Measurement method and associated measurement device

Abstract

A method for determining a parameter of interest related to at least one target on a substrate is disclosed. The method comprises: obtaining measurement data comprising at least one asymmetry signal, the at least one asymmetry signal comprising a difference or imbalance of a measurement parameter from a target; obtaining a trained model that has been trained or configured to correlate the at least one asymmetry signal to a parameter of interest, the trained model comprising at least one proxy for at least one interfering component of the at least one asymmetry signal; and inferring the parameter of interest for the at least one target from the at least one asymmetry signal using a trained model.

Description

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims priority to EP application 22155715.0 filed on February 8, 2022, the entire contents of which are incorporated herein by reference. Technical Field

[0003] The present invention relates to a photolithography process, and more particularly to a method for measuring parameters of a photolithography process. Background Art

[0004] A lithographic apparatus is a machine that applies a desired pattern to a substrate (usually a target portion of a substrate). A lithographic apparatus can be used to manufacture integrated circuits (ICs). In this case, a pattern forming device (also referred to as a mask or reticle) can be used to generate a circuit pattern to be formed on a single layer of an IC. The pattern can be transferred to a target portion (e.g., a portion including one or more dies) on a substrate (e.g., a silicon wafer). The transfer of the pattern is usually by imaging onto a layer of radiation-sensitive material (resist) provided on the substrate. Typically, a single substrate will contain a network of adjacent target portions that are continuously patterned. In the lithographic process, it is desirable to frequently measure the created structure, for example, for process control and verification. Various tools are known for making such measurements, including scanning electron microscopes, which are typically used to measure critical dimensions (CDs), and specialized tools for measuring overlay (a measure of the accuracy of the alignment of two layers in a device). Overlay can be described by the degree of misalignment between two layers, for example, a 1 nm overlay mentioned as measured can describe a situation where the two layers are misaligned by 1 nm.

[0005] Recently, various forms of scatterometers have been developed for use in the field of photolithography. These devices direct a beam of radiation toward a target and measure one or more properties of the scattered radiation (e.g., intensity versus wavelength at a single reflection angle; intensity versus reflection angle at one or more wavelengths; or polarization versus reflection angle) to obtain a "spectrum" from which properties of interest of the target can be determined. Determination of the properties of interest can be performed by a variety of techniques: for example, reconstruction of the target by iterative methods such as rigorous coupled wave analysis or finite element methods; library searching; and principal component analysis.

[0006] The targets used by conventional scatterometers are relatively large, e.g. a 40 μm x 40 μm grating, while the spot produced by the measurement beam is smaller than the grating (i.e. the grating is underfilled). This simplifies the mathematical reconstruction of the target, since it can be considered infinite. However, in order to reduce the size of the targets, e.g. to 10 μm x 10 μm or less, e.g. in order to locate them in product features rather than in scribe lines, metrology methods have been proposed in which the grating is smaller than the measurement spot (i.e. the grating is overfilled). Typically, such targets are measured using a dark field scatterometry method, in which the zeroth order diffraction (corresponding to the specular reflection) is blocked and only the higher orders of diffraction are processed. Examples of dark field metrology methods can be found in international patent applications WO 2009 / 078708 and WO 2009 / 106279, the entire contents of which are hereby incorporated by reference. Patent publications US20110027704A, US20110043791A and US20120242970A describe further developments of the technology. US2010201963A1 and US2011102753A1 describe improvements to the device to increase throughput. The contents of all of these applications are also incorporated herein by reference. Diffraction-based overlay uses dark field detection of diffraction orders to enable overlay measurement of smaller targets. These targets may be smaller than the irradiation point and may be surrounded by product structures on the wafer. The target may include multiple gratings, which can be measured in one image.

[0007] There are several methods for overlay inference. A known method for determining overlay from metrology images such as those obtained using dark field methods, while making some correction for non-overlay asymmetry, is known as the A+ / A- regression method. The method includes measuring an offset target having two differently offset sub-targets using radiation having at least two different wavelengths, and plotting the intensity asymmetry from one of the sub-targets relative to the intensity asymmetry from the other of the sub-targets for each wavelength. A line with a slope indicative of overlay is produced through the regression of each data point.

[0008] It would be desirable to improve upon this known overlay inference method. Summary of the invention

[0009] In a first aspect, the present invention provides a method for determining a parameter of interest associated with at least one target on a substrate. The method comprises: obtaining measurement data including at least one asymmetry signal, the at least one asymmetry signal comprising a difference or imbalance in a measured parameter; obtaining a trained model that has been trained or configured to relate the at least one asymmetry signal to the parameter of interest, the trained model comprising at least one proxy for at least one interference component of the at least one asymmetry signal; and using the trained model to infer the parameter of interest for the at least one target from the at least one asymmetry signal.

[0010] In a second aspect, the present invention provides a method for training a model to relate an asymmetry signal to a parameter of interest, the model comprising at least one agent for at least one interference component of the asymmetry signal, the method comprising: obtaining training data comprising multiple training asymmetry signals associated with multiple training objectives; and training the model by optimizing corresponding training parameters for each of the at least one agent.

[0011] In a third aspect, the present invention provides a measurement device operable to perform the method of the first aspect or the second aspect.

[0012] In another aspect of the invention there is provided a computer program comprising program instructions operable, when run on a suitable apparatus, to perform the method of the first aspect.

[0013] Other features and advantages of the present invention and the structure and operation of various embodiments of the present invention will be described in detail below in conjunction with the accompanying drawings. It should be noted that the present invention is not limited to the specific embodiments described herein. Such embodiments are provided herein only for illustrative purposes. Based on the teachings contained herein, additional embodiments will be apparent to those skilled in the relevant art(s). BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Embodiments of the present invention will now be described, by way of example only, with reference to the accompanying drawings, in which:

[0015] Figure 1 A lithographic apparatus according to an embodiment of the present invention is shown;

[0016] Figure 2 A lithography cell or lithography cluster according to an embodiment of the present invention is shown;

[0017] Figure 3The invention comprises (a) a schematic diagram of a dark field scatterometer for measuring a target using a first pair of illumination apertures, (b) details of a diffraction spectrum of a target grating for a given illumination direction, (c) a second pair of illumination apertures that provides an additional illumination mode when performing diffraction-based overlay measurements using the scatterometer, and (d) a third pair of illumination apertures that combines the first and second pairs of apertures;

[0018] Figure 4 A plurality of grating targets of known form and the outlines of the measurement points on the substrate are shown;

[0019] Figure 5 Depicted in Figure 3 The scatterometer obtained Figure 4 An image of the target;

[0020] Figure 6 is a flow chart of (a) a training or calibration phase and (b) a generation or inference phase of a first embodiment of the present invention; and

[0021] Figure 7 Flowchart of (a) the training or calibration phase and (b) the generation or inference phase of the first embodiment of the present invention. DETAILED DESCRIPTION

[0022] Before describing the embodiments of the present invention in detail, an example environment in which the embodiments of the present invention can be implemented is introduced.

[0023] Figure 1 A lithographic apparatus LA is schematically shown. The apparatus comprises an illumination optical 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 table) 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, a substrate table (e.g. wafer stage) WT configured to hold a substrate (e.g. resist-coated wafer) W and connected to a second positioner PW configured to accurately position the substrate according to certain parameters, and a projection optical system (e.g. 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.

[0024] The illumination optics system may include various types of optical or non-optical components, such as refractive, reflective, magnetic, electromagnetic, electrostatic or other types of components, or any combination thereof, for directing, shaping or controlling the radiation.

[0025] The patterning device support 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 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 may be, for example, a frame or table that may be fixed or moved as desired. The patterning device support may ensure that the patterning device is in a desired position, for example, relative to a projection system. Any use of the term "reticle" or "mask" herein may be considered synonymous with the more general term "patterning device".

[0026] The term "patterning device" as used herein should be broadly interpreted as referring to any device that can be used to impart a pattern to a cross-section of a radiation beam, such as to create a pattern in a target portion of a 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 created in the target portion, such as an integrated circuit.

[0027] The patterning device may be transmissive or reflective. Examples of patterning devices include masks, programmable mirror arrays, and programmable LCD panels. Masks are well known in lithography and include mask types such as binary, alternating phase shift, and attenuated phase shift, as well as various hybrid mask types. An example of a programmable mirror array employs a matrix arrangement of small mirrors, each of which can be individually tilted to reflect an incoming radiation beam in different directions. The tilted mirrors impart a pattern in the radiation beam, which is reflected by the matrix of mirrors.

[0028] As shown here, the device is of the transmissive type (eg, using a transmissive mask). Alternatively, the device may be of the reflective type (eg, using a programmable mirror array of the type described above, or using a reflective mask).

[0029] The lithographic apparatus may also be of a type in which at least a portion of the substrate may be covered by a liquid having a relatively high refractive index (e.g., water) so as 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 between the mask and the projection system. Immersion techniques are well known in the art and are used to increase the numerical aperture of the projection system. The term "immersion" as used herein does not mean that the structure (such as the substrate) must be immersed in the liquid, but only means that the liquid is located between the projection system and the substrate during exposure.

