Method for calibrating a simulation process based on a defect-based process window

Abstract

A method for improving simulation processes and solutions associated with chip manufacturing (e.g., retargeting patterns) is described herein. The method includes obtaining a plurality of dose-focus settings and a reference distribution based on measured values of a characteristic of a printed pattern associated with each of the plurality of dose-focus settings. The method also includes determining a probability density function (PDF) of the characteristic based on a tuning model and the plurality of dose-focus settings, such that an error between the PDF and the reference distribution is reduced. The PDF can be a function of the tuning model and a variance associated with the dose, the tuning model being configured to change a proportion of a nonlinear dose sensitivity contribution to the PDF. A process window can be adjusted based on the determined PDF of the characteristic.

Description

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims priority to U.S. application 62 / 980,068, filed on February 21, 2020, and the entire contents of which are incorporated herein by reference. Technical Field

[0003] The present disclosure relates to techniques for improving the performance of a device manufacturing process, which can be used in conjunction with a lithographic apparatus or a metrology apparatus. Background Art

[0004] A lithographic apparatus is a machine that applies a desired pattern to a target portion of a substrate. A lithographic apparatus can be used, for example, in the manufacture of integrated circuits (ICs). In this case, a patterning device, alternatively referred to as a mask or reticle, can be used to produce circuit patterns corresponding to individual layers of the IC, and such patterns can be imaged onto a target portion (e.g., a portion comprising a die, a die, or several dies) on a substrate (e.g., a silicon wafer) having a layer of radiation-sensitive material (resist). Typically, a single substrate will contain a network of adjacent target portions that are exposed successively. Known lithographic apparatus include so-called steppers, in which the target portions are irradiated by exposing the entire pattern onto each target portion at once, and so-called scanners, in which each target portion is irradiated by scanning the substrate synchronously parallel to or antiparallel to a given direction (the "scanning" direction) while scanning the pattern via a beam.

[0005] Before the circuit pattern is transferred from the pattern forming device to the substrate, the substrate can undergo various processes, such as priming, resist coating and soft baking. After exposure, the substrate may undergo other processes, such as post-exposure baking (PEB), developing, hard baking, and measurement / inspection of the circuit pattern after transfer. This array of processes is used as the basis for the manufacture of a separate layer of a device such as an IC. The substrate can then undergo various processes, such as etching, ion implantation (doping), metallization, oxidation, chemical mechanical polishing, etc., all of which are expected to ultimately complete the separate layer of the device. If several layers are needed in the device, the entire process or its variation is repeated for each layer. Ultimately, a device will be present in each target portion on the substrate. Subsequently, these devices are separated from each other by techniques such as dicing or sawing, so that a separate device can be mounted on a carrier, connected to a pin, or the like.

[0006] Thus, manufacturing devices such as semiconductor devices typically involves processing a substrate (e.g., a semiconductor wafer) using a number of fabrication processes to form various features and multiple layers of the device. These layers and features are typically manufactured and processed using, for example, deposition, lithography, etching, chemical mechanical polishing, and ion implantation. Multiple devices can be fabricated on multiple dies on a substrate, and the devices can then be separated into individual devices. This device manufacturing process can be considered a patterning process. The patterning process involves performing a patterning step using a pattern forming device in a lithographic apparatus, such as optical lithography and / or nanoimprint lithography, to transfer the pattern on the pattern forming device to the substrate, and the patterning process typically but optionally involves one or more related pattern processing steps, such as developing a resist by a developing apparatus, baking the substrate using a baking tool, using an etching apparatus, etching using the pattern, and the like. Summary of the Invention

[0007] According to an embodiment, a method for calibrating a simulation process is provided. The method includes obtaining (i) characteristic limits of a characteristic of a printed pattern based on a threshold failure rate of the printed pattern and (ii) a reference process window based on the characteristic limits; and calibrating the simulation process so that the simulation process window is within an acceptable threshold of the reference process window. Calibrating the simulation process includes executing one or more process models to determine a simulated pattern; and adjusting parameter values associated with the one or more process models until the characteristic of the simulated pattern satisfies the characteristic limits.

[0008] Furthermore, according to an embodiment, a method for generating a retargeting pattern associated with a patterning process is provided. The method comprises: obtaining (i) characteristic limits associated with a targeting pattern and (ii) a source mask optimization (SMO) process, wherein the characteristic limits are values of a characteristic beyond which a printed pattern corresponding to the targeting pattern will be considered defective, the source mask optimization (SMO) process being configured to calculate dose and / or mask parameters based on a threshold failure rate associated with the characteristic of the targeting pattern; and generating the retargeting pattern by simulating the source mask optimization process using the targeting pattern, wherein the characteristic associated with the retargeting pattern further falls within the characteristic limits associated with the targeting pattern.

[0009] Furthermore, according to an embodiment, a method for adjusting a process window is provided. The method includes obtaining (i) a dose probability density function (dose PDF) and (ii) a mask probability density function (mask PDF), the dose probability density function (dose PDF) being used to determine a probability of a dose, the dose PDF being a function of (a) a characteristic of a feature and (b) a deviation of a mask characteristic, the mask characteristic being associated with a mask used to print the feature on a substrate, the mask probability density function (mask PDF) being used to determine the probability of the deviation of the mask characteristic; determining the probability density function associated with the characteristic by convolving (i) the dose PDF with (ii) the mask PDF within a given range of mask characteristic values; and adjusting a process window associated with a patterning process based on the determined probability density function associated with the characteristic.

[0010] Furthermore, according to an embodiment, a method for adjusting a process window is provided. The method includes: obtaining (i) a plurality of dose-focus settings and (ii) a reference distribution based on measured values of a characteristic of a printed pattern associated with each of the plurality of dose-focus settings; determining a probability density function (PDF) of the characteristic based on an adjustment model and the plurality of dose-focus settings such that an error between the PDF and the reference distribution is reduced, the PDF being a function of the adjustment model and a variance associated with the dose, the adjustment model being configured to change a proportion of a nonlinear dose sensitivity contribution to the PDF; and adjusting a process window associated with a patterning process based on the determined PDF of the characteristic.

[0011] Furthermore, according to an embodiment, a non-transitory computer-readable medium is provided, the non-transitory computer-readable medium including instructions that, when executed by one or more processors, result in operations including: obtaining (i) characteristic limits for a characteristic of a printed pattern based on a threshold failure rate of the printed pattern and (ii) a reference process window based on the characteristic limits; and calibrating the simulation process so that the simulated process window is within an acceptable threshold of the reference process window. Calibrating the simulation process includes executing one or more process models to determine a simulated pattern; and adjusting parameter values associated with the one or more process models until the characteristic of the simulated pattern satisfies the characteristic limits.

[0012] In addition, according to an embodiment, a non-transitory computer-readable medium is provided, which includes instructions that, when executed by one or more processors, cause operations including: obtaining (i) characteristic limits associated with a target pattern and (ii) a source mask optimization (SMO) process, wherein the characteristic limits are values of some characteristics beyond which a printed pattern corresponding to the target pattern will be considered defective, the source mask optimization (SMO) process being configured to calculate dose and / or mask parameters based on a threshold failure rate associated with the characteristics of the target pattern; and simulating the source mask optimization process using the target pattern to produce a retargeted pattern, wherein the characteristics associated with the retargeted pattern further fall within the characteristic limits associated with the target pattern.

[0013] In addition, according to an embodiment, a non-transitory computer-readable medium is provided, which includes instructions that, when executed by one or more processors, cause operations including the following: obtaining (i) a dose probability density function (dose PDF) and (ii) a mask probability density function (mask PDF), wherein the dose probability density function (dose PDF) is used to determine the probability of a dose, wherein the dose PDF is a function of (a) a characteristic of a feature and (b) a deviation of a mask characteristic, wherein the mask characteristic is associated with a mask used to print the feature on a substrate, and the mask probability density function (mask PDF) is used to determine the probability of the deviation of the mask characteristic; determining the probability density function associated with the characteristic by convolving (i) the dose PDF with (ii) the mask PDF within a given range of mask characteristic values; and adjusting a process window associated with a patterning process based on the determined probability density function associated with the characteristic.

[0014] In addition, according to an embodiment, a non-transitory computer-readable medium is provided, which includes instructions that, when executed by one or more processors, cause operations including the following: obtaining (i) a plurality of dose-focus settings and (ii) a reference distribution based on measured values of a characteristic of a printed pattern associated with each of the plurality of dose-focus settings; determining a probability density function (PDF) of the characteristic based on an adjustment model and the plurality of dose-focus settings so that an error between the PDF and the reference distribution is reduced, the PDF being a function of the adjustment model and a variance associated with the dose, the adjustment model being configured to change a proportion of a nonlinear dose sensitivity contribution to the PDF; and adjusting a process window associated with a patterning process based on the determined PDF of the characteristic. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 schematically depicts a lithographic apparatus according to an embodiment;

[0016] Figure 2 schematically depicts an embodiment of a lithographic cell or lithographic cluster according to an embodiment;

[0017] Figure 3 schematically depicting exemplary detection devices and measurement techniques according to embodiments;

[0018] Figure 4 schematically depicts an exemplary detection device according to an embodiment;

[0019] Figure 5 FIGURE 1 illustrates the relationship between an illumination spot and a measurement target of a detection device according to an embodiment;

[0020] Figure 6 Schematically depicting a process of deriving a plurality of variables of interest based on measurement data according to an embodiment;

[0021] Figure 7 shows exemplary categories of process variables according to an embodiment;

[0022] Figure 8 Schematically illustrating a process for a patterning simulation method according to an embodiment;

[0023] Figure 9 Schematically illustrating a process for measuring a simulation method according to an embodiment;

[0024] Figure 10 is a flow chart of an example of an existing process for retargeting associated with a specific feature, according to an embodiment;

