Measurement by computer

Abstract

To provide techniques of improving the performance of a device manufacturing process.SOLUTION: A method includes: determining first distribution of a first parameter associated with an error or residual in performing a device manufacturing process; determining second distribution of a second parameter associated with an error or residual in performing the device manufacturing process; and determining distribution of a parameter of interest associated with the device manufacturing process using a function operating on the first and second distributions. The function may include a correlation.SELECTED DRAWING: Figure 9

Description

Technical Field

[0001] The present disclosure relates to techniques for improving the performance of device manufacturing processes. These techniques may be used in connection with lithographic apparatus or metrology apparatus.

Background Art

[0002] A lithographic apparatus is a machine that applies a desired pattern onto a target portion of a substrate. The lithographic apparatus can be used, for example, in the manufacture of integrated circuits (ICs). In that context, a patterning device, alternatively referred to as a mask or a reticle, can be used to generate a circuit pattern corresponding to an individual layer of the IC, and this pattern can be exposed onto a part of a substrate (e.g., a silicon wafer) having a layer of a radiation-sensitive material (resist) on a target portion (e.g., one or more dies). In general, a single substrate will contain a network of adjacent target portions that are successively exposed. Known lithographic apparatus include so-called steppers that irradiate each target portion by exposing the entire pattern onto the target portion at once, and so-called scanners that irradiate each target portion by scanning the pattern through a beam while synchronously scanning the substrate in a specified direction (the “scan” direction) parallel or antiparallel to this direction.

[0003] Before transferring the circuit pattern from the patterning device to the substrate, the substrate may go through various steps such as priming, resist coating, soft baking, etc. After exposure, the substrate is further subjected to other steps such as post-exposure bake (PEB), development, hard baking, measurement / inspection of the transferred circuit pattern, etc. This series of steps is used as the basis for creating individual layers (such as ICs) of the device. Next, the substrate can go through various processes such as etching, ion implantation (doping), metallization, oxidation, chemical mechanical polishing, etc. to finish all the individual layers of the device. If multiple layers are required for the device, the entire steps or their variations are repeated for each layer. Finally, there are devices present at each target portion on the substrate. Thereafter, these devices are separated from each other by techniques such as dicing and sawing, and the individual devices can be attached to the carrier.

[0004] Therefore, the manufacture of devices such as semiconductor devices typically involves processing a substrate (e.g., a semiconductor wafer) using a number of manufacturing processes to form various features and multiple layers of the device. Such layers and features are typically fabricated and processed using, for example, deposition, lithography, etching, chemical mechanical polishing, and ion implantation. Multiple devices can be created on a plurality of dies on the substrate and separated into individual devices. This device manufacturing process can be regarded as a patterning process. The patterning process typically, but optionally, includes patterning steps such as optical and / or nanoimprint lithography using the patterning device of a lithographic apparatus to transfer the pattern on the patterning device to the substrate, and one or more associated pattern processing steps including resist development by a developing device, baking of the substrate using a baking tool, etching using the pattern with an etching device, etc.

Summary of the Invention

[0005] In one embodiment, a method is disclosed that includes determining a first distribution of a first parameter related to an error or residual when executing a device manufacturing process, and determining a second distribution of a second parameter related to an error or residual when executing the device manufacturing process. Then, a hardware computer uses a function operating on the first and second distributions to determine a distribution of a parameter of interest related to the device manufacturing process.

[0006] In one embodiment, a method is provided that includes obtaining a contribution underlying a lithographic apparatus to an overlay as part of a patterning process. Then, a hardware computer combines the underlying contribution with a further contribution of the substrate to the overlay to obtain an estimate of the overlay of the substrate.

[0007] In one embodiment, a method is provided that includes determining a first distribution of measured alignment data when executing a device manufacturing process, determining a second distribution of alignment data derived from process parameters of the device manufacturing process, and determining, by a hardware computer system, a distribution of alignment data related to the device manufacturing process as a function of the first and second distributions.

[0008] In one embodiment, a method is provided that includes obtaining an alignment data distribution over at least a portion of a substrate processed using a patterning process based on measured alignment data, and obtaining an estimate of the alignment data of the substrate by a hardware computer combining an alignment fingerprint resulting from process parameters other than the measured alignment with the alignment data distribution.

[0009] In one embodiment, a computer program product is provided that includes a non-transitory computer-readable medium having instructions recorded thereon that, when executed by a computer implementing any of the methods herein. BRIEF DESCRIPTION OF THE DRAWINGS

[0010]

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DETAILED DESCRIPTION OF THE INVENTION

[0011] Before describing the embodiments in detail, it is beneficial to present an exemplary environment in which the embodiments can be implemented.

[0012] Figure 1 schematically shows an embodiment of a lithographic apparatus LA. Configuration of the apparatus: An illumination system (illuminator) IL configured to adjust a radiation beam B (UV radiation or DUV radiation); A support structure (e.g., a mask table) MT connected to a first positioner PM constructed to support a patterning device (e.g., a mask) MA and configured to accurately position the patterning device according to certain parameters; A substrate table (e.g., a wafer table) WT connected to a second positioner PW constructed to hold a substrate (e.g., a resist-coated wafer) W and configured to accurately place the substrate according to certain parameters; A projection system (e.g., a refractive projection lens system) PS configured to project a pattern imparted to a radiation beam B by the patterning device MA onto a target portion C (including one or more dies, often called a field of the substrate W); The projection system is supported on a reference frame (RF).

[0013] As shown herein, the apparatus is of the transmissive type (e.g., using a transmissive mask). Alternatively, the apparatus may be of the reflective type (e.g., using a programmable mirror array of the type mentioned above, or a reflective mask).

[0014] The illuminator IL receives a radiation beam from a radiation source SO. For example, if the radiation source is an excimer laser, the radiation source and the lithographic apparatus may be separate entities. In such a case, the radiation source is not considered to form part of the lithographic apparatus, and the radiation beam is sent from the radiation source SO to the illuminator IL using a beam delivery system BD including the beam, e.g., by means of suitable directing mirrors and / or expanders. In other cases, the source is part of the apparatus, for example, if the light source is a mercury lamp. The radiation source SO and the illuminator IL, together with the beam delivery system BD if necessary, may be referred to as a radiation system.

[0015] Illuminator IL may change the intensity distribution of the beam. The illuminator can be arranged to limit the radial range of the radiation beam such that the intensity distribution becomes non-zero within an annular region in the pupil plane of the illuminator IL. Additionally or alternatively, the illuminator IL may be operable to limit the distribution of the beam in the pupil plane such that the intensity distribution becomes non-zero within a plurality of equally spaced sectors in the pupil plane. The intensity distribution of the radiation beam in the pupil plane of the illuminator IL may be referred to as the illumination mode.

[0016] Accordingly, the illuminator IL may comprise an adjuster AM configured to adjust the (angular / spatial) intensity distribution of the beam. Generally, at least the outer and / or inner radius ranges (usually referred to as σ-outer and σ-inner respectively) of the intensity distribution within the pupil plane of the illuminator can be adjusted. The illuminator IL may be operable to change the angular distribution of the beam. For example, the illuminator may be operable to change the number and angular range of the sectors in the pupil plane where the intensity distribution is non-zero. By adjusting the intensity distribution of the beam within the pupil plane of the illuminator, different illumination modes can be achieved. For example, by limiting the radial and angular ranges of the intensity distribution within the pupil plane of the illuminator IL, the intensity distribution may have a multipole distribution such as, for example, a dipole, quadrupole or hexapole distribution. The desired illumination mode can be obtained, for example, by inserting an optical system providing that illumination mode into the illuminator IL or by using a spatial light modulator.

[0017] Illuminator IL may be operable to change the polarization of the beam and may be operable to adjust the polarization using adjuster AM. The polarization state of the radiation beam across the pupil plane of illuminator IL may be referred to as a polarization mode. The use of different polarization modes may make it possible to achieve greater contrast in the image formed on substrate W. The radiation beam may not be polarized. Alternatively, the illuminator may be arranged to linearly polarize the radiation beam. The polarization direction of the radiation beam may vary across the pupil plane of illuminator IL. The polarization direction of the radiation may be different in different regions of the pupil plane of illuminator IL. The polarization state of the radiation can be selected according to the illumination mode. In the case of the multipole illumination mode, the polarization of each pole of the radiation beam may be substantially perpendicular to the position vector of that pole within the pupil plane of illuminator IL. For example, in the case of the dipole illumination mode, the radiation may be linearly polarized in a direction substantially perpendicular to the line bisecting the two opposing sectors of the dipole. The radiation beam is polarized in one of two different orthogonal directions called the X-polarization state and the Y-polarization state. In the case of the quadrupole illumination mode, the radiation of each sector of the pole can be linearly polarized in a direction substantially perpendicular to the line bisecting that sector. This polarization mode may be called XY polarization. Similarly, in the case of the hexapole illumination mode, the radiation of each sector of the pole can be linearly polarized in a direction substantially perpendicular to the line bisecting that sector. This polarization mode may be called TE polarization.

[0018] Furthermore, illuminator IL generally includes various other components such as integrator IN and capacitor CO. The illumination system can include various types of optical components such as those for refraction, reflection, magnetic, electromagnetic, electrostatic, or radiation directing, shaping, or controlling, or any combination thereof, or other types of optical components.

[0019] Thus, the illuminator provides an adjusted radiation beam B having a desired uniformity and intensity distribution in its cross-section.

[0020] The support structure MT supports the patterning device in a way that depends on the orientation of the patterning device, the design of the lithographic apparatus, and other conditions such as whether the patterning device is held in a vacuum environment. The support structure can hold the patterning device using mechanical, vacuum, electrostatic, or other clamping techniques. The support structure may be, for example, a frame or table that can be made fixed or movable as required. The support structure can ensure that the patterning device is in the desired position relative to, for example, the projection system. All uses of the terms "reticle" or "mask" in this specification can be regarded as synonymous with the more general term "patterning device".

[0021] The term "patterning device" as used in this specification should be broadly construed to refer to a device that can be used to impart a pattern to a target portion of a substrate. In one embodiment, the patterning device is any device that can be used to impart a pattern to a cross-section of a radiation beam in order 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 of the target portion of the substrate, for example when the pattern includes phase-shift features or so-called assist features. In general, the pattern imparted to the radiation beam corresponds to a particular functional layer of the device being created in the target portion, such as an integrated circuit.

[0022] 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, attenuated phase-shift, and various hybrid mask types. In the example of a programmable mirror array, a matrix arrangement of small mirrors is used. Each mirror can be individually tilted to reflect an incident radiation beam in a different direction. The tilted mirrors impart a pattern to the radiation beam, which is reflected by the mirror matrix.

[0023] As used herein, the term "projection system" should be broadly construed to encompass any type of projection system, including refractive, reflective, catadioptric, magnetic, electromagnetic, and electro - static optical systems, or combinations thereof appropriate for the exposure radiation being used. In the case of other factors, such as the use of an immersion liquid or the use of a vacuum. All uses of the term "projection lens" in this specification can be considered synonymous with the more general term "projection system".

[0024] The projection system PS has a non - uniform optical transfer function and can affect the pattern imaged on the substrate W. In the case of non - polarized radiation, such effects are described as a scalar map of the transmission (apodization) and relative phase, depending on the position within the pupil plane, of the radiation emerging from the projection system PS. These scalar maps may be referred to as transmission maps and relative phase maps and may be represented as a linear combination of a complete set of basis functions. A particularly convenient set is the Zernike polynomials, which form a set of orthogonal polynomials defined on the unit circle. The determination of each scalar map involves the determination of the coefficients in such an expansion. Since the Zernike polynomials are orthogonal on the unit circle, the Zernike coefficients can be determined by calculating the inner product of the measured scalar map with each Zernike polynomial and dividing this by the square of the norm of that Zernike polynomial.

[0025] The transmission map and the relative phase map are field- and system-dependent. That is, in general, each projection system PS will have a different Zernike expansion for each field point (i.e., for each spatial position in its image plane). The relative phase of the projection system PS in its pupil plane can be determined, for example, by projecting radiation from a point source in the object plane of the projection system PS (i.e., the plane of the patterning device MA) through the projection. The system PS and a shearing interferometer are used to measure the wavefront (i.e., the locus of points of the same phase). The shearing interferometer is a common-path interferometer and thus, advantageously, no secondary reference beam is required to measure the wavefront. The shearing interferometer may comprise a diffraction grating, e.g., a two-dimensional grid, in the image plane of the projection system (i.e., the substrate table WT) and a detector configured to detect an interference pattern in a plane conjugate to the pupil plane of the projection system PS. The interference pattern is related to the derivative of the phase of the radiation with respect to the coordinates of the pupil plane in the shearing direction. The detector may comprise an array of sensing elements, e.g., charge-coupled devices (CCDs).

[0026] Since the projection system PS of a lithographic apparatus may not generate visible fringes, for example, a technical phase step such as the movement of a diffraction grating can be used to improve the accuracy of the determination of the wavefront. Steps can be executed in a direction perpendicular to the scanning direction of the measurement within the plane of the diffraction grating. The stepping range is one grating period and at least three (evenly distributed) phase steps are used. Thus, for example, three scanning measurements can be executed in the y direction, each scanning measurement being executed for a different position in the x direction. This stepping of the diffraction grating effectively converts phase variations into intensity variations, enabling the phase information to be determined. The grating can be stepped in a direction perpendicular to the diffraction grating (the z direction) to calibrate the detector.

[0027] The diffractive grating can be scanned continuously in two perpendicular directions that coincide with the axes (x and y) of the coordinate system of the projection system PS or are at an angle such as 45 degrees with respect to these axes. The scan may be performed over an integer grating period, for example, over one grating period. By the scan, the phase fluctuations in one direction are averaged out and the phase fluctuations in the other direction can be reconstructed. Thereby, the wavefront can be determined as a function of both directions.

[0028] The transmission (apodization) of the projection system PS in its pupil plane can be determined, for example, by projecting the radiation from a point source in the object plane of the projection system PS (i.e., the plane of the patterning device MA). Using the projection system PS and the detector, the intensity of the radiation in a plane conjugate to the pupil plane of the projection system PS is measured. The same detector that is used to measure the wavefront to determine the aberration may be used.

[0029] The projection system PS may comprise a plurality of optical (e.g., lens) elements and may further comprise an adjustment mechanism AM configured to adjust one or more of the optical elements so as to correct aberrations (phase variations across the pupil plane of the entire field of view). To achieve this, the adjustment mechanism may be operable to manipulate one or more of the optical (e.g., lens) elements within the projection system PS in one or more different ways. The projection system may have a coordinate system whose optical axis extends in the z direction. The adjustment mechanism may be operable to perform any of the following combinations: displace one or more of the optical elements, tilt one or more of the optical elements, and / or deform one or more of the optical elements. The displacement of the optical element is in any direction (x, y, z, or combinations thereof). The tilt of the optical element typically deviates from the plane perpendicular to the optical axis by rotating about an axis in the x and / or y direction, although rotation about the z axis can be used for rotationally asymmetric aspherical optical elements. The deformation of the optical element may include low-frequency shapes (e.g., coma) and / or high-frequency shapes (e.g., free-form aspheres). The deformation of the optical element may be performed, for example, by using one or more actuators to apply a force to one or more sides of the optical element and / or by using one or more heating elements to heat one or more selected regions of the optical element. In general, it is not possible to adjust the projection system PS to correct apodization (variation in transmittance across the pupil plane). The transmission map of the projection system PS can be used when designing the patterning device (e.g., mask) MA of the lithographic apparatus LA. Using computational lithography techniques, the patterning device MA may be designed to at least partially correct for apodization.

[0030] The lithographic apparatus may be of a type having two (dual stage) or more tables (e.g., two or more substrate tables WTa, WTb, two or more patterning device tables, a substrate table WTa and a table WTb not under the projection system, e.g., a substrate dedicated to facilitating measurement and / or cleaning, etc.). In such a "dual stage" machine, additional tables can be used in parallel or preparation steps can be carried out on one or more tables while one or more other tables are used for exposure. For example, alignment measurements using an alignment sensor AS and / or level (height, tilt, etc.) measurements using a level sensor LS can be performed.

[0031] The lithographic apparatus may be of a type in which at least a portion of the substrate is covered by a liquid having a relatively high refractive index, such as water. Water for filling the space between the projection system and the substrate. The immersion liquid can also be applied to other spaces in the lithographic apparatus, such as between the patterning device and the projection system. Immersion techniques for increasing the numerical aperture of the projection system are well known in the art. As used herein, the term "immersion" does not mean that a structure such as a substrate has to be submerged in a liquid, but only means that the liquid is present between the projection system and the substrate during exposure.

[0032] Accordingly, during operation of a lithographic apparatus, the radiation beam is conditioned and provided by an illumination system IL. The radiation beam B is incident on a patterning device (e.g., a mask) MA held on a support structure (e.g., a mask table) MT and is patterned by the patterning device. After traversing the patterning device MA, the radiation beam B passes through a projection system PS, which focuses the beam onto a target portion C of a substrate W. The second positioner PW and the position sensor IF (e.g., an interferometric device, a linear encoder, a 2D encoder, or a capacitance sensor), the substrate table WT can be moved accurately. Similarly, a first positioner PM and another position sensor (not explicitly shown in FIG. 1) can be used to accurately position the patterning device MA with respect to the path of the radiation beam B, e.g., after mechanically retrieving from a mask library or during a scan. In general, the movement of the support structure MT can be realized with the aid of a long-stroke module (coarse positioning) and a short-stroke module (fine positioning) forming part of the first positioner PM. Similarly, the movement of the substrate table WT can be realized using a long-stroke module and a short-stroke module forming part of the second positioner PW. In that case, the support structure MT of a stepper (as opposed to a scanner) may be connected to or fixed to only short-stroke actuators. The patterning device MA and the substrate W can be aligned using patterning device alignment marks M1, M2 and substrate alignment marks P1, P2. The illustrated substrate alignment marks occupy dedicated target portions, but they may also be located in the spaces between the target portions (these are known as scribe lane alignment marks). Similarly, in situations where more than one die is provided on the patterning device MA, the patterning device alignment marks may be located between the dies.

[0033] The illustrated apparatus can be used in at least one of the following modes: 1. In step mode, the support structure MT and substrate table WT are kept essentially stationary and the entire pattern imparted to the radiation beam is projected onto the target portion C in one go (i.e. a single static exposure). The substrate table WT is then shifted in the X and / or Y direction so that a different target portion C can be exposed. In step mode, the maximum size of the exposure field limits the size of the target portion C imaged in a single static exposure. 2. In scan mode, the support structure MT and the substrate table WT are scanned synchronously while a pattern imparted to the radiation beam is projected onto a target portion C (i.e. a single dynamic exposure). The velocity and direction of the substrate table WT relative to the support structure MT may be determined by the (de-)magnification and image reversal characteristics of the projection system PS. In scan mode, the maximum size of the exposure field limits the width (non-scan direction) of the target portion in a single dynamic exposure, while the length of the scanning movement determines the height (in the scan direction) of the target portion. 3. In another mode, the support structure MT is kept essentially stationary holding a programmable patterning device, and the substrate table WT is moved or scanned while a pattern imparted to the radiation beam is projected onto a target portion C. A radiation source is used and the programmable patterning device is updated after each movement of the substrate table WT, or between successive radiation pulses during a scan, as required. This mode of operation is readily adaptable to maskless lithography employing a programmable patterning device such as a programmable mirror array of the type referred to above.

[0034] Combinations and / or variations on the above described modes of use or entirely different modes of use may also be employed.

[0035] Although there may be particular reference in this document to the use of lithographic apparatus in the manufacture of ICs, the lithographic apparatus to be described herein may have applications in, for example, the manufacture of integrated optical systems, magnetic domain memories, liquid crystal displays (LCDs), thin film magnetic heads, etc. Those skilled in the art will appreciate that in the context of such alternative applications, the terms "wafer" or "die" can be regarded as synonymous with the more general terms "substrate" or "target portion", respectively. The substrate referred to in this document may be processed, before and / or after exposure, for example, by a track (a tool generally used to apply a resist layer to the substrate and to develop the exposed resist) or a metrology or inspection tool. Where applicable, the disclosure herein may be applied to such and other substrate processing tools. Further, for example, in order to create a multi-layer IC, the substrate may be processed multiple times, and thus the term "substrate" as used herein may also refer to a substrate already comprising multiple processed layers.

[0036] As used herein, the terms "radiation" and "beam" encompass all types of electromagnetic radiation, including ultraviolet (UV) radiation (e.g., having a wavelength of 365, 248, 193, 157 or 126 nm) and extreme ultraviolet (EUV) radiation (e.g., having a wavelength in the range of 5 to 20 nm), as well as particle beams such as ion beams or electron beams.

[0037] The various patterns on or provided by a patterning device have different process windows, i.e., a space of process variables within which the pattern is generated within the specifications. Examples of pattern specifications related to potential systematic defects include necking, line pullback, line spacing, CD, edge placement, overlap, resist top loss, resist undercut and / or bridging checks. The process window or region thereof for all patterns on the patterning device can be obtained by merging (e.g., overlapping) the process windows of each individual pattern. The boundaries of the process window for all patterns include the boundaries of the process windows of some of the individual patterns. That is, these individual patterns limit the process window for all patterns. These patterns may be referred to as "hot spots" or "process window limiting patterns (PWLP)". When controlling the patterning process, it is possible and economical to focus on the hot spots. If there are no defects in the hot spots, there may be no defects in all patterns.

[0038] As shown in Figure 2, the lithographic apparatus LA can form part of a lithographic cell LC, sometimes also referred to as a litho cell or cluster, and also includes apparatus for performing pre-exposure and post-exposure processes on a substrate. Conventionally, these include one or more spin coaters SC for depositing one or more resist layers, one or more developers DE for developing the exposed resist, one or more chill plates CH and / or one or more bake plates BK. A substrate handler, or robot RO, picks up one or more substrates from input / output ports I / O1, I / O2, moves them between different process devices and delivers them to the loading bay LB of the lithographic apparatus. These devices, often collectively referred to as a track, are under the control of a track control unit TCU controlled by a supervisory control system SCS, which also controls the lithographic apparatus via a lithography control unit LACU. Thus, different devices can be operated to maximize throughput and processing efficiency.

