Measurement method

Abstract

A metrology method related to measurement of a structure on a substrate, the structure experiencing process variations is disclosed. The method comprises: obtaining first measurement data related to a phase of measurement radiation that has been scattered from one or more markers and to a plurality of measurement conditions; obtaining second measurement data relating to the intensity of the measurement radiation and to the plurality of measurement conditions; obtaining a weighting of the first measurement data and the second measurement data, the weighting comprising a modulus component associated with a modulus of a complex weight and an argument component associated with an argument of the complex weight; and determining a first parameter value of a first parameter from the first measurement data and the second measurement data weighted by the weighting.

Description

Cross Reference to Related Applications

[0001] This application claims priority to European application 23167496.1, filed on April 12, 2023, and which is incorporated herein in its entirety by reference. TECHNICAL FIELD

[0002] The present invention relates to methods and apparatuses, for example usable in manufacturing devices by lithographic techniques, and to methods of manufacturing devices using lithographic techniques. More specifically, the present invention relates to metrology sensors and lithographic apparatuses having such metrology sensors. BACKGROUND

[0003] A lithographic apparatus is a machine that applies a desired pattern onto a substrate, usually onto part of the substrate. The lithographic apparatus can be used, for example, in the manufacture of integrated circuits (ICs). In that situation, a patterning device (which is alternatively referred to as a mask or a reticle) can be used to generate a circuit pattern to be formed on a single layer of the IC. This pattern can be transferred onto a target portion (for example, comprising part of, one, or several dies) of the substrate (for example, a silicon wafer). The pattern can be transferred, for example, via 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 each to be imaged. These target portions are commonly referred to as “fields”.

[0004] In the manufacture of complex devices, it is common to perform many lithographic patterning steps to form functional features in successive layers on the substrate. A key aspect of lithographic apparatus performance is therefore the ability to place accurately and precisely the applied pattern with respect to features laid down in previous layers (by the same apparatus or a different lithographic apparatus). To this end, 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, typically an optical position sensor. The lithographic apparatus includes one or more alignment sensors by which the position of the marks on the substrate can be measured accurately. Different types of marks and different types of alignment sensors are known from different manufacturers and different products of the same manufacturer.

[0005] In other applications metrology sensors are used to measure exposure structures on a substrate (exposure structures in resist and / or exposure structures after etching). A fast and non-invasive dedicated inspection tool is a scatterometer in which a beam of radiation is directed onto a target on the substrate surface and properties of the scattered or reflected beam are measured. Examples of known scatterometers are angle resolved scatterometers of the type described in US2006033921A1 and US2010201963A1. In addition to measuring feature shape by reconstruction it is also possible to use such apparatuses to measure diffraction based overlay as described in published patent application US2006066855A1. Diffraction based overlay metrology using dark field imaging of diffraction orders enables overlay measurements on smaller targets. Examples of dark field imaging metrology can be found in international patent applications WO 2009 / 078708 and WO 2009 / 106279 which are incorporated herein in their entirety by way of reference. Further developments of this technique 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 product structures on the wafer. The use of composite grating targets can enable multiple gratings to be measured in one image. The contents of all these applications are also incorporated herein by reference.

[0006] In some metrology applications, such as in some scatterometers or alignment sensors, defects in the metrology target can cause wavelength / polarization dependent variations in the measured values from that target. Accordingly, sometimes correction for and / or mitigation of this variation is achieved by performing the same measurement using multiple different wavelengths and / or polarizations (or more generally, multiple different measurement conditions). It is desirable to improve one or more aspects of measurement using multiple measurement conditions. SUMMARY

[0007] The present invention provides in a first aspect a metrology method relating to measurement of a structure on a substrate, the structure undergoing process variation, the method comprising: obtaining first measurement data relating to phase of measurement radiation that has been scattered from one or more marks and relating to a plurality of measurement conditions; obtaining second measurement data relating to intensity of the measurement radiation and relating to the plurality of measurement conditions; obtaining a weighting of the first measurement data and the second measurement data, the weighting comprising a modulus component relating to modulus of a complex weight and an argument component relating to argument of the complex weight; and determining a first parameter value of a first parameter from the first measurement data and the second measurement data weighted by the weighting.

[0008] Also disclosed is a computer program, an alignment sensor and a lithographic apparatus operable to perform the method of the first aspect.

[0009] The above described aspects and other aspects of the present invention will be understood by considering the examples described below. BRIEF DESCRIPTION OF DRAWINGS

[0010] Embodiments of the present invention will now be described, by way of example only, with reference to the accompanying drawings in which: Figure 1 A lithographic apparatus is depicted; Figure 2 Measurement and exposure processes in the apparatus are schematically illustrated Figure 1 Figure 3 is a schematic illustration of an alignment sensor applicable according to embodiments of the present invention; and Figure 4 is a schematic illustration of a measurement for an alignment mark. DETAILED DESCRIPTION

[0011] Before a detailed description of embodiments of the application, it is beneficial to present an example environment in which various embodiments of the application can be implemented.

