JP2025165596A - Movement control method, drawing method, estimation method, computer-readable program, and movement control device - Google Patents

Abstract

The position of an object in the sub-scanning direction during main scanning is adaptively controlled.
[Solution] As a preliminary step, an approximation equation indicating the relationship between the main scanning position and the sub-scanning position of the object is found from a group of measurement values 611 of the main scanning position and the sub-scanning position, and a residual estimator 631 is constructed that estimates the residual based on the main scanning position, etc., using the difference between the sub-scanning position indicated by the group of measurement values 611 and the sub-scanning position indicated by the approximation equation as the residual for each main scanning position. During main scanning of the object, an estimated residual value is obtained by the residual estimator 631 at each time using the measurement value of the main scanning position obtained by a measurement unit 22, etc. Online learning is performed using the measurement value of the sub-scanning position obtained by the measurement unit 22 and the estimated residual value, and estimated coefficients in the approximation equation are obtained. An approximate value of the sub-scanning position is found using the approximate equation to which the estimated coefficients are applied. An estimated sub-scanning position is obtained using the estimated residual value and the approximate value, and the position of the object in the sub-scanning direction is corrected.
[Selected Figure] Figure 4

Description

The present invention relates to technology for controlling a moving mechanism and technology for estimating parameter values.

In recent years, control devices that use not only feedback control but also machine learning models such as neural networks have been proposed for controlling the movement of stages and other devices. However, even if a control device that uses a machine learning model is optimized at a certain point in time, it may no longer achieve the desired control performance as the device is relocated or changes over time.

Patent Document 1 proposes a method for redetermining parameter values through reinforcement learning in a control device using a neural network. This method minimizes degradation of control accuracy due to changes in the state of the controlled object. The control device in Patent Document 2 includes: a first compensator that generates a first signal based on a control deviation; a compensator that corrects the control deviation using one of multiple adjustment units that generate a correction signal by correcting the control deviation according to an arithmetic expression with an adjustable coefficient; a second compensator that generates a second signal using a neural network based on the correction signal; and a calculator that generates a control signal based on the first and second signals. Because the time required to adjust the multiple adjustment units is shorter than the time required to re-learn the neural network, appropriate control characteristics can be adjusted in a short time even if changes occur in the state of the controlled object or in the external disturbance environment.

In the exposure apparatus of Patent Document 3, a straightness correction table is prepared that indicates the amount of correction for correcting the position of the stage in the sub-scanning direction according to the position of the stage in the main scanning direction, and when the stage is driven in the main scanning direction, the position of the stage in the sub-scanning direction is corrected based on this straightness correction table. This ensures straightness when driving the stage in the main scanning direction, making it possible to irradiate light from the exposure head to the appropriate position on the substrate placed on the stage.

Japanese Patent Application Laid-Open No. 2022-11044 JP 2022-92690 A Japanese Patent Application Laid-Open No. 2022-137849

However, when using a correction table to correct the position of an object in the sub-scanning direction during a main scan, as in Patent Document 3, it is necessary to re-acquire the correction table when changes in the state occur, such as when the device is relocated or deteriorates over time. Even with the method of Patent Document 1, which uses reinforcement learning in a neural network, it is difficult to estimate the amount of training data required in advance, and operating the actual device to acquire training data may require an unrealistic amount of data. Furthermore, the method of Patent Document 2 requires determining optimal parameters for multiple adjustment units in accordance with anticipated changes in the control state, which may make it difficult to prevent a decrease in control accuracy depending on the state change. Therefore, there is a need for a new method that can adaptively control the position of an object in the sub-scanning direction during a main scan. There is also a need for a method that adaptively estimates the value of a second parameter that changes in accordance with fluctuations in the value of a first parameter.

The present invention was developed in consideration of the above-mentioned problems, and aims to adaptively control the position of an object in the sub-scanning direction during main scanning, and also to adaptively estimate the value of a second parameter that changes in response to fluctuations in the value of a first parameter.

Aspect 1 of the present invention is a movement control method for controlling a movement mechanism that moves an object in mutually intersecting main scanning and sub-scanning directions, comprising: a) a step of determining an approximation equation indicating the relationship between the main scanning position and the sub-scanning position from a group of measurement values of the main scanning position and the sub-scanning position of the object acquired by a measurement unit while the object is moving in the main scanning direction; b) a step of constructing a residual estimator that estimates the residual based on at least the main scanning position, using the difference between the sub-scanning position indicated by the group of measurement values and the sub-scanning position indicated by the approximation equation for each main scanning position as a residual; c) a step of moving the object in the main scanning direction; and d) a step of acquiring an estimated position of the sub-scanning position of the object at each time at a predetermined interval while performing step c), and correcting the position of the object in the sub-scanning direction to match a predetermined target position, wherein step d) comprises: d1) acquiring an estimated position of the sub-scanning position of the object at each time d2) performing online learning at each time to estimate at least one coefficient in the approximation formula using the measurement value of the sub-scanning position by the measurement unit and the estimated value of the residual, and obtaining an estimate of the at least one coefficient; d3) using the approximation formula to which the estimated value of the at least one coefficient at each time is applied to obtain an approximate value of the sub-scanning position at each time; d4) obtaining the estimated position of the sub-scanning position using the estimated value and approximate value of the residual at each time; and d5) moving the object in the sub-scanning direction based on the difference between the estimated position of the sub-scanning position obtained for each time and the target position.

Aspect 2 of the present invention is the movement control method of aspect 1, wherein the approximation equation is a linear regression equation, and the at least one coefficient is the intercept and/or slope of the linear regression equation.

Aspect 3 of the present invention is the movement control method of aspect 1 (or aspect 1 or 2), in which the online learning is performed using a Kalman filter.

Aspect 4 of the present invention is a movement control method according to Aspect 1 (which may be any one of Aspects 1 to 3), in which the residual estimator is a trained model that outputs the estimated value of the residual in response to inputs including the torque of a main scanning motor included in the movement mechanism and/or the main scanning speed of the object, and the main scanning position.

Aspect 5 of the present invention is a drawing method for drawing a pattern on a substrate, comprising: a movement step of moving the stage, which is the object, in the main scanning direction using the movement control method of any one of aspects 1 to 4; and a drawing step of drawing a pattern on the substrate held on the stage by controlling a drawing unit in synchronization with the movement of the stage in the main scanning direction.

Aspect 6 of the present invention is a drawing method according to aspect 5, in which, after the drawing step is completed, the movement step and the drawing step are repeated for another substrate, and in the movement step for the other substrate, steps a) and b) of the movement control method are omitted, and the initial value of the at least one coefficient in the online learning of step d2) is determined from the relationship between the main scanning position and the sub-scanning position obtained in the movement step for the substrate on which drawing was performed immediately before.

