Method for determining the spatial distribution of a parameter of interest for at least one substrate or part thereof - Patents.com

Abstract

A method for determining a spatial distribution of a parameter of interest for at least one substrate or portion thereof subjected to a semiconductor manufacturing process is disclosed, the method comprising obtaining a statistical description describing a predicted fingerprint component of the spatial distribution and a noise component describing a predicted level of measurement noise associated with the parameter of interest, obtaining metrology data related to the parameter of interest, and estimating by Bayesian estimation the spatial distribution of the parameter of interest for the at least one substrate or portion thereof using the statistical description as a prior distribution and the metrology data as observations.

Description

[Technical field]

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority to European Application No. 22164691.2, filed March 28, 2022, the entire contents of which are incorporated by reference into this specification. [Background technology]

[0002] The present invention relates to a method and apparatus for applying a pattern to a substrate in a lithographic process.

[0003]

[0003] A lithographic apparatus is a machine that applies a desired pattern onto a substrate, usually onto a target portion of the substrate. Lithographic apparatus can be used, for example, in the manufacture of integrated circuits (ICs). A patterning device, also called a mask or reticle, can then be used to generate a circuit pattern formed on an individual layer of the IC. This pattern can be transferred onto a target portion (e.g. comprising part of a die, or one or more dies) on the substrate (e.g. a silicon wafer). Usually, the transfer of the pattern is by imaging onto a layer of radiation-sensitive material (resist) provided on the substrate. In general, a single substrate will contain a network of adjacent target portions that are successively patterned. Known lithographic apparatus include so-called steppers, in which each target portion is irradiated by exposing the entire pattern onto the target portion at once, and so-called scanners, in which each target portion is irradiated by scanning the pattern with a radiation beam in a certain direction (the "scan" direction) while simultaneously scanning the substrate parallel or anti-parallel to this direction. It is also possible to transfer the pattern from the patterning device to the substrate by imprinting the pattern onto the substrate.

[0004]

[0004] To monitor the lithographic process, parameters of the patterned substrate are measured. The parameters may include, for example, the overlay error between successive layers formed in or on the patterned substrate and the critical linewidth (CD) of the developed photosensitive resist. The measurements may be performed on the product substrate and / or on a dedicated metrology target. Various techniques exist for making measurements of the microstructures formed in the lithographic process, including the use of scanning electron microscopes and various specialized inspection tools. A fast and non-invasive form of specialized inspection tool is the scatterometer, in which a beam of radiation is directed at a target on the surface of the substrate and properties of the scattered or reflected beam are measured. Two main types of scatterometers are known. Spectroscopic scatterometers direct a broadband beam of radiation onto the substrate and measure the spectrum (intensity as a function of wavelength) of the radiation scattered into a specific narrow angular range. Angularly resolved scatterometers use a monochromatic beam of radiation and measure the intensity of the scattered radiation as a function of angle.

[0005]

[0005] Examples of known scatterometers include angle resolved scatterometers of the type described in US2006033921A1 and US2010201963A1. The target used by such scatterometers is relatively large, for example a 40 μm×40 μm grating, and the measurement beam produces a spot smaller than the grating (i.e. the grating is underfilled). In addition to measuring feature shapes by reconstruction, diffraction-based overlay can be measured using an apparatus such as that described in published patent application US2006066855A1. Diffraction-based overlay metrology using dark-field imaging of the diffraction orders allows overlay measurements on smaller targets. Examples of dark-field imaging metrology can be found in International Patent Applications WO2009 / 078708 and WO2009 / 106279, which are incorporated herein by reference in their entirety. Further developments of this technology are described in published patent publications US20110027704A, US20110043791A, US2011102753A1, US20120044470A, US20120123581A, US20130258310A, US20130271740A and WO2013178422A1. These targets may be smaller than the illumination spot and may be surrounded by product structures on the wafer. Multiple grating targets can be used to measure multiple gratings in one image. The contents of all these applications are also incorporated herein by reference.

[0006]

[0006] During semiconductor manufacturing processes, such as lithography processes, such as applying a pattern onto a substrate or measuring such a pattern, process control methods are used to monitor and control the process. Such process control techniques are typically performed to obtain correction values ​​for controlling the semiconductor manufacturing process. It is desirable to improve such process control methods. In particular, process corrections are typically performed based on modeled metrology data, where the modeling may be based on fitting basis functions to the measured data. Basis function-based modeling is not optimal because it is not based on domain knowledge or actual observed properties of the fingerprint. This can lead to fitting inaccurate or inappropriate models to the metrology data (e.g., sub-optimal basis functions). Summary of the Invention

[0007]

[0007] In a first aspect of the present invention, there is provided a method for determining a spatial distribution of a parameter of interest for at least one substrate or portion thereof subjected to a semiconductor manufacturing process, the method comprising obtaining a statistical description describing a predicted fingerprint component of the spatial distribution and a noise component describing a predicted level of measurement noise associated with the parameter of interest, obtaining metrology data related to the parameter of interest, and estimating the spatial distribution of the parameter of interest for at least one substrate or portion thereof by Bayesian estimation using the statistical description as a prior distribution and the metrology data as observations.

