Computational measurement

Abstract

A method includes determining a first distribution of a first parameter associated with an error or residual when performing a device manufacturing process; determining a second distribution of a second parameter associated with the error or residual when performing the device manufacturing process; and determining a distribution of a parameter of interest associated with the device manufacturing process using a function that operates on the first distribution and the second distribution. The function may include a correlation.

Description

[0001] This application is a divisional application of the international application PCT / EP2018 / 053412, which entered the Chinese national phase on August 22, 2019 and has application number 201880013446.4.

[0002] CROSS-REFERENCE TO RELATED APPLICATIONS

[0003] This application claims priority to U.S. Application No. 62 / 462,201, filed on February 22, 2017, and U.S. Application No. 62 / 545,578, filed on August 15, 2017, the entire contents of which are incorporated herein by reference. Technical Field

[0004] The present disclosure relates to techniques for improving the performance of a device manufacturing process. These techniques may be used in conjunction with a lithography apparatus or a metrology apparatus. Background Art

[0005] A lithographic apparatus is a machine that applies a desired pattern to a target portion of a substrate. For example, a lithographic apparatus may be used in the manufacture of integrated circuits (ICs). In this case, a pattern forming device (alternatively referred to as a mask or reticle) may be used to produce a circuit pattern corresponding to a single layer of the IC, and the pattern may be imaged onto a target portion (e.g., a portion including a die, one or several dies) on a substrate (e.g., a silicon wafer) having a layer of radiation-sensitive material (resist). Typically, a single substrate will include a network of adjacent target portions that are exposed in succession. Known lithographic apparatus include so-called steppers, in which each target portion is irradiated by exposing the entire pattern to the target portion at once, and so-called scanners, in which each target portion is irradiated by scanning the pattern along a given direction (the "scanning" direction) by the beam, while simultaneously scanning the substrate in a direction parallel or antiparallel to the direction.

[0006] Before the circuit pattern is transferred from the pattern forming device to the substrate, the substrate may undergo various processes, such as primer coating, resist coating and soft baking. After exposure, the substrate may undergo other processes, such as post-exposure baking (PEB), development, hard baking and measurement / inspection of the transferred circuit pattern. This series of processes is used as the basis for manufacturing a single layer of a device (e.g., IC). Afterwards, the substrate may undergo various processes, such as etching, ion implantation (doping), metallization, oxidation, chemical mechanical polishing, etc., all of which are intended to eventually complete a single layer of the device. If multiple layers are needed in the device, all processes or their variations are repeated for each layer. Ultimately, the device will be present in each target portion on the substrate. Afterwards, these devices are separated from each other by techniques such as slicing or sawing, whereby individual devices can be mounted on a carrier, connected to pins, etc.

[0007] Therefore, manufacturing devices (such as semiconductor devices) typically involves processing a substrate (e.g., a semiconductor wafer) using multiple fabrication processes to form various features and multiple layers of the device. These layers and features are typically manufactured and processed using, for example, deposition, lithography, etching, chemical mechanical polishing, ion implantation. Multiple devices can be made on multiple dies on a substrate and then separated into individual devices. This device manufacturing process can be considered a patterning process or a patterning process. The patterning process involves a patterning step using a patterning device in a lithography apparatus, such as optical and / or nanoimprint lithography, to transfer the pattern on the patterning device to the substrate, and the patterning process typically but optionally involves one or more related pattern processing steps, such as resist development by a developing apparatus, baking the substrate using a baking tool, etching using a pattern using an etching apparatus, etc. Summary of the invention

[0008] In an embodiment, a method is disclosed, comprising: determining a first distribution of a first parameter associated with an error or residual when performing a device manufacturing process; determining a second distribution of a second parameter associated with the error or residual when performing the device manufacturing process; and determining, by a hardware computer, a distribution of a parameter of interest associated with the device manufacturing process using a function that operates on the first distribution and the second distribution.

[0009] In an embodiment, a method is provided, comprising: obtaining a base contribution to overlay of a lithographic device as part of a patterning process; and combining, by a hardware computer, the base contribution with a further contribution to overlay of a substrate to obtain an estimate of the overlay of the substrate.

[0010] In an embodiment, a method is provided, comprising: determining a first distribution of alignment data measured when performing a device manufacturing process; determining a second distribution of alignment data derived from processing parameters during 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 distribution and the second distribution.

[0011] In an embodiment, a method is provided, comprising: obtaining, based on measured alignment data, an alignment data distribution across at least a portion of a substrate processed using a patterning process; and combining, by a hardware computer, the alignment data distribution with an alignment fingerprint attributable to processing parameters other than the measured alignment to obtain an estimate of the alignment data for the substrate.

[0012] In an embodiment, a computer program product is provided, comprising a non-transitory computer-readable medium having recorded thereon instructions, the instructions implementing any of the methods herein when executed by a computer. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 A lithographic apparatus according to an embodiment is schematically depicted.

[0014] Figure 2 Embodiments of lithographic cells or clusters are schematically depicted.

[0015] Figure 3 Example inspection equipment and metrology techniques are schematically depicted.

[0016] Figure 4 An example inspection device is schematically depicted.

[0017] Figure 5 The relationship between the illumination spot of the inspection device and the measurement target is schematically illustrated.

[0018] Figure 6 The process of deriving multiple variables of interest based on measured data is schematically depicted.

[0019] Figure 7 Categories of example treatment variables are shown.

[0020] Figure 8 Schematically shows how changes in process variables may contribute to the measured data.

[0021] Fig. 9 An example of deriving combined contributions to patterning process parameters is schematically shown.

[0022] Fig.10 An example of deriving contributions to process variables from metrology data is schematically shown.

[0023] Fig.11 The flow for a method according to an embodiment is schematically shown.

[0024] Fig.12 The flow for a method according to an embodiment is schematically shown.

[0025] Fig.13 The flow for a method according to an embodiment is schematically shown.

[0026] Fig.14 An exemplary embodiment of selection of contributions / fingerprints and profiles is schematically depicted.

[0027] Fig.15 An exemplary embodiment of contribution / fingerprint and modification of the profile is schematically depicted.

[0028] Fig.16A , Fig. 16B and 16C An embodiment of a defect analysis process is schematically depicted.

[0029] Fig.17A , Fig. 17B and 17C An embodiment of a defect analysis process is schematically depicted.

[0030] Fig.18 An example of deriving combined contributions for alignment is shown schematically.

[0031] Fig.19 An example of deriving combined contributions for alignment is shown schematically.

[0032] Fig. 20 An example of how a patterning process corrected using a fingerprint determined from an existing alignment measurement scheme is converted into an overlay error fingerprint is schematically shown.

[0033] Fig.21 An example of how a patterning process corrected using a derived aligned fingerprint calculated as described herein translates into an overlay error is schematically shown.

[0034] Fig. 22 The flow for a method according to an embodiment is schematically shown.

[0035] Fig.23 and Fig.24 Adjustment of the calibration factor to predict the distribution is shown schematically.

[0036] Fig.25 The probability of determining the correct prediction is shown schematically.

[0037] Fig.26 is a block diagram of an example computer system. DETAILED DESCRIPTION

[0038] Before describing the embodiments in detail, it is instructive to provide an exemplary environment in which the embodiments can be implemented.

[0039] Figure 1 An embodiment of a lithographic apparatus LA is schematically depicted. The apparatus comprises:

[0040] - an illumination system (illuminator) IL configured to condition a radiation beam B (e.g. a UV radiation beam or a DUV radiation beam);

[0041] a support structure (e.g. mask table) MT configured to support a patterning device (e.g. mask) MA and connected to a first positioner PM configured to accurately position the patterning device according to certain parameters;

[0042] a substrate table (e.g., wafer stage) WT (e.g., WTa, WTb, or both) configured to hold a substrate (e.g., a resist-coated wafer) W and connected to a second positioner PW configured to accurately position the substrate according to certain parameters; and

[0043] - a projection system (e.g. a refractive projection lens system) PS, which is configured to project the pattern imparted to the radiation beam B by the pattern forming device MA onto a target portion C (e.g. comprising one or more dies and often referred to as a field) of the substrate W, the projection system being supported on a reference frame (RF).

[0044] As depicted here, the device is transmissive (eg, employing a transmissive mask). Alternatively, the device may be reflective (eg, employing a programmable mirror array of the type mentioned above, or employing a reflective mask).

[0045] The illuminator IL receives a radiation beam from a radiation source SO. The source and the lithographic apparatus may be separate entities (for example when the source is an excimer laser). In this case, the source is not considered to form part of the lithographic apparatus, and the radiation beam is transferred from the source SO to the illuminator IL by means of a beam delivery system BD comprising, for example, suitable directional mirrors and / or a beam expander. In other cases, for example when the source is a mercury lamp, the source may be an integral part of the apparatus. The source SO and illuminator IL, and the beam delivery system BD provided if necessary, may be referred to together as a radiation system.

[0046] The illuminator IL may vary the intensity distribution of the beam. The illuminator may be arranged to limit the radial extent of the radiation beam so that the intensity distribution is non-zero within an annular region in a 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 so that the intensity distribution is non-zero in 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 an illumination mode.

[0047] Thus, the illuminator IL may comprise an adjuster AM configured to adjust the (angular / spatial) intensity distribution of the beam. Typically, at least the outer radial extent and / or the inner radial extent (typically referred to as σ-outer and σ-inner, respectively) of the intensity distribution in a pupil plane of the illuminator may 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 extent of sectors in the pupil plane where the intensity distribution is non-zero. By adjusting the intensity distribution of the beam in the pupil plane of the illuminator, different illumination modes may be achieved. For example, by limiting the radial extent and the angular extent of the intensity distribution in the pupil plane of the illuminator IL, the intensity distribution may have a multipolar distribution such as (for example) a dipole, quadrupole or sextupole distribution. The desired illumination mode may be obtained by inserting an optical device providing the illumination mode into the illuminator IL or by using a spatial light modulator.

[0048] The illuminator IL may be operable to change the polarization of the beam and may be operable to adjust the polarization by using an adjuster AM. The polarization state of the radiation beam across the pupil plane of the illuminator IL may be referred to as a polarization mode. Using different polarization modes may allow a greater contrast to be achieved in the image formed on the substrate W. The radiation beam may be unpolarized. 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 the illuminator IL. In the pupil plane of the illuminator IL, the polarization direction of the radiation in different regions may be different. The polarization state of the radiation may be selected depending on the illumination mode. For a multipolar illumination mode, the polarization of each pole of the radiation beam may generally be substantially perpendicular to the position vector of the pole in the pupil plane of the illuminator IL. For example, for a dipole illumination mode, the radiation may be linearly polarized in a direction substantially perpendicular to a line bisecting two opposite sectors of the dipole. The radiation beam may be polarized in one of two different orthogonal directions, which may be referred to as the X polarization and Y polarization states. For a quadrupole illumination mode, the radiation in the sectors of each pole may be linearly polarized in a direction substantially perpendicular to a line bisecting the sectors. The polarization mode may be referred to as XY polarization. Similarly, for a hexapole illumination mode, the radiation in the sectors of each pole may be linearly polarized in a direction substantially perpendicular to a line bisecting the sectors. The polarization mode may be referred to as TE polarization.

[0049] In addition, the illuminator IL typically includes various other components, such as an integrator IN and a condenser CO. The illumination system may include various types of optical components, such as refractive, reflective, magnetic, electromagnetic, electrostatic or other types of optical components, or any combination thereof, to direct, shape or control the radiation.

[0050] The illuminator thus provides a conditioned radiation beam B having a desired uniformity and intensity distribution in its cross-section.

[0051] The support structure MT supports the patterning device in a manner that depends on the orientation of the patterning device, the design of the lithographic apparatus, and other conditions such as whether the patterning device is maintained in a vacuum environment. The support structure can hold the patterning device using mechanical, vacuum, electrostatic or other clamping techniques. The support structure can be a stand or a table, for example, which can be fixed or movable as required. The support structure can ensure that the patterning device is located in a desired position (for example relative to a projection system). Any term "reticle" or "mask" used in this article can be considered to be synonymous with the more general term "patterning device".

[0052] The term "patterning device" as used herein should be broadly interpreted as meaning any device that can be used to impart a pattern in a target portion of a substrate. In an embodiment, the patterning device is any device that can be used to impart a radiation beam pattern in its cross-section to form a pattern on the target portion of the substrate. It should be noted that the pattern imparted to the radiation beam may not exactly correspond to the desired pattern on the target portion of the substrate (for example, if the pattern includes phase-shifting features or so-called assist features). Typically, the pattern imparted to the radiation beam will correspond to a specific functional layer in a device (such as an integrated circuit) produced in the target portion.

[0053] The pattern forming device can be transmissive or reflective. Examples of pattern forming devices include masks, programmable mirror arrays, and programmable LCD panels. Masks are well known in lithography and include mask types such as binary mask types, alternating phase shift mask types, attenuated phase shift mask types, and various hybrid mask types. An example of a programmable mirror array employs a matrix arrangement of small mirrors, each of which can be individually tilted to reflect an incident radiation beam in different directions. The tilted mirrors impart a pattern to the radiation beam reflected by the mirror matrix.

[0054] The term "projection system" as used herein should be broadly interpreted to include any type of projection system, including refractive optical systems, reflective optical systems, catadioptric optical systems, magnetic optical systems, electromagnetic optical systems and electrostatic optical systems or any combination thereof, for example as appropriate for the exposure radiation used or for other factors such as the use of immersion liquid or the use of a vacuum. Any use of the term "projection lens" herein may be considered synonymous with the more general term "projection system".

[0055] The projection system PS has an optical transfer function that may be non-uniform, which may affect the pattern imaged on the substrate W. For unpolarized radiation, this effect can be well described by two scalar maps that describe the transmission (apodization) and relative phase (aberration) of the radiation leaving the projection system PS as a function of position in its pupil plane. These scalar maps, which may be referred to as transmission maps and relative phase maps, can be expressed as linear combinations 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 may involve determining 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 in turn and dividing the inner product by the square of the norm of the Zernike polynomial.

[0056] Transmission mapping and relative phase mapping 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 by projecting radiation (e.g., from a point source in the object plane (i.e., the plane of the pattern forming device MA)) through the projection system PS and measuring the wavefront (i.e., the trajectory of points with the same phase) using a shearing interferometer. A shearing interferometer is an interferometer with a common path, so advantageously, no secondary reference beam is required to measure the wavefront. The shearing interferometer may include a diffraction grating (e.g., a two-dimensional grating) in the image plane (i.e., the substrate table WT) of the projection system, and a detector arranged to detect an interference pattern in a plane conjugate with 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 in the pupil plane in the shear direction. The detector may include an array of sensing elements (such as, for example, a charge coupled device (CCD)).

[0057] The projection system PS of the lithographic apparatus may not produce visible fringes, so a phase stepping technique (such as, for example, moving a diffraction grating) can be used to enhance the accuracy of the wavefront determination. The stepping can be performed in the plane of the diffraction grating and in a direction perpendicular to the scanning direction of the measurement. The stepping range can be one grating period, and at least three (evenly distributed) phase steps can be used. Thus, for example, three scanning measurements can be performed in the y direction, each scanning measurement being performed for a different position in the x direction. This stepping of the diffraction grating effectively converts phase changes into intensity changes, allowing the phase information to be determined. The grating can be stepped in a direction perpendicular to the diffraction grating (z direction) to calibrate the detector.

[0058] The diffraction grating may be scanned sequentially in two perpendicular directions, which may coincide with the axes (x and y) of the coordinate system of the projection system PS, or may be at an angle (such as 45 degrees) to these axes. The scan may be performed over an integer number of grating periods (e.g. one grating period). The scan averages the phase changes in one direction allowing reconstruction of the phase changes in the other direction. This allows the wavefront to be determined as a function of the two directions.

[0059] The transmission (apodization) of the projection system PS in a pupil plane of the projection system PS may be determined by projecting radiation, for example 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 system PS and measuring the intensity of the radiation in a plane conjugate to the pupil plane of the projection system PS using a detector. The same detectors may be used as those used to measure the wavefront to determine the aberrations.

[0060] The projection system PS may include a plurality of optical (e.g., lens) elements, and may further include an adjustment mechanism AM configured to adjust one or more of these optical elements in order to correct aberrations (phase variations across the pupil plane throughout the field). To achieve this, the adjustment mechanism may be operable to manipulate one or more 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 combination of: shifting one or more optical elements; tilting one or more optical elements; and / or deforming one or more optical elements. The displacement of the optical element may be in any direction (x, y, z, or a combination thereof). By rotating about an axis in the x and / or y direction, the optical element tilt is typically out of a plane perpendicular to the optical axis, although rotation about the z axis may be used for non-rotationally symmetric aspheric optical elements. The deformation of the optical element may include low-frequency shapes (e.g., astigmatism) and / or high-frequency shapes (e.g., free-form aspheric surfaces). Deformation of the optical element may be performed, for example, by using one or more actuators for applying forces to one or more sides of the optical element and / or by using one or more heating elements for heating one or more selected regions of the optical element. Typically, the projection system PS may not be adjusted to correct for apodization (variations in transmission across a pupil plane). When designing a patterning device (e.g., a mask) MA for the lithographic apparatus LA, a transmission map of the projection system PS may be used. Using computational lithography techniques, the patterning device MA may be designed to at least partially correct for apodization.

[0061] The lithographic apparatus may be a machine having two tables (dual stage) or more tables (e.g. two or more substrate tables WTa, WTb, two or more patterning device tables, substrate tables WTa and WTb below the projection system without dedicated substrates, e.g. to facilitate measurement and / or cleaning, etc.). In such a "multi-stage" machine, additional tables may be used in parallel, or preparatory steps may be performed on one or more tables while one or more other tables are being used for exposure. For example, alignment measurements may be made using an alignment sensor AS and / or level (height, tilt, etc.) measurements may be made using a level sensor LS.

[0062] The lithographic apparatus may also be of a type in which at least a portion of the substrate may be covered by a liquid having a relatively high refractive index, such as water, so as to fill the space between the projection system and the substrate. Immersion liquid may also be applied to other spaces in the lithographic apparatus, such as the space between the pattern forming device and the projection system. It is well known in the art that immersion techniques are used to increase the numerical aperture of the projection system. The term "immersion" as used herein does not mean that structures such as the substrate must be immersed in the liquid; rather, "immersion" only means that the liquid is located between the projection system and the substrate during exposure.

[0063] Thus, in operation of the lithographic apparatus, a radiation beam is conditioned and provided by the illumination system IL. The radiation beam B is incident on the pattern forming device (e.g. mask) MA held on the support structure (e.g. mask table) MT and is patterned by the pattern forming device. Having traversed the pattern forming device MA, the radiation beam B passes through the projection system PS, which focuses the beam onto a target portion C of the substrate W. With the aid of a second positioner PW and a position sensor IF (e.g. interferometer device, linear encoder, two-dimensional encoder or capacitive sensor), the substrate table WT can be accurately moved, for example in order to position different target portions C in the path of the radiation beam B. Similarly, the first positioner PM and the further position sensor ( Figure 1 The support structure MT is a device for accurately positioning the pattern forming device MA relative to the path of the radiation beam B (not explicitly shown in the figure). In general, the movement of the support structure MT can be realized with the help of a long-stroke module (coarse positioning) and a short-stroke module (fine positioning) which form part of the first positioner PM. Similarly, the movement of the substrate table WT can be realized with a long-stroke module and a short-stroke module which form part of the second positioner PW. In the case of a stepper (as opposed to a scanner), the support structure MT may be connected only to a short-stroke actuator, or may be fixed. The pattern forming device MA and the substrate W can be aligned by using pattern forming device alignment marks M1, M2 and substrate alignment marks Pl, P2. Although the substrate alignment marks shown in the figure occupy dedicated target portions, they can be located in the spaces between multiple target portions (these are commonly known as scribe alignment marks). Similarly, in the case where more than one tube core is arranged on the pattern forming device MA, the pattern forming device alignment marks can be located between these tube cores.

[0064] The depicted device can be used in at least one of the following modes:

[0065] 1. In step mode, the support table MT and the substrate table WT are held substantially stationary while an entire pattern imparted to the radiation beam is projected at once onto a target portion C (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 that is imaged in a single static exposure.

[0066] 2. In scan mode, the support structure MT and 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 speed 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 of the target portion in a single dynamic exposure (in the non-scanning direction), while the length of the scanning motion determines the height of the target portion (in the scanning direction).

[0067] 3. In another mode, the support structure MT holding the programmable patterning device is held substantially stationary and the substrate table WT is moved or scanned while a pattern imparted to the radiation beam is projected onto a target portion C. In this mode, a pulsed radiation source is typically employed and the programmable patterning device is updated as required after each movement of the substrate table WT or between successive radiation pulses during a scan. This mode of operation may be readily applicable to maskless lithography using a programmable patterning device such as a programmable mirror array of the type mentioned above.

[0068] Combinations and / or variations on the above described modes of use, or entirely different modes of use, may also be employed.

[0069] Although specific reference is made herein to the use of lithographic apparatus in the manufacture of integrated circuits, it is to be understood that the lithographic apparatus described herein may have other applications, such as the manufacture of integrated optical systems, guidance and detection patterns of magnetic domain memories, liquid crystal displays (LCDs), thin film magnetic heads, etc. It will be understood by those skilled in the art that in the context of such alternative applications, any term "wafer" or "die" used herein may be considered synonymous with the more general term "substrate" or "target portion", respectively. The substrate referred to herein may be processed before or after exposure, such as in a coating and developing device or track (a tool that typically applies a resist layer to a substrate and develops the exposed resist), a metrology tool, or an inspection tool. Where applicable, the disclosure herein may be applied to such and other substrate processing tools. In addition, the substrate may be processed more than once, such as for the production of a multi-layer IC, so that the term "substrate" used herein may also refer to a substrate that already contains multiple processed layers.

[0070] The terms "radiation" and "beam" as used herein include all types of electromagnetic radiation, including ultraviolet (UV) radiation (e.g., having a wavelength of 365 nm, 248 nm, 193 nm, 157 nm or 126 nm) and extreme ultraviolet (EUV) radiation (e.g., having a wavelength in the range of 5 nm to 20 nm), as well as particle beams such as ion beams or electron beams.

