TW201937300A - Prediction of out of specification physical items - Google Patents

Abstract

A method including: obtaining a value of a characteristic of a physical item instance of a physical system or object, using a non-probabilistic model; obtaining an attribute of a distribution of a residue of the non-probabilistic model with respect to an ensemble of physical item instances that is based on an attribute of a distribution of a residue of the non-probabilistic model with respect to at least one physical item instance corresponding to at least one physical item type of the ensemble; determining an attribute of a distribution of the characteristic based on the attribute of the distribution of the residue with respect to an ensemble of physical item instances and on the value of the characteristic of the physical item instance; and determining a probability that the physical item instance is out of specification, based on the attribute of the distribution of the characteristic.

Description

Forecast of out-of-specification physical items

The description in this article is about a method of predicting an out-of-specification physical item, such as an out-of-specification pattern instance on a substrate generated by a device manufacturing process.

A lithographic apparatus is a machine that applies a desired pattern onto a target portion of a substrate. Lithography devices can be used, for example, in the manufacture of devices such as integrated circuits (ICs). In this case, a patterned device (e.g., a reticle or a reticle) can be used to generate a pattern corresponding to the individual layers of the device ("design layout"), and by, for example, via This pattern can be transferred to a target portion (e.g., containing a portion of a die, one or more dies) on a substrate (e.g., a silicon wafer) having, for example, a layer of radiation-sensitive material (resist). On the target part. Generally speaking, a single substrate will contain a plurality of adjacent target portions, and the pattern is sequentially transferred from the lithographic apparatus to the plurality of adjacent target portions, one target portion at a time. In one type of lithographic device, the pattern on the entire patterned device is transferred to a target portion at one time; this device is often referred to as a stepper. In an alternative device commonly referred to as a step-and-scan apparatus, the projected beam is scanned across the patterned device in a given reference direction (the "scanning" direction) while being parallel or anti-parallel to it The substrate is moved synchronously with reference to the direction. Different portions of the pattern on the patterned device are progressively transferred to a target portion. Because the lithographic projection device will generally have a reduction factor M (usually> 1), the speed F of moving the substrate is multiplied by the factor M and the speed at which the projection beam scans the patterning device.

Before the pattern is transferred from the patterned device to the device manufacturing process of the substrate of the device manufacturing process, the substrate may undergo various device manufacturing processes of the device manufacturing process, such as priming, resist coating, and soft baking. After exposure, the substrate can be subjected to the device fabrication process of the device manufacturing process, such as post-exposure baking (PEB), development, hard baking, and measurement / inspection of the transferred pattern. This device fabrication process array is used as a basis for manufacturing individual layers of a device such as an IC. The substrate may then go through various device manufacturing processes of the device manufacturing process, such as etching, ion implantation (doping), metallization, oxidation, chemical-mechanical polishing, etc., all of which are intended to finish individual layers of the device. If several layers are required in the device, the entire procedure or a variant thereof is repeated for each layer. Eventually, there will be devices in each target portion on the substrate. If there are a plurality of devices, these devices are then separated from each other by a technique such as dicing or sawing, whereby individual devices can be mounted on a carrier, connected to pins, and the like.

Therefore, manufacturing devices such as semiconductor devices typically involves processing substrates (eg, semiconductor wafers) using several fabrication processes to form the various features and multiple layers of such devices. Such layers and features are typically manufactured and processed using, for example, deposition, lithography, etching, chemical mechanical polishing, and ion implantation. Multiple devices can be fabricated on a plurality of dies on a substrate, and then these devices are separated into individual devices. This device manufacturing process can be considered a patterning process. The patterning process involves using a patterning device in a lithography device to perform a patterning step (such as optical and / or nano-imprint lithography) to transfer the pattern on the patterning device to a substrate. The situation involves one or more related pattern processing steps, such as resist development by a developing device, baking a substrate using a baking tool, etching using a pattern using an etching device, and the like.

Whether the physical item of the physical system or object (for example, a pattern feature on the substrate) exceeds the specification (for example, a defect) is in the control, modification, design, etc. of the physical item or object or a program involving the physical item or object, etc. Important considerations. Therefore, a technology is expected to improve the prediction of physical items that exceed specifications, for example, an improved measurement sampling plan for measuring physical items (for example, pattern items on a substrate generated by a device manufacturing process).

In one embodiment, a method is provided, which includes: using a non-probability model to obtain a value of a property of an entity item instance of an entity system or object; obtaining a residual of the non-probability model relative to the entity item instance An attribute of a distribution of a set of items (ensemble), the attribute of the residual relative to the distribution of a set of entity item instances is based on a residual of the non-probability model relative to at least one entity corresponding to the set An attribute of one of the distributions of at least one entity item instance of the item type; based on the attribute of the distribution relative to the distribution of a set of entity item instances and the value of the characteristic of the entity item instance, determining An attribute of a distribution of the characteristic; and a probability of determining that the entity item instance exceeds the specification based on the attribute of the distribution of the characteristic.

In one embodiment, a method is provided, including: obtaining a test value of a characteristic of a plurality of entity item instances of an entity system or object; using a non-probability model to obtain a calculated value of the characteristic; and based on the test values And the calculated values to obtain a value of a residual of the non-probability model; to obtain an attribute of a first distribution of the residual based on the values of the residual; and to obtain an attribute of the first distribution based on the attribute of the first distribution, obtain An attribute of a residual of the non-probability model relative to a second distribution of a set of entity item instances.

In one embodiment, a method is provided, which includes: obtaining a probability that a group of entity items of an entity system or object will exceed the specifications, using a non-probability model of a residual relative to a set of entity item instances Determining a probability based on an attribute of a distribution based on an attribute of a distribution of a residual of the non-probability model relative to one of at least one entity item instance corresponding to at least one entity item type of the set; and An ordered list of entity item instances to be detected based on these probabilities.

In one embodiment, a computer program product is provided that includes a non-transitory computer-readable medium having instructions recorded thereon that, when executed by a computer system, implement any method or part of a method herein.

Before describing the embodiments in detail, it is instructive to present an example environment in which the embodiments can be implemented.

FIG. 1 schematically depicts an embodiment of the lithographic apparatus LA. The device contains:
-A lighting system (illuminator) IL, which is configured to regulate the radiation beam B (for example, electromagnetic radiation such as UV radiation or DUV radiation);
-A support structure (e.g., a photomask stage) MT that is configured to support a patterned device (e.g., a photomask) MA and is connected to a first positioning configured to accurately position the patterned device based on certain parameters器 PM; PM
-A substrate table (e.g., wafer table) WT (e.g., WTa, WTb, or both), which is constructed to hold a substrate (e.g., a resist-coated wafer) W, and is connected to Certain parameters to accurately position the second positioner PW of the substrate; and
-A projection system (e.g., a refraction, reflection, or refraction projection system) PS configured to project a pattern imparted to the radiation beam B by the patterning device MA onto a target portion C of the substrate W (e.g., including one or Multiple grains and often referred to as a field), the projection system is supported on a reference frame (RF).

As depicted herein, the device is of a transmissive type (eg, using a transmissive mask or an LCD matrix). Alternatively, the device may be of a reflective type (eg, using a programmable mirror array or using a reflective mask).

The illuminator IL receives a radiation beam from a radiation source SO (for example, a mercury lamp or an excimer laser). For example, when the radiation source is an excimer laser, the radiation source and the lithography device may be separate entities. Under these conditions, the radiation source is not considered to form a part of the lithographic device, and the radiation beam is transferred from the radiation source SO to the illuminator IL by means of a beam delivery system BD comprising, for example, a suitably guided mirror and / or a beam expander. In other situations, for example, when the radiation source is a mercury lamp, the radiation source may be an integral part of the device. The radiation source SO and the illuminator IL together with the beam delivery system BD may be referred to as a radiation system when needed.

The illuminator IL can change the intensity distribution of the light beam. The illuminator may be configured to limit the radial range of the radiation beam such that the intensity distribution in the annular region in the pupil plane of the illuminator IL is non-zero. Additionally or alternatively, the illuminator IL is operable to limit the distribution of the light beam in the pupil plane such that the intensity distribution in a plurality of equally spaced segments in the pupil plane is non-zero. The intensity distribution of the radiation beam in the pupil plane of the illuminator IL may be referred to as an illumination mode.

Thus, the illuminator IL may include an adjuster AM configured to adjust the (angle / space) intensity distribution of the light beam. Generally, at least the outer radial range and / or the inner radial range of the intensity distribution in the pupil plane of the illuminator can be adjusted (usually referred to as σ-outer and σ-inner, respectively). The illuminator IL is operable to change the angular distribution of the light beam. For example, the illuminator is operable to change the number and angular range of sections in a pupil plane whose intensity distribution is non-zero. By adjusting the intensity distribution of the light beam in the pupil plane of the illuminator, different illumination modes can be achieved. For example, by limiting the radial and angular ranges of the intensity distribution in the pupil plane of the illuminator IL, the intensity distribution may have a multipolar distribution, such as a dipole, quadrupole, or hexapole distribution. The desired lighting mode can be obtained, for example, by inserting an optical element providing the other lighting mode into the illuminator IL or using a spatial light modulator.

The illuminator IL is operable to change the polarization of the light beam and is operable to adjust the polarization 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. The use of different polarization modes allows greater contrast in the images formed on the substrate W. The radiation beam may be unpolarized. Alternatively, the illuminator may be configured to linearly polarize the radiation beam. The polarization direction of the radiation beam can be changed across the pupil plane of the illuminator IL. The polarization direction of the radiation may be different in different regions in the pupil plane of the illuminator IL. The polarization state of the radiation can be selected depending on the illumination mode. For a multi-polar illumination mode, the polarization of each pole of the radiation beam may be substantially perpendicular to the position vector of the other 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 that is substantially perpendicular to the line that bisects two opposing sections of the dipole. The radiation beam may be polarized in one of two different orthogonal directions, which may be referred to as an X-polarized state and a Y-polarized state. For the quadrupole illumination mode, the radiation in the segments of each pole may be linearly polarized in a direction substantially perpendicular to the line that bisects the other segment. This polarization mode can be referred to as XY polarization. Similarly, for a six-pole illumination mode, the radiation in the segments of each pole may be linearly polarized in a direction that is substantially perpendicular to the line that bisects the other segment. This polarization mode can be referred to as TE polarization.

In addition, the illuminator IL generally contains various other components such as a light collector IN and a condenser CO. The lighting system may include various types of optical components for directing, shaping, or controlling radiation, such as refractive, reflective, magnetic, electromagnetic, electrostatic, or other types of optical components, or any combination thereof.

Thus, the luminaire provides an adjusted radiation beam B having the desired uniformity and intensity distribution in cross section.

The support structure MT supports the patterned device in a manner that depends on the orientation of the patterned device, the design of the lithographic device, and other conditions, such as whether the patterned device is held in a vacuum environment. The support structure may use mechanical, vacuum, electrostatic, or other clamping techniques to hold the patterned device. The support structure may be, for example, a frame or a table, which may be fixed or movable as required. The photomask support structure can ensure that the patterned device is in a desired position relative to the projection system, for example. Any use of the term "reduction mask" or "reticle" herein may be considered synonymous with the more general term "patterned device."

The term "patterned device" as used herein should be interpreted broadly to mean any device that can be used to impart a pattern in a target portion of a substrate. In one embodiment, a patterned device is any device that can be used to impart a pattern to a radiation beam in a cross-section of the radiation beam to produce a pattern in a target portion of a substrate. It should be noted that, for example, if the pattern imparted to the radiation beam includes a phase shift feature or a so-called auxiliary feature, the pattern may not exactly correspond to a desired pattern in a target portion of the substrate. Generally, 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.

The patterned device may be transmissive or reflective. Examples of patterned devices include photomasks, programmable mirror arrays, and programmable LCD panels. Masks are well known to us in lithography and include mask types such as binary, alternating phase shift, and attenuation phase shift, as well as various hybrid mask types. An example of a programmable mirror array uses a matrix configuration of small mirrors, each of which can be individually tilted so that the incident radiation beam is reflected in different directions. The oblique mirror surface imparts a pattern in the radiation beam reflected by the mirror matrix.

The term "projection system" as used herein should be broadly interpreted to cover any type of projection system, including refraction, suitable for the exposure radiation used or other factors such as the use of immersed liquids or the use of vacuum. Reflective, refraction, magnetic, electromagnetic, and electrostatic optical systems, or any combination thereof. Any use of the term "projection lens" herein may be considered synonymous with the more general term "projection system."

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 the optical elements in order to correct aberrations (crossing the pupil across the field Phase change in the plane). To achieve this, the adjustment mechanism is 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, wherein the optical axis of the projection system extends in the z direction. The adjustment mechanism is operable to perform any combination of: displacing 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 can be performed in any direction (x, y, z, or a combination thereof). The tilting of the optical element usually occurs from a plane perpendicular to the optical axis by rotating around an axis in the x and / or y direction, but for non-rotationally symmetric aspherical optical elements a rotation around the z axis can be used. The deformation of the optical element may include a low-frequency shape (for example, astigmatism) and / or a high-frequency shape (for example, a free-form aspheric surface). Optics may be performed, for example, by using one or more actuators to apply a force to one or more sides of the optical element and / or by using one or more heating elements to heat one or more selected areas of the optical element Deformation of components. In general, it is not possible to adjust the projection system PS to correct apodizations (transmission changes across the pupil plane). When designing a patterned device (eg, a reticle) MA for the lithographic apparatus LA, a transmission image of the projection system PS can be used. Using computational lithography techniques, the patterned device MA may be designed to at least partially correct apodization.

Lithography devices can belong to two (dual stage) or more than two (e.g., two or more substrate stages WTa, WTb, two or more patterned device stages, Types of substrate tables WTa and WTb) below the projection system for substrates that facilitate measurement and / or cleaning, etc. In these "multi-stage" machines, additional stages can be used in parallel, or preliminary steps can be performed on one or more stages while one or more other stages are used for exposure. For example, an alignment measurement using the alignment sensor AS and / or a level measurement (height, tilt, etc.) measurement using the level sensor LS may be performed.

Therefore, in the operation of the lithographic apparatus, the radiation beam is adjusted and provided by the illumination system IL. The radiation beam B is incident on a patterned device (eg, a photomask) MA that is held on a support structure (eg, a photomask stage) MT, and is patterned by the patterned device. In the case where the patterned device MA has been traversed, the radiation beam B passes through the projection system PS, and the projection system PS focuses the beam onto the target portion C of the substrate W. With the second positioner PW and the position sensor IF (for example, an interference measurement device, a linear encoder, a 2D encoder, or a capacitive sensor), the substrate table WT can be accurately moved, for example, in the radiation beam B Locate different target parts C in the path. Similarly, for example, after a mechanical acquisition from a photomask library or during a scan, a first positioner PM and another position sensor (which is not explicitly depicted in FIG. 1) may be used relative to the radiation beam The path of B accurately positions the patterned device MA. Generally speaking, the movement of the support structure MT is achieved by means of a long-stroke module (coarse positioning) and a short-stroke module (fine positioning) that form the components of the first positioner PM. Similarly, the long-stroke module and the short-stroke module forming part of the second positioner PW can be used to realize the movement of the substrate table WT. In the case of a stepper (as opposed to a scanner), the support structure MT may be connected to a short-stroke actuator only, or may be fixed. By using the alignment system, the patterned device MA and the substrate W can be aligned using the patterned device alignment marks M1, M2 and the substrate alignment marks P1, P2. Although the substrate alignment marks occupy dedicated target portions as illustrated, the marks may be located in the space between the target portions (these marks are referred to as scribe lane alignment marks). Similarly, in the case where more than one die is provided on the patterned device MA, the patterned device alignment mark may be located between the die. Small alignment marks can also be included in the crystal grains in the device features. In this case, it is necessary to make the marks as small as possible without requiring any imaging or procedural conditions that are different from neighboring features.

The depicted device may be used in at least one of the following modes:

1. In the step mode, when the entire pattern imparted to the radiation beam is projected onto the target portion C at one time, the supporting structure MT and the substrate table WT are kept substantially stationary (ie, a single static exposure). Next, the substrate table WT is shifted in the X and / or Y direction so that different target portions C can be exposed. In the step mode, the maximum size of the exposure field limits the size of the target portion C imaged in a single static exposure.

2. In the scan mode, when the pattern imparted to the radiation beam is projected onto the target portion C, the support structure MT and the substrate table WT are scanned synchronously (ie, a single dynamic exposure). The speed and direction of the substrate table WT relative to the support structure MT can be determined by the magnification (reduction rate) and image inversion characteristics of the projection system PS. In the scanning 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), and the length of the scanning motion determines the height of the target portion (in the scanning direction).

