Apparatus and method for optimizing actuator forces used for distortion correction

Abstract

To provide a method and a system for optimizing forces applied to actuators during a nanoimprint lithography process.SOLUTION: A first set of forces within a first set of force limits is selected to be applied to edges of a template. When the first set of forces is applied to the edges of the template, first residual distortion representative of a first predicted overlay error associated with a simulated imprinting method is estimated. A second set of forces is selected within a second set of force limits to be applied to the edges of the template. When the second set of forces is applied to the edges of the template, second residual distortion representative of a second predicted overlay error associated with the simulated imprinting method is estimated. An initial set of forces having the narrowest set of force limits and residual distortion below threshold allowance is selected from among the first set of forces and the second set of forces.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] This disclosure relates to a control system in nanoimprint lithography, and more specifically, to a system for controlling forces applied by actuators during an imprint lithography process. [Background technology]

[0002] In nanoimprint lithography, the goal is to transfer the pattern of an imprint template to a corresponding field on a substrate. To achieve this, a curable liquid resist is dispensed onto the substrate, the template is brought into contact with the substrate, and as a result, after the curing process, the pattern on the template is transferred to a specific field on the substrate. To facilitate this process, force is applied to the template by an actuator to modify the template shape, which helps reduce the difference in shape between the template and the substrate.

[0003] This distortion is generated by using multiple actuators that apply force to the edges of the template. The force applied to each actuator is used simultaneously to correct a first set of distortion errors, which are used to correct a set of distortion parameters during the closed-loop alignment correction process, and a second set of distortion parameters, called residual overlay errors, which are different from the first set of distortion parameters. As a result, at any given time, the force exerted by each actuator is the sum of the force required for alignment correction and the force required for residual error correction.

[0004] One method for determining the force for each actuator that can be used to compensate for residual overlay errors is to use constrained linear least-squares optimization, aiming to minimize the amount of force that should be applied by each actuator to compensate for the residual error. However, this approach has drawbacks when the calculated residual force is combined with the amount of force that should be applied during alignment control and compensation. More specifically, in this combination, each actuator often becomes saturated, meaning that the force applied to each actuator has reached its maximum or minimum allowable limit. The result of saturation negatively impacts the alignment control and compensation process, leading to a decrease in overlay processing and also causing slippage of the imprint template, which can affect other aspects of the imprint lithography process. Therefore, the force used for residual error compensation needs to be optimized. [Overview of the project]

[0005] The present disclosure provides a method and system for optimizing the forces applied to an actuator during a nanoimprint lithography process by: selecting a first set of forces within a first set of force limits applied to the edge of a template; estimating a first residual distortion representing a first predicted overlay error associated with an imprint method simulated when the first set of forces is applied to the edge of the template; selecting a second set of forces within a second set of force limits applied to the edge of the template; estimating a second residual distortion representing a second predicted overlay error associated with an imprint method simulated when the second set of forces is applied to the edge of the template; and selecting an initial set of forces from the first set of forces and the second set of forces having the narrowest set of force limits and residual distortion below a threshold tolerance.

[0006] In one embodiment, the residual distortion is a statistical measure of the set of predicted overlay error values, the statistical measure being one of the standard deviation, range, maximum, mean, and median.

[0007] In another embodiment, the second force limit is within the first force limit, the second residual distortion is higher than the first residual distortion, the second residual distortion is lower than the residual threshold, and the initial set force is the second set force.

[0008] In a further embodiment, the force of the second set is selected as the force of the initial set if the second residual distortion is within the acceptable range of the reproducibility of the first residual distortion, or is higher than the first residual distortion.

[0009] In another embodiment, a film is imprinted on the field using the force of the initial set, which includes adjusting the force of the initial set within the widest range of the force limits of the first set and the force limits of the second set, in response to alignment signals received while the film is being imprinted.

[0010] In another embodiment, the residual distortion relates to a desired distortion of the template based on the measured or predicted substrate distortion in the substrate imprinted by the template.

[0011] In yet another embodiment, the force limit of the first set is the force limit of the widest set that can be used during imprinting, the residual threshold is the sum of the first residual distortion and the allowable threshold, and the force of the initial set is the force of the second set when the second residual distortion is less than the residual threshold.

[0012] In a further embodiment, the force limit of the first set is wider than the force limit of the second set, the residual threshold is the sum of the first residual distortion and the tolerance threshold, and the force of the initial set is the force of the second set when the second residual distortion is less than the residual threshold.

[0013] 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, the drawings, and the claims.

Brief Description of the Drawings

[0014] [Figure 1] FIG. 1 shows a side view of a nanoimprint lithography system.

[0015] [Figure 2] FIG. 2 shows a side view of the substrate of FIG. 1.

[0016] [Figure 3] FIG. 3 shows the configuration of a deformation mechanism.

[0017] [Figure 4A-4B] FIGS. 4A and 4B are flowcharts of a force optimization algorithm.

[0018] [Figure 5A-5B] FIGS. 5A and 5B are graphical representations of the force values applied by respective deformation mechanisms.

[0019] [Figure 6] FIG. 6 is a graph of force reduction for a particular deformation mechanism based on the optimization algorithm of the present disclosure.

[0020] [Figures 7A-7B] FIGS. 7A and 7B illustrate the improvements provided by the force optimization algorithm of the present disclosure. [Modes for carrying out the invention]

[0021] Figure 1 shows an imprint lithography apparatus 100 for forming a relief pattern on a substrate 102. The substrate 102 may be coupled to a substrate chuck 104. In some examples, the substrate chuck 104 includes a vacuum chuck, a pin chuck, a groove chuck, an electromagnetic chuck, or other suitable chuck. Exemplary chucks are described in U.S. Patent No. 6,873,087, which is incorporated herein by reference. The substrate 102 and the substrate chuck 104 may be further supported by a stage 106. The stage 106 provides motion with respect to the x, y, and z axes, as well as rotation around the z axis (e.g., θ). In this regard, the stage 106 may refer to an XYθ stage. The stage 106, the substrate 102, and the substrate chuck 104 may be positioned on a base (not shown).