[0030] refer to Figure 1, the illuminator IL receives a radiation beam from a radiation source SO. For example, when the source is an excimer laser, the source and the lithographic apparatus may be separate entities. In this case, the source is not considered to form part of the lithographic apparatus, the radiation beam being transferred from the source SO to the illuminator IL by means of a beam delivery system BD, which comprises, for example, suitable guide 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. The source SO and the illuminator IL, and if necessary, the beam delivery system BD, may be referred to as a radiation system.

[0031] The illuminator IL may include an adjuster AD for adjusting the angular intensity distribution of the radiation beam. Typically, at least the outer and / or inner radial extent of the intensity distribution in a pupil plane of the illuminator (commonly referred to as σ-outer and σ-inner, respectively) may be adjusted. Furthermore, the illuminator IL may include various other components, such as an integrator IN and a converger CO. The illuminator may be used to adjust the radiation beam so that its cross-section has a desired uniformity and intensity distribution.

[0032] The radiation beam B is incident on a patterning device (e.g. a mask) MA, which is held on a patterning device support (e.g. a mask table MT) and patterned by the patterning device. After passing through the patterning device (e.g. a mask) MA, the radiation beam B passes through a projection optical system PS, which focuses the beam onto a target portion C of the substrate W, thereby projecting an image of the pattern onto the target portion C. With the aid of a second positioner PW and a position sensor IF (e.g. an interferometer, a linear encoder, a 2-D encoder or a capacitive sensor), the substrate table WT 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.

[0033] The pattern forming device (e.g., mask) MA and substrate W can be aligned using mask alignment marks M1, M2 and substrate alignment marks P1, P2. Although the substrate alignment marks shown occupy dedicated target portions, they can be located in the space between target portions (these are called scribe lane alignment marks). Similarly, where multiple dies are provided on the pattern forming device (e.g., mask) MA, the mask alignment marks can be located between the dies. Small alignment marks can also be included within the die, located within the device features, in which case it is desirable that the marks be as small as possible and do not require imaging or process conditions that are different from adjacent features. The alignment system for detecting the alignment marks will be further described below.

[0034] The lithography apparatus LA in this example is a so-called dual-stage type, which has two substrate tables WTa, WTb and two stations (exposure station and measurement station), and the substrate table can be exchanged between the two stations. When 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 preparation steps can be performed. The preparation steps may include mapping the surface control of the substrate using a horizontal sensor LS and measuring the position of the alignment mark on the substrate using an alignment sensor AS. This makes it possible to greatly improve the throughput of the equipment.

[0035] The apparatus shown can be used in a variety of modes including, for example, step mode or scan mode.The construction and operation of lithographic apparatus are well known to those skilled in the art and no further description is required to understand the present invention.

[0036] like Figure 2 As shown, the lithography apparatus LA forms part of a lithography system, referred to as a lithography cell LC or a lithography cell or a lithography cluster. The lithography cell LC may also include devices for performing pre-exposure and post-exposure processes on a substrate. Typically, these devices include a spin coater SC for depositing a resist layer, a developer DE for developing the exposed resist, a cooling plate CH, and a baking plate BK. The substrate handler or robot RO picks up substrates from input / output ports I / O1, I / O2, moves them between different process devices, and then transfers them to the loading station LB of the lithography apparatus. These devices are generally collectively referred to as tracks, which are controlled by a track control unit TCU, which itself is controlled by a monitoring system SCS, which also controls the lithography apparatus via a lithography control unit LACU. Thus, different devices can be operated to maximize throughput and processing efficiency.

[0037] In order for the substrates exposed by the lithography equipment to be correctly and consistently exposed, it is necessary to inspect the exposed substrates to measure characteristics such as overlay errors between subsequent layers, line thickness, critical dimensions (CD), etc. Therefore, the manufacturing facility where the lithography unit LC is located also includes a measurement system MET, which receives part or all of the substrates W that have been processed in the lithography unit. The measurement results are provided directly or indirectly to the monitoring system SCS. If an error is detected, the exposure of subsequent substrates can be adjusted, especially if the inspection can be completed quickly and fast enough so that other substrates of the same batch still need to be exposed. In addition, the already exposed substrates can be stripped and reprocessed to improve the yield, or discarded to avoid further processing of substrates that are known to be faulty. In the case where only some target parts in the substrate are faulty, further exposure can be performed only on those good target parts.

[0038] In a metrology system MET, an inspection device is used to determine the properties of a substrate, in particular to determine how the properties of different substrates or different layers of the same substrate vary from layer to layer. The inspection device may be integrated into the lithographic apparatus LA or the lithographic cell LC, or may be a stand-alone device. To achieve the fastest measurement, it is desirable for the inspection device to measure the properties in the exposed resist layer immediately after exposure. However, the contrast of the latent image in the resist is very low - the difference in refractive index between the parts of the resist exposed to radiation and the parts not exposed to radiation is very small - and not all inspection devices have sufficient sensitivity to make useful measurements of the latent image. Therefore, the measurement can be made after a post-exposure bake step (PEB), which is usually the first step performed on the exposed substrate and increases the contrast between the exposed and unexposed parts of the resist. At this stage, the image in the resist may be referred to as a semi-latent image. Measurements can also be made on a developed resist image (when the exposed or unexposed parts of the resist have been removed), or after a pattern transfer step such as etching. The latter possibility limits the possibility of reworking defective substrates, but can still provide useful information.

[0039] Figure 3 (a) shows a measurement device. Figure 3(b) shows in more detail the target T and the diffracted rays of the measuring radiation used to illuminate the target. The metrology apparatus shown is of a type known as a dark field metrology apparatus. The metrology apparatus described here is purely exemplary and is used to explain dark field metrology. The metrology apparatus can be a stand-alone device or can be incorporated into the lithography apparatus LA (e.g., at a measurement station) or the lithography cell LC. The optical axis (which has multiple branches throughout the apparatus) is represented by the dashed line O. In the apparatus, light emitted by a source 11 (e.g., a xenon lamp) is directed onto the substrate W by an optical system (including lenses 12, 14 and an objective lens 16) via a beam splitter 15. These lenses are arranged in a double sequence of a 4F arrangement. Different lens arrangements can be used as long as it still provides an image of the substrate onto the detector and at the same time allows access to the intermediate pupil plane for spatial frequency filtering. Therefore, the angular range of radiation incident on the substrate can be selected by defining the spatial intensity distribution in a plane presenting the spatial spectrum of the substrate plane (here called the (conjugate) pupil plane). In particular, this can be achieved by inserting an aperture plate 13 of appropriate form between the lenses 12 and 14 in the plane of the back-projected image of the objective pupil plane. In the example shown, the aperture plate 13 has different forms, labeled 13N and 13S, allowing different illumination modes to be selected. The illumination system in this example forms an off-axis illumination mode. In a first illumination mode, the aperture plate 13N provides off-axis from a direction designated as "North", for descriptive purposes only. In a second illumination mode, an aperture plate 13S is used to provide similar illumination, but from the opposite direction labeled "South". By using different apertures, other illumination modes can be achieved. The rest of the pupil plane is desirably dark, because any unnecessary light outside the desired illumination mode will interfere with the desired measurement signal.

[0040] like Figure 3 As shown in (b), the target T is placed so that the substrate W is perpendicular to the optical axis O of the objective lens 16. The substrate W may be supported by a support (not shown). The rays of measurement radiation I impinge on the target T from an angle offset from the axis O, producing a zero-order ray (solid line 0) and two first-order rays (dash-dotted line +1 and dash-dotted line -1). It should be remembered that for a small overfilled target, these rays are only one of many parallel rays covering the substrate area (including the measurement target T and other features). Since the aperture in the plate 13 has a finite width (needed to allow a useful amount of light), the incident ray I will actually occupy a certain angle range, and the diffracted rays 0 and +1 / -1 will be somewhat scattered. According to the point spread function of the small target, each order +1 and -1 will be further distributed over a certain angle range, rather than a single ideal ray as shown. Note that the grating pitch and illumination angle of the target can be designed or adjusted so that the first-order rays entering the objective are closely aligned with the central optical axis. Figure 3 (a) and Figure 3The rays shown in (b) are slightly off-axis purely to make them easier to distinguish in the figure.

[0041] At least the 0th and +1st orders diffracted by the target T on the substrate W are collected by the objective lens 16 and directed back through the beam splitter 15. Figure 3 (a), the figure shows the first and second illumination modes, represented by designated diametrically opposed apertures marked as north (N) and south (S). When the incident ray I of the measurement radiation comes from the north side of the optical axis, that is, when the first illumination mode is applied using the aperture plate 13N, the +1 diffracted ray marked as +1 (N) enters the objective lens 16. In contrast, when the second illumination mode is applied using the aperture plate 13S, the -1 diffracted ray (marked as -1 (S)) enters the lens 16.

[0042] A second beam splitter 17 splits the diffracted beam into two measurement branches. In the first measurement branch, an optical system 18 forms a diffraction spectrum (pupil plane image) of the target on a first sensor 19 (e.g., a CCD or CMOS sensor) using the zero-order and first-order diffracted beams. Each diffraction order hits a different point on the sensor so that image processing can compare and contrast the diffraction orders. The pupil plane image captured by the sensor 19 can be used for focusing a metrology device and / or for normalizing the intensity measurement of the first-order beam. The pupil plane image can also be used for many measurement purposes, such as reconstruction.

