Alignment control in nanoimprint lithography using feedback and feedforward control

Abstract

A system and method for controlling the position of a movable stage supporting a substrate are provided. First position information representing the position of the substrate relative to a mark on an object is obtained from a sensor. Alignment prediction information is generated based on the obtained first position, wherein the generated alignment prediction information includes at least one parameter value. First trajectory information including the at least one parameter value is generated based on the obtained first position information and the generated alignment prediction information. Second trajectory information is generated based on the generated alignment prediction information, the first trajectory information, and the second position information, wherein the second position information represents the position of the movable stage. An output control signal is generated based on the second trajectory information, and the output control signal is used to control the movable stage to approach a target position based on the generated output signal.

Description

Technical Field

[0001] The present disclosure relates to alignment control in nanoimprint lithography, and more particularly, to real-time feedback and feedforward control. Background Art

[0002] In nanoimprint lithography, the technique of zone-by-zone alignment has been used to achieve nanometer-scale overlay accuracy. In some examples, the initial alignment error between the imprint template and the corresponding zone on the substrate can be corrected by moving the template relative to the substrate (e.g., a wafer). However, for nanoimprint lithography, fast and consistent alignment is a challenge. More specifically, changes in the initial state and dilute liquid friction are two major difficulties. Current alignment schemes typically utilize a single control algorithm that can be manually adjusted via an adjustment knob. In addition to the conventional disadvantages associated with manually adjusting control algorithms such as delay times to achieve modifications to the control algorithm, the variations and nonlinearities of the current scheme are insufficient to handle different RLTs (residual layer thickness of the curable liquid between the template and the substrate), positions, and transitions. This leads to various problems, including slow convergence, overshoot, undershoot, stalling, oscillation, and repeatability. These problems continue to affect the yield and efficiency of mass production, and it is therefore desirable that these problems be corrected. Summary of the Invention

[0003] According to the present disclosure, a method for controlling the position of a movable stage on which a substrate is supported is provided. First position information representing the position of the substrate relative to a mark on an object is obtained from a sensor. Alignment prediction information is generated based on the obtained first position, wherein the generated alignment prediction information includes at least one parameter value. First trajectory information is generated based on the obtained first position information and the generated alignment prediction information, and the first trajectory information includes the at least one parameter value. Second trajectory information is generated based on the generated alignment prediction information, the first trajectory information, and the second position information, wherein the second position information represents the position of the movable stage. An output control signal is generated based on the second trajectory information, and the output control signal is used to control the movable stage to approach a target position based on the generated output signal.

[0004] In other embodiments according to the present disclosure, an error value is determined based on a sensor indicating a position of a substrate relative to a mark on an object moved according to second trajectory information, and an updated output control signal is generated based on the error value being within a predetermined range, and the movable stage is controlled to approach a target position based on the updated output control signal.

[0005] In other embodiments according to the present disclosure, the alignment prediction information and at least one parameter value included in the alignment prediction information are updated based on updated first position information obtained by the image capturing device after the movable stage moves according to the output control signal.

[0006] According to the present disclosure, the alignment prediction information is a first feedforward signal, and the generated first trajectory information is a first feedback signal generated by obtaining a difference between the obtained first position information and the feedforward alignment prediction information, and the generated second trajectory information is a second feedback signal.

[0007] The present invention provides further embodiments that, in response to determining that an error value indicating the position of the substrate relative to a mark on the object at the end position of the alignment prediction information based on a sensor is outside a predetermined range, generate new alignment prediction information including at least one updated parameter value determined based on the updated first position information, combine the new alignment prediction information with the second trajectory information to generate an updated output control signal, and control the movable stage based on the updated output control signal. In this manner, the output control signal is further based on the combination of the third feedforward control signal and the second trajectory information.

[0008] Advantages of the general aspects and implementations described herein include feedforward and feedback control of alignment errors based on real-time system identification, resulting in rapid and accurate correction of alignment errors in imprint lithography. Rapid and accurate correction with smooth transition of substrate movement to an aligned condition results in improved alignment productivity and overlay accuracy.

[0009] The details of one or more implementations of the subject matter described in this specification are set forth in the accompanying drawings and the description below. Other potential features, aspects, and advantages of the subject matter will become apparent from the description, drawings, and claims. BRIEF DESCRIPTION OF THE DRAWINGS

[0010] Figure 1 Depicted is a side view of a nanoimprint lithography system.

[0011] Figure 2 Depicts Figure 1 Side view of the substrate.

[0012] Figure 3 Depicted are side views of a nanoimprint lithography template in contact with liquid imprint resist on a substrate, showing the initial alignment error X0 between a pair of example alignment marks on the template and substrate, respectively.

[0013] Figure 4 Depicted is a block diagram illustrating feed-forward and feedback control for aligning marks on a template and a substrate.

[0014] Figures 5A to 5C Pictured Figure 4 Different types of feedforward controllers are shown in Figure 3.

[0015] Figure 6 is a flow chart illustrating the alignment control algorithm in detail.

[0016] Figure 7 is a graphical representation of the feedforward signals used to generate various motion trajectories.

[0017] Figure 8A and Figure 8B Is a graphical representation of the time it takes for a control signal to converge to a target position. DETAILED DESCRIPTION

[0018] Figure 1 An imprint lithography system 100 is illustrated for forming a concave-convex pattern on a substrate 102. The substrate 102 can be coupled to a substrate chuck 104. In some examples, the substrate chuck 104 includes a vacuum chuck, a pin-type chuck, a slot-type chuck, an electromagnetic chuck, or other suitable chuck. An exemplary chuck is described in U.S. Patent No. 6,873,087, which is incorporated herein by reference. The substrate 102 and the substrate chuck 104 can be further supported by a stage 106. The stage 106 provides motion about the x-axis, the y-axis, and the z-axis, as well as rotation about the z-axis (e.g., θ). In this regard, the stage 106 can be referred to as an XYθ stage. The stage 106, the substrate 102, and the substrate chuck 104 can also be disposed on a base (not shown).

[0019] The imprint lithography system 100 includes an imprint lithography template 108 separated from the substrate 102. In some examples, the template 108 includes a mesa 110 (mold 110) extending from the template 108 toward the substrate 102. In some examples, the mold 110 includes a patterned surface 112. The template 108 and / or the mold 110 can be formed of materials including, but not limited to, fused silica, quartz, silicon, organic polymers, siloxane polymers, borosilicate glass, fluorocarbon polymers, metals, hardened sapphire, or other suitable materials. In the illustrated example, the patterned surface 112 includes a plurality of features defined by spaced-apart grooves 124 and protrusions 126. The pattern formed as described above is for example purposes only, and any type of pattern can be present on the patterned surface 112. As such, the patterned surface 112 can define any pattern that forms the basis of a pattern to be formed on the substrate 102 via an imprint process.