3. In another mode, when the pattern imparted to the radiation beam is projected onto the target portion C, the support structure MT is kept substantially stationary, thereby holding the programmable patterning device, and moving or scanning the substrate table WT . In this mode, a pulsed radiation source is typically used and the programmable patterned device is updated as needed after each movement of the substrate table WT or between successive radiation pulses during scanning. This mode of operation can be easily applied to maskless lithography using a programmable patterned device such as a programmable mirror array of the type mentioned above.

Combinations and / or variations of the usage modes described above or completely different usage modes can also be used.

As shown in FIG. 2, the lithographic apparatus LA may form part of a lithographic manufacturing unit LC (sometimes also referred to as a lithocell or cluster). The lithographic manufacturing unit LC also includes Device for pre-exposure procedure and post-exposure procedure. Conventionally, such devices include one or more spin coaters SC for depositing one or more resist layers, one or more developers DE for developing exposed resist, one or more The cooling plate CH and / or one or more baking plates BK. The substrate handler or robot RO picks up one or more substrates from the input / output ports I / O1, I / O2, moves them between different process devices and delivers them to the loading box LB of the lithographic device. These devices, often collectively referred to as the coating and developing system (track), are controlled by the coating and developing system control unit TCU. The coating and developing system control unit TCU itself is controlled by the supervisory control system SCS, and the supervisory control system SCS is also controlled by the lithographic control unit LACU. And control the lithography device. Therefore, different devices can be operated to maximize throughput and processing efficiency.

Examples of physical items (such as pattern features on a substrate) of a physical system or object may not be perfect in meeting the associated specifications. That is, the physical item characteristics (eg, size, shape, etc.) of the physical item instance group may have significant variability in meeting specifications. This variability can be systematic or random. Therefore, it may be difficult to predict whether an entity item is out of specification, especially due to random changes. Therefore, the technology provided in this article can improve the prediction of physical items that exceed specifications (for example, pattern instances on substrates produced by device manufacturing processes) for use in, for example, physical items or objects or involving physical items or objects. Control, modification, design, etc. of procedures and / or establishment of improved measurement sampling plans for measuring physical items.

Now, in order to explain the embodiments of the technology without intending to limit the generality of the present invention, the present invention focuses on pattern instances on a substrate generated by a device manufacturing process as examples of physical item instances of a physical system or object, and focuses on The defects in these pattern instances are that the entity item instances exceed the specifications. The embodiments of the present invention are not limited to these specific examples.

Therefore, in the case of considering the pattern examples on the substrate, the pattern patterns generated by the device manufacturing process may not all be perfect. If some of the patterns exceed their respective design specifications, they can be considered defects. Defects can be caused by many factors. Factors may include system imperfection of lithographic devices or other hardware used in the device manufacturing process. If these factors can be measured, the defects caused by these factors alone can be predicted with a relatively high degree of certainty, because the relationship between these factors and the pattern is clear. Factors may include random variations of lithographic devices or other hardware used in the device manufacturing process. Random changes can be attributed to a variety of mechanisms, such as photon shot noise, thermal noise, mechanical vibration, and more. Because of the random nature of these factors, it can be extremely difficult to clearly predict defects caused by at least some of these factors.

FIG. 3 schematically depicts a method for predicting defects in a device manufacturing process. Examples of defects may include necking, wire end pullback, wire thinning, incorrect CD, overlap, bridging, and / or other defects. The defect may be in a resist image, an optical image, or an etched image (that is, a pattern transferred to a substrate layer by etching using the resist thereon as a photomask). At 213, the model is used to calculate characteristics 214 (eg, presence, location, type, shape, etc.) of the pattern based on one or more program parameters 211 and / or one or more layout parameters 212 of the device manufacturing process. The program parameters 211 are parameters that are associated with the device manufacturing process but are not associated with the layout. For example, the program parameters 211 may include characteristics of illumination (e.g., intensity, pupil profile, etc.), characteristics of projection optics, dose, focus, characteristics of resist, characteristics of resist development, resist Characteristics of baking after exposure of the agent, and / or characteristics of etching. The layout parameters 212 may include the shape, size, relative position and / or absolute position of various features on the layout, and / or the overlap of features on different layouts. In one example, the model is an empirical model. In the empirical model, the patterns that can be in the resist image, aerial image, or etch image are not simulated. In fact, the empirical model is based on the input of the empirical model (for example, one or more The correlation between the program parameters 211 and / or the layout parameters 212) and the characteristics 214 (eg, presence, location, type, shape, etc.) of the pattern determines the characteristics. In one example, the model is a computational model in which at least a portion of a pattern is simulated and a characteristic 214 is determined from that portion, or the characteristic 214 is simulated without simulating the pattern itself. At 215, it is determined whether the pattern is a defect or the probability of a pattern-based defect based on the characteristic 214. For example, a wire-end pull-back defect can be identified by finding the end of the wire that is too far away from the desired portion of the wire; a bridging defect can be identified by finding a location where the two wires are not ideally joined.

Examples of applicable calculation methods are described in US Patent Application Publication No. US 2015-0227654, PCT Patent Application Publication No. WO 2016-128189, PCT Patent Application Publication No. WO 2016-202546, PCT Patent Application Publication No. WO 2017-114662 and US Patent Application No. 62 / 365,662, each of which is incorporated herein by reference in its entirety.

In one embodiment, the model may be in the form of a polynomial, including one or more program parameters of the device manufacturing process as variables. For example, the polynomial can be characterized by one or more of the following: focus, dose, moving average (MA) of servo error of lithography device stage, moving standard deviation (MSD) of servo error of lithography device stage, Patterned device pattern error and / or etch parameters. In one embodiment, one or more variables may be characterized spatially on the substrate (eg, having X and Y coordinates, having radial coordinates, etc.). As an example, the polynomial can be specified based on at least the focus and dose, where the focus and dose are spatially characterized on the substrate.

An exemplary flowchart of a method of modeling and / or simulating portions of a patterning process in FIG. 3, such as a pattern in a modeling and / or simulation image (e.g., resist image, aerial image, etch image) Characteristics of at least a portion or pattern. As should be appreciated, the models may represent different patterning procedures and need not include all models described below.

As described above, in the lithographic projection device, the illumination system provides illumination (ie, radiation) to the patterned device, and the projection optics directs the illumination from the patterned device onto the substrate. Therefore, in one embodiment, the projection optics enable the formation of an aerial image (AI), which is the radiation intensity distribution at the substrate. The resist layer on the substrate is exposed, and an aerial image is transferred to the resist layer as a latent "resist image" (RI) therein. The resist image (RI) can be defined as the spatial distribution of the solubility of the resist in the resist layer. In one embodiment, the simulation of the lithography process can simulate the generation of aerial images and / or resist images.

The illumination model 31 represents the optical characteristics (including radiation intensity distribution and / or phase distribution) of the illumination mode used to generate the patterned radiation beam. The lighting model 31 may represent the optical characteristics of the lighting, including but not limited to numerical aperture settings, lighting standard deviation (σ) settings, and any particular lighting mode shape (eg, off-axis radiation shapes such as ring, quadrupole, dipole, etc.) Where 0 (or standard deviation) is the outer radial range of the luminaire.

The projection optics model 32 represents the optical characteristics of the projection optics (including changes to the radiation intensity distribution and / or phase distribution caused by the projection optics). The projection optics model 32 may include optical aberrations caused by various factors such as heat generation of components of the projection optics, and stress caused by mechanical connection of the components of the projection optics. The projection optics model 32 may represent the optical characteristics of the projection optics, including one or more of the following: aberration, distortion, refractive index, entity size, entity dimension, absorption rate, and so on. The lithographic projection device's optical properties (eg, properties of lighting, patterning device patterns, and projection optics) specify aerial images. Since the patterned device pattern used in the lithographic projection device can be changed, it is necessary to separate the optical properties of the patterned device pattern from the optical properties of the rest of the lithographic projection device including at least illumination and projection optics. The illumination model 31 and the projection optics model 32 can be combined into a transmission cross-coefficient (TCC) model.

Patterned device pattern model 33 represents the optical characteristics of patterned device patterns (e.g., device design layouts corresponding to the characteristics of integrated circuits, memory, electronic devices, etc.) (including radiation exposure caused by a given patterned device pattern Changes in intensity distribution and / or phase distribution), patterned device pattern is a representation of the configuration of features on or formed by a patterned device. The patterned device model 33 captures how design features are arranged in the pattern of the patterned device, and may include detailed physical attributes of the patterned device and a representation of the patterned device pattern, for example, as described in U.S. Patent No. 7,587,704. Patents are incorporated herein by reference in their entirety.

The resist model 37 may be used to calculate a resist image from an aerial image. An example of this resist model can be found in US Patent No. 8,200,468, which is incorporated herein by reference in its entirety. Resist models typically describe the effects of chemical procedures that occur during resist exposure, post-exposure bake (PEB), and development in order to predict, for example, the contours of resist features formed on a substrate, and therefore they are usually only related to These properties of the resist layer, such as the effects of chemical processes that occur during exposure, post-exposure baking, and development, are related. In one embodiment, optical properties of the resist layer, such as refractive index, film thickness, propagation, and polarization effects, can be captured as part of the projection optics model 32.

With these models, the self-illumination model 31, the projection optics model 32, and the patterned device pattern model 33 can simulate an aerial image 36. Aerial image (AI) is the radiation intensity distribution at the substrate level. The optical properties of lithographic projection devices (eg, properties of lighting, patterning devices, and projection optics) specify aerial images.

As mentioned above, the resist layer on the substrate is exposed by an aerial image, and the aerial image is transferred to the resist layer as a latent "resist image" (RI) therein. The resist image 37 may be simulated from the aerial image 36 using the resist model 37. Therefore, in general, the connection between the optical model and the resist model is the simulated aerial image intensity in the resist layer, which results from the projection of radiation onto the substrate, refraction at the resist interface, and resist Multiple reflections in a film stack. The radiation intensity distribution (air image intensity) is converted into a latent "resist image" by absorption of incident energy, and the latent resist image is further modified by a diffusion process and various loading effects. An efficient simulation method fast enough for full-chip applications approximates the actual 3-dimensional intensity distribution in a resist stack by 2-dimensional aerial (and resist) images.

In one embodiment, a resist image can be used as an input to the post-pattern program model 39. The post-pattern process model 39 defines that one or more post-resist development processes (eg, etching, CMP, etc.) are performed and a post-etch image 40 can be generated. That is, the etched image 40 can be simulated from the resist image 36 using the pattern transfer program model 39.

Therefore, this model formulates most, if not all, of the total procedures known physical and chemical methods, and each of the model parameters ideally corresponds to a distinct entity or chemical effect. Therefore, model formulation sets an upper limit on how well a model can be used to simulate the total manufacturing process.

For example, simulations of the patterning process can predict contours in the air, resist and / or etched images, CDs, edge placement (eg, edge placement errors), pattern shifts, and so on. That is, the characteristics of the pattern (eg, the presence, location, type, shape, etc. of the pattern) may be determined using the aerial image 34, the resist image 36, or the etched image 40. Therefore, the objective of the simulation is to accurately predict, for example, the edge placement and / or contour of the printed pattern, and / or the pattern shift, and / or the slope of the aerial image intensity, and / or the CD and so on. This value can be compared to the expected design to, for example, correct the patterning process, identify where the defect is predicted to occur, and so on. Prospective designs are often defined as pre-OPC design layouts that can be provided in a standardized digital file format such as GDSII or OASIS or other file formats.

Used to transform patterned device patterns into various lithographic images (e.g., aerial images, resist images, etc.), use their technologies and models to apply OPC, and evaluate techniques and models implemented (e.g., according to program windows) Details are described in U.S. Patent Application Publication Nos. US 2008-0301620, 2007-0050749, 2007-0031745, 2008-0309897, 2010-0162197, 2010-0180251, and 2011-0099526. The disclosure of one is incorporated herein by reference in its entirety.

To facilitate the speed of the evaluation model, one or more portions can be identified from the patterned device pattern, which is referred to as a "clip." In a particular embodiment, a collection of clips is extracted, which represents a complex pattern in a patterned device pattern (typically about 50 to 1000 clips, but any number of clips can be used). As those skilled in the art will appreciate, these patterns or clips represent a small portion of the design (ie, a circuit, cell, or pattern), and in particular, these clips represent a small portion that requires specific attention and / or inspection. In other words, the clip can be part of a patterned device pattern, or it can be similar or have critical features identified by experience (including clips provided by the customer), identified by trial and error, or performed by performing a full-chip simulation Similar behavior of the patterned part of the patterned device. Clips usually contain one or more test patterns or gauge patterns. The initial large set of clips can be provided a priori by the customer based on known critical feature areas in the patterned device pattern that require specific considerations. In one embodiment, an initial larger set of clips can be extracted from the entire patterned device pattern by using some kind of automatic (such as machine vision) or manual algorithm to identify critical feature areas.

In addition, various patterns on or provided by a patterned device may have different program windows, that is, a space for processing variables, under which the pattern will be produced within specifications. Examples of pattern specifications for potential systemic defects include inspection necking, line end pullback, line thinning, CD, edge placement, overlap, resist top loss, resist undercut, and / or bridging. The program windows of all the patterns on the patterned device or its area can be obtained by merging the program windows of each individual pattern (eg, overlapping the program windows). The boundaries of the program windows of all patterns include the boundaries of some of the program windows of individual patterns. In other words, these individual patterns limit the program window for all patterns. These patterns may be referred to as "hot spots" or "program window restriction patterns (PWLP)", and "hot spots" and "program window restriction patterns (PWLP)" are used interchangeably herein. Focusing on hot spots is possible and economical when designing, modifying, and the like as part of a patterning program using modeling such as described herein. When the hot spot is not defective, it is most likely that all patterns are not defective.

Therefore, current methods that identify actual defects on a substrate based on relatively fast optical inspection may encounter resolution issues when trying to detect small defects (eg, sub-10 nm defects). Electron beam systems, on the other hand, are often too slow to be used in high-volume manufacturing (HVM) to detect defects in a large number of locations. Therefore, as described above, calculation methods can be used to help identify where defects should be located on the substrate, and then guide an electron beam inspection (EBI) tool to those locations. This can increase the effective detection speed of EBI and make it useful for finding small defects (e.g., sub-10 nm defects) in HVM.

Of course, the effectiveness of using computational methods to identify potential defects to improve detection speed depends on the model used to guide the EBI tool to the relevant defect site with high accuracy. However, a problem with these calculation methods when looking for small defects (for example, sub-10 nm defects) is that the modeling used to identify the defect site cannot perfectly predict how a pattern will be produced on a product substrate. Therefore, there is a model residual, that is, a difference between a predicted size and a measured size of a pattern.

The magnitude of these model residuals (e.g., noise) can be commensurate with the small defects that the computational method attempts to predict. This leads to significant uncertainty as to whether the defect will appear at the predicted location. Therefore, in order to achieve an acceptable certainty level during which all defects are found on the substrate during inspection, the EBI tool should access all parts of the calculation method that indicate the possibility of a defect; that is, the limits used to identify defects may require Better wide to ensure that all or most defects are captured. This means that EBI tools will have to detect a significant number of unnecessary sites (obstructions) in order to capture actual defects. This may cause unnecessary detection time and poor correlation between the number of measured points and the actual number of defects. That is, for example, the number of points on any given substrate that will need to be sampled to determine the actual number of defects is significantly greater than the actual number of defects, and its ratio to the actual number of defects on any given substrate is not Must be constant. Therefore, the detection time may be significantly longer than required.

Now, although random changes are random, their statistics may not be so. Therefore, it is possible to predict defects statistically, in other words, it is possible to predict the probability of defects. Therefore, in an embodiment, a probability model or method is used at 213 in FIG. 3, that is, a model or method for calculating the probability of a characteristic of a defect having a certain value. For example, a probability model or method can predict the probability that a pattern in an image has a certain shape or a certain CD. Rather than using only non-probability models, probabilistic models or methods are better at capturing random changes in the device manufacturing process.

