Cost function data generation method, cost function data generation program, and cost function data generation device

Abstract

To provide a technique capable of properly designing a cost function for optimizing control parameters of a processing device.SOLUTION: A cost function data generation method includes a discharge pressure data preparation step S1, a ranking step S2, and a weight determination step S3. In the discharge pressure data preparation step S1, a plurality of pieces of discharge pressure data 99 are prepared which are obtained by measuring discharge pressure when a coating device 1 is controlled with control parameters of a plurality of patterns. In the ranking step S2, the plurality of pieces of discharge pressure data 99 are ranked. In the weight determination step S3, a weight of a cost function which outputs a cost value obtained by integrating weights of index values V1 to V10 of a plurality of evaluation items extracted from the discharge pressure data 99 is determined.SELECTED DRAWING: Figure 18

Description

[Technical Field]

[0001] The subject matter disclosed herein relates to techniques for generating cost function data. [Background technology]

[0002] Industrial machinery control devices have a variety of control parameters, which are often adjusted before shipment. This parameter adjustment work is generally performed by engineers. However, there is a strong demand for automation of the adjustment work to reduce costs by reducing labor and to suppress variability. For this reason, several methods for efficiently optimizing parameters have been proposed.

[0003] For example, Patent Document 1 proposes optimizing the state parameters and external environmental conditions related to the design life of a spacecraft using a Bayesian optimization method. Specifically, a heat conduction model that predicts temperature from various parameters is used to calculate the absolute difference between the predicted temperature and the actually measured temperature, and various parameters that minimize this absolute difference are found using Bayesian optimization.

[0004] Furthermore, Patent Document 2 proposes that a pulse waveform used in pulse arc welding that further reduces the amount of spatter is determined by a Bayesian optimization method. [Prior art documents] [Patent documents]

[0005] [Patent Document 1] Japanese Patent Application Publication No. 2019-215750 [Patent Document 2] Japanese Patent Publication No. 2020-157347 Summary of the Invention [Problem to be solved by the invention]

[0006] In both Patent Documents 1 and 2, a clear single evaluation value such as temperature or sputter amount is used as a cost function (objective function), and optimization is performed to minimize the cost function. However, when a single quantitative evaluation value (index) for output does not exist, or when its existence is unknown, it is possible to design an appropriate cost function by combining multiple indexes.

[0007] For example, in a coater developer used in flat panel display (FPD) manufacturing, a pump drives a processing solution to be ejected from a slit nozzle and applied to a substrate as it is transported. To achieve ideal coating, the control parameters of the pump drive must be adjusted. To adjust the control parameters, a typical procedure involves actually ejecting the processing solution and visually evaluating the pressure waveform observed by a pressure sensor installed near the nozzle. The quality of the pressure waveform is determined based on multiple evaluation criteria, such as the time it takes for the pressure to reach a specified value, the pressure rise rate, and the presence or absence of overshoot. However, proper evaluation of the pressure waveform requires skilled experience and knowledge. Therefore, a technology that can accurately evaluate the pressure waveform is needed, even for those with limited experience and knowledge.

[0008] Furthermore, in order to properly evaluate the pressure waveform, it is conceivable to design a cost function that integrates multiple indices and optimize the pump drive control parameters based on the value output by the cost function. However, properly designing a cost function that integrates multiple indices requires skilled experience and knowledge. Furthermore, if the characteristics of the waveform output change due to a change in the device configuration, it is often necessary to redesign the cost function. Redesigning a cost function that integrates multiple indices requires considering the balance between the indices, making it difficult to redesign the cost function.

[0009] An object of the present invention is to provide a technique that can appropriately design a cost function for optimizing control parameters of a processing device. [Means for solving the problem]

[0010] In order to solve the above problem, the first aspect is Implemented using a computer A cost function data generation method, comprising: a) The computer a step of preparing a plurality of measurement data obtained by measuring the operating state of the processing device when the processing device is controlled using a plurality of patterns of control parameters; and b) The computer a step of assigning a rank to the plurality of measurement data; and c) The computer and determining weights in a cost function that outputs a cost value obtained by weighting and integrating index values ​​of a plurality of items extracted from the measurement data, wherein step c) determines a weight in a cost function that outputs a cost value obtained by weighting and integrating index values ​​of a plurality of items extracted from the measurement data, so that the correlation between the cost value output by the cost function for each of the measurement data and the rank assigned to each of the measurement data in step b) is high. The computer Adjusting the weights in the cost function.

[0011] A second aspect is the cost function data generation method of the first aspect, wherein the step c) comprises the steps of: c-1) The computer The method includes displaying correlation information indicating the correlation between the rank and the cost value based on the adjusted weight.

[0012] A third aspect is the cost function data generation method of the second aspect, wherein the correlation information includes a distribution indicating the relationship between the rank and the cost value based on the adjusted weight for each measurement data.

[0013] A fourth aspect is the cost function data generation method according to the third aspect, wherein the correlation information includes a regression line indicating the relationship between the rank and the cost value.

[0014] A fifth aspect is the cost function data generation method according to any one of the second to fourth aspects, wherein the correlation information includes a correlation coefficient indicating a relationship between the rank and the cost value.

[0015] A sixth aspect is the cost function data generation method according to any one of the second to fifth aspects, wherein the step c) comprises the steps of: c-2) The computerc-3) displaying an indicator on a display unit for adjusting the weight for the index value for each of the plurality of items; The computer the indicator displayed on the display unit of operation Based on and adjusting the weights, wherein step c-1) The computer The method includes a step of displaying the correlation information based on the weight adjusted in step c-3).

[0016] A seventh aspect is the cost function data generation method of the first aspect, wherein the cost function includes a neural network that receives index values ​​of the plurality of items as input and outputs the cost value, and the step c) The computer and performing machine learning using the neural network.

[0017] An eighth aspect is the cost function data generation method of the seventh aspect, wherein the neural network receives the index values ​​for two or more of the measurement data as input and outputs the cost values ​​for the two or more measurement data, and the step c) comprises: The computer The method includes a step of performing machine learning using, as an objective function, a correlation coefficient between the cost value for the two or more pieces of measurement data and the rank assigned to the two or more pieces of measurement data.

[0018] A ninth aspect is a cost function data generation method according to any one of the first to eighth aspects, wherein the processing device is a device that applies an ejection pressure to a processing liquid and ejects the processing liquid from a nozzle, and the measurement data is data indicating the ejection pressure.

[0019] A tenth aspect is the cost function data generation method according to any one of the first to ninth aspects, The computer The method includes a step of assigning a rank to the plurality of measurement data on a scale of 10 or less.

[0020] An eleventh aspect is a cost function data generation program that causes a computer to execute the cost function data generation method according to any one of the first to tenth aspects.

[0021] A twelfth aspect is a cost function data generating device comprising: a memory unit that stores a plurality of measurement data that measure the operating state of the processing device when the processing device is controlled with a plurality of patterns of control parameters; a rank assigning unit that assigns ranks to the plurality of measurement data based on a predetermined operation input; and a weight determination unit that determines weights in a cost function that outputs a cost value obtained by weighting and integrating index values ​​of a plurality of items extracted from the measurement data, wherein the weight determination unit adjusts the weights in the cost function so that there is a high correlation between the cost value output by the cost function for each of the measurement data and the rank assigned to each of the measurement data by the rank assigning unit.

[0022] A thirteenth aspect is the cost function data generating device of the twelfth aspect, further comprising a display unit that displays correlation information indicating the correlation between the rank and the cost value based on the adjusted weight.

[0023] A 14th aspect is a cost function data generation device according to the 12th or 13th aspect, wherein the cost function is represented by a neural network that takes index values ​​of the plurality of items as input and outputs the cost values, and the weight determination unit includes a learning unit that performs machine learning using the neural network. [Effects of the Invention]

[0024] According to the cost function data generation method of the first aspect, the weights of the cost function are determined so that the cost values ​​output by the cost function for the measurement data correlate with the pre-assigned ranks. This makes it possible to appropriately design a cost function that weights and integrates the index values ​​of multiple items of the measurement data even if one has little experience or knowledge in evaluating the measurement data.

[0025] According to the cost function data generating method of the second aspect, the validity of the adjusted weights can be evaluated based on the correlation information.