[0020] The template 108 can be coupled to a template chuck 128. In some examples, the template chuck 128 includes a vacuum chuck, a pin-type chuck, a slot-type chuck, an electromagnetic chuck, or any suitable chuck. Exemplary chucks are described in U.S. Patent No. 6,873,087. In some embodiments, the template chuck 128 can be of the same type as the substrate chuck 104. In other embodiments, the template chuck 128 and the substrate chuck can be different types of chucks. Additionally, the template chuck 128 can be coupled to an imprint head 130 such that the template chuck 128, the imprint head 130, or both are configured to facilitate movement of the template 108. Movement of the template 108 includes movement within the plane of the template relative to the template (in-plane movement) and movement out of the plane of the template (out-of-plane movement). In-plane movement includes movement of the template 108 within the plane of the template (e.g., in a plane such as Figure 1 ) and rotation of the template in the plane of the template (e.g., in the XY plane depicted in ) and rotation of the template in the plane of the template (e.g., in the XY plane and about the Z axis). Translation or rotation of the template 108 relative to the substrate 102 can also be achieved by translation or rotation of the substrate. In-plane movement of the template 108 also includes increasing or decreasing the compressive force on opposite sides of the template (e.g., using an amplifying actuator) to increase or decrease the size of the template in the XY plane of the template. Out-of-plane movement of the template 108 includes translation of the template along the Z axis (e.g., by increasing or decreasing the distance between the template and the substrate to increase or decrease the force applied to the substrate via the template) and rotation of the template about an axis in the XY plane of the template. Rotation of the template 108 about an axis in the XY plane of the template changes the angle between the XY plane of the template 108 and the XY plane of the substrate 102, and is referred to herein as "tilting" the template relative to the substrate, or changing the "tilt" or "tilt angle" of the template relative to the substrate. US Patent No. 8,387,482 discloses moving a template via an imprint head in an imprint lithography system and is incorporated herein by reference.

[0021] The imprint lithography system 100 may also include a fluid dispensing system 132. The fluid dispensing system 132 may be used to deposit a polymerizable material 134 onto the substrate 102. The polymerizable material 134 may be disposed on the substrate 102 using techniques such as droplet dispensing, spin coating, dip coating, chemical vapor deposition (CVD), physical vapor deposition (PVD), thin film deposition, thick film deposition, or other suitable methods. In some examples, the polymerizable material 134 is disposed on the substrate 102 before or after a desired volume is defined between the mold 110 and the substrate 102. The polymerizable material 134 may include a monomer as described in U.S. Patent No. 7,157,036 and U.S. Patent Application Publication No. 2005 / 0187339, both of which are incorporated herein by reference. In some examples, the polymerizable material 134 is disposed on the substrate 102 as a plurality of droplets 136.

[0022] Reference Figure 1 and Figure 2 The imprint lithography system 100 may further include an energy source 138 coupled to the direct energy 140 along a path 142. In some examples, the imprint head 130 and the stage 106 are configured to position the template 108 and the substrate 102 in an overlapping manner with the path 142. The imprint lithography system 100 may be regulated by a controller 144 in communication with the stage 106, the imprint head 130, the fluid distribution system 132, the energy source 138, or any combination thereof, and may operate according to a computer-readable program stored in a memory 146.

[0023] In some examples, the imprint head 130, the stage 106, or both vary the distance between the mold 110 and the substrate 102 to define a desired volume therebetween to be filled with the polymerizable material 134. For example, the imprint head 130 can apply a force to the template 108 so that the mold 110 contacts the polymerizable material 134. After the desired volume is filled with the polymerizable material 134, the energy source 138 generates energy 140, such as broadband ultraviolet radiation, to cause the polymerizable material 134 to polymerize and conform to the shape of the patterned surface 112 and the surface 148 of the substrate 102, thereby defining a polymerized patterned layer 150 on the substrate 102. In some examples, the patterned layer 150 includes a residual layer 152 and a plurality of features, shown as protrusions 154 and recesses 156, where the protrusions 154 have a thickness t1 and the residual layer 152 has a thickness t2.

[0024] The above-described systems and processes may also be implemented in the imprint lithography processes and systems described in U.S. Patent No. 6,932,934, U.S. Patent Application Publication No. 2004 / 0124566, U.S. Patent Application Publication No. 2004 / 0188381, and U.S. Patent Application Publication No. 2004 / 0211754, which are incorporated herein by reference in their entireties.

[0025] The imprint lithography substrate and template may include a corresponding pair of alignment marks that allow real-time alignment of the template and substrate. After the patterned template is positioned above the substrate (e.g., superimposed above the substrate), the alignment of the template alignment marks relative to the substrate alignment marks is determined. As disclosed in U.S. Patent Nos. 6,916,585; 7,170,589; 7,298,456 and 7,420,654, which are all incorporated herein by reference, an alignment scheme may include a "through-the-table" (TTM) measurement of alignment errors associated with a pair of corresponding alignment marks, followed by compensation for these errors to achieve precise alignment of the template with the desired imprint location on the substrate. Alignment errors may be caused by relative positioning of the substrate and the template, deformation of the substrate or template, or a combination thereof.

[0026] Figure 3 A side view of an imprint lithography template 108 in contact with a liquid imprint resist 134 on a substrate 102 is shown, illustrating a first or initial alignment error X0 between a pair of example alignment marks 302 and 304 on the template 108 and substrate 102, respectively. The alignment error X0 can be measured by an image capture device, such as a sensor 158. In some examples, the sensor 158 comprises a TTM alignment instrument configured to detect diffracted light from the alignment marks 302 and 304, where the diffracted light can pass through the liquid imprint resist 134. The initial alignment error X0 may exceed a tolerable alignment error, which can be less than 10 nm, with a repeatability of, for example, 1 nm or less. While the sensor 158 is described as an image capture device, this is merely exemplary, and the image capture device can include any device capable of detecting, capturing, and transmitting diffracted light in real time.

[0027] The alignment error X0 may be primarily caused by placement error, rotation error, and / or compliance and hysteresis of the stage 106 (e.g., an XYθ stage), and may include rotation about the z-axis (θ) as well as errors in the x-axis and y-axis. For example, placement error typically refers to an XY positioning error between the template and the substrate (i.e., Figure 1 , translation along the X-axis, Y-axis, or both, where the X-axis and Y-axis lie in the plane of or are parallel to the imprinting surface of the template or substrate). Rotational (θ) error typically refers to relative orientation error about the Z-axis (i.e., Figure 1 , a rotation about the Z axis, where the Z axis is orthogonal to the XY plane).

