Parameter optimization method, recording medium, and substrate processing apparatus

Abstract

The present invention provides a technique capable of appropriately and effectively implementing parameter optimization in a device that ejects a treatment liquid. A coating device (1) of the present invention includes: an ejection control section (910) that controls ejection of a coating liquid from a nozzle (71) based on a plurality of parameters including a first parameter and a second parameter; an ejection characteristic measurement section (911) that measures an ejection characteristic when the nozzle (71) ejects the coating liquid; a first optimization section (915) that optimizes the first parameter through global search based on the ejection characteristic; and a second optimization section (917) that optimizes the second parameter through local search based on the ejection characteristic. The first parameter includes parameters V1 to V4, T1 to T9 corresponding to a rising period in which an ejection speed of the coating liquid from the nozzle (71) is increased to a stable ejection speed. The second parameter includes a parameter V5 corresponding to a stable ejection period in which the ejection speed is maintained at the stable ejection speed.

Description

TECHNICAL FIELD

[0001] The subject matter disclosed in this specification relates to a parameter optimization method, a recording medium, and a substrate processing apparatus. BACKGROUND

[0002] As shown in Patent Literature 1, in coating a processing liquid sprayed from a nozzle on a substrate, the spray pressure applied to the processing liquid has a great influence on the thickness of the processing liquid coated on the substrate. Therefore, in Patent Literature 1, the object is to optimize parameters related to the spray pressure.

[0003] Specifically, the optimization method of Patent Literature 1 has: a simulated spraying process of spraying the processing liquid to the outside of the substrate; a spray property measurement process of measuring the spray property of the processing liquid in the simulated spraying process; a state quantity derivation process of deriving a state quantity of the deviation of the measured spray property from a target property; and a learning process of constructing a learning model by machine learning of the state quantity that changes with the change of the parameters. In addition, during the period when the state quantity exceeds a prescribed allowable range, the simulated spraying process, the spray property measurement process, the state quantity derivation process, and the learning process are repeatedly performed on the basis of the change of the parameters based on the learning model. When the state quantity falls within the allowable range, the last changed parameters are set as the parameters at the time of spraying the processing liquid in the processing liquid supply process.

[0004] PRIOR ART DOCUMENTS

[0005] PATENT LITERATURE

[0006] Patent Literature 1: Japanese Patent Application Publication No. 2020-040046

[0007] According to the optimization method of Patent Literature 1, since the adjustment work of the parameters can be automated by utilizing machine learning, the workload of the technicians can be reduced. However, the learning of the machine learning model generally requires a large amount of learning data or a large number of repeated trials. Therefore, in the case of simply automating the optimization work of the parameters, there is a risk that the time required for optimization or the amount of processing liquid consumed with the simulated spraying will increase, compared to the case where the parameter adjustment work is performed by a technician with knowledge and experience. SUMMARY

[0008] An object of the present application is to provide a technology that can appropriately and efficiently perform parameter optimization in a device that sprays a processing liquid.

[0009] To solve the above problems, a first aspect is a parameter optimization method for optimizing parameters for controlling ejection of a treatment liquid from a nozzle in a substrate processing apparatus that supplies the treatment liquid to a substrate, the parameter optimization method including a first optimization process of optimizing a first parameter by global search and a second optimization process of optimizing a second parameter by local search, the first parameter including a parameter corresponding to a rising period in which an ejection speed of the treatment liquid from the nozzle is increased to a stable ejection speed, the second parameter including a parameter corresponding to a stable ejection period in which the ejection speed is maintained at the stable ejection speed.

[0010] A second aspect is the parameter optimization method of the first aspect, in which the process b) is executed after the process a).

[0011] A third aspect is the parameter optimization method of the first aspect, in which the first optimization process includes a process of optimizing the first parameter by Bayesian optimization.

[0012] A fourth aspect is the parameter optimization method of any one of the first to third aspects, in which the parameter is a control amount that controls operation of a pump that feeds the treatment liquid to the nozzle.

[0013] A fifth aspect is the parameter optimization method of any one of the first to fourth aspects, in which the process a) includes a process of optimizing the first parameter based on a cost value derived from a feature amount of an ejection characteristic when the treatment liquid is ejected from the nozzle.

[0014] A sixth aspect is the parameter optimization method of any one of the first to fifth aspects, in which the process b) includes a process of optimizing the second parameter based on a ratio of an ejection speed at the start of the stable ejection period to an ejection speed at the end of the stable ejection period.

[0015] A seventh aspect is a recording medium that a computer readable records a program for causing the computer to execute optimization of parameters for controlling ejection of a treatment liquid from a nozzle, the program causing the computer to execute a first optimization process of optimizing a first parameter by global search and a second optimization process of optimizing a second parameter by local search, the first parameter including a parameter corresponding to a rising period in which an ejection speed of the treatment liquid from the nozzle is increased to a stable ejection speed, the second parameter including a parameter corresponding to a stable ejection period in which the ejection speed is maintained at the stable ejection speed.

[0016] The eighth aspect is a substrate processing apparatus that supplies a processing liquid ejected from a nozzle to a substrate, includes an ejection control section that controls ejection of the processing liquid from the nozzle based on a plurality of parameters including a first parameter and a second parameter, an ejection characteristic measurement section that measures an ejection characteristic when the processing liquid is ejected from the nozzle, a first optimization section that optimizes the first parameter by global search based on the ejection characteristic, and a second optimization section that optimizes the second parameter by local search based on the ejection characteristic, the first parameter including a parameter corresponding to a rise period in which an ejection speed of the processing liquid from the nozzle is increased to a stable ejection speed, and the second parameter including a parameter corresponding to a stable ejection period in which the ejection speed is maintained at the stable ejection speed.

[0017] According to the parameter optimization method of the first to sixth aspects, since the parameter corresponding to the stable ejection speed, which is relatively easy to optimize, is optimized by local search, the amount of calculation can be reduced compared to the case where all parameters are optimized by global search. Thus, optimization of parameters corresponding to ejection of the processing liquid can be performed appropriately and efficiently.

[0018] According to the parameter optimization method of the second aspect, the second parameter can be optimized based on the first parameter that is optimized.

[0019] According to the parameter optimization method of the third aspect, the first parameter can be optimized by Bayesian optimization.

[0020] According to the parameter optimization method of the fifth aspect, the first parameter can be optimized based on the cost value.

[0021] According to the parameter optimization method of the sixth aspect, since the second parameter is optimized based on the ratio of the ejection speeds at the start and end of the stable ejection period, the second parameter can be optimized so that the ejection speed during the stable ejection period is constant at the stable ejection speed. BRIEF DESCRIPTION OF DRAWINGS

[0022] Figure 1 FIG. 1 is a diagram schematically showing the overall configuration of a coating apparatus according to an embodiment.

[0023] Figure 2 FIG. 2 is a diagram showing the configuration of a coating liquid supply mechanism.

[0024] Figure 3 FIG. 3 is a diagram showing the configuration of a pump. Figure 2 FIG. 4 is a diagram showing the movement pattern of the working disk section of the pump shown in FIG. 3.

[0025] Figure 4 FIG. 5 is a diagram showing an ejection characteristic.

[0026] Figure 5 FIG. 6 is a block diagram showing a configuration example of a control unit.

[0027] Figure 6 is a flowchart showing a parameter optimization process performed in the coating apparatus.

[0028] Figure 7 is a flowchart showing Figure 6 details of the first optimization process shown in FIG. 7.

[0029] Figure 8 is a flowchart showing Figure 6 details of the second optimization process shown in FIG. 8.

[0030] Figure 9 is a graph showing a pressure waveform after the parameters are optimized by the first optimization process.

[0031] Figure 10 is a graph showing a result of linear regression on the characteristic quantity Fv.

[0032] Figure 11 is a graph for explaining each period of the pressure waveform.

[0033] Figure 12 is a graph schematically showing one example of an operation performed by the cost value derivation section on the pressure waveform.