[0039] In order for a substrate to be correctly exposed by a lithographic apparatus, it is desirable to inspect a substrate or other object for measurement or determination in order to monitor one or more properties such as alignment, overlay, etc. (e.g., between upper layer structures or between structures of the same layer provided individually to a layer by, for example, a double patterning process), line thickness, critical dimension (CD), focus offset, material properties, etc. in a patterning process (e.g., a device manufacturing process) that consistently and / or includes at least one pattern transfer step (e.g., a photolithography step). Thus, a manufacturing facility in which a litho cell LC is disposed typically also includes a metrology system MET that measures some or all of a substrate W processed in the litho cell or other object within the litho cell. The metrology system MET may be part of the litho cell LC, or may be part of, for example, a lithographic apparatus LA (such as an alignment sensor AS).

[0040] One or more measurement parameters may include, for example, overlay between consecutive layers formed in or on a patterned substrate, critical dimension (CD) of features formed in or on a patterned substrate (e.g., critical line width), focus or focus error of an optical lithography process, dose or dose error of an optical lithography process, optical aberration of an optical lithography process, etc. This measurement may be performed on the target of the product substrate itself and / or on a dedicated metrology target provided on the substrate. The measurement can be performed after resist development and before etching, or after etching.

[0041] There are various techniques for measuring structures formed in a patterning process, including the use of scanning electron microscopes, image-based measurement tools, and / or various dedicated tools. As described above, a high-speed, non-invasive special measurement tool is one in which a radiation beam is directed at a target on the substrate surface and the characteristics of the scattered (diffracted / reflected) beam are measured. By evaluating one or more characteristics of the radiation scattered by the substrate, one or more characteristics of the substrate can be determined. This may be referred to as diffraction-based measurement. One such application of this diffraction-based measurement is the measurement of the asymmetry of features within a target. This can be used, for example, as a measure of overlay, although other applications are also known. For example, the asymmetry can be measured by comparing opposite portions of the diffraction spectrum (e.g., comparing the -1st and +1st orders of the diffraction spectrum of a periodic grating). This can be done as described above, for example, as described in U.S. Patent Application Publication US2006-066855, which is hereby incorporated by reference in its entirety. Another use of diffraction-based measurement is the measurement of feature width (CD) within a target. Such techniques can use the apparatus and methods described below.

[0042] Thus, in a device manufacturing process (e.g., a patterning process or a lithography process), during or after the process, a substrate or other object can be subjected to various types of measurements. The measurements can determine whether a particular substrate has defects, establish adjustments to the process and the apparatus used in the process (e.g., alignment of two layers on a substrate or alignment of a patterning device to a substrate), measure the performance of the process, or be for other purposes. Examples of measurements include optical imaging (such as an optical microscope), non-imaging optical measurements (diffraction-based measurements such as an ASML YieldStar measurement tool, an ASML SMASH measurement system), mechanical measurements (profiling using a stylus, atomic force microscopy (AFM)), and / or non-optical imaging (e.g., scanning electron microscopy (SEM)). The SMASH (SMart Alignment Sensor Hybrid) system described in U.S. Patent No. 6,961,116, which is hereby incorporated by reference in its entirety, uses a self-referencing interferometer that generates two overlapping and relatively rotating images of an alignment marker, detects the intensity of the pupil plane where the Fourier transform of the images interferes, and extracts position information from the phase difference between the diffraction orders of the two images that appears as intensity variations in the interference order.

[0043] The measurement results are provided directly or indirectly to a monitoring control system SCS. If an error is detected in an exposed substrate, subsequent exposure of substrates (especially if the inspection can be performed early enough such that one or more other substrates in a batch have not yet been exposed) and / or adjustment of subsequent exposures can be performed. Also, substrates that have already been exposed can be stripped and reprocessed or discarded to improve yield, thereby avoiding further processing of substrates known to have defects. If only a portion of a target portion of a substrate has a defect, only the good target portion is exposed.

[0044] Within metrology system MET, a metrology apparatus is used to determine one or more characteristics of a substrate, in particular how one or more characteristics of different substrates change, and how different layers of the same substrate change from layer to layer. As described above, the metrology apparatus may be integrated into a lithography apparatus LA or a lithocell LC, or may be a stand-alone device.

[0045] To enable metrology, one or more targets can be provided on the substrate. In one embodiment, the target is specially designed and can include a periodic structure. In one embodiment, the target is part of a device pattern, for example a periodic structure of a device pattern. In one embodiment, the device pattern is a periodic structure of a memory device (e.g., a structure such as a bipolar transistor (BPT), a bit line contact (BLC), etc.).

[0046] In one embodiment, the target on the substrate can include one or more 1-D periodic structures (e.g., a grating) printed such that periodic structural features are formed by solid resist lines after development. In one embodiment, the target can include one or more 2-D periodic structures (e.g., a grating) printed such that solid resist pillars or vias in the resist are formed after development. Alternatively, bars, pillars, or vias may be etched into the substrate (e.g., into one or more layers on the substrate).

[0047] In one embodiment, one of the target parameters of the patterning process is the overlay. The overlay can be measured using dark-field scattering measurement. Specular reflection (corresponding) is blocked and only higher orders are processed. Examples of dark-field measurement are PCT Patent Application Publication Nos. WO2009 / 078708 and WO2009 / 106279, which are hereby incorporated by reference in their entirety. Further developments of this technology are described in U.S. Patent Application Publication Nos. US2011-0027704, US2011-0043791 and US2012-0242970, which are hereby incorporated by reference in their entirety. Diffraction-based overlays using dark-field detection of diffraction orders enable overlay measurements on smaller targets. These targets can be smaller than the illumination spot and may be surrounded by device product structures on the substrate. In one embodiment, multiple targets can be measured with a single radiation capture.

[0048] Figure 3 shows an exemplary inspection apparatus (e.g., a scatterometer). It includes a broadband (white light) radiation projector 2 that projects radiation onto a substrate W. The redirected radiation is passed to a spectrometer detector 4 that measures the spectrum 10 of the specularly reflected radiation (intensity as a function of wavelength). As shown, for example, in the lower left graph. From this data, the structure or profile that gives rise to the detected spectrum is reconstructed by a processor PU. By rigorous coupled-wave analysis and non-linear regression, or by comparison with a library of simulated spectra as shown in the lower right of Figure 3. Generally, in the reconstruction, the general form of the structure is known, some variables are assumed from the knowledge of the process by which the structure was created, and the variables of the structure determined from the measurement data are very few. Such an inspection apparatus may be configured as a normal incidence inspection apparatus or as an oblique incidence inspection apparatus.

[0049] Another inspection apparatus that can be used is shown in FIG. 4. In this device, the radiation emitted from the radiation source 2 is collimated using the lens system 12, passes through the interference filter 13 and the polarizer 17, is reflected by the partial reflection surface 16, and is focused on the spot S of the substrate W through the objective lens 15 having a numerical aperture (NA) desirably of at least 0.9 or at least 0.95. An immersion inspection apparatus (using a fluid with a relatively high refractive index such as water) may have a numerical aperture exceeding 1.

[0050] One or more substrate tables may be provided to hold the substrate W during the measurement operation, such as in a lithographic apparatus LA. The substrate table may be similar or identical in form to the substrate table WT of FIG. 1. In an example where the inspection apparatus is integrated with a lithographic apparatus, they may be the same substrate table. The coarse and fine positioners may be provided in a second positioner PW configured to accurately position the substrate with respect to the measurement optical system. For example, various sensors and actuators are provided to acquire the position of interest and bring it to a position under the objective lens 15. Usually, many measurements are made on targets at different positions of the substrate W. The substrate support can move in the X and Y directions to acquire different targets and move the optical system in the Z direction to acquire the desired position of the target with respect to focus. For example, it is convenient to describe the operation considering that in practice the optical system is substantially stationary, but the objective lens moves to different positions with respect to the substrate (typically in the X and Y directions, and thus in the Z direction). When the relative position of the substrate and the optical system is correct, in principle it does not matter whether the substrate or the optical system or a combination of parts of the optical system (e.g., in the Z and / or tilt directions) is actually moving. The rest of the optical system is stationary and the substrate is moving (e.g., not only in the X and Y directions but optionally also in the Z and / or tilt directions).

[0051] Next, the radiation whose direction has been changed by the substrate W passes through the partial reflection surface 16 and enters the detector 18 in order to detect the spectrum. The detector 18 may be arranged on the inverse projection focal plane 11 (i.e., at the focal length of the lens system 15), or the plane 11 may be re-imaged onto the detector 18 by an auxiliary optical system (not shown). The detector may be a two-dimensional detector so as to be able to measure the two-dimensional angular scattering spectrum of the substrate target 30. The detector 18 may be, for example, an array of CCD or CMOS sensors and may use, for example, an integration time of 40 milliseconds per frame.

[0052] A reference beam can be used to measure, for example, the intensity of the incident radiation. To do this, when the radiation beam is incident on the partial reflection surface 16, a part of it passes through the partial reflection surface 16 as a reference beam directed towards the reference mirror 14. The reference beam is then projected onto different parts of the same detector 18 or alternatively onto different detectors (not shown).

[0053] One or more interference filters 13 are available to select wavelengths of interest, for example in the range from 405 to 790 nm or even lower ranges such as from 200 to 300 nm. The interference filter is more adjustable than including a set of different filters. A grating can be used instead of the interference filter. An aperture stop or a spatial light modulator (not shown) may be provided in the illumination path to control the range of the angle of incidence of the radiation on the target.

[0054] The detector 18 can measure the intensity of the radiation redirected at a single wavelength (or a narrow wavelength range), individually at multiple wavelengths, or the intensity integrated over a certain wavelength range. Furthermore, the detector may separately measure the intensities of the horizontally magnetically polarized radiation and the horizontally electrically polarized radiation, and / or the phase difference between the horizontally magnetically polarized radiation and the horizontally electrically polarized radiation.

[0055] The target 30 on the substrate W may be a one-dimensional grating printed such that after development, bars are formed by solid resist lines. The target 30 may be a 2D grating printed such that after development, the grating is formed by solid resist pillars or vias in the resist. The bars, pillars, or vias may be etched within or on the substrate (e.g., one or more layers on the substrate). The pattern (bars, pillars, vias, etc.) is sensitive to changes in the processing of the patterning process (optical aberrations of the lithographic projection apparatus, particularly the projection system PS, changes in focus, changes in dose, etc.). It appears as a change in the printed grating. Thus, the measured data of the printed grating is used to reconstruct the grating. One or more parameters of a 1-D grating such as line width and / or shape, or one or more parameters of a 2-D grating such as the width or length or shape of the pillars or vias can be input into the reconstruction process.

[0056] In addition to the measurement of parameters by reconstruction, angular resolved scatterometry is useful for the measurement of the asymmetry of features of the product and / or the resist pattern. A particular use of symmetry measurement is overlay measurement, where the target 30 includes one set of periodic features overlaid on another set. The concept of asymmetry measurement using the apparatus of FIG. 3 or FIG. 4 is described, for example, in U.S. Patent Application Publication US2006-066855, which is incorporated herein by reference in its entirety. Briefly, the position of the diffraction order in the diffraction spectrum of the target is determined only by the periodicity of the target, but the asymmetry of the diffraction spectrum indicates the asymmetry of the individual features that make up the target. In the apparatus of FIG. 4 where the detector 18 can be an image sensor, the asymmetry of the diffraction order appears directly as the asymmetry of the pupil image recorded by the detector 18. This asymmetry can be measured by digital image processing in the unit PU and calibrated against a known value of the overlay.

[0057] FIG. 5 shows a plan view of a typical target 30 and the range of the illumination spot S in the apparatus of FIG. 4. In one embodiment, the target 30 is a periodic structure (e.g., a grating) that is larger than the width (e.g., diameter) of the illumination spot S in order to obtain a diffraction spectrum without interference from the surrounding structure. S may be smaller than the width and length of the target. In other words, the target is "underfilled" by the illumination, and the diffraction signal substantially does not include signals from features of the product outside the target itself. The illumination devices 2, 12, 13, 17 may be configured to provide illumination of uniform intensity across the rear focal plane of the objective lens 15. Alternatively, for example, by including an aperture in the illumination path, the illumination may be restricted in the on-axis or off-axis direction.

[0058] FIG. 6 schematically shows an exemplary process for determining the value of one or more variables of interest of the target pattern 30 based on measurement data obtained using measurement. The radiation detected by the detector 18 provides the measured radiation distribution 108 of the target 30'.

[0059] For a given target 30‘, for example, using a numerical Maxwell solver 210, a radiation distribution 208 can be calculated / simulated from the parameterized model 206. The parameterized model 206 constitutes the target and shows exemplary layers of various materials associated therewith. The parameterized model 206 can include one or more variables regarding the characteristics and layers of the portion of the target under consideration, which can be changed and derived. As shown in FIG. 6, one or more of the variables include the thickness t of one or more layers, the width w (e.g., CD) of one or more features, the height h of one or more features, and / or the sidewall angle α of one or more features. Although not shown, one or more of the variables can further include, but are not limited to, the refractive index of one or more layers (e.g., real refractive index or complex refractive index, refractive index tensor, etc.), the absorption coefficient of one or more layers, the absorption of one or more layers, loss during development, the footing of one or more features, and / or the line edge roughness of one or more features. The initial values of the variables may be the values expected for the target during measurement. The measured radiation distribution 108 is then compared with the radiation distribution 208 calculated at 212, and the difference between the two is determined. If there is a difference, the value of one or more variables of the parameterized model 206 is changed, a new calculated radiation distribution 208 is calculated, and compared with the measured radiation distribution 108 until the measured radiation distribution 108 and the calculated radiation distribution 208 are in sufficient agreement. At that point, the values of the variables of the parameterized model 206 provide a good or best match to the geometry of the actual target 30‘. In one embodiment, sufficient agreement exists if the difference between the measured radiation distribution 108 and the calculated radiation distribution 208 is within an acceptable threshold.

[0060] The variables of the patterning process are referred to as "process variables". The patterning process may include processes upstream and downstream of the actual transfer of the pattern within the lithographic apparatus. FIG. 7 shows an example of categories of process variables 370. The first category may be variables 310 of the lithographic apparatus or any other apparatus used in the lithographic process. Examples of this category include variables such as the illumination of the lithographic apparatus, the projection system, the substrate stage, etc. The second category may be variables 320 of one or more steps performed in the patterning process. Examples of this category include focus control or focus measurement, dose control or dose measurement, bandwidth, exposure time, development temperature, chemical composition used in development, etc. The third category may be variables 330 of the design layout, and may be in the patterning device or its implementation using the patterning device. Examples of this category include the shape and / or position of assist features, the adjustments applied by resolution enhancement techniques (RET), the CD of mask features, etc. The fourth category is variables 340 of the substrate, and includes, for example, the characteristics of the structure under the resist layer, the chemical composition and / or physical dimensions of the resist layer, etc. The fifth category may be the characteristics 350 of the temporal variation of one or more variables of the patterning process. Examples of this category include the characteristics of the movement of the high-frequency stage (frequency, amplitude, etc.), the change in the high-frequency laser bandwidth (frequency, amplitude, etc.), and / or the change in the wavelength of the high-frequency laser. These high-frequency changes or movements exceed the response time of the mechanism that adjusts the underlying variables (stage position, laser intensity, etc.). The sixth category may be the characteristics 360 of processes upstream or downstream of pattern transfer in the lithographic apparatus, such as spin coating, post-exposure bake (PEB), development, etching, deposition, doping, and / or packaging.

[0061] As will be appreciated, many, if not all, of these variables affect the parameters of the patterning process and often affect the parameters of interest. Non-limiting examples of parameters of the patterning process include critical dimension (CD), critical dimension uniformity (CDU), focus, overlay, edge position or placement, sidewall angle, pattern shift, and the like. Often, these parameters represent an error from a nominal value (design value, average value, etc.). The parameter value may be a characteristic value of an individual pattern or a statistical value (average, variance, etc.) of the characteristics of a group of patterns.

[0062] Some or all of the values of the process variables, or the parameters associated therewith, can be determined in an appropriate manner. For example, the values may be determined from data obtained with various measurement tools (e.g., substrate measurement tools). The values can be obtained from various sensors or systems of the patterning process apparatus (e.g., sensors of a lithography apparatus such as a leveling sensor or an alignment sensor, a control system (e.g., a substrate or patterning device table control system), a lithography apparatus, sensors of a track tool, etc.). The values may be from an operator of the patterning process.

[0063] Currently, an increasing number of measurements are becoming a burden, mainly in terms of time. This is particularly true, for example, when multiple patterning techniques have emerged in the semiconductor industry. Multiple patterning techniques such as litho-etch-litho-etch (LELE) and sidewall assist double patterning (SADP) have significantly increased the number of processing steps, so the amount of measurement steps used for control and yield monitoring has increased. Further, as more layers are used in the multiple patterning steps and more patterning steps are used for each layer, the amount of measurement per node increases (i.e., the reduction of feature size).

[0064] In addition or as an alternative, there is an increasing demand for defect determination and / or induced defect inspection. This includes considerably higher density focus, overlay, and / or CD measurements than before.

[0065] In addition or as an alternative, the specifications for CD, overlay, and / or focus performance on the device are becoming stricter. This drives the manufacturing equipment specifications, such as for exposure tools and processing tools (e.g., deposition, etching, track, chemical mechanical polishing (CMP), etc.), from one node to the next. As a result, this promotes more precise control and monitoring of performance, thereby increasing the ever-growing demand for measurements for control and monitoring.

[0066] In addition or as an alternative, with the tightening of the specifications for CD, focus, and / or overlay performance on the device, higher-order corrections may be required. Higher-order correction is basically a selective correction action (e.g., correction at high spatial resolution) at a small spatial scale over all or part of the substrate. Since higher-order correction involves high-density sampling for each substrate for measurement, the measurement load may increase beyond the practical limit of the productivity of the measurement equipment.

[0067] In addition or as an alternative, substrate-to-substrate variations may require additional individual substrate-level control (e.g., compared to lot-level control) and related monitoring to achieve the desired CD, focus, and / or overlay performance. This enables more substrates to be measured per lot, so the amount of measurement used may increase beyond the practical limit of the productivity of the measurement equipment.

[0068] However, to meet the increasing data demand, simply adding measurement equipment or improving the productivity of measurement equipment may not be sufficient. Furthermore, it may not be possible to solve all problems, such as obtaining high-density CD, focus, and / or overlay profiles in a timely manner across the entire substrate.

[0069] Therefore, measurement efficiency is desirable. This is for obtaining data, for example, when the data density per substrate is high and the number of substrates per lot is large.

[0070] Therefore, in one embodiment, a method is provided that, for example, helps improve measurement efficiency. In this method, measurement data from multiple sources are combined and manipulated to derive accurate estimated values of one or more patterning process parameters (such as CD, focus, overlay, edge placement, etc.) for each of multiple positions on a substrate. In one embodiment, high-density measurement data (e.g., per square mm) is then provided, for example, for all substrates processed in a patterning process and for all layers processed on such substrates in a patterning process.

[0071] In practice, in one embodiment, the result of the method is a "virtual" or emulated distribution of the values of one or more patterning process parameters across the substrate, which is achieved by such a combination of various measurement data. This method can provide an efficient way of hybrid measurement of one or more patterning process parameters (such as focus, CD, overlay, etc.). And while the embodiments herein mainly consider specific examples of patterning process parameters, namely focus, CD, and overlay, it should be understood that one or more other or additional patterning process parameters can be the subject of this technology.

[0072] As described above, this method includes measurements and combinations of sources from various data, other data. In one embodiment, this method combines measured values of patterning process parameters of interest with data from one or more devices in the patterning process, such as data from one or more sensors of a lithography apparatus. Then, this combination of data is used to predict the performance of the product in the form of patterning process parameters such as CD, overlay, focus, pattern shift, edge placement (such as edge placement error), or derived parameters such as yield, defects (e.g., risk of defects, defect count).

[0073] Thus, the principle underlying this method is to isolate and estimate the individual root causes of changes in patterning process parameters of interest and combine them to calculate the performance of the product. The goal is to avoid an increasing amount of offline (and / or online) measurements using as much available information as possible and to determine the patterning process parameters of interest using tools as described with respect to Figure 3.

[0074] Thus, in one embodiment, it is desirable to identify the various contributions to changes in a patterning process parameter of interest (such as CD error, focus error, overlay, etc.). These contributions can then be used in various combinations to achieve a desired estimate of performance on the product. Typically, these contributions are errors and / or residuals. For example, a device may generate an error when making a correction, which can then appear as a change in the patterning process parameter of interest. As another example, a sensor system may measure an error, which may be or contribute to a change in the patterning process parameter. As a further example, a mathematical model used to determine a device or device setting may not be able to achieve a particular desired or best physical effect (e.g., the difference between a desired physical correction and the physical correction achievable by the device, the difference between a desired physical effect such as dose, focus, etc. and the physical effect achievable by the device, the difference between a desired physical correction or effect and the correction or effect determinable by the mathematical model), resulting in a change or a residual contributing to a change in the parameters of the patterning process. In one embodiment, the contributions can be determined experimentally or empirically.

[0075] Each of these contributions to the patterning process parameter of interest that is spatially distributed across the die, field, or entire substrate is characterized as a fingerprint. Similarly, a combination of contributions across the die, field, or entire substrate can be characterized as a fingerprint.

[0076] Thus, a plurality of these contributions can be combined to generate a derived fingerprint. For example, a focus fingerprint on a product substrate is, for example, a synthesis of focus contributions, which are due to the non - flatness of the substrate, the focus error associated with the projection system of the lithography apparatus during exposure of the substrate, the height error due to the substrate position control loop during exposure, and the residual fingerprint of the focus setting of the lithography apparatus. This example will be described below with reference to FIG. 9.