[0043] In the second measurement branch, the optical systems 20, 22 form an image of the target T on a sensor 23 (e.g., a CCD or CMOS sensor). In the second measurement branch, an aperture stop 21 is provided in a plane conjugate to the pupil plane. The aperture stop 21 serves to block the zero-order diffraction beam so that the target image formed on the sensor 23 is formed only by the -1 or +1 first-order beam. The image captured by the sensors 19 and 23 is output to a processor PU which processes the image, the functionality of which depends on the specific type of measurement being performed. Note that the term "image" is used here in a broad sense. If only one of the -1 and +1 orders is present, no image of the grating lines is formed.

[0044] Figure 3The specific forms of aperture plate 13 and field stop 21 shown in are merely examples. In another embodiment of the invention, on-axis illumination of the target is used, and an aperture stop with an off-axis aperture is used to pass substantially only first-order diffracted light of the diffracted light to the sensor. In other examples, a two-quadrant aperture may be used. This enables simultaneous detection of positive and negative orders, as described in US2010201963A1 mentioned above. Embodiments with a wedge (segmented prism or other suitable element) in the detection branch can be used to separate the orders for spatial imaging in a single image, as described in US2011102753A1 mentioned above. In yet other embodiments, 2nd, 3rd and higher order beams ( Figure 3 In other embodiments, a segmented prism may be used instead of the aperture stop 21 to enable simultaneous capture of the +1 and -1 orders at spatially separated locations on the image sensor 23.

[0045] To adapt the measurement radiation to these different types of measurements, the aperture plate 13 may include a plurality of aperture patterns formed around a disk, which is rotated to put the desired pattern in place. Note that aperture plates 13N or 13S can only be used to measure gratings oriented in one direction (X or Y, depending on the setup). For measurements of orthogonal gratings, the target can be rotated 90° and 270°. Figure 3 (c) and Figure 3 (d) shows different aperture plates. The use of these aperture plates and many other variations and applications of the device are described in the above-mentioned previously published applications.

[0046] Figure 4Describe the overlay target or composite overlay target formed on the substrate according to known practice. The overlay target in this example includes four sub-targets (e.g., gratings) 32 to 35, which are closely positioned together so that they are all located in the measurement point 31 formed by the measurement radiation irradiation beam of the measurement device. Therefore, the four sub-overlay targets are irradiated simultaneously and imaged on the sensor 23 simultaneously. In an example dedicated to overlay measurement, the sub-targets 32 to 35 themselves are composite structures formed by overlay gratings, which are patterned in different layers of the semiconductor device formed on the substrate W. The sub-targets 32 to 35 can have overlay offsets with different biases to facilitate measuring the overlay between the layers of different parts of the composite sub-targets formed therein. The directions of the sub-targets 32 to 35 can also be different, as shown in the figure, so as to diffract the incident radiation in the X and Y directions. In one example, sub-targets 32 and 34 are X-direction sub-targets with two different biases (e.g., the biases are +d, -d, respectively). Sub-targets 33 and 35 are Y-direction sub-targets with two different offsets (e.g., offsets of +d and -d, respectively). Individual images of these sub-targets can be identified in the image captured by sensor 23. This is just one example of an overlay target. An overlay target may include more or less than 2 sub-targets in each direction.

[0047] Figure 5 Shows the use of Figure 3 In the device Figure 4 In the overlay target, use the Figure 3 An example of an image that the aperture plate 13NW or 13SE in (d) can form on and be detected by the sensor 23. While the pupil plane image sensor 19 cannot distinguish between different individual sub-targets 32 to 35, the image sensor 23 can. The shaded area 40 represents the area of ​​the image on the sensor where the illumination point 31 on the substrate is imaged into the corresponding circular area 41. Within this circular area 41, the rectangular areas 42-45 represent the images of the small overlay target sub-targets 32 to 35. If the overlay target is located in the product area, product features may also be visible at the periphery of this image area. The image processor and controller PU use pattern recognition to process these images to identify the individual images 42 to 45 of the sub-targets 32 to 35. In this way, the images do not have to be aligned very accurately at specific locations within the sensor frame, which greatly improves the throughput of the entire measurement device.

[0048] Once the individual images of the overlay target are identified, the intensity of these individual images can be measured, for example, by averaging or summing the intensity values ​​of selected pixels within the identified area. The intensity and / or other characteristics of the images can be compared to each other. The results can be combined to measure different parameters of the lithography process. Overlay performance is an important example of such a parameter.

[0049] For example, using the method described in the above-mentioned application US20110027704A, the overlay (i.e., undesired and unintentional overlay misalignment) between two layers within sub-targets 32 to 35 is measured. This method may be referred to as micro-diffraction based overlay (μDBO). The measurement may be made by overlay target asymmetry, such as by comparing the intensities in the +1 and -1 order dark field images (other complementary higher order intensities may be compared, e.g., +2 and -2 orders) to obtain a measure of intensity asymmetry.

[0050] There are several methods to perform overlay inference from such measurements, aiming to separate or isolate the desired overlay signal from other interfering contributions (e.g., non-overlay target asymmetry, etc.). These methods may vary depending on the data dimensions used in the model, the model itself, and / or the model / scheme setup. Many methods have been developed that use multiple wavelength data dimensions. Other methods use additional data dimensions, such as multiple target locations, to extract more information from the diverse inputs. These methods may also require conditions specific to the model / scheme setup, such as external reference data.

[0051] Current overlay inference methods, especially post-development inspection (ADI) (i.e., pre-etch inspection) overlay inference methods (e.g., compatible with faster metrology techniques such as dark field metrology), have many disadvantages, including:

[0052] • Overlay estimation models lack flexibility with respect to process variations during production.

[0053] • The estimated overlay (eg, symmetry and asymmetry) process variations lack accuracy and stability.

[0054] Inefficient use of existing signal dimensions in the data that provide the potential for more accurate overlay estimates.

[0055] In understanding the concepts disclosed herein, it should be recognized that the measured asymmetry signal A is a function of the overlay and any process variations:

[0056]

[0057] Where A is the measured asymmetry signal, OV is the unknown true overlay (parameter of interest), PA is the asymmetry process variation, and PS describes the symmetry process variation. These are geometrical properties: wavelength and polarization independent, and typically depend on the target position i on the wafer and the pixel position j in the captured image (or region of interest ROI). describes the sensitivity of the measured asymmetry to each unknown parameter and depends on wavelength and polarization. Thus, the first term describes the overlay signal component, the second term describes the asymmetric non-overlay signal contribution (first interfering component), and the third term describes the symmetric non-overlay signal component (second interfering component).

[0058] Examples of asymmetric process variations include, among others: differences in side wall angle dSWA (e.g., between two walls of a grating feature), (non-overlay) grating asymmetry, floor tilt. Examples of symmetric process variations include, among others: layer thickness variations, CD variations, grating imbalance GI, and symmetric SWA variations.

[0059] The intensity image can be decomposed into:

[0060] I=S+A

[0061] Where S is the symmetric part and A is the asymmetric part. The asymmetric part contains the overlay information. For an infinite grating pair, A(ov) is periodic with a pitch of P, so A(ov) can be written as:

[0062]

[0063] Using the atan approximation, we can simply take the first term of the above expression without expanding sin(x):

[0064]

[0065] In this formula, K is a measure of the sensitivity (Jacobian) of the intensity asymmetry component to overlay.

[0066] The measured asymmetry signal can be the intensity asymmetry of the complementary diffraction orders or the phase difference asymmetry from the complementary sub-target pair (“M pad” and “W pad”), depending on whether the metrology method is intensity-based (e.g., μDBO) or phase-based (e.g., continuous DBO or cDBO). Therefore, for intensity-based applications, A can be defined as and (Conveniently written as A ± =(I +1 -i -1 ) ±b ), where I +1 ,I +1 are the respective intensities of the +1 and -1 diffraction orders from each sub-target with respective biases +b, -b.

[0067] For phase-based applications, the asymmetry signal A can be defined as the phase difference between a diffraction order from the “M pad” and the corresponding diffraction order from the “W pad”, optionally averaging the two diffraction orders of a complementary pair of diffraction orders: For example, A = (φ M -φ W ) +1 +(φ M -φ W )-1 Among them (φ M -φ W ) +1 , (φ M -φ W )-1 is the phase difference measured between the "M pad" and the "W pad" of the +1 diffraction order and the -1 diffraction order, respectively. Therefore, it can be understood that the concepts described in this article are applicable to different types of asymmetry signals. The principles of cDBO are described in Matsunobu et al., Novel diffraction-based overlaymetrology utilizing phase-based overlay for improved robustness, Proc. SPIE11611, Metrology, Inspection, and Process Control for Semiconductor Manufacturing XXXV, 1161126 (22 February 2021), which is incorporated herein by reference.