[0028] Placement errors of the template alignment marks 302 and corresponding substrate alignment marks 304 offset in the XY plane can be compensated for by relative movement of the template and substrate (e.g., by controlled movement of the substrate, the template, or both in the XY plane). Rotational errors can be compensated for by changing the relative angle of the template and substrate in the XY plane (e.g., by rotating the substrate, the template, or both).

[0029] The present disclosure describes a control mechanism for controlling the above relative Figures 1 to 3The operation of the imprint system is described to reduce the amount of time it takes for the alignment marks 302 and 304 to converge to be properly aligned in order to ensure that the pattern defined on the table 110 is successfully imprinted on the substrate 102. In other words, a control algorithm will be described below that causes a reduced error value, generally indicated by X0, to be below a predetermined error threshold within a predetermined time period. Preferably, the result will result in a relative distance between the marks on the template and the marks on the substrate being less than a predetermined distance value. However, due to the various physical properties of both the substrate and the polymer used to imprint the pattern thereon, there are certain difficulties in achieving an acceptable level of error within an acceptable time period. More specifically, from the time the polymer (e.g., imprint resist) is deposited on the substrate and energy is applied thereto during curing, it is challenging to align the substrate with the template so that the relative distance between the alignment marks on each is within a predetermined relative distance from each other.

[0030] To align the markings on the template and substrate, a control signal is generated for controlling the movement of the gantry in the X, Y, and θ directions. The control signal includes one or more parameter values that are converted into electrical signals that are applied to a gantry motor (not shown) for moving the gantry to the desired target position. The parameter values that constitute the control signal can be any one or more of acceleration values, velocity values, rotation values, and time values indicating when the movement will occur.

[0031] Depending on the parameter values determined during the alignment process, one of two common problems can arise. One possible issue involves overshooting the target position because one or more parameter values together result in a trajectory that causes the stage to move in such a way that a mark on the substrate passes over a mark on the template, thereby requiring further alignment correction. Another possible issue involves misalignment. Misalignment indicates that the parameter values of the control signals cause the stage to move too slowly. In this way, the energy applied to the substrate by the template causes the liquid resist to solidify and polymerize, causing the alignment process to become misaligned before the marks are aligned. These problems are remedied by using the control algorithm described herein, which utilizes at least two feedforward signals per sample that are integrated with feedback signals to continuously modify and update the control signals used to move the stage toward the target position. By continuously monitoring the positional information of the substrate and stage relative to the template and using these measurements, the system described herein successfully reduces the error value between alignment marks more quickly, within a predetermined time before the polymerizable material 134 polymerizes, and without negatively impacting the properties of the substrate 102.

[0032] Figure 4 An example control block diagram of feedforward and feedback control is shown. The control system as described herein is shown implemented as Figure 11 and 1 . The controller 144 includes at least one central processing unit (CPU) and memory and can execute instructions stored in the memory to perform one or more of the described operations and / or functions. The controller 144 communicates with one or more memories (e.g., RAM and / or ROM) and, in some examples, executes the stored instructions to perform one or more control operations. In other examples, the controller 144 can temporarily store data in one or more memories for calculation and generation of various signals described below. Thus, the controller 144 controls the operation of the system 100 by using data stored in the RAM and / or ROM and a computer program (one or more series of stored instructions executable by the CPU). Figure 1 Here, the controller 144 may include one or more dedicated hardware or graphics processing units (GPUs) different from the CPU (or may communicate with them), and the GPU or dedicated hardware may perform part of the processing by the CPU. As examples of dedicated hardware, there are application-specific integrated circuits (ASICs), field programmable gate arrays (FPGAs), and digital signal processors (DSPs). In one embodiment, the control system 100 may be implemented as follows: Figure 1 100 is a portion of the controller 144 shown in . In some embodiments, the controller 144 can be a dedicated controller. In other cases, the control system 100 can include multiple controllers that communicate with each other and other components of the control system 100 for implementing the operations described herein.

[0033] Next, the control functions according to the present disclosure will be described. Figure 4 144 to perform the functions described herein. In other embodiments, each controller described herein may be implemented as a separate integrated circuit, each having its own CPU and memory, and dedicated to performing the processing associated therewith. In other embodiments, one or more of the controllers described herein may be implemented as a single integrated circuit. Additionally, in some embodiments, some of the described controllers may be dedicated processing units and communicate with the CPU of the controller that is executing stored instructions to perform the functional operations described herein.

[0034] Figure 4The system includes a sensor 158, a feedforward controller 410, an alignment feedback controller 430, a stage feedback controller 450, and a stage amplifier 470 (hereinafter referred to as "amplifier 470"). Disposed between the aforementioned components are a plurality of nodes that combine the signals output by the various controllers feeding the signals by adding, subtracting, or convolving the signals with one another. Each of the aforementioned components operates as described below to move the stage supporting the substrate to a target position representing an alignment error value within a predetermined alignment error range. In one embodiment, the target position represents a substantially zero alignment error value indicating direct alignment of a mark on the substrate with a mark on the template.

[0035] Each of the alignment feedback controller 430 and the gantry feedback controller 450 may be implemented as a proportional-integral-derivative (PID) controller or any other feedback controller. Thus, an exemplary control function for processing the respective input signals to generate the output signals may be a control function such as the following:

[0036]

[0037] Among them, K p , K i and K d respectively represent the proportional, integral, and derivative control terms used to control the specific operation of the controller implementing them. The manner in which the feedback controller performs this control function is known and need not be further described, and it continues to calculate error values based on the inputs received therein. A first node 420 is provided between the feedforward controller 410 and the sensor 158 and generates a first input signal 422 for the alignment feedback controller 430 by obtaining the difference between a first feedforward control signal 412 and a measurement signal 402 representing the position of a mark on the template relative to the mark on the substrate. The first feedforward signal 412 represents alignment reference trajectory information and is generated based on the reference trajectory information stored in a memory and the measurement signal 402. The first feedforward signal 412 includes at least one parameter defining one or more aspects of the movement operation of the control gantry. For example, the at least one parameter may include one or more of: (a) a desired position value, (b) a desired velocity value, (c) a desired acceleration value, (d) a desired rotation value, and (e) a desired start time for initiating movement of the gantry along the determined trajectory. The first feedforward signal can be a feedforward trajectory in the phase plane (x-axis: position, y-axis: velocity), which is then mapped to the time domain (x-axis: time, y-axis: position) to generate a feedforward signal on a per-sample basis. Based on the friction changes observed from the feedforward and feedback signals, this trajectory in the phase plane is optimized offline or online through model prediction and iterative learning. This optimization will achieve minimal overshoot and undershoot with minimal oscillation and convergence time, thereby aligning the marks on the template and substrate with each other.