[0012] Figure 1 ​A lithographic apparatus LA is schematically depicted. The apparatus includes an illumination system (illuminator) IL configured to condition a radiation beam B (e.g., UV or DUV radiation), a patterning device support or support structure (e.g., a mask table) MT constructed to support a patterning device (e.g., a mask) MA and connected to a first positioner PM configured to accurately position the patterning device in accordance with certain parameters, two substrate tables (e.g., wafer tables) WTa or WTb each constructed 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 in accordance with 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 patterning device MA onto a target portion C (e.g., comprising one or more dies) of the substrate W. A reference frame RF links the various items and serves as a reference for setting and measuring the position of the patterning device as well as the position of the substrate and features on the substrate.

[0013] The illumination system can 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 radiation.

[0014] 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, such as for example whether the patterning device is to be held in a vacuum environment. The patterning device support can be mechanical, vacuum, electrostatic, or electrodynamic clamping technology, or another type of apparatus for holding the patterning device. It will be appreciated that the patterning device support, which can be referred to or be a frame or table, for example, can be stationary or movable as needed. The patterning device support can ensure that the patterning device is at a desired location, for example in relation to the projection system.

[0015] The term“patterning device” used herein should be interpreted in its broadest sense as a device that can be used in the process of pattern formation on a substrate. It should be noted that the pattern that is imparted to the radiation beam can not exactly correspond to the desired pattern on the substrate, for example if the pattern includes phase shift features or so-called assist features. Generally, the pattern that is imparted to the radiation beam will correspond to a particular functional layer in a device, such as an integrated circuit, that is formed on the substrate.

[0016] As described herein, the apparatus is of a transmissive type (e.g. employing transmissive patterning devices). Alternatively, the apparatus can be of a reflective type (e.g. employing a programmable mirror array of a type as referred to above, or employing a reflective mask). Examples of patterning devices comprise masks, programmable mirror arrays and programmable LCD panels. Any use of the terms "mask" or "reticle" herein can be considered as synonymous with the more general term "patterning device". The term "patterning device" can also be interpreted as a device that stores data that describes a pattern in digital form, which is used for the control of the programmable pattern formation device.

[0017] The term "projection system" used herein should be interpreted as a broad term as encompassing any type of projection system, including refractive, reflective, catadioptric, magnetic, electromagnetic and electrostatic optical systems, or any combination thereof, as appropriate for the exposure radiation being used, or for other factors such as the use of an immersion liquid or the use of a vacuum. Any use of the term "projection lens" herein can be considered as synonymous with the more general term "projection system".

[0018] The lithographic apparatus can also be of a type that includes a substrate table, which is designed to hold a substrate in a fixed position with respect to the projection system, while an immersion liquid is provided in a reservoir, for example, a space, between the substrate table and the projection system. The reservoir can have an arbitrary shape, for example, without limitation, rectangular, oval, triangular, or even with a plurality of surfaces that are at an angle, to each other. Immersion liquids having higher refractive indices than air are commonly used as they allow for a higher numerical aperture to be used, which, allows for improved resolution. Immersion liquids can also be used to high numerical aperture projection systems other than those of the type described above.

[0019] In operation, the illuminator IL receives a radiation beam from a radiation source SO. The source and the lithographic apparatus can be separate entities, for example, when the source is an excimer laser. In such cases, the source is not considered to form part of the lithographic apparatus and the radiation beam is passed from the source SO to the illuminator IL with the aid of a beam delivery system BD including, for example, suitable directing mirrors and / or a beam expander. In other cases not specifically described herein, the source can be an integral part of the lithographic apparatus. The source SO and the illuminator IL, together with the beam delivery system BD if required, can be referred to as a radiation system.

[0020] The illuminator IL can include an adjuster AD for adjusting the angular intensity distribution of the radiation beam. Generally, at least the outer and / or inner radial extent of the luminous intensity distribution in a pupil plane of the illuminator can be adjusted.

[0021] A radiation beam B is incident on the patterning device MA, held on the patterning device support MT, and patterned by the patterning device. After passing through the patterning device (e.g., mask) MA, the radiation beam B passes through the projection system PS, which focuses the beam onto a target portion C of the substrate W. The substrate table WTa or WTb can be accurately moved by means of the second positioner PW and position sensor IF (e.g., an interferometer, a linear encoder, a 2-D encoder, or a capacitive sensor), so as to position different target portions C in the path of the radiation beam B. Similarly, the patterning device (e.g., mask) MA can be positioned relative to the path of the radiation beam B by means of the first positioner PM and another position sensor (not explicitly shown in the figure) after mechanical retrieval from the mask library, or during a scan. Figure 1 The other position sensor is not explicitly shown in the figure.

[0022] The patterning device (e.g., mask) MA can be aligned to the substrate W using mask alignment marks M1, M2 and substrate alignment marks P1, P2. While the substrate alignment marks (as illustrated) occupy dedicated target portions, these marks can be located in spaces between target portions (they are referred to as scribe-lane alignment marks). Similarly, in case more than one die is provided on the patterning device (e.g., mask) MA, mask alignment marks can be located between the dies. In addition to device features, smaller alignment marks can be included within the dies, in which case it is desirable that the marks are as small as possible and do not require any imaging or process conditions that are different from the adjacent features. An alignment system that detects the alignment marks is further described below.