[0077] Similarly, a derived or measured fingerprint can be used to generate a (further) derived fingerprint by removing one or more fingerprints therefrom. For example, from the measured focus fingerprint of a substrate, the focus contribution of the non-flatness of the substrate, the focus error related to the projection system of the lithographic apparatus during exposure of the substrate, the height error during exposure by the substrate position control loop, and the residual fingerprint of the focus setting of the lithographic apparatus can be removed. This may result in a residual focus fingerprint caused by errors not captured by the removed fingerprints. This example will be described below with reference to FIG. 10.

[0078] Thus, in one embodiment, the method can derive a fingerprint, for example, by decomposing the fingerprint into individual contributing fingerprints and / or by combining fingerprints.

[0079] Accordingly, referring to FIG. 8, an embodiment of a combination of contributions (fingerprints) is shown. A change in process variable 311 (e.g., in the case of focus, height error) has a contribution 312 to the patterning process parameter 352 (e.g., in the case of focus, focus) of the pattern on the substrate, and a change in process variable 321 (e.g., in the case of focus, the residual of the focus setup) may have a contribution 322 to the patterning process parameter 352. That is, the patterning process parameter 352 may have a combined contribution of changes in one or more process variables. These contributions 312 and 322 may be simply additive (which may include weighted or linear addition), or may be combined by other functions (e.g., using (de)convolution, using neural networks, RMS addition, scaling, etc.). The patterning process parameter 352 may have contributions from changes in other variables. Accordingly, as further described below, this implementation can be used to determine various contributions or to derive an estimated value of the patterning process parameter. In one embodiment, the contributions 312 and / or 322 may be determined by modeling one or more applicable process variables. The contributions 312 and / or 322 may be represented as a function of one or more applicable process variables. The function may be linear or non-linear.

[0080] FIG. 9 schematically shows an example of obtaining a derived contribution 470 to the patterning process parameters of a substrate, the derived contribution being a combination of contributions of a plurality of process variables (one or more of which may be the derived contribution). In this case, the derived contribution 470 is the (de)focus. Thus, the derived contribution 470 can be obtained using contributions of a plurality of process variables such as a focus error (FE) related to the projection system of the lithographic apparatus during exposure 400 of the substrate, a height error (e.g., moving standard deviation (MSDz)) created by the substrate position control loop during exposure 410, and non-flatness (P) of the substrate 420. Importantly, this data can be obtained from the lithographic apparatus and may be a by-product when manufacturing the substrate as part of the patterning process. None of these identified contributions necessarily require measurement of the patterned features on the substrate, for example using the tools as described with respect to FIGS. 3-6. The contributions can be obtained by simulation, mathematical modeling and / or measurement / experiment as required. For example, the contribution degrees can be obtained by simulation based on physical models, empirical modeling, and / or dedicated measurements.

[0081] Therefore, in the case of focus, an example of the contribution of process variable 400 to the focus is shown as contribution 430, an example of the contribution of process variable 410 to the focus is shown as contribution 440, and an example of the contribution of process variable 420 to the focus is shown as contribution degree 450. Next, each of these contributions is combined together (460), and the derived contribution 470 is realized. Element 460 (and other elements in the figure) shows a plus sign, but the operation at 460 does not have to be addition and can be, for example, multiplication or convolution by using a neural network or the like. The operation may be different for one or more contributions from another one or more contributions (e.g., addition and summation from 430 to 440 and convolution of contribution 450). In the example, the combined contribution can be expressed as F(x, y) = a1 * F(FE)(x, y) + b1 * F(MSDz)(x, y) + c1 * F(P)(x, y) + ···. Various functions can be obtained by simulation, mathematical modeling, and / or measurement / experiment. Further, there may be cross terms not shown here (such as focus as a function of FE and MSD). To obtain the absolute value of the focus, the nominal value or simulated value of the focus can be combined with the contribution. Coefficients such as a, b, c are the sensitivities of the focus with respect to the respective process variables or their functions. In this example, the contribution is over the entire substrate, but in one embodiment, one or more of the contributions can be per die / field (and then, for example, can be repeated over the entire substrate according to the applicable conditions for each instance). As described above, since the contribution degree 470 can be spatially defined over the substrate / die / field, it can be characterized as a fingerprint. Further, the conversion of the contribution to the absolute value can be spatially defined over the entire substrate / die / field and is thus characterized as a fingerprint. As will be understood, the respective contributions can be derived using data from the processing of multiple substrates using a patterning process. Since this data may be a byproduct of substrate processing, it may already be available.

[0082] Currently, in the context of CDs, the same approach as described with respect to FIG. 9 can be used. For example, the derivation contribution 470 to the CD can be a combination of contributions (which can include the derivation contribution) due to a plurality of process variables such as the focus (F) 400, the moving standard deviation of the substrate movement (MSDz) 410, the normal direction of the substrate, and the moving standard deviation of the substrate movement in the direction parallel to the substrate (MSDx) 420. Thus, in this case, an example of the contribution of the focus (F) 400 to the CD is contribution 430, an example of the contribution of the moving standard deviation (MSDz) 410 to the CD is contribution 440, and an example of the contribution of the moving standard deviation (MSDx) 420 to the CD is 440. Next, each of these contributions is combined together (460) to achieve the derived contribution 470. In the example, the combined contribution can be expressed as CD(x,y)=a1*CD(F 2 )(x,y)+b1*CD(MSDx)(x,y)+c1*CD(MSDz 2 )(x,y)+··. Furthermore, there may be cross terms not shown here and the relationships may be different (for example, the relationships such as focus and MSDz can have linear and cubic terms and not be purely quadratic). In one embodiment, contributions 430, 440, 450 can be the distributions of the focus (F) 400, the moving standard deviation (MSDz) 410, and the moving standard deviation (MSDx) 420, respectively, and in this case, a CD model is used to combine them into the distribution of the CD. Furthermore, there may be cross terms not shown here (such as CD as a function of F times MSD, etc.). To obtain the absolute value of the CD, the nominal value or the simulation value of the CD can be combined with the contributions. Coefficients such as a, b, c are the sensitivities of the CD with respect to the process variables or functions thereof.

[0083] Applying the above principle, FIG. 10 schematically shows an example of obtaining a derived contribution 510 from the measurement data of a patterned substrate of a patterning process parameter of interest for a substrate by removing the contribution to the patterning process parameter of interest. The patterning substrate measurement data in this context is the value of a parameter of interest obtained by measuring features (e.g., device pattern features, measurement targets other than device patterns, etc.) on a substrate that has been at least partially processed by patterning. Such measurement data can typically be obtained using a measurement tool or inspection tool as described with respect to FIGS. 3 to 6.

[0084] The patterning substrate measurement data 500 of the parameter of interest can have at least two contributions. Thus, by removing one or more other contributions within the patterning substrate measurement data, one or more contributions within the patterning substrate measurement data can be obtained. Thus, the contribution 510 can be obtained by removing the contribution 520 from the patterning substrate measurement data 500 (505). Element 505 (and other elements in the figure) shows a minus sign, but the operation at 505 does not have to be subtraction. For example, there are multiplication using a neural network, etc., (de)convolution, etc. The contribution degree 520 can be a derived contribution degree such as the contribution degree 470, or can be a contribution degree derived from one or more of other data such as any one or more of the contribution degrees 430, 440, and 450. Further, a plurality of contributions can be deleted. For example, the optional contribution 540 associated with the process variable 530 can be removed from the patterning substrate measurement data 500 together with the contribution 520. As will be understood, the measurement data of the patterned substrate can be obtained using data from the processing of a plurality of substrates using the patterning process.

[0085] In one embodiment, the patterned substrate measurement data is from a pattern separate from the device pattern, such as a non-functional area of the die, measurement features between dies, or on a test substrate. Thus, for example, the contribution of one or more process variables can be removed from such measurement data, thereby obtaining the remaining contribution of one or more process variables to such measurement data. Comparable contributions to the measurement data of device patterns on the same or different substrates can be obtained based on the remaining contributions. It is not necessary to actually obtain measurement data from the device pattern. For example, since one or more applicable process variables have an effect comparable to that of a pattern separate from the device pattern, the contribution to the measurement of the device pattern is presumed to be the same as the remaining contribution. In one embodiment, the separate pattern is a pattern for test purposes (e.g., measurement target), and performing measurements on the separate pattern does not affect the device pattern on the substrate.

[0086] Thus, by combining contributions or removing contributions from the patterned substrate measurement data, an estimated value of a parameter of interest of the substrate can be obtained without necessarily obtaining the patterned measurement data of that substrate. This is done by recognizing the nature of the various contributions.

[0087] In one embodiment, the contribution of one or more process variables can be device-specific (e.g., a lithography apparatus). That is, the contribution is specific to a particular actual device or combination of devices. Thus, in one embodiment, the contribution of one or more process variables may be repeatedly used across any substrate. Thus, the contribution of one or more process variables can be characterized in advance and obtained from a database for various combination / removal processes. The contribution can be device-specific as a whole or for a particular part of the device (e.g., an etching chamber). Examples of such variables include, but are not limited to, various characteristics of processes upstream or downstream of pattern transfer in a lithography apparatus, such as spin coating, post-exposure bake, development, etching, deposition, doping, and / or packaging.

[0088] In one embodiment, the contribution of one or more process variables is not specific to a particular substrate (and thus can be used across substrates). Thus, the contribution of one or more process variables can be characterized in advance and retrieved from a database for later use in various combination / removal processes. This contribution of one or more process variables can be applied to a particular substrate by combining it with the data and sensitivity relationships of one or more variables for that particular substrate. Examples of such variables include, but are not limited to, illumination variables, projection systems, focus, dose, bandwidth, exposure time, characteristics of the movement of the high-frequency stage (e.g., standard deviation of the movement of the substrate stage (MSD), moving average of the movement of the substrate stage, frequency, amplitude, etc.), changes in the high-frequency laser bandwidth (e.g., frequency, amplitude, etc.), changes in the wavelength of the high-frequency laser, and / or the substrate.

[0089] In one embodiment, the contribution of one or more process variables can be substrate-specific. For example, the contribution may be determined for each substrate or a particular group of substrates. Examples of such variables include the shape of the substrate (height map, deformation map), substrate processing conditions, illumination variables, projection system variables, focus, dose, bandwidth, exposure time, movement of the high-frequency stage movement (e.g., standard deviation of the movement of the substrate stage (MSD), moving average of the movement of the substrate stage, etc.), changes in the high-frequency laser bandwidth (e.g., frequency, amplitude, etc.), changes in the high-frequency laser wavelength, and / or the flatness of the substrate.

[0090] In one embodiment, the contribution of one or more process variables can be pattern or patterning device specific. That is, the contribution is specific to a particular actual patterning device or a particular pattern provided by a patterning device. This contribution may further be independent of the substrate. Thus, the pattern or patterning device specific contributions can be pre-characterized and later retrieved from a database for various combination processes. Examples of such variables include patterning device feature CDs, the shape and / or position of assist features, the adjustments applied by resolution enhancement techniques (RET), and the like.

[0091] In one embodiment, the contributions associated with different process variables can have different spatial uniformities. For example, the contributions of some process variables can be essentially spatially uniform across the substrate, while the contributions of some other process variables may not be as spatially uniform across the substrate. This difference can be due to the nature of the process variables. For example, the contributions of one or more process variables related to the resist layer, the development of the resist layer, and / or the etching of the substrate tend to be essentially spatially uniform across the substrate as the entire substrate is typically coated, developed, or etched in the same conditions simultaneously, or tend to be symmetric due to, for example, the rotation of the substrate during many of these processes. For example, the contributions of one or more process variables related to pattern transfer or lithographic apparatus tend to be location specific for pattern transfer, and since one or more process variables can vary between pattern transfers at one location and pattern transfers at another location, they tend not to be spatially uniform. Thus, if non-essentially spatially uniform contributions can be removed from the patterning substrate measurement data, essentially spatially uniform contributions can be obtained from the patterning substrate measurement data.

[0092] Therefore, in certain examples, process variable data for each point exposed on the substrate, such as leveling information, moving average (MA) of substrate movement, MSDxyz, dose, laser bandwidth, pupil shape, etc., can be collected from the lithography apparatus. This data is usually already available in the lithography apparatus, for example in a diagnostic file. From this data, the contributions described above can be generated using a model of the target parameter that describes the sensitivity of the target parameter to one or more process variables. One or more sensitivities can be obtained from simulations or experiments. The contributions generated in this way are expected to be seen during measurements after resist development, assuming that the calibration of the track and resist model is complete. For example, when the substrate is measured after development or etching, the contributions are removed from the patterned substrate measurement data. The remaining contributions are due to contributions from pre-pattern transfer or post-transfer processes (e.g., generally between fields by track and / or etching apparatus) and the patterning device (within the field). The errors of the lithography apparatus are corrected from the patterned substrate measurement data. Similarly, the contributions of the patterning device can be measured and removed to leave the contributions from pre-pattern transfer or the pattern transfer process. The contributions can be removed for each process flow (e.g., patterning process steps and / or combination of apparatuses used), or for each specific apparatus or part thereof (e.g., etching apparatus or etching chamber).

[0093] Thus, by these techniques, contributions to the parameter of interest can be obtained through the modeled relationships or by removing known contributions from the patterned substrate measurement data. Furthermore, one or more contributions can be device-specific, but may also be substrate-independent. However, one or more other contributions may be substrate-specific. Therefore, by appropriate mixing and matching of the contributions, an estimated value of the parameter of interest at a specific point in the patterning process can be estimated.

[0094] Accordingly, some specific examples of the application of these contributions are described in the context of focus, CD, and overlay to determine the respective estimated values of focus, CD, and overlay of the substrate. As will be understood, additional or other parameters of interest can be processed and estimated.

[0095] To enable these examples, various data are used. For example, a lithographic apparatus incorporates important measurement functions used for pattern transfer control. Examples of such integrated measurements are a position measuring device (e.g., sensor IF) for a substrate and / or patterning device for servo control, a leveling sensor (e.g., sensor LS) for measuring the surface of the substrate for leveling control, an alignment sensor (e.g., sensor AS) for measuring the orientation, position, and / or deformation of the substrate to enable overlay control, and / or an aberration sensor (e.g., the shear interferometer described above) for controlling the wavefront of the projection system. The lithographic apparatus uses the data from these sensors to control at a level where its overall CD, overlay, and / or focus budget is met, while at the same time tracking the residuals and / or errors remaining after control. These residuals and / or errors are used to calculate what CD, overlay, and / or focus errors occur during pattern transfer, i.e., the contributions to the CD, overlay, and / or focus fingerprint of the lithographic apparatus. As will be understood, other devices used in the patterning process may have similar information regarding the applicable metrology of the device.

[0096] Furthermore, the setup or control of a lithographic apparatus can use one or more mathematical models to determine respective calibration or control corrections. However, such one or more models may have built-in assumptions or limitations that cause non-zero residual errors. The residuals of such models calculate what CD, overlay, and / or focus errors have occurred, i.e., the contribution of the model to CD, overlay, and / or focus fingerprints. As will be appreciated, other apparatus used in the patterning process can have similar model information.

[0097] Furthermore, in-situ resist measurements can be used to set up the lithographic apparatus and assist in removing global and local fingerprints of one or more parameters (such as focus, overlay, etc.). However, the global fingerprint may drift over time since the last calibration was performed. To monitor and control this setup state, a monitor substrate can be exposed and measured to monitor the global fingerprint. The monitor substrate can be a basic substrate having a clear pattern on the substrate that is coated with a resist layer, exposed with a pattern related to the clear pattern, developed, and then measured. Once the measurement is complete, the resist on the monitor substrate can be stripped to leave the clear pattern and a new resist layer can be applied. Based on these measurements, corrections can be made to the lithographic apparatus, and these corrections need to be considered when determining the contribution. In one embodiment, the monitor substrate can be used to determine overlay by using the clear pattern and / or to determine focus by using the resist pattern.

[0098] Looking at an example of a focus, this approach basically includes two main parts. The first part is a setup process that determines the basic focus contribution of a lithography apparatus that is not reflected in the process variables of one or more types of lithography apparatus used to determine an estimated value of the focus of a particular substrate in an estimation process. The second part is an estimation process that uses the focus contribution associated with one or more types of processing apparatus for the variables of the substrate under consideration to determine an estimated value of the focus of the particular substrate.

[0099] Thus, in a setup process according to one embodiment, patterning substrate focus measurement data is acquired for one or more substrates, and then the contribution of one or more types of lithography apparatus process variables is removed as described above with respect to FIG. 10. One type of contribution that can be removed is, for example, the focus contribution of a substrate height residual or error map associated with a leveling sensor of the lithography apparatus. A further type of contribution that can be removed is the focus contribution of an image plane deviation (IPD) of the projection system, which can be obtained, for example, from a shear interferometer and / or a model residual of the projection system. A further type of contribution that can be removed is the focus contribution of the patterning device and / or substrate servo control (e.g., MA), which is obtained from the residuals of applicable positioners, position measurement devices (e.g., sensor IF) and / or servo control models. As described above, the conversion from process variables to focus contributions can be determined through simulation, mathematical modeling, and / or experimentation.

[0100] If desired, the contribution fingerprint can be re-gridded (which can be the same grid as any grid of the contribution fingerprint or a different grid) to the same grid. Similarly, the contribution fingerprint can be re-gridded to the patterning substrate measurement data. In one embodiment, the re-gridding includes upsampling or downsampling.

[0101] In one embodiment, filtering (e.g., moving average, deconvolution, FFT, etc.) is applied to the contributions, desirably before combining it with another contribution.

[0102] In one embodiment, since the focus contribution underlying the lithographic apparatus can be effectively determined once and used for various focus estimations, the measurement amount can be significantly reduced by comparing with the measurement of each substrate. In one embodiment, the patterned substrate focus measurement data can be obtained by relatively sparse sampling of positions on the substrate (e.g., 500 or fewer targets on the substrate) and / or the number of substrates from one or more lots (e.g., fewer than 10 substrates from a lot of 25 or more substrates).

[0103] In one embodiment, the patterning substrate focus measurement data can be the measured focus fingerprint of the monitor substrate as described above. Therefore, the data that has already been captured can be used. Thus, the measured focus fingerprint corrects the influence of the lithographic apparatus obtained from the sensor information of the lithographic apparatus, such as the focus contribution of the image plane deviation (IPD) of the projection system, the residual of the substrate height or the focus contribution of the error map, the focus contribution of the patterning device and / or the substrate servo control, etc., and can reach the focus contribution underlying the lithographic apparatus.

[0104] Next, the focus contribution underlying the lithographic apparatus is saved for use in in-product focus estimation. The focus contribution underlying the lithographic apparatus can be determined for a plurality of lithographic apparatuses. The focus contribution underlying the lithographic apparatus can be determined for a specific combination of devices of the lithographic apparatus used. For example, the lithographic apparatus can have a plurality of substrate tables capable of exposing substrates, and thus the focus contribution underlying the lithographic apparatus can be determined for a specific combination and / or a plurality of combinations of the devices used.

[0105] Next, for product-level estimation, for a substrate of interest, errors or residuals of one or more types of lithography apparatus process variables related to focus are obtained, and their focus contributions are determined. For example, the focus contribution of the image plane deviation (IPD) of the projection system, the focus contribution of the substrate height residual or error map, and / or the focus contribution of the patterning device and / or substrate servo control can be obtained for the substrate. A further type of contribution that can be added is the focus contribution of patterning device errors due to the patterning device used for a particular substrate of interest, which can be obtained by measurement. This contribution can be used in particular when the applicable underlying focus contribution of the lithography apparatus is obtained without using the patterning device.

[0106] Furthermore, as described above, the applicable underlying focus contribution of the lithography apparatus is obtained. Next, in a similar manner to that described above with respect to FIG. 9, the applicable underlying focus contribution of the lithography apparatus is combined with one or more specific focus contributions of the target substrate to obtain an estimated focus fingerprint of the target substrate. Thus, an estimated value of the focus error can be determined at any location, or almost any location, on any substrate.

[0107] Looking at the example of CD, in principle, there are several process variables that can cause CD variations in the substrate. In this embodiment, specific CD variations across the substrate are considered. In particular, the contributions of CD variations are considered with respect to focus, defocus, dose, and the overall process. The patterning device, which is the in-field contribution of CD variations, can also be considered but is not further described for the sake of simplicity.

[0108] The focus contribution to the CD can be based on a combination of the above-mentioned focus contributions, specifically, the focus contribution of the underlying lithography apparatus and the focus contribution of one or more process variables of the lithography apparatus for the substrate under consideration. This dense focus information can in principle be converted into the ΔCD contribution for the entire field of the pattern features and / or the entire substrate, provided that, for example, the Bossung behavior of the features (after lithography and / or after etching) is known through experiments or simulations. Thus, for any position (x, y) on the substrate with a focus value, the CD value corresponding to that substrate position (x, y) can be calculated. CD (HDFM x,y ) = Φ1 (HDFM x,y ) Here, HDFM corresponds to a focus map such as a high-density focus map derived as described above in the example of the focus.

[0109] The contribution of focus blur to the CD can be obtained using lithography apparatus data such as servo information (e.g., MSD in the z direction). The focus blur information can be converted into the ΔCD contribution in the scan direction and over the entire substrate. This conversion from the focus blur data to the CD is also feature-specific and can be known through experiments or simulations. CD (fblur x,y ) = Φ2 (fblur x,y ) Here, fblur corresponds to the focus blur.