[0026] According to the cost function data generating method of the third aspect, the validity of the adjusted weights can be evaluated based on the distribution indicating the relationship between the ranks and the cost values.

[0027] According to the cost function data generating method of the fourth aspect, the validity of the adjusted weight can be evaluated based on the regression line that indicates the relationship between the rank and the cost value.

[0028] According to the cost function data generating method of the fifth aspect, the cost function can be appropriately generated based on the correlation coefficient.

[0029] According to the cost function data generation method of the sixth aspect, the weights can be easily adjusted by operating the indicators. Furthermore, by displaying correlation information based on the adjusted weights, the adjusted weights can be evaluated based on the correlation information.

[0030] According to the cost function data generation method of the seventh aspect, machine learning using a neural network is performed, thereby making it possible to appropriately generate data of a cost function expressed by a neural network.

[0031] According to the cost function data generating method of the tenth aspect, the number of rank stages is set to 10 or less, so that the measurement data can be easily ranked. [Brief explanation of the drawings]

[0032] [Figure 1] 1 is a diagram schematically illustrating the overall configuration of a coating apparatus according to a first embodiment. [Figure 2] FIG. 2 is a diagram showing the configuration of a coating liquid supply mechanism. [Figure 3] FIG. 2 is a block diagram showing an example of the configuration of a control unit. [Figure 4] 10 is a flowchart illustrating an example of a discharge pressure evaluation method executed based on a discharge pressure evaluation program. [Figure 5] 10A and 10B are diagrams for explaining periods used in evaluating the discharge pressure. [Figure 6]10A and 10B are diagrams illustrating an example of a calculation performed by a pressure evaluation unit in response to a change in discharge pressure over time. [Figure 7] 10 is a diagram for explaining evaluation items for evaluating the change over time in the discharge pressure based on the feature amount Fv1. FIG. [Figure 8] 10 is a diagram for explaining evaluation items for evaluating the change over time in the discharge pressure based on the feature amount Fv2. FIG. [Figure 9] FIG. 10 is a diagram for explaining evaluation items for evaluating the change over time in the discharge pressure based on the feature amount Fv3. [Figure 10] FIG. 10 is a diagram for explaining a feature amount Fv4. [Figure 11] FIG. 10 is a diagram for explaining a feature amount Fv5. [Figure 12] FIG. 10 is a diagram for explaining evaluation items for evaluating the change over time in the discharge pressure based on the feature amount Fv6. [Figure 13] FIG. 10 is a diagram for explaining evaluation items for evaluating the change over time in the discharge pressure based on the feature amount Fv7. [Figure 14] FIG. 10 is a diagram for explaining evaluation items for evaluating the change over time in the discharge pressure based on the feature amount Fv8. [Figure 15] FIG. 10 is a diagram for explaining an evaluation item for evaluating the change over time in the discharge pressure based on the feature amount Fv9. [Figure 16] FIG. 10 is a diagram for explaining an evaluation item for evaluating the change over time in the discharge pressure based on the feature amount Fv10. [Figure 17] FIG. 10 is a diagram conceptually illustrating a procedure for generating cost function data. [Figure 18] FIG. 10 is a diagram showing a flow of a procedure for generating cost function data. [Figure 19] FIG. 19 is a diagram showing the flow of the weight determination process shown in FIG. 18. [Figure 20] FIG. 10 is a diagram showing an example of a weight adjustment window AW1. [Figure 21] FIG. 11 is a diagram illustrating a cost function data generator according to the second embodiment. [Figure 22] FIG. 1 illustrates a neural network representing a cost function. DETAILED DESCRIPTION OF THE INVENTION

[0033] Hereinafter, an embodiment of the present invention will be described with reference to the accompanying drawings. Note that the components described in the embodiment are merely examples and are not intended to limit the scope of the present invention. In the drawings, the dimensions and numbers of each part may be exaggerated or simplified as necessary to facilitate understanding.

[0034] 1. First embodiment FIG. 1 is a diagram schematically illustrating the overall configuration of a coating apparatus 1 according to a first embodiment. The coating apparatus 1 is a substrate processing apparatus that applies a coating liquid to the upper surface Sf of a substrate S. The substrate S is, for example, a glass substrate for a liquid crystal display device. The substrate S may also 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 or optical disk, a glass substrate for an organic electroluminescence (EL) display, a glass or silicon substrate for a solar cell, or various other substrates for electronic devices, such as flexible substrates and printed circuit boards. The coating apparatus 1 is, for example, a slit coater. An XYZ coordinate system is defined in the drawings to explain the relative positions of the elements of the coating apparatus 1. The transport direction of the substrate S is the "X direction." The direction in which the substrate S advances in the X direction (toward downstream in the transport direction) is the +X direction, and the opposite direction (toward upstream in the transport direction) is the -X direction. The direction perpendicular to the X direction is the Y direction, and the direction perpendicular to both the X and Y directions is the Z direction. In the following description, the Z direction is the vertical direction, and the X and Y directions are the horizontal directions. In the Z direction, the +Z direction is the upward direction, and the −Z direction is the downward direction.

[0035] The coating apparatus 1 includes, in order in the +X direction, an input conveyor 100, an input transfer unit 2, a floating stage unit 3, an output transfer unit 4, and an output conveyor 110. The input conveyor 100, the input transfer unit 2, the floating stage unit 3, the output transfer unit 4, and the output conveyor 110 form a transport path along which the substrate S passes. The coating apparatus 1 also includes a substrate transport unit 5, a coating mechanism 7, a coating liquid supply mechanism 8, and a control unit 9.

[0036] 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 rotation drive mechanism 102. The rotation drive mechanism 102 rotates each roller of the roller conveyor 101. Due to the rotation of each roller of the roller conveyor 101, the substrate S is transported downstream (+X direction) in a horizontal position. The "horizontal position" refers to a state in which the main surface (the surface with the largest area) of the substrate S is parallel to the horizontal plane (XY plane).

[0037] The input transfer section 2 is equipped with 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 and raises and lowers the roller conveyor 21. The rotation of the roller conveyor 21 transports the substrate S downstream (+X direction) in a horizontal position. The elevation of the roller conveyor 21 also changes the position of the substrate S in the Z direction. The substrate S is transferred from the input conveyor 100 to the floating stage section 3 via the input transfer section 2.

[0038] As shown in FIG. 1, the floating stage unit 3 is substantially flat. The floating stage unit 3 is divided into three sections along the X direction. The floating stage unit 3 includes, in order along the +X direction, an entrance floating stage 31, a coating stage 32, and an exit floating stage 33. The upper surfaces of the entrance floating stage 31, the coating stage 32, and the exit floating stage 33 are on the same plane. The floating stage unit 3 further includes a lift pin drive mechanism 34, a floating control mechanism 35, and an elevation drive mechanism 36. The lift pin drive mechanism 34 raises and lowers several lift pins arranged on the entrance floating stage 31. The floating control mechanism 35 supplies compressed air to the entrance floating stage 31, the coating stage 32, and the exit floating stage 33 to float the substrate S. The elevation drive mechanism 36 raises and lowers the exit floating stage 33.

[0039] A large number of nozzle holes for ejecting compressed air supplied from the levitation control mechanism 35 are arranged in a matrix on the upper surface of the entrance levitation stage 31 and the upper surface of the exit levitation stage 33. When compressed air is ejected from each nozzle hole, the substrate S is levitated upward relative to the levitation stage part 3. Then, the lower surface Sb of the substrate S is supported in a horizontal position while being spaced apart from the upper surface of the levitation stage part 3. When the substrate S is in a levitated state, the distance (levitation amount) between the lower surface Sb of the substrate S and the upper surface of the levitation stage part 3 is, for example, 10 μm or more and 500 μm or less.

[0040] On the upper surface of the coating stage 32, jet holes for ejecting compressed air supplied from the levitation control mechanism 35 and suction holes for sucking gas are alternately arranged in the X and Y directions. The levitation control mechanism 35 controls the amount of compressed air ejected from the jet holes and the amount of air sucked through the suction holes. This precisely controls the amount of levitation of the substrate S relative to the coating stage 32 so that the position in the Z direction of the upper surface Sf of the substrate S passing above the coating stage 32 becomes a specified value. The amount of levitation of the substrate S relative to the coating stage 32 is calculated by the control unit 9 based on the detection results of a sensor 61 or a sensor 62, which will be described later. Preferably, the amount of levitation of the substrate S relative to the coating stage 32 can be adjusted with high precision by airflow control.