5A, 5B, 5C, and 5D schematically show that the probability model method can better consider the random variation than the calculation method using only the non-probability model, and therefore, for example, better guides the inspection of the device manufacturing process. Generated in the substrate. 5A and 5B each show a non-probability model calculating a value 420 of a characteristic of an example of a pattern on a substrate generated by a device manufacturing process. A non-exhaustive list of characteristic examples may include one or more of the following: the position of the pattern relative to the substrate, the position of the pattern relative to one or more other pattern instances on the substrate, the geometric size (e.g., CD ), Geometry, and / or measures of random effects (eg, CD uniformity (CDU), line width roughness (LWR), line edge roughness (LER), etc.). If the characteristic fails to meet the condition (in this case, for example, if the characteristic is less than the threshold 410), the pattern instance is defective; if the characteristic meets the condition (for example, if the characteristic is greater than the threshold 410), then The legend items are not defects. The value 420 is greater than the threshold value 410 in the example shown in FIGS. 5A and 5B. Therefore, based on the non-probability model, this pattern instance should not be considered a defect.

However, like any model, the non-probability model may not be completely accurate. The calculated values of the characteristics of the pattern instances by the non-probability model may differ from the actual values of the characteristics of the generated pattern instances. This difference is called the residual. Residuals can be attributed to, for example, random variations, flaws in non-probability models, inputs to non-probability models, or a combination thereof. In the example of FIGS. 5A and 5B, if the residual is sufficiently large (for example, greater than the difference between the value 420 and the threshold value 410), the actual value of the characteristics of the pattern instance of the determination value 420 may be less than the threshold 410, and the pattern items are defects.

In practice, the residuals may have a distribution (for example, distribution 430 in FIG. 5A and distribution 431 in FIG. 5B), which is characterized by, for example, the number of occurrences of the residual value, the occurrence probability of the residual value, and the like. For example, in practice, specific patterns can be generated in different sizes on the substrate, but the predicted sizes of their pattern instances on the substrate can be the same or can be predicted from changes that are different from the actual generated size. Therefore, there will be a distribution of residual values.

The distribution 430 of the residuals in the example of FIG. 5A is wider than the distribution 431 of the residuals in the example of FIG. 5B. In detail, the probability that the residual error in the example of FIG. 5A is greater than the difference between the value 420 and the threshold 410 is greater than the example of FIG. 5B. In other words, in the example of FIG. 5A, the probability that the actual value of the pattern instance of the determination value 420 is less than the threshold 410 is greater than that of the example of FIG. 5B; the probability of the pattern instance in the example of FIG. 5A is greater than that of FIG. 5B. Instance. The non-probability model cannot capture the distribution of residuals (e.g., distributions 430 and 431), and therefore cannot capture some defects (or many of the defects in the example of FIG. 5A).

Similarly, non-probability models may predict non-defects as defects. FIG. 5C and FIG. 5D each show a value 421 of the characteristic of another pattern instance on the substrate calculated by the non-probability model. In one embodiment, the pattern of the calculated value 421 is the same as the pattern of the calculated value 420. The difference in the judgment value may be due to, for example, a general pattern transfer condition that is different from the pattern example of the calculated value 421 compared to the pattern transfer condition of the calculated value 420. As an example, compared to the pattern instance of the calculated value 420, the pattern instance of the calculated value 421 may have different conditions such as focus and dose, thereby causing a difference between the calculated values 420 and 421.

Therefore, if the characteristics of the pattern instance (for example, the value 421) cannot satisfy the condition (in this article, for example, if the characteristic is less than the threshold 410), the pattern instance is defective; if the characteristic meets the condition (in this article, for example, If the characteristic is greater than the threshold value 410), the pattern instance is not a defect. In this example, the value 421 is less than the threshold 410, as shown in FIGS. 5C and 5D. Therefore, based on the non-probability model, this pattern instance should not be considered a defect.

However, in the examples of FIGS. 5C and 5D, if the residual is sufficiently large (for example, greater than the difference between the value 421 and the threshold 410), the actual value of the characteristics of the pattern instance may be greater than the threshold 410, And that pattern is not a defect. The distribution 430 of the residuals in the example of FIG. 5C is wider than the distribution 431 of the residuals in the example of FIG. 5D. In detail, the probability that the residual error in the example of FIG. 5C is greater than the difference between the value 421 and the threshold 410 is greater than the example of FIG. 5D. In other words, in the example of FIG. 5C, the probability that the actual value of the pattern instance of the determination value 421 is greater than the threshold 410 is greater than the example of FIG. 5D; the probability of the pattern instance in the example of FIG. 5C is not a defect is greater than that of FIG. Instance. Non-probability models cannot capture the distribution of residuals (eg, distributions 430 and 431), and therefore predict some non-defects (or many non-defects in the example of FIG. 5C) as defects.

Therefore, in one embodiment, the probability calculation method is used to generate a “statistical defect”, which is a probability that a specific part identified by the calculation method of determining whether the part is a defect is actually a defect. In one embodiment, the probability may be a probability number between 0 and 1.

In one embodiment, the probability calculation method uses a set of one or more hotspots (where hotspots are program-sensitive features within the die to be patterned) and program information obtained using metrology to assign each hotspot considered to be its Probability of defects in one or more locations on the substrate printed with instances of each hot spot. In one embodiment, the total number of defects on the substrate that are statistically expected from a set of hotspot instances under consideration is the sum of all probabilities of hot spots at all predicted locations on the substrate.

FIG. 6 schematically shows how a probability calculation method is used to predict defects according to an embodiment. The non-probability model 555 is used to calculate the value 520 of the characteristics of the instance of the pattern 510 on the substrate generated by the device manufacturing process. A non-exhaustive list of characteristic examples may include one or more selected from the following: position relative to the substrate, position relative to one or more other pattern instances on the substrate, geometric size (e.g., CD), Geometry, and / or a measure of random effects (eg, CD uniformity (CDU), line width roughness (LWR), etc.). The non-probability model 555 may calculate the value 520 based on one or more program parameters or layout parameters or empirically. In one embodiment, the distribution 530 of residuals of the non-probability model 555 is added to the value 520 to generate a distribution 540 of characteristics. The distribution 540 can be used to calculate the probability that the pattern 510 is a defect (eg, the probability that the characteristic exceeds a range between the threshold 551 and 552).

FIG. 7 shows a flowchart of a method of calculating a probability of a defect on a substrate generated by a device manufacturing process according to an embodiment. At 610, an attribute 620 of the distribution of the residuals of the non-probability model is obtained. An example of attribute 620 is the probability density function (PDF) of the residuals. In one embodiment, the PDF can be normalized such that the sum of the probability in the distribution is a specific value, for example, 1. Another example of an attribute 620 is the cumulative distribution function (CDF) or empirical cumulative distribution function (eCDF) of the residuals (also known as the empirical distribution function (EDF)). The eCDF can be determined from the value of the residual. eCDF is a distribution function associated with an empirical measure of a sample (eg, residual values obtained from a plurality of pattern instances, as discussed below). eCDF is a step function that rises by 1 / n at each of the n data points (eg, residual values obtained from a plurality of pattern instances). The eCDF can be defined using: , Where ( x ₁ ,…, x _n ) are the values in the sample, and It is the indicator of event A. The value of eCDF at any given value t Is the score of the sample less than or equal to t. According to Glivenko-Cantelli's theorem, it converges with probability 1 to the basic distribution with increasing n. CDF can be estimated based on eCDF. ECDF can be based on e.g. Dvorestzky-Kiefer-Wolfowitz (DKW) inequality To estimate the CDF . The estimated CDF error based on eCDF is bounded by the following DKW inequality: . The DKW inequality is shown, and the estimation error cannot be used to construct the EDF To determine the number of residual values n.

In one embodiment, the attribute 620 is an attribute representing the dispersion (eg, variance and / or standard deviation) of the distribution. In one embodiment, the attribute 620 is used for a specific pattern type or a set of pattern types. In one embodiment, the attribute 620 is used for a specific hotspot or a set of hotspots. As should be understood, a plurality of different attributes 620 are obtained, each of which corresponds to a different pattern type or set of pattern types.

At 630, a non-probability model is used to calculate a value 640 for the characteristics of the pattern instances on the substrate. A non-exhaustive list of characteristic examples may include one or more selected from the following: position relative to the substrate, position relative to one or more other pattern instances on the substrate, geometric size (e.g., CD), Geometry, and / or a measure of random effects (eg, CD uniformity (CDU), line width roughness (LWR), etc.). In one embodiment, a value 640 is calculated for the pattern type where the attribute 620 exists (eg, it matches the pattern type of the attribute 620 or a set of pattern types that match the attribute 620).

At 650, an attribute 660 of the characteristic distribution is determined based on the attribute 620 of the distribution of the residuals and based on the value 640 calculated using the non-probability model. In one example, the attribute 660 is the sum of the value 640 calculated using the non-probability model and the attribute 620 of the distribution of the residuals.

At 670, a probability 680 that the pattern instance is defective is determined based on the attribute 660. In one example, the attribute 660 is a PDF of the characteristic, and the probability 680 may be an integration of the PDF within the characteristic range. For example, the probability 680 may be the integration of PDFs within a range below the defect threshold and / or above a defect threshold. In an example, the attribute 660 is the CDF or eCDF of the characteristic, and the probability 680 may be the value of the CDF or eCDF at the upper limit of the characteristic range (for example, the defect occurs below the defect threshold) and / or 1 (assuming the CDF or eCDF characterizes the probability in the range of 0 to 1) minus the value of CDF or eCDF at the lower limit of the range (for example, a defect occurs above a defect threshold). In one embodiment, the attribute 660 is normalized. For example, the expected value of the total number of defects of one or more pattern instances on the substrate under consideration is expected to be equal to one or more of the images on the substrate. Each case item is the sum of the probability of a defect.

As should be understood, steps 610, 630, 650, and 670 may be repeated for as many pattern instances as necessary, and may be repeated for as many different pattern types as necessary. In one embodiment, steps 610, 630, 650, and 670 are repeated for each instance of the pattern type on the substrate.

As mentioned above, the method of FIGS. 6 and 7 involves the attribute 620 of the distribution of the residuals of the non-probability model. FIG. 8 schematically illustrates how the attribute 620 of the distribution of the residuals of the non-probability model can be obtained according to an embodiment (eg, as in step 610 of FIG. 7).

A plurality of pattern instances (eg, 710a, 710b, ... 710i, ...) on the substrate generated by the device manufacturing process are selected. In one embodiment, the examples may all have the same pattern type. In one embodiment, each item may have a different pattern type. In an embodiment, the instances may include a plurality of instances for each of a plurality of different pattern types. Where there are multiple pattern types, one or more criteria may be used to select a set of multiple pattern types. For example, in one embodiment, the pattern types of the set are pattern types having similar shapes, similar sizes, similar functions, and / or spatial proximity. In one embodiment, the pattern types of the set are pattern types having similar sensitivity to changes in the device manufacturing process. In this context, similar differences may not exceed 20% of the applicable standards, 15% of the applicable standards, 10% of the applicable standards, not more than 5% of the applicable standards, or 1% of the applicable standards. Therefore, in general, pattern types of collections have similar behaviors related to defects when they are generated. As an example, the plurality of pattern types may each be an isolated contact hole type, each of the dense contact hole types, and the like. As discussed above, each of the one or more pattern types may be a hot spot (which enables focusing on pattern features that may be defective rather than pattern features with little risk of defect).

A non-probability model is used to obtain calculated values for the characteristics of these pattern instances (eg, 730a, 730b, ... 730i, ...). A non-exhaustive list of feature examples may include one or more of the following: the position of the pattern instance relative to the substrate, the position of the pattern instance relative to one or more other pattern instances on the substrate, the geometric size (Eg, CD), geometry, and / or measures of random effects (eg, CD uniformity (CDU), line width roughness (LWR), line edge roughness (LER), etc.). The test values of the characteristics of these pattern instances (for example, 720a, 720b, ... 720i, ...) may be actual values of characteristics obtained by measuring the pattern instances, for example, using a suitable metrology tool, or using a rigorous model Analog value of the characteristic performed. Examples of metrology tools may include optical metrology tools that measure optical images, diffraction, scattering, or other suitable optical signals from a substrate, and / or metrology tools that use a beam of charged particles (eg, electrons). The value of the residual of the non-probability model is obtained from the difference between the test value and the calculated value of each of these pattern instances.

An attribute 620 of the distribution of the residual is obtained from the value of the residual. In one example, the attribute 620 is a PDF of the residuals, which can be determined from a histogram of the residuals. In another example, attribute 620 is the CDF or eCDF of the residual.

In an embodiment, the attribute 620 may be obtained for each of a plurality of different pattern types and / or pattern type groups. That is, in one embodiment, the calculated values (for example, 730a, 730b, ... 730i, ...) of the characteristics of the related pattern type items (for example, 710a, 710b, ... 710i, ...) and related pattern type examples can be used Residuals calculated from the test values (eg, 720a, 720b, ..., 720i, ...) of the characteristics of the term obtain a plurality of attributes 620. For example, at least one of the attributes 620 may be used for a different pattern type than the other of the attributes 620. Additionally or alternatively, at least one of the attributes 620 may be used for a different set of pattern types than the other of the attributes 620.

FIG. 9 shows a flowchart of a method (for example, step 610 in FIG. 7) of a method for obtaining an attribute 880 (for example, property 620 in FIG. 7) of a residual of a non-probability model according to an embodiment. At 810, for example, by measuring a pattern instance using a metrology tool or by performing a simulation using a rigorous model, a check value 820 of the characteristics of the plurality of pattern instances on the substrate is obtained. At 830, a non-probability model of the pattern instance is used to obtain a calculated value 840 of the characteristic.

At 850, a value 860 of the residual of the non-probability model is obtained based on the test value 820 and the calculated value 840. In one example, the residual value 860 is the difference between the calculated value 840 and the test value 820. At 870, an attribute 880 of the distribution of the residual is obtained based on the value 860 of the residual (for example, the attribute 620 in FIG. 7 in the form of, for example, PDF or CDF or eCDF). In an embodiment, the number of instances of the difference between the calculated value 840 and the check value 820 may be changed to the probability of their difference in order to generate a PDF in the form of a probability (eg, a probability in the range of 0 to 1) CDF or eCDF.

As should be understood, steps 810, 830, 850, and 870 may be repeated for each attribute 880 desired (e.g., for different pattern types, different sets of multiple pattern types, etc.). In addition, once one or more attributes 880 and a range of characteristics of the pattern are considered defects (eg, one or more defect thresholds where applicable), one or more attributes 880 are used as one or more attributes 620 and The range in which a pattern is considered a characteristic of a defect (for example, one or more defect thresholds where applicable) can be used for a large number or production of the methods of FIGS. 6 and 7. That is, a range of characteristics (e.g., one or more defect thresholds that apply) where one or more attributes 620 and patterns are considered to be defects may be obtained in the initial (e.g., one) learning phase, then in Figures 6 and 6 The method of FIG. 7 is reused for one or more substrates in bulk or manufacturing applications.

In the case where the inspection value 820 is obtained by metrology, the attribute 880 may be obtained using results from one generated substrate, or the attribute 880 may be obtained using results from more than one generated substrate. In one embodiment, the inspection value 820 may be obtained using one or more "test" substrates. The "test" substrate may be one or more substrates manufactured using a device manufacturing process or one or more specially produced substrates (e.g., Depending on, for example, the characteristics of interest, CDU substrates, Focus Exposure Matrix (FEM) substrates, programmed stacked substrates, etc.).

10A, 10B, 10C, 10D, 10E, 10F, and 10G each show an example histogram of residuals as an example of an attribute 880. The probability of the frequency or value of the horizontal axis residual value and the vertical axis value. The histograms shown in FIGS. 10A to 10G are used for each of one of the seven pattern type sets, each set having a nominal CD different from the other set for one or more of the pattern types.

The attribute of the characteristic distribution (for example, 660 in FIG. 7) is a factor that determines the probability of a pattern defect, but is not necessarily the only factor. Selecting the range in which a pattern is considered a characteristic of a defect (eg, one or more defect thresholds where applicable) may be another factor. Other factors are also possible. In one example shown schematically in FIG. 11, the probability of a pattern-based defect is CD 1030 (an example of a property of a distribution of characteristics) integrated within a range of negative infinity to a threshold value of 1010. Practical considerations 1020 will affect the choice of threshold 1010. For example, the variance of an acceptance characteristic from its nominal value in a device manufacturing process specifies, at least in part, a threshold value of 1010. That is, only a certain amount of variance can be tolerated, at which point the pattern instance is considered a defect (for example, the device may not operate properly). As another example, if the total number of inspections or the amount of time available for inspection is limited, the threshold 1010 may be made smaller or larger depending on the circumstances, thereby reducing the number of pattern instances identified as potential defects, And thus reducing the number of inspections or inspection time that reduces the number of potential defects.

