Alignment method and related alignment and lithographic apparatus

Abstract

A method for determining at least one set of correction weights to correct metrology data is disclosed. The method includes obtaining first measurement data and second measurement data associated with a first layer and a second layer, respectively. Each of the first measurement data and the second measurement data is fitted to a model for representing the measurement data to determine a first set of fitting residuals and a second set of fitting residuals. At least one set of correction weights is determined as at least one set of correction weights to minimize a difference between the first set of fitting residuals and the second set of fitting residuals.

Description

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims priority to EP application 22206356.2 filed on November 9, 2022, which is hereby incorporated by reference in its entirety. Technical Field

[0003] The present invention relates to methods and apparatus which can be used, for example, to manufacture devices by lithography, and to methods of manufacturing devices using lithography.The present invention relates to metrology equipment, and more particularly to metrology equipment for measuring position, such as alignment sensors and lithography equipment having such alignment sensors. Background Art

[0004] A lithographic apparatus is a machine that applies a desired pattern to a substrate, typically to a target portion of the substrate. A lithographic apparatus can be used, for example, in the manufacture of an integrated circuit (IC). In this case, a pattern forming device (or mask or reticle) can be used to produce a circuit pattern to be formed on an individual layer of the IC. This pattern can be transferred to a target portion (e.g., including a portion of a die, one die, or several dies) on a substrate (e.g., a silicon wafer). The transfer of the pattern is typically performed by imaging onto a layer of radiation-sensitive material (resist) disposed on the substrate. Typically, a single substrate will contain a network of adjacent target portions that are continuously patterned. These target portions are typically referred to as "fields."

[0005] In the manufacture of complex devices, many lithographic patterning steps are typically performed to form functional features in successive layers on a substrate. Therefore, a key aspect of the performance of a lithographic apparatus is the ability to correctly and accurately place the applied pattern relative to features laid out in previous layers (either by the same apparatus or by a different lithographic apparatus). 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 at a later time using a position sensor or alignment sensor (the two terms are used synonymously) - typically an optical position sensor.

[0006] The lithographic apparatus comprises one or more alignment sensors by which the position of a mark on a substrate can be accurately measured. Different types of marks and different types of alignment sensors are known from different manufacturers and from different products of the same manufacturer. One type of sensor widely used in current lithographic apparatus is based on a self-referencing interferometer as described in US 6961116 (den Boef et al.). Various enhancements and modifications of position sensors have been developed, such as disclosed in US2015261097A1. The contents of all these publications are hereby incorporated by reference.

[0007] Imperfections in an alignment mark can result in wavelength / polarization-dependent variations in the measurements from that mark. Thus, correction and / or mitigation of this variation is sometimes achieved by performing the same measurement using multiple different wavelengths and / or polarizations (or more generally, multiple different illumination conditions).

[0008] One method to minimize the error caused by such marking defects is to use a weighted average between two or more colors, where the color weights are found by minimizing the residuals of the wafer model fit. Such a method may be referred to as a multi-color minimum residual (MCLR) method and is described in WO 2022184405A1, which is incorporated herein by reference. The measurements of each color may be modeled separately to obtain the model residuals for each color, and then a fit (e.g., a least squares fit) may be performed to find the optimal color weight that minimizes the model residuals on the wafer or wafer group.

[0009] At least in certain applications or use cases, there is a need to improve one or more aspects of measurements using multiple illumination conditions, such as described in WO 2022184405A1. Summary of the invention

[0010] The present invention provides in a first aspect a method for determining at least one set of correction weights to correct measurement data, the method comprising: obtaining first measurement data associated with a first set of illumination settings for measurement radiation used to perform measurement of a first layer; fitting the first measurement data to a model for representing the measurement data, and determining a first set of fitting residuals as residuals of the first measurement data relative to the model; obtaining second measurement data associated with a second set of illumination settings for measurement radiation used to perform measurement of a second layer, the second set of illumination settings comprising a plurality of illumination settings, wherein each illumination setting comprises a different wavelength, polarization, or a combination thereof; fitting the second measurement data to a model for representing the measurement data, and determining a second set of fitting residuals as residuals of the second measurement data relative to the model; and determining the at least one set of correction weights as at least one set of correction weights that minimizes a difference between the first set of fitting residuals and the second set of fitting residuals.

[0011] Also disclosed are a computer program, an alignment sensor and a lithographic apparatus operable to perform the method of the first aspect.

[0012] The above and other aspects of the invention will be understood by considering the examples described below. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Embodiments of the present invention will now be described, by way of example only, with reference to the accompanying drawings, in which:

[0014] Figure 1 A photolithographic apparatus is depicted;

[0015] Figure 2 Schematically shows Figure 1 Measurement and exposure processes in devices;

[0016] Figure 3 is a schematic diagram of an alignment sensor applicable according to an embodiment of the present invention;

[0017] Figure 4 is a flow chart of a color selection method according to an embodiment of the present invention;

[0018] Figure 5 conceptually illustrates an example of indirect alignment, showing how two layers may each reference a reference layer or each other; and

[0019] Figure 6 An example of indirect alignment is conceptually illustrated, showing overlay between a top layer pair and an immediately previous layer pair. DETAILED DESCRIPTION

[0020] Before describing embodiments of the present invention in detail, it is helpful to provide an example environment in which embodiments of the present invention may be implemented.

[0021] Figure 1 A lithographic apparatus LA is schematically shown. The apparatus comprises an illumination system (illuminator) IL configured to condition a radiation beam B (e.g., UV radiation or DUV radiation); a patterning device support or support structure (e.g., mask stage) MT configured to support a patterning device (e.g., mask) MA and connected to a first positioner PM configured to accurately position the patterning device according to certain parameters; two substrate tables (e.g., wafer stages) WTa and WTb, each configured to hold a substrate (e.g., a resist-coated wafer) W and each 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 to the radiation beam B by the patterning device 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 device and the substrate and features thereon.

[0022] The illumination system 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 directing, shaping or controlling the radiation.

[0023] The patterning device support MT holds the patterning device in a manner that depends on the orientation of the patterning device, the design of the lithographic apparatus, and other conditions (e.g., whether the patterning device is held in a vacuum environment). The patterning device support may use mechanical, vacuum, electrostatic, or other clamping techniques to hold the patterning device. The patterning device support MT may be, for example, a frame or a stage that may be fixed or moved as required. The patterning device support may ensure that the patterning device is in a desired position, e.g., relative to a projection system.

[0024] The term "patterning device" as used herein should be broadly interpreted as referring to any device that can be used to impart a radiation beam with a pattern in its cross-section so as to produce a pattern in a target portion of the substrate. It should be noted that the pattern imparted to the radiation beam may not exactly correspond to the desired pattern in the target portion of the substrate, for example if the pattern includes phase-shifting features or so called assist features. Typically, the pattern imparted to the radiation beam will correspond to a specific functional layer in a device (e.g. an integrated circuit) being created in the target portion.

[0025] As shown, the device is transmissive (e.g., employing a transmissive patterning device). Alternatively, the device may be reflective (e.g., employing a programmable mirror array of the type described above, or employing a reflective mask). Examples of patterning devices include masks, programmable mirror arrays, and programmable LCD panels. Any use of the term "reticle" or "mask" herein may be considered synonymous with the more general term "patterning device." The term "patterning device" may also be interpreted as referring to a device that stores pattern information in digital form for use in controlling such a programmable patterning device.

[0026] The term "projection system" as used herein should be broadly interpreted to include any type of projection system, including refractive, reflective, catadioptric, magnetic, electromagnetic and electrostatic optical systems, or any combination thereof, as appropriate to the exposure radiation used, or to other factors such as the use of an immersion liquid or the use of a vacuum. Any use of the term "projection lens" herein may be considered synonymous with the more general term "projection system".

[0027] The lithographic apparatus may also be of a type in which at least a portion of the substrate may be overlaid with a liquid having a relatively high refractive index, such as water, to fill the space between the projection system and the substrate. Immersion liquid may also be applied to other spaces in the lithographic apparatus, such as the space between the mask and the projection system. Immersion techniques are well known in the art and are used to increase the numerical aperture of a projection system.

