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

Abstract

As preliminary preparation, from a measured value group (611) of main scanning positions and sub-scanning positions of an object, an appropriate expression indicating the relationship between the main scanning positions and the sub-scanning positions is obtained, and a residual estimator (631) for estimating a residual on the basis of the main scanning position or the like is constructed, the residual being a difference between a sub-scanning position indicated by the measured value group (611) for each main scanning position and a sub-scanning position indicated by the approximate expression. During main scanning of the object, at each time point, an estimated value of the residual is acquired by the residual estimator (631) using the measured value or the like of the main scanning position obtained by a measurement unit (22). Online training is performed using the measured value of the sub-scanning position obtained by the measurement unit (22) and the estimated value of the residual, and the estimated value of a coefficient in the approximate expression is acquired. An approximate value of the sub-scanning position is obtained using the approximate expression to which the estimated value of the coefficient is applied. The estimated position of the sub-scanning position is acquired using the estimated value of the residual and the approximate value, and the position of the object in the sub-scanning direction is corrected.

Description

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

[0001] The present invention relates to a technique for controlling a moving mechanism and a technique for estimating parameter values. [Reference to Related Applications] This application claims the benefit of priority from Japanese Patent Application JP2024-69741, filed on April 23, 2024, the entire disclosure of which is incorporated herein by reference.

[0002] 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, etc. However, even if a control device that uses a machine learning model is optimized at a certain point in time, it may no longer be able to achieve the desired control performance due to the relocation or aging of the device.

[0003] Therefore, Japanese Patent Laid-Open Publication No. 2022-11044 (Document 1) proposes a method for redetermining parameter values ​​through reinforcement learning in a control device using a neural network. This method suppresses a decrease in control accuracy due to changes in the state of the controlled object. The control device of Japanese Patent Laid-Open Publication No. 2022-92690 (Document 2) includes a first compensator that generates a first signal based on a control deviation, a corrector that corrects the control deviation using one of multiple adjusters 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 signal and the second signal. Since the time required to adjust the multiple adjusters 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 in the state of the controlled object or changes in the disturbance environment occur.

[0004] In the exposure apparatus of JP 2022-137849 A (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 the straightness correction table. This ensures straightness when driving the stage in the main scanning direction, and makes it possible to irradiate light from the exposure head to an appropriate position on the substrate placed on the stage.

[0005] However, when using a correction table to correct the position of an object in the sub-scanning direction during a main scan, as in Literature 3, it is necessary to re-acquire the correction table when changes in the state occur, such as relocating the device or changes over time. Even with the method of Literature 1, which uses reinforcement learning of a neural network, it is difficult to estimate the amount of training data required in advance, and operating an actual device to acquire training data may require an unrealistic amount of data. Furthermore, the method of Literature 2 requires determining optimal parameters for multiple adjustment units in accordance with anticipated changes in the control state, which may make it difficult to suppress a decrease in control accuracy depending on the state change. Therefore, a new method is needed 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.

[0006] The present invention aims to adaptively control the position of an object in the sub-scanning direction during main scanning, and also aims to adaptively estimate the value of a second parameter that changes in accordance with fluctuations in the value of a first parameter.

[0007] A first aspect of the present invention is 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, the method comprising: a) a step of determining an approximation equation that indicates 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 is moved 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 a 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 the c) step, and correcting the position of the object in the sub-scanning direction to match a predetermined target position, wherein the d) step 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 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 determine 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 the approximate value of the residual at each time; and 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.

[0008] According to the present invention, the position of an object in the sub-scanning direction during main scanning can be adaptively controlled.

[0009] A second aspect of the present invention is the movement control method of the first aspect, wherein the approximation equation is a linear regression equation, and the at least one coefficient is an intercept and / or a slope of the linear regression equation.

[0010] Aspect 3 of the present invention is the movement control method of aspect 1 (which may be aspect 1 or 2), in which the online learning is performed by a Kalman filter.

[0011] 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.

[0012] Aspect 5 of the present invention is a drawing method for drawing a pattern on a substrate, comprising: a movement step of moving the target object, a stage, in the main scanning direction by 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.