[0023] The described apparatus can be used in various modes. In scan mode, during which a pattern imparted to the radiation beam is projected onto a target portion C, the patterning device support (e.g., mask table) MT and the substrate table WT are scanned synchronously in a sinusoidal pattern (i.e., a single dynamic exposure). The speed and direction of the substrate table WT relative to the patterning device support (e.g., mask table) MT can be determined by the magnification (reduction) and image reversal characteristics of the projection system PS. In scan 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, whereas the length of the scanning motion determines the height of the target portion (in the scanning direction). Other types of lithography apparatuses and modes of operation can also be possible. For example, a step-and-repeat mode is known. In so-called "maskless" lithography, a programmable patterning device is held static but has a varying pattern, and the substrate table WT is moved or scanned.

[0024] Combinations and / or variations on the above described modes of use or entirely different modes of use can also be employed.

[0025] The lithography apparatus LA is of the so-called twin- stage type, having two substrate tables WTa, WTb and two stations - an exposure station EXP and a measurement station MEA - between which the substrate tables can be exchanged. While one substrate on one substrate table is being exposed in the exposure station, the other substrate can be loaded onto the other substrate table at the measurement station and various preparatory steps performed. This results in a significant increase in throughput of the apparatus. The preparatory steps can include mapping the surface height profile of the substrate using a level sensor LS and measuring the position of alignment marks on the substrate using an alignment sensor AS. If the position sensor IF is unable to measure the position of the substrate table while it is at the measurement station as well as at the exposure station, a second position sensor can be provided to enable the position of the substrate table relative to the reference frame RF to be tracked at both stations. Other arrangements are also known and can be used instead of the twin-stage arrangement shown. For example, other lithography apparatus are known which provide a substrate table and a measurement table which are docked together when performing preparatory measurements and then undocked while the substrate table is being exposed.

[0026] Figure 2 The steps of exposing a target portion (e.g. a die) on a substrate W in a twin-stage apparatus of the type shown in Figure 1 are shown. The left-hand side within the dashed box are steps performed at the measurement station MEA, while the right-hand side shows steps performed at the exposure station EXP. At times, one of the substrate tables WTa, WTb will be at the exposure station, while the other of the substrate tables WTa, WTb is at the measurement station, as described above. For the purposes of the description, it is assumed that the substrate W has already been loaded into the exposure station. At step 200, a new substrate W' is loaded into the apparatus by means not shown. Both substrates are processed in parallel to increase the throughput of the lithography apparatus.

[0027] Referring first to the newly loaded substrate W', this can be a substrate which has not previously been processed, prepared with new photoresist for a first exposure in the apparatus. However, typically, the lithography process described will be only one step in a series of exposure and processing steps, so the substrate W' will already have been through the apparatus and / or other lithography apparatus several times, and can also have undergone subsequent processes. In particular, for the problem of improving overlay performance, the goal is to ensure that the new pattern is correctly applied to the correct position on a substrate which has already undergone one or more cycles of patterning and processing. These processing steps will gradually introduce distortions in the substrate, so that the distortions must be measured and corrected to achieve satisfactory overlay performance.

[0028] As just mentioned, previous and / or subsequent patterning steps can be performed in other lithography apparatuses, and even in different types of lithography apparatuses. For example, some layers in a device manufacturing process for which the parameters such as resolution and overlay are of high importance can be performed in more advanced lithography tools than others for which the requirements are lower. Thus, some layers can be exposed in an immersion lithography tool, while others are exposed in a "dry" tool. Some layers can be exposed in a tool working at DUV wavelengths, while others are exposed using EUV wavelength radiation.

[0029] At 202, the alignment measurements using the substrate marks P1 etc. and the image sensor (not shown) are used to measure and record the alignment of the substrate relative to the substrate table WT a / WT b. In addition, a number of alignment marks across the substrate W' will be measured using the alignment sensor AS. In one embodiment, these measurements are used to establish a "wafer grid" which very accurately maps the distribution of the marks across the substrate including any distortion relative to a nominal rectangular grid.

[0030] At step 204, the wafer height (Z) map relative to the X-Y position is also measured using the level sensor LS. Typically, the height map is only used to achieve accurate focus of the exposed pattern. The height map can additionally be used for other purposes.

[0031] When the substrate W' is loaded, the recipe data 206 is received which defines the exposure to be performed and also defines the nature of the wafer and the patterns previously formed and to be formed on the wafer. The measurements of the wafer position, wafer grid and height map performed at 202, 204 are added to these recipe data so that a complete set of recipe and measurement data 208 can be passed to the exposure station EXP. For example, the measurements of the alignment data include the X and Y positions of the alignment targets formed in a fixed or nominally fixed relationship to the product pattern which is the product of the lithography process. These alignment data obtained just prior to exposure are used to generate an alignment model with parameters which 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 interpolates between the measured positions. Conventional alignment models can include four, five or six parameters which together define the translation, rotation and scaling of an 'ideal' grid in different dimensions. Advanced models are known which use more parameters.