[0068] Like the μDBO target, the cDBO target contains multiple pads or sub-targets (optional for each direction), each sub-target having overlapping gratings in the corresponding layer for which overlay values ​​need to be measured. Instead of having gratings of the same pitch in both layers like the μDBO target, the cDBO target includes sub-targets, each of which has gratings of different pitches in both layers. More specifically, a typical cDBO target includes an arrangement of two different types of sub-targets (e.g., for each direction): an "M pad" or "M sub-grating", in which the pitch of the bottom grating is smaller than that of the top grating, and a "W pad" or "W sub-grating", in which these gratings are inverted (i.e., they have the same pitch as the M pad, but the pitch of the top layer is larger).

[0069] Different example arrangements of cDBO targets are described in PCT application WO2021224009A1, which is incorporated herein by reference. The cDBO target may include at least one pair of similar target areas arranged so that the entire target arrangement, or at least the target areas for measurement in a single direction, are centrally symmetric together (i.e., if rotated 180 degrees, the arrangement is the same). Such an arrangement can help solve matching problems caused by distortions in the measurement tool optics. Typically, in order to infer overlay in cDBO, the target arrangement includes two (or more) sub-target clusters, each cluster including at least one M pad and one W pad in each direction (in some designs, pads can be shared between clusters). Therefore, each cluster can be used independently to infer overlay. However, in order to solve the matching problem, the overlay can be determined as the average of the calculated overlay for each cluster:

[0070]

[0071] Among them, c i is the i-th cluster, p1 and p2 are the grating pitches of the gratings in each layer.

[0072] In intensity-based applications, the measured symmetry signal can be determined as the sum of the intensities measured through the normal branch and the complementary branch, i.e., S ±b =(I +1 +I -1 ) ±b In phase-based applications such as cDBO measurements, the phase symmetry cannot be measured directly without a phase reference. However, in cDBO measurements, the amplitude is independent of the phase measurement and can therefore be accessed directly. Therefore, for cDBO applications, the symmetry signal can be defined as: S M,W =(a +1 +a -1 ) M,W . where a is the amplitude signal (the difference between the maximum and minimum intensity of each pad (M, W)).

[0073] Therefore, symmetric and asymmetric process variations each induce a corresponding component in the measurement signal. In order to achieve an accurate and reliable overlay inference, the sensitivity of the measurement signal to process variations should be suppressed. However, the information from a single measurement alone cannot distinguish overlay from other interfering contributions described by PA and PS. Moreover, process variations are highly stack- and application-dependent. Therefore, a more flexible model is needed.

[0074] This paper describes an improved overlay inference method (e.g., for ADI overlay) that improves the accuracy and robustness of inferences about symmetry and asymmetry process variations. One aspect of the proposal includes multidimensional regression that uses diversity in multiple information channels: e.g., intensity channel, e.g., related to some or all of: positive bias / W pad, negative bias / M pad, normal diffraction orders, complementary diffraction orders, different pixels within the ROI, measurement wavelength, target position on the wafer. This can most effectively exploit the diversity present in the information channels of the currently implemented measurement strategy and does not require additional metrology compared to current (e.g., μDBO / cDBO) methods.

[0075] Alternatively or additionally, another aspect of the proposed method is the use of a parameterized model that includes at least a symmetry proxy for at least symmetric process variations, and optional separate symmetry and asymmetry proxies for symmetric process variations and asymmetric process variations, respectively. This helps to make the overlay inference model more flexible. In addition, the inference method can be data-driven or training-based; the model parameters can be trained or calibrated based on available external reference data; or in a self-referenced embodiment, based on a known target bias (e.g., for μDBO applications). For a cDBO self-referenced embodiment, the model parameters can be trained or calibrated based on inferred equality from pairs of sub-target clusters.

[0076] Thus, a method for determining a parameter of interest (such as overlay) is described, the method comprising: obtaining an asymmetry signal (e.g., an asymmetry signal captured in an image plane, such as an intensity asymmetry and / or a phase difference asymmetry signal); obtaining a trained model that has been trained to associate the measurement signal with the parameter of interest, the parameter of interest involving at least one proxy for at least one interference component; and inferring the parameter of interest from the measurement signal using the trained model.

[0077] In one embodiment, the trained model has been trained to relate the asymmetry signal to a parameter of interest via at least two proxies, an asymmetry first proxy for asymmetric interference components and a symmetry proxy for symmetric interference components.The trained model may be a multidimensional regression model.

[0078] For intensity-based embodiments, such as μDBO, the method may include measuring the intensity asymmetry of the complementary diffraction orders from each offset subtarget, the intensity sum of the symmetry proxy, and the second-order intensity asymmetry of the asymmetry proxy. In cDBO applications, the phase difference between the M and W pads (e.g., averaged over complementary diffraction order pairs), amplitude symmetry, and at least one amplitude asymmetry may be measured.

[0079] A method of training the model is also disclosed to relate an asymmetry signal to a parameter of interest via at least one proxy, wherein the at least one proxy is for at least one interference component (optionally, at least an asymmetry first proxy for an asymmetric interference component, and a symmetry proxy for a symmetric interference component). In another embodiment, more than one asymmetry proxy may be defined. Training may use external training data (reference values ​​for the parameter of interest), or may be self-referenced by training on known properties of a target design (e.g., a target bias for μDBO and a target cluster for a centrally symmetric cDBO target).

[0080] This approach exploits the variation of available information channels in the measurement data (e.g., data obtained from dark field images). There are multiple information channels (data dimensions) in the measured dark field images obtained by, for example, μDBO or cDBO metrology. Exploiting this diversity, the proposed method aims to separate the true overlay signal from the interfering components. Furthermore, the proposed method aims to suppress the sensitivity to interfering process variations (e.g., symmetry and asymmetry) by combining multiple information channels (e.g., intensity or phase (optionally per pixel or image area), wavelength, and target position). In order to effectively and efficiently incorporate additional dimensions, the overlay estimation problem can be formulated as a multidimensional regression problem.

[0081] In order to suppress the effects of process variations, a data-driven approach is proposed to learn the sensitivity and amplitude of process variations. This can be achieved by parameterizing the overlay inference model with the sensitivity to process variations. The exact values ​​and types of symmetric and asymmetric process variations are unknown, and direct measurement is impossible or impractical. For this reason, in one embodiment, it is proposed to define a symmetry proxy P and at least one asymmetry proxy G for these variations based on measured data. If these overlays (or derived overlay parameters v) with programmed or known overlays are used, the overlay parameters v ± ), then the training parameters M and N associated with the agent on the training target can be calibrated or trained and the learned model applied to the production target. Therefore, in an embodiment based on external reference strength (μDBO) (i.e., where known reference overlay values ​​are available for labeling training data), for positive and negative bias target pads (sub-targets) +b and –b, the model can take the following form:

[0082] v -b,i =([1P +b,i ]M +b +[1G i T ]N +b )ΔI +b,i

[0083] v -b,i =([1P -b,i ]M -b +[1G i T ]N -b )ΔI -b,i

[0084] This can be expressed more conveniently as:

[0085] v ±b，i =([1P ±b，i ]M ±b +[1G i T ]N ±b )ΔI±b，i (1)

[0086] For example, depending on whether a sinusoidal or linear overlay transform is used, the overlay parameter v ±b，i Can take one of the following forms:

[0087] or

[0088] where ov is the real envelop. Note that bold lowercase letters denote vectors, bold uppercase letters denote matrices, and plain letters denote scalars.

[0089] The training or calibration of the model involves the training of the parameters M ±b and N ±b Perform the following minimization:

[0090]

[0091] in: is the measured intensity asymmetry, is a symmetry proxy for changes in symmetry processes, is an asymmetric proxy for changes in the asymmetric process. The training parameters have dimensions N λ is the number of measured wavelengths, N t is the number of target locations, N p is the number of pixels (if a single intensity value is used for each sub-target, it can be treated as a single pixel, e.g. averaging over the ROI, as is currently done in μDBO / cDBO). This can be conveniently expressed as:

[0092]

[0093] in Note that the ±b notation describes two biases, so minimization consists of minimizing a pair of functions: one for the +b bias and one for the -b bias.

[0094] In one embodiment, the symmetry proxy may include the sum of measurements (e.g., intensities or phase differences) of a pair of complementary diffraction orders. In one embodiment, the asymmetry proxy may include a second order measurement difference comprising the difference of a first measurement difference of a corresponding diffraction order (e.g., normal or +1 order) from each of the first biased (or M) subtarget and the second biased (or W) subtarget and a second measurement difference of a corresponding diffraction order (e.g., complementary or -1 order) from the first biased (or M) subtarget and the second biased (or W) subtarget; for example, using the intensity example:

[0095]

[0096] Once training is complete, the training parameters N ±b and N ±b can be used to measure the asymmetry signal ΔI ±b，i Inferred Overlay v ±，i ΔI ±b，i :

[0097]

[0098] The actual true engraving ov for each target i i This can be done by pairing two values: +，i , v -，i Perform the inverse transform and take the average of these values ​​to determine:

[0099]

[0100] For the cDBO embodiment, the overlay equation can be defined as:

[0101]

[0102] In this cDBO embodiment, agents can be defined independently for each cluster, as shown below: c and G c shown.