[0071] Various patterns on or provided by the pattern forming device can have different process windows, i.e., the space of process variables (under which the pattern will be produced within the specification). Examples of pattern specifications for potential systematic defects include checks for necking, line pullback, line thinning, CD, edge placement, overlap, resist top loss, resist undercut and / or bridging. The process windows of all patterns on the pattern forming device or on a region thereof can be obtained by merging (e.g., overlapping) the process windows of each individual pattern. The boundaries of the process windows of all patterns contain the boundaries of the process windows of some individual patterns. In other words, these individual patterns limit the process windows of all patterns. These patterns can be referred to as "hot spots" or "process window limiting patterns (PWLP)", which are used interchangeably herein. When controlling the patterning process, it is possible and economical to focus on hot spots. When there are no defects in the hot spots, it is likely that all patterns are defect-free.

[0072] like Figure 2As shown, the lithographic apparatus LA may form part of a lithographic cell LC, sometimes also referred to as a lithocell or lithographic cluster, which may also include equipment for performing pre-exposure and post-exposure processes on a substrate. Conventionally, these equipment 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 baking plates BK. A substrate handling device or robot RO picks up one or more substrates from input / output ports I / O1, I / O2, moves the substrates between different process devices, and then transfers the substrates to a feed station LB of the lithographic apparatus. These devices are often collectively referred to as tracks or coating and developing devices, and are controlled by a track control unit TCU, which itself is controlled by a management control system SCS, which also controls the lithographic apparatus through a lithographic control unit LACU. Thus, different equipment may be operated to maximize throughput and processing efficiency.

[0073] In order to ensure that substrates exposed by a lithographic apparatus are correctly and consistently exposed, and / or in order to monitor a patterning process (e.g. a device manufacturing process) comprising at least one pattern transfer step (e.g. an optical lithography step), it is desirable to inspect the substrate or other object to measure or determine one or more properties, such as alignment, overlay (e.g., which may be between structures in overlapping layers, or between structures that have been separately provided into the same layer, e.g. by a double patterning process), line thickness, critical dimension (CD), focus offset, material properties, etc. Thus, a manufacturing facility in which a lithocell LC is located also typically comprises a metrology system MET, which measures some or all of the substrates W that have been processed in the lithocell or in other objects in the lithocell. The metrology system MET may be part of the lithocell LC, for example it may be part of the lithographic apparatus LA (such as an alignment sensor AS).

[0074] The one or more measured parameters may include, for example, overlap between successive layers formed in or on a patterned substrate, critical dimensions (CD) (e.g., critical line width) of features formed in or on a patterned substrate, focus or focus error of an optical lithography step, dose or dose error of an optical lithography step, optical aberration of an optical lithography step, etc. The measurements may be performed on a target on the product substrate itself and / or on a dedicated metrology target disposed on the substrate. The measurements may be performed after development of the resist but before etching, or may be performed after etching.

[0075] There are various techniques for measuring the structure formed in the patterning process, including the use of scanning electron microscopes, image-based measurement tools and / or various special tools. As described above, a fast and non-invasive special measurement tool is a tool in which a radiation beam is directed to a target on a substrate surface and the properties of the scattered (diffraction / reflection) beam are measured. By evaluating one or more properties of the radiation scattered by the substrate, one or more properties of the substrate can be determined. This can be referred to as diffraction-based measurement. One such application of the diffraction-based measurement is in the measurement of feature asymmetry within a target. For example, this can be used as a measure of overlap, but other applications are also known. For example, asymmetry can be measured by comparing relative portions of the diffraction spectrum (e.g., comparing the -1 order and +1 order in the diffraction spectrum of a periodic grating). This can be done as described above and as described in U.S. Patent Application Publication US2006-066855, which is incorporated herein by reference in its entirety. Another application of diffraction-based measurement is in the measurement of feature width (CD) within a target. These techniques may use the devices and methods described below.

[0076] Therefore, in a device manufacturing process (e.g., a patterning process or a lithography process), a substrate or other object may be subjected to various types of measurements during or after the process. The measurement may determine whether a particular substrate is defective, may establish adjustments to the process and equipment used in the process (e.g., aligning two layers on a substrate or aligning a pattern forming device with a substrate), may measure the performance of the process and equipment, or may be used for other purposes. Examples of measurements include optical imaging (e.g., an optical microscope), non-imaging optical measurements (e.g., diffraction-based measurements, such as ASML EyedStar metrology tools, ASML SMASH metrology systems), mechanical measurements (e.g., drawing using a stylus, atomic force microscope (AFM)), and / or non-optical imaging (e.g., a scanning electron microscope (SEM)). The SMASH (Smart Alignment Sensor Hybrid) system, as described in U.S. Pat. No. 6,961,116 (the entire contents of which are incorporated herein by reference), employs a self-referencing interferometer that produces two overlapping and relatively rotated images of an alignment mark, detects intensity in a pupil plane where the Fourier transform of the images results in interference, and extracts position information based on the phase difference between the diffraction orders of the two images (which manifests itself as intensity variations in the interfered orders).

[0077] The measurement results may be provided directly or indirectly to the supervisory control system SCS. If an error is detected, the exposure of subsequent substrates may be adjusted (particularly in the case where the inspection can be completed quickly and quickly enough that one or more other substrates of the batch are still to be exposed) and / or the subsequent exposure of the exposed substrate may be adjusted. In addition, substrates that have already been exposed may be stripped and reworked to improve yield, or scrapped, thereby avoiding further processing of substrates that are known to be defective. In the case where only some target portions of the substrate are defective, further exposure may be performed only on those target portions that are good.

[0078] Within the metrology system MET, a metrology apparatus is used to determine one or more properties of a substrate, and in particular to determine how one or more properties of different substrates vary, or how properties of different layers of the same substrate vary between different layers. As described above, the metrology apparatus may be integrated into the lithographic apparatus LA or the lithocell LC, or may be a stand-alone device.

[0079] In order to enable measurement, one or more targets may be provided on the substrate. In an embodiment, the target is specially designed and may include a periodic structure. In an embodiment, the target is a part of a device pattern, such as a periodic structure of a device pattern. In an embodiment, the device pattern is a periodic structure of a memory device (e.g., a bipolar transistor (BPT), a shared bit bus (BLC), etc.).

[0080] In an embodiment, the target on the substrate may include one or more 1-D periodic structures (e.g., gratings) that are printed such that after development, the periodic structural features are formed by solid resist lines. In an embodiment, the target may include one or more 2-D periodic structures (e.g., gratings) that are printed such that after development, the one or more periodic structures are formed by solid resist pillars or through holes in the resist. The bars, pillars, or through holes may alternatively be etched into the substrate (e.g., etched into one or more layers on the substrate).

[0081] In an embodiment, one of the parameters of interest in the patterning process is overlap. Overlap can be measured using dark field scatterometry, where the zero-order diffraction (corresponding to specular reflection) is blocked and only higher-order diffraction is processed. Examples of dark field metrology can be found in PCT Patent Application Publication No. WO 2009 / 078708 and WO 2009 / 106279, and these patent applications are hereby incorporated by reference in their entirety. In addition, developments in the technology have been described in U.S. Patent Application Publications US2011-0027704, US2011-0043791, and US2012-0242970, and these U.S. Patent Applications are hereby incorporated by reference in their entirety. Diffraction-based overlap using dark field detection of diffraction orders enables overlap measurement of smaller targets. These targets may be smaller than the irradiation spot and may be surrounded by product structures on the substrate. In an embodiment, multiple targets may be measured in one radiation capture.

[0082] Figure 3 An example inspection device (e.g., a scatterometer) is depicted. It comprises a broadband (white light) radiation projector 2 that projects radiation onto a substrate W. The redirected radiation is passed to a spectrometer detector 4, which measures a spectrum 10 (intensity as a function of wavelength) of the specularly reflected radiation, as shown, for example, in the graph at the bottom left. From the data, the structure or profile that gave rise to the detected spectrum can be reconstructed by a processing unit PU, for example by rigorous coupled wave analysis and nonlinear regression, or with Figure 3 The reconstruction is performed by comparison with a library of simulated spectra on the bottom right. Typically, for the reconstruction, the general form of the structure is known and some variables are assumed based on knowledge of the process by which the structure was made, leaving only a few variables of the structure to be determined from the measured data. Such an inspection device can be configured as a normal incidence inspection device or an oblique incidence inspection device.

[0083] You can use Figure 4 Another inspection apparatus is shown. In the device, radiation emitted by a radiation source 2 is collimated using a lens system 12 and transmitted through an interference filter 13 and a polarizer 17, reflected by a partially reflective surface 16, and focused to a spot S on a substrate W via an objective lens 15, which has a high numerical aperture (NA) of desirably at least 0.9 or at least 0.95. Immersion inspection apparatus (using a relatively high refractive index fluid, such as water) can even have a numerical aperture of more than 1.

[0084] As in the lithographic apparatus LA, one or more substrate tables may be provided to hold a substrate W during measurement operations. The substrate table may be similar in form to Figure 1The substrate table WT of the inspection apparatus is similar or identical to or is identical to the substrate table WT of the inspection apparatus. In an example where the inspection apparatus is integrated with the lithographic apparatus, the substrate table may even be the same substrate table. A coarse positioner and a fine positioner may be provided to a second positioner PW, which is configured to accurately position the substrate relative to the measuring optical system. Various sensors and actuators are provided, for example, to obtain the position of an object of interest and to bring the object of interest into position below the objective lens 15. Typically, many measurements will be made on the target at different locations across the substrate W. The substrate support can be moved in the X and Y directions to obtain different targets, and can be moved in the Z direction to obtain the desired location of the target relative to the focus of the optical system. When (for example) in practice the optical system may remain substantially stationary (typically in the X and Y directions, but perhaps also in the Z direction) and only the substrate moves, it is convenient to consider and describe the operation as if the objective lens is being brought to different locations relative to the substrate. If the relative position of substrate and optical system is correct, it does not matter in principle which of the substrate and the optical system moves in the real world, or whether both are moving, or a combination of one part of the optical system moving (e.g. in Z and / or tilt direction) and the rest of the optical system being stationary, and the substrate moving (e.g. in X and Y direction, but optionally also in Z and / or tilt direction).

[0085] The radiation redirected by the substrate W is then passed through the partially reflective surface 16 to the detector 18 for detection of the spectrum. The detector 18 may be located in the back-projected focal plane 11 (at the focal length of the lens system 15), or the plane 11 may be re-imaged onto the detector 18 with auxiliary optics (not shown). The detector may be a two-dimensional detector, so that a two-dimensional angular scattering spectrum of the substrate target 30 may be measured. The detector 18 may be, for example, an array of CCD or CMOS sensors, and an integration time of, for example, 40 milliseconds per frame may be used.

[0086] For example, a reference beam may be used to measure the intensity of the incident radiation. To this end, when the radiation beam is incident on the partially reflective surface 16, a portion of it is transmitted as a reference beam through the partially reflective surface 16 towards the reference mirror 14. The reference beam is then projected onto a different portion of the same detector 18, or alternatively onto a different detector (not shown).

[0087] One or more interference filters 13 may be used to select wavelengths of interest in the range of, for example, 405-790 nm or even lower (e.g., 200-300 nm). The interference filters may be tunable, rather than comprising a set of different filters. Gratings may be used in place of interference filters. An aperture stop or spatial light modulator (not shown) may be provided in the illumination path to control the range of angles of incidence of the radiation on the target.

[0088] The detector 18 can measure the intensity of the redirected radiation at a single wavelength (or narrow wavelength range), the intensity integrated at multiple wavelengths or over a wavelength range. In addition, the detector can measure the intensity of the transverse magnetic polarization and transverse electric polarization radiation and / or the phase difference between the transverse magnetic polarization and transverse electric polarization radiation.

[0089] The target 30 on the substrate W can be a 1-D grating, which is printed so that after development, the bars are formed by solid resist lines. The target 30 can be a 2-D grating, which is printed so that after development, the grating is formed by solid resist columns or through holes in the resist. The bars, columns or through holes can be etched into or onto the substrate (for example, etched into one or more layers on the substrate). The pattern (for example, the bars, columns or through holes) is sensitive to changes in the processing during the patterning process (for example, optical aberrations, focus changes, dose changes, etc. in the lithographic projection equipment (particularly the projection system PS)) and will be reflected in the changes in the printed grating. Therefore, 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 shape) or one or more parameters of a 2-D grating (such as width or length or shape of a column or via) can be input into the reconstruction process performed by processing unit PU based on knowledge of the printing steps and / or other inspection processes.

[0090] In addition to measuring parameters by reconstruction, angle-resolved scatterometry is useful in measuring asymmetry of features in a product and / or resist pattern. A particular application of asymmetry measurement is for measuring overlays, where the target 30 includes a set of periodic features that are superimposed on each other. For example, the use of Figure 3 or Figure 4 The invention relates to the concept of measuring asymmetry in an instrument of a patent application which is incorporated herein in its entirety. In short, while the positions of the diffraction orders in the diffraction spectrum of a target are determined solely by the periodicity of the target, the asymmetry in the diffraction spectrum is indicative of the asymmetry in the individual features that make up the target. Figure 4In an instrument of FIG. 1 , in which the detector 18 may be an image sensor, this asymmetry of the diffraction orders appears directly as an asymmetry in the pupil image recorded by the detector 18. The asymmetry may be measured by digital image processing in the unit PU and calibrated relative to a known value of the overlap.

[0091] Figure 5 A plan view of a typical target 30 is shown, and Figure 4 The range of the illumination spot S in the device. In order to obtain a diffraction spectrum that is not disturbed by surrounding structures, in an 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. The width of the spot S may be smaller than the width and length of the target. In other words, the target is "not filled" with illumination, and the diffraction signal is substantially unaffected by any signal from product features, etc., other than the target itself. The illumination arrangement 2, 12, 13, 17 may be configured to provide illumination of uniform intensity across the back focal plane of the objective lens 15. Alternatively, the illumination may be limited to an on-axis direction or an off-axis direction, for example by including a hole in the illumination path.

[0092] Figure 6 An example process of determining values ​​of one or more variables of interest for a target pattern 30' based on measurement data obtained using metrology is schematically depicted.The radiation detected by the detector 18 provides a measured radiation distribution 108 for the target 30'.

[0093] For a given target 30', a radiation distribution 208 may be calculated / simulated from a parameterized model 206 using, for example, a numerical Maxwell solver 210. The parameterized model 206 shows example layers of various materials that make up and are associated with the target. The parameterized model 206 may include one or more variables for features and layers of the portion of the target under consideration that may be varied and derived. Figure 6As shown, the one or more variables may 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, the one or more variables may also include, but are not limited to, the refractive index (e.g., real or complex refractive index, refractive index tensor, etc.) of one or more layers, the extinction coefficient of one or more layers, the absorbance of one or more layers, the resist 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 these variables may be the expected values ​​of the target being measured. The measured radiation distribution 108 is then compared to the calculated radiation distribution 208 at 212 to determine the difference between the two. If there is a difference, the value of one or more of the variables of the parameterized model 206 may be changed, and the new calculated radiation distribution 208 is calculated and compared with the measured radiation distribution 108 until there is a sufficient match between the measured radiation distribution 108 and the calculated radiation distribution 208. At this 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 an embodiment, a sufficient match exists when the difference between the measured radiation distribution 108 and the calculated radiation distribution 208 is within a tolerance threshold.

[0094] The variations of the patterning process are referred to as “process variations.” The patterning process may include processes both upstream and downstream of the actual transfer of the pattern in the lithographic apparatus. Figure 7Example categories of process variables 370 are shown. The first category may be variables 310 of the lithographic apparatus or any other apparatus used in the lithographic process. Examples of such categories include variables of the illumination, projection system, substrate stage, etc. of the lithographic apparatus. The second category may be variables 320 of one or more processes performed during the patterning process. Examples of such categories include focus control or focus measurement, dose control or dose measurement, bandwidth, exposure duration, development temperature, chemical composition used in development, etc. The third category may be variables 330 of the design layout and its implementation in or using the patterning device. Examples of such categories may include the shape and / or location of assist features, adjustments applied by resolution enhancement technology (RET), CD of mask features, etc. The fourth category may be variables 340 of the substrate. Examples include characteristics of structures beneath the resist layer, chemical composition and / or physical dimensions of the resist layer, etc. The fifth category may be characteristics of time variations of one or more variables of the patterning process 350. Examples of such categories include characteristics of high frequency stage movement (e.g., frequency, amplitude, etc.), high frequency laser bandwidth changes (e.g., frequency, amplitude, etc.), and / or high frequency laser wavelength changes. These high frequency changes or movements are high frequency changes or movements that are higher than the response time of the mechanism used to adjust the basic variables (e.g., stage position, laser intensity). A sixth category can be 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.

[0095] As will be appreciated, many, if not all, of these variables will have an impact on parameters of the patterning process and often parameters of interest. Non-limiting examples of parameters of the patterning process may include critical dimension (CD), critical dimension uniformity (CDU), focus, overlay, edge position or placement, sidewall angle, pattern offset, etc. Often, these parameters represent errors from nominal values ​​(e.g., design values, averages, etc.). The parameter values ​​may be values ​​of a characteristic of an individual pattern or statistical measures of a characteristic of a group of patterns (e.g., averages, variances, etc.).

[0096] The values ​​of some or all of these process variables or parameters related thereto may be determined by suitable methods. For example, these values ​​may be determined from data obtained using various metrology tools (e.g., substrate metrology tools). These values ​​may be obtained from various sensors or systems of equipment in the patterning process (e.g., sensors of the lithographic equipment (such as leveling sensors or alignment sensors), control systems of the lithographic equipment (e.g., substrate or patterning device stage control systems), sensors in track tools, etc.). These values ​​may come from an operator of the patterning process.

[0097] Nowadays, more and more metrology has become a major burden in terms of time spent. For example, especially in the case of multiple patterning or techniques that will emerge in the semiconductor industry. With multiple patterning techniques or patterning (such as lithography-etch-lithography-etch (LELE) and / or sidewall assisted double patterning (SADP), the number of processing steps increases significantly, and therefore the number of metrology steps for control and yield monitoring also increases significantly. In addition, as more layers are used in the multiple patterning steps, the metrology measurements per node increase (i.e., the feature size decreases), and more patterning steps are used per layer.

[0098] Additionally or alternatively, it is desirable to increase defect determination and / or guided defect inspection. This involves substantially more intensive focus, overlay and / or CD metrology than before.

[0099] Additionally or alternatively, there are increasingly tighter specifications for CD, overlay, and / or focus performance on devices. This drives the specifications of manufacturing equipment, such as exposure tools and processing tools (e.g., deposition, etch, track, chemical mechanical polishing (CMP), etc.), from one node to the next. This can, therefore, drive tighter control and monitoring of performance, which in turn drives the need for increasing quantities of measurement for control and monitoring.

[0100] Additionally or alternatively, higher order corrections may be required depending on tightening specifications for CD, focus and / or overlay performance on the device. Higher order corrections are essentially corrective actions that are selective on a small spatial scale across all or part of the substrate (e.g., corrections with high spatial resolution). Higher order corrections involve denser sampling of each substrate for metrology, thereby increasing the metrology burden which may exceed the practical limits of metrology equipment productivity.

[0101] Additionally or alternatively, substrate-to-substrate variations may require additional individual substrate level control (compared to, for example, batch level control) and associated monitoring in order to achieve desired CD, focus and / or overlay performance. This may result in more substrates being measured per batch, driving the amount of measurements used to increase, possibly beyond the practical limits of metrology equipment productivity.

[0102] However, to meet the increased data demands, simply adding metrology equipment or improving metrology equipment productivity may not be enough. In addition, it may not solve all problems, such as obtaining dense CD, focus and / or overlay profiles across the substrate in a timely manner.

[0103] Therefore, metrology efficiency is desirable in order to obtain, for example, a higher density of data per substrate and a higher number of substrates per batch.

[0104] Thus, in an embodiment, a method is provided that, for example, helps improve metrology efficiency. In the method, metrology data from multiple sources are combined and manipulated to derive accurate estimates of one or more patterning process parameters (e.g., CD, focus, overlay, edge placement, etc.) for each of multiple locations where a needle traverses a substrate. In an embodiment, dense metrology data (e.g., for each square millimeter) is then provided for, for example, all substrates processed in a patterning process and for, for example, all layers processed on these substrates in a patterning process.

[0105] Indeed, in embodiments, the result of the method is a "virtual" or modeled distribution of values ​​of one or more patterning process parameters across the substrate, obtained by such combination of various metrology data. Such an approach can then provide an efficient method for hybrid metrology for one or more patterning process parameters (e.g., focus, CD, overlay, etc.). And, while the embodiments herein will primarily consider specific examples of patterning process parameters, namely focus, CD, and overlay, it will be appreciated that one or more other or additional patterning process parameters may be the subject of the techniques herein.

[0106] As mentioned above, the method involves combining metrology with other data from various sources. In an embodiment, the method involves combining measurements 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 the lithographic apparatus. This combination of data is then used to predict on-product performance in the form of, for example, patterning process parameters such as CD, overlay, focus, pattern offset, edge placement (e.g., edge placement error), etc. and / or parameters derived therefrom such as yield, defects (e.g., defect risk, defect count, etc.).

[0107] The method is therefore based on the principle of isolating and estimating the individual root causes of variations in the patterning process parameters of interest, which are then combined to calculate the on-product performance. The goal is to use as much available information as possible to avoid an ever-increasing amount of off-line (and / or on-line) measurements to use, for example, Figure 3-6 The tools described are used to determine patterning process parameters of interest.

[0108] Therefore, in an embodiment, it is desirable to identify various contributions to changes in patterning process parameters of interest (such as CD error, focus error, overlap, etc.). These contributions can then be used in various combinations to achieve an estimate of the desired performance on the product. Typically, these contributions will be errors and / or residuals. For example, the device may generate errors when making corrections, which can then become facts in the changes of the patterning process parameters of interest. As another example, the sensor system can measure errors that are or contribute to the changes in the patterning process parameters. As another example, the device or the mathematical model used to determine the settings of the device may not be able to achieve a certain desired or optimal physical effect (e.g., the difference between the desired physical correction and the physical correction that can be achieved by the device, the difference between the desired physical effect (such as dose, focus, etc.) and the physical effect that can be achieved by the device, the difference between the desired physical correction or effect and the correction or effect that can be determined by the mathematical model, etc.), and therefore cannot achieve a residual that is or contributes to the change of the patterning process parameters. In an embodiment, the contribution can be determined experimentally or empirically.