[0032] At 210, the wafers W' and W are exchanged so that the measured substrate W' becomes the substrate W which enters the exposure station EXP. At 212, the exposure is performed. The exposure can be performed using the recipe data 206 and the measurements of the wafer position, wafer grid and height map 208. The exposure can also be performed using the alignment model generated from the alignment data. Figure 1In the exemplary apparatus, such an exchange is performed by swapping the supports WTaand WTbwithin the apparatus, such that the substrates W, W' remain clamped and positioned accurately on these supports, to maintain the relative alignment between the substrate table and the substrate itself. Thus, once the table has been exchanged, the relative position between the projection system PS and the substrate table WTb(previously WTa) is determined, which is the parameter required to use the measurement information 202, 204 of the substrate W (previously W') in controlling the exposure step. At step 212, reticle alignment is performed using the reticle alignment marks Ml, M2. In steps 214, 216, 218, a scan motion and a pulse of radiation are applied at successive target positions across the substrate W, in order to complete the exposure of a plurality of patterns.

[0033] By using the alignment data and height map obtained at the measurement station in performing the exposure step, the patterns can be accurately aligned relative to the desired positions, in particular relative to features previously laid down on the same substrate. From the exposed patterns, the exposed substrate (now labeled W") is unloaded from the apparatus at step 220 to undergo etching or other processes.

[0034] The skilled person will appreciate that the above description is a simplified overview of many very specific steps involved in one example of a real manufacturing scenario. For example, using the same or different marks, there will typically be different phases of coarse and fine measurements, rather than measuring alignment in one process or step. Coarse and / or fine alignment measurement steps can be performed before or after height measurements, or interleaved.

[0035] In the manufacture of complex devices, many lithographic patterning steps are typically performed, shaping functional features in successive layers on the substrate. A key aspect of lithographic apparatus performance is therefore the ability to place the applied patterns correctly and accurately relative to features laid down in previous layers (by the same apparatus or a different lithographic apparatus). To this end, the substrate is provided with one or more sets of marks. Each mark is a structure whose position can be measured at a later time using a position sensor (typically an optical position sensor). The position sensor can be referred to as an "alignment sensor", and the marks can be referred to as "alignment marks".

[0036] A lithographic apparatus can include one or more (e.g., multiple) alignment sensors by which the position of alignment marks provided on a substrate can be accurately measured. Alignment (or position) sensors can use optical phenomena such as diffraction and interference to obtain position information from alignment marks formed on a substrate. An example of an alignment sensor used in current lithographic apparatuses is based on a self-referencing interferometer as described in US 6961116. Various enhancements and modifications to position sensors have been developed, for example as disclosed in US 2015261097 Al. All of these disclosures are incorporated herein by reference.

[0037] A mark or alignment mark can comprise a series of bars formed on or in a layer provided on a substrate or (directly) in a substrate. These bars can be regularly spaced apart and act as grating lines, such that the mark can be considered as a diffractive grating with a known spatial period (pitch). Depending on the orientation of these grating lines, the mark can be designed to allow measurement of position along an X-axis or along a Y-axis (which is oriented substantially perpendicular to the X-axis). A mark comprising bars arranged at +45 degrees and / or -45 degrees with respect to both the X-axis and the Y-axis allows X and Y measurements combined using the techniques described in US 2009 / 195768 A, incorporated herein by reference.

[0038] An alignment sensor optically scans each mark with a spot of radiation to obtain a periodically varying signal, such as a sinusoidal 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 is in turn fixed relative to a reference frame of the lithographic apparatus. So-called coarse marks and fine marks can be provided in relation to different (coarse and fine) mark sizes, so that the alignment sensor can distinguish between different periods of the periodic signal and the exact position (phase) within the period. Marks of different pitches can also be used for this purpose.

[0039] Measuring the position of a mark can also provide information about the deformation of the substrate on which the mark is provided, for example in the form of a wafer grid. Deformation of the substrate can occur, for example, by electrostatic clamping of the substrate to a substrate table, and / or heating of the substrate when the substrate is exposed to radiation.

[0040] Figure 3 is a schematic block diagram of an embodiment of a known alignment sensor AS. A radiation source RSO provides a beam of radiation RB of one or more wavelengths, which is turned into an illumination spot SP on a mark, such as a mark AM located on a substrate W, by turning optics. In this example, the turning optics comprise a spot mirror SM and an objective lens OL. The diameter of the illumination spot SP used to illuminate the mark AM can be slightly smaller than the width of the mark itself.

[0041] Radiation diffracted by the mark AM (in this example via the objective lens OL) is collimated into an information-bearing beam IB. The term "diffracted" is intended to include the complementary higher diffraction orders from the mark (e.g. +1 and -1 diffraction orders (marked +1, -1)), and optionally the zeroth order diffraction (which can be referred to as a reflection). A self-referencing interferometer SRI (e.g. of the type disclosed in US6961116 mentioned above) interferes the beam IB with itself, after which it is received by a photodetector PD. In the case that more than one wavelength is produced by the radiation source RSO, additional optics (not shown) can be included to provide separate beams. The photodetector can be a single element, or it can comprise multiple pixels, if desired. The photodetector can comprise a sensor array.

[0042] The turning optics, which in this example comprise a spot mirror SM, can 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 essential for the measurement, but improves the signal to noise ratio).

[0043] The SRI intensity signal SSI is provided to a processing unit PU. By a combination of optical processing in the self-referencing interferometer SRI and computational processing in the unit PU, values of the X and Y positions on the substrate relative to a reference frame are output.