In an embodiment, the threshold value 1010 may be configured using data from, for example, one or more generated test or manufacturing substrates. For example, a threshold value of 1010 may be selected so that, based on the threshold value, the total probability of defects calculated using the probability calculation method is equal to or equivalent to the actual number of defects on one or more test or manufacturing substrates ( (For example, within an order of magnitude of the actual number). For example, the method as described above with respect to FIGS. 6 and 7 may be used with one or more attributes 620, such as using the method of FIGS. 8 and 9 using one or more test or manufacturing substrates Judgment is to use the initial threshold of 1010 to determine the probability of a defect. The probability of a defect can then be used to calculate the number of defects (eg, the sum of the probabilities) on one or more manufacturing or substrates. This predicted number of defects can be compared to the number of defects measured on one or more test or manufacturing substrates using their initial threshold of 1010. If the number of defects measured by them is equal to or equal to the predicted number of defects (for example, within an order of magnitude of the predicted number), the threshold 1010 is sufficient and can be used for a large number of the methods of FIGS. 6 and 7. Or manufacturing use. However, if the measured number of defects is not equal to or equal to the predicted number of defects (for example, within an order of magnitude of the predicted number), then the threshold 1010 can be adjusted, and then the adjusted threshold 1010 can be used to Repeat the analysis using the method of FIGS. 6 and 7 with one or more attributes 620 to obtain the predicted number of defects. This new prediction of the number of defects can be compared with the measured defects judged using the adjusted threshold 1010, and their comparison can be used to determine the threshold 1010 or the process needs to be repeated until an appropriate threshold 1010 is obtained . This may be characterized as a machine learning process that reaches an appropriate threshold of 1010 (or more generally, the range of characteristics of the pattern that are considered defects (eg, one or more defect thresholds where applicable)).

In one embodiment, the probability calculation method can adjust (by machine learning) the statistical defect accuracy obtained over time by adding data points when the probability calculation method is used in a large amount or in a manufacturing application. For example, data from one or more substrates analyzed using the probabilistic method of Figures 6 and 7 from one or more substrates may be used to calculate updated or additional values and / or patterns for one or more attributes 620 are considered as The range of characteristics of the defect (eg, one or more defect thresholds that apply). In one embodiment, from time to time, data from one or more test substrates analyzed outside the bulk or manufacturing uses of the probabilistic methods of FIGS. 6 and 7 may be used to calculate updated or Additional values and / or patterns are considered to be a range of characteristics of the defect (eg, one or more defect thresholds that apply). For example, periodically or continuously updating PDFs through feedback mechanisms from inspection data can significantly improve predictions (adaptive predictions) (for example, if measuring about 1 substrate / batch, it can be about 200 wafers / day, There are about 2000 measurements / substrates and more than 100 CD values / measurements. For example, each lithographic device generates more than 40 million data points per day, which is significantly improved prediction data).

The probability of one or more pattern instances being defects can be used for various purposes. For example, the probability can be used to derive a statistical defect count for each substrate, which should be close to the actual number of defects actually present on any given substrate. In one embodiment, a statistical process chart may be established based on the statistical defect count. This also allows the decision to further process substrates analyzed using this probability calculation method with, for example, fast turnaround times.

Probability and / or statistical defect counts can be used to prioritize parts to be inspected with a metrology tool, such as an electron beam inspection tool. Based on the probability and / or statistical defect count, a sampling scheme can be defined in which sites are added to the sampling scheme until, for example, the desired capture rate level is achieved (e.g., when the sum of the probability of sampling sites reaches 90%) or the desired Obstacle rate level. The capture rate can be defined as the number of true positive defects divided by the sum of true positive defects and false negative defects. The nuisance rate can be defined as the number of false positive defects divided by the sum of true positive defects and false positive defects. Therefore, an improved (shorter) detection time can be achieved. As a related benefit, the complete set of sampling sites identified in this way should provide on the substrate a spatial feature that is analyzed using a method of predicting the probability of a defect, which may be related to the correlation of the "fingerprint" processing one or more specific process steps Or improve the correlation as part of the device manufacturing method. Processing "fingerprints" is the spatial distribution of errors usually caused by one or more specific process steps. For example, the substrate table may have warpage in the support surface, which will always introduce certain errors at certain locations on the substrate patterned using that substrate table. Therefore, the sampling site can provide the user with information to help identify and / or resolve the root cause of the defect on the substrate.

The probability of a pattern-based defect can be used to guide the inspection of a substrate generated by a device manufacturing process. Pattern instances with a higher probability of defect can be prioritized in the detection of pattern instances with a lower probability of defect. FIG. 12 schematically shows a flowchart of a method of determining which pattern instances on a substrate should be detected and the order in which such pattern instances should be detected according to the probability of using pattern instances as defects according to an embodiment. For example, using the method shown in FIG. 6 and FIG. 7, the probability of obtaining a set of pattern examples on the substrate is 1110 is a defect, respectively. The legend items can have the same pattern type or different pattern types. For example, the design layout shown on the substrate may be used to obtain the portion 1120 of the pattern example.

At 1130, an ordered list 1140 of pattern instances to be detected is determined based on the probability 1110, and optionally based on the location 1120. At 1150, pattern instances in the ordered list 1140 are detected following the order of the ordered list.

In one embodiment, the number of pattern instances to be detected for each pattern type or a specific set of pattern types may be determined based on a statistical expectation of the number of defects for each pattern type or a set of specific pattern types. (Or the measurement part where their pattern examples are located). In one embodiment, for each pattern type or a specific set of pattern types, the detection location can be determined based on, for example, (i) the probability of defects and (ii) the spatial distribution of the associated pattern instances on the substrate. To, for example, maximize the benefits of measuring light spots, FOVs, or images obtained with metrology tools. In one embodiment, a fixed fraction of the detection time may be assigned to uniform sampling and measurement of certain anchoring features.

In an example, the ordered list 1140 includes their pattern instances with the highest probability of defects; in other words, the ordered list 1140 includes a subset of the pattern instances in the set of pattern instances, where the pattern instances in the subset are defects The probability is higher than the pattern instances in the set instead of the subset. The number of pattern instances in the ordered list 1140 can be determined by the detection processing amount or empirically. The number of pattern instances in the ordered list 1140 may be limited by the amount of time used to detect the arrival of the next substrate. The number of pattern instances in the ordered list 1140 may be limited by the amount of radiation allowed to the substrate during the inspection. In an example, the order of the pattern items in the ordered list 1140 may be a descending probability order. In other words, the order may be to detect pattern instances with a higher probability of defects before the pattern instances with a lower probability of occurrence ("decreasing probability order"). In an example, the order of the pattern instances in the ordered list 1140 may be the order that caused the cost function to be at its extreme value. In one embodiment, the cost function is a function of the order of the pattern instances, and may represent the probability, the amount of time required to detect the pattern instances, the distance from one pattern instance to the next pattern instance, and / or detection execution Other indicators. In the optional step 1160, the probability 1110 is updated based on the data obtained from detecting the pattern items in the ordered list 1140.

13A and 13B schematically show that the descending probability order may be worse in terms of detection processing amount compared to another order. In the example in FIGS. 13A and 13B, there are three pattern items 1211, 1212, and 1213 on the substrate. Case item 1211 in the figure shows the highest probability of defects (as indicated by the size of the circle). Case item 1212 in the figure is the second largest probability of defects, which is slightly smaller than the probability of pattern 1211. The case item 1213 in the figure is that the probability of the defect is the smallest, which is much smaller than the probability of the pattern 1211 and the probability of the pattern 1212. The figure case item 1212 is far from the pattern case items 1211 and 1213; the pattern case items 1211 and 1213 are close to each other. FIG. 13A shows the order of the ordered list of pattern items 1211 → pattern example 1212 → pattern example 1213, which is a descending probability order. FIG. 13B shows the different order of the ordered list of pattern items 1211 → pattern example 1213 → pattern example 1212, which is not a descending probability order. By following the order in FIG. 13A, the weights and measures tool must travel a relatively long distance from the pattern instance 1211 to the pattern instance 1212 and from the pattern instance 1212 to the pattern instance 1213. By following the order in FIG. 13B, the weights and measures tool must travel a relatively short distance from the pattern instance 1211 to the pattern instance 1213, and a relatively long distance from the pattern instance 1213 to the pattern instance 1212. Therefore, by following the order in FIG. 13B, the total time required to detect the three pattern instances is shorter (and therefore the amount of detection processing is higher).

The metrology tool is capable of detecting multiple pattern instances without moving the field of view ("FOV") or measuring the light spot. For example, some metrology tools that use charged particle beams have FOVs that can cover multiple pattern instances, but moving FOVs is relatively slow. Multiple pattern instances detected before moving the weights and measures tool can be considered as one-time detection. FIG. 14A and FIG. 14B schematically show that, when using this measurement and weighing tool for detection, compared with another order, the descending probability order may be worse in terms of detection processing amount. In the example shown in FIGS. 14A and 14B, there are seventeen pattern items on the substrate, and these pattern items can be surrounded by three FOVs 1311, 1312, and 1313. The case item in the figure is represented by a + sign, and the associated circle represents the probability that the pattern item is defective. The larger the circle, the greater the chance. Because moving FOV is relatively slow, using more than three FOVs to detect pattern instances reduces the amount of detection processing. Of the three FOVs, the total probability of defects within FOV 1311 (that is, the sum of the probability of each of the pattern instances in FOV 1311 being the defect) is the largest. The total probability of defects in FOV 1313 is the smallest, but FOV 1313 has patterns that are most likely to be defective among the seventeen pattern instances (as shown by its relatively large circle). FOV 1312 is far from FOV 1311 and 1313; FOV 1311 and 1313 are close to each other. FIG. 14A shows the order of an ordered list of pattern items in FOV 1311 → pattern items in FOV 1312 → pattern examples in FOV 1313. FIG. 14B shows different orders of an ordered list of pattern instances in FOV 1311 → pattern instances in FOV 1313 → pattern instances in FOV 1312. By following the order in FIG. 14A, the weights and measures tool must move the FOV a relatively long distance from FOV 1311 to FOV 1312 and from FOV 1312 to FOV 1313. By following the order in FIG. 14B, the metrology tool must travel a relatively short distance from FOV 1311 to FOV 1313 and a relatively long distance from FOV 1313 to FOV 1312. Therefore, by following the order in FIG. 14B, the total time required to detect the three pattern instances is shorter.

Therefore, in one embodiment, a probability calculation method is provided for determining a model residual, for example, by using a measurement of a substrate (for example, a measurement characteristic (for example, CD) value and a prediction characteristic value). Difference between), assigning a probability distribution to one or more pattern instance types (eg, one or more hotspot instance types). The probability distribution can be used to determine, for example, the probability of a defect in a pattern instance of one or more pattern instance types. The probability of defects can be used for statistical process control (for example, by using statistical defects). That defect probability can be used to assist in finding actual defects on the substrate using a metrology tool, ideally, high capture rates and / or low obstruction rates and / or improved inspection times (e.g., within target criteria (e.g., defect size, and, for example, Capture rate and / or obstruction rate), no or less than the required measurement is required.

Now, as discussed above, the properties of the residual distribution are calculated based on a plurality of pattern instances with the same pattern type or a collection containing a plurality of different pattern types (where pattern types often share similar behavior, as described above) ). Next, the attribute probability 660/880 is used in the probability method of FIGS. 6 and 7 to determine the probability of a defect (which can then be used for various purposes as described above, such as establishing a list of sampling locations for a metrology tool). In one embodiment, one or more pattern types are hot spots.

However, compared to the probability that a single pattern instance deviates from the specification, the probability that any one pattern instance in a relatively large set of pattern instances deviates significantly from the specification (for example, it is actually a defect) is more localized and reaches To peak. Therefore, in one embodiment, prediction of the degree of defects in a set of pattern instances is provided, which means that a probability calculation method that can predict the statistical behavior of a group of pattern instances to determine whether any group member is a defect. Therefore, in an embodiment, this can better distinguish the detection site (eg, FOV) with a defect from the detection site without a defect. In turn, this should reduce the number of sites that are sampled by the metrology tool to capture defects, as compared to, for example, a situation where a metrology tool is directed to individually access the pattern instance parts.

Referring to FIG. 15, an example method of obtaining the attribute 660/880 of the residual distribution of the probability calculation method based on the statistical behavior of the set of pattern instances is presented. At 1400, an attribute 1410 (e.g., attribute 660/880) of the distribution of non-probabilistic (e.g., deterministic) model residuals ("noise") is determined using techniques such as described with respect to FIGS. 7 and 8. In short, for example, a test value of a characteristic (eg, CD) obtained from each of a plurality of pattern instances measured on a substrate produced under nominal conditions is obtained. In addition, a non-probabilistic (eg, deterministic) model for predicting characteristics is used to obtain a predicted value of a characteristic (eg, CD) of a pattern instance. Then, the distribution of the residuals is obtained by, for example, determining a pattern difference between a prediction characteristic (for example, CD _pred ) of the pattern instance and a test characteristic (for example, CD _meas ) of the same pattern instance (for example, ΔCD = CD _meas -CD _pred ). An example of attribute 1410 in PDF form of this residual distribution determined from synthetic data is shown in Figure 16 as curve 1500, where the horizontal axis is ΔCD in nanometers and the vertical axis is in the range of 0 to 1. Probability score. In this example, the distribution of residuals is characterized by a standard deviation of σ = 1 nm. This attribute 1410 in the form of a PDF can be used for statistical prediction, as discussed above with respect to FIGS. 6 and 7. According to PDF, CDF or eCDF can be calculated by integrating PDF. Therefore, the attribute 1410 may be in the form of a CDF or an eCDF and, like the attribute 1410 in the form of a PDF, may be used for statistical prediction, as discussed above with respect to FIGS. 6 and 7. An example of the attribute 1410 in the form of an eCDF from the residual distribution determined from the synthetic data corresponding to PDF 1500 is shown as a curve 1510 in FIG. 16. As described above with reference to FIGS. 6 and 7, PDF, CDF, or eCDF can be calculated for a plurality of pattern instances of a specific pattern type or a collection of a plurality of pattern types, where data can be obtained from the plurality of pattern instances scattered on a substrate .

At 1420, the concept of defectivity within the set of predicted pattern instances is introduced. In one embodiment, this involves calculating the attributes 1430 of the residuals for a set of N pattern instances. In an embodiment, the attribute of the residual of the set is determined 1430 based on the attribute (eg, PDF, CDF, or eCDF) of the residual of at least one or more of the pattern types of the set of N pattern instances. . In one embodiment, the attribute 1430 includes a cumulative distribution function of a set of N pattern instances or simply eCDF _N. This attribute is sometimes referred to as the extreme statistical property. In an embodiment, the attribute 1430 is specified for a specific pattern type and / or a set of a plurality of pattern types. Therefore, in the case where there are a plurality of attributes 1430, each attribute may be specified for a different pattern type and / or a different set of a plurality of pattern types.

In one embodiment, the N pattern instances of the set include one or more hotspot instances. In the case where the N pattern instances of the set correspond to the measurement site (such as FOV or image), the modeling technology described in this article can be used to identify one or more measurement sites of at least one pattern system hot spot and determine The number of the same or similar patterns (such as hot spots) in the measurement part is measured to form a collection of patterns in the measurement part.

In one embodiment, the value of N corresponds to the number of pattern instances of interest (and associated with the eCDF) within the measurement site of the metrology tool. In one embodiment, the value of N corresponds to all the patterns of interest in the measurement site. In one embodiment, the measurement site corresponds to a field of view or a measurement light spot of a metrology tool, such as an electron beam metrology tool. In one embodiment, the measurement site corresponds to a measurement site that can be effectively measured at one time by a suitable metrology tool. The reason for specifying the value of N for the measurement site is to be able to more effectively select the measurement site where the defect is expected to actually occur; transferring from one measurement site to another will inevitably exist for a certain amount of time, so It is desirable to be able to identify their one or more measurement sites for defects that may actually occur, which may reduce, for example, wasteful measurement and / or time between measurement sites. In one embodiment, the value of N is 10 or more, 20 or more, 50 or more, 100 or more, 200 or more, 400 or more, 500 or more, 1000 or more, 2000 or greater or 5000 or greater. In one embodiment, the value of N may be different for different measurement locations (for example, FOV or image).