[0041] The substrate S carried into the floating stage unit 3 is imparted with a propulsive force in the +X direction by the roller conveyor 21, and is transported onto the entrance floating stage 31. The entrance floating stage 31, the coating stage 32, and the exit floating stage 33 support the substrate S in a floating state. For example, the configuration described in Japanese Patent No. 5346643 may be adopted as the floating stage unit 3.

[0042] The substrate transport unit 5 is disposed below the floating stage unit 3. The substrate transport unit 5 includes a chuck mechanism 51 and a suction / travel control mechanism 52. The chuck mechanism 51 includes a suction pad (not shown) provided on a suction member. The chuck mechanism 51 supports the substrate S from below by bringing the suction pad into contact with the peripheral edge of the lower surface Sb of the substrate S. The suction / travel control mechanism 52 applies negative pressure to the suction pad, thereby suctioning the substrate S to the suction pad. The suction / travel control mechanism 52 also causes the substrate transport unit 5 to travel back and forth in the X direction.

[0043] The chuck mechanism 51 holds the substrate S in a state where the lower surface Sb of the substrate S is positioned higher than the upper surface of the floating stage part 3. With the peripheral edge of the substrate S held by the chuck mechanism 51, the buoyancy applied by the floating stage part 3 keeps the substrate S in a horizontal position.

[0044] 1, the coating device 1 is equipped with a sensor 61 for measuring plate thickness. The sensor 61 is disposed near the roller conveyor 21. The sensor 61 detects the position in the Z direction of the upper surface Sf of the substrate S held by the chuck mechanism 51. Furthermore, a chuck (not shown) that is not holding the substrate S is positioned directly below the sensor 61, so that the sensor 61 can detect the position in the vertical direction Z of the suction surface, which is the upper surface of the suction member.

[0045] The chuck mechanism 51 moves in the +X direction while holding the substrate S that has been carried into the floating stage section 3. As a result, the substrate S is transported from above the entrance floating stage 31, via above the coating stage 32, to above the exit floating stage 33. Then, the substrate S is moved from the exit floating stage 33 to the output transfer section 4.

[0046] The output transfer unit 4 moves the substrate S from a position above the exit floating stage 33 to the output conveyor 110. The output transfer unit 4 includes a roller conveyor 41 and a rotation / lifting drive mechanism 42. The rotation / lifting drive mechanism 42 drives the roller conveyor 41 to rotate and also raises and lowers the roller conveyor 41 in the Z direction. As each roller of the roller conveyor 41 rotates, the substrate S moves in the +X direction. Furthermore, as the roller conveyor 41 rises and falls, the substrate S is displaced in the Z direction.

[0047] The output conveyor 110 includes a roller conveyor 111 and a rotation drive mechanism 112. The output conveyor 110 transports the substrate S in the +X direction by the rotation of each roller of the roller conveyor 111, and delivers the substrate S to the outside of the coating apparatus 1. 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 may be incorporated into a device separate from the coating apparatus 1.

[0048] The coating mechanism 7 coats the upper surface Sf of the substrate S with a coating liquid. The coating mechanism 7 is disposed above the transport path of the substrate S. The coating mechanism 7 has a nozzle 71. The nozzle 71 is a slit nozzle having a slit-shaped discharge outlet on its lower surface. The nozzle 71 is connected to a positioning mechanism (not shown). The positioning mechanism moves the nozzle 71 between a coating position above the coating stage 32 (the position indicated by the solid line in FIG. 1) and a maintenance position, which will be described later. The coating liquid supply mechanism 8 is connected to the nozzle 71. The coating liquid supply mechanism 8 supplies the coating liquid to the nozzle 71, causing the coating liquid to be discharged from a discharge outlet disposed on the lower surface of the nozzle 71.

[0049] FIG. 2 is a diagram showing the configuration of the coating liquid supply mechanism 8. The coating liquid supply mechanism 8 includes 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 drive unit 87. The pump 81 is a supply source for supplying the coating liquid to the nozzle 71 and supplies the coating liquid by changing its volume. For example, the pump 81 may be a bellows-type pump described in Japanese Patent Laid-Open No. 10-61558. As shown in FIG. 2, the pump 81 has a flexible tube 811 that is elastically expandable and contractible in the radial direction. One end of the flexible tube 811 is connected to the coating liquid replenishment unit 83 via a pipe 82. The other end of the flexible tube 811 is connected to the nozzle 71 via a pipe 84.

[0050] As shown in Fig. 2, the pump 81 has a bellows 812 that is elastically deformable in the axial direction. The bellows 812 has a small bellows section 813, a large bellows section 814, a pump chamber 815, and an operating disk section 816. The pump chamber 815 is disposed between the flexible tube 811 and the bellows 812. An incompressible medium is sealed in the pump chamber 815. The operating disk section 816 is connected to the drive section 87.

[0051] The coating liquid replenishment unit 83 has a storage tank 831 that 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 opens and closes in response to a command 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. 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.

[0052] 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 opens and closes in response to commands from the control unit 9. The on-off valve 85 opens and closes to switch between sending and stopping the coating liquid to the nozzle 71. A pressure gauge 86 is disposed in the pipe 84. The pressure gauge 86 detects the pressure (discharge pressure) of the coating liquid sent to the nozzle 71, and outputs a signal indicating the detected pressure value to the control unit 9.

[0053] In response to a command from the control unit 9, the drive unit 87 displaces the operating disc portion 816 in the axial direction in a predetermined movement pattern (a pattern that indicates a change in the speed of the operating disc portion 816 over time). The displacement of the operating disc portion 816 changes the internal volume of the bellows 812. This causes the flexible tube 13 to expand and contract radially, performing a pumping operation, and the coating liquid replenished from the coating liquid replenishment unit 83 is fed toward the nozzle 71. In this way, the movement pattern of the operating disc portion 816 is closely related to the discharge characteristics (change in discharge pressure over time) of the coating liquid discharged from the nozzle 71, and therefore predetermined discharge characteristics can be obtained according to the movement pattern.

[0054] As shown in FIG. 2, a sensor 62 is disposed on the nozzle 71 to which the coating liquid is supplied 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 floating substrate S and the upper surface of the coating stage 32. Then, based on the measured separation distance, the control unit 9 adjusts the coating position of the nozzle 71 using the positioning mechanism. Note that an optical sensor or an ultrasonic sensor can be used as the sensor 62.

[0055] The coating mechanism 7 includes a nozzle cleaning standby unit 72. The nozzle cleaning standby unit 72 performs predetermined maintenance on the nozzle 71 positioned at the maintenance position. The nozzle cleaning standby unit 72 includes a roller 721, a cleaning section 722, and a roller vat 723. The nozzle cleaning standby unit 72 cleans the nozzle 71 and forms a liquid pool, thereby preparing the discharge port of the nozzle 71 for a coating process. Furthermore, in the coating device 1, in order to evaluate the discharge pressure applied to the coating liquid, a simulated discharge is performed in which the coating liquid is discharged from the nozzle 71 while the nozzle 71 is positioned at the maintenance position.

[0056] 3 is a block diagram showing an example of the configuration 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 and includes a calculation unit 91, a storage unit 93, and a user interface 95. The calculation unit 91 is a processor configured with a CPU (Central Processing Unit) or a GPU (Graphics Processing Unit). The storage unit 93 is configured with a transient storage device such as a RAM (Random Access Memory) and a non-transient auxiliary storage device such as an HDD (Hard Disk Drive) and an SDD (Solid State Drive).

[0057] The user interface 95 has a display that displays information to the user and an input device that accepts input operations by the user. The control unit 9 can be, for example, a desktop, laptop, or tablet computer.

[0058] The storage unit 93 stores a discharge pressure evaluation program 97 and a cost function data generation program 98. The discharge pressure evaluation program 97 and the cost function data generation program 98 are provided by, for example, a recording medium M. The recording medium M records the discharge pressure evaluation program 97 or the cost function data generation program 98 so as to be readable by the control unit 9, which is a computer. 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.

[0059] The calculation unit 91 executes the discharge pressure evaluation program 97 to function as a measurement execution unit 911 that measures the discharge pressure and a pressure evaluation unit 913 that evaluates the measured discharge pressure using a cost function. In addition, the calculation unit 91 executes the cost function data generation program 98 to function as a cost function data generation unit 915.