[0013] A sixth aspect of the present invention is a drawing method according to the fifth aspect, wherein, after the drawing process is completed, the moving process and the drawing process are repeated for another substrate, and in the moving process for the other substrate, steps a) and b) in 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 moving process for the substrate on which drawing was performed immediately before.

[0014] A seventh aspect of the present invention is a method for estimating a value of a second parameter that changes in response to fluctuations in the value of a first parameter, the method 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 the residual based on at least the value of the first parameter, using 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 approximation formula for each value of the first parameter as a residual; and c) acquiring an estimate of the second parameter at each time at a predetermined interval while the value of the first parameter fluctuates; The c) step includes: 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) at each time instant, performing online learning to estimate at least one coefficient in the approximation formula using the measurement value of the second parameter by the measurement unit and the estimate of the residual, and acquiring an estimate of the at least one coefficient; c3) at each time instant, using the approximation formula to which the estimate of the at least one coefficient at each time instant is applied, to obtain an approximation of the second parameter at each time instant; and c4) acquiring the estimate of the second parameter by using the estimate and the approximation of the residual at each time instant. In Aspect 7 of the present invention, the value of the second parameter can be adaptively estimated.

[0015] 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 a main scanning direction and a sub-scanning direction that intersect with each other, and 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 from a group of measurement values ​​of the main scanning position and the sub-scanning position of the object, the measurement values ​​being acquired by a measurement unit when the object is moved 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. the d) step comprises: 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) determining 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; d4) acquiring the estimated position of the sub-scanning position using the estimated value and the approximate value of the residual at each time; and 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.

[0016] A ninth aspect of the present invention is 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, the movement control device comprising: an approximation equation acquisition unit that obtains an approximation equation that indicates 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 is moved 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 a 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 that, at each time point, acquires an estimated position of the sub-scanning position of the object the residual acquisition unit is configured to acquire 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 is configured to perform 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 acquire an estimated value of the at least one coefficient; an approximate value calculation unit is configured to calculate 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 is configured to acquire the estimated position of the sub-scanning position using the estimated value and the approximate value of the residual at each time; and a correction control unit is configured to move 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.

[0017] The above and other objects, features, aspects and advantages will become more apparent from the following detailed description of the invention which proceeds with reference to the accompanying drawings.

[0018] 1 is a front view showing a drawing device; FIG. 2 is a side view showing a drawing device; FIG. 3 is a diagram showing the configuration of a computer; FIG. 4 is a block diagram showing the functional configuration realized by the computer; FIG. 5 is a diagram showing the flow of advance preparation for drawing processing; FIG. 6 is a diagram showing changes in sub-scanning position relative to main scanning position, and lines of an approximation equation; FIG. 7 is a diagram showing changes in residual error relative to main scanning position; FIG. 8 is a diagram showing the flow of drawing processing in a drawing device; FIG. 9 is a diagram showing the flow of correction control of sub-scanning position; FIG. 10 is a diagram for explaining changes in the state of a moving mechanism; and FIG. 11 is a diagram for explaining the accuracy of correction control of sub-scanning position.

[0019] FIG. 1 is a front view of a drawing apparatus 1 according to one embodiment of the present invention, and FIG. 2 is a side view of the drawing apparatus 1. The drawing apparatus 1 is a direct drawing apparatus (also called an exposure apparatus) that irradiates a main surface of a substrate 9, such as a semiconductor substrate coated with a photosensitive material, with spatially modulated light to draw a pattern on the main surface. In FIGS. 1 and 2, the X, Y, and Z directions, which are orthogonal to each other, 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.

[0020] The imaging device 1 includes a base 10, a stage 21, a moving mechanism 3, a measuring unit 22, an imaging unit 4, and a computer 5. As will be described later, the computer 5 is responsible for overall control of the imaging device 1. The base 10 is a support table that supports the moving mechanism 3 and the imaging 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 fix the substrate 9 and multiple suction holes that suction the substrate 9.

[0021] The moving mechanism 3 is a mechanism for transporting the stage 21. The moving mechanism 3 moves the stage 21 in the Y direction and the X direction relative to the base 10. As will be described later, in 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 FIGS. 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.

[0022] 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 in the sub-scanning direction. Each main scanning guide 331 extends linearly along the main scanning direction. For example, an air guide is used as the main scanning guide 331, and the main scanning plate 31 is guided in the main scanning direction in a levitated state.