[0034] Figure 13 is a graph for explaining an evaluation item for evaluating a time variation of the discharge pressure based on the characteristic quantity Fv1.

[0035] Figure 14 is a graph for explaining an evaluation item for evaluating a time variation of the discharge pressure based on the characteristic quantity Fv2.

[0036] Figure 15 is a graph for explaining an evaluation item for evaluating a time variation of the discharge pressure based on the characteristic quantity Fv3.

[0037] Figure 16 is a graph for explaining the characteristic quantity Fv4.

[0038] Figure 17 is a graph for explaining the characteristic quantity Fv5.

[0039] Figure 18 is a graph for explaining an evaluation item for evaluating a time variation of the discharge pressure based on the characteristic quantity Fv6.

[0040] Figure 19 is a graph for explaining an evaluation item for evaluating a time variation of the discharge pressure based on the characteristic quantity Fv7.

[0041] Figure 20 is a graph for explaining an evaluation item for evaluating a time variation of the discharge pressure based on the characteristic quantity Fv8.

[0042] Figure 21is a graph for explaining an evaluation item for evaluating a time change in the discharge pressure based on the feature quantity Fv9.

[0043] Figure 22 is a graph for explaining an evaluation item for evaluating a time change in the discharge pressure based on the feature quantity Fv10. DETAILED DESCRIPTION

[0044] Embodiments of the present application will be described below with reference to the drawings. Note that the components described in these embodiments are merely examples and do not limit the scope of the present application. In the drawings, the size, the relative shape, and the like of each component are exaggerated or simplified for the sake of explanation and ease of understanding.

[0045] Figure 1 is a graph schematically showing the overall configuration of the coating apparatus 1 of the embodiment. The coating apparatus 1 is a substrate processing apparatus that coats a coating liquid onto the upper surface Sf of a substrate S. The substrate S is, for example, a glass substrate for a liquid crystal display device. Note that the substrate S can be a semiconductor wafer, a glass substrate for a photomask, a glass substrate for a plasma display, a glass or ceramic substrate for a magnetic / optical disc, a glass substrate for an organic EL, a glass or silicon substrate for a solar cell, other flexible substrates and printed substrates, and the like, which are various processed substrates for electronic devices. The coating apparatus 1 is, for example, a slot coater.

[0046] In Figure 1 In order to explain the positional relationship of the components of the coating apparatus 1, an XYZ coordinate system is defined. The conveyance direction of the substrate S is the "X direction". The direction in which the substrate S advances in the X direction (the direction toward the downstream of the conveyance direction) is denoted as the +X direction, and the opposite direction (the direction toward the upstream of the conveyance direction) is denoted as the -X direction. In addition, the direction orthogonal to the X direction is the Y direction, and the direction orthogonal to the X direction and the Y direction is the Z direction. In the following description, the Z direction is the vertical direction, and the X direction and the Y direction are the horizontal directions. In the Z direction, the +Z direction is denoted as the upward direction, and the -Z direction is denoted as the downward direction.

[0047] In the coating apparatus 1, an input conveyor 100, an input transfer section 2, a float stage section 3, an output transfer section 4, and an output conveyor 110 are provided in this order in the +X direction. The input conveyor 100, the input transfer section 2, the float stage section 3, the output transfer section 4, and the output conveyor 110 form a conveyance path through which the substrate S passes. In addition, the coating apparatus 1 further includes a substrate conveyance section 5, a coating mechanism 7, a coating liquid supply mechanism 8, and a control unit 9.

[0048] The substrate S is transported from the upstream side to the input conveyor 100. The input conveyor 100 includes a roller conveyor 101 and a rotary drive mechanism 102. The rotary drive mechanism 102 rotates each roller of the roller conveyor 101. By rotating each roller of the roller conveyor 101, the substrate S is transported downstream (in the +X direction) in a horizontal orientation. "Horizontal orientation" means that the main surface (the surface with the largest area) of the substrate S is parallel to the horizontal plane (XY plane).

[0049] The input transfer unit 2 includes a roller conveyor 21 and a rotation-lifting drive mechanism 22. The rotation-lifting drive mechanism 22 rotates each roller of the roller conveyor 21 while simultaneously raising and lowering the roller conveyor 21. The rotation of the roller conveyor 21 transports the substrate S horizontally downstream (in the +X direction). Furthermore, the position of the substrate S in the Z direction is changed by raising and lowering the roller conveyor 21. The substrate S is transferred from the input conveyor 100 to the floating platform unit 3 via the input transfer unit 2.

[0050] like Figure 1 As shown, the floating stage section 3 is generally flat. The floating stage section 3 is divided into three parts along the X direction. In the floating stage section 3, an inlet floating stage 31, a coating stage 32, and an outlet floating stage 33 are sequentially arranged along the +X direction. The upper surfaces of the inlet floating stage 31, the coating stage 32, and the outlet floating stage 33 are on the same plane. The floating stage section 3 also includes a lifting pin drive mechanism 34, a floating control mechanism 35, and a lifting drive mechanism 36. The lifting pin drive mechanism 34 raises and lowers several lifting pins disposed on the inlet floating stage 31. The floating control mechanism 35 supplies compressed air to the inlet floating stage 31, the coating stage 32, and the outlet floating stage 33 to make the substrate S float. The lifting drive mechanism 36 raises and lowers the outlet floating stage 33.

[0051] On the upper surfaces of the inlet floating stage 31 and the outlet floating stage 33, a large number of ejection holes are arranged in a matrix for ejecting compressed air supplied from the floating control mechanism 35. When compressed air is ejected from each ejection hole, the substrate S floats above the floating stage 3. Thus, the substrate S is supported in a horizontal position with its lower surface Sb separated from the upper surface of the floating stage 3. When the substrate S is in the floating state, the distance (floatation amount) between the lower surface Sb of the substrate S and the upper surface of the floating stage 3 is, for example, 10 μm or more and 500 μm or less.

[0052] On the upper surface of the coating stage 32, ejector holes for ejecting compressed air supplied from the levitation control mechanism 35 and intake holes for drawing in air are alternately arranged in the X and Y directions. The levitation control mechanism 35 controls the amount of compressed air ejected from the ejector holes and the amount of air drawn in from the intake holes. This precisely controls the levitation amount of the substrate S relative to the coating stage 32, so that the position of the upper surface Sf of the substrate S above the coating stage 32 in the Z direction is a predetermined value. It should be noted that the levitation amount of the substrate S relative to the coating stage 32 is calculated by the control unit 9 based on the detection results of sensor 61 or sensor 62 (described later). Furthermore, the levitation amount of the substrate S relative to the coating stage 32 is preferably adjustable with high precision via airflow control.

[0053] The substrate S, which is moved into the floating platform section 3, is given a pushing force in the +X direction by the roller conveyor 21 and is transported to the inlet floating platform 31. The inlet floating platform 31, the coating platform 32, and the outlet floating platform 33 support the substrate S in a floating state. As the floating platform section 3, for example, the configuration described in Japanese Patent No. 5346643 can be adopted.

[0054] The substrate transport unit 5 is positioned below the floating platform unit 3. The substrate transport unit 5 includes a chuck mechanism 51 and an adsorption-running control mechanism 52. The chuck mechanism 51 includes an adsorption pad (not shown) disposed on the adsorption member. The chuck mechanism 51 supports the substrate S from below by bringing the adsorption pad into contact with the periphery of the lower surface Sb of the substrate S. The adsorption-running control mechanism 52 applies negative pressure to the adsorption pad, causing the substrate S to adsorb onto the adsorption pad. Furthermore, the adsorption-running control mechanism 52 causes the substrate transport unit 5 to reciprocate in the X direction.

[0055] The chuck mechanism 51 keeps the substrate S in a position where the lower surface Sb of the substrate S is higher than the upper surface of the lifting stage 3. While the peripheral portion of the substrate S is held by the chuck mechanism 51, the buoyancy provided by the lifting stage 3 keeps the substrate S in a horizontal position.