[0008] The invention further provides a processing apparatus, a metrology device and a lithographic apparatus comprising the computer program of the first aspect.

[0009]

[0009] Further aspects, features, and advantages of the present invention, as well as the structure and operation of various embodiments of the present invention, are described in detail below with reference to the accompanying drawings. It should be noted that the present invention is not limited to the specific embodiments described herein. Such embodiments are shown herein for illustrative purposes only. Additional embodiments will be apparent to those skilled in the art based on the teachings herein. [Brief description of the drawings]

[0010]

[0010] Some embodiments of the invention will now be described, by way of example, with reference to the accompanying drawings, in which:

[0011] [Figure 1] 1 illustrates a lithographic apparatus which, together with other equipment, forms a semiconductor device production facility. [Diagram 2] FIG. 2 is a schematic diagram of a scatterometer for use in measuring a target according to an embodiment of the present invention; [Diagram 3] 1 is a flow diagram illustrating a method according to one embodiment. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

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

[0013]

[0012] 200 in Fig. 1 shows a lithography apparatus LA as part of an industrial production facility performing a large-scale lithographic manufacturing process. In this example, the manufacturing process is adapted to the manufacture of semiconductor products (integrated circuits) on substrates such as semiconductor wafers. Those skilled in the art will understand that a wide variety of products can be manufactured by processing different types of substrates in various variations of this process. The production of semiconductor products is used purely as an example with great commercial significance today.

[0014]

[0013] Within the lithographic apparatus (or "lithotool" for short 200) a measurement station MEA is indicated at 202, an exposure station EXP is indicated at 204, and a control unit LACU is indicated at 206. In this example, each substrate visits a measurement station and an exposure station so that a pattern is imparted to the substrate. In an optical lithographic apparatus, for example, a projection system is used to transfer the product pattern from a patterning device MA onto the substrate using conditioned radiation. This is done by forming an image of the pattern in a layer of radiation-sensitive resist material.

[0015]

[0014] The term "projection system" as used herein should be broadly interpreted to encompass any type of projection system, including refractive, reflective, catadioptric, magnetic, electromagnetic and electrostatic optical systems, or any combination thereof, appropriate for the exposure radiation used, or for other factors such as the use of an immersion liquid or the use of a vacuum. The patterning device MA may be a mask or a reticle, which imparts a pattern to a radiation beam that is transmitted or reflected by the patterning device. Well-known modes of operation include stepping and scanning modes. As is known, the projection system may cooperate with support and positioning systems for the substrate and the patterning device in various ways to impart the desired pattern to many target portions across the substrate. Instead of a reticle with a fixed pattern, a programmable patterning device may be used. The radiation may include electromagnetic radiation, for example, in the deep ultraviolet (DUV) or extreme ultraviolet (EUV) wavebands. The present disclosure is also applicable to other types of lithographic processes, such as imprint lithography and direct write lithography, such as with an electron beam.

[0016]

[0015] The lithographic apparatus control unit LACU controls all movements and measurements of the various actuators and sensors to receive the substrate W and reticle MA and to perform the patterning operations. The LACU also contains signal processing and data processing capabilities to perform the required calculations related to the operation of the apparatus. In practice, the control unit LACU is realized as a system of many sub-units, each of which handles real-time data acquisition, processing and control of a subsystem or component within the apparatus.

[0017]

[0016] Before a pattern is applied to the substrate at the exposure station EXP, the substrate may be processed at the measurement station MEA to perform various preparatory steps. The preparatory steps may include mapping the surface height of the substrate using a level sensor and measuring the position of alignment marks on the substrate using an alignment sensor. The alignment marks are usually arranged in a regular grid pattern. However, due to imprecision in the creation of the marks and due to deformations of the substrate occurring during processing, the marks deviate from the ideal grid. Therefore, if the apparatus is to print product features in a precise position with very high accuracy, in addition to measuring the position and orientation of the substrate, the alignment sensor must actually measure the position of many marks in detail over the entire substrate area. The apparatus may be of the so-called dual stage type, having two substrate tables each equipped with a positioning system controlled by a control unit LACU. Various preparatory steps may be performed by exposing one substrate on one substrate table at the exposure station EXP while another substrate can be placed on the other substrate table at the measurement station MEA. Measuring the alignment marks is therefore very time consuming and the provision of two substrate tables allows a significant increase in the throughput of the apparatus. If the position sensor IF is not able to measure the position of the substrate table when it is in the measurement station and when it is in the exposure station, the provision of a second position sensor may make it possible to track the position of the substrate table in both stations. The lithographic apparatus LA may be of a so-called dual stage type having two substrate tables and two stations (an exposure station and a measurement station) between which the substrate tables can be exchanged.