Aspect 7 of the present invention is an estimation method for estimating the value of a second parameter that changes in response to fluctuations in the value of a first parameter, comprising: a) a step of determining an approximation equation indicating the relationship between the value of the first parameter and the value of the second parameter from a group of measured values of the first parameter and the second parameter acquired by a measurement unit when the value of the first parameter fluctuates; b) a step of constructing a residual estimator that estimates the residual based on at least the value of the first parameter, using the difference between the value of the second parameter indicated by the group of measured values and the value of the second parameter indicated by the approximation equation as the residual; and c) a step of acquiring an estimated value of the second parameter at each time point at a predetermined interval while the value of the first parameter fluctuates. The c) step includes: c1) at each time, using the residual estimator to obtain an estimate of the residual using at least the measurement value of the first parameter by the measurement unit; c2) at each time, using the measurement value of the second parameter by the measurement unit and the estimate of the residual, performing online learning to estimate at least one coefficient in the approximation formula and obtain an estimate of the at least one coefficient; c3) using the approximation formula to which the estimate of the at least one coefficient at each time is applied to find an approximate value of the second parameter at each time; and c4) using the estimate and approximate value of the residual at each time to obtain the estimate of the second parameter.

Aspect 8 of the present invention is a computer-readable program that causes a computer to control a movement mechanism that moves an object in main scanning and sub-scanning directions that intersect with each other. Execution of the program by a computer includes the following steps: a) determining an approximation formula that indicates the relationship between the main scanning position and the sub-scanning position of the object from a group of measurement values of the main scanning position and the sub-scanning position of the object acquired by a measurement unit while the object is moving in the main scanning direction; b) constructing a residual estimator that estimates the residual based on at least the main scanning position, using the difference between the sub-scanning position indicated by the group of measurement values and the sub-scanning position indicated by the approximation formula for each main scanning position as a residual; c) moving the object in the main scanning direction; and d) acquiring an estimated position of the sub-scanning position of the object at each time point at a predetermined interval while performing step c), and correcting the position of the object in the sub-scanning direction to match a predetermined target position. and the d) step includes: d1) at each time, acquiring an estimated value of the residual by the residual estimator using at least the measurement value of the main scanning position by the measurement unit; d2) at each time, performing online learning to estimate at least one coefficient in the approximation formula using the measurement value of the sub-scanning position by the measurement unit and the estimated value of the residual, and acquiring an estimated value of the at least one coefficient; d3) using the approximation formula to which the estimated value of the at least one coefficient at each time is applied to obtain an approximate value of the sub-scanning position at each time; d4) acquiring the estimated position of the sub-scanning position using the estimated value and approximate value of the residual at each time; and d5) moving the object in the sub-scanning direction based on the difference between the estimated position of the sub-scanning position acquired for each time and the target position.

A ninth aspect of the present invention is a movement control device that controls a movement mechanism that moves an object in mutually intersecting main scanning and sub-scanning directions, and includes: an approximation equation acquisition unit that determines an approximation equation indicating the relationship between the main scanning position and the sub-scanning position from a group of measurement values of the main scanning position and the sub-scanning position of the object acquired by a measurement unit when the object moves in the main scanning direction; an estimator construction unit that constructs a residual estimator that estimates the residual based on at least the main scanning position, using the difference between the sub-scanning position indicated by the group of measurement values and the sub-scanning position indicated by the approximation equation for each main scanning position as a residual; and a movement control unit that acquires an estimated position of the sub-scanning position of the object at each time point at predetermined intervals while moving the object in the main scanning direction, and corrects the position of the object in the sub-scanning direction to match a predetermined target position, and the movement control unit acquires an estimated position of the sub-scanning position of the object at each time point at least The system includes a residual acquisition unit that acquires an estimated value of the residual using the residual estimator based on the measurement value of the main scanning position obtained by the measurement unit; a coefficient acquisition unit that performs online learning to estimate at least one coefficient in the approximation formula using the measurement value of the sub-scanning position obtained by the measurement unit and the estimated value of the residual at each time, and acquires an estimated value of the at least one coefficient; an approximate value calculation unit that calculates an approximate value of the sub-scanning position at each time using the approximation formula to which the estimated value of the at least one coefficient at each time is applied; an estimated position acquisition unit that acquires the estimated position of the sub-scanning position using the estimated value and approximate value of the residual at each time; and a correction control unit that moves the object in the sub-scanning direction based on the difference between the estimated position of the sub-scanning position obtained for each time and the target position.

In aspects 1 to 6, as well as aspects 8 and 9 of the present invention, the position of the object in the sub-scanning direction during main scanning can be adaptively controlled. In aspect 7 of the present invention, the value of the second parameter can be adaptively estimated.

FIG. 2 is a front view showing the imaging device. FIG. 2 is a side view showing the imaging device. FIG. 1 illustrates the configuration of a computer. FIG. 2 is a block diagram showing a functional configuration realized by a computer. FIG. 10 is a diagram showing a flow of advance preparation for drawing processing. 10A and 10B are diagrams showing changes in sub-scanning position relative to main scanning position, and lines of approximation equations; FIG. 10 is a diagram showing a change in residual error with respect to the main scanning position. FIG. 2 is a diagram showing the flow of drawing processing in the drawing device. FIG. 10 is a diagram showing a flow of correction control of the sub-scanning position. 10A and 10B are diagrams for explaining state changes of a moving mechanism. 10A and 10B are diagrams for explaining the accuracy of correction control of the sub-scanning position.

Figure 1 is a front view of an imaging device 1 according to one embodiment of the present invention, and Figure 2 is a side view of the imaging device 1. The imaging device 1 is a direct imaging device (also called an exposure device) that irradiates spatially modulated light onto a main surface of a substrate 9, such as a semiconductor substrate coated with a photosensitive material, to image a pattern on the main surface. In Figures 1 and 2, the mutually orthogonal X, Y, and Z directions are indicated by arrows. In this embodiment, the X and Y directions are approximately horizontal, and the Z direction is approximately vertical, but the X, Y, and Z directions may be changed as desired.

The drawing device 1 comprises a base 10, a stage 21, a movement mechanism 3, a measurement unit 22, a drawing unit 4, and a computer 5. As described below, the computer 5 is responsible for overall control of the drawing device 1. The base 10 is a support platform that supports the movement mechanism 3 and the drawing unit 4, and has a flat outer shape that extends in the Y and X directions. The stage 21 is a flat plate that holds the substrate 9. The stage 21 has a flat upper surface. The substrate 9 is placed on the upper surface of the stage 21 in a substantially horizontal position. The stage 21 may have chuck pins that secure the substrate 9 and multiple suction holes that hold the substrate 9 by suction.

The moving mechanism 3 is a mechanism for transporting the stage 21. The moving mechanism 3 moves the stage 21 in the Y and X directions relative to the base 10. As will be described later, during the drawing process in the drawing device 1, the stage 21 moves continuously in the Y direction and intermittently in the X direction. Therefore, hereinafter, the Y direction will be referred to as the "main scanning direction" and the X direction will be referred to as the "sub-scanning direction." As shown in Figures 1 and 2, the moving mechanism 3 includes a main scanning plate 31, a sub-scanning plate 32, a main scanning mechanism 33, a sub-scanning mechanism 34, and a rotation mechanism 35.