[0056] like Figure 1 As shown, the coating apparatus 1 includes a sensor 61 for measuring plate thickness. The sensor 61 is positioned near the roller conveyor 21. The sensor 61 detects the position of the upper surface Sf of the substrate S held in the chuck mechanism 51 in the Z direction. In addition, by positioning the chuck (not shown) which is not holding the substrate S directly below the sensor 61, the sensor 61 can detect the vertical Z position of the upper surface of the adsorption member, i.e., the adsorption surface.

[0057] The chuck mechanism 51 moves while holding the substrate S which is carried into the floating stage section 3, in the +X direction. Thus, the substrate S is carried from above the entrance floating stage 31, through above the coating stage 32, to above the exit floating stage 33. Further, the substrate S is moved from the exit floating stage 33 to the output transfer section 4.

[0058] The output transfer section 4 moves the substrate S from the position above the exit floating stage 33 to the output conveyor 110. The output transfer section 4 has a roller conveyor 41 and a rotation-lift driving mechanism 42. The rotation-lift driving mechanism 42 rotationally drives the roller conveyor 41 and lifts the roller conveyor 41 in the Z direction. The substrate S is moved in the +X direction by rotating the rollers of the roller conveyor 41. Further, the substrate S is displaced in the Z direction by lifting the roller conveyor 41.

[0059] The output conveyor 110 has a roller conveyor 111 and a rotation driving mechanism 112. The output conveyor 110 carries the substrate S in the +X direction by rotating the rollers of the roller conveyor 111 and pushes the substrate S out of the coating apparatus 1. Note that the input conveyor 100 and the output conveyor 110 are part of the coating apparatus 1. However, the input conveyor 100 and the output conveyor 110 can be assembled into a device different from the coating apparatus 1.

[0060] The coating mechanism 7 coats the substrate S with a coating liquid on the upper surface Sf thereof. The coating mechanism 7 is disposed above the carrying path of the substrate S. The coating mechanism 7 has a nozzle 71. The nozzle 71 is a slit nozzle having a slit-shaped ejection port on the lower surface thereof. The nozzle 71 is connected to a positioning mechanism (not shown). The positioning mechanism moves the nozzle 71 between a coating position (position shown by a solid line) above the coating stage 32 and a maintenance position described later. Figure 1 The coating liquid supply mechanism 8 is connected to the nozzle 71. The coating liquid supply mechanism 8 ejects the coating liquid from the ejection port provided on the lower surface of the nozzle 71 by supplying the coating liquid to the nozzle 71.

[0061] Figure 2 is a view showing the configuration of the coating liquid supply mechanism 8. The coating liquid supply mechanism 8 has a pump 81, a pipe 82, a coating liquid replenishment unit 83, a pipe 84, an on-off valve 85, a pressure gauge 86, and a driving section 87. The pump 81 is a delivery source for delivering the coating liquid to the nozzle 71 and delivers the coating liquid by changing the volume. For example, the pump 81 can employ a bellows type pump described in Japanese Patent Application Publication No. 10-61558. As shown in Figure 2 the pump 81 has a flexible tube 811 which freely expands and contracts in the radial direction. One end of the flexible tube 811 is connected to the coating liquid replenishment unit 83 via the pipe 82. The other end of the flexible tube 811 is connected to the nozzle 71 via the pipe 84.

[0062] The pump 81 has a bellows 812 which is axially freely elastically deformable. The bellows 812 has a small bellows portion 813, a large bellows portion 814, a pump chamber 815, and a working disk portion 816. The pump chamber 815 is disposed between the flexible tube 811 and the bellows 812. The pump chamber 815 is filled with an incompressible medium. The working disk portion 816 is connected to the drive portion 87.

[0063] The coating liquid replenishing unit 83 has a storage tank 831 which stores the coating liquid. The storage tank 831 is connected to the pump 81 via a pipe 82. An on-off valve 833 is inserted in the pipe 82. The on-off valve 833 is opened and closed in accordance with an instruction from the control unit 9. When the on-off valve 833 is opened, the coating liquid can be replenished from the storage tank 831 to the flexible tube 811 of the pump 81. In addition, when the on-off valve 833 is closed, the replenishment of the coating liquid from the storage tank 831 to the flexible tube 811 of the pump 81 is restricted.

[0064] The pipe 84 is connected to the output side of the pump 81. An on-off valve 85 is inserted in the pipe 84. The on-off valve 85 is opened and closed in accordance with an instruction from the control unit 9. By opening and closing the on-off valve 85, the supply and stop of the coating liquid to the nozzle 71 are switched. A pressure gauge 86 is disposed in the pipe 84. The pressure gauge 86 detects the pressure (discharge pressure) of the coating liquid supplied to the nozzle 71, and outputs a signal indicating the detected pressure value to the control unit 9.

[0065] Figure 3 is a graph showing a movement pattern of the working disk portion 816 of the pump 81. Figure 2 is a graph showing a movement pattern of the working disk portion 816 of the pump 81. Figure 3 In FIG. 8, the horizontal axis represents time, and the vertical axis represents the moving speed of the working disk portion 816. The drive portion 87 moves the working disk portion 816 in accordance with the movement pattern shown in Figure 3 is a graph showing a movement pattern of the working disk portion 816 of the pump 81. Figure 4 is a graph showing a movement pattern of the working disk portion 816 of the pump 81.

[0066] Figure 4 is a graph showing a movement pattern of the working disk portion 816 of the pump 81. Figure 4 (a) of FIG. 9 is a graph showing a target characteristic which is a preferred discharge characteristic. Figure 4 (b) of FIG. 9 is an example of actually measured discharge characteristics. In Figure 4 In FIG. 9, the horizontal axis represents time, and the vertical axis represents the pressure value (or the discharge speed).

[0067] In the present embodiment, by adjusting various parameters (acceleration time, constant speed, constant speed time, deceleration time, etc.) that regulate the movement of the work table section 816, appropriate optimization processing is performed to make the ejection characteristics (specifically, the temporal change in the ejection speed (ejection pressure)) of the coating liquid ejected from the nozzle 71 coincide with or approximate the desired target characteristics (the graph shown in (a) of FIG. 10). Figure 4 Details will be described later.

[0068] As shown in FIGS. 11 and 12, a sensor 62 is disposed on the nozzle 71 that supplies the coating liquid from the coating liquid supply mechanism 8. The sensor 62 detects the height of the substrate S in the Z direction in a non-contact manner. The sensor 62 is electrically connected to the control unit 9. Based on the detection result of the sensor 62, the control unit 9 measures the distance (separation distance) between the floated substrate S and the upper surface of the coating stage 32. In addition, the control unit 9 adjusts the coating position of the nozzle 71 by the positioning mechanism based on the measured separation distance. Note that, as the sensor 62, an optical sensor or an ultrasonic sensor can be applied. Figure 1 Figure 2 As shown in FIGS. 11 and 12, a sensor 62 is disposed on the nozzle 71 that supplies the coating liquid from the coating liquid supply mechanism 8. The sensor 62 detects the height of the substrate S in the Z direction in a non-contact manner. The sensor 62 is electrically connected to the control unit 9. Based on the detection result of the sensor 62, the control unit 9 measures the distance (separation distance) between the floated substrate S and the upper surface of the coating stage 32. In addition, the control unit 9 adjusts the coating position of the nozzle 71 by the positioning mechanism based on the measured separation distance. Note that, as the sensor 62, an optical sensor or an ultrasonic sensor can be applied.

[0069] The coating mechanism 7 is provided with a nozzle cleaning standby unit 72. The nozzle cleaning standby unit 72 performs prescribed maintenance on the nozzle 71 disposed at the maintenance position. The nozzle cleaning standby unit 72 has a roller 721, a cleaning section 722, and a roller stand 723. The nozzle cleaning standby unit 72 adjusts the ejection port of the nozzle 71 to a state suitable for the coating process by cleaning the nozzle 71 and forming a puddle. In addition, in the coating apparatus 1, in order to evaluate the ejection pressure applied to the coating liquid, the simulation ejection of the coating liquid from the nozzle 71 is performed in a state in which the nozzle 71 is disposed at the maintenance position.