[0023] 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 driving 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 be configured to move the stage 21 using, for example, a rotary motor and a ball screw (the same applies to the sub-scanning mechanism 34).

[0024] 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 along the sub-scanning direction. For example, a ball guide is used for the sub-scanning guide 341, and it smoothly guides the sub-scanning plate 32 in the sub-scanning direction relative to the main scanning plate 31.

[0025] 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 driving 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.

[0026] 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.

[0027] 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 an 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 disposed 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 the mirror 251 are not shown in FIG. 1.

[0028] As shown in FIG. 1 , the mirror 252 is fixed to the edge of the stage 21 in the sub-scanning direction. The sub-scanning length measuring device 24 is a laser length measuring device and is disposed opposite the mirror 252 in the sub-scanning direction. The sub-scanning length measuring device 24 emits laser light toward the mirror 252 and receives the laser light reflected by the mirror 252. The sub-scanning length measuring device 24 measures the position of the stage 21 in the sub-scanning direction (hereinafter simply referred to as the "sub-scanning position") based on the phase difference between the emitted light and the reflected light, and outputs the measured value to the computer 5. In the example shown in FIGS. 1 and 2 , the mirrors 251 and 252 are attached to the side of the stage 21. However, they may also be provided upright on the top surface of the stage 21. 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. However, the drawing apparatus 1 may be provided with a main-scanning encoder and a sub-scanning encoder as needed.

[0029] As shown in FIGS. 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 disposed 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 Grating Light Valve (GLV) (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 Digital Micromirror Device (DMD) in which multiple micromirrors are two-dimensionally arranged.

[0030] In the drawing process in the drawing apparatus 1, the main scanning mechanism 33 continuously moves the substrate 9 (and the 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 upper surface of the substrate 9. Furthermore, the control unit 6, which will be described later, controls the spatial light modulator of the drawing unit 4 in synchronization with the movement of the irradiation position on the upper surface. As a result, the drawing unit 4 draws a pattern in a strip-shaped region extending in the main scanning direction on the upper surface. Next, the sub-scanning mechanism 34 moves the substrate 9 a predetermined distance in the sub-scanning direction. Thereafter, while the substrate 9 moves in the main scanning direction, the spatial light modulator of the drawing unit 4 is controlled to draw a pattern in another strip-shaped region. 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 approximately the entire upper surface.

[0031] FIG. 3 is a diagram showing the configuration of the computer 5. The computer 5 has a typical computer system configuration including a CPU 51, a ROM 52, a RAM 53, a storage device 54, a display 55, an input unit 56, a reading device 57, a communication unit 58, a GPU 59, and a bus 50. The CPU 51 performs various arithmetic operations. The GPU 59 performs various arithmetic operations related to image processing and the like. The ROM 52 stores basic programs. The RAM 53 and the storage device 54 store various types of information. The display 55 displays various types of information such as images. The input unit 56 includes a keyboard 56a and a mouse 56b for receiving input from an operator. The reading device 57 reads information from a computer-readable recording medium M1 such as an optical disk, a magnetic disk, a magneto-optical disk, or a memory card. The communication unit 58 transmits and receives signals between the movement mechanism 3 and the drawing unit 4. The bus 50 is a signal circuit that connects the CPU 51, the GPU 59, the ROM 52, the RAM 53, the storage device 54, the display 55, the input unit 56, the reading device 57, and the communication unit 58. The computer 5 may be provided with a touch panel, and the input unit 56 and the display 55 may be realized by the touch panel.

[0032] In the computer 5, the program 540 is read in advance from the recording medium M1 via the reading device 57 and stored in the storage device 54. The program 540 may be stored in the storage device 54 via a network. The CPU 51 and the GPU 59 execute arithmetic processing using the RAM 53 and the storage device 54 in accordance with the program 540. The CPU 51 and the GPU 59 function as a calculation unit in the computer 5. Other components that function as a calculation unit may be employed in addition to the CPU 51 and the GPU 59.

[0033] 4 is a block diagram showing the functional configuration realized by the computer 5. In the drawing device 1, the computer 5 executes arithmetic processing and the like in accordance with a program 540, thereby realizing the control unit 6. 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 electric circuit, or each function may be realized by an individual program. The control unit 6 may also be realized by multiple computers. In FIG. 4, the moving mechanism 3, drawing unit 4, and measurement unit 22 are also shown as blocks.