[0103] Furthermore, since the phase difference between the M and W pads is measured as well as the amplitude of each pad, one or both of two different asymmetry proxies can be defined:

[0104]

[0105] and / or

[0106]

[0107] In which a M / W =(I max -I min ) M / W .

[0108] In embodiments with three (or more) agents, additional corresponding training parameters need to be defined, e.g., a third amplitude / sensitivity matrix, e.g. Multiple symmetry and / or asymmetry agents may be defined. In such an embodiment, each agent may include variables associated with a particular type of process variation. For example, a three agent embodiment may include a first (symmetry) agent associated with a symmetrical process variation, a second (asymmetry) agent associated with, for example, dSWA, and a third (asymmetry) agent associated with, for example, floor tilt. In this way, the contribution of each process variation to the overlay signal may be better distinguished, thereby defining a better model to extract / suppress the effects of the overlay signal. Since amplitude and phase measurements are accessible in cDBO, there are more signal dimensions to identify relevant agents. However, additional (e.g., more than two) agents may also be defined for μDBO in general.

[0109] The model disclosed herein can be derived as follows (this derivation is provided for the μDBO example, although the concepts are generally similar for cDBO). For a single pixel, a single wavelength λ, and a single target location on the wafer, and assuming a 2-offset grating target design (in each direction) for μDBO (e.g., Figure 4 As shown), the dual-wave model for 1D signal extraction can be written as:

[0110]

[0111] in In the single-wavelength overlay inference method, K is eliminated by offsetting the grating and is calculated as follows:

[0112]

[0113] Compared to existing methods based on eliminating K, the proposed method exploits K to learn about process variations. It can be shown that K is correlated with both symmetric and asymmetric process variations. In other words, while usually only the asymmetric part of the intensity signal is used, the symmetric variations are included due to the dependence of K on the symmetric variations. Therefore, K can be used as a proxy for process variations in training-based algorithms.

[0114] Applying variable changes and simplifying the notation to:

[0115] v i :=sin(ov i ±b i ), A linear transformation can be used here instead of a sine transform. Rearranging the equation to describe the sensitivity of the overlay parameter v to changes in the measured signal ΔI (rather than the sensitivity v of ΔI to changes in v) yields:

[0116]

[0117] Where weight w = K -1

[0118] We can define a proxy P for symmetric and asymmetric process changes j，λ，i , G j，λ，i To do this, we can separate the weights associated with the symmetric and asymmetric process changes and rewrite the estimated model as:

[0119]

[0120] where w j，λ =(z j，λ +r j，λ ), where z j，λ and r j，λ The weights included are functions of the symmetric and asymmetric process variations respectively:

[0121] Symmetry process changes: z j，λ (P j，λ，i ):

[0122]

[0123] Asymmetric process changes: r j，λ (G j，λ，i );

[0124]

[0125] That is, the difference between the two offset images of the normal or +1st diffraction order and the complementary or -1st diffraction order.

[0126] It can be assumed that z j，λ and r j，λ They are P j，λ，i and G j，λ，i By vectorizing z for all considered wavelengths and pixels j，λ， r j，λ , P j，λ，i and G j，λ，i , which can reduce the dependence on wavelength and pixel, thus generating and Linearize z vs. P around the nominal operating point i and r to G i The dependency of , we get:

[0127]

[0128] definition and in get:

[0129]

[0130] Similarly, define and in It turns out that:

[0131]

[0132] Combining the above, the overlay inference model becomes:

[0133]

[0134] The above models and theories rely on the presence of known training labels or known parameter values ​​of interest (e.g., overlay) in the training data. Such known values ​​can be measured using accurate metrology techniques (such as scanning electron microscopes), or obtained, for example, by any other suitable method. The known values ​​may include scanner setting values ​​for a wafer with programmed overlay. When the training data includes simulated data (the training data can be measured and / or simulated), the parameter / overlay values ​​of interest can be simulated values. However, reference values ​​may not always be available. Therefore, a self-referencing embodiment will now be described, which is an adaptation of the above embodiment.

[0135] In this embodiment, it is proposed Use all target locations to jointly find model training parameters Based on the assumption that the overlays on the two subgoals must be the same:

[0136]

[0137] in:

[0138] ov +b :=v +b -b

[0139] ov -b :=v -b +b

[0140] Also assume that v +b and v -b can be captured by the same model, namely Therefore, the training problem consists of solving a single minimization problem to minimize In the previous embodiment, the training problem consists of solving a pair of minimization problems (one cost function for each sub-goal bias +b, -b) to minimize and

[0141] Therefore, plugging the equation into v-space yields the training problem:

[0142]

[0143] This can be conveniently written as:

[0144]

[0145] in:

[0146]

[0147] This training is fully self-referential, where the training uses the known biases b of the sub-goals instead of the external overlays.

[0148] During the inference phase or manufacturing phase, the overlay can be determined according to the following formula.

[0149]

[0150] Again, this is a single equation, rather than a pair of equations (one for each bias) as in the previous external reference embodiment, so that the information ΔI from the two biased sub-targets is +b，i ΔI -b，i The transformed overlay value v can then be used as in the previous embodiment. +b，i 、v +b，i The inverse transform and averaging are performed to determine the final overlay value ov for each object.

[0151] For the cDBO self-referencing embodiment, the following assumptions can be made:

[0152] ov c1 =ov c2 → c1 -ov c2 =0;

[0153]

[0154] Where c1 and c2 represent the corresponding different (e.g., centrosymmetric) target clusters in a pair of clusters. This training can then be performed to enforce this formula; that is, find training parameters that minimize the overlay inference difference between two (or more) centrosymmetric target design clusters. The training equation can be written as:

[0155]

[0156] And, once training is complete, the overlay can be determined from the following formula:

[0157]

[0158] The final overlay includes the average overlay of the two clusters (i is the target position index):

[0159]

[0160] The proposed method based on the above concepts may include two stages: a solution setting stage or training stage (which can be combined with the existing qualification certification process); and a manufacturing stage or overlay inference stage.

[0161] Figure 6 is a flowchart showing the first embodiment or the external reference embodiment. Figure 6 (a) is a flow chart showing the training phase for this embodiment. The training data TD includes one or more of the following: measurement data MEA DAT and simulation data SIM DAT (e.g., obtained using computational lithography techniques) obtained by performing measurements on one or more training wafers TW. In each case, the training data may relate to a plurality of different wavelengths λ1-λ n The target may include two offsets (or two offsets for each direction in the substrate plane), such as Figure 4 , or may be a cDBO target as previously described. The targets should all be similar. The measurement data may include a single measurement per sub-target or pad (e.g., averaged over the ROI), a measurement per pixel, or a measurement for an image region or group of pixels (e.g., averaged over the intermediate granularity between two listed extremes).

[0162] In addition to the training data, external reference data POI Ref is acquired, which includes known reference values ​​(e.g., known overlay values) of the parameters of interest. This may include measured values ​​(e.g., using SEM metrology), other AEI reference values, or (scanner model corrected) scanner setting values ​​for a wafer with programmed overlay for the measured data MEA DAT and / or programmed / calculated / setting values ​​for the simulation data SIM DAT.

[0163] The reference data POI Ref and the training data TD are used for a training or optimization step TRA to find / train at least the training parameters TPM ±b , N ±b (or per cluster in the cDBO example). Of course, in embodiments where more agents are defined, there will be more training parameters. This step can use the minimization function Equation 2 and can be solved by a closed-form solution and / or a multi-pixel version (described below). In this training phase, the parameter estimation problem is reduced to an optimization problem that requires solving the model parameters in multiple dimensions (e.g., intensity, wavelength, and target position on the wafer) simultaneously. This training phase can be performed online or offline.

[0164] Figure 6(b) is a flow chart illustrating the inference phase or production phase. The measurement data MD includes the measurement data MD from the production wafer PW for two (or more) complementary diffraction orders (e.g., +1 and -1) for a plurality of different wavelengths λ1-λ n The measurement data MD may be related to one or more target locations.

[0165] In the inference phase, based on the training parameters TP (e.g., M ±b , N ±b ), the parameters of interest POI of the new measurement data MD are calculated using the trained model TM. This can be done using formula (3). The parameter of interest POI inference can be done jointly for all targets, a subset of all targets on a per-target basis. At this stage, in order to prevent deviations from the process during manufacturing, the use of one or more monitoring KPIs is optionally proposed. These KPIs can be used to identify deviations from the training model TM. Monitoring KPIs can mark changes that are not descriptive enough for the learning model. This can be used in the control loop to trigger additional solution settings or training phases.

[0166] Figure 7 Included with Figure 6 The flowchart is equivalent to the flowchart for the self-referenced embodiment. In this embodiment, and with reference to Figure 7 In the training phase shown in (a), training data TD is obtained from the wafer W. The training data TD includes measurement data MEA DAT obtained by performing measurements on the wafer W, the measurement data being for a plurality of different wavelengths λ1-λ n The measurement data may include two (or more) complementary diffraction orders (e.g., +1 and -1) for each of the sub-targets and multiple different target locations (e.g., all target locations on wafer W). As before, the measurement data may include a single measurement for each sub-target or pad (e.g., averaged over the ROI), a measurement for each pixel, or a measurement for an image area or group of pixels (e.g., averaged over intermediate granularities between two listed extremes).