[0038] By utilizing the real-time measured position of the substrate relative to the template and the reference trajectory information, the first feedforward signal 412 can represent a polynomial or exponential decay line in the position-velocity phase plane converted to the time domain. In this way, by combining the alignment reference trajectory information of the first feedforward signal 412 with the measured position value encoded in the measurement signal 402 obtained in real time from the sensor 158, the alignment controller 430 can generate an alignment trajectory (sometimes referred to as a control command or control force) that will align the substrate and the mark on the template more quickly. The alignment controller 430 generates alignment trajectory information 432 based on the first input signal 422 and outputs the alignment trajectory information 432 to the second node 440. In other words, the alignment feedback controller continues to calculate the alignment error value according to the following formula

[0039] e TTM (t)=FF1(t)–POS TTM (t)

[0040] Among them, e TTM represents the error value at a given time, FF1 is the value of the first feedforward signal 412 generated by the feedforward controller 410, and POS TTM is the current position of the template relative to the substrate supported by the stage 106 obtained by the sensor 158. After calculating the error value, the alignment feedback controller 430 outputs the alignment trajectory information as U AL (t). As described below, the alignment trajectory information 432 will be used to generate a trajectory (or control force) along which the stage moves to align the substrate and template.

[0041] The feedforward controller 410 also outputs a second feedforward control signal 414 to the second node 440. In one embodiment, the first feedforward signal 412 is identical to the second feedforward signal 414. In another embodiment, the second feedforward signal is generated based on the first feedforward signal 412. For example, in one embodiment, the second feedforward signal 414 can be a magnitude or time-shifted version of the first feedforward signal 412, where the first feedforward signal 412 is shifted to start from an initial start time. For example, in one embodiment, the second feedforward signal 414FF2 can be a magnitude-shifted version of the first feedforward signal 412FF1, where the first feedforward signal 412 is shifted by magnitude FF as described below. shift .

[0042] FF2(t)=FF1(t)+FF shift

[0043] Thus, if the target position to which the stage is to be moved represents an alignment error of substantially zero, the second feedforward signal 414 has the same value as the first feedforward signal 412, but begins at zero at the target position, as compared to the first feedforward signal 412, which begins at the measurement position 402. Other examples of generating the second feedforward signal 414 include applying a transfer function f() to the first feedforward signal 412 as described below, where f() is a nonlinear transfer function including a time offset.

[0044] FF2(t)=f(FF1(t)) The transfer function f() may represent nonlinear friction that causes the motion sensed by the gantry position sensor 476 and the mark sensor 158 to be asynchronous. In another embodiment, the second feedforward signal 414 is generated independently of the first feedforward signal 412.

[0045] In addition to the alignment trajectory information 432 and the second feedforward signal 414, the second node 440 receives as input gantry position information 474 obtained from a gantry position sensor 476 of the amplifier 470. The gantry position information 474 represents the current measured position of the gantry 106 at the end of the gantry movement operation requested by the amplifier 470. The second node 440 combines the alignment information 432 with the second feedforward signal 414 and then obtains the difference between the combined signal and the gantry position information 474 to generate a second input signal 442. The second input signal 442 is input to the gantry feedback controller and generates gantry trajectory information 452 as an output therefrom. Although the gantry position sensor 476 is shown as being separate from the gantry 106, this is merely exemplary and is shown to facilitate understanding of system operation. It should be understood that the gantry position sensor 476 can be included in the gantry 106.

[0046] It should be noted that the stage sensor feedback 474 sensed by the stage position sensor 476 is not the same signal as the mark sensor feedback 402, even though both feedback signals are derived from the operation of the stage 106 at each sample. This is because the mark sensor feedback 402 and the stage sensor feedback 474 are not in the same coordinate space and are therefore not synchronized. The stage sensor feedback 474 has an initial position that is typically set to zero and is set to the same as the entire device (e.g., machine) in the global coordinate system relative to the coordinate space in which these exist. However, when the mark error between the template and the substrate is zero, the mark sensor feedback 402 is set to zero. This can be seen in the following example: Figure 3 The coordinate space of the mark sensor 158 is the space relative to the template and substrate. In other words, the coordinate space of the mark sensor 158 that generates the mark sensor feedback 402 is the local coordinate system. The prediction information implemented as feedforward signals 412 and 414 is generated by taking into account the offset of the two coordinate spaces.

[0047] In addition to the offset due to the different coordinate spaces, nonlinear friction between the template and the substrate may also cause nonlinear scaling and a time and magnitude offset between the first feedforward signal 412 and the second feedforward signal 414. For example, in extreme cases, very large friction between the substrate and the template may cause the mark sensor 158 to detect that a misalignment has occurred (e.g., the substrate is stuck to the template) even though the stage sensor feedback 474 indicates that the stage 106 is moving. In embodiments such as this, the generation of the first feedforward signal 412 and the second feedforward signal 414 may require the implementation of a nonlinear transfer function as part of the operation of the feedforward controller 410.

[0048] The stage feedback controller 450 continues to calculate an error value associated with the position of the stage as controlled by the amplifier 470. This error value may be calculated by the stage feedback controller 450 using the following equation:

[0049] e stage (t) = U AL (t)+FF2(t)–POS stage (t)

[0050] Among them, e stage Indicates the error value of the stage position, U AL (t) represents the alignment trajectory information 432, FF2(t) represents the constant offset (FF) of the second feedforward signal 414 (eg, FF1(t)). shift ) added form), and POS stage is the current position of the gantry 106 as operated by the amplifier 470 and sensed by the gantry position sensor 476. In this process, the second feedforward signal 414 (FF2(t)) also includes a value associated with at least one parameter value from the first feedforward signal 412. In one embodiment, the parameter values in the second feedforward signal 414 are the same as the parameter values in the first feedforward signal 412, except for the offset resulting from the addition of the constant offset discussed above. In another embodiment, given an error value determined as part of the alignment trajectory information processing, one or more of the at least one parameter value representing movement control (e.g., position, velocity, rotation, acceleration) can be updated based on the determined error value, thereby improving the gantry trajectory information 452 output by the gantry feedback controller 450.

[0051] In one embodiment, the gantry trajectory information 452 is output directly to an amplifier 470, which converts the gantry trajectory information 452 into an electrical signal that is then applied to a Figure 14 and 5. The gantry 106 is moved to a desired position by moving the gantry 106 toward the desired position. At the end of the gantry motion at the end of the gantry trajectory defined in signal 452, the internal gantry amplifier 470 receives a command from the gantry feedback controller 450 and outputs the command as a gantry electrical signal for generating gantry motion. The new gantry position is obtained by the gantry position sensor and fed back to the second node 440 and used to determine the error value as discussed above. The gantry control command information 452 may be output as U stage (t)(output control signal 472).