[0018]

[0017] In a production facility, the apparatus 200 forms part of a "litho cell" or "lithocluster" that also includes a coating apparatus 208 for applying photosensitive resist and other coatings to multiple substrates W for patterning by the apparatus 200. At the output of the apparatus 200, a bake apparatus 210 and a developer apparatus 212 are provided for developing the exposed pattern into a physical resist pattern. Between all these apparatuses, a substrate handling system is responsible for supporting the substrates and transporting them from one apparatus to the next. These apparatuses, often collectively referred to as a "track", are under the control of a track control unit controlled by a supervisory control system SCS, which also controls the lithography apparatus via a lithography apparatus control unit LACU. In this way, the different apparatuses can be operated to maximize throughput and processing efficiency. The supervisory control system SCS receives recipe information R that provides in detail a definition of the steps to be performed to create each patterned substrate.

[0019]

[0018] After patterning and development in the lithocell, the patterned substrate 220 is transferred to other processing equipment as shown at 222, 224, 226. A wide range of processing steps are performed by various equipment in a typical manufacturing facility. By way of example, the equipment 222 in this embodiment is an etching station, and the equipment 224 performs a post-etch annealing step. Further physical and / or chemical processing steps are applied in further equipment 226, etc. Many types of operations may be required to create the actual device, for example, material deposition, surface material property modification (oxidation, doping, ion implantation, etc.), chemical mechanical polishing (CMP), etc. The equipment 226 may actually represent a series of different processing steps performed in one or more equipment. As another example, equipment and processing steps may be provided to perform self-aligned multiple patterning to generate multiple smaller features based on the precursor pattern created by the lithography equipment.

[0020]

[0019] As is known, in the manufacture of semiconductor devices, such processes are repeated many times to build device structures layer by layer on a substrate using appropriate materials and patterns. Thus, the substrate 230 arriving at the lithography cluster may be a freshly prepared substrate, or a substrate that has been previously processed in this cluster or another whole machine. Similarly, depending on the processing required, the substrate 232 leaving the machine 226 may be returned for a subsequent patterning operation in the same lithography cluster, may be transported for a patterning operation in a different cluster, or may be a finished product sent for dicing and packaging.

[0021]

[0020] Each layer of the product structure requires a different sequence of processing steps, and the equipment 226 used for each layer may be completely different in type. Furthermore, even if the processing steps applied by the equipment 226 are nominally the same, in a large facility there may be several seemingly identical machines operating in parallel to perform the step 226 on different substrates. Small differences in the setup or faults between these machines mean that they affect different substrates in different ways. Even a step that is relatively common to each layer, such as etching (equipment 222), may be performed by several etching equipment that are nominally identical but operate in parallel to maximize throughput. In practice, furthermore, different layers require different etching processes, such as chemical etching, plasma etching, and special requirements such as isotropic etching, depending on the details of the material to be etched.

[0022]

[0021] The preceding and / or subsequent processes may be performed in other lithography apparatus as described above, or may be performed in different types of lithography apparatus. For example, some layers in a device manufacturing process that are highly demanding in parameters such as resolution and overlay may be formed in more advanced lithography tools than other layers that are less demanding. Thus, some layers may be exposed in an immersion lithography tool, while other layers are exposed in a "dry" tool. Some layers may be exposed in a tool operating at DUV wavelengths, while other layers are exposed using EUV wavelength radiation.

[0023]

[0022] To ensure that substrates exposed by the lithographic apparatus are correctly and consistently exposed, it is desirable to inspect the exposed substrate to measure properties such as overlay error between subsequent layers, line thickness, critical dimension (CD), etc. The manufacturing facility in which the lithocell LC is located therefore also includes a metrology system that receives some or all of the substrates W processed in the lithocell. The metrology results are provided directly or indirectly to a supervisory control system SCS. If an error is detected, particularly if metrology can be performed early enough before other substrates of the same batch are exposed, adjustments can be made to the exposure of subsequent substrates. Also, exposed substrates can be stripped and reworked to improve yield or discarded, thereby avoiding further processing on substrates known to be defective. If only some target portions of a substrate are defective, further exposures can only be performed on good target portions.

[0024]

[0023] Figure 1 also shows a metrology device 240 that is provided to perform measurements of parameters of the product at a desired stage in the manufacturing process. A typical example of a metrology station in a modern lithography production facility is a scatterometer, such as a dark field scatterometer, an angle resolved scatterometer or a spectroscopic scatterometer, which can be applied to measure the properties of the substrate developed in 220 before etching in the device 222. Using the metrology device 240, it can be determined that important performance parameters, such as overlay or critical dimension (CD), do not meet certain accuracy requirements of the developed resist. Before the etching step, there is an opportunity to strip the developed resist and reprocess the substrate 220 through the lithocluster. The metrology results 242 from the device 240 can be used to maintain the accurate performance of the patterning operation in the lithocluster by the supervisory control system SCS and / or the control unit LACU 206 making small adjustments over time, thereby minimizing the risk that the product will be out of specification and will require rework.

[0025] Additionally, metrology tool 240 and / or other metrology tools (not shown) can be applied to measure properties of processed substrates 232, 234, and subsequent substrates 230. Metrology tools can be used on processed substrates to determine important parameters such as overlay and CD.