[0060] 4 is a flowchart showing an example of a discharge pressure evaluation method executed based on the discharge pressure evaluation program 97. In the discharge pressure measurement step S101, the measurement execution unit 911 moves the actuation disk unit 816 based on a movement pattern defined in the discharge pressure evaluation program 97, thereby discharging the discharge liquid from the nozzle 71 (simulated discharge). As a result, the actuation disk unit 816 accelerates from zero speed to a predetermined target speed in a global sense, moves at a constant speed at the target speed for a predetermined period, and then decelerates from the target speed to zero speed. Note that, as described in Patent Document 2, the speed (parameter) of the actuation disk unit 816 is adjusted to set the movement pattern during a local period from when the speed of the actuation disk unit 816 reaches its maximum speed until it stabilizes at the target speed.

[0061] In this example, the discharge pressure evaluation program 97 defines the movement pattern of the operating disk portion 816 so that the discharge pressure changes in the following procedure. The discharge pressure increases from the initial pressure Pi to a target pressure Pt that is greater than the initial pressure Pi. The discharge pressure stabilizes at the target pressure Pt. The discharge pressure decreases from the target pressure Pt to the initial pressure Pi.

[0062] In the discharge pressure measurement step S101, the measurement execution unit 911 periodically acquires measured values ​​of the discharge pressure by the pressure gauge 86 at a predetermined sampling period, in parallel with discharging the coating liquid from the nozzle 71 in accordance with the movement of the operating disk unit 816. The measurement execution unit 911 measures the discharge pressure applied to the coating liquid during the discharge period Tt (see FIG. 5) in which the coating liquid is discharged from the nozzle 71, and stores the acquired discharge pressure in the storage unit 93 as discharge pressure data 99. The discharge pressure data 99 is data that indicates a time and a value of the discharge pressure measured at that time in association with each other.

[0063] In the measurement result evaluation step S102, the pressure evaluation unit 913 evaluates the change over time of the discharge pressure indicated by the discharge pressure data 99 using a cost function. The cost function has an index value calculation function as an internal function. The index value calculation function calculates an index value Vi (feature amount) for each predetermined evaluation item from the change over time of the discharge pressure indicated by the discharge pressure data 99. The cost function also weights and integrates (sums up) the calculated index values ​​Vi. The cost function is expressed by the following equation, where x is the discharge pressure data 99 and Vi is the index value calculation function. y=Σw(i)×Vi(x) Next, the index values ​​calculated by the index value calculation function will be described in detail for each evaluation item.

[0064] Fig. 5 is a diagram for explaining each period used in evaluating the discharge pressure. The graph shown in Fig. 5 shows the change in discharge pressure over time, with the horizontal axis representing time and the vertical axis representing discharge pressure. Note that in each graph shown in Fig. 6 and subsequent figures, the horizontal axis also represents time and the vertical axis represents discharge pressure.

[0065] 5, in the discharge pressure measurement step S101, the measurement execution unit 911 acquires discharge pressure data 99 from before the nozzle 71 starts discharging the coating liquid until after the nozzle 71 has finished discharging the coating liquid (i.e., before and after the discharge period Tt). The discharge pressure at time ta when the nozzle 71 starts discharging the coating liquid and the discharge pressure at time te when the nozzle 71 finishes discharging the coating liquid are the initial pressure Pi. However, the pressures at the start and end of discharge do not always match the initial pressure Pi.

[0066] 5, the discharge period Tt is divided into a rise period Ta, a transition period Tb, a steady period Tc, and a fall period Td. The rise period Ta is the period from time ta when the coating liquid supply mechanism 8 starts discharging the coating liquid from the nozzle 71 (i.e., time ta when the coating liquid supply mechanism 8 starts moving the operating disk portion 816) to time tb when the discharge pressure reaches the target pressure Pt. In other words, when the discharge of the coating liquid from the nozzle 71 starts at time ta, the discharge pressure increases from the initial pressure Pi to the target pressure Pt between time ta and time tb.

[0067] The transition period Tb is the period from time tb to time tc, when a predetermined vibration damping period has elapsed. This vibration damping period is the period required for the time change in the discharge pressure to stabilize, and is set in advance, for example, by a user through an input operation on the user interface 95 and stored in the storage unit 93.

[0068] The steady period Tc is the period from time tc to time td when the coating solution supply mechanism 8 starts to reduce the discharge pressure (i.e., time td when the coating solution supply mechanism 8 starts to decelerate the operating disc portion 816 from the target speed). In other words, the coating solution supply mechanism 8 moves the operating disc portion 816 at a constant speed from time tc to time td, and starts to decelerate the operating disc portion 816 at time td. Note that during the steady period Tc, the discharge pressure is basically stable at the target pressure Pt. However, even during the steady period Tc, the change in the discharge pressure over time includes minute vibrations. For this reason, during the steady period Tc, the discharge pressure may become larger or smaller than the target pressure Pt.

[0069] The transition period Tb and the steady period Tc constitute a constant pressure period Tbc, which is the period from time tb to time td.

[0070] The fall period Td is the period from time td to time te when the coating liquid supply mechanism 8 finishes discharging the coating liquid from the nozzle 71 (i.e., time te when the coating liquid supply mechanism 8 stops the operating disk portion 816). In other words, the discharge pressure decreases to the initial pressure Pi between time td and time te, and at time te, the discharge of the coating liquid from the nozzle 71 stops.

[0071] 6 is a diagram schematically illustrating an example of a calculation performed by the pressure evaluation unit 913 on the time change in the discharge pressure. As shown in FIG. 6, the pressure evaluation unit 913 calculates a first derivative D1 of the time change in the discharge pressure by differentiating the time change in the discharge pressure. Furthermore, the pressure evaluation unit 913 calculates a second derivative D2 of the time change in the discharge pressure by differentiating the first derivative D1 of the time change in the discharge pressure by time. The pressure evaluation unit 913 also calculates a mean absolute error (MAE) and a root mean square error (RMSE) based on the following equations. MAE(α, β)=(1 / n)·(Σ|α-β|) RMSE(α, β)=((1 / n)·(Σ(α-β) 2 )) 1 / 2 n is the number of data.

[0072] Fig. 7 is a diagram illustrating an evaluation item for evaluating the time change of the discharge pressure based on the feature value Fv1. In the evaluation item shown in Fig. 7, the time change of the discharge pressure indicated by the discharge pressure data 99 is evaluated based on the error (ideal trapezoid absolute error) between a trapezoidal waveform having an amplitude corresponding to the difference between the average value of the discharge pressure during the steady period Tc (i.e., the steady pressure Pm) and the initial pressure Pi, and the discharge pressure data 99.

[0073] Specifically, a linear regression analysis is performed on the time change in the discharge pressure between a predetermined lower reference pressure and a predetermined upper reference pressure that is greater than the lower reference pressure during the rise period Ta, and a rise regression line Lr_R is calculated. This rise regression line Lr_R linearly increases from the initial pressure Pi to the steady-state pressure Pm between time t11 and time t12.

[0074] Similarly, a linear regression analysis is performed on the time change in the discharge pressure between the upper and lower reference pressures during the falling period Td to calculate a falling regression line Lr_F, which linearly decreases from the steady pressure Pm to the initial pressure Pi between time t13 and time t14.

[0075] 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, for example, by a user through an input operation on the user interface 95 and stored in the storage unit 93. For example, the lower reference pressure may be a pressure obtained by adding, to the initial pressure Pi, a pressure that is 20% of the absolute value of the difference between the initial pressure Pi and the target pressure Pt. The upper reference pressure may be a pressure obtained by adding, to the initial pressure Pi, a pressure that is 80% of the absolute value of the difference between the initial pressure Pi and the target pressure Pt.

[0076] Also, for the period from time ta to time t11, an initial approximation straight line Lr_s is set. This initial approximation straight line Lr_s is a straight line with a slope of zero indicating the initial pressure Pi. That is, the initial approximation straight line Lr_s is a straight line connecting from the start point of the discharge of the coating liquid from the nozzle 71 (time ta) to the start point of the rising regression straight line Lr_R. Depending on the state (slope) of the regression straight line, time t11 may be earlier than time ta, and time t12 may be later than time tb. Thus, when t11 < ta, the initial approximation straight line Lr_s is omitted.

