Aberration effects on systems, models, and manufacturing processes

Abstract

Scanner aberration impact modeling in semiconductor manufacturing processes is described. Scanner aberration impact modeling can facilitate co-optimization of multiple scanners. Scanner aberration impact modeling can include executing a calibration model and controlling a scanner based on output from the model. The model is configured to receive patterning system aberration data. The model is calibrated with patterning system aberration calibration data and corresponding patterning process impact calibration data. New patterning process impact data for the received patterning system aberration data can be determined based on the model. The model includes a hyperdimensional function configured to associate the received patterning system aberration data with the new patterning process impact data. The hyperdimensional function is configured to associate the received patterning system aberration data with the new patterning process impact data in an approximate form, rather than full simulation, and without involving computation of aerial images or representations thereof.

Description

[0001] Cross-references to related applications

[0002] This application claims priority to US application 63 / 037,494, filed June 10, 2020, and US application 63 / 147,831, filed February 10, 2021, which is incorporated herein by reference in its entirety. Technical Field

[0003] This article generally deals with photolithography in semiconductor manufacturing, and more specifically, computational photolithography. Background Technology

[0004] Photolithography projection equipment can be used, for example, in the manufacture of integrated circuits (ICs). A patterning apparatus (e.g., a mask) can contain or provide a pattern corresponding to a single layer (“design layout”) of the IC, and can transfer this pattern onto a target portion (e.g., comprising one or more dies) on a substrate (e.g., a silicon wafer) already coated with a layer of radiation-sensitive material (“resist”) by methods such as irradiating the target portion through the pattern on the patterning apparatus. Typically, a single substrate contains multiple adjacent target portions, and the photolithography projection equipment continuously transfers the pattern onto the target portions one target portion at a time. In one type of photolithography projection equipment, the entire pattern on the patterning apparatus is transferred onto a target portion in one operation. This type of equipment is often referred to as a stepper. In an optional equipment (often referred to as a step-scanning apparatus), a projection beam scans across the patterning apparatus in a given reference direction (“scanning” direction) while the substrate is moved parallel or antiparallel to that reference direction. Different portions of the pattern on the patterning apparatus are progressively transferred onto a target portion. Typically, because photolithography projection equipment will have a reduction ratio M (e.g., 4), the substrate movement speed F will be 1 / M times the speed of the projection beam scanning pattern forming apparatus. More information about photolithography apparatuses can be found, for example, in US 6,046,792, which is incorporated herein by reference.

[0005] Before a pattern is transferred from a patterning apparatus to a substrate, the substrate can undergo various processes, such as primer coating, resist coating, and soft baking. After exposure, the substrate can undergo other processes (“post-exposure processes”), such as post-exposure baking (PEB), development, hard baking, and measurement / inspection of the transferred pattern. This series of processes serves as the basis for fabricating individual layers of a device, such as an IC. The substrate can then undergo various processes, such as etching, ion implantation (doping), metallization, oxidation, chemical mechanical polishing, etc., all of which are designed to complete the individual layers of the device. If several layers are required in the device, the entire process or its variations are repeated for each layer. Ultimately, the device will exist in each target portion of the substrate. These devices are then separated from each other using techniques such as dicing or sawing so that individual devices can be mounted on a carrier, connected to pins, etc.

[0006] Therefore, manufacturing devices (such as semiconductor devices) typically involves processing a substrate (e.g., a semiconductor wafer) using multiple manufacturing processes to form various features and multiple layers of the device. These layers and features are typically fabricated and processed using techniques such as deposition, photolithography, etching, chemical mechanical polishing, and ion implantation. Multiple devices can be fabricated on multiple chips on a substrate and then separated into individual devices. This device fabrication process can be viewed as a patterning process. A patterning process involves patterning steps such as optical and / or nanoimprint lithography using a patterning apparatus in a photolithography device to transfer a pattern from the patterning apparatus to the substrate, and typically, but optionally, involves one or more associated patterning processing steps, such as developing with a resist in a developing apparatus, baking the substrate using a baking tool, etching the pattern using an etching apparatus, etc.

[0007] Photolithography is a central step in the fabrication of devices such as integrated circuits (ICs), in which patterns formed on a substrate define the functional elements of the device, such as microprocessors and memory chips. Similar photolithography techniques are also used to form flat panel displays, microelectromechanical systems (MEMS), and other devices.

[0008] As semiconductor manufacturing processes continue to advance, the size of functional components continues to shrink. Simultaneously, the number of functional components (such as transistors) in each device has been steadily increasing, following a trend commonly known as "Moore's Law." In the current state of technology, photolithography projection devices are used to fabricate the layers of devices. These devices project a design layout onto a substrate using irradiation from a deep ultraviolet light source, resulting in individual functional components with dimensions well below 100 nm (i.e., less than half the wavelength of radiation from the irradiation source, such as a 193 nm source).

[0009] The process of printing features with dimensions smaller than the classical resolution limit of photolithography projection equipment is often referred to as low-k1 lithography, according to the resolution formula CD = k1 × λ / NA, where λ is the wavelength of the radiation used (currently mostly 248 nm or 193 nm), NA is the numerical aperture of the projection optics in the photolithography projection equipment, CD is the "critical size" (typically the smallest feature size to be printed), and k1 is an empirical resolution factor. Generally, the smaller k1 is, the more difficult it becomes to reproduce patterns on a substrate that resemble the shape and size planned by the circuit designer to achieve specific electrical functions and performance. To overcome these difficulties, complex fine-tuning steps can be applied to the photolithography projection equipment, layout design, or patterning apparatus. These steps include, but are not limited to: optimization of NA and optical coherence settings, self-limiting illumination schemes, use of phase-shifting patterning apparatus, optical proximity correction (OPC, sometimes also called "optical and process correction") in the layout design, or other methods generally defined as "resolution enhancement techniques" (RET).

[0010] OPC and other RETs utilize robust electronic models that describe the lithography process. Therefore, a calibration procedure for such a lithography model is expected to provide an effective, robust, and accurate model throughout the process window. Currently, calibration is performed using a number of one-dimensional and / or two-dimensional gauge patterns, utilizing wafer measurements. More specifically, one-dimensional gauge patterns include line spacing patterns with varying pitch and critical dimensions (CD), isolation lines, multiple lines, etc. Two-dimensional gauge patterns typically include line ends, contacts, and randomly selected SRAM (Static Random Access Memory) patterns. Summary of the Invention

[0011] According to an embodiment, a non-transitory computer-readable medium is provided, having instructions on it. When executed by a computer, the instructions cause the computer to execute a calibration model configured to receive patterned systematic aberration data. The model is calibrated using the patterned systematic aberration calibration data and corresponding patterned process influence calibration data. The instructions are configured to cause the computer to determine new patterned process influence data based on the model for the received patterned systematic aberration data. The model includes a hyperdimensional function configured to correlate the received patterned systematic aberration data with the new patterned process influence data without simulating, generating, or otherwise calculating a spatial image or its representation.

[0012] In some embodiments, the hyperdimensional function is configured to correlate the received patterned system aberration data with the new patterning process effect data in an approximate and / or simplified form, rather than in a full simulation.

[0013] In some embodiments, the model is calibrated by: providing patterned system aberration calibration data to a base model to obtain a prediction of the patterning process's influence on the calibration data, and using the patterning process's influence on the calibration data as feedback to update one or more configurations of the base model. One or more configurations are updated based on a comparison between the patterning process's influence on the calibration data and the prediction of the patterning process's influence on the calibration data.

[0014] In some embodiments, the model includes one or more nonlinear, linear, and / or quadratic algorithms.

[0015] In some embodiments, updating one or more configurations of the base model includes one or more parameters of the calibration algorithm.

[0016] In some embodiments, the received patterning system aberration data includes received wavefront data, and wherein the new patterning process influence data includes one or more patterning process measures.

[0017] In some embodiments, the one or more patterning process metrics include critical dimensions associated with the patterning process, pattern placement error, edge placement error, critical dimension asymmetry, optimal focus offset, or defect count.

[0018] In some embodiments, the model includes one or more key feature components and one or more general components, the key feature components being configured to model the variation of key features of the patterning process between patterning systems; and the one or more general components being configured to model the general performance of the patterning system for non-key features of the patterning process.

[0019] In some embodiments, the new patterning process impact data from the model is configured to be provided to a cost function to help determine the costs associated with each patterning process metric and / or the costs associated with each patterning process variable.

[0020] In some embodiments, the cost function includes a first component associated with critical features of the patterning process, a second component associated with non-critical features of the patterning process, and a third component associated with physical functional limitations of one or more patterning systems.

[0021] In some embodiments, the cost function further includes a fourth component associated with the wavefront conditioning penalty of the patterning process.

[0022] In some embodiments, the new patterning process impact data output from the model is configured to facilitate the collaborative optimization of multiple patterning systems.

[0023] In some embodiments, the plurality of patterning systems include scanners, and the collaborative optimization includes using lens actuators as variables and using a gradient-based nonlinear optimizer to collaboratively determine the actuator positions of the plurality of scanners.

[0024] In some embodiments, the new patterning process influence data from the model is configured to determine a patterning process control metric set, which is configured to be determined by a linear solver.

[0025] In some embodiments, the new patterning process influences data representation of the effects of the corresponding patterning system aberrations on one or more of the critical size, pattern placement error, edge placement error, critical size asymmetry, optimal focus offset, or defect count associated with the patterning process.

[0026] In some embodiments, the new patterning process influence data from the model is configured to be provided to a cost function to help determine the costs associated with each patterning process metric. The costs associated with each patterning process metric are configured to be provided back to the model to help determine the costs associated with patterning process wavefront conditioning. The costs associated with the patterning process wavefront conditioning are configured to be provided to a driver lens model to help determine the costs associated with each patterning process variable. The costs associated with each patterning process variable are configured to be provided to an optimizer to facilitate the coordinated optimization of multiple patterning systems.

[0027] In some embodiments, the model is calibrated such that the new patterning process influence data is configured to help enhance control over the heating of one or more mirrors and / or lenses of the patterning system.

[0028] In some embodiments, the aberration data of the patterning system is simulated based on the associated pupil shape and pattern forming apparatus design.

[0029] In some embodiments, the patterning process influence data includes a cost function s(Z) of the corresponding patterning system aberrations. The patterning system aberrations s(Z) are defined by the received patterning system aberration data.

[0030] In some embodiments, the cost function s(Z) represents the impact of the corresponding patterning system aberrations on the patterning process.

[0031] In some embodiments, the new patterning process influence data from the model is configured to be provided to a second model to facilitate dynamic field aberration control of the patterning system. In some embodiments, the second model is a projection optics correction model.

[0032] In some embodiments, the patterning system includes a scanner. Dynamic field control of the scanner includes generating a corrected formula of scanner control parameters to optimize a set of lithography performance metrics for a given scanner aberration.

[0033] In some embodiments, the new patterning process influence data from the model is configured to determine a patterning process control metric set. The patterning process control metric set is configured to be determined by a linear solver.

[0034] In some embodiments, the patterning process control metrics include lithography metrics.

[0035] In some embodiments, the new patterning process influence data from the model includes a cost function, Hessian. Determining the patterning process control metric set includes performing singular value decomposition on the Hessian.

[0036] In some embodiments, the new patterning process influence data indicates the effect of the corresponding patterning system aberrations on one or more of the critical size, pattern placement error, edge placement error, critical size asymmetry, optimal focus offset, or defect count associated with the patterning process.

[0037] In some embodiments, the model is calibrated such that the new patterning process influence data is configured to help enhance control over the heating of one or more mirrors and / or lenses of the patterning system.

[0038] In some embodiments, the model is calibrated such that the new patterning process impact data is configured to help enhance control over focus, dose, and / or stage variation (MSD) associated with the patterning system.

[0039] According to another embodiment, a method for determining patterning process influence data is provided. The method includes: performing a calibration model configured to receive patterned systematic aberration data, and calibrating the model using patterned systematic aberration calibration data and corresponding patterning process influence calibration data. The method further includes determining new patterning process influence data based on the model for the received patterned systematic aberration data. The model includes a hyperdimensional function configured to correlate the received patterned systematic aberration data with the new patterning process influence data without simulating, generating, or otherwise computing a spatial image representation.

[0040] In some embodiments, the hyperdimensional function is configured to correlate the received patterned system aberration data with the new patterning process influence data in an approximate and / or simplified form, rather than in a full simulation.

[0041] In some embodiments, the model is calibrated by: providing patterned system aberration calibration data to a base model to obtain a prediction of the patterning process's influence on the calibration data, and using the patterning process's influence on the calibration data as feedback to update one or more configurations of the base model. One or more configurations are updated based on a comparison between the patterning process's influence on the calibration data and the prediction of the patterning process's influence on the calibration data.

[0042] In some embodiments, the model includes one or more nonlinear, linear, and / or quadratic algorithms.

[0043] In some embodiments, updating one or more configurations of the base model includes one or more parameters of the calibration algorithm.

[0044] In some embodiments, the received patterning system aberration data includes received wavefront data, and wherein the new patterning process influence data includes one or more patterning process measures.

[0045] In some embodiments, the one or more patterning process metrics include critical dimensions associated with the patterning process, pattern placement error, edge placement error, critical dimension asymmetry, optimal focus offset, or defect count.

[0046] In some embodiments, the model includes one or more key feature components and one or more general components, the key feature components being configured to model the variation of key features of the patterning process between patterning systems; and the one or more general components being configured to model the general performance of the patterning system for non-key features of the patterning process.

[0047] In some embodiments, the new patterning process impact data from the model is configured to be provided to a cost function to help determine the costs associated with each patterning process metric and / or the costs associated with each patterning process variable.

[0048] In some embodiments, the cost function includes a first component associated with critical features of the patterning process, a second component associated with non-critical features of the patterning process, and a third component associated with physical functional limitations of one or more patterning systems.

[0049] In some embodiments, the cost function further includes a fourth component associated with the wavefront conditioning penalty of the patterning process.

[0050] In some embodiments, the new patterning process impact data output from the model is configured to facilitate the collaborative optimization of multiple patterning systems.

[0051] In some embodiments, the plurality of patterning systems include scanners, and the collaborative optimization includes using lens actuators as variables and using a gradient-based nonlinear optimizer to collaboratively determine the actuator positions of the plurality of scanners.

[0052] In some embodiments, the new patterning process influence data from the model is configured to determine a patterning process control metric set, which is configured to be determined by a linear solver.

[0053] In some embodiments, the new patterning process influence data indicates the effect of the corresponding patterning system aberrations on one or more of the critical size, pattern placement error, edge placement error, critical size asymmetry, optimal focus offset, or defect count associated with the patterning process.