The main scanning mechanism 33 is a mechanism for transporting the stage 21 in the main scanning direction. The main scanning mechanism 33 moves the main scanning plate 31 in the main scanning direction relative to the base 10. The main scanning mechanism 33 includes a pair of main scanning guides 331, a main scanning motor 332, and a main scanning circuit 333. The pair of main scanning guides 331 are provided on the upper surface of the base 10 with a gap between them in the sub-scanning direction. Each main scanning guide 331 extends linearly along the main scanning direction. The main scanning guides 331 may be, for example, air guides, which guide the main scanning plate 31 in the main scanning direction while levitating it.

The main scanning motor 332 is disposed between a pair of main scanning guides 331. In this embodiment, the main scanning motor 332 is a linear motor having a stator 332a and a slider 332b. The stator 332a is provided on the upper surface of the base 10 along the main scanning direction. The slider 332b is fixed to the lower surface of the main scanning plate 31. In the main scanning motor 332, the slider 332b moves in the main scanning direction along the stator 332a due to magnetic attraction and repulsion generated between the stator 332a and slider 332b. This causes the main scanning plate 31 to move in the main scanning direction relative to the base 10. The main scanning circuit 333 is electrically connected to the main scanning motor 332 and controls the drive of the main scanning motor 332. The main scanning circuit 333 also acquires the torque and movement speed (hereinafter referred to as the "main scanning speed") of the main scanning motor 332 and outputs them to the computer 5. The main scanning mechanism 33 may also move the stage 21 using, for example, a rotary motor and a ball screw (the same applies to the sub-scanning mechanism 34).

The sub-scanning mechanism 34 is a mechanism for transporting the stage 21 in the sub-scanning direction. The sub-scanning mechanism 34 moves the sub-scanning plate 32 in the sub-scanning direction relative to the main scanning plate 31. The sub-scanning mechanism 34 includes a pair of sub-scanning guides 341, a sub-scanning motor 342, and a sub-scanning circuit 343. The pair of sub-scanning guides 341 are provided on the upper surface of the main scanning plate 31 with a gap in the main scanning direction. Each sub-scanning guide 341 extends linearly in the sub-scanning direction. The sub-scanning guides 341 may be, for example, ball guides, and smoothly guide the sub-scanning plate 32 in the sub-scanning direction relative to the main scanning plate 31.

The sub-scanning motor 342 is disposed between a pair of sub-scanning guides 341. In this embodiment, the sub-scanning motor 342 is a linear motor having a stator 342a and a slider 342b. The stator 342a is provided on the upper surface of the main scanning plate 31 along the sub-scanning direction. The slider 342b is fixed to the lower surface of the sub-scanning plate 32. In the sub-scanning motor 342, the slider 342b moves in the sub-scanning direction along the stator 342a due to magnetic attraction and repulsion generated between the stator 342a and slider 342b. This causes the sub-scanning plate 32 to move in the sub-scanning direction relative to the main scanning plate 31. The sub-scanning circuit 343 is electrically connected to the sub-scanning motor 342 and controls the drive of the sub-scanning motor 342. The sub-scanning circuit 343 also acquires the torque of the sub-scanning motor 342 and outputs it to the computer 5.

The rotation mechanism 35 is a mechanism for adjusting the rotation angle of the stage 21 around a rotation axis R1 extending in the Z direction. The rotation mechanism 35 has, for example, a rotation motor, and rotates the stage 21 around the rotation axis R1 relative to the sub-scanning plate 32. The rotation mechanism 35 can adjust the rotation angle (yawing angle) of the stage 21 around the rotation axis R1.

The measuring unit 22 includes a main scanning length measuring device 23, a sub-scanning length measuring device 24, and mirrors (plane mirrors) 251 and 252. As shown in FIG. 2, the mirror 251 is fixed to the edge of the stage 21 in the main scanning direction. The main scanning length measuring device 23 is a laser length measuring device and is positioned opposite the mirror 251 in the main scanning direction. The main scanning length measuring device 23 emits laser light toward the mirror 251 and receives the laser light reflected by the mirror 251. The main scanning length measuring device 23 measures the position of the stage 21 in the main scanning direction (hereinafter simply referred to as the "main scanning position") based on the phase difference between the emitted light and the reflected light, and outputs the measured value to the computer 5. The main scanning length measuring device 23 and mirror 251 are not shown in FIG. 1.

As shown in Figure 1, mirror 252 is fixed to the edge of stage 21 in the sub-scanning direction. Sub-scanning length measuring device 24 is a laser length measuring device, and is positioned opposite mirror 252 in the sub-scanning direction. Sub-scanning length measuring device 24 emits laser light toward mirror 252 and receives the laser light reflected by mirror 252. Sub-scanning length measuring device 24 measures the position of stage 21 in the sub-scanning direction (hereinafter simply referred to as "sub-scanning position") based on the phase difference between the emitted light and the reflected light, and outputs the result to computer 5. In the examples shown in Figures 1 and 2, mirrors 251 and 252 are attached to the side of stage 21, but they may also be installed upright on the top surface of stage 21, for example. As will be described later, the movement of the stage 21 is controlled using the main scanning position measured by the main scanning length measuring device 23 and the sub-scanning position measured by the sub-scanning length measuring device 24, but the imaging device 1 may also be provided with a main scanning encoder and a sub-scanning encoder as needed.

As shown in Figures 1 and 2, the drawing unit 4 includes a head 41, an illumination optical system 42, and a laser oscillator 43. The laser oscillator 43 emits laser light. The laser light is guided to the head 41 via the illumination optical system 42. The head 41 is fixed to the base 10 via a frame (not shown) and is positioned above the substrate 9 on the stage 21. A spatial light modulator is provided inside the head 41. The spatial light modulator is, for example, a GLV (Grating Light Valve) (registered trademark), which is a diffraction grating-type light modulator. Light spatially modulated by the spatial light modulator is irradiated onto the upper surface of the substrate 9. This exposes the photosensitive material on the upper surface of the substrate 9. The spatial light modulator may be a type other than a GLV, and may be, for example, a DMD (Digital Micromirror Device) in which multiple micromirrors are arranged two-dimensionally.

During the drawing process in the drawing device 1, the main scanning mechanism 33 continuously moves the substrate 9 (and stage 21) in the main scanning direction. As a result, the irradiation position of light from the drawing unit 4 moves relatively in the main scanning direction on the top surface of the substrate 9. The control unit 6, described below, also controls the spatial light modulator of the drawing unit 4 in synchronization with the movement of the irradiation position on the top surface. As a result, the drawing unit 4 draws a pattern in a strip-shaped area extending in the main scanning direction on the top surface. Next, the sub-scanning mechanism 34 moves the substrate 9 a predetermined distance in the sub-scanning direction. Thereafter, while the substrate 9 continues to move in the main scanning direction, the spatial light modulator of the drawing unit 4 is controlled to draw a pattern in another strip-shaped area. In this way, by repeating the continuous movement of the substrate 9 in the main scanning direction and the intermittent movement in the sub-scanning direction, a pattern is drawn on almost the entire top surface.