[0044] A single measurement of the type shown fixes the position of the mark only to within a certain range corresponding to one period of the mark. A coarse measurement technique (i.e. a more coarse measurement technique) is used in conjunction with this to identify which period of the sinusoidal wave is the one that includes the mark position. Regardless of the material from which the mark is made and the material on and / or under which it is provided, the same process is repeated at different wavelengths, at a coarser level and / or at a finer level, to obtain increased accuracy and / or robust detection of the mark. Improvements are disclosed below to perform and process such multi-wavelength measurements.

[0045] It is known that alignment marks (and other metrology targets) can be distorted due to process variation (PV) from substrate to substrate, resulting in overlay errors on the product. The term "mark" will be used herein to refer to any structure that can be measured in the methods disclosed herein; such structures can include alignment marks formed for alignment purposes, other metrology marks or targets formed for metrology purposes, and / or product structures that can be measured to obtain metrology and / or position values.

[0046] In the context of wafer alignment, concepts such as OCW (optimal color weighting) and related OCIW (optimal color and intensity weighting) are used or have been proposed to correct for mark positions (e.g. mark asymmetry, i.e. asymmetry in the alignment mark, leading to position errors or offsets) for such process variations. These concepts are described in more detail in the publications US2019 / 0094721, WO2017032534A2, US2020 / 0272061A1 and US2020 / 0081356A1, all of which publications are incorporated herein by reference. Another concept includes MCLR (multi-color lowest residual) described in more detail in PCT publication WO2022184405A1, which PCT publication is incorporated herein by reference.

[0047] measured (e.g. alignment and / or phase) data Δ MEAS (ω) will include a component due to process variations (e.g. mark asymmetry or mark deformation) Δ MD (ω) and a desired wafer deformation component Δ WD (i.e. the desired position values or first parameter values) (e.g. the sum of). The process variation component shows a variation between colors (i.e. color dependency, i.e. angular frequency dependency), while the desired wafer deformation component Δ WD does not have this dependency (at least for positive ω). The definition of the angular frequency ω is given below in the description of the Figure 4 attached figures.

[0048] To solve this problem, many alignment sensors are provided with a functionality to measure each alignment mark using a plurality of different measurement conditions (e.g. combinations of wavelength and polarization; note that throughout this specification “color” will be used as a short hand for the measurement condition, i.e. the wavelength and polarization combination). In a more basic technique, one or more of the better performing measurements and / or an average of these per color measurements are used to determine the position of the alignment. In OCW, a per color weighting for the measurement data (e.g. alignment data) can be determined, said weighting including (e.g. trained) positive and negative weights that minimize the influence of process variations on the parameter of interest such as overlay (or e.g. any other placement parameter such as edge placement error). The sum of the weights should be one to keep the alignment signal.

[0049] The OCIW is an improvement over the OCW in which the metrology tool / alignment sensor has additional intensity channel functionality that can separately measure the intensity from two complementary diffraction orders (e.g., the +1 and -1 orders, but higher order pairs are theoretically possible as well) from each mark. In the OCIW, additional intensity weighting is determined for intensity imbalance signals (e.g., imbalance, such as difference or ratio, based on these +1 and -1 diffraction orders). In the OCIW, the color weighting and intensity weighting can be trained together in order to again minimize the impact of process variations on the parameter of interest, such as overlay.

[0050] The primary physical mechanism of the OCW and OCIW is that the weighting produces (near) orthogonality to the process variations observed in the training data.

[0051] Another weighting technique can include weighting based on a “wafer quality” WQ or other mark reflectivity metric (e.g., a (normalized) reflectivity of a mark). The term wafer quality or WQ will be used herein to refer to any such measurement of a mark reflectivity (or signal amplitude) from a target. In WQ weighting, only positive weights are used, and these weights do not require training. However, these weights are determined for each alignment mark, e.g., from a (normalized) reflectivity of that alignment mark. The primary physical mechanism of WQ weighting is that the weighting of target reflectivity improves convergence of the target asymmetry dispersion sum rule(s). Other metrics that can be used include signal intensity metrics (e.g., intensity or amplitude metrics) and / or measurement noise metrics.

[0052] A problem with current OCW and OCIW weighting is that it is not adaptive, meaning that the algorithm itself cannot adapt in real-time to (new) process variations that are not present in the training data. Another problem is that negative weights cause an increase in the weight vector length (2-norm of the weights) compared to the best color or average color recipe, which can cause measurement noise to be amplified. A problem with the WQ weighting algorithm is that it does not point to the geometry point of interest for the customer, but rather to the optical density centroid of the deformed grating. And this optical density centroid of the deformed grating still depends on the mark deformation.

[0053] Accordingly, a method of OCIW including complex weighting is proposed, in which the weights applied are complex in that they include a modulus component and an (e.g., trained) argument component. This allows a first principles physically supported weighting scheme for first measurement data (e.g., phase data or alignment data) and second measurement data (e.g., intensity imbalance data), in which the modulus of the complex weight includes a reflectivity metric, WQ, signal intensity metric, and / or measurement noise metric, and the argument of the complex weight is a trained component.

[0054] The advantage of complex weights over positive and negative weights is that it allows for a reduction in the number of parameters (e.g. weights) to train compared to current OC(I)W techniques, which can reduce the necessary amount of training data.