[0026]

[0025] Figure 2(a) shows a metrology apparatus suitable for use in an embodiment of the present invention. Figure 2(b) shows a target T and the diffracted rays of the measurement radiation used to illuminate the target in more detail. The metrology apparatus shown is of the type known as a dark-field metrology apparatus. The metrology apparatus may be a stand-alone device or may be integrated into a lithography apparatus LA, for example in a measurement station or in a lithography cell LC. An optical axis with several branches throughout the apparatus is shown by a dotted line O. In this apparatus, light emitted by a source 11 (for example a xenon lamp) is directed onto a substrate W via a beam splitter 15 by an optical system including lenses 12, 14 and an objective lens 16. These lenses are arranged in a double sequence in a 4F configuration. Other lens arrangements can be used as long as they provide an image of the substrate on the detector and at the same time allow access to an intermediate pupil plane for spatial frequency filtering. Thus, by defining the spatial intensity distribution in a plane (herein called the (conjugate) pupil plane) representing the spatial spectrum of the substrate plane, the angular range at which the radiation is incident on the substrate can be selected. In particular, this can be done by inserting an aperture plate 13 of suitable form between the lenses 12 and 14 in a plane which is the back-projected image of the objective pupil plane. In the illustrated example, the aperture plate 13 has different forms, labelled 13N and 13S, which allow the selection of different illumination modes. 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 "north" for ease of explanation only. In a second illumination mode, the aperture plate 13S is used to provide a similar illumination from the opposite direction, labelled "south". By using different apertures, other illumination modes are also possible. It is desirable for the remainder of the pupil plane to be dark, since unwanted light outside the desired illumination mode would interfere with the desired measurement signal.

[0027] As shown in FIG. 2(b), the target T is placed with the substrate W perpendicular to the optical axis O of the objective lens 16. The substrate W may be supported by a support (not shown). A measurement radiation beam I impinging on the target T from an angle off the axis O results in a zeroth order beam (solid line 0) and two first order beams (dashed lines +1 and dashed lines -1). Note that due to the overfilled small target, these beams are only a part of many parallel beams covering the area of ​​the substrate including the metrology target T and other features. Since the aperture in the plate 13 has a finite width (necessary to pass a useful amount of light), the incident beam I will in fact occupy a range of angles, and the diffracted beams 0 and +1 / -1 will be somewhat spread out. According to the point spread function of the small target, the +1 and -1 orders will be further spread out over a range of angles and will not be one ideal beam 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. The rays shown in Figures 2(a) and 2(b) are shown to a certain degree off-axis simply to make them more easily distinguishable in the figures.

[0028]

[0027] At least the zeroth and first 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. Returning to Fig. 2(a), both the first and second illumination modes are illustrated with diametrically opposite apertures labeled as North (N) and South (S). If the incident ray I of measurement radiation comes from the north side of the optical axis, i.e. if the first illumination mode is applied using the aperture plate 13N, the +1 diffracted ray, labeled +1(N), is incident on the objective lens 16. Conversely, if the second illumination mode is applied using the aperture plate 13S, the -1 diffracted ray (labeled 1(S)) is the ray incident on the lens 16.

[0029]

[0028] A second beam splitter 17 splits the diffracted beam into two measurement branches. In the first measurement branch, an optical system 18 uses the zeroth and first diffracted order beams to form a diffraction spectrum (pupil plane image) of the target on a first sensor 19 (e.g. a CCD or CMOS sensor). Since each diffraction order hits a different point on the sensor, the orders can be compared by image processing. The pupil plane image captured by the sensor 19 can be used for many measurement purposes, such as the reconstruction used in the methods described herein. The pupil plane image can also be used to focus the metrology device and / or to normalize the intensity measurements of the first beam order.

[0030] In the second measurement branch, the optical system 20, 22 forms an image of the target T on a sensor 23 (for example 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 has the function of blocking the zeroth order diffracted beam so that the image of the target formed on the sensor 23 is formed only from the -1st or +1st order beam. The images captured by the sensors 19 and 23 are output to a processor PU which processes the images, the function of which depends on what type of measurement is being performed. Note that in this document the term "image" is used in a broad sense. For this reason, an image of the grating lines will not be formed if only the -1st and +1st orders are present.

[0031]

[0030] The particular configuration of aperture plate 13 and field stop 21 shown in Figure 2 is merely an example. 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 one first order diffracted light to the sensor. In yet other embodiments, second, third and even higher order beams (not shown in Figure 2) can be used for the measurement instead of or in addition to the first order beam.

[0032]

[0031] The target T may include multiple gratings, which may have different biased overlay offsets to facilitate measurement of the overlay between the layers on which different parts of the composite grating are formed. The gratings may also be oriented differently to diffract incident radiation in the X and Y directions. In one example, a target may include two X-direction gratings with biased overlay offsets +d and -d, and a Y-direction grating with biased overlay offsets +d and -d. Separate images of these gratings may be identified in the images captured by the sensor 23. Once the separate images of the gratings are identified, the intensities of these individual images may be measured, for example, by averaging or summing the intensity values ​​of selected pixels within the identified regions. The intensities and / or other characteristics of the images may be compared to each other. These results may be combined to measure separate parameters of the lithography process.