In one embodiment, eCDF _N can be calculated as: eCDF _N = [1-(1-eCDF) ^N ]. In one embodiment, eCDF _N = [1-(1-eCDF) ^N ] is used, and we are interested in the probability of the smallest pattern or hotspot instance in the measurement area (for example, the smallest CD in FOV). Mathematically, the cumulative probability distribution (eCDF _N ) of a collection of N similar pattern instances (e.g., within FOV) is therefore clearer than the cumulative probability distribution (eCDF ₁ ) of a single pattern instance: eCDF _N = eCDF ₁ ^ N. Therefore, for the case where it is desired to find the cumulative probability of the characteristic value of the set of pattern instances being less than a certain threshold (or greater than a certain threshold), the attribute 1430 (for example, in the form of eCDF _N , where The number of case items in the graph is N) to calculate this probability.

An example of attribute 1430 in the form of eCDF _N of the residual distribution determined from the self-synthesized data corresponding to PDF 1500 and eCDF 1510 is shown as curve 1520 in FIG. 16. In this example, eCDF _N 1520 is determined for the set of N = 400 similar pattern instances in the field of view of the electron beam detection tool in this example.

In the case where the attribute 1430 is established, substantially the same probability calculation method 1440 as described with reference to FIGS. 6 and 7 can be used to calculate the probability 1450 of the pattern instance. For example, instead of using PDF, CDF, or eCDF, the method may use attributes 1430, for example, in the form of eCDF _N. In one embodiment, the probability that the measurement site (eg, FOV) contains at least one defect is calculated. In one embodiment, the computer rate (if any) can be calculated for all measurement locations on the substrate (for example, all possible FOVs on the substrate). Probabilities 1450 can be used for purposes as described herein, such as for statistical program chart establishment, for sampling plan establishment, and so on.

For example, as appropriate, the probability 1450 can be used to establish a sampling plan for measurement by a substrate metrology tool. The sampling plan can be used to identify defects on the substrate; the identified defects can be used for device manufacturing process modification, control, design, etc. The probability that an extreme value characteristic (eg, CD) of a certain measurement site (eg, FOV or image) exceeds a control limit (ie, contains defects) provides a method of prioritizing a site to be detected with a metrology tool. For example, starting with the measurement site with the highest probability, a sampling scheme can be defined in which sites are added until the desired defect capture criteria are achieved (e.g., the level of capture rate or obstruction rate is achieved, or, for example, the probability When the sum reaches 80% or higher, 85% or higher, 90% or higher, or 95% or higher). In this way, an improved (shorter) detection time can be achieved.

As a more specific example, in one embodiment, the probability values of the measurement locations may be sorted in order of increasing values, and then used to calculate the cumulative probability. An example of this cumulative probability represented as several predicted defects is shown in Figure 17, where the horizontal axis corresponds to the number of ordered measurement locations (e.g., FOV or image) and the vertical axis corresponds to the predicted number of measurement locations Cumulative number of defects. Curve 1600 is an example of the cumulative number of predicted defects based on the probability calculation method of PDF, CDF, or eCDF used to synthesize a data set. Curve 1610 is an example of the cumulative number of predicted defects based on the attribute calculation method 1430 for the synthetic data set, in which case the probability calculation method in the form of eCDF _N. The number of samples to be found is given by intercepting the number of measurement sites. For example, 90% or more defects (or 85% or higher, or 95% or higher), and the curve is at the total number of defects. Purpose 90%. In this example, as seen in the curve, the total number of defects is about 29 (asymptotic lines for curves 1600 and 1610). Therefore, 90% of them are about 26 defects, which are shown by line 1620. In the case where the line 1620 intersects the curves 1600 and 1610, the number of the measurement positions of the respective sorts to be detected should be respectively indicated so as to detect 26 defects. In the case of curve 1600, this is shown by line 1630 as approximately 220 images. For the calculated number of images corresponding to curve 1600, the obstruction rate is calculated to be about 86%. In contrast, in the case of curve 1610, this is shown by line 1640 as approximately 103 images. For the calculated number of images corresponding to curve 1610, the obstruction rate is calculated to be approximately 71%. Therefore, for this specific situation, the detection time is improved by about 2 times (103 images to 220 images), and the effective interference rate is improved by about 18%.

Using two sampling plans according to curves 1600 and 1610, it is visualized how the two sampling plans are compared (i.e., predictions for specific pattern instances (e.g., hot spots) by PDF, CDF or eCDF versus The set (eg, defined for measurements such as FOV or imaging) using, for example, the prediction of eCDF _N ) contains the actual measurement site of the defect. Figure 18 shows this highly schematic visualization of the measurement site on at least a portion of the substrate 1700, where the solid circle 1710 corresponds to the measurement site with actual defects, and the internal (or smaller) hollow circle corresponds to the PDF, CDF Or eCDF is a sample measurement location predicted for a specific pattern instance (e.g., a hot spot), and the outer (or larger) hollow circle corresponds to a definition by a collection of pattern instances (e.g., for measurements such as FOV or images ) Sampling measurement sites using eCDF _N prediction, for example. As seen in FIG. 18, compared to sample measurement locations predicted by PDF, CDF, or eCDF for specific pattern instances (e.g., hot spots), a set of pattern instances (e.g., for quantities such as FOV or image) (Definition and definition) using, for example, eCDF _N prediction, the sample measurement site is significantly closer to the defective fingerprint 1710.

Therefore, in one embodiment, a probability calculation method is provided that performs defect prediction based on statistical data of a set (or group) of similar pattern instances (eg, hotspot instances). Using the other method, in the embodiment, a probability distribution of at least one measurement site (for example, FOV or image) with a defect can be formed, and a sampling strategy based on the predicted probability or the number of defects can be established based on the ranking.

In one embodiment, this probability calculation method involves calculating statistics for a set of pattern instances within a measurement site such as a field of view (FOV) of a metrology tool (eg, an electronic metrology system) in order to establish The probability that a specific pattern instance (for example, a hot spot) becomes a defect on a specific part of the substrate of the case item. This statistic can be determined by comparing the measured values (eg, CD) of the pattern instances on the substrate with the predicted values of their pattern instances. In one embodiment, the statistics of the set can be used to predict the probability of defects in the pattern instances. For example, the statistics of a set of groups of pattern instances in a specified measurement site (for example, FOV or image) can be used to determine whether any pattern instance of a group within a measurement site is predicted to be a defect . For example, a relatively large field-of-view metrology system can measure a collection of pattern instances substantially at a time. Therefore, it may be advantageous to consider the probability of a specific set of FOVs on the substrate, so that it is possible to more effectively determine whether to measure the measurement site on the substrate corresponding to the FOV and / or select the measurement site, for example to reduce the detection time. In one embodiment, the probability that the one or more measurement sites have defects is high, and then the one or more measurement sites may be detected.

In one embodiment, this method uses the actual distribution function of the residuals (eg, based on measurements), which are expected to be non-Gaussian. Therefore, the practical use of this distribution should bring additional benefits in terms of sampling (e.g., lower effective interference rates).

In one embodiment, the probability calculation takes into account changes in the residual distribution on the substrate. That is, the attributes 660/880/1430 may vary on the substrate. This can be done in one of several ways. For example, by using a specific area on the substrate (e.g., at each measurement site (e.g., FOV or image), on each die, on a device that can be manufactured (such as a lithographic device, etc.) The range or standard deviation of the local characteristic distribution (e.g., CDU distribution) calculated over the area where the control actuator is addressed, scales the attributes. This will further improve the purity of the sampling (e.g., achieve a lower effective interference rate).

In one embodiment, the device manufacturing process used to generate pattern instances on any given substrate has been evaluated to have drifted or suffered a particular offset. By comparing the number of statistical defects determined for a particular substrate with one or more previous statistical defects calculated on one or more previous substrates and / or one or more actual defects observed on one or more previous substrates Number to complete this assessment. For example, if the number of statistical defects exceeds this previous number of defects by a certain amount (for example, 5% or greater, 10% or greater, 15% or greater, 20% or greater), the user may be flagged This drift / offset can remove the substrate from which the statistical defect number is applied from being processed, stop the device manufacturing process, and modify, control, etc. the device manufacturing process to eliminate or reduce drift / offset and so on. In one embodiment, this type of evaluation can also be used to evaluate the data used in the probability calculation method. In an embodiment, the anchoring feature in the substrate may be measured to determine whether the current measurement is statistically different from the baseline (eg, previous measurement) (eg, using a confidence interval). If the current measurement is considered to be off baseline, it can alert that the predicted defect is invalid or potentially invalid due to drift or offset.

In one embodiment, the variability of hotspot instance data (local critical size uniformity (LCDU), line edge roughness (LER), etc.) is compared with each hotspot instance type or a set of multiple similar hotspot instance types. Can be analyzed for variability (for example, using, for example, the image logarithmic slope (ILS), MSD, etc. in the Z direction) to obtain similar attributes for predicting variability as discussed above, which can be used for One or more predictors in probabilistic methods to enhance defect prediction. For example, based on hotspot instances generated using a certain focus value, the PDF of a particular hotspot instance type or a collection of multiple similar hotspot instance types may change, because it is compared with other features in focus, Out-of-focus features have lower ILS and therefore will have wider PDFs.

Therefore, this article provides, for example, a method of calculating the probability of defects on a substrate produced by a device manufacturing process, a method of obtaining the attributes of the distribution of residuals of a non-probability model, and a method of determining pattern instances to be detected based on the probability of defects. An ordered list approach.

In one embodiment, a method is provided, which includes: using a non-probability model to obtain a value of a characteristic of a pattern instance on a substrate generated by a device manufacturing process; and obtaining a residual of the non-probability model. An attribute of a distribution; an attribute of a distribution of the characteristic is determined based on the attribute of the distribution of the residual and the value of the characteristic of the pattern instance; and the attribute of the distribution based on the characteristic , Determine that the pattern instance is a probability of a defect.

According to an embodiment, the attribute of the distribution of the residual includes a probability density function (PDF) of the residual. According to an embodiment, the attribute of the distribution of the residual includes a cumulative distribution function (CDF) of the residual or an empirical cumulative distribution function (eCDF) of the residual. According to an embodiment, the attribute of the distribution of the residuals represents a dispersion of the distribution of the residuals. According to an embodiment, the attribute of the distribution of the residual is the variance or standard deviation of the distribution of the residual. According to an embodiment, the characteristic is selected from one or more of the following: a position relative to the substrate, a position relative to one or more other pattern instances on the substrate, a geometric size, a Geometry, a measure of a random effect, and / or any combination selected from the foregoing. According to an embodiment, determining the attribute of the distribution of the characteristic includes adding the attribute of the distribution of the residual and the value of the characteristic. According to an embodiment, the attribute of the distribution of the characteristic is a PDF of the characteristic. According to an embodiment, determining the probability includes integrating the PDF with the characteristic within a range of the characteristic. According to an embodiment, the method further includes normalizing the attribute of the distribution of the characteristic. According to an embodiment, the attribute determining the distribution of the characteristic is further based on a range of the characteristic, within which the pattern is considered a defect.

In one embodiment, a method is provided, including: obtaining a test value of a characteristic of a plurality of pattern instances on a substrate generated by a device manufacturing process; using a non-probability model to obtain a calculated value of the characteristic; Obtaining a value of a residual of the non-probability model based on the test values and the calculated values; and obtaining an attribute of a distribution of the residual based on the values of the residual.

According to an embodiment, the characteristic is selected from one or more of the following: a position relative to the substrate, a position relative to one or more other pattern instances on the substrate, a geometric size, a Geometry, a measure of a random effect, and / or any combination selected from the foregoing. According to an embodiment, obtaining the inspection values includes using a metrology tool to measure the pattern instances or using a strict model for simulation. According to an embodiment, the metrology tool is configured to measure the pattern instances using a charged particle beam. According to an embodiment, obtaining the values of the residual includes obtaining the difference between the calculated values and the test values. According to an embodiment, the attribute of the distribution of the residual includes a PDF of the distribution of the residual. According to an embodiment, the method further includes obtaining the pattern instances based on the shape, size, function, or spatial proximity of the pattern type of the plurality of pattern instances.

In one embodiment, a method is provided, which includes: obtaining a probability that a set of pattern instances on a substrate generated by a device manufacturing process are defects, respectively; and determining a pattern instance to be detected based on the probabilities. An ordered list; and following one of the ordered lists to detect pattern items in the ordered list.

According to an embodiment, the method further includes obtaining parts of the set of pattern instances. According to an embodiment, determining the ordered list is further based on the locations. According to an embodiment, the ordered list includes a subset of the pattern instances in the set of pattern instances, wherein the pattern instances in the subset are more likely to be defective than the pattern instances in the set and not the subset . According to an embodiment, determining the ordered list is further based on a detection throughput, an amount of time allowed to be detected, and / or an amount of radiation allowed to be received by the substrate during the inspection. According to an embodiment, the order is a descending probability order. According to an embodiment, determining that the ordered list includes calculating a cost function as a function of the order. According to an embodiment, the cost function represents the probabilities, an amount of time to detect the set of pattern instances, and / or a distance among the set of pattern instances. According to an embodiment, the method further comprises updating the probabilities based on data obtained from detecting the pattern instances in the ordered list.

In one embodiment, a method is provided, which includes: using a non-probability model to obtain a value of a property of an entity item instance of an entity system or object; obtaining a residual of the non-probability model relative to the entity item instance An attribute of a distribution of one set of items, the attribute of the residual relative to that of a set of entity item instances. The attribute of the distribution is based on a residual of the non-probability model relative to at least one entity item type corresponding to the set. An attribute of at least one entity item instance distribution; based on the residual relative to the attribute of the distribution of a set of entity item instances and the value of the characteristic of the entity item instance, determining the characteristic An attribute of a distribution; and a probability of determining that the entity item instance exceeds the specification based on the attribute of the distribution of the characteristic.

In one embodiment, the attribute of the residual relative to the distribution of the set includes a cumulative distribution function of the set of entity item instances. In one embodiment, the attribute of the residual relative to the distribution of the set relates to the attribute of the residual relative to the distribution of at least one entity item instance corresponding to at least one entity item type of the set being greater than the The power of several physical item instances in the collection. In one embodiment, the property of the residual relative to the distribution of the set is at least a function defined by [1-(1-eCDF) ^N ] or [1-(1-CDF) ^N ], where N Is the number of entity item instances in the set, CDF is a cumulative distribution function of the residual relative to at least one entity item instance corresponding to at least one entity item type of the set, and eCDF is the residual relative to the corresponding An empirical cumulative distribution function for at least one entity item instance of at least one entity item type in the set. In one embodiment, the number of entity item instances in the set is greater than ten. In one embodiment, the physical item instance corresponds to a pattern instance on a substrate generated by a device manufacturing process. In one embodiment, in a measurement site or field of view of a metrology tool, the number of entity item instances in the set corresponds to a specific entity item type or a set of a specific plurality of entity item types. The number of entity item instances. In an embodiment, the method further includes determining, based on the probability, that at least one physical item instance exceeding a specification exists in a measurement location or field of view of one of the metrology tools. In one embodiment, there are a plurality of attributes of the distribution relative to the distribution of the residual, and for different physical parts, the residual is different with respect to each of the plurality of attributes of the distribution of the collection. of. In one embodiment, the characteristic is selected from one or more of the following: a position relative to a substrate, a position relative to one or more other entity item instances, a geometric size, a geometric shape , A measure of a random effect, and / or any combination selected from the foregoing. In one embodiment, determining the attribute of the distribution of the characteristic includes the attribute of the distribution and the value of the characteristic relative to the set to which the residual is added. In one embodiment, determining the probability is further based on a range of the characteristics, within which the entity item instance is considered to be out of specification. In an embodiment, the method further includes determining a sampling plan of the measurement site for measurement based on the probability to determine an entity item instance (if any) that exceeds the specification.

In one embodiment, a method is provided, including: obtaining a test value of a characteristic of a plurality of entity item instances of an entity system or object; using a non-probability model to obtain a calculated value of the characteristic; and based on the test values And the calculated values to obtain a value of a residual of the non-probability model; to obtain an attribute of a first distribution of the residual based on the values of the residual; and to obtain an attribute of the first distribution based on the attribute of the first distribution, obtain An attribute of a residual of the non-probability model relative to a second distribution of a set of entity item instances.