[0109] Each of these contributions to the patterning process parameters of interest (as contributions spatially distributed across a die, field, or substrate) can then be characterized as a fingerprint. And, similarly, the combined contribution across a die, field, or substrate can be characterized as a fingerprint.

[0110] Thus, multiple of these contributions may be combined to produce a derived fingerprint. For example, a focus fingerprint on a product substrate may be a composite of focus contributions due, for example, to unevenness of the substrate, focus errors associated with the projection system of the lithographic apparatus during exposure of the substrate, height errors produced by the substrate position control loop during exposure, and residual fingerprints of focus settings of the lithographic apparatus. Fig. 9 Describe an example thereof.

[0111] Similarly, a derived or measured fingerprint may have one or more fingerprints removed from it to produce a (further) derived fingerprint. For example, a measured focus fingerprint of a substrate may have removed from it the focus contribution of the unevenness of the substrate, the focus error associated with the projection system of the lithographic apparatus during exposure of the substrate, the height error produced by the substrate position control loop during exposure, and the residual fingerprint of the focus setting of the lithographic apparatus. This may produce a residual focus fingerprint due to errors captured by the fingerprints that were not removed. Refer below Fig.10 Describe an example thereof.

[0112] Thus, in embodiments, the method may decompose the fingerprint into separate contributing fingerprints and / or derive fingerprints, for example, by combining these fingerprints.

[0113] Therefore, reference Figure 8 , depicting an embodiment of a combination of contributions (fingerprints). A change in a process variable 311 (e.g., a height error in the context of focus) may have a contribution 312 to a patterning process parameter 352 (e.g., focus in the context of focus) for a pattern on a substrate, and a change in a process variable 321 (e.g., a residual of a focus setting in the context of focus) 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 simple additions (which may include weighted or linear additions) 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 of changes in other variables. Therefore, through such implementations discussed further below, various contributions may be determined or various contributions may be used to derive estimates of patterning process parameters. In an embodiment, the contributions 312 and / or 322 may be determined by modeling one or more applicable process variables. Contributions 312 and / or 322 may be expressed as a function of one or more applicable process variables. The function may be linear or non-linear.

[0114] Fig. 9 An example of obtaining a derived contribution 470 to a patterning process parameter of a substrate is schematically shown, the derived contribution being a combination of contributions of a plurality of process variables (one or more of which may be derived contributions). In this case, the derived contribution 470 is (de)focusing. Thus, the derived contribution 470 may be obtained using contributions of a plurality of process variables, such as a focus error (FE) associated with a projection system of a lithographic apparatus during exposure 400 of the substrate, a height error (e.g., moving standard deviation (MSD)) generated by a substrate position control loop during exposure 410, and a height error (e.g., moving standard deviation (MSD)) generated by a substrate position control loop during exposure 410. z ), and the unevenness (P) of the substrate 420. Notably, the data may be obtained from a lithographic apparatus and may be a by-product of producing a substrate as part of a patterning process. None of these identified contributions necessarily require the use of (for example) a reference such as Figure 3-6 The described tools are used to measure features patterned on a substrate. If applicable, these contributions can be obtained by simulation, mathematical modeling, and / or measurement / experimentation. For example, these contributions can be obtained by simulation based on physical models, empirical modeling, and / or dedicated measurements.

[0115] Thus, in the focused case, an example of a focused contribution to process variable 400 is shown as contribution 430, an example of a focused contribution to process variable 410 is shown as contribution 440, and an example of a focused contribution to process variable 420 is shown as contribution 450. Each of these contributions is then combined together 460 to obtain a derived contribution 470. Although element 460 (and other elements in the figure) are shown as a plus sign, the operation at 460 need not be an addition, for example, by using a neural network it can be a multiplication, convolution, etc. The operation for one or more contributions can be different from another one or more contributions (e.g., addition of 430 with 440, and convolution of the sum with contribution 450). In an example, the combined contribution can be represented as F(x,y)=a1*F(FE)(x,y)+b1*F(MSD z )(x,y)+c1*F(P)(x,y)+…. Various functions can be obtained through simulation, mathematical modeling and / or measurement / experimentation. In addition, there may be cross terms not shown here (such as focus as a function of FE times MSD, etc.). In order to obtain the absolute value of focus, the nominal value or simulated value of focus can be combined with these contributions. These coefficients (such as a1, b1, c1) are the sensitivity of focus to the corresponding process variables or functions thereof. In this example, these contributions are across the substrate, but in an embodiment, one or more contributions can be for each tube core / field (which is then repeated across the substrate, depending on, for example, the conditions applicable at each of these instances). As noted above, contribution 470 can be characterized as a fingerprint because the contribution can be spatially defined across the substrate / tube core / field. In addition, the conversion of the contribution to an absolute value can be characterized as a fingerprint because it can be spatially defined on the substrate / tube core / field. As will be understood, data obtained from processing multiple substrates using a patterning process can be used to derive the corresponding contributions. This data may already be available as it may be a by-product of processing these substrates.

[0116] Now, in the context of CD, you can use Fig. 9 For example, the derived contribution to CD 470 may be a combination of contributions due to multiple process variables (which may include derived contributions), such as focus (F) 400, the standard deviation of the movement of the substrate in the direction normal to the substrate (MSD z ) 410, and the moving standard deviation (MSD) of the substrate moving in a direction parallel to the substrate x ) 420. Thus, in this case, an example of a contribution to the CD of focus (F) 400 would be contribution 430, to the moving standard deviation (MSD zAn example of a contribution to the CD of 410 would be the contribution 440 to the moving standard deviation (MSD x An example of a contribution of CD of F 420 would be contribution 440. Each of these contributions are then combined together 460 to obtain a derived contribution 470. In an example, the combined contribution may be represented as CD(x,y)=a1*CD(F 2 )(x,y)+b1*CD(MSD x )(x,y)+c1*CD(MSD z 2 )(x,y)+…. In addition, there may be cross-terms not shown here, and these relationships may be different (e.g., such as focus and / or MSD z The relationship may not be purely quadratic and may have linear and cubic terms. In an embodiment, the contributions 430, 440, 450 may be focus (F) 400, moving standard deviation (MSD) 410, 420, 430, 440, 450, respectively. z )410 and moving standard deviation (MSD x )420 distributions, in which case the CD model will be used to combine them into a CD distribution. In addition, 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 CD, the nominal or simulated value of CD can be combined with these contributions. The coefficients (such as a1, b1, c1) are the sensitivity of CD to the process variable or its function.

[0117] Applying the principles described above, Fig.10 An example of a derived contribution 510 is schematically shown from patterned substrate metrology data for a patterning process parameter of interest for a substrate by removing the contribution to the patterning process parameter of interest. Patterned substrate metrology data in this context is a value of the parameter of interest obtained by measuring features on a substrate at least partially processed by a patterning process (e.g., device pattern features, metrology targets separate from the device pattern, etc.). Such metrology data can typically be measured using, for example, Figure 3-6 The measurement or inspection tool described is used to obtain the result.

[0118] The patterned substrate measurement data 500 for the parameter of interest may have at least two contributions. Therefore, by removing one or more other contributions within the patterned substrate measurement data, one or more contributions within the patterned substrate measurement data may be obtained. Therefore, contribution 510 may be obtained by removing 505 contribution 520 from the patterned substrate measurement data 500. Although element 505 (and other elements in the figure) are shown as a minus sign, the operation at 505 does not need to be a subtraction, for example, it may be a multiplication, (de)convolution by using a neural network, etc. Contribution 520 may be a derived contribution (such as contribution 470) or may be a contribution derived from other data (such as any one or more of contributions 430, 440, and 450). In addition, multiple contributions may be removed. For example, an optional contribution 540 associated with a process variable 530 may be removed from the patterned substrate measurement data 500 and contribution 520. As will be appreciated, data obtained from processing multiple substrates using a patterning process may be used to obtain patterned substrate measurement data.

[0119] In an embodiment, patterned substrate measurement data is from a pattern separate from the device pattern, such as a measurement feature at a non-functional area of ​​a die, 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. A comparable contribution to measurement data of a device pattern on the same or different substrate can then be obtained based on the remaining contribution without actually obtaining measurement data from the device pattern. For example, the contribution to the measurement of the device pattern can be estimated to be the same as the residual contribution because the applicable one or more process variables have an effect comparable to the device pattern and the separate pattern. In an embodiment, the separate pattern is a pattern used for test purposes (e.g., a measurement target), and performing measurements on the separate pattern does not affect the device pattern on the substrate.

[0120] Thus, by combining and / or removing contributions from patterned substrate metrology data, an estimate of a parameter of interest of a substrate can be obtained without having to obtain patterned substrate metrology data for the substrate. This is achieved by recognizing the nature of the various contributions.

[0121] In an embodiment, the contribution of one or more process variables may be specific to an apparatus (e.g., a lithographic apparatus); that is, the contribution is specific to a particular actual apparatus or combination of apparatuses. Thus, in an embodiment, the contribution of one or more process variables may be reused across each substrate. Thus, the contribution of one or more process variables may be pre-characterized and obtained from a database for various combination / removal processes. The contribution may be specific to an overall apparatus or a specific portion of an apparatus (e.g., an etching chamber). Examples of these variables may include, but are not limited to, various characteristics of processes upstream or downstream of pattern transfer in a lithographic apparatus (such as spin coating, post-exposure baking, development, etching, deposition, doping, and / or packaging).

[0122] In an embodiment, the contribution of one or more process variables is not specific to a particular substrate (and therefore can be used across substrates). Therefore, the contribution of one or more process variables can be pre-characterized and obtained from a database for subsequent use in various combination / removal processes. By combining such contribution of one or more process variables with data and sensitivity relationships of one or more variables for a particular substrate, such contribution of the one or more process variables can be applied to a particular substrate. Examples of these variables may include, but are not limited to, variables of irradiation, variables of the projection system, focus, dose, bandwidth, exposure duration, characteristics of high-frequency stage movement (e.g., moving standard deviation (MSD) of movement of the substrate stage, moving average of movement of the substrate stage, frequency, amplitude, etc.), high-frequency laser bandwidth variation (e.g., frequency, amplitude, etc.), high-frequency laser wavelength variation, and / or flatness of the substrate.

[0123] In an embodiment, the contribution of one or more process variables may be substrate specific. For example, the contribution of each substrate or a particular group of substrates may be determined. Examples of these variables may include, but are not limited to, substrate geometry (height map, deformation map), substrate processing conditions, irradiation variables, projection system variables, focus, dose, bandwidth, exposure duration, characteristics of high-frequency stage movement (e.g., moving standard deviation (MSD) of the movement of the substrate stage, moving average of the movement of the substrate stage, etc.), high-frequency laser bandwidth variation (e.g., frequency, amplitude, etc.), high-frequency laser wavelength variation, and / or flatness of the substrate.

[0124] In an embodiment, the contribution of one or more process variables may 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 be independent of additional substrates. Thus, contributions specific to patterns or patterning devices may be pre-characterized and obtained from a database for subsequent use in various combination processes. Examples of these variables may include, but are not limited to, patterning device feature CD, shape and / or location of assist features, adjustments applied by resolution enhancement techniques (RET), etc.

[0125] In an embodiment, the contribution associated with different process variables may have different spatial uniformity. For example, the contribution of some process variables may be substantially uniform across the entire substrate space, while the contribution of some other process variables may not be spatially uniform across the entire substrate. This difference may be attributed to the different properties of the process variables. For example, the contribution of one or more process variables associated with the resist layer, the development of the resist layer and / or the etching of the substrate tends to be substantially uniform in space, because the entire substrate is usually coated with a resist layer, developed or etched at the same time and under the same conditions, or tends to be symmetrical, because (for example) the substrate is rotated during many of these processes. For example, the contribution of one or more process variables associated with pattern transfer or lithography equipment tends to be less uniform in space, because the pattern transfer tends to be specific to the position and one or more process variables can be changed between the pattern transfer for one position and the pattern transfer for another position. Therefore, if the contribution that is not substantially uniform in space can be removed from the patterned substrate measurement data, a substantially uniform contribution in space can be obtained from the patterned substrate measurement data.

[0126] Thus, in a particular example, 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. The data is usually already available in the lithography apparatus, for example in a diagnostic file. Based on the data, for the parameter of interest, the contribution described above can be generated using the model, which describes the sensitivity of the parameter of interest to one or more process variables. One or more sensitivities can be obtained from simulations or experiments. Assuming that the track and resist model calibration will be perfect, the contribution generated in this way is expected to be visible during the measurement after resist development. Once the substrate is measured, for example after development or after etching, the contribution is removed from the patterned substrate measurement data. The remaining contribution is now the contribution of the pattern transfer process before or after the pattern transfer process (for example, by the track and / or etching equipment, which is usually between fields) and the pattern forming device (within the field). The lithography apparatus error will be corrected based on the patterned substrate measurement data. Similarly, the patterning device contribution can be measured and its contribution removed to leave the contribution before or after the pattern transfer process. The contribution can be removed per process flow (e.g., combination of patterning process steps and / or equipment used) or per specific equipment or portion thereof (e.g., etching equipment or etching chamber).

[0127] Thus, with these techniques, contributions to a parameter of interest can be obtained by modeling relationships or by removing known contributions from patterned substrate metrology data. Furthermore, one or more contributions can be device-specific but at the same time substrate-independent. However, one or more other contributions can be substrate-specific. Thus, by appropriate mixing and matching of contributions, an estimate of a parameter of interest at a point in the patterning process can be estimated.

[0128] Therefore, some specific examples of the application of these contributions will now be described in the context of focus, CD and overlay to determine respective estimates of focus, CD and overlay for a substrate.As will be appreciated, additional or other parameters of interest may be processed and estimated.

[0129] In order to enable these examples, various data are used. For example, the lithographic apparatus has a significant measurement capability integrated therein for pattern transfer control. Examples of such integrated measurements are position measurement devices (e.g., sensors IF) for substrates and / or patterning devices for servo control, leveling sensors (e.g., sensors LS) that measure the substrate surface for leveling control, alignment sensors (e.g., sensors AS) that measure the direction, position, and / or deformation of the substrate to enable overlap control, and / or aberration sensors (e.g., shearing interferometers described above) that are used to control the wavefront of the projection system. The lithographic apparatus will use data from these sensors to control at the following levels: meet its total CD, overlap, and / or focus budgets but also keep track of the residuals and / or errors left after control. These residuals and / or errors can be used to calculate the CD, overlap, and / or focus errors generated during pattern transfer (i.e., the contribution of the lithographic apparatus to CD, overlap, and / or focus fingerprints). As will be understood, other equipment used in the patterning process may have information similar to the applicable measurements used for the equipment.

[0130] In addition, the lithographic apparatus settings or controls may use one or more mathematical models to determine corresponding calibration or control corrections. However, such one or more models may have built-in assumptions or limitations that result in non-zero residual errors. Such model residuals may be used to calculate the resulting CD, overlay and / or focus errors (i.e., the model's contribution to CD, overlay and / or focus fingerprints). As will be appreciated, other equipment used in the patterning process may have similar model information.

[0131] In addition, the lithographic equipment can be set up by using in-resist measurements to help remove any global and local fingerprints of one or more parameters (e.g., focus, overlap, etc.). However, the global fingerprint may drift over time since the last calibration was performed. In order to monitor and control this setup state, a monitoring substrate can be exposed and measured to monitor the global fingerprint. The monitoring substrate can be a basic substrate, and there is a well-defined pattern in the substrate, a resist layer is applied to the substrate, exposed with a pattern related to the well-defined pattern, developed and then measured. Once measured, the resist on the monitoring substrate can be stripped to leave the well-defined pattern so that a new resist layer can be applied. Based on these measurement results, the lithographic equipment can be corrected, so these corrections need to be factored in when determining these contributions. In an embodiment, the monitoring substrate can be used to determine overlap by using the well-defined pattern and / or to determine focus by using the resist pattern.

[0132] Turning to the focus example, the technique mainly involves two main parts. The first part is actually a setup process for determining a base focus contribution for the lithographic apparatus that is not reflected in one or more types of lithographic apparatus process variables used to determine the focus estimate for a particular substrate in the estimation process. The second part is an estimation process that uses the focus contributions associated with these one or more types of lithographic apparatus process variables for the substrate under consideration to determine an estimate of the focus for a particular substrate.

[0133] Thus, in a setup according to an embodiment, patterned substrate focus metrology data is obtained for one or more substrates and then used as described above. Fig.10 The contribution of one or more types of lithographic apparatus process variables may be removed in a similar manner as described. One type of contribution that may be removed is the focus contribution of a substrate height residual or error map associated with, for example, a leveling sensor of the lithographic apparatus. Another type of contribution that may be removed is the focus contribution of a projection system image plane deviation (IPD), which may be obtained, for example, from a shearing interferometer and / or projection system model residual. Another type of contribution that may be removed is the focus contribution of a patterning device and / or substrate servo control (e.g., MA), which may be obtained from residuals of an applicable positioner, position measurement device (e.g., sensor IF), and / or servo control model. As described above, the conversion from process variables to focus contributions may be determined by simulation, mathematical modeling, and / or experiment.

[0134] As desired, the contribution fingerprints may be re-gridded to the same grid (which may be the same grid as that of one of the contribution fingerprints, or a different grid). Similarly, the contribution fingerprints may be re-gridded to patterned substrate metrology data, or vice versa. In an embodiment, the re-gridding comprises upsampling or downsampling.

[0135] In an embodiment, filtering (eg, moving averaging, deconvolution, FFT, etc.) is applied to a contribution, desirably before combining the contribution with another contribution.

[0136] In an embodiment, the base focus contribution of the lithographic apparatus can be efficiently determined once and used for various focus estimates, so that the quantity measurements can be significantly reduced compared to measuring each substrate. In an embodiment, patterned substrate focus metrology data can be obtained by relatively sparsely sampling locations on a substrate (e.g., 500 targets or less on a substrate) and / or locations on a large number of substrates from one or more batches (e.g., 10 or less substrates from a batch of 25 or more substrates).

[0137] In an embodiment, the patterned substrate focus metrology data may be a measured focus fingerprint of a monitoring substrate as described above. Thus, data that has already been captured may be used. Thus, the measured focus fingerprint may be corrected for lithographic apparatus effects derived from lithographic apparatus sensor information to arrive at a base focus contribution of the lithographic apparatus, such as the focus contribution of the projection system image plane deviation (IPD), the focus contribution of the substrate height residual or error map, and / or the focus contribution of the patterning device and / or substrate servo controller.

[0138] The base focus contribution of the lithographic apparatus is then stored for on-product focus estimation. The base focus contribution of the lithographic apparatus may be determined for a plurality of lithographic apparatuses. The base focus contribution of the lithographic apparatus may be determined for a specific combination of devices of the lithographic apparatus used. For example, a lithographic apparatus may have more than one substrate table on which a substrate may be exposed, and thus the base focus contribution of the lithographic apparatus may be determined for a specific combination and / or multiple combinations of devices used.

[0139] Then, for on-product estimation, errors or residuals of one or more types of lithographic apparatus process variables related to focus are obtained for the substrate of interest, and their focus contributions are determined. For example, the focus contribution of the projection system image plane deviation (IPD), the focus contribution of the substrate height residual or error map, and / or the focus contribution of the patterning device and / or substrate servo controller can be obtained for the substrate of interest. Another type of contribution that can be added is the focus contribution of the patterning device error, which is attributable to the patterning device being used for the specific substrate of interest, which can be obtained by measurement. This contribution can be used specifically if an applicable base focus contribution of the lithographic apparatus is obtained for the substrate of interest without using the patterning device.

[0140] In addition, the applicable base focus contributions of the lithographic apparatus (as described above) are obtained. The applicable base focus contributions of the lithographic apparatus are then combined (similar to the above description of Fig. 9 As described above, one or more specific focus contributions of the substrate of interest are used to obtain an estimated focus fingerprint for the substrate of interest. Thus, an estimate of the focus error can be determined at any location or nearly any location on any substrate.

[0141] Now, turning to the CD example, in principle, there are many process variables that may lead to CD variations in the substrate. In the described embodiments, some CD variations across the substrate are considered. In particular, CD variation contributions with respect to focus, focus blur, dose and overall process are considered. The patterning device (which is an intra-field contributor to CD variations) may also be considered, but for convenience only, it will not be described further.

[0142] The focus contribution to CD may be based on the focus contribution as described above, in particular, based on a combination of the base lithographic apparatus focus contribution and the focus contribution of one or more process variables of the lithographic apparatus for the substrate under consideration. In principle, the dense focus information may be converted into a ΔCD contribution for any pattern feature across the field and / or across the substrate, assuming, for example, that the Bossung behavior of the feature (after lithography and / or after etching) is known experimentally or by simulation. Thus, for any location (x, y) on the substrate with a focus value, the CD value corresponding to the substrate location (x, y) may be calculated:

[0143] CD (HDFM x,y )=Φ1(HDFM x,y )

[0144] Wherein HDFM corresponds to a focusing map, such as the derived high density focusing map described above in the focusing example.

[0145] The focus blur contribution to CD can be obtained using lithographic apparatus data, such as servo information (e.g., MSD in the z-direction). The focus blur information can be converted into a ΔCD contribution in the scan direction and across the substrate. This conversion of focus blur data to CD is also feature specific and can be known by experiment or simulation:

[0146] CD(fblur x,y )=Φ2(fblur x,y )

[0147] where fblur corresponds to focus blur.

[0148] The dose contribution to CD is due to the dose variation of the lithographic apparatus (e.g. determined by a dose mapping system). The dose variation across the substrate during exposure can be converted to a ΔCD contribution using a suitable dose sensitivity for the applicable feature, which can be known experimentally or by simulation:

[0149] CD (dose x,y )=Φ3(dose x,y )

[0150] The total process contribution to CD is the CD variation resulting from various process steps as part of the patterning process, separate only from the pattern transfer. Thus, in an embodiment, the total process contribution is the state of the CD variation after the final etching step, and is not attributed to various other CD variations that are considered when estimating the CD variation. Thus, in an embodiment, the contribution is for all unaccounted for cumulative effects of process variations resulting from, for example, film deposition variations, baking and / or development variations, and / or etching process variations. Examples of process variables that contribute to the total process contribution to CD may include characteristics of the structure below the resist layer, the chemical composition and / or physical dimensions of the resist layer, and / or characteristics of one or more processes upstream or downstream of the pattern transfer in the lithographic apparatus, such as spin coating, post-exposure baking, development, etching, deposition, doping, and / or packaging. Also, while the total process contribution to CD is described in terms of after etching, the total process contribution may be obtained for different points in the patterning process, for example, after development but before etching.