[0022] The imprint lithography system 100 includes an imprint lithography template 108 positioned spaced apart 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 patterning surface 112. The template 108 and / or mold 110 may be formed from materials including, but are 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 patterning surface 112 includes a number of features defined by spaced recesses 124 and protrusions 126. The patterns formed as described above are for illustrative purposes only, and any type of pattern may be represented on the patterning surface 112. Therefore, the patterning surface 112 can define any pattern that forms the basis of the pattern formed on the substrate 102 via the imprint process.

[0023] The template 108 may be coupled to a template chuck 128. In some examples, the template chuck 128 includes a vacuum chuck, a pin chuck, a groove 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 may be of the same type as the substrate chuck 104. In other embodiments, the template chuck 128 and the substrate chuck may be of different types. Furthermore, the template chuck 128 may be coupled to the imprint head 130, or both, so as to facilitate the movement of the template 108. The movement of the template 108 includes in-plane movement of the template and out-of-plane movement of the template relative to the template. In-plane movement includes translation of template 108 within the plane of the template (e.g., in the XY plane as shown in Figure 1) and rotation of the template within the plane of the template (e.g., in the XY plane and around the Z axis). Translation or rotation of template 108 relative to substrate 102 can also be achieved by translation or rotation of the substrate. In-plane movement of template 108 also includes increasing or decreasing compressive forces on both sides of the template (e.g., using a magnification actuator) to increase or decrease the dimensions of the template in the XY plane of the template. Mechanisms and controls for applying and adjusting forces are described below with respect to Figures 3-10. Out-of-plane movement of template 108 includes translation of the template along the Z axis (e.g., to increase or decrease the force applied to the substrate via the template by increasing or decreasing the distance between the template and the substrate) and rotation of the template around an axis in the XY plane of the template. Rotation of template 108 around an axis in the template's XY plane changes the angle between the XY plane of template 108 and the XY plane of substrate 102, and is referred to herein as “tilting” the template with respect to the substrate, or changing the “tilt” or “tilt angle” of the template with respect to the substrate.U.S. Patent No. 8,387,482 discloses the movement of a template via an imprint head in an imprint lithography system, which is incorporated herein by reference.

[0024] The imprint lithography apparatus 100 may further include a fluid dispensing system 132. The fluid dispensing system 132 may be used to deposit a polymerizable material 134 onto a substrate 102. The polymerizable material 134 may be placed 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 placed 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 monomers such as those 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 placed on the substrate 102 as a plurality of droplets 136.

[0025] Referring to Figures 1 and 2, the imprint lithography system 100 may further include an energy source 138 coupled to guide energy 140 along a path 142. In some examples, the imprint head 130 and stage 106 are configured to position a template 108 and substrate 102 in align with the path 142. The imprint lithography apparatus 100 may be coordinated by a controller 144 that communicates with the stage 106, imprint head 130, fluid dispensing system 132, energy source 138, or any combination thereof, and may operate on a computer-readable program stored in memory 146.

[0026] 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 between them to be filled by the polymerizable material 134. For example, the imprint head 130 may apply force to the template 108 so that the mold 110 is in contact with the polymerizable material 134. After the desired volume has been filled by the polymerizable material 134, an energy source 138 generates energy 140, such as broadband ultraviolet radiation, to polymerize the polymerizable material 134, conforming the shape of the surface 148 of the substrate 102 to the patterning surface 112, and defining a polymer patterned layer 150 on the substrate 102. In some examples, the patterned layer 150 includes a residual layer 152 and a plurality of features indicated as protrusions 154 and recesses 156, where the protrusions 154 have a thickness t1 and the residual layer 152 has a thickness t2.

[0027] The systems and processes described above may be further implemented in the imprint lithography processes and systems referenced 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, all of which are incorporated herein by reference.

[0028] Imprint lithography substrates and templates may include corresponding pairs of alignment marks that enable real-time alignment of the template and the substrate. After the patterned template is positioned on the substrate (e.g., after being superimposed on the substrate), the alignment of the template alignment marks with respect to the substrate alignment marks is determined. The alignment method may include "through mesa" (TTM) measurement of the alignment error associated with the corresponding pair of alignment marks, as disclosed in U.S. Patent Nos. 6,916,585, 7,170,589, 7,298,456, and 7,420,654, all of which are incorporated herein by reference, and subsequent compensation of such error to achieve precise alignment between the template and the desired imprint position on the substrate. The alignment error may be caused by the relative positioning of the substrate and the template, deformation of the substrate or the template, or a combination thereof. Alignment errors can also be caused by vibrations introduced by the imprint lithography process and one or more movements of the machine performing the imprint lithography process.

[0029] Figure 3 shows an exemplary deformation mechanism 310 and a control system that selectively determines and applies control values ​​transmitted, communicated, or otherwise transmitted to each of the multiple deformation mechanisms 310. These control signals cause each deformation mechanism 310 to modify by applying a compressive force applied to the template 108 shown in Figure 1 so that the imprint pattern 112 can form a better match with the substrate 102 and transfer the imprint pattern 112 thereto. The deformation mechanism 310 can deform the pattern area 112 of the template 108 by applying force to the four sides 302a-302d of the template 108. As shown herein, this exemplary embodiment includes 16 deformation mechanisms 310. Each deformation mechanism 310 includes an actuator 312 connected to a contact portion 314, the contact portion 314 in contact with at least a portion of the adjacent template sides 302a-302d. Each deformation mechanism 310 is connected to a controller 144 (indicated by dashed lines). The controller 144 executes at least one control algorithm that selectively determines the amount of force applied by each of the individual deformation mechanisms 310 to modify the shape of the sides 302a to 302d of the template 108.