In one embodiment, the attribute of the residual relative to the second distribution of the set includes a cumulative distribution function of the set of entity item instances. In an embodiment, the attribute of the residual relative to the second distribution of the set relates to the power of the attribute of the first distribution of the residual to a number of entity item instances in the set. In an embodiment, the attribute of the residual relative to the second distribution of the set is at least one function defined by [1-(1-eCDF) ^N ] or [1-(1-CDF) ^N ], Where N is the number of physical item instances in the set, CDF is a cumulative distribution function with respect to the first distribution, and eCDF is an empirical cumulative distribution with respect to the first distribution. In one embodiment, the number of entity item instances in the set is greater than ten. In one embodiment, the physical item instances correspond to pattern instances on a substrate generated by a device manufacturing process. In one embodiment, in a measurement site or field of view of a metrology tool, the number of entity item instances in the set corresponds to a specific entity item type or a set of a specific plurality of entity item types. The number of entity item instances. In one embodiment, there are a plurality of attributes of the residual relative to the second distribution of the set, and for different entity parts, the residual is relative to each of the plurality of attributes of the second distribution of the set One property is different. In one embodiment, the characteristic is selected from one or more of the following: a position relative to a substrate, a position relative to one or more other entity item instances, a geometric size, a geometric shape , A measure of a random effect, and / or any combination selected from the foregoing. In one embodiment, obtaining the inspection values includes using a metrology tool to measure the entity project instances or using a rigorous model for simulation. In one embodiment, the metrology tool is configured to measure the physical item instances using a charged particle beam. In one embodiment, obtaining the values of the residual includes obtaining the difference between the calculated values and the test values. In one embodiment, the attribute of the first distribution of the residual is a CDF or eCDF of the first distribution of the residual. In one embodiment, the method further includes obtaining the plurality of physical item instances based on shape, size, function, or spatial proximity.

In one embodiment, a method is provided, which includes: obtaining a probability that a group of entity items of an entity system or object will exceed the specifications, using a non-probability model of a residual relative to a set of entity item instances Determining a probability based on an attribute of a distribution based on an attribute of a distribution of a residual of the non-probability model relative to one of at least one entity item instance corresponding to at least one entity item type of the set; and An ordered list of entity item instances to be detected based on these probabilities.

In one embodiment, the attribute of the residual relative to the distribution of the set includes a cumulative distribution function of the set of entity item instances. In one embodiment, the attribute of the residual relative to the distribution of the set relates to the attribute of the residual relative to the distribution of at least one entity item instance corresponding to at least one entity item type of the set being greater than the The power of several physical item instances in the collection. In one embodiment, the property of the residual relative to the distribution of the set is at least a function defined by [1-(1-eCDF) ^N ] or [1-(1-CDF) ^N ], where N Is the number of entity item instances in the set, CDF is a cumulative distribution function of the residual relative to at least one entity item instance corresponding to at least one entity item type of the set, and eCDF is the residual relative to the corresponding An empirical cumulative distribution function for at least one entity item instance of at least one entity item type in the set. In one embodiment, the number of entity item instances in the set is greater than ten. In one embodiment, the physical item instances correspond to pattern instances on a substrate generated by a device manufacturing process. In one embodiment, in a measurement site or field of view of a metrology tool, the number of entity item instances in the set corresponds to a specific entity item type or a set of specific entity item types in the collection. Number of project instances. In an embodiment, determining the ordered list further includes determining, based on the probabilities, the predicted existence of at least one defect in a measurement site or field of view of the metrology tool. In one embodiment, there are a plurality of attributes of the distribution relative to the distribution of the residual, and for different physical parts, the residual is different with respect to each of the plurality of attributes of the distribution of the collection. of. In one embodiment, the characteristic is selected from one or more of the following: a position relative to a substrate, a position relative to one or more other entity item instances, a geometric size, a geometric shape , A measure of a random effect, and / or any combination selected from the foregoing. In an embodiment, the method further includes obtaining parts of the set of entity item instances, and determining the ordered list is further based on the parts. In an embodiment, the ordered list includes a subset of the entity item instances in the set of entity item instances, where the probability of the entity item instances in the subset exceeding the specification is greater than the set and not the subset. The physical item count is high. In an embodiment, determining the ordered list is further based on an inspection throughput, an amount of time allowed to be detected, and / or an amount of radiation allowed to be received by a substrate during the inspection. In an embodiment, the ordered list is in descending order of probability. In one embodiment, the method further includes updating the probabilities based on information obtained from detecting the entity item instances in the ordered list. In an embodiment, the method further includes detecting the physical item instances in the ordered list following the order of the ordered list.

FIG. 19 is a block diagram illustrating a computer system 100 that can assist in implementing all or part of 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 to process information. The computer system 100 may also include a main memory 106, such as a random access memory (RAM) or other dynamic storage device, coupled to the bus 102 to store and / or supply information and instructions to be executed by the processor 104. The main memory 106 may be used to store and / or supply temporary variables or other intermediate information during execution of instructions to be executed by the processor 104. The computer system 100 may further include a read-only memory (ROM) 108 or other static storage device coupled to the bus 102 to store and / or supply static information and instructions for the processor 104. A storage device 110 such as a magnetic disk or an optical disk may be provided, and the storage device 110 may be coupled to the bus 102 to store and / or supply information and instructions.

The computer system 100 may be coupled to a display 112, such as a cathode ray tube (CRT) or a flat panel display or a touch panel display, for displaying information to a computer user via a bus 102. An input device 114 including alphanumeric and other keys can be coupled to the bus 102 to communicate information and command selections to the processor 104. Another type of user input device may be a cursor control 116, such as a mouse, trackball, or cursor direction button, used to communicate direction information and command choices to the processor 104 and control the movement of the cursor on the display 112. This input device typically has two degrees of freedom on two axes, a first axis (eg, x) and a second axis (eg, y), which allows the device to specify a position in a plane. Touch panel (screen) displays can also be used as input devices.

According to one embodiment, part of the method disclosed herein 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. Execution of the sequence of instructions contained in the main memory 106 causes the processor 104 to execute the program steps described herein. One or more processors in a multi-processing configuration may be used to execute a sequence of instructions contained in the main memory 106. In one embodiment, hard-wired circuits may be used instead of or in combination with software instructions. Therefore, the description herein is not limited to any specific combination of hardware circuits and software.

The term "computer-readable medium" as used herein refers to any medium that participates in providing instructions to the processor 104 for execution. This media can take many forms, including but not limited to non-volatile media, volatile media, and transmission media. Non-volatile media includes, for example, optical or magnetic disks, such as the storage device 110. Volatile media includes dynamic memory, such as main memory 106. Transmission media include coaxial cables, copper wires, and optical fibers, including wires including the busbar 102. Transmission media can also be in the form of sound or light waves, such as those generated during radio frequency (RF) and infrared (IR) data communications. Common forms of computer-readable media include, for example, floppy disks, flexible disks, hard disks, magnetic tapes, any other magnetic media, CD-ROMs, DVDs, any other optical media, punched cards, paper tape, patterned with holes Any other physical media, RAM, PROM and EPROM, FLASH-EPROM, any other memory chip or cassette, carrier wave as described below, or any other media that can be read by a computer.

Various forms of computer-readable media may be involved in carrying one or more sequences of one or more instructions to processor 104 for execution. For example, the instructions may initially be carried on a disk or memory of a remote computer. The remote computer can load the instructions into its dynamic memory and send the instructions above the communication path. The computer system 100 can receive data from the path and place the data on the bus 102. The bus 102 carries data to the main memory 106, and the processor 104 fetches instructions from the main memory and executes the instructions. The instructions received by the main memory 106 may be stored on the storage device 110 before or after being executed by the processor 104 as appropriate.

The computer system 100 may include a communication interface 118 coupled to the bus 102. The communication interface 118 provides a two-way data communication coupling to the network link 120, and the network link 120 is connected to the network 122. For example, the communication interface 118 may provide a wired or wireless data communication connection. In any such implementation, the communication interface 118 sends and receives electrical, electromagnetic, or optical signals that carry digital data streams representing various types of information.

The network link 120 typically provides data communication to other data devices via one or more networks. For example, the network link 120 may provide a connection to the host computer 124 or to a data device operated by an Internet Service Provider (ISP) 126 via the network 122. The ISP 126 then provides data communication services via a global packet data communication network (now commonly referred to as the "Internet") 128. Both the network 122 and the Internet 128 use electrical signals, electromagnetic signals, or optical signals that carry digital data streams. The signals via various networks and the signals on the network link 120 and via the communication interface 118 (the signals carry digital data to and from the computer system 100) are exemplary for conveying information Form of carrier.

The computer system 100 can send messages and receive data, including code, via the network, the network link 120, and the communication interface 118. In the Internet example, the server 130 may transmit the requested code for the application program via the Internet 128, ISP 126, network 122, and communication interface 118. For example, one such downloaded application may provide code to implement the methods herein. The received code may be executed by the processor 104 when 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.

FIG. 20 schematically depicts another exemplary lithographic apparatus 1000. The lithographic apparatus 1000 includes:

-Source collector module SO

-Lighting system (illuminator) IL, which is configured to regulate the radiation beam B (e.g. EUV radiation).

-A support structure (e.g., a photomask stage) MT, which is constructed to support a patterned device (e.g., a photomask or a reduction mask) MA, and is connected to a first positioning configured to accurately position the patterned device器 PM; PM

-A substrate table (e.g., wafer table) WT configured to hold a substrate (e.g., resist-coated wafer) W and connected to a second positioner PW configured to accurately position the substrate; and

-A projection system (e.g., a reflective projection system) PS configured to project a pattern imparted to the radiation beam B by the patterning device MA onto a target portion C (e.g., containing one or more dies) of a substrate W on.

As depicted herein, the device 1000 is of a reflective type (eg, using a reflective mask). It should be noted that because most materials are absorptive in the EUV wavelength range, the patterned device may have a multi-layer reflector including multiple stacks such as molybdenum and silicon. In one example, the multi-stack reflector has a 40-layer pair of molybdenum and silicon. X-ray lithography can be used to generate even smaller wavelengths. Since most materials are absorptive at EUV and x-ray wavelengths, a thin patterned absorbing material on the patterned device configuration (e.g., a TaN absorber on top of a multilayer reflector) defining features will print (positive Resist) or not printed (negative resist).

Referring to FIG. 20, the illuminator IL receives an extreme ultraviolet (EUV) radiation beam from a source collector module SO. Methods of generating EUV radiation include, but are not necessarily limited to, converting a material into a plasma state, which has at least one element, for example, xenon, lithium, or tin, with one or more emission lines in the EUV range. In one such method (often referred to as laser-generated plasma "LPP"), a fuel (such as a small droplet, stream, or Cluster) to produce plasma. The source collector module SO may be a component of an EUV radiation system including a laser (not shown in FIG. 20), which is used to provide a laser beam for exciting the fuel. The resulting plasma emits output radiation (e.g., EUV radiation), which is collected using a radiation collector disposed in a source collector module. For example, when a CO2 laser is used to provide a laser beam for fuel excitation, the laser and source collector modules may be separate entities.

Under these conditions, the laser is not considered to be a component forming a lithographic device, and the radiation beam is transmitted from the laser to the source collector module by means of a beam delivery system including, for example, a suitably guided mirror and / or a beam expander . In other situations, for example, when the source is a plasma generating EUV generator (often referred to as a DPP source), the source may be an integral part of the source collector module.

The illuminator IL may include an adjuster configured to adjust the angular intensity distribution of the radiation beam. Generally, at least the outer radial range and / or the inner radial range of the intensity distribution in the pupil plane of the illuminator can be adjusted (usually referred to as σ-outer and σ-inner, respectively). In addition, the illuminator IL may include various other components such as a faceted field mirror device and a faceted pupil mirror device. The illuminator can be used to condition the radiation beam to have the desired uniformity and intensity distribution in its cross section.

The radiation beam B is incident on a patterned device (eg, a photomask) MA that is held on a support structure (eg, a photomask stage) MT, and is patterned by the patterned device. After being reflected from the patterned device (eg, the mask) MA, the radiation beam B is passed through the projection system PS, which focuses the beam on the target portion C of the substrate W. With the second positioner PW and the position sensor PS2 (for example, an interference measurement device, a linear encoder, or a capacitive sensor), the substrate table WT can be accurately moved, for example, for positioning in the path of the radiation beam B Different Objectives Part C. Similarly, the first positioner PM and another position sensor PS1 can be used to accurately position the patterned device (eg, the mask) MA relative to the path of the radiation beam B. The patterned device alignment marks M1, M2 and the substrate alignment marks P1, P2 may be used to align the patterned device (for example, a photomask) MA and the substrate W.

The depicted device may be used in at least one of the following modes:

1. In the step mode, while supporting the entire pattern given to the radiation beam onto the target portion C at one time, the supporting structure (for example, the mask stage) MT and the substrate stage WT are kept substantially stationary (that is, , Single static exposure). Next, the substrate table WT is shifted in the X and / or Y direction so that different target portions C can be exposed.

2. In the scan mode, while projecting a pattern imparted to the radiation beam onto the target portion C, the supporting structure (for example, a mask stage) is simultaneously scanned in a given direction (the so-called "scanning direction") MT And substrate stage WT (ie, single dynamic exposure). The speed and direction of the substrate stage WT relative to the supporting structure (eg, a mask stage) MT can be determined from the magnification (reduction rate) and image inversion characteristics of the projection system PS.

3. In another mode, while the pattern imparted to the radiation beam is projected onto the target portion C, the supporting structure (for example, the photomask stage) MT is kept substantially stationary, thereby holding the programmable patterned device, And the substrate table WT is moved or scanned. In this mode, a pulsed radiation source is typically used and the programmable patterned device is updated as needed after each movement of the substrate table WT or between successive radiation pulses during scanning. This mode of operation can be easily applied to maskless lithography using a programmable patterned device such as a programmable mirror array of the type mentioned above.

FIG. 21 shows the device 1000 in more detail, which includes a source collector module SO, a lighting system IL, and a projection system PS. The source collector module SO is constructed and configured so that a vacuum environment can be maintained in the enclosure structure 2120 of the source collector module SO. An EUV radiation-emitting plasma 2110 can be formed by generating a plasma source by discharging. EUV radiation may be generated by a gas or vapor (eg, Xe gas, Li vapor, or Sn vapor), with an extreme pyroelectric plasma 2110 being generated to emit radiation in the EUV range of the electromagnetic spectrum. For example, an extremely hot plasma 2110 is generated by causing a discharge of at least partially ionized plasma. For efficient generation of radiation, Xe, Li, Sn vapors, or any other suitable gas or vapor, may be required, for example, at a partial pressure of 10 Pa. In one embodiment, an excited tin (Sn) plasma is provided to generate EUV radiation.

The radiation emitted by the thermoelectric plasma 2110 is via a gas barrier or a contaminant trap 2130 (in some cases, also called a pollutant barrier or foil, if appropriate) positioned in or behind the opening in the source chamber 2111 Sheet retainer) from the source chamber 2111 into the collector chamber 2112. The contaminant trap 2130 may include a channel structure. The pollutant trap 2130 may also include a gas barrier, or a combination of a gas barrier and a channel structure. As is known in the art, the contaminant trap or contaminant trap 2130 further indicated herein includes at least a channel structure.

The source chamber 2111 may include a radiation collector CO, which may be a so-called grazing incidence collector. The radiation collector CO has an upstream radiation collector side 2151 and a downstream radiation collector side 2152. The radiation traversing the collector CO may be reflected from the grating spectral filter 2140 to focus in the virtual source point IF along the optical axis indicated by the dotted-line "O". The virtual source point IF is often referred to as an intermediate focus, and the source collector module is configured such that the intermediate focus IF is located at or near the opening 2121 in the enclosure structure 2120. The virtual source point IF is an image of the radiation-emitting plasma 2110.

Subsequently, the radiation traverses the illumination system IL, which may include a faceted field mirror device 2192 and a faceted pupil mirror device 2194, a faceted field mirror device 2192, and a faceted pupil mirror device 2194 configured to The desired angular distribution of the radiation beam 2191 at the patterned device MA and the required uniformity of the radiation intensity at the patterned device MA are provided. After the reflection of the radiation beam 2191 at the patterned device MA held by the support structure MT, a patterned beam 2196 is formed, and the patterned beam 2196 is imaged by the projection system PS to the substrate through the reflection elements 2198, 3190. The substrate WT is held on the substrate W.

More elements than those shown may generally be present in the illumination optics unit IL and the projection system PS. Depending on the type of lithographic device, a grating spectral filter 2140 may be present as appropriate. In addition, there may be more specular surfaces than those shown in the figures, for example, there may be 1 to 6 additional reflective elements in the projection system PS than the reflective elements shown in FIG. 21.

The collector optics CO as illustrated in FIG. 21 is depicted as a nested collector with grazing incidence reflectors 2153, 2154, and 2155, and is merely an example of a collector (or collector mirror). The grazing incidence reflectors 2153, 2154, and 2155 are arranged axially symmetrically about the optical axis O, and this type of collector optics CO is ideally used in combination with a discharge generating plasma source (often referred to as a DPP source). Alternatively, the source collector module SO may be part of an LPP radiation system.