[0151] Therefore, similar to the setup process of the focusing example, all of these ΔCD contributions due to focus, focus blur and dose can be used and subtracted from the substrate CD measurement results to estimate the total process contribution. That is, in an embodiment, the total process contribution after etching can be generated from the anchor feature CD measurement results after etching, from which the ΔCD contributions of focus, focus blur and dose (for the anchor feature) are removed. As mentioned, the total process contribution is estimated based on the appropriate anchor feature. Therefore, in an embodiment, the total process contribution of other features can be determined based on the anchor feature. For example, the remaining part of the total process contribution can be represented as part of the characteristics of the anchor feature. In the case where the total process contribution is obtained for different points in the patterning process (for example, obtained after development but before etching), the CD measurement results after development but before etching can be used.

[0152] In embodiments, the total process contribution can be efficiently determined once and used for various CD estimates, so the amount of measurements can be significantly reduced compared to measuring each substrate. In embodiments, patterned substrate focus metrology data can be obtained by relatively sparsely sampling locations on a substrate (e.g., 500 targets on a substrate or less) and / or many substrates from one or more batches (e.g., 10 or fewer substrates from a batch of 25 or more substrates).

[0153] The total process contribution is then stored for CD estimation on the product. The total process contribution can be determined for a specific and / or multiple equipment configurations (e.g., one or more specific etch chambers, one or more specific combinations of etch chambers and bake plates, one or more specific combinations of substrate stages and etch chambers, etc.).

[0154] Then, similar to the focus estimation step described above, an on-product CD estimate may be obtained. In an embodiment, errors or residuals of one or more types of lithographic apparatus process variables related to CD are obtained for the substrate of interest and their CD contributions are determined. For example, CD contributions of focus, focus blur and / or dose may be obtained for the substrate of interest. Another type of contribution that may be added is the CD contribution of patterning device errors, which may be attributable to the patterning device being used for the particular substrate of interest, which may be obtained by measurement.

[0155] In addition, the applicable total process contribution to CD is obtained, as described above. Then, the applicable total process contribution to CD is combined (similar to the above description of Fig. 9 As described above, one or more CD contributions specific to the substrate of interest are used to obtain an estimated CD fingerprint for the substrate of interest. Thus, an estimate of the CD error can be determined at any location or nearly any location on any substrate.

[0156] In addition, estimates of one or more specific pattern features of interest on the substrate, such as hot spots, can be obtained. As mentioned above, the total process contribution to CD is determined for a specific anchor feature, but can be scaled for one or more specific features of interest. In addition, the CD contribution of one or more types of lithographic equipment process variables (such as focus, focus blur and / or dose) can be calculated based on appropriate sensitivities for one or more specific features between CD variation and one or more types of lithographic equipment process variables. Such sensitivities can be obtained, for example, by simulation and / or experiment. Thus, multiple CD substrate fingerprints can be obtained, each for a different hot spot or other feature of interest of the pattern.

[0157] The method can be improved, for example, by using more parameters in one or more relevant models (e.g., patterning device and / or aberration models). The method can be extended by estimating the total process contribution, for example, by decomposing the total process contribution into different contributing factors (e.g., deposition, lithography, and / or etching) having different sensitivities to different features.

[0158] In an embodiment, a dose correction applied as part of the patterning process may be corrected for use in the result. For example, the lithography unit may apply a dose correction using, for example, ASML's Dosemapper system. Thus, this correction is taken into account when determining the CD estimate.

[0159] Turning now to the overlay example, data from at least two different patterns transferred onto the substrate are used. These techniques are similar to those described above with respect to the focus and CD examples.

[0160] The technique essentially involves two main parts. The first part is actually a setup process for determining a base overlay contribution for the lithographic apparatus that is not reflected in one or more types of lithographic apparatus process variables used to determine the overlay estimate for a particular substrate in the estimation process. Optionally, the total process overlay contribution can also be determined in a manner similar to the total process CD contribution of the CD example discussed above. The second part is an estimation process for determining an estimate of overlay for a particular substrate using the overlay contributions associated with these one or more types of lithographic apparatus process variables for the substrate under consideration for each of the at least two pattern transfers.

[0161] Thus, in a setup according to an embodiment, patterned substrate overlay metrology data is obtained for one or more substrates and then for each of at least two pattern transfers, as described above. Fig.10 The contribution of one or more types of lithographic equipment process variables is removed in a similar manner as described. One type of contribution that can be removed is the overlap contribution of the substrate height map obtained, for example, from the leveling sensor of the lithographic equipment. Differences can be found for the substrate height maps used for two pattern transfers, and then the differences can be converted into overlap values ​​and thus into overlap contributions. For example, by treating the height difference as a warp or bend of the substrate and using first principles to calculate the X and / or Y displacement (for example, in the clamped area of ​​the substrate, for example, the displacement can be the ratio of the change in Z to the change in X or Y multiplied by half of the substrate thickness, or in the unclamped area of ​​the substrate, for example, the Kirchoff-Love plate theory can be used to calculate the displacement), the Z height difference can be converted into X and / or Y displacement. In an embodiment, the conversion of height to overlap contribution can be determined by simulation, mathematical modeling and / or experiment. Therefore, by using this substrate height information for each pattern transfer, the overlap effect caused by focusing or chuck spot can be observed and considered.

[0162] Another type of contribution that can be removed is the overlap contribution of the patterning device and / or substrate servo control (e.g., MA) in the X and / or Y directions (including rotation about Z), which can be obtained from the residuals of the applicable positioner, position measurement device (e.g., sensor IF), and / or servo control model. The difference can be found for the servo control values ​​across the substrate for the two pattern transfers, which can then represent the overlap contribution. The conversion from servo control values ​​to overlap contributions can be determined by simulation, mathematical modeling, and / or experimentation, if desired.

[0163] Another type of contribution that can be removed is the overlap contribution of projection system aberrations (which can be observed, for example, from a shearing interferometer) and / or projection system model residuals. The conversion from aberrations and / or residuals to overlap contributions can be determined by simulation, mathematical modeling and / or experiments.

[0164] Another type of contribution that can be removed is the overlap contribution to the alignment system model residuals, which can be provided by the lithographic apparatus. The conversion from residuals to overlap contributions can be determined by simulation, mathematical modeling and / or experimentation. In an embodiment, the alignment system model residuals can be different for different pattern transfer steps, so combinations / differences of alignment system model residuals can be used for different pattern transfer steps to obtain overlap contributions. In an embodiment, the alignment model residuals can be corrected for substrate height.

[0165] If desired, the contribution fingerprints can be re-gridded into the same grid. Similarly, the contribution fingerprints can be re-gridded into patterned substrate metrology data, or vice versa.

[0166] In an embodiment, the base overlay contribution of a lithographic apparatus can be efficiently determined once and used for various overlay estimates, so that the quantity measurements can be significantly reduced compared to measuring each substrate. In an embodiment, patterned substrate overlay metrology data can be obtained by relatively sparsely sampling locations on a substrate (e.g., 500 targets on a substrate or less) and / or many substrates from one or more batches (e.g., 10 or fewer substrates from a batch of 25 or more substrates).

[0167] In an embodiment, the patterned substrate overlay measurement data may be a measured overlay fingerprint of a monitoring substrate as described above. Thus, data that has already been captured may be used. Thus, the measured overlay fingerprint may be corrected for lithographic equipment effects derived from lithographic equipment sensor information to obtain a base overlay contribution of the lithographic equipment, such as an overlay contribution of the projection system, an overlay contribution of substrate height, an overlay contribution of alignment model residuals, and / or an overlay contribution of a pattern forming device and / or substrate servo control. In an embodiment, the measured overlay fingerprint data will be captured once for the first pattern transfer of a product substrate, and then captured again for the second pattern transfer (and the monitoring substrates between pattern transfers will be reworked). In an embodiment, the patterned substrate overlay measurement data is an overlay delta fingerprint, which is obtained by the difference between an overlay fingerprint measured from one or more monitoring substrates after the first pattern transfer and an overlay fingerprint measured from one or more monitoring substrates after the second pattern transfer. Thus, by exposing a set of monitoring substrates at approximately the same time as the product layer, the overlay equipment contribution to overlay in terms of short-term drift may be quantified. That is, using the overlay delta fingerprint at that time, the lithographic tool contribution to the overlay out of field due to the short-term drift between the first pattern transfer and the second pattern transfer can be obtained.

[0168] Optionally, in the case of an overlap after an expected etching, an etching process contribution to the overlap can be determined, which is an overlap change caused by etching. In order to obtain the etching process overlap contribution, the patterned substrate measurement data after development but before etching can be removed from the patterned substrate measurement data after etching to obtain the etching process overlap contribution. In an embodiment, the etching process overlap contribution can be effectively determined once and used for overlap estimation, so that the amount measurement can be significantly reduced compared to measuring each substrate. In an embodiment, the patterned substrate overlap measurement data can be obtained by relatively sparsely sampling a portion on the substrate (e.g., 500 targets on the substrate or less) and / or a number of substrates from one or more batches (e.g., 10 or less substrates from a batch with 25 or more substrates). Assuming that the etching fingerprint after each pattern transfer is the same, the etching process fingerprint induced at the first pattern transfer or the second pattern transfer can be derived from the delta fingerprint between the overlap measurement after development but before etching and the overlap measurement after etching of the other of the first pattern transfer and the second pattern transfer.

[0169] The basic overlap contribution of the lithographic apparatus (and optionally the etch process overlap contribution) is then stored for on-product overlap estimation. The basic overlap contribution of the lithographic apparatus can be determined for multiple lithographic apparatuses. The basic overlap contribution of the lithographic apparatus can be determined for a specific combination of devices of the lithographic apparatus used. For example, a lithographic apparatus can have more than one substrate table on which a substrate can be exposed, and thus the basic overlap contribution of the lithographic apparatus can be determined for a specific combination and / or multiple combinations of devices used. The etch process overlap contribution can be determined for a specific and / or multiple equipment configurations (e.g., one or more specific etching chambers).

[0170] Then, for the on-product estimation, errors or residuals of one or more types of lithographic apparatus process variables related to overlay are obtained for the substrate of interest, and their overlay contributions are determined. Overlay contributions of the projection system, overlay contributions of substrate height, overlay contributions of alignment model residuals, and / or overlay contributions of patterning devices and / or substrate servo control may be obtained for the substrate of interest to obtain a base overlay contribution of the lithographic apparatus. In an embodiment, only the overlay contribution of substrate height is obtained.

[0171] In addition, an applicable base overlay contribution for the lithographic apparatus as described above is obtained, and optionally, an applicable overlay contribution for the etching process is obtained. The applicable base overlay contribution for the lithographic apparatus (and optionally, the optional overlay contribution for the etching process) is then combined (similar to the above description of Fig. 9 As described above, and one or more specific overlap contributions of the substrate of interest are used to obtain an estimated overlap fingerprint for the substrate of interest. Thus, an estimate of the overlap at almost any location on any substrate can be determined.

[0172] In an embodiment, an overlay correction applied as part of the patterning process may be corrected for use in the result. For example, the lithography unit may apply an overlay correction based on measurements of a monitored substrate using, for example, ASML's Baseliner system. Thus, this correction is taken into account when determining the overlay estimate.

[0173] In an embodiment, in a multiple patterning process, it is desirable that the exposure and lithography apparatus conditions (e.g., exposure dose, patterning device transmission, patterning device qualification error, illumination settings, lithography apparatus substrate clamping error, etc.) are very similar between the first pattern transfer step and the second pattern transfer step. Furthermore, it is desirable that the exposure and heating marks at the level within the field are similar between the first pattern transfer step and the second pattern transfer step, so this effect on the overlap should be small.

[0174] Additionally, in embodiments, multiple predictions may be combined. For example, an overlap prediction may be combined with a CD prediction. For example, in a multiple patterning scenario where different pattern transfer steps are used to create structures adjacent to each other and the structures have gaps between them, the combination of CD, one or more different pattern transfer steps, and the overlap of the different pattern transfer steps may give a better prediction of the gap size than either the overlap or CD estimates alone.

[0175] Fig.11 A flow for a method according to an embodiment is then schematically shown. In particular, it is shown how generalized contributions (such as a base focus contribution of a lithographic apparatus, a total process contribution to CD and / or a base overlap contribution of a lithographic apparatus (and optionally, an applicable etch process overlap contribution) can be applied to specific information of a substrate of interest to obtain an estimate of the parameter of interest for said substrate. Thus, contribution 912 corresponds to one or more process variables for a specific substrate and, for example, to one or more process variables for a hotspot. This can be determined by modeling, root device information, etc. In addition, contributions 922 applicable to multiple substrates are obtained, such as a base focus contribution of a lithographic apparatus, a total process contribution to CD and / or a base overlap contribution of a lithographic apparatus (and optionally, an applicable etch process overlap contribution). The total process contribution and / or the base overlap contribution of the lithographic apparatus (and optionally, the applicable etch process overlap contribution). Contribution 922 may be obtained using any of the techniques described herein. Contribution 912 may be determined for multiple substrates (e.g., for each substrate of interest), while contribution 922 may be reused across many substrates. Contribution 912 and contribution 922 are combined to obtain an estimate 950 of a parameter of interest for (e.g.) a hotspot, without necessarily obtaining patterned substrate metrology data for the hotspot. In operation 970, an action is taken to determine, such as whether a defect is present at the hotspot, based on the estimate of the parameter of interest.

[0176] Thus, the device sensor data may be utilized to enhance the metrology in the resist and / or after etching to obtain computed metrology that may, for example, provide dense metrology per substrate without having to have dense sampling of substrates and / or provide metrology for many, if not every, substrates without having to obtain patterned substrate metrology data for each such substrate. Additionally, for example, the dense computed metrology may enable higher order corrections. The computed metrology may also enable greater control, possibly including per substrate control, without having to obtain patterned substrate metrology data for each such substrate and / or without having to densely measure patterned substrate metrology data on a substrate.

[0177] Furthermore, estimates based on these computed metrology techniques may enable various applications such as patterning process control (eg, adjusting one or more process variables), patterning process monitoring, fault detection, defect prediction, patterning process design, and the like.

[0178] In an embodiment, the derived contribution may be used (such as using Fig.10 The derived contribution) is used to parameterize the mathematical model to determine the contribution of changes in one or more process variables to the parameter of interest. That is, a mathematical model can be fitted to the derived contribution to obtain the value of one or more parameters, constants, etc. of the mathematical model. Therefore, as an example, it is desirable to have a model and any sensitivity represented in the model to accommodate changes in the process and / or substrate stack. Therefore, in an embodiment, a predicted substrate fingerprint can be generated for each substrate to be measured. To this end, a model of the parameter of interest can be established, for example, for CD, the model includes CD=a1*DOSE+a2*FOCUS 2 +a3*MSDx+a4*MSDy+a5*MSDz+... For the measurement of the substrate, the fingerprints before and / or after the process (e.g., coating development (track) / etching) and the fingerprint of the pattern forming device can be removed. The remaining fingerprint measurement results can be compared with the predicted values. In this case, there is now a set of equations (as many equations as measurement points) in which CD, dose, focus, MSD-xyz, aberrations, etc. are known. The set of equations can be solved for the desired sensitivity (a1, a2,...). When this is performed for several substrates measured for a certain device pattern, there will be a large amount of data for re-estimating the desired sensitivity. If data from multiple lithography devices and / or data from focus exposure matrix exposure are used in the same way, sufficient changes in the input signal (e.g., focus, dose, MSD, CD, etc.) can achieve correct sensitivity estimates. In addition, the technology can be applied to other parameters of interest, such as depth of focus, exposure latitude, overlap, edge position, etc.

[0179] In embodiments, a training algorithm may be used to add additional accuracy. For example, when solving for sensitivities to aberrations, boundary conditions may be considered where the aberrations can only vary across the slit and the CD (or overlap) data is pre-filtered before fitting these sensitivities. In embodiments, by re-estimating these sensitivities from time to time or continuously, these sensitivities may become more robust to variations in the patterning process.

[0180] Return to reference Figure 6and its associated description, in an embodiment, one or more of the variables in the parameterized model 206 may have a stronger effect 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 significant difference in the calculated radiation distribution. Such variables may be referred to as strong variables. Strong variables may include, but are not limited to, the critical dimension of a feature. On the other hand, a large percentage 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 may include, but are not limited to, the side wall angle of a feature, the height of a feature, the thickness of a layer, the resist loss during development, the footing of a feature, the refractive index of a layer, the absorptivity of a layer, and / or the extinction coefficient of a layer.

[0181] Both the strong variables and the weak variables in the parameterized model 206 can be used by a user (e.g., a person, a control system, etc.) to estimate one or more steps of the patterning process. Specifically, one or more weak variables can be used to determine whether there are defects on the target 30' or other pattern, which can be used in one or more processes (such as spin coating, PEB, development, etching, deposition, doping and / or packaging) upstream or downstream of pattern transfer in a lithographic device. For example, when the sidewall angle of the pattern on the substrate exceeds a certain threshold, one or more defects may be generated during subsequent etching. In this way, defects that may be caused by etching can be predicted based on the value of the sidewall angle of the pattern on the substrate before the etching process occurs. These examples are non-limiting.

[0182] However, determining the value of weak variables directly based on measurement results is challenging. This is because the signals that can be used to determine the value of weak variables in the inspection system are often weak and sometimes too weak to be detected. In addition, it is difficult to provide a certain level of accuracy in determining the value of weak variables, especially when there are many variables in the parameterized model and the value of the strong variable is unknown.

[0183] In order to pass Figure 6 The reconstruction process described obtains more accurate values ​​of one or more weak variables for various purposes (eg, for predicting defects), it is desirable to determine the values ​​of one or more strong variables (eg, CD) in the parameterized model outside of the reconstruction process itself.

[0184] Fig.12A flow chart of a method for determining the value of a strong variable on a substrate according to an embodiment (the method can avoid performing measurements on the strong variable on the substrate) is shown. The process can be used to obtain the values ​​of multiple different strong variables. As shown, a fingerprint of a strong variable 1640 of a substrate can be obtained by combining a first contribution 1610 from a first set of one or more variables related to a lithographic apparatus (such as focus, dose, MSD, aberration, pupil shape, etc., and which can be spatially specified and repeated across the substrate for each tube die / field under application conditions, or spatially specified across the substrate), a second contribution 1620 from a second set of one or more variables related to one or more manufacturing processes before or after pattern transfer in the lithographic apparatus (such as etching, development, etc., and which can be spatially specified across the substrate), and a third contribution 1630 from a third set of one or more variables related to a pattern forming device used in a patterning process (such as mask CD, etc., and which can be spatially specified and repeated across the substrate for each tube die / field under application conditions, or spatially specified across the substrate). For any particular portion of the substrate, such as a portion of target 30', a fingerprint of strong variables 1640 may be obtained.

[0185] The first group of one or more variables related to the lithographic apparatus may be one or more variables described above. The first contribution 1610 may be specific to the lithographic apparatus; that is, the first contribution 1610 is specific to a particular actual lithographic apparatus. In an embodiment, the first contribution 1610 is not specific to a particular substrate (and can therefore be used across substrates). Therefore, the first contribution 1610 may be pre-characterized and later obtained from a database for use in the reconstruction process. The first contribution 1610 may be applied to a particular substrate by combining it with data and sensitivity relationships of one or more variables of a particular substrate. The first contribution 1610 may be substrate specific. For example, the first contribution 1610 may be determined for each substrate or a particular group of substrates so that the fingerprint of the strong variable 1640 is specific to the substrate or the group of substrates. Examples of the first group of variables may include, but are not limited to, variables of illumination, variables of the projection system, focus, dose, bandwidth, exposure duration, characteristics of the high-frequency stage movement (e.g., moving standard deviation (MSD) of the movement of the substrate stage, moving average of the movement of the substrate stage, etc.), high-frequency laser bandwidth variation (e.g., frequency, amplitude, etc.), high-frequency laser wavelength variation, and / or flatness of the substrate.

[0186] The third set of one or more variables related to the patterning device may be one or more variables described above. The third contribution 1630 may be pattern or patterning device specific; that is, the third contribution 1630 is specific to a certain actual patterning device or a specific pattern provided by a patterning device. The third contribution 1630 may be substrate independent. Thus, the third contribution 1630 may be pre-characterized and later obtained from a database for use in the reconstruction process. Examples of the third set of variables may include, but are not limited to, mask CD, shape and / or location of assist features, adjustments applied by resolution enhancement techniques (RET), etc.

[0187] The second group of one or more variables related to one or more manufacturing processes before or after pattern transfer in the lithographic apparatus may be one or more variables described above. Similar to the first contribution 1610, the second contribution 1620 may be substrate independent or substrate dependent. In an embodiment, the second contribution 1620 may be reused across each substrate. Therefore, the second contribution 1620 may be pre-characterized and obtained from a database during the reconstruction process. Examples of the second group of one or more variables may include, but are not limited to, various characteristics of processes upstream or downstream of pattern transfer in the lithographic apparatus (such as spin coating, PEB, development, etching, deposition, doping and / or packaging).

[0188] The first contribution 1610, the second contribution 1620 and / or the third contribution 1630 may be provided by, for example, Figure 8-11 In one embodiment, the third contribution 1630 (ie, the patterning device fingerprint) can be obtained by directly measuring the patterning device using a patterning device metrology tool.

[0189] After determining the fingerprint 1640 of the strong variable, the value of the strong variable 1660 can be obtained by combining the fingerprint 1640 of the strong variable with a certain value 1650 of the strong variable. In an embodiment, the certain value of the strong variable can be a nominal design value. In an embodiment, the strong variable can be an average of a set of measurements of the strong variable on a substrate. The set of measurements of the strong variable can be performed on the same feature in two or more dies on a substrate.

[0190] Given the values ​​of one or more strong variables in the parameterized model (e.g., by fixing the values ​​of the one or more strong variables, or by limiting the value of each of the one or more strong variables to a predetermined range (e.g., within 10%, within 5%, within 3%, within 1%)), one or more weak variables can be adjusted until 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. When the calculated radiation distribution is substantially similar to the measured radiation distribution, or the difference is within a predetermined tolerance threshold, the values ​​of the one or more weak variables can be output.