[0070] Figure 5 is a block diagram showing a configuration example of the control unit 9. The control unit 9 controls the operation of each element of the coating apparatus 1. The control unit 9 is a computer provided with an arithmetic section 91, a storage section 93, and a user interface 95. The arithmetic section 91 is a processor constituted by a CPU (Central Processing Unit) or a GPU (Graphics Processing Unit), etc. The storage section 93 is constituted by a RAM (Random Access Memory) or the like, a nonvolatile auxiliary storage device such as an HDD (Hard Disk Drive) and an SDD (Solid State Drive), etc.

[0071] ​The user interface 95 has a display that displays information to the user and an input device that accepts user input operations. As the control unit 9, for example, a desktop, laptop, or tablet computer can be used.

[0072] The storage section 93 stores a program 931. The program 931 is provided by a recording medium M. That is, the recording medium M records the program 931 in a manner that the control unit 9 of the computer can read. The recording medium M is, for example, a USB (Universal Serial Bus) memory, an optical disk such as a DVD (Digital Versatile Disc), a magnetic disk, or the like.

[0073] The arithmetic section 91 functions as an ejection control section 910, an ejection characteristic measurement section 911, a cost value derivation section 913, a first optimization section 915, and a second optimization section 917 by executing the program 931.

[0074] The ejection control section 910 controls the operation (feed operation) of the pump 81 that delivers the coating liquid to the nozzle 71 based on a parameter set in advance.

[0075] The ejection characteristic measurement section 911 measures the ejection characteristic. Specifically, the ejection characteristic measurement section 911 measures the pressure waveform based on the ejection pressure (pressure value of the coating liquid) output from the pressure gauge 86 in the simulation ejection. That is, the ejection characteristic measurement section 911 periodically acquires the ejection pressure measured by the pressure gauge 86 at a prescribed sampling period. Thereby, the ejection pressure applied to the coating liquid during the ejection of the coating liquid from the nozzle 71 is acquired and stored as ejection pressure measurement data in the storage section 93. The ejection pressure measurement data is data indicating the time and the ejection pressure measured at the time.

[0076] The cost value derivation section 913 derives the cost value based on a prescribed cost function from the ejection characteristic (pressure waveform) measured by the ejection characteristic measurement section 911. The cost value is used when the first optimization section 915 performs the optimization operation. The first optimization section 915 optimizes the parameter by a global search method. As the optimization of the global search, in this example, Bayesian optimization is performed. Note that the global search method is not limited to the Bayesian optimization, and a genetic algorithm can be employed. The second optimization section 917 optimizes the parameter by a local search method. The optimization of the local search will be described later.

[0077] In the coating apparatus 1, in order to coat the coating liquid ejected from the nozzle 71 on the upper surface Sf of the substrate S with a uniform film thickness, it is important to adjust the ejection characteristic, that is, the ejection speed of the coating liquid at the time of ejection from the nozzle 71. For example, by adjusting the ejection characteristic, the ejection characteristic measurement section 911 measures the ejection characteristic of the coating liquid, and the cost value derivation section 913 derives the cost value from the ejection characteristic. Figure 4The coating liquid is ejected from the nozzle 71 with the target property of (a) shown in FIG. 7, and the uniformity of the film thickness can be improved. Therefore, it is important to optimize the parameters closely related to the ejection property in such a manner that the ejection property approaches the target property. In the present embodiment, as shown in FIG. 8, the following 16 setting values for pump control, which have determined the movement of the work disk portion 816, are taken as the parameters of the optimization object. Figure 3

[0078] • Stable speed V1.

[0079] • Acceleration time T1: time from the stop state to the stable speed V1.

[0080] • Stable speed time T2: time of continuation of the stable speed V1.

[0081] • Stable speed V2.

[0082] • Acceleration time T3: time from the stable speed V1 to the stable speed V2.

[0083] • Stable speed time T4: time of continuation of the stable speed V2.

[0084] • Stable speed V3.

[0085] • Acceleration time T5: time from the stable speed V2 to the stable speed V3.

[0086] • Stable speed time T6: time of continuation of the stable speed V3.

[0087] • Stable speed V4.

[0088] • Acceleration time T7: time from the stable speed V3 to the stable speed V4.

[0089] • Stable speed time T8: time of continuation of the stable speed V4.

[0090] • Stable speed V5.

[0091] • Acceleration time T9: time from the stable speed V4 to the stable speed V5.

[0092] • Stable speed time T10: time of continuation of the stable speed V5.

[0093] • Deceleration time T11: time from the stable speed V5 to the stop state.

[0094] The above parameters correspond to the control amount for controlling the operation (feed operation) of the pump 81 that feeds the coating liquid to the nozzle 71. Note that the kind and number of the parameters are not particularly limited, and can be arbitrarily set as long as the control amount for controlling the feed operation of the pump 81. ​

[0095] The above parameters can be adjusted, for example, by changing the method depending on the type of coating treatment. Additionally, there are cases where parameters are adjusted based on user input via an input device. Of the 16 parameters mentioned above, V5 can mostly be adjusted by slightly altering the value of the stable speed V4. Therefore, V5 is relatively easy to optimize. On the other hand, the parameters other than V5 (V1~V4, T1~T11) are relatively difficult to optimize because adjustments are made while continuously trying different coating liquids to grasp the spraying characteristics.

[0096] Therefore, in this embodiment, for the optimization of parameters other than V5 (the first parameter), a general and globally searchable Bayesian optimization is applied. On the other hand, for the optimization of V5 (the second parameter), after adjustment through the above-described Bayesian optimization, a local search method described later is applied.

[0097] Figure 6 This is a flowchart illustrating the parameter optimization process performed in the coating apparatus 1. When the parameter optimization process begins, the nozzle moving step S1 is performed first. In the nozzle moving step S1, the nozzle 71 is moved to the aforementioned maintenance position. Through the nozzle moving step S1, simulated spraying can be performed in the coating apparatus 1.

[0098] When the nozzle movement step S1 is completed, the first optimization step S2 is executed. In the first optimization step S2, the first optimization unit 915 optimizes parameters other than V5 (V1 to V4, T1 to T11). It should be noted that in the first optimization step S2, parameter V5 is fixed to a predetermined value. Then, after the first optimization step S2, the second optimization step S3 is performed. In the second optimization step S3, V5 is optimized.

[0099] like Figure 3 As shown, the moving speed of the working disc section 816 is maintained within the range corresponding to V5. Figure 4 (b) shows the "stable ejection period". The "stable ejection period" is the range in which the ejection rate (ejection pressure) of the coating liquid from nozzle 71 remains almost constant (stable ejection rate). That is, the second optimization step S3 of optimization V5 is equivalent to the step of optimizing the parameters corresponding to the stable ejection period.

[0100] In addition, among the parameters other than V5, V1~V4 and T1~T9 are corresponding... Figure 4 The parameters for the "rise period" are shown in (b). The "rise period" is the interval from zero to a stable ejection velocity. The first optimization step S2, which optimizes parameters V1 to V4 and T1 to T9, is equivalent to the step that optimizes the parameters corresponding to the rise period.

[0101] <First Optimization (Optimization via Global Search)>

[0102] Figure 7 It is shown Figure 6 The flowchart showing the details of the first optimization process S2 is shown below. Figure 7 As shown, in the first optimization step S2, the aforementioned 16 parameters are first set (step S21). The initial values ​​of the parameters are, for example, values ​​generated from random numbers or values ​​specified by the user. After step S21, the ejection characteristic measurement unit 911 measures the pressure waveform as an ejection characteristic (step S22). After step S22, the cost value derivation unit 913 derives the cost value from the measured pressure waveform (step S23).