[0028] In operation, the illuminator IL receives a radiation beam from a radiation source SO. The source and the lithographic apparatus may be separate entities, for example when the source is an excimer laser. In this case, the source is not considered to form part of the lithographic apparatus, and the radiation beam is delivered from the source SO to the illuminator IL by means of a beam delivery system BD comprising, for example, suitable directing mirrors and / or a beam expander. In other cases, the source may be an integral part of the lithographic apparatus, for example when the source is a mercury lamp. If desired, the source SO and the illuminator IL together with the beam delivery system BD are referred to as a radiation system.

[0029] The illuminator IL may, for example, comprise an adjuster AD for adjusting the angular intensity distribution of the radiation beam, an integrator IN and a condenser CO. The illuminator may be used to condition the radiation beam, to have a desired uniformity and intensity distribution in its cross-section.

[0030] The radiation beam B is incident on a patterning device MA held on a patterning device support MT and is patterned by the patterning device. After passing through the patterning device (e.g. a mask) MA, the radiation beam B passes through a projection system PS which focuses the radiation beam onto a target portion C of the substrate W. With the aid of a second positioner PW and a position sensor IF (e.g. an interferometric device, a linear encoder, a 2-D encoder or a capacitive sensor), the substrate table WTa or WTb can be precisely moved, for example in order to position a different target portion C in the path of the radiation beam B. Similarly, a first positioner PM and a further position sensor ( Figure 1 ) can be used to accurately position the patterning device (e.g. mask) MA relative to the path of the radiation beam B, for example after mechanical retrieval from a mask library or during scanning.

[0031] Mask alignment marks M1, M2 and substrate alignment marks P1, P2 can be used to align the pattern forming device (e.g., mask) MA and substrate W. Although the substrate alignment marks shown occupy dedicated target portions, they can be located in the spaces between target portions (these are called scribe alignment marks). Similarly, in the case where more than one die is set on the pattern forming device (e.g., mask) MA, the mask alignment marks can be located between the dies. In device features, small alignment marks can also be included within the die, in which case it is desirable that the mark be as small as possible and do not require any imaging or processing conditions that are different from adjacent features. The alignment system for detecting alignment marks is further described below.

[0032] The described apparatus can be used in a variety of modes. In scanning mode, the pattern forming device support (e.g., mask table) MT and the substrate table WT are scanned synchronously while the pattern imparted to the radiation beam is projected onto a target portion C (i.e., a single dynamic exposure). The speed and direction of the substrate table WT relative to the pattern forming device support (e.g., mask table) MT can be determined by the (reduced) magnification and image reversal characteristics of the projection system PS. In scanning mode, the maximum size of the exposure field limits the width (in the non-scanning direction) of the target portion in a single dynamic exposure, while the length of the scanning movement determines the height (in the scanning direction) of the target portion. As is known in the art, other types of lithographic equipment and operating modes are also possible. For example, stepping modes are known. In so-called "maskless" lithography, the programmable pattern forming device remains stationary but has a changing pattern, and the substrate table WT is moved or scanned.

[0033] Combinations and / or variations on the above described modes of use or entirely different modes of use may also be employed.

[0034] The lithographic apparatus LA is of a so-called dual-stage type, having two substrate tables WTa, WTb and two stations (exposure station EXP and measurement station MEA), between which the substrate table can be exchanged. While a substrate on one substrate table is exposed at the exposure station, another substrate can be loaded onto another substrate table at the measurement station, and various preparatory steps are performed. This significantly increases the throughput of the apparatus. The preparatory steps may include drawing the surface height profile of the substrate using a horizontal sensor LS, and measuring the position of the alignment mark on the substrate using an alignment sensor AS. If the position sensor IF cannot measure the position of the substrate table when the substrate table is at the measurement station and the exposure station, a second position sensor may be provided so that the position of the substrate table can track the position of the substrate table relative to the reference frame RF at the two stations. Other arrangements are known and can be used to replace the dual-stage arrangement shown. For example, other lithographic apparatus are known in which a substrate table and a measurement table are provided. These are docked together when performing preparatory measurements, and then not docked when the substrate table is exposed.

[0035] Figure 2 Shown in Figure 1 200 , a new substrate W' is loaded into the apparatus by a mechanism not shown. The two substrates are processed in parallel to increase the throughput of the lithography apparatus.

[0036] Reference is first made to a newly loaded substrate W', which may be a previously unprocessed substrate, which is prepared with a new photoresist for a first exposure in the apparatus. However, typically, the lithographic process described will be only one step in a series of exposure and processing steps, so that the substrate W' has passed through the apparatus and / or other lithographic apparatus several times and may also have subsequent processes to undergo. In particular for the problem of improving overlay performance, the task is to ensure that the new pattern is applied accurately at the correct position on a substrate that has undergone one or more patterning and processing cycles. These processing steps gradually introduce distortions in the substrate that must be measured and corrected to achieve satisfactory overlay performance.

[0037] The previous and / or the next patterning step can be performed in other lithographic equipment, as just mentioned, and can even be performed in different types of lithographic equipment. For example, some layers that are very demanding on parameters such as resolution and overlay in the device manufacturing process can be performed in more advanced lithographic tools than other layers with lower requirements. Thus, some layers can be exposed in immersion lithographic tools, while other layers are exposed in "dry" tools. Some layers can be exposed in tools operating at DUV wavelengths, while other layers are exposed using EUV wavelength radiation.

[0038] At 202, alignment measurements using substrate marks P1 etc. and an image sensor (not shown) are used to measure and record the alignment of the substrate relative to the substrate table WTa / WTb. In addition, several alignment marks across the substrate W' will be measured using an alignment sensor AS. These measurements are used in one embodiment to establish a "wafer grid" that very accurately maps the distribution of the marks across the substrate, including any distortion relative to a nominal rectangular grid.

[0039] In step 204, a map of wafer height (Z) versus X-Y position is also measured using a level sensor LS. Typically, the height map is only used to achieve accurate focus of the exposure pattern. In addition, it can be used for other purposes.

[0040] When the substrate W' is loaded, recipe data 206 is received, which defines the exposure to be performed, as well as the characteristics of the wafer and the previous production and the pattern to be produced thereon. The measurements of the wafer position, wafer grid and height map made at 202, 204 are added to these recipe data so that the entire set of recipe and measurement data 208 can be transferred to the exposure station EXP. The measurement of alignment data includes, for example, the X and Y positions of alignment targets, which are formed in a fixed or nominally fixed relationship relative to the product pattern as the product of the lithography process. These alignment data taken just before exposure are used to generate an alignment model with parameters that make the model suitable for 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 in use interpolates the position deviations between the measured positions. Traditional alignment models can include four, five or six parameters, which together define the translation, rotation and scaling of the "ideal" grid in different dimensions. Advanced models using more parameters are known.

[0041] At 210, wafers W' and W are exchanged so that the measured substrate W' becomes the substrate W entering the exposure station EXP. Figure 1 In the example apparatus of , the exchange is performed by exchanging supports WTa and WTb within the apparatus so that the substrate W, W' remains accurately clamped and positioned on these supports to maintain the relative alignment between the substrate table and the substrate itself. Therefore, once the tables have been exchanged, determining the relative position between the projection system PS and the substrate table WTb (formerly WTa) is necessary to utilize the measurement information 202, 204 of the substrate W (formerly W') in the control of the exposure steps. In step 212, reticle alignment is performed using the mask alignment marks M1, M2. In steps 214, 216, 218, scanning movements and radiation pulses are applied at consecutive target positions across the substrate W so as to complete the exposure of a plurality of patterns.

[0042] By using the alignment data and height map obtained at the measurement station in the performance of the exposure step, these patterns are accurately aligned relative to the desired locations, in particular relative to features previously placed on the same substrate. At step 220, the exposed substrate, now marked as W", is unloaded from the equipment for etching or other processing according to the exposed patterns.