[0110] The contribution of dose to the CD is due to dose variations in the lithography apparatus (e.g., determined by a dose mapping system). The dose variations over the entire substrate during exposure can be converted into the ΔCD contribution using the appropriate dose sensitivity of the applied features. This can be known through experiments or simulations. CD (dose x,y ) = Φ3 (dose x,y )

[0111] The overall process contribution to CD is the variation in CD resulting from various process steps as part of a patterning process distinct from just pattern transfer. Thus, in one embodiment, the overall process contribution is the state of CD variation after the final etch step and is not due to the various other CD variations considered in the estimation of CD variation. Thus, in one embodiment, this contribution is all the cumulative effects that do not consider process variations arising, for example, from variations in film deposition, baking and / or development, and / or variations in the etching process. Examples of process variables that contribute to the overall process contribution to CD include the characteristics of the structure under the resist layer, the chemical composition and / or physical dimensions of the resist layer, and / or the characteristics of one or more processes (spin coating, post-exposure bake, development, etching, deposition, doping, packaging, etc.) upstream or downstream of pattern transfer in the lithography apparatus. And while the overall process contribution to CD is explained from the post-etch perspective, the overall process contribution is obtained at various points in the patterning process, for example, after development and before etching.

[0112] Thus, similar to the setup process for a set of focus examples, all of the contributions of these ΔCDs due to focus, focus blur, and dose can be used and subtracted from the measured value of the substrate CD to estimate the overall process contribution. That is, in one embodiment, the overall post-etch process contribution can be generated from the post-etch anchor feature CD measurement, from which the ΔCD contributions of focus, focus blur, and dose (of the anchor feature) are removed. As described above, the overall process contribution is estimated from an appropriate anchor function. Thus, in one embodiment, the overall process contribution to other features can be determined from the anchor feature. For example, the remainder of the overall process contribution can be expressed as a proportion of the characteristics of the anchor feature. When the overall process contribution is obtained at different points in the patterning process, for example, after development but before etching, it can be used before the post-development but pre-etch CD measurement.

[0113] In one embodiment, the contribution of the entire process can be effectively determined and used for various CD estimations, thus significantly reducing the amount of measurement compared to the measurement of each substrate. In one embodiment, the patterned substrate focus measurement data can be obtained by relatively sparse sampling of positions on the substrate (e.g., less than 500 targets on the substrate) and / or the number of substrates from one or more lots (e.g., less than 10 substrates from a lot of 25 or more substrates).

[0114] The overall process contribution is saved for use in the estimation of CD on the product. The overall process contribution can be determined for specific and / or multiple device configurations (e.g., one or more specific etching chambers, one or more specific combinations of etching chambers and bake plates, one or more specific combinations of substrate tables and etching chambers, etc.).

[0115] Next, similar to the above focus estimation step, an estimated value of the CD on the product can be obtained. In one embodiment, errors or residuals of one or more types of lithographic apparatus process variables related to the CD are obtained for the substrate of interest, and its CD contribution is determined. For example, for the target substrate, the CD contributions of focus, defocus, and / or dose can be obtained. An additional type of contribution that can be added is the CD contribution of the patterning device error resulting from the patterning device used for the specific substrate of interest, which can be obtained by measurement.

[0116] Furthermore, as described above, the overall process contribution applicable to the CD is obtained. Next, similar to what was described above with respect to FIG. 9, the overall process contribution applicable to the CD is combined with one or more specific CD contributions of the target substrate to obtain the estimated CD fingerprint of the target substrate. Thus, the estimated value of the CD error can be determined at any location, or almost any location, on any substrate.

[0117] Furthermore, estimated values can be obtained for one or more specific pattern features of interest on the substrate, such as hot spots. As described above, the overall contribution to CD was determined for specific anchor features, but can be scaled for one or more specific features of interest. Additionally, the CD contribution of one or more types of lithographic apparatus process variables (such as focus, defocus, and / or dose) can be calculated based on the appropriate sensitivity of the CD variation to one or more specific features among one or more types of lithographic apparatus process variables. Such sensitivity can be obtained, for example, by simulation and / or experimentation. Thus, multiple CD substrate fingerprints can be obtained, each of which can be used for different hot spots or other target features of the pattern.

[0118] The methodology can be improved, for example, by increasing the parameters of one or more related models, such as patterning device and / or aberration models. This methodology can be extended, for example, by estimating the overall contribution to the process by dividing it into different contributions, such as deposition, lithography, and / or etching, with different sensitivities to different features.

[0119] In one embodiment, the dose correction applied as part of the patterning process can be corrected in the result. For example, a litho cell can apply dose correction using, for example, ASML's Dosemapper system. Thus, this correction is taken into account in the determination of the estimated value of CD.

[0120] Looking at an example of overlay here, data from at least two different pattern transfers to the substrate is used. This technique is similar to that described above with respect to focus and CD.

[0121] This method essentially includes two main parts. The first part is a setup process that determines the contribution of the underlying overlay of the lithography apparatus that is not reflected in one or more types of lithography apparatus process variables used to determine the estimated value of the overlay of a particular substrate in the estimation process. Optionally, the contribution of the overall process overlay can also be determined in the same way as the contribution of the overall process CD in the CD example described above. The second part is an estimation process that uses the contribution of the overlay related to one or more types of lithography apparatus process variables of the substrate under consideration for each of at least two pattern transfers to determine the estimated value of the overlay of a particular substrate.

[0122] Thus, in the setup process according to one embodiment, patterned substrate overlay measurement data is obtained for one or more substrates, and then the contribution of one or more types of lithography apparatus process variables is removed for each of at least two pattern transfers. One type of contribution that can be removed is, for example, the overlay contribution of the substrate height map obtained from the leveling sensor of the lithography apparatus. The difference between the substrate height maps of the two pattern transfers can be found and the difference can be converted into an overlay value. For example, using the first principle of calculating the X and / or Y displacements considering the height difference as the warp or bend of the substrate, the Z height difference can be converted into X and / or Y displacements (e.g., the displacement is half of the change in Z versus the change in X or Y times the thickness of the substrate, e.g., the thickness of the substrate or the displacement can be calculated using Kirchhoff plate theory in a non-attenuating region of the substrate). In one embodiment, the conversion to the overlay contribution of height can be determined through simulation, mathematical modeling, and / or experimentation. Therefore, by using such substrate height information for each pattern transfer, the influence of the overlay by the focus or chuck spot can be observed and explained.

[0123] A further type of contribution that can be removed is the overlay contribution of the patterning device and / or substrate servo control (such as MA) in the X and / or Y directions (including rotation about the Z axis), which can be obtained from the corresponding positioner. A difference in the servo control values for the entire substrate may be seen in two pattern transfers, and this difference may represent the overlay contribution. If necessary, the conversion from the servo control values to the overlay contribution can be determined through simulation, mathematical modeling, and / or experimentation.

[0124] A further type of contribution that can be removed is the aberration of the projection system (which can be obtained, for example, from a shearing interferometer) and / or the overlay contribution of the projection system. The conversion from the aberration and / or residual to the overlay contribution can be determined through simulation, mathematical modeling, and / or experimentation.

[0125] A further type of removable contribution is the overlay contribution of the residual of the alignment system model, which can be provided by the lithographic apparatus. The conversion from the residual to the overlay contribution can be determined through simulation, mathematical modeling, and / or experimentation. In one embodiment, the residual of the alignment system model may be different for different pattern transfer steps, and thus the combination / difference of the alignment system model residuals for different pattern transfer steps can be used to obtain the overlay contribution. In one embodiment, the residual of the alignment model can be corrected for the height of the substrate.

[0126] If necessary, the contribution fingerprint can be regridded to the same grid. Similarly, the contribution fingerprint can be regridded to the patterning substrate measurement data.

[0127] In one embodiment, the contribution of the overlay that forms the basis of the lithographic apparatus can be effectively determined once and used for various overlay estimations, thus significantly reducing the amount of measurement compared to the measurement and comparison of each substrate. In one embodiment, the patterned substrate overlay measurement data can be obtained by relatively sparse sampling of positions on the substrate (e.g., targets of 500 or less on the substrate) and / or the number of substrates from one or more lots (e.g., less than 10 substrates from a lot of 25 or more substrates).

[0128] In one embodiment, the patterned substrate overlay measurement data can be the measured overlay fingerprint of the monitor substrate as described above. Thus, the data that has already been captured can be used. Therefore, the measured overlay fingerprint can be corrected for the influence of the lithographic apparatus derived from lithographic apparatus sensor information such as the overlay contribution of the projection system, the overlay contribution of the substrate height, the overlay contribution of the alignment model residual, or the overlay contribution of the patterning device and / or substrate servo control in order to reach the overlay contribution that forms the basis of the lithographic apparatus. In one embodiment, the measured overlay fingerprint data is captured once for the first pattern transfer of the product substrate and then captured for the second pattern transfer (involving reprocessing of the monitor substrate during the pattern transfer). In one embodiment, the patterned substrate overlay measurement data is the overlay delta fingerprint obtained from the difference between the overlay fingerprint measured from one or more monitor substrates after the first pattern transfer and the overlay fingerprint measured from one or more later monitor substrates. Thus, by exposing a set of monitor substrates approximately simultaneously with the product layer, the contribution of the lithographic apparatus to the overlay in terms of short-term drift can be quantified. That is, thereafter, by overlaying the delta fingerprint, the contribution of the lithographic apparatus to the inter-field overlay due to short-term drift between the first and second pattern transfers can be obtained.

[0129] Optionally, if an overlay after etching is desired, the contribution from the etching process to the overlay can be determined, which is the overlay variation resulting from etching. To obtain the etching process overlay contribution, the metrology data of the patterned substrate after development but before etching can be subtracted from the metrology data of the patterned substrate after etching to obtain the etching process overlay contribution. In one embodiment, the overlay contribution of the etching process is effectively determined once and used for overlay estimation, and thus the amount of measurement can be significantly reduced compared to the measurement of each substrate. In one embodiment, the patterned substrate overlay metrology data can be obtained by relatively sparse sampling of positions on the substrate (e.g., targets of 500 or less on the substrate) and / or the number of substrates from one or more lots (e.g., less than 10 substrates from a lot of 25 or more substrates). The etching process fingerprint induced by the first or second pattern transfer can be estimated by the delta fingerprint between after development and before etching overlay measurement and after other post-etching overlay measurements of the first or second pattern transfer. Each pattern transfer is the same.

[0130] Subsequently, the overlay contribution of the lithography apparatus (and optionally the etching process overlay contribution) is stored for use in the product overlay estimation on the lithography apparatus. The overlay contribution of the lithography apparatus can be determined for multiple lithography apparatuses. The overlay contribution of the lithography apparatus can be determined for a specific combination of devices of the lithography apparatus used. For example, a lithography apparatus may have multiple substrate tables on which a substrate may be exposed, and thus the overlay contribution under the lithography apparatus may have a specific combination of devices used and / or multiple combinations. The overlay contribution of the etching process can be determined for specific and / or multiple apparatus configurations (e.g., one or more specific etching chambers).

[0131] Next, for product-level estimation, for a target substrate, errors or residuals of one or more types of lithography apparatus process variables related to the overlay are obtained, and the overlay contribution thereof is determined. For example, the contribution of the overlay of the projection system, the contribution of the overlay of the substrate height, the contribution of the residual overlay of the alignment model, and / or the contribution of the overlay of the patterning device and / or substrate servo control can be obtained for the target substrate in order to arrive at the contribution of the underlying overlay of the lithography apparatus. In one embodiment, only the overlay contribution of the substrate height is obtained.

[0132] Furthermore, as described above, the applicable underlying overlay contribution of the lithography apparatus is obtained, and optionally, the overlay contribution of the applicable etching process is obtained. Next, the applicable underlying overlay contribution of the lithography apparatus (and optionally, the overlay contribution of any etching process) is combined in the same manner as described above. FIG. 9 shows the contribution of one or more specific overlays of the target substrate for obtaining the estimated overlay fingerprint of the target substrate. Thus, the overlay estimate can be determined at substantially all locations on any substrate.

[0133] In one embodiment, the overlay correction applied as part of the patterning process can be corrected in the result. For example, the lithocell may apply an overlay correction based on measurements of a monitor substrate using, for example, ASML's Baseliner system. Thus, this correction is taken into account in the determination of the overlay estimate.

[0134] In one embodiment, in a multiple patterning process, it is desirable that both exposure conditions and lithography apparatus conditions, such as exposure dose, patterning device transmittance, patterning device qualification error, illumination setting, substrate clamping error of the lithography apparatus, etc., be very similar between the first and second pattern transfer steps. Further, since the characteristics of exposure and heating at the in-field level are expected to be similar between the first and second pattern transfer steps, such effects on overlay should be small.

[0135] Furthermore, in one embodiment, multiple predictions can be combined. For example, an overlay prediction and a CD prediction can be combined. For example, in a multiple patterning situation where different pattern transfer steps are used to create adjacent structures to each other and there is a gap between those structures, by combining the CDs of one or more different pattern transfer steps and the overlay of different pattern transfer steps, the size of the gap can be predicted more accurately than an estimation of only the overlay or the CD.

[0136] FIG. 11 schematically shows the flow of a method according to one embodiment. In particular, it shows generalized contributions such as the focus contribution underlying the lithographic apparatus, the overall process contribution to CD, and / or the overlay contribution underlying the lithographic apparatus (and optionally the overlay contribution of an applicable etching process). By applying to specific information of a substrate of interest, an estimated value of a parameter of interest of the substrate can be obtained. Thus, contribution 912 corresponds to one or more process variables of a specific substrate, for example with respect to hot spots. This can be determined by modeling, for example from device information. Further, a contribution 922 applicable to a plurality of substrates is obtained, such as the focus contribution underlying the lithographic apparatus, the overall process contribution to CD, and / or the overlay contribution underlying the lithographic apparatus (and optionally the etching process overlay contribution). Contribution 922 can be obtained using any of the techniques described herein. Contribution 912 may be determined for a plurality of substrates (e.g., for any substrate of interest), while contribution 922 may be used repeatedly across many substrates. By combining contribution 912 and contribution 922, an estimated value 950 of a parameter of interest, for example with respect to hot spots, is obtained, without necessarily obtaining patterning substrate measurement data of the hot spots. In step 970, an action such as determining whether there is a defect in the hot spot is performed based on the estimation of the parameter of interest.

[0137] Thus, by leveraging device sensor data, measurements in and / or after the resist can be enhanced, providing high-density measurements for each substrate, without the need to densely sample the substrate or obtain patterning substrate measurement data for each substrate, and providing measurements for many, if not all, substrates. Further, the high-density computed measurements enable, for example, higher-order corrections. The computed measurements enable better control, including control for each substrate. There is no need to obtain patterning substrate measurement data for each such substrate, nor to densely measure patterning substrate measurement data on the substrate.

[0138] Furthermore, based on the estimations from these calculated metrology techniques, various applications such as patterning process control (such as adjusting one or more process variables), monitoring of the patterning process, defect detection, defect prediction, and patterning process design become possible.

[0139] In one embodiment, a mathematical model that determines the contribution of changes in one or more process variables to a parameter of interest can be parameterized using derived contributions (such as those derived using FIG. 10). That is, the mathematical model can be fitted to the derived contributions, thereby obtaining values for one or more parameters, constants, etc. of the mathematical model. Thus, as an example, it is desirable to have a model and the sensitivity represented by the model to adapt to changes in the process and / or substrate stack. Therefore, in one embodiment, a predicted substrate fingerprint can be generated for all substrates to be measured. For this reason, a model of the parameter of interest (for example, in the case of CD, CD = a1*DOSE + a2*FOCUS + a3*MSDx + a4*MSDy + a5*MSDz +...) can be established. By measuring the substrate, the fingerprints of the pre-treatment and / or post-treatment (such as track / etching) and the patterning device can be removed. The remaining fingerprint measurements can be compared with the predicted values. In this situation, there is a set of equations (the same number of equations as the measurement points) where CD, dose, focus, MSD-xyz, aberration, etc. are known. This set of equations can be solved for the required sensitivities (a1, a2,...). When this is performed for a large number of substrates measured for a specific device pattern, there is a lot of data for re-evaluating the required sensitivities. When using data from multiple lithography apparatuses and / or using data from focus exposure matrix exposures in the same way, the sensitivities can be appropriately estimated due to sufficient variation in the input signals (such as focus, dose, MSD, CD, etc.). Furthermore, this technique can be applied to other parameters of interest such as depth of focus, exposure latitude, overlay, edge position, etc.

[0140] In one embodiment, additional accuracy can be added using a training algorithm. For example, once the sensitivity to aberration is resolved, boundary conditions can be considered. Aberration only varies at the slit, and CD (or overlay) data can be pre-filtered before adjusting these sensitivities. In one embodiment, the sensitivities can be made robust to variations in the patterning process by re-evaluating them occasionally or continuously.

[0141] Referring again to FIG. 6 and its associated description, in one embodiment, one or more of the variables of the parameterized model 206 may have a stronger influence on the calculated radiation distribution than one or more other variables. For example, a small percentage change in one or more variables may result in a large difference in the calculated radiation distribution. Such variables may be referred to as strong variables. Strong variables include, but are not limited to, the critical dimension of a feature. On the other hand, a large change in one or more other variables may result in a small difference in the calculated radiation distribution. Such variables may be referred to as weak variables. Weak variables include, but are not limited to, the sidewall angle of a feature, the height of a feature, the thickness of a layer, resist loss during development, the footing of a feature, the refractive index of a layer, the absorption of a layer, and / or the extinction coefficient of a layer.

[0142] Both the strong and weak variables of the parameterized model 206 can be used by a user (e.g., a human, a control system, etc.) to evaluate one or more steps of the patterning process. Specifically, one or more weak variables may be useful for determining whether there are defects in a target 30' or other pattern that can be used in one or more processes upstream or downstream of the pattern transfer of a lithography apparatus, such as spin coating, PEB, development, etching, deposition, doping, packaging. For example, if the sidewall angle of a pattern on a substrate exceeds a certain threshold, one or more defects may occur during subsequent etching. As such, possible defects due to etching can be predicted before the etching process occurs based on the value of the sidewall angle of the pattern on the substrate. Such examples are non-limiting.

[0143] However, it is difficult to determine the value of a weak variable directly based on measurement. This is because the signal used to determine the value of a weak variable in an inspection system is usually very weak and sometimes too weak to detect. Furthermore, it is difficult to provide a certain level of accuracy in determining the value of a weak variable, especially when there are many variables in a parameterized model and the values of the strong variables are unknown.

[0144] Through the reconstruction process described in FIG. 6, to obtain more accurate values of one or more weak variables for various applications (e.g., predicting defects), it is preferable to determine the values of one or more strong variables (e.g., CD) within a parameterized model external to the reconstruction process itself.

[0145] FIG. 12 shows a flow of a method for determining the value of a strong variable on a substrate (thereby avoiding performing the measurement of the strong variable on the substrate). By applying this process, the values of a plurality of different strong variables can be obtained. As shown, the strong variable 1640 of the substrate is a first contribution 1610 of a first group of one or more variables related to the lithographic apparatus (spatially specified for each die / field, such as focus, dose, MSD, aberration, pupil shape, etc., and repeated across the substrate under the application conditions or spatially specified across the substrate), a second contribution 1620 of a second group of one or more variables related to one or more manufacturing processes before and after pattern transfer in the lithographic apparatus (such as etching, development, etc., which can be spatially specified across the substrate), and a contribution 1630 of a third group of one or more variables related to the patterning device used in the patterning process (such as mask CD, etc., which can be spatially specified for each die / field and repeatedly arranged or spatially specified across the substrate under the application conditions). The fingerprint of the strong variable 1640 can be obtained for a specific part of the substrate, such as a part of the target 30'.

[0146] The first group of one or more variables related to the lithographic apparatus can be one or more variables as described above. The first contribution 1610 can be specific to the lithographic apparatus. That is, the first contribution 1610 is specific to a particular actual lithographic apparatus. In one embodiment, the first contribution 1610 is not specific to a particular substrate (and thus can be used across multiple substrates). Thus, the first contribution 1610 may be pre-characterized and later retrieved from a database for the reconfiguration process. This first contribution 1610 can be applied to a particular substrate by combining it with data on one or more variables regarding the particular substrate and the sensitivity relationship. The first contribution 1610 can be substrate-specific. For example, the first contribution 1610 may be determined for each substrate or a particular group of substrates such that the fingerprint of the strong variable 1640 is specific to the substrate or group of substrates. Examples of the first group of variables include illumination variables, projection system, focus, dose, bandwidth, exposure time, characteristics of high-frequency stage movement (e.g., movement standard deviation (MSD) of the substrate stage, moving average of the movement of the substrate stage, etc.), changes in high-frequency laser bandwidth (frequency, amplitude, etc.), changes in the wavelength of the high-frequency laser, and / or flatness of the substrate.

[0147] The third group of one or more variables related to the patterning device can be the one or more variables described above. The third contribution 1630 can be specific to the pattern or the patterning device. That is, the third contribution 1630 is specific to a particular actual patterning device or a particular pattern provided by the patterning device. The third contribution 1630 may be independent of the substrate. Thus, the third contribution 1630 may be pre-characterized and later retrieved from a database for the reconfiguration process. Examples of the third group of variables include mask CD, shape and / or position of assist features, adjustments applied by resolution enhancement techniques (RET), etc.

[0148] A second group of one or more variables associated with one or more manufacturing processes before or after pattern transfer in a lithographic apparatus can be the one or more variables described above. Similar to the first contribution 1610, the second contribution 1620 may or may not be substrate-dependent. In one embodiment, the second contribution 1620 may be repeatedly used across all substrates. Thus, the second contribution 1620 may be pre-characterized and retrieved from a database during the reconstruction process. Examples of the second group of one or more variables include, but are not limited to, various characteristics of processes upstream or downstream of pattern transfer in a lithographic apparatus, such as spin coating, PEB, development, etching, deposition, doping, and / or packaging.

[0149] The first contribution 1610, the second contribution 1620, and / or the third contribution 1630 can be characterized experimentally or retrieved from previous production data, for example, using any of the flows of FIGS. 8 to 11. In one embodiment, the third contribution 1630 (i.e., the patterning device fingerprint) can be obtained by directly measuring the patterning device using a patterning device metrology tool.