[0054] In some embodiments, the new patterning process influence data from the model is configured to be provided to a cost function to help determine the costs associated with each patterning process metric. The costs associated with each patterning process metric are configured to be provided back to the model to help determine the costs associated with patterning process wavefront conditioning. The costs associated with the patterning process wavefront conditioning are configured to be provided to a driver lens model to help determine the costs associated with each patterning process variable. The costs associated with each patterning process variable are configured to be provided to an optimizer to facilitate the coordinated optimization of multiple patterning systems.

[0055] In some embodiments, the model is calibrated such that the new patterning process influence data is configured to help enhance control over the heating of one or more mirrors and / or lenses of the patterning system.

[0056] In some embodiments, patterning system aberration calibration data are simulated based on the associated pupil shape and pattern forming apparatus design.

[0057] In some embodiments, the new patterning process influence data includes a cost function s(Z) of the corresponding patterning system aberrations. The patterning system aberrations s(Z) are defined by the received patterning system aberration data.

[0058] In some embodiments, the cost function s(Z) represents the impact of the corresponding patterning system aberrations on the patterning process.

[0059] In some embodiments, the new patterning process influence data from the model is configured to be provided to a second model to facilitate dynamic field aberration control of the patterning system. In some embodiments, the second model is a projection optics correction model.

[0060] In some embodiments, the patterning system includes a scanner. Dynamic field control of the scanner includes generating a corrected formula of scanner control parameters to optimize a set of lithography performance metrics for a given scanner aberration.

[0061] In some embodiments, the new patterning process influence data from the model is configured to determine a patterning process control metric set. The patterning process control metric set is configured to be determined by a linear solver.

[0062] In some embodiments, the patterning process control metrics include lithography metrics.

[0063] In some embodiments, the new patterning process influence data from the model includes a cost function, Hessian. Determining the patterning process control metric set includes performing singular value decomposition on the Hessian.

[0064] In some embodiments, the new patterning process influence data indicates the effect of the corresponding patterning system aberrations on one or more of the critical size, pattern placement error, edge placement error, critical size asymmetry, optimal focus offset, or defect count associated with the patterning process.

[0065] In some embodiments, the model is calibrated such that the new patterning process influence data is configured to help enhance control over the heating of one or more mirrors and / or lenses of the patterning system.

[0066] In some embodiments, the model is calibrated such that the new patterning process impact data is configured to help enhance control over focus, dose, and / or stage variation (MSD) associated with the patterning system.

[0067] According to another embodiment, a non-transitory computer-readable medium having instructions thereon is provided. When the instructions are executed by a computer, they cause the computer to perform the methods described in any of the preceding paragraphs.

[0068] According to another embodiment, a non-transitory computer-readable medium is provided having instructions on it that, when executed by a computer, cause the computer to execute an electronic model for determining patterning process influence data without calculating a spatial image representation of the patterning process. The patterning process influence data is configured to facilitate the collaborative optimization of multiple scanners used in the patterning process. The operations caused by the instructions include: providing patterning system aberration data to the model, the model including a hyperdimensional function configured to correlate the received patterning system aberration data with the patterning process influence data; and, based on the model, determining new patterning process influence data from the received patterning system aberration data, wherein the new patterning process influence data from the model is configured to be provided to a cost function to facilitate the determination of costs associated with each patterning process metric and / or costs associated with each patterning process variable, and wherein the costs associated with each patterning process metric and / or costs associated with each patterning process variable are configured to facilitate the collaborative optimization of multiple scanners.

[0069] In some embodiments, the patterned system aberration data provided to the model includes wavefront data, and wherein the new patterning process influence data includes one or more patterning process measures.

[0070] In some embodiments, the model includes one or more key feature components configured to model variations in key features of the patterning process between scanners; and one or more general components configured to model general performance of the scanner for non-key features of the patterning process.

[0071] In some embodiments, the cost function includes a first component associated with critical features of the patterning process, a second component associated with non-critical features of the patterning process, and a third component associated with physical functional limitations of one or more scanners.

[0072] In some embodiments, the collaborative optimization includes using lens actuators as variables and using a gradient-based nonlinear optimizer to collaboratively determine the actuator positions of multiple scanners.

[0073] According to another embodiment, one or more non-transitory computer-readable media are provided, the non-transitory computer-readable media storing a prediction model and instructions, the instructions providing the prediction model when executed by one or more processors. The prediction model generates the following steps: obtaining patterned system aberration data and corresponding patterned process influence data; providing the patterned system aberration data to a base prediction model to obtain a prediction result of the patterned process influence data; and using the patterned process influence data as feedback to update one or more configurations of the base prediction model, wherein the one or more configurations are updated based on a comparison between the patterned process influence data and the prediction result of the patterned process influence data. The prediction model includes a hyperdimensional function configured to correlate the patterned system aberration data with the patterned process influence data without computing a spatial image.

[0074] In some embodiments, the prediction model includes a linear or quadratic algorithm.

[0075] In some embodiments, updating one or more configurations of the prediction model includes one or more parameters of a calibration function.

[0076] In some embodiments, the aberration data of the patterning system is simulated based on the associated pupil shape and pattern forming apparatus design.

[0077] In some embodiments, the patterning process influence data includes a cost function s(Z) of the corresponding patterning system aberrations, which are defined by the patterning system aberration data. Attached Figure Description

[0078] The accompanying drawings, which are included in and form part of this specification, illustrate one or more embodiments and explain these embodiments together with the specification. Embodiments of the invention will now be described by way of example only with reference to the accompanying drawings, wherein corresponding reference numerals indicate corresponding parts, and wherein:

[0079] Figure 1 A block diagram of various subsystems of a photolithography projection apparatus according to an embodiment is shown.

[0080] Figure 2 An exemplary flowchart for fully simulating lithography in a lithography projection apparatus according to an embodiment is shown.

[0081] Figure 3 The method according to an embodiment is shown.

[0082] Figure 4 A comparison between the operation of the aberration influence model of the present invention according to an embodiment and the operation of a full simulation is shown.

[0083] Figure 5 An example operation for constructing the aberration effect model of the present invention according to an embodiment is shown.

[0084] Figure 6 The following illustrates how to construct the aberration influence model of the present invention (e.g., during the offline or R&D phase) according to an embodiment. Figure 5 (The operation shown in the figure) is then used in the manufacturing stage.

[0085] Figure 7 An example is shown whereby a cost function is configured according to an aberration influence model for use by a projection optics correction model to determine a set of control metrics for the patterning process, based on an embodiment.

[0086] Figure 8 Dynamic aberration control according to an embodiment is shown (using mirror heating as an example).

[0087] Figure 9 The document illustrates the conversion of a cost function (from an aberration influence model) into a format of lithographic metrics according to an embodiment (e.g., to facilitate the determination of a patterning process control metric set via a projection optics correction model).

[0088] Figure 10 The aberration influence model of the present invention, according to an embodiment, illustrates how dynamic aberration correction per substrate (e.g., per wafer or even per layer) can be achieved.

[0089] Figure 11 A summary flow of the above-described operation according to an embodiment is shown.

[0090] Figure 12 The components of the cost function according to an embodiment are shown.

[0091] Figure 13 An example optimized architecture according to an embodiment is shown.

[0092] Figure 14 This is a block diagram of an example computer system according to an embodiment.

[0093] Figure 15 This is a schematic diagram of a photolithography projection apparatus according to an embodiment.

[0094] Figure 16 This is a schematic diagram of another photolithography projection device according to an embodiment.

[0095] Figure 17 This is a detailed view of a photolithography projection apparatus according to an embodiment.

[0096] Figure 18 This is a detailed view of the source collector module of a photolithography projection apparatus according to an embodiment. Detailed Implementation

[0097] Modeling scanner aberration effects in semiconductor manufacturing processes is advantageous. The models described in this paper have a wide range of applications. Scanner aberration effect modeling can facilitate collaborative optimization of multiple scanners, model-based output field control of scanners, and / or other uses. The models described in this paper include hyperdimensional functions configured to correlate received patterned system aberration data with new patterning process effect data. These hyperdimensional functions are configured to correlate received patterned system aberration data with new patterning process effect data in an approximate form without involving the computation of spatial images or their expressions, instead of full simulation. This can save computation time, computational resources, and / or offer other advantages.

[0098] For example, mirror heating properties and / or other dynamically changing variables that cause aberrations in patterning process scanners (e.g., EUV scanners) require rapid field control to achieve stable imaging performance in manufacturing environments. Previous attempts at such rapid field control have involved defining a merit function based on the scanner's pupil-level properties (e.g., the RMS of the delta wavefront relative to a reference state), but without knowing the imaging performance properties at the substrate (e.g., wafer) level. Therefore, while aberrations at the pupil level are minimized, imaging performance (at the substrate or wafer level) is not optimized.

[0099] Alternative imaging performance-based methods are known, but these are not suitable for dynamic field scanner control. For example, one approach requires calculating Zernike sensitivities across a large number of key dimensions, making it computationally intensive and requiring significant online and offline data transfer. Using this approach, lithographic performance metrics are limited to critical dimensions. This approach is not flexible enough to cover other types of custom metrics, including discrete metrics such as defect counts. As another example, different approaches involve performing aberration (wavefront) optimization using a source mask optimization engine to match the performance of different scanners. However, this approach is designed for cold lens setups without considering mirror heating, and it performs iterative optimization, requiring a complete imaging simulation for each iteration. This makes it computationally intensive and unsuitable for dynamic field scanner control.

[0100] Advantageously, this disclosure describes systems and methods for performing fast and dynamic scanner aberration (wavefront) control. These systems and methods are imaging performance-aware and suitable for dynamic in-situ scanner aberration control (e.g., for controlling aberrations caused by mirror heating and / or other dynamic aspects of the patterning apparatus and / or patterning process). The systems and methods include a calibrated aberration influence model configured to receive patterned system aberration data and determine new patterning process influence data on the received patterned system aberration data. The model is calibrated using the patterned system aberration data and the corresponding patterning process influence calibration data. Compared to existing systems, this model includes a relatively simple hyperdimensional function configured to correlate the received patterned system aberration data with the new patterning process influence data. The hyperdimensional function is configured to correlate the received patterned system aberration data with the new patterning process influence data in an approximate form, rather than a full simulation. For example, in some embodiments, the model includes linear or quadratic algorithms. New patterning process influence data from this model are configured (e.g., formatted output from this model) to be provided to a second model (such as a projection optics correction model) to facilitate dynamic field aberration control of the patterning system (e.g., a scanner).

[0101] As another example, the same design layout (used in the patterning process) might be printed differently on different scanners or at different slit locations. This variation is disadvantageous because it is generally not something that can be corrected by optical proximity correction (OPC) or retargeting, as is the case with uniform printing errors. For existing systems, ensuring that the same design layout is printed identically on different scanners or at different slit locations requires a complete imaging simulation for each iteration. This is computationally intensive and requires identifying a reference scanner, which is often not an obvious choice for the operator (and thus leads to additional variations). Matching each scanner individually to a reference scanner does not necessarily minimize variations in key features.

[0102] Advantageously, calibrated aberration influence models can be used for wavefront tuning (e.g., replacing full imaging simulations in existing systems). As described above, this model includes a relatively simple hyperdimensional function configured to correlate received patterned system aberration data with new patterning process influence data. This hyperdimensional function is configured to correlate received patterned system aberration data with new patterning process influence data in an approximate form, rather than a full simulation (which eliminates the need to compute spatial images). Multiple models can be used to describe the imaging performance of multiple scanners. The models described herein facilitate the use of a four-component cost function to capture imaging performance, wavefront residuals, and / or actuator consumption, as well as various other possibilities. Furthermore, imaging performance can be arbitrarily specified by the user (instead of being requested by the hard scanner). The models described herein also facilitate the use of actuators as variables (e.g., instead of Zernikes) and the use of a general nonlinear optimizer (e.g., instead of a linear solver) to solve for the optimal actuator positions for multiple scanners (e.g., instead of a single scanner).

[0103] Embodiments of this disclosure are described in detail with reference to the accompanying drawings, which are provided as illustrative examples to enable those skilled in the art to practice this disclosure. It should be noted that the following drawings and examples are not intended to limit the scope of this disclosure to a single embodiment, but rather other embodiments are possible by interchangeing some or all of the elements described or illustrated. Furthermore, where certain elements of this disclosure may be implemented partially or entirely using known components, only those portions of such known components necessary for understanding this disclosure will be described, and detailed descriptions of other portions of these known components will be omitted so as not to obscure this disclosure. Embodiments are described as being implemented in software, but embodiments are not intended to be limited thereto, but may include implementations implemented in hardware or a combination of software and hardware, and vice versa, as will be apparent to those skilled in the art, unless otherwise stated herein. Embodiments illustrating a single component in this specification should not be considered limiting; rather, this disclosure is intended to cover other embodiments including a plurality of identical components, and vice versa, unless expressly stated herein. Furthermore, the applicant does not intend to assign any terminology in the specification or claims an unusual or particular meaning unless expressly stated otherwise. Furthermore, this disclosure covers existing and future known components that are equivalent to the known components mentioned herein by way of description.

[0104] While references to IC manufacturing may be made specifically herein, it should be clearly understood that the description herein has many other possible applications. For example, other possible applications include the manufacture of integrated optical systems, guide and detection patterns for magnetic domain memory, liquid crystal display panels, thin-film magnetic heads, etc. Those skilled in the art will understand that, in the context of such alternative applications, any use of the terms “mask,” “wafer,” or “die” herein should be considered interchangeable with the more general terms “mask,” “substrate,” and “target portion,” respectively.

[0105] In this document, the terms “radiation” and “beam” are used to cover all types of electromagnetic radiation, including ultraviolet radiation (e.g., with wavelengths of 365 nm, 248 nm, 193 nm, 157 nm, or 126 nm) and EUV (extreme ultraviolet radiation, e.g., with wavelengths in the range of about 5–100 nm).

[0106] The term "projection optics" as used herein should be interpreted broadly to include various types of optical systems, such as refractive optics, reflective optics, aperture optics, and catadioptric optics. The term "projection optics" may also include components for any of these design types used to guide, shape, or control a projected radiation beam, either jointly or individually. The term "projection optics" can include any optical component in a lithography projection apparatus, regardless of where the optical component is located in the optical path of the lithography projection apparatus. Projection optics can include optical components for shaping, adjusting, and / or projecting radiation from a source before it passes through a (e.g., semiconductor) patterning apparatus, and / or for shaping, adjusting, and / or projecting radiation after it has passed through the patterning apparatus. Projection optics typically do not include a source or a patterning apparatus.