[0034] 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 measurement value set 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 measurement value set 611. The estimator construction unit 63 constructs a residual estimator 631 that estimates a residual, which is the difference between the sub-scanning position indicated by the measurement value set 611 and the sub-scanning position indicated by the approximate equation.

[0035] 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 coefficients in the approximate formula and acquires estimated values ​​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 values ​​of the coefficients are 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.

[0036] Next, the preparation for the drawing process in the drawing apparatus 1 will be described with reference to FIG. 5 . In the preparation for the drawing process, first, under the control of the control unit 6, the movement mechanism 3 positions 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 region on the substrate 9 by one continuous movement of the stage 21 in the main scanning direction (i.e., one main scan). The multiple target positions are the positions of the multiple strip-shaped regions in the sub-scanning direction. Next, the stage 21 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 the 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 measured by the measurement unit 22. The same applies to the "sub-scanning position."

[0037] 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 reciprocates multiple times in the main scanning direction at the target position. These measurement values ​​are stored and prepared as a measurement value group 611 in the memory unit 61 of the control unit 6 (step S11). Note that a dummy substrate may be placed on the stage 21 when the measurement value group 611 is obtained.

[0038] 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 an explanatory variable and the sub-scanning position as a response variable. This results in a linear regression equation indicating the relationship between the main scanning position and the sub-scanning position (step S12). FIG. 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 FIG. 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 FIG. 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.

[0039] Once approximate expression L12 is determined, the estimator construction unit 63 determines a 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 is a diagram showing how the residual changes with respect to the main scanning position. Then, machine learning is performed using the main scanning position, the main scanning speed of the stage 21, and the motor torque as explanatory variables and the residual as a target variable, and a residual estimator 631 is constructed (created) (step S13).

[0040] The residual estimator 631 is a trained model that outputs an estimated residual value for inputs including the main scanning position, the main scanning speed, and the 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 having, for example, three input layer variables, two intermediate layers, each with 32 variables, and one output layer variable. The structure of the neural network (the number of input layer variables, the number of intermediate layers, the number of variables in each intermediate layer, etc.) may be changed 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. A supervised machine learning algorithm other than a neural network may also be used. In the residual estimator 631, the value of each variable in the input layer is normalized (standardized) to the order of 1, for example, by dividing the value obtained by dividing by the average value by the standard deviation.

[0041] 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 divided into the approximate equation L12, which is a linear component, and the residual, which is a curve component; that is, the change is essentially divided into a trend component, an offset component, and a curve component. This completes the preparations prior to the drawing process shown in FIG. 5 . In practice, the approximate equation L12 is obtained and the residual estimator 631 is constructed by similar operations for each target position other than the target position. The above steps S11 to S13 are operations that are performed, for example, when the drawing apparatus 1 is installed, and may be omitted in drawing processes for ordinary substrates 9.

[0042] Next, the drawing process in the drawing apparatus 1 will be described with reference to FIG. 8 . In the drawing process in the drawing apparatus 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 is initiated (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 acquired at each time during 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.

[0043] 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. The 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 due to 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 the drawing of the pattern on the substrate 9 at the target position, i.e., the 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 manner, the pattern is drawn over the entire pattern drawing area.

[0044] Next, the correction control of the sub-scanning position will be described with reference to FIG. 9 . In the correction control of the sub-scanning position, 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 in the main scan of the stage 21 (hereinafter referred to as the "target time") is taken into consideration, first, the measured values ​​of the main-scanning position, main-scanning speed, and motor torque at the target time are 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 value of the residual at the target time (step S221).

[0045] Furthermore, 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 by a Kalman filter.

[0046]

[0047] 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 component and trend component at time t. Here, the trend component uses the slope (fixed value) obtained by the simple regression analysis in step S12. 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. 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 acquire 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 starts 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.

[0048] Next, the approximate value calculation unit 663 changes the intercept in the approximate formula to the estimated value of the offset component at the time of interest. In this approximate formula, 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 formula 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.

[0049] 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.

