients (Z4, Z9, and Z16 in the above embodiment) by using the weight matrix W. With this configuration, for example, the adjustment amount can be calculated taking into account the importance of the above coefficients in the Zernike polynomial. Therefore, since it is possible to calculate the adjustment amount taking into account the characteristics such as the importance of multiple order terms in the Zernike polynomial, a more appropriate adjustment amount can be calculated.

[0162] Furthermore, the weighting may be set so that, among the terms of multiple degrees, the terms of lower degrees are weighted more heavily than the terms of higher degrees. In the above embodiment, the weighting coefficients W1, W2, and W3 corresponding to the three coefficients are set so as to satisfy the relationship W1>W2>W3. With the above configuration, the terms of lower degrees of the Zernike polynomials, which may generally have higher importance, are weighted more heavily than the terms of higher degrees, so that a more appropriate adjustment amount can be calculated.

[0163] The weighting may be set based on the variance of each basis function of multiple order terms related to the diameter of the target substrate. In this case, the conditions for calculating the adjustment amount can be adjusted based on the variance of the basis function, so that a more appropriate adjustment amount can be calculated.

[0164] The one or more coefficients related to the concentric curved components in the approximation formula may be coefficients corresponding to multiple types of order terms related to the diameter of the target substrate in the Zernike polynomial, for example, Z4, Z9, and Z16 in the above embodiment. In addition, before creating the approximation formula, a low-order approximation formula may be created using a low-order Zernike polynomial that includes only terms with orders smaller than those of the Zernike polynomial used in creating the approximation formula. Furthermore, it may further include determining whether each of the film thickness values ​​is an abnormal value based on the difference between the film thickness value at a point corresponding to the multiple measurement points included in the low-order approximation formula and the film thickness value at the multiple measurement points. In this case, since the low-order approximation formula is created using the low-order Zernike polynomial, a simple approximation formula can be created. Then, for example, a film thickness value with a large deviation between the low-order approximation formula and the film thickness value can be determined to be an abnormal value. Therefore, when an abnormal value is included in the film thickness values ​​at multiple measurement points, it is possible to appropriately identify it.

[0165] When creating the approximation formula, a thickness value different from the thickness value determined to be an abnormal value among the thickness values ​​at the multiple measurement points may be approximated to a Zernike polynomial to create an approximation formula related to the thickness distribution of the target film. In this case, it is possible to create an approximation formula without using the thickness value determined to be an abnormal value, so that it is possible to create an approximation formula that more accurately reflects the actual thickness state of the target film.

[0166] [Variations] Although various exemplary embodiments have been described above, the present invention is not limited to the above-described exemplary embodiments, and various omissions, substitutions, and modifications may be made. In addition, elements in different embodiments can be combined to form other embodiments.

[0167] For example, the method of measuring the thickness of the coating film AF on the workpiece W is not limited to the method described in the above embodiment. In the above embodiment, the film thickness is measured by irradiating laser light, but the method of analyzing the film thickness described in the above embodiment can be applied as long as a measured value (estimated value) of the film thickness of the coating film AF formed on the workpiece W is obtained. Therefore, it is sufficient to obtain information on the film thickness at multiple measurement points on the workpiece W using a known film thickness measurement method, and the method is not particularly limited.

[0168] Even when the film thickness measuring method described in the above embodiment is used, the layout and configuration of each part may be changed as appropriate.

[0169] In the above example, the thickness of the coating film AF of the processing liquid (resist) for forming a resist film is estimated. In contrast, the analysis method related to the film thickness described in the above embodiment may estimate the thickness of the coating film of the processing liquid for forming a film other than the resist film (e.g., an underlayer film or an overlayer film). It may also be applied to a developer for developing a resist film.

[0170] Furthermore, the method of deriving the calculation matrices M and N and the method of calculating the coefficient matrix Z described in the above embodiment are merely examples, and can be changed as appropriate depending on the liquid processing conditions, etc.