[0055] The fact that the modulus of the complex weight is equal to the WQ of each mark means that the applied weighting is adaptive, which is expected to be beneficial when process variations occur that are not present in the training data (i.e. it improves extrapolation behavior and / or generalization performance).

[0056] The argument of the complex weight is the trained fact, allowing the algorithm to be trained to determine the specific point or location of interest to apply (i.e. the location of interest from the perspective of the overlay), rather than the (mark deformation dependent) optical density centroid of the deformed grating. The same trained weight can be used to apply weighting to both color and intensity (intensity asymmetry indicator).

[0057] Figure 4 An exemplary alignment mark AM is shown that includes a grating deformation and pitch P, which uses an electric field The described alignment illumination to measure, and the captured diffraction orders are described by electric fields 、 wherein: wherein I + , I - are the measured intensities of each diffraction order of a complementary pair (e.g. pair of +1 and -1), φ + , φ - are the phases of these orders, ω = 2πc / λ, λ is the measurement wavelength, and c is the speed of light.

[0058] The alignment data Δ MEAS (ω) is related to the measured phase difference, for example as measured by the phase channel of the alignment sensor:

[0059] In addition, an intensity asymmetry indicator a(ω) can be measured, for example in the intensity channel of the alignment sensor: where P > 0 denotes the (apparent) grating period, and n is a positive integer indicating the diffraction order. It can be understood that the intensity asymmetry indicator a(ω) has the same units as the measured position Δ MEAS (ω).

[0060] The dependence on the angular frequency ω stems from the Fourier transform rather than originating from illumination with a specific wavelength; thus, negative angular frequencies ω < 0 need to be considered. It can be shown that reversing the direction of propagation has no effect on the observed intensity, thus and This means and This in turn means that the real-valued electric field , and the wafer deformation Δ WD has some dependence on the angular frequency ω (i.e., .

[0061] It has been proposed to apply (e.g., Kramers-Kronig) dispersion relations to analyze the measured data. In the Hilbert transform notation such a dispersion relation can include an asymmetry relation: and its inverse: or, in an alternative variant, based on the product formula : and its inverse: and thus: .

[0062] An OCIW example based on dispersion physics can be constructed. If F(ω) and G(ω) are square-integrable, then . Thus, if (weighting) and , then based on : Assuming, and solving for Δ WD : .

[0063] However, while this dispersion physics-based approach has a sound theoretical basis, the requirements for performing a Hilbert transform make this approach difficult to implement in practice. This is because the finite wavelength range and sampling density used in the alignment measurement (e.g., typically spanning 12 wavelengths across a single octave), whereas Kramers-Kronig type dispersion analysis requires a set of wavelengths 0 < λ < ∞ as input (or at least an approximation of multiple octaves). The existing OCIW algorithm addresses this problem by, for example, training the results of a Hilbert transform. However, an improved approach will be described herein that removes the need to perform any Hilbert transform and thus eliminates the problem of the finite wavelength range of the measured radiation.

[0064] The proposed approach uses the concept of complex weighting. The complex weight is defined as and note that if then Then: if then

[0065] The complex weight is redefined as and note that the inverse Fourier transform of W(ω) is the causal function Since the Hilbert transform is a linear transform, it follows that if then .

[0066] It is proposed herein that, in embodiments, the complex weight is defined as where θ(ω) > 0. It can be appreciated that the standard θ(ω) > 0 enforces that the inverse Fourier transform of W(ω) is causal. This standard can be thought of as a generalization of real-valued (i.e., positive, zero and / or negative) weighting.

[0067] Because wafer quality is the measured quantity, wafer quality has finite energy and causal inverse Fourier transform. Thus, in embodiments, the weighted modulus r(ω) can describe wafer quality or reflectivity metrics (per mark or per measurement location), while only the argument θ(ω) is trained. As previously described, training can be performed using, for example, first data (e.g., alignment data) and corresponding reference data (e.g., overlay data) measured from training wafers. The concept is not limited to alignment data color weighting, and thus the first data can be suitable for the application; for example, for weighted overlay data (e.g., as measured by scatterometers), the first data can be overlay data, where the reference data is reference overlay data (e.g., as measured using scanning electron microscopes / e-beam tools).

[0068] For a first parameter value or desired (wafer deformation component) position value Δ WD , solve where θ(ω) ≥ 0, to obtain: .

[0069] Complex weighting can be physically interpreted as follows. Consider that: If θ(ω) ≥ 0, then and are causal. Thus, is also causal, because the convolution of two causal functions is causal. Thus, complex weighting can be interpreted as the average color of The product of the complex weight can be thought of as a conformal mapping function.

[0070] An alternative and more convenient statement of the formula for a first parameter value or desired (wafer deformation component) position value Δ WD may include: and thus: where, as previously described, the training argument or polar angle θ(ω) and r(ω) can be wafer quality or reflectivity metrics WQ(ω). Thus, the first parameter value can be determined from a weighted first measurement data (or a weighted derivative in frequency (or wavelength) of the first measurement data) and a weighted derivative in frequency (or wavelength) of the second measurement data.