[0033]

[0032] Lithography process control methods typically rely on measurements of parameters of interest at multiple points on a wafer or a portion thereof (such as an exposure field) that are indicative of the quality of the circuits being manufactured, and thus the functionality / yield. These measurements can be modeled to interpolate values ​​of the parameters of interest at locations between the measurement points where the values ​​are actually known. The modeled measurements are sometimes called fingerprints, which are the spatial distribution of the parameters of interest (or another parameter) on the wafer or a portion thereof. Alternatively, the modeled measurements can include a temporal distribution or a contextual distribution. The parameters of interest can be any parameter that is indicative of or related to the functionality / yield of the device. Common examples are overlay, alignment or positioning parameters (grid position / modeling of the wafer lattice), layer-by-layer position parameters such as edge placement error (EPE), critical dimensions (CD), leveling parameters (e.g. height of the wafer surface), etching parameters, other process parameters, and metrology parameters that result in a metrology fingerprint. Such fingerprints can be used, for example, for diagnosis and control of the lithography process (after applying optimizations, e.g., converting the fingerprints into scanner operating parameters).

[0034]

[0033] The main problem in modeling the fingerprint of a parameter of interest is to find the best way to estimate the parameter of interest at any location on the wafer (or part thereof) given a finite set of measurement points of the parameter of interest. It is known to model the measured data of the parameter of interest by fitting a set of predefined basis functions (selected during the model setup) to the measured data. The basis functions can then be evaluated at any location to obtain a prediction for the entire wafer. Computational metrology is another method with the same basic approach, but uses different types of additional data (data from different domains) to improve the prediction of the parameter of interest (for example, if the parameter of interest is overlay, the additional data can be one or more of alignment, leveling, and / or servo error data reported by the scanner).

[0035]

[0034] A currently identified limitation of such estimation methods is the degradation of performance for sampling layouts exceeding about 500 points per wafer. When measuring fewer points, basis function-based estimation models work well. However, when sampling exceeds 500 points, they are outperformed by models that do not perform global estimation and model per field (e.g., per exposure correction or CPE). Most of the physical causes of wafer fingerprints are not related to the exposure field, so the fingerprints do not show per field behavior. Therefore, the CPE model cannot be expected to perform best in practice, which means that there must be better estimation models for this range beyond 500 points.

[0036]

[0035] A fundamental limitation of the current approach is that it is not directly based on physical knowledge. As a specific example, it has been determined that current estimation models do not perform well for ring-shaped fingerprints that are often found in 3D-NAND structures. This problem has been successfully solved by implementing new basis functions that are more suitable for capturing these fingerprints. However, the need to design such new basis functions adds an additional layer of non-physical content to the basic physical knowledge of how ring fingerprints occur.

[0037]

[0036] To address this issue, a new modeling approach for fingerprint determination has been proposed that relies on actual physical knowledge about the fingerprint or spatial distribution of the parameters of interest. More specifically, the proposed approach is based on Bayesian approximation or Bayesian estimation.

[0038]

[0037] Bayesian estimation is a method of statistical estimation that uses Bayes' theorem to update the probability of a hypothesis as more evidence or information becomes available. Bayesian estimation derives the posterior probability as a result of two assumptions: the prior probability and a "likelihood function" derived from a statistical model or description of the observed (measured) data. The result is a continuously updated estimate or fingerprint that is updated whenever new data becomes available.

[0039]

[0038] The proposed method may use a formal statistical description (prior distribution) of how the fingerprint of the target parameter (including noise) is expected to behave, and metrology data (e.g., metrology data of at least the target parameter including a set of measurements of the target parameter). The metrology data may also optionally include other metrology data of different types than the target parameter (e.g., alignment data, leveling data, servo error data, data of after development inspection (ADI) overlay vs. after etch inspection (AEI) overlay, and EPE data, among others). Thus, the prior distribution may include elements or parameters other than the target parameter.

[0040]

[0039] Figure 3 is a conceptual flow diagram of such a method. The statistical description SD is used as a Bayesian prior distribution, which is updated by the solver SLV based on new metrology data MD (observations). Based on these two inputs SD, MD, the solver SLV decides which set of root causes is most likely to explain the observations (i.e., the metrology data MD). This is a formal mathematical problem that can be induced to be solvable with only one matrix inversion if certain criteria are met (i.e., all distributions in the prior distribution are Gaussian and the relationship between the parameters of the prior distribution and the observations is linear). The output can include a fingerprint CFP of the target parameters that is continuously updated.

[0041]

[0040] The statistical description or prior distribution may include a known predicted behavior of the target parameter, for example, based on previous observations, known physical knowledge, and / or expert knowledge. For example, the prior distribution may include a spatial distribution (fingerprint) shape of one or more predicted target parameters. As an example of overlay, it has been found that the measure of overlay is the sum of at least the following shape-related components: • The inter-field shape is predicted to be smooth. • The shape within the field is predicted to be smooth. • Slit fingerprints are predicted to be smooth. ?The scan-up and scan-down shapes are predicted to be smooth. ?Step Left Step Right The shape is predicted to be smooth. The edge roll-off profile, which depends only on the radius, is predicted to be smooth. The shape per exposure field is expected to be smooth. Measurement noise is expected to be smooth.