Figure 3 shows the configuration of computer 5. Computer 5 has the configuration of a typical computer system, including a CPU 51, ROM 52, RAM 53, storage device 54, display 55, input unit 56, reading device 57, communication unit 58, GPU 59, and bus 50. CPU 51 performs various arithmetic operations. GPU 59 performs various arithmetic operations related to image processing, etc. ROM 52 stores basic programs. RAM 53 and storage device 54 store various types of information. Display 55 displays various types of information, such as images. Input unit 56 includes a keyboard 56a and mouse 56b for accepting input from an operator. Reading device 57 reads information from a computer-readable recording medium M1, such as an optical disk, magnetic disk, magneto-optical disk, or memory card. Communication unit 58 transmits and receives signals between movement mechanism 3 and drawing unit 4, etc. The bus 50 is a signal circuit that connects the CPU 51, GPU 59, ROM 52, RAM 53, storage device 54, display 55, input unit 56, reading device 57, and communication unit 58. The computer 5 may be provided with a touch panel, which may implement the input unit 56 and display 55.

In computer 5, program 540 is read in advance from recording medium M1 via reader 57 and stored in storage device 54. Program 540 may also be stored in storage device 54 via a network. CPU 51 and GPU 59 execute arithmetic processing using RAM 53 and storage device 54 in accordance with program 540. CPU 51 and GPU 59 function as arithmetic units in computer 5. Other components that function as arithmetic units may also be employed in addition to CPU 51 and GPU 59.

Figure 4 is a block diagram showing the functional configuration realized by the computer 5. In the drawing device 1, the control unit 6 is realized by the computer 5 executing arithmetic processing and the like in accordance with the program 540. That is, the CPU 51, GPU 59, ROM 52, RAM 53, storage device 54, etc. of the computer 5 realize the control unit 6. All or part of the control unit 6 may be realized by a dedicated electrical circuit, or each function may be realized by an individual program. The control unit 6 may also be realized by multiple computers. In Figure 4, the movement mechanism 3, drawing unit 4, and measurement unit 22 are also shown as blocks.

The control unit 6 includes a stage control unit 60 and a drawing control unit 69. The drawing control unit 69 controls the drawing unit 4. The stage control unit 60 includes a memory unit 61, an approximate equation acquisition unit 62, an estimator construction unit 63, and a movement control unit 66. The memory unit 61 stores a set of measurement values 611 of the main scanning position and sub-scanning position of the stage 21 acquired by the measurement unit 22 when the stage 21 moves in the main scanning direction. The approximate equation acquisition unit 62 obtains an approximate equation indicating the relationship between the main scanning position and the sub-scanning position from the set of measurement values 611. The estimator construction unit 63 constructs a residual estimator 631 that estimates the residual, which is the difference between the sub-scanning position indicated by the set of measurement values 611 and the sub-scanning position indicated by the approximate equation.

The movement control unit 66 includes a residual acquisition unit 661, a coefficient acquisition unit 662, an approximate value calculation unit 663, an estimated position acquisition unit 664, and a correction control unit 665. The residual acquisition unit 661 acquires an estimated value of the residual using the residual estimator 631. The coefficient acquisition unit 662 performs online learning to estimate the coefficients in the approximate formula and acquires an estimated value of the coefficients. The approximate value calculation unit 663 calculates an approximate value of the sub-scanning position using the approximate formula to which the estimated value of the coefficients is applied. The estimated position acquisition unit 664 acquires an estimated position of the sub-scanning position by adding the estimated value of the residual to the approximate value. The correction control unit 665 moves the stage 21 in the sub-scanning direction based on the difference between the estimated position of the sub-scanning position and a predetermined target position.

Next, the preparations for the drawing process in the drawing device 1 will be described with reference to FIG. 5. In the preparations for the drawing process, the control unit 6 controls the movement mechanism 3 to position the stage 21 at one of multiple target positions in the sub-scanning direction (hereinafter referred to as the "target position"). As described above, in the drawing process, a pattern is drawn in one strip-shaped area on the substrate 9 by a single continuous movement of the stage 21 in the main scanning direction (i.e., a single main scan). The multiple target positions are the sub-scanning direction positions of the multiple strip-shaped areas. The stage 21 then moves continuously in the main scanning direction. The stage 21 moves from one end to the other of its range of movement in the main scanning direction during the drawing process. In parallel with the movement of the stage 21 in the main scanning direction, the measurement unit 22 measures the main scanning position and sub-scanning position of the stage 21. In the following description, the term "main scanning position" simply refers to the measurement value of the main scanning position obtained by the measurement unit 22. The same applies to the "sub-scanning position."

As the stage 21 moves in the main scanning direction, the main scanning speed of the stage 21 at each main scanning position and the torque of the main scanning motor 332 (hereinafter simply referred to as "motor torque") are also measured by the main scanning mechanism 33. In this embodiment, the sub-scanning position, main scanning speed, and motor torque at each main scanning position are obtained while the stage 21 moves back and forth multiple times in the main scanning direction at the target position. These measurement values are stored and prepared in the memory unit 61 of the control unit 6 as a measurement value group 611 (step S11). Note that a dummy substrate may be placed on the stage 21 when obtaining the measurement value group 611.

Next, the approximate equation acquisition unit 62 of the stage control unit 60 performs a simple regression analysis using the main scanning position included in the measurement value set 611 as the explanatory variable and the sub-scanning position as the target variable. This results in a linear regression equation indicating the relationship between the main scanning position and the sub-scanning position (step S12). Figure 6 shows the change in the sub-scanning position relative to the main scanning position of the stage 21 moving in the main scanning direction at the target position, and the line of the approximate equation. In Figure 6, line L11 indicates the change in the sub-scanning position relative to the main scanning position, and line L12 indicates the approximate equation. As mentioned above, the approximate equation (hereinafter, denoted by the symbol L12, like line L12 in Figure 6) is a linear regression equation, and the approximate equation acquisition unit 62 determines the slope and intercept of the approximate equation L12 (the value of the approximate equation when the main scanning position is 0). In the following description, the slope and intercept of the approximate equation L12 are also referred to as the "trend component" and "offset component," respectively.

Once approximate expression L12 is determined, the estimator construction unit 63 determines the residual, which is the difference between the sub-scanning position indicated by the measurement value group 611 and the sub-scanning position indicated by approximate expression L12, for each main scanning position. Figure 7 shows how the residual changes with respect to the main scanning position. Machine learning is then performed using the main scanning position, main scanning speed of the stage 21, and motor torque as explanatory variables, and the residual as the objective variable, to construct (create) a residual estimator 631 (step S13).