[0150] After the fingerprint 1640 of the strong variables is determined, the value of the strong variables 1660 can be obtained by combining the fingerprint 1640 of the strong variables with the specific values 1650 of the strong variables. In one embodiment, the specific value of the strong variables can be the nominal design value. In one embodiment, the strong variables may be the average of a group of measured values of the strong variables on the substrate. The measurement group of the strong variables is performed for the same feature on two or more dies on the substrate.

[0151] When the values of one or more strong variables of a parameterized model are given (for example, fixing the values of one or more strong variables, or restricting the respective values of one or more strong variables within a predetermined range (for example, within 10%, within 5%, within 3%, within 1%)), the calculated radiation distribution is substantially similar to the measured radiation distribution, or the difference between the calculated radiation distribution and the measured radiation distribution is within a predetermined tolerance threshold, one or more weak variables may be adjusted. When the calculated radiation distribution is substantially similar to the measured radiation distribution, or the difference is within the predetermined tolerance threshold, the values of one or more weak variables may be output.

[0152] As described above, the values of one or more weak variables are used to predict whether there are defects in one or more downstream processes after exposure, such as PEB, development of the resist layer, etching, deposition, doping, and / or packaging. If a defect is predicted, the values of one or more variables in the first group of one or more variables, the second group of one or more variables, and / or the third group of one or more variables are adjusted to obtain a new fingerprint of the strong variables. This is because a new set of values of one or more weak variables is reconstructed using the above process. Such adjustment may be repeatedly performed based on the new set of values of one or more weak variables until no defect is predicted.

[0153] In a further application of the above contributions / fingerprints, one or more contributions / fingerprints can be used to predict the outline of a pattern. In this regard, the outline is the outline of the shape of the features of the pattern transferred to the substrate. The outline can be visualized, for example, by processing an image of the substrate (e.g., a scanning electron microscope image) to extract the outer boundary of the shape of the pattern features transferred to the substrate. However, it is also possible to generate an outline by a mathematical process (such as a simulation) to create an electronic representation of the pattern features expected to be transferred to the substrate. Usually, the outline is in the form of a line, but the outline used here can be generalized by the data describing the boundaries of the features. The outline does not have to be continuous. That is, if a discontinuous outline and / or data sufficiently describes the boundaries of the features, the outline and / or data may be discontinuous around the features. In one embodiment, the outline can be two-dimensional (i.e., defining a plane) or three-dimensional. In one embodiment, the outline can extend in a plane substantially parallel to the surface of the substrate on which the pattern is formed. In one embodiment, the outline can extend in a plane substantially perpendicular to the surface of the substrate on which the pattern is formed. In that case, it can be characterized as a profile and can be in two-dimensional or three-dimensional form.

[0154] To predict the outline, one or more contributions / fingerprints can be obtained as described herein and used to select a specific nominal outline and / or modify the nominal outline to reach the predicted outline. Referring to FIG. 13, an embodiment of a flowchart of a method for predicting an outline is shown. At 1700, the nominal outline of the features of the pattern is determined. In one embodiment, the nominal outline is the outline expected in the resist. In one embodiment, the nominal outline is the outline expected in the developed resist.

[0155] In one embodiment, the nominal profile can be obtained by mathematical calculations via a model and / or simulation. In one embodiment, a simulator or model, for example, a simulator such as ASML's Tachyon product, can determine the expected profile of a pattern feature with applicable design values of one or more process variables of the feature patterning process. This profile obtained by calculation can be designated as the nominal profile. Similarly, the simulator or model can determine the profile with different values of one or more process variables (e.g., one or more optical settings or conditions such as different focus settings or conditions, different dose settings or conditions, different projection system aberration settings, or conditions, different illumination pupil shape settings or conditions, etc.) to obtain multiple profiles of the feature. Each profile is a different value of one or more process variables. These profiles obtained by calculation can be designated as nominal profiles with each nominal profile associated with different values of one or more processes. In one embodiment, the nominal focus is determined for different focus settings or conditions, and thus each of the nominal profiles can be associated with different focus settings or conditions (such as a specific dispersion from the best focus). The following description focuses on focus settings or conditions, but the nominal profile can be determined for settings or conditions different from focus and can be determined for various combinations of settings or conditions.

[0156] In one embodiment, the influence of one or more process variables on one or more other process variables whose nominal profile is determined is evaluated. In one embodiment, the one or more other process variables being evaluated are one or more process variables that affect the shape and / or size of the profile. Thus, in embodiments where the nominal profile is determined for focus setting, the influence of focus on one or more other process variables (such as CD) is determined. In one embodiment, this influence can be determined using a focus exposure matrix (FEM) type process, where a particular pattern is evaluated at at least different focus settings or conditions. The CD at these different focus settings or conditions can be determined to evaluate the degree of change in CD due to the change in focus. In one embodiment, the influence described above can be determined experimentally using one or more processed substrates, which are then measured by a measurement tool. In one embodiment, the influence described above can be determined using a simulator.

[0157] In addition to, or instead of, determining the nominal profile computationally, in one embodiment, the nominal profile can be obtained experimentally. For example, features can be created on one or more substrates with applicable design values of one or more process variables of a patterning process and measured (e.g., using a scanning electron microscope) to derive the profile of the features. This profile obtained by measurement can be designated as the nominal profile. Additionally or alternatively, features can be created and measured (e.g., using a scanning electron microscope) on one or more substrates with different values of one or more process variables (such as one or more of the optical settings or conditions described above) to derive multiple profiles of the features, each profile being at a different value of one or more process variables. These profiles obtained by measurement can then be designated as nominal profiles with each nominal profile associated with different values of one or more process variables. Thus, as a specific example, each nominal profile can be associated with different focus settings or conditions (such as a specific dispersion from best focus).

[0158] Thus, in one embodiment, the nominal contour can provide an indication of the shape of the contour. For example, the nominal contour can indicate the shape of the contour under specific focus conditions. Thus, in the case of multiple nominal contours obtained with multiple different focus conditions, each nominal contour can provide an indication of the predicted contour shape under the applicable focus conditions.

[0159] Thus, in one embodiment, as further discussed, the shape of the contour can be predicted for more processing variables by referring to the nominal contour, based on nominal contours each associated with a different value of one or more processing variables (e.g., focus). If the nominal contour cannot be used for a particular value of one or more processing variables, the contour can be generated by interpolation, extrapolation, etc. Thus, as an example, for any focus value at a particular location on the substrate, the shape of the contour of the corresponding pattern feature of interest can be predicted.

[0160] Thus, at 1710, for one or more processing variables for which the nominal contour has been determined, a first contribution / fingerprint can be obtained. The first contribution / fingerprint can be obtained using any of the techniques described herein. In one embodiment, this first contribution / fingerprint corresponds to the situation prior to etching.

[0161] In one embodiment, the first contribution / fingerprint is in focus and thus, in one embodiment, the first contribution / fingerprint is a focus map of the entire substrate. In one embodiment, the first contribution / fingerprint can be generated based on data obtained from a lithography apparatus used to pattern the substrate. For example, the lithography apparatus can provide focus information (e.g., focus residual error, etc.) and / or characteristics of high-frequency stage movement (e.g., MSD) to construct the focus map. FIG. 14 shows an exemplary focus map 1800 for a patterning process, where different shadings schematically represent different dispersions from a nominal focus (e.g., best focus, average focus, etc.).

[0162] In 1720, using the first contribution / fingerprint 1710, a nominal contour of the feature of interest is selected. For example, at a specific location on the substrate, for a specific feature of interest, the values of one or more process variables for which the nominal contour has been determined are determined from the first contribution / fingerprint 1710 and then used to select the associated nominal contour. Thus, in an example where the first contribution / fingerprint 1710 is a focus map, the focus estimation at the substrate location within the focus map can be used to obtain the associated nominal contour as a prediction of the contour. Thus, the predicted contour can be determined for each feature and each substrate location.

[0163] Referring back to FIG. 14, an example of such a selection is shown. In FIG. 14, the nominal contours 1810, 1812, 1814 at the best focus are shown. Here, at the position on the focus map 1800 associated with the nominal contour 1812, the focus map indicates that the focus was at or near the best focus. Thus, for that location, the nominal contour 1812 would be selected as the predicted contour. In the case of the location associated with the nominal contour 1810, the focus map indicates that the focus was at the negative defocus -F. Thus, in that case, instead of using the nominal contour 1810, the nominal contour determined for the negative defocus -F, i.e., the nominal contour 1820, is selected. As shown in FIG. 14, the nominal contour 1820 has the characteristics of the feature but a different shape due to the negative defocus -F. Similarly, in the case of the location associated with the nominal contour 1814, the focus map indicates that the focus was at the positive defocus +F. Thus, in that case, instead of using the nominal contour 1814, the nominal contour determined for the positive defocus +F, i.e., the nominal contour 1830, is selected. As seen in FIG. 14, the nominal contour 1830 has the characteristics of the feature but a different shape due to the positive defocus +F. Thus, when the focus is -F, the nominal contour of the optimal focus changes shape, and similarly, when the focus is +F, the nominal contour of the optimal focus changes shape. Thus, for example, if F is the dispersion from the best focus and the absolute values of +F and -F are the same, the changes in the respective contour shapes may be the same as shown in FIG. 14.

[0164] Referring back to FIG. 13, at 1730, for one or more process variables other than the one or more process variables for which the nominal contour was determined, a second contribution / fingerprint can be obtained. The second contribution / fingerprint 1730 can be obtained using any of the techniques described herein. In one embodiment, the second contribution / fingerprint corresponds to the situation after etching.

[0165] In one embodiment, the second contribution / fingerprint 1730 is a critical dimension, and thus, in one embodiment, the second contribution / fingerprint is a critical dimension map (e.g., a critical dimension uniformity map) of the entire substrate. In one embodiment, the contribution / fingerprint can be generated based on data measured on one or more substrates having patterns after the etching step of the patterning process using a metrology tool. FIG. 15 shows an exemplary critical dimension map 1900 of a patterning process, where different shades schematically represent different dispersions from a nominal critical dimension (e.g., a design critical dimension, an average critical dimension, etc.). Thus, for example, the critical dimension map 1800 can represent critical dimensions measured in an anchor aspect and plotted as a percentage of the average critical dimension.

[0166] In one embodiment, the second contribution / fingerprint is corrected for the influence of one or more process variables associated with the first contribution / fingerprint on one or more process variables of the second contribution / fingerprint. Thus, for example, if the first contribution / fingerprint is a focus map and the second contribution / fingerprint is a critical dimension map, the second contribution / fingerprint is corrected for the influence of focus (e.g., focus information (e.g., focus residual error, etc.) and / or characteristics of the movement of the high-frequency stage) on the critical dimension with respect to the second contribution / fingerprint. Details for determining such influence have been described above. For example, using FEM, the influence of focus on CD occurring during the pattern transfer step can be separated and removed from the CD measurement after etching. Additionally or alternatively, measurement signals of various lithography apparatuses can be processed to arrive at an estimated value of focus during pattern transfer and its influence on the CD, and the influence can be removed from the CD after etching. As will be understood, the correction can be performed in various ways, such as by directly incorporating the correction into the second contribution / fingerprint, or by performing the correction after a value has been selected from the second contribution / fingerprint as will be described below in relation to 1740.

[0167] At 1740, the second contribution / fingerprint 1730 is used to correct the nominal contour of the feature of interest. In one embodiment, the nominal contour is the nominal contour selected at 1720. However, if a predetermined nominal contour has already been selected for the feature of interest without using the selection step at 1720, the selection at 1720 can be skipped (although the change is still performed). Similarly, if the nominal contour is selected at step 1720 and no change is required, the change at 1740 can be skipped.

[0168] Thus, in 1740, for example, at a particular location on the substrate, for a particular target feature, the values of one or more other process variables are obtained from the second contribution / fingerprint 1730 and used to determine an appropriate modification to the nominal profile. In one embodiment, the modification is a change in the size of the nominal profile. Thus, in one example, if the second contribution / fingerprint 1730 is a critical dimension map, the critical dimension estimate at the substrate location within the critical dimension map is used to change the size of the nominal profile (e.g., the nominal profile selected at 1720) as a prediction of the profile. Thus, the predicted profile can be determined for each feature and each substrate location.

[0169] In one embodiment, it is assumed that the values of one or more other process variables obtained from the second contribution / fingerprint 1730 at a particular location are applied to the entire feature of interest. Thus, if the critical dimension of the feature represented by the second contribution / fingerprint 1730 deviates by a particular amount (e.g., 5%) from a particular critical dimension (average critical dimension), all critical dimensions of the feature deviate by the same amount at the same location. Thus, this assumption means that the complete profile is sized by the same amount as the deviation of the critical dimension. Thus, assuming that the complete profile size of the feature at a particular location on the substrate changes by approximately the same amount as the critical dimension of the anchor aspect at the same location measured to obtain the second contribution / fingerprint 1730, the nominal profile critical dimension shrinks by x when it decreases by x and the nominal profile expands by x when the critical dimension increases by x. The change is provided uniformly across the profile.

[0170] Referring back to FIG. 15, an example of such a size change is shown. In FIG. 15, nominal contours 1910, 1912, 1914 are shown. Here, at the position on the critical dimension map 1900 associated with the nominal contour 1912 (which can be selected using step 1720), the critical dimension map shows that the critical dimension corresponds to the nominal critical dimension (e.g., design critical dimension, average critical dimension, etc.). Thus, for that location, the nominal contour 1912 is selected as the predicted contour. In the case of the location associated with the nominal contour 1910, the critical dimension map shows that the critical dimension is lower by a certain amount (e.g., -x). Thus, in that case, instead of using the nominal contour 1910, the nominal contour 1910 is shrunk by a certain amount (e.g., -x) to obtain the predicted contour 1920. As seen in FIG. 15, the contour 1920 has the characteristics of the feature but is smaller in size due to the smaller critical dimension. Similarly, in the case of the location associated with the nominal contour 1914, the critical dimension map shows that the critical dimension is higher by a certain amount (e.g., +x). Thus, in that case, instead of using the nominal contour 1914, the size of the nominal contour 1914 is increased by a certain amount (e.g., +x) to obtain the predicted contour 1930. As seen in FIG. 15, the contour 1930 has the characteristics of the feature but is larger in size due to the higher critical dimension. Thus, when the critical dimension is -x, the nominal contour shrinks uniformly but the shape is maintained. When the critical dimension is +x, the nominal contour increases uniformly in size but the shape is maintained.

[0171] Thus, in one embodiment, based on these two assumptions (i.e., the value of a particular one or more process variables (e.g., focus) can predict the contour shape and the value of a particular one or more other process variables (e.g., CD) can predict the contour size), and values selected from one or more contributions / fingerprints, the contour shape and size of the feature can be predicted. In particular, for all locations on the substrate, the complete contour of one or more target features can be predicted. In one embodiment, the feature of interest is a determined hot spot.

[0172] In certain embodiments, the contour is predicted from critical dimension and focus measurements. In certain embodiments, the fingerprint of critical dimension and focus is used to estimate the contour.

[0173] At 1750, the predicted contour can be used in various applications. For example, the contour can be checked by itself or in relation to one or more other contours to determine if a defect is predicted (e.g., one or more checks can be performed for necking, bridging, line pullback, line thinning, overlapping, resist top loss, and / or resist undercut). This approach is particularly useful, for example, when identifying bridging defects. These defects are caused by two features contacting each other and can in principle occur at any point on the contours of the two features (varying depending on the particular CD, focus, and / or overlay conditions at that location). Using the contour allows for a more robust assessment of such defects, for example, by evaluating and comparing dimensions at the cut lines of adjacent features.

[0174] As another example, contours can be used to evaluate edge placement positions and / or errors (and can also be used to identify defects such as bridging). In practice, this approach can provide a computational form of measurement to determine edge placement errors. For example, using the predicted contour, a "virtual" edge placement error can be predicted. This can be used, for example, in edge placement error-driven multi-patterning defect prediction. Thus, defects due to edge placement errors can be estimated using CD and focus fingerprint.

[0175] An example where potential defects can be identified using the predicted contour is the spacer and cut layer process. This example is shown in FIGS. 16A-C. FIG. 16A shows an exemplary spacer cut layer process in which line 2000 is "cut" using pattern 2010. FIG. 16A shows a nominal process where line 2000 and pattern 2010 are in the desired alignment, size, etc. The result of such a process is a clean cut of intermediate line 2000 by pattern 2010. Now, the process of FIG. 13 is applied using maps 1800 and 1900 schematically shown in FIG. 16 to arrive at the determination of the predicted contours of line 2000 and pattern 2010. In this example shown in FIG. 16B, it is predicted that the size of the contour of pattern 2010 will increase (although the shape is not changed in this example, it could be changed), while the predicted contour of line 2000 is as expected. Here, FIG. 16C shows the result when the predicted contour of pattern 2010 is used in the spacer and cut layer process. As seen at 2020, pattern 2010 unnecessarily cuts a portion of the upper line 2000 and the lower line 2000. Thus, in one embodiment, the predicted behavior of the spacer and cut layer process can be flagged as potentially generating a defect when using pattern 2010 to cut line 2000.

[0176] As another example, using the predicted contours, potential defects in a litho-etch (LELE) process can be determined. This example is shown in FIGS. 17A-C. FIG. 17A shows an exemplary litho and etch process, where line 2100 is created in a first litho-etch process and pattern 2110 is interleaved with line 2100 through a second litho-etch process. FIG. 17A shows a nominal process where line 2100 and pattern 2110 are in the desired alignment, size, etc. The result of such a process would be the designed separation between pattern 2110 and line 2100. Here, the process of FIG. 13 is applied using maps 1800 and 1900 schematically shown in FIG. 17, and the predicted contours of line 2100 and pattern 2110 can be reached. In this example shown in FIG. 17B, the contour of pattern 2110 is predicted to be larger in size and changed in shape, while the predicted contour of line 2100 is determined to be as expected. Now, FIG. 17C shows the result when the predicted contour of pattern 2110 is used in the litho-etch process. As seen at 2120, pattern 2110 is undesirably too close to the lower line 2100 (e.g., the spacing between features is less than a specific threshold). That is, it is an overlap area or violates the minimum distance requirement. This can result in a bridging defect. Further, pattern 2110 may have a necking defect 2130 where the feature is changed to be too narrow (e.g., the width is below the threshold). Thus, in one embodiment, the predicted operation of the litho-etch process can be flagged as generating one or more potential defects when pattern 2110 is created in relation to line 2100. Thus, in one embodiment, for defect prediction in multiple-exposure LELE type applications, the predicted contours must improve the prediction ability for necking and / or bridging defects compared to using only defect indicators / cut lines.

[0177] In another possible usage of the predicted contour, the predicted contour, which can be used in the calibration of the model, particularly in the calibration of the optical proximity effect correction model, enables the correction of the measured gauge (contour) etching fingerprint and / or focus fingerprint. For example, this predicted contour can be used to adjust the preparation of the mask model after etching.

[0178] Thus, in one embodiment, this technique enables the prediction of the contour from the virtual substrate. Therefore, this approach combines measurement and calculation to generate the contour without measurement. In one embodiment, this technique enables the prediction of the variability of the contour and edge placement error across the entire substrate when an appropriate fingerprint (e.g., the critical dimension fingerprint after etching and the focus fingerprint of the lithographic apparatus) is provided. In one embodiment, this technique improves the prediction ability of multi-patterning. In one embodiment, this technique enables pattern control by using edge placement optimization based on the predicted contour.

[0179] In a further embodiment, the techniques described herein can be applied to alignment measurements. As is known in the art, various alignment marks (e.g., in the form of diffraction gratings) are provided on at least the substrate and the patterning device (e.g., the mask). Alignment marks can also be provided on other structures such as the substrate table. The alignment marks are measured with an alignment sensor to determine the spatial position of one or more specific locations in the plane on the surface of the substrate and / or the patterning device (e.g., a location on the substrate and the patterning device). The measured spatial position is used, for example, to facilitate proper positioning in the X-Y plane of the transfer of the pattern to the substrate, i.e., to ensure that the pattern is provided at the proper location on the patterning receiving surface of the substrate.

[0180] If a pattern has been previously applied to a substrate and a subsequent pattern needs to be aligned with the previous pattern, such proper positioning is particularly important. A misalignment of the patterns can be characterized as an overlay error as described in this document. To facilitate proper alignment between a first device pattern and a second device pattern applied thereafter, alignment marks can be generated for use in proper positioning of the second device pattern during generation of the first device pattern. For example, a patterning device pattern for generating the first device pattern can have one or more alignment mark patterns that are transferred to the substrate when the first device pattern is transferred to the substrate. Thus, one or more alignment marks associated with the first device pattern are processed with the first device pattern to generate an alignment mark structure in a layer of the substrate associated with the first device pattern. Next, when it is necessary to apply the second device pattern, one or more alignment marks associated with the first device pattern are measured (usually by overlaying one or more layers such as a resist), and the position of the first device pattern is determined so that the second device pattern associated with the first device pattern can be accurately positioned.

[0181] With accurate alignment, excellent overlay performance is guaranteed and production yield is improved. However, the space constraints of the substrate designed to create the device mean that alignment marks cannot be provided everywhere on the substrate (after all, most of the substrate should be used to apply patterns for generating the device). Additionally, due to time constraints, the number of alignment marks per production substrate that can be measured during production is limited while maintaining an appropriate throughput of the manufacturing system (e.g., the number of production substrates processed per hour).

[0182] Therefore, in a typical arrangement, a certain number of alignment marks are measured across the substrate (usually, a plurality of dies / fields extend across the entire substrate onto which the pattern is transferred from the patterning device), providing a significant spatial coverage at the locations of the places on that substrate. In an exemplary scheme, the substrate alignment measurement sequence can measure 20 to 100 alignment marks (positions) across the substrate. The results of these measurements capture the overall fingerprint of the entire substrate at a relatively low spatial frequency for each substrate. The measurement results are used in combination with an alignment mathematical model. The purpose of the model is to represent the deviation between the transferred positions of the device pattern features compared to an ideal grid. Thereby, for example, appropriate corrections can be made by the apparatus of the device manufacturing process based on the output of the model. As will be understood, more than 20 to 100 alignment marks can be provided across the substrate, but only 20 to 100 (e.g., 20 to 40) alignment marks are sampled, for example due to throughput constraints. Further, all or most of these sampled alignment marks can be provided in areas not available for the device pattern, such as the scribe lane.