[0171] From the foregoing, it will be understood that various embodiments of the present disclosure have been described herein for purposes of illustration, and that various modifications may be made without departing from the scope and spirit of the present disclosure. Accordingly, the various embodiments disclosed herein are not intended to be limiting, with the true scope and spirit being indicated by the appended claims. [Explanation of symbols]

[0172] 1...substrate processing system, 2...coating and developing apparatus, 60...measurement section, 70A to 70C...light emitting and receiving device, 100...control device, 112...processing information storage section, 114...liquid processing control section, 120...film thickness adjustment section, 121...film thickness estimation function, 122...film thickness adjustment function, 124...light projection control section, 126...signal acquisition section, 128...feature acquisition section, 130...model information storage section, 132...film thickness calculation section, 134...condition acquisition section, 136...film thickness estimation result acquisition section, 138...polynomial approximation section, 140...calculation matrix storage section, 142...film thickness adjustment condition calculation section, 144...calculation matrix creation section.

Claims

1. A method for measuring a thickness of a target film formed on a target substrate by supplying a processing liquid to the target substrate while rotating the target substrate under predetermined liquid processing conditions, the method comprising: acquiring film thickness values ​​at a plurality of measurement points different from each other along a radial direction of the target film; creating an approximation equation relating to a thickness distribution of the target film by approximating the film thickness values ​​at the plurality of measurement points to one Zernike polynomial; Including, In creating the approximation formula, a coefficient related to a film thickness of the entire target substrate and one or more coefficients related to a concentric curved component are identified from among a plurality of coefficients included in the Zernike polynomial, thereby creating the approximation formula; the one or more coefficients relating to the concentric curved component in the approximation formula are coefficients corresponding to a plurality of order terms relating to a diameter of the target substrate in the Zernike polynomial, a Zernike polynomial including only terms related to a diameter of the target substrate whose degree is smaller than that of a Zernike polynomial used in creating the approximation equation, to create a low-order approximation equation related to a thickness distribution of the target film, and determining whether or not each of the thickness values ​​at the multiple measurement points is an abnormal value based on a difference between a thickness value at a point corresponding to the multiple measurement points included in the low-order approximation equation and the thickness values ​​at the multiple measurement points.

2. A film thickness analysis method as described in claim 1, in which, in creating the approximation equation, film thickness values ​​at the multiple measurement points that are different from the film thickness value determined to be the abnormal value are approximated to the Zernike polynomials to create an approximation equation relating to the film thickness distribution of the target film.

3. Obtaining the liquid processing conditions during formation of the target film on the target substrate; calculating an adjustment amount of the setting value when the film thickness distribution of the target film is brought closer to a target value by applying an adjustment amount calculation matrix, which is a calculation matrix relating an adjustment amount of the setting value included in the liquid processing conditions and a change amount of a plurality of coefficients included in the created approximation formula, to a coefficient matrix obtained from an approximation formula related to a film thickness distribution of the target film on the target substrate; The method for film thickness analysis according to claim 1 or 2, further comprising:

4. Obtaining film thickness values ​​at a plurality of measurement points along a radial direction of a target film formed on a target substrate by supplying a processing liquid to the target substrate while rotating the target substrate under predetermined liquid processing conditions; creating an approximation equation relating to a thickness distribution of the target film by approximating the film thickness values ​​at the plurality of measurement points to one Zernike polynomial; Including, In creating the approximation formula, a coefficient related to a film thickness of the entire target substrate and one or more coefficients related to a concentric curved component are identified from among a plurality of coefficients included in the Zernike polynomial, thereby creating the approximation formula; acquiring the liquid processing conditions during formation of the target film on the target substrate; calculating an adjustment amount of the setting value when the film thickness distribution of the target film is brought closer to a target value by applying an adjustment amount calculation matrix, which is a calculation matrix relating an adjustment amount of the setting value included in the liquid processing conditions and a change amount of a plurality of coefficients included in the created approximation formula, to a coefficient matrix obtained from an approximation formula related to a film thickness distribution of the target film on the target substrate; The film thickness analysis method further comprises:

5. 5. The film thickness analysis method according to claim 3, wherein the liquid processing conditions include a plurality of set values ​​for processes that are independent of each other.