The residual estimator 631 is a trained model that outputs residual estimates for inputs including the main scanning position, main scanning speed, and motor torque. When constructing the residual estimator 631, the parameter values included in the model and the model structure are determined. In this embodiment, the residual estimator 631 is a neural network with, for example, three input layer variables, two intermediate layers, each with 32 variables, and one output layer variable. The neural network structure (the number of input layer variables, the number of intermediate layers, the number of variables in each intermediate layer, etc.) may be modified as appropriate. The output of an acceleration sensor provided on the stage 21, the torque of the sub-scanning motor 342, etc. may also be used as explanatory variables. Supervised machine learning algorithms other than neural networks may also be used. In the residual estimator 631, the values of each input layer variable are normalized (standardized) to the order of 1, for example, by dividing the value obtained by dividing by the average value by the standard deviation.

By obtaining the approximate equation L12 (step S12) and constructing the residual estimator 631 (step S13), the change in the sub-scanning position relative to the main-scanning position is separated into the linear component, approximate equation L12, and the residual, which is a curve component. In other words, it is essentially separated into a trend component, an offset component, and a curve component. This completes the pre-preparation before the drawing process shown in Figure 5. In practice, similar operations are performed to obtain the approximate equation L12 and construct the residual estimator 631 for each target position other than the target position. Steps S11 to S13 are operations that are performed, for example, when installing the drawing device 1, and may be omitted in drawing processes for normal boards 9.

Next, the drawing process in the drawing device 1 will be described with reference to FIG. 8. In the drawing process in the drawing device 1, first, the substrate 9 is placed on the stage 21. Next, under the control of the movement control unit 66, the stage 21 is positioned at a target position in the sub-scanning direction (hereinafter referred to as the "target position", as in the advance preparation), and then continuous movement in the main scanning direction begins (step S21). In this embodiment, the stage 21 moves at a constant speed. The movement control unit 66 performs sub-scanning position correction control in parallel with the movement of the stage 21 in the main scanning direction (step S22). In the sub-scanning position correction control, an estimated sub-scanning position of the stage 21 is obtained at each time in the main scanning of the stage 21, and the position of the stage 21 in the sub-scanning direction is corrected to match the target position. The sub-scanning position correction control will be described later.

Furthermore, in synchronization with the movement of the stage 21 in the main scanning direction, the drawing control unit 69 controls the drawing unit 4 based on the drawing data (step S23). As a result, a pattern is drawn on the main surface of the substrate 9 held on the stage 21. Drawing of the pattern on the substrate 9 is performed in parallel with the correction control of the sub-scanning position. When the irradiation position of the drawing unit 4 moves from one end of the main scanning direction to the other end of the pattern drawing area (the area where the pattern is to be drawn) on the substrate 9 as a result of the movement of the stage 21 in the main scanning direction, the movement of the stage 21 in the main scanning direction is stopped (step S24). This completes drawing of the pattern on the substrate 9 at the target position, i.e., drawing of the pattern in one strip-shaped area. In practice, the above steps S21 to S24 are repeated for each target position other than the target position. In this way, the pattern is drawn over the entire pattern drawing area.

Next, sub-scanning position correction control will be described with reference to FIG. 9. In sub-scanning position correction control, an estimated sub-scanning position of the stage 21 is obtained at each time interval during the main scan of the stage 21, and the position of the stage 21 in the sub-scanning direction is corrected. Specifically, when a time during the main scan of the stage 21 (hereinafter referred to as the "target time") is taken into consideration, the measured values of the main scanning position, main scanning speed, and motor torque at the target time are first input to the residual acquisition unit 661. As described above, the main scanning position is measured by the measurement unit 22, and the main scanning speed and motor torque are measured by the main scanning mechanism 33. The residual acquisition unit 661 inputs the measured values of the main scanning position, main scanning speed, and motor torque to the residual estimator 631, thereby obtaining an estimated residual value at the target time (step S221).

In addition, the coefficient acquisition unit 662 performs online learning to estimate the offset component (intercept) of the approximation equation during the main scan of the stage 21. In this embodiment, the state space model of Equation 1 is used, and the offset component is estimated using a Kalman filter.

In Equation 1, v(t) and w(t) are white noise, and y(t) is the value obtained by subtracting the estimated residual at time t from the measured value of the sub-scanning position by the measurement unit 22 at time t. offset(t) and trend(t) are the offset and trend components at time t. Here, the trend component uses the slope (fixed value) obtained by the simple regression analysis in step S12 above. laserY(t) is the measured value of the main scanning position by the measurement unit 22 at time t. The coefficient acquisition unit 662 sequentially estimates the offset component of the approximation formula at each time using the measured values of the main scanning position and sub-scanning position by the measurement unit 22 and the estimated residual value using a Kalman filter. Therefore, an estimated value of the offset component of the approximation formula is obtained at the time of interest (step S222). The Kalman filter can obtain an estimated value of the offset component while reducing the influence of noise in the measurement values. In this processing example, the main scanning position where correction control of the sub-scanning position begins is set to the origin (Y = 0), and the initial value of the offset component in online learning is the intercept of the approximation equation obtained in step S12 above.

Next, the approximate value calculation unit 663 changes the intercept in the approximate equation to the estimated value of the offset component at the time of interest. In this approximate equation, the value of the sub-scanning position obtained for the measured value of the main scanning position at the time of interest is calculated as the approximate value of the sub-scanning position at the time of interest (step S223). In this way, the approximate value calculation unit 663 calculates the approximate value of the sub-scanning position using the approximate equation to which the estimated value of the offset component at the time of interest is applied. Note that the trend component is the slope (fixed value) obtained by the simple regression analysis in step S12 above.

The estimated position acquisition unit 664 adds the estimated residual value for the time of interest acquired by the residual acquisition unit 661 to the approximate value of the sub-scanning position at the time of interest calculated by the approximate value calculation unit 663. This acquires the estimated sub-scanning position of the stage 21 (step S224). The correction control unit 665 moves the stage 21 in the sub-scanning direction based on the difference between the estimated sub-scanning position acquired for the time of interest and the target position (step S225). For example, if the estimated sub-scanning position of the stage 21 is located on the +X side of the target position, the stage 21 is moved to the -X side by the distance of the difference. If the estimated sub-scanning position of the stage 21 is located on the -X side of the target position, the stage 21 is moved to the +X side by the distance of the difference. This positions the stage 21 at approximately the target position in the sub-scanning direction.

In practice, the operations of steps S221 to S225 are repeated at regular intervals until the irradiation position of the drawing unit 4 moves from one end of the pattern drawing area on the substrate 9 in the main scanning direction to the other (step S226). When the irradiation position of the drawing unit 4 reaches the other end of the pattern drawing area, correction control of the sub-scanning position for the target position ends (step S226). As described above, patterns are drawn for each target position other than the target position while performing the same sub-scanning position correction control as above. The interval at which the operations of steps S221 to S225 are performed may be determined arbitrarily, such as several times the control cycle. Furthermore, this interval may vary if, for example, the movement speed of the stage 21 fluctuates during one main scanning pass.