[0183] However, such relatively sparse sampling of this type of alignment mark does not capture the fingerprint of the substrate at high spatial frequencies. As a result, the overlay performance may degrade.

[0184] To capture local effects (i.e., obtain higher spatial frequencies), an in-field alignment scheme can be used. However, there are one or more drawbacks. For example, it is necessary to perform relatively dense measurements of alignment marks, which is probably impossible to achieve without affecting throughput. Furthermore, valuable die space needs to be occupied by alignment marks. Also, due to constraints (such as throughput), in-field alignment may be limited to fewer parameters than the parameters that can be corrected by the apparatus (e.g., a lithographic apparatus) in the device manufacturing process. For example, a model of in-field alignment has six parameters (e.g., magnification (M) of the patterning device pattern, rotation (R) around the z-axis, parallel translations in x and y (Cx, Cy), magnification in the y-direction per field (My), and scan skew (RI)), even if the lithographic apparatus can correct higher orders for each transfer of the device pattern.

[0185] Therefore, for example, it would be desirable to have a denser alignment fingerprint without the need to perform more alignment mark measurements (such as dense in-field alignment). For this purpose, in the method described herein, a relatively dense alignment fingerprint (or hybrid dense alignment map (HDAM)) is calculated by combining the measured alignment data and context information from relevant factors of alignment. That is, similar to what was described for other parameters such as overlay and CD, a combination of fingerprints can be combined to obtain a derived fingerprint for alignment.

[0186] In particular, in production, local effects such as, for example, contamination, aberrations of the projection system, writing errors of the patterning device (i.e., errors in pattern creation or by the pattern creation device, etc.), heating, fluctuations in substrate height due to process effects (chemical mechanical polishing (CMP), etching, etc.) cause misalignment of at least a part of the alignment marks (and device patterns). One or more of these local effects can effectively have a fingerprint of a relatively high spatial frequency, but may not usually be captured in the alignment mark measurement sampling used in manufacturing (constrained by throughput, available die / field space, etc. for the alignment marks).

[0187] Accordingly, in one embodiment, the alignment contributions of one or more of these local effects are determined and combined with alignment measurements at a relatively low density to generate a higher density alignment fingerprint. The alignment contributions of one or more different local effects can be derived from other metrology measurements of the lithocell (e.g., within a lithographic apparatus) and / or can be calculated / measured "offline" (i.e., it is not necessary to calculate or measure during the processing of a particular substrate through the lithocell for which the HDAM is determined).

[0188] Accordingly, FIG. 18 schematically shows an example of obtaining a derived contribution 2275 to the alignment of a substrate, which is a combination of contributions of a plurality of process parameters (one or more of which may be derived contributions). Thus, the derived contribution 2275 can be obtained using the measurement contribution from the alignment mark measurement 2200 combined with the respective contributions of one or more process parameters (e.g., local effect process parameters) such as substrate height 2205 due to contamination, one or more process effects 2210 (chemical mechanical polishing (CMP), etching, etc.), heating 2215 (e.g., of the patterning device by an illumination beam to obtain a patterned beam for exposure of the substrate), projection system anomalies 2220, and / or patterning device write errors 2225. Importantly, the process parameter data can be obtained from a lithographic apparatus or other patterning process apparatus and can be a by-product of manufacturing the substrate as part of the patterning process. The contributions associated with one or more of these process parameters do not necessarily require measurement of alignment marks on the substrate using an alignment sensor.

[0189] Therefore, in this alignment case, an example of the alignment fingerprint (A') of the alignment mark measurement 2200 is shown as contribution 2240, an example of the contribution to the alignment of the substrate height or flatness (SH) is contribution 2245 (the schematic shows the substrate height data of the entire substrate, and this data can be converted into the corresponding effects of the alignment described herein), an example of the contribution due to one or more process effects (PE) is contribution 2250 (the schematic shows one or more process effect data of the entire substrate such as data or etching effect data, and can be converted into the corresponding effects of the alignment as described herein if necessary), an example of the contribution to the alignment of the heating (RH) 2215 is contribution 2255 (the schematic shows the mask heating data of the entire exposure field of the mask, and can be converted into the corresponding effects of the alignment as described herein), an example of the contribution to the alignment of the projection system aberration (PA) 2220 is contribution 2260, and an example of the contribution to the alignment due to the patterning device writing error (RWE) 2225 is shown as contribution 2265. As can be understood, it is not necessary to combine all of these contributions 2245 - 2260 with contribution 2240. Rather, one or more of the contributions 2245 - 2260 can be combined with contribution 2240. The contributions can be obtained by simulation, mathematical modeling, and / or measurement / experiment as necessary. For example, the contribution degree can be obtained by simulation based on physical models, empirical modeling, and / or dedicated measurements.

[0190] One or more of these contributions 2245-2260 can be combined (2270) with contribution 2240 respectively to achieve the derived contribution 2275. Although element 2270 indicates a plus sign, the operation at 2270 does not necessarily have to be addition. For example, multiplication and convolution can be performed using a neural network or the like. The operations may be different for one or more contributions from another one or more contributions (e.g., addition of contributions 2245 and 2250 to contribution 2240, and convolution of the sum with one or more contributions 2255 to 2265). In the example, the combined contribution to the alignment can be expressed as A(x,y)=A‘(x,y)+b1*F(SH)(x,y)+c1*F(PE)(x,y)+d1*F(RH)(x,y)+e1*F(PA)x,y)+f1*F(RWE)(x,y).... Various functions can be obtained by simulation, mathematical modeling, and / or experiment. Additionally, there may be cross terms not shown here (such as a focus as a function of the product of RH and PA). To obtain the absolute value of the alignment, the nominal or simulated value of the alignment can be combined with the contributions. Coefficients such as b1, c1, etc. are the sensitivity of the alignment to the respective processing parameters or their functions. Some of the contributions are over the entire substrate (e.g., process effects, substrate height, non-flatness, etc.). In one embodiment, one or more contributions (e.g., contribution of heating (RH) 2215, aberration of the projection system (PA) 2220, writing error of the patterning device (RWE) 2225, etc.) are per die / field (and may be repeated over the entire substrate depending on the conditions applicable in each instance). As described above, since contribution 2275 can be spatially defined over the substrate / die / field, it is characterized as a fingerprint. Further, the conversion of the contributions to the absolute value can be spatially defined over the substrate / die / field, so it is characterized as a fingerprint. As will be understood, the respective contributions can be derived using data from the processing of multiple substrates using the patterning process. Since this data may be a by-product of substrate processing, it may already be available.

[0191] Returning to the example of the processing parameter related to the local effect, the contribution 2205 of the height or non-flatness of the substrate to the alignment is a leveling substrate height map converted into in-plane displacement within the substrate (e.g., there may be 5000 points or more, 10,000 points or more, 20,000 points or more, or 50,000 points or more per substrate, and the corresponding in-plane displacement corresponding to the alignment contribution). The in-plane displacement that affects alignment and corresponds to the height or non-flatness of the substrate can be obtained by simulation, mathematical modeling, and / or measurement / experiment. Therefore, using a leveling measurement sensitive to process-induced contamination converted into in-plane displacement, the alignment measurement can be refined and enhanced at a higher density. In one embodiment, the leveling measurement relates to the state of the substrate when the alignment measurement is performed. Thus, in an embodiment, the fingerprint related to the height or non-flatness of the substrate can be specific to the particular substrate under consideration.

[0192] Using certain techniques such as 3D-NAND, the height map of the leveling substrate can probe for alignment displacements, especially at the in-field level, after removing one or more process-dependent artifacts (e.g., more leveling points are used). As is known with optical level sensors, different substrates, and different parts of a substrate, interact with the measurement beam of radiation in different ways. In other words, the height measurements obtained by the level sensor are susceptible to process-dependent effects and do not always give the true height. In particular, when the light reflected from the substrate undergoes a so-called Goos-Hänchen shift, it is known that a depression in the apparent surface occurs. This effect varies by material and depends strongly on the structure and material of several layers. Thus, the depressions in the apparent surface can vary significantly between layers and between regions of the entire substrate. For example, metallized regions reflect light more reliably than regions that are mainly dielectric. Thus, one or more techniques such as U.S. Patent No. 7,265,364, U.S. Patent Application Publication No. US2010 / 0233600, and U.S. Patent Application Publication No. US2016-0370711, which are hereby incorporated by reference in their entirety, can be used to correct and / or identify one or more process-dependent artifacts.

[0193] Another contribution due to process parameters related to local effects is a fingerprint related to one or more process effects (e.g., one or more other process steps from processes other than etching, CMP, and / or lithography pattern transfer steps). Data on one or more process effects can be determined using, for example, "offline" measurements using the measuring devices illustrated and described with respect to FIGS. 3 through 6. In one embodiment, the fingerprint of one or more process effects can be the derived contribution determined as described above. In-plane displacements that affect the alignment corresponding to one or more process effects can be obtained by simulation, mathematical modeling, and / or measurement / experiment. In one embodiment, the process effect data is associated with the creation of alignment marks before alignment measurements are made for a particular lithography pattern transfer step based on the alignment marks. In one embodiment, if the substrate under consideration is subject to the same process effects, the fingerprint associated with the process effects may not depend on the particular substrate being processed. However, in some cases, the fingerprint associated with the process effects may be specific to a particular substrate where different substrates may be affected by different values of the process effects.

[0194] A further possible process parameter is the aberration of the projection system, which can cause pattern shifts. In one embodiment, the aberration of the projection system can be measured in a lithographic apparatus using a sensor (e.g., the ASML ILIAS sensor, which is an interferometer type measuring device used to measure aberrations and other parameters). In one embodiment, the projection system aberration of the alignment mark pattern shift is calculated based on the aberration residuals measured by the sensor. The in-plane displacements affecting alignment corresponding to the aberration of the projection system can be obtained by simulation, mathematical modeling, and / or measurement / experiment. In one embodiment, the aberration data of the projection system is associated with the creation of the alignment marks before alignment measurements are made for a particular lithographic pattern transfer step based on those alignment marks. In one embodiment, a fingerprint related to the aberration of the projection system is determined for a die / field and can then be repeatedly applied to one or more other dies / fields across the substrate. Thus, the fingerprint related to the aberration of the projection system may be independent of the particular substrate being processed.

[0195] Heating is another possible process parameter that can cause a pattern shift. In one embodiment, heating is heating of the patterning device (e.g., mask) and / or the projection system. In one embodiment, heating is due to long exposure of the patterning device and / or the projection system to the illumination for pattern transfer. In one embodiment, heating can be measured in the lithographic apparatus using a sensor (e.g., a temperature sensor). In one embodiment, heating can be calculated based on first principles using the characteristics (e.g., thermal material characteristics) of one or more patterning devices and / or the projection system and the irradiation dose. In-plane displacements that affect the alignment corresponding to the heating can be obtained by simulation, mathematical modeling and / or measurement / experiment. In one embodiment, heating is associated with the creation of alignment marks before alignment measurements are made for a particular lithographic pattern transfer step based on those alignment marks. In one embodiment, the fingerprint associated with heating is determined for a die / field and can then be repeatedly applied to one or more other dies / fields across the substrate. Thus, the fingerprint associated with heating may not be dependent on the particular substrate being processed.

[0196] The write error of the patterning device is a further possible processing parameter and can cause pattern shift. In one embodiment, the write error of the patterning device is an error related to forming a pattern on or by the patterning device itself. For example, the pattern of the absorber of the mask may not be created completely, and thus the variation from the designed pattern is characterized as a write error of the patterning device. In one embodiment, the write error of the patterning device can be obtained by "offline" measurement using a measuring device. The in-plane displacement affecting alignment corresponding to the write error of the patterning device can be obtained by simulation, mathematical modeling, and / or measurement / experiment. In one embodiment, the write error of the patterning device is associated with the creation of alignment marks before alignment measurement is performed for a specific lithography pattern transfer step based on those alignment marks. In one embodiment, the fingerprint related to the write error of the patterning device is determined for a die / field and can then be repeatedly applied to one or more other dies / fields of the entire substrate. Thus, the fingerprint related to the write error of the patterning device may not depend on the specific substrate being processed.

[0197] Information regarding other possible process parameters, such as servo control (X, Y, and / or Z moving average (MA) and / or moving standard deviation (MSD)), patterning device shape (such as Z-direction bending), impact on the pellicle of the patterning device, and variation of the reference axis of the projection system, can be included if possible. The corresponding in-plane displacements affecting alignment can be obtained by simulation, mathematical modeling, and / or measurement / experiment. In one embodiment, one or more process parameters (such as the shape of the patterning device, the impact of the pellicle, the reference axis of the projection system, etc.) are associated with the creation of alignment marks before alignment measurements are made for a specific lithography pattern transfer step based on those alignment marks. Information regarding these one or more other possible process parameters is derived from metrology measurements of the lithography apparatus (or lithocell), from "offline" metrology measurements, or from calculations (such as simulations, calibration mathematical models, first principles, etc.).

[0198] Therefore, by combining alignment measurement data with the impact on alignment by one or more process parameters related to local effects (which process parameter data is, for example, lithography apparatus or other lithocell metrology data and / or may depend on the process and application), a hybrid high-density alignment map (HDAM), which is a pre-lithography pattern transfer output for the control of lithography pattern transfer, can be calculated. Since the hybrid high-density alignment map uses data obtained from individual sources, in this calculation-based measurement, the contributions of the process and the application can be shown separately.

[0199] An example of a specific non-limiting workflow for calculating the HDAM is shown in FIG. 19. That is, FIG. 19 schematically shows an example of deriving the combined contribution for alignment. Here, the example HDAM 2275 is created using the first four inputs listed in the workflow example of FIG. 18. In this example, the alignment fingerprint 2240 of the alignment mark measurement of the specific substrate under consideration, which cannot be obtained in the alignment measurement but is converted into the effect on alignment as described above, is combined with three other contributions to obtain the HDAM 2275. The other three inputs are the contribution 2245 of the substrate height or flatness 2205 to alignment (the schematic shows the substrate height data for the entire substrate, and this data can be converted into the corresponding effect on alignment described here), the contribution 2250 of one or more process effects such as chemical mechanical polishing (CMP), etching, etc. to alignment (the schematic shows the data of one or more process effects (such as etching effect data) for the entire substrate, and the data can be converted into the corresponding effect on alignment as needed), and the contribution 2255 of the patterning device heating to alignment (the schematic shows the patterning device heating data for the entire exposure field of the mask, and this data can be converted into the corresponding effect on the alignment of the substrate described, and the effect at the die / field can be repeated for the entire substrate). As understood, various contributions can be re-gridded and / or scaled as appropriate to form the HDAM. Further, the density of various contributions can be adjusted as needed to adjust the overall density of the HDAM. Therefore, by combining the alignment data with the alignment effects of one or more processing parameters, a calculated alignment map with a much higher density than the alignment data alone can be created.

[0200] HDAM can be used for various purposes. An example of use is as an input to the control of a patterning process. For example, HDAM can be an input to the control of pattern transfer in a lithographic apparatus. In that respect, it can be used as an input to an inter-field and / or intra-field substrate alignment model used to determine corrections to the lithographic apparatus. The combined high-density alignment substrate map provides high-density measurement information at both the inter-field level and the intra-field level, and thus can support the use of a higher-order substrate alignment model as part of a control loop better than when alignment data is used alone.

[0201] Depending on the use case and input data, the alignment density can be increased as needed at both the inter-field level and the intra-field level. Compared with the common alignment methods used in production, such high-density measurement enables higher-order inter-field and / or intra-field alignment models. The accuracy of the model content may be improved (in the case of a higher-order alignment model), and the overlay performance at the substrate level is enhanced. For example, FIG. 20 schematically shows an example of how a patterning process modified using a fingerprint determined according to an existing alignment measurement method is converted into an overlay error fingerprint. Alignment fingerprint 2240 is obtained using existing alignment measurement techniques and is used to modify the patterning process using an alignment model. The overlay fingerprint of the modified patterning process is shown as 2300. As can be seen in fingerprint 2300, there are a fairly large number of vectors, indicating that there are relatively significant overlay errors at various positions across the substrate. In comparison, FIG. 21 schematically shows an example of how a patterning process modified using a derived fingerprint of alignment calculated as described herein is converted into an overlay error. The derived fingerprint or HDAM 2275 is obtained using the techniques described herein and is used to modify the patterning process using an alignment model (which can be a higher-order model than that used only for alignment fingerprint 2240). In this example, the sampling position per substrate of the HDAM is approximately 1000, which is significantly higher than when only alignment measurement is used during production (when there are time constraints in production), the pattern coverage on the device is much higher than when alignment measurement is used, and the overlay fingerprint of the patterning process modified alone (when there are indium / fi eld space constraints in the placement of alignment marks) during production is shown as 2310.As can be seen in the fingerprint 2310, there are few relatively large vectors, indicating that there are few relatively significant overlay errors at various positions across the substrate. In fact, in the example, after high-order correction calculated from the hybrid high-density output using alignment measurements, the overlay can be significantly improved compared to existing alignment methods (e.g., reducing the overlay [average plus 3 standard deviations] from 4 nm to 1 nm).

[0202] In one embodiment, the contributions or HDAM can be analyzed to identify possible significant alignment errors or residuals (e.g., due to contamination issues). This can be done, for example, by statistical analysis of the data, application of thresholds to the data, or both. If there are significant alignment errors, the measurement sampling can be re-distributed (e.g., increased, spatially concentrated, etc.) to enable improvement of the computational measurement inputs and / or improvement of the modeling complexity (e.g., providing a higher-order model), for example, to avoid unnecessary rework of the substrate and enable improved operation of the patterning process. As an example, in the case of dominant heating contributions at the substrate-to-substrate level, this computational measurement can use a higher-order in-field substrate alignment model without throughput hits and without sacrificing large space by providing a high measurement density at the in-field level.

[0203] Accordingly, in one embodiment, a computer-based alignment measurement method is provided that can construct a hybrid dense alignment map based on data other than alignment measurement values (e.g., data from measurements by lithography apparatus sensors other than alignment sensors, data from measurements by other sensors in the patterning process). The HDAM can be created "inline" and can be created before a lithography pattern transfer step that can use the HDAM for correction. Thereby, the HDAM data can be used, for example, in a feed-forward manner or corrected immediately before or during pattern transfer. In one embodiment, the hybrid dense alignment map can be combined with "offline" measurements (e.g., based on measurements from write errors of the patterning device, process effects (effects such as CMP, etching, etc.)) that can be combined with "inline" such as alignment measurements.

[0204] Computation-based alignment measurement can construct a hybrid high-density alignment map with increased density of substrate alignment fingerprint compared to alignment measurement data, for example, without causing a decrease in substrate processing throughput and / or without sacrificing space within the substrate. In computation-based alignment measurement, a hybrid high-density alignment map can be constructed. This enables in-field alignment in a higher-order field based on the hybrid high-density alignment map as compared to using only alignment measurement data. In one embodiment, one or more of the contributions to the hybrid dense alignment map can be determined using a physical model, thereby avoiding model fitting. For example, (offline) simulation or model-based alignment fingerprint due to pattern shift caused by heating can be calculated at the in-field level. This enables in-field substrate alignment and compensates for dominant displacements at the inter-substrate level. As a further example, (offline) simulation or model-based alignment fingerprint due to optical aberration-induced pattern shift can be calculated to generate high-density measurement data at the in-field level, such as using an in-field substrate alignment model. As another example, (offline) simulation or model-based alignment fingerprint due to pattern shift caused by a writing error of a patterning device can be calculated to generate high-density measurement data at the in-field level, such as using an in-field substrate alignment model. Measured values of heating, optical aberration, and / or writing error of the patterning device can be input into the determination of each alignment fingerprint.

[0205] The advantages of HDAM are high-density alignment measurements compared to existing alignment measurement processes, for example, being able to capture substrate fingerprints at higher spatial frequencies than existing alignment measurement processes. Additional or alternative advantages are that this computational metrology with multiple inputs (contributions) allows for clustering of pre-lithography errors and inclusion of multiple automatic process control threads with different priorities in the patterning process. Additional or alternative advantages are that his computational metrology can be run "in-line", i.e., during the processing of the substrate, making it suitable for feed-forward correction and / or suitable as a tool for identifying process drifts (such as rework, discard of the substrate if possible). Additional or alternative advantages are that this enables more accurate capture of alignment substrate fingerprints due to the high sampling density of the computational measurement. Additional or alternative advantages are that this computational metrology can improve overlay substrate-to-substrate performance with more accurate alignment inputs.

[0206] The results of the method of the present specification (or other results derived from the results of the method of the present specification, such as defect prediction) can be used for various purposes, including control of the patterning process or apparatus therein, monitoring of substrates produced by the patterning process, design of the process or apparatus of the patterning process, and the like. For example, the results or other results derived therefrom can be used to modify the apparatus or process of the patterning process for further processing of the substrate or processing of another substrate. For example, defects can be predicted using the results. Prediction of defects can be used, for example, to control measurement tools to inspect the affected areas and / or to modify the apparatus or process of the patterning process for further processing of the substrate or processing of another substrate. Further, the results can be used to design the patterning process, for example, by deriving a dose recipe for correction of a lithography apparatus, enabling design of the patterning device and its pattern, process setup, and the like. Further, the results can be used to calibrate models, for example, calibration of an optical proximity effect correction model, a source mask optimization model, a lithography manufacturing inspection model, a resist model, an imaging model, a measurement model (e.g., a measurement process), etc., to determine one or more variables of the process (e.g., optimal exposure and / or optimal dose) and can be used for various purposes. As will be understood, there can be many other uses.