[0043] Those skilled in the art will appreciate that the above description is a simplified overview of the multiple very detailed steps involved in one example of an actual manufacturing situation. For example, rather than measuring alignment in a single pass, there will typically be different stages of coarse and fine measurement using the same or different markers. The coarse and / or fine alignment measurement steps may be performed before or after the height measurement, or interleaved.

[0044] In the manufacture of complex devices, many lithographic patterning steps are typically performed to form functional features in successive layers on a substrate. Therefore, a key aspect of the performance of a lithographic apparatus is the ability to correctly and accurately place an applied pattern relative to features arranged in a previous layer (either by the same apparatus or by a different lithographic apparatus). To this end, a substrate has one or more sets of marks. Each mark is a structure whose position can be measured at a later time using a position sensor (usually an optical position sensor). The position sensor may be referred to as an "alignment sensor" and the mark may be referred to as an "alignment mark".

[0045] The lithographic apparatus may include one or more (e.g., multiple) alignment sensors, by which the positions of alignment marks disposed on the substrate can be accurately measured. The alignment (or position) sensor may use optical phenomena such as diffraction and interference to obtain position information from alignment marks formed on the substrate. An example of an alignment sensor used in a current lithographic apparatus is based on a self-referencing interferometer as described in US 6961116. Various enhancements and modifications of position sensors have been developed, such as those disclosed in US2015261097A1. The contents of all these publications are incorporated herein by reference.

[0046] The mark or alignment mark may comprise a series of strips formed on or in a layer provided on a substrate or (directly) in the substrate. These strips may be regularly spaced and act as grating lines so that the mark may be viewed as a diffraction grating with a well-known spatial period (pitch). Depending on the orientation of these grating lines, the mark may be designed to allow measurement of the position along the X-axis or along the Y-axis (oriented substantially perpendicular to the X-axis). A mark comprising strips arranged at +45 degrees and / or -45 degrees relative to the X-axis and the Y-axis allows combined X- and Y-measurements to be performed using techniques as described in US2009 / 195768A, which is incorporated herein by reference.

[0047] The alignment sensor optically scans each mark with a radiation 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 and thus the position of the substrate relative to the alignment sensor, which in turn is fixed relative to the reference frame of the lithographic apparatus. So-called coarse and fine marks associated with different (coarse and fine) mark sizes can be provided so that the alignment sensor can distinguish different periods of the periodic signal as well as the exact position (phase) within a period. Marks of different pitches can also be used for this purpose.

[0048] Measuring the position of the marks may also provide information about deformation of the substrate on which the marks are provided, for example in the form of a wafer grid.Deformation of the substrate may occur, for example, by electrostatically clamping the substrate to a substrate table and / or heating the substrate when the substrate is exposed to radiation.

[0049] Figure 3 is a schematic block diagram of an embodiment of a known alignment sensor AS. A radiation source RSO provides a beam RB of one or more wavelengths, which is steered by a steering optic onto a mark, such as a mark AM located on a substrate W, as an illumination spot SP. In this example, the steering optic comprises a spot mirror SM and an objective lens OL. The diameter of the illumination spot SP illuminating the mark AM may be slightly smaller than the width of the mark itself.

[0050] Radiation diffracted by the mark AM is collimated (in this example via the objective lens OL) into an information-bearing 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 zeroth order diffraction from the mark (which may be referred to as reflection). A self-referencing interferometer SRI, for example of the type disclosed in the aforementioned US 6961116, causes the beam IB to interfere with itself, after which the beam is received by a photodetector PD. Additional optics (not shown) may be included to provide separate beams in the event that the radiation source RSO produces more than one wavelength. If desired, the photodetector may be a single element, or it may comprise a plurality of pixels. The photodetector may comprise an array of sensors.

[0051] The steering optics comprising a spot mirror SM in this example may also be used to block zeroth order radiation reflected from the mark so that the information bearing beam IB comprises only higher order diffracted radiation from the mark AM (this is not necessary for the measurement but improves the signal to noise ratio).

[0052] The SRI intensity signal SSI is provided to the processing unit PU. By a combination of optical processing in the self-referencing interferometer SRI and computational processing in the unit PU, the values ​​of the X and Y position on the substrate relative to the reference frame are output.

[0053] A single measurement of the type shown only fixes the position of the mark within a specific range corresponding to one pitch of the mark. A coarser measurement technique is used in conjunction with this to identify which period of the sine wave is the period that contains the position of the mark. The same process is repeated at different wavelengths at coarser and / or finer levels to improve the accuracy of the mark and / or the robust detection capability of the mark regardless of the material from which the mark is made, and whether the mark is placed above and / or below the material. Improvements in performing and processing such multi-wavelength measurements are disclosed below.

[0054] In the case of wafer alignment, the following methods are used or have been proposed to correct mark asymmetry of mark positions (asymmetry in alignment marks that causes position errors or offsets): OCW (Optimum Color Weighting - which is described in more detail in U.S. publication US2019 / 094721A1, which is incorporated herein by reference), OCIW (Optimum Color and Intensity Weighting - which is described in more detail in PCT publication WO 2017032534A2) and WAMM (Wafer Alignment Model Mapping - which is described in more detail in PCT publications WO2019001871A1 and WO 2017060054A1).

[0055] An example using OCW is that in OCW, according to a set of weights including a weight for each color Perform a least squares optimization of the alignment model fitting coefficients X. When these weights Enables alignment and overlay measurement These weights minimize the difference between is considered optimal; that is, the optimization finds the weights that best satisfy

[0056]

[0057] In each of these prior art methods, training on reference overlay data is required or desired. Other methods may rely on specific assumptions made about the spatial distribution of mark deformations on the wafer. This means that these corrections can only be performed accurately if sufficient reference data is available and if process variations in the reference data represent variations that require correction. The reference data may be measured by a reference sensor, such as hindsight overlay data, as used in the OCW example just given. This overlay metrology data is used as a reference in a feedback mode: after the wafer has been exposed, the resulting measurement errors are observed in the hindsight by overlay metrology and corrected for future exposures.

[0058] There are important disadvantages to using overlay metrology in this manner. For example, overlay metrology is expensive, not all exposed wafers are typically measured, the measurement occurs relatively long after exposure so that corrections may be out of date by the time they are applied, and overlay metrology also suffers from very similar mark deformation errors and is therefore an imperfect reference.

[0059] To address this issue, a multi-color minimum residual (MCLR) method has been designed, as described in WO 2022184405A1. This describes a method for correcting mark asymmetry using only alignment data, for example, without relying on overlay measurement feedback. The method described is based on the observed correlation between wafer alignment model residuals (the difference between the measured alignment data and the alignment model fitted to the alignment data) and overlay performance. Due to mark asymmetry, each color measures a slightly different wafer shape, and the color that best fits the model can be selected as the recipe color. The concept can be extended to determine color weightings for multiple colors in a manner similar to OCW, but without relying on reference overlay data. For the avoidance of doubt, all references to "color" in this disclosure should be understood to cover (and be a shorthand for) specific wavelength and polarization combinations.

[0060] The goal of the described MCLR method is to determine a set of color weights that minimizes the alignment model residuals. The specific exemplary method described below determines the set of color weights by performing a linear least squares optimization of the model residuals for each measurement. However, it should be understood that this is only one optimization option and alternative optimization methods may be performed instead. For example, by including a regularization term in an optimization based on the L1 norm.

[0061] The method includes obtaining alignment data including an alignment value for each color (i.e., there are multiple alignment values ​​for each alignment mark, one for each color). Model residuals may be calculated for each alignment mark and for each color by fitting the measured values ​​for each color with an alignment model and recording the fit residuals. The alignment model may be any suitable alignment model for alignment modeling. The fit residuals may be represented as a residual matrix R, where each element includes a residual for an alignment mark index m (1-M) and a color channel n (1-N)

[0062]

[0063] The residuals can be computed over multiple wafers and stacked vertically in R.