[0191] As described above, the value of one or more weak variables can be used to predict whether there are defects caused by one or more downstream processes (e.g., PEB, development of the resist layer, etching, deposition, doping and / or packaging) after exposure. If a defect is predicted, the value 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 can be adjusted to obtain a new fingerprint of the strong variable. This is done so that a new set of values ​​for one or more weak variables can be reconstructed using the process described above. Such adjustments can be performed iteratively until no defects are predicted based on a new set of values ​​for the one or more weak variables.

[0192] In other applications of the contribution / fingerprint discussed above, one or more contributions / fingerprints can be used to predict the contour of a pattern. In this context, a contour is the contour of the shape of the feature of the pattern transferred to the substrate. For example, the contour can be visualized 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 feature transferred to the substrate. However, the contour can also be generated by a mathematical process (e.g., simulation) to create an electronic representation of the pattern feature because it is expected to be transferred to the substrate. Although the contour is typically in the form of a line, the contour used here can be more hyper-encapsulated into data describing the boundary of the feature. The contour does not need to be continuous; that is, if the discontinuous contour and / or data fully describe the boundary of the feature, the contour and / or data can be discontinuous around the feature. In an embodiment, the contour can be two-dimensional (i.e., defined as a plane) or three-dimensional. In an embodiment, the contour can extend in a plane substantially parallel to the surface of the substrate on which the pattern is formed. In an embodiment, the contour may extend in a plane that is substantially perpendicular to the surface of the substrate on which the pattern is formed; in this case, the contour may be characterized as a profile, and may be in two or three dimensions.

[0193] To predict the profile, one or more contributions / fingerprints may be obtained as described herein and used to select a nominal profile and / or to modify the nominal profile in order to obtain a predicted profile. Fig.13 , depicts an embodiment of a flow diagram of a method for predicting a profile. At 1700, a nominal profile of a feature of a pattern is determined. In an embodiment, the nominal profile is the profile expected in the resist. In an embodiment, the nominal profile is the profile expected in the developed resist.

[0194] In an embodiment, the nominal profile may be obtained by mathematical calculation via a model and / or simulation. In an embodiment, a simulator or model (e.g., a simulator such as ASML's Tachyon product) may determine the expected profile of the feature of the pattern at an applicable design value for one or more process variables of the patterning process of the feature. The profile obtained by calculation may then be designated as the nominal profile. Similarly, the simulator or model may determine the profile at various different values ​​of the 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 being at different values ​​of the one or more process variables. These profiles obtained by calculation may then be designated as nominal profiles, and each nominal profile is associated with different values ​​of the one or more process variables. In an embodiment, these nominal profiles are determined for different focus settings or conditions, so each nominal profile may be associated with different focus settings or conditions (such as a certain deviation from optimal focus). Although the following description focuses on focus settings or conditions, the nominal profile may be determined for settings or conditions other than focus, and may be determined for various combinations of settings or conditions.

[0195] In an embodiment, the impact of one or more process variables is evaluated, and the impact of the nominal profile on one or more other process variables is determined for the one or more process variables. In an embodiment, the one or more other process variables evaluated are one or more process variables that have an impact on the shape and / or size of the profile. Therefore, in an embodiment, the impact of focus on one or more other process variables (such as CD) is determined when the nominal profile is determined for a focus setting. In an embodiment, the impact can be determined using a focus exposure matrix (FEM) type process, where a pattern is evaluated under at least different focus settings or conditions. The CD at those different focus settings or conditions can then be determined in order to evaluate how much of a change in CD is caused by focus. In an embodiment, the impact described above can be determined experimentally using one or more processed substrates (which are then measured by a metrology tool). In an embodiment, the impact described above can be determined using a simulator.

[0196] In addition to or as an alternative to determining the nominal profile by calculation, in an embodiment, the nominal profile can be obtained experimentally. For example, the feature can be created on one or more substrates at applicable design values ​​of one or more process variables for the patterning process, and then the feature is measured (e.g., using a scanning electron microscope) to derive the profile of the feature. The profile obtained by measurement can then be designated as the nominal profile. In addition or alternatively, the feature can be created on one or more substrates at various different values ​​of one or more process variables (e.g., one or more optical settings or conditions as described herein), and then the feature is measured (e.g., using a scanning electron microscope) to derive multiple profiles of the feature, each profile being at a different value of the one or more process variables. These profiles obtained by measurement can then be designated as nominal profiles, and each nominal profile is associated with a different value of the one or more process variables. Therefore, as a specific example, each nominal profile can be associated with a different focus setting or condition (such as a certain deviation from optimal focus).

[0197] Thus, in embodiments, the nominal profile may provide an indication of the shape of the profile. For example, the nominal profile may provide an indication of the shape of the profile under a particular focus condition. Thus, where multiple nominal profiles are obtained under multiple different focus conditions, each nominal profile may provide an indication of the shape of the predicted profile under the applicable focus condition.

[0198] Thus, in embodiments and as will be discussed further, in the case of multiple nominal profiles, each associated with a different value of one or more process variables (e.g., focus), the shape of the profile may be predicted by reference to the nominal profiles for any value of the one or more process variables. If the nominal profiles are not available for a particular value of the one or more process variables, the profile may be generated by interpolation, extrapolation, etc. Thus, as an example, for any focus value at a location on a substrate, the shape of the profile of an applicable pattern feature of interest may be predicted.

[0199] Thus, at 1710, a first contribution / fingerprint may be obtained for one or more process variables for which a nominal profile has been determined. The first contribution / fingerprint may be obtained using any of the techniques described herein. In an embodiment, the first contribution / fingerprint corresponds to the situation before etching.

[0200] In an embodiment, the first contribution / fingerprint has focus, thus, in an embodiment, the first contribution / fingerprint is a focus map across the substrate. In an embodiment, the first contribution / fingerprint may be generated based on data obtained from a lithographic apparatus used to pattern the substrate. For example, the lithographic apparatus may provide focus information (e.g., focus residual error, etc.) and / or characteristics of high frequency stage movement (e.g., MSD) to construct a focus map. Fig.14 An example focus map 1800 for a patterning process is shown, where different shading schematically represents different deviations from a nominal focus (eg, best focus, average focus, etc.).

[0201] At 1720, the first contribution / fingerprint 1710 is used to select a nominal profile for a feature of interest. For example, at a particular location on the substrate and for a particular feature of interest, values ​​of one or more process variables (for which nominal profiles have been determined) may be determined from the first contribution / fingerprint 1710, and then the associated nominal profile may be selected using these values. Thus, in examples where the first contribution / fingerprint 1710 is a focus map, the focus estimate at the substrate location within the focus map may be used to obtain the associated nominal profile as a prediction of the profile. Thus, a predicted profile may be determined for each feature and each substrate location.

[0202] Reference again Fig.14 , depicts an example of this choice. Fig.14, nominal profiles 1810, 1812, 1814 are shown at best focus. Now, at a location on focus map 1800 associated with nominal profile 1812, the focus map indicates that the focus is at or close to best focus. Therefore, for that location, nominal profile 1812 will be selected as the predicted profile. For the location associated with nominal profile 1810, the focus map indicates that the focus is at negative defocus -F. Therefore, in that case, instead of using nominal profile 1810, the nominal profile determined for negative defocus -F, i.e. nominal profile 1820, will be selected. Fig.14 As can be seen, nominal profile 1820 has the characteristics of the feature, but has a different shape due to the negative defocus -F. Similarly, for the location associated with nominal profile 1814, the focus map indicates that the focus is at positive defocus +F. Therefore, in this case, instead of using nominal profile 1814, the nominal profile determined for positive defocus +F will be selected, namely nominal profile 1830. Fig.14 As can be seen, the nominal profile 1830 has the characteristics of the features described, but has a different shape due to the positive defocus +F. Thus, at a focus of -F, the nominal profile at best focus changes shape and similarly, for a focus of +F, the nominal profile at best focus changes shape. Thus, for example, if F is the deviation from best focus and +F and -F have the same absolute value, the corresponding profile shape change may be similar to Fig.14 Same as shown in .

[0203] Return to reference Fig.13 At 1730, a second contribution / fingerprint may be obtained for one or more process variables other than the one or more process variables for which the nominal profile has been determined. The second contribution / fingerprint 1730 may be obtained using any of the techniques described herein. In an embodiment, the second contribution / fingerprint corresponds to a post-etch situation.

[0204] In an embodiment, the second contribution / fingerprint 1730 has a critical dimension, and thus, in an embodiment, the second contribution / fingerprint is a critical dimension map across the substrate (e.g., a critical dimension uniformity map). In an embodiment, the contribution / fingerprint is generated based on data measured on one or more substrates having a pattern using a metrology tool after an etching step of a patterning process. Fig.15 An example CD map 1900 for a patterning process is shown, where different shading schematically represents different deviations from a nominal CD (e.g., a designed CD, an average CD, etc.). Thus, for example, CD map 1800 may represent a CD measured in terms of anchoring and plotted as a % of the average CD.

[0205] In an embodiment, the second contribution / fingerprint is corrected for the effect 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, where the first contribution / fingerprint is a focus map and the second contribution / fingerprint is a critical dimension map, the second contribution / fingerprint may be corrected for the effect of focus (e.g., focus information (e.g., focus residual error, etc.) and / or characteristics of high frequency stage movement)) on the critical dimension in the second contribution / fingerprint. Details of determining such effects are described above. For example, a FEM may be used to isolate the effect of focus on the CD produced during the pattern transfer step, and then remove the effect from the CD measurement after etching. Additionally or alternatively, various lithographic apparatus signals may be processed to obtain an estimate of focus and its effect on CD during pattern transfer, and then remove the effect from the CD measurement after etching. As will be appreciated, the correction may be performed in a variety of ways, including incorporating the correction directly into the second contribution / fingerprint, performing the correction after selecting a value from the second contribution / fingerprint (as discussed below with respect to 1740), and the like.

[0206] At 1740, the second contribution / fingerprint 1730 is used to modify the nominal profile for the feature of interest. In an embodiment, the nominal profile is the nominal profile selected at 1720. However, if a given nominal profile has already been selected for the feature of interest without using the selection step at 1720, the selection at 1720 may be skipped (but the modification is performed). Similarly, if a nominal profile is selected at step 1720 and it does not need to be modified, the modification at 1740 may be skipped.

[0207] Thus, at 1740, for example, at a particular location on the substrate and for a particular feature of interest, values ​​of one or more other process variables are obtained from the second contribution / fingerprint 1730, and the values ​​are then used to determine an appropriate modification of the nominal profile. In an embodiment, the modification is a change in the size of the nominal profile. Thus, in examples where the second contribution / fingerprint 1730 is a critical dimension map, the critical dimension estimate at the substrate location within the critical dimension map can be used to modify the size of the nominal profile (e.g., the nominal profile selected at 1720) as a prediction of the profile. Thus, a predicted profile can be determined for each feature and each substrate location.

[0208] In an embodiment, it is assumed that the values ​​of one or more other process variables obtained at a certain location from the second contribution / fingerprint 1730 apply to the entire feature of interest. Therefore, if the critical dimension of a feature represented in the second contribution / fingerprint 1730 deviates from a certain critical dimension (e.g., the average critical dimension) by a certain amount (e.g., 5%), all critical dimensions of any feature at the same location will deviate by the same amount. Therefore, this assumption means that the entire profile is resized by the same amount as the deviation of the critical dimension. Therefore, assuming that the overall profile size of a feature at a certain location on the substrate is relatively changed by the same amount as the critical dimension of the anchoring aspect at the same location (which has been measured to obtain the second contribution / fingerprint 1730), the nominal profile can be reduced by x% when the critical dimension is reduced by x%, and expanded by x% when the critical dimension is increased by x%. The change is provided uniformly across the entire profile.

[0209] Reference again Fig.15 , depicts an example of this size variation. Fig.15 , nominal profiles 1910, 1912, 1914 are shown. Now, at a location on critical dimension map 1900 that is associated with nominal profile 1912 (which may be selected using step 1720), the critical dimension map indicates that the critical dimension corresponds to the nominal critical dimension (e.g., a designed critical dimension, an average critical dimension, etc.). Therefore, for that location, nominal profile 1912 will be selected as the predicted profile. For the location associated with nominal profile 1910, the critical dimension map indicates that the critical dimension is reduced by a certain amount (e.g., -x%). Therefore, in this case, instead of using nominal profile 1910, nominal profile 1910 is reduced by a certain amount (e.g., -x%) to obtain predicted profile 1920. As shown in FIG. Fig.15 As shown, profile 1920 has the features of the features described, but has smaller dimensions due to the lower critical dimension. Similarly, for the location associated with nominal profile 1914, the critical dimension map indicates that the critical dimension is increased by a certain amount (e.g., +x%). Therefore, in this case, instead of using nominal profile 1914, the dimensions of nominal profile 1914 are increased by a certain amount (e.g., +x%) to obtain predicted profile 1930. Fig.15 As shown, profile 1930 has the characteristics of the feature, but has a larger size due to the larger critical dimension. Thus, when having a critical dimension of -x%, the nominal profile shrinks uniformly but still maintains its shape, and when having a critical dimension of +x%, the nominal profile increases in size uniformly but still maintains its shape.

[0210] Thus, in an embodiment, given these two assumptions (i.e., that the value of some one or more process variables (e.g., focus) can predict the profile shape, and the value of some one or more other process variables (e.g., CD) can predict the profile size), the profile shape and size can be predicted for a feature based on values ​​selected from one or more contributions / fingerprints. In particular, for each location on the substrate, the full profile of one or more features of interest can be predicted. In an embodiment, the features of interest are identified hot spots.

[0211] In certain embodiments, the profile is predicted from critical dimension and focus measurements. In certain embodiments, the profile is estimated using critical dimension and focus fingerprints.

[0212] At 1750, the predicted profile can be used in a variety of applications. For example, the profile can be checked by itself, or with respect to one or more other profiles, to determine whether a defect is predicted (e.g., one or more checks can be performed for necking, bridging, line backing, line thinning, overlap, resist top loss, and / or resist undercut). For example, the technique can be used to determine bridging defects. These defects are caused by two features that touch each other, which in principle occur at any point on the profile of the two features (depending on the specific CD, focus, and / or overlap conditions at the site). The use of the profile enables a more robust assessment of such defects than, for example, the assessment of dimensions at a cut line on an adjacent feature.

[0213] As another example, the profile can be used to assess edge placement position and / or error (which can also be used to identify defects such as bridging). In fact, the technique can provide a computational form of metrology to determine edge placement error. For example, using the predicted profile, a "virtual" edge placement error can be predicted. For example, this can be used for edge placement error driven multi-patterning defect prediction. Thus, CD and focus fingerprints can be used to estimate edge placement error driven defects.

[0214] Examples of where the predicted profile can be used to identify potential defects are in the spacer and cut layer processes. Fig.16A - shown in C. Fig.16A An example spacer and cutting layer process is depicted where pattern 2010 is used to "cut" line 2000 . Fig.16A A nominal process is depicted, where the line 2000 and pattern 2010 are in the desired alignment, size, etc. The result of such a process would be a center line 2000 clearly cut by the pattern 2010. Now, the diagrams 1800 and 1900 shown schematically in FIG. 16 may be used to apply Fig.13 The process of obtaining the predicted contours of the line 2000 and the pattern 2010 is determined. Fig. 16B In the example shown in , it is determined that the outline of pattern 2010 has been predicted to increase in size (although in the example, the shape has not changed but the shape can change), while the predicted outline of line 2000 is as expected. Now, Fig. 16C The result of the predicted profile if pattern 2010 is used in the spacer and cut layer process is shown. As seen at 2020, it would be undesirable for pattern 2010 to cut a portion of the upper and lower lines 2000. Therefore, in an embodiment, when pattern 2010 is used to cut line 2000, the predicted operation of the spacer and cut layer process can be marked as producing a potential defect.

[0215] As another example, the predicted profile can be used to determine potential defects in a lithography-etch-lithography-etch (LELE) process. Fig.17A - shown in C. Fig.17A An example lithography-etch and lithography-etch process is depicted, where lines 2100 are created in a first lithography-etch process, and patterns 2110 are interleaved with lines 2100 by a second lithography-etch process. Fig.17A A nominal process is depicted, where the line 2100 and pattern 2110 are in the desired alignment, size, etc. The result of such a process would be a designed separation between pattern 2110 and line 2100. Now, the diagrams 1800 and 1900 schematically shown in FIG. 17 may be used to apply Fig.13 The process is to achieve the determination of the predicted contours of the line 2100 and the pattern 2110. Fig. 17B In the example shown in , it is determined that the outline of pattern 2110 has been predicted to increase in size and change in shape, while the predicted outline of line 2100 is as expected. Fig. 17C The results of using the predicted profile of pattern 2110 in the lithography-etch and lithography-etch processes are shown. As seen at 2120, it would be undesirable for pattern 2110 to be too close to the lower line 2100 (e.g., the spacing between these features is below a certain threshold); that is, it is an overlapping area or violates the minimum distance requirement. This may lead to bridging defects. In addition, pattern 2110 may have a necking defect 2130, where the feature has been reshaped so that it has become too narrow (e.g., the width has been below a threshold). Therefore, in an embodiment, when pattern 2110 is created together with line 2100, the predicted operation of the lithography-etch and lithography-etch processes can be marked as producing one or more potential defects. Therefore, in an embodiment, for defect prediction in multi-exposure LELE type applications, the predicted profile should be able to improve the prediction ability of necking and / or bridging defects compared to using only defect indicators / cut lines.

[0216] In another possible use of the predicted profile, the predicted profile can be used for model calibration, in particular calibration of an optical proximity effect correction model. The predicted profile enables etch fingerprint and / or focus fingerprint correction in the measured gauge (profile). For example, the predicted profile can be used for mask data preparation of a model after calibration etching.

[0217] Thus, in embodiments, the techniques enable profile prediction from a virtual substrate; thus, the techniques combine metrology with computation to generate profiles without having to measure them. In embodiments, the techniques enable prediction of profile and edge placement error variations across a substrate assuming appropriate fingerprints (e.g., critical dimension fingerprints after etching and lithography equipment focus fingerprints). In embodiments, the techniques enable better prediction capabilities for multiple patterning. In embodiments, the techniques enable pattern control based on predicted profiles using edge placement optimization.

[0218] In other embodiments, 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 at least on the substrate and the pattern forming device (e.g., mask). Alignment marks can also be provided on other structures (such as substrate stages). Alignment marks are measured using alignment sensors to determine the spatial position of one or more specific parts in the plane on the substrate surface and / or on the pattern forming device (including, for example, the relative position between the parts on the substrate and the pattern forming device). The measured spatial position is used to facilitate the proper positioning in the (e.g.) XY plane when the pattern is transferred to the substrate, that is, the pattern is provided to the appropriate part on the pattern forming receiving surface of the substrate.

[0219] Such proper positioning is particularly important in cases where a pattern has previously been applied to a substrate and a subsequent pattern should be aligned with the previous pattern; misalignment of a pattern can be characterized as an overlay error, as described herein. In order to help facilitate the correct alignment of a first device pattern with a second device pattern that is subsequently applied, alignment marks for proper positioning of the second device pattern can be generated when the first device pattern is generated. For example, the pattern forming device pattern that generates 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, those one or more alignment marks associated with the first device pattern are processed together with the first device pattern to generate an alignment mark structure in a layer in the substrate associated with the first device pattern. Then, when it is desired to apply the second device pattern, those one or more alignment marks associated with the first device pattern (often typically applied on top through one or more layers, such as a resist) can be measured to determine, for example, the location of the first device pattern so that the second device pattern associated with the first device pattern can be accurately placed.

[0220] Accurate alignment helps ensure good overlay performance and thus high yield in production. However, space limitations on a substrate designed to create a device mean that the alignment marks cannot be placed anywhere on the substrate (after all, a large portion of the substrate should be used to apply the pattern used to create the device). In addition, time constraints limit the number of alignment marks per production substrate that can be measured during production while maintaining sufficient throughput of the manufacturing system (e.g., the number of production substrates processed per hour).

[0221] Therefore, in a typical arrangement, a certain number of alignment marks across the substrate (which will typically have multiple dies / fields across the substrate where the pattern is transferred from the pattern forming device) are measured to provide very good spatial coverage of the location of the site on the substrate across the substrate. In an example scheme, the substrate alignment measurement sequence can measure 20-100 alignment marks (sites) across the substrate. The results of these measurements capture the global fingerprint across the substrate, and the spatial frequency of each substrate is relatively low. The measurement results are used in conjunction with an alignment mathematical model. The purpose of the model is to represent the deviation between the transfer position of the device pattern features and the ideal grid, so that, for example, appropriate corrections made by the equipment during the device manufacturing process can be performed based on the output of the model. As will be understood, more than 20-100 alignment marks can be set across the substrate, but due to (for example) production volume restrictions or constraints, only 20-100 (for example, 20-40) alignment marks are sampled. In addition, all or most of these sampled alignment marks can be set in an area that cannot be used for device patterns, such as device patterns in scribing lines.

[0222] However, this relatively sparse sampling of alignment marks cannot capture substrate fingerprints with high spatial frequency. As a result, overlay performance may suffer.

[0223] In order to capture local effects (i.e., to obtain higher spatial frequencies), an alignment scheme within a field can be used. However, it may have one or more disadvantages. For example, it is necessary to perform relatively dense measurements of alignment marks, which may not be achieved without affecting production volume. In addition, valuable intra-die space will need to be occupied by alignment marks. And due to constraints (such as production volume), alignment within a field can be limited to fewer parameters than those corrected by equipment (e.g., lithography equipment) during device manufacturing. For example, a model for alignment within a field can be defined as 6 parameters per field (e.g., magnification (M) of the pattern forming device pattern, rotation (R) around the z-axis, translation (Cx, Cy) on x and y, magnification (My) in the y direction, and scanning skew (RI)), even though the lithography equipment may be able to correct higher-order pattern transfers per device.