[0025] Figure 11 is a flow chart of a simulation process for implementing a defect-based process window and characteristic limits to improve conventional patterning process simulation according to an embodiment;

[0026] Figure 12A FIGURE 1 shows a method for calibrating (eg, Figure 11 ) exemplary rubrics for the simulation process;

[0027] Figure 12B Illustrated are exemplary gauges according to an embodiment and instructions for calibrating each gauge (e.g., Figure 11 ) The corresponding defect-based CD limit and resist CD limit of the simulation process;

[0028] Figure 12C is an exemplary resist profile illustrating a pattern or gauge of top CD locations and bottom CD locations according to an embodiment;

[0029] Figure 13 illustrates an exemplary defect-based process window associated with the top and bottom of a resist profile according to an embodiment;

[0030] Figure 14A FIGURE 1 shows a method for calibrating (eg, Figure 11 ) an exemplary DB-PW process window of experimental data for a simulated process;

[0031] Figure 14B The diagram shows the process from (eg, Figure 11 ) An example of a simulated process window obtained by a calibration simulation process;

[0032] Figure 14C shows exemplary CD margins achievable at different locations on a resist according to an embodiment;

[0033] Figure 15 According to the embodiment Figure 11 Flowchart of calibration of similar simulation process;

[0034] Figure 16 illustrates a desired exemplary target pattern after etching, and the results of an exemplary post-patterning process, according to an embodiment;

[0035] Figure 17 illustrates an exemplary retargeted pattern and associated process parameter values generated based on a target and calibrated SMO process after etching the pattern, according to an embodiment;

[0036] Figure 18 is a block diagram of an exemplary retargeting process according to an embodiment;

[0037] Figure 19 The diagram will confirm Figure 18 Examples of margins used in the retargeting process;

[0038] Figure 20A and Figure 20B illustrates exemplary behavior of margin due to dose variation according to an embodiment;

[0039] Figure 21 is a flow chart of a method for generating a retargeting pattern associated with a patterning process according to an embodiment;

[0040] Figure 22 is a plot of an exemplary CD distribution fit according to an embodiment;

[0041] Figure 23 a plot illustrating the deviation of measured resist LCDU relative to mask CD associated with each mask contact hole plotted;

[0042] Figure 24 is a flow chart of a method for determining a probability density function associated with characteristics of features to be printed on a substrate, according to an embodiment;

[0043] Figure 25 illustrates an exemplary relationship between a mask size and a change in CD on a wafer due to the change in mask size according to an embodiment; and

[0044] Figure 26 According to the embodiment for different δCD mask Two exemplary relationships between the dose (D) and the CD on the substrate;

[0045] Figure 27 illustrates an exemplary distribution of raw CD data and a Gaussian fit on the raw data according to an embodiment;

[0046] Figure 28 are sample results generated by an existing CD model for different dose-focus settings according to an embodiment;

[0047] Figure 29 is a flow chart of a method for determining a probability density function associated with a characteristic of a pattern to be printed on a substrate according to an embodiment;

[0048] Figure 30A and Figure 30B is a plot of adjustment values associated with an adjustment model for adjusting dose contribution to characteristic (e.g., CD) variation according to an embodiment;

[0049] Figure 31 are sample results generated by a characteristic model (eg, a CD model) for different dose-focus settings according to an embodiment, wherein the characteristic model is generated by Figure 29 Method to determine;

[0050] Figure 32 According to the embodiment Figure 1 The block diagram of the simulation model corresponding to the subsystem in;

[0051] Figure 33 A flow chart illustrating a general method of optimizing a lithographic projection apparatus according to an embodiment;

[0052] Figure 34 A flow chart showing a method of optimizing a lithographic projection apparatus according to an embodiment, wherein optimization of all design variables is performed alternately;

[0053] Figure 35 An exemplary method of optimization according to an embodiment is shown;

[0054] Figure 36is a block diagram of an exemplary computer system according to an embodiment;

[0055] Figure 37 is a schematic diagram of another lithographic projection apparatus according to an embodiment;

[0056] Figure 38 According to the embodiment Figure 37 A more detailed view of the device in; and

[0057] Figure 39 According to the embodiment Figure 37 and Figure 38 A more detailed view of the source collector module of the device. DETAILED DESCRIPTION

[0058] Before describing the embodiments in detail, it is instructive to present an exemplary environment in which the embodiments may be implemented.

[0059] Figure 1 An embodiment of a lithographic apparatus LA is schematically depicted. The apparatus comprises:

[0060] - an illumination system (illuminator) IL configured to condition a radiation beam B (e.g. UV radiation or DUV radiation);

[0061] a support structure (e.g., mask table) MT configured to support a patterning device (e.g., mask) MA and connected to a first positioner PM configured to accurately position the patterning device according to certain parameters;

[0062] a substrate table (e.g., wafer stage) WT (e.g., WTa, WTb, or both) configured to hold a substrate (e.g., a resist-coated wafer) W and connected to a second positioner PW configured to accurately position the substrate according to certain parameters; and

[0063] - a projection system (e.g., a refractive projection lens system) PS, which is configured to project the pattern imparted to the radiation beam B by the pattern forming device MA onto a target portion C (e.g., comprising one or more tube cores and often referred to as a field) of the substrate W, and the projection system is supported on a reference frame (RF).

[0064] As depicted here, the device is of the transmissive type (eg using a transmissive mask). Alternatively, the device may be of the reflective type (eg using a programmable mirror array of the type mentioned above, or using a reflective mask).

[0065] The illuminator IL receives a radiation beam from a radiation source SO. For example, when the source is an excimer laser, the source and the lithographic apparatus may be separate entities. In such a case, the source is not considered to form part of the lithographic apparatus, and the radiation beam is transferred from the source SO to the illuminator IL by means of a beam delivery system BD comprising, for example, suitable directing mirrors and / or a beam expander. In other cases, for example, when the source is a mercury lamp, the source may be an integral part of the apparatus. The source SO and illuminator IL, together with the beam delivery system BD (where necessary), may be referred to as a radiation system.

[0066] The illuminator IL can vary the intensity distribution of the beam. The illuminator can be arranged to limit the radial extent of the radiation beam so that the intensity distribution is non-zero within an annular region in a pupil plane of the illuminator IL. Additionally or alternatively, the illuminator IL can be operable to limit the distribution of the beam in the pupil plane so that the intensity distribution is non-zero in a plurality of equally spaced segments in the pupil plane. The intensity distribution of the radiation beam in the pupil plane of the illuminator IL can be referred to as an illumination pattern.

[0067] Thus, the illuminator IL may include an adjuster AM configured to adjust the (angular / spatial) intensity distribution of the beam. Typically, at least the outer radial extent and / or the inner radial extent (typically referred to as σ-outer and σ-inner, respectively) of the intensity distribution in the pupil plane of the illuminator may be adjusted. The illuminator IL may be operable to change the angular distribution of the beam. For example, the illuminator may be operable to change the number and angular extent of the segments in the pupil plane where the intensity distribution is non-zero. By adjusting the intensity distribution of the beam in the pupil plane of the illuminator, different illumination patterns may be achieved. For example, by limiting the radial extent and the angular extent of the intensity distribution in the pupil plane of the illuminator IL, the intensity distribution may have a multipolar distribution, such as, for example, a dipole, quadrupole, or hexapole distribution. Such illumination patterns may be obtained, for example, by inserting optics providing the desired illumination pattern into the illuminator IL or by using a spatial light modulator.

[0068] The illuminator IL can be operable to change the polarization of the beam and can be operable to adjust the polarization using the adjuster AM. The polarization state of the radiation beam across the pupil plane of the illuminator IL can be referred to as a polarization mode. Using different polarization modes can allow for greater contrast in the image formed on the substrate W. The radiation beam can be unpolarized. Alternatively, the illuminator can be arranged to linearly polarize the radiation beam. The polarization direction of the radiation beam can vary across the pupil plane of the illuminator IL. The polarization direction of the radiation can be different in different zones in the pupil plane of the illuminator IL. The polarization state of the radiation can be selected depending on the illumination mode. For a multipolar illumination mode, the polarization of each pole of the radiation beam can typically be perpendicular to the position vector of the pole in the pupil plane of the illuminator IL. For example, for a dipole illumination mode, the radiation can be linearly polarized in a direction substantially perpendicular to a line bisecting two opposing sections of the dipole. The radiation beam can be polarized in one of two different orthogonal directions, which can be referred to as the X polarization state and the Y polarization state. For a quadrupole illumination mode, the radiation in the segments of each pole can be linearly polarized in a direction substantially perpendicular to a line bisecting the segments. This polarization mode can be referred to as XY polarization. Similarly, for a hexapole illumination mode, the radiation in the segments of each pole can be linearly polarized in a direction substantially perpendicular to a line bisecting the segments. This polarization mode can be referred to as TE polarization.

[0069] In addition, the illuminator IL typically includes various other components, such as an integrator IN and a condenser CO. The illumination system may include various types of optical components for directing, shaping or controlling the radiation, such as refractive, reflective, magnetic, electromagnetic, electrostatic or other types of optical components, or any combination thereof.

[0070] The illuminator thus provides a conditioned radiation beam B having a desired uniformity and intensity distribution in its cross-section.

[0071] The support structure MT supports the patterning device in a manner that depends on the orientation of the patterning device, the design of the lithographic apparatus, and other conditions such as, for example, whether the patterning device is held in a vacuum environment. The support structure may use mechanical, vacuum, electrostatic, or other clamping techniques to hold the patterning device. The support structure may be, for example, a frame or table, which may be fixed or movable as required. The support structure may ensure that the patterning device is in a desired position, for example, relative to a projection system. Any use of the terms "reticle" or "mask" in this disclosure may be considered synonymous with the more general term "patterning device."