6. The one or more coefficients relating to the concentric curved component in the approximation formula are coefficients corresponding to a plurality of order terms relating to a diameter of the target substrate in the Zernike polynomial, 6. The film thickness analysis method according to claim 3, wherein, in calculating the adjustment amount of the set value, a coefficient of each term in the Zernike polynomial is weighted, and then the adjustment amount calculation matrix is ​​applied to a coefficient matrix obtained from the approximation formula.

7. 7. The film thickness analysis method according to claim 6, wherein the weighting is set such that, among the terms of the plurality of kinds of orders, terms of lower orders are weighted greater than terms of higher orders.

8. 8. The film thickness analysis method according to claim 7, wherein the weighting is set based on variances of basis functions of a plurality of types of order terms related to a diameter of the target substrate.

9. A film thickness analysis method described in any one of claims 1 to 8, wherein, in the approximation, the approximation equation is created using a coefficient matrix, which is a matrix that specifies the relationship between each of the measurement points and multiple coefficients contained in the Zernike polynomial.

10. A film thickness analysis method described in any one of claims 1 to 8, wherein the approximate equation includes four types of terms, namely, zeroth order, second order, fourth order, and sixth order, related to the diameter of the target substrate.

11. an acquisition unit that acquires film thickness values ​​at a plurality of measurement points along a radial direction of a target film formed on a target substrate by supplying a processing liquid to the target substrate while rotating the target substrate based on predetermined liquid processing conditions; an approximation equation creation unit that creates an approximation equation relating to a thickness distribution of the target film by approximating the film thickness values ​​at the plurality of measurement points to one Zernike polynomial; having the approximation formula creation unit creates the approximation formula by identifying a coefficient relating to a film thickness of the entire target substrate and one or more coefficients relating to a concentrically curved component from among a plurality of coefficients included in the Zernike polynomial; the one or more coefficients relating to the concentric curved component in the approximation formula are coefficients corresponding to a plurality of order terms relating to a diameter of the target substrate in the Zernike polynomial, a thickness distribution of the target film by approximating the film thickness values ​​at the multiple measurement points to a low-order Zernike polynomial, the low-order Zernike polynomial including only terms whose orders of terms relating to a diameter of the target substrate are smaller than those of the Zernike polynomials used in creating the approximation equation, and determining whether or not each of the film thickness values ​​at the multiple measurement points is an abnormal value based on a difference between a film thickness value at a point corresponding to the multiple measurement points included in the low-order approximation equation and the film thickness values ​​at the multiple measurement points.

12. An acquisition unit that acquires film thickness values ​​at a plurality of different measurement points along a radial direction of a target film formed on a target substrate to be analyzed by supplying a processing liquid while rotating the target substrate based on predetermined liquid processing conditions; an approximation equation creation unit that creates an approximation equation relating to a thickness distribution of the target film by approximating the film thickness values ​​at the plurality of measurement points to one Zernike polynomial; having the approximation formula creation unit creates the approximation formula by identifying a coefficient relating to a film thickness of the entire target substrate and one or more coefficients relating to a concentrically curved component from among a plurality of coefficients included in the Zernike polynomial; a condition acquisition unit that acquires the liquid processing conditions when the target film is formed on the target substrate; a film thickness adjustment condition calculation unit that calculates adjustment amounts of the set values ​​when the film thickness distribution of the target film is brought closer to a target value by applying an adjustment amount calculation matrix, which is a calculation matrix that relates adjustment amounts of set values ​​included in the liquid processing conditions to changes in a plurality of coefficients included in the created approximation formula, to a coefficient matrix obtained from an approximation formula related to a film thickness distribution of the target film on the target substrate; and The film thickness analysis apparatus further comprises:

13. A computer-readable storage medium storing a program for causing an apparatus to execute the film thickness analysis method according to any one of claims 1 to 10.

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