[0042]

[0041] Thus, a statistical description of an overlay may include one or more, two or more, three or more, four or more, five or more, six or more, or all of the (geometric) components listed immediately above. A prior distribution may therefore be constructed from any number of such geometric components based on previously observed overlay shapes. The prior distribution may include a statistical distribution (e.g., a spatial distribution and a measurement noise component representing the error bars of this spatial distribution), so that this prior distribution can be sampled directly. At least some of these (geometric) components may be applicable to other parameters of interest, such as edge placement error.

[0043]

[0042] In each of these (shape) components, other than noise, the shape of the distribution or fingerprint components is expected to be smooth. In this context, smoothness can be specifically quantified by the bending energy of the model for a given shape m(x,y).

number

[0044]

[0043] Alternative definitions of smoothness that can be used instead of bending energy include the rotation or divergence of the distribution components or fingerprint components (eg, vector fields).

[0045]

[0044] If the shape is predicted to behave in a certain way, e.g. "predicted to be smooth", this is a statistical description. This involves the solver finding the most likely solution, as described above. To this end, the solver finds the solution that minimizes the bending energy of each component in the prior distribution. In this way, tuning parameters in the model (e.g. how smooth the shape is predicted to be, how large the measurement noise is predicted to be) have a physical meaning, unlike choices in traditional models (e.g. the choice of the degree of the polynomial to fit). Moreover, the classification into physical effects is very useful for diagnosis.

[0046]

[0045] It should be understood that the solver may fit all the aforementioned geometric components simultaneously. Thus, using the given overlay example, the solver may fit the fingerprint model by simultaneously minimizing the bending energy of each geometric component included in the prior distribution, and by minimizing the measurement noise component (if included).

[0047]

[0046] Furthermore, fitting can be done simultaneously for all measured wafers, instead of wafer by wafer, as is usually the case. This can greatly improve performance when the wafers do not have a common sampling scheme, and a common shape can be found using all wafers. The same result cannot be achieved by first averaging, and then the overall content of each wafer goes into this average wafer. Therefore, it is possible to efficiently use sampling changes per field or per wafer. For example, it has been shown that an accurate SUSD fingerprint can be determined by sampling a very small number of points both in the scan upfield and the scan downfield.

[0048]

[0047] It should be noted that the concept of Bayesian approximation is not limited to the above examples of statistical description. In particular, it is possible that the statistical description can be extended or improved by more specific knowledge. For example, the description can be improved by including one or more of wafer heating data, a map of wafer height Z versus XY position, servo error data, scanner grating deformation, pattern shift data, heating data (e.g., one or more of lens heating data, reticle heating data, wafer heating data), drift data (e.g., intra-wafer drift data, intra-lot drift data, long-term drift data), mark printing error, ADI-ACI (after clean inspection) matching data, radial inner wafer model, variation mode (e.g., as part of principal component analysis (PCA)), advanced process correction data, intra-field etch impact data. Also, the prior distribution can be improved as knowledge changes. For example, quantification of overall shape and smoothness other than that described may prove to be better in the future.

[0049] In one embodiment, the solver may be used in the scanner for each wafer, for example immediately following or immediately after measuring the alignment data.

[0050]

[0049] It can be seen that the proposed methodology is easily extendable with new physical effects since new effects can be added to the statistical description without the need to provide / determine a new modeling flow.