[0167] The training data TD is used in a training or optimization step TRA to find / train the training parameters TP M, N. This step uses the minimization function Eq. 4 and can be solved by a closed form solution and / or a multi-pixel version (as described below). No external reference is used and the training is performed on a known bias.

[0168] Figure 7(b) is a flow chart showing the inference phase or production phase of the self-referencing embodiment. The measurement data MD includes the measurement values ​​of a single target on the same wafer W used for training. Likewise, the measurement data MD may be related to the measurement values ​​for a plurality of different wavelengths λ1-λ n The two (or more) complementary diffraction orders (e.g., +1 and -1) for each wavelength in the training data are related, which wavelengths can be the same wavelengths as in the training phase, or a smaller (appropriate) subset of the wavelengths used for training (e.g., a small subset of less than 6, less than 5, less than 4, or less than 3 wavelengths). Based on the training parameters TP M, N determined in the training phase, the training model TM is used to calculate the parameters of interest POI of the new measurement data MD. This can be done using, for example, formula (5). In this embodiment, the parameters of interest POI inference is performed on a per-target basis.

[0169] Closed-form solution to the optimization problem

[0170] The proposed multidimensional regression problem has a closed-form solution. The external reference problem (Formula (2)) can be rewritten as:

[0171]

[0172] in During the training phase, the solution can be found by computing the pseudo-inverse:

[0173]

[0174] Among them, H + represents the pseudo-inverse of H. Additionally, to avoid instability and apply regularization, the number of values ​​used to compute the pseudo-inverse H can be limited by applying a threshold to the singular values ​​of H. + mode.

[0175] After calculating M and N in the training phase, the embedding vector v ±b It can be calculated as follows:

[0176]

[0177] Similarly, for the self-referencing embodiment, the closed-form solution to equation (4) can be:

[0178]

[0179] Where H = H +b -H -b

[0180] It will be apparent to one skilled in the art that a closed-form solution for the cDBO embodiment can be similarly constructed.

[0181] We can also add explicit regularization to the optimization problem. For example, the optimization problem with Tikhonov regularization can be written as

[0182]

[0183] in This leads to the closed-form solution:

[0184]

[0185] A similar regularization formula can be formulated for the self-referencing version, leading to the closed-form solution

[0186]

[0187] Pixel Example

[0188] As described above, the regression problem can be solved using information from multiple pixels within the image ROI. p To solve, we can also use N p Set to 1 (standard mean value within the ROI).

[0189] However, if multiple pixel information is to be used, the size of the data matrix P, G, ΔI is known to be N p N λ ×N t , the size of the unknown training matrix is In order to be able to solve the problem efficiently, a data reduction step is proposed to reduce the number of free parameters. This can be achieved by applying data compression using singular value decomposition (SVD) as shown below:

[0190] During the training phase, SVD is applied to each of the data matrices P, G, ΔI:

[0191]

[0192] in is a left singular vector, is a diagonal matrix containing singular values, are right singular vectors.

[0193] The compressed version of the data matrix, i.e., P, G, ΔI can be calculated as follows:

[0194]

[0195] in The matrices U are P , U g and U a The first qp ,q g and q a In this case, q p ,q g and q a is the compressed length of the data matrix and is chosen so that the data matrix can be adequately approximated by these mode numbers.

[0196] Applying data compression, the regression problem (Formula 2) can be rewritten as:

[0197]

[0198] in and is the reduced left singular vector expanded by 1 on the diagonal and and is a reduced version of the training matrices M, N, where:

[0199]

[0200] The regression problem can be equivalently written as:

[0201]

[0202] To find the solution to this optimization problem, a compressed version of the data matrix (P c , G c and ΔI c ) to train the training parameter matrix (M r , N r ). For example, the training phase can consist of solving:

[0203]

[0204] And in the inference stage, the overlay value can be obtained in the following ways:

[0205]

[0206] It will be apparent to one skilled in the art that this approach can be adapted and used with the self-reference embodiment and / or the cDBO embodiment.

[0207] It will also be appreciated that a dimensionality reduction step (such as an SVD step) may be applied independently of single pixel processing, for example, as may be applied to any other embodiment disclosed herein.

[0208] Reduce target size

[0209] In one embodiment, the overlay method disclosed herein can allow for the removal of one bias grating from a μDBO target (e.g., per direction), thereby halving the target area. Similarly, by having only one cluster per cDBO target (e.g., only one M pad and W pad), the cDBO target can be made smaller (e.g., halved in size). Thus, a target with only one sub-target per direction, either with a single bias or no bias (μDBO), or two sub-targets, one for each of the M pad and the W pad (cDBO) can be used for in-line ADI overlay monitoring.

[0210] In a first variation of this embodiment, the bias can be varied across different single bias targets (the scope of the term "single bias target" in this context includes zero bias / no bias targets) to provide a collective multi-bias. Thus, each wafer can include multiple targets, all with a single bias (optionally per direction), but with the bias varied between targets such that there are two (or more) biases on the wafer. This allows the proxy P to be used in a variety of ways. j，λ，i and G j，λ，i can be defined in the same way as already described; in particular, it allows the use of an asymmetric proxy G j，λ，i , which agent relies on the presence of different biases to determine the second order differences, as already described. More specifically, to determine the asymmetry agent in such an embodiment, the required signal differences between sub-targets of different biases can now be obtained from different target locations rather than from the same target location. and (Right now, and Involved with In such an embodiment, the two target locations used to determine the asymmetry proxy may be close or adjacent, where it can be assumed that the asymmetry process effect is similar for the two target locations.

[0211] A similar distributed approach may be applied to cDBO targets, where targets on a wafer may include first targets of a first cluster type at certain wafer locations, and targets of a second cluster type at other wafer locations.

[0212] In an alternative embodiment, all targets on the wafer may have the same single bias / same cluster type. However, for μDBO embodiments, this only allows the use of symmetry agents. Therefore, in such μDBO embodiments, the asymmetry agent is omitted or set to zero: G j,λ,i =0 and its corresponding training parameter N ±b Not trained and not used for inference.

[0213] In summary, this paper describes an ADI metrology approach that can be used for fast metrology techniques (e.g., dark-field metrology) for in-line overlay monitoring. Thus, this approach extends training-based inference methods to dark-field applications. This approach incorporates both asymmetric and symmetric process variations into the model.

[0214] Since this method can be used to collectively estimate the overlay of multiple target locations on the wafer, this approach can improve accuracy and robustness to process variations. The proposed methods can be used to reduce the target size. In addition, these methods allow the incorporation of pixel intensity information in dark field images into the overlay inference problem. This provides an opportunity to jointly develop calibration and inference methods within the same framework, incorporating pixel selection and ROI refinement methods (such as pixel mapping) directly into the overlay inference problem.

[0215] As mentioned above, although the disclosed embodiments are primarily described for μDBO or more generally intensity-based applications, the same approach can be extended to cDBO or more generally phase-based applications.

[0216] While the targets described above are metrology targets that are specifically designed and formed for measurement purposes, in other embodiments, characteristics may be measured on a target that is a functional component of a device formed on a substrate. Many devices have a regular grating-like structure. The terms "target grating" and "target" as used herein do not require that the structure be provided specifically for the measurement being performed. In such embodiments, the target grating and the dielectric grating may all comprise a product structure, or only one or both of the target gratings may comprise a product structure, wherein the dielectric grating is specifically formed to adjust the allowed pitch so that measurements can be made directly on the product structure. In addition, the pitch of the metrology target is close to the resolution limit of the scatterometer optical system, but may be much larger than the size of a typical product feature made in the target portion C by a photolithography process. In practice, the lines and / or spaces of the overlaid grating within the target can be made to include smaller structures of similar size to the product features.

[0217] One embodiment may include a computer program comprising one or more sequences of machine-readable instructions describing a method of measuring a target on a substrate and / or analyzing the measurements to obtain information about a lithography process. The computer program may be used, for example, in Figure 3 The unit PU and / or Figure 2 A data storage medium (e.g. a semiconductor memory, a magnetic disk or an optical disk) in which such a computer program is stored may also be provided. Figure 3 When a computer program product of the type shown in FIG. 1 is already in production and / or in use, the present invention may be implemented by providing an updated computer program product to cause a processor to perform the steps required to calculate overlay error.

[0218] The program may optionally be arranged to control the optical system, substrate support etc. to carry out the steps required to calculate the overlay error for measuring asymmetry on a suitable plurality of targets.

[0219] Further embodiments according to the invention are given in the following numbered clauses:

[0220] 1. A method for determining a parameter of interest associated with at least one target on a substrate, the method comprising:

[0221] obtaining measurement data including at least one asymmetry signal including a difference or imbalance in a measured parameter from the target;

[0222] obtaining a trained model that has been trained or configured to relate the at least one asymmetry signal to the parameter of interest, the trained model comprising at least one proxy for at least one interference component of the at least one asymmetry signal; and

[0223] The parameter of interest for the at least one target is inferred from the at least one asymmetry signal using the trained model.