[0224] Thus, it is desirable to have a denser alignment fingerprint (for example) without having to perform more alignment mark measurements (such as a dense intra-field alignment). Thus, using the techniques described herein, a relatively dense alignment fingerprint (or hybrid dense alignment map (HDAM)) is computed by combining the measured alignment data with contextual information from relevant contributors to the alignment. That is, a combination of fingerprints can be combined to obtain a derived fingerprint for alignment, in the context of other parameters such as overlap and CD, similar to those described above.

[0225] In particular, in production, the shifting of at least parts of the alignment marks (and parts of the device pattern) may be caused by local effects such as substrate height variations due to, for example, contamination, projection system aberrations, patterning device writing errors (i.e., errors in creating the pattern on or by the patterning device, such as errors in creating the pattern in an absorber layer of a mask), heating, process effects (such as chemical mechanical planarization (CMP), etching, etc.), etc. One or more of these local effects may effectively have a relatively high spatial frequency fingerprint, but the fingerprint may not be captured by typical alignment mark measurement sampling used in production (which is limited by, for example, production throughput, and / or available die / field space for alignment marks).

[0226] Thus, in an embodiment, the alignment contribution of one or more of these local effects is determined and combined with the alignment measurements at a relatively low density to produce a higher density alignment fingerprint. The contribution to the alignment of one or more of the various local effects may be derived from other metrology measurements in a lithocell (e.g., in a lithographic apparatus) and / or calculated / measured "offline" (i.e., without the need for the contribution to be calculated or measured by the lithocell (for which the HDAM is determined) during processing of a particular substrate).

[0227] therefore, Fig.18 An example of obtaining a derived contribution 2275 to the alignment of a substrate is schematically shown, the derived contribution being a combination of contributions of multiple process parameters (one or more of which may be derived contributions). Thus, the derived contribution 2275 may be obtained using a measured contribution from alignment mark measurement 2200 combined with contributions of each of one or more process parameters (e.g., local effect process parameters), such as substrate height 2205 due to, for example, contamination, one or more process effects 2210 (such as chemical mechanical planarization (CMP), etching, etc.), heating 2215 (e.g., heating of the patterning device due to an irradiation beam to obtain a patterned beam for exposure of the substrate), projection system aberrations 2220, and / or patterning device write errors 2225. It is noted that the process parameter data may be obtained from a lithography apparatus or other patterning process apparatus, and may be a byproduct of producing a substrate as part of a patterning process. None of the contributions associated with these one or more process parameters necessarily require measurement of alignment marks on the substrate using an alignment sensor.

[0228] Thus, in the alignment scenario, an example of an alignment fingerprint (A') of an alignment mark measurement 2200 is shown as contribution 2240, an example of a contribution to alignment of a substrate height or unevenness (SH) 2205 is shown as contribution 2245 (a schematic diagram showing substrate height data across the substrate, which can be converted into corresponding effects on alignment as described herein), an example of a contribution to alignment of one or more process effects (PE) 2210 (such as chemical mechanical planarization (CMP), etching, etc.) is shown as contribution 2250 (a schematic diagram showing one or process effect data ( 2240). An example of a contribution to the alignment of heating (RH) 2215 is shown as contribution 2255 (a schematic diagram shows mask heating data across the exposure field of the mask, which can be converted into a corresponding effect on the alignment at the substrate as described herein), an example of a contribution to the alignment of projection system aberrations (PA) 2220 is shown as contribution 2260, and an example of a contribution to the alignment of patterning device write errors (RWE) 2225 is shown as contribution 2265. It will be understood that not all of these contributions 2245-2260 need to be combined with contribution 2240; rather, one or more contributions 2245-2260 can be combined with contribution 2240. If applicable, these contributions can be obtained by simulation, mathematical modeling and / or measurement / experimentation. For example, these contributions can be obtained by simulation based on physical models, empirical modeling and / or dedicated measurement results.

[0229] Each of one or more of these contributions 2245-2260 may be combined 2270 with contribution 2240 to obtain a derived contribution 2275. Although element 2270 is shown as a plus sign, the operation at 2270 need not be an addition, for example, it may be a multiplication, convolution, etc. by using a neural network. The operation on one or more contributions may be different from another one or more contributions (e.g., the addition of contributions 2245 and 2250 with contribution 2240, and the convolution of the sum with one or more contributions 2255 to 2265). In an example, the combined contribution to the alignment may be represented as A(x,y)=A′(x,y)+b1*F(SH)(x,y)+c1*F(PE)(x,y)+d1*F(RH)(x,y)+e1*

[0230] F(PA)(x,y)+f1*F(RWE)(x,y)…. Various functions may be obtained by simulation, mathematical modeling and / or experimentation. In addition, there may be cross-terms not shown here (such as focus as a function of RH times PA, etc.). In order to obtain an absolute value of the alignment, a nominal or simulated value of the alignment may be combined with these contributions. These coefficients (such as b1, c1, etc.) are the sensitivity of the alignment to the corresponding processing parameters or functions thereof. Some contributions are across the substrate (e.g., process effects, substrate height or unevenness, etc.), but in an embodiment, one or more contributions may be repeated across the substrate for each tube die / field (which may then depend on (for example) the applicable conditions in each instance) One or more contributions such as the contribution of heating (RH) 2215, the contribution of projection system aberrations (PA) 2220, and the contribution of pattern forming device write errors (RWE) 2225. As noted above, the contribution 2275 can be characterized as a fingerprint because the contribution can be spatially defined across the substrate / die / field. Additionally, the conversion of contributions to absolute values ​​can be characterized as a fingerprint, since the contribution can be spatially defined across the substrate / die / field. As will be appreciated, data from processing multiple substrates using a patterning process can be used to derive the corresponding contribution. This data may already be available, as it may be a byproduct of processing these substrates.

[0231] Returning to the example of processing parameters related to local effects, the contribution to alignment of substrate height or unevenness 2205 can be a leveled substrate height map converted into in-plane displacements within the substrate (e.g., there can be more than 1000 points, more than 5000 points, more than 10000 points, more than 20000 points, or more than 50000 points per substrate, so the corresponding in-plane displacements correspond to the alignment contribution). The in-plane displacements that affect alignment and correspond to substrate height or unevenness can be obtained through simulation, mathematical modeling and / or measurement / experimentation. Therefore, leveling measurements that are sensitive to process-induced contamination and converted into in-plane displacements can be used to refine and improve alignment measurement results to a higher density. In an embodiment, the leveling measurement is a measurement of the substrate state when the alignment measurement is performed. Therefore, in an embodiment, the fingerprint associated with substrate height or unevenness may be specific to the particular substrate under consideration.

[0232] Using special techniques (such as 3D-NAND), after removing one or more process-dependent artifacts, leveling the substrate height map can particularly explore alignment shifts at the level within the field (for example, using a higher number of leveling points). It is well known that using optical level sensors, different substrates and different parts of the substrate will interact with the measuring radiation beam in different ways. In other words, the height measurement results obtained by the level sensor are subject to process-dependent effects and do not always give the true height. In particular, it is known that apparent surface depressions will be caused when the light reflected from the substrate is subject to the so-called Goos-Haenchen shift. This effect is different for different materials and depends to a large extent on the structure and materials of several layers. Therefore, the apparent surface depression may vary significantly from layer to layer and across the substrate. For example, heavily metallized areas will reflect light more reliably than areas that are mainly dielectric materials. Thus, one or more techniques (such as described in U.S. Patent No. 7,265,364, U.S. Patent Application Publication No. US2010 / 0233600, and U.S. Patent Application Publication No. US2016-0370711, the entire contents of which are incorporated herein by reference) can be used to correct and / or identify one or process-dependent artifacts for removal.

[0233] Another contribution due to processing parameters related to local effects is a fingerprint associated with one or more process effects due to processing other than the lithographic pattern transfer step (e.g., effects on alignment marks due to etching, CMP, and / or one or more other process steps). Figure 3-6 The metrology equipment depicted and described uses "offline" measurements to determine data for one or more process effects. In an embodiment, the fingerprint of one or more process effects may be a derived contribution determined as described above. In-plane shifts that affect alignment corresponding to one or more process effects may be obtained by simulation, mathematical modeling and / or measurement / experimentation. In an embodiment, process effect data is associated with the creation of alignment marks before alignment measurements are performed for a specific lithographic pattern transfer step based on the alignment marks. In an embodiment, if the substrate under consideration is subject to the same process effect, the fingerprint associated with the process effect may not depend on the specific substrate being processed. However, in some cases, the fingerprint associated with the process effect may be specific to a specific substrate, where different substrates may be subject to different process effect values.

[0234] Another possible processing parameter is a projection system aberration that may induce a pattern shift. In an embodiment, a sensor (e.g., ASML's ILIAS sensor, which is an interferometer-type measuring device for measuring aberrations and other parameters) may be used in a lithographic device to measure projection system aberrations. In an embodiment, the projection system aberrations of the alignment mark pattern shift are calculated based on the aberration residuals measured by the sensor. The in-plane displacement that affects the alignment corresponding to the projection system aberrations can be obtained by simulation, mathematical modeling and / or measurement / experimentation. In an embodiment, before performing alignment measurements for a specific lithographic pattern transfer step based on the alignment mark, the projection system aberration data is associated with the creation of the alignment mark. In an embodiment, a fingerprint associated with the projection system aberration can be determined for a die / field and then repeatedly applied to one or more other dies / fields across the substrate. Therefore, the fingerprint associated with the projection system aberration may not depend on the specific substrate being processed.

[0235] Heating is another possible processing parameter that may induce pattern shift. In an embodiment, heating is heating of a pattern forming device (e.g., a mask) and / or heating of a projection system. In an embodiment, heating is caused by prolonged exposure of the pattern forming device and / or projection system to irradiation for pattern transfer. In an embodiment, the heating can be measured in a lithographic apparatus using a sensor (e.g., a temperature sensor). In an embodiment, the heating can be calculated based on first principles using one or more pattern forming devices and / or projection system properties (e.g., thermal material properties) and irradiation doses, and / or based on a mathematical model calibrated with appropriate data derived from a lithographic apparatus to calculate the heating. The in-plane displacement that affects the alignment corresponding to the heating can be obtained by simulation, mathematical modeling and / or measurement / experimentation. In an embodiment, the heating is associated with the creation of an alignment mark before an alignment measurement is performed for a specific lithographic pattern transfer step based on the alignment mark. In an embodiment, a fingerprint associated with heating can be determined for a die / field and then repeatedly applied to one or more other dies / fields across a substrate. Therefore, the fingerprint associated with heating may not depend on the specific substrate being processed.

[0236] Patterning device write errors are another possible processing parameter that may induce pattern shifts. In an embodiment, patterning device write errors are errors associated with images that constitute the patterning device itself or the image constituted by the patterning device itself. For example, the pattern in the absorber of the mask may not be perfectly created, so the change from the designed pattern can be characterized as a patterning device write error. In an embodiment, the patterning device write error can be obtained by "offline" measurement using a metrology device. The in-plane shift that affects the alignment corresponding to the patterning device write error can be obtained by simulation, mathematical modeling and / or measurement / experimentation. In an embodiment, the patterning device write error is associated with the creation of the alignment mark before the alignment measurement is performed for a specific lithographic pattern transfer step based on the alignment mark. In an embodiment, the fingerprint associated with the patterning device write error can be determined for a tube die / field and then repeatedly applied to one or more other tube die / fields across the substrate. Therefore, the fingerprint associated with the patterning device write error may not depend on the specific substrate being processed.

[0237] Information about one or more other possible process parameters may also or alternatively be included (if available), such as servo control (moving average (MA) and / or moving standard deviation (MSD) in X, Y and / or Z), patterning device shape (e.g., bow in Z direction), effect of pellicle on patterning device, projection system reference axis variation, etc. The corresponding in-plane shifts that affect alignment may be obtained by simulation, mathematical modeling, and / or measurement / experimentation. In an embodiment, one or more of these process parameters (e.g., patterning device shape, effect of pellicle, projection system reference axis, etc.) are associated with the creation of alignment marks before alignment measurements are made for a particular lithographic pattern transfer step based on said alignment marks. Information about these one or more other possible process parameters may be derived from metrology measurements in the lithographic apparatus (or lithocell), derived from "offline" metrology measurements, or determined by calculation (e.g., simulation, calibrated mathematical model, first principles, etc.).

[0238] Thus, by combining alignment measurement data and the impact on alignment due to one or more process parameters related to local effects (the process parameter data may be, for example, lithographic apparatus or other lithocell metrology data, and / or it may be process and application dependent), a hybrid dense alignment map (HDAM) may be calculated, the HDAM being a pre-lithographic pattern transfer output for control of, for example, lithographic pattern transfer. Since the hybrid dense alignment map uses data obtained from separate sources, the calculated metrology based may have an indication of contributions from process contribution and application contribution, respectively.

[0239] Fig.19 A specific, non-limiting example workflow for computing HDAM is shown in FIG. That is, Fig.19 An example of deriving combined contributions for alignment is shown schematically, where Fig.18 An example HDAM 2275 is created from the four first inputs listed in the example workflow of . In the example, an alignment fingerprint 2240 of alignment mark measurements of the particular substrate under consideration is combined with three other contributions that are not obtained through alignment measurements but are converted into effects on alignment as described above to obtain the HDAM 2275. The other three inputs are a contribution 2245 to alignment of substrate height or unevenness 2205 (a schematic diagram shows substrate height data across the substrate, which can be converted into corresponding effects on alignment as described herein), a contribution 2250 to alignment of one or more process effects (such as chemical mechanical planarization (CMP), etching, etc.) (a schematic diagram shows one or process effect data (such as etching effect data) across the substrate, which effect data (if necessary) can be converted into corresponding effects on alignment as described herein), and a contribution 2255 to alignment of patterning device heating (a schematic diagram shows patterning device heating data across the exposure field of the mask, which heating data can be converted into effects on alignment at the substrate as described herein, and the effects in the die / field can be repeated across the substrate). As will be appreciated, the various contributions may be remeshed and / or appropriately scaled to form the HDAM. Additionally, the density of the various contributions may be adjusted as desired to adjust the overall density of the HDAM. Thus, by combining the alignment data with the alignment effects of one or more processing parameters, a significantly more computationally intensive alignment map may be created than the alignment data alone.

[0240] HDAM can be used for various purposes. An example use is as an input to control a patterning process. For example, HDAM can be an input to control pattern transfer of a lithographic apparatus. In this regard, it can be used as an input to determine a corrected inter-field and / or intra-field substrate alignment model in a lithographic apparatus. The combined dense alignment substrate map provides dense metrology information at both the inter-field and intra-field levels, and thus can support the use of a high-order substrate alignment model as part of a control loop rather than using alignment data alone.

[0241] Depending on the use case and input data, the alignment density can be enhanced as desired at both the inter-field and intra-field levels. Using this higher density of metrology, higher order inter-field and / or intra-field alignment models can have potentially higher accuracy for model content (if a higher order alignment model is available) compared to typical alignment techniques used in production, which in turn improves overlay performance at the per-substrate level. For example, Fig. 20An example of how a patterning process corrected using a fingerprint determined according to an existing alignment measurement scheme is converted into an overlay error fingerprint is schematically shown. An alignment fingerprint 2240 is obtained using an existing alignment measurement technique, and the alignment fingerprint 2240 is used to correct the patterning process using an alignment model. The overlay fingerprint of the corrected patterning process is shown as 2300. As can be seen from the fingerprint 2300, there are quite a few vectors with relatively high magnitudes, indicating that there are relatively significant overlay errors at different locations across the substrate. In contrast, Fig.21 An example of how a patterning process corrected using a derived alignment fingerprint calculated as described herein is converted into an overlay error is schematically shown. A derived fingerprint or HDAM 2275 is obtained using the techniques described herein and is used to correct the patterning process using an alignment model (which may be a higher order model than that used for the alignment fingerprint 2240 alone). In this example, the HDAM has a sampling of approximately 1000 sites per substrate, which is significantly higher than using alignment measurements alone during production (given the time constraints of production) and is significantly denser and has a larger pattern coverage on the device than using alignment measurements alone during production (given the intra-die / field space constraints for placing alignment marks). The overlay fingerprint of the corrected patterning process is shown as 2310. As can be seen from the fingerprint 2310, there are very low magnitude vectors, showing that there are relatively insignificant overlay errors at different sites across the substrate. Indeed, in an example, overlay can be significantly improved (eg, overlay [mean plus three standard deviations] reduced from 4 nm to 1 nm) compared to existing alignment techniques after using high-order corrections computed from the output of hybrid dense alignment metrology.

[0242] In an embodiment, the contribution or HDAM can be analyzed to identify possible significant alignment errors or residuals (e.g., due to contamination issues). This can be done by, for example, statistical analysis of the data, by applying thresholds to the data, or both. If significant alignment errors are present, the measurement sampling can be redistributed (e.g., increased, spatially concentrated, etc.) to enable improved computational measurement inputs and / or refine the complexity of the modeling (e.g., provide a higher order model) in the case where it is desired, for example, to avoid unnecessary substrate rework, thereby enabling improved patterning process operation. As an example, in the case of a dominant heating contribution at the substrate-to-substrate level, such computational measurement can help provide high measurement density at the intra-field level so that a higher order intra-field substrate alignment model can be used without a throughput hit and without sacrificing die space.

[0243] Thus, in an embodiment, a computationally based alignment metrology is provided that can construct a hybrid dense alignment map based on data from outside alignment measurements (e.g., data from other sensor measurements from the patterning process, such as data from lithography device sensor measurements other than the alignment sensor). The HDAM can be generated "online" and can be generated prior to a lithography pattern transfer step, where the HDAM can be used for correction; this can enable the use of the HDAM data in a (for example) feed-forward manner and can be used to correct only before or during pattern transfer. In an embodiment, a hybrid dense alignment map can be constructed based on measurement results from "offline" metrology (e.g., pattern forming device write errors, process effects (such as the effects of CMP, etching, etc.), which can be combined with "online" metrology (such as alignment measurements).

[0244] Based on the calculated alignment measurements, a hybrid dense alignment map can be constructed, which has an increased density of substrate alignment fingerprints compared to alignment measurement data alone, and doing so (for example) does not result in a decrease in substrate processing throughput and / or does not sacrifice space within the substrate field / die. Based on the calculated alignment measurements, a hybrid dense alignment map can be constructed, which can achieve higher-order alignment within the field based on the hybrid dense alignment map compared to alignment measurement data alone. In an embodiment, one or more of these contributions to the hybrid dense alignment map can be determined using a physical model, so that model fitting can be avoided. For example, an (offline) simulation or model-based alignment fingerprint caused by heating-induced pattern shifts can be calculated at the level within the field, which can achieve substrate alignment within the higher order field to compensate for the main shift at the substrate to substrate level. As a further example, an (offline) simulation or model-based alignment fingerprint caused by optical aberration-induced pattern shifts can be calculated to produce dense measurement data at the level within the field (for example) for use in a substrate alignment model within the field. As another example, a (offline) simulated or model-based alignment fingerprint due to patterning device write error induced pattern shifts may be calculated to generate dense metrology data at the intra-field level (e.g.) for use in an intra-field substrate alignment model. Measurements of heating, optical aberrations and / or patterning device write errors may be input to the determination of the corresponding alignment fingerprint.

[0245] An advantage of HDAM over existing alignment measurement processes is a higher density of alignment measurements, which can, for example, capture substrate fingerprints at a higher spatial frequency than existing alignment measurement processes. An additional or alternative advantage is that such computational measurements with multiple inputs (contributions) can enable pre-lithography transfer grouping of errors and can enable the ability to include multiple automatic process control threads with different priorities in, for example, a patterning process. An additional or alternative advantage is that its computational measurements can be performed "online", i.e., during processing of the substrate, and can therefore be suitable for feed-forward correction and / or as a tool to identify process offsets (so that the substrate can be reprocessed, scrapped, etc.). An additional or alternative advantage is that due to the high sampling density, the computational measurements can enable determination of a more accurate capture of the aligned substrate fingerprint. An additional or alternative advantage is that due to the more accurate alignment inputs, the computational measurements can enable improved overlay substrate-to-substrate performance.

[0246] The results of the methods herein (or another result derived from the results of the methods herein (e.g., defect prediction)) can be used for various purposes, including controlling a process or equipment therein in a patterning process, monitoring a substrate produced by a patterning process, designing a process or equipment for a patterning process, and the like. For example, these results or results derived therefrom can be used to change an equipment or process for a patterning process for additional processing of a substrate or for processing of another substrate. For example, these results can be used to predict defects. For example, the prediction of defects can be used to control a metrology tool to inspect the affected area and / or change an equipment or process for a patterning process for additional processing of a substrate or for processing of another substrate. In addition, these results can be used to design a patterning process by, for example, deriving a dose selection scheme for correction of a lithographic apparatus, thereby enabling the design of a patterning device and its pattern, process settings, and the like. In addition, these results can be used for model calibration of, for example, an optical proximity effect correction model, a source mask optimization model, a lithography manufacturing verification model, a resist model, an imaging model, a measurement model (e.g., modeling a measurement process), and the like. These results can be used to determine one or more variables of the process (eg, optimal exposure and / or optimal dose), which can then be used for various purposes. As will be appreciated, many other uses are possible.

[0247] In an embodiment, a method is provided, comprising: determining a first distribution of a first parameter associated with an error or residual when performing a device manufacturing process; determining a second distribution of a second parameter associated with the error or residual when performing the device manufacturing process; and determining, by a hardware computer, a distribution of a parameter of interest associated with the device manufacturing process using a function that operates on the first distribution and the second distribution.