[0072] The term "patterning device" as used in the present invention should be broadly interpreted as referring to any device that can be used to impart a pattern in a target portion of a substrate. In an embodiment, the patterning device is any device that can be used to impart a pattern in its cross-section to a radiation beam so as to produce a pattern in the target portion of the substrate. It should be noted that, for example, if the pattern imparted to the radiation beam includes phase-shifting features or so-called assist features, the pattern may not exactly correspond to the desired pattern in the target portion of the substrate. Typically, the pattern imparted to the radiation beam will correspond to a specific functional layer in a device (such as an integrated circuit) produced in the target portion.

[0073] The patterning device may be transmissive or reflective. Examples of patterning devices include masks, programmable mirror arrays, and programmable LCD panels. Masks are well known in photolithography and include types such as binary, alternating phase-shift, and attenuated phase-shift, as well as various hybrid mask types. An example of a programmable mirror array uses a matrix arrangement of small mirrors, each of which can be individually tilted to reflect an incident radiation beam in different directions. The tilted mirrors impart a pattern in the radiation beam that is reflected by the mirror matrix.

[0074] The term "projection system" as used herein should be interpreted broadly to encompass any type of projection system, as appropriate to the exposure radiation used or to other factors such as the use of an immersion liquid or the use of a vacuum, including refractive, reflective, catadioptric, 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."

[0075] The projection system PS has an optical transfer function that can be non-uniform and can affect the pattern imaged onto the substrate W. For unpolarized radiation, this effect can be fairly well described by two scalar maps that describe the transmission (apodization) and relative phase (aberration) of the radiation exiting the projection system PS as a function of its position in the pupil plane. These scalar maps, which can be referred to as transmittance maps and relative phase maps, can be expressed as linear combinations of a full set of basis functions. A particularly suitable set is the Zernike polynomials, which form a set of orthogonal polynomials defined on the unit circle. Determining each scalar map can involve determining the coefficients in such an expansion. Since the Zernike polynomials are orthogonal on the unit circle, the Zernike coefficients can be determined by successively calculating the inner product of the measured scalar map with each Zernike polynomial and dividing this inner product by the square of the norm of the Zernike polynomial.

[0076] The transmittance map and the relative phase map are field- and system-dependent. That is, typically, each projection system PS will have a different Zernike expansion for each field point (i.e., for each spatial location in the image plane of the projection system). The relative phase of the projection system PS in its pupil plane can be determined by projecting radiation, for example, from a point-like source in the object plane of the projection system PS (i.e., the plane of the patterning device MA) through the projection system PS and measuring the wavefront (i.e., the locus of points with the same phase) using a shearing interferometer. The shearing interferometer is a common-path interferometer and therefore advantageously does not require a secondary reference beam to measure the wavefront. The shearing interferometer may comprise a diffraction grating (e.g., a two-dimensional grid) in the image plane of the projection system (i.e., the substrate table WT), and a detector arranged to detect an interference pattern in a plane conjugate to the pupil plane of the projection system PS. The interference pattern is related to the derivative of the phase of the radiation with respect to the coordinate in the pupil plane in the shear direction. The detector may comprise an array of sensing elements, such as, for example, a charge-coupled device (CCD).

[0077] The projection system PS of the lithographic apparatus may not produce visible fringes and therefore a phase stepping technique (such as, for example, moving a diffraction grating) may be used to enhance the accuracy of the determination of the wavefront. The stepping may be performed in the plane of the diffraction grating and in a direction perpendicular to the scanning direction of the measurement. The stepping range may be one grating period and at least three (uniformly distributed) phase steps may be used. Thus, for example, three scanning measurements may be performed in the y direction, each for a different position in the x direction. Such stepping of the diffraction grating effectively converts phase changes into intensity changes, thereby allowing the phase information to be determined. The grating may be stepped in a direction perpendicular to the diffraction grating (z direction) to calibrate the detector.

[0078] The diffraction grating can be scanned sequentially in two perpendicular directions, which can coincide with the axes (x and y) of the coordinate system of the projection system PS or can be at an angle (such as 45 degrees) to these axes. The scan can be performed over an integer number of grating periods (e.g., one grating period). The scan averages the phase change in one direction, thereby allowing the phase change in the other direction to be reconstructed. This allows the wavefront to be determined as a function of the two directions.

[0079] The transmission (apodization) of the projection system PS in the pupil plane of the projection system PS can be determined by projecting radiation, for example, from a point-like source in the object plane of the projection system PS (i.e., the plane of the patterning device MA) through the projection system PS and measuring the intensity of the radiation in a plane conjugate to the pupil plane of the projection system PS using a detector. The same detectors as those used to measure the wavefront to determine aberrations can be used.

[0080] The projection system PS may include multiple optical (e.g., lens) elements and may further include an adjustment mechanism AM configured to adjust one or more of the optical elements to correct for aberrations (phase variations in the pupil plane across the field). To achieve this adjustment, the adjustment mechanism may be operable to manipulate one or more optical (e.g., lens) elements within the projection system PS in one or more different ways. The projection system may have a coordinate system in which the optical axis of the projection system extends in the z-direction. The adjustment mechanism may be operable to perform any combination of the following: shifting one or more optical elements; tilting one or more optical elements; and / or deforming one or more optical elements. Displacement of the optical elements may be performed in any direction (x, y, z, or a combination thereof). Tilting of the optical elements is typically performed out of a plane perpendicular to the optical axis by rotating about axes in the x and / or y directions, although rotation about the z-axis may be used for non-rotationally symmetric aspheric optical elements. Deformation of the optical element may include low-frequency shape (e.g., astigmatism) and / or high-frequency shape (e.g., free-form asphericity). Deformation of the optical element may be performed, for example, by using one or more actuators to apply forces to one or more sides of the optical element and / or by using one or more heating elements to heat one or more selected regions of the optical element. Typically, it is not possible to adjust the projection system PS to correct for apodization (transmittance variation across the pupil plane). A transmittance map of the projection system PS may be used when designing a patterning device (e.g., mask) MA for the lithographic apparatus LA. Using computational lithography techniques, the patterning device MA may be designed to at least partially correct for apodization.

[0081] The lithographic apparatus may be of a type having two (dual stage) or more tables (e.g. two or more substrate tables WTa, WTb, two or more patterning device tables, a substrate table WTa and table WTb below the projection system without a dedicated substrate table, for example to facilitate measurement and / or cleaning, etc.). In these "multi-stage" machines, the additional tables may be used in parallel, or preparatory steps may be carried out on one or more tables while one or more other tables are being used for exposure. For example, alignment measurements may be performed using an alignment sensor AS and / or level (height, inclination, etc.) measurements may be performed using a level sensor (or leveling sensor) LS.

[0082] The lithographic apparatus may also be of a type in which at least a portion of the substrate may be covered by a liquid having a relatively high refractive index (e.g., water) so as to fill the space between the projection system and the substrate. Immersion liquid may also be applied to other spaces in the lithographic apparatus, such as the space between the patterning device and the projection system. Immersion techniques are well known in the art for increasing the numerical aperture of projection systems. The term "immersion" as used herein does not imply that a structure such as a substrate is necessarily immersed in the liquid, but only that the liquid is located between the projection system and the substrate during exposure.

[0083] Thus, in operation of the lithographic apparatus, a radiation beam is conditioned and provided by the illumination system IL. The radiation beam B is incident on a patterning device (e.g. a mask) MA held on a support structure (e.g. a mask table) MT and is patterned by the patterning device. Having traversed the patterning device MA, the radiation beam B passes through a projection system PS which focuses the beam onto a target portion C of the substrate W. With the aid of a second positioner PW and a position sensor IF (e.g. an interferometer, a linear encoder, a 2-D encoder or a capacitive sensor), the substrate table WT can be accurately moved, for example in order to position different target portions C in the path of the radiation beam B. Similarly, for example after mechanical retrieval from a mask library or during scanning, a first positioner PM and a further position sensor (the further position sensor in Figure 1 The support structure MT may be arranged to move along the pattern forming device MA relative to the path of the radiation beam B. In general, movement of the support structure MT may be achieved by means of a long-stroke module (coarse positioning) and a short-stroke module (fine positioning) which form part of the first positioner PM. Similarly, movement of the substrate table WT may be achieved using a long-stroke module and a short-stroke module which form part of the second positioner PW. In the case of a stepper (as opposed to a scanner), the support structure MT may be connected to the short-stroke actuator only, or may be fixed. The pattern forming device MA and the substrate W may be aligned using the pattern forming device alignment marks M1, M2 and the substrate alignment marks P1, P2. Although the substrate alignment marks as shown occupy dedicated target portions, the substrate alignment marks may be located in the space between target portions (these marks are referred to as scribe line alignment marks). Similarly, in the case where more than one die is provided on the pattern forming device MA, the pattern forming device alignment marks may be located between the dies.

[0084] The depicted device can be used in at least one of the following modes:

[0085] 1. In step mode, the entire pattern imparted to the radiation beam is projected onto a target portion C at once while the support structure MT and substrate table WT are held essentially stationary (i.e. a single static exposure). Subsequently, the substrate table WT is shifted in the X and / or Y direction so that a different target portion C can be exposed. In step mode, the maximum size of the exposure field limits the size of the target portion C imaged in a single static exposure.

[0086] 2. In scan mode, the support structure MT and substrate table WT are scanned synchronously while a pattern imparted to the radiation beam is projected onto a target portion C (i.e., a single dynamic exposure). The speed and direction of the substrate table WT relative to the support structure MT may be determined by the (de-)magnification and image reversal characteristics of the projection system PS. In scan mode, the maximum size of the exposure field limits the width of the target portion (in the non-scanning direction) in a single dynamic exposure, while the length of the scanning motion determines the height of the target portion (in the scanning direction).