Embodiments may be further described using the following items:
1. A method comprising:
Use a non-probability model to obtain a value of a property of a physical system instance of a physical system or object;
Obtain an attribute of a distribution of a residual of the non-probability model relative to one of a set of entity item instances, and an attribute of the distribution of the residual relative to a set of an entity item instance based on a residual of the non-probability model An attribute corresponding to one of at least one entity item instance corresponding to at least one entity item type of the set;
Determining an attribute of a distribution of the characteristic based on the attribute of the distribution with respect to the distribution of a set of entity item instances and based on the value of the characteristic of the entity item instance; and the distribution based on the characteristic This attribute determines the probability that the entity project instance exceeds the specification.
2. The method of item 1, wherein the attribute of the residual relative to the distribution of the set includes a cumulative distribution function of the set of entity item instances.
3. The method of clause 1 or clause 2, wherein the attribute of the distribution of the residual relative to the set relates to the instance of the residual relative to at least one entity item of at least one entity item type corresponding to the set The property of the distribution is greater than the power of several physical item instances in the set.
4. The method of any one of clauses 1 to 3, wherein the attribute of the residual relative to the distribution of the set is at least [1-(1-eCDF) ^N ] or [1-(1-CDF ) ^N ] defines a function, where N is the number of entity item instances in the set, and CDF is a cumulative distribution function of the residual relative to at least one entity item instance corresponding to at least one entity item type of the set And eCDF is an empirical cumulative distribution function of the residual relative to at least one entity item instance corresponding to at least one entity item type of the set.
5. The method of any one of clauses 1 to 4, wherein the number of entity item instances in the set is greater than 10.
6. The method of any one of clauses 1 to 5, wherein the physical item instance corresponds to a pattern instance on a substrate generated by a device manufacturing process.
7. The method of any one of clauses 1 to 6, wherein the number of entity item instances in the set corresponds to a specific entity item type or a specific plural number in a measurement site or field of view of a metrology tool The number of one of these entity item instances that is a collection of one entity item type.
8. The method of any one of clauses 1 to 7, further comprising determining, based on the probability, that at least one physical item instance that exceeds the specification exists in a measurement location or field of view in one of the metrology tools.
9. The method of any one of clauses 1 to 8, wherein there are a plurality of attributes of the distribution of the residual relative to the set, and for different entity parts, the residual relative to the distribution of the set Each of the plurality of attributes is different.
10. The method of any one of clauses 1 to 9, wherein the characteristic is selected from one or more of the following: relative to a position of a substrate, relative to one or more other entity project instances A position, a geometric size, a geometric shape, a measure of a random effect, and / or any combination selected from the foregoing.
11. The method of any one of clauses 1 to 10, wherein the attribute of the distribution of the characteristic is determined to include the attribute of the distribution and the value of the characteristic relative to the set to which the residual is added.
12. The method of any one of clauses 1 to 11, wherein the probability is determined further based on a range of the characteristics, within which the entity project instance is considered to be out of specification.
13. The method of any one of clauses 1 to 12, further comprising determining a sampling plan for a measurement site for measurement based on the probability to determine a physical item instance (if any) that exceeds the specification.
14. A method comprising:
Obtaining a test value of one of a plurality of entity item instances of an entity system or object;
Use a non-probability model to obtain the calculated value of the characteristic;
Obtaining the value of a residual of the non-probability model based on the test values and the calculated values;
Obtaining an attribute of a first distribution of the residuals based on the values of the residuals; and obtaining a set of residuals of the non-probability model relative to a set of entity item instances based on the attributes of the first distributions An attribute of a second distribution.
15. The method of clause 14, wherein the attribute of the residual relative to the second distribution of the set includes a cumulative distribution function of the set of entity item instances.
16. The method of clause 14 or clause 15, wherein the attribute of the residual relative to the second distribution of the set relates to the attribute of the first distribution of the residual to the number of physical items in the set The power of the instance.
17. The method of any of clauses 14 to 16, wherein the attribute of the residual relative to the second distribution of the set is at least [1-(1-eCDF) ^N ] or [1-(1 -CDF) ^N ] defines a function, where N is the number of entity item instances in the set, CDF is a cumulative distribution function with respect to the first distribution, and eCDF is an empirical accumulation with respect to the first distribution distributed.
18. The method of any one of clauses 14 to 17, wherein the number of entity item instances in the set is greater than ten.
19. The method of any one of clauses 14 to 18, wherein the physical item instances correspond to pattern instances on a substrate generated by a device manufacturing process.
20. The method according to any one of clauses 14 to 19, wherein the number of entity item instances in the set corresponds to a specific entity item type or a specific plural within a measurement site or field of view of a metrology tool The number of one of these entity item instances that is a collection of one entity item type.
21. The method of any one of clauses 14 to 20, wherein there are a plurality of attributes of the residual relative to the second distribution of the set, and for different entity parts, the residual relative to the first Each of the plurality of attributes of the two distributions is different.
22. The method of any of clauses 14 to 21, wherein the characteristic is selected from one or more of the following: relative to a position of a substrate, relative to one or more other entity project instances A position, a geometric size, a geometric shape, a measure of a random effect, and / or any combination selected from the foregoing.
23. The method of any one of clauses 14 to 22, wherein obtaining the test values comprises measuring the entity project instances using a weights and measures tool or using a rigorous model for simulation.
24. The method of clause 23, wherein the weights and measures tool is configured to use a charged particle beam to measure the physical item instances.
25. The method of any of clauses 14 to 24, wherein obtaining the values of the residual includes obtaining the difference between the calculated values and the test values.
26. The method of any one of clauses 14 to 25, wherein the attribute of the first distribution of the residuals is a CDF or eCDF of the first distribution of the residuals.
27. The method of any one of clauses 14 to 26, further comprising obtaining the plurality of entity project instances based on shape, size, function, or spatial proximity.
28. A method comprising:
Obtain the probability that a group of entity items of an entity system or object will exceed the specifications, and use an attribute of a residual of a non-probability model to a distribution of a set of entity items to determine the probability. The determination is based on an attribute of a residual of the non-probability model relative to one of at least one entity item instance corresponding to at least one entity item type of the set; and an entity item instance to be detected based on the probabilities An ordered list.
29. The method of clause 28, wherein the attribute of the distribution relative to the distribution of the set includes a cumulative distribution function of the set of entity item instances.
30. The method of clause 28 or clause 29, wherein the attribute of the distribution of the residual relative to the set relates to at least one entity item instance of the residual relative to at least one entity item type corresponding to the set The property of the distribution is greater than the power of several physical item instances in the set.
31. The method of any one of clauses 28 to 30, wherein the attribute of the distribution relative to the distribution of the set is at least [1-(1-eCDF) ^N ] or [1-(1-CDF ) ^N ] defines a function, where N is the number of entity item instances in the set, and CDF is a cumulative distribution function of the residual relative to at least one entity item instance corresponding to at least one entity item type of the set And eCDF is an empirical cumulative distribution function of the residual relative to at least one entity item instance corresponding to at least one entity item type of the set.
32. The method of any one of clauses 28 to 31, wherein the number of entity item instances in the set is greater than ten.
33. The method of any one of clauses 28 to 32, wherein the physical item instances correspond to pattern instances on a substrate generated by a device manufacturing process.
34. The method of any one of clauses 28 to 33, wherein the number of entity item instances in the set corresponds to a specific entity item type or a specific plurality of objects in a measurement site or field of view of one of the metrology tools The number of one of these entity item instances that is a collection of entity item types.
35. The method of any one of clauses 28 to 34, wherein determining the ordered list further comprises determining, based on the probabilities, the predicted presence of at least one defect in a measurement site or field of view of the metrology tool.
36. The method of any one of clauses 28 to 35, wherein there are a plurality of attributes of the distribution relative to the distribution of the set, and for different entities, the residual is relative to the distribution of the set Each of the plurality of attributes is different.
37. The method of any one of clauses 28 to 36, wherein the characteristic is selected from one or more of the following: relative to a position of a substrate, relative to one or more other entity project instances A position, a geometric size, a geometric shape, a measure of a random effect, and / or any combination selected from the foregoing.
38. The method of any one of clauses 28 to 37, further comprising obtaining locations of the set of entity item instances, and determining the ordered list is further based on those locations.
39. The method of any one of clauses 28 to 38, wherein the ordered list includes a subset of the entity item instances in the set of entity item instances, wherein the entity item instances in the subset exceed the specification The probability is higher than the physical item instances in the set rather than the subset.
40. The method of any one of clauses 28 to 39, wherein determining the ordered list is further based on an inspection throughput, an amount of time allowed for inspection, and / or an amount of radiation allowed to be received by a substrate during the inspection .
41. The method of any one of clauses 28 to 40, wherein the ordered list is in descending order of probability.
42. The method of any one of clauses 28 to 41, further comprising updating the probabilities based on information obtained from detecting the entity item instances in the ordered list.
43. The method of any one of clauses 28 to 42, further comprising detecting entity items in the ordered list following the order of the ordered list.
44. A computer program product comprising a non-transitory computer-readable medium having recorded thereon instructions which, when executed by a computer system, implement the method of any one of clauses 1 to 43.

The lithographic device may be of a type in which at least a portion of the substrate may be covered with a liquid having a relatively high refractive index, for example, water, so as to fill a space between the projection system and the substrate. Wetting liquid can also be applied to other spaces in the lithographic apparatus, such as the space between the patterning device and the projection system. Infiltration techniques are known to increase the numerical aperture of projection systems. The term "wetting" as used herein does not mean that a structure such as a substrate must be immersed in a liquid, but only means that the liquid is located between the projection system and the substrate and / or the patterned device and the projection system during exposure. .

The term "projection system" or "projection optics" as used herein should be broadly interpreted to cover any type suitable for the exposure radiation used or for other factors such as the use of immersion liquids or the use of vacuum Projection systems, including refraction, reflection, refraction, magnetic, electromagnetic and electrostatic optical systems, or any combination thereof. The term "projection optics" or "projection system" may also include components that operate in accordance with any of these design types for collectively or individually directing, shaping, or controlling a beam of projection radiation.

The concepts disclosed herein can be used to simulate or mathematically model any device manufacturing process that involves a pattern transfer step, and can be particularly useful when using emerging imaging technologies that can produce increasingly smaller wavelengths. Emerging technologies that are already in use include the ability to generate deep ultraviolet (DUV) lithography with a wavelength of 193 nanometers by using ArF lasers and even 157 nanometers by using fluorine lasers. In addition, EUV lithography can generate wavelengths in the range of 5 to 20 nanometers, for example, by using a synchrotron or by using high-energy electrons to strike a material (solid or plasma) in order to generate photons in this range.

The term "mask" or "patterned device" as used herein can be broadly interpreted to mean a general patterned device that can be used to impart a patterned cross section to an incident radiation beam, which corresponds to The pattern to be generated in the target portion of the substrate; the term "light valve" can also be used in the context of this content. In addition to classic photomasks (transmission or reflection; binary, phase shift, hybrid, etc.), examples of other such patterned devices include: programmable mirror arrays and programmable LCD arrays.

The patterned devices mentioned above include or can form a design layout. Computer-aided design (CAD) programs can be used to generate design layouts. This procedure is often referred to as Electronic Design Automation (EDA). Most CAD programs follow a set of predetermined design rules to produce a functional design layout / patterned device. These rules are set by processing and design constraints. For example, design rules define the space tolerance between circuit devices (such as gates, capacitors, etc.) or interconnect lines in order to ensure that these circuit devices or lines do not interact with each other in an undesirable manner. Design rule limits are often referred to as "critical dimensions" (CD). The critical dimension of a circuit can be defined as the minimum width of a line or hole, or the minimum space between two lines or two holes. Therefore, the CD determines the total size and density of the designed circuit. Of course, one of the goals in the fabrication of integrated circuits is to faithfully reproduce the original circuit design (via patterned devices) on a substrate.

Although the concepts disclosed herein can be used for device fabrication on substrates such as silicon wafers, it should be understood that the concepts disclosed can be used with any type of pattern transfer system, for example, An imaged pattern transfer system on a round substrate.

As mentioned, lithography is an important step in the manufacture of devices such as ICs, where patterns formed on a substrate define functional elements of the IC, such as microprocessors, memory chips, and so on. Similar lithographic techniques are also used to form flat panel displays, micro-electromechanical systems (MEMS), and other devices. Although specific reference may be made to the fabrication of integrated circuits herein, it should be clearly understood that the description herein has many other possible applications. For example, it can be used to manufacture integrated optical systems, guidance and detection patterns for magnetic domain memory, liquid crystal display panels, thin-film magnetic heads, micro-mechanical systems (MEM), and the like. Those skilled in the art should understand that in the context of these alternative applications, any use of the terms "reduction mask", "wafer", or "die" in this article should be considered separately and more generally The terms "patterned device", "substrate" and "target portion" are synonymous or interchangeable with these more general terms. The substrates mentioned herein can be processed before or after exposure in, for example, a coating development system (a tool that typically applies a resist layer to a substrate and develops the exposed resist) or a metrology or inspection tool. Where applicable, the disclosure herein can be applied to these and other substrate processing tools. In addition, the substrate may be processed more than once, for example in order to produce, for example, a multilayer IC, so that the term substrate used herein may also refer to a substrate that already contains multiple processed layers.

In this document, the terms "radiation" and "beam" are used to cover all types of radiation, including ultraviolet radiation (e.g., 365 nm, 248 nm, 193 nm, 157 nm, or 126 nm) And extreme ultraviolet radiation (EUV, for example, in the wavelength range of 5 to 20 nm), and particle beams such as ion beams or electron beams.

Although the above may have specifically referred to the use of embodiments in the context of optical lithography, it should be understood that one embodiment of the present invention can be used in other applications (e.g., embossed lithography) and in the context of content Where permitted, it is not limited to optical lithography. In embossed lithography, the configuration in a patterned device defines a pattern that is generated on a substrate. The configuration of the patterned device may be pressed into a resist layer supplied to a substrate, and on the substrate, the resist is cured by applying electromagnetic radiation, heat, pressure, or a combination thereof. After the resist is cured, the patterned device is removed from the resist, leaving a pattern in it. Therefore, a lithographic apparatus using imprint technology usually includes a template holder for holding an imprint template, a substrate table for holding a substrate, and a relative movement between the substrate and the imprint template so that the The pattern of the embossing template is embossed onto one or more actuators on a layer of the substrate.

Aspects of the invention may be implemented in any convenient form. For example, embodiments may be implemented by one or more suitable computer programs, which may be on a tangible carrier medium (e.g., a magnetic disk) or an intangible carrier medium (e.g., a communication signal) Appropriate carrier media. Embodiments of the invention may be implemented using suitable devices that may specifically take the form of a programmable computer that executes a computer program configured to implement the methods as described herein. Therefore, the embodiments of the present invention can be implemented in hardware, firmware, software, or any combination thereof. Embodiments of the invention may also be implemented as instructions stored on a machine-readable medium, which may be read and executed by one or more processors. A machine-readable medium may include any mechanism for storing or transmitting information in a form readable by a machine (eg, a computing device). For example, machine-readable media may include read-only memory (ROM); random access memory (RAM); magnetic disk storage media; optical storage media; flash memory devices; electrical, optical, acoustic, or other forms Signals (such as carrier waves, infrared signals, digital signals, etc.), and other media. In addition, firmware, software, routines, and instructions may be described herein as performing specific actions. It should be understood, however, that such descriptions are merely for convenience and that such actions are actually caused by computing devices, processors, controllers, or other devices executing firmware, software, routines, instructions, and so on.

In the block diagrams, the illustrated components are depicted as discrete functional blocks, but embodiments are not limited to systems where the functionality described herein is organized as illustrated. The functionality provided by each of the components can be provided by software or hardware modules that are organized in a different way than currently depicted, for example, can be blended, combined, replicated, decomposed, distributed ( (E.g., within a data center or geographically), or organize this software or hardware differently. The functionality described herein may be provided by one or more processors executing one or more computers of code stored on a tangible, non-transitory machine-readable medium. In some cases, a third-party content delivery network may host some or all of the information transmitted over the network, in which case, where the information (e.g., content) is allegedly supplied or otherwise provided, This information can be provided by sending instructions to retrieve that information from the content delivery network.