[0103] The cost value represents the evaluation result of the pressure waveform numerically. As described later, the cost value derivation unit 913 derives the cost value based on a cost function that takes the pressure waveform as input and outputs the cost value. In this embodiment, the cost function is set to the pressure waveform ( Figure 4 (b) and the pressure waveform as the target ( Figure 4 The more different (a) is, the greater the cost value.

[0104] After step S23, it is determined whether the cost value is less than a predetermined threshold (step S24). If the cost value is determined to be above the predetermined threshold (no in step S24), the first optimization unit 915 obtains the next search point (i.e., new parameters) based on the currently set parameters and the cost value derived from step S23 (step S25). Furthermore, after step S25, step S21 is executed again. Thus, by simulating ejection based on the new parameters as the next search point, the pressure waveform measurement is performed again (step S22).

[0105] On the other hand, in step S24, if the cost value is determined to be less than the specified threshold (yes in step S24), the parameters are considered to have been optimized, and the first optimization unit 915 ends the first optimization process S2.

[0106] <Second optimization process (optimization through local search)>

[0107] Figure 8 It is shown Figure 6 The flowchart shows the details of the second optimization process S3. When the second optimization process S3 begins, firstly, the second optimization unit 917 calculates the characteristic quantity Fv based on the pressure waveform after the parameters have been optimized by the first optimization process S2 (step S31). (Refer to...) Figure 9 Explain the steps for calculating the characteristic quantity Fv.

[0108] Figure 9is a graph showing a pressure waveform after the parameters are optimized by the first optimization process S2. The second optimization section 917 extracts data of the stable ejection period in the pressure waveform in order to calculate the characteristic quantity Fv. In addition, the second optimization section 917 performs linear regression on the data of the stable ejection period. By this linear regression, the second optimization section 917 acquires the regression straight line Ll shown in Figure 9 In addition, the second optimization section 917 acquires the pressure Ps at the start of the stable ejection period and the pressure Pe at the end of the stable ejection period, respectively, on the basis of the regression straight line Ll. Furthermore, the second optimization section 917 calculates the value of the ratio of the pressure Ps to the pressure Pe (= Ps / Pe) as the characteristic quantity Fv. The pressure Ps corresponds to the ejection speed at the start of the stable ejection period. The pressure Pe corresponds to the ejection speed at the end of the stable ejection period.

[0109] Returning to Figure 8 After step S31, the second optimization section 917 updates V5 (step S32). Specifically, the second optimization section 917 acquires a value obtained by multiplying the current V5 by the characteristic quantity Fv as the new V5.

[0110] After step S32, the ejection characteristic measurement section 911 measures the pressure waveform while performing the simulation ejection (step S33). Then, the second optimization section 917 calculates the characteristic quantity Fv of the pressure waveform acquired in step S33 (step S34). Step S34 performs the same steps as step S31.

[0111] After step S34, the second optimization section 917 determines whether the characteristic quantity Fv is within the range of 1 ± a (step S35). Here, "a" is an arbitrary decimal number set in advance. As described above, since the stable ejection period is an interval in which the coating liquid is ejected at a constant speed, the pressure Ps at the start should coincide with the pressure Pe at the end. Therefore, in step S35, it is determined whether the current V5 is appropriate by determining whether the characteristic quantity Fv is within the range of 1 ± a.

[0112] In step S35, in a case where it is determined that the characteristic quantity Fv is within the range of 1 ± a (YES in step S35), the second optimization section 917 considers that V5 has been optimized, and ends the second optimization process S3. On the other hand, in step S35, in a case where it is determined that the characteristic quantity Fv is outside the range of 1 ± a (NO in step S35), the second optimization section 917 performs linear regression on the characteristic quantities Fv acquired in step S31 and step S34 (step S36).

[0113] Figure 10 is a graph showing the result of the linear regression on the characteristic quantity Fv. In Figure 10 , the horizontal axis represents V5, and the vertical axis represents the characteristic quantity Fv. Figure 10The plurality of (three) dots shown indicate the feature quantity Fv acquired in step S31 or step S34. As shown in the figure, the feature quantity Fv is acquired by performing linear regression on the feature quantity Fv. Figure 10 As shown, the regression straight line L2 is acquired by performing linear regression on the feature quantity Fv.

[0114] Returning to Figure 8 After step S36, the second optimization section 917 updates V5 (step S37). Specifically, the second optimization section 917 calculates the value of V5 (= V5') at which Fv is 1, based on the regression straight line L2 acquired by step S36. Then, the second optimization section 917 updates V5 to the calculated value. Next, based on the updated V5, step S33 is executed again. In this way, in the second optimization process S3, steps S33 to S37 are repeatedly executed until the feature quantity Fv is within the range of 1 ± α.

[0115] As described above, in the coating device 1, of all the parameters related to the ejection of the coating liquid, optimization is applied to the parameter V5 for which optimization is relatively easy by local search. Thereby, compared to a case where optimization by global search such as Bayesian optimization is applied to all the parameters, the amount of calculation can be reduced. Therefore, in the coating device 1 that ejects the coating liquid, optimization of the parameters can be appropriately and efficiently performed. In addition, since the number of trials of the simulation ejection can be reduced, the amount of consumption of the coating liquid can be suppressed.

[0116] Note that optimization by local search can also be applied to parameters other than the parameter V5.

[0117] <Cost value calculation method>

[0118] Next, the calculation method of the cost value used for optimization in the first optimization process S2 will be described. The cost value is calculated by adding each of the feature quantities Fv1 to Fv10 calculated from the pressure waveform for each of the prescribed evaluation items. Hereinafter, the feature quantities Fv1 to Fv10 for each of the evaluation items will be described.

[0119] Figure 11 is a graph for explaining each period of the pressure waveform. Figure 11 In the graph, the horizontal axis indicates the time, and the vertical axis indicates the ejection pressure. Note that in Figure 11 The horizontal axis indicates the time, and the vertical axis indicates the ejection pressure in each of the graphs that follow.

[0120] As shown in Figure 11 The ejection pressure at the time ta at which the ejection of the coating liquid from the nozzle 71 is started and the ejection pressure at the time te at which the ejection of the coating liquid from the nozzle 71 is ended are the initial pressure Pi. However, the pressure at each of the start and the end of the ejection does not necessarily always coincide with the initial pressure Pi.

[0121] As shown in Figure 11As shown, the ejection period Tt is divided into an ascending period Ta, a transition period Tb, a stable period Tc, and a descending period Td. The ascending period Ta is a period from a time ta at which the coating liquid supply mechanism 8 starts to eject the coating liquid from the nozzle 71 (i.e., a time ta at which the coating liquid supply mechanism 8 starts to move the work-plate section 816) to a time tb at which the ejection pressure reaches the target pressure Pt. That is, when the ejection of the coating liquid from the nozzle 71 is started at the time ta, the ejection pressure is increased from the initial pressure Pi to the target pressure Pt during the period from the time ta to the time tb.

[0122] The transition period Tb is a period from the time tb to a time tc after a prescribed vibration decay period. The vibration decay period is a time required for the ejection pressure to be stabilized in time, which is set in advance by the user through an input operation to the user interface 95, for example, and stored in the storage section 93.

[0123] The stable period Tc is a period from the time tc to a time td at which the coating liquid supply mechanism 8 starts to decrease the ejection pressure (i.e., a time td at which the coating liquid supply mechanism 8 starts to decelerate the work-plate section 816 from the target speed). That is, the coating liquid supply mechanism 8 moves the work-plate section 816 at a constant speed (V5 described above) during the period from the time tc to the time td, and starts to decelerate the work-plate section 816 at the time td. Note that, in the stable period Tc, the ejection pressure is substantially stabilized at the target pressure Pt. However, even in the stable period Tc, the time variation of the ejection pressure includes a slight vibration. Therefore, in the stable period Tc, the ejection pressure can be greater or less than the target pressure Pt.

[0124] The transition period Tb and the stable period Tc constitute a constant-pressure period Tbc. That is, the constant-pressure period Tbc is a period from the time tb to the time td.