[0030] As shown in Figure 1, the controller (control unit) 144 includes at least one central processing unit (CPU) and memory, and can execute instructions stored in memory to perform one or more of the operations and / or functions described. The controller 144 communicates with one or more memories (e.g., RAM and / or ROM) and, in some examples, executes stored instructions to perform one or more control operations. In other examples, the controller 144 may temporarily store data used for the calculation and generation of various signals, as described below, in one or more memories. Thus, the controller 144 controls the system 100 in Figure 1 by using a computer program (one or more stored instructions that can be executed by the CPU) and data stored in RAM and / or ROM. Here, the controller 144 may include (or communicate with) one or more dedicated hardware or GPUs (graphics processing units) separate from the CPU, and the GPUs or dedicated hardware may perform some of the processing performed by the CPU. Examples of dedicated hardware include ASICs (application specific integrated circuits), FPGAs (field-programmable gate arrays), and DSPs (digital signal processors). In some embodiments, the controller 144 may be a dedicated controller. In other embodiments, the control system 100 may include a plurality of controllers that communicate with other components of the control system 100 in order to perform the operations described herein.

[0031] The connection between the controller 144 and each deformation mechanism 310 allows one or more control signals (time-series control values) to be transmitted (communicated) to each deformation mechanism 310, which controls the actuator 312 to apply various levels of force to the sides 302a-302d via each contact portion 314. These control signals may be transmitted, transmitted, or otherwise communicated to each of the deformation mechanisms 310 via a wired or wireless communication path. The actuator 312 drives the contact portion 314 to generate a force that is applied to a portion of the side of the template 108 adjacent to it. Although shown herein as two separate components, the actuator 312 and the contact portion 314 may be formed integrally with each other. The actuator 312 portion of the deformation mechanism 310 may include, but is not limited to, any operating mechanism including a pneumatic coil, piezoelectric coil, magnetostrictive coil, and voice coil. In one embodiment, the deformation mechanisms 310 are mounted on a frame and linked to each other via a link system, thereby allowing control signals for controlling the movement and operation of the deformation mechanisms 310 to be provided to the link system.

[0032] An exemplary control algorithm includes operating a deformation mechanism 310 as a correction mechanism that physically deforms the template 108 by applying external forces from sides 302a to 302d of the template 108. By applying these forces, the shape of the pattern area 112 is corrected so that the difference between the shape of the pattern (shot area) formed on the substrate and the shape of the pattern area 112 can be reduced. This improves the overlay accuracy (superposition accuracy) between the pattern formed on the substrate and the pattern of the imprint material newly formed on the substrate. Exemplary components of the shape (including size) of the pattern area 112 that can be controlled by the deformation mechanism 310 include, for example, magnification components and distortion components (e.g., rhombus, trapezoidal, and higher-order components).

[0033] The example of 16 deformation mechanisms as shown in FIG. 3 is for illustrative purposes only and shows only one possible embodiment. In other embodiments, there may be N deformation mechanisms 310, where N is at least 2. The number of deformation mechanisms used can be determined based on the size of the template and the amount of force that needs to be applied to various sides of the template. In one embodiment, there are the same number of deformation mechanisms 310 on each side 302a - 302d of the template 108.

[0034] During the imprint process, the force applied by each deformation mechanism 310 is used for the first control and correction process and the second control and correction process. The first control and correction process includes alignment and control processes to ensure that the template is properly aligned with the substrate and that the pattern on the template is applied to the substrate by lithographic imprint, as described above. The second control and correction process includes determining the additional force applied by each deformation mechanism 310 to correct residual overlay errors not corrected by the first control and correction process. The force determined for each deformation mechanism is aggregated and used to deform the template to improve the position and conformity of the template with respect to the substrate.

[0035] The distortion components corrected in the x and y directions by the first control and correction process and the second control and correction process are generally represented by the following equation (1). JPEG2023064048000002.jpg18169 Here, e x is the overlay error in the X direction, and e y is the overlay error in the Y direction. k 1x is the shift in the X direction, k [[ID=1,6]] 2x is the magnification in the X direction, k 3x is the skew in the X direction, k 4x is the trapezoidal correction in the X direction. k 1y is the shift in the Y direction, k [[ID=2,4]] 2y is the magnification in the Y direction, k 3y is the skew in the Y direction, k 3y 4yThis is trapezoidal correction in the Y direction. f is the final imprint force value, k tiltx is the tilt in the X direction, and k tilty is the tilt in the Y direction. These include a first set of distortion components, also known as low-order distortion components. In the above equation, there is a second set of distortion components, also known as high-order distortion components, which represent the residual error in the X direction. JPEG2023064048000003.jpg1111, and representing the residual error in the Y direction. This is JPEG2023064048000004.jpg1111. In one embodiment, the second set of distortion may also include some of the lower-order components of the overlay, such as magnification, skew, and trapezoidal error, in addition to the higher-order distortion components.

[0036] Typically, a first control and correction process is used to correct a first set of distortion components using a combination of real-time feedback and feedforward closed-loop processing, and a second control and correction process is used to correct a second set of distortion components. Typically, these second sets of distortion components are not measured in real time and are not actively corrected, and estimates of these overlay distortions are obtained in prior test experiments where the second set of distortions are not corrected. These distortion estimates are then obtained from overlay data measured on these test substrates using measurement tools such as the Archer® tool (KLA Corporation, Mulpitas, CA). Also, since the estimates are obtained from prior test wafers, these correction forces can be determined before imprinting on the device substrate and applied as feedforward for each imprint field (region) on the substrate. In another embodiment, the above estimates can also be measured in real time with the addition of a sufficient number of measurement tools capable of measuring a large number of fields on the substrate. Exemplary alignment processing algorithms are described in U.S. Patent Nos. 7,828,984, 8,845,317, 9,579,843 and 9,573,319, all of which are incorporated herein by reference, and closed-loop control processing is described in U.S. Patent Nos. 10,635,072 and 10,216,104, all of which are incorporated herein by reference.