[0071] Thus, any of the equations for Δ WD above can be used to determine a first parameter value from a first measurement data or phase measurement data Δ MEAS(ω) (e.g., with values for each mark and each measurement condition), second measurement data or intensity imbalance measurement data a(ω) (e.g., again with values for each mark and each measurement condition), wafer quality / reflectivity metric data WQ(ω), and a trained polar angle θ(ω) to obtain a corrected position Δ (e.g., for each mark) WD .

[0072] The training can be substantially the same as current OCW and OCIW techniques, e.g., it can include finding a weighting that maximizes performance of the reference data. This can include finding a weighting that minimizes (e.g., de-corrected) overlay (reference data) when applied to corresponding first training data or phase training data Δ MEAS (ω) and second training data or intensity training data a(ω). The training data can be obtained from training wafers and / or actual production wafers.

[0073] In an alternative, the training can determine a weighting such that the weighting maximizes performance of the first parameter value (e.g., corrected position or overlay), i.e., performance of the first parameter is the goal. This can cover both training and / or evaluation (i.e., after training) scenarios. Ultimately, the training goal represents only evaluation (i.e., after training) performance.

[0074] In another embodiment, it can be appreciated that since the Hilbert transform is angular frequency shift invariant, the above presented algorithm can also be angular frequency shift invariant. Thus, the trained polar angle θ(ω) can be selected to be angular frequency shift invariant; i.e., such that θ(ω) = θ. In an embodiment, this polar angle can be ±45°, as it can prove advantageous in terms of measurement noise, signal energy, and geometric invariance. This results in:

[0075] Thus, in this embodiment, the magnitude of the polar angle is fixed and does not need to be trained; only the sign (i.e., whether the sum or difference of the phase measurement data and intensity imbalance measurement data is used to determine the wafer deformation Δ WD ) is trained. Thus, the sign of each mark selection can be trained (or otherwise determined, e.g., using the dispersion sum rule) and used in combination with wafer quality (e.g., for r(ω) or r(λ)) to determine the weighting. Thus, the argument component of the weighting in this embodiment can include a +1 or -1 binary weighting applied to the second measurement data or intensity imbalance measurement data a(ω).

[0076] Thus, the proposed method addresses the inaccuracy of the Hilbert transform when performing measurements at only a limited wavelength by introducing complex weighting. A first-principle, dispersion- physics-derived algorithm prototype is described that makes the OCIW adaptive, includes an intensity channel in the WQ weighting, and includes negative weights in the WQ weighting.

[0077] While specific embodiments of the application have been described above, it will be appreciated that the application can be practiced otherwise than as described.

[0078] Although the use of embodiments of the application can have been specifically referred to above in the context of optical lithography, it will be appreciated that the application is not limited to optical lithography and that the application can be used in other applications such as imprint lithography where the context allows. In imprint lithography, the topography of the patterning device defines the pattern formed on the substrate. The topography of the patterning device can be pressed into a resist layer provided to the substrate and the resist is then solidified by the application of electromagnetic radiation, heat, pressure or a combination thereof. After the resist is solidified, the patterning device is removed from the resist, leaving the pattern therein.

[0079] The terms “radiation” and “beam” used herein encompass all types of electromagnetic radiation, including ultraviolet (UV) radiation (e.g. having a wavelength of or about 365, 355, 248, 193, 157 or 126 nm) and extreme ultra violet (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.

[0080] The term “lens”, where the context allows, can refer to any one or combination of various types of optical components, including refractive, reflective, magnetic, electromagnetic, and electrostatic optical components. Reflective components can be used in devices operating in the UV and / or EUV range.

[0081] Aspects of the application are set out in the following clauses. 1. A metrology method relating to measurement of a structure on a substrate, the structure undergoing process variation, the method comprising: obtaining first measurement data relating to a phase of measurement radiation that has been scattered from one or more marks and relating to a plurality of measurement conditions; obtaining second measurement data relating to an intensity of the measurement radiation and relating to the plurality of measurement conditions; obtaining a weighting of the first measurement data and the second measurement data, the weighting comprising a modulus component relating to a modulus of a complex weight and an argument component relating to an argument of the complex weight; and determining a first parameter value of a first parameter from the first measurement data and the second measurement data weighted by the weighting. 2. The method of clause 1, wherein the first measurement data comprises alignment data, and the first parameter value is a position value. 3. The method of clause 1, wherein the first measurement data comprises overlay data, and the first parameter value is an overlay value. 4. The method of any preceding clause, wherein the second measurement data comprises intensity imbalance measurement data. 5. The method of any preceding clause, wherein the modulus component comprises one or more of: a reflectivity metric for each of the marks, a wafer quality metric, a signal strength metric, and / or a measurement noise metric. 6. The method of any preceding clause, wherein the first parameter value is determined from weighted first measurement data and weighted second measurement data, the weighted second measurement data comprising a weighted derivative in frequency or wavelength of the second measurement data. 7. The method of clause 6, wherein the weighted first measurement data comprises a weighted derivative in frequency or wavelength of the first measurement data. 8. The method of clause 6 or 7, wherein the first parameter value is determined from a difference between the weighted first measurement data and the weighted second measurement data. 9. The method of any of clauses 6 to 8, wherein the weighted first measurement data is weighted by a real part of the complex weight, and the weighted second measurement data is weighted by an imaginary part of the complex weight. 10. The method of any preceding clause, wherein a real part of the complex weight comprises a product of the modulus component and a first function of the argument component, and an imaginary part of the complex weight comprises a product of the modulus component and a second function of the argument component; and wherein the first function and the second function comprise periodic functions having a respective difference in argument of π / 2. 11. The method of any of clauses 1 to 6, wherein the argument component is substantially constant in angular frequency. 12. The method of clause 11, wherein the argument describes a polar angle of +45° or -45°. 13. The method of clause 11 or 12, wherein the argument component comprises a +1 or -1 binary weighting of the second measurement data. 14. The method of any of clauses 11 to 13, wherein the determining a first parameter value comprises determining the first parameter from a derivative in frequency or wavelength of a product of the modulus component and a sum of the first measurement data and weighted second measurement data. 15. The method of any preceding clause, wherein said determining parameter values comprises normalizing said first parameter values. 16. The method of any preceding clause, wherein, for each mark, said weighting applies a respective weight to said first measurement data for each measurement condition. 17. The method of any preceding clause, wherein said argument component has been previously trained in a training phase. 18. The method of any of clauses 1 to 16, wherein a modulus of said argument component has been previously trained in a training phase, and a sign of said argument component is determined after measuring said second measurement data. 19. The method of any preceding clause, comprising performing said training phase, said training phase comprising: obtaining first training data of a same data type as said first measurement data; obtaining second training data of a same data type as said second measurement data; obtaining reference data corresponding to said first training data and said second training data; and determining said argument component such that said weighting maximizes a performance of any of: said first parameter values; or said reference data when applied to said first training data and said second training data. 20. The method of clause 19, wherein said reference data comprises overlap data. 21. The method of clause 20, wherein said overlap data is processed to remove any corrections applied in accordance with said first measurement data. 22. The method of any preceding clause, comprising performing a subsequent exposure on said substrate in accordance with said first parameter values. 23. A computer program comprising program instructions operable to perform the method of any of clauses 1 to 21 when run on a suitable device. 24. A non-transitory computer program carrier comprising the computer program of clause 23. 25. A processing system comprising a processor and a storage device, said storage device comprising the computer program of clause 23. 26. An alignment sensor operable to perform the method of any of clauses 1 to 21. 27. A lithographic apparatus comprising: a patterning device support to support a patterning device; a substrate support to support a substrate; and an alignment sensor of clause 26.

[0082] The breadth and scope of the present application should not be limited to any of the above-described exemplary embodiments, but should be defined only in accordance with the following claims and their equivalents.

Claims

1. A metrology method relating to measurement of a structure on a substrate, the structure being subject to process variation, the method comprising: obtaining first measurement data relating to phase of measurement radiation that has been scattered from one or more marks, and relating to a plurality of measurement conditions; obtaining second measurement data relating to intensity of the measurement radiation and relating to the plurality of measurement conditions; obtaining a weighting of the first measurement data and the second measurement data, the weighting comprising a modulus component relating to modulus of a complex weight and an argument component relating to argument of the complex weight; and determining a first parameter value of a first parameter from the first measurement data and the second measurement data weighted by the weighting.

2. The method of claim 1, wherein the first measurement data comprises alignment data, and the first parameter value is a position value.

3. The method of claim 1, wherein the first measurement data comprises overlay data, and the first parameter value is an overlay value.

4. The method of any preceding claim, wherein the second measurement data comprises intensity imbalance measurement data.

5. The method of any preceding claim, wherein the modulus component comprises one or more of: reflectivity metric of each of the marks, wafer quality metric, signal strength metric and / or measurement noise metric.

6. The method of any preceding claim, wherein the first parameter value is determined from weighted first measurement data and weighted second measurement data, the weighted second measurement data comprising a weighted derivative in frequency or wavelength of the second measurement data.

7. The method of claim 6, wherein the weighted first measurement data comprises a weighted derivative in frequency or wavelength of the first measurement data.

8. The method of claim 6 or 7, wherein the first parameter value is determined from a difference of the weighted first measurement data and the weighted second measurement data.

9. The method of any of claims 6 to 8, wherein the weighted first measurement data is weighted by a real part of the complex weight, and the weighted second measurement data is weighted by an imaginary part of the complex weight.

10. The method of any one of the preceding claims, wherein a real part of the complex weight comprises a product of the modulus component and a first function of the argument component, and an imaginary part of the complex weight comprises a product of the modulus component and a second function of the argument component; and wherein, the first function and the second function comprising periodic functions having a respective difference in argument of n / 2.

11. The method of any of claims 1 to 6, wherein the argument component is substantially constant in angular frequency.

12. The method of any one of the preceding claims, wherein the determining parameter values comprises: normalising the first parameter value.

13. The method of any preceding claim, wherein, for each mark, the weighting applies a respective weight to the first measurement data for each measurement condition.

14. The method of any preceding claim, comprising performing the training phase, the training phase comprising: obtaining first training data of the same data type as the first measurement data; obtaining second training data of the same data type as the second measurement data; obtaining reference data corresponding to the first training data and the second training data; and determining the argument component such that the weighting maximises performance of any one of: the first parameter value; or the reference data when applied to the first training data and the second training data.

15. An alignment sensor operable to perform the method of any preceding claim.

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