[0207] In one embodiment, a method is provided that includes determining a first distribution of a first parameter related to an error or residual when executing a device manufacturing process, determining a second distribution of a second parameter related to an error or residual when executing the device manufacturing process, and using a function operating on the first and second distributions by a hardware computer to determine a distribution of a parameter of interest related to the device manufacturing process.

[0208] In one embodiment, the first parameter, the second parameter, and the parameter of interest are the same. In one embodiment, the first distribution is specific to the device manufacturing process but not specific to a particular substrate processed using the device manufacturing process. In one embodiment, the second distribution is specific to a particular substrate processed using the device manufacturing process but not common to other substrates processed using the device manufacturing process. In one embodiment, the first distribution and / or the second distribution includes one or more selected from the contribution of servo error to the respective first and / or second parameters, the contribution of alignment model residuals to the respective first and / or second parameters, the contribution of projection system aberration or image plane deviation to the respective first and / or second parameters, the contribution of projection system model residuals to the respective first and / or second parameters, and / or the contribution of substrate surface height to the respective first and / or second parameters. In one embodiment, determining the first distribution further includes obtaining measurement data of the first parameter and removing the contribution of a particular device of the device manufacturing process to the first parameter therefrom. In one embodiment, the contribution of the particular device includes one or more selected from the contribution of servo error, the contribution of alignment model residuals, the contribution of projection system aberration or image plane deviation, the contribution of projection system model residuals, and / or the contribution of the height of the substrate surface. In one embodiment, the measured first parameter data includes the first parameter data measured from a monitor substrate. In one embodiment, the first distribution, the second distribution, and / or the distribution of the parameter of interest includes a spatial substrate fingerprint. In one embodiment, the method further includes performing one or more selected from predicting substrate defects using the distribution of the target parameter, controlling the device manufacturing process, monitoring the device manufacturing process, designing device aspects, and calibrating the manufacturing process and / or the mathematical model. In one embodiment, the first parameter, the second parameter, and / or the parameter of interest are one or more selected from overlay, CD, focus, dose, and / or edge position. In one embodiment, the device manufacturing process includes a lithography process and / or a semiconductor manufacturing process.In one embodiment, the function includes one or more selected from arithmetic addition, convolution, and / or neural network. In one embodiment, the first parameter and / or the second parameter are different from the target parameter and further include the first parameter and / or the second parameter in the target parameter. In one embodiment, the method further includes determining the first distribution and / or the second distribution using data provided by a lithography apparatus and / or an etching apparatus used in the device manufacturing process.

[0209] In one embodiment, a method is provided that includes obtaining a fundamental contribution to an overlay as part of a patterning process and obtaining an estimated value of the overlay of the substrate by combining, by a hardware computer, the fundamental contribution with a further contribution of the substrate to the overlay.

[0210] In one embodiment, a further contribution includes the contribution of the substrate surface height of the substrate to the overlay. In one embodiment, a further contribution includes the contribution of the substrate servo error of the substrate to the overlay. In one embodiment, a further contribution includes the contribution of the residual of the alignment and / or projection system model. In one embodiment, the method further includes combining the underlying contribution and the contribution of the substrate surface height with the contribution of the etching process of the substrate to the overlay. In one embodiment, the contribution of the etching process is specific to the patterning process but not specific to a particular substrate processed using the patterning process. In one embodiment, the underlying contribution is specific to a particular patterning process but not specific to a particular substrate processed using the patterning process. In one embodiment, obtaining the underlying contribution further includes obtaining measured overlay data and removing therefrom the contribution of a particular component of the lithographic apparatus to the overlay. In one embodiment, the contribution of a particular component is the contribution of the servo error, the contribution of the alignment model residual, the contribution of the projection system aberration, the contribution of the projection system model residual, and / or the contribution of the substrate surface height. In one embodiment, the measured overlay data includes the overlay data measured from a monitor substrate. In one embodiment, the contribution includes a spatial substrate fingerprint. In one embodiment, the method further includes using the estimate to predict defects of the substrate, control the patterning process, monitor the patterning process, design aspects of the patterning process, and / or calibrate a mathematical model.

[0211] In one embodiment, a method is provided that includes: determining a first distribution of measured alignment data when executing a device manufacturing process; determining a second distribution of alignment data derived from process parameters of the device manufacturing process; and determining, by a hardware computer system, a distribution of alignment data associated with the device manufacturing process as a function of the first and second distributions.

[0212] In one embodiment, the process parameters include one or more selected from the height or non-flatness of the substrate, process effects, heating of the optical element, optical aberrations, and / or writing errors of the patterning device. In one embodiment, the second distribution is derived from a plurality of process parameters of the device manufacturing process. In one embodiment, the process parameters include the height or non-flatness of the substrate, process effects, and heating of the optical element. In one embodiment, the second distribution is specific to the device manufacturing process but not specific to a particular substrate processed using the device manufacturing process. In one embodiment, the second distribution is specific to a particular substrate processed using the device manufacturing process but not common to other substrates processed using the device manufacturing process. In one embodiment, the second distribution is derived from measured values of the process parameters. In one embodiment, the method further includes performing one or more selected from predicting substrate defects, controlling the device manufacturing process, monitoring the device manufacturing process, designing aspects of the device manufacturing process, and / or calibrating a mathematical model using the distribution of alignment data. In one embodiment, the method further includes changing the sampling of measurement data based on the distribution of alignment data. In one embodiment, the method further includes using a higher-order alignment model that includes the distribution of alignment data compared to that used with only the measured alignment data. In one embodiment, the method further includes determining the first distribution and / or the second distribution using data provided by a lithographic apparatus used in the device manufacturing process. In one embodiment, the first distribution, the second distribution, and / or the distribution of the parameter of interest includes a spatial substrate fingerprint. In one embodiment, the device manufacturing process includes a lithography process and / or a semiconductor manufacturing process. In one embodiment, the function includes one or more selected from arithmetic addition, convolution, and / or neural networks.

[0213] In one embodiment, a method is provided that includes obtaining an alignment data distribution over at least a portion of a substrate processed using a patterning process based on measured alignment data. Then, a hardware computer combines the alignment fingerprint due to processing parameters other than the measured alignment with the alignment data distribution to obtain an estimated value of the alignment data of the substrate.

[0214] In one embodiment, the alignment fingerprint includes the contribution of the height of the substrate or the non - flatness of the substrate to alignment. In one embodiment, the alignment fingerprint includes the contribution of the process effect of the substrate to alignment by a part of the patterning process other than lithographic pattern transfer. In one embodiment, the alignment fingerprint includes the contribution of heating of the substrate to alignment. In one embodiment, the alignment fingerprint is specific to the patterning process but not specific to a particular substrate processed using the patterning process. In one embodiment, the alignment fingerprint is specific to a particular substrate processed using the patterning process but not common to other substrates processed using the patterning process. In one embodiment, the alignment fingerprint is derived from measured values of processing parameters. In one embodiment, the alignment fingerprint includes a spatial substrate fingerprint. In one embodiment, the method further includes using the estimated value to predict defects of the substrate, control the patterning process, monitor the patterning process, design aspects of the patterning process, and / or calibrate a mathematical model.

[0215] The input factors for overlay computational metrology (CM) are the measurements collected by the exposure sensors of the scanner and inspection tools. For example, it includes level sensor and alignment sensor measurements, stage dynamic servo logging, overlay, and other off - line metrology measurements.

[0216] When using the alignment input as an example of a contribution, it is used to calculate model content from alignment measurements based on a higher-order alignment model, such as a cubic polynomial. The content of such a model may be dominated by the contribution of wafer deformation along with the deformation of the alignment marks. However, for accurate overlay measurement monitoring, control, or defect prediction, only the contribution of wafer deformation is the true signal. The deformation of the alignment marks is irrelevant and is the cause of an error (or "noise") to be excluded. The result of including such inaccurate model content is an inconsistent performance of computational metrology (CM). In the case of a wafer where only slight deformation of the alignment marks occurs, the alignment input using a higher-order model increases the signal-to-noise ratio, thus improving measurement accuracy. In the case of a wafer with severe deformation of the alignment marks, this input may reduce measurement accuracy due to a low signal-to-noise ratio. The error (or "noise") is proportional to the degree of the model being used. Usually, it occurs at the location of the wafer edge where the alignment marks are most deformed due to the influence caused by the process. Due to such limitations, a lower-order model is selected to limit the amplitude of the "noise", but the true wafer deformation signal that can only be captured by the higher-order model is missing from the input, thus limiting the performance of CM.

[0217] It should be noted that these limitations generally exist in other input contributions such as level sensor measurement wafer height maps, scanner dynamics, offline measurement measurement etch-induced overlay, bottom grating asymmetry measurement, CD measurement, etc.

[0218] When including measurement values from a scanner or off-line measurement as input factors into the CM, the orthogonality between the factors is a useful assumption. With this assumption, contributions can be added and correlated without crosstalk with parameters of interest such as patterning process parameters like the overlay after development, the overlay after etching, the CD of SEM measurement or the overlay, etc. However, these factors may interfere with each other, especially under specific spatial frequency conditions. Depending on the parameter of interest, these contributions can also be correlated with the parameter of interest under different conditions.

[0219] In the frequency distribution of multiple input factors of the CM, in the high (> 100 Hz) frequency range, scanner measurement inputs (e.g., level sensors that measure wafer height maps) may predict overlay content with a small amount of crosstalk from other factors (e.g., scanner dynamics servo errors).

[0220] However, in the low (< 100 Hz) frequency range, the contributions share a common frequency window. These factors include, for example, wafer alignment model content, monitor wafer model content, level sensor measurements, dynamic servo data. This means that the content of such models may interfere with each other. However, it also shows that these contributions may be correlated with a specific part of the overlay content under specific frequency conditions, here called the frequency window. Signals outside these frequency windows may become part of the "noise" with unwanted contributions, potentially degrading the accuracy of the CM. Therefore, it is advantageous to exclude such "noise" from the input factors of the CM, for example, through low / high / band-pass frequency filters, to increase the signal-to-noise ratio. The embodiments described below provide a methodology for the CM to exclude such "noise".

[0221] Such a function also helps to adjust the CM results for various interest parameters with respect to the generalized data usage of other applications. For example, between an optically measured overlay and an overlay that depends on device features measured by SEM, the targets have different responses to the patterning process because of different dimensions and designs. Such a function helps to exclude uncorrelated overlay content between the optically measured contribution and the response of the actual device features from the perspective of defect prediction.

[0222] In one embodiment, a model or an NCE (non-correctable error) model functions as a frequency low-pass / high-pass filter, and a set of specific model parameters can function as a frequency band-pass filter. This is because a pair of specific model parameters (i.e., contribution or any patterning process parameter) estimated from either of the two input data shows a correlation within each pair, and here the weight between the two input data, called the calibration coefficient, can be appropriately determined.

[0223] In one embodiment, a methodology is provided for estimating the calibration coefficient of the correlation model parameters between any two input contributions or parameters of interest. For the sake of understanding, the methodology will be explained from the perspective of predicting one domain from another. The input contribution used for prediction is defined as domain A. The parameter of interest is defined as domain B.

[0224] The domain A of the input contribution is a processing variable such as an alignment variable as explained with reference to FIG. 7. The domain B of interest may be a patterning process parameter such as an overlay as explained with reference to FIGS. 7 and 8.

[0225] FIG. 22 schematically shows the flow of a method according to one embodiment.

[0226] Parameters of an interested distribution 2322 (DB), such as an overlay distribution, are determined. This is a first distribution 2322 of a first parameter 2321 related to errors or residuals during the execution of a device manufacturing process. To determine the distribution 2322, a first distribution of values 2325 of the first parameter 2321 is obtained. Next, the first distribution 2325 of values is modeled 2328 to obtain a first modeled distribution 2322 (DB) of values. Thus, in this embodiment, the determined first distribution (parameter of interest) includes the first modeled distribution of values 2322 (DB).

[0227] An input contribution distribution 2312 (DA), such as an alignment distribution, is determined. This is a second distribution 2312 of a first parameter 2311 related to errors or residuals during the execution of a device manufacturing process. To determine the distribution, a second distribution 2315 of values of the first parameter 2311 is obtained. Then, the first distribution 2315 of values is modeled 2318 to obtain a second modeled distribution 2312 (DA) of values. Thus, in this embodiment, the determined second distribution (input contribution) includes the first modeled distribution of values 2312 (DA).

[0228] For modeling 2328, 2318, a scale of variation 2304 (SV) (e.g., frequency < 100 Hz) is determined 2302, and for this, values of the first distribution 2325 and the second distribution 2315 exceed a threshold. Next, according to the determined scale of variation 2304 (SV), the first and second distributions of values are modeled (2328, 2318) to obtain a first modeled distribution and a second modeled distribution 2322 (DB), 2312 (DA) of values.

[0229] Next, a hardware computer uses a function operating on the first and second distributions 2322 (DB), 2312 (DA) to determine a distribution of a parameter of interest (in this embodiment, a first parameter such as an overlay). The function of this embodiment includes a correlation 2332 (CORR) operating on the first and second distributions 2322, 2312.

[0230] The determination of the distribution of the target parameter 2352 (DB') is based on the scaling 2335 of the modeled second distribution 2312 (DA) using a scaling coefficient 2334 (calibration coefficient CF) obtained by a mapping 2332 between a first model coefficient associated with the first modeled distribution value 2322 and a second model coefficient associated with the second modeled distribution value 2312. The modeled component can be excluded from the step of determining the distribution of the target parameter 2352 using the scaling coefficient 2334 (calibration coefficient, CF). For example, if the scaling coefficient is below a threshold 2333, the model coefficient associated with the first modeled distribution of the value 2312 (DA) may be excluded from the scaling.

[0231] Figures 23 and 24 schematically show how the calibration coefficient is adjusted to predict the distribution of the target parameter. A correlation between two domains A (alignment) and domain B (overlay) can be defined. For two domains described by the same set of parameters, such as linear, higher-order, or combined polynomial coefficients, a set of scaling coefficients or calibration coefficients can be defined, for example, by dividing the coefficients of domain B by the coefficients of domain A using simple linear algebra.

[0232] When one domain receives corrections from the other domain, there is a high likelihood of a good correlation between these two domains, and a large number of data points are provided. For example, the scanner uses information from alignment measurements to correct the substrate grid (deformation). There is an assumption that there is a strong correlation between the alignment and the overlay of the parameters of the maximum fifth-order polynomial component used in the alignment model. That is, domain B (overlay) receives corrections from domain A (alignment), and there is a strong correlation between domain A and domain B.

[0233] Figures 23 and 24 show a method of predicting one domain DB' by projecting another domain DA using the calibration coefficients of all model parameters. First, all model parameters are calculated for each domain. For two model parameters MPA and MPB, eight points PI to P8 are aggregated respectively.

[0234] Regarding Figure 23, Table 2362 shows the values of MPA for domain A (DA) and domain B (DB). Graph 2366 is a plot of MPA for domain A and MPA for domain B, including the data points in Table 2362. The correlation is determined by fitting a linear model (y = a * x) to determine the calibration coefficient between the parameter sets of model parameter MPA, which is 0.50 here (y = 0.5 * x).

[0235] Regarding Figure 24, Table 2364 shows the values of MPB for domain A (DA) and domain B (DB). Graph 2368 is a plot of MPB for domain A and MPB for domain B, including the data points in Table 2364. The correlation is determined by fitting a linear model (y = a * x) to determine the calibration coefficient between the parameter sets of model parameter MPB, which is 0.33 here (y = 0.33 * x).

[0236] For each of the model parameters MPA and MPB, as shown in Table 2370 of Figure 23 and 2372 of Figure 24, use the calibration coefficient to predict the model parameters of the target DB' (e.g., overlay) from the domain A parameter values.

[0237] Even if there is a perfect correlation between domain A and domain B, it does not guarantee that the weight between the two parameter sets is 1. For example, the conversion value between wafers for alignment measurement may be twice the value of the conversion observed in the case of overlay error. In this case, there is a perfect correlation between the two parameter sets, but the scale is not always 1. In other words, when there is a strong correlation between two parameter sets, domain B can be predicted more accurately by adjusting the calibration coefficient of the parameter multiplied by the parameter of domain A. The input sampling of domain A and domain B is preferably restricted to avoid crosstalk between model parameters due to the asymmetric layout of the input sampling.

[0238] When alignment and overlay are correlated with a scale of 1, it means that the overlay correction is based on information representing the actual wafer deformation, in this case true and actual alignment information. In this case, the calibration coefficients of the two parameter sets are all 1 and are the same as the observed scale.

[0239] If the alignment measurement is affected by the asymmetry of the alignment marks or the measurement, the uncertainty of the measurement means that there is incorrect information from the deformed alignment marks regarding the alignment. If the alignment model is calculated using this incorrect information, such errors resulting from the deformation of the marks are reflected in the overlay prediction. In one embodiment, the calibration coefficient between alignment and overlay for each parameter can be calculated by examining only the correlation model parameters between alignment and overlay with a sufficiently good correlation. By applying these selected calibration coefficients to the alignment data, the overlay prediction caused by the incorrect deformation of the alignment marks can be calibrated (filtered) for all parameters.

[0240] Due to the deformation of the measurement overlay target, there is usually an offset between the measurement target overlay and the device overlay. This offset budget can be divided into the categories of "batch" and "wafer-to-wafer" (W2W). The "batch" offset is calculated based on the actual device overlay. However, in the case of W2W, if there is a stable correlation between the measurement and the device overlay, the measured values can be defined and calibrated / predicted as W2W in a way that explains this offset. This can be understood by replacing domain A with the "metrology overlay" and domain B with the "device overlay".

[0241] The calibration / prediction of the overlay can be extended using context information. The concept of context-based grouping is used. When production lots are divided into several groups and each group is processed individually with different process tools, the fingerprints of each group (or the degree of deformation / asymmetry of the wafer / mark) are different from each other. In this case, the entire dataset can be grouped into sub-datasets, and the correlation / calibration coefficients can be recalculated for each group. The calculated calibration / prediction is applied individually to each group, and the calibration / prediction results become more appropriate.

[0242] Figure 25 schematically shows the determination of the possibility of correct prediction. The vertical axis DB is the domain B model parameter value, and the horizontal axis DA is the domain A model parameter value.

[0243] When calculating the calibration coefficient for each dataset, under the assumption that the data points are evenly distributed, the framework described below can be used to define the possibility of correct prediction.

[0244] (1) If a specific data point is in the region 2704 between the gradient of the correlation coefficient line 2706 and the axis of domain B (DB), the predicted value is always greater than zero and less than the value of domain B. Domain B can be correctly predicted / forecasted.

[0245] (2) When the data point is on the inclined plane 2706, the projection / prediction is complete.

[0246] (3) When the point is in the region 2708 between the gradients 2706 and half of the gradient 2710, prediction is possible. However, the predicted value will be greater than the value in domain B. The calibration for this data point changes the sign of the calibrated result.

[0247] (4) For data points in regions other than these three (2704, 2706, and 2708), the calibration of domain B using the method described here will worsen the result compared to the original value.

[0248] Thus, at an angle θ between the axis A region and the inclination 2706, the region of correct prediction can be defined as follows. As the inclination approaches the x-axis, the probability of correct projection / prediction becomes 50% of the maximum value at the angle θ1. However, the advantage of using this projection method is that the calibration coefficient approaches zero as it gets closer to zero. Therefore, it is very important to find a specific frequency window or condition with a good correlation between the two domains (for example, using the separation of the entire dataset into subsets). This creates a distribution of data points concentrated on the gradients within the three regions (2704, 2706, 2708) described above. Also, a trade-off between the calibration coefficient and the correctability is possible. The calibration coefficient defined in the correlation (setup) phase can be adjusted to be smaller than the original defined value. This correctly increases the number of data points. Although predicted / adjusted, the merit becomes smaller than before.

[0249] Calibration coefficient (F cal ) = (tan θ) Probability of prediction = 1 / 2 - 1 / π · (tan -1 (F cal / 2))

[0250] Embodiments provide a generalized methodology for projecting one domain onto another for measurement prediction / calibration, with calibration coefficients between frequencies filtered from any of the domains, herein called correlation model parameters, and determining values of the calibration coefficients.

[0251] Embodiments can calibrate overlay predictions from wafer deformation / alignment mark asymmetry due to domain deformation across multiple wavelengths (colors) within a sensor, multi-reference measurements (wafer) over time, and multiple spatial frequencies (positions) within the measurement.

[0252] Embodiments divide data into subsets to enhance correlation and prediction accuracy between two domains.

[0253] Embodiments can deselect content from uncorrelated model parameters of both domains to suppress noise in predictions derived from input contributions.

[0254] Embodiments can provide metrics for wafers that require actual production measurements. For example, if scanner metrology measured from a new domain A does not correspond to a previously observed population, an action to measure actual wafers in domain B and update the previously defined population can be triggered.

[0255] Embodiments calibrate a portion of the measured content that is incorrect, measured by overlay measurement from a scanner or prediction, i.e., asymmetry of alignment marks, mis-corrected wafer deformation, or uncorrelated content within the input contributions.

[0256] Embodiments can be used for any input data and parameters of interest, i.e., offline wafer shape measurement or SEM measurement.

[0257] In the case of wafer-to-wafer variation feedforward, the embodiments can predict the wafer-to-wafer correction of the next layer from the alignment of the previous layer if there is a correlation between these two. For example, in the case of a layer that has undergone Litho-Etch-Litho-Etch processing.

[0258] FIG. 26 is a block diagram showing a computer system 100 that can assist in implementing the methods and flows disclosed herein. The computer system 100 includes a bus 102 or other communication mechanism for communicating information, and a processor 104 (or processors 104 and 105) coupled to the bus 102 for processing information. The computer system 100 also includes a main memory 106, such as a random access memory (RAM) or other dynamic storage device, coupled to the bus 102 for storing information and instructions to be executed by the processor 104. The main memory 106 may be used to store temporary variables or other intermediate information during execution of instructions by the processor 104. The computer system 100 further includes a read only memory (ROM) 108 or other static storage device coupled to the bus 102 for storing static information and instructions for the processor 104. A storage device 110, such as a magnetic disk or optical disk, is provided and coupled to the bus 102 for storing information and instructions.