[0077] Also, for the period from time t14 to time te, an end approximation straight line Lr_e is set. This end approximation straight line Lr_e is a straight line with a slope of zero indicating the initial pressure Pi. That is, the end approximation straight line Lr_e is a straight line connecting from the end point of the falling regression straight line Lr_F to the end point of the discharge of the coating liquid from the nozzle 71 (time te). When te < t14, the end approximation straight line Lr_e is omitted.

[0078] Furthermore, for the period from time t12 to time t13, a steady straight line Lr_m is set. This steady straight line Lr_m is a straight line with a slope of zero indicating the steady pressure Pm. That is, the steady straight line Lr_m is a straight line indicating the steady pressure Pm that connects the end point (time t12) of the rising regression straight line Lr_R and the start point (time t13) of the falling regression straight line Lr_F.

[0079] As described above, the pressure evaluation unit 913 calculates an approximate waveform WF1 composed of the initial approximation straight line Lr_s, the rising regression straight line Lr_R, the steady straight line Lr_m, the falling regression straight line Lr_F, and the end approximation straight line Lr_e arranged in time series. Then, the pressure evaluation unit 913 calculates the mean absolute error MAE (ideal trapezoid absolute error) between the discharge pressure data 99 and the approximate waveform WF1 over the entire discharge period Tt from time ta to time te as the feature quantity Fv1. The pressure evaluation unit 913 stores the calculated feature quantity Fv1 in the storage unit 93 as the index value V1.

[0080] According to the evaluation based on the feature Fv1 in Figure 7, if the change in the discharge pressure over time throughout the entire discharge period Tt deviates significantly from the ideal shape (i.e., a trapezoidal shape), a large score (i.e., a negative evaluation) can be given to this discharge pressure.

[0081] FIG. 8 is a diagram illustrating an evaluation item for evaluating the time change of the discharge pressure based on the feature value Fv2. The evaluation item in FIG. 8 evaluates the smoothness of the rise of the discharge pressure. Specifically, during the rise period Ta, a curve regression analysis is performed on the time change of the discharge pressure between the lower reference pressure P2_l and the upper reference pressure P2_u, which is greater than the lower reference pressure P2_l, to calculate the rise regression curve Nr. This curve regression analysis is performed using a quadratic curve.

[0082] The lower reference pressure P2_l is set to the initial pressure Pi. 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, for example, by a user through an input operation on the user interface 95 and stored in the storage unit 93. The upper reference pressure P2_u may be set to 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. This rising regression curve Nr increases from the lower reference pressure P2_l (initial pressure Pi) to the upper reference pressure P2_u between time t21 and time t22. Note that time t21 coincides with time ta, and time t22 is after time ta and before time tb.

[0083] The pressure evaluation unit 913 calculates a waveform WF2 configured from the rising regression curve Nr. Then, the pressure evaluation unit 913 calculates the root mean square error RMSE between the discharge pressure data 99 and the waveform WF2 as a feature value Fv2 during an initial rising period Ta_s from time t21 to time t22. The pressure evaluation unit 913 then stores the calculated feature value Fv2 in the storage unit 93 as an index value V2.

[0084] 8, if an abnormality occurs in the discharge pressure immediately after the start of discharge due to the influence of the state before the start of discharge of the coating liquid from the nozzle 71, a large score (i.e., a negative evaluation) can be given to this discharge pressure. Note that the curve that can be used in the curve regression analysis is not limited to a quadratic curve, and other curves such as an exponential function may also be used.

[0085] 9 is a diagram illustrating an evaluation item for evaluating a change in discharge pressure over time based on a feature value Fv3. The evaluation item in FIG. 9 evaluates whether the rise period Ta falls within a certain period. Specifically, the pressure evaluation unit 913 calculates, as the feature value Fv3, the length of the rise period Ta (=tb-ta), which is the period from time ta to time tb required for the discharge pressure to increase from the initial pressure Pi to the target pressure Pt. The pressure evaluation unit 913 then stores the calculated feature value Fv3 in the storage unit 93 as an index value V3.

[0086] According to the evaluation based on the feature amount Fv3 in FIG. 9, a large score (that is, a negative evaluation) can be given to a discharge pressure that takes time to rise to the target pressure Pt.

[0087] Fig. 10 is a diagram illustrating the feature Fv4. Fig. 10(A) is a diagram illustrating an evaluation item for evaluating the time change in the discharge pressure based on the feature Fv4. Fig. 10(B) is a diagram illustrating an example of the time change in the discharge pressure that is determined to be inappropriate by evaluation based on the feature Fv4. The evaluation item in Fig. 10(A) evaluates whether there is an abnormality in the rise of the discharge pressure.

[0088] Specifically, the pressure evaluation unit 913 calculates a first-order derivative D1 of the time change in the discharge pressure during the rise period Ta, from time ta to time tb, to obtain a first-order derivative waveform WF4. The pressure evaluation unit 913 then calculates the number of times the first-order derivative waveform WF4 crosses a predetermined threshold value Th4 during the rise period Ta as a feature value Fv4. In the example of FIG. 10(A), the first-order derivative waveform WF4 crosses the threshold value Th4 (e.g., 0.002) at both time t41 and time t42, resulting in a total number of crossings (feature value Fv4) of two. The pressure evaluation unit 913 stores the calculated feature value Fv4 in the storage unit 93 as an index value V4.

[0089] According to the evaluation based on the feature Fv4 in Figure 10(A), if a step occurs in the time change of the discharge pressure during the rise period Ta (for example, as shown in Figure 10(B)), a large score (i.e., a negative evaluation) can be given to this discharge pressure.

[0090] Fig. 11 is a diagram illustrating the feature Fv5. Fig. 11(A) is a diagram illustrating an evaluation item for evaluating the time change in the discharge pressure based on the feature Fv5. Fig. 11(B) is a diagram illustrating an example of the time change in the discharge pressure that is determined to be inappropriate by evaluation based on the feature Fv5. The evaluation item in Fig. 11(A) evaluates whether or not there is an abnormality in the rise of the discharge pressure.

[0091] Specifically, the pressure evaluation unit 913 calculates the second-order derivative D2 of the time change in the discharge pressure during the rise period Ta, from time ta to time tb, to obtain a second-order derivative waveform WF5. The pressure evaluation unit 913 then calculates the number of times the absolute value of the second-order derivative waveform WF5 intersects with a predetermined threshold value Th5 during the rise period Ta as a feature value Fv5. In the example of FIG. 11A, the absolute value of the second-order derivative waveform WF5 intersects with the threshold value Th5 (e.g., 0.0002) at times t51, t52, t53, and t54, resulting in a total of four intersections (feature value Fv5). The pressure evaluation unit 913 stores the calculated feature value Fv5 in the storage unit 93 as an index value V5.

[0092] According to the evaluation based on the feature Fv5 in Figure 11(A), if a step occurs in the time change of the discharge pressure during the rise period Ta (for example, as shown in Figure 11(B)), a large score (i.e., a negative evaluation) can be given to this discharge pressure.

[0093] 12 is a diagram illustrating an evaluation item for evaluating the time change in the discharge pressure based on the feature Fv6. The evaluation item in FIG. 12 evaluates whether the rise in the discharge pressure stalls in the latter half. Specifically, the pressure evaluation unit 913 calculates the second-order derivative D2 of the time change in the discharge pressure for the rise period Ta from time ta to time tb to obtain a second-order derivative waveform WF6.

[0094] The pressure evaluation unit 913 then determines, during the rising period Ta, the time T_1st at which the second-order differential waveform WF6 exceeds a predetermined positive threshold (Th5) and the time T_2nd at which the second-order differential waveform WF6 falls below a predetermined negative threshold (-Th5). The positive and negative thresholds have the same absolute value (Th5) but different signs. The absolute value (Th5) of the positive and negative thresholds is equal to the threshold Th5 used in the evaluation using the feature Fv5. The pressure evaluation unit 913 then determines the ratio of these times (=T_1st / T_2nd) as the feature Fv6. Furthermore, the pressure evaluation unit 913 converts the feature Fv6 based on the following equation: Fv6 = |1-Fv6|

[0095] The pressure evaluation unit 913 stores the converted feature amount Fv6 in the storage unit 93 as an index value V6.