[0224] 2. The method of clause 1, wherein the metrology data comprises post-development metrology data measured prior to an etching step of the just exposed layer.

[0225] 3. A method according to clause 1 or 2, wherein the at least one asymmetry signal comprises at least one asymmetry signal measured at an image plane or a conjugate thereof of a metrology tool used to obtain the metrology data.

[0226] 4. A method according to any of the preceding clauses, wherein the trained model comprises configured training parameters for each of the at least one agent.

[0227] 5. A method according to any of the preceding clauses, wherein the at least one agent comprises one or both of the following:

[0228] using at least one symmetry proxy for a symmetric interference component of each of the at least one asymmetry signal; and / or

[0229] At least one asymmetry proxy for an asymmetric interference component of each of the at least one asymmetry signal is used.

[0230] 6. A method according to clause 5, wherein the at least one asymmetry signal comprises: a measured parameter asymmetry between each diffraction order in a pair of complementary diffraction orders.

[0231] .A method according to clause 6, wherein the measured parameter is an intensity or related parameter.

[0232] 8. A method according to clause 6 or 7, wherein the at least one symmetry proxy comprises a sum of respective measured parameter values ​​from each diffraction order in a pair of complementary diffraction orders.

[0233] 9. A method according to clause 6, 7 or 8, wherein the at least one asymmetry proxy comprises the difference between:

[0234] a first measured parameter value difference for a first corresponding diffraction order of each of a first sub-target type and a different second sub-target type from the at least one target; and

[0235] A second measured parameter value difference for a second corresponding diffraction order from each of the first sub-target type and the second sub-target type that is complementary to the first corresponding diffraction order.

[0236] 10. The method of clause 9, wherein the first sub-target type and the second sub-target type are each included in a respective target arrangement at each target location.

[0237] 11. The method of clause 9, wherein the first sub-target type and the second sub-target type are each distributed over different target locations on the substrate.

[0238] 12. A method according to any of the preceding clauses, wherein each of the at least one target comprises only a single sub-target type, or each measurement direction comprises a single sub-target type.

[0239] 13. A method according to claim 5, wherein the at least one asymmetry signal comprises a phase difference between radiation scattered by a first sub-target type of the at least one target and radiation scattered by at least a second sub-target type of the at least one target, each sub-target type comprising a first grating and a second grating having different pitches, and wherein the order of the gratings is opposite within the target layer between the two sub-target types.

[0240] 14. A method according to claim 13, wherein the at least one asymmetry signal is determined from the average value of the phase difference, the phase difference being obtained from: a first diffraction order from a complementary diffraction order pair for each sub-target type and a second diffraction order from a complementary diffraction order pair for each sub-target type.

[0241] 15. A method according to clause 13 or 14, wherein the at least one symmetry proxy comprises a sum of respective amplitude values ​​of each diffraction order from a pair of complementary diffraction orders.

[0242] 16. A method according to any one of clauses 13 to 15, wherein the at least one asymmetry agent comprises one or more of: the difference between: a first phase difference of a first corresponding diffraction order from each of the first sub-target type and the second sub-target type, and a second phase difference of a second corresponding diffraction order complementary to the first corresponding diffraction order from each of the first sub-target type and the second sub-target type; and / or the sum of: a first amplitude difference (optionally normalized) between complementary diffraction orders of radiation scattered by the first sub-target type and a second amplitude difference (optionally normalized) between complementary diffraction orders of radiation scattered by the second sub-target type.

[0243] 17. A method according to any one of clauses 13 to 16, wherein the at least one target includes at least a first cluster type, the first cluster type includes a first arrangement of sub-targets, the first arrangement of sub-targets includes at least a first sub-target type and a second sub-target type, the second cluster type includes a second arrangement of sub-targets, the second arrangement of sub-targets includes at least a first sub-target type and a second sub-target type.

[0244] 18. The method of clause 17, wherein the first cluster type and the second cluster type are each included within a respective target arrangement at each target location.

[0245] 19. The method of clause 17, wherein the first cluster type and the second cluster type are each distributed over different target locations on the substrate.

[0246] 20. A method according to any of the preceding clauses, wherein the measurement data comprises multiple asymmetry signals associated with multiple targets at different target positions; and the step of inferring the parameter of interest comprises using the trained model and the multiple asymmetry signals to simultaneously infer the parameter of interest for each of the targets.

[0247] 21. A method according to any of clauses 1 to 19, wherein the step of inferring the parameter of interest comprises inferring the parameter of interest separately for each target on the substrate.

[0248] 22. A method according to any of the preceding clauses, wherein the trained model is trained using training data comprising a plurality of training asymmetry signals associated with a plurality of training targets, the plurality of training targets being the same or similar to the at least one target.

[0249] 23. A method according to any of the preceding clauses, wherein the trained model is trained using external reference data for the parameter of interest.

[0250] 24. A method according to clause 23, wherein the trained model includes a first training model and a second training model, the first training model is used to infer the parameter value of interest of the first sub-target type or cluster type for each target of the at least one target, and the second training model is used to infer the parameter value of interest of the second sub-target type or cluster type for each target of the at least one target; and the inference step includes: using the first training model to determine the first parameter value of interest for each first sub-target type or cluster type, and using the second training model to determine the second parameter value of interest for each second sub-target type or cluster type; and inferring the parameter of interest for each target as a combination or average of the first parameter value of interest for the first sub-target type or cluster type for the target and the second parameter value of interest for the second sub-target type or cluster type for the target.

[0251] 25. A method according to clause 23 or 24, comprising an initial step of performing a method according to any one of clauses 30 to 41 to train the trained model.

[0252] 26. A method according to any one of clauses 1 to 22, wherein the training of the trained model is self-referential and the training targets are the same targets located on the same substrate as the at least one target.

[0253] 27. A method according to clause 26, wherein the model assumes that the parameters of interest are the same for each sub-goal type or sub-goal cluster type of the at least one goal; and a single model is used to infer the parameters of interest for each sub-goal type or sub-goal cluster type.

[0254] 28. A method according to clause 26 or 27, wherein the model is trained based on bias magnitudes of the sub-goals or assumed common overlays from different clusters of sub-goals.

[0255] 29. A method according to clause 26, 27 or 28, comprising an initial step of performing a method according to any one of clauses 30 to 35 or clause 42 to train the trained model.

[0256] 30. A method according to any of the preceding clauses, wherein the measurement data comprises a plurality of asymmetry signals from each sub-target of each target of the at least one target, the plurality of asymmetry signals from each sub-target being associated with different regions within a measurement image of the sub-target from which the asymmetry signals originate; wherein inferring the parameter of interest comprises inferring the parameter of interest separately using the plurality of asymmetry signals associated with different regions within the measurement image of each sub-target.

[0257] 31. A method according to clause 30, wherein each asymmetry signal of the different regions within the measurement image of each sub-target is obtained from the measurement value of the corresponding pixel of the corresponding measurement image of the sub-target.

[0258] 32. A method according to any of the preceding clauses, wherein the model is a compressed model comprising a compressed asymmetry signal matrix and a compression matrix for each of the at least one agent.

[0259] 33. A method according to any of the preceding clauses, wherein the parameter of interest is overlay.

[0260] 34. A method according to any of the preceding clauses, wherein the training model is a multidimensional regression model, the dimensions comprising two or more of: diffraction order, sub-target or cluster type, measurement wavelength, target position on the substrate, and the area within the measurement image from which the asymmetry signal originates.

[0261] 35. A method according to any of the preceding clauses, comprising performing measurement on the at least one target to obtain the measurement data.

[0262] 36. The method of clause 35, wherein the measurement comprises dark field measurement.

[0263] 37. A method for training a model to relate an asymmetry signal to a parameter of interest, the model comprising at least one agent for at least one interference component of the asymmetry signal, the method comprising: acquiring training data comprising a plurality of training asymmetry signals associated with a plurality of training targets on one or more training substrates; and training the model by optimizing corresponding training parameters of each of the at least one agent.

[0264] 38. A method according to clause 37, wherein the at least one agent comprises at least one of: at least one symmetric agent for a symmetric interference component of the at least one asymmetric signal; and / or at least one asymmetric first agent for an asymmetric interference component of the at least one asymmetric signal.

[0265] 39. A method according to clause 38, wherein the training asymmetry signals each comprise: a measured parameter asymmetry between each diffraction order in a pair of complementary diffraction orders.

[0266] 40. The method of clause 39, wherein the measured parameter is an intensity or related parameter.

[0267] 41. A method according to clause 39 or 40, wherein the at least one symmetry proxy comprises a sum of respective measured parameter values ​​for each diffraction order in a pair of complementary diffraction orders.

[0268] 42. A method according to clauses 39, 40 or 41, wherein the at least one asymmetry proxy comprises a difference between: a first measured parameter value difference for a first corresponding diffraction order from each of a first sub-target type and a different second sub-target type included in the training target; and a second measured parameter value difference for a second corresponding diffraction order complementary to the first corresponding diffraction order from each of the first sub-target type and the second sub-target type.