[0107] Patterning apparatuses (e.g., semiconductors) can include or form one or more design layouts. Design layouts can be generated using CAD (Computer-Aided Design) programs, a process often referred to as EDA (Electronic Design Automation). Most CAD programs follow a predetermined set of design rules to create functional design layouts / patterning apparatuses. These rules are set through processing and design constraints. For example, design rules define spatial tolerances or interconnects between devices (such as gates, capacitors, etc.) to ensure that devices or lines do not interact with each other in undesirable ways. Design rules can include and / or specify particular parameters, parameter limits and / or ranges, and / or other information. One or more of the design rule constraints and / or parameters can be referred to as “critical dimensions” (CDs). A critical dimension of a device can be defined as the minimum width of a line or via, or the minimum spacing between two lines or two vias, or other characteristics. Therefore, CDs determine the overall size and density of the designed device. Of course, one of the goals in device fabrication is to faithfully reproduce the original design intent on the substrate (via the patterning apparatus).

[0108] As used herein, the terms "mask" or "patterning apparatus" can be broadly interpreted to refer to a general patterning apparatus that can be used to impart a patterned cross-section to an incident radiation beam, the patterned cross-section corresponding to a pattern to be generated in a target portion of a substrate; the term "light valve" can also be used in this context. Examples of such patterning apparatuses, in addition to classical masks (transmissive or reflective masks; binary masks, phase-shifting masks, hybrid masks, etc.), include programmable mirror arrays and programmable LCD arrays.

[0109] An example of a programmable mirror array can be a matrix-addressable surface with a viscoelastic control layer and a reflective surface. The basic principle behind such a device is that, for example, addressed regions of the reflective surface reflect incident radiation as diffracted radiation, while unaddressed regions reflect incident radiation as non-diffracted radiation. By using suitable filters, the non-diffracted radiation can be filtered out from the reflected beam, retaining only the diffracted radiation; in this way, the beam is patterned according to the addressing pattern of the matrix-addressable surface. The desired matrix addressing can be performed using suitable electronics. An example of a programmable LCD array is given in U.S. Patent No. 5,229,872, which is incorporated herein by reference.

[0110] As used herein, the term "patterning process" generally refers to the process of producing an etched substrate by applying light with a specific pattern as part of a photolithography process. However, "patterning process" can also include plasma etching, as many of the features described herein can provide benefits for forming printed patterns using plasma processing.

[0111] As used herein, the term “target pattern” refers to an idealized pattern to be etched onto a substrate.

[0112] As used herein, the term "printed pattern" refers to a physical pattern etched onto a substrate based on a target pattern. For example, a printed pattern may include grooves, channels, recesses, edges, or other two-dimensional and three-dimensional features produced by a photolithography process.

[0113] As used herein, the terms “predictive model,” “process model,” and / or model (which may be used interchangeably) refer to a model that includes one or more models simulating the patterning process. For example, a predictive and / or process model may include an optical model (e.g., modeling a lens system / projection system used to deliver light during the photolithography process, and may include modeling the final optical image of the light arriving on the photoresist), a resist model (e.g., modeling the physical effects of the resist, such as chemical effects due to light), and / or an OPC model (e.g., which may be used to create the target pattern and may include sub-resolution resist features (SRAF), etc.), and / or other models.

[0114] As used herein, the term “calibration” refers to modifying (e.g., improving or adjusting) and / or validating something (such as a process model).

[0115] A patterning system can be a system that includes any or all of the components described above, as well as other components configured to perform any or all of the operations associated with these components. For example, a patterning system may include a photolithography projection device, a scanner, and / or other systems.

[0116] As an introduction, Figure 1 A diagram illustrating various subsystems of an exemplary photolithography projection apparatus 10A is shown. The main components are: a radiation source 12A, which may be a deep ultraviolet excimer laser source or other types of sources including extreme ultraviolet (EUV) sources (as mentioned above, the photolithography projection apparatus itself does not need to have a radiation source); irradiation optics, which, for example, define partial coherence (denoted as sigma or σ) and may include optics 14A, 16Aa, and 16Ab for shaping the radiation from source 12A; a pattern forming apparatus 18A; and a transmissive optics 16Ac that projects an image of a pattern from the pattern forming apparatus onto a substrate plane 22A. An adjustable filter or aperture 20A at the pupil plane of the projection optics can limit the angular range of the beam incident on the substrate plane 22A, wherein the maximum possible angle defines the numerical aperture NA of the projection optics as nsin(Θ). max ), where n is the refractive index of the medium between the substrate and the final element of the projection optics, and Θ maxIt is the maximum angle at which the beam emitted from the projection optics can still be incident on the substrate plane 22A.

[0117] In a photolithography projection apparatus, a source provides illumination (i.e., irradiation) to a patterning apparatus, and projection optics are shaped and guided onto a substrate by the patterning apparatus. The projection optics may include at least some of components 14A, 16Aa, 16Ab, and 16Ac. The spatial image (AI) is the distribution of radiation intensity at the substrate level. A resist image can be calculated from the spatial image using a resist model, examples of which can be found in U.S. Patent Application Publication No. US2009-0157630, the disclosure of which is incorporated herein by reference in its entirety. The resist model relates to the properties of the resist layer (e.g., the effects of chemical processes occurring during exposure, post-exposure baking (PEB), and development). The optical properties of the photolithography projection apparatus (e.g., the properties of the irradiation, the patterning apparatus, and the projection optics) determine the spatial image and can be defined in the optical model. Because the patterning apparatus used in a photolithography projection apparatus can be modified, it is desirable to separate the optical properties of the patterning apparatus from the optical properties of the remainder of the photolithography projection apparatus, which includes at least the source and the projection optics. Details of the techniques and models used to convert design layouts into various lithographic images (e.g., spatial images, resist images, etc.), the application of OPC using these techniques and models, and the evaluation of performance (e.g., in terms of process windows) are described in U.S. Patent Application Publications Nos. US2008-0301620, US2007-0050749, US2007-0031745, US2008-0309897, US2010-0162197, and US2010-0180251, the disclosures of each of which are incorporated herein by reference in their entirety.

[0118] One or more tools can be used to generate results that can be used for designing, controlling, monitoring, and other aspects of patterning processes. One or more tools can be provided for computationally controlling, designing, or otherwise implementing patterning processes, such as pattern design for a patterning apparatus (including, for example, adding sub-resolution auxiliary features or optical proximity correction), irradiation of the patterning apparatus, etc. Therefore, in systems that computationally control, design, or otherwise involve patterning manufacturing processes, manufacturing system components and / or processes can be described by various functional modules and / or models. In some embodiments, one or more electronic (e.g., mathematical, parametric, etc.) models can be provided that describe one or more steps and / or devices of the patterning process. In some embodiments, one or more electronic models can be used to perform simulations of the patterning process to simulate how the patterning process uses a design pattern provided by the patterning apparatus to form a patterned substrate.

[0119] An exemplary flowchart for simulating lithography in a lithography projection device is shown in... Figure 2 This can be an exemplary full lithography simulation. Irradiation model 31 represents the optical characteristics of irradiation (including the radiation intensity distribution and / or phase distribution). Projection optics model 32 represents the optical characteristics of projection optics (including variations in the radiation intensity distribution and / or phase distribution caused by the projection optics). Design layout model 35 represents the optical characteristics of the design layout (including variations in the radiation intensity distribution and / or phase distribution caused by a given design layout), which represents the arrangement of features on or formed by the patterning apparatus. Spatial image 36 can be simulated using irradiation model 31, projection optics model 32, and design layout model 35. Resist image 38 can be simulated based on spatial image 36 using resist model 37. For example, the simulation of lithography can predict the contours and / or CDs in the resist image.

[0120] More specifically, the illumination model 31 can represent the optical characteristics of the illumination, including but not limited to NA-Sigma (σ) settings and any particular illumination shape (e.g., off-axis illumination, such as ring, quadrupole, dipole, etc.). The projection optics model 32 can represent the optical characteristics of the projection optics, including aberrations, distortion, refractive index, physical size, or dimension. The design layout model 35 can also represent one or more physical characteristics of the physical patterning apparatus, such as those described in U.S. Patent No. 7,587,704, which is incorporated herein by reference in its entirety. The optical characteristics associated with the lithography projection apparatus (e.g., the characteristics of the illumination, patterning apparatus, and projection optics) determine the spatial image. Since the patterning apparatus used in the lithography projection apparatus can be modified, it is desirable to separate the optical characteristics of the patterning apparatus from those of the rest of the lithography projection apparatus (including at least the illumination and projection optics, and therefore the design layout model 35).

[0121] Resist model 37 can be used to calculate resist images from spatial images, examples of which can be found in U.S. Patent No. 8,200,468, which is incorporated herein by reference in its entirety. Resist models are generally related to the properties of the resist layer (e.g., the effects of chemical processes that occur during exposure, post-exposure baking, and / or development).

[0122] One of the purposes of full simulation is to accurately predict, for example, edge placement, spatial image intensity slope, and / or CD, which can then be compared with the expected design. The expected design is typically defined as a pre-OPC design layout, which can be provided in standardized digital file formats such as GDS, GDSII, or OASIS, or other file formats.

[0123] Based on this design layout, one or more portions, referred to as "segments," can be identified. In embodiments, a set of segments is extracted, which represents a complex pattern in the design layout (typically around 50 to 1000 segments, but any number of segments can be used). As those skilled in the art will understand, these patterns or segments represent small parts of the design (e.g., circuits, cells, etc.), and in particular, segments represent small parts that require specific attention and / or verification. In other words, a segment can be a part of the design layout, or can resemble a part of the design layout or exhibit similar behavior to a part of the design layout, where key features are identified through experience (including segments provided by the customer), trial and error, or running full-chip simulations. Segments typically contain one or more test patterns or gauge patterns. The customer can pre-provide a large initial set of segments based on known key feature regions in the design layout that require specific image optimization. Alternatively, in another embodiment, a large initial set of segments can be extracted from the entire design layout by using automated (such as machine vision) or manual algorithms to identify key feature regions.

[0124] For example, simulation and modeling can be used to configure one or more features of a pattern forming apparatus pattern (e.g., performing optical proximity correction), one or more features of illumination (e.g., changing one or more properties of the spatial / angular intensity distribution of illumination, such as changing shape), and / or one or more features of a projection optics (e.g., numerical aperture, etc.). This configuration can generally be referred to as mask optimization, source optimization, and projection optimization, respectively. These optimizations can be performed individually or in combination in different ways. One such example is source mask optimization (SMO), which involves configuring one or more features of a pattern forming apparatus pattern together with one or more features of illumination. Optimization techniques can focus on one or more segments. Optimization can be performed using the machine learning models described herein to predict values ​​for various parameters, including images, etc.

[0125] In some embodiments, the optimization process of a system can be represented as a cost function. The optimization process may include finding the set of system parameters (design variables, process variables, etc.) that minimizes the cost function. Depending on the optimization objective, the cost function can have any suitable form. For example, the cost function can be the weighted root mean square (RMS) of the deviations of certain characteristics (evaluation points) of the system relative to expected values ​​(e.g., ideal values) of these characteristics. The cost function can also be the maximum value of these deviations (i.e., the worst-case deviation). The term "evaluation point" should be interpreted broadly to include any characteristic of the system or manufacturing method. Due to the practicality of implementing the system and / or method, the design and / or process variables of the system can be constrained to a limited range and / or interdependent. In the case of photolithography projection equipment, such constraints are typically associated with the physical properties and characteristics of the hardware (such as tunability range and / or manufacturability design rules for patterning apparatus). For example, evaluation points may include physical points on a resist image on a substrate, as well as non-physical characteristics (such as dosage and focus).

[0126] In photolithography projection equipment, as an example, the cost function can be expressed as follows:

[0127]

[0128] Among them, (z1, z2, ..., z N ) are N design variables or their values, and f p (z1,z2,···,z N ) can be design variables (z1, z2, ..., z N Functions such as design variables (z1, z2, ..., z) N The difference between the actual and expected values ​​of a set of properties. In some embodiments, w p Is with f p (z1,z2,···,z N The associated weighting constants. For example, a characteristic could be the location of the edge of a pattern measured at a given point on the edge. Different f p (z1,z2,···,z N ) can have different weights w p For example, if a particular edge has a narrow range of allowed locations, then f represents the difference between the actual and expected locations of the edge. p (z1,z2,···,z N The weight w p It can be given a higher value. f p (z1,z2,···,z N It can also be a function of interlayer characteristics, which are design variables (z1, z2, ..., z...). NThe function is CF(z1,z2,...,z). N The expression is not limited to the form of the above equation, and CF(z1,z2,...,z) N () can be any other suitable form.

[0129] The cost function can represent any one or more suitable characteristics of the photolithography projection equipment, photolithography process, or substrate, such as focus, CD, image shift, image distortion, image rotation, random variation, yield, local CD variation, process window, interlayer characteristics, or combinations thereof. In some embodiments, the cost function may include a function representing one or more characteristics of the resist image. For example, f p (z1,z2,···,z N It can be simply the distance between a point in the resist image and the expected location of that point (i.e., edge placement error EPE). P (z1,z2,···,z N Parameters (such as design variables) can include any adjustable parameters, such as those of the source, patterning apparatus, projection optics, dose, focus, etc.

[0130] Parameters (e.g., design variables) can have constraints, which can be represented as (z1, z2, ..., z...). N Let Z be a set of possible values ​​for the design variables. One possible constraint on the design variables can be imposed by the expected output of the lithography projection apparatus. Without such a constraint imposed by the expected output, optimization may produce a set of unrealistic design variable values. Constraints should not be interpreted as necessary conditions. For example, the output may be affected by the pupil fill ratio. For some illumination designs, a low pupil fill ratio may discard radiation, resulting in a lower output. The output may also be affected by the resist chemistry. Slower resists (e.g., resists that require higher radiation doses for proper exposure) will result in a lower output.

[0131] In some embodiments, the illumination model 31, the projection optics model 32, the design layout model 35, the resist model 37, and / or other models associated with and / or included in the integrated circuit manufacturing process can be empirical models of the operations performed by the methods described herein. Empirical models can predict outputs based on correlations between various inputs (e.g., one or more characteristics of a mask or wafer image, one or more characteristics of a design layout, one or more characteristics of a patterning apparatus, one or more characteristics of the illumination used in the lithography process (such as wavelength), etc.).

[0132] As an example, an empirical model may include one or more algorithms. As another example, an empirical model may be a machine learning model and / or any other parameterized model. In some embodiments, a machine learning model may be and / or include mathematical equations, algorithms, plots, graphs, networks (e.g., neural networks), and / or other tools and machine learning model components. For example, a machine learning model may be and / or include one or more neural networks having an input layer, an output layer, and one or more intermediate or hidden layers. In some embodiments, one or more neural networks may be and / or include deep neural networks (e.g., neural networks with one or more intermediate or hidden layers between the input and output layers).