[0087] 3. In another mode, the support structure MT is held essentially stationary, thereby holding the programmable patterning device, and the substrate table WT is moved or scanned while the pattern imparted to the radiation beam is projected onto a target portion C. In this mode, a pulsed radiation source is typically used, and the programmable patterning device is updated as required after each movement of the substrate table WT or between successive radiation pulses during a scan. This mode of operation can be readily applied to maskless lithography utilizing a programmable patterning device, such as a programmable mirror array of the type mentioned above.

[0088] Combinations and / or variations on the above-described modes of use or entirely different modes of use may also be employed.

[0089] Although specific reference may be made to the use of lithographic equipment in IC manufacturing in the present invention, it should be understood that the lithographic equipment described in the present invention may have other applications, such as manufacturing integrated optical systems, guidance and detection patterns for magnetic domain memories, liquid crystal displays (LCDs), thin film heads, etc. Those skilled in the art will understand that in the context of these alternative applications, any use of the term "wafer" or "die" in the present invention may be considered synonymous with the more general term "substrate" or "target portion", respectively. The substrates referred to in the present invention may be processed before or after exposure in, for example, a coating and development system or track (a tool that typically applies a resist layer to a substrate and develops the exposed resist), or a measurement or inspection tool. Where applicable, the disclosure of the present invention may be applied to these and other substrate processing tools. In addition, a substrate may be processed more than once, for example to produce a multi-layer IC, so that the term substrate used in the present invention may also refer to a substrate that already contains multiple processed layers.

[0090] The terms "radiation" and "beam" as used in the present invention encompass all types of electromagnetic radiation, including ultraviolet (UV) radiation (e.g., having a wavelength of 365 nm, 248 nm, 193 nm, 157 nm or 126 nm) and extreme ultraviolet (EUV) radiation (e.g., having a wavelength in the range of 5 nm to 20 nm), as well as particle beams, such as ion beams or electron beams.

[0091] The various patterns on or provided by a pattern forming device can have different process windows, i.e., the space of process variables within which a pattern within specification will be produced. Examples of pattern specifications related to potential systematic defects include checking for necking, line pullback, line thinning, CD, edge placement, overlap, resist top loss, resist undercut and / or bridging. The process windows of all patterns on a pattern forming device or a region thereof can be obtained by merging the process windows of each individual pattern (e.g., overlapping the process windows). The boundaries of the process windows of all patterns contain the boundaries of the process windows of some of the individual patterns. In other words, these individual patterns limit the process windows of all patterns. These patterns can be referred to as "hot spots" or "process window limiting patterns (PWLPs)", and "hot spots" or "process window limiting patterns (PWLPs)" are used interchangeably in the present invention. When controlling a portion of a patterning process, it is possible and economical to focus on hot spots. When the hot spots are defect-free, it is most likely that all patterns are defect-free.

[0092] like Figure 2 As shown in , the lithography equipment LA can form part of a lithography cell LC (sometimes also referred to as a litho cell or litho cluster), which also includes equipment for performing pre-exposure and post-exposure processes on a substrate. Conventionally, these devices include one or more spin coaters SC for depositing one or more resist layers, one or more developers DE for developing the exposed resist, one or more chill plates CH and / or one or more bake plates BK. A substrate handling device or robot RO picks up one or more substrates from input / output ports I / O1, I / O2, moves these substrates between different process equipment and transfers these substrates to a feed station LB of the lithography equipment. These devices, often collectively referred to as coating and developing systems or tracks, are controlled by a coating and developing system control unit or track control unit TCU, which is itself controlled by a management control system SCS, which also controls the lithography equipment via the lithography control unit LACU. Thus, different devices can be operated to maximize throughput and processing efficiency.

[0093] In order to correctly and consistently expose a substrate exposed by a lithographic apparatus and / or to monitor a portion of a patterning process (e.g., a device manufacturing process) that includes at least one pattern transfer step (e.g., an optical lithography step), it is desirable to inspect the substrate or other object to measure or determine one or more properties, such as alignment, overlay (the overlay may be, for example, overlay between structures in overlapping layers or overlay between structures in the same layer that have been provided separately from the layer by, for example, a double patterning process), line thickness, critical dimension (CD), focus offset, material properties, etc. Therefore, a fabrication facility in which a lithocell LC is located typically also includes a metrology system MET that measures some or all of the substrates W processed in the lithocell, or other objects in the lithocell. The metrology system MET may be a component of the lithocell LC, for example, the metrology system MET may be a component of the lithographic apparatus LA (such as an alignment sensor AS).

[0094] For example, one or more measured parameters may include: overlap between successive layers formed in or on a patterned substrate, critical dimensions (CD) of features formed in or on a patterned substrate (e.g., critical line width), focus or focus error of an optical lithography step, dose or dose error of an optical lithography step, optical aberrations of an optical lithography step, etc. Such measurements may be performed on a target on the product substrate itself and / or on a dedicated metrology target provided on the substrate. The measurements may be performed after resist development but before etching, or may be performed after etching.

[0095] There are various techniques for measuring structures formed during the patterning process, including the use of scanning electron microscopes, image-based metrology tools, and / or various specialized tools. As discussed above, a fast and non-invasive form of a specialized metrology tool is a measurement tool in which a radiation beam is directed onto a target on the surface of the substrate and the properties of the scattered (diffracted / reflected) beam are measured. By evaluating one or more properties of the radiation scattered by the substrate, one or more properties of the substrate can be determined. This can be referred to as diffraction-based metrology. One such application of such diffraction-based metrology is to measure the characteristics of asymmetry within a target. This can be used as a measure of overlap, for example, but other applications are also known. For example, asymmetry can be measured by comparing relative parts of the diffraction spectrum (e.g., comparing the -1 order and the +1 order in the diffraction spectrum of a periodic grating). This can be done as described above and as described, for example, in U.S. Patent Application Publication No. US2006-066855, which is incorporated herein by reference in its entirety. Another application of diffraction-based metrology is the measurement of feature width (CD) within a target. Such techniques may employ the apparatus and methods described below.

[0096] Thus, during a device fabrication process (e.g., a patterning process or a lithography process), a substrate or other object may be subjected to various types of measurements during or after the process. The measurements may determine whether a particular substrate is defective, may adjust the process and equipment used in the process (e.g., aligning two layers on a substrate or aligning a patterning device with a substrate), may measure the performance of the process and equipment, or may be used for other purposes. Examples of measurements include optical imaging (e.g., optical microscopy), non-imaging optical measurements (e.g., diffraction-based measurements, such as ASML YieldStar metrology tools, ASML SMASH metrology systems), mechanical measurements (e.g., profiling using a stylus, atomic force microscopy (AFM)), and / or non-optical imaging (e.g., scanning electron microscopy (SEM)). The SMASH (Smart Alignment Sensor Hybrid) system, as described in U.S. Pat. No. 6,961,116, which is incorporated herein by reference in its entirety, uses a self-referencing interferometer that produces two overlapping and relatively rotated images of an alignment mark, detects intensities in the pupil plane where the Fourier transforms of the images cause interference, and extracts position information from the phase differences between the diffraction orders of the two images, which are expressed as intensity variations in the interference orders.

[0097] The measurement results can be provided directly or indirectly to the supervisory control system SCS. If an error is detected, the exposure of subsequent substrates (especially if the inspection of one or more other substrates in the batch that are still to be exposed can be completed quickly and sufficiently) and / or the subsequent exposure of the exposed substrate can be adjusted. In addition, the exposed substrate can be stripped and reworked to improve the yield, or discarded, thereby avoiding further processing of substrates known to be defective. In the case where only some target portions of the substrate are defective, further exposure can be performed only on those target portions that are good.

[0098] Within the metrology system MET, metrology equipment is used to determine one or more properties of a substrate, and in particular, to determine how one or more properties vary between different substrates or how different layers of the same substrate vary between layers. As mentioned above, the metrology equipment can be integrated into the lithographic apparatus LA or lithocell LC, or can be a separate device.

[0099] To enable measurement, one or more targets may be provided on the substrate. In an embodiment, the target is specially designed and may include a periodic structure. In an embodiment, the target is part of a device pattern, for example, a periodic structure of the device pattern. In an embodiment, the device pattern is a periodic structure of a memory device (e.g., a bipolar transistor (BPT), a bit line contact (BLC), or the like).

[0100] In an embodiment, the target on the substrate may include one or more one-dimensional periodic structures (e.g., gratings) that are printed such that after development, the periodic structural features are formed by solid resist lines. In an embodiment, the target may include one or more two-dimensional periodic structures (e.g., gratings) that are printed such that after development, the one or more periodic structures are formed by solid resist guide posts or vias in the resist. The bars, guide posts, or vias may alternatively be etched into the substrate (e.g., etched into one or more layers on the substrate).

[0101] In an embodiment, one of the parameters of interest for the patterning process is overlay. Overlay can be measured using dark field scatterometry, where the zero order diffraction (corresponding to specular reflection) is blocked and only higher orders are processed. Examples of dark field metrology can be found in PCT patent application publications WO 2009 / 078708 and WO 2009 / 106279, which are hereby incorporated by reference in their entirety. Further developments of the technology have been described in U.S. patent application publications US2011-0027704, US2011-0043791, and US2012-0242970, which are hereby incorporated by reference in their entirety. Diffraction-based overlay using dark field detection of diffraction orders enables overlay measurement of smaller targets. These targets can be smaller than the illumination spot and can be surrounded by device product structures on the substrate. In an embodiment, multiple targets can be measured in a single radiation capture.

[0102] Figure 3 An exemplary inspection apparatus (e.g., a scatterometer) is depicted. The scatterometer comprises a broadband (white light) radiation projector 2 that projects radiation onto a substrate W. The redirected radiation is passed to a spectrometer detector 4, which measures the spectrum 10 (intensity as a function of wavelength) of the radiation reflected by the specular surface, as shown, for example, in the lower left graph. From this data, the processor PU can generate a spectrum of the specular spectrum 10 (intensity as a function of wavelength), for example, by rigorous coupled wave analysis and nonlinear regression, or by comparing the specular spectrum to the specular spectrum. Figure 3 The structure or profile that resulted in the detected spectrum is reconstructed by comparing the simulated spectra shown in the lower right corner of the image to the library of simulated spectra. Typically, for reconstruction, the general form of the structure is known, and some variables are assumed based on knowledge of the process used to make the structure, leaving only a few variables to determine the structure based on the measured data. Such an inspection device can be configured as a normal-incidence inspection device or an oblique-incidence inspection device.