[0125] The descending period Td is a period from the time td to a time te at which the coating liquid supply mechanism 8 ends the ejection of the coating liquid from the nozzle 71 (i.e., a time te at which the coating liquid supply mechanism 8 stops the work-plate section 816). That is, during the period from the time td to the time te, the ejection pressure is decreased to the initial pressure Pi, and the ejection of the coating liquid from the nozzle 71 is stopped at the time te.

[0126] Figure 12 FIG. 9 is a diagram schematically showing one example of an operation performed by the cost value derivation section 913 on the pressure waveform. As shown, the cost value derivation section 913 calculates a first-order differential Dl of the pressure waveform by time-differentiating the pressure waveform. Further, the cost value derivation section 913 calculates a second-order differential D2 of the time variation of the ejection pressure by differentiating the first-order differential Dl of the time variation of the ejection pressure with respect to time. In addition, the cost value derivation section 913 calculates the mean absolute error MAE and the root mean square error RMSE based on the following equations. Figure 12 As shown, the cost value derivation section 913 calculates a first-order differential Dl of the pressure waveform by time-differentiating the pressure waveform. Further, the cost value derivation section 913 calculates a second-order differential D2 of the time variation of the ejection pressure by differentiating the first-order differential Dl of the time variation of the ejection pressure with respect to time. In addition, the cost value derivation section 913 calculates the mean absolute error MAE and the root mean square error RMSE based on the following equations.

[0127] MAE (a, b) = (1 / n) · (Σ|a - b|)

[0128] RMSE (a, b) = ((1 / n) · (Σ(a - b) 2 )) 1 / 2

[0129] n is the amount of data.

[0130] Figure 13 is a graph for illustrating an evaluation item for evaluating the time variation of the discharge pressure based on the feature quantity Fv1. In the evaluation item shown in Figure 13 In the evaluation item shown in FIG. 8, the error (ideal trapezoidal absolute error) from the actual pressure waveform is evaluated based on the trapezoidal waveform having an amplitude equivalent to the difference between the average value of the discharge pressure in the stable period Tc (i.e., the stable pressure Pm) and the initial pressure Pi.

[0131] Specifically, in the rising period Ta, linear regression analysis is performed on the time variation of the discharge pressure between the prescribed lower reference pressure and the prescribed upper reference pressure that is greater than the lower reference pressure, and the rising regression straight line Lr_R is calculated. The rising regression straight line Lr_R linearly increases from the initial pressure Pi to the stable pressure Pm between the time tll and the time tl2.

[0132] Likewise, in the falling period Td, linear regression analysis is performed on the time variation of the discharge pressure between the upper reference pressure and the lower reference pressure, and the falling regression straight line Lr_F is calculated. The falling regression straight line Lr_F linearly decreases from the stable pressure Pm to the initial pressure Pi between the time tl3 and the time tl4.

[0133] Note that the lower reference pressure and the upper reference pressure are pressures that are greater than the initial pressure Pi and less than the target pressure Pt, and are set by the user through input operations on the user interface 95, for example, and are stored in the storage section 93. For example, the lower reference pressure can be a pressure obtained by adding 20% of the absolute value of the difference between the initial pressure Pi and the target pressure Pt to the initial pressure Pi. In addition, the upper reference pressure can be a pressure obtained by adding 80% of the absolute value of the difference between the initial pressure Pi and the target pressure Pt to the initial pressure Pi.

[0134] Further, a start-time approximation straight line Lr_s is set for the interval from time ta to time tll. This start-time approximation straight line Lr_s is a straight line indicating that the slope of the initial pressure Pi is zero. That is, the start-time approximation straight line Lr_s is a straight line connecting from the time point (time ta) at which the coating liquid starts to be ejected from the nozzle 71 to the start time point of the rising regression straight line Lr_R. Note that, depending on the state (slope) of the regression straight line, time tll can be before time ta, and time t12 can be after time tb. In this case, when tll < ta, the start-time approximation straight line Lr_s is omitted.

[0135] Further, an end-time approximation straight line Lr_e is set for the interval from time t14 to time te. This end-time approximation straight line Lr_e is a straight line indicating that the slope of the initial pressure Pi is zero. That is, the end-time approximation straight line Lr_e is a straight line connecting from the end time point of the falling regression straight line Lr_F to the time point (time te) at which the ejection of the coating liquid from the nozzle 71 ends. Note that, when te < t14, the end-time approximation straight line Lr_e is omitted.

[0136] Further, a stable straight line Lr_m is set for the interval from time t12 to time t13. This stable straight line Lr_m is a straight line indicating that the slope of the stable pressure Pm is zero. That is, the stable straight line Lr_m is a straight line connecting the end time point (time t12) of the rising regression straight line Lr_R to the start time point (time t13) of the falling regression straight line Lr_F, and indicating the stable pressure Pm.

[0137] As described above, the cost value derivation section 913 calculates the approximation waveform WF1 constituted by the start-time approximation straight line Lr_s, the rising regression straight line Lr_R, the stable straight line Lr_m, the falling regression straight line Lr_F, and the end-time approximation straight line Lr_e arranged in time series. Further, the cost value derivation section 913 calculates the average absolute error MAE (ideal trapezoidal absolute error) between the pressure value of the pressure waveform and the approximation waveform WF1 in the entire ejection period Tt from time ta to time te, as the characteristic quantity Fv1. The cost value derivation section 913 stores the calculated characteristic quantity Fv1 in the storage section 93.

[0138] According to the evaluation based on the characteristic quantity Fv1, in the case where the time variation of the ejection pressure in the entire ejection period Tt greatly deviates from the ideal shape (i.e., the trapezoidal shape), a large score (i.e., a negative evaluation) can be given to the ejection pressure.

[0139] Figure 14 is a view for explaining an evaluation item for evaluating the time variation of the ejection pressure based on the characteristic quantity Fv2. In Figure 14The evaluation item is to evaluate the smoothness of the increase in the discharge pressure. Specifically, during the increase period Ta, a time change in the discharge pressure between the lower reference pressure P2_l and the upper reference pressure P2_u that is greater than the lower reference pressure P2_l is subjected to curve regression analysis, and an increase regression curve Nr is calculated. The curve regression analysis is performed by a quadratic curve.

[0140] The lower reference pressure P2_l is set to the initial pressure Pi. In addition, the upper reference pressure P2_u is a pressure that is greater than the lower reference pressure P2_l and less than the target pressure Pt. The upper reference pressure P2_u is set by the user, for example, by an input operation to the user interface 95, and is stored in the storage section 93. The upper reference pressure P2_u can be a pressure that is obtained by adding 20% of the absolute value of the difference between the initial pressure Pi and the target pressure Pt to the initial pressure Pi. The increase regression curve Nr increases from the lower reference pressure P2_l (the initial pressure Pi) to the upper reference pressure P2_u during a period from the time t21 to the time t22. Note that the time t21 coincides with the time ta, and the time t22 is a time after the time ta and before the time tb.

[0141] The cost value derivation section 913 calculates a waveform WF2 constituted by the increase regression curve Nr. In addition, the cost value derivation section 913 calculates a root mean square error RMSE between the pressure values of the pressure waveform measured in the increase initial period Ta_s from the time t21 to the time t22 and the waveform WF2 as the feature quantity Fv2. In addition, the cost value derivation section 913 stores the calculated feature quantity Fv2 in the storage section 93.

[0142] According to the evaluation based on the feature quantity Fv2, in a case where the abnormality in the discharge pressure occurs immediately after the start of the discharge of the coating liquid from the nozzle 71, which is affected by the state before the start of the discharge, a large score (i.e., a negative evaluation) can be given to the discharge pressure. Note that the curve that can be used for the curve regression analysis is not limited to a quadratic curve. Other curves such as an exponential function can also be used.