[0096] The conveyance speed of the substrate S to be coated with the coating liquid reaches the target speed without stalling even in the latter half of the acceleration period. Therefore, it is preferable that the discharge pressure applied to the coating liquid also reaches the target pressure Pt without stalling during the rising period Ta. On the other hand, according to the evaluation based on the feature amount Fv6 in FIG. 12, when the discharge pressure stalls during the rising period Ta, a large score (i.e., a negative evaluation) can be given to this discharge pressure.

[0097] FIG. 13 is a diagram for explaining an evaluation item for evaluating the time change of the discharge pressure based on the feature amount Fv7. In the evaluation item of FIG. 13, the sharpness of the time change of the discharge pressure at the end of the rise is evaluated. Specifically, in the rising period Ta, linear regression analysis is performed on the time change of the discharge pressure between the lower reference pressure P7_l and the upper reference pressure P7_u greater than the lower reference pressure P7_l, and a regression line Lr at the end of the rise is calculated. Here, the lower reference pressure P7_l is the pressure obtained by adding the pressure of 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 the pressure obtained by adding the pressure of 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 between the time t71 and the time t72.

[0098] This regression line Lr at the end of the rise increases with the passage of time and reaches the steady pressure Pm (the average value of the discharge pressure during the steady period Tc) at the time t73. Thus, the regression line Lr at the end of the rise is set for the section from the time t71 to the time t73. Further, the pressure evaluation unit 913 sets an extended line Lm with a slope of zero indicating the steady pressure Pm between the time t73 and the time tb. As described above, the time tb is the time when the discharge pressure reaches the target pressure Pt and corresponds to the end time of the rising period Ta. That is, this extended line Lm is provided so as to extend from the end point of the regression line Lr at the end of the rise to the end point of the rising period Ta. When tb < t73, the extended line Lm is omitted.

[0099] In this way, an approximate waveform WF7 composed of the rise end regression line Lr and the extension line Lm arranged in chronological order is calculated. Then, the pressure evaluation unit 913 calculates, as a feature value Fv7, a value indicating the difference between the discharge pressure data 99 and the approximate waveform WF7 during the rise end period Ta_e from time t72, when the discharge pressure reaches 90% of the target pressure Pt, to time tb, when the discharge pressure reaches 100%. Specifically, a weighted reference time width Tw=t73-t72 is set. Then, a weighted root-mean-square error sum is calculated based on the following equation: Fv7=(Σ(P_measure-WF7) 2 ×W) 1 / 2 P_measure = Discharge pressure data 99 W=1 in the range of time t≦t73+2×Tw W=w in the range of time t>t73+2×Tw w is a weighting factor greater than 1, e.g., 10

[0100] The pressure evaluation unit 913 stores the calculated feature value Fv7 as an index value V7 in the pressure evaluation unit 913. According to the evaluation based on the feature value Fv7 in Fig. 13, if the change in the discharge pressure over time shows a rounded waveform with a weak rising momentum, a large score (i.e., a negative evaluation) can be given to this discharge pressure.

[0101] FIG. 14 is a diagram illustrating evaluation items for evaluating temporal changes in the discharge pressure based on the feature amount Fv8. The evaluation items in FIG. 14 evaluate the degree of overshoot that occurs when the discharge pressure rises. Specifically, the pressure evaluation unit 913 calculates the sign (positive / negative) of the second-order derivative D2 of the discharge pressure at time t81, when the discharge pressure reaches the maximum value Pmax. The pressure evaluation unit 913 then calculates time t82, when the sign of the second-order derivative D2 of the discharge pressure switches twice from the sign at time t81. The time change in the discharge pressure during the initial oscillation period Tb_s from time t81 to time t82 is then evaluated.

[0102] Specifically, the minimum value P8min of the time change of the discharge pressure during this initial vibration period Tb_s is obtained, and the smaller of the steady-state pressure Pm and the pressure P8min is selected as the target pressure Pg. Then, the feature value Fv8 is calculated based on the difference between the maximum pressure Pmax and the target pressure Pg, i.e., based on the following equation. Fv8=Pmax-Pg

[0103] The pressure evaluation unit 913 stores the calculated feature value Fv8 as an index value V8 in the storage unit 93. According to the evaluation based on the feature value Fv8 in Fig. 14, if the discharge pressure has a strong rising momentum and shows a large overshoot as a result of the change over time in the discharge pressure, a large score (i.e., a negative evaluation) can be given to this discharge pressure.

[0104] Fig. 15 is a diagram illustrating evaluation items for evaluating temporal changes in the discharge pressure based on the feature Fv9. The evaluation items in Fig. 15 evaluate the stability of temporal changes in the discharge pressure during the transition period Tb. Specifically, the pressure evaluation unit 913 calculates the root mean square error RMSE(P_measure, Pm) as the feature Fv9 for the discharge pressure during the transition period Tb and the steady pressure Pm, which is the average value of the discharge pressure during the steady period Tc, based on the following equation. Fv9=RMSE(P_measure,Pm) P_measure = Discharge pressure data 99

[0105] The pressure evaluation unit 913 stores the calculated feature value Fv9 as an index value V9 in the storage unit 93. According to the evaluation based on the feature value Fv9 in Fig. 15, if the time change of the discharge pressure shows ringing during the transition period Tb, a large score (i.e., a negative evaluation) can be given to this discharge pressure.

[0106] FIG. 16 is a diagram illustrating evaluation items for evaluating temporal changes in the discharge pressure based on the feature amount Fv10. The evaluation items shown in FIG. 16 evaluate the stability of temporal changes in the discharge pressure during the constant pressure period Tbc. Specifically, the pressure evaluation unit 913 obtains the maximum value Pmax and minimum value P10min of the discharge pressure during the constant pressure period Tbc. The pressure evaluation unit 913 then calculates the feature amount Fv10 based on the difference between the maximum pressure Pmax and the minimum pressure P10min during the constant pressure period Tbc, i.e., the following equation. Fv10=Pmax-P10min

[0107] The pressure evaluation unit 913 stores the calculated feature value Fv10 as an index value V10 in the storage unit 93. According to the evaluation based on the feature value Fv10 in Fig. 16, if the change in the discharge pressure over time shows a large variation in the steady period Tc that has a large effect on the film thickness of the coating liquid, a large score (i.e., a negative evaluation) can be given to this discharge pressure.

[0108] In the measurement result evaluation step S102, the pressure evaluation unit 913 calculates index values ​​V1 to V10 based on the results of extracting each of the feature amounts Fv1 to Fv10 from the discharge pressure data 99. Then, the pressure evaluation unit 913 calculates a final evaluation value (final evaluation value) for the change in the discharge pressure over time indicated by the discharge pressure data 99 from the index values ​​V1 to V10. Specifically, the discharge pressure data 99 is input into a cost function. Then, the index values ​​V1 to V10 are calculated by an internal index value calculation function, and the cost value obtained by weighting and adding these values ​​together is acquired as the final evaluation value. Next, a procedure for generating cost function data 991 indicating the weights (wi) in the cost function will be described.

[0109] <Procedure for generating cost function data> Fig. 17 is a diagram conceptually showing the procedure for generating the cost function data 991. Fig. 18 is a diagram showing the flow of the procedure for generating the cost function data 991.

[0110] To generate the cost function data 991, first, multiple patterns of discharge pressure data 99 are prepared (FIG. 18: discharge pressure data preparation step S1). Specifically, as shown in FIG. 17, multiple patterns of discharge pressure data 99 are prepared when the coating apparatus 1 is operated with multiple patterns of control parameters A, B, C, etc. The discharge pressure data 99 is an example of measurement data that indicates the operating state of the coating apparatus 1.

[0111] Once multiple patterns of discharge pressure data 99 are prepared in the discharge pressure data preparation step S1, a rank is assigned to each of the discharge pressure data 99 (rank assignment step S2). Specifically, the ranking is achieved by classifying the multiple discharge pressure data 99 into multiple ranks (classes) set in advance. The multiple ranks are configured, for example, as 5 to 10 ranks, such as "very good," "good," "average," "poor," and "very poor." The cost function data generation unit 915 assigns a rank (a numerical value such as "1," "2," "3," etc.) to the discharge pressure data 99 according to the rank assigned by the user. In this example, the closer the pressure waveform of the discharge pressure data 99 is to the ideal discharge waveform (i.e., the better the pressure waveform), the smaller the assigned rank value is set.