[0103] Figure 4Another inspection apparatus that can be used is shown in . In this arrangement, radiation emitted by a radiation source 2 is collimated using a lens system 12 and transmitted through an interference filter 13 and a polarizer 17, and is reflected by a partially reflective surface 16 and focused via an objective lens 15 into a spot S on a substrate W, the objective lens having a relatively high numerical aperture (NA), desirably at least 0.9 or at least 0.95. Immersion inspection apparatuses (using a relatively high refractive index fluid, such as water) can even have a numerical aperture exceeding 1.

[0104] As in the lithographic apparatus LA, one or more substrate tables may be provided to hold the substrate W during measurement operations. The substrate table may be of a similar form to that of Figure 1 The substrate table WT is similar or identical to that of the substrate table WT. In an example where the inspection apparatus is integrated with the lithographic apparatus, the substrate table may even be the same substrate table. Coarse positioning means and fine positioning means may be provided to a second positioner PW, which is configured to accurately position the substrate relative to the measuring optical system. Various sensors and actuators are provided, for example, for acquiring the position of an object of interest and bringing the object of interest into position below the objective lens 15. Typically, many measurements will be made of the target at different locations across the substrate W. The substrate support may be moved in the X and Y directions to acquire different targets and in the Z direction to acquire the desired location of the target relative to the focal length of the optical system. For example, when in practice the optical system can remain substantially stationary (typically in the X and Y directions, but possibly also in the Z direction) and only the substrate moves, it is convenient to consider and describe the operation as if the objective lens is brought into different locations relative to the substrate. Provided that the relative position of the substrate to the optical system is correct, it does not matter in principle which of the substrate and the optical system moves in the real world, or whether both move, or a combination of a part of the optical system moving (e.g. in the Z direction and / or tilt direction) while the rest of the optical system is stationary and the substrate moves (e.g. in the X and Y directions, and optionally also in the Z direction and / or tilt direction).

[0105] The radiation redirected by the substrate W then passes through the partially reflective surface 16 into the detector 18 for spectrum detection. The detector 18 can be located at the back-projected focal plane 11 (i.e., at the focal length of the lens system 15), or the plane 11 can be re-imaged onto the detector 18 using auxiliary optics (not shown). The detector can be a two-dimensional detector, enabling measurement of a two-dimensional angular scatter spectrum of the substrate target 30. The detector 18 can be, for example, a CCD or CMOS sensor array, and can use an integration time of, for example, 40 milliseconds per frame.

[0106] The reference beam can be used, for example, to measure the intensity of incident radiation. To perform such a measurement, when the radiation beam is incident on partially reflective surface 16, a portion of the radiation beam is transmitted through partially reflective surface 16 as a reference beam toward reference mirror 14. The reference beam is then projected onto a different portion of the same detector 18 or, alternatively, onto a different detector (not shown).

[0107] One or more interference filters 13 can be used to select wavelengths of interest within a range of, for example, 405 nm to 790 nm, or even lower, such as 200 nm to 300 nm. The interference filters can be adjustable, rather than comprising a collection of different filters. Gratings can be used in place of interference filters. An aperture stop or spatial light modulator (not shown) can be placed in the illumination path to control the range of angles of incidence of the radiation on the target.

[0108] The detector 18 can measure the intensity of the redirected radiation at a single wavelength (or a narrow wavelength range), the intensity of the redirected radiation at multiple wavelengths separately, or the intensity of the redirected radiation integrated over a certain wavelength range. In addition, the detector can separately measure the intensity of transverse magnetic polarized radiation and transverse electric polarized radiation, and / or the phase difference between the transverse magnetic polarized radiation and the transverse electric polarized radiation.

[0109] The target 30 on the substrate W can be a one-dimensional grating that is printed so that after development, the bars are formed by solid lines of resist. The substrate target 30 can be a two-dimensional grating that is printed so that after development, the grating is formed by solid resist guide posts or through holes in the resist. The bars, guide posts or through holes can be etched into or onto the substrate (for example, etched into one or more layers on the substrate). The pattern (for example, the pattern of bars, guide posts or through holes) is sensitive to changes in the patterning process (for example, optical aberrations in the lithographic projection equipment (specifically, the projection system PS), focal length changes, dose changes, etc.) and will show changes in the printed grating. Therefore, the measured data of the printed grating is used to reconstruct the grating. One or more parameters of a one-dimensional grating (such as line width and / or shape) or one or more parameters of a two-dimensional grating (such as guide post or via width or length or shape) can be input to the reconstruction process performed by the processor PU based on knowledge of the printing step and / or other inspection processes.

[0110] In addition to the measurement of parameters by reconstruction, angle-resolved scatterometry is also used to measure the asymmetry of features in the product and / or resist pattern. A particular application of asymmetry measurement is for overlay measurements, where the target 30 comprises a set of periodic features that are overlaid on another set of periodic features. Figure 3 or Figure 4 The concept of asymmetry measurement of an instrument is described, for example, in U.S. Patent Application Publication No. US2006-066855, which is incorporated herein in its entirety. Briefly, while the positions of the diffraction orders in the diffraction spectrum of a target are determined solely by the periodicity of the target, asymmetry in the diffraction spectrum indicates asymmetry in the individual features that make up the target. Figure 4 In an instrument (where the detector 18 may be an image sensor), such asymmetry in the diffraction orders manifests itself directly as asymmetry in the pupil image recorded by the detector 18. Such asymmetry can be measured by digital image processing in the unit PU and can be calibrated relative to a known overlay value.

[0111] Figure 5 illustrates a plan view of a typical target 30, and Figure 4 The range of the illumination spot S in the device is determined by the illumination method. In order to obtain a diffraction spectrum without interference from surrounding structures, in an embodiment, the target 30 is a periodic structure (e.g., a grating) that is larger than the width (e.g., diameter) of the illumination spot S. The width of the spot S can be smaller than the width and length of the target. In other words, the target is "underfilled" with illumination, and the diffraction signal is essentially free of any signal from product features and the like located outside the target itself. The illumination arrangements 2, 12, 13, 17 can be configured to provide illumination of uniform intensity across the entire back focal plane of the objective lens 15. Alternatively, the illumination can be limited to an on-axis direction or an off-axis direction by, for example, including an aperture in the illumination path.

[0112] Figure 6 An exemplary process of determining values of one or more variables of interest for a target pattern 30' based on measurement data obtained using metrology is schematically depicted.The radiation detected by the detector 18 provides a measured radiation distribution 108 for the target 30'.

[0113] For a given target 30', a radiation distribution 208 can be calculated / simulated according to a parameterized model 206 using, for example, a numerical Maxwell solver 210. The parameterized model 206 shows exemplary layers of various materials that make up and are associated with the target. The parameterized model 206 may include one or more variables for the features and layers of the portion of the target under consideration that may be varied and derived. Figure 6As shown in , one or more of the variables may include the thickness t of one or more layers, the width w (e.g., CD) of one or more features, the height h of one or more features, and / or the sidewall angle α of one or more features. Although not shown, one or more of the variables may also include, but are not limited to: the refractive index of one or more layers in the layers (e.g., real refractive index or complex refractive index, refractive index tensor, etc.), the extinction coefficient of one or more layers, the absorptivity of one or more layers, the resist loss during development, the footing of one or more features, and / or the line edge roughness of one or more features. The initial values of the variables may be the initial values expected for the target being measured. The measured radiation distribution 108 is then compared to the calculated radiation distribution 208 at 212 to determine the difference between the two. If a difference exists, the values of one or more of the variables of the parameterized model 206 can be varied, a new calculated radiation distribution 208 calculated, and the new calculated radiation distribution 208 compared to the measured radiation distribution 108 until a sufficient match exists between the measured radiation distribution 108 and the calculated radiation distribution 208. At this point, the values of the variables of the parameterized model 206 provide a good or optimal match to the geometry of the actual target 30'. In an embodiment, a sufficient match exists when the difference between the measured radiation distribution 108 and the calculated radiation distribution 208 is within a tolerance threshold.

[0114] The variations in the patterning process are referred to as “process variations.” The patterning process may include processes both upstream and downstream of the actual transfer of the pattern in the lithographic apparatus. Figure 7Example categories of process variables 370 are shown. The first category may be variables 310 of the lithographic apparatus or any other equipment used in the lithographic process. Examples of this category include variables of the lithographic apparatus's illumination, projection system, substrate stage, etc. The second category may be variables 320 of one or more processes performed during the patterning process. Examples of this category include focus control or focus measurement, dose control or dose measurement, bandwidth, exposure duration, development temperature, chemical composition used in development, etc. The third category may be variables 330 of the design layout and its implementation in or using the patterning device. Examples of this category may include the shape and / or location of assist features, adjustments applied by resolution enhancement technology (RET), the CD of mask features, etc. The fourth category may be variables 340 of the substrate. Examples include properties of structures beneath the resist layer, the chemical composition and / or physical dimensions of the resist layer, etc. The fifth category may be temporal characteristics 350 of one or more variables of the patterning process. Examples of this category include characteristics of high-frequency stage movement (e.g., frequency, amplitude, etc.), high-frequency laser bandwidth changes (e.g., frequency, amplitude, etc.), and / or high-frequency laser wavelength changes. These high-frequency changes or movements are high-frequency changes or movements that exceed the response time of the mechanism used to adjust the basic variables (e.g., stage position, laser intensity). A sixth category can be characteristics 360 of processes upstream or downstream of pattern transfer in the lithographic apparatus, such as spin coating, post-exposure bake (PEB), development, etching, deposition, doping, and / or packaging.