[0064] The goal of the algorithm is to find a set of color weights This minimizes the residual R (e.g., in a least squares sense), i.e., obtains:

[0065]

[0066] This system of equations can be solved, for example, via linear least squares regression with the additional constraint that the sum of the color weights must equal 1:

[0067]

[0068] This constraint ensures that the determined alignment correction is invariant to translations of all colors, and also avoids trivial solutions where all weights equal zero.

[0069] Once the system of equations is solved, applying the resulting optimal weights w to the alignment data will result in the minimum model residuals (e.g., the minimum root sum of squares / root mean square of the model residuals) across the wafer(s) considered in the input. The weights may be applied to the alignment data to correct for mark asymmetries in the alignment data when determining the alignment grid for future exposures.

[0070] The MCLR method can be implemented as an external training algorithm in a similar manner to OCW. Alignment data from one or more wafers can be used as training data in order to determine a set of color weights that can then be applied to one or more (future) wafers. However, relying solely on alignment data without the need for reference overlay data also means that the same method can be used to perform inline alignment corrections for each wafer; for example, in a scanner or a separate alignment station. After all alignment marks have been measured (for example, in the measurement stage of a dual-stage system or in a separate alignment station), but before the wafers are transferred to an exposure stage or exposure station, the proposed method can be used to determine a set of color weights that minimize the model residuals for each wafer on a per wafer basis. In this way, the alignment grid of each wafer can be corrected with an optimal set of color weights determined specifically for that wafer.

[0071] Typically, a set of color weights obtained using the above method will include non-zero values ​​for each color. For example, some alignment sensors can measure with up to 24 illumination settings (e.g., 12 wavelengths and two polarizations), and thus, the method disclosed herein can determine 24 color weights.

[0072] In one embodiment, it may be advantageous to limit the number of color weights used in the solution, such as limiting the number of colors used for measurement (e.g., to a maximum of 4, 5, 6, or 7 colors), thereby determining a preferred subset of the plurality of illumination settings. Advantages of such an embodiment include greater robustness to overfitting to outliers in the training data, and less stringent requirements on future wafers on which the recipe will be applied, since all colors with non-zero weights must also be valid (e.g., sufficient signal strength).

[0073] A first method for reducing the number of color weights (which may be applied alone or in combination with other such methods described herein) may include applying appropriate thresholds to exclude colors with very small associated weights, and / or removing colors that do not contribute significantly to the result (e.g., colors with associated weights below a threshold may be excluded).

[0074] Figure 4 is a flow chart describing a method that can be used to reduce the number of colors (e.g., to determine a set of enabled colors for measurement as a subset of available colors). This describes one method of removing colors by backward stepwise selection of predictors. Another method is to use forward stepwise selection, or a combination of the two.

[0075] At step 402, a color impact metric and a current performance metric are determined from the residual (RES) R and the weight (WT) w. The current performance can be determined from the regression error (e.g., the square root of the regression error ). The color influence metric can be constructed by multiplying each color (column) of the residual matrix by the corresponding color weight. Based on this, the RMS (or other suitable statistical metric) for each color can be determined, resulting in a color influence vector with values ​​for each color.

[0076] The method described by the flowchart can be repeated in multiple runs, for example, each time potentially removing a color. At step 404, it is determined whether this is the first run, and if so, a starting performance metric 408 is initialized 406 using the current performance metric determined in the previous step. At step 412, it is determined whether the difference between the current performance metric and the starting performance metric 408 is outside a performance threshold 410. If so, it is determined 414 based on the performance whether the previous run resulted in the removal of a color. If so, the algorithm restores 416 the weights from the previous run 418 and ends 420 with these weights and presents the enabled colors.

[0077] If either of steps 412, 414 is negative, then at step 422, it is determined whether the current number of enabled colors 426 is greater than the specified maximum number of enabled colors 424. If not, then at step 430, it is determined whether any weight has a magnitude below a minimum weight threshold 428. If not, then at step 440, it is determined whether the difference between the current performance metric and the starting performance metric 408 is within the performance threshold 410. If not, the process ends 444 with the current weights and enabled colors.

[0078] For any of steps 422, 430, 440, if the determination is yes, the current weights for the run are stored 442, and a determination is made at step 432 whether the number of colors is greater than 1. If no, the process ends 444 with the current weights. If yes, based on the currently enabled colors 434, the colors with the lowest associated color influence are removed to determine an updated set of enabled colors 438. Further runs may then be performed based on the updated enabled colors 438 and their associated weights 442.

[0079] Another method of reducing the number of colors may include a brute force approach, where all color combinations are considered and the best combination (preferred subset) is selected (e.g., the combination that satisfies all conditions). More specifically, the method may include calculating a solution for each possible set of color weights starting with each single color, and gradually increasing the colors and evaluating each combination. Thus, this may include starting with all 1-color solutions, then all 2-color solutions, then all 3-color solutions, and so on to all color solutions. The optimal solution may be the solution that uses the least number of colors and satisfies a certain performance threshold.

[0080] The above method describes the minimization of the model residual relative to a single layer or reference layer (e.g., L0), as is typically done in alignment. In many cases, this will indeed produce the best results. However, in some cases, it may be preferable to minimize the point-to-point difference or Δ of the model residual between two specific layers (e.g., the overlay of two specific layers), even if this results in higher residuals for each of these layers relative to the bottom / reference layer.

[0081] Figure 5 An example of indirect alignment is conceptually shown, where both layers L1 and L2 align AL back to the same underlying or reference layer L0, and device yield depends primarily on the overlay OV L2-L1 between layer L1 and layer L2 (rather than relative to L0). The above-described MCLR method will minimize the residual between layer L1 and reference layer L0, and between layer L2 and reference layer L0. The proposed method aims to determine one or more sets of weights that minimize the difference in residuals between layers L1 and L2. When the alignment model residuals of layer L2 match the alignment model residuals of layer L1, the overlay between layer L1 and layer L2 may be close to optimal. This effectively means that the same error is repeated in both layers, eliminating the error between the layers, so that there is minimal overlay between layer L1 and layer L2. As previously described, the method can use only alignment data, for example, to determine the alignment data residuals with respect to a fitted alignment model; post-exposure overlay data is not required.

[0082] There are many different implementations to achieve this. In one embodiment, the color weight recipe of the bottom layer L1 can be fixed so that only the color weights of the top layer L2 are allowed to change during optimization. Alternatively, the color weights of both layers can be allowed to change. In one such embodiment, a common color recipe is determined for both layers. In another such embodiment, each of the two layers can be allowed to have a corresponding different set of optimization weights that are not necessarily the same. If the bottom layer recipe is also allowed to change, greater performance gains can be achieved, although this may be at the expense of poorer bottom layer performance.

[0083] Thus, a method for determining at least one set of correction weights to correct measurement data is disclosed. The method includes: obtaining first measurement data related to a first set of illumination settings for measurement radiation used to perform measurement of a first layer; fitting the first measurement data to a model representing the measurement data, and determining a first set of fitting residuals as residuals of the first measurement data relative to the model; obtaining second measurement data related to a second set of illumination settings for measurement radiation used to perform measurement of a second layer, wherein each illumination setting in the first set of illumination settings and the second set of illumination settings includes a different wavelength, polarization, or a combination thereof; fitting the second measurement data to a model used to represent the measurement data, and determining a second set of fitting residuals as residuals of the second measurement data relative to the model; and determining the at least one set of correction weights as at least one set of correction weights that minimizes the difference between the first set of fitting residuals and the second set of fitting residuals.

[0084] Specifically, the first metrology data may include (optionally) first alignment data from a multi-color alignment measurement of the first layer, and the second metrology data may include second alignment data from a multi-color alignment measurement of the second layer. The first metrology data and the second metrology data may be obtained from a single alignment sensor (e.g., as part of a single lithographic apparatus (scanner) or a separate alignment station), or from different alignment sensors (e.g., in respective different lithographic apparatuses or separate alignment stations, or possibly within a single lithographic apparatus).