[0248] In an embodiment, the first parameter, the second parameter and the parameter of interest are the same. In an embodiment, the first distribution is specific to the device manufacturing process, but not specific to any specific substrate processed using the device manufacturing process. In an embodiment, the second distribution is specific to a specific substrate processed using the device manufacturing process, but not universal to other substrates processed using the device manufacturing process. In an embodiment, the first distribution and / or the second distribution include one or more selected from the following: the contribution of servo errors to the corresponding first parameter and / or second parameter, the contribution of alignment model residuals to the corresponding first parameter and / or second parameter, the contribution of projection system aberrations or image plane deviations to the corresponding first parameter and / or second parameter, the contribution of projection system model residuals to the corresponding first parameter and / or second parameter, and / or the contribution of substrate surface height to the corresponding first parameter and / or second parameter. In an embodiment, determining the first distribution also includes obtaining data of the measured first parameter and removing the contribution of the specific device of the device manufacturing process to the first parameter. In an embodiment, the contribution of a specific device includes one or more selected from the following: a contribution of a servo error, a contribution of an alignment model residual, a contribution of a projection system aberration or image plane deviation, a contribution of a projection system model residual, and / or a contribution of a substrate surface height. In an embodiment, the data of the measured first parameter includes data of the first parameter measured from a monitoring substrate. In an embodiment, the first distribution, the second distribution, and / or the distribution of the parameter of interest include a spatial substrate fingerprint. In an embodiment, the method further includes using the distribution of the parameter of interest to perform any one or more selected from the following: predicting defects of 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. In an embodiment, the first parameter, the second parameter, and / or the parameter of interest are one or more selected from the following: overlap, CD, focus, dose, and / or edge position. In an embodiment, the device manufacturing process includes a lithography process and / or a semiconductor manufacturing process. In an embodiment, the function includes one or more selected from the following: arithmetic addition, convolution, and / or a neural network. In an embodiment, the first parameter and / or the second parameter are different from the parameter of interest, and also include converting the first parameter and / or the second parameter into the parameter of interest. In an embodiment, the method further comprises determining the first distribution and / or the second distribution using data provided by a lithography apparatus and / or an etching apparatus used in a device manufacturing process.

[0249] In an embodiment, a method is provided, comprising: obtaining a base contribution to overlay of a lithographic device as part of a patterning process; and combining, by a hardware computer, the base contribution with a further contribution to overlay of a substrate to obtain an estimate of the overlay of the substrate.

[0250] In an embodiment, the additional contribution includes the contribution of the substrate surface height of the substrate to the overlap. In an embodiment, the additional contribution includes the contribution of the substrate servo error of the substrate to the overlap. In an embodiment, the additional contribution includes the contribution of the alignment and / or projection system model residuals. In an embodiment, the method further includes combining the basic contribution and the contribution of the substrate surface height, the contribution of the etching process to the overlap of the substrate. In an embodiment, the etching process contribution is specific to the patterning process, but not specific to any specific substrate processed using the patterning process. In an embodiment, the basic contribution is specific to a specific patterning process, but not specific to any specific substrate processed using the patterning process. In an embodiment, obtaining the basic contribution also includes obtaining the measured overlap data and removing the contribution of the specific components of the lithographic device to the overlap therefrom. In an embodiment, the contribution of the specific components includes one or more selected from the following: 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 an embodiment, the measured overlap data includes overlap data measured from the monitoring substrate. In an embodiment, the contribution includes a spatial substrate fingerprint. In an embodiment, the method further comprises using the estimate to perform any one or more selected from: predicting defects of the substrate, controlling a patterning process, monitoring a patterning process, designing aspects of a patterning process, and / or calibrating a mathematical model.

[0251] In an embodiment, a method is provided, comprising: determining a first distribution of alignment data measured when performing a device manufacturing process; determining a second distribution of alignment data derived from processing parameters during the device manufacturing process; and determining, by a hardware computer system, a distribution of a parameter of interest associated with the device manufacturing process as a function of the first distribution and the second distribution.

[0252] In an embodiment, the processing parameters include one or more selected from the following: substrate height or unevenness, processing effects, optical aberrations and / or pattern forming device writing errors. In an embodiment, the second distribution is derived from a plurality of processing parameters of the device manufacturing process. In an embodiment, these processing parameters include substrate height or unevenness, process effects and optical element heating. In an embodiment, the second distribution is specific to the device manufacturing process, but not specific to any specific substrate processed using the device manufacturing process. In an embodiment, the second distribution is specific to a specific substrate processed using the device manufacturing process, but not universal for other substrates processed using the device manufacturing process. In an embodiment, the second distribution is derived from the measurement results of the processing parameters. In an embodiment, the method also includes using the distribution of alignment data to perform any one or more selected from the following: predicting defects of the substrate, controlling the device manufacturing process, monitoring the device manufacturing process, designing aspects of the device manufacturing process and / or calibrating the mathematical model. In an embodiment, the method also includes changing the sampling of the measurement data based on the distribution of alignment data. In an embodiment, the method also includes using a higher-order alignment model with a distribution of alignment data than an alignment model with a distribution used only with the measured alignment data. In an embodiment, the method further comprises determining the first distribution and / or the second distribution using data provided by a lithographic apparatus used in a device manufacturing process. In an embodiment, the first distribution, the second distribution and / or the distribution of the parameter of interest comprises a spatial substrate fingerprint. In an embodiment, the device manufacturing process comprises a lithographic process and / or a semiconductor manufacturing process. In an embodiment, the function comprises one or more selected from: arithmetic addition, convolution and / or a neural network.

[0253] In an embodiment, a method is provided, comprising: obtaining, based on measured alignment data, an alignment data distribution across at least a portion of a substrate processed using a patterning process; and combining, by a hardware computer, the alignment data distribution with an alignment fingerprint attributable to processing parameters other than the measured alignment to obtain an estimate of the alignment data for the substrate.

[0254] In an embodiment, the alignment fingerprint includes the contribution of the substrate height or unevenness of the substrate to the alignment. In an embodiment, the alignment fingerprint includes the contribution of the process effect of the substrate (caused by the portion of the patterning process other than the photolithographic pattern transfer) to the alignment. In an embodiment, the alignment fingerprint includes the contribution of the heating of the substrate to the alignment. In an embodiment, the alignment fingerprint is specific to the patterning process, but not specific to any particular substrate processed using the patterning process. In an embodiment, the alignment fingerprint is specific to a particular substrate processed using the patterning process, but not universal to other substrates processed using the patterning process. In an embodiment, the alignment fingerprint is derived from the measurement results of the processing parameters. In an embodiment, the alignment fingerprint includes a spatial substrate fingerprint. In an embodiment, the method further includes using the estimate to perform any one or more selected from the following: predicting defects in the substrate, controlling the patterning process, monitoring the patterning process, designing aspects of the patterning process, and / or calibrating a mathematical model.

[0255] Input contributors to the calculated metrology (CM) for overlay can be measurements collected by the scanner and exposure sensors of the inspection tool. For example, they can include level sensor and alignment sensor measurements, graded dynamic servo recording, overlay and other offline metrology measurements.

[0256] If we take the alignment input as an example contributor, a high-order alignment model (e.g., based on a cubic polynomial) is used to compute the model content from the alignment measurement results. This model content can be dominated by both the wafer deformation contribution and the alignment mark deformation. But for accurate overlay measurement monitoring, control, or defect prediction, only the wafer deformation contribution is the real signal. The alignment mark deformation is irrelevant and is a source of error (or "noise") that should be excluded. The consequence of including such incorrect model content is inconsistent performance of computational metrology (CM). For wafers that are only subject to minor alignment mark deformation, an alignment input with a high-order model can improve measurement accuracy due to a higher signal-to-noise ratio. For wafers that are subject to severe alignment mark deformation, the input may reduce measurement accuracy due to a low signal-to-noise ratio. The error (or "noise") is proportional to the order of the model used. Typically, it occurs at locations (e.g.) at the edge of the wafer where the alignment mark deformation is the largest due to process-induced effects. This limitation leads to the selection of low-order models to limit the amplitude of the "noise", but then the performance of the CM is limited because the true wafer deformation signal (captured only by the high-order model) is lost from the input.

[0257] Note that these limitations typically exist for other input contributors, e.g., wafer height map measured by level sensors, scanner dynamics, etch-induced overlay measured by offline metrology, bottom grating asymmetry measurements, CD measurements, etc.

[0258] When including measurements from scanners or offline metrology as input contributors to CM, orthogonality between these contributors is a useful assumption. With this assumption, these contributors can be added and correlated without crosstalk with parameters of interest (e.g., patterning process parameters such as overlay after development, overlay after etching, or SEM-measured CD or overlay). However, these contributors may still interfere with each other, especially under certain spatial frequency conditions. Depending on the parameter of interest, these contributors may also be correlated with the parameter of interest under different conditions.

[0259] In the frequency distribution of multiple input contributors for CM, in the high (>100 Hz) frequency range, the scanner metrology input (e.g., a level sensor measuring the wafer height map) can predict overlapping content with small crosstalk from other contributors (e.g., scanner dynamics servo errors).

[0260] However, at low (<100 Hz) frequency ranges, the contributors share a common frequency window. These contributors include, for example, wafer alignment model content, monitoring wafer model content, level sensor measurements, dynamic servo data. This means that such model content may interfere with each other. But it also shows that these contributors can be associated with specific parts of the overlapping content for specific frequency conditions (here called frequency windows). For signals outside these frequency windows, the unwanted contributions may become part of the "noise" and may reduce the accuracy of the CM. Therefore, it is advantageous to exclude this "noise" from the input contributors of the CM via (for example) frequency low / high / bandpass filters to increase the signal-to-noise ratio. The embodiment described below provides a method for CM to exclude such "noise".

[0261] Such a feature is also useful for calibrating the results of CM for different parameters of interest (use of generalized data for other applications). For example, between the overlap of optical measurements and the overlap of device features that rely on SEM measurements, the target responds differently to the patterning process due to different sizes and designs. From a defect prediction perspective, such a feature is useful to exclude irrelevant overlap content between the optically measured contributors and the response of the actual device features.

[0262] In an embodiment, the model or NCE (uncorrectable error) model can be used as a frequency low / high pass filter, and a specific set of model parameters can be used as a frequency band pass filter. This means that as long as a specific pair of model parameters (i.e., contributors or any patterning process parameters) derived from any of the two input data show correlation within each pair, the weight (referred to herein as a calibration factor) between the two input data can be determined accordingly.

[0263] In an embodiment, a method of deriving a calibration factor for a correlation model parameter between any of the two input contributors or parameters of interest is provided. To aid understanding, we describe the method in terms of predicting from one domain to another other domain. The input contributors used for prediction are defined as domain A. The parameter of interest is defined as domain B.

[0264] Enter the contributor field A for reference Figure 7 The process variables described, such as alignment variables. The parameter domain B of interest can be reference Figure 7 and Figure 8 Patterning process parameters such as overlay are described.

[0265] Fig. 22 The flow for a method according to an embodiment is schematically shown.

[0266] A parameter distribution 2322 (DB) of interest is determined, such as an overlap distribution. This is a first distribution 2322 of a first parameter 2321 associated with an error or residual when performing a device manufacturing process. To determine the distribution 2322, a first distribution of values ​​2325 of the first parameter 2321 is obtained. The first distribution of values ​​2325 is then modeled 2328 to obtain a first modeled distribution 2322 (DB) of values. Thus, in the embodiment, the determined first distribution (parameter of interest) includes a first modeled distribution 2322 (DB) of values.

[0267] An input contributor distribution 2312 (DA) is determined, such as an alignment distribution. This is a second distribution 2312 of a first parameter 2311 associated with an error or residual when performing a device manufacturing process. To determine the distribution, a second distribution of values ​​2315 of the first parameter 2311 is obtained. The first distribution of values ​​2315 is then modeled 2318 to obtain a second modeled distribution 2312 (DA) of values. Thus, in the described embodiment, the determined second distribution (input contributor) includes the first modeled distribution 2312 (DA) of values.

[0268] For modeling 2328, 2318, a variation range or scale 2304 (SV) (e.g., frequency < 100 Hz) is determined 2302 for which the correlation between the values ​​2325 of the first distribution and the values ​​2315 of the second distribution exceeds a threshold. The first distribution and the second distribution of values ​​are then modeled 2328, 2318 in dependence on the determined variation scale 2304 (SV) to obtain a first modeled distribution 2322 (DB) and a second modeled distribution 2312 (DA) of values.

[0269] Next, the hardware computer determines the distribution of the parameter of interest (which in the embodiment is the first parameter, such as overlap) using a function operating on the first distribution 2322 (DB) and the second distribution 2312 (DA). The function in the embodiment includes a correlation 2332 (CORR) operating on the first distribution 2322 and the second distribution 2312.

[0270] The determination of the distribution 2352 (DB') of the parameter of interest is based on scaling 2335 the modeled second distribution 2312 (DA) using a scaling factor 2334 (calibration factor CF) obtained by mapping 2332 (CORR) between first model coefficients associated with the first modeled distribution 2322 (DB) of values ​​and second model coefficients associated with the second modeled distribution 2312 (DA) of values. The scaling factor 2334 (calibration factor, CF) can be used to exclude modeling components from the step of determining the distribution 2352 of the parameter of interest. For example, if the scaling factor is lower than or equal to a threshold value 2333, the model coefficients associated with the first modeled distribution 2312 (DA) of values ​​can be excluded from the scaling.

[0271] Fig.23 and Fig.24 Schematically showing the adjustment of calibration factors for predicting the distribution of a parameter of interest. A correlation between two domains A (aligned) and domain B (overlapped) can be defined. For two domains that can be described by the same set of parameters (e.g., linear, high-order, or combined polynomial coefficients), a set of scaling factors or calibration factors for the correlation coefficients can be defined by dividing the coefficients of domain B by the coefficients of domain A using simple linear algebra.

[0272] In the case where one domain receives corrections from another domain, there is a high probability of good correlation between the two domains, given a large number of data points. For example, the scanner uses information from the alignment measurement to correct the substrate grid (deformation). There is an assumption that there is a strong correlation between alignment and overlay for parameters up to 5th degree polynomial components used in the alignment model. In other words, domain B (overlay) receives corrections from domain A (alignment) and there is a strong correlation between domain A and domain B.

[0273] Fig.23 and Fig.24 It is illustrated that prediction of one domain DB' is by projecting another domain DA with calibration factors of all model parameters. First, all model parameters of each domain are calculated. Two model parameters MPA and MPB each have eight points P1 to P8 shown in their table.

[0274] about Fig.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 versus MPA for Domain B, including the data points in Table 2362. The calibration factor between these sets of parameters for the model parameter MPA is determined by fitting a linear model (y=a*x) to determine the correlation, here 0.50 (y=0.5*x).

[0275] about Fig.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 versus MPB for domain B, including the data points in Table 2364. The calibration factor between these sets of parameters for the model parameter MPB is determined by fitting a linear model (y=a*x) to determine the correlation, here 0.33 (y=0.33*x).

[0276] For the model parameters MPA and MPB, respectively, Fig.23 Table 2370 and Fig.24 As shown in Table 2372 in , the calibration factors are used to predict these model parameters from the parameter of interest DB' (eg, overlap) in the parameter values ​​of domain A.

[0277] Even though there may be a perfect correlation between domain A and domain B, there is no guarantee that the weight between the two sets of parameters is 1. For example, the wafer-to-wafer translation value of the alignment measurement may be twice the translation observed in the context of overlay error. In this case, even if there is a perfect correlation between the two sets of parameters, the scaling value is not always 1. In other words, if there is a strong correlation between the two sets of parameters, domain B can be predicted more accurately by adjusting the calibration factor of the parameters multiplied by the parameters of domain A. Note that in order to have a good prediction quality, due to the asymmetric layout of the input samples, it is preferred that the input samples of domain A and domain B are restricted to avoid crosstalk between the model parameters.

[0278] If the alignment and overlay are associated with a scaling of 1, it means that the overlay correction is based on information that represents the true wafer deformation. In this case, the alignment information is correct and true. In this case, the calibration factors from both sets of parameters are 1, which is the same as the observed scaling.

[0279] If the alignment measurement is affected by alignment mark asymmetry or metrology measurement uncertainty, it means that there is wrong information for the alignment from the deformed alignment marks. If the alignment model is calculated with this wrong information, these errors induced from mark deformation will be dialed into the overlay prediction. In an embodiment, by looking at only those relevant model parameters between alignment and overlay (whose correlation is good enough), a calibration factor between alignment and overlay can be calculated for each parameter. By applying these selected calibration factors to the alignment data, overlay predictions induced by wrong alignment mark deformation can be calibrated (filtered) for all parameters.

[0280] Due to deformation of the measurement overlay target, there is often an offset between the measurement target overlay and the device overlay. The offset budget can be divided into "batch" and "wafer to wafer" (W2W) categories. While the "batch" offset is calculated based on the actual device overlay measurement, in the case of W2W, if there is a stable correlation between the measurement and device overlay, a calibration factor can be defined and used to calibrate / predict the offset to W2W in the manner described above. This can be understood by replacing domain A with "measurement overlay" with domain B with "device overlay".

[0281] The context information can be used; the overlapping calibration / prediction can be extended using the concept of context-based grouping. For the case where the production batches are divided into several groups and each group is processed separately with different process tools, the fingerprint (or degree of wafer / mark deformation / asymmetry) of each group will be different from each other. In this case, the total data set can be grouped into sub-data sets and the correlation / calibration factor can be calculated again for each group. The calculated calibration / prediction will be applied to each group separately, resulting in better calibration / prediction results.

[0282] Fig.25 The probability of determining a correct prediction is schematically shown. The vertical axis DB is the domain B model parameter value, and the horizontal axis DA is the domain A model parameter value.

[0283] When calculating the calibration factor for each data set, the likelihood of a correct prediction can be defined using the framework described below, assuming that the data points are uniformly distributed.

[0284] (1) If a data point is located in the region 2704 between the slope of the correlation factor 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. Then, a certain portion of domain B can be correctly projected / predicted.

[0285] (2) If the data point is exactly on slope 2706, then the projection / prediction is perfect.

[0286] (3) If a point is in region 2708 between slope 2706 and half of slope 2710, a prediction can be made, but the predicted value is greater than the value of region B. Calibration of the data point changes the sign of the result of the calibration.

[0287] (4) For data points located in regions other than these three (2704, 2706, and 2708), calibrating domain B using the method described herein makes the results worse than the original values.

[0288] Thus, the area of ​​correct prediction can be defined below using the angle θ between the axis, the axis of domain A and the slope 2706. As the slope becomes closer to the x-axis, at angle θ1, the possibility of correct projection / prediction becomes its maximum value of 50%. However, as the calibration factor approaches zero, the benefit of using the projection becomes closer to zero. Therefore, it is very important to find conditions with good correlation between a specific frequency window or two domains (for example, using the total data set to be divided into subsets). This will focus the distribution of data points on the slope, which will be within the three regions (2704, 2706 and 2708) explained above. A trade-off can also be made between the calibration factor and the possibility of correction. The calibration factor defined during the correlation (setup) phase can be adjusted to be less than its originally defined value. This will increase the number of correctly predicted / calibrated data points, but the benefit will be less than it will have.

[0289] Calibration factor (Fcal) = tan().

[0290] Embodiments provide a general method for determining calibration factors (referred to herein as relevant model parameters) between filtered frequencies based on any of these domains, and for projecting one domain into another for measurement prediction / calibration purposes, and the ability to correct the domain projection is related to the value of the calibration factor.

[0291] Embodiments are able to calibrate overlay predictions from wafer deformation / alignment marks and asymmetries of domain projection across multiple wavelengths (colors) in the sensor, multiple reference measurements in time (wafer), and multiple spatial frequencies (sites) within a measurement.

[0292] An embodiment divides the data into subsets, thereby increasing the correlation and prediction accuracy between the two domains.

[0293] Embodiments can deselect the content from non-correlated model parameters of the two domains to suppress noise in the prediction induced from the input contributors.

[0294] Embodiments can provide an indication of wafers that require actual production measurement. For example, if the measured scanner metrology from new domain A no longer falls within the previously observed population, an action can be triggered to measure actual wafers in domain B to update the previously defined population.

[0295] Embodiments calibrate out a portion of the spurious content measured by any overlay measurements measured by the scanner or from predictions, namely alignment mark asymmetry, miscorrected wafer deformation, or any irrelevant content within the input contributors.

[0296] Embodiments may be used for either input data and parameters of interest (ie, offline wafer shape measurements or SEM measurements).

[0297] For wafer-to-wafer variation feed-forward, embodiments can predict wafer-to-wafer corrections for a subsequent layer based on the alignment of the previous layer (when there is a correlation between the previous and subsequent layers). For example, for a layer that has been processed by lithography-etch-lithography-etch.

[0298] Fig.26 1 is a block diagram illustrating a computer system 100 that can assist in implementing the methods and processes disclosed herein. The computer system 100 includes a bus 102 or other communication mechanism for communicating information, and a processor 104 (or multiple 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 can also be used to store temporary variables or other intermediate information during the execution of instructions to be executed by the processor 104. The computer system 100 also 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.

[0299] The computer system 100 can be coupled to a display 112, such as a cathode ray tube (CRT) or a flat panel display or a touch panel display, via the bus 102 for displaying information to a computer user. An input device 114 including alphanumeric keys and other keys is coupled to the bus 102 for communicating information and command selections to the processor 104. Another type of user input device is a cursor controller 116 (such as a mouse, trackball, or cursor direction keys) for communicating direction information and command selections to the processor 104 and for controlling cursor movement on the display 112. Such an input device typically has two degrees of freedom in two axes, a first axis (e.g., x) and a second axis (e.g., y), which allows the device to specify a position in a plane. A touch panel (screen) display can also be used as an input device.

[0300] According to one embodiment, portions of the process may be performed by the computer system 100 in response to the processor 104 executing one or more sequences of one or more instructions contained in the main memory 106. Such instructions may be read into the main memory 106 from another computer-readable medium, such as the storage device 110. The execution of the sequence of instructions contained in the main memory 106 causes the processor 104 to perform the process steps described herein. One or more processors in a multi-processing arrangement may also be used to execute the sequence of instructions contained in the main memory 106. In alternative embodiments, hard-wired circuits may be used in place of or in combination with software instructions. Therefore, the description herein is not limited to any particular combination of hardware circuitry and software.

[0301] The term "computer-readable medium" as used herein refers to any medium that participates in providing instructions to the processor 104 for execution. Such media can take many forms, including but not limited to non-volatile media, volatile media, and transmission media. Non-volatile media include, for example, optical or magnetic disks, such as storage device 110. Volatile media include dynamic memory, such as main memory 106. Transmission media include coaxial cables, copper wires, and optical fibers, including wires containing bus 102. Transmission media can also take the form of sound waves or light waves, such as sound waves or light waves generated during radio frequency (RF) and infrared (IR) data communications. Common forms of computer-readable media include, for example, floppy disks, flexible disks, hard disks, magnetic tapes, any other magnetic media, CD-ROMs, DVDs, any other optical media, punch cards, paper tapes, any other physical media with hole patterns, RAM, PROMs and EPROMs, FLASH-EPROMs, any other memory chips or boxes, carriers as described below, or any other media from which a computer can read.