[0115] As will be appreciated, many, if not all, of these variables will have an impact on the parameters of the patterning process and often on the parameters of interest. Non-limiting examples of parameters of the patterning process may include critical dimension (CD), critical dimension uniformity (CDU), focal length, overlay, edge position or placement, sidewall angle, pattern shift or offset, etc. Often, these parameters express the error relative to a nominal value (e.g., a design value, an average value, etc.). The parameter value may be a value of a characteristic of an individual pattern or a statistic of a characteristic of a group of patterns (e.g., a mean value, a variance, etc.).

[0116] The values of some or all of the process variables, or parameters related to the process variables, can be determined by suitable methods. For example, the values can be determined based on data obtained using various metrology tools (e.g., substrate metrology tools). The values can be obtained from various sensors or systems of equipment in the patterning process (e.g., sensors such as leveling sensors or alignment sensors of the lithographic apparatus, control systems of the lithographic apparatus (e.g., substrate or patterning device stage control systems), sensors in coating and developing system tools or track tools, etc.). The values can also be obtained from an operator of the patterning process.

[0117] Figure 8 An exemplary flow chart for modeling and / or simulating portions of a patterning process is illustrated in . As will be appreciated, the models can represent different patterning processes and need not include all of the models described below. Source model 1200 represents the optical characteristics of the illumination of the patterning device (including the radiation intensity distribution, bandwidth, and / or phase distribution). Source model 1200 can represent the optical characteristics of the illumination, including, but not limited to, a numerical aperture setting, an illumination sigma (σ) setting, and any specific illumination shape (e.g., an off-axis radiation shape such as a toroidal, quadrupole, dipole, etc.), where σ (or sigma) is the outer radial extent of the illuminator.

[0118] The projection optics model 1210 represents the optical characteristics of the projection optics (including changes in the radiation intensity distribution and / or phase distribution caused by the projection optics). The projection optics model 1210 can represent the optical characteristics of the projection optics, including aberrations, distortion, one or more refractive indices, one or more physical sizes, one or more physical dimensions, etc.

[0119] The patterning device / design layout model module 1220 captures how the design features are arranged in the pattern of the patterning device and may include a representation of the detailed physical properties of the patterning device, as described, for example, in U.S. Patent No. 7,587,704, which is incorporated by reference in its entirety. In embodiments, the patterning device / design layout model module 1220 represents the optical properties (including the changes in radiation intensity distribution and / or phase distribution resulting from a given design layout) of a design layout (e.g., a device design layout corresponding to features of an integrated circuit, memory device, electronic device, etc.), which is a representation of the arrangement of features on or formed by the patterning device. Because the patterning device used in a lithographic projection apparatus can vary, it is desirable to separate the optical properties of the patterning device from the optical properties of the rest of the lithographic projection apparatus, including at least both the illumination device and the projection optics. The goal of simulations is often to accurately predict, for example, edge placement and CD, which can then be compared to the device design. The device design is typically defined as a pre-OPC patterning device layout and is provided in a standardized digital file format such as GDSII or OASIS.

[0120] An aerial image 1230 can be simulated based on the source model 1200, the projection optics model 1210, and the patterning device / design layout model 1220. The aerial image (AT) is the radiation intensity distribution at substrate level. The optical properties of the lithographic projection apparatus (e.g., the properties of the illuminator, patterning device, and projection optics) dictate the aerial image.

[0121] A resist layer on a substrate is exposed by an aerial image, and the aerial image is transferred to the resist layer as a potential "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. A resist model 1240 can be used to simulate a resist image 1250 based on the aerial image 1230. A resist model can be used to calculate a resist image based on an aerial image, an example of which can be found in U.S. Patent Application Publication No. US 2009-0157360, the disclosure of which is hereby incorporated by reference in its entirety. A resist model typically describes the effects of chemical processes occurring during resist exposure, post-exposure baking (PEB), and development in order to predict, for example, the profile of a resist feature formed on a substrate, and is therefore typically only related to these properties of the resist layer (e.g., the effects of chemical processes occurring during exposure, post-exposure baking, and development). In an embodiment, optical properties of the resist layer, such as refractive index, film thickness, propagation and polarization effects, may be captured as part of the projection optics model 1210 .

[0122] Therefore, typically, the connection between the optical model and the resist model is the simulated spatial image intensity within the resist layer, which originates from the projection of radiation onto the substrate, refraction at the resist interface, and multiple reflections in the resist film stack. The radiation intensity distribution (spatial image intensity) is converted into a latent "resist image" by absorbing the incident energy, which is further modified by diffusion processes and various loading effects. Efficient simulation methods that are fast enough for full-chip applications approximate the actual three-dimensional intensity distribution in the resist stack through a two-dimensional spatial (and resist) image.

[0123] In an embodiment, the resist image may be used as input to the post-pattern transfer process model module 1260. The post-pattern transfer process model 1260 defines the performance of one or more post-resist development processes (eg, etching, developing, etc.).

[0124] The simulation of the patterning process can, for example, predict the profile, CD, edge placement (e.g., edge placement error), etc. in the resist and / or etch image. Thus, the goal of the simulation is to accurately predict, for example, the edge placement, and / or the aerial image intensity slope, and / or the CD, etc., of the printed pattern. These values can be compared to the intended design to, for example, correct the patterning process, identify locations where defects are predicted to occur, etc. The intended design is typically defined as a pre-OPC design layout that can be provided in a standardized digital file format such as GDSII or OASIS or other file formats.

[0125] Thus, the model formula describes most (if not all) known physical and chemical effects of the overall process, and each of the model parameters desirably corresponds to a different physical or chemical effect. Thus, the model formula sets an upper limit on how well the model can be used to simulate the overall manufacturing process.

[0126] Figure 9 An exemplary flow chart for modeling and / or simulating a measurement process is illustrated in FIG. As will be appreciated, the following models may represent different measurement processes and need not include all of the models described below (e.g., some models may be combined). The source model 1300 represents the optical characteristics of the illumination of the measurement target (including radiation intensity distribution, radiation wavelength, polarization, etc.). The source model 1300 may represent the optical characteristics of the illumination, including but not limited to wavelength, polarization, illumination sigma (σ) settings (where σ (or sigma) is the radial extent of the illumination in the illuminator), any specific illumination shape (e.g., off-axis radiation shapes such as annular, quadrupole, dipole, etc.), etc.

[0127] The metrology optics model 1310 represents the optical properties of the metrology optics (including changes in the radiation intensity distribution and / or phase distribution caused by the metrology optics). The metrology optics 1310 can represent the optical properties of the illumination of the metrology target by the metrology optics and the optical properties of the transfer of the redirected radiation from the metrology target toward the detector of the metrology device. The metrology optics model can represent various properties related to the illumination of the target and the transfer of the redirected radiation from the metrology target toward the detector, including aberrations, distortion, one or more refractive indices, one or more physical sizes, one or more physical dimensions, and the like.

[0128] The measurement target model 1320 can represent the optical properties of the illumination redirected by the measurement target (including the changes in the intensity distribution and / or phase distribution of the illumination radiation caused by the measurement target). Thus, the measurement target model 1320 can model the conversion of the illumination radiation to the redirected radiation by the measurement target. Thus, the measurement target model can simulate the resulting illumination distribution of the redirected radiation from the measurement target. The measurement target model can represent various properties related to the illumination of the target and the generation of the redirected radiation according to the measurement, including one or more refractive indices, one or more physical dimensions of the measurement, the physical layout of the measurement target, etc. Because the measurement target used can be changed, it is necessary to separate the optical properties of the measurement target from the optical properties of the rest of the measurement apparatus, including at least the illumination and projection optics and the detector. The simulated target is often used to accurately predict, for example, intensity, phase, etc., which can then be used to derive parameters of interest for the patterning process, such as overlay, CD, focal length, etc.

[0129] A pupil or aerial image 1330 can be simulated based on the source model 1300, the metrology optics model 1310, and the metrology target model 1320. The pupil or aerial image is the radiation intensity distribution at the level of the detector. The optical properties of the metrology optics and the metrology target (e.g., the properties of the illumination, the metrology target, and the metrology optics) define the pupil or aerial image.

[0130] The detector of the measurement device is exposed to the pupil or aerial image and detects one or more optical properties of the pupil or aerial image (e.g., intensity, phase, etc.). The detection model module 1320 represents how the radiation from the measurement optics is detected by the detector of the measurement device. The detection model can describe how the detector detects the pupil or aerial image and can include signal-to-noise ratio, sensitivity to incident radiation on the detector, etc. Therefore, in general, the connection between the measurement optics model and the detector model is a simulated pupil or aerial image that results from the illumination of the measurement target by the optics, the redirection of the radiation by the target, and the transfer of the redirected radiation to the detector. The radiation distribution (pupil or aerial image) is converted into a detection signal by absorbing the incident energy on the detector.

[0131] The metrology simulation can, for example, predict the spatial intensity signal, spatial phase signal, and other values at the detector based on the pupil or aerial image detected by the detector, or predict other calculated values from the detection system, such as overlay and CD. Thus, the goal of the simulation is to accurately predict, for example, the detector signal corresponding to the metrology target or derived values such as overlay and CD. These values can be compared with expected design values to, for example, correct the patterning process, identify locations where defects are predicted to occur, and so on.

[0132] Thus, the model formula describes most, if not all, known physical and chemical effects of the entire measurement process, and each of the model parameters desirably corresponds to a different physical and / or chemical effect in the measurement process.

[0133] In embodiments, the methods described herein may be used with Figure 8 The data from the simulation process described in

[15] and the metrology data from the metrology tools or metrology simulations discussed above can be used to establish relationships between characteristics associated with the substrate, process variables, and / or mask parameters. For example, the relationship between the CD of a feature printed on the substrate, the dose value, and the mask CD. In embodiments, additional relationships can be implemented in one or more models of the simulation process to generate, for example, defect-aware patterning processes, retargeting of target layouts, and the like.

[0134] The various patterns set on or provided by a pattern forming device can have different process windows, i.e., the space of process variables within which a pattern within specification will be produced. Examples of pattern specifications related to potential systematic defects include checking for necking, line pullback, line thinning, CD, edge placement, overlap, resist top loss, resist undercut, and / or bridging. For example, a process window is defined over two process variables (i.e., dose and focus) such that the CD obtained after patterning can be within ±10% of the desired CD of the features of the pattern. The process window for all patterns on a pattern forming device or region thereof can be obtained by merging the process windows of the individual patterns (e.g., overlapping the process windows).

[0135] Typically, a pattern may include several instances of one or more features arranged in a certain manner to form the pattern (e.g., 10 instances of feature A). 6 instances, 10 of feature B 4 Examples include, for example, a single-shot process window (e.g., a single-shot process window, a single-shot process window, and a single-shot process window). During the patterning process, one or more features may fail under certain, for example, dose / focus settings, resulting in defects in the substrate, thereby affecting the yield of the patterning process. Therefore, selecting an appropriate range of dose / focus values or process windows is important for achieving a desired or selected yield. For example, a high yield (e.g., 99.9%) or a selected yield range (e.g., 98% to 99.99%) may be selected, for example, by a designer or manufacturer.

[0136] For example, attempts have been made to improve the process window for specific features using rule-based modifications to the pre-OPC layout, known as "retargeting." See K. Lucas et al., "Process, Design, and OPC Requirements for the 65nm Device Generation," (Proc. SPIE, Vol. 5040, p. 408, 2003). One approach to rule-based retargeting for pre-OPC layout involves selective biasing and pattern shifting. This approach can improve the full process window performance for certain critical features by selectively changing the target edge placement that the OPC software uses as the desired end result, while still calculating the OPC correction only under nominal process conditions. Thus, instead of minimizing the error between the design dimensions and the simulated edge placement, the OPC software instead minimizes the error between the retarget dimensions and the simulated edge placement.

[0137] Users of OPC software can retarget designs in a variety of ways to improve process window performance. In the simplest example of retargeting, rules can be applied to specific features to improve their printability and process window. For example, it is well known that isolated lines have a worse process window than dense lines, but process margins improve as feature size increases. A simple rule can be applied to increase the size of smaller isolated lines, thereby improving the process window. Other rule-based retargeting methods have been developed in which metrics other than CD are used to determine the retargeted edge placement, such as Normalized Image Log Slope (NILS) or sensitivity to mask CD error (MEF or Mask Error Enhancement Factor (MEEF)).

[0138] Rule-based retargeting methods can improve the printability of features across the entire process window, but they suffer from several drawbacks. These methods can become quite complex and are based solely on pre-OPC layouts. Once OPC corrections are added to the design, the printing performance as a function of process conditions can become quite different from what was expected from the pre-OPC design, introducing significant error sources and preventing retargeting from achieving the desired results.

[0139] Figure 10Another example of an existing process for retargeting related to a specific feature is shown. In process P10, the semiconductor manufacturing process begins with the development of a specific design intent 1001 (e.g., lines connected by vias having a specific critical dimension CD in the after-etch image AEI) with associated (preliminary) design rules. For example, the design rules include a minimum line pitch / CD, a minimum via pitch / CD, a 2D line, or a 1D line that can be supported. In process P20, an initial target CD (e.g., the CD of the pattern in the after-development image ADI) is set for imaging. The initial target CD can be based on experience / extrapolation from previous nodes (e.g., previously manufactured substrates) and early defect inspection experiments.

[0140] Additionally, in step P30, a source-mask optimization (SMO) is performed to determine the optimal illumination pupil, typically based on a weighting function that minimizes deviations (also referred to as drift) in various gauges of the segment (e.g., selected patterns or features for measurement purposes) given these target CDs caused by dose / mask / focus drift or variations.

[0141] After the SMO process, in step P40, a mask pattern (e.g., >1k features, each with many gauges) is selected from the results of the SMO to manufacture a mask and the mask is used to image a pattern on a substrate (interchangeably referred to as exposure or printing). The pattern on the imaged substrate is used to calibrate process parameters such as resist parameters, metrology parameters (e.g., dozens of parameters), or other patterning process-related parameters through patterning process simulation including an OPC process. The OPC calibration is verified by exposing another substrate using the OPCed mask pattern and measuring the CD of the exposed substrate. A certain residual error is accepted here.

[0142] Once the OPC process is calibrated, a design of experiments (DOE) is performed in step P50, for example using a focal exposure matrix (FEM) to expose the substrate. The exposed substrate is inspected for defects using a bright field or electron beam inspection tool (e.g., a scanning electron microscope (SEM) or a transmission electron microscope (TEM)). For more mature processes, electrical test structures and inspection tools (such as SEM / TEM) are used to refine the detection algorithm to capture an appropriate number of defects with a high capture rate and a low nuisance rate.

[0143] In step P60, process adjustments are made and / or design rules are updated (e.g., certain assist features are added to the OPC set, while some assist features may be removed from the OPC set). Due to the non-ideal selection of the target CD relative to the failure rate, the target CD is also updated (i.e., "retargeted") to improve the defectivity at ADI, AEI, and AEI(2L) to an acceptable failure rate, thereby achieving the minimum patterning-related yield. After retargeting, the processes including SMO, OPC, inspection, etc. can be re-executed and the CD further retargeted to further improve the yield.

[0144] The existing process discussed above may take up to 1 year for each tested device for a customer, wherein the semiconductor manufacturing process is adjusted until it has sufficient yield for each individual process step and integrated layer of the substrate. In parallel, other solutions (e.g., OVL targets, and control and monitoring solutions for process tools) are also developed to limit variations in manufacturing and improve overall yield. Several test devices of increasing complexity may be required to obtain a final high-volume manufacturing process or high-volume manufacturing (HVM) process that produces chips with sufficient patterning yield. In examples, the yield is due to patterning geometric tolerances or design rules. However, there is also parameter yield or yield loss due to more random / less predictable drift (e.g., particles). For example, parameter yields related to the operation of the chip, such as electrical performance, thermal performance, are used to determine whether the device is working, whether the device is too slow or consumes more power relative to requirements, etc.

[0145] One of the challenges of the existing processes discussed above is that, due to the various interdependencies between the process itself, patterning process parameters, and process variables, learning from the first cycle (or iteration) needs to be accounted for in the next cycle (or iteration). This makes parallelization difficult except by brute force. Consequently, development time is extended due to lengthy cycle times.

[0146] Existing processes have several drawbacks. First, several new masks must be manufactured for each process iteration. Second, the metrology / inspection cycle can be very lengthy (typically weeks). Third, conventional SMO processes are unaware of limits at the extremes of the target CD (e.g., oversized / undersized features) based on actual failure rates. Conventional SMO optimizes only for optimal variability, such as the optimal variability of process variables ±dose, ±focus, or ±mask bias for a given target CD. This optimization can be suboptimal because it relies heavily on the user providing the correct CD target based on an (often proprietary) inspection model.

[0147] The present invention describes an alternative mechanism for determining characteristic limits (e.g., characteristic limits associated with resist CD) based on metrology / inspection data using a defect-based process window. The defect-based process window refers to process variable values determined based on failure rate data associated with a pattern to be printed on a substrate. In one embodiment, determining a defect-based process window associated with a patterning process (e.g., via computer hardware system 100) involves obtaining (i) characteristic limits for a characteristic (e.g., CD) associated with the patterning process based on failure rate measurements of the patterning process and (ii) a probability density function (PDF) of the characteristic (e.g., CD), defined as a function of process variables and / or the variance of the process variables for the patterning process. Based on the characteristic limits and the PDF of the characteristic, an estimated failure rate for the patterning process is determined. Additionally, the defect-based process window is determined based on the process variables such that the estimated failure rate of the characteristic is less than a selected failure rate threshold (interchangeably referred to as a desired failure rate or a target failure rate). For example, identifying the process window involves determining a range of the process variable between the intersection of the estimated failure rate and the selected threshold.

[0148] In an embodiment, the characteristic limits are obtained by converting a probability density function of a process variable (e.g., dose) for a given setting into a probability density function of a characteristic (e.g., CD) for that setting based on a conversion function. The conversion function is determined based on a function of the process variable. The characteristic limits are determined based on a characteristic distribution (e.g., CD distribution) for a given process variable setting and a measurement of the failure rate of the characteristic.

[0149] Examples of methods for determining characteristic limits (also referred to as parameter limits associated with a feature) and defect-based process windows are described in U.S. Patent Application No. 62,609,755, filed on December 22, 2017, and U.S. Patent Application No. 62 / 773,259, filed on November 30, 2018 (also filed as PCT Application No. PCT / EP2018 / 085159), which are incorporated herein by reference in their entireties. Metrology data or inspection data is obtained from several features for calibrating a failure rate model that can be used to determine characteristic limits in a simulator for any (e.g., interpolated) feature size.

[0150] According to the present invention, defect-based process windows are used to improve simulation results and retarget. Figure 11 is a flow chart of an exemplary simulation process for implementing defect-based process windows and characteristic limits to improve conventional patterning process simulations (eg, SMO, retargeting, OPC, etc.) according to an embodiment of the present invention.

[0151] Method 1100 begins at step P30, which is to simulate an SMO process on a target layout (e.g., a fragment of a full chip layout), such as Figure 10 As discussed in . For example, the target layout may include more than a million or hundreds of thousands of features. The results of the SMO simulation can be FEM, optimized mask parameters (e.g., mask bias and CD), optimized source, optimized focal length, optimized illumination pupil, etc.