[0085] The first set of illumination settings and the second set of illumination settings may include a common set of illumination settings. However, this is not necessary, and at least some embodiments may use different respective illumination settings for the first measurement data and the second measurement data (of course, the latter is not possible for the embodiments described below that optimize the first and second layers using common weights). In addition, while all embodiments require that the second measurement data of the second layer (top layer) be associated with multiple illumination settings (e.g., have been measured using two or more measurement setups), embodiments that only optimize the top layer weights do not require that the first measurement data (first layer) be associated with multiple illumination settings; for example, the layer may be measured using only a single illumination setup because it is not optimized.

[0086] In all cases, the same alignment marks should be measured for each of the two layers (same number of marks at a common set of measurement locations). If not, the optimization can be performed only on the intersection of the two sets of measurements (common measurement points). This is because the point-to-point delta can only be calculated at each point where two measurements (first layer and second layer) are available. If there is a point where one measurement is missing, that point cannot be included in the point-to-point delta. The intersection of the two layer measurements represents the set of points where both the first layer and second layer measurements are available and valid.

[0087] Each of these methods will now be described individually.

[0088] Optimize only top-level weights

[0089] The inter-layer differences (increments) can be optimized by applying a MCLR algorithm (e.g., as described and disclosed in WO 2022184405A1) to the residuals of each color of the second (or top) layer L2 and the increments of the fixed residuals of the first layer L1. Note that the terms "first layer" and "second layer" are only used to distinguish the layers and describe the relative order (i.e., the first layer is exposed before the second layer). However, one or more layers may be exposed on the substrate before the first layer and / or possibly between the exposure of the first and second layers.

[0090] This approach can include correcting the weights w for the second layer. L2 An optimization is performed; for example, by finding the second layer correction weights w that minimize the residual difference between the second set of fitted residuals (second layer residuals) and the vector comprising the first set of fitted residuals (first layer residuals) L2 :

[0091]

[0092] Where R L2 is a matrix including the residuals for each label and each color of the second layer L2, and is R L1 A vector with the residuals for each token but not each color of the first layer L1. The vector R L1 Can be determined as:

[0093]

[0094] Where R L1 is a matrix with the residuals for each label and each color of the first layer L1, and w L1 are the first layer weights (eg, as determined in a previous optimization). In each case, the superscript T denotes the transposed matrix.

[0095] In this embodiment, the basic MCLR method is unchanged and can be performed as already described. The difference is the input (ie, the residual difference rather than the single layer residual).

[0096] Optimizing the first and second layers with common weights

[0097] In this method, a common set of correction weights w for both the first measurement data (first layer) and the second measurement data (second layer) is determined. L1，L2 , that is, the weights are optimized jointly using the constraint that the weights of the two layers are the same. L2The second set of fitted residuals and the first layer R L1 The MCLR method is performed on the residual differences between the first set of fitted residuals. In each case, the residuals for each color can be used. The matrix R L1 and R L2 should have the same size. Thus, the matrix R L1 and R L2 The data in may represent the residuals from the same marker positions (in rows) measured in layers L1 and L2 respectively, and measured with the same set of colors (in columns). The optimization may minimize the following:

[0098]

[0099] As with the previous embodiments, the basic MCLR method is unchanged and can be performed as already described.The differences are the input; that is, residual differences (now two layers per color) rather than a single layer residual.

[0100] Optimizing the first and second layers with independent weights

[0101] If both layers are allowed to obtain independent weights, the weights w can be corrected according to the first measurement data / first layer of the first layer L1 and the second measurement data / the second layer correction weight w L2 to solve the quadratic equality constraint problem that minimizes their residual difference. For example, the cost function to be solved may include:

[0102]

[0103] This can no longer be solved using the MCLR method already described (e.g., with modified inputs). Instead, the MCLR method itself can be modified to solve for two sets of weights. A solution can be found by rewriting the problem as an unconstrained problem, which can be solved by, for example, subspace modeling or quadratic optimization / quadratic programming. These are only examples, and there are many such mathematical techniques and methods for solving such cost functions, which are well known to those skilled in the art and therefore will not be described further here.

[0104] Additionally, to prevent the solution from straying too far from a good solution, a prior for the weights can be imposed such that only small deviations from the prior are allowed. This avoids the situation where the layer weighted residuals of two layers become very large but equal so that their deltas are still small. Regular MCLR weights (e.g., optimizing the first and second layer (e.g., residuals towards zero) in sequence) are used to get the first set of initial weights w. L1，L0 and a second set of initial weights w L2，L0 ) can be used for such a prior. In addition, a regularization term for each set of weights can be applied where the size of the regularization term λ describes the amount of regularization. Thus, λ=0 means no regularization, making the solution the same as in the previous section. Large values ​​of the regularization term λ will force the solution to be at or very close to the initial weights w L1，L0 and w L2，L0 For example, such a regularization term may favor simple solutions and / or smaller weights. Note that similar regularization terms may be used in the other embodiments described above (in each case, there is only one set of weights, so only a single regularization term is required).

[0105] Thus, in one embodiment, the cost function may be:

[0106]

[0107] Now, due to the previous solution w L1，L0 and w L2，L0 already sum to 1, deviations from those priors can be constrained to sum to 0:

[0108]

[0109] Any embodiments disclosed herein may disclose any color reduction method described herein.

[0110] A further approach will now be described, applying similar ideas as described above to an overlay (more generally, parameter of interest) trained OCW technique, which uses reference metrology data (e.g., overlay data) to train the recipe. An overlay trained OCW is described above, the goal of which is to find weightings that minimize the error or difference between the weighted alignment data and the corresponding reference metrology data or overlay data from the same substrate. Typically, the color weight recipe is optimized sequentially and independently for each layer in the stack. However, this may not be optimal when indirect alignment is used.

[0111] In both direct and indirect alignment, the overlay between layer L2 and layer L1 is affected by the exposure of layer L2 (the position of the top grating of the overlay target) as well as by the exposure of layer L1 (the position of the bottom grating of the overlay target). Therefore, changes in the alignment recipe of layer L1 can affect the overlay L2-L1 in addition to changes in the alignment recipe of layer L2. However, the main difference between direct and indirect alignment is that in direct alignment, any change in the alignment of layer L1 also changes the position of the newly printed alignment marks in L1 (as seen from layer L2). Therefore, any change in layer L1 can be measured and corrected at layer L2: that is, layer L2 can observe and follow the changes in L1. In indirect alignment, changes in the alignment of L1 are not observed on the next layer, because layer L2 is still referenced to the same alignment marks in reference layer L0, which has not been changed by the exposure of layer L1. In this way, layer L2 does not see and cannot follow any changes in layer L1; more generally, a later layer cannot follow changes in any previous layer (after layer L0).

[0112] For this reason, in indirect alignment, it is important to consider the impact of both layer L1 alignment and layer L2 alignment. A change in the L1 alignment recipe will require a corresponding change in the L2 alignment to follow the change in layer L1 and keep the L2-L1 overlay error within specification.

[0113] Multi-layer co-determination or co-optimization of a color weight recipe or multi-layer OCW will now be described. It is proposed to co-optimize (at least) the indirect alignment of two layers L2, L1 (e.g., relative to a reference layer L0) to minimize the overlay L2-L1 while ensuring that the overlay L1-L-1 remains within specification with the previous layer (e.g., the immediately previous layer, such that layer L-1 directly precedes L1). Figure 6 This engraving is also shown in Figure 6 Shown with Figure 5 A similar arrangement, but with overlay L2-L1 and overlay L1-L-1 explicitly shown. Such an approach may be particularly beneficial when the tolerance of overlay L2-L1 is tighter than the tolerance of overlay L1-L-1. In this way, overlay L2-L1 may be significantly improved. It will be appreciated that while this improvement will be at the expense of slightly worse overlay performance of overlay L1-L-1, this will be acceptable as long as the overlay remains within specification.

[0114] In practice, in a typical indirect alignment tree, many layers are aligned back to the same reference layer. In this case, each layer has an indirect impact on the overlay L2-L1, because the L2-L1 overlay is affected by the L1 alignment, which is affected by the L-1 alignment, which is affected by the L-2 alignment, and so on.