[0052] In another embodiment, Figure 4 As shown in FIG, the control system includes a third node 460 disposed between the gantry feedback controller 450 and the gantry amplifier 470. The third node 460 combines the gantry trajectory information 452 with the third feedforward signal 416 generated and output by the feedforward controller 410. The third feedforward signal 416 is a motion control command prediction signal. In one embodiment, the gantry is controlled by obtaining the difference between the target position of the gantry with substantially zero alignment error and the second feedforward signal 414 and multiplying the difference by the value used by the gantry feedback controller 450 to control the gantry 106 ( Figure 1 ) is used to generate the third feedforward signal 416. The third feedforward signal 416 can be calculated according to the following formula:

[0053] FF3=(POS target -FF2(t))×P gain

[0054] Wherein, FF3 is the third feedforward signal 416, POS target represents the target stage position where the alignment error is essentially zero, and P gain represents the gain to be applied by the gantry feedback controller 450 to control the movement of the gantry. The third node 460 connects FF3 to U stage (t) to generate a gantry motion control signal 462 that is used as an input to a gantry amplifier 470. The gantry amplifier 470 converts the signal into a voltage or current (output control signal 472) that is used to control the gantry motion according to the gantry motion control signal 462 obtained by combining the third feedforward signal 416 (FF3) with the gantry command information 452 (U stage (t)) and the motion control signal generated by the combination to drive the stage 106.

[0055] By generating and using the third feedforward signal 416 and the stage trajectory information 452, there is less phase delay due to the stage feedback controller processing, resulting in faster alignment. Other advantages presented by using the third feedforward signal 416 allow greater design freedom to reduce shear forces and overcome static friction and nonlinear kinematic friction during the alignment and curing processes. In addition, the third feedforward signal 416 focuses on the residual error between the second feedforward signal 414 and the target position. This advantageously improves the ability to adjust the stage trajectory information by updating the stage trajectory information based on the third feedforward signal 416 so that the stage moves along a trajectory that will align the substrate and the mark on the template more quickly. This can also be used to minimize the desynchronization between the first feedforward and the second feedforward caused by nonlinear friction between the template and the substrate; and reduces the design complexity of the feedback controllers 430 and 450 in handling smaller feedback errors.

[0056] Based on the above, Figure 4 The control system advantageously enables the first and second feedforward signals to be focused on respective feedback loops, thereby allowing the alignment feedback controller 430 and the gantry feedback controller 450 to be more easily adjusted because their processing is focused on the residual error between the current position and the respective first and second feedforward trajectory information generated by the feedforward controller 410. This allows the third feedforward signal to be based on the latest end position of the gantry defined by the previous gantry trajectory to bring the gantry closer to the target position. Figure 7 An exemplary time trace illustrating the feedforward signal is shown in FIG. Time (in seconds) is shown along the x-axis and position (in nanometers) is shown along the y-axis. This illustrates the position difference at a particular time, showing the relative distances between the substrate and template and the target position. Figure 7 , the target mark alignment is represented by a target mark distance of 0, designated as 702. A first feedforward signal 412 is based on position information sensed by the mark sensor 158 and begins slightly after an initial time of 0 seconds. As indicated herein, the first feedforward signal 412 is used to generate alignment trajectory information. A second feedforward signal 414, having substantially the same characteristics as the first feedforward signal 412, is offset, and instead of starting at the position sensed by the sensor 158, the second feedforward signal 414 is reinitialized to begin at the current stage position, which may be zero for the first initialization or the last stage position prior to reinitialization. As indicated herein, the second feedforward signal 414 is used to generate stage trajectory information. Based thereon, substantially simultaneously, a third feedforward signal 416 representing motion control command prediction information is generated based on the second feedforward signal 414. Thus, over time, the sensed mark positions and motion prediction information indicated in the alignment trajectory converge, indicating alignment of the substrate and the template.

[0057] If the initial error from the mark sensor is within a predetermined range, the feedforward controller replaces the first feedforward with the target mark position, and the second and third feedforwards are set to zero. If the initial error from the mark sensor is outside the predetermined range, the first feedforward will be generated to bring the mark error to zero, and the second and third feedforwards will be generated as described above. If the generated feedforward has been used and the mark error at the end of the trajectory from the mark sensor is still greater than the predetermined range, the feedforward will be regenerated based on the mark error at the end of the feedforward as the new initial error. The second feedforward will also be regenerated by using the end of the previous feedforward trajectory as the starting point. The predetermined range can be position, velocity, or acceleration based on the mark sensor error. If the error from the mark sensor reaches the target before the feedforward completes the last sample, the feedforward signal can jump to the last sample, or continue until the last sample.

[0058] When viewing Figure 8A and Figure 8B The other advantage of the third feedforward presented by the present control system is clear when Figure 8A and Figure 8B The gantry reaches the target position and uses two feedforward control signals ( Figure 8A ) and three feedforward control signals ( Figure 8B ) is a graphical representation of the length of time it takes to align the substrate and template. Figure 8B As seen in Figure 8A Compared to the first two feedforwards, the time it takes for all trajectories to converge to target position zero is reduced. This is a direct result of the third feedforward overcoming time delays and static friction. Another benefit is that, compared to a solution with only two feedforwards, misalignment is overcome more quickly at the end of the smaller stage motion control signal with the third feedback. The smaller stage control command force near the end of alignment can reduce the amount of force experienced by polymerizable material 134 while being supplied with energy for polymerization.

[0059] Although Figure 4 The diagram shows the overall control system implemented by various controllers and sensors, but Figures 5A to 5C The illustrations illustrate how additional configurations of various components may be implemented. Figure 5A A more detailed view of the feedforward controller 410 in an embodiment in which two feedforward control signals are generated and integrated with the various feedback control signals described above is illustrated. As shown herein, each block may represent a respective CPU that performs the calculations described above. Figure 5A, the feedforward controller 410 may include a first feedforward generator 502, which is a processing unit (CPU) that receives input from the sensor 158 to generate a first feedforward control signal 412 representing alignment reference trajectory information. In addition, the first feedforward generator 502 may output the first feedforward signal to a second feedforward generator 504, which is a processing unit (the same as the first feedforward generator or a separate CPU). The second feedforward generator 504 then generates a second feedforward signal 414 for output to the gantry controller 450. Although shown herein as a signal directly output to the controllers 430 and 450, it should be noted that this may indicate a second feedforward signal for the gantry controller 450. Figure 4 Alternatively, the functions performed by the nodes may be encapsulated in each of the alignment feedback controller 430 and the gantry feedback controller 450. Figure 5B The embodiment in which the third feedforward signal including motion prediction information can be generated is shown. In this embodiment, the feedforward controller 410 includes a third feedforward generator 506, which itself can be its own processing unit CPU or can be part of a processing unit having one or both of the first feedforward generator and the second feedforward generator. In addition, as Figure 5B As shown by the dashed boxes in FIG, the exemplary configuration implements the feedforward controller 410 and the alignment feedback controller 430 on a single processing unit separate from the gantry feedback controller 450. Figure 5C Including Figure 5B Components are similar to those shown in , except that the dashed boxes indicate that the feedforward controller 410, alignment feedback controller 430, and gantry feedback controller 450 are implemented on a single processing unit.