[0259] Computer system 100 can be coupled via bus 102 to a display 112, such as a cathode ray tube (CRT), flat panel, or touch panel display, for displaying information to a computer user. An input device 114, including alphanumeric and other keys, is coupled to bus 102 for communicating information and command selections to processor 104. Another type of user input device is a cursor control 116, such as a mouse, trackball, or cursor direction keys, for transmitting direction information and command selections to processor 104 and controlling cursor movement on display 112. This input device typically has two degrees of freedom in two axes, i.e., a first axis (such as x) and a second axis (such as y), enabling the device to specify a position within a plane. A touch panel (screen) display can also be used as an input device.

[0260] According to one embodiment, in response to processor 104 executing one or more sequences of one or more instructions contained in main memory 106, computer system 100 can perform a portion of a process. Such instructions may be read into main memory 106 from another computer-readable medium, such as storage device 110. Execution of the sequence of instructions contained in main memory 106 causes processor 104 to perform the process steps described herein. One or more processors in a multiprocessing configuration can also be used to execute the sequence of instructions contained in main memory 106. In alternative embodiments, hardwired circuitry can be used in place of, or in combination with, software instructions. Accordingly, the description herein is not limited to a particular combination of hardware circuitry and software.

[0261] As used herein, the term "computer-readable medium" refers to any medium that participates in providing instructions to processor 104 for execution. Such a medium may take many forms, including but not limited to non-volatile media, volatile media, and transmission media. Non-volatile media includes, for example, optical or magnetic disks, such as storage device 110. Volatile media includes dynamic memory, such as main memory 106. Transmission media includes coaxial cables, copper wire, fiber optics, including the wires that make up bus 102. Transmission media can also take the form of acoustic or light waves, such as those generated during radio frequency (RF) and infrared (IR) data communications. Common forms of computer-readable media include, for example, floppy (registered trademark) disks, flexible disks, hard disks, magnetic tape, other magnetic media, CD-ROM, DVD, other optical media, punch cards, paper tape, other physical media with patterns of holes, RAM, PROM, and EPROM, FLASH-EPROM, other memory chips or cartridges, the carrier waves described below, or other media that can be read by a computer.

[0262] [[ID=*]]Various forms of computer-readable media may be involved in carrying one or more sequences of one or more instructions to processor 104 for execution. For example, the instructions are initially created on a magnetic disk of a remote computer. The remote computer can load the instructions into dynamic memory and transmit the instructions over a telephone line using a modem. A modem local to computer system 100 can receive the data over the telephone line and convert the data into an infrared signal using an infrared transmitter. An infrared detector coupled to bus 102 can receive the data carried in the infrared signal and place the data on bus 102. Bus 102 carries the data to main memory 106, from which processor 104 retrieves and executes the instructions. The instructions received by main memory 106 may optionally be stored in storage device 110 either before or after execution by processor 104.

[0263] Computer system 100 preferably also includes a communication interface 118 coupled to bus 102. Communication interface 118 provides bi-directional data communication coupling to a network link 120 connected to local network 122. For example, communication interface 118 can be an integrated services digital network (ISDN) card or modem that provides a data communication connection to a corresponding type of telephone line. As another example, communication interface 118 can be a local area network (LAN) card that provides a data communication connection to a compatible LAN. A wireless link may be implemented. In such an implementation, communication interface 118 transmits and receives electrical, electromagnetic, or optical signals that carry a digital data stream representing various types of information.

[0264] Network link 120 typically provides data communication through one or more networks to other data devices. For example, network link 120 can provide a connection through local network 122 to data equipment operated by host computer 124 or an Internet service provider (ISP) 126. ISP 126 provides data communication services through a worldwide packet data communication network now commonly referred to as the "Internet" 128. Both local network 122 and the Internet 128 use electrical, electromagnetic, or optical signals that carry a digital data stream. Signals through various networks that carry digital data to and from computer system 100 and signals through network link 120 and communication interface 118 are examples of forms of carrier waves that carry information.

[0265] Computer system 100 can send messages and receive data including program code via a network, network link 120, and communication interface 118. In an example of the Internet, server 130 may send the code requested by an application program via Internet 128, ISP 126, local network 122, and communication interface 118. One such downloaded application may provide, for example, lighting optimization of the embodiments. The received code can be executed by processor 104 when received and / or stored in storage device 110 or other non-volatile storage for later execution. In this way, computer system 100 can obtain application code in the form of a carrier wave.

[0266] Further embodiments are disclosed in the following numbered list of embodiments. 1. A method comprising: Determining a first distribution of a first parameter related to an error or residual in executing a device manufacturing process, Determining a second distribution of a second parameter related to an error or residual in executing a device manufacturing process, Using a function operating on the first and second distributions to determine, by a hardware computer, a distribution of a parameter of interest related to the device manufacturing process. 2. The method of embodiment 1, wherein the first parameter, the second parameter, and the parameter of interest are the same. 3. The method of embodiment 1, wherein the first distribution is specific to the device and not specific to a particular substrate processed using the device manufacturing process. 4. The method of embodiment 1, wherein the second distribution is specific to a particular substrate processed using the device manufacturing process but not general to other substrates processed using the device manufacturing process. 5. The method of Embodiment 1, wherein the first distribution and / or the second distribution includes one or more selected from the contribution of servo error to the respective first and / or second parameters, the contribution of alignment model residuals to the respective first and / or second parameters, the contribution of projection system aberration or image plane deviation to the respective first and / or second parameters, the contribution of projection system model residuals to the respective first and / or second parameters, and / or the contribution of substrate surface height to the respective first and / or second parameters. 6. The method of Embodiment 1, wherein determining the first distribution further includes obtaining measurement data of the first parameter and removing the contribution to the first parameter of a specific device in the device manufacturing process therefrom. 7. The method of Embodiment 6, wherein the contribution of a specific device includes one or more selected from the contribution of servo error, the contribution of alignment model residuals, the contribution of projection system aberration or image plane deviation, the residuals of the projection system model, and / or the contribution of substrate surface height. 8. The method of Embodiment 6, wherein the measured first parameter data includes the first parameter data measured from a monitor substrate. 9. The method of Embodiment 1, wherein the first distribution, the second distribution, and / or the distribution of the parameter of interest includes a spatial substrate fingerprint. 10. The method of Embodiment 1 further includes using the distribution of the parameter of interest to perform any one or more selected from predicting substrate defects, controlling the device manufacturing process, monitoring the device manufacturing process, designing aspects of the device manufacturing process, and / or calibrating a mathematical model. 11. The method of Embodiment 1, wherein the first parameter, the second parameter, and / or the parameter of interest is one or more selected from overlay, CD, focus, dose, and / or edge position. 12. The method of Embodiment 1, wherein the device manufacturing process includes a lithography process and / or a semiconductor manufacturing process. 13. The method of Embodiment 1, wherein the function includes one or more selected from arithmetic addition, convolution, and / or a neural network. 14. The method of Embodiment 1, further comprising converting the first parameter and / or the second parameter into a parameter of interest when the first parameter and / or the second parameter is different from the parameter of interest. 15. The method of Embodiment 1, further comprising determining a first distribution and / or a second distribution using data provided by a lithography apparatus and / or an etching apparatus used in a device manufacturing process. 16. The method of Embodiment 1, wherein the function includes a correlation acting on the first and second distributions. 17. The method of Embodiment 16, wherein the determined first distribution includes a first modeled distribution of values, the determined second distribution includes a second modeled distribution of values, the parameter of interest is the first parameter, obtaining a first distribution of values of the first parameter, obtaining a second distribution of values of the second parameter, modeling the first and second distributions of values to obtain first and second modeled distributions of values, determining a distribution of the parameter of interest based on scaling of the modeled second distribution using a scaling coefficient obtained by mapping between a first model coefficient associated with the first modeled distribution of values and a second model coefficient associated with the second modeled distribution of values. 18. The method of Embodiment 17, determining a scale of variation where the correlation between the values of the first distribution and the values of the second distribution exceeds a threshold, modeling the values of the first and second distributions with the determined scale of variation to obtain the modeled values of the first and second distributions according to the determined scale of variation. 19. The method of Embodiment 17, comprising using a scaling coefficient to exclude a modeled component from the step of determining a distribution of the parameter of interest. 20. Obtaining a fundamental contribution to the overlay of a lithographic apparatus as part of a patterning process, A method of obtaining an estimated value of the overlay of a substrate by a hardware computer, combining the fundamental contribution with a further contribution to the overlay of the substrate. 21. The method of embodiment 20, wherein the further contribution includes a contribution to the overlay of the substrate surface height of the substrate. 22. The method of embodiment 20, wherein the further contribution includes a contribution of the substrate servo error of the substrate to the overlay. 23. The method of embodiment 20, wherein the further contribution includes a contribution of an alignment and / or projection system model residual. 24. The method of embodiment 20, further comprising combining the fundamental contribution, the contribution of the height of the substrate surface, and the contribution of the etching process to the overlay of the substrate. 25. The method of embodiment 24, wherein the contribution of the etching process is specific to the patterning process but not specific to a particular substrate processed using the patterning process. 26. The method of embodiment 20, wherein the fundamental contribution is specific to a particular patterning process but not specific to a particular substrate processed using the patterning process. 27. Obtaining the fundamental contribution further includes obtaining measured overlay data and removing from it the contribution to the overlay of a specific component of the lithographic apparatus. 28. The method of embodiment 27, wherein the contribution of the specific component includes one or more selected from the contribution of the servo error, the contribution of the alignment model residual, the contribution of the projection system aberration, the contribution of the projection system model residual, and / or the contribution of the height of the substrate surface. 29. The method of embodiment 27, wherein the measured overlay data includes the overlay data measured from a monitor substrate. 30. The method of embodiment 20, wherein the contribution includes a spatial substrate fingerprint. 31. The method of embodiment 20 further includes performing one or more selected from predicting defects in a substrate, controlling a patterning process, monitoring a patterning process, designing aspects of a patterning process, and / or calibrating a mathematical model using a presumption. 32. When executing a device manufacturing process, determining a first distribution of measurement alignment data, determining a second distribution of alignment data derived from process parameters of a device manufacturing process, A method of determining, by a hardware computer system, a distribution of alignment data related to a device manufacturing process as a function of the first and second distributions. 33. The method of embodiment 32, wherein the process parameters include one or more selected from the height or non-flatness of a substrate, process effects, heating of an optical element, optical aberration, and / or writing errors of a patterning device. 34. The method of embodiment 32, wherein the second distribution is derived from a plurality of process parameters of a device manufacturing process. 35. The method of embodiment 34, wherein the process parameters include the height or non-flatness of a substrate, process effects, and heating of an optical element. 36. The method of embodiment 32, wherein the second distribution is specific to a device manufacturing process but not specific to a particular substrate processed using the device manufacturing process. 37. The method of embodiment 32, wherein the second distribution is specific to a particular substrate processed using a device manufacturing process but not common to other substrates processed using the device manufacturing process. 38. The method of embodiment 32, wherein the second distribution is derived from measured values of process parameters. 39. The method of embodiment 32 further includes performing one or more selected from predicting defects in a substrate, controlling a device manufacturing process, monitoring a device manufacturing process, designing aspects of a device manufacturing process, and / or calibrating a mathematical model using the distribution of alignment data. The method of embodiment 32, further comprising changing the sampling of measurement data based on the distribution of alignment data. The method of embodiment 32, further comprising using a higher-order alignment model in the distribution of alignment data as compared to that used with only the measured alignment data. The method of embodiment 32, further comprising determining the first distribution and / or the second distribution using data provided by a lithographic apparatus used in a device manufacturing process. The method of embodiment 32, wherein the first distribution, the second distribution, and / or the distribution of the parameter of interest includes a spatial substrate fingerprint. The method of embodiment 32, wherein the device manufacturing process includes a lithography process and / or a semiconductor manufacturing process. The method of embodiment 32, wherein the function includes one or more selected from arithmetic addition, convolution, and / or neural networks. Based on the measured alignment data, obtaining an alignment data distribution over at least a part of a substrate processed using a patterning process, A method of obtaining an estimated value of the alignment data of a substrate by combining, by a hardware computer, the alignment data distribution with an alignment fingerprint resulting from processing parameters other than the measured alignment. The method of embodiment 46, wherein the alignment fingerprint includes a contribution of the height of the substrate or the non-flatness of the substrate to alignment. The method of embodiment 46, wherein the alignment fingerprint includes a contribution of a process effect of the substrate on alignment resulting from a part of a patterning process other than lithographic pattern transfer. The method of embodiment 46, wherein the alignment fingerprint includes a contribution of heating of the substrate to alignment. The method of embodiment 46, wherein the alignment fingerprint is specific to the patterning process but not specific to a particular substrate processed using the patterning process. 51. The method of embodiment 46, wherein the alignment fingerprint is unique to a particular substrate processed using a patterning process but not common to other substrates processed using the patterning process. 52. The method of embodiment 46, wherein the alignment fingerprint is derived from measured values of processing parameters. 53. The method of embodiment 46, wherein the alignment fingerprint includes a spatial substrate fingerprint. 54. The method of embodiment 46, further comprising performing one or more selected from predicting defects of a substrate, controlling a patterning process, monitoring a patterning process, designing aspects of a patterning process, and / or calibrating a mathematical model using an estimate. 55. A computer program product including a non-transitory computer-readable medium having instructions recorded thereon, when executed by a computer implementing the method of any of embodiments 1 to 54.

[0267] Embodiments of the present disclosure may be implemented in hardware, firmware, software, or any combination thereof. Embodiments of the present disclosure may also be implemented as instructions stored on a machine-readable medium, which may be read and executed by one or more processors. A machine-readable medium can include any mechanism for storing or transmitting information in a form readable by a machine (e.g., a computing device). For example, a machine-readable medium may include read only memory (ROM), random access memory (RAM), magnetic disk storage media, optical storage media, flash memory devices, electrical, optical, acoustical, or other forms of propagated signals (such as carrier waves, infrared signals, digital signals, etc.). Further, firmware, software, routines, instructions may be described herein as performing particular actions. However, such descriptions are merely for convenience and such actions actually result from computing devices, processors, controllers, or other devices executing firmware, software, routines, instructions, etc.

[0268] In the block diagrams, the illustrated components are depicted as individual functional blocks, but the embodiments are not limited to a system in which the functions described herein are organized as illustrated. The functions provided by each component may be provided by software or hardware modules in a different organization than that currently shown. For example, such software or hardware may be intermixed, combined, replicated, divided, distributed (e.g., within a data center or geographically), or otherwise organized. The functions described herein may be provided by one or more processors of one or more computers executing code stored on a tangible non-transitory machine-readable medium. In some cases, a third-party content delivery network may host some or all of the information transmitted over the network, in which case it is provided by sending an instruction to obtain that information from the content delivery network to the extent that the information (such as content) is said to be supplied or provided.

[0269] Unless otherwise specified, as will be apparent from the discussion, throughout the discussion in this specification, "processing", "computing", "calculating", "determining", etc. refer to actions or processes of a specific apparatus such as a dedicated computer or a similar dedicated electronic processing / calculating device.

[0270] The reader should understand that this application describes several inventions. Instead of separating these inventions into multiple independent patent applications, the applicant has grouped these inventions into a single document because the related subject matter is useful for the economics of the application process. However, the distinct advantages and aspects of such inventions should not be confused. In some cases, embodiments address all of the deficiencies described herein, but the invention is independently useful and some embodiments may address only a subset of such problems or provide other unmentioned advantages that will be apparent to those skilled in the art. Due to cost constraints, some of the inventions disclosed herein may not currently be claimed and may be claimed in a later application such as a continuation application or by amending the current claims. Similarly, due to space constraints, neither the summary section nor the body of this document should be construed to include an exhaustive list of all such inventions or all aspects of such inventions.

[0271] The description and drawings are not intended to limit the invention to the particular forms disclosed, but on the contrary, to cover all modifications, equivalents, and alternatives within the spirit and scope of the invention as defined by the appended claims.

[0272] Modifications and alternative embodiments of various aspects of the present invention will be apparent to those skilled in the art in view of this description. Accordingly, this description and the drawings should be construed as illustrative only and are for the purpose of teaching those skilled in the art a general way of implementing the present invention. It should be understood that the forms of the present invention shown and described herein should be construed as examples of embodiments. Elements and materials may be substituted for those illustrated and described herein, and after those skilled in the art have obtained the benefit of this description of the present invention, parts and processes may be reversed, the order may be changed or omitted, specific features may be utilized independently, and embodiments or features of embodiments may be combined in all possible ways. Changes may be made to the elements described herein without departing from the spirit and scope of the present invention as recited in the appended claims. The headings used herein are for organizational purposes only and are not intended to limit the scope of the description.

[0273] As used throughout this application, the word "may" is used in a permissive sense (i.e., meaning "might") rather than a mandatory sense (i.e., meaning "must"). Words such as "including", "includes", and "include" mean including, but not limited to. As used throughout this application, the singular forms "a", "an", and "the" include plural referents unless explicitly indicated otherwise in the content. Thus, for example, a reference to "an" element or "a" element includes combinations of two or more elements, despite the use of other terms and phrases for one or more elements such as "one or more". The term "or" is non-exclusive, i.e., includes both "and" and "or", unless otherwise specified. When multiple attributes or functions are mapped to multiple objects (e.g., one or more processors that perform steps A, B, C, and D), functions are included that are mapped to subsets of all such attributes or functions that are mapped to subsets of all such objects or attributes (e.g., all processors that perform steps A through D, and processor 1 performs step A, processor 2 performs steps B and part of step C, and processor 3 performs part of step C and step D, unless otherwise specified). Further, unless otherwise specified, a description that one value or action is "based on" another condition or value includes both cases where the condition or value is the sole factor and cases where the condition or value is one of multiple factors. Unless otherwise specified, a statement that a property exists for "each" instance of a collection should not be read to exclude cases where identical or similar members of a larger collection do not have the property, i.e., where each does not necessarily mean all.

[0274] To the extent that a particular U.S. patent, U.S. patent application, or other material (e.g., article) is incorporated by reference, the text of such U.S. patent, U.S. patent application, and other material is incorporated by reference only to the extent that it does not conflict. If such a conflict occurs, such conflicting text in the incorporated U.S. patent, U.S. patent application, and other material is not specifically incorporated herein by reference.

[0275] Although particular embodiments of the disclosure have been described above, it will be understood that the embodiments may be practiced otherwise than as described.

Claims

1. obtaining a first spatial distribution of a target parameter including an error or residual of focus, CD, or overlay, based on data from a lithography apparatus used in the execution of a device manufacturing process; obtaining a second spatial distribution of the target parameter from measurement results including an error or residual of focus, CD, or overlay introduced by the device manufacturing process; determining, by a hardware computer, a third spatial distribution of the target parameter that is denser than the second spatial distribution, based on a combination of the first spatial distribution and the second spatial distribution; wherein the measurement results include overlay measurement data.

2. The method according to claim 1, wherein the first spatial distribution is specific to a particular substrate processed using the device manufacturing process, but not common to other substrates processed using the device manufacturing process.

3. The method according to claim 1, wherein the first spatial distribution includes one or more selected from a contribution of servo error in position control of a patterning device and / or a substrate to the target parameter, a contribution of an alignment model residual to the target parameter, a contribution of projection system aberration or image plane deviation to the target parameter, and / or a contribution of substrate surface height to the target parameter.

4. The method according to claim 1, wherein the measurement results include focus measurement data, and the first spatial distribution includes a contribution of substrate surface height to the target parameter.

5. The method according to claim 4, wherein the focus measurement data is obtained by sparse sampling of positions on the substrate compared to the third spatial distribution of the target parameter, and the third spatial distribution of the target parameter includes a spatial distribution of focus parameters across the substrate.

6. The method according to claim 1, wherein the measurement results include critical dimension (CD) measurement data, and the first spatial distribution includes a contribution of substrate surface height to the target parameter.

7. The method according to claim 6, wherein the CD measurement data is obtained by sparse sampling of positions on the substrate compared to the third spatial distribution of the target parameter, and the third spatial distribution of the target parameter includes a spatial distribution of focus parameters across the substrate.

8. The overlay measurement data is obtained by sparser sampling of positions on the substrate than the third spatial distribution of the target parameter, and the third spatial distribution of the target parameter includes the spatial distribution of the overlay parameter across the substrate, the method according to claim 1.

9. The first spatial distribution, the second spatial distribution, and the third spatial distribution include focus or CD errors or residuals, The method further includes using the third spatial distribution of the target parameter to predict the shape and / or size of one or more contours of a pattern at a hot spot on the substrate, the method according to any one of claims 1 to 8.

10. The second spatial distribution is based on data from an inspection device and / or a measurement device, the method according to claim 1.

11. Determining a first spatial distribution of a target parameter including focus, CD, or overlay errors or residuals based on data from a lithography apparatus used in the execution of a device manufacturing process; Determining a second spatial distribution of the target parameter from measurement results including focus, CD, or overlay errors or residuals introduced by the device manufacturing process; Configuring a computer to execute computer-readable instructions for determining a third spatial distribution of the target parameter that is denser than the second spatial distribution based on a combination of the first spatial distribution and the second spatial distribution; The measurement results are a computer program including overlay measurement data.

12. The measurement results include focus measurement data, and the first spatial distribution includes the contribution of the substrate surface height to the target parameter, the computer program according to claim 11.

13. The measurement results include CD measurement data, and the first spatial distribution includes the contribution of the substrate surface height to the target parameter, the computer program according to claim 11.

14. The first spatial distribution, the second spatial distribution, and the third spatial distribution include focus or CD errors or residuals, The computer program according to any one of claims 11 to 13 further comprises instructions for use in predicting the shape and / or size of one or more contours of a pattern at a hot spot on a substrate as the third spatial distribution of the target parameter.

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