When performing drawing processing on the next substrate 9 after completing the drawing processing on one substrate 9, steps S11 to S13 in FIG. 5 are omitted, and steps S21 to S24 in FIG. 8 are performed for each target position on the next substrate 9. At this time, during drawing processing on the first substrate 9, the measurement unit 22 acquires a set of measurement values for the main scanning position and sub-scanning position of the stage 21 during drawing at each target position. As in step S12 above, the approximate equation acquisition unit 62 performs simple regression analysis using the main scanning position as the explanatory variable and the sub-scanning position as the target variable to obtain an approximate equation that shows the relationship between the main scanning position and the sub-scanning position. Then, during drawing processing on the next substrate 9, the offset component of the approximate equation acquired during the drawing processing on the first substrate 9 is used as the initial value of the offset component. As described below, if online learning is also performed on the trend component, the trend component of the approximate equation acquired during the drawing processing on the first substrate 9 may be used as the initial value of the trend component in the drawing processing on the next substrate 9.

Furthermore, if a certain amount of time has passed between the drawing process on one substrate 9 and the drawing process on the next substrate 9 (for example, the drawing process on the first substrate 9 each day), it is preferable to perform a main scan of the stage 21 and obtain a set of measurements of the main scanning position and sub-scanning position of the stage 21 using the measurement unit 22 as a confirmation step before the drawing process. In this case, an approximation formula showing the relationship between the main scanning position and the sub-scanning position is found from the set of measurements, and the offset component of the approximation formula is used as the initial value of the offset component in the drawing process on the next substrate 9.

The state of the moving mechanism 3 changes over time due to factors such as temperature and humidity. Figure 10 is a diagram illustrating the change in state of the moving mechanism 3. In Figure 10, line L31 shows the change in the value obtained by subtracting the estimated residual value (curve component) from the measured value of the sub-scanning position by the measurement unit 22 at each main scanning position during main scanning of the stage 21 after the state of the moving mechanism 3 changes from the state during preparatory work shown in Figure 5. Line L32 also shows the approximate equation obtained during preparatory work. As mentioned above, the approximate equation obtained during preparatory work (hereinafter, denoted by the symbol L32, like line L32 in Figure 10) is a linear component in the relationship between the main scanning position and the sub-scanning position. Line L31, which shows the change in the value obtained by subtracting the estimated residual value from the measured value of the sub-scanning position by the measurement unit 22, can be considered a component corresponding to the linear component. Comparing line L31 in Figure 10 with approximation L32, it can be seen that the trend component (slope) changes slightly due to changes in the state of the movement mechanism 3, but the offset component (intercept) changes significantly.

Figure 11 is a diagram illustrating the accuracy of correction control of the sub-scanning position. In Figure 11, line L41 shows the change in the difference (hereinafter referred to as "error") between the measured value of the sub-scanning position by the measurement unit 22 at each time during main scanning and the target position when performing correction control of the sub-scanning position of Figure 9 after the state of the moving mechanism 3 changes from the state during the preliminary preparation of Figure 5, omitting online learning in step S222 and using the approximate equation obtained in the preliminary preparation as is. Line L42 also shows the change in the error when online learning in step S222 is performed. Figure 11 shows that performing online learning re-learns the offset component, resulting in a smaller error than when online learning is omitted. Thus, performing online learning in correction control of the sub-scanning position enables adaptation to changes in the state of the moving mechanism 3, enabling accurate control of the position in the sub-scanning direction (i.e., improved control performance).

In the above processing example, with regard to changes in the state of the moving mechanism 3, the offset component is assumed to be a component that changes over time, while the curve component and trend component are components that do not change over time, and online learning is performed only on the offset component. However, both the offset component and trend component may also be treated as components that change over time and online learning may be performed. In this case, in step S222, estimated values of the offset component and trend component are obtained by online learning (Kalman filter) using Equation 2, and in step S223, an approximate value of the sub-scanning position is obtained using an approximation formula that applies the estimated values of the offset component and trend component.

Depending on the structure of the movement mechanism 3, only the trend component may be treated as the component that changes over time. In this way, the stage control unit 60 performs online learning to estimate at least one coefficient in the approximation formula. In the correction control of the sub-scanning position, a regression formula of second order or higher may be used as the approximation formula. In this case, too, in step S222, online learning is performed to estimate at least one coefficient in the approximation formula.

As described above, the movement control method for controlling the movement mechanism 3 that moves the stage 21 includes a preparatory step (step S12) of calculating an approximate equation indicating the relationship between the main scanning position and the sub-scanning position from a set of measured values 611 of the main scanning and sub-scanning positions of the stage 21 acquired by the measurement unit 22 as the stage 21 moves in the main scanning direction, and a step (step S13) of constructing a residual estimator 631 that estimates the residual based on the main scanning position, etc., using the difference between the sub-scanning position indicated by the set of measured values 611 and the sub-scanning position indicated by the approximate equation for each main scanning position as the residual. The movement control method also includes a step (step S21) of moving the stage 21 in the main scanning direction during pattern writing, and a step (step S22) of acquiring an estimated sub-scanning position of the stage 21 at predetermined intervals and correcting the position of the stage 21 in the sub-scanning direction to match a predetermined target position, while performing step S21.

In step S22, at each time, the residual estimator 631 acquires an estimated residual value using the main scanning position measurement value obtained by the measurement unit 22 (step S221). At that time, the residual estimator 631 performs online learning to estimate at least one coefficient (the offset component and/or trend component in the above example) in the approximation formula using the sub-scanning position measurement value obtained by the measurement unit 22 and the residual estimate value obtained by the measurement unit 22, and acquires an estimated value of that coefficient (step S222). Next, the approximation formula to which the estimated coefficient value at that time is applied is used to obtain an approximate value of the sub-scanning position at that time (step S223). The estimated and approximate residual values at that time are used to acquire an estimated sub-scanning position (step S224). Finally, the stage 21 is moved in the sub-scanning direction based on the difference between the estimated sub-scanning position acquired for that time and the target position (step S225).

Here, consider a comparative example in which a trained model is constructed that directly obtains an estimated sub-scanning position. In this comparative example, if the state of the moving mechanism 3 changes due to device relocation or aging, the trained model must be re-trained, but re-training requires a huge amount of data and takes a long time. In contrast, the above-mentioned method of online learning to estimate the coefficients of the approximation equation allows for sequential (short-term) re-training without acquiring a huge amount of data. Furthermore, advanced estimation of curve components is performed using the residual estimator 631. As a result, even if the state of the moving mechanism 3 changes, it is possible to adaptively control the position of the stage 21 in the sub-scanning direction during main scanning, thereby improving control performance. Note that the above-mentioned movement control may be used in combination with feedback control, etc.

Preferably, the approximation equation determined in step S12 is a linear regression equation, and the coefficient estimated in the online learning in step S222 is the intercept and/or slope of the linear regression equation. This makes it possible to more reliably improve the control performance of the position in the sub-scanning direction when the linear component in the relationship between the main scanning position and the sub-scanning position fluctuates due to changes in the state of the movement mechanism 3.