[0050] 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 end (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. The interval between the operations of steps S221 to S225 may be determined arbitrarily, such as several times the control cycle. Furthermore, this interval may vary if, for example, the moving speed of the stage 21 during one main scanning pass fluctuates.

[0051] When performing the drawing process on the next substrate 9 after completing the drawing process 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 the drawing process on the first substrate 9, the measurement unit 22 acquires a group of measurement values ​​for the main scanning position and the sub-scanning position of the stage 21 during drawing at each target position. As in step S12 above, the approximate expression acquisition unit 62 performs a simple regression analysis using the main scanning position as the explanatory variable and the sub-scanning position as the objective variable to obtain an approximate expression that indicates the relationship between the main scanning position and the sub-scanning position. Then, during the drawing process on the next substrate 9, the offset component of the approximate expression acquired during the drawing process on the first substrate 9 is used as the initial value of the offset component. As will be described later, if online learning is also performed on the trend component, the trend component of the approximate expression acquired during the drawing process on the first substrate 9 may be used as the initial value of the trend component during the drawing process on the next substrate 9.

[0052] Furthermore, if a certain amount of time has elapsed between the drawing process on one substrate 9 and the drawing process on the next substrate 9 (for example, in the case of the first drawing process on the substrate 9 every day), it is preferable to perform a check before the drawing process by main-scanning the stage 21 and obtaining a group of measurement values ​​for the main-scanning position and sub-scanning position of the stage 21 using the measurement unit 22. In this case, an approximation formula showing the relationship between the main-scanning position and the sub-scanning position is found from the group of measurement values, 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.

[0053] The state of the moving mechanism 3 changes over time due to the influence of temperature, humidity, and the like. FIG. 10 is a diagram illustrating the change in the state of the moving mechanism 3. In FIG. 10, line L31 shows the change in the value obtained by subtracting the estimated residual value (curve component) from the measurement 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 the advance preparation shown in FIG. 5. Furthermore, line L32 shows the approximate equation obtained during the advance preparation. As described above, the approximate equation obtained during the advance preparation (hereinafter, denoted by the symbol L32, like line L32 in FIG. 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 measurement value of the sub-scanning position by the measurement unit 22, can be considered to be a component corresponding to the linear component. Comparing line L31 in FIG. 10 with approximate expression L32, it can be seen that the trend component (slope) changes slightly due to changes in the state of the moving mechanism 3, but the offset component (intercept) changes significantly.

[0054] FIG. 11 is a diagram illustrating the accuracy of correction control of the sub-scanning position. In FIG. 11, line L41 shows the change in the difference (hereinafter referred to as "error") between the measured value of the sub-scanning position measured 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 FIG. 9 after the state of the moving mechanism 3 changes from the state during the advance preparation of FIG. 5, omitting online learning in step S222 and using the approximate formula obtained in advance preparation as is. Line L42 also shows the change in the error when online learning in step S222 is performed. It can be seen from FIG. 11 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).

[0055] In the above processing example, with regard to the change 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 assumed to be components that do not change over time, and online learning is performed only on the offset component, but online learning may also be performed by treating both the offset component and the trend component as components that change over time. 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 to which the estimated values ​​of the offset component and trend component are applied.

[0056]

[0057] Depending on the structure of the moving mechanism 3, only the trend component may be treated as a 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.

[0058] As described above, the movement control method for controlling the movement mechanism 3 that moves the stage 21 includes, as a preparation step, a step (step S12) of determining an approximation equation indicating the relationship between the main scanning position and the sub-scanning position from a set of measurement values ​​611 of the main scanning position and the sub-scanning position of the stage 21 acquired by the measurement unit 22 when the stage 21 moves in the main scanning direction, and a step (step S13) of constructing a residual estimator 631 that estimates a residual based on the main scanning position, etc., using the difference between the sub-scanning position indicated by the set of measurement values ​​611 and the sub-scanning position indicated by the approximation equation for each main scanning position as a 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 estimated positions of the 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.