[0051] Further embodiments of the present invention are disclosed in the following list of numbered clauses: 1. A method for determining a spatial distribution of a parameter of interest for at least one substrate or portion thereof subjected to a semiconductor manufacturing process, comprising: obtaining a statistical description describing a predicted fingerprint component of the spatial distribution and a noise component describing a predicted level of measurement noise associated with the parameter of interest; obtaining metrology data associated with the parameter of interest; and estimating the spatial distribution of the parameter of interest for the at least one substrate or portion thereof by Bayesian estimation using the statistical description as a prior distribution and the metrology data as observations. 2. The method of claim 1, wherein the statistical description describes a distribution associated with a semiconductor manufacturing process. 3. The method of claim 2, wherein the distribution is a spatial, temporal, or contextual distribution. 4. The method of any one of clauses 1 to 3, wherein the statistical description includes at least one predictive component of the spatial distribution of the parameter of interest. 5. The method of claim 4, wherein the at least one predictive component includes multiple predictive components of the spatial distribution of the parameter of interest, and the estimating step includes simultaneously fitting each of the predictive components to the metrology data. 6. The method of clause 4 or 5, wherein the metrology data includes a plurality of metrology data sets, each of the metrology data sets relating to a respective substrate of the plurality of substrates, and the estimating step includes simultaneously fitting each of the at least one predicted component to each of the metrology data sets. 7. The method of claim 6, wherein the measurement sampling for each metrology data set varies for the metrology data set. 8. The method of any of clauses 4 to 7, wherein at least one predictive component comprises one or more predictive shape components of the spatial distribution of the parameter of interest. 9. The method of claim 8, wherein the statistical description includes a plurality of predicted shape components of the spatial distribution of the parameter of interest. 10. The method according to clause 8 or 9, wherein some or each of the one or more predicted shape components is predicted to be smooth according to a statistical description. 11. The method of claim 10, wherein each of the one or more predicted shape components is predicted to have low bending energy, divergence, or curl. 12. The method of claim 11, wherein the estimating step includes fitting one or more feature components to metrology data to minimize bending energy, divergence, or curl of each feature component predicted to be smooth. 13. The method of any of clauses 8-12, wherein the semiconductor manufacturing process is a lithography process and each of the one or more predicted shape components includes one or more of an inter-field shape, an intra-field shape, a slit fingerprint, a scan-up scan-down shape, a step-left step-right shape, an edge roll-off shape that is dependent only on radius, and a shape per exposure field. 14. The method of any of clauses 8-12, wherein each of the one or more predicted shape components includes two or more of an inter-field shape, an intra-field shape, a slit fingerprint, a scan-up-scan-down shape, a step-left-step-right shape, an edge roll-off shape that is only dependent on radius, and a shape per exposure field. 15. The method of any of clauses 8-12, wherein each of the one or more predicted shape components includes three or more of an inter-field shape, an intra-field shape, a slit fingerprint, a scan-up-scan-down shape, a step-left-step-right shape, an edge roll-off shape that is only dependent on radius, and a shape per exposure field. 16. A method as described in any of clauses 8 to 12, wherein each of the one or more predicted shape components includes each of an inter-field shape, an intra-field shape, a slit fingerprint, a scan-up scan-down shape, a step-left step-right shape, an edge roll-off shape that is only dependent on radius, and a shape per exposure field. 17. The method of any of clauses 4 to 16, wherein each of the at least one prediction component comprises a statistical spatial distribution for the substrate or a portion thereof. 18. The method of any of clauses 4 to 17, wherein at least one prediction component includes a noise component describing predicted measurement noise. 19. The method of claim 18, wherein describing the expected measurement noise includes predicting that the measurement noise is small. 20. The method of any of clauses 18 or 19, wherein the estimating step includes fitting one or more components to metrology data such that measurement noise is minimized. 21. The method of any of clauses 4-20, wherein at least one prediction component includes one or more components related to shape or other characteristics, including one or more of wafer heating data, a map of wafer height Z versus X-Y position, servo error data, scanner grating deformation, pattern shift data, heating data, drift data, mark printing errors, ADI-ACI matching data, radial inner wafer model, modes of variation as part of principal component analysis, advanced process correction data, and intra-field etch effect data. 22. The method of any one of clauses 1 to 21, wherein the metrology data comprises a set of measurements of a parameter of interest. 23. A method according to any of clauses 1 to 22, wherein the metrology data comprises a set of measurements of a parameter other than the parameter of interest and / or a set of measurements relating to a domain other than the domain of the parameter of interest. 24. The method of any of clauses 1-23, wherein the method is repeated each time new metrology data becomes available. 25. The method of any of clauses 1 to 24, comprising performing the method on each substrate before performing a semiconductor manufacturing exposure process on each substrate. 26. The method of clause 25, comprising performing the method while performing an alignment process and a lithographic exposure process on each substrate. 27. A method according to any of clauses 1 to 26, further comprising using the spatial distribution of the target parameter to control a lithographic apparatus configured to provide a product structure on a substrate in a lithographic process. 28. A computer program comprising program instructions operable, when executed on a suitable device, to perform the method according to any of the preceding clauses. 29. A non-transitory computer program carrier containing a computer program as referred to in clause 28. 30. A processing arrangement comprising a computer program carrier containing a computer program according to clause 29, and a processor operable to execute the computer program. 31. A metrology device including a processing arrangement according to clause 30. 32. A lithographic apparatus including a processing arrangement according to clause 30. 33. A method for determining a spatial distribution of a parameter of interest for at least one substrate or portion thereof subjected to a semiconductor manufacturing process, comprising: obtaining a statistical description describing a predicted fingerprint component of the spatial distribution and a noise component describing a predicted level of measurement noise associated with the parameter of interest; obtaining metrology data associated with the parameter of interest; and estimating the spatial distribution of the parameter of interest for the at least one substrate or portion thereof by Bayesian estimation using the statistical description as a prior distribution and the metrology data as observations. 34. The method of clause 33, wherein the target parameter is a parameter associated with a semiconductor manufacturing process. 35. The method of claim 33 or 34, wherein the predictive fingerprint components include multiple shape components of the spatial distribution of the parameter of interest. 36. The method of claim 35, wherein the estimating step includes simultaneously fitting each geometric component of the plurality of geometric components to the metrology data. 37. A method according to any of clauses 33 to 36, wherein the metrology data includes a plurality of metrology data sets, each of which relates to a respective substrate of the plurality of substrates, and the estimation step includes simultaneously fitting the predicted fingerprint components to each of the metrology data sets. 38. A method according to any of clauses 35 to 37, wherein some or each of the plurality of shape components is predicted to be smooth according to a statistical description. 39. The method of claim 35, wherein some or each of the plurality of shape components is predicted to have low bending energy, divergence, or curl. 40. The method of clause 35, wherein the estimating step includes fitting one or more of the plurality of geometric components to metrology data to minimize bending energy, divergence, or curl of each geometric component that is predicted to be smooth. 41. A method according to any of clauses 35-40, wherein the estimating step includes fitting one or more shape components of the plurality of shape components to the metrology data such that a predicted level of measurement noise is minimized. 42. A method according to any of clauses 35 to 41, wherein the semiconductor manufacturing process is a lithography process and the plurality of feature components include one or more of an inter-field feature, an intra-field feature, a slit fingerprint, a scan-up scan-down feature, a step-left step-right feature, an edge roll-off feature that is dependent only on radius, and a feature per exposure field. 43. A method according to any of clauses 33 to 42, wherein the metrology data comprises a set of measurements of a parameter other than the parameter of interest and / or a set of measurements relating to a domain other than the domain of the parameter of interest. 44. A computer program comprising program instructions operable, when executed on a suitable device, to perform the method according to any of clauses 33 to 43. 45. A non-transitory computer program carrier containing a computer program as referred to in clause 44. 46. ​​A processing arrangement comprising a computer program carrier containing a computer program according to clause 45, and a processor operable to execute the computer program. 47. A metrology device including a processing arrangement according to clause 46.