[0133] As an example, one or more neural networks can be based on a large number of neural units (or artificial neurons). One or more neural networks can loosely mimic the workings of a biological brain (e.g., through large clusters of biological neurons connected by axons). Each neural unit of the neural network can be connected to many other neural units in the network. Such connections can strengthen or inhibit their influence on the activation state of the connected neural units. In some embodiments, each individual neural unit can have a summation function that combines the values ​​of all its inputs. In some embodiments, each connection (or the neural unit itself) can have a threshold function such that a signal must exceed a threshold before being allowed to propagate to other neural units. Compared to conventional computer programs, these neural network systems can be self-learning and self-training rather than explicitly programmed, and can perform better in solving problems in certain domains. In some embodiments, one or more neural networks can include multiple layers (e.g., signal paths traverse from previous layers to subsequent layers). In some embodiments, the neural network can utilize backpropagation techniques, where forward stimulation is used to reset the weights on “previous” neural units. In some embodiments, stimulation and inhibition of one or more neural networks can flow more freely, with connections interacting in more chaotic and complex ways. In some embodiments, the intermediate layers of one or more neural networks include one or more convolutional layers, one or more recursive layers, and / or other layers.

[0134] One or more neural networks can be trained (i.e., the parameters of the neural network are determined) using a training information set. The training information can include a set of training samples. Each sample can be a pair consisting of an input object (usually a vector, which may be called a feature vector) and a desired output value (also called a management signal). The training algorithm analyzes the training information and adjusts the behavior of the neural network by adjusting the parameters of the neural network (e.g., the weights of one or more layers) based on the training information. For example, given a set of parameters of the form {(x1,y1),(x2,y2),…,(x...}... N ,y N A set of N training samples of )} such that xi y is the feature vector of the i-th sample. i Let X be the management signal of the i-th sample. The training algorithm finds a neural network g: X→Y, where X is the input space and Y is the output space. A feature vector is an n-dimensional vector representing the numerical features of some object (e.g., a simulated spatial image, a wafer design, a fragment, etc.). The vector space associated with these vectors is usually called the feature space. After training, the neural network can be used to make predictions using new samples.

[0135] This system and method include a calibrated model configured to predict the potential impact of patterning system (e.g., scanner) aberrations on the patterning process. For example, the calibrated model may be referred to herein as an aberration influence model. The aberration influence model is configured to receive patterning system aberration data (e.g., data describing the characteristics of a particular aberration) and determine new patterning process influence data (e.g., data describing the impact of aberrations on the corresponding patterning process outcome) for the received patterning system aberration data. The aberration influence model is calibrated using patterning system aberration calibration data and corresponding patterning process influence calibration data. Compared to existing systems, this aberration influence model includes a relatively simple hyperdimensional function configured to correlate the received patterning system aberration data with the new patterning process influence data. The hyperdimensional function is configured to correlate the received patterning system aberration data with the new patterning process influence data in a simplified form, rather than a full simulation. For example, the aberration influence model may include linear or quadratic algorithms. As mentioned above, a full simulation can include simulations of the source, mask, dose, focusing, and / or other aspects of the lithography process (see, for example, [link to full simulation]). Figure 2 Modeling with aberration-influence models without full simulation includes modeling, at least without generating, simulating, or otherwise computing a spatial image representation. Aberration-influence models are configured to generate predictions based on input patterned system aberration data, without requiring additional information related to source, mask, dose, focus, etc., that would be needed in a full simulation.

[0136] New patterning process influence data from the model (e.g., formatting the output from the model) can be provided to a second model (such as a projection optics correction model) to enable dynamic in-situ aberration control of the patterning system, such as aberrations caused by mirror heating in an EVU lithography system or lens heating in a DUV lithography system. Advantageously, this facilitates rapid and dynamic scanner aberration (and wavefront) control that is perceptible to imaging performance (e.g., controlling aberrations caused by mirror heating and / or patterning apparatus and / or other dynamic aspects of the patterning process).

[0137] Figure 3An exemplary method 300 according to an embodiment of this disclosure is illustrated. In some embodiments, method 300 includes calibrating an aberration influence model 302, receiving patterning system aberration data 304, predicting and / or otherwise determining patterning process influence data 306, providing patterning process influence data to a second model 308, performing dynamic field aberration control of the patterning system 310, and / or other operations. The operations of method 300 presented below are intended to be illustrative. In some embodiments, method 300 may be performed with one or more additional operations not described and / or without one or more of the operations discussed. For example, operations 308, 310, and / or other operations may be optional. Furthermore, the order of operations of method 300 is as follows: Figure 3 The contents are shown and described below, and are not intended to be limiting.

[0138] In operation 302, the aberration influence model is calibrated. For example, the aberration influence model could be a predictive model. Calibration can include model generation, training, tuning, and / or other operations. The model is calibrated using patterned system aberration calibration data and corresponding patterning process influence calibration data. The patterning system can be and / or includes a scanner (such as...) Figure 1 (And the photolithography projection apparatus shown in the accompanying figures). In a scanner, aberrations can occur when the surface of a lens element (e.g., a lens, mirror, and / or other element) in the scanner is not in the expected position. For example, the surface of a lens element may be out of the expected position due to heating of the lens element, but there can be many different reasons. Patterned system aberration data includes data describing the characteristics of a particular aberration, the cause of the aberration, and / or other data. Patterned system aberration data may include measured and / or simulated aberrations, system and / or process parameters associated with the aberration, and / or other wavefront information. Wavefront aberration (or “aberration” as used herein) can refer to the deviation (degree of inconsistency) between the ideal wavefront and the actual wavefront.

[0139] For example, when a lens element is heated, shape changes (which can lead to aberrations) may occur due to laser power levels, pupil shape, target design, exposure dose, and / or other factors. Any and / or all of these and other factors can be included in the patterning system aberration dataset. Patterning process impact data includes data describing the effect of aberrations on the corresponding patterning process. For example, patterning process impact data may indicate the effect of corresponding patterning system aberrations on imaging performance on the substrate, such as critical dimensions associated with the patterning process, pattern placement errors, edge placement errors, critical dimension asymmetry, optimal focus offset, defect counts associated with the patterning process, and / or other parameters. Patterning process impact data may include values ​​of various parameters, cost and / or value functions (e.g., as described below), and / or other information.

[0140] Patterning system aberration calibration data and corresponding patterning process influence calibration data include known and / or otherwise previously determined data. Patterning system aberration and / or process influence calibration data can be measured, simulated, and / or determined in other ways. In some embodiments, calibration data are obtained by performing a full simulation model based on associated pupil shape, pattern forming apparatus design, and various aberration inputs (e.g., the full simulation model may include one or more of illumination model 31, projection optics model 32, design layout model 35, resist model 37, and / or other models).

[0141] In some embodiments, an aberration influence model is calibrated by providing patterned system aberration calibration data to a base (prediction) model to obtain predictions of the patterning process influence calibration data, and using the patterning process influence calibration data as feedback to update one or more configurations of the base model. For example, one or more configurations of the aberration influence model are updated based on a comparison between the patterning process influence calibration data and the predictions of the patterning process influence calibration data. Calibration data used to calibrate the aberration influence model may include pairs or sets of inputs (e.g., known patterned system aberration data) and corresponding known outputs (e.g., known patterning process influence calibration data). In some embodiments, the aberration influence model can self-learn using the provided training information pairs. The calibrated aberration influence model can then be used to make predictions (e.g., the influence on the patterning process) based on various input information (such as different patterned system aberration data as described above).

[0142] In some embodiments, the aberration influence model includes a hyperdimensional function configured to correlate received patterned system aberration data with patterned process influence data. In some embodiments, the calibrated model includes updating one or more configurations of the underlying model by tuning and / or otherwise adjusting one or more parameters of the function. In some embodiments, tuning includes adjusting one or more model parameters such that the predicted patterned process influence data better matches or corresponds to known patterned process influence calibration data. In some embodiments, tuning includes training or retraining the model using additional calibration information, including new and / or additional input / output calibration data pairs.

[0143] In some embodiments, the aberration influence model (e.g., a hyperdimensional function) includes one or more of nonlinear algorithms, linear algorithms, quadratic algorithms, or combinations thereof, but may also include any suitable arbitrary mathematical function. For example, the hyperdimensional function may have any power polynomial form, piecewise polynomial form, exponential form, Gaussian form, sigmoid form, decision tree-type form, convolutional neural network-type form, etc. These algorithms may include any number of parameters, weights, and / or other features, in any combination such that the hyperdimensional function is configured to mathematically correlate patterned system aberrations with the influence of the patterning process in a simplified form, rather than a full simulation. Without limiting the scope of this disclosure to the examples below, exemplary linear algorithms may include linear forms of Zernike terms, wherein linear coefficients are computed via linear regression of the dependencies of CD, PPE, EPE, asymmetry, defects, and / or other parameters on individual Zernike terms. Exemplary quadratic algorithms may include linear and quadratic forms of Zernike terms, wherein linear and quadratic coefficients are computed via nonlinear regression of the dependencies of CD, PPE, and / or other parameters on individual Zernike terms.

[0144] In some embodiments, the form of the function (e.g., nonlinear, linear, quadratic, etc.), the parameters of the function, the weights in the algorithm, and / or other properties of the function may be automatically determined based on the above-described calibration, based on accuracy and runtime performance specifications provided by the user, based on information selections made by the user through a user interface included in the system, and / or other methods. In some embodiments, the form of the function (e.g., nonlinear, linear, quadratic, etc.), the parameters of the function, and / or other properties of the function may vary with the various layers of the substrate (e.g., with processing parameters and / or other conditions that may cause and / or affect aberration changes), and / or based on other information. For example, different models may be calibrated for different layers of the substrate produced during the patterning operation in semiconductor device fabrication.

[0145] Fully simulated models are typically computationally expensive and time-consuming, making them unsuitable for handling real-time aberration drift for compensation during high-volume manufacturing. As a non-limiting example, Figure 4 A comparison of the operation of this aberration influence model 400 with the operation of the full simulation 402 is shown. As mentioned above, the full simulation may include simulations of the source, mask, dose, focusing, and / or other aspects of the lithography process (see, for example, [link to full simulation]). Figure 2 Modeling using this aberration influence model instead of a full simulation includes modeling, at least without computing (e.g., simulating or generating) a spatial image or its representation. The aberration influence model is configured to generate predictions based on input patterned system aberration data without requiring additional information related to source, mask, dose, focus, etc., that would be needed in a full simulation.

[0146] like Figure 4 As shown, prior to the system and method of the present invention, a full lithography simulation 406 is performed using a measured, modeled, and / or otherwise determined aberration Z (e.g., defined by patterning system aberration data) 404. Then, the lithography process cost 408 is evaluated using the full lithography simulation 406 (e.g., defined by and / or including patterning process influence data). Depending on the specific application, the user may choose to focus on different lithography performance metrics (such as CD, PPE, EPE, CD asymmetry, defect count, etc.). The cost (value) function s(CD, PPE, ...) is defined according to user requirements. For any given aberration Z, a full lithography simulation is performed to obtain CD, PPE, EPE, and then s(CD, PPE, ...) is evaluated. Full lithography simulation is slow and expensive. Therefore, iteratively repeating such simulations is unsuitable for dynamic in-situ aberration control. In contrast, the aberration influence model 400 can be applied faster than a full simulation, at least due to its lower computational complexity. For example, as... Figure 4 As shown, process costs can be modeled 410 and directly defined as a function of aberrations (e.g., s(Z) shown). The function s(Z) can represent the impact on the patterning process as a function of aberrations. Embodiments of this disclosure are described in great detail with reference to aberrations and aberration correction. For example, as discussed herein, wavefront aberration can refer to the deviation (degree of inconsistency) between the ideal wavefront and the actual wavefront. However, the mechanisms disclosed herein can also be applied to the monitoring or correction of other wavefront aspects in the lithography process without departing from the scope of this disclosure.

[0147] As another non-restrictive example, Figure 5 Example operation 500 for constructing this aberration influence model 400 is shown. As described above, it can be based on different aberrations (e.g., Z1…Z2). n Repeated simulations 502 and the effects of different aberrations on the patterning process generate calibration data 501 503, wherein the effects can be represented by a comprehensive cost function s(Z). The calibration data 503 is used to calibrate a basic model 506 504 (e.g., having a deterministic form—linear, quadratic, etc.) to produce an aberration effect model 400.

[0148] return Figure 3In operation 304, the aberration influence model receives patterned system aberration data. The received patterned system aberration data may include data describing the characteristics of a particular aberration, the cause of the aberration, and / or other data. Patterned system aberration data may include measured and / or simulated aberrations, system and / or process parameters associated with the aberration, and / or other information. The model receives the data as input to generate predictions. Data may be received electronically from one or more other parts of the system (e.g., from a different processor), from a remote computing system never associated with the system, and / or from other sources. Data may be received wirelessly and / or wired via portable storage media and / or from other sources. For example, data may be uploaded and / or downloaded from another source (such as a cloud storage device), and / or received in other ways.

[0149] In some embodiments, patterned system aberration data is received during substrate fabrication. For example, aberration drift can be measured during or just before substrate layer processing in semiconductor fabrication (e.g., and / or patterned system aberration data can be determined). The relatively time-consuming and computationally intensive configuration and calibration of the aberration influence model is performed before it can be used in mass production. The calibrated model has a simplified form and does not require predictions using illumination model 31, projection optics model 32, design layout model 35, resist model 37, or other models, advantageously enabling real-time or near-real-time calculations to obtain accurate compensation for scanner (patterned system) aberrations. Furthermore, since the calibrated model can be configured to optimize one or more imaging performance factors with respect to the substrate, the determined aberration compensation can advantageously produce optimal imaging performance on the substrate.

[0150] As a non-restrictive example, Figure 6 This illustrates the construction of an aberration influence model 400 (e.g., using operation 500) during the offline R&D phase 600. Figure 5 (as shown in the operation), and then model 400 is used in the mass production stage 602. Figure 5 As shown, in manufacturing stage 602, model 400 is configured to receive measured aberration 604 data (e.g., patterning system aberration data) and output new patterning process influence data s(Z). In some embodiments, the aberration influence model does not need to "output" imaging performance data. As described below, the output from model 400 (e.g., s(Z)) (and / or calculation results, which are not the model's "output") is configured to be used by a second model 610 to facilitate dynamic field scanner aberration control 612. However, this is merely exemplary. In some other embodiments, the aberration influence model integrates functions of the second model.

[0151] return Figure 3In operation 306, in response to the received patterning system aberration data, patterning process influence data is determined. New patterning process influence data is determined based on an aberration influence model and / or other information. The generated patterning process influence data refers to the effect of a corresponding patterning system aberration on the substrate in one or more aspects of critical dimensions, pattern placement errors, edge placement errors, critical dimension asymmetry, optimal focus offset, defect count, and / or other parameters of the patterning process associated with the patterning process. In some embodiments, determining new patterning process influence data includes predicting new patterning process influence data using an aberration influence model. The patterning process influence data is predicted based on the received patterning system aberration data (e.g., aberrations measured in real time during high-volume manufacturing). In some embodiments, the predicted patterning process influence data indicates a high probability or likelihood that a given aberration will cause a corresponding patterning process influence.

[0152] In some embodiments, the aberration impact model includes the value s(Z) of a cost (or value) function of the corresponding patterning system aberration. The cost function s(Z) represents the impact on the patterning process (e.g., on any one or more of the parameters listed above) caused by the corresponding patterning system aberration drift. In some embodiments, the aberration drift is primarily caused by lens heating or mirror heating during operation of the lithography apparatus. The cost (or value) function s(Z) determined by the aberration impact model may include parameters associated with the scanner tuning knob, lithography performance metrics (e.g., CD, EPE, defect count, asymmetry parameters, etc. selected by the user), and / or other parameters (see the examples and discussions provided below related to operations 308 and 310, and...). Figures 7-9 ).

[0153] In some embodiments, method 300 includes providing 308 new patterning process influence data to a second model to facilitate dynamic in-situ aberration control of a patterning system (e.g., a scanner). For example, providing new patterning process influence data includes providing a cost function s(Z) and / or other information. In some embodiments, the second model is a projection optics correction model and / or other models. In some embodiments, the new patterning process influence data (e.g., the cost function) from the aberration influence model is configured to determine a set of patterning process control metrics (e.g., by the projection optics correction model). In some embodiments, the patterning process control metrics include lithography performance metrics and / or other information. In some embodiments, the set of patterning process control metrics is configured to be determined by a linear solver and / or by other operations.

[0154] In some embodiments, method 300 includes performing 310 dynamic field aberration control of a patterning system (e.g., a scanner and / or other patterning system). In some embodiments, dynamic field control of the scanner includes generating a corrected scanner control parameter recipe for a given scanner aberration to optimize a set of lithography performance metrics. In some embodiments, dynamic field control includes controlling aberrations during high-volume manufacturing. For example, in some embodiments, operations 302-310 may be performed such that new patterning process influence data (e.g., a cost function output by an aberration influence model) are configured to facilitate real-time or near-real-time enhancement of compensation and / or control (e.g., to reduce and / or eliminate scanner aberrations) of heating (e.g., EUV) to one or more mirrors, lenses, and / or other elements of the patterning system during manufacturing. EUV mirror heating control is useful because scanners typically require a limited number of knobs to dynamically correct aberrations caused by mirror heating. As another example, operations 302-310 can be performed such that new patterning process influence data (e.g., the cost function output by an aberration influence model) are configured to facilitate real-time or near-real-time enhancement of control over focus, dose, and / or stage variation (MSD) associated with the patterning system (e.g., a scanner) during manufacturing. Other examples are conceivable.

[0155] It should be noted that an aberration influence model can be provided to different projection optics boxes to control CD, EPE, and / or other parameters. Because the aberration influence model can be configured to construct a cost (value) function based on simulation results, it can define (e.g., for calibration) any desired metric, such as CD, PPE, EPE, CD asymmetry, optimal focus offset, defect count, etc. In this way, the aberration influence model can be configured to automatically reflect the desired metrics.

[0156] Through several non-restrictive examples, Figure 7-11 The diagram illustrates various operations involved in providing (e.g., operation 308) new patterning process influence data to a second model to facilitate dynamic field aberration control of the scanner (e.g., operation 310). For example, Figure 7 An example is provided to illustrate how to configure a cost function based on an aberration influence model for use by a projection optics correction model, thereby determining a set of control metrics for the patterning process. Figure 7 A visual representation 700 of the cost function 702 in the aberration (or wavefront aberration) space 704 is provided. Figure 7The target state (or the scanner's initial state or cold state) "A" 706 and the isocost curve 708 are shown. As described above, the aberration influence model determines the cost function s(Z). The projection optics correction model defines a (scanner) lens (element, such as a lens, mirror, etc.) dependency matrix D such that the scanner performance fingerprint = D*δ, where δ represents a variable scanner control knob setting. In some embodiments, the cost function from the aberration influence model can be defined as:

[0157] s(Z(δ))=s(ΔZ+Dδ)

[0158] Where ΔZ represents the aberration drift from the scanner, D is the dependency matrix, δ represents the variable scanner control knob setting, and Dδ represents the performance fingerprint (or in other words, the required correction). A nonlinear optimizer can be used to minimize s(δ) such that δ* = argmin s(δ), where δ* represents the required dynamic scanner knob correction.

[0159] continue Figure 7 The visual illustration shown is 700. Figure 8 Dynamic aberration control / correction is shown (using (lens) mirror heating as an example). Figure 8 A projection optics correction model is shown, which attempts to correct scanner aberrations based on a cost function determined by an aberration influence model. Figure 8 View 800 shows cold state A706 (before the mirror is heated during scanner operation), view 802 shows hot state B (after the mirror is heated during scanner operation), and view 804 shows hot state C after correction. In cold state A, ΔZ = 0 and δ = 0. The cost function s(Z(δ)) is at its minimum, s = 0. In hot state B before correction, ΔZ ≠ 0 and δ = 0. The cost function s = ΔZ T HΔZ, where H is the cost function Hessian and T denotes the transpose operation. In the corrected thermal state C, ΔZ≠0 and δ≠0. The projection optics correction model is attempting to adjust the knob (δ) to minimize the cost s(δ).

[0160] As described above, in some embodiments, new patterning process influence data (e.g., cost function) from the aberration influence model is configured to be used (e.g., by a projection optics correction model) to determine a set of patterning process control metrics. In some embodiments, the patterning process control metrics include lithography performance metrics (or “lithography metrics”) and / or other information. In some embodiments, the set of patterning process control metrics is configured to be determined by a linear solver and / or by other operations. For example, the form of the aberration influence model (and / or the cost function output by the aberration influence model) is set (for this example) to be a positive definite quadratic form, such as:

[0161]

[0162] Where, the total aberration Z = ΔZ + Dδ, ΔZ is the aberration drift (e.g., aberration caused by mirror heating), δ represents the scanner knob, and Dδ represents the correction. Then:

[0163]

[0164] The cost function described above can be transformed into a lithographic metric set. In some embodiments, the new patterning process influence data from the model includes the cost function Hessian (e.g., H in the equation above). Determining the patterning process control metric set involves performing singular value decomposition (SVD) on the Hessian. Hessian(H) is a positive definite matrix. Performing SVD on the Hessian transforms the cost function into a "lithographic metric" format.

[0165] For example, Figure 9 The transformation of the cost function (from the aberration effect model) into a lithographic metric format is shown (e.g., to help determine the patterning process control metric set through the projection optics correction model). Figure 9 A comparison is shown between what the projection optics correction model will achieve (900) and what the projection optics correction model can typically achieve (902). In some embodiments, "will achieve" means minimizing a previously defined lithography performance function; "what the projection optics correction model can typically achieve" means achieving certain objectives of a linear combination set of Zernike variables in an RMS sense. Figure 9 The cost function Hessian 904 and lithographic metric 906 are shown. To bridge the gap between the two expressions, singular value decomposition (SVD) can be performed on the Hessian according to the following equation:

[0166]

[0167] (where eigenvalues ​​are absorbed into the eigenvectors) such that:

[0168]

[0169] like Figure 9 As shown. SVD essentially eliminates cross terms through high-dimensional rotation.

[0170] Figure 10 This demonstrates how this aberration influence model enables dynamic aberration correction per substrate (e.g., per wafer or per layer). Figure 10 Using a reflector for heating as an example. Figure 10The aberrations (e.g., Zernikei) 1001 caused by mirror heating over time (in a given production batch) 1003 are plotted. Figure 10 The image shows wafers 1–8 (w1, w2, …, w8) within a production batch. Figure 10 The original 1005 aberration drift that would occur without correction (e.g., the change of Zernike 1001 over time 1003 due to mirror heating) was plotted. In contrast, Figure 10 The diagram also shows the mirror heating residue 1007, the projection optics correction model residue 1009, the final field 1011 of the mirror heating residue 1007 (which is equal to the worst mirror heating residue), and the correction 1013 for each wafer. As described above, correction is applied via the projection optics correction model. Due to the dynamic nature of the aberration-affected model, correction can be applied on a per-wafer basis, in contrast to prior art systems that provide static corrections that can only be performed offline (e.g., not in a manufacturing setup).

[0171] Figure 11 The outline of the above operations is shown. Figure 11 This illustrates the construction of the aberration influence model 400 during the offline or R&D phase 600 (e.g., Figure 5 The operation shown), and then the model is used in manufacturing stage 602 (e.g. Figure 6 (As shown). During stage 600, the aberration influence model 400 can be calibrated based on simulated patterned system aberration calibration data and / or corresponding patterned process influence calibration data. Simulations can be performed using simulation engine 1101, based on different mask designs 1103, pupil shapes 1105, and / or other information. In some embodiments, simulations can be performed on the entire chip layout to obtain a cost function, dependency matrix, or Hessian matrix for the entire chip layout. As described herein, the cost function from the aberration influence model 400 is configured to be used by the projection optics correction model 610 (in conjunction with measured aberration data 1107 from the scanner (patterned system) 1109) to determine a set of patterned process control metrics and to facilitate dynamic field aberration control 612. For example, the aberration influence model 400 can take the form of an ADLASSLA file and / or any other scanner-friendly lightweight data format. Figure 11 As shown, multiple different projection optics correction models 610 (associated with several different scanners 1109) can be used with a single calibration aberration effect model.

[0172] Dynamic field aberration control 612 includes adjusting the semiconductor device manufacturing process during the manufacturing phase. Adjustments can be made based on the output of a projection optics correction model and / or other information. For example, manufacturing process parameter adjustments can be determined (e.g., the amount by which a given parameter should be changed), and the manufacturing process parameters can be adjusted from a previous parameter setpoint to a new parameter setpoint. In some embodiments, the determined and / or adjusted semiconductor device manufacturing process parameters include one or more of pupil shape, dose, focus, power setting, and / or other semiconductor device manufacturing process parameters. As an example, if the process parameter is (e.g., a new) pupil shape or a new dose, the scanner can be adjusted from an old or previous pupil shape or dose to the determined (e.g., new) pupil shape or dose. Several other similar examples are also envisioned.

[0173] As described above, the model presented herein has a wide range of applications. Another example application (e.g., in addition to mirror heating and other examples mentioned above) is the use of aberration influence modeling to collaboratively optimize multiple patterned systems. Patterned systems may include scanners and / or other patterned systems. For example, a calibrated aberration influence model can be used for wavefront tuning (e.g., replacing full imaging simulation in prior art systems) to ensure that the same design layout is printed identically on different scanners or at different slit locations.

[0174] As a reminder, the aberration effect model described herein includes a relatively simple hyperdimensional function configured to correlate the received patterned system aberration data with the new patterning process effect data. This hyperdimensional function is configured to correlate the received patterned system aberration data with the new patterning process effect data in an approximate form, rather than a full simulation (requiring no computation of the spatial image). Multiple models can be used to describe the imaging performance of multiple scanners.

[0175] This (aberration effects) model is a compact model that offers a reduced range and improved runtime performance compared to existing models. At least because the predicted effects are based (only) on aberration data, and because the predicted effects can be specifically applied to pre-selected metrics (such as critical size, defect count, etc.), this model is accurate, fast, and / or possesses other advantageous characteristics, making it suitable for co-optimization applications. This model can be specifically designed for use cases where tuning is based solely on relevant aberration data. Due to the lightweight nature of this model and / or their other advantageous characteristics, co-optimization of multiple patterned systems is possible.

[0176] For example, in some embodiments, one or more processors (e.g., one or more computers) may execute one or more electronic models (e.g., aberration influence models) to determine patterning process influence data without computing a spatial image representation of the patterning process. The patterning process influence data may be configured to facilitate the cooperative optimization of multiple patterning systems used in the patterning process. New patterning process influence data output from the model may be configured to facilitate the cooperative optimization of multiple scanners used in the patterning process. Cooperative optimization may include using lens actuators as variables and employing a gradient-based nonlinear optimizer to cooperatively determine the actuator positions of the multiple scanners. In some embodiments, the new patterning process influence data from the model is configured to determine a patterning process control metric set, wherein the patterning process control metric set is configured to be determined by a linear solver (e.g., as described below).

[0177] Patterned system aberration data can be provided to a model (or multiple models) such that the model (e.g., a hyperdimensional function) correlates the received patterned system aberration data with patterning process influence data. Different (aberration influence) models may correspond to different patterned systems (scanners). New patterning process influence data can be determined for the received patterned system aberration data. As a non-limiting example, the received patterned system aberration data may include received wavefront data, and the new patterning process influence data may include one or more patterning process measures. For example, wavefront data may include measured or simulated wavefront data in the form of a Zernike list or pixelated bitmap, and / or other wavefront data. In this example, one or more patterning process measures may include critical size, pattern placement error, edge placement error, critical size asymmetry, optimal focus offset, defect count, and / or other measures associated with the patterning process. In some embodiments, the new patterning process impact data represents the effect of the corresponding patterning system aberrations on one or more of the following metrics associated with the patterning process: critical size, pattern placement error, edge placement error, critical size asymmetry, optimal focus offset, defect count, and / or other metrics.

[0178] In some embodiments, a given model includes one or more key feature components (e.g., one or more dimensions of a hyperdimensional function) configured to model variations between scanners for key features of the patterning process; one or more regular components (e.g., one or more other dimensions of the hyperdimensional function) configured to model the general performance of the scanners for non-key features of the patterning process; and / or other components. Key feature components of a given model are defined for (all) patterning systems (e.g., scanners) in a group of patterning systems undergoing co-optimization. Key feature components are configured to represent variations in key features (e.g., key dimensions as an example) in the pattern between patterning systems (e.g., scanners). Regular components of the model can be configured to represent non-key features of the pattern. Regular components of the model can represent the general performance of a given scanner (or other patterning system) with respect to non-key features of the pattern. This separate arrangement of key feature components / regular components allows users to customize the key feature components of the model based on, for example, the performance of the patterning system at a given manufacturing location, or other unique factors affecting key features of the patterning process, while keeping invariant or non-key factors the same (or similar). For example, a user can provide a specific CD sensitivity, which can be represented by one or more key feature components of the model for the key features of the pattern, but then allow the model's regular components to generate outputs of non-key features of the pattern, where it is not meaningful to spend a lot of resources on modeling and / or optimization.

[0179] In other words, users can specify key features based on any suitable criteria (e.g., features of particular interest to the user and / or features that address one or more problems). Other features can be considered regular features. The key feature components and regular components of a given model can be two different functions associated with these different types of features. In some embodiments, users can define regular features / functions (e.g., in addition to and / or in place of key feature components / functions), but if a user defines regular features / functions, the system can be configured such that the user-defined features / functions (by definition) become key. Advantageously, the model handles any features / functions not specified by the user in a uniform manner known for regular features / functions.

[0180] In some embodiments, new patterning process impact data from the model is configured to be provided to the cost function to help determine the costs associated with each patterning process metric and / or with each patterning process variable. The costs associated with each patterning process metric and / or with each patterning process variable are configured to contribute to the collaborative optimization of multiple scanners and / or for other purposes.

[0181] Figure 12 The components of an example cost function 1200 according to an embodiment are shown. Figure 12 As shown, the cost function 1200 includes a first component 1202 associated with critical features of the patterning process, a second component 1204 associated with non-critical features of the patterning process, and a third component 1206 associated with physical functional limitations of one or more scanners and / or other patterning systems. Component 1202 is defined for all patterning systems (e.g., scanners) in the group of patterning systems undergoing co-optimization. Component 1202 is configured to represent variations in critical features (e.g., critical dimensions as an example) between patterning systems (e.g., scanners). Component 1204 may be the total lithographic metric of common non-critical features in the patterning systems. Component 1204 may represent the general performance of a given scanner with respect to non-critical features (e.g., features that would print well even without tuning). Component 1206 is unique for a given patterning system and is associated with specific physical limitations of the given patterning system (e.g., the range of motion of a particular component, any offset, specific parameters that move consistently and regularly on the machine in the same manner, etc.). In some embodiments, the cost function 1200 also includes a fourth component 1208 associated with the conventional penalty for the wavefront during the patterning process. Component 1208 is defined per individual scanner. Component 1208 is configured to represent and / or otherwise indicate any additional user preferences regarding the wavefront itself (rather than its associated lithographic performance characteristics). For example, if two sets of wavefronts have the same lithographic performance characteristics, the user may prefer a wavefront with a smaller root mean square (RMS) amplitude.

[0182] Figure 13 An example (cooperative) optimized architecture 1300 according to an embodiment is shown. Figure 13As shown, in some embodiments, new patterning process influence data 1302 from model 1304 (e.g., an aberration influence model as described herein) is configured to be provided to cost function 1200 (e.g., including key features and general features) to help determine costs 1306 associated with various patterning process metrics (e.g., ds / dCD, etc.). Costs 1306 associated with various patterning process metrics are configured to be provided back to model 1304 to help determine costs associated with patterning process wavefront conditioning 1308 (e.g., ds / dwf). Costs associated with patterning process wavefront conditioning 1308 may also be determined based on wavefront conditioning penalty 1310 (e.g., provided by the user) and / or other information. For example, costs 1308 associated with patterning process wavefront conditioning are configured to be provided to driver lens model 1312 to help determine costs associated with various patterning process variables 1314 (e.g., ds / dv). For example, driver lens model 1312 may be a model specifying how the tuning action of an actuator knob affects the wavefront. Costs 1308 can also be determined based on physical functional constraints 1316 (e.g., actuator consumption penalties) and / or other constraints of one or more scanners and / or other patterning systems. Costs 1314 associated with the individual patterning process variables are configured to be provided to an optimizer 1318 to facilitate collaborative optimization of multiple patterning systems (e.g., scanners). Typically, an optimizer is a computer algorithm that finds the minimum of a given cost function. For example, optimizer 1318 could be a gradient-based nonlinear optimizer (e.g., L-BFGS-B) configured to collaboratively determine the actuator positions of multiple scanners. Optimizer 1318 can be formed by one or more processors configured to differently balance possible process variables (e.g., each variable within its own permissible range) relative to manufacturing capabilities or costs associated with different metrics (e.g., critical dimensions, pattern placement errors, edge placement errors, critical dimension asymmetry, optimal focus offset, defect counts, and / or other metrics associated with the patterning process).

[0183] Similarly, Figure 13 As shown, optimizer 1318 can be configured to output one or more process variables (v) (e.g., lens actuator variables in this example) 1320, which are fed into driver lens model 1312 and converted into wavefront data 1322 (wf) (as described above, wavefront data is provided to model 1304). Driver lens model 1312 is configured to predict the resulting wavefront when the lens actuator variables are tuned.

[0184] Figure 14This is a diagram of an exemplary computer system CS, which can be used for one or more of the operations described herein. The computer system CS includes a bus BS or other communication mechanism for communicating information, and a processor PRO (or multiple processors) coupled to the bus BS for processing information. The computer system CS also includes main memory MM, such as random access memory (RAM) or other dynamic storage devices, coupled to the bus BS for storing instructions and information to be executed by the processor PRO. The main memory MM can also be used to store temporary variables or other intermediate information during instruction execution by the processor PRO. The computer system CS also includes a read-only memory (ROM) or other static storage device coupled to the bus BS for storing static information and instructions for the processor PRO. A storage device SD, such as a disk or optical disk, is provided and coupled to the bus BS for storing information and instructions.

[0185] A computer system CS can be coupled via a bus BS to a display DS for displaying information to the computer user, such as a cathode ray tube (CRT), flat panel display, or touch panel display. Input devices ID, including alphanumeric keys and other keys, are coupled to the bus BS for communicating information and command selections to the processor PRO. Another type of user input device is a cursor controller CC, such as a mouse, trackball, or cursor direction keys, used to communicate directional information and command selections to the processor PRO and to control cursor movement on the display DS. Such input devices typically have two degrees of freedom on two axes (i.e., a first axis (e.g., x) and a second axis (e.g., y)), allowing the device to specify its position in a plane. Touch panel (screen) displays can also be used as input devices.

[0186] In some embodiments, a portion of one or more methods as described herein may be performed by a computer system CS in response to a processor PRO executing one or more sequences of one or more instructions contained in main memory MM. These instructions may be read from another computer-readable medium, such as a storage device SD, into main memory MM. Execution of the sequence of instructions contained in main memory MM causes the processor PRO to perform the process steps (operations) described herein. One or more processors arranged in a multiprocessor configuration may also be employed to execute the sequence of instructions contained in main memory MM. In some embodiments, a hard-wired circuit system may be used instead of or in combination with software instructions. Therefore, the description herein is not limited to any particular combination of hardware circuitry and software.

[0187] As used herein, the term "computer-readable medium" refers to any medium that participates in providing instructions to a processor (PRO) for execution. Such media can take many forms, including but not limited to non-volatile media, volatile media, and transmission media. Non-volatile media include, for example, optical discs or magnetic disks, such as storage devices (SDs). Volatile media include dynamic memory, such as main memory (MMs). Transmission media include coaxial cables, copper wires, and optical fibers, including wires containing a bus (BS). Transmission media can also take the form of sound waves or light waves, such as those generated during radio frequency (RF) and infrared (IR) data communications. Computer-readable media can be non-transitory, such as floppy disks, floppy disks, hard disks, magnetic tape, any other magnetic media, CD-ROMs, DVDs, any other optical media, punched cards, paper tape, any other physical media with a perforated pattern, RAM, PROMs and EPROMs, FLASH-EPROMs, any other memory chips or cartridges. Non-transitory computer-readable media may have instructions recorded thereon. When executed by a computer, the instructions can perform any of the operations described herein. For example, a temporary computer-readable medium may include a carrier wave or other medium that propagates electromagnetic signals.

[0188] Various forms of computer-readable media can be used to carry one or more sequences of one or more instructions to the processor PRO for execution. For example, the instructions can initially be carried on the disk of a remote computer. The remote computer can load the instructions into its dynamic memory and transmit them over a telephone line using a modem. A modem local to the computer system CS can receive data over the telephone line and convert the data into an infrared signal using an infrared transmitter. An infrared detector coupled to the bus BS can receive the data carried in the infrared signal and place the data on the bus BS. The bus BS carries the data to the main memory MM, and the processor PRO retrieves and executes the instructions from the main memory MM. The instructions received by the main memory MM can optionally be stored on the storage device SD before or after execution by the processor PRO.

[0189] The computer system CS may also include a communication interface CI coupled to the bus BS. The communication interface CI provides bidirectional data communication coupling with a network link NDL connected to a local area network (LAN). For example, the communication interface CI may be an Integrated Services Digital Network (ISDN) card or a modem to provide data communication connectivity to a corresponding type of telephone line. As another example, the communication interface CI may be a LAN card to provide data communication connectivity to a compatible LAN. Wireless links may also be implemented. In any such implementation, the communication interface CI transmits and receives electrical, electromagnetic, or optical signals carrying digital data streams representing various types of information.

[0190] A network link (NDL) typically provides data communication to other data devices via one or more networks. For example, a network link NDL can provide a connection to a host computer (HC) via a local area network (LAN). This can include data communication services provided via a global packet data communication network (now commonly referred to as the "Internet" INT). A LAN (Internet) can use electrical, electromagnetic, or optical signals to carry digital data streams. Signals passing through various networks and signals on the network data link (NDL) and through the communication interface (CI) (which carries digital data to and from the computer system (CS)) are example forms of carriers for transmitting information.

[0191] A computer system CS can send messages and receive data, including process code, via a network, network data link (NDL), and communication interface (CI). In the Internet example, a host computer HC can transmit requested code for an application via the Internet (INT), network data link (NDL), local area network (LAN), and communication interface (CI). For example, such a downloaded application can provide all or part of the methods described herein. The received code can be executed by the processor PRO upon reception and / or stored in storage device (SD) or other non-volatile storage device for later execution. In this way, the computer system CS can obtain application code in carrier form.

[0192] Figure 15 This is a schematic diagram of a photolithography projection apparatus according to an embodiment. The photolithography projection apparatus may include an illumination system IL, a first stage MT, a second stage WT, and a projection system PS. The illumination system IL can adjust the radiation beam B. In this embodiment, the illumination system also includes a radiation source SO. The first stage (e.g., a patterning apparatus stage) MT may be provided with a patterning apparatus holder to hold the patterning apparatus MA (e.g., a mask) and connected to a first locator to accurately position the patterning apparatus relative to the stage PS. The second stage (e.g., a substrate stage) WT may be provided with a substrate holder to hold the substrate W (e.g., a silicon wafer coated with resist) and connected to a second locator to accurately position the substrate relative to the stage PS. The projection system (e.g., it includes lenses) PS (e.g., a refractive optical system, a reflective optical system, or a catadioptric optical system) can image the illuminated portion of the patterning apparatus MA onto a target portion C (e.g., including one or more dies) of the substrate W. For example, the patterning apparatus MA and the substrate W can be aligned using patterning apparatus alignment marks M1, M2 and substrate alignment marks P1, P2.

[0193] As described, the device can be transmissive (i.e., having transmissive pattern forming apparatus). However, it can also typically be reflective, for example (having reflective pattern forming apparatus). The device can employ different kinds of pattern forming apparatus to form typical masks; examples include programmable mirror arrays or LCD matrices.

[0194] A source SO (e.g., a mercury lamp or excimer laser, LPP (laser-generated plasma) EUV source) generates a radiation beam. This beam is fed, for example, directly or after passing through a conditioning device (such as a beam expander) or a beam delivery system BD (including a directional mirror, beam expander, etc.) into an irradiation system (irradiator) IL. The irradiator IL may include a conditioning device AD ​​for setting the outer and / or inner radial ranges (typically referred to as σ-outer and σ-inner, respectively) of the intensity distribution in the beam. Additionally, the conditioning device AD ​​typically includes various other components, such as an integrator IN and a concentrator CO. In this way, the beam B irradiated onto the patterning apparatus MA has the desired uniformity and intensity distribution in its cross-section.

[0195] In some embodiments, the source SO can be inside the housing of the photolithography projection apparatus (e.g., this is typically the case when the source SO is a mercury lamp), but the source SO can also be located away from the photolithography projection apparatus. For example, the radiation beam generated by the source SO can be directed into the apparatus (e.g., by means of a suitable guiding mirror). For example, the latter case may be the case when the source SO is an excimer laser (e.g., based on KrF, ArF, or F2 lasers).

[0196] The beam PB can then be incident on the pattern forming apparatus MA held on the pattern forming apparatus stage MT. Having traversed the pattern forming apparatus MA, the beam B can pass through the lens PL, which focuses the beam B onto the target portion C of the substrate W. With the aid of a second positioning device (and an interferometric measuring device IF), the substrate stage WT can be accurately moved, for example, to position the different target portions C in the path of the beam B. Similarly, for example, after mechanically retrieving the pattern forming apparatus MA from the pattern forming apparatus library, or during scanning, the first positioning device can be used to accurately position the pattern forming apparatus MA relative to the path of the beam B. Typically, the movement of the stages MT and WT can be achieved by means of a long-stroke module (coarse positioning) and a short-stroke module (fine positioning). However, in the case of a stepper (relative to a stepping scanning tool), the pattern forming apparatus stage MT may be connected only to the short-stroke actuator, or it may be fixed.

[0197] The described tool can be used in two different modes: step mode and scan mode. In step mode, the pattern forming apparatus stage MT remains essentially stationary, and the entire pattern forming apparatus image is projected onto the target portion C in a single operation (i.e., a single "flash"). The substrate stage WT can move in the x and / or y directions, allowing the beam PB to irradiate different target portions C. In scan mode, essentially the same scenario is applied, except that the given target portion C is not exposed in a single "flash". Instead, the pattern forming apparatus stage MT can move at a speed v along a given direction (e.g., the "scanning direction" or the "y" direction), thereby scanning the projected beam B across the pattern forming apparatus image. Simultaneously, the substrate stage WT moves at a speed V = Mv in the same or opposite directions, where M is the magnification of the lens (typically, M = 1 / 4 or 1 / 5). In this way, a relatively large target portion C can be exposed without sacrificing resolution.

[0198] Figure 16 This is a schematic diagram of another lithographic projection apparatus (LPA) that can be used for and / or facilitate one or more of the operations described herein. The LPA may include a source collector module SO, an irradiation system (irradiator) IL configured to modulate a radiation beam B (e.g., EUV radiation), a support structure MT, a substrate stage WT, and a projection system PS. The support structure (e.g., a patterning apparatus stage) MT may be configured to support a patterning apparatus (e.g., a mask or photomask) MA and connected to a first positioner PM configured to accurately position the patterning apparatus. The substrate stage (e.g., a wafer stage) WT may be configured to hold a substrate (e.g., a wafer coated with resist) W and connected to a second positioner PW configured to accurately position the substrate. The projection system (e.g., a reflective projection system) PS may be configured to project a pattern, imparted by the radiation beam B by the patterning apparatus MA, onto a target portion C (e.g., comprising one or more dies) of the substrate W.

[0199] As described in this example, the LPA can be reflective (e.g., employing a reflective patterning apparatus). It should be noted that because most materials are absorptive in the EUV wavelength range, the patterning apparatus can have multilayer reflectors, which, for example, comprise multiple stacks of molybdenum and silicon. In one example, the multilayer reflector has 40 layers of molybdenum and silicon pairs, where the thickness of each layer is a quarter wavelength. Even smaller wavelengths can be produced using X-ray lithography. Since most materials are absorptive at both EUV and X-ray wavelengths, the patterned absorbent material blob on the morphology of the patterning apparatus (e.g., a TaN absorber on top of a multilayer reflector) defines whether the feature will be printed (positive resist) or not (negative resist).

[0200] The irradiator IL can receive an extreme ultraviolet (EUV) radiation beam from the source collector module SO. Methods for generating EUV radiation include, but are not necessarily limited to, converting a material into a plasma state having at least one element (e.g., xenon, lithium, or tin) using one or more emission lines in the EUV range. In one such method (commonly referred to as laser-generated plasma (“LPP”), plasma can be generated by irradiating fuel (such as droplets, streams, or clusters of material having a line-emitting element) with a laser beam. Figure 16 (Not shown in the image). The resulting plasma emits output radiation (e.g., EUV radiation), which is collected using a radiation collector disposed in the source collector module. The laser and the source collector module can be separate entities, for example, when a CO2 laser is used to provide a laser beam for fuel excitation. In this example, the laser is not considered part of the lithography apparatus, and the radiation beam can be delivered from the laser to the source collector module by means of a beam delivery system including, for example, suitable directional mirrors and / or beam expanders. In other examples, for example, when the source is a discharge-generated plasma EUV generator (often referred to as a DPP source), the source can be part of the source collector module.

[0201] An irradiator IL may include adjusters for adjusting the angular intensity distribution of the radiation beam. Typically, at least the outer radial range and / or inner radial range (often referred to as σ-outer and σ-inner, respectively) of the intensity distribution in the pupil plane of the irradiator can be adjusted. Additionally, the irradiator IL may include various other components, such as faceted fields and pupil reflector devices. The irradiator can be used to adjust the radiation beam to have a desired uniformity and intensity distribution in its cross-section.

[0202] A radiation beam B is incident on a pattern forming apparatus (e.g., a mask) MA held on a support structure (e.g., a pattern forming apparatus stage) MT and is patterned by the pattern forming apparatus. After being reflected from the pattern forming apparatus (e.g., the mask) MA, the radiation beam B passes through a projection system PS, which focuses the beam onto a target portion C of the substrate W. The substrate stage WT can be accurately moved (e.g., to position different target portions C in the path of the radiation beam B) by means of a second locator PW and a position sensor PS2 (e.g., an interferometric measuring device, a linear encoder, or a capacitive sensor). Similarly, a first locator PM and another position sensor PS1 can be used to accurately position the pattern forming apparatus (e.g., the mask) MA relative to the path of the radiation beam B. Pattern forming apparatus alignment marks M1, M2 and substrate alignment marks P1, P2 can be used to align the pattern forming apparatus (e.g., the mask) MA and the substrate W.

[0203] The described apparatus LPA can be used in at least one of the following modes: step mode, scan mode, and static mode. In step mode, the support structure (e.g., patterning apparatus stage) MT and substrate stage WT are kept substantially stationary (i.e., single static exposure) while the entire pattern applied to the radiation beam is projected onto the target portion C in a single pass. The substrate stage WT is then shifted in the X and / or Y directions, allowing different target portions C to be exposed. In scan mode, the support structure (e.g., patterning apparatus stage) MT and substrate stage WT are scanned synchronously while the pattern applied to the radiation beam is projected onto the target portion C (i.e., single dynamic exposure). The speed and direction of the substrate stage WT relative to the support structure (e.g., patterning apparatus stage) MT can be determined by the magnification (reduction) and image inversion characteristics of the projection system PS. In static mode, the support structure (e.g., patterning apparatus stage) MT is kept substantially stationary while the pattern applied to the radiation beam is projected onto the target portion C, thereby maintaining the programmable patterning apparatus, and the substrate stage WT is moved or scanned. In this mode, a pulsed radiation source is typically used, and the programmable patterning apparatus is updated as needed after each movement of the substrate stage WT or between consecutive radiation pulses during scanning. This operating mode can be readily applied to maskless lithography utilizing programmable patterning apparatuses, such as programmable mirror arrays as described above.

[0204] Figure 17 yes Figure 16 A detailed view of the photolithography projection equipment shown. (See attached image.) Figure 17 As shown, the LPA may include a source collector model SO, an irradiation system IL, and a projection system PS. The source collector model SO is configured such that a vacuum environment can be maintained within the enclosed structure 20 of the source collector model SO. An EUV radiation emitting plasma 210 can be formed by generating a plasma source through a discharge. The EUV radiation can be generated by a gas or vapor (e.g., Xe gas, Li vapor, or Sn vapor), wherein a heated plasma 210 is generated to emit radiation in the EUV range of the electromagnetic spectrum. The heated plasma 210 can be generated, for example, by a discharge that causes at least partial ionization of the plasma. A partial pressure of Xe, Li, Sn vapor, or any other suitable gas or vapor, such as 10 Pa, may be required to efficiently generate the radiation. In some embodiments, a plasma of excited tin (Sn) is provided to generate EUV radiation.

[0205] Radiation emitted by the hot plasma 210 enters the collector chamber 212 from the source chamber 211 via an optional gas barrier or contaminant trap 230 (also referred to in some cases as a contaminant barrier or vane trap), which is positioned in or behind the opening of the source chamber 211. The contaminant trap 230 may include a channel structure. The contaminant trap 230 may also include a gas barrier or a combination of a gas barrier and a channel structure. The contaminant trap or contaminant barrier trap 230 also includes a channel structure. The collector chamber 211 may include a radiation collector CO, which may be a grazing incidence collector. The radiation collector CO has an upstream radiation collector side 251 and a downstream radiation collector side 252. Radiation passing through the collector CO may be reflected by a grating spectral filter 240 to be focused along the optical axis indicated by the dashed line "O" at a virtual source point IF. The virtual source point IF is often referred to as the intermediate focus, and the source collector module is arranged such that the intermediate focus IF is positioned at or near the opening 221 of the enclosed structure 220. The virtual source point IF is an image of the radiative emission plasma 210.

[0206] Subsequently, the radiation passes through the illumination system IL, which may include a faceted field mirror assembly 22 and a faceted pupil mirror assembly 24, arranged to provide a desired angular distribution of the radiation beam 21 at the patterning apparatus MA and a desired uniformity of radiation intensity at the patterning apparatus MA. When the radiation beam 21 is reflected at the patterning apparatus MA (held by the support structure MT), a patterned beam 26 is formed, and the patterned beam 26 is imaged onto the substrate W held by the substrate stage WT via the projection system PS through reflective elements 28 and 30. Typically, more elements than are shown can be present in the illumination optics unit IL and the projection system PS. For example, a grating spectral filter 240 may be optionally present depending on the type of lithography apparatus. Furthermore, more mirrors than are shown in the figures may be present, for example, compared to… Figure 15 As shown, there may be 1-6 additional reflective elements in the projection system PS.

[0207] like Figure 17 The collector optics CO illustrated in the figure are depicted as a nested collector with grazing incidence reflectors 253, 254, and 255, which is merely an example of a collector (or collector mirror). The grazing incidence reflectors 253, 254, and 255 are configured to be axially symmetrical about the optical axis O, and this type of collector optics CO can be used in conjunction with a discharge-generated plasma source (commonly referred to as a DPP source).

[0208] Figure 18This is a detailed view of the source-collector module SO of the photolithography projection apparatus LPA (shown in the previous figures). The source-collector module SO can be part of the LPA radiation system. The laser LA can be arranged to deposit laser energy into a fuel such as xenon (Xe), tin (Sn), or lithium (Li), thereby generating a highly ionized plasma 210 with an electron temperature of several 10 eV. High-energy radiation generated during the deexcitation and recombination of these ions is emitted from the plasma, collected by near-normal incident collector optics CO, and focused onto an opening 221 in the enclosed structure 220.

[0209] The concepts disclosed in this paper can be used to simulate or mathematically model any general imaging system for imaging sub-wavelength characteristics, and may be particularly useful for emerging imaging techniques capable of generating increasingly shorter wavelengths. Emerging techniques include EUV (Extreme Ultraviolet) and DUV lithography, which can generate wavelengths of 193 nm using ArF lasers, and even 157 nm using fluorine lasers. Furthermore, EUV lithography can generate wavelengths in the 20 nm–50 nm range using synchrotrons or by bombarding materials (solid-state or plasma) with high-energy electrons to produce photons within this range.

[0210] The embodiments of this disclosure can be further described by the following clauses.

[0211] 1. A non-transitory computer-readable medium having instructions thereon, which, when executed by a computer, cause the computer to execute an electronic model for determining patterning process influence data without calculating a spatial image representation of the patterning process, the patterning process influence data being configured to facilitate the cooperative optimization of multiple scanners used in the patterning process, the operations caused by the instructions including:

[0212] Patterned system aberration data is provided to the model, which includes a hyperdimensional function configured to correlate the received patterned system aberration data with patterning process influence data; and

[0213] Based on the model, new patterning process influence data is determined for the received patterning system aberration data, wherein the new patterning process influence data from the model is configured to be provided to a cost function to help determine the costs associated with each patterning process metric and / or with each patterning process variable, and wherein the costs associated with each patterning process metric and / or with each patterning process variable are configured to facilitate collaborative optimization of multiple scanners.

[0214] 2. The medium according to item 1, wherein the patterned system aberration data provided to the model includes wavefront data, and wherein the new patterning process influence data includes one or more patterning process measures.

[0215] 3. The medium according to clause 1 or 2, wherein the model includes one or more key feature components configured to model the variation of key features of the patterning process between scanners; and one or more general components configured to model the general performance of the scanner for non-key features of the patterning process.

[0216] 4. The medium according to any one of clauses 1-3, wherein the cost function includes a first component associated with critical features of the patterning process, a second component associated with non-critical features of the patterning process, and a third component associated with physical functional limitations of one or more scanners.

[0217] 5. The medium according to any one of clauses 1-4, wherein the collaborative optimization includes using lens actuators as variables and using a gradient-based nonlinear optimizer to collaboratively determine the actuator positions of multiple scanners.

[0218] 6. A non-transitory computer-readable medium having instructions thereon, the instructions causing the computer to:

[0219] Perform a calibration model, which is configured to receive patterned system aberration data; and

[0220] Based on the model, the influence of the new patterning process on the received patterned system aberration data is determined;

[0221] The model includes a hyperdimensional function configured to correlate received patterned system aberration data with new patterning process influence data without computing a spatial image representation.

[0222] 7. The medium according to clause 6, wherein the hyperdimensional function is configured to correlate the received patterned system aberration data with the new patterning process influence data in an approximate form, rather than in a full simulation.

[0223] 8. The medium according to any one of clauses 6-7, wherein the model comprises one or more nonlinear, linear or quadratic algorithms.

[0224] 9. The medium according to any one of clauses 6-8, wherein the received patterning system aberration data includes received wavefront data, and wherein the new patterning process influence data includes one or more patterning process measures.

[0225] 10. The medium according to clause 9, wherein the one or more patterning process metrics include critical dimensions, pattern placement error, edge placement error, critical dimension asymmetry, optimal focus offset, or defect count associated with the patterning process.

[0226] 11. The medium according to any one of clauses 6-9, wherein the model comprises one or more key feature components and one or more general components, the key feature components being configured to model the variation of key features of the patterning process between patterning systems; and the one or more general components being configured to model the general performance of the patterning system for non-key features of the patterning process.

[0227] 12. The medium according to any one of clauses 6-11, wherein the new patterning process impact data from the model is configured to be provided to a cost function to help determine the costs associated with each patterning process metric and / or the costs associated with each patterning process variable.

[0228] 13. The medium according to clause 12, wherein the cost function includes a first component associated with a critical feature of the patterning process, a second component associated with a non-critical feature of the patterning process, and a third component associated with physical functional limitations of one or more patterning systems.

[0229] 14. The medium according to clause 13, wherein the cost function further includes a fourth component associated with the wavefront modulation penalty of the patterning process.

[0230] 15. The medium according to any one of clauses 6-14, wherein the new patterning process influence data output from the model is configured to facilitate the collaborative optimization of multiple patterning systems.

[0231] 16. The medium according to clause 15, wherein the plurality of patterning systems includes scanners, and wherein the collaborative optimization includes using lens actuators as variables and using a gradient-based nonlinear optimizer to collaboratively determine the actuator positions of the plurality of scanners.

[0232] 17. The medium according to any one of clauses 6-16, wherein the new patterning process influence data from the model is configured to determine a patterning process control metric set, the patterning process control metric set being configured to be determined by a linear solver.

[0233] 18. The medium according to any one of clauses 6-17, wherein the new patterning process influence data indicates the effect of the corresponding patterning system aberrations on one or more of the following associated with the patterning process: critical size, pattern placement error, edge placement error, critical size asymmetry, optimal focus offset, or defect count.

[0234] 19. The medium according to any one of clauses 6-18, wherein:

[0235] The new patterning process impact data from the model is configured to be provided to the cost function to help determine the costs associated with each patterning process metric.

[0236] The costs associated with each patterning process metric are configured to be returned to the model to help determine the costs associated with wavefront modulation of the patterning process.

[0237] The costs associated with wavefront conditioning of the patterning process are configured to be provided to the driver lens model to help determine the costs associated with each patterning process variable; and

[0238] The costs associated with each patterning process variable are configured to be provided to the optimizer to facilitate the collaborative optimization of multiple patterning systems.

[0239] 20. The medium according to any one of clauses 6-8, wherein the model is calibrated such that the new patterning process influence data is configured to help enhance the control of heating of one or more mirrors and / or lenses of the patterning system.

[0240] 21. A method for determining patterning process influence data without calculating the spatial image representation of the patterning process, the method comprising:

[0241] Perform a calibration model, which is configured to receive patterned system aberration data; and

[0242] Based on the model, new patterning process influence data are determined for the received patterned system aberration data;

[0243] The model includes a hyperdimensional function configured to correlate received patterned system aberration data with new patterning process influence data without computing the spatial image representation.

[0244] 22. The method according to clause 21, wherein the hyperdimensional function is configured to correlate the received patterned system aberration data with the new patterning process influence data in an approximate form, rather than a full simulation.

[0245] 23. The method according to any one of clauses 21-22, wherein the model comprises one or more nonlinear, linear or quadratic algorithms.

[0246] 24. The method according to any one of clauses 21-23, wherein the received patterned system aberration data includes received wavefront data, and wherein the new patterning process influence data includes one or more patterning process measures.

[0247] 25. The method according to clause 24, wherein the one or more patterning process metrics include critical dimensions, pattern placement error, edge placement error, critical dimension asymmetry, optimal focus offset, or defect count associated with the patterning process.

[0248] 26. The method according to any one of clauses 21-25, wherein the model comprises one or more key feature components and one or more general components, the key feature components being configured to model the variation of key features of the patterning process between patterning systems; and the one or more general components being configured to model the general performance of the patterning system for non-key features of the patterning process.

[0249] 27. The method according to any one of clauses 21-26, wherein the new patterning process impact data from the model is configured to be provided to a cost function to help determine the costs associated with each patterning process metric and / or the costs associated with each patterning process variable.

[0250] 28. The method according to clause 27, wherein the cost function includes a first component associated with critical features of the patterning process, a second component associated with non-critical features of the patterning process, and a third component associated with physical functional limitations of one or more patterning systems.

[0251] 29. The method according to clause 28, wherein the cost function further includes a fourth component associated with the wavefront conditioning penalty of the patterning process.

[0252] 30. The method according to any one of clauses 21-29, wherein the new patterning process influence data output from the model is configured to facilitate the collaborative optimization of multiple patterning systems.

[0253] 31. The method according to clause 30, wherein the plurality of patterning systems includes scanners, and wherein the collaborative optimization includes using lens actuators as variables and using a gradient-based nonlinear optimizer to collaboratively determine the actuator positions of the plurality of scanners.

[0254] 32. The method according to any one of clauses 21-31, wherein the new patterning process influence data from the model is configured to determine a patterning process control metric set, the patterning process control metric set being configured to be determined by a linear solver.

[0255] 33. The method according to any one of clauses 21-32, wherein the new patterning process influence data indicates the effect of the corresponding patterning system aberrations on one or more of the critical dimensions, pattern placement errors, edge placement errors, critical dimension asymmetry, optimal focus offset, or defect counts associated with the patterning process.

[0256] 34. The method according to any one of clauses 21-33, wherein:

[0257] The new patterning process impact data from the model is configured to be provided to the cost function to help determine the costs associated with each patterning process metric.

[0258] The costs associated with each patterning process metric are configured to be returned to the model to help determine the costs associated with wavefront modulation of the patterning process.

[0259] The costs associated with wavefront conditioning of the patterning process are configured to be provided to the driver lens model to help determine the costs associated with each patterning process variable; and

[0260] The costs associated with each patterning process variable are configured to be provided to the optimizer to facilitate the collaborative optimization of multiple patterning systems.

[0261] 35. The method according to any one of clauses 21-34, wherein the model is calibrated such that the new patterning process influence data is configured to help enhance the control of heating of one or more mirrors and / or lenses of the patterning system.

[0262] 36. One or more non-transitory computer-readable media storing a prediction model and instructions, the instructions providing the prediction model when executed by one or more processors, the prediction model generating the following steps:

[0263] Obtain aberration data of the patterning system and corresponding data on the effects of the patterning process;

[0264] The patterning system aberration data is fed into a basic prediction model to obtain prediction results for the influence data of the patterning process; and

[0265] The patterning process influence data is used as feedback to update one or more configurations of the base prediction model, wherein the one or more configurations are updated based on a comparison between the patterning process influence data and the prediction results of the patterning process influence data.

[0266] The prediction model includes a hyperdimensional function configured to correlate the patterned system aberration data with the patterning process influence data without computing a spatial image representation.

[0267] 37. The medium according to item 36, wherein the prediction model comprises a linear or quadratic algorithm.

[0268] 38. The medium according to clause 37, wherein updating one or more configurations of the prediction model includes one or more parameters of a calibration function.

[0269] 39. The medium according to any one of clauses 36-38, wherein the aberration data of the patterning system is simulated based on the associated pupil shape and pattern forming apparatus design.

[0270] 40. The medium according to any one of clauses 36-39, wherein the patterning process influence data includes a cost function s(Z) of the corresponding patterning system aberrations, the patterning system aberrations being defined by the patterning system aberration data.

[0271] 41. A non-transitory computer-readable medium having instructions thereon, the instructions causing the computer to:

[0272] A calibration model is executed, the calibration model being configured to receive patterned system aberration data, and the model is calibrated using the patterned system aberration calibration data and corresponding patterning process influence calibration data; and

[0273] Based on the model, new patterning process influence data are determined for the received patterned system aberration data;

[0274] The model includes a hyperdimensional function configured to correlate received patterned system aberration data with new patterning process influence data without computing the spatial image representation.

[0275] 42. The medium according to clause 41, wherein the hyperdimensional function is configured to correlate the received patterned system aberration data with the new patterning process influence data in a simplified form, rather than in a full simulation.

[0276] 43. The medium according to clause 41 or 42, wherein the model is calibrated by: providing the patterning system aberration calibration data to a base model to obtain a prediction of the patterning process affecting the calibration data, and using the patterning process affecting the calibration data as feedback to update one or more configurations of the base model, wherein the one or more configurations are updated based on a comparison between the patterning process affecting the calibration data and the prediction of the patterning process affecting the calibration data.

[0277] 44. The medium according to any one of clauses 41-43, wherein the model comprises a linear or quadratic algorithm.

[0278] 45. The medium according to any one of clauses 43-44, wherein updating one or more configurations of the underlying model includes one or more parameters of a calibration function.

[0279] 46. ​​The medium according to any one of clauses 41-45, wherein the aberration calibration data of the patterning system is simulated based on the associated pupil shape and pattern forming apparatus design.

[0280] 47. The medium according to any one of clauses 41-46, wherein the new patterning process influence data includes a cost function s(Z) of the corresponding patterning system aberrations, the patterning system aberrations being defined by the patterning system aberration data.

[0281] 48. The medium according to clause 47, wherein the cost function s(Z) represents the effect of the corresponding patterning system aberrations on the patterning process.

[0282] 49. The medium according to any one of clauses 41-48, wherein the new patterning process influence data from the model is configured to be provided to the second model to facilitate dynamic field aberration control of the patterning system.

[0283] 50. The medium according to clause 49, wherein the second model is a projection optics calibration model.

[0284] 51. The medium according to clause 49 or 50, wherein the patterning system includes a scanner, and wherein dynamic field control of the scanner includes generating a corrected scanner control parameter formula for a given scanner aberration to optimize a set of lithographic performance metrics.

[0285] 52. The medium according to any one of clauses 41-51, wherein the new patterning process influence data from the model is configured to determine a patterning process control metric set, the patterning process control metric set being configured to be determined by a linear solver.

[0286] 53. The medium according to clause 52, wherein the patterning process control measure includes photolithography measurement.

[0287] 54. The medium according to clause 52 or 53, wherein the new patterning process influence data from the model includes a cost function Hessian, and wherein determining the patterning process control metric set includes performing singular value decomposition on the Hessian.

[0288] 55. The medium according to any one of clauses 41-54, wherein the new patterning process influence data indicates the effect of the corresponding patterning system aberrations on one or more of the critical dimensions, pattern placement errors, edge placement errors, critical dimension asymmetry, optimal focus offset, or defect counts associated with the patterning process.

[0289] 56. The medium according to any one of clauses 41-55, wherein the model is calibrated such that the new patterning process influence data is configured to help enhance the control of heating of one or more mirrors and / or lenses of the patterning system.

[0290] 57. The medium according to any one of clauses 41-56, wherein the model is calibrated such that the new patterning process influence data is configured to help enhance control over focus, dose, and / or stage variation (MSD) associated with the patterning system.

[0291] 58. A method for determining the impact of a patterning process on data, the method comprising:

[0292] A calibration model is executed, the calibration model being configured to receive patterned system aberration data, and the model is calibrated using the patterned system aberration calibration data and corresponding patterning process influence calibration data; and

[0293] Based on the model, new patterning process influence data are determined for the received patterned system aberration data;

[0294] The model includes a hyperdimensional function configured to correlate received patterned system aberration data with new patterning process influence data without computing the spatial image representation.

[0295] 59. The method according to clause 58, wherein the hyperdimensional function is configured to correlate the received patterned system aberration data with the new patterning process influence data in a simplified form, rather than a full simulation.

[0296] 60. The method according to clause 58 or 59, wherein the model is calibrated by: providing the patterned system aberration calibration data to a base model to obtain a prediction of the patterning process affecting the calibration data, and using the patterning process affecting the calibration data as feedback to update one or more configurations of the base model, wherein the one or more configurations are updated based on a comparison between the patterning process affecting the calibration data and the prediction of the patterning process affecting the calibration data.

[0297] 61. The method according to any one of clauses 58-60, wherein the model comprises a linear or quadratic algorithm.

[0298] 62. The method according to any one of clauses 60-61, wherein updating one or more configurations of the base model includes one or more parameters of a calibration function.

[0299] 63. The method according to any one of clauses 58-62, wherein the aberration calibration data of the patterning system is simulated based on the associated pupil shape and pattern forming apparatus design.

[0300] 64. The method according to any one of clauses 58-63, wherein the new patterning process influence data includes a cost function s(Z) of the corresponding patterning system aberrations, the patterning system aberrations being defined by the patterning system aberration data.

[0301] 65. The method according to clause 64, wherein the cost function s(Z) represents the effect of the corresponding patterning system aberrations on the patterning process.

[0302] 66. The method according to any one of clauses 58-65, wherein the new patterning process influence data from the model is configured to be provided to a second model to facilitate dynamic field aberration control of the patterning system.

[0303] 67. The method according to clause 66, wherein the second model is a projection optics correction model.

[0304] 68. The method according to clause 66 or 67, wherein the patterning system includes a scanner, and wherein dynamic field control of the scanner includes generating a corrected scanner control parameter formula for a given scanner aberration to optimize a set of lithography performance metrics.

[0305] 69. The method according to any one of clauses 58-68, wherein the new patterning process influence data from the model is configured to determine a patterning process control metric set, the patterning process control metric set being configured to be determined by a linear solver.

[0306] 70. The method according to item 69, wherein the patterning process control metrics include lithographic metrics.

[0307] 71. The method according to clause 69 or 70, wherein the new patterning process influence data from the model includes a cost function Hessian, and wherein determining the patterning process control metric set includes performing singular value decomposition on the Hessian.

[0308] 72. The method according to any one of clauses 58-71, wherein the new patterning process influence data indicates the effect of the corresponding patterning system aberrations on one or more of the critical dimensions, pattern placement errors, edge placement errors, critical dimension asymmetry, optimal focus offset, or defect counts associated with the patterning process.

[0309] 73. The method according to any one of clauses 58-72, wherein the model is calibrated such that the new patterning process influence data is configured to help enhance the control of heating of one or more mirrors and / or lenses of the patterning system.

[0310] 74. The method according to any one of clauses 58-73, wherein the model is calibrated such that the new patterning process influence data is configured to help enhance control over focus, dose, and / or stage variation (MSD) associated with the patterning system.

[0311] 75. A non-transitory computer-readable medium having instructions thereon, which, when executed by a computer, cause the computer to perform the method according to any one of claims 58-74.

[0312] While the concepts disclosed herein can be used to manufacture wafers on substrates such as silicon wafers, it should be understood that the disclosed concepts can be used in any type of manufacturing system (e.g., a manufacturing system for manufacturing on substrates other than silicon wafers).

[0313] Furthermore, the combinations and sub-combinations of the disclosed elements may include separate embodiments. For example, an aberration effect model and a projection optics model may be included in separate embodiments, or they may be included together in the same embodiment.

[0314] The above description is intended to be illustrative and not restrictive. Therefore, it will be apparent to those skilled in the art that modifications can be made to the described invention without departing from the scope of the claims set forth below.

Claims

1. A non-transitory computer-readable medium having instructions thereon, the instructions causing the computer to: A calibration model is executed, the calibration model being configured to receive patterned system aberration data, calibrate the model using the patterned system aberration calibration data and corresponding patterning process influence calibration data, and the patterning process influence data indicating the effect on the substrate patterned using the patterned system; and Based on the model, the influence of the new patterning process on the received patterned system aberration data is determined; in, The model includes a hyperdimensional function configured to correlate the received patterned system aberration data with the new patterning process influence data in a simplified form, without requiring computation of a spatial image representation.

2. The medium according to claim 1, wherein, The model is calibrated by: providing the patterned system aberration calibration data to the base model to obtain a prediction result of the patterning process affecting the calibration data, and using the patterning process affecting the calibration data as feedback to update one or more configurations of the base model, wherein the one or more configurations are updated based on a comparison between the patterning process affecting the calibration data and the prediction result of the patterning process affecting the calibration data.

3. The medium according to claim 1, wherein, The model includes linear algorithms, quadratic algorithms, or combinations thereof.

4. The medium according to claim 2, wherein, The aberration calibration data of the patterning system is simulated based on the associated pupil shape and the pattern forming device design of a specific layer.

5. The medium according to claim 1, wherein, The new patterning process impact data includes a cost function s(Z) for the corresponding patterning system aberration, which is defined by the received patterning system aberration data, wherein the cost function s(Z) represents the impact on the patterning process caused by the corresponding patterning system aberration.

6. The medium according to claim 1, wherein, The new patterning process influence data from the model is configured to be provided to a second model to enable dynamic in-situ aberration control of the patterning system, wherein the second model is a projection optics correction model.

7. The medium according to claim 6, wherein, The patterning system includes a scanner, and the dynamic field control of the scanner includes generating a corrected scanner control parameter configuration scheme to optimize a set of lithography performance metrics for a given scanner aberration.

8. The medium according to claim 1, wherein, The new patterning process influence data from the model is configured to determine a patterning process control metric set, which is configured to be determined by a linear solver.

9. The medium according to claim 8, wherein, Determining the patterned process control metric set includes performing singular value decomposition on the cost function Hessian.

10. The medium according to claim 8, wherein, The patterning process control metrics include lithographic metrics, and wherein the new patterning process influence data indicates the effect of the corresponding patterning system aberrations on one or more of the following associated with the patterning process: critical size, pattern placement error, edge placement error, critical size asymmetry, optimal focus offset, or defect count.

11. The medium according to claim 1, wherein, The model is calibrated such that the new patterning process influence data is configured to help enhance control over the effects of heating one or more mirrors and / or lenses of the patterning system.

12. The medium according to claim 1, wherein, The new patterning process impact data from the model is configured to be provided to a cost function to help determine the costs associated with each patterning process metric and / or with each patterning process variable, wherein the costs associated with each patterning process metric and / or with each patterning process variable are configured to facilitate collaborative optimization of multiple scanners.

13. The medium according to claim 12, wherein, The model includes one or more key feature components configured to model the variation of key features of the patterning process between scanners; and one or more general components configured to model the general performance of the scanner for non-key features of the patterning process.

14. The medium according to claim 12, wherein, The cost function includes two or more of the following: a first component associated with critical features of the patterning process, a second component associated with non-critical features of the patterning process, and a third component associated with physical functional limitations of one or more scanners.

15. The medium according to claim 12, wherein, The collaborative optimization involves using lens actuators as variables and employing a gradient-based nonlinear optimizer to collaboratively determine the actuator positions of multiple scanners.

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