The drawing method includes a movement step in which the stage 21 is moved in the main scanning direction using the movement control method described above, and a drawing step in which a pattern is drawn on the substrate 9 held on the stage 21 by controlling the drawing unit 4 in synchronization with the movement of the stage 21 in the main scanning direction. As described above, the movement step improves the positional accuracy of the stage 21 in the sub-scanning direction during main scanning, allowing the pattern to be drawn accurately on the substrate 9.

Preferably, when the movement process and drawing process are repeated for another substrate 9 after the drawing process for one substrate 9 is completed, steps S12 and S13 (preparation) in the movement control method are omitted in the movement process for the other substrate 9. Furthermore, the initial value of the coefficient in the online learning in step S222 is determined from the relationship between the main scanning position and the sub-scanning position acquired in the movement process for the substrate 9 on which drawing was performed immediately before. This makes it possible to accurately estimate the coefficient of the approximation formula in the movement process for the other substrate 9.

The online learning in step S222 of the above movement control can also be performed using a method other than a Kalman filter. For example, an extended Kalman filter, an unscented Kalman filter, an ensemble Kalman filter, a particle filter, etc. can be used. While these filters offer greater versatility, they also require a greater amount of calculation. Therefore, from the perspective of obtaining coefficient estimates with a minimal amount of calculation, it is preferable to perform online learning using a Kalman filter.

The stage control unit 60, which is a movement control device, executes the movement control method and includes an approximate equation acquisition unit 62 that calculates the approximate equation, an estimator construction unit 63 that constructs the residual estimator 631, and a movement control unit 66 that corrects the position of the stage in the sub-scanning direction while moving the stage 21 in the main scanning direction. The movement control unit 66 includes a residual acquisition unit 661 that acquires an estimated residual value using the residual estimator 631 at each time during main scanning of the stage 21, a coefficient acquisition unit 662 that performs online learning at that time and acquires estimated values of the coefficients of the approximate equation, an approximate value calculation unit 663 that calculates an approximate value of the sub-scanning position using the approximate equation to which the estimated coefficient value at that time is applied, an estimated position acquisition unit 664 that acquires an estimated sub-scanning position using the estimated and approximate residual value at that time, and a correction control unit 665 that moves the stage 21 in the sub-scanning direction based on the difference between the estimated sub-scanning position and the target position. This enables adaptive control of the position of the stage 21 in the sub-scanning direction during main scanning.

Various variations are possible with the above movement control method, drawing method, and movement control device.

In the above embodiment, a residual estimator 631 is constructed that receives inputs of the main scanning position, the torque of the main scanning motor 332, and the main scanning speed of the stage 21, but one of the motor torque and the main scanning speed may be omitted. In other words, the residual estimator 631 may be a trained model that outputs an estimated residual value for inputs that include the torque of the main scanning motor 332 included in the movement mechanism 3 and/or the main scanning speed of the stage 21, and the main scanning position of the stage 21.

Depending on the control performance required in the movement control method, the residual estimator 631 may output an estimated value of the residual from, for example, a table or function. The table or function may specify an estimated value of the residual based solely on the main scanning position of the stage 21. In this way, the residual estimator 631 may estimate the residual based on at least the main scanning position. In this case, in step S221, the residual estimator 631 obtains an estimated value of the residual using at least the measured value of the main scanning position by the measurement unit 22. On the other hand, to accurately estimate the residual, it is preferable that the residual estimator 631 be the above-mentioned trained model.

In the measurement unit 22, the main scanning position and sub-scanning position of the stage 21 may be measured by means other than a laser length measuring device.

The main scanning direction and sub-scanning direction in the movement mechanism 3 need only intersect with each other, and depending on the design of the movement mechanism 3, the main scanning direction and sub-scanning direction may intersect at an acute angle.

The drawing unit 4 may be configured to irradiate the substrate 9 with an electron beam or the like.

The substrate 9 held on the stage 21 may be a substrate other than a semiconductor substrate (for example, a glass substrate or a printed wiring board). The object moved by the movement mechanism 3 may be something other than the stage 21. For example, if the drawing unit 4 in the drawing device 1 moves in the main scanning direction, the drawing unit 4 may be the object. The movement control method described above may also be used in devices other than the drawing device 1.

The above movement control method obtains an estimated value of the sub-scanning position, which changes in response to fluctuations in the main-scanning position of the stage 21. If the main-scanning position and sub-scanning position are referred to as the first parameter and the second parameter, respectively, then the above technique can be understood as an estimation method for estimating the value of the second parameter, which changes in response to fluctuations in the value of the first parameter. This estimation method includes the steps of: determining an approximate equation indicating the relationship between the value of the first parameter and the value of the second parameter from a set of measured values 611 of the first parameter and the second parameter obtained by the measurement unit 22 when the value of the first parameter fluctuates (step S12); constructing a residual estimator 631 that estimates the residual based on at least the value of the first parameter, using the difference between the value of the second parameter indicated by the set of measured values 611 and the value of the second parameter indicated by the approximate equation for each value of the first parameter as the residual (step S13); and obtaining an estimated value of the second parameter at each time at a predetermined interval while the value of the first parameter fluctuates (step S22).

The acquisition of the estimated value of the second parameter involves, at each time, a step (step S221) of acquiring an estimated value of the residual using the residual estimator 631 using at least the measured value of the first parameter by the measurement unit 22, and a step (step S222) of performing online learning to estimate at least one coefficient in an approximate equation using the measured value of the second parameter by the measurement unit 22 and the estimated value of the residual at that time, thereby acquiring an estimated value of that coefficient. Next, a step (step S223) of calculating an approximate value of the second parameter at that time using the approximate equation to which the estimated value of the coefficient at that time is applied, and a step (step S224) of acquiring an estimated value of the second parameter using the estimated value and approximate value of the residual at that time are performed. This allows the value of the second parameter to be adaptively estimated. The above estimation method can be used for various control purposes other than movement control. For example, in fluid flow control, the above estimation method may be used with the valve opening as the first parameter and the fluid flow rate as the second parameter. The above estimation method may also be used for purposes other than control.

The configurations in the above embodiments and variations may be combined as appropriate as long as they are not mutually inconsistent.