Unless specifically stated otherwise, it should be understood that throughout this specification, discussions using terms such as "processing", "computing / calculating", "judgment" or the like refer to, for example, a dedicated computer or The action or program of a particular device similar to a dedicated electronic processing / computing device

The reader should be aware that this application describes several inventions. These inventions have been grouped into a single document rather than separating their inventions into separate patent applications, because the subject matter of those inventions contributes to economic development in the application. But the distinct advantages and aspects of these inventions should not be combined. In some cases, embodiments address all of the deficiencies mentioned herein, but it should be understood that the inventions are independently useful, and some embodiments address only a subset of these issues or provide other unmentioned benefits, These benefits will be apparent to those skilled in the art who review the present invention. Due to cost constraints, some of the inventions disclosed herein may not be claimed at present, and such inventions may be claimed in later applications (such as continuing applications or by amending this technical solution). Similarly, due to space constraints, neither the [Abstracts] nor [Summary] sections of this document should be considered as containing a comprehensive list of all such inventions or all aspects of these inventions.

It should be understood that the description and drawings are not intended to limit the invention to the particular form disclosed, but on the contrary, the intention is to cover all modifications and equivalents falling within the spirit and scope of the invention as defined by the scope of the appended patents And alternatives.

In view of this description, modifications and alternative embodiments of various aspects of the invention will be apparent to those skilled in the art. Accordingly, this description and drawings are to be interpreted as illustrative only and for the purpose of teaching those skilled in the art the general manner of carrying out the invention. It should be understood that the forms of the invention shown and described herein should be considered as examples of embodiments. Elements and materials can replace the elements and materials described and described herein, parts and procedures can be reversed or omitted, certain features can be used independently, and embodiments or features of the embodiments can be combined, as they are familiar with It will be apparent to those skilled in the art after obtaining the benefits of this description. Changes may be made in the elements described herein without departing from the spirit and scope of the invention as described in the following patent application scope. The headings used herein are for organizational purposes only and are not meant to limit the scope of the description.

As used throughout this application, the word "may" is used in a permitted meaning (ie, meaning possible) rather than in a mandatory meaning (ie, meaning necessary). The word "include / including / includes" and the like means including but not limited to. As used throughout this application, the singular form "a / an / the" includes plural references unless the content clearly dictates otherwise. Thus, for example, reference to "an element / a element" includes a combination of two or more elements, although other terms and phrases such as "a or Multiple. " Unless otherwise indicated, the term "or" is non-exclusive, that is, it covers both "and" and "or". Terms that describe conditional relationships, such as "response to X while Y", "after X, that is Y", "if X, then Y", "when X, Y", and the like cover causality, where The premise is a necessary causal condition, the premise is a sufficient causal condition, or the premise is a contributing causal condition of the result, for example, "the condition X appears after condition Y is obtained", for "only X appears after Y" and " After Y and Z, X "appears universally. These conditional relationships are not limited to the results obtained by immediately following the premise. This is because some results can be delayed, and in the conditional statement, the premise is connected to its result, for example, the premise is related to the possibility of the result. Unless otherwise indicated, a statement that a plurality of attributes or functions are mapped to a plurality of objects (e.g., performing one or more processors of steps A, B, C, and D) covers all such attributes or functions that are mapped to all These subsets of objects and attributes or functions are mapped to both subsets of attributes or functions (for example, all processors perform steps A through D, respectively, among which processor 1 performs step A, processor 2 performs steps B and C Part of the process, and the processor 3 executes part of step C and the status of step D). In addition, unless otherwise indicated, a statement of a value or action is "based on" another condition or value, and the description covers both the case where the condition or value is a separate factor and the case where the condition or value is one of a plurality of factors. Unless otherwise instructed, each "instance" of a set should not be read to have a certain property to exclude the condition that some other same or similar members in the larger set do not have that property, that is, every One does not necessarily mean every one. References to selection from a range include the endpoints of the range.

In the above description, any procedure, description or block in the flowchart should be understood as a module, section or part representing code, which includes one or more of the specific logical functions or steps for implementing the procedure Executable instructions, and alternative implementations are included within the scope of the illustrative examples of progress of the present invention, where functions may be performed out of the order shown or discussed depending on the functionality involved, including substantially simultaneously or in the opposite order Sequential execution, as understood by those skilled in the art.

Where certain U.S. patents, U.S. patent applications, or other materials (e.g., papers) have been incorporated by reference, the text of these U.S. patents, U.S. patent applications, and other materials has The stated statements and drawings are incorporated by reference without conflict. Where such conflicts exist, any such conflicting text in such incorporated U.S. patents, U.S. patent applications, and other materials is not specifically incorporated herein by reference.

Although certain embodiments have been described, these embodiments have been presented by way of example only, and are not intended to limit the scope of the invention. In fact, the novel methods, devices, and systems described herein may be implemented in many other forms; furthermore, various forms of methods, devices, and systems described herein may be omitted without departing from the spirit of the present invention. , Replacement and change. The scope of the accompanying patent application and its equivalent are intended to cover such forms or modifications as would fall within the scope and spirit of the invention.

31‧‧‧lighting model

32‧‧‧ Projection Optics Model

33‧‧‧Pattern device pattern model / patterned device model

36‧‧‧ aerial image / resist image

37‧‧‧ resist model

38‧‧‧resist image

39‧‧‧Procedure model after pattern transfer

40‧‧‧Etched image / Etched image

100‧‧‧ computer system

102‧‧‧Bus

104‧‧‧Processor

105‧‧‧ processor

106‧‧‧Main memory

108‧‧‧Read Only Memory

110‧‧‧Storage device

112‧‧‧Display

114‧‧‧input devices

116‧‧‧Cursor Control

118‧‧‧ communication interface

120‧‧‧ network link

122‧‧‧Internet

124‧‧‧Host computer

126‧‧‧Internet Service Provider (ISP)

128‧‧‧Internet

130‧‧‧Server

211‧‧‧program parameters

212‧‧‧Layout parameters

213‧‧‧step

214‧‧‧Features

215‧‧‧step

410‧‧‧Threshold

420‧‧‧value

421‧‧‧value

430‧‧‧ distribution

431‧‧‧ distribution

510‧‧‧ pattern

520‧‧‧value

530‧‧‧ distribution

540‧‧‧ distribution

551‧‧‧Threshold

552‧‧‧Threshold

555‧‧‧ Non-Probability Model

610‧‧‧step

620‧‧‧Attribute

630‧‧‧step

640‧‧‧value

650‧‧‧step

660‧‧‧Attribute

670‧‧‧step

680‧‧‧ chance

710a‧‧‧Pattern example

710b‧‧‧Pattern example

710c‧‧‧Pattern example

710d‧‧‧Pattern example

710e‧‧‧Pattern example

710f‧‧‧Pattern example

710g‧‧‧Illustration item

710h‧‧‧Pattern example

710i‧‧‧Pattern example

720a‧‧‧Calculated

720b‧‧‧Calculated

720c‧‧‧calculated value

720d‧‧‧calculated value

720e‧‧‧Calculated

720f‧‧‧Calculated value

720g‧‧‧calculated value

720h‧‧‧Calculated value

720i‧‧‧calculated value

730a‧‧‧Calculated

730b‧‧‧Calculated

730c‧‧‧Calculated

730d‧‧‧Calculated

730e‧‧‧Calculated

730f‧‧‧Calculated

730g‧‧‧Calculated

730h‧‧‧Calculated value

730i‧‧‧Calculated

810‧‧‧step

820‧‧‧test value

830‧‧‧step

840‧‧‧Calculated value

850‧‧‧step

860‧‧‧value

870‧‧‧step

880‧‧‧Attribute

1010‧‧‧Threshold

1020‧‧‧actual considerations

1030‧‧‧ Probability Density Function (PDF)

1110‧‧‧ chance

1120‧‧‧parts

1130‧‧‧step

1140 ‧ ‧ ‧ ordered list

1150‧‧‧step

1160‧‧‧step

1211‧‧‧ Pattern Examples / Patterns

1212‧‧‧ Pattern Examples

1213‧‧‧ Pattern Examples

1311‧‧‧Field of View (FOV)

1312‧‧‧Field of View (FOV)

1313‧‧‧Field of View (FOV)

1400‧‧‧step

1410‧‧‧ Properties

1420‧‧‧step

1430‧‧‧ Properties

1440‧‧‧ Probability calculation method

1450‧‧‧ chance

1500‧‧‧curve

1510‧‧‧ curve

1520‧‧‧ curve

1600‧‧‧ curve

1610‧‧‧ Curve

1620‧‧‧line

1630‧‧‧line

1640‧‧‧line

1700‧‧‧ substrate

1710‧‧‧Solid circle / defective fingerprint

AS‧‧‧ Alignment Sensor

B‧‧‧ radiation beam

BD‧‧‧Beam Delivery System

BK‧‧‧Baking plate

C‧‧‧ Target section

CH‧‧‧ cooling plate

CO‧‧‧ Concentrator / radiation collector / collector optics

DE‧‧‧Developer

IF‧‧‧Position Sensor / Virtual Source

IL‧‧‧lighting system / luminaire / lighting optics unit

IN‧‧‧Light Accumulator

I / O1‧‧‧ input / output port

I / O2‧‧‧ input / output port

LA‧‧‧lithography device

LACU ‧ ‧ lithography control unit

LB‧‧‧Loading Box

LC‧‧‧Weiying Manufacturing Unit

LS‧‧‧Order Sensor

MA‧‧‧ Patterned Device

MT‧‧‧ support structure

M1‧‧‧ Patterned Device Alignment Mark

M2‧‧‧ patterned device alignment mark

O‧‧‧ Optical axis

PM‧‧‧First Positioner

PS‧‧‧ projection system

PS1‧‧‧Position Sensor

PS2‧‧‧Position Sensor

PW‧‧‧Second Positioner

P1‧‧‧Substrate alignment mark

P2‧‧‧ substrate alignment mark

RF‧‧‧ Reference Frame

RO‧‧‧ substrate handler or robot

SC‧‧‧ Spinner

SCS‧‧‧Supervision Control System

SO‧‧‧ radiation source / source collector module

TCU‧‧‧ Coating Development System Control Unit

W‧‧‧ substrate

WT‧‧‧ Substrate

WTa‧‧‧ Substrate

WTb‧‧‧ Substrate

For those skilled in the art, after reviewing the following description of a specific embodiment in conjunction with the accompanying drawings, the above and other aspects and features will become apparent, in these drawings:

FIG. 1 is a schematic block diagram of a lithographic apparatus.

FIG. 2 schematically depicts one embodiment of a lithographic manufacturing unit or cluster.

FIG. 3 schematically depicts a method for predicting defects in a device manufacturing process.

FIG. 4 is a flowchart illustrating a method of simulating at least a portion of a pattern or a characteristic of a pattern in an image.

5A, 5B, 5C, and 5D schematically show that the probability calculation method can better consider the random variation than the method using only the non-probability model, and thus, for example, better guides the inspection in the device manufacturing process The resulting substrate.

FIG. 6 schematically shows how a probability calculation method is used to predict defects according to an embodiment.

FIG. 7 shows a flowchart of a method of calculating a probability of a defect on a substrate generated by a device manufacturing process according to an embodiment.

FIG. 8 schematically shows how the properties of the distribution of the residuals of the non-probability model can be obtained according to an embodiment.

FIG. 9 shows a flowchart of a method for obtaining attributes of a distribution of residuals of a non-probability model according to an embodiment.

10A, 10B, 10C, 10D, 10E, 10F, and 10G each show an example of the residual histogram as an attribute of the distribution of the residual.

FIG. 11 schematically shows an example in which the probability of a pattern-based defect is the integration of PDF within a range from infinity to a threshold value.

FIG. 12 schematically shows a flowchart of a method for determining which pattern instances on a substrate should be detected and the order in which such pattern instances should be detected according to an embodiment using the probability of pattern-based defects.

13A and 13B schematically show that the descending probability order may be worse in terms of detection processing amount compared to another order.

14A and 14B schematically show that the descending probability order may be worse in terms of detection processing amount compared to another order.

FIG. 15 shows the attributes of the distribution of the residuals of the non-probability model, the probability of calculating defects on the substrate generated by the device manufacturing process, and using the probability to determine which pattern instances on the substrate are to be detected according to an embodiment Method flow chart.

FIG. 16 is a graph showing an example of the probability distribution based on the characteristics of the pattern instances of the synthesized data.

FIG. 17 is an example graph of the cumulative number of predicted defects based on synthetic data as a function of the number of measurement sites.

FIG. 18 is an example visualization of a sampling plan for measuring substrates.

Figure 19 is a block diagram of an example computer system.

FIG. 20 is a schematic diagram of another lithographic apparatus.

FIG. 21 is a more detailed view of the device in FIG. 20.

Embodiments will now be described in detail with reference to the drawings, which are provided as illustrative examples to enable those skilled in the art to practice the embodiments. In particular, the figures and examples are not meant to limit the scope to a single embodiment, but other embodiments are possible through the interchange of some or all of the described or illustrated elements. Wherever convenient, the same reference numbers will be used throughout the drawings to refer to the same or like parts. Where known components may be used to partially or fully implement certain elements of these embodiments, only those portions of these known components necessary to understand the embodiments will be described and will be omitted Detailed descriptions of other parts of these known components, so as not to confuse the description of the embodiments. In this description, embodiments showing singular components should not be considered limiting; in fact, the category is intended to cover other embodiments including a plurality of the same components, and vice versa, unless explicitly stated otherwise herein. Furthermore, unless so explicitly stated, applicants do not intend to attribute any term in this specification or the scope of the patent application to an unusual or specific meaning. In addition, the scope covers the present and future known equivalents of the components mentioned herein as illustrations.

Claims (15)

A method comprising: Use a non-probability model to obtain a value of a property of a physical system instance of a physical system or object; Obtain an attribute of a distribution of a residual of the non-probability model relative to one of a set of entity item instances, and an attribute of the distribution of the residual relative to a set of an entity item instance based on a residual of the non-probability model An attribute corresponding to one of at least one entity item instance corresponding to at least one entity item type of the set; Determine an attribute of a distribution of the characteristic based on the attribute of the distribution with respect to the distribution of the entity item instance and based on the value of the characteristic of the entity item instance; and Based on the attribute of the distribution of the characteristic, a probability that the entity item instance exceeds the specification is determined. The method of claim 1, wherein the attribute of the residual relative to the distribution of the set includes a cumulative distribution function of the set of entity item instances. The method as claimed in item 1, wherein the attribute of the residual relative to the distribution of the set relates to the attribute of the residual relative to the distribution of at least one entity item instance corresponding to at least one entity item type of the set Than the power of several physical item instances in the set. The method of claim 1, wherein the attribute of the residual relative to the distribution of the set is at least one function defined by [1-(1-eCDF) ^N ] or [1-(1-CDF) ^N ], Where N is the number of entity item instances in the set, CDF is a cumulative distribution function of the residual relative to at least one entity item instance corresponding to at least one entity item type of the set, and eCDF is relative to the residual An empirical cumulative distribution function for at least one entity item instance corresponding to at least one entity item type of the set. The method as claimed in item 1, wherein the number of entity item instances in the set is greater than ten. The method of claim 1, wherein the physical item instance corresponds to a pattern instance on a substrate generated by a device manufacturing process. The method of claim 1, wherein the number of entity item instances in the set corresponds to a specific entity item type or a specific entity item type set in a measurement site or field of view of a metrology tool. One of these entity project instances. The method of claim 1, further comprising determining, based on the probability, that at least one physical item instance that exceeds the specification exists in a measurement location or field of view of one of the metrology tools. The method of claim 8, wherein the metrology tool is configured to measure the entity project instances using a charged particle beam. As in the method of claim 1, wherein there are a plurality of attributes of the distribution relative to the distribution of the residual, and for different entity parts, each of the plurality of attributes of the distribution relative to the distribution of the residual Department is different. The method of claim 1, wherein the characteristic is selected from one or more of the following: a position relative to a substrate, a position relative to one or more other entity item instances, a geometric size, a Geometry, a measure of a random effect, and / or any combination selected from the foregoing. The method of claim 1, wherein the attribute of the distribution of the characteristic is determined to include the attribute of the distribution and the value of the characteristic relative to the set to which the residual is added. As in the method of claim 1, wherein the probability is determined further based on a range of the characteristics, within which the entity project instance is considered to be out of specification. The method of claim 1, further comprising, based on the probability, determining a sampling plan for a measurement site for measurement to determine an entity item instance (if any) that exceeds the specification. A computer program product comprising a non-transitory computer-readable medium having instructions recorded thereon, which when executed by a computer system implements the method of claim 1.