[0060] It should be understood that the above description of the feedforward controller 410 illustrates that at least two, but sometimes three, feedforward signals are generated and used to control the movement of the gantry 106. As described above, this control can be performed using the first feedforward signal 412 and the second feedforward signal 414. In addition, the above description indicates that the third feedforward signal 416 can be used in combination with the first feedforward signal 412 and the second feedforward signal 414. It should also be understood that the algorithm can also use the first feedforward signal only with the third feedforward signal 416. Alternatively, only the second feedforward signal 414 and the third feedforward signal 416 can be used. How and when to determine the three feedforward signals depends on the error calculation performed and whether the calculated error is outside a predetermined range, so that more (or less) positive prediction information needs to be generated to control the gantry movement to align the markings on the template with the markings on the substrate. The goal of various combinations of feedforward signals (412, 414, 416) can be to predict a set of fast and stable positions and control trajectories before the control forces are applied. A further goal can be to minimize the feedback errors (422 and 442). In an embodiment, there is an ideal relationship between the three feedforwards that are synchronized which can be described as follows:

[0061] Sys 412 (FF1)=Sys 414 (FF2)+Sys 416 (FF3)

[0062] Among them, Sys xxx 4. The open-loop system response with inputs of feedforward signals 412, 414, and 416 is shown. In another embodiment, the waveforms of the three feedforward signals may be determined by model reference design, iterative learning, and / or repetitive control. In an embodiment, two or more feedforward signals may be optimized taking into account one or more of the following: coordinate system differences between stage alignment and mark alignment, and nonlinear friction between the substrate and the template.

[0063] Now go to Figure 6 , Figure 6 An exemplary control algorithm for achieving alignment control according to the present disclosure is shown. Figures 1 to 4 The associated reference numerals indicate the processing units that execute the algorithm control. As shown herein, the algorithm represents a method for controlling the position of a movable stage on which a substrate is supported. In step S602, first position information representing the measured position of the substrate relative to a mark on a template is obtained by sensor 158. The first position information represents the current measured position of stage 106 and the relative distance between the substrate and the mark on the template. The first position information is provided to each of feedforward controller 410 and alignment feedback controller 430.

[0064] In step S604, the feedforward controller 410 generates alignment reference trajectory information based on the obtained first position. The generated alignment reference trajectory information represents a first feedforward signal 412, a second feedforward signal 414, and a third feedforward signal 416 output from the feedforward controller 410, and includes at least one parameter value for controlling the movement of the movable stage to a target position such that the determined alignment error between the substrate and the mark on the template is substantially zero. The at least one parameter includes one or more of (a) a desired position value, (b) a desired velocity value, (c) a desired acceleration value, and (d) a desired start time for initiating movement of the stage along the determined trajectory.

[0065] In step S606, the alignment feedback controller generates first trajectory information. The first trajectory information represents alignment trajectory information output by the alignment feedback controller 420 and includes at least one parameter value based on the obtained first position information and the generated alignment prediction information. The first trajectory information is a first feedback signal 422 generated by obtaining the difference between the obtained first position information and the feedforward alignment reference trajectory information.

[0066] In step S608, second trajectory information 452 is generated. The second trajectory information 452 is generated by the stage feedback controller 450 and is generated based on the alignment prediction information 414 and an error value determined from the second reference trajectory information 432 and the stage position information 474 indicating the current position of the movable stage. Thus, the generated second trajectory information 452 includes at least one updated parameter value that has been updated based on the calculated error value. The second trajectory information represents a second feedback signal generated by combining the second feedforward signal 414, the alignment trajectory information 432, and the position signal indicating the current position of the stage 106. In some embodiments, S608 may further include a second error determination process that determines a second error value based on the current position of the movable stage moved according to the second trajectory information and the target position.

[0067] In step S610, the gantry feedback controller 450 generates an output control signal 472 including the updated at least one parameter value and outputs the control signal to the gantry amplifier 470. In step S612, the gantry amplifier 470 controls the movable gantry to approach the target position based on the generated output signal. The output control signal 472 generated in step S610 may also include a third feedforward signal determined by the second error processing described above, so that the gantry can be controlled to move according to the updated parameter value in step S612.

[0068] In step S614, the sensor 158 determines whether the error value associated with the relative position of the mark on the substrate and the mark on the template and the mark are within a predetermined error range. If the result of the determination in S614 is affirmative, indicating that the error value is within an acceptable range, then the determination indicates that the mark on the template and the mark on the substrate are aligned with each other and the control algorithm ends in S615.

[0069] If the determination result is negative, this indicates that the marking on the substrate is misaligned with the marking on the template. In this case, the algorithm repeats steps S602 to S612. In this manner, each of the information and trajectory values described herein is updated, such that one or more parameters contained therein and used to control the motion of the gantry are modified based on both feedback and feedforward control. These updates are based on the updated first position information obtained by the sensor after the movable gantry moves in accordance with output control signal 472 and reaches an end position that is not the target position.

[0070] In addition to repeating steps S602 to S612, in response to a negative determination, the algorithm generates motion prediction information as a third feedforward signal 416 in step S616. In this manner, in response to determining that the end position of the movable stage based on the output control signal 472 is outside a predetermined distance from the target position (e.g., an error value greater than a predetermined error threshold), motion controller prediction information is generated, and the motion controller prediction information includes an updated at least one parameter value determined based on the end position of the movable stage. The updated at least one parameter value is updated based on the difference between the end position and the second trajectory information. The motion controller prediction information is combined with the second trajectory information to generate an updated output control signal 472, which is then used to control the movable stage based on the updated output control signal 472.

[0071] According to the algorithm described above, the relative position of the template and the substrate can be successfully controlled by receiving alignment information representing the relative positions of the marks on the template relative to the alignment marks on the substrate. A feedforward alignment trajectory based on the alignment information is then generated, and the feedforward alignment trajectory can include one or more parameters such as the desired position, desired velocity, desired acceleration, and desired start time of the feedforward alignment trajectory. Based on this, an alignment error time series can be generated, representing the feedforward alignment trajectory minus the measured alignment trajectory, where each of these trajectories includes one or more parameters such as position, velocity, and acceleration. The alignment error time series can be converted into an alignment closed-loop feedback control output time series, which is then used to generate stage trajectory information for use as input by the amplifier, as the sum of the alignment closed-loop feedback control output time series and the stage feedforward trajectory. A stage feedback controller receives stage controller input information and feedback information from a stage position sensor, which measures the stage position and continuously updates and modifies the stage trajectory information. This stage trajectory information is then used by the stage feedback controller to drive the stage position toward a target.

[0072] The present disclosure provides a dynamic feedforward reinitialization mechanism, whereby new feedforward trajectory information is generated if the stage's ending position causes the stage to be outside a predetermined threshold of the target position. In this manner, the feedforward controller is reinitialized to generate an updated feedforward signal based on the stage's latest position and determined by sensor 158, which senses the relative position between the substrate and template. Due to the feedforward reinitialization, position errors, as well as overall system complexity and feedback gain, can be reduced. In operation, sensor 158 measures the relative distance between the substrate and template, which is used to measure the absolute distance the stage has moved. When acquiring the first sample, the generated feedforward begins at an initial position based on the sensor data and is subsequently reinitialized to start from the total control force that led to the stage's ending position during the previous sample. In this way, the dual feedback loop can be reinitialized at the beginning of each feedforward reinitialization. This operation advantageously enables the presently described control system to provide fast and consistent alignment for imprint lithography, compensating for physical changes in the substrate and internal friction of the liquid resist at the start of imprinting. The above algorithm overcomes the disadvantages associated with the variations and nonlinearities associated with feedback control systems to reduce overshoot, undershoot, and offset during imprint lithography. As such, the control algorithm provided herein improves the yield and efficiency of batch fabrication of one or more articles from a substrate.

[0073] Therefore, the control algorithm detailed above can be used in a semiconductor manufacturing process for manufacturing one or more articles or devices. The processes to which a substrate that has been successfully aligned according to the control algorithm described herein is subjected include, but are not limited to: imprint lithography; photolithography; baking; oxidation; layer formation; deposition; doping; etching; descumming; slicing; bonding; packaging, etc. Other known steps and processes for article manufacturing can also be used to process the substrate, including, for example, inspection, curing, oxidation, layer formation, deposition, doping, planarization, etching, formable material removal, slicing, bonding, packaging, etc. Based on the above, the substrate can be processed to produce multiple articles (devices).

[0074] In one example, a process may include dispensing an imprint resist (e.g., a liquid) onto a substrate and contacting the imprint resist with an object such that the object having a pattern thereon contacts the imprint resist. The process includes an alignment process to align the substrate and the object (e.g., a template) to a predetermined alignment position, and then processing the substrate having the imprint resist thereon to produce the article. Energy is then applied to the substrate to cure the resist and form a pattern on the substrate corresponding to the pattern on the template. This process is repeated such that the object and substrate are aligned before the resist is cured by the applied energy.

[0075] A number of implementations have been described. However, it will be appreciated that various modifications may be made without departing from the spirit and scope of this disclosure. Accordingly, other implementations are within the scope of the following claims.

[0076] The embodiments of the present disclosure may be implemented by providing a program that implements one or more functions of the above-described embodiments to a system or device via a network or storage medium and reading and executing the program using one or more processors in a computer of the system or device. In addition, the embodiments of the present disclosure may be implemented by a circuit (e.g., an application-specific integrated circuit (ASIC)) that implements one or more functions.

[0077] The embodiments of the present disclosure may also be implemented by a computer of a system or device that reads and executes computer-executable instructions (e.g., one or more programs) recorded on a storage medium (which may also be more fully referred to as a "non-transitory computer-readable storage medium") to perform one or more functions of the above-described embodiments and / or includes one or more circuits (e.g., application-specific integrated circuits (ASICs)) for performing one or more functions of the above-described embodiments, and by a method performed by a computer of the system or device, for example, reading and executing computer-executable instructions from a storage medium to perform one or more functions of the above-described embodiments and / or controlling one or more circuits to perform one or more functions of the above-described embodiments. The computer may include one or more processors (e.g., a central processing unit (CPU), a microprocessing unit (MPU)), and may include a network of separate computers or separate processors to read and execute computer-executable instructions. The computer-executable instructions may be provided to the computer, for example, from a network or a storage medium. The storage medium may include, for example, a hard disk, a random access memory (RAM), a read-only memory (ROM), a memory of a distributed computing system, an optical disk (such as a compact disk (CD), a digital versatile disk (DVD), a Blu-ray Disc (BD), etc.) TM ), one or more of flash memory devices, memory cards, etc.

[0078] With reference to the description, specific details are set forth in order to provide a thorough understanding of the disclosed examples. In other instances, well-known methods, procedures, components, and circuits have not been described in detail so as not to unnecessarily lengthen aspects of the present disclosure.

[0079] It should be understood that when an element or portion is referred to as being "on," "against," "connected to," or "coupled to" another element or portion, it can be directly on, abut, connected to, or coupled to the other element or portion, or intervening elements or portions may be present. In contrast, when an element is referred to as being "directly on," "directly connected to," or "directly coupled to" another element or portion, there may be no intervening elements or portions. When used, the term "and / or" includes any and all combinations of one or more of the associated listed items, if so provided.

[0080] For ease of description, spatial relative terms such as "below", "below", "under", "down", "above", "above", "proximal end", "distal end" and the like may be used herein to describe the relationship between an element or feature and another (some) element or feature as illustrated in the various figures. However, it should be understood that spatial relative terms are intended to encompass different orientations of the device in use or operation in addition to the orientation depicted in the accompanying drawings. For example, if the device in the accompanying drawings is flipped, the element described as being "below" or "below" other elements or features will be oriented as being "above" other elements or features. Therefore, relative spatial terms such as "below" can encompass both the above orientation and the below orientation. The device can be oriented in other ways (rotated 90 ° or in other orientations), and the spatial relative descriptors used herein will be interpreted accordingly. Similarly, where applicable, the relative spatial terms "proximal end" and "distal end" may also be interchangeable.

[0081] As used herein, the term "about" means, for example, within 10%, within 5%, or less. In some embodiments, the term "about" may mean within measurement error.

[0082] The terms first, second, third, etc. can be used in this article to describe various elements, components, regions, parts and / or intervals. It should be understood that these elements, components, regions, parts and / or intervals should not be restricted by these terms. These terms are only used to distinguish an element, component, region, part or interval from another region, part or interval. Therefore, without departing from the teaching herein, the first element, component, region, part or interval discussed below can be referred to as the second element, component, region, part or interval.

[0083] The terms used herein are for the purpose of describing particular embodiments only and are not intended to be limiting. As used herein, the singular forms "a," "an," and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It should be further understood that when used in this specification, the terms "comprise" and / or "comprising" specify the presence of stated features, integers, steps, operations, elements, and / or parts, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, parts, and / or groups thereof that are not explicitly stated.

[0084] The foregoing merely illustrates the principles of the present disclosure. Various modifications and alterations to the described exemplary embodiments will be apparent to those skilled in the art in view of the teachings herein.

[0085] In describing the example embodiments illustrated in the drawings, specific terminology is employed for the sake of clarity. However, the disclosure of this patent specification is not intended to be limited to the specific terminology so selected, and it is to be understood that each specific element includes all technical equivalents that operate in a similar manner.

Claims

1. A method of controlling the position of a movable stage having a substrate supported thereon, the method comprising: obtaining first position information representing a position of the substrate relative to the marking on the object from a sensor; generating alignment prediction information based on the obtained first position information, wherein the generated alignment prediction information includes at least one parameter value; generating first trajectory information including the at least one parameter value based on the obtained first position information and the generated alignment prediction information; generating second trajectory information based on the generated alignment prediction information, the first trajectory information, and the second position information, wherein the second position information indicates a position of the movable stage; generating an output control signal based on the second trajectory information; controlling the movable stage to approach a target position based on the generated output signal; and The alignment prediction information and the at least one parameter value included in the alignment prediction information are updated based on updated first position information obtained by the image capture device after the movable stage has moved according to the output control signal.

2. The method according to claim 1, further comprising: determining an error value based on the sensor indicating a position of the substrate relative to the marker on the object moved according to the second trajectory information; as well as generating an updated output control signal based on the error value being within a predetermined range; as well as The movable stage is controlled to approach the target position based on the updated output control signal.

3. The method according to claim 1, wherein The alignment prediction information is a first feedforward signal, and the generated first trajectory information is a first feedback signal generated by obtaining a difference between the obtained first position information and the alignment prediction information.

4. The method according to claim 1, further comprising: generating new alignment prediction information including updated at least one parameter value determined based on the updated first position information in response to determining that an error value indicating a position of the substrate relative to a mark on the object at an end position of the alignment prediction information based on the sensor is outside a predetermined range; as well as adjusting one or more controls used in said generating: aligning prediction information; First trajectory information; and second trajectory information; as well as combining the new alignment prediction information with the second trajectory information to generate an updated output control signal; as well as The movable stage is controlled based on the updated output control signal.

5. The method according to claim 1, wherein The alignment prediction information includes: a first feedforward control signal; a second feedforward control signal; and a third feedforward control signal; Wherein, the generation of the first trajectory information is further based on the first feedforward control signal; Wherein, the generation of the second trajectory information is further based on the second feedforward control signal; The generation of the output control signal is further based on the third feedforward control signal.

6. The method according to claim 5, wherein: The feedforward control group consists of the first feedforward control signal; the second feedforward control signal; and the third feedforward control signal; and Herein, at least one of the control signals in the feedforward control group is based on one or two of the other control signals in the feedforward control group.

7. An imprint lithography system for controlling alignment of an imprint lithography template relative to a substrate, the system comprising: a movable stage configured to hold a substrate and movable such that a position of the movable stage can be modified; as well as a sensor configured to sense a position of the substrate relative to the imprint lithography template; as well as at least one controller in communication with the movable stage and the sensor, the at least one controller configured to contact the imprint resist with the imprint lithography template based on the substrate: obtaining first position information representing a position of the substrate relative to a mark on the imprint lithography template from a sensor; generating alignment prediction information based on the obtained first position information, wherein the generated alignment prediction information includes at least one parameter value; generating first trajectory information including the at least one parameter value based on the obtained first position information and the generated alignment prediction information; generating second trajectory information based on the generated alignment prediction information, the first trajectory information, and the second position information, wherein the second position information indicates a position of the movable stage; generating an output control signal based on the second trajectory information; controlling the movable stage to approach a target position based on the generated output signal; and The alignment prediction information and the at least one parameter value included in the alignment prediction information are updated based on updated first position information obtained by the image capture device after the movable stage has moved according to the output control signal.

8. The system according to claim 7, wherein: The at least one controller is further configured to: determining an error value based on the sensor indicating a position of the substrate relative to a mark on the imprint lithography template moved according to the second trajectory information; as well as generating an updated output control signal based on the error value being within a predetermined range; as well as The movable stage is controlled to approach the target position based on the updated output control signal.

9. The system according to claim 7, wherein: The alignment prediction information is a first feedforward signal, and the generated first trajectory information is a first feedback signal generated by obtaining a difference between the obtained first position information and the alignment prediction information.

10. The system according to claim 7, wherein: The at least one controller is further configured to: generating new alignment prediction information including updated at least one parameter value determined based on the updated first position information in response to determining that an error value based on the sensor indicating a position of the substrate relative to a mark on the imprint lithography template at an end position of the alignment prediction information is outside a predetermined range; as well as combining the new alignment prediction information with the second trajectory information to generate an updated output control signal; as well as The movable stage is controlled based on the updated output control signal.

11. A method for manufacturing an article, comprising using the method for controlling a movable stage according to claim 1, the method further comprising: dispensing an imprint resist on a substrate; bringing the imprint resist into contact with an object having a pattern thereon in contact with the imprint resist; The substrate to which the imprint resist has been dispensed is processed to fabricate an article.

12. A method of controlling the position of a movable stage having an object supported thereon, the method comprising: obtaining first position information representing a position of the object from a sensor; generating first feedforward information and second feedforward information based on the obtained first position information; inputting information based on the obtained first position information and the generated first feedforward information into a first feedback controller; inputting information based on the generated second feedforward information, the output from the first feedback controller, and second position information into the second feedback controller, the second position information indicating the position of the movable stage; controlling the movable stage based on an output from the second feedback controller; as well as Alignment prediction information and at least one parameter value included in the alignment prediction information are updated based on third position information indicating the position of the substrate relative to the mark on the object obtained by the sensor after the movable stage has moved according to the output from the second feedback controller.

13. A method of manufacturing an article, the method comprising: dispensing an imprint resist on a substrate supported by a movable stage; bringing the imprint resist into contact with an object having a pattern thereon in contact with the imprint resist; Controlling a movable stage using the method according to claim 12; The substrate in which the imprint resist has been patterned is processed to produce an article.

14. A system for controlling the position of a movable stage having an object supported thereon, the system comprising: a controller configured to control a position of the movable stage, The controller includes: a feedforward controller configured to generate first feedforward information and second feedforward information based on first position information representing a position of the object from a sensor configured to sense the position of the object; a first feedback controller configured to obtain information based on the obtained first position information and the generated first feedforward information; and a second feedback controller configured to obtain information based on the generated second feedforward information, an output from the first feedback controller, and second position information representing a position of the movable stage, wherein the controller controls the movable stage based on an output from the second feedback controller, and wherein the controller updates the alignment prediction information and at least one parameter value included in the alignment prediction information based on third position information indicating the position of the substrate relative to the mark on the object obtained by the sensor after the movable stage has moved according to the output from the second feedback controller.

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