[0059] In step S22, the following steps are performed at each time: a step S221 in which the residual estimator 631 acquires an estimated value of the residual using the main-scanning position measurement value obtained by the measurement unit 22, and a step S222 in which online learning is performed to estimate at least one coefficient (the offset component and / or trend component in the above example) in an approximate equation using the sub-scanning position measurement value obtained by the measurement unit 22 and the residual estimate value at that time, and an estimate of the coefficient is acquired. Subsequently, the following steps are performed: a step S223 in which the approximate equation to which the estimate value of the coefficient at that time is applied is used to obtain an approximate value of the sub-scanning position at that time; a step S224 in which the estimate and approximate value of the residual at that time are used to acquire an estimated position of the sub-scanning position; and a step S225 in which the stage 21 is moved in the sub-scanning direction based on the difference between the estimated position of the sub-scanning position acquired for that time and the target position.

[0060] Consider a comparative example in which a trained model is constructed to directly obtain an estimated sub-scanning position. In this comparative example, if the state of the moving mechanism 3 changes due to device relocation, aging, or other reasons, the trained model must be retrained. However, retraining requires a huge amount of data and takes a long time. In contrast, the above-described online learning method for estimating the coefficients of the approximation equation allows for sequential (short) retraining without acquiring a huge amount of data. Furthermore, advanced estimation of the curve components is performed using the residual estimator 631. As a result, even if the state of the moving mechanism 3 changes, the position of the stage 21 in the sub-scanning direction during main scanning can be adaptively controlled, improving control performance. The above-described movement control may be combined with feedback control, etc.

[0061] Preferably, the approximation equation obtained in step S12 is a linear regression equation, and the coefficients estimated in the online learning in step S222 are 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 a change in the state of the movement mechanism 3.

[0062] The drawing method includes a moving step of moving the stage 21 in the main scanning direction by the above-described movement control method, and a drawing step of controlling the drawing unit 4 in synchronization with the movement of the stage 21 in the main scanning direction, thereby drawing a pattern on the substrate 9 held on the stage 21. As described above, in the moving step, the positional accuracy in the sub-scanning direction during the main scanning of the stage 21 is improved, so that the pattern can be drawn on the substrate 9 with high accuracy.

[0063] Preferably, when the moving step and the drawing step are repeated for another substrate 9 after the drawing step for one substrate 9 is completed, steps S12 and S13 (preparation) in the movement control method are omitted in the moving step 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 moving step 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 moving step for the other substrate 9.

[0064] The online learning in step S222 of the movement control can be performed using a filter other than the Kalman filter. For example, an extended Kalman filter, an unscented Kalman filter, an ensemble Kalman filter, a particle filter, etc. can be used. On the other hand, these filters are more versatile but require a larger amount of calculation. Therefore, from the viewpoint of obtaining coefficient estimates with a smaller amount of calculation, it is preferable to perform the online learning using the Kalman filter.

[0065] 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 21 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 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 values ​​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.

[0066] The movement control method, drawing method and movement control device can be modified in various ways.

[0067] In the above embodiment, the residual estimator 631 is constructed to receive as input 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 value of the residual in response to inputs including the torque of the main scanning motor 332 included in the moving mechanism 3 and / or the main scanning speed of the stage 21, and the main scanning position of the stage 21.

[0068] 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 a function. The table or function may specify an estimated value of the residual based only 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 acquires 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 trained model described above.

[0069] In the measuring unit 22, the main scanning position and the sub-scanning position of the stage 21 may be measured by a device other than a laser length measuring device.

[0070] The main scanning direction and the sub-scanning direction in the moving mechanism 3 only need to intersect with each other, and depending on the design of the moving mechanism 3, the main scanning direction and the sub-scanning direction may intersect at an acute angle.

[0071] The drawing unit 4 may be a unit that irradiates the substrate 9 with an electron beam or the like.

[0072] 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, when the drawing unit 4 moves in the main scanning direction in the drawing apparatus 1, the drawing unit 4 may be the object. The movement control method described above may be used in devices other than the drawing apparatus 1.

[0073] In the above-described movement control method, an estimated value of the sub-scanning position that changes in response to fluctuations in the main-scanning position of the stage 21 is obtained. If the main-scanning position and the sub-scanning position are referred to as a first parameter and a second parameter, respectively, then the above-described technique can be regarded as an estimation method for estimating the value of the second parameter that changes in response to fluctuations in the value of the first parameter. The estimation method includes a step (step S12) of determining an approximate expression indicating the relationship between the value of the first parameter and the value of the second parameter from a measurement value group 611 of the first parameter and the second parameter acquired by the measurement unit 22 when the value of the first parameter fluctuates, a step (step S13) of constructing a residual estimator 631 that estimates a residual based on at least the value of the first parameter, using the difference between the value of the second parameter indicated by the measurement value group 611 and the value of the second parameter indicated by the approximate expression as the residual, and a step (step S22) of acquiring an estimated value of the second parameter at each time at a predetermined interval while the value of the first parameter fluctuates.