[0115] For indirect alignment, it is not optimal to optimize the color weight recipe of each layer sequentially, i.e. optimize layer L1 first and then optimize layer L2 while keeping layer L1 fixed. Instead, better performance can be achieved by co-optimizing both layers simultaneously to obtain the best overlay L2-L1.

[0116] The joint optimization of these two layers requires a preparatory step to "de-correct" the active alignment corrections of each of layer L2 and layer L1 (e.g., the first set of effective weights and the second set of effective weights). Lx (where x is 1 and 2 in the examples below) is the weighted alignment data for that layer according to the current or effective recipe. Thus:

[0117]

[0118] where w Lx is the weight of layer Lx, X Lx is the measured alignment data of layer Lx, w i is the weight of each color (index i) and X(λ i ) is the alignment data for each color. In the context of the present disclosure, de-correction may include removing corrections such as corrections performed during alignment (i.e., removing alignment corrections). Thus, de-corrected overlay data may include overlay data with the alignment correction for each layer previously applied removed.

[0119] In a first step, the measured overlay L2-L1y should be compared with the effective alignment of layer L2. L2-L1 Perform solution correction (remove the effective L2 correction) to obtain the solution-corrected overlay L2-L1 y L2-L1，dL2 This simulates "undoing" an alignment correction to the top structure (e.g., the top grating of an overlay target):

[0120] y L2-L1，dL2 =y L2 - L1 +X L2 =y L2-L1 +X L2 ·w L2

[0121] Then, for effective alignment of layer L1, the resulting decorrected overlay should be further decorrected (to obtain a "doubly decorrected" overlay y L2-L1,dL2,dL1 ). This also simulates "undoing" the alignment correction on the bottom layer. The decorrection in this step should be performed with a sign flip, since it is applied to the bottom raster:

[0122] y L2-L1，dL2，dL1 =y L2-L1，dL2 +(-X L1 )=y L2-L1+X L2 ·w L2 -X L1 ·w L1

[0123] To simulate the impact of the new (potentially better) alignment recipes at layer L2 and layer L1, both recipes can be applied to the double solution-corrected overlay to obtain the new overlay data y L2-L1，new :

[0124] y L2-L1，new =y L2-L1，dL2，dL1 -X L2 ·w L2，new +X L1 ·w L1，new

[0125] where w L2，new , w L1，new These are new recipes for layer L2 and layer L1 respectively.

[0126] Optimized color weight recipe w for layer L2 and layer L1 L2,opt , w L1,opt It is possible to find both in a single optimization, for example by concatenating the alignment and weights of a measure:

[0127]

[0128] As mentioned before, the two weights w L2,opt , w L1,opt The constraint is that the sum is 1 to prevent trivial solutions.

[0129] Optionally, the method just described can be regularized to penalize the layer L1 weights W L1，opt Deviate from the prior weight formula w L1,prior A solution that is too far away. While the optimization routine just described will find an optimal combination of weights for layers L2 and L1, it does not take into account the overlay L1-L-1, which is of course affected by the weighting applied to layer L1. Allowing the optimization to freely choose any weights for layer L1 (to optimize L2-L1 overlay) may result in the overlay L1-L-1 being severely affected (e.g., out of specification). To address this issue, a known good a priori recipe for layer L1 can be included in the cost function (e.g., as part of a regularization term), and the solution can be constrained so that the new weights at layer L1 remain close to the a priori recipe. In this case, the overlay L1-L-1 may still degrade slightly to improve the overlay L2-L1, but it is not allowed to deviate too far from the initial recipe.

[0130] The prior solution can be included via a regularization penalty that penalizes large deviations of the new formulation relative to the prior:

[0131]

[0132] where λ L1 is a regularization parameter. This regularization parameter provides a trade-off between overlay L2-L1 and overlay L1-L-1 (i.e., determines how much overlay L1-L-1 is allowed to deteriorate in order to improve overlay L2-L1). In this way, λ can be tuned according to the corresponding specifications of overlay L2-L1 and / or overlay L1-L-1. L1 .

[0133] A priori set of correction weights can be determined using conventional OCW recipe training (single-layer optimization) for that layer (e.g., in this case for layer L1), or, as will be described, it can use the results of a previous optimization to optimize the parameters of interest between L1 and the layer before the first layer (e.g., layer L-1).

[0134] In a typical indirect alignment use case, many consecutive layers L3, L2, L1, L-1, L-2, ... are all aligned back to the same bottom layer L0, and the overlay between each consecutive layer (L3-L2, L2-L1, L1-L-1, L-1-L-2, ...) is critical. The joint optimization routine described so far can be applied sequentially to each layer pair, for example, while constraining the solution of the bottom layer to be close to the previous solution through the described regularization penalty.

[0135] As an example, starting from the layer pair L-1-L-2, the weights of layers L-1 and L-2 can be optimized as already described; for example:

[0136]

[0137] The weights found for layer L-1 will become the priors for optimizing the next layer L1-L-1; that is, the weights can be used as the prior w L-1，prior The optimization finds a better formulation for layer L-1, a prior for L1, etc.; for example:

[0138]

[0139] This can be repeated for each successive layer. For example, the cost function for the overlay L2-L1 given above can be used to optimize the next layer, where the w just determined is L1，opt Used for L1，prior .

[0140] At each step, the regularization parameter λ can be tuned based on the criticality of the overlay of the layer pair Lx For example, if the overlay L1-L-1 is not very critical, the regularization parameter λ used in the next regularization step can be relaxed. L1, so that the new recipe for layer L1 can deviate a little more from the prior. This may result in a slightly worsened overlay L1-L-1 (which is not critical) and an improved overlay L2-L1.

[0141] Co-optimization is particularly useful for indirect alignment, because, for example, changes in layer L1 cannot be observed from layer L2, because layer L2 is not aligned with layer L1. However, it is understood that the concepts disclosed herein can be applied to direct alignment. However, the added value of this approach for direct alignment is not expected to be large, because changes in layer L1 can already be observed and then layer L2.

[0142] The concepts disclosed herein can be generalized to determining a set of color weights (or illumination setting weights, where the illumination setting is a combination of measurement wavelength and polarization) for correcting measurement data for multiple color / illumination settings by minimizing the delta model residual between two layers according to the weights, wherein the model residual is obtained by fitting each set of measurement data to a model used to represent the measurement data.

[0143] While specific embodiments of the invention have been described above, it will be appreciated that the invention may be practiced otherwise than as described.

[0144] Although specific reference has been made above to the use of embodiments of the invention in the context of optical lithography, it will be appreciated that the invention may be used in other applications, such as imprint lithography, and that the invention is not limited to optical lithography where the context permits. In imprint lithography, the topography in the patterning device defines the pattern produced on the substrate. The topography of the patterning device may be pressed into a layer of resist provided to the substrate, whereupon the resist is cured by application of electromagnetic radiation, heat, pressure, or a combination thereof. The patterning device removes the resist, leaving a pattern therein after the resist has cured.

[0145] As used herein, the terms "radiation" and "beam" encompass all types of electromagnetic radiation, including ultraviolet (UV) radiation (e.g., having a wavelength of approximately 365, 355, 248, 193, 157 or 126 nm) and extreme ultraviolet (EUV) radiation (e.g., having a wavelength in the range of 1-100 nm), as well as particle beams, such as ion beams or electron beams.

[0146] The term "lens", where the context permits, may refer to any one or combination of various types of optical components, including refractive, reflective, magnetic, electromagnetic, and electrostatic optical components. Reflective components may be used in devices operating in the UV and / or EUV range.

[0147] Various aspects of the invention are set out in the following clauses.

[0148] 1. A method for determining at least one set of correction weights to correct measurement data; the method comprising: obtaining first measurement data associated with a first set of illumination settings for measurement radiation used to perform measurement of a first layer; fitting the first measurement data to a model representing the measurement data, and determining a first set of fit residuals as residuals of the first measurement data relative to the model; obtaining second measurement data associated with a second set of illumination settings for measurement radiation used to perform measurement of a second layer, the second set of illumination settings comprising a plurality of illumination settings, wherein each illumination setting comprises a different wavelength, polarization, or a combination thereof; fitting the second measurement data to a model representing the measurement data, and determining a second set of fit residuals as residuals of the second measurement data relative to the model; and determining the at least one set of correction weights as at least one set of correction weights that minimizes a difference between the first set of fit residuals and the second set of fit residuals.