[0269] 43. A method according to clause 42, wherein the first sub-target type and the second sub-target type are each included in a respective target arrangement at each target position on the or each training substrate.

[0270] 44. A method according to clause 42, wherein the first sub-target type and the second sub-target type are each distributed at different target locations on the or each training substrate; and the asymmetry agent is determined based on two training targets at two different target locations on the training substrate.

[0271] 45. A method according to any one of clauses 44, wherein each of the training targets includes only a single sub-target type, or each measurement direction includes only a single sub-target type.

[0272] 46. ​​A method according to clause 38, wherein the at least one asymmetry signal comprises a phase difference between radiation scattered by a first sub-target type included in the training target and radiation scattered by at least a second sub-target type included in the training target, each sub-target type comprising a first grating and a second grating having different pitches, and wherein in the target layer between the two sub-target types, the orders of the gratings are opposite.

[0273] 47. A method according to claim 46, wherein the at least one asymmetry signal is determined based on the average value of the phase difference, which is obtained from: the first diffraction order of the complementary diffraction order pair of each sub-target type, and the second diffraction order of the complementary diffraction order pair of each sub-target type.

[0274] 48. A method according to clause 46 or 47, wherein the at least one symmetry agent comprises a sum of respective amplitude values ​​of each diffraction order in a pair of complementary diffraction orders.

[0275] 49. A method according to any one of clauses 46 to 48, wherein the at least one asymmetry agent comprises one or more of: the difference between: a first phase difference of a first corresponding diffraction order from each of the first sub-target type and the second sub-target type, and a second phase difference of a second corresponding diffraction order complementary to the first corresponding diffraction order from each of the first sub-target type and the second sub-target type; and / or the sum of: a first amplitude difference (optionally normalized) between complementary diffraction orders of radiation scattered by the first sub-target type and a second amplitude difference (optionally normalized) between complementary diffraction orders of radiation scattered by the second sub-target type.

[0276] 50. A method according to any one of clauses 46 to 49, wherein the at least one target includes at least a first cluster type, the first cluster type includes a first arrangement of sub-targets, the first arrangement of sub-targets includes at least a first sub-target type and a second sub-target type, the second cluster type includes a second arrangement of sub-targets, the second arrangement of sub-targets includes at least a first sub-target type and a second sub-target type.

[0277] 51. The method of clause 50, wherein the first cluster type and the second cluster type are each included within a respective target arrangement at each target location.

[0278] 52. The method of clause 50, wherein the first cluster type and the second cluster type are each distributed over different target locations on the substrate.

[0279] 53. A method according to any one of clauses 37 to 52, wherein the training data comprises multiple training asymmetry signals from each sub-target of each training target, wherein the multiple training asymmetry signals from each sub-target are associated with different regions within a training image of the sub-target from which the asymmetry signals originate; and wherein the training step solely uses the multiple training asymmetry signals associated with different regions within the training image of each sub-target.

[0280] 54. A method according to any one of clauses 37 to 53, wherein a singular value decomposition step is performed before the training step to reduce the dimensionality of the training data.

[0281] 55. A method according to any one of clauses 37 to 54, comprising obtaining known parameter values ​​of interest corresponding to the training data; and using the known parameter values ​​of interest to mark the training data before the training step, wherein the first measurement value difference and the second measurement value difference are obtained from two different targets at different target positions.

[0282] 56. A method according to clause 55, wherein the optimization step includes determining a training parameter value for each of the training parameters, the training parameter value minimizing the difference between the known parameter values ​​of interest and the product of the training parameter value and the asymmetry signal convolved with each of the proxy.

[0283] 57. A method according to clause 55 or 56, wherein the model includes a first model for inferring parameter values ​​of interest for a first sub-goal type of the training goal, and a second training model for inferring parameter values ​​of interest for a second sub-goal type of the training goal.

[0284] 58. A method according to any one of clauses 37 to 54, wherein the optimization step comprises determining a training parameter value for each of the training parameters, the training parameter value minimizing the difference between: the bias amplitude of the training objective or a multiple thereof, and the product of: the training parameter value; and the difference between: the convolution of the asymmetry signal with each of the agents of the first sub-objective type for the training objective, and the convolution of the asymmetry signal with each of the agents of the second sub-objective type for the training objective.

[0285] 59. A processing device comprising a processor and configured to perform the method of any of the preceding clauses.

[0286] 60. A measurement device comprising a processor according to clause 59.

[0287] 61. A computer program comprising program instructions capable of performing a method according to any one of clauses 1 to 58 when run on a suitable apparatus.

[0288] 62. A non-transitory computer program carrier comprising a computer program according to clause 61.

[0289] Although specific reference may have been made above to embodiments of the invention being used in the context of optical lithography, it should be understood that the invention may be used in other applications, such as imprint lithography, and that the invention is not limited to optical lithography as 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 supplied to the substrate, and the resist is then cured by applying electromagnetic radiation, heat, pressure, or a combination thereof. After the resist is cured, the patterning device is removed from the resist, leaving a pattern therein.

[0290] As used herein, the terms "radiation" and "beam" encompass all types of electromagnetic radiation, including ultraviolet (UV) radiation (e.g., having a wavelength of about 365 nm, 355 nm, 248 nm, 193 nm, 157 nm, or 126 nm) and extreme ultraviolet (EUV) radiation (e.g., having a wavelength in the range of 5-20 nm), A as well as A particle beam, such as A ion beam or an electron beam.

[0291] The term "lens," where the context permits, may refer to any one or more types of components, including refractive, reflective, magnetic, electromagnetic, and electrostatic components.

[0292] The description of the above specific embodiments will fully reveal the general nature of the present invention, and others can easily modify and / or adjust these specific embodiments for various applications without departing from the general concept of the present invention by applying knowledge within the technical scope of the art, without excessive experimentation. Therefore, based on the teachings and guidance provided herein, these adjustments and modifications are intended to fall within the meaning and scope of equivalents of the disclosed embodiments. It should be understood that the wording or terminology herein is for illustration, not for limitation, and therefore, those skilled in the art should interpret the terms or wording of this specification in accordance with the teachings and guidance.

[0293] 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 a parameter of interest associated with at least one target on a substrate, the method comprising: obtaining measurement data including at least one asymmetry signal including a difference or imbalance in a measured parameter from the target; obtaining a trained model that has been trained or configured to relate the at least one asymmetry signal to the parameter of interest, the trained model comprising at least one proxy for at least one interference component of the at least one asymmetry signal; as well as The parameter of interest for the at least one target is inferred from the at least one asymmetry signal using the trained model.

2. The method of claim 1, wherein the metrology data comprises post-development metrology data measured prior to an etching step of a just exposed layer.

3. The method according to claim 1 or 2, wherein the at least one asymmetry signal comprises at least one asymmetry signal measured at an image plane or a conjugate thereof of a metrology tool used to obtain the metrology data. 4 . The method according to claim 1 , wherein the trained model comprises configured training parameters for each of the at least one agent.

5. The method according to any one of the preceding claims, wherein the at least one agent comprises one or both of the following: using at least one symmetry proxy for a symmetric interference component of each of the at least one asymmetry signal; and / or At least one asymmetry proxy for an asymmetric interference component of each of the at least one asymmetry signal is used.

6. The method of claim 5, wherein the at least one asymmetry signal comprises: A measured parameter asymmetry between each diffraction order in a complementary pair of diffraction orders. The method according to claim 6 , wherein the measured parameter is an intensity or related parameter.

8. A method according to claim 6 or 7, wherein the at least one symmetry proxy comprises a sum of corresponding measured parameter values ​​from each diffraction order in a pair of complementary diffraction orders.

9. The method of claim 6, 7 or 8, wherein the at least one asymmetry proxy comprises the difference of: a first measured parameter value difference for a first corresponding diffraction order of each of a first sub-target type and a different second sub-target type from the at least one target; and A second measured parameter value difference for a second corresponding diffraction order complementary to the first corresponding diffraction order from each of the first sub-target type and the second sub-target type.

10. The method of claim 9, wherein the first sub-target type and the second sub-target type are each included in a respective target arrangement at each target location.

11. The method of claim 9, wherein the first sub-target type and the second sub-target type are each distributed on different target locations on the substrate.

12. A method according to any one of the preceding claims, wherein each of the at least one target comprises only a single sub-target type, or each measurement direction comprises a single sub-target type.

13. A method according to claim 5, wherein the at least one asymmetry signal comprises a phase difference between radiation scattered by a first sub-target type of the at least one target and radiation scattered by at least a second sub-target type of the at least one target, each sub-target type comprising a first grating and a second grating having different pitches, and wherein the order of the gratings is opposite between the two sub-target types within the target layer.

14. A method according to claim 13, wherein the at least one asymmetry signal is determined from the average value of the phase difference, and the phase difference is obtained from: the first diffraction order of a complementary diffraction order pair from each sub-target type and the second diffraction order of the complementary diffraction order pair from each sub-target type.

15. A method according to claim 13 or 14, wherein the at least one symmetry proxy comprises a sum of respective amplitude values ​​of each diffraction order from a pair of complementary diffraction orders.

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