[0052]

[0051] The terms "radiation" and "beam" as used in connection with a lithographic apparatus encompass all types of electromagnetic radiation including ultraviolet (UV) (e.g. having a wavelength of 365 nm, 355 nm, 248 nm, 193 nm, 157 nm or 126 nm, or wavelengths approximately these values), and extreme ultraviolet (EUV) (e.g. having a wavelength in the range of 5 to 20 nm), as well as particulate beams such as ion beams and electron beams.

[0053] The term "lens", where the context allows, may refer to any one or combination of various types of optical components, including refractive, reflective, magnetic, electromagnetic and electrostatic optical components.

[0054]

[0053] The above description of the specific embodiments sufficiently reveals the general nature of the present invention, so that others can easily modify and / or adapt such specific embodiments for various applications by applying knowledge within the art without undue experimentation and without departing from the general concept of the present invention. Therefore, such adaptations and modifications are intended to be within the meaning and range of equivalents of the disclosed embodiments based on the teaching and guidance presented herein. It should be understood that the expressions or terms in this specification are for the purpose of explanation by example and not limitation, and therefore the terms or terms in this specification should be interpreted by those skilled in the art in light of the teaching and guidance.

[0055]

[0054] 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. 1. A method for determining a spatial distribution of a parameter of interest for at least one substrate or a portion thereof subjected to a semiconductor manufacturing process, comprising the steps of: obtaining a statistical description describing a predicted fingerprint component of the spatial distribution and a noise component describing a predicted level of measurement noise associated with the parameter of interest; acquiring metrology data related to the parameter of interest; estimating the spatial distribution of the parameter of interest for the at least one substrate or portion thereof by Bayesian estimation using the statistical description as a prior distribution and the metrology data as observations; A method comprising:

2. The method of claim 1 , wherein the parameter of interest is a parameter associated with the semiconductor manufacturing process.

3. The method of claim 1 , wherein the predictive fingerprint components include multiple shape components of the spatial distribution of the parameter of interest.

4. The method of claim 3 , wherein the estimating step includes simultaneously fitting each geometric component of the plurality of geometric components to the metrology data.

5. 2. The method of claim 1, wherein the metrology data includes a plurality of metrology data sets, each of which is associated with a respective substrate of a plurality of substrates, and the estimating step includes fitting the predicted fingerprint components to each of the metrology data sets simultaneously.

6. The method of claim 3 , wherein some or each of the plurality of geometric components is predicted to be smooth according to the statistical description.

7. The method of claim 3 , wherein some or each of the plurality of shape components is predicted to have low bending energy, divergence, or curl.

8. 4. The method of claim 3, wherein the estimating step comprises fitting one or more of the plurality of geometric components to the metrology data to minimize the bending energy, divergence, or curl of each geometric component that is predicted to be smooth.

9. The method of claim 3 , wherein the estimating step comprises fitting one or more of the plurality of geometric components to the metrology data such that the predicted level of measurement noise is minimized.

10. 4. The method of claim 3, wherein the semiconductor manufacturing process is a lithography process and the plurality of feature components include one or more of an inter-field feature, an intra-field feature, a slit fingerprint, a scan-up-scan-down feature, a step-left-step-right feature, an edge roll-off feature that is radius only dependent, and a feature per exposure field.

11. The method of claim 1 , wherein the metrology data comprises a set of measurements of parameters other than the parameter of interest and / or a set of measurements relating to domains other than the domain of the parameter of interest.

12. A computer program comprising program instructions operable to perform the method according to any of claims 1 to 11 when executed on a suitable device.

13. A non-transitory computer program carrier comprising a computer program according to claim 12.

14. A computer program carrier comprising a computer program according to claim 13; a processor operable to execute the computer program; A processing configuration including:

15. A metrology device comprising the processing arrangement of claim 14.

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