[0037] The algorithm described herein, when executed during the imprint lithography process, favorably optimizes the magnitude of the forces in each deformation mechanism used to compensate for a second set of distortion parameters (residual errors), thereby increasing the range of forces available for use in compensating for the first set of distortion parameters. This is advantageous because problems associated with compensating for residual overlay arise due to the relatively high magnitude of forces required to compensate for residual overlay errors, which can lead to each of the deformation mechanisms 310 reaching their respective force saturation points (either maximum or minimum force levels). This results in a smaller range of forces that can be used for alignment correction and control provided to compensate for the first set of distortion parameters (e.g., lower-order distortion components).

[0038] To optimize the force to be used to compensate for residual overlay errors and to make available additional force to be used as part of the closed-loop alignment and correction control process, the optimization algorithm described herein iterates (or sweeps) through the range of available forces within a predetermined range of forces for each deformation mechanism 310. This iteration is performed field by field, where the field is the area on the substrate where the imprint is performed. Outside the predetermined range of forces that each deformation mechanism 310 can use to compensate for residual overlay errors are the lower force range and the upper force range used for the alignment and control process. The lower force range starts at the minimum force value of the predetermined range of forces and approaches zero, while the upper force range starts at the maximum force value of the predetermined range of forces. The total force range available for each deformation mechanism starts at the lowest force value in the lower force range and ends at the maximum force value in the upper force range, thereby including the lower force range, the predetermined force range, and the upper force range. The force optimization algorithm advantageously iterates through force ranges for each distortion mechanism applied to a particular imprint field to correct for a target second set of distortions, calculates residual values ​​at each force limit, and identifies and selects the optimal minimum-maximum force range to achieve residual values ​​within a given tolerance. In one embodiment, the residual values ​​using the optimal minimum-maximum force range are within an acceptable threshold for residual values ​​obtained within the initial minimum-maximum force range. As used herein, comparing residual values, or comparing the difference in residual values ​​to a threshold, refers to a statistical index of the residual error distribution. In one embodiment, the statistical index is the standard deviation (or three times the standard deviation), but may be other statistical indexes such as variance, range, mean, median, or maximum. For each imprint field, a set of outliers is measured, an outlier residual for each outlier forming the set is calculated, and then a statistical index of the set of outliers is calculated. The statistical index may be a statistical index, or a function of one or more statistical indexes, such as the mean plus three times the standard deviation. By minimizing the force required for overlay correction, there is an expansion of available forces that can be utilized and applied during alignment control and correction processing on a specific field for correcting the first set of distortions.

[0039] The optimization algorithms described herein are executed by the controllers 144 shown in Figures 1 and 3. Each controller 144 may have a set of stored instructions executed by the CPU of the controller 144 to perform the functions described herein. In other embodiments, each controller described herein may be embodied as an individual integrated circuit, each having its own CPU and memory, 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. Furthermore, in some embodiments, some of the controllers described herein may be dedicated processing units that communicate with the CPU of the controller executing stored instructions to complete the functional operations described herein.

[0040] In step S400, the optimization process is initiated and performed for each of the individual fields on the substrate to be imprinted during the lithography imprint process, and for each of the respective deformation mechanisms 310. In step S402, the residual overlay value ε is calculated using the initial optimization method based on the initial maximum and minimum force values. x and ε y The following is calculated. This initial minimum-maximum force range can extend across the entire force range available on each deformation mechanism 310. More generally, the initial minimum-maximum force range extends across the majority of the force range available on each deformation mechanism 310. In one embodiment, the initial optimization method is carried out such that the residual overlay value calculated in S402 is performed based on the following equation (2). JPEG2023064048000005.jpg39169 Here, T x and T y (nm) is the higher-order distortion component (second set of distortion) of the overlay in the x and y directions at a predetermined number of measurement points m. MagX and A MagY (nm / N) represents the deformation mechanism actuator force C magThis is a transformation matrix that transforms (N) into template distortion (nm) along the X and Y axes, respectively. heatX and A heatY is the heating power density C heat (W / m 2 This is a transformation matrix that converts ) to wafer / substrate overlay distortion (nm). Target distortion T x and T y (nm) is the second set of distortion obtained from the overlay measured on a pre-test board that has not been corrected for the second set of distortion. In another embodiment, these measurements can be performed in real time using additional measurement tools. Since these target distortions may differ for each field on the imprinted board, different solutions are calculated for each field. The purpose of the regression / optimization described above is F min ~F max and C heat min ~C heat max Within the constraints, the residual value ε in each field x and ε y The effort vector C that minimizes [the specified value]. Mag (N) and C heat (W / m 2 The goal is to find ε. x and ε y This represents the overlay error that remains uncorrected by this higher-order distortion correction mechanism. For the purposes of this disclosure, the relevant value used by the optimization algorithm described herein is F min ~F max These values ​​are obtained based on the final force values ​​of each deformation mechanism 310 in a prior test run in which the distortion of the second set had not been corrected.

[0041] Figures 5A and 5B schematically illustrate the calculation in step S402. Figure 5A shows each of the 16 deformation mechanisms on the x-axis and the respective final forces applied to the substrate by each deformation mechanism during execution, as shown on the y-axis, where higher-order distortions are not corrected (normalized to force ranges). From this, the plot shown in Figure 5B can be calculated, which shows the range of forces available for each of the deformation mechanisms that can be used to correct other distortions, such as higher-order distortions. Initial minimum and maximum force limits F for each finger for optimization. min and F max This is calculated by subtracting the force of the corresponding finger in Figure 5A from the minimum and maximum force ranges available for each compensation mechanism. This generally means that the initial minimum-maximum force range is the widest force range that can be used to compensate for the second set of distortions in the process. Using these force limits, equation (2) is solved for the residual value (ε x , ε y This is determined. This represents the least squares residual estimate, but it is not the most efficient from the standpoint of actuator force utilization, because input effort utilization is as inefficient as possible. This is important because, as mentioned above, the hardware (e.g., deformation mechanism) is shared between higher-order distortion correction and dynamic alignment control / correction functions (e.g., closed-loop control of lower-order errors).