[0074] 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 by 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 the coefficient. Subsequently, 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.

[0075] The configurations in the above-described embodiment and each modification may be combined as appropriate as long as they are not mutually contradictory.

[0076] While the invention has been particularly illustrated and described, it should be understood that the foregoing description is illustrative and not restrictive, and that numerous modifications and variations are possible without departing from the scope of the invention.

[0077] 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

1. 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 that indicates 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 is moved 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) a step of acquiring an estimated value of the residual by the residual estimator at each time using at least the measurement value of the main scanning position acquired by the measurement unit; d2) at each of the times, 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 obtaining 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 of the times is applied to obtain an approximate value of the sub-scanning position at each of the times; d4) using the estimated value and the approximate value of the residual at each of the times to obtain the estimated position of the sub-scanning position; and d5) moving the object in the sub-scanning direction based on a difference between the estimated position of the sub-scanning position obtained for each of the times and the target position.

2. A movement control method according to claim 1, wherein the approximation formula is a linear regression formula, and the at least one coefficient is the intercept and / or slope of the linear regression formula.

3. A mobility control method according to claim 1, wherein the online learning is performed by a Kalman filter.

4. A movement control method according to claim 1, 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.

5. A drawing method for drawing a pattern on a substrate, comprising: a movement step of moving a stage, which is the object, in the main scanning direction by a movement control method according to any one of claims 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.

6. A drawing method as claimed in claim 5, wherein, after completion of the drawing step, 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) in 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.

7. An estimation method for estimating a value of a second parameter that changes in accordance with fluctuations in the value of a first parameter, comprising: a) a step of determining an approximation formula indicating a 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 obtained 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 formula for each value of the first parameter as a residual; and c) a step of acquiring an estimate of the second parameter at each time at a predetermined interval while the value of the first parameter fluctuates; wherein the c) step comprises: c1) a step of acquiring an estimate of the residual at each time by the residual estimator using at least the measured value of the first parameter obtained by the measurement unit; c2) at each of the times, performing online learning 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) using the approximation formula to which the estimated value of the at least one coefficient at each of the times is applied to obtain an approximate value of the second parameter at each of the times; and c4) using the estimated value and the approximate value of the residual at each of the times to obtain the estimated value of the second parameter.

8. A computer-readable program that causes a computer to control a movement mechanism that moves an object in mutually intersecting main scanning and sub-scanning directions, wherein execution of the program by a computer causes the computer to execute the following steps: a) determining an approximation formula that indicates 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, the measurement values ​​being obtained by a measurement unit when the object is moved 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 the residual; c) moving the object in the main scanning direction; and d) concurrently with step c), obtaining an estimated position of the sub-scanning position of the object at each time at predetermined intervals, and correcting the position of the object in the sub-scanning direction to match a predetermined target position; and step d) is d1) at each of the time instants, 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 of the time instants, 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) determining an approximate value of the sub-scanning position at each of the time instants using the approximation formula to which the estimated value of the at least one coefficient at each of the time instants is applied; d4) acquiring the estimated position of the sub-scanning position using the estimated value and the approximate value of the residual at each of the time instants; and 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 of the time instants and the target position.

9. A movement control device that controls a movement mechanism that moves an object in mutually intersecting main scanning and sub-scanning directions, comprising: an approximate equation acquisition unit that obtains an approximate equation that indicates 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 is moved 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 approximate 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 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, wherein the movement control unit comprises: a residual acquisition unit that acquires an estimated value of the residual by the residual estimator at each time using at least the measurement values ​​of the main scanning position acquired 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 by the measurement unit and the estimated value of the residual at each time, and acquires the estimated value of the at least one coefficient; an approximate value calculation unit that uses the approximation formula to which the estimated value of the at least one coefficient at each time is applied to determine an approximate value of the sub-scanning position at each time; 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; and 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.

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