[0149] 2. The method according to clause 1, wherein each of the fitting steps comprises fitting the first measurement data and the second measurement data corresponding to each illumination setting to the model, and recording the fitting residual for each illumination setting.

[0150] 3. A method according to clause 1 or 2, wherein determining the at least one set of correction weights comprises determining a single set of correction weights.

[0151] 4. The method of clause 3, wherein the single set of correction weights comprises a second layer of correction weights for correcting only the second set of measurement data, wherein the second layer comprises a top layer and the first layer comprises a layer below the second layer.

[0152] 5. A method according to clause 4, wherein the determining step comprises performing an optimization of the second layer correction weights so that they minimize the difference between the second set of fitting residuals and the residual vector associated with the first set of residual data.

[0153] 6. A method according to clause 5, wherein the residual vector comprises a set of fitted residuals for each target or each marker determined based on the first set of residual data and fixed first layer correction weights.

[0154] 7. The method of clause 6, comprising performing an initial optimization on only the first measurement data to determine the first set of residual data and fixed first layer correction weights.

[0155] 8. A method according to clause 5, 6 or 7, wherein the second set of fitting residuals is included in a residual matrix, the residual matrix comprising the measurement data arranged by target or marker in a first dimension and by shooting condition in a second dimension.

[0156] 9. The method of clause 3, wherein the single set of correction weights comprises a common set of correction weights for correcting each of the first set of measurement data and the second set of measurement data.

[0157] 10. A method according to clause 9, wherein the determining step includes performing an optimization of the common correction weight group so that they minimize the difference between a first residual matrix and a second residual matrix, wherein the first residual matrix includes the first measurement data arranged according to the target or label in the first dimension and according to the shooting condition in the second dimension, and the second residual matrix includes the second measurement data arranged according to the target or label in the first dimension and according to the shooting condition in the second dimension.

[0158] 11. The method according to clause 1 or 2, wherein the determining the at least one set of correction weights comprises determining a first layer of correction weights for correcting the first measurement data and a second layer of correction weights for correcting the second measurement data.

[0159] 12. A method according to clause 11, wherein the determining step includes performing a joint optimization of the first layer correction weights and the second layer correction weights so that they minimize the difference between the first set of fitting residuals weighted by the first layer correction weights and the second set of fitting residuals weighted by the second layer correction weights.

[0160] 13. The method of clause 12, comprising applying a prior that minimizes the size of the first set of fit residuals weighted by the first layer correction weights and the size of the second set of fit residuals weighted by the second layer correction weights.

[0161] 14. The method of clause 13, wherein the prior is based on a first set of initial weights that optimize the first set of fit residuals towards zero and a second set of initial weights that optimize the second set of fit residuals towards zero.

[0162] 15. The method of clause 14, comprising performing a first initial optimization on the first measurement data to obtain the first set of initial weights, and performing a second initial optimization on the second measurement data to obtain the second set of initial weights.

[0163] 16. A method according to any one of clauses 11 to 15, wherein the first set of fitting residuals is included in a first residual matrix, the first residual matrix includes the measurement data arranged according to the target or label in a first dimension and according to the shooting condition in a second dimension, and the second set of fitting residuals is included in a second residual matrix, the second residual matrix includes the measurement data arranged according to the target or label in the first dimension and according to the shooting condition in the second dimension.

[0164] 17. A method according to any preceding clause, wherein the first set of illumination settings comprises a plurality of illumination settings, wherein each illumination setting comprises a different wavelength, polarization or a combination thereof.

[0165] 18. A method according to any preceding clause, wherein the determining step uses regularization that favors smaller weight values ​​for the at least one set of weights.

[0166] 19. A method according to any preceding clause, wherein the determining step uses at least one least squares optimization.

[0167] 20. A method according to any preceding clause, wherein each of the at least one set of correction weights comprises a correction weight for each illumination setting in the set of illumination settings.

[0168] 21. A method according to any preceding clause, further comprising determining a preferred subset of the set of illumination settings.

[0169] 22. A method according to clause 21, wherein the step of determining a preferred subset comprises: evaluating candidate combinations of illumination settings based on a performance metric and an impact metric; and removing or adding illumination settings to the candidate combinations of illumination settings based on the performance metric and the impact metric.

[0170] 23. The method of clause 22, wherein the removing or adding step comprises removing the illumination condition with the lowest impact metric to obtain an updated candidate combination of illumination settings if a performance threshold is met.

[0171] 24. A method according to clause 22 or 23, comprising performing the evaluating and removing or adding steps until the candidate combination of illumination settings includes a desired number of illumination settings.

[0172] 25. A method according to clause 21, wherein the step of determining a preferred subset comprises evaluating all possible combinations of illumination settings; and selecting the preferred subset as a combination of illumination settings that meets a performance threshold using a minimum number of illumination settings.

[0173] 26. A method according to any preceding clause, comprising removing any illumination setting for which the determined correction weight is below a significance threshold.

[0174] 27. A method according to any preceding clause, wherein the determining step is constrained so that the sum of each of the at least one set of correction weights is equal to one.

[0175] 28. A method according to any preceding clause, wherein the first metrology data and the second metrology data each comprise alignment data.

[0176] 29. A method according to clause 28, comprising applying each of the at least one set of correction weights to a respective alignment measurement of the substrate performed at a plurality of illumination setups to obtain corrected alignment measurements.

[0177] 30. The method of clause 29, comprising performing the alignment measurements.

[0178] 31. A method according to clause 29 or 30, wherein the method is performed to determine the at least one set of correction weights using a training substrate in an initial training phase, the determined at least one set of correction weights being used for application to a plurality of subsequent substrates.

[0179] 32. A method according to clause 29 or 30, wherein the method is performed between performing an alignment measurement step and a lithography exposure step; wherein the alignment measurement step is performed to obtain the alignment measurement so that the first alignment data includes the alignment measurement, and the method further comprises: performing the lithography exposure step using the alignment measurement corrected by applying at least one set of correction weights determined.

[0180] 33. A method according to clause 32, wherein the at least one set of correction weights is determined individually for each substrate before each exposure step.

[0181] 34. A method as described in any of clauses 28 to 33, wherein the method comprises: when the amount of available overlay data reaches a threshold, switching to optimization based on minimizing the difference between the overlay data and the alignment data.

[0182] 35. A method according to any of clauses 28 to 34, wherein said determining the correction weights comprises performing a joint optimization between said minimizing the fit residual and minimizing the difference between the overlay data and the alignment data.

[0183] 36. A method according to any one of clauses 1 to 27, wherein the metrology data comprises overlay data.

[0184] 37. A method according to any preceding clause, wherein the first group of illumination settings and the second group of illumination settings comprise a common group of illumination settings.

[0185] 38. A method according to any preceding clause, wherein the first measurement data and the second measurement data are each associated with a common set of measurement locations.

[0186] 39. A computer program comprising program instructions operable, when run on suitable apparatus, to perform the method of any of clauses 1 to 38.

[0187] 40. A computer program carrier comprising a non-transitory version of the computer program of clause 39.

[0188] 41. A processing system comprising a processor and a storage device, the storage device comprising a computer program according to clause 40.

[0189] 42. An alignment sensor operable to perform the method of any of clauses 1 to 38.

[0190] 43. A lithographic apparatus comprising: a patterning device support for supporting a patterning device; a substrate support for supporting a substrate; and an alignment sensor according to clause 42.

[0191] 44. A metrology apparatus operable to perform the method of any of clauses 1 to 38.