[0042] As a result of S402, the overlay residual value is calculated using the initial maximum and minimum force values ​​across the full force range available to the actuator, and then the force limit range is further optimized by S406-S416 to find an efficient force range that balances overlay correction and force utilization. In step S404, the maximum force limit used in S402 is reduced by a predetermined step size. In one embodiment, the predetermined step size is a force value in the range of 1N to 5N. For example, in S404, the initial Fmax value calculated in S402 is reduced by a predetermined magnitude of 5N, and the overlay residual value ε x and ε yThe recalculation is performed, and it is determined whether the recalculated residual value is within a predetermined tolerance threshold for the overlay residual value in S402. In other words, the difference between the residual value with a wider initial force range and the residual value with a narrower force range is calculated, and the difference value is 3 * Statistical indicators such as standard deviation are obtained from the difference, and the difference is then compared to a predetermined tolerance threshold. The predetermined tolerance threshold is a distance in nanometers that is acceptable as an overlay error, and by reducing the maximum force, the resulting correction still allows an acceptable overlay error while increasing the amount of force available to other correction mechanisms such as alignment control and correction. In another embodiment, it is determined that the recalculated residual value is within a predetermined tolerance threshold representing the absolute overlay residual value.

[0043] In one embodiment, a predetermined tolerance is based on the reproducibility of the overlay in the nanolithography imprint process. The tolerance threshold (Δ) may be determined (or set) according to the following: In one exemplary embodiment, the tolerance thresholds represent acceptable residual values ​​of 0.05 nm, 0.1 nm, and 0.2 nm. In another embodiment, the tolerance thresholds may be based on a percentage of the target overlay budget. For example, the tolerance threshold may be less than or equal to 10% of the total overlay error variance. In an exemplary embodiment where the overlay error budget is 3σ = 2 nm (3 standard deviations of overlay error in the device) and the tolerance threshold for this optimization is set as 10% of the overlay error variance, the threshold is determined accordingly as follows: JPEG2023064048000007.jpg15169

[0044] Therefore, step S404 calculates the updated residual value and determines whether the difference between the updated residual value and the original residual value is less than a predetermined threshold tolerance, as shown in step S406. If the difference between the updated residual value from S404 and the original residual value in S402 is less than (or equal to) the tolerance threshold (e.g., TRUE), the value of Fmax is updated to the reduced force value, as in S408, and the process proceeds to S410, which is described below. If the determination in S406 indicates that the difference between the updated residual value from S404 and the original residual value in S402 is not less than the tolerance threshold (e.g., FALSE), the algorithm proceeds to S407, where a further determination is made as to whether the overlay residual value difference from step 412 in the previous iteration is less than the tolerance threshold. In S407, the value to be determined is the overlay residual value difference from S412 taken from the output of S410 in the previous iteration (indicated as i-1 in the flowchart). If the determination in S407 is negative, the algorithm proceeds to S416, where the Fmax value is set to equal to the previous maximum force value and Fmin is set to the previous minimum force value. If the determination in S407 is positive, in S409 the value of Fmax is maintained at the determined previous Fmax value (which may be the value determined in S402 for the first iteration), and then the process proceeds to S410.

[0045] In S410, the algorithm obtains the minimum force value Fmin calculated in S402 and increments the minimum force value by a predetermined step size. In one embodiment, the predetermined step size is a force value in the range of 1N to 5N. For example, in S410, the initial Fmin value calculated in S402 is increased by a predetermined size of 5N, and the residual value ε x and ε y The value is recalculated, and it is determined whether the recalculated residual value is within a predetermined tolerance threshold of the original residual value calculated in S402. The recalculation of the residual value performed in S410 may be based on the updated Fmax value set in S408, or it may use the previous Fmax value set in S409.

[0046] In step S412, a further comparison of the updated residual values ​​calculated in S410 is made against an acceptable threshold, as described in S406. If the difference between the updated residual value from S410 and the original residual value in S402 is less than (or equal to) the acceptable threshold (e.g., TRUE), the value of Fmin is updated to the increased force value, as in S413, and the process returns to S404 to determine whether another optimization iteration can be performed to further decrease and increase the values ​​of Fmax and Fmin, respectively. If the determination in S412 indicates that the difference between the updated residual value from S410 and the original residual value in S402 is greater than the acceptable threshold (e.g., FALSE), then in S414, a further determination is made to determine whether the overlay residual difference from step 406 in the same iteration is less than the acceptable threshold (e.g., the question from S406). If the question in S414 is affirmative (e.g., TRUE), the algorithm proceeds to S415, where the value of Fmin is kept at the previous Fmin value (which may be the value determined in S402 for the first iteration), and then returns to S406 to perform another optimization iteration. If the decision in S414 is negative, the algorithm proceeds to S416, where Fmin is set to the previous minimum force value and Fmax is set to equal to the previous maximum force value.

[0047] When it is determined that increasing the Fmax value and decreasing the Fmin value will result in the residual difference exceeding the allowable threshold, then in S416, the current Fmax and Fmin values ​​are set for the specific imprint field, and the algorithm in Figure 4 is repeated for subsequent imprint fields on the substrate. In other words, for both S412 and S406, as soon as the overlay residual value falls outside the allowable threshold of the original overlay residual value in S402, the optimization is stopped and the previous minimum and maximum force limits are selected for the field. This routine allows the actuator to use the minimum force range to compensate for the second set of distortions. Thus, this optimization algorithm favorably improves the available force range that can be made available to each of the deformation mechanisms for real-time feedforward compensation of distortions other than higher-order distortions (the first set of distortions).

[0048] The improvements provided by the execution of the algorithm in Figure 4 can be visualized in the graph in Figure 6. Here, an exemplary plot of residual distortion based on Fmax determined for multiple deformable members (determined so that each deformable member can exhaust its available maximum force range) is shown. As shown herein, the point labeled 602 represents three standard deviations of the overlay residual value calculated with Fmax values ​​that utilize the force up to the actuator's maximum force limit according to step S402. By further improving the optimization process by stepping down the Fmax level while keeping the overlay residual value below the acceptable threshold of the original residual value (602), the resulting Fmax value can be reduced as shown by the point labeled 604. By thus reducing the force required to perform higher-order distortion correction (correction of the second set of distortions), available force is freed up that can be used for lower-order distortion correction (first set of distortions) during real-time feedback alignment control processing. This benefit is explained for single-field overlay distortion data. However, it should be understood that determining the optimal upper and lower force limits for each field can provide distortion performance within predetermined tolerance thresholds in the nanometer range.