[0112] In the ranking process S2, the control unit 9 displays the pressure waveforms of the multiple discharge pressure data 99 to be ranked on a display, and the user visually checks each of the pressure waveforms displayed on the display and assigns a rank to each of the pressure waveforms. The cost function data generation unit 915 then assigns a rank to each of the discharge pressure data 99 in response to a user's input. The ranks assigned to each of the discharge pressure data 99 are appropriately stored in the storage unit 93. In this manner, the cost function data generation unit 915 functions as a rank assigning unit that assigns ranks to the discharge pressure data 99. The pressure evaluation unit 913 may calculate index values ​​V1 to V10 for each of the discharge pressure data 99, and the calculated index values ​​V1 to V10 may be displayed on a display together with the discharge pressure data 99. This allows the user to perform ranking using the index values ​​V1 to V10 as indexes, thereby improving the accuracy of the ranking.

[0113] As shown in FIG. 18, once the ranking step S2 is completed, a weight determination step S3 is executed. In the weight determination step S3, weights for the index values ​​V1 to V10 in the cost function are determined. FIG. 19 is a diagram showing the flow of the weight determination step S3 shown in FIG. 18. As shown in FIG. 19, in the weight determination step S3, first, the user adjusts the weights of the cost function (weight adjustment step S31). This weight adjustment is performed via a GUI (weight adjustment window AW1) described later. After the weights are adjusted, the cost function data generation unit 915 calculates cost values ​​for each discharge pressure data 99 using the cost function to which the adjusted weights have been applied (cost value calculation step S32). After the cost values ​​are calculated, the cost function data generation unit 915 displays correlation information indicating the correlation between the rank and the cost value for each discharge pressure data 99 on a display (correlation information display step S33).

[0114] FIG. 20 is a diagram showing an example of a weight adjustment window AW1. The weight adjustment window AW1 is one element of the GUI that the cost function data generation unit 915 displays on the display. The weight adjustment window AW1 has a weight adjustment area AR1, a distribution display area AR2, a distribution display selection area AR3, a correlation coefficient display area AR4, and a confirm button BT1. The weight adjustment area AR1 is an area where icons for adjusting the weights of each index value are displayed. The weight adjustment area AR1 has multiple indicators ID1 for adjusting the weights of multiple index values ​​(here, three index values ​​X, Y, and Z). The indicator ID1 has arrow icons indicating the weight values. The user can decrease or increase the weight of the corresponding index value by moving the arrow icon left or right. In this way, the process in which the user operates the indicator ID1 corresponds to the weight adjustment process S31 in which the weights are adjusted.

[0115] The distribution display area AR2 is an area where a distribution (hereinafter referred to as a "rank-cost value distribution") showing the relationship between the pre-assigned ranks and the cost values ​​output by the cost function for each discharge pressure data 99 is displayed. The rank-cost value distribution is an example of correlation information showing the correlation between ranks and cost values. As shown in FIG. 20, the rank-cost value distribution is displayed in the distribution display area AR2 with the rank value on the horizontal axis and the cost value on the vertical axis. The distribution display selection area AR3 is an area where the type of distribution to be displayed in the distribution display area AR2 is selected. In this example, the distribution display selection area AR3 has radio buttons that allow the user to select one of two types: a "scatter plot" and a "box-and-whisker plot." When the "scatter plot" is selected, the rank-cost value distribution is displayed in the distribution display area AR2 as a scatter plot, as shown in FIG. 20. When the "box-and-whisker plot" is selected, the rank-cost value distribution is displayed in the distribution display area AR2 as a box-and-whisker plot represented by "boxes" and "whisker" symbols. The cost function data generating unit 915 may display a regression line RL1 indicating the relationship between the rank and the cost value together with the rank-cost value distribution. The regression line RL1 is correlation information indicating the correlation between the rank and the cost value. By displaying the regression line RL1, the user can appropriately adjust the weight of each index value using the regression line RL1 as an index.

[0116] In the rank-cost value distribution shown in Fig. 20, several discharge pressure data 99 are classified into each of five ranks. As shown in the figure, even if the assigned rank is the same, if the cost value is different, the dots representing the discharge pressure data 99 will be distributed in a spread manner along the vertical axis according to the magnitude of the cost value within the same rank.

[0117] The correlation coefficient display area AR4 is an area for displaying correlation coefficients. The cost function data generation unit 915 calculates correlation coefficients indicating the relationship between ranks and cost values ​​from the rank-cost value distribution, and displays the calculated correlation coefficients in the correlation coefficient display area AR4. The correlation coefficients are an example of correlation information indicating the relationship between ranks and cost values.

[0118] Each time the user adjusts the weight by operating indicator ID1, the cost function data generation unit 915 calculates a cost value based on the adjusted weight (cost value calculation step S32). Then, the cost function data generation unit 915 updates the correlation information (rank-cost value distribution, correlation coefficient, regression line RL1) displayed on the display. This allows the user to adjust the weight of the cost function while checking the correlation information updated in real time. While checking the correlation information displayed on the display, the user adjusts the weight of the cost function so that the correlation between the rank and the cost value is as high as possible. This adjusts the weight of the cost function so that a cost value corresponding to the visual ranking is output.

[0119] The Confirm button BT1 is an icon that is pressed when confirming the adjusted weights. When the user confirms the weights, he or she presses the Confirm button BT1. The cost function data generation unit 915 determines whether the Confirm button BT1 has been pressed (FIG. 19: determination step S34). When the Confirm button BT1 has been pressed, the cost function data generation unit 915 confirms the adjusted weights as the final weights of the cost function. The confirmed weights are stored in the storage unit 93 as cost function data 991 (see FIG. 3, etc.). In this way, the cost function data generation unit 915 functions as a weight determination unit that determines weights.

[0120] For the index values ​​V1 to V10, the weight may be conditionally branched depending on the magnitude of the value. For example, a threshold may be set for each index value, and if the index value is less than the threshold, the weight (coefficient) for that threshold may be set to zero. Also, if the index value is equal to or greater than the threshold, the weight may be set to one.

[0121] <Effects> It is possible to determine multiple feature values ​​Fv1 to Fv10 from the pressure waveform of the discharge pressure data 99 and obtain the respective index values ​​V1 to V10. However, designing a cost function (objective function) for evaluating the discharge pressure data 99 based on the index values ​​V1 to V10 typically requires skilled experience and knowledge. In contrast, in this embodiment, the discharge pressure data 99 is visually ranked, and the weight of the cost function is adjusted so that the correlation between the output (cost value) of the cost function and the rank is high. This allows the cost function to be designed to output a cost value that matches the visual ranking. Therefore, even if one has little skilled experience or knowledge regarding the evaluation of the discharge pressure data 99, the cost function can be appropriately designed.

[0122] Furthermore, ranking can be made easier by making the number of ranking stages (M stages) smaller than the number (N) of target discharge pressure data 99. In particular, by making the number of ranking stages sufficiently smaller than the number of discharge pressure data 99 (for example, 5 to 10 stages), ranking can be easily performed for each discharge pressure data 99. Therefore, even a user with little experience or knowledge regarding evaluation of discharge pressure data 99 can appropriately design a cost function.

[0123] 2. Second embodiment In the first embodiment, the final weights (cost function data 991) are determined based on the weights adjusted by the user. However, the method of determining the weights is not limited to this manual method, and may be performed automatically.

[0124] FIG. 21 is a diagram showing a cost function data generation unit 915 according to the second embodiment. FIG. 22 is a diagram showing a neural network NN1 that expresses a cost function. As shown in FIG. 21, the cost function data generation unit 915 includes a learning unit 916. The learning unit 916 performs machine learning using the neural network NN1 shown in FIG. 22. The neural network NN1 has an input layer L11, an intermediate layer L13, and an output layer L15. Index values ​​(index values ​​V1 to V10) of multiple evaluation items are input to the input layer L11. The output layer outputs cost values. The neural network NN1 is configured to receive the index values ​​V1 to V10 of multiple discharge pressure data 99 as input, and to output a set of cost values ​​corresponding to the multiple discharge pressure data 99.