[0143] Figure 15 is a graph for explaining an evaluation item for evaluating the time change in the discharge pressure based on the feature quantity Fv3. In Figure 15 In the evaluation item, it is evaluated whether the increase period Ta falls within the constant period. Specifically, the cost value derivation section 913 calculates the length (= tb-ta) of the increase period Ta from the time ta to the time tb required for the discharge pressure to increase from the initial pressure Pi to the target pressure Pt as the feature quantity Fv3. In addition, the cost value derivation section 913 stores the calculated feature quantity Fv3 in the storage section 93.

[0144] According to the evaluation based on the feature quantity Fv3, a large score (i.e., a negative evaluation) can be given to the discharge pressure for which the period of rising to the target pressure Pt is shorter or longer than the prescribed constant period.

[0145] Figure 16 (A) of FIG. 9 is a graph for explaining the feature quantity Fv4. Figure 16 (A) of FIG. 9 is a graph for explaining the evaluation item based on the feature quantity Fv4 to evaluate the time variation of the discharge pressure. Figure 16 (B) of FIG. 9 is a graph showing an example of the time variation of the discharge pressure judged as unsuitable by the evaluation based on the feature quantity Fv4. In Figure 16 In the evaluation item of (A) of FIG. 9, it is evaluated whether or not there is an abnormality in the rising of the discharge pressure.

[0146] Specifically, the cost value deriving section 913 calculates the first-order differential Dl of the time variation of the discharge pressure for the rising period Ta from the time ta to the time tb, and obtains the first-order differential waveform WF4. Then, the cost value deriving section 913 obtains the number of times that the first-order differential waveform WF4 crosses a prescribed threshold value Th4 in the rising period Ta as the feature quantity Fv4. In Figure 16 In the example of (A) of FIG. 9, the first-order differential waveform WF4 crosses the threshold value Th4 (for example, 0.002) at the time t41 and the time t42, respectively, and the number of crossings (the feature quantity Fv4) is twice. The cost value deriving section 913 stores the calculated feature quantity Fv4 in the storage section 93.

[0147] According to the evaluation based on the feature quantity Fv4, in the case where the time variation of the discharge pressure appears in steps in the rising period Ta (for example, Figure 16 (B) of FIG. 9), a large score (i.e., a negative evaluation) can be given to the discharge pressure.

[0148] Figure 17 (A) of FIG. 10 is a graph for explaining the feature quantity Fv5. Figure 17 (A) of FIG. 10 is a graph for explaining the evaluation item based on the feature quantity Fv5 to evaluate the time variation of the discharge pressure. Figure 17 (B) of FIG. 10 is a graph showing an example of the time variation of the discharge pressure judged as unsuitable by the evaluation based on the feature quantity Fv5. In Figure 17 In the evaluation item of (A) of FIG. 10, it is evaluated whether or not there is an abnormality in the rising of the discharge pressure.

[0149] Specifically, the cost value deriving section 913 calculates the second-order differential D2 of the time variation of the discharge pressure for the rising period Ta from the time ta to the time tb, and obtains the second-order differential waveform WF5. In addition, the cost value deriving section 913 obtains the number of times that the absolute value of the second-order differential waveform WF5 crosses a prescribed threshold value Th5 in the rising period Ta as the feature quantity Fv5. In Figure 17In the example of (A) of FIG. 9, the absolute values of the second-order differential waveform WF5 cross the threshold value Th5 (for example, 0.0002) at times t51, t52, t53, and t54, and the number of crossings (feature quantity Fv5) is four. The cost value deriving section 913 stores the calculated feature quantity Fv5 in the storage section 93.

[0150] According to the evaluation based on the feature quantity Fv5, in a case where the time variation of the discharge pressure in the rising period Ta appears in steps (for example, as shown in (B) of FIG. 9), a large score (that is, a negative evaluation) can be given to the discharge pressure. Figure 17

[0151] Figure 18 is a graph for explaining an evaluation item for evaluating the time variation of the discharge pressure based on the feature quantity Fv6. In the evaluation item of (A) of FIG. 10, the rising of the discharge pressure is evaluated whether or not it stalls in the latter half. Specifically, the cost value deriving section 913 calculates the second-order differential D2 of the time variation of the discharge pressure in the rising period Ta from time ta to time tb, and obtains a second-order differential waveform WF6. Figure 18

[0152] In addition, the cost value deriving section 913 obtains a time T_1st at which the second-order differential waveform WF6 is greater than a prescribed positive threshold value (Th5) and a time T_2nd at which the second-order differential waveform WF6 is less than a prescribed negative threshold value (-Th5) in the rising period Ta, respectively. Here, the positive threshold value and the negative threshold value have the same absolute value (Th5) and different signs from each other. The absolute value (Th5) of the positive threshold value and the negative threshold value is equal to the absolute value of the threshold value Th5 used in the evaluation of the feature quantity Fv5 described above. In addition, the cost value deriving section 913 obtains a ratio (=T_1st / T_2nd) of these times as the feature quantity Fv6. Furthermore, the cost value deriving section 913 converts the feature quantity Fv6 based on the following equation.

[0153] Fv6 = |1 - Fv6|

[0154] The cost value deriving section 913 stores the converted feature quantity Fv6 in the storage section 93.

[0155] The conveyance speed of the substrate S that is the coating target of the coating liquid does not stall in the latter half of the acceleration period and reaches the target speed. Therefore, it is preferable that the discharge pressure applied to the coating liquid does not stall in the rising period Ta and reaches the target pressure Pt. According to the evaluation based on the feature quantity Fv6, in a case where the discharge pressure stalls in the rising period Ta, a large score (that is, a negative evaluation) can be given to the discharge pressure.

[0156] Figure 19 is a graph for explaining an evaluation item for evaluating the time variation of the discharge pressure based on the feature quantity Fv7. In the evaluation item of (A) of FIG. 11, the rising of the discharge pressure is evaluated whether or not it stalls in the latter half. Specifically, the cost value deriving section 913 calculates the second-order differential D2 of the time variation of the discharge pressure in the rising period Ta from time ta to time tb, and obtains a second-order differential waveform WF7. Figure 19 ​​the time variation of the discharge pressure at the end of the evaluation upstroke. Specifically, during the upstroke Ta, a linear regression analysis is performed on the time variation of the discharge pressure between a lower reference pressure P7_l and an upper reference pressure P7_u that is greater than the lower reference pressure P7_l, and a regression line Lr at the end of the upstroke is calculated. Here, the lower reference pressure P7_l is a pressure obtained by adding 80% of the absolute value of the difference between the initial pressure Pi and the target pressure Pt to the initial pressure Pi, and the upper reference pressure P7_u is a pressure obtained by adding 90% of the absolute value of the difference between the initial pressure Pi and the target pressure Pt to the initial pressure Pi, and the discharge pressure increases from the lower reference pressure P7_l to the upper reference pressure P7_u during a period from time t71 to time t72.

[0157] The regression line Lr at the end of the upstroke increases with time, and time t73 reaches the steady pressure Pm (the average of the discharge pressure during the steady period Tc). Thus, the regression line Lr at the end of the upstroke is set for the interval from time t71 to time t73. Further, the cost value derivation section 913 sets an extension line Lm having a slope of zero from time t73 to time tb that represents the steady pressure Pm. As described above, time tb is the time at which the discharge pressure reaches the target pressure Pt, and corresponds to the end time of the upstroke Ta. That is, the extension line Lm is set to extend from the end time point of the regression line Lr at the end of the upstroke to the end time point of the upstroke Ta. Note that when tb < t73, the extension line Lm is omitted.

[0158] As described above, the approximate waveform WF7 composed of the regression line Lr at the end of the upstroke and the extension line Lm arranged in time series is calculated. Further, the cost value derivation section 913 calculates the value of the difference between the pressure value P_measure representing the pressure waveform and the approximate waveform WF7 in the upstroke end period Ta_e from time t72 at which the discharge pressure is 90% of the target pressure Pt to time tb at which the discharge pressure is 100% of the target pressure Pt, as the characteristic quantity Fv7. Specifically, a weighted reference time width Tw = t73 - t72 is set. Further, the weighted root mean square error sum is calculated based on the following equation.