[0049] Figure 4A illustrates an algorithm that iteratively steps down the maximum force level determined by the initial optimization in S404-S408 and steps up the minimum force level determined by the initial optimization in S410-S414. In another embodiment, the optimization algorithm may include either the actions performed in S404-S408 or the actions performed in S410-S414. In any of these embodiments, step S402 for calculating the residual value having the maximum force range available to the actuator / deformation mechanism (allowable maximum Fmax, minimum Fmin) precedes the above reference block such that in S402 only the maximum force is iteratively stepped down from the initial maximum force limit, or in S402 the minimum force is iteratively increased from the initial minimum force limit.

[0050] In an embodiment where the optimization algorithm seeks to optimize the maximum force limit (Fmax), the algorithm includes S400-S408 and S416. In this iteration, the initial Fmax value is calculated in S402, and then the Fmax value is stepped down by a predetermined step value representing a given force (N), and the updated residual value is calculated in S404. In S406, the difference between the updated residual value and the original residual value is compared with an allowable threshold. If the difference in residual values ​​is smaller than a predetermined allowable threshold, the stepped-down value of Fmax is set as the new Fmax value. This process is repeated until the comparison in S406 results in a difference in residual values ​​that is greater than the threshold allowable range at the time the latest Fmax (the last Fmax for which condition S406 is true) is set as the Fmax value, and the algorithm is applied to the next imprint field.

[0051] In an embodiment where the optimization algorithm seeks to optimize the minimum force limit value (Fmin), the algorithm includes S400-S402, S410-S413, and S416. An initial Fmin value is calculated in S402, and then the Fmin value is increased by a predetermined step value representing a given force (N), and the updated residual value is calculated in S410. In S412, the difference between the updated residual value and the original residual value is compared with an allowable threshold. If the difference in residual values ​​is smaller than a predetermined allowable threshold, in S413, the increased value of Fmin is set as the new Fmin value. This process is repeated until the comparison in S412 results in a difference in residual values ​​that is greater than the threshold allowable range at the time the latest Fmin (the last Fmin for which condition S412 is true) is set as the Fmin value, and the algorithm is applied to the next imprint field.

[0052] In another embodiment of the optimization algorithm shown in Figure 4B, steps S404-S408 are executed concurrently with steps S410-S414. In this embodiment, the initial optimization process begins in S450, and the residual values ​​are calculated in S452, which reflect the operation described above in S402. In S452, the overlay residual values ​​are obtained using the initial maximum and minimum force limits (over the entire usable force range for the actuator / deformation mechanism). Once obtained, in S454, an estimation process is performed to estimate the updated maximum and updated minimum force values. This is done by subtracting a predetermined step size from the maximum force value and adding a predetermined step size to the minimum force value. In one embodiment, the step sizes to be subtracted and added are the same value. However, these step size values ​​do not need to be the same. Next, in S456, the updated residual value is calculated using these force limits. If the difference between the updated residual value (in S452) and the original residual value is smaller than the threshold tolerance, which is expressed by a predefined value in nanometers, the algorithm continues back to S454, iterating in a single step of decreasing the maximum force limit and increasing the minimum force limit. If the question in S456 indicates that the difference between the updated residual value and the original residual value is greater than the tolerance threshold, further optimization is performed in S458 to generate a first further residual value. In the first further optimization, the updated maximum force limit is calculated by adding the step size to the current maximum force value (the purpose of which is to advance to the previous maximum force limit) and maintaining the current minimum force value. This is used to calculate the first further residual value. Simultaneously, in S459, a second further optimization is performed to obtain a second further residual. To obtain the second further residual value, the current maximum force limit is maintained and the step size is subtracted from the current minimum force value. In step 460, a comparison is made between the first additional residual value and the original residual value (calculated using the initial minimum and maximum force limits), and between the second additional residual value and the original residual value. In S462, the maximum and minimum force values ​​are set based on the following results.If only the difference between the first additional residual value and the original residual value is less than the allowable threshold, the maximum and minimum force values ​​used to generate the first additional residual value are retained, and processing continues on the further imprint field. If this comparison does not result in a residual difference less than the threshold, further processing is performed. If only the difference between the second additional residual value and the original residual value is less than the allowable threshold, the maximum and minimum force values ​​used to calculate the second additional residual value are retained, and processing continues on the further imprint field. However, if both of the residual differences resulting above are less than the allowable threshold, the maximum and minimum force values ​​that produced the smallest difference from the allowable threshold are retained, and processing continues on the further imprint field.

[0053] In another embodiment, the above optimization may be modified so that a coarse optimization is performed first, and if the coarse optimization does not result in a difference between the updated residual value and the original residual value that is smaller than an acceptable threshold, the above further optimization used to generate a first further residual value and a second further residual value is performed using a different step size than the original step size used. By making the step size for the initial optimization coarser than that of subsequent optimizations having finer step sizes, the iterations may be reduced through force values ​​at both the maximum and minimum levels to obtain efficient and acceptable maximum and minimum force values ​​for the deformation mechanism.

[0054] The improved results of the optimization algorithm can be seen in the graphs in Figures 7A and 7B. Figure 7A shows the frequency (number of instances) at which different force values ​​are applied by the deformation mechanism when using only the initial optimization performed in S402 described above. These are the frequencies for all imprint fields on the wafer. Figure 7B shows the results when the overall optimization algorithm of Figure 4 (and any additional described embodiments) is performed. Comparing the frequency at which the upper and lower force values ​​are applied in Figure 7B with that in Figure 7A, a significant decrease in the frequency at the upper and lower force values ​​is observed, but it resulted in substantially the same overlay on the substrate, with the residual difference within the tolerance threshold (in this example, the tolerance threshold was set to 0.1 nm). The reduction in the upper and lower force ranges is advantageous in that it increases the available range for closed-loop alignment control and correction processing, i.e., for correcting the first set of distortions.