[0125] The learning unit 916 performs machine learning so as to increase the correlation between the set of cost values ​​that are the output of the neural network NN1 and the set of ranks that have been assigned in advance to the discharge pressure data 99. That is, the learning unit 916 performs machine learning so as to maximize the correlation coefficient, which is the objective function of the correlation coefficient between the cost values ​​and the ranks. The weight parameters in the neural network NN1 are adjusted by the machine learning of the learning unit 916. Then, when the machine learning is completed, the weights are finally determined. The neural network NN1, whose weights have been determined in this way, can be used as a cost function that calculates cost values ​​from multiple index values ​​V1 to V10.

[0126] If the cost function data generation unit 915 includes the learning unit 916, the weights in the cost function (neural network NN1) can be automatically determined by machine learning. This reduces the effort required to determine the weights of the cost function compared to manually adjusting the weights.

[0127] Preparing a sufficient amount of training data for training the neural network NN1 requires a large amount of work and a lot of effort. In contrast, as described above, when performing machine learning using multiple discharge pressure data 99 as input and the correlation coefficient between a set of ranks and a set of cost values ​​as the objective function, the training data can be artificially inflated by rearranging the discharge pressure data 99 used as training data. Therefore, machine learning can be performed appropriately while reducing the effort required for collecting and ranking the discharge pressure data 99.

[0128] The depth of the neural network NN1 should be selected depending on the complexity of the learning target. For example, if all that is required is to multiply each indicator by a coefficient and add them up, the intermediate layer L13 may be omitted. Reducing the number of layers in the neural network NN1 makes it difficult to express complex weighting rules. However, stable learning can be achieved with a small amount of learning data.

[0129] <3. Modifications> Although the embodiments have been described above, the present invention is not limited to the above and various modifications are possible.

[0130] For example, in the above embodiment, the discharge characteristics are measured based on the pressure value detected by the pressure gauge 86 attached to the piping 82, but the installation position of the pressure gauge 86 is not limited to this, and the installation position can be any position as long as it is a position where the pressure of the coating liquid supplied to the nozzle 71 can be detected.

[0131] Furthermore, in the above embodiment, a bellows type pump 81 is used, but the type of pump is not limited to this, and for example, a syringe type pump using a piston (for example, Japanese Patent Application Laid-Open No. 2008-101510) may also be used.

[0132] Furthermore, in the above embodiment, the present invention is applied to a coating apparatus 1 that supplies a coating liquid to the upper surface Sf of the substrate S while the substrate S is in a floating state, but the application of the present invention is not limited to this, and the present invention can be applied to general substrate processing techniques in which a processing liquid is supplied to a nozzle, and then the processing liquid is supplied from the nozzle to the upper surface of the substrate to perform a predetermined process.

[0133] The cost function does not necessarily weight and evaluate all of the index values ​​V1 to V10 of the above feature amounts Fv1 to Fv10. The cost function may be configured to output a cost value based on only some of these index values ​​V1 to V10.

[0134] Furthermore, the pressure evaluation unit 913 and the cost function data generation unit 915 are realized by the control unit 9, which is an element of the coating apparatus 1. However, the pressure evaluation unit 913 or the cost function data generation unit 915 may be realized by a device (cost function data generation device) separate from the coating apparatus 1.

[0135] In the above embodiments, the measurement data is described as the discharge pressure data 99 of the coating device 1, but the measurement data is not limited to this. The measurement data may be any measurable data, such as temperature data or speed data in a processing device that processes an object. Furthermore, the measurement data is not limited to data obtained by actual observation, but may also be data obtained by simulation. For example, a simulated discharge in the coating device 1 may be simulated on a computer, and the change over time in the pressure applied to the coating liquid at that time may be obtained as the discharge pressure data 99.

[0136] Although the present invention has been described in detail, the above description is merely illustrative in all respects and does not limit the present invention. It is understood that countless variations not illustrated can be envisioned without departing from the scope of the present invention. The configurations described in the above embodiments and variations can be combined or omitted as appropriate as long as they are not mutually inconsistent. [Explanation of symbols]

[0137] 1 Coating device 71 nozzle 93 Memory section 98 Cost function data generator 915 Cost function data generation unit 916 Learning Department 991 Cost Function Data AR1 weight adjustment area AR2 distribution display area AR3 Distribution display selection area AR4 Correlation Coefficient Display Area AW1 Weight adjustment window NN1 Neural Network RL1 regression line

Claims

1. A cost function data generation method executed by a computer, comprising: a) preparing a plurality of measurement data sets obtained by measuring the operating state of the processing device when the processing device is controlled by the computer using a plurality of patterns of control parameters; b) the computer assigning ranks to the plurality of measurement data; c) determining weights in a cost function that outputs a cost value obtained by weighting and integrating index values ​​of a plurality of items extracted from the measurement data; Including, The cost function data generation method, wherein the step c) includes a step in which the computer adjusts weights in the cost function so that there is a high correlation between the cost value output by the cost function for each of the measurement data and the rank assigned to each of the measurement data in the step b).

2. 2. The cost function data generation method according to claim 1, The step c) c-1) a step in which the computer displays correlation information indicating a correlation between the rank and the cost value based on the adjusted weight; A cost function data generation method, comprising:

3. 3. The cost function data generation method according to claim 2, A cost function data generation method, wherein the correlation information includes a distribution indicating the relationship between the rank and the cost value based on the adjusted weight for each measurement data.

4. 4. The cost function data generation method according to claim 3, The cost function data generating method, wherein the correlation information includes a regression line that indicates the relationship between the rank and the cost value.

5. 5. The cost function data generation method according to claim 2, further comprising: The cost function data generating method, wherein the correlation information includes a correlation coefficient indicating a relationship between the rank and the cost value.

6. 6. A cost function data generation method according to claim 2, further comprising: The step c) c-2) a step in which the computer displays an indicator on a display unit for adjusting the weights for the index values ​​of the plurality of items; c-3) adjusting the weight based on an operation of the indicator displayed on the display unit by the computer; The step c-1) comprises: The cost function data generating method includes a step of displaying the correlation information based on the weights adjusted in step c-3) by the computer.

7. 2. The cost function data generation method according to claim 1, the cost function includes a neural network that receives index values ​​of the plurality of items as input and outputs the cost value; The cost function data generating method, wherein the step c) includes a step in which the computer performs machine learning using the neural network.

8. 8. The cost function data generation method according to claim 7, the neural network receives the index values ​​for two or more pieces of measurement data as input and outputs the cost values ​​for the two or more pieces of measurement data; The step c) includes a step in which the computer performs machine learning using, as an objective function, a correlation coefficient between the cost value for the two or more pieces of measurement data and the rank assigned to the two or more pieces of measurement data.

9. 9. A cost function data generation method according to claim 1, further comprising: the treatment device is a device that applies a discharge pressure to a treatment liquid and discharges the treatment liquid from a nozzle, The cost function data generating method, wherein the measurement data is data indicating the discharge pressure.

10. 10. A cost function data generation method according to claim 1, further comprising: The cost function data generating method, wherein the step b) includes a step in which the computer assigns ranks to the plurality of pieces of measurement data on a scale of 10 or less.

11. A cost function data generation program, A cost function data generating program that causes a computer to execute the cost function data generating method according to any one of claims 1 to 10.

12. A cost function data generating device, a storage unit that stores a plurality of measurement data obtained by measuring the operating state of the processing device when the processing device is controlled using a plurality of patterns of control parameters; a rank assigning unit that assigns ranks to the plurality of measurement data based on a predetermined operation input; a weight determination unit that determines weights in a cost function that outputs a cost value obtained by weighting and integrating index values ​​of a plurality of items extracted from the measurement data; Equipped with The weight determination unit adjusts the weight in the cost function so that there is a high correlation between the cost value output by the cost function for each piece of measurement data and the rank assigned to each piece of measurement data by the rank assigning unit.

13. 13. The cost function data generating device according to claim 12, a display unit that displays correlation information indicating a correlation between the rank and the cost value based on the adjusted weight; The cost function data generating device further comprises:

14. 14. The cost function data generating device according to claim 12 or 13, the cost function is expressed by a neural network that receives index values ​​of the plurality of items as input and outputs the cost value; The cost function data generating device, wherein the weight determination unit includes a learning unit that performs machine learning using the neural network.

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