[0159] Fv7 = (Σ(P_measure - WF7) 2 x W) 1 / 2

[0160] W = 1 in the range of time t ≤ t73 + 2 x Tw.

[0161] W = w in the range of time t > t73 + 2 x Tw.

[0162] w is a weighting coefficient greater than 1, for example, 10

[0163] The cost value derivation section 913 stores the calculated feature quantity Fv7 in the storage section 93. According to the evaluation based on the feature quantity Fv7, in the case where the time variation of the discharge pressure represents a weakly rising trend and a waveform with a radian, a large score (i.e., a negative evaluation) can be given to the discharge pressure.

[0164] Figure 20 is a graph for explaining an evaluation item for evaluating the time variation of the discharge pressure based on the feature quantity Fv8. In the evaluation item of Figure 20 The degree of overshoot occurring when the discharge pressure rises is evaluated. Specifically, the cost value derivation section 913 obtains the sign (positive / negative) of the second-order differential D2 of the discharge pressure at the time t81 at which the discharge pressure reaches the maximum value Pmax. Then, the cost value derivation section 913 calculates the time t82 at which the sign of the second-order differential D2 of the discharge pressure switches twice from the sign at the time t81. Then, the time variation of the discharge pressure during the initial vibration period Tb_s from the time t81 to the time t82 is evaluated.

[0165] Specifically, the minimum value P8min of the time variation of the discharge pressure in the initial vibration period Tb_s is obtained, and the pressure smaller of the stable pressure Pm and the pressure P8min is selected as the target pressure Pg. Then, the feature quantity Fv8 is calculated based on the difference between the maximum pressure Pmax and the target pressure Pg, i.e., the following expression.

[0166] Fv8 = Pmax - Pg

[0167] The cost value derivation section 913 stores the calculated feature quantity Fv8 in the storage section 93. According to the evaluation based on the feature quantity Fv8, in the case where the time variation of the discharge pressure represents a strong rising trend and a large overshoot, a large score (i.e., a negative evaluation) can be given to the discharge pressure.

[0168] Figure 21 is a graph for explaining an evaluation item for evaluating the time variation of the discharge pressure based on the feature quantity Fv9. In the evaluation item of Figure 21 The stability of the time variation of the discharge pressure during the transition period Tb is evaluated. Specifically, the cost value derivation section 913 calculates the root mean square error RMSE(P_measure, Pm) of the stable pressure Pm which is the average of the discharge pressure during the transition period Tb and the discharge pressure during the stable period Tc, as the feature quantity Fv9 based on the following expression.

[0169] Fv9 = RMSE(P_measure, Pm)

[0170] The cost value derivation section 913 stores the calculated feature quantity Fv9 in the storage section 93. According to the evaluation based on the feature quantity Fv9, in a case where the time variation of the discharge pressure indicates a transient during the transition period Tb, a large score (i.e., a negative evaluation) can be given to the discharge pressure.

[0171] Figure 22 is a graph for explaining an evaluation item for evaluating the time variation of the discharge pressure based on the feature quantity FvlO. In the evaluation item shown in Figure 22 In the evaluation item shown, the stability of the time variation of the discharge pressure during the constant pressure period Tbc is evaluated. Specifically, the cost value derivation section 913 calculates the maximum value Pmax and the minimum value P10min of the discharge pressure during the constant pressure period Tbc. In addition, the cost value derivation section 913 calculates the feature quantity FvlO based on the difference between the maximum pressure Pmax and the minimum pressure P10min during the constant pressure period Tbc, i.e., the following expression.

[0172] Fv10 = Pmax - P10min

[0173] The cost value derivation section 913 stores the calculated feature quantity Fv9 in the storage section 93. According to the evaluation based on the feature quantity Fv9, in a case where the time variation of the discharge pressure indicates a transient during the transition period Tb, a large score (i.e., a negative evaluation) can be given to the discharge pressure.

[0174] The cost value derivation section 913 can derive the sum of the feature quantities Fvl to FvlO as the cost value. However, the cost value derivation section 913 can also weight each of the feature quantities Fvl to FvlO. That is, the cost value derivation section 913 can derive the weighted sum of the feature quantities Fvl to FvlO as the cost value.

[0175] Note that the above-described feature quantities Fvl to FvlO are examples. Therefore, other feature quantities can also be used for the calculation of the cost value. In addition, a part of the feature quantities Fvl to FvlO can also be used for the calculation of the cost value.

[0176] Although the present application has been described in detail, the above description is merely exemplary, and the present application is not limited thereto. Numerous modifications can be conceived which are not enumerated, and can be interpreted as modifications which can be conceived within the scope of the present application. The respective configurations described in each of the embodiments and each of the modifications can be appropriately combined or omitted, as long as they do not contradict each other.

[0177] Explanation of Reference Signs

[0178] 1 coating device (substrate processing device)

[0179] 9 control unit

[0180] 71 nozzle

[0181] 81 pump

[0182] 91 arithmetic unit

[0183] 93 storage unit

[0184] 910 ejection control unit

[0185] 911 ejection characteristic measurement unit

[0186] 913 cost value derivation unit

[0187] 915 first optimization unit

[0188] 917 second optimization unit

[0189] 931 program

[0190] M recording medium

[0191] S substrate

Claims

1. A parameter optimization method of optimizing, by a computer, parameters for controlling ejection of a processing liquid from a nozzle in a substrate processing apparatus that supplies a substrate with the processing liquid ejected from the nozzle, wherein the method comprises: a first optimization process in which the computer optimizes a first parameter by global search; and a second optimization process in which the computer optimizes a second parameter by local search, the first parameter includes a parameter corresponding to a rising period in which an ejection speed of the processing liquid from the nozzle is increased to a stable ejection speed, and the second parameter includes a parameter corresponding to a stable ejection period in which the ejection speed is maintained at the stable ejection speed.

2. The parameter optimization method according to claim 1, wherein the second optimization process is executed after the first optimization process.

3. The parameter optimization method according to claim 1, wherein the first optimization process includes a process of optimizing the first parameter by Bayesian optimization.

4. The parameter optimization method according to any one of claims 1 to 3, wherein the parameter is a control amount that controls operation of a pump that feeds the processing liquid to the nozzle.

5. The parameter optimization method according to any one of claims 1 to 3, wherein in the first optimization process, a process of optimizing the first parameter based on a cost value derived from a feature quantity of an ejection characteristic at the time of ejection of the processing liquid from the nozzle is included.

6. The parameter optimization method according to any one of claims 1 to 3, wherein in the second optimization process, a process of optimizing the second parameter based on a ratio of an ejection speed at the start of the stable ejection period to an ejection speed at the end of the stable ejection period is included.

7. A recording medium that is a recording medium on which a program is recorded, the program being used to cause a computer to execute optimization of parameters for controlling ejection of a processing liquid from a nozzle, wherein the program causes the computer to execute: a first optimization process of optimizing a first parameter by global search; and a second optimization process of optimizing a second parameter by local search, the first parameter includes a parameter corresponding to a rising period in which an ejection speed of the processing liquid from the nozzle is increased to a stable ejection speed, and the second parameter includes a parameter corresponding to a stable ejection period in which the ejection speed is maintained at the stable ejection speed.

8. A substrate processing apparatus that supplies a substrate with a processing liquid ejected from a nozzle, wherein the apparatus comprises: an ejection control section that controls ejection of the processing liquid from the nozzle based on a plurality of parameters including a first parameter and a second parameter; an ejection characteristic measurement section that measures an ejection characteristic at the time of ejection of the processing liquid from the nozzle; a first optimization section that optimizes the first parameter by global search based on the ejection characteristic; and a second optimization section that optimizes the second parameter by local search based on the ejection characteristic, the first parameter includes a parameter corresponding to a rising period in which an ejection speed of the processing liquid from the nozzle is increased to a stable ejection speed, and the second parameter includes a parameter corresponding to a stable ejection period in which the ejection speed is maintained at the stable ejection speed. ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​

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