[0055] To statistically evaluate the performance of this new method using the current method, performance across the entire wafer can be evaluated to see the improvements shown in Figures 6, 7A, and 7B. Minimal distortion correction is obtained by providing a trade-off for distortion correction within a given threshold tolerance (e.g., 0.05 nm), but the distribution of the number of deformation mechanisms observed in different force ranges is improved after the improvement in higher-order distortion correction. When closed-loop control for alignment is initiated, it is desirable that fewer deformation mechanisms be in higher force ranges closer to the maximum force range, as the probability of saturation increases for these deformation mechanisms. Returning to Figure 7A, without the optimization algorithm, 450 (339 + 77 + 20 + 14) instances of deformation mechanisms are in force ranges greater than 69% of the normalized force, and therefore have a higher probability of saturation for these deformation mechanisms. Referring to Figure 7B, the results when the efficient force-limit optimization algorithm described above is performed are shown, and the number of instances of deformation mechanisms greater than 69% of the normalized force decreases from 450 to 61 (49 + 3 + 5 + 4). In general, Figure 7B shows a significant reduction in the number of instances of the deformation mechanism that fall within the upper and lower force ranges.

[0056] As a result, the algorithm described herein determines an efficient set of forces for a deformation mechanism without sacrificing the overlay correction potential for higher-order distortion correction. In doing so, the set of forces applied to the edges of a particular template is redistributed and relaxed in the calculation such that the new set of forces is equal to or narrower than the set of forces used in conventional optimization methods, and the overlay residual values ​​remain within tolerance usage determined to depend on the reproducibility of the imprint process and tools. Thus, the new overlay residual values ​​remain substantially the same as the previous overlay residual values.

[0057] Several embodiments have been described. However, it should be understood that various modifications may be made without departing from the spirit and scope of this disclosure. Accordingly, other embodiments are within the scope of the appended claims.

[0058] One embodiment of the present disclosure can be realized by providing a program that performs one or more of the functions of the embodiments described above to a system or device via a network or storage medium, and by reading and executing the program on one or more processors in the computer of that system or device. Alternatively, one embodiment of the present disclosure can be realized by a circuit (for example, an application-specific integrated circuit (ASIC)) that performs one or more functions.

[0059] Embodiments of the present disclosure may be implemented by a computer of a system or device including one or more circuits (e.g., application-specific integrated circuits (ASICs)) for performing one or more functions of the embodiments described above, by reading and executing computer-executable instructions (e.g., one or more programs) recorded on a storage medium (which may be more entirely called a “non-temporary computer-readable storage medium”) for performing one or more functions of the embodiments described above, and / or by controlling, for example, one or more circuits for performing one or more functions of the embodiments described above, by the computer of the system or device. The computer may comprise one or more processors (e.g., a central processing unit (CPU), a microprocessor unit (MPU)) and may include a separate computer or a network of separate processors for reading and executing computer-executable instructions. Computer-executable instructions may be provided to the computer from, for example, a network or a storage medium. The storage medium may include, for example, one or more of the following: hard disk, random access memory (RAM), read-only memory (ROM), storage devices for distributed computing systems, optical discs (e.g., compact discs (CD), digital versatile discs (DVD), or Blu-ray discs (BD) (trademark)), flash memory devices, memory cards, etc.

[0060] When referring to the description, specific details are provided to give a complete understanding of the disclosed embodiments. In other examples, well-known methods, procedures, components, and circuits are not described in detail so as not to unnecessarily lengthen this disclosure.

[0061] Where an element or part is referred to herein as being “on,” “against,” “connected to,” or “coupled to” another element or part, it should be understood that it may be directly on, against, connected to, or coupled to the other element or part, or there may be an intervening element or part. In contrast, where an element is referred to as being “directly on,” “directly connected to,” or “directly coupled to” another element or part, there is no intervening element or part. Where used, the terms “and / or” include any and all combinations of one or more of the enumerated items relating to the subject, as provided therefor.

[0062] Spatial relative terms such as “under,” “beneath,” “below,” “above,” “upper,” “proximal,” and “distal” may be used herein to facilitate explanation and describe the relationship between one element or feature and another, as shown in various diagrams. However, it should be understood that spatial relative terms are intended to encompass different orientations of a device in use or operation, in addition to the orientation shown in the diagrams. For example, if a device in a diagram is upside down, an element described as “below” or “beneath” another element or feature will be oriented “above” that other element or feature. Thus, spatial relative terms such as “below” can encompass both upward and downward orientations. A device may also be in other orientations (90° or other orientations), and the spatial relative descriptors used herein should be interpreted accordingly. Similarly, the spatial relative terms "proximal" and "distal" may be interchangeable where applicable.

[0063] As used herein, the term "about" means, for example, within 10%, within 5%, or less. In some embodiments, the term "about" may mean within the measurement error.

[0064] Terms such as First, Second, Third, etc., may be used herein to describe various elements, components, areas, parts, and / or sections. It should be understood that these elements, components, areas, parts, and / or sections should not be limited by these terms. These terms are used solely to distinguish one element, component, area, part, or section from another. Therefore, the First element, component, area, part, or section described below may be referred to as the Second element, component, area, part, or section without departing from the teachings herein.

[0065] The terms used herein are intended solely to describe specific embodiments and are not intended to limit them. Where used herein, the singular forms “a,” “an,” and “the” are intended to include the plural forms unless the context clearly indicates otherwise. The terms “includes” and / or “including,” where used herein, identify the presence of the described features, integers, steps, actions, elements, and / or components, but should be further understood not to exclude the presence or addition of one or more other features, integers, steps, actions, elements, components, and / or groups thereof that are not expressly stated.

[0066] The above is merely illustrative of the principles of this disclosure. Various modifications and changes to the exemplary embodiments described herein will be apparent to those skilled in the art, given the teachings herein.