3 Movement mechanism 4 Drawing unit 5 Computer 9 Board 21 Stage 22 Measurement unit 60 Stage control unit 62 Approximation formula acquisition unit 63 Estimator construction unit 66 Movement control unit 332 Main scanning motor 540 Program 611 Measurement value group 631 Residual estimator 661 Residual acquisition unit 662 Coefficient acquisition unit 663 Approximation value calculation unit 664 Estimated position acquisition unit 665 Correction control unit S11 to S13, S21 to S24, S221 to S226 Steps

Claims (9)

A movement control method for controlling a movement mechanism that moves an object in a main scanning direction and a sub-scanning direction that intersect with each other, comprising:
a) determining an approximation formula indicating a relationship between the main scanning position and the sub-scanning position from a group of measurements of the main scanning position and the sub-scanning position of the object acquired by a measurement unit while the object is moving in the main scanning direction;
b) constructing a residual estimator that estimates a residual based on at least the main scanning position, the residual being the difference between the sub-scanning position indicated by the group of measurement values and the sub-scanning position indicated by the approximation formula;
c) moving the object in the main scanning direction;
d) acquiring an estimated position of the sub-scanning position of the object at each time point at a predetermined interval while performing the c) step, and correcting the position of the object in the sub-scanning direction to match a predetermined target position;
Equipped with
The step d)
d1) at each time, acquiring an estimated value of the residual by the residual estimator using at least the measurement value of the main scanning position by the measurement unit;
d2) performing online learning at each time point to estimate at least one coefficient in the approximation formula using the measured value of the sub-scanning position by the measurement unit and the estimated value of the residual, and acquiring an estimated value of the at least one coefficient;
d3) calculating an approximate value of the sub-scanning position at each time by using the approximate expression to which the estimated value of the at least one coefficient at each time is applied;
d4) obtaining the estimated position of the sub-scanning position using the estimated value and the approximate value of the residual at each time;
d5) moving the object in the sub-scanning direction based on a difference between the estimated position of the sub-scanning position acquired for each time and the target position;
A movement control method comprising: The movement control method according to claim 1,
the approximation equation is a linear regression equation,
The movement control method, wherein the at least one coefficient is an intercept and/or a slope of the linear regression equation. The movement control method according to claim 1,
A movement control method in which the online learning is performed by a Kalman filter. The movement control method according to claim 1,
A movement control method, wherein the residual estimator is a trained model that outputs the estimated value of the residual in response to inputs including the torque of a main scanning motor included in the movement mechanism and/or the main scanning speed of the object, and the main scanning position. A method for drawing a pattern on a substrate, comprising:
a moving step of moving the stage, which is the object, in the main scanning direction by the movement control method according to any one of claims 1 to 4;
a drawing step of drawing a pattern on a substrate held on the stage by controlling a drawing unit in synchronization with movement of the stage in the main scanning direction;
A drawing method comprising: 6. The drawing method according to claim 5,
After the drawing step is completed, the moving step and the drawing step are repeated for another substrate;
A drawing method in which, in the movement process for the other substrate, the a) and b) steps in the movement control method are omitted, and the initial value of the at least one coefficient in the online learning of the d2) step is determined from the relationship between the main scanning position and the sub-scanning position obtained in the movement process for the substrate on which drawing was performed immediately before. An estimation method for estimating a value of a second parameter that changes in response to a variation in a value of a first parameter, comprising:
a) determining an approximation formula indicating a relationship between a value of the first parameter and a value of the second parameter from a group of measured values of the first parameter and the second parameter acquired by a measurement unit when the value of the first parameter fluctuates;
b) constructing a residual estimator that estimates a residual based on at least the value of the first parameter, the residual being a difference between the value of the second parameter indicated by the group of measured values and the value of the second parameter indicated by the approximate expression;
c) obtaining an estimate of the second parameter at each time point at a predetermined interval while the value of the first parameter is varying;
Equipped with
The step c) is
c1) at each time instant, acquiring an estimate of the residual by the residual estimator using at least the measurement value of the first parameter by the measurement unit;
c2) performing online learning at each time point to estimate at least one coefficient in the approximation formula using the measurement value of the second parameter by the measurement unit and the estimated value of the residual, and obtaining an estimated value of the at least one coefficient;
c3) calculating an approximate value of the second parameter at each time using the approximate formula to which the estimated value of the at least one coefficient at each time is applied;
c4) obtaining the estimated value of the second parameter using the estimated value and the approximated value of the residual at each time;
An estimation method comprising: A computer-readable program that causes a computer to control a movement mechanism that moves an object in a main scanning direction and a sub-scanning direction that intersect with each other, wherein the execution of the program by a computer includes causing the computer to:
a) determining an approximation formula indicating a relationship between the main scanning position and the sub-scanning position from a group of measurements of the main scanning position and the sub-scanning position of the object acquired by a measurement unit while the object is moving in the main scanning direction;
b) constructing a residual estimator that estimates a residual based on at least the main scanning position, the residual being the difference between the sub-scanning position indicated by the group of measurement values and the sub-scanning position indicated by the approximation formula;
c) moving the object in the main scanning direction;
d) acquiring an estimated position of the sub-scanning position of the object at each time point at a predetermined interval while performing the c) step, and correcting the position of the object in the sub-scanning direction to match a predetermined target position;
Execute
The step d)
d1) at each time, acquiring an estimated value of the residual by the residual estimator using at least the measurement value of the main scanning position by the measurement unit;
d2) performing online learning at each time to estimate at least one coefficient in the approximation formula using the measured value of the sub-scanning position by the measurement unit and the estimated value of the residual, and acquiring an estimated value of the at least one coefficient;
d3) calculating an approximate value of the sub-scanning position at each time by using the approximate expression to which the estimated value of the at least one coefficient at each time is applied;
d4) obtaining the estimated position of the sub-scanning position using the estimated value and the approximate value of the residual at each time;
d5) moving the object in the sub-scanning direction based on a difference between the estimated position of the sub-scanning position acquired for each time and the target position;
A computer readable program comprising: A movement control device that controls a movement mechanism that moves an object in a main scanning direction and a sub-scanning direction that intersect with each other,
an approximate equation acquisition unit that obtains an approximate equation indicating a relationship between the main scanning position and the sub-scanning position from a group of measurement values of the main scanning position and the sub-scanning position of the object acquired by a measurement unit when the object moves in the main scanning direction;
an estimator constructing unit that constructs a residual estimator that estimates a residual based on at least the main scanning position, using a difference between the sub-scanning position indicated by the measurement value group and the sub-scanning position indicated by the approximation formula as a residual for each main scanning position;
a movement control unit that acquires an estimated position of the sub-scanning position of the object at each time point at a predetermined interval while moving the object in the main scanning direction, and corrects the position of the object in the sub-scanning direction to match a predetermined target position;
Equipped with
The movement control unit
a residual error acquisition unit that acquires an estimated value of the residual error by the residual error estimator using at least the measurement value of the main scanning position obtained by the measurement unit at each time;
a coefficient acquisition unit that performs online learning to estimate at least one coefficient in the approximation formula using the measurement value of the sub-scanning position by the measurement unit and the estimated value of the residual at each time, and acquires an estimated value of the at least one coefficient;
an approximate value calculation unit that calculates an approximate value of the sub-scanning position at each time by using the approximate expression to which the estimated value of the at least one coefficient at each time is applied;
an estimated position acquisition unit that acquires the estimated position of the sub-scanning position using the estimated value and the approximate value of the residual at each time;
a correction control unit that moves the object in the sub-scanning direction based on a difference between the estimated position of the sub-scanning position acquired for each time and the target position;
A movement control device comprising: