Method for determining positioning correction of photolithographic process

Abstract

A method of determining a positioning correction of a substrate in a lithographic process is disclosed. The method includes obtaining a trained first model for various training data sets, the trained first model having been trained to minimize a force balance residual of a force on a substrate after performing at least one action causing a physical deformation of the substrate, the physical deformation is affected by a non-linear frictional interaction between the substrate and a substrate support supporting the substrate; obtaining estimated substrate deformation data associated with the substrate; inputting the estimated substrate deformation data into the trained first model to obtain, after the action, modeled substrate deformation data relating to the substrate, the modeled substrate deformation data taking into account the non-linear frictional interaction between the substrate and the substrate support; and determining a positioning correction of the substrate in exposure using the modeled substrate deformation data.

Description

Cross-reference to related applications

[0001] This application claims priority to EP application 23195431.4, filed on September 5, 2023, which is incorporated herein by reference in its entirety. Technical Field

[0002] This invention relates to methods and apparatuses for manufacturing equipment, for example, using photolithography, and to methods for manufacturing equipment using photolithography. More particularly, this invention relates to measurement sensors and photolithography apparatuses having such measurement sensors. Background Technology

[0003] A photolithography apparatus is a machine that applies a desired pattern onto a substrate (typically onto a target portion of the substrate). For example, a photolithography apparatus can be used to fabricate integrated circuits (ICs). In this instance, a patterning apparatus (alternatively referred to as a mask or photomask) can be used to generate a circuit pattern to be formed on a separate layer of the IC. This pattern can then be transferred onto a target portion (e.g., comprising a portion of a die, a die, or several dies) on a substrate (e.g., a silicon wafer). The transfer of the pattern is typically achieved by imaging onto a layer of radiation-sensitive material (resist) provided on the substrate. Typically, a single substrate will contain a network of adjacent target portions patterned sequentially. These target portions are generally referred to as "fields."

[0004] In the fabrication of complex devices, numerous photolithographic patterning steps are typically performed to form functional features in successive layers on a substrate. Therefore, a key aspect of the performance of a photolithography apparatus is its ability to correctly and accurately place the applied pattern with respect to features laid in previous layers (by the same apparatus or different photolithography apparatuses). For this purpose, the substrate is provided with one or more sets of alignment marks. Each mark is a structure whose position can be measured later using a position sensor (typically an optical position sensor). A photolithography apparatus includes one or more alignment sensors whose positions on the substrate can be accurately measured. Different types of marks and different types of alignment sensors are known from different manufacturers and from different products from the same manufacturer.

[0005] In other applications, measurement sensors are used to measure exposed structures on a substrate (in resist and / or after etching). A fast and non-invasive form of dedicated inspection tool is a scatterometer, in which a radiation beam is directed onto a target on the substrate surface, and the nature of the scattered or reflected beam is measured. Examples of known scatterometers include angle-resolved scatterometers of the type described in US2006033921A1 and US2010201963A1. In addition to reconstructing the shape of the measured feature, diffraction-based overlay measurements can also be performed using such a device, as described in published patent application US2006066855A1. Diffraction-based overlay measurements using dark-field imaging with diffraction order enable overlay measurements on smaller targets. Examples of dark-field imaging measurements can be found in international patent applications WO 2009 / 078708 and WO 2009 / 106279, which are incorporated herein by reference in their entirety. Further developments of this technology have been described in published patent publications US20110027704A, US20110043791A, US2011102753A1, US20120044470A, US20120123581A, US20130258310A, US20130271740A, and WO2013178422A1. These targets can be smaller than the illumination spot and can be surrounded by the product structure on the wafer. Multiple gratings can be measured in a single image using composite grating targets. The contents of all these applications are also incorporated herein by reference.

[0006] Alignment measurements are used to determine positioning corrections to correct substrate deformation. Alignment measurements typically involve measuring alignment marks on the substrate and fitting them as a model to the resulting alignment data, which describes the substrate deformation. For optimal accuracy, it is desirable to measure more alignment marks (if feasible) from the perspective of throughput and / or wafer area.

[0007] There is a desire to improve the methods used to determine substrate deformation. Summary of the Invention

[0008] The present invention provides, in a first aspect, a method for determining positioning correction of a substrate in a photolithography process, the method comprising: obtaining a trained first model for various training datasets, the trained first model being trained to minimize a force balance residual on the substrate after performing at least one action that causes physical deformation of the substrate, the physical deformation being affected by frictional interaction between the substrate and a substrate support supporting the substrate; obtaining estimated substrate deformation data associated with the substrate; inputting at least the estimated substrate deformation data into the trained first model to obtain at least modeled substrate deformation data associated with the substrate after the at least one action, the modeled substrate deformation data taking into account the frictional interaction between the substrate and the substrate support; and using the modeled substrate deformation data to determine positioning correction of the substrate during exposure.

[0009] A computer program and a photolithography apparatus operable to perform the method of the first aspect are also disclosed.

[0010] The above and other aspects of the present invention will be understood by considering the following examples. Attached Figure Description

[0011] Embodiments of the present invention will now be described by way of example only with reference to the accompanying drawings, wherein: Figure 1 A schematic overview of the photolithography apparatus is provided; Figure 2 A schematic overview of the photolithography unit is described; Figure 3 schematically illustrated Figure 1 Measurement and exposure processes in the apparatus; Figure 4 A schematic representation of overall photolithography is depicted, illustrating the collaboration between three key technologies to optimize semiconductor manufacturing; Figure 5 This is a schematic representation of an alignment sensor adaptable to embodiments of the present invention; Figure 6 The flowchart describes a method for training a model to obtain a high-resolution wafer deformation map based on low-resolution alignment data, according to an embodiment; and Figure 7 The description of the use according to the embodiments is as follows. Figure 6 The flowchart describes a method for obtaining high-resolution wafer deformation maps from low-resolution alignment data using a model trained by this method. Detailed Implementation

[0012] Before describing the embodiments of the present invention in detail, it is beneficial to present an example environment in which the embodiments of the present invention can be implemented.

[0013] Figure 1A lithography apparatus LA is schematically depicted. The apparatus includes: an irradiation system (irradiator) IL configured to modulate a radiation beam B (e.g., UV or DUV radiation); a patterning apparatus support or support structure (e.g., a mask stage) MT configured to support a patterning apparatus (e.g., a mask) MA and connected to a first positioner PM configured to accurately position the patterning apparatus according to certain parameters; two substrate stages (e.g., wafer stages) WTa and WTb 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 according to certain parameters; and a projection system (e.g., a refractive projection lens system) PS 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. A reference frame RF connects the various components and serves as a reference for setting and measuring the positions of the patterning apparatus and the substrate, and the features on them.

[0014] Irradiation systems may include various types of optical components, such as refractive, reflective, magnetic, electromagnetic, electrostatic, or other types of optical components or any combination thereof, for guiding, shaping, or controlling radiation.

[0015] A patterning apparatus support MT holds the patterning apparatus in a manner dependent on the orientation of the patterning apparatus, the design of the lithography apparatus, and other conditions, such as whether the patterning apparatus is held in a vacuum environment. The patterning apparatus support MT can use mechanical, vacuum, electrostatic, or other clamping techniques to hold the patterning apparatus. The patterning apparatus support MT can be a frame or a table, which can be fixed or movable as needed. The patterning apparatus support ensures that the patterning apparatus is positioned in a desired location, such as relative to the projection system.

[0016] The term "patterning apparatus" as used herein should be interpreted broadly to refer to any apparatus that can be used to impart a pattern of radiation beams in its cross-section, such as to create a pattern in a target portion of a substrate. It should be noted that the pattern imparted by the radiation beams may not perfectly correspond to the desired pattern in the target portion of the substrate, for example, if the pattern includes phase-shifting features or so-called auxiliary features. Typically, the pattern imparted by the radiation beams will correspond to a specific functional layer in the apparatus (such as an integrated circuit) created in the target portion.

[0017] As depicted herein, the apparatus is transmissive (e.g., employing a transmissive patterning device). Alternatively, the apparatus may be reflective (e.g., employing a programmable mirror array of the type referenced above, or a reflective mask). Examples of patterning devices include masks, programmable mirror arrays, and programmable LCD panels. Any use of the terms "mask" or "mask" herein may be considered synonymous with the more general term "patterning device." The term "patterning device" may also be interpreted as a device that stores pattern information in digital form for use in controlling such a programmable patterning device.

[0018] The term “projection system” as used herein should be interpreted broadly to encompass any type of projection system, including refractive, reflective, reflective-refractive, magnetic, electromagnetic, and electrostatic optical systems or any combination thereof, as appropriate for the exposure radiation used or other factors such as the use of immersion or vacuum. Any use of the term “projection lens” in this document may be considered synonymous with the more general term “projection system.”

[0019] Photolithography apparatuses can also be of the type in which at least a portion of the substrate can be covered with a liquid (e.g., water) having a relatively high refractive index to fill the space between the projection system and the substrate. Immersion liquid can also be applied to other spaces within the photolithography apparatus, such as the space between the mask and the projection system. Immersion techniques are well known in the art for increasing the numerical aperture of the projection system.

[0020] In operation, the irradiator IL receives a radiation beam from the radiation source SO. The source and the lithography apparatus can be separate entities, such as when the source is an excimer laser. In this case, the source is not considered part of forming the lithography apparatus, and the radiation beam is delivered from the source SO to the irradiator IL by means of a beam delivery system BD, which includes, for example, suitable directional mirrors and / or beam expanders. In other cases, the source can be an integrated part of the lithography apparatus, such as when the source is a mercury lamp. The source SO, the irradiator IL, and (if necessary) the beam delivery system BD can be referred to as the radiation system.

[0021] The irradiator IL may, for example, include an adjuster AD, an integrator IN, and a concentrator CO for adjusting the angular intensity distribution of the radiation beam. The irradiator can be used to adjust the radiation beam to have a desired uniformity and intensity distribution within its cross-section.

[0022] A radiation beam B is incident on a patterning apparatus MA held on a patterning apparatus support MT and patterned by the patterning apparatus. After passing through the patterning apparatus (e.g., a 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 WTa or WTb can be precisely moved, for example, to position different target portions C within the path of the radiation beam B, by means of a second positioner PW and a position sensor IF (e.g., an interferometer, linear encoder, 2D encoder, or capacitive sensor). Similarly, for example, after mechanical retrieval from a mask library or during scanning, the first positioner PM and another position sensor (not in use) can be moved. Figure 1 (As explicitly described in the text) can be used to accurately position a patterning device (e.g., a mask) MA relative to the path of the radiation beam B.

[0023] Patterning apparatus (e.g., mask) MA and substrate W can be aligned using mask alignment marks M1, M2 and substrate alignment marks P1, P2. Although the illustrated substrate alignment marks occupy dedicated target portions, they can be located in the space between target portions (these are referred to as scribing alignment marks). Similarly, when more than one die is provided on patterning apparatus (e.g., mask) MA, mask alignment marks can be located between dies. Small alignment marks can also be included within the die, included in apparatus features, in which case it is desirable that the marks be as small as possible and do not require any imaging or process conditions different from adjacent features. Alignment systems for detecting alignment marks will be described further below.

[0024] The depicted apparatus can be used in a variety of modes. In scanning mode, as the pattern imparted by the radiation beam is projected onto the target portion C (i.e., a single dynamic exposure), the patterning apparatus support (e.g., mask stage) MT and the substrate stage WT are scanned synchronously. The velocity and direction of the substrate stage WT relative to the patterning apparatus support (e.g., mask stage) MT can be determined by the magnification (reduction) and image inversion characteristics of the projection system PS. In scanning mode, the maximum size of the exposure field limits the width of the target portion (in the non-scanning direction) in a single dynamic exposure, while the length of the scanning motion determines the height of the target portion (in the scanning direction). As is known in the art, other types of lithography apparatuses and operating modes are possible. For example, stepping modes are known. In so-called “maskless” lithography, the programmable patterning apparatus remains stationary but has a changing pattern, and the substrate table WT is moved or scanned.

[0025] Combinations and / or variations of the above usage patterns, or entirely different usage patterns, may also be adopted.

[0026] A lithography apparatus (LA) can be of a so-called dual-stage type, having two substrate stages WTa and WTb and two stations—an exposure station EXP and a measurement station MEA—with the substrate stages interchangeable between them. While one substrate on one stage is exposed at the exposure station, another substrate can be loaded onto the other substrate stage at the measurement station, and various preparation steps are performed. This can significantly increase the apparatus's throughput. Preparation steps may include mapping the surface height profile of the substrate using a horizontal sensor LS and measuring the position of alignment marks on the substrate using an alignment sensor AS. If a position sensor IF cannot measure the position of the substrate stage when it is located at both the measurement and exposure stations, a second position sensor can be provided so that the position of the substrate stage can be tracked relative to a reference frame RF at both stations. Other arrangements are known and available instead of the dual-stage arrangement shown. For example, other lithography apparatuses that provide substrate and measurement stages are known. These are docked together during preparation measurements and then disconnected during exposure of the substrate stages.

[0027] like Figure 2 As shown, a lithography apparatus LA can form part of a lithography unit LC, sometimes also called a lithography unit or (lithography) cluster, which typically also includes apparatus for performing pre- and post-exposure processes on a substrate W. Conventionally, these include a spin coater SC for depositing a resist layer, a developer DE for developing the exposed resist, a chiller CH for regulating the temperature of the substrate W (e.g., for regulating the solvent in the resist layer), and a baking plate BK. A substrate handler or robot RO picks up the substrate W from input / output ports I / O1, I / O2, moves them between different process units, and delivers the substrate W to the feed stage LB of the lithography apparatus LA. The equipment in the lithography unit (often collectively referred to as tracks) may be controlled by a track control unit TCU, which itself may be controlled by a supervisory control system SCS, which may also control the lithography apparatus LA (e.g., via the lithography control unit LACU).

[0028] In photolithography, frequent measurements of the created structure are desirable, for example, for process control and verification. The tools used to perform these measurements are referred to as metrology tools (MTs). Different types of metrology tools (MTs) for performing such measurements are known, including scanning electron microscopes (SEMs) or various forms of scatterometer metrology tools (MTs). A scatterometer is a versatile instrument that allows the measurement of parameters of the photolithography process by placing a sensor in or near the pupil of the scatterometer objective (these measurements are often referred to as pupil-based measurements) or by placing a sensor in or near the image plane (in this case, these measurements are often referred to as image- or field-based measurements). Such scatterometers and associated measurement techniques are further described in patent applications US20100328655, US2011102753A1, US20120044470A, US20110249244, US20110026032, or EP1,628,164A, all of which are incorporated herein by reference in their entirety. The aforementioned scatterometer can measure gratings using light from hard X-rays (HXR), soft X-rays (SXR), extreme ultraviolet (EUV), visible to near-infrared (IR), and the IR wavelength range. If the radiation is hard or soft X-rays, the aforementioned scatterometer can optionally be a small-angle X-ray scattering measurement tool.

[0029] To ensure correct and consistent exposure of the substrate W by the photolithography unit LA, it is desirable to inspect the substrate to measure properties of the patterned structure, such as overlay errors between subsequent layers, line thickness, critical dimension (CD), structural shape, etc. For this purpose, inspection tools and / or measurement tools (not shown) may be included in the photolithography unit LC. If errors are detected, adjustments may be made, for example, to the exposure of subsequent substrates or other processing steps to be performed on the substrate W, particularly if the inspection is completed before other substrates W in the same batch or group are still to be exposed or processed.

[0030] An inspection apparatus (also referred to as a measurement apparatus) is used to determine the properties of a substrate W, particularly how the properties of different substrates W vary, or how the properties associated with different layers of the same substrate W change between layers. The inspection apparatus may alternatively be configured to identify defects on the substrate W, and may be, for example, part of a photolithography unit LC, or integrated into a photolithography apparatus LA, or even a stand-alone device. The inspection apparatus can measure the properties of latent images (images in the resist layer after exposure), semi-latent images (images in the resist layer after the PEB baking step), developed resist images (where exposed or unexposed portions of the resist have been removed), or even etched images (after pattern transfer steps such as etching).

[0031] In the first embodiment, the scatterer MT is an angle-resolved scatterer. In such a scatterer, a reconstruction method can be applied to the measured signal to reconstruct or calculate the properties of the grating. For example, this reconstruction might be caused by simulating the interaction between the scattered radiation and a mathematical model of the target structure and comparing the simulation results with the measurement results. The parameters of the mathematical model are adjusted until the simulated interaction produces a diffraction pattern similar to that observed from a real target.

[0032] In the second embodiment, the scatterer MT is a spectroscopic scatterer MT. In this spectroscopic scatterer MT, radiation emitted by a radiation source is directed onto the target, and reflected, transmitted, or scattered radiation from the target is directed to a spectroscopic detector that measures the spectrum of specularly reflected radiation (i.e., intensity based on wavelength). Using this data, for example through rigorous coupled-wave analysis and nonlinear regression, or by comparison with a simulated spectral library, the structure or profile of the target from the detected spectrum can be reconstructed.

[0033] In the third embodiment, the scatterer MT is an ellipsometer. An ellipsometer allows the determination of parameters of a photolithography process by measuring the scattered or transmitted radiation for each polarization state. This measurement device emits polarized light (such as linear, circular, or elliptical) by using, for example, a suitable polarization filter in the illumination section of the measurement device. A source suitable for the measurement device can also provide polarized radiation. Various embodiments of existing ellipsometers are described in U.S. Patent Applications 11 / 451,599, 11 / 708,678, 12 / 256,780, 12 / 486,449, 12 / 920,968, 12 / 922,587, 13 / 000,229, 13 / 033,135, 13 / 533,110, and 13 / 891,410, all of which are incorporated herein by reference.

[0034] In one embodiment of a scattering instrument (MT), the scattering instrument MT is adapted to measure the overlay of two misaligned gratings or periodic structures by measuring the reflectance spectrum and / or detecting asymmetry in the configuration, the asymmetry being related to the degree of overlay. Two (potentially overlapping) grating structures can be applied to two different layers (not necessarily consecutive layers) and can be formed at substantially the same location on the wafer. The scattering instrument can have a symmetrical detection configuration, for example, described in the co-owned patent application EP1,628,164A, such that any asymmetry is readily distinguishable. This provides a direct way to measure misalignment in gratings. Other examples involving overlay errors between two layers of a periodic structure when the target is measured by asymmetry of the periodic structure can be found in PCT patent application publication WO 2011 / 012624 or U.S. patent application US 20160161863, both of which are incorporated herein by reference in their entirety.

[0035] Other parameters of interest may be focus and dose. Focus and dose can be determined simultaneously by scattering measurements (or alternatively by scanning electron microscopy), as described in U.S. Patent Application US2011-0249244, which is incorporated herein by reference in its entirety. A single structure may be used that has a unique combination of critical size and sidewall angle measurements for each point in the focus energy matrix (FEM, also known as the focus exposure matrix). If these unique combinations of critical size and sidewall angles are available, the focus and dose values ​​can be uniquely determined based on these measurements.

[0036] The measurement target can be a single composite grating formed by photolithography, primarily within a resist, but can also be formed after other manufacturing processes, such as etching. The pitch and linewidth of the structure within the grating may depend significantly on the measurement optics (particularly the NA of the optics) to capture the diffraction order from the measurement target. As previously indicated, the diffraction signal can be used to determine the shift between two layers (also known as 'overlap') or to reconstruct at least a portion of the original grating produced by the photolithography process. This reconstruction can be used to provide guidance on the quality of the photolithography process and can be used to control at least a portion of the photolithography process. The target can have smaller sub-subdivisions configured to mimic the dimensions of functional portions of the design layout within the target. Due to these sub-subdivisions, the target's behavior will be more similar to the functional portions of the design layout, making the overall process parameter measurements more similar to the functional portions of the design layout. The target can be measured in either underfill or overfill modes. In underfill mode, the measurement beam generates a spot smaller than the overall target. In overfill mode, the measurement beam generates a spot larger than the overall target. In this overfilling mode, it may also be possible to measure different targets simultaneously, thereby determining different processing parameters at the same time.

[0037] The overall measurement quality of lithography parameters for a specific target is determined at least in part by the measurement scheme used to measure those parameters. The term "substrate measurement scheme" can include one or more parameters of the measurement itself, one or more parameters of one or more patterns being measured, or both. For example, if the measurement used in the substrate measurement scheme is a diffraction-based optical measurement, the one or more parameters measured can include the wavelength of the radiation, the polarization of the radiation, the angle of incidence of the radiation relative to the substrate, the radiation orientation relative to the pattern on the substrate, etc. One criterion for selecting a measurement scheme can be, for example, the sensitivity of one of the measurement parameters to handling variations. Further examples are described in U.S. Patent Application US2016-0161863 and published U.S. Patent Application US2016 / 0370717A1, both of which are incorporated herein by reference in their entirety.

[0038] Figure 3 The illustration shows that in Figure 1 The steps for exposing a target portion (e.g., a die) on a substrate W in a dual-stage lithography apparatus are described. The left side within the dashed box shows the steps performed at the measurement station MEA, while the right side shows the steps performed at the exposure station EXP. Sometimes, one of the substrate stages WTa and WTb will be at the exposure station, while the other substrate stage will be at the measurement station, as described above. For the purposes of this description, it is assumed that the substrate W has already been loaded into the exposure station. In step 200, a new substrate W' is loaded into the apparatus via a mechanism not shown. The two substrates are processed in parallel to increase the throughput of the lithography apparatus.

[0039] Initially, a newly loaded substrate W' is referenced, which may be a previously untreated substrate, prepared with a new photoresist for its first exposure in the apparatus. However, typically, the described lithography process will only be one step in a series of exposure and processing steps, such that the substrate W' has already passed through the apparatus and / or other lithography apparatuses multiple times, and may also have undergone subsequent processes. Specifically addressing the issue of improving overlay performance, the task is to ensure that the new pattern is applied precisely to the correct position on the substrate that has already been patterned and processed through one or more cycles. These processing steps progressively introduce distortions into the substrate that must be measured and corrected to achieve satisfactory overlay performance.

[0040] Previous and / or subsequent patterning steps can be performed in other lithography apparatuses, as just mentioned, and even in different types of lithography apparatuses. For example, some layers in the manufacturing process that have very high requirements for parameters such as resolution and overlay can be performed in more advanced lithography tools than other layers with lower requirements. Therefore, some layers may be exposed in immersion lithography tools, while others are exposed in 'dry' tools. Some layers may be exposed in tools that operate at DUV wavelengths, while others are exposed using EUV wavelength radiation.

[0041] At 202, alignment measurements using substrate marker P1 and an image sensor (not shown) are used to measure and record the alignment of the substrate relative to the substrate stage WTa / WTb. Additionally, several alignment marks on the substrate W' will be measured using an alignment sensor AS. In one embodiment, these measurements are used to establish a "wafer grid" that maps the distribution of the marks on the substrate very accurately, including any distortion relative to a nominal rectangular grid.

[0042] In step 204, the wafer height (Z) map relative to the XY position is also measured using a horizontal sensor LS. Typically, the height map is only used to achieve accurate focusing of the exposure pattern. However, it can also be used for other purposes.

[0043] When the substrate W' is loaded, scheme data 206 is received, defining the exposure to be performed, as well as the properties of the wafer and the previously fabricated and to be patterned thereon. This scheme data is added to measurements of wafer position, wafer grid, and height map taken in 202 and 204, allowing the complete set of scheme and measurement data 208 to be transferred to the exposure station EXP. Alignment data measurements include, for example, the X and Y positions of alignment targets, which are formed in a fixed or nominally fixed relationship with the product pattern as a product of the lithography process. This alignment data, obtained just before exposure, is used to generate an alignment model whose parameters fit the model to the data. These parameters and the alignment model will be used during the exposure operation to correct the position of the pattern applied in the current lithography step. The model used inserts positional deviations between the measured positions. A typical alignment model may include four, five, or six parameters that together define the translation, rotation, and scaling of an 'ideal' grid at different sizes. Higher-level models using more parameters are known.

[0044] At 210, wafers W' and W are swapped, so that the substrate W' being measured becomes the substrate W entering the exposure station EXP. Figure 1 In the example apparatus, this swapping is performed by exchanging supports WTa and WTb within the device, ensuring that substrates W and W' are accurately clamped and positioned on these supports to maintain relative alignment between the substrate stage and the substrate itself. Therefore, once the substrate stage has been swapped, determining the relative position between the projection system PS and the substrate stage WTb (formerly WTa) is necessary in controlling the exposure steps using measurement information 202, 204 of substrate W (formerly W'). In step 212, mask alignment is performed using mask alignment marks M1, M2. In steps 214, 216, 218, scanning motion and radiation pulses are applied to successive target locations on the substrate W to complete the exposure of multiple patterns.

[0045] By using alignment data and height maps obtained at the measurement station during the exposure step, these patterns are accurately aligned relative to the desired location, particularly relative to features previously laid on the same substrate. In step 220, the exposed substrate (now labeled W'') is unloaded from the apparatus to be etched or processed according to the exposed pattern.

[0046] Those skilled in the art will appreciate that the above description is a simplified overview of several very detailed steps involved in an example of a real manufacturing scenario. For instance, instead of measuring alignment in a single pass, there are typically separate stages of coarse and fine measurements using the same or different markings. The coarse and / or fine alignment measurement steps may be performed before or after the height measurement, or they may be performed alternately.

[0047] In the fabrication of complex devices, numerous photolithographic patterning steps are typically performed to form functional features in successive layers on a substrate. Therefore, a key aspect of the performance of a photolithography apparatus is its ability to correctly and accurately align the applied pattern with respect to features formed in previous layers (by the same apparatus or different photolithography apparatuses). For this purpose, the substrate is provided with one or more sets of markers. Each marker is a structure whose position can be measured later using a position sensor (typically an optical position sensor). The position sensor may be referred to as an "alignment sensor," and the marker may be called an "alignment marker."

[0048] A photolithography apparatus may include one or more alignment sensors by which the position of alignment marks provided on a substrate can be accurately measured. The alignment (or position) sensor may use optical phenomena, such as diffraction and interference, to obtain positional information from the alignment marks formed on the substrate. Examples of alignment sensors used in current photolithography apparatuses are based on the self-reference interferometer described in US6961116. Various enhancements and modifications of position sensors have been developed, for example, as disclosed in US2015261097A1. All of these disclosures are incorporated herein by reference.

[0049] Markings or alignment marks may comprise a series of strips formed on or within a layer provided on a substrate, or (directly) formed in the substrate. The strips may be regularly spaced and act as grating lines, such that the markings can be considered diffraction gratings with a well-known spatial period (pitch). Depending on the orientation of these grating lines, the markings may be designed to allow measurements of positions along the X-axis or along the Y-axis (which is substantially perpendicular to the X-axis). Markings comprising strips arranged at +45 degrees and / or -45 degrees relative to the X and Y axes allow for combined X and Y measurements using the techniques described in US2009 / 195768A (which is incorporated herein by reference).

[0050] The alignment sensor optically scans each mark with a radiating spot to obtain a periodically varying signal, such as a sine wave. The phase of this signal is analyzed to determine the position of the mark relative to the alignment sensor, thereby determining the position of the substrate relative to the alignment sensor, which is in turn fixed relative to the reference frame of the photolithography apparatus. So-called coarse and fine marks, associated with different (coarse and fine) mark sizes, can be provided, allowing the alignment sensor to distinguish different cycles of the periodic signal and the precise position (phase) within each cycle. Marks with different pitches can also be used for this purpose.

[0051] The location of the measurement marks can also provide information about the deformation of the substrate to which the marks are provided, for example, in the form of a wafer grid. When the substrate is exposed to radiation, the deformation of the substrate can occur, for example, by electrostatically clamping the substrate to a substrate stage and / or heating the substrate.

[0052] Patterning in the photolithography (LA) apparatus is one of the most critical steps in the process, requiring highly accurate dimensional determination and placement of the structure on the substrate W. To ensure this high accuracy, three systems can be combined into a so-called "holistic" control environment, such as... Figure 4 The diagram illustrates this schematically. One of these systems is the lithography apparatus LA, which is (essentially) connected to the metrology tool MT (second system) and the computer system CL (third system). The key to this "holistic" environment is optimizing the collaboration between these three systems to enhance the overall process window and providing a tight control loop to ensure that the patterning performed by the lithography apparatus LA remains within the process window. The process window defines a range of process parameters (e.g., dose, focus, overlay) within which a specific manufacturing process will produce a defined result (e.g., a functional semiconductor device). Within this range, process parameters in the lithography or patterning process may be allowed to vary.

[0053] The computer system CL can use a portion of the design layout to be patterned to predict which resolution enhancement techniques will be used, and perform computational lithography simulations and calculations to determine which mask layouts and lithography setups will achieve the maximum overall process window (within) the patterning process. Figure 4 (Depicted by double arrows in the first scale SC1). Resolution enhancement techniques can be arranged to match the patterning possibilities of the lithography apparatus LA. The computer system CL can also be used to detect where the lithography apparatus LA is currently operating within the process window (e.g., using input from the metrology tool MET) to predict whether defects may exist due to, for example, suboptimal processing (in... Figure 4 (The arrow pointing to "0" in the second ruler SC2 is used to depict this).

[0054] The measurement tool MT can provide input to the computer system CL for accurate simulation and prediction, and can provide feedback to the lithography apparatus LA to identify possible drift, for example, under the calibration conditions of the lithography apparatus LA (in Figure 4 (The middle part is depicted by multiple arrows in the third ruler SC3).

[0055] Figure 5This is a schematic block diagram of a known alignment sensor AS. A radiation source RSO provides a radiation beam RB of one or more wavelengths, which is redirected as an illumination spot SP onto a marker (such as a marker AM located on a substrate W) by optics. In this example, the redirecting optics include a spot reflector SM and an objective lens OL. The diameter of the illumination spot SP on which the marker AM is illuminated can be slightly smaller than the width of the marker itself.

[0056] The radiation diffracted by the marked AM is collimated (in this example, via the objective lens OL) into the information-carrying beam IB. The term "diffraction" is intended to include complementary higher diffraction orders; for example, +1 and -1 diffraction orders (labeled +1, -1), and optionally, zero-order diffraction from the marked AM (which may be referred to as reflection). A self-referenced interferometer SRI (such as the type disclosed in US6961116 mentioned above) causes the beam IB to interfere with itself, after which the beam is received by a photodetector PD. In cases where more than one wavelength is created by the radiation source RSO, additional optics (not shown) may be included to provide a separate beam. The photodetector may be a single element, or it may comprise several pixels, if desired. The photodetector may comprise a sensor array.

[0057] In this example, the steering optics that include the spot reflector SM can also be used to block the zero-order radiation reflected from the marker, so that the information-carrying beam IB only includes the higher-order diffraction radiation from the marker AM (which is not essential for the measurement, but improves the signal-to-noise ratio).

[0058] The SRI intensity signal SSI is supplied to the processing unit PU. Through a combination of optical processing in the self-referenced interferometer SRI and computational processing in the unit PU, the values ​​of the X and Y positions on the substrate relative to the reference frame are output.

[0059] A single measurement of the type illustrated fixes the position of the marker within a specific range corresponding to one pitch of the marker. Coarse measurement techniques are used in conjunction with this measurement to identify which period of the sine wave contains the marked position. The same process is repeated at different wavelengths at coarser and / or finer levels to improve the accuracy and / or robustness of marker detection, regardless of the material on which the marker is made or the material at and / or below the location where the marker is provided. Improvements to performing and processing such multi-wavelength measurements are disclosed below.

[0060] As already described, alignment data describing the measured XY position (substrate plane position) of each alignment mark is used to fit an alignment model, for example, which includes a set of polynomials. The fitted model approximately describes the substrate deformation across the entire wafer and is used as input for subsequent exposures on the substrate for overlay correction.

[0061] The accuracy of the fitted model depends in particular on the number of alignment marks measured (e.g., measurement density): model accuracy improves with increasing measurement density (at least at some point). However, in practical high-volume manufacturing (HVM), simply increasing the number of measurement marks is not feasible because each measurement takes time, and in an HVM environment, the number of marks expected in terms of measurement modeling accuracy would take too long. Additionally, each mark occupies a considerable amount of space on the wafer (including a limited area, of course), thus imposing a limitation on the actual number of marks that can be accommodated, and further limiting the practical maximum measurement density.

[0062] This paper discloses a method for obtaining high-resolution deformation data from low-resolution or low-density alignment data; for example, alignment data obtained from a typical number of markers currently measured in HVM, such as fewer than 80, 70, or 60 markers per wafer. This method can be used to effectively improve wafer alignment without increasing the number of alignment markers / measurements.

[0063] High-resolution deformation data largely depends on the unknown initial unclamped substrate shape or unknown (high-resolution) unclamped substrate deformation data (and other unknown physical parameters). This method may include modeling the clamping of the substrate using a trained first model, thereby estimating the clamped substrate shape at high resolution based on the (unknown) unclamped substrate deformation data, i.e., the (high-resolution) clamped substrate deformation data.

[0064] In an embodiment, this may include starting with an initial estimate of substrate deformation data, such as an initial estimate of unclamped substrate deformation data (e.g., and substrate physical parameters), and using a trained first model to estimate clamped substrate deformation data based on the unclamped substrate deformation data. Optimization may be performed to optimize (e.g., iteratively or using a second trained model) the unclamped substrate deformation data (e.g., and optionally the unclamped substrate physical parameters) to minimize the difference between the modeled clamped substrate deformation data and the alignment data measured at the measurement (alignment mark) location (optionally including horizontal sensor data in the 3D deformation embodiment). Once optimized, the final clamped substrate deformation data can be used as high-resolution substrate deformation data instead of conventional fitted alignment data (e.g., sampled at a higher resolution than the conventional fitted alignment data).

[0065] In this context, substrate physical parameters may include, in particular, one or more of the following: protrusion stiffness, coefficient of friction, backfill gas pressure, substrate / substrate support temperature, protrusion contact data, and friction model data. These are parameters that are already or may be included in a physical wafer load grid (WLG) model (which has been developed but is slow to arrive at a solution) and are related to the thermomechanical description of the substrate-fixture interaction. The physical WLG model aims to minimize the force balance residuals and iteratively describes the force balance on the substrate. Such a physical WLG model arrives at a solution in hours over a period of time. In the method disclosed herein, a first model can be trained by inputting the output of a first model into the equations of the physical WLG model and minimizing the resultant force balance residuals. Because the first model uses the same governing equations as the physical model, these physical parameters can be fixed constants or set as variables and become inputs to the first model, so that they can then be inferred from unfixed substrate deformation data using measurement data (e.g., in the described fitting step).

[0066] In short, WLG is a type of overlay distortion related to the unevenness of the substrate (wafer) during clamping and the finite coefficient of friction between the protrusions and the substrate, where the protrusions are protrusions on the substrate support (wafer stage) that support the substrate. Perfectly mounting the substrate onto the substrate support means that once the mounted substrate is fully positioned (and clamped) onto the multiple protrusions, no strain is left in the mounted substrate. Any strain locked into the substrate can cause deformation of the substrate in the XY plane, resulting in overlay errors. When the substrate is mounted onto the substrate support, localized slippage can occur. The residual deformation in the substrate caused by this localized slippage leads to overlay errors. WLG is a measure used to quantify the error introduced by this deformation.

[0067] Wafer clamping can include a wafer loading sequence from electronic pins to a substrate holder or wafer stage. This process can include carrying the substrate down onto the electronic pins to a substrate stage, the substrate contacting the substrate holder and being clamped on the substrate holder (e.g., by vacuum or electrostatic ground, depending on the scanner type), thereby locking stress in the substrate.

[0068] The proposed method can use a trained first model (such as a neural network model) that has been trained to determine modeled substrate deformation data, such as modeled clamped substrate deformation data (e.g., high-resolution wafer deformation maps) (and physical parameters) based on estimated substrate deformation data (such as estimated unclamped substrate deformation data).

[0069] Alternatively or additionally, the trained first model can model the wafer heating-induced deformation (i.e., wafer heating-induced expansion). This can be done in parallel with WLG modeling, for example, modeling the wafer from an unclamped to a clamped state, taking into account any thermal load on the substrate and the resulting expansion. Alternatively, the trained first model can predict (e.g., EUV) exposure-induced wafer deformation in real time, independently of WLG modeling. During exposure (after clamping), the wafer will deform again due to the thermal load (e.g., EUV) of each die being exposed. Real-time prediction of this wafer deformation / expansion makes it possible to determine the feedforward correction for the exposure. In either case, the first model can receive temperature data as input (e.g., from the thermal modeling step of the lithography apparatus and / or a temperature sensor, such as a substrate support temperature sensor). In an embodiment, this temperature data can be input into a linear wafer heating or linear wafer expansion model to obtain linear expansion data, and the first model is used to convert this linear expansion data into nonlinear expansion data to better reflect the actual expansion of the substrate, while taking into account the frictional interaction between the substrate and the substrate support. Alternatively, the temperature data can be directly input into the first model to generate nonlinear expansion data. In the WLG embodiment, the temperature data, or linear expansion data, can be provided in parallel with the estimated unclamped substrate deformation data. This linear wafer expansion or wafer heating (WH) model is currently used in some lithography apparatuses and assumes linear wafer expansion over time. Therefore, the currently used linear WH model suffers in terms of accuracy because many of the mechanisms modeled are highly nonlinear; in particular, the aforementioned nonlinear frictional interactions between the substrate and substrate support. A physics-based nonlinear WH model has been developed, incorporating modeling of substrate contact mechanics and nonlinear protrusion friction effects. However, this model has not yet been deployed in HVM due to the extremely slow speed of deriving a solution (e.g., several hours per substrate).

[0070] In any of these embodiments, the trained first model can model time-varying deformation or distortion (e.g., during the clamping process) by sequentially determining the distortion at multiple time points, where the output of each time step is used as the input for the next time step. The trained first model can address physical phenomena related to nonlinear frictional interactions between the substrate and substrate support during wafer clamping (e.g., due to protrusion friction effects between the substrate backside and protrusions) and optionally other factors such as thermal load (distortion due to wafer temperature variations) and / or frictional model data.

[0071] The method may include: obtaining a trained first model for various training datasets, the trained first model being trained to minimize the force balance residual of forces on the substrate after performing at least one action that causes physical deformation of the substrate, the physical deformation being affected by nonlinear frictional interactions between the substrate and a substrate support supporting the substrate; obtaining estimated substrate deformation data associated with the substrate; inputting at least the estimated substrate deformation data into the trained first model to obtain at least modeled substrate deformation data associated with the substrate after the at least one action, the modeled substrate deformation data taking into account the nonlinear frictional interactions between the substrate and the substrate support; and using the modeled substrate deformation data to determine positioning corrections of the substrate during exposure.

[0072] In a more specific embodiment, the method may include: obtaining a trained first model for various unclamped substrate deformation datasets (e.g., various unclamped substrate shapes), the trained first model being trained to minimize the force balance residuals of forces on the clamped substrate after clamping the substrate to a substrate support; obtaining measurement data (e.g., alignment data) associated with the substrate; obtaining estimated unclamped substrate deformation data associated with the substrate prior to clamping; inputting at least the estimated unclamped substrate deformation data into the trained first model to obtain at least estimated clamped substrate deformation data associated with the clamped substrate; determining final unclamped substrate deformation data that minimizes the difference between the estimated clamped substrate deformation data estimated by the first model and the measurement data; and performing a substrate positioning operation in a subsequent exposure using output substrate deformation data, the output substrate deformation data including estimated clamped substrate deformation data corresponding to the final unclamped substrate deformation data (e.g., the estimated clamped substrate deformation data corresponding to the final unclamped substrate deformation data may be an input-output pair of the first model). The output substrate deformation data may include higher resolution than the measurement data.

[0073] In addition to substrate deformation data, the method may also include inputting estimates of other substrate physical parameter data into the trained first model, such as those already described.

[0074] The optimization can also optimize the unclamped substrate deformation data, thereby optimizing the output substrate deformation data in the direction perpendicular to the substrate plane (Z direction). This can include parameterizing the substrate deformation data wafer (unclamped and clamped) at three dimensions and performing optimization relative to alignment data and horizontal sensor data (substrate height data). Therefore, the optimization can minimize the difference between the estimated clamped substrate deformation data in this Z direction and a known value from the horizontal sensor data. Thus, the method can also include obtaining the horizontal sensor data.

[0075] The method may include using a trained first model at multiple time steps during the clamping period in which the substrate is clamped (i.e., from an unclamped configuration to a fully clamped configuration), wherein the model output from the (immediately adjacent) previous time step is used as the input to the trained first model for each consecutive time step.

[0076] At each time step, the first model can output at least substrate deformation data describing the deformation of the substrate within that time step. Additionally, the first model can output protrusion contact data and / or friction model data. Protrusion contact data can describe the order or sequence of protrusion contact with the substrate during clamping (e.g., the order in which protrusions of a substrate stage contact the wafer). Friction model data can describe the frictional model of the substrate, i.e., the position of the substrate in a graph of frictional force versus time (e.g., whether the force increases or decreases and at what rate). It is well known that frictional force depends on its history (hysteresis), and nonlinear models can be used to describe this behavior, such as the Maxwell friction model. A suitable frictional model was published by Al-Bender et al. in 2004 in the International Journal of Nonlinear Mechanics, Vol. 39, pp. 1721-1735. Theoretical analysis of the dynamic behavior of hysteresis elements in Mechanical systems (theoretical analysis of the dynamic behavior of hysteresis elements in mechanical systems) It is described in [the original text], and is incorporated herein by reference.

[0077] The trained second model can be used to determine unclamped substrate deformation data and / or initial WLG physics model parameters from measurement data using a dataset generated by the trained first model, enabling rapid inference. The first trained model can provide a fast mapping from the initial unclamped state to the final clamped state. For a given set of measurement data, backpropagation (gradient descent) can be performed to optimize the initial state; however, this can take longer than ideal, as it requires multiple iterations. An alternative is to train a second model or a second neural network that directly learns the mapping from the final clamped state to the initial unclamped state by leveraging the 1000x faster data generation achieved by the trained first model.

[0078] The first trained model (and the second trained model) can include machine learning models, such as neural networks.

[0079] The trained first model can also model other effects, such as thermal effects (thermal expansion). In this embodiment, the trained model can recover the correct nonlinear substrate thermal expansion from linear thermal expansion (i.e., taking into account nonlinear friction effects), for example, as determined by a linear WLG model that ignores friction effects, such that the wafer and fixture are modeled together as a rigid body.

[0080] The training of the first model does not employ typical "black box" machine learning methods, where the model is taught to map from inputs to outputs using paired input-output training data (i.e., labeled training data). Instead, the first model is trained by directly substituting its output into the governing equations (i.e., force balance) of the WLG physics model and minimizing the force balance residuals (e.g., using a suitable cost function). Therefore, the residuals are defined as the cost function. The force balance equations can include the same equations developed for the aforementioned nonlinear WLG and WH physics models, which were developed but were too slow to achieve the solution used by HVM. Since a correct solution should result in zero residuals (the substrate is stationary), the first model output is physically correct by definition by minimizing the loss function. Due to the very fast forward computation of the first model, a significant reduction in computation time is foreseeable compared to iterative solutions using the physically nonlinear WLG or WH models.

[0081] Training can be performed at multiple time steps in the deformation process, with the first model output of the previous time step being used as the first model input of the next time step.

[0082] The first model can be trained with many different initial wafer shapes by randomly sampling input vectors that include data on unclamped substrate distortion. Depending on data availability, process fingerprint information can also be encoded into the input vectors. A key point is that, unlike conventional deep learning methods that require many input-output pairs for training (computationally demanding and nearly impossible for slow solvers), training here is accomplished by directly applying physical laws to the output and using the residuals as a cost function. Therefore, generating training data is simple and inexpensive, such as random shape descriptions, random linear thermal expansion maps, etc.

[0083] Figure 6 This is a flowchart illustrating the method used to train the first model. Obtaining training (unclamped) substrate deformation data (SDD) TR Training substrate deformation data (SDD) TR Parameterization can be achieved using an input vector containing multiple elements. Training substrate deformation data (SDD) TR Training data can be generated for many different shapes (e.g., through measurement and / or simulation). For example, this can be simulated by randomly sampling input vectors. The training data does not require labels and / or any output pairs. Substrate deformation data can describe deformation in the substrate plane and optionally, deformation normal to the substrate plane. If modeling thermal expansion effects is desired, the training data may also optionally include thermal expansion data.

[0084] Training substrate deformation data SDD TRIt can be used to export input data DAT IN In addition to substrate deformation data, it also includes input data DAT. IN Input data DAT IN It may also include WLG physical model parameters. WLG physical model parameters may include one or more of the following: temperature data, linear expansion data, joint contact data, friction model data, joint stiffness data, friction coefficient data, and backfill gas pressure data. (Corresponding to time t) i-1 Input data DAT IN The input is fed into the first model MOD, and the model MOD is trained to be at a later time point t during the clamping period. i Estimated equivalent data DAT OUT This minimizes the cost function CF1, for which force balance is the cost to be minimized, such as the force from the protrusion to the wafer at each time step, such that the total force on the wafer is zero. This is performed over multiple consecutive time steps from unclamped to fully clamped wafer, over all training substrate deformation data SDD. TR The output data DAT of the previous time step OUT DAT, used as input data for the next time step IN In this way, for many different unclamped wafer shapes, the trained first model MOD will be able to estimate the distortion within the clamped wafer (on two or three dimensions).

[0085] Figure 7 This is a flowchart describing how to obtain high-resolution substrate deformation data using a trained model based on low-resolution alignment data. The process involves obtaining (unclamped) input substrate deformation data (SDD). IN The initial estimate includes, for example, an initial shape (process fingerprint) parameterized by an input vector (including multiple elements). Unclamped substrate deformation data (SDD) IN It can be used to export other input data DAT. IN and / or combined with it, such as about Figure 6 Description. Input data DAT IN It may also include data related to one or more other WLG physical model parameters, as already described. In an embodiment, this may include linear expansion data determined using a linear WH model based on temperature sensor data. The input data is SDD. IN It is fed into the first model MOD after training to compare the input data DAT. IN t i-1 Late time t i Obtain substrate deformation data. This can be performed over multiple consecutive time steps from when the wafer is not clamped to when it is fully clamped, with the output data DAT from the previous time step being used.OUT DAT, used as input data for the next time step IN .

[0086] Output data DAT OUT With measurement data or alignment data AL IN The comparison allows the alignment data AL at the marked position to be aligned. IN The measured deformation value inside and the output data DAT at the same location OUT The distortion values ​​included in the data (including estimated clamping substrate deformation data) are compared. The cost function CF2 can be used to find the input data DAT. IN (For example, unclamped substrate distortion data), this input data will measure the output data DAT at the measurement location. OUT and alignment data AL IN The difference between them is minimized. This fitting may also optionally include fitting one or more WLG physical model parameters for the unclamped substrate (alternatively or additionally, one or more of these WLG physical parameters may be fixed at the estimated values). Once minimized, the final output data WDD includes high-resolution substrate distortion data. OUT It can be used for substrate alignment so that subsequent exposure can be performed on the substrate. In an embodiment, the horizontal sensor data can be combined with the alignment data AL. IN Used in combination to achieve 3D fitting of substrate deformation.

[0087] It can be understood that the optimizations implemented in the cost function CF2 and Figure 7 The optimization outlined herein is not model training. For this optimization, the first model MOD is fixed (all parameters are fixed) and only fits the input vector (e.g., other input physical parameters). In an embodiment, the cost of the cost function CF2 may include the mean square error of the mismatch between the output wafer deformation and the alignment measurements at the marked locations. Since the cost function CF2 is correlated with the unclamped wafer deformation data through the first model, which is fully differentiable, by minimizing CF2 (backpropagation), the unknown input vector (initial wafer shape) evolves into a best match with the sparse measurement data, while simultaneously determining the complete wafer deformation map.

[0088] Therefore, the proposed first model is a real-time nonlinear solver for 2D or 3D wafer load meshes, simulating the entire physical process from any initial wafer shape to fully clamped wafer deformation. It enables physically-based wafer alignment, enhancing alignment through prior knowledge of wafer load physics. This allows for the computation of high-resolution full-wafer deformation maps from low-resolution alignment measurements without increasing the number of alignment markers. Training the model does not require expensive (labeled or input-output paired) training data. Instead, simple, inexpensive input-only training data can be used, without any corresponding output data or labels.

[0089] As already described, the first model can be used to determine the substrate deformation (expansion) of the clamped substrate, for example, during exposure. This can include inputting linear substrate expansion data, such that the first model transforms this linear substrate expansion data to allow for corrections to nonlinear friction effects. The model can be trained in substantially the same manner as described in the WLG embodiments (i.e., minimizing the force balance residuals using the same relationships), but the training data includes a variety of different linear expansion data. Generating such linear expansion data is inexpensive, so the first model can be trained using highly variable linear expansion data without requiring a computationally expensive correct solution.

[0090] As used herein, the terms "optimizing" and "optimization" refer to or imply adjusting lithography apparatus, equipment manufacturing processes, etc., to achieve more desirable characteristics in the lithography or equipment manufacturing results and / or processes, such as higher accuracy in projecting design layouts onto the substrate, a larger process window, etc. Therefore, as used herein, the terms "optimizing" and "optimization" refer to or imply a process that identifies one or more values ​​of one or more parameters that provide an improvement in at least one relevant metric, such as a local optimum, compared to an initial set of one or more values ​​for those parameters. "Optimum" and other related terms should be interpreted accordingly. In embodiments, optimization steps may be applied iteratively to provide further improvements to one or more metrics.

[0091] While specific embodiments of the invention have been described above, it should be understood that the invention may be practiced in other ways than those described.

[0092] Although the use of embodiments of the invention may have been specifically referenced above in the context of optical lithography, it is to be understood that the invention can be used in other applications, such as imprint lithography, and is not limited to optical lithography where the context permits. In imprint lithography, the morphology in a patterning apparatus defines a pattern created on a substrate. The morphology of the patterning apparatus can be pressed into a resist layer supplied to the substrate, whereby the resist is cured by applying electromagnetic radiation, heat, pressure, or a combination thereof. After the resist has been cured, the patterning apparatus is removed from the resist, thereby leaving a pattern therein.

[0093] Other embodiments of the present invention are disclosed in the following list of numbered clauses: 1. A method for determining the positioning correction of a substrate in a photolithography process, the method comprising: obtaining a trained first model for various training datasets, the trained first model being trained to minimize the force balance residual of forces on the substrate after performing at least one action that causes physical deformation of the substrate, the physical deformation being affected by frictional interaction between the substrate and a substrate support supporting the substrate; and obtaining estimated substrate deformation data associated with the substrate. The estimated substrate deformation data is input into the trained first model to obtain, after the at least one action, modeled substrate deformation data related to the substrate, which takes into account the frictional interaction between the substrate and the substrate support; and to determine a positioning correction for the substrate, which is configured to correct the exposure steps of the lithography process using the modeled substrate deformation data. 2. The method according to Clause 1, wherein: the at least one action includes at least clamping the substrate onto the substrate support; the estimated substrate deformation data includes estimated unclamped substrate deformation data associated with the substrate prior to the clamping; and the modeled substrate deformation data includes modeled clamped substrate deformation data associated with the substrate after the clamping. 3. The method according to Clause 2, comprising: obtaining measurement data related to the substrate; and determining final unclamped substrate deformation data, said final unclamped substrate deformation data being data in which the difference between the corresponding modeled clamped substrate deformation data estimated by the first model based on the final unclamped substrate deformation data and the measurement data is minimized. 4. The method according to Clause 3, wherein the step of determining the positioning correction includes determining the positioning correction of the substrate in a subsequent exposure using output substrate deformation data, the output substrate deformation data including the modeled clamped substrate deformation data corresponding to the final unclamped substrate deformation data. 5. The method according to Clause 3 or 4, wherein determining the final unclamped substrate deformation data includes performing a fitting of at least the unclamped substrate deformation data in at least the substrate plane to minimize the difference. 6. The method according to Clause 5, wherein the performing fit includes fitting physical parameter data related to one or more physical parameters of a physical model of the interaction between the substrate and the substrate support. 7. The method according to any one of clauses 3 to 6, wherein the output substrate deformation data has a higher resolution than the measurement data. 8. The method according to any one of Clauses 3 to 7, wherein the estimated unclamped substrate deformation data, the final unclamped substrate deformation data, the modeled clamped substrate deformation data, and the output clamped substrate deformation data are parameterized in at least the substrate planar dimensions. 9. The method according to any one of Clauses 3 to 8, wherein determining the final unclamped substrate deformation data includes performing fitting of the unclamped substrate deformation data in a direction perpendicular to the substrate plane to minimize the difference. 10. The method according to Clause 9, wherein the estimated unclamped substrate deformation data, the final unclamped substrate deformation data, the modeled clamped substrate deformation data, and the output clamped substrate deformation data are parameterized in three dimensions; and the measurement data further includes substrate height data. 11. The method according to any one of Clauses 3 to 10, wherein the measurement data includes at least alignment data. 12. The method according to any one of the preceding clauses, wherein the estimated substrate deformation data includes linear substrate expansion data caused by temperature changes of the substrate. 13. The method according to Clause 12 includes: obtaining temperature data related to the temperature of the substrate and / or substrate support; obtaining a linear substrate thermal expansion model; and using the linear substrate thermal expansion model to generate the linear substrate expansion data based on the temperature data. 14. The method according to Clause 12 or 13, wherein the method includes feedforward correction for heating the substrate during exposure. 15. The method according to any one of the preceding clauses, comprising using the trained first model at multiple time steps during a clamping period in which the substrate is clamped, wherein for each consecutive time step, the model output from the previous time step is used as the input to the trained first model. 16. The method according to Clause 15, wherein the model has been trained to minimize the force balance residual at each time step. 17. The method according to any one of the preceding clauses, comprising: obtaining a trained second model; and using the trained second model to determine at least the unclamped substrate deformation data based on the measurement data output using the trained first model. 18. The method according to any one of the preceding clauses, wherein at least the trained first model comprises a machine learning model and / or a neural network. 19. The method according to any one of the preceding clauses, wherein the trained model models thermal effects on the substrate, and the at least the estimated unclamped substrate deformation data further includes thermal load data. 20. The method according to any one of the preceding clauses, comprising a training step of training the first model on training data, the training comprising minimizing the force balance residual on the clamping substrate modeled by the first model with respect to the training data. 21. The method according to Clause 20, wherein the training data comprises at least a plurality of unclamped substrate deformation datasets describing a plurality of different substrate shapes. 22. The method according to Clause 21 includes randomly generating the training data by randomly sampling an input vector describing the distortion of the unclamped substrate. 23. The method according to clauses 20, 21 or 22, wherein the training data includes at least multiple substrate expansion datasets associated with multiple different thermal loads on the substrate and / or the substrate support. 24. The method according to Clause 23 includes using a linear substrate thermal expansion model to generate the training data. 25. The method according to any one of clauses 21 to 24, wherein the training data further includes physical parameter data relating to one or more physical parameters of a physical model of the interaction between the substrate and the substrate support. 26. The method according to any one of clauses 20 to 25, comprising inputting the output of the first model at each time step of the training step into the physical wafer load grid model equation and minimizing the resultant force balance residual. 27. The method according to any one of clauses 20 to 26, wherein the training data includes unlabeled training data without corresponding paired output training data. 28. The method according to any one of the preceding clauses further includes inputting physical parameter data into the trained first model, the physical parameter data being related to one or more physical parameters of a physical model of the interaction between the substrate and the substrate support. 29. The method according to any one of the preceding clauses includes performing exposure on the substrate based on the positioning correction. 30. A computer program comprising program instructions that, when run on a suitable apparatus, are operable to perform the method according to any one of clauses 1 to 29. 31. A processing system comprising a processor and a storage device, the storage device including a computer program according to clause 30. 32. A photolithography apparatus capable of operating to perform the method according to any one of clauses 1 to 29. 33. A lithography apparatus according to Clause 32, comprising: an alignment sensor operable to measure at least a portion of the measurement data. 34. The lithography apparatus according to Clause 33 further includes a horizontal sensor operable to measure at least a portion of the measurement data.

[0094] The terms “radiation” and “beam” used in this article cover all types of electromagnetic radiation, including ultraviolet (UV) radiation (e.g., having wavelengths equal to or about 365 nm, 355 nm, 248 nm, 193 nm, 157 nm, or 126 nm) and extreme ultraviolet (EUV) radiation (e.g., having wavelengths in the range of 1 nm to 100 nm) as well as particle beams, such as ion beams or electron beams.

[0095] Where the context permits, the term "lens" can refer to any one or a combination of various types of optical components, including refractive, reflective, magnetic, electromagnetic, and electrostatic optical components. Reflective components are likely to be used in devices operating in the UV and / or EUV range.

[0096] The breadth and scope of this invention should not be limited by any of the exemplary embodiments described above, but should be defined only by the following claims and their equivalents.

Claims

1. A method of determining a positioning correction of a substrate in a lithography process, the method comprising: obtaining a trained first model for various training data sets, the trained first model having been trained to minimize a force balance residual of a force on the substrate after performing at least one action resulting in a physical deformation of the substrate, the physical deformation being influenced by a frictional interaction between the substrate and a substrate support supporting the substrate; obtaining estimated substrate deformation data related to the substrate; inputting at least the estimated substrate deformation data into the trained first model to obtain at least modeled substrate deformation data related to the substrate after the at least one action, the modeled substrate deformation data taking into account the frictional interaction between the substrate and the substrate support; and determining a positioning correction of the substrate, the positioning correction being configured to correct an exposure step of the lithography process using the modeled substrate deformation data.

2. The method according to claim 1, wherein: the at least one action comprises at least clamping the substrate onto the substrate support; the estimated substrate deformation data comprises estimated unclamped substrate deformation data related to the substrate prior to the clamping; and the modeled substrate deformation data comprises modeled clamped substrate deformation data related to the substrate after the clamping.

3. The method according to claim 2, comprising: obtaining metrology data related to the substrate; and determining a final unclamped substrate deformation data, the final unclamped substrate deformation data being data for which a difference between corresponding modeled clamped substrate deformation data estimated by the first model based on the final unclamped substrate deformation data and the metrology data is minimized.

4. The method according to claim 3, wherein the step of determining a positioning correction comprises determining a positioning correction of the substrate in a subsequent exposure using output substrate deformation data, the output substrate deformation data comprising the modeled clamped substrate deformation data corresponding to the final unclamped substrate deformation data.

5. The method according to any of claims 3 to 4, wherein the output substrate deformation data has a higher resolution than the metrology data.

6. The method according to any of claims 3 to 5, wherein the metrology data comprises at least alignment data.

7. The method according to claim 1, wherein the estimated substrate deformation data comprises linear substrate expansion data caused by a temperature change of the substrate.

8. The method according to claim 7, comprising: obtaining temperature data related to a temperature of the substrate and / or substrate support; obtaining a linear substrate heating expansion model; and generating the linear substrate expansion data from the temperature data using the linear substrate heating expansion model.

9. The method according to claim 8, wherein the method comprises generating a feedforward correction to mitigate heating of the substrate during an exposure step. ​ ​ ​ 10. The method of claim 1, comprising using the trained first model in a plurality of time steps during a clamping cycle in which the substrate is clamped, for each successive time step, the model output from the previous time step is used as input to the trained first model.

11. The method of claim 1, comprising: obtaining a trained second model; and using the trained second model to determine at least the unclamped substrate deformation data from the metrology data using the output of the trained first model.

12. The method of claim 1, wherein at least the trained first model comprises a machine learning model and / or a neural network.

13. The method of claim 1, wherein the trained model models thermal effects on the substrate, the at least the estimated unclamped substrate deformation data further comprising thermal loading data.

14. The method of claim 1, further comprising a training step of training the first model on training data, the training comprising minimizing the force balance residual on the clamped substrate modeled by the first model for the training data.

15. A computer program comprising program instructions operable to perform the method of claim 1 when run on a suitable apparatus. ​

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