[0067] Certain terminology is used for clarity when describing exemplary embodiments shown in the drawings. However, it should be understood that the disclosures in this patent specification are not intended to be limited to the specific terminology thus chosen, and each specific element includes all technical equivalents that function similarly.

Claims

A method for determining the magnitude of the force of each of a plurality of deformation mechanisms that sequentially apply a first set of forces and a second set of forces to a template during an imprint process, comprising: selecting, as the force of each of the plurality of deformation mechanisms applied to the edge of the template, a first set of forces from the force range available to each deformation mechanism; estimating a first residual distortion representing a first predicted overlay error associated with an imprint method simulated when the first set of forces is applied to the edge of the template; selecting, as the force of each of the plurality of deformation mechanisms applied to the edge of the template, a second set of forces from the force range available to each deformation mechanism; estimating a second residual distortion representing a second predicted overlay error associated with an imprint method simulated when the second set of forces is applied to the edge of the template; selecting, from among the first set of forces and the second set of forces, the set of forces for which the difference between the maximum value and the minimum value of the force of each of the plurality of deformation mechanisms is the smallest, and for which the residual distortion of the template after sequentially applying the first set of forces and the second set of forces is less than an acceptable threshold; A method, characterized by including the above. The method according to claim 1, characterized in that the residual distortion is a statistical indicator of a set of predicted overlay error values.

3. The method according to claim 2, characterized in that the statistical indicator is one of standard deviation, range, maximum value, mean, and median.

4. The force range of the second set is within the force range of the first set, the second residual distortion is higher than the first residual distortion, the initial set of forces is the second set of forces. The method according to claim 1, characterized by the above.

5. The second set of forces is selected as the initial set of forces when the second residual distortion is within an acceptable range of reproducibility of the first residual distortion, or the second residual distortion is higher than the first residual distortion. The method according to claim 1, characterized by the above.

6. further comprising performing an imprint process on a field of a substrate using the initial set of forces. Adjusting the force of the initial set within the force range having the widest difference between the maximum and minimum values among the force range of the first set and the force range of the second set in response to an alignment signal received during the imprinting process, the method according to claim 1, characterized in that.

7. The residual distortion is based on the measured or predicted substrate distortion in the substrate imprinted by the template, the method according to claim 1, characterized in that.

8. The force range of the first set is the widest set of force ranges that can be used during imprinting, The value of the residual distortion is the sum of the first residual distortion and the tolerance threshold, The force of the initial set is the force of the second set when the second residual distortion is less than the value of the residual distortion, The method according to claim 1, characterized in that.

9. The force range of the first set is wider than the force range of the second set, The value of the residual distortion is the sum of the first residual distortion and the tolerance threshold, The force of the initial set is the force of the second set when the second residual distortion is less than the value of the residual distortion, The method according to claim 1, characterized in that.

10. An apparatus for performing an imprinting process, A plurality of actuators for sequentially applying a first set of forces and a second set of forces to a template during the imprinting process, A controller coupled to each of the plurality of actuators, Comprising, The controller, Selecting a first set of forces from the force ranges available to each actuator as the force of each of the plurality of actuators applied to the edge of the template, Estimating a first residual distortion representing a first predicted overlay error associated with a simulated imprinting method when the first set of forces is applied to the edge of the template, Selecting a second set of forces from the force ranges available to each actuator as the force of each of the plurality of actuators applied to the edge of the template, Estimating a second residual distortion representing a second predicted overlay error associated with a simulated imprinting method when the second set of forces is applied to the edge of the template, Select, from among the forces of the first set and the forces of the second set, the set of forces for which the difference between the maximum value and the minimum value of the force of each of the plurality of actuators is the smallest, and which is the initial set of forces for which the residual distortion of the template after sequentially adding the force of the first set and the force of the second set is less than the allowable threshold value. An apparatus characterized by this.

11. The apparatus according to claim 10, wherein the residual distortion is a statistical index of a set of predicted overlay error values.

12. The apparatus according to claim 11, wherein the statistical index is one of a standard deviation, a range, a maximum value, an average, and a median.

13. The force range of the second set is within the force range of the first set, The second residual distortion is higher than the first residual distortion, The initial set of forces is the force of the second set, An apparatus characterized by this, according to claim 10.

14. The force of the second set is such that the second residual distortion is within the allowable range of reproducibility of the first residual distortion, or higher than the first residual distortion, is selected as the initial set of forces, an apparatus characterized by this, according to claim 10.

15. The controller configures the apparatus to perform an imprint process on a field of a substrate using the initial set of forces, and adjusts the initial set of forces within the force range having the widest difference between the maximum value and the minimum value among the force range of the first set and the force range of the second set in response to an alignment signal received during the imprint process. An apparatus characterized by this, according to claim 10.

16. The apparatus according to claim 10, wherein the residual distortion is based on measured or predicted substrate distortion in a substrate imprinted by the template.

17. The force range of the first set is the widest set of force ranges that can be used during imprinting, the value of the residual distortion is the sum of the first residual distortion and the allowable threshold value, the initial set of forces is the force of the second set when the second residual distortion is less than the value of the residual distortion, An apparatus characterized by this, according to claim 10.

18. The force range of the first set is wider than that of the second set, The value of the residual distortion is the sum of the first residual distortion and the tolerance threshold, The force of the initial set is the force of the second set when the second residual distortion is smaller than the value of the residual distortion, The device according to claim 10, characterized in that.

19. An article manufacturing method including using the method according to claim 1, Dispensing an imprint resist onto a substrate, Bringing the template having a pattern in contact with the imprint resist into contact with the imprint resist, Processing the substrate on which the imprint resist is dispensed so as to manufacture an article, Further comprising, an article manufacturing method characterized in that.

20. Processing the substrate further includes applying energy to the substrate to cure the imprint resist and forming a pattern corresponding to the pattern of the template on the substrate, The method is repeatedly executed while the template is in contact with the imprint resist so that the template and the substrate are aligned before the imprint resist is cured by the application of the energy, The article manufacturing method according to claim 19, characterized in that.

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