[0302] Various forms of computer readable media may be involved in transmitting one or more sequences of one or more instructions to processor 104 for execution. For example, the instructions may initially be carried on a disk of a remote computer. The remote computer may load the instructions into its dynamic memory and send the instructions over a telephone line using a modem. A modem local to computer system 100 may receive the data on the telephone line and convert the data into an infrared signal using an infrared transmitter. An infrared detector coupled to bus 102 may receive the data carried in the infrared signal and place the data on bus 102. Bus 102 transmits 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 on storage device 110 before or after execution by processor 104.

[0303] The computer system 100 also preferably includes a communication interface 118 coupled to the bus 102. The communication interface 118 provides a two-way data communication coupled to a network link 120, which is connected to a local network 122. For example, the communication interface 118 can be an integrated services digital network (ISDN) card or a modem for providing a data communication connection with a corresponding type of telephone line. As another example, the communication interface 118 can be a local area network (LAN) card for providing a data communication connection with a compatible LAN. A wireless link can also be implemented. In any such implementation, the communication interface 118 sends and receives electrical signals, electromagnetic signals, or optical signals that carry digital data streams representing various types of information.

[0304] The network link 120 typically provides data communication to other data devices through one or more networks. For example, the network link 120 may provide a connection to a host computer 124 or to data equipment operated by an Internet Service Provider (ISP) 126 through a local network 122. The ISP 126, in turn, provides data communication services through the global packet data communication network now commonly referred to as the "Internet" 128. Both the local network 122 and the Internet 128 use electrical, electromagnetic or optical signals that carry digital data streams. The signals through the various networks and the signals on the network link 120 and through the communication interface 118, which transmit the digital data to and from the computer system 100, are example forms of carrier waves that transport the information.

[0305] The computer system 100 can send messages and receive data, including program code, through the network, network link 120, and communication interface 118. In the Internet example, the server 130 can transmit the requested code for an application through the Internet 128, ISP 126, local network 122, and communication interface 118. For example, one such downloaded application can be provided for irradiation optimization of an embodiment. The received code can be executed by the processor 104 as it is received, and / or stored in the storage device 110 or other non-volatile storage for later execution. In this way, the computer system 100 can obtain application code in the form of a carrier wave.

[0306] Additional embodiments are disclosed in the following list of numbered embodiments:

[0307] 1. A method comprising:

[0308] determining a first distribution of a first parameter associated with an error or residual when performing a device manufacturing process;

[0309] determining a second distribution of a second parameter associated with the error or residual when performing the device manufacturing process; and

[0310] A distribution of a parameter of interest associated with the device manufacturing process is determined by a hardware computer using a function operating on the first distribution and the second distribution.

[0311] 2. The method of embodiment 1, wherein the first parameter, the second parameter, and the parameter of interest are the same.

[0312] 3. The method of embodiment 1, wherein the first profile is specific to the device fabrication process but not specific to any particular substrate processed using the device fabrication process.

[0313] 4. The method of embodiment 1, wherein the second profile is specific to a particular substrate processed using the device fabrication process, but is not generic to other substrates processed using the device fabrication process.

[0314] 5. The method of embodiment 1, wherein the first distribution and / or the second distribution comprises one or more selected from the following:

[0315] the contribution of servo error to the corresponding first parameter and / or second parameter, the contribution of alignment model residual to the corresponding first parameter and / or second parameter, the contribution of projection system aberration or image plane deviation to the corresponding first parameter and / or second parameter, the contribution of projection system model residual to the corresponding first parameter and / or second parameter, and / or the contribution of substrate surface height to the corresponding first parameter and / or second parameter.

[0316] 6. The method of embodiment 1, wherein determining the first distribution further comprises obtaining measured data of the first parameter and removing a contribution of specific means of the device manufacturing process to the first parameter from the measured data.

[0317] 7. The method of embodiment 6, wherein the contribution of the specific device comprises one or more selected from the following:

[0318] The contribution of servo errors, the contribution of alignment model residuals, the contribution of projection system aberrations or image plane deviations, the contribution of projection system model residuals and / or the contribution of substrate surface height.

[0319] 8. The method of embodiment 6, wherein the first parameter data measured comprises the first parameter data measured from a monitoring substrate.

[0320] 9. The method of embodiment 1, wherein the first distribution, the second distribution and / or the distribution of the parameter of interest comprises a spatial substrate fingerprint.

[0321] 10. The method of embodiment 1, further comprising using the distribution of the parameter of interest to perform any one or more selected from the following:

[0322] predicting defects of a substrate, controlling the device manufacturing process, monitoring the device manufacturing process, designing aspects of the device manufacturing process, and / or calibrating a mathematical model.

[0323] 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:

[0324] Overlap, CD, focus, dose and / or edge position.

[0325] 12. The method according to embodiment 1, wherein the device manufacturing process comprises a photolithography process and / or a semiconductor manufacturing process.

[0326] 13. The method of embodiment 1, wherein the function comprises one or more selected from: arithmetic addition, convolution, and / or neural network.

[0327] 14. The method of embodiment 1, wherein the first parameter and / or the second parameter is different from the parameter of interest, and further comprising converting the first parameter and / or the second parameter to the parameter of interest.

[0328] 15. The method of embodiment 1, further comprising determining the first distribution and / or the second distribution using data provided by a lithography apparatus and / or an etching apparatus used in a manufacturing process of the device.

[0329] 16. The method of embodiment 1, wherein the function comprises a correlation operating on the first distribution and the second distribution.

[0330] 17. The method of embodiment 16, wherein:

[0331] The determined first distribution comprises a first modeled distribution of values; and

[0332] The determined second distribution comprises a second modeled distribution of values; and

[0333] The parameter of interest is the first parameter,

[0334] And the method comprises:

[0335] obtaining a first distribution of values ​​of the first parameter;

[0336] obtaining a second distribution of values ​​of the second parameter;

[0337] modeling the first distribution of values ​​and the second distribution of values ​​to obtain the first modeled distribution of values ​​and the second modeled distribution of values; and

[0338] The distribution of the parameter of interest is determined based on scaling the second modeled distribution using a scaling factor obtained by mapping between first model coefficients associated with the first modeled distribution of values ​​and second model coefficients associated with the second modeled distribution of values.

[0339] 18. The method of embodiment 17, comprising:

[0340] determining a measure of variation in the correlation between values ​​of the first distribution and values ​​of the second distribution exceeding a threshold; and

[0341] The first distribution of values ​​and the second distribution of values ​​are modeled in dependence on the determined scale of variation to obtain the first modeled distribution of values ​​and the second modeled distribution of values.

[0342] 19. The method of embodiment 17, comprising using the scaling factor to exclude a modeling component from the step of determining the distribution of the parameter of interest.

[0343] 20. A method comprising:

[0344] Obtaining the basis contribution of the lithographic equipment to the overlay as part of the patterning process; and

[0345] The base contribution is combined with an additional contribution to the overlap of the substrate by a hardware computer to obtain an estimate of the overlap of the substrate.

[0346] 21. The method of embodiment 20, wherein the additional contribution comprises a contribution of a substrate surface height of the substrate to the overlap.

[0347] 22. The method of embodiment 20, wherein the additional contribution comprises a contribution of a substrate servo error of the substrate to the overlay.

[0348] 23. The method of embodiment 20, wherein the additional contributions include contributions of alignment and / or projection system model residuals.

[0349] 24. The method according to embodiment 20 further includes combining the base contribution with the contribution of the substrate surface height and the contribution of the overlap of the etching process on the substrate.

[0350] 25. The method of embodiment 24, wherein the etching process contribution is specific to the patterning process but not specific to any particular substrate processed using the patterning process.

[0351] 26. The method of embodiment 20, wherein the basis contribution is specific to a particular patterning process but not specific to any particular substrate processed using the patterning process.

[0352] 27. The method of embodiment 20, wherein obtaining the base contribution further comprises obtaining measured overlay data and removing the contribution of the specific components of the lithographic device to the overlay from the measured overlay data.

[0353] 28. A method according to embodiment 27, wherein the contribution of the specific component includes one or more selected from: contribution of servo error, contribution of alignment model residual, projection system aberration, contribution of projection system model residual and / or contribution of substrate surface height.

[0354] 29. The method of embodiment 27, wherein the measured overlay data comprises overlay data measured from a monitor substrate.

[0355] 30. The method of embodiment 20, wherein the contribution comprises a spatial substrate fingerprint.

[0356] 31. The method of embodiment 20, further comprising using the estimation to perform any one or more selected from: predicting defects of the substrate, controlling a patterning process, monitoring a patterning process, designing aspects of a patterning process, and / or calibrating a mathematical model.

[0357] 32. A method comprising:

[0358] determining a first distribution of alignment data measured while performing a device manufacturing process;

[0359] determining a second distribution of alignment data derived from process parameters during fabrication of the device; and

[0360] A distribution of alignment data associated with the device manufacturing process is determined by a hardware computer system as a function of the first distribution and the second distribution.

[0361] 33. The method of embodiment 32, wherein the processing parameters include one or more selected from: substrate height or unevenness, process effects, optical element heating, optical aberrations, and / or pattern forming device writing errors.

[0362] 34. The method of embodiment 32, wherein the second distribution is derived from a plurality of processing parameters of the device manufacturing process.

[0363] 35. The method of embodiment 34, wherein the processing parameters include substrate height or unevenness, process effects, and optical element heating.

[0364] 36. The method of embodiment 32, wherein the second profile is specific to the device fabrication process but not specific to any particular substrate processed using the device fabrication process.

[0365] 37. The method of embodiment 32, wherein the second profile is specific to a particular substrate processed using the device fabrication process, but is not generic to other substrates processed using the device fabrication process.

[0366] 38. The method of embodiment 32, wherein the second distribution is derived from measurements of the processing parameters.

[0367] 39. The method according to embodiment 32 also includes using the distribution of alignment data to perform any one or more selected from the following: predicting defects of the substrate, controlling the device manufacturing process, monitoring the device manufacturing process, designing aspects of the device manufacturing process and / or calibrating mathematical models.

[0368] 40. The method of embodiment 32, further comprising changing the sampling of the metrology data based on the distribution of the alignment data.

[0369] 41. The method of embodiment 32 further comprises using an alignment model having a higher order distribution of alignment data than using an alignment model having only a distribution of measured alignment data.

[0370] 42. The method according to embodiment 32 further includes determining the first distribution and / or the second distribution using data provided by a lithography equipment used in the device manufacturing process.

[0371] 43. The method of embodiment 32, wherein the first distribution, the second distribution, and / or the distribution of the parameter of interest comprises a spatial substrate fingerprint.

[0372] 44. The method according to embodiment 32, wherein the device manufacturing process includes a photolithography process and / or a semiconductor manufacturing process.

[0373] 45. The method of embodiment 32, wherein the function comprises one or more selected from: arithmetic addition, convolution, and / or neural network.

[0374] 46. ​​A method comprising:

[0375] obtaining an alignment data distribution across at least a portion of a substrate processed using the patterning process based on the measured alignment data; and

[0376] The alignment data distribution is combined by a hardware computer with an alignment fingerprint attributable to process parameters other than the measured alignment to obtain an estimate of alignment data for the substrate.

[0377] 47. The method of embodiment 46, wherein the alignment fingerprint comprises a contribution of substrate height or unevenness of the substrate to alignment.

[0378] 48. The method of embodiment 46, wherein the alignment fingerprint comprises a contribution to alignment from process effects of the substrate due to portions of the patterning process other than lithographic pattern transfer.

[0379] 49. The method of embodiment 46, wherein the alignment fingerprint comprises a contribution of heating of the substrate to the alignment.

[0380] 50. The method of embodiment 46, wherein the alignment fingerprint is specific to the patterning process but not specific to any particular substrate processed using the patterning process.

[0381] 51. The method of embodiment 46, wherein the alignment fingerprint is specific to a particular substrate processed using the patterning process, but is not universal for other substrates processed using the patterning process.

[0382] 52. The method of embodiment 46, wherein the alignment fingerprint is derived from measurements of the processing parameters.

[0383] 53. A method according to embodiment 46, wherein the alignment fingerprint includes a spatial substrate fingerprint.

[0384] 54. The method of embodiment 46 further comprises using the estimate to perform any one or more selected from: predicting defects of the substrate, controlling a patterning process, monitoring a patterning process, designing aspects of a patterning process, and / or calibrating a mathematical model.

[0385] 55. A computer program product comprising a non-transitory computer-readable medium having recorded thereon instructions, the instructions, when executed by a computer, implementing the method according to any one of embodiments 1-54.

[0386] The embodiments of the present disclosure may be implemented in hardware, firmware, software, or any combination thereof. The embodiments of the present disclosure may also be implemented as instructions stored on a machine-readable medium, which can be read and executed by one or more processors. A machine-readable medium may include any mechanism for storing or transmitting information in a form that can be read by a machine (e.g., a computing device). For example, a machine-readable medium may include a read-only memory (ROM); a random access memory (RAM); a disk storage medium; an optical storage medium; a flash memory device; an electrical, optical, acoustic, or other form of propagation signal (e.g., a carrier wave, an infrared signal, a digital signal, etc.), etc. In addition, herein, firmware, software, routines, instructions may be described as performing certain actions. However, it should be understood that such descriptions are merely for convenience, and that these actions are actually generated by a computing device, a processor, a controller, or other devices that execute firmware, software, routines, instructions, etc.

[0387] In the block diagram, although the illustrated components are depicted as discrete functional blocks, embodiments are not limited to systems in which the functionality described herein is organized as shown. The functions provided by each of the components may be provided by software or hardware modules, which are organized in a manner different from that currently depicted, such as being blended, combined, replicated, dissolved, distributed (e.g., within a data center or by region), or otherwise organized in a different manner. The functions described herein may be provided by one or more processors of one or more computers executing code stored on a tangible, non-temporary machine-readable medium. In some cases, a third-party content distribution network may be the host of some or all of the information transmitted on the network, in which case, to the extent that information (e.g., content) is considered to be supplied or otherwise provided, the information may be provided by sending instructions to obtain the information from the content distribution network.

[0388] Unless otherwise expressly stated, it should be understood from this discussion that throughout the specification, discussions utilizing terms such as "processing," "computing," "calculating," "determining," etc., refer to actions or processes of a specific apparatus, such as a special purpose computer or similar special purpose electronic processing / computing device.

[0389] The reader should understand that this application describes several inventions. Rather than separating these inventions into multiple independent patent applications, the applicant has combined these inventions into a single file, because their related themes apply themselves to the economy during the application process. However, the different advantages and aspects of these inventions should not be merged. In some cases, although the embodiments solve all the deficiencies mentioned herein, it should be understood that the invention is independently useful, and some embodiments only solve a subset of these problems or provide other unmentioned benefits, which are clear to the technician who consults the disclosure. Due to cost constraints, some inventions disclosed herein may not be claimed at present, and these inventions may be claimed in a later application (such as continuing this application or by amending the claims). Similarly, due to space constraints, "summary" and "content of the invention" sections should not be considered as a comprehensive enumeration of all these inventions or all aspects of these inventions.

[0390] It should be understood that the specification and drawings are not intended to limit the invention to the particular forms disclosed, but on the contrary, the invention is to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the invention as defined by the appended claims.

[0391] In view of this specification, those skilled in the art will understand modifications and alternative embodiments of various aspects of the present invention. Therefore, this specification and the accompanying drawings are interpreted as illustrative only, and are for the purpose of teaching those skilled in the art the general way of implementing the present invention. It should be understood that the forms of the present invention shown and described herein will be regarded as examples of embodiments. Elements and materials can be used to replace those elements and materials illustrated and described herein, parts and processes can be reversed, changed in order or omitted, and certain features can be used independently, and embodiments or features of embodiments can be combined, all of which will be clear to those skilled in the art after benefiting from the description of the present invention. Without departing from the spirit and scope of the present invention as described in the appended claims, changes can be made to the elements described herein. The titles used herein are only for organizational purposes and are not meant to limit the scope of the specification.

[0392] As used throughout this application, the words "may" and "could" are used in a permissible sense (i.e., meaning potentially possible) rather than a mandatory sense (i.e., meaning must). The words "include," "including," and "includes," and the like mean including, but not limited to. As used throughout this application, the singular forms "a," "an," and "the" include plural references unless the context clearly indicates otherwise. Thus, for example, reference to "an element and an element" includes combinations of two or more elements, even though other terms and phrases such as "one or more" are used for one or more elements. Unless otherwise indicated, the term "or" is non-exclusive, i.e., includes "and" and "or." Terms describing conditional relationships, such as "in response to X, Y", "when X, Y", "if X, then Y", "when X, Y", etc., include causal relationships, where the antecedent is a necessary causal condition, the antecedent is a sufficient causal condition, or the antecedent is a contributing causal condition of the result, for example, "the statement that state X occurs when condition Y is achieved" is superordinate to "X occurs only when Y" and "X occurs when Y and Z". Such conditional relationships are not limited to results immediately after the antecedent is achieved, because some results may be delayed, and in the conditional statement, the antecedent is associated with their results, such as the antecedent is associated with the likelihood of the result occurring. A statement in which multiple attributes or functions are mapped to multiple objects (e.g., one or more processors that perform steps A, B, C, and D) includes all of these attributes or functions being mapped to all of these objects and subsets of the attributes or functions being mapped to subsets of the attributes or functions (e.g., all processors each perform steps AD, and the case in which processor 1 performs step A, processor 2 performs step B and part of step C, and processor 3 performs part of step C and step D), unless otherwise specified. Furthermore, unless otherwise stated, a statement that a value or action is "based on" another condition or value encompasses both instances where the condition or value is the only factor and instances where the condition or value is one of multiple factors. Unless otherwise stated, a statement that "each" instance of a certain set has a certain property should not be interpreted as excluding the case where some other identical or similar components in the larger set do not have the property, i.e., each does not necessarily mean every or any one.

[0393] To the extent that certain U.S. patents, U.S. patent applications, or other materials (e.g., articles) have been incorporated by reference, the text of such U.S. patents, U.S. patent applications, and other materials is incorporated only to the extent that there is no conflict between such materials and the statements and figures set forth herein. In the event of such a conflict, any such conflicting text in such incorporated by reference U.S. patents, U.S. patent applications, and other materials is not specifically incorporated by reference herein.

[0394] While specific embodiments of the disclosure have been described above, it will be appreciated that these embodiments may be practiced otherwise than as described.

Claims

1. A method for calculating a measurement, the method comprising: obtaining a first distribution of a first parameter associated with an error or residual associated with a lithographic apparatus used in performing a device fabrication process; obtaining a second distribution of a second parameter from measurements associated with errors or residuals in performing a device manufacturing process; and A distribution of a parameter of interest associated with a device manufacturing process is determined by a hardware computer based on combining the first distribution and the second distribution. 2 . The method of claim 1 , wherein the first parameter, the second parameter, and the parameter of interest are parameters of the same type.

3. The method of claim 1, wherein the first profile is specific to a particular substrate processed using the device fabrication process but is not generally applicable to other substrates processed using the device fabrication process.

4. A method as claimed in claim 1, wherein the first distribution includes one or more selected from the following: a contribution of servo error to the first parameter, a contribution of alignment model residuals to the first parameter, a contribution of projection system aberrations or image plane deviations to the first parameter, a contribution of projection system model residuals to the first parameter, and / or a contribution of substrate surface height to the first parameter.

5. The method of claim 1, wherein: The metrology results include focus metrology data, and the first distribution includes a contribution of substrate surface height to the first parameter.

6. The method of claim 5, wherein the focus metrology data is obtained by relatively sparsely sampling locations on a substrate, and the distribution of the parameter of interest comprises a relatively dense spatial distribution of focus parameters across the substrate.

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

8. The method of claim 7, wherein the CD metrology data is obtained by relatively sparsely sampling locations on a substrate, and the distribution of the parameter of interest comprises a relatively dense spatial distribution of focus parameters across the substrate.

9. The method of claim 1, wherein the measurement results include overlapping measurement data.

10. The method of claim 9, wherein the overlay metrology data is obtained by relatively sparse sampling of locations on a substrate, and the distribution of the parameter of interest comprises a relatively dense spatial distribution of the overlay parameter across the substrate.

11. The method of claim 1 , further comprising using the distribution of the parameter of interest to predict hot spots on a substrate.

12. The method of claim 11, wherein the hotspot is predicted based on at least a first parameter of interest and a second parameter of interest, the first parameter of interest being CD and the second parameter of interest being a coverage parameter.

13. The method of claim 1, further comprising using the distribution of the parameter of interest to predict a shape and / or size of one or more contours of a pattern.

14. The method of claim 1, wherein the first parameter and / or the second parameter are different from the parameter of interest and further comprising converting the first parameter and / or the second parameter to the parameter of interest.

15. The method of claim 1, wherein the first distribution is based on data from the lithographic apparatus and the second distribution is based on data from an inspection and / or metrology apparatus.

16. A computer program product comprising a non-transitory computer-readable medium having instructions therein, wherein the instructions, when executed by a computer system, are configured to cause the computer system to at least: obtaining a first distribution of a first parameter associated with an error or residual associated with a lithographic apparatus used in performing a device fabrication process; obtaining a second distribution of a second parameter from measurements associated with errors or residuals in performing a device manufacturing process; and A distribution of a parameter of interest associated with a device manufacturing process is determined based on combining the first distribution and the second distribution.

17. The computer program product of claim 16, wherein the metrology results include focus metrology data and the first distribution includes a contribution of substrate surface height to the first parameter.

18. The computer program product of claim 17, wherein the metrology results include critical dimension metrology data and the first distribution includes a contribution of substrate surface height to the first parameter.

19. The computer program product of claim 16, wherein the instructions are further configured to cause the computer system to predict hot spots on a substrate using the distribution of the parameter of interest.

20. The computer program product of claim 19, wherein the instructions configured to cause the computer system to predict the hotspot are configured to do so using at least two parameters of interest as input: a first parameter of interest is a critical dimension and a second parameter of interest is an overlay parameter.

21. The computer program product of claim 16, wherein the instructions are further configured to cause the computer system to use the distribution of the parameter of interest to predict a shape and / or size of one or more contours of a pattern.

22. The computer program product of claim 16, wherein the first parameter and / or the second parameter are different from the parameter of interest, and wherein the instructions are further configured to cause the computer system to convert the first parameter and / or the second parameter to the parameter of interest.

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