[0192] 45. A method for determining a first set of correction weights for a first layer and a second set of correction weights for a second layer; the method comprising:

[0193] obtaining reference measurement data related to a parameter of interest between the first layer and the second layer;

[0194] demodulating the reference metrology data for a first metrology correction performed when exposing the first layer and a second metrology correction performed when exposing the second layer to obtain demodulated reference metrology data; and

[0195] The first set of correction weights and the second set of correction weights are jointly determined so that when the first set of correction weights are applied to first measurement data related to the first layer to obtain first weighted measurement data, and the second set of correction weights are applied to second measurement data related to the second layer to obtain second weighted measurement data, the first set of correction weights and the second set of correction weights improve the parameters of interest between the first layer and the second layer.

[0196] 46. ​​A method according to clause 45, wherein the step of jointly determining includes jointly determining the first set of correction weights and the second set of correction weights so as to minimize reference measurement data corrected by the solution using the first weighted measurement data and the second weighted measurement data.

[0197] 47. A method according to clause 45 or 46, wherein:

[0198] The first measurement correction includes the first measurement data weighted by a first set of effective weights of the first layer; and

[0199] The second measurement correction includes the second measurement data weighted by a second set of effective weights of the second layer.

[0200] 48. A method according to any of clauses 45 to 47, wherein the step of jointly determining comprises constraining the jointly determining to penalize solutions where the first set of correction weights deviate significantly from the a priori first set of correction weights.

[0201] 49. A method according to clause 48, wherein the constraining step is applied via a regularization term comprising a regularization parameter, and the method comprises selecting and / or tuning the regularization parameter based on a specification for the parameter of interest between the first layer and the second layer and / or the parameter of interest between a previous layer and the first layer.

[0202] 50. A method according to clause 48 or 49, wherein the a priori first set of correction weights comprises a set of correction weights determined in a previous optimization to optimize the parameter of interest between the first layer and a layer preceding the first layer.

[0203] 51. A method according to clause 50, comprising performing the method to optimize successive groups of correction weights for successive pairs of layers, using the results of previous optimizations to determine the a priori first set of correction weights for each successive jointly determined.

[0204] 52. A method according to clause 48 or 49, wherein the a priori first set of correction weights comprises the set of correction weights determined in a single layer optimization for the first layer.

[0205] 53. A method according to any of clauses 45 to 52, wherein the reference metrology data comprises overlay data and the parameter of interest is the overlay between the second layer and the first layer.

[0206] 54. A method according to any of clauses 45 to 53, wherein the first metrology correction and the second metrology correction each comprise an alignment correction, and the first metrology data and the second metrology data each comprise alignment data referenced to a common reference layer.

[0207] 55. The method of clause 54, comprising applying the first set of correction weights to a first alignment measurement of a first layer on a substrate, and applying the second set of correction weights to a second alignment measurement of a second layer on the substrate, each of the first alignment measurement and the second first alignment measurement being performed using a plurality of illumination settings such that each set of correction weights applies weighted measurements corresponding to different illumination settings.

[0208] 56. The method of clause 55, comprising performing the first alignment measurement and the second alignment measurement.

[0209] 57. A method according to clause 55 or 56, wherein the method is performed to determine the at least one set of correction weights using a training substrate in an initial training phase, the determined at least one set of correction weights being used for application to a plurality of subsequent substrates.

[0210] 58. Method according to any of clauses 45 to 57, wherein the first measurement data and the second measurement data each relate to a common set of measurement locations.

[0211] 59. A computer program comprising program instructions operable to perform the method of any of clauses 45 to 58 when the program instructions are run on suitable apparatus.

[0212] 60. A non-transitory computer program carrier comprising a computer program according to clause 59.

[0213] 61. A processing system comprising a processor and a storage device, the storage device comprising a computer program according to clause 60.

[0214] 62. An alignment sensor operable to perform the method of any of clauses 45 to 58.

[0215] 63. A lithographic apparatus comprising: a patterning device support for supporting a patterning device; a substrate support for supporting a substrate; and an alignment sensor according to clause 62.

[0216] 64. A measurement device operable to perform the method of any of clauses 45 to 58.

[0217] The breadth and scope of the present invention should not be limited by any of the above-described exemplary embodiments, but should be defined only in accordance with the following claims and their equivalents.

Claims

1. A method for determining at least one set of correction weights for correcting measurement data; the method comprising: obtaining first metrology data relating to a first set of illumination settings of a measurement radiation for performing measurements of a first layer; fitting the first measurement data to a model for representing the measurement data, and determining a first set of fitting residuals as residuals of the first measurement data with respect to the model; obtaining second metrology data associated with a second set of illumination settings of measurement radiation for performing measurements of the second layer, the second set of illumination settings comprising a plurality of illumination settings, wherein each illumination setting comprises a different wavelength, polarization, or a combination thereof; fitting the second measurement data to a model for representing the measurement data, and determining a second set of fitting residuals as residuals of the second measurement data with respect to the model; as well as The at least one set of correction weights is determined as at least one set of correction weights that minimizes a difference between the first set of fit residuals and the second set of fit residuals.

2. The method of claim 1, wherein each of the fitting steps comprises fitting the first measurement data and the second measurement data corresponding to each illumination setting to the model, and recording the fitting residual for each illumination setting.

3. The method of claim 1 or 2, wherein said determining said at least one set of correction weights comprises determining a single set of correction weights.

4. The method of claim 3, wherein the single set of correction weights comprises a second layer of correction weights for correcting only the second set of measurement data, wherein the second layer comprises a top layer and the first layer comprises a layer below the second layer.

5. A method as claimed in claim 4, wherein the determining step includes performing an optimization of the second layer correction weights so that they minimize the difference between the second set of fitting residuals and the residual vector associated with the first set of residual data.

6. A method as claimed in claim 5, wherein the residual vector includes a set of fitting residuals for each target or each marker determined based on the first set of residual data and fixed first layer correction weights.

7. The method of claim 6, comprising performing an initial optimization on only the first measurement data to determine the first set of residual data and fixed first layer correction weights.

8. A method as claimed in claim 5, 6 or 7, wherein the second set of fitting residuals is included in a residual matrix, which includes the measurement data arranged by target or marker in a first dimension and by shooting condition in a second dimension.

9. The method of claim 3, wherein the single set of correction weights comprises a common set of correction weights for correcting each of the first set of measurement data and the second set of measurement data.

10. A method as claimed in claim 9, wherein the determining step includes performing an optimization of the common correction weight group so that they minimize the difference between a first residual matrix and a second residual matrix, wherein the first residual matrix includes the first measurement data arranged by target or label in a first dimension and by shooting conditions in a second dimension, and the second residual matrix includes the second measurement data arranged by target or label in the first dimension and by shooting conditions in the second dimension.

11. The method of claim 1 or 2, wherein the determining the at least one set of correction weights comprises determining a first layer of correction weights for correcting the first measurement data and a second layer of correction weights for correcting the second measurement data.

12. A method as claimed in claim 11, wherein the determining step includes performing co-optimization of the first layer correction weights and the second layer correction weights so that they minimize the difference between the first set of fitting residuals weighted by the first layer correction weights and the second set of fitting residuals weighted by the second layer correction weights.

13. The method of claim 12, comprising applying a prior that minimizes the size of the first set of fit residuals weighted by the first layer correction weights and the size of the second set of fit residuals weighted by the second layer correction weights.

14. The method of claim 13, wherein the prior is based on a first set of initial weights that optimize the first set of fit residuals toward zero and a second set of initial weights that optimize the second set of fit residuals toward zero.

15. The method of claim 14, comprising performing a first initial optimization on the first measurement data to obtain the first set of initial weights, and performing a second initial optimization on the second measurement data to obtain the second set of initial weights.

16. The method of any preceding claim, wherein the first set of illumination settings and the second set of illumination settings comprise a common set of illumination settings.

17. A method as claimed in any preceding claim, wherein the first measurement data and the second measurement data both relate to a common set of measurement locations.

18. An alignment sensor operable to perform the method of any one of claims 1 to 17.

19. A lithographic apparatus comprising: a pattern forming device support for supporting the pattern forming device; a substrate support for supporting a substrate; as well as An alignment sensor as claimed in claim 18.

20. A metrology device operable to perform a method according to any one of claims 1 to 17.

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