[0152] Step P1101 involves performing a defect-based process window (DB-PW) calibration on a calibration set (e.g., comprising dozens of gauges or selected patterns of a target layout) to determine characteristic limits (e.g., CD limits) and local CD uniformity associated with the pattern to be printed on the substrate. After DB-PW calibration, the characteristic limits can be applied to any given pattern of the target layout. Examples of methods for determining characteristic limits (also known as parameter limits associated with a feature) and defect-based process windows are described in PCT Application No. PCT / EP2018 / 085159, which is incorporated herein by reference in its entirety.

[0153] In parallel with P1101, a calibration involving OPC (e.g., Figure 10 In one embodiment, OPC calibration is performed on a much larger number of gauges or patterns than those used for DB-PW. In another embodiment, DB-PW calibration and OPC calibration are separated. DB-PW calibration may take more time because DB-PW calibration involves performing metrology measurements to determine the actual CD and defects on the printed substrate, while OPC calibration does not involve any metrology measurements or defect-based calculations.

[0154] In an embodiment, OPC calibration involves calibrating, for example, resist parameters to ensure that the simulated pattern on the substrate is close to the desired resist target (e.g., CD in the resist). In an embodiment, the output of OPC is a mask pattern including, for example, assist features, main features, curved mask patterns, and straight line patterns. In an embodiment, OPC calibration uses a relatively large number of patterns or gauges (e.g., 100,000 gauges), while DB-PW uses only a subset of gauges (e.g., tens of gauges).

[0155] In an embodiment, DB-PW calibration generates or uses a failure rate model and probability density function of the characteristics of a feature. For example, the CD distribution associated with a pattern can be modeled based on measurement data of the printed substrate. In an embodiment, such a failure rate model and CD distribution model can be used to determine CD limits, since only a few dozen gauges are calibrated and then what CD will be printed for any gauge or pattern. For example, the CD distribution and failure rate model can be a Gaussian model fitted to metrology-based data (e.g., measured CD and failure rate). The fitted model can be used to determine CD limits for a desired or target failure rate. In an embodiment, the CD limit can be considered a hard limit, e.g., below which the feature is considered a defect.

[0156] In an embodiment, the DB-PW calibration also calibrates the response of how the local CD uniformity (LCDU) behaves. In an example, Bossung behavior describes the dose sensitivity of CD, while the local LCDU describes the CD variance, which can give a measure of the underlying CD distribution.

[0157] The outputs from steps P1101 and P40 (e.g., CD limits and resist parameters, dose-focus matrix, mask parameters, etc.) can be used to perform "dynamic retargeting" in step P1103. Figure 15 Let's discuss exemplary dynamic retargeting.

[0158] In an embodiment, in process P1104, method 1100 can also be extended to determine the optimal process window based on the after-development image (ADI) and / or after-etch image (AEI) data. For example, the ADI process window can be determined based on the CD behavior at the development step. The AEI process window can be determined based on the CD behavior at the post-etch step. In an embodiment, an ADI and / or AEI model that describes how CD changes with changes in ADI or AEI parameters can be used to determine the CD behavior. In an example, the AEI model can predict the CD after etching. The post-etch CD can be checked against the CD limit to determine whether the post-etch CD is within an acceptable range. If it is not within the acceptable range, a retargeted layout can be generated, or the etching process can be modified so that the post-etch CD is within the CD limit determined by DB-PW. In an embodiment, in process P1105, the optimal process window can also be used to predict the yield of the entire chip.

[0159] An exemplary method for determining the CD limit can be expressed in the following equation (1), which is discussed in detail in PCT Application No. PCT / EP2018 / 085159, the entirety of which is incorporated herein by reference.

[0160]

[0161] In the above equation (1), (i) R fail Failure rate of features for each set of process variables (e.g., dose, resist-related, and / or etch-related); (ii) PDF CD (CD, d) refers to the CD PDF model based on the measurement data in process P1101 under a certain process condition (denoted by "d"); and (iii) CDF CD (CD lim , d) is PDF CD The cumulative distribution function of (CD, d) provides the cumulative distribution function of (CD, d) at and beyond CD lim The total probability of failure when . The CD limit can be determined at one or more settings of process variables (e.g., dose, resist related, etch variables) with corresponding failure rates, where the characteristics of the failures do not affect each other's failure rates (i.e., one skilled in the art can consider each failure to be an "isolated failure"), but there are a sufficient number of characteristics of the failures to limit the variance of the failure rates being measured or determined. In an embodiment, the PDF can be determined according to the present invention as described below. CD For example, PDF CD can be determined as a function of dose and mask variation. In another example, the PDF can be determined based on the adjustment model CD , the adjustment model adjusts for variations due to dose contributions.

[0162] The failure rate model can also be used to determine a process window over a range of process variables (e.g., dose, resist, etch) (see PCT Application No. PCT / EP2018 / 085159 for more details). For example, a process window can be a range of dose values ("d") within which the estimated failure rate can be less than 10 -9 In an embodiment, the desired yield (e.g., for 10 6 characteristics, with a yield of 99.9%) determine the expected failure rate:

[0163] R fail (d)=(1-Y(d)) …(2)

[0164] In an embodiment, the yield rate may be calculated using the estimated failure rate (e.g., in Equation 2) as follows:

[0165] Y(d)=(1-R fail (d)) N …(3)

[0166] In equation (3) above, Y(d) is the yield at a specific dose (d) for N individual features, and R fail (d) is the estimated failure rate (eg, in Equation 2). Based on this calculated yield, a process window can be selected in which the calculated yield is greater than or equal to the desired yield (eg, 99.9%).

[0167] FIG. 12A to FIG. 12B An exemplary method for determining CD limit and failure rate data using a calibration set of patterns is illustrated. In an embodiment, the simulated resist pattern may correspond to measurement data of a DB-PW calibration (in process P1101) performed using equation (4) as explained below.

[0168] CD lim =a+b.(H2-H1) …(4)

[0169] In the above equation (4), CD lim is an example of a characteristic limit based on the CD of a feature determined from DB-PW data, H2-H1 is a characteristic limit based on a simulated resist profile (e.g., reference 1) at two different heights (e.g., H1 at the top of the resist layer, and H2 at the bottom of the resist layer). Figure 12C In an embodiment, the SMO or related process simulator can be modified to include equation (4) to determine the CD margin at the top or bottom of the resist (see Figure 12C ).

[0170] In an embodiment, Figure 12A As shown in FIG, gauge #G may be a hole array having four parameters px, py, CDx, and CDy that may vary, wherein p represents the pitch in the x direction and CDx represents the CD in the x direction. In an embodiment, based on gauge #G, multiple gauges #G0, #G1, #G2, #G3, and #G4 may be generated, as shown in FIG. Figure 12B For example, in Figure 12B In the example, #G1 is a single row feature, #G2 is a vertical column feature, and #G3 is a diagonal feature. For each gauge, a CD limit can be determined. For example, the CD limit can be CD L，G0 、CD L，G1 、CD L，G2 、CD L，G3 and CD L，G4 Similarly, for each gauge, the simulator can generate, for example, resist CD H1 / H2 G0 、H1 / H2 G1 、H1 / H2 G2 、H1 / H2 G3 and H1 / H2G4 In this way, Equation (4) converts CD lim Correlated to the simulated CD value. Figure 12C An exemplary resist profile is illustrated in FIG, along with the top and bottom locations where the CD is measured.

[0171] Figure 13 An exemplary method for determining a defect-based process window using CD at the top and bottom of a resist profile according to an embodiment of the present invention is shown. In this example, a process simulation is performed using an annular illumination model for a 20 nm contact hole. In an embodiment, the process window and CD are determined using, for example, a failure rate model based on measured data. lims Furthermore, such a process window can be simulated using a modified process as discussed herein. For example, using a calibrated simulation process including equation (4) (e.g., regarding Figure 14A and Figure 14B Thus, the defect-based process window PW1 can be advantageously simulated early in the semiconductor manufacturing process. For example, by measuring at the bottom and top of the resist and assuming that the defect-based process window PW1 is lims A process window PW1 can be determined based on a certain margin. The edge of the process window PW1 shows how the profile or these limits behave at different depths in the resist profile. In an embodiment, the margin is the amount of CD variation that can be applied to the bottom and top of the resist. The process window PW1 can then be determined from the dose and focus matrix. Therefore, based on the resist profile, the CD limits can be compared; and the process window can be determined based on the CD limits. In such an embodiment, a defect-based process window PW1 is obtained assuming no local CD variation. In some other embodiments, the LCDU is taken into account, and the process window can be changed accordingly.

[0172] Figure 14A and Figure 14B An exemplary method for determining a calibrated simulation process according to an embodiment of the present invention is shown. Figure 14A An exemplary DB-PW based on experimental data obtained from printed substrates and inspection data of printed substrates is shown (for more details see PCT application number PCT / EP2018 / 085159). Figure 14A , a failure rate can be determined by executing a failure rate model (e.g., P1101) for each process condition (e.g., on a processor of the computer hardware system 100). Additionally, based on a given expected failure rate or acceptable failure rate, an acceptable process window PW2 (dashed line) can be determined. Furthermore, an ellipse fit (or any other suitable fit) can be performed on the acceptable process window PW2 to determine, for example, an ellipse process window PW3 having a maximum exposure latitude.

[0173] exist Figure 14A In Figure 1, the process window cPW is the process window obtained based on a conventional OPC simulation of 29 contact points with an average contact hole size of 20 nm. The profile of PW2 is at a fixed failure rate or an acceptable failure rate, and the profile of PW3 is an ellipse fit within the window PW2. From the perspective of focus and CD, PW3 can be considered the maximum process window. It can be observed that the classic process window cPW is different from the DB-PW PW2 / PW3. Based on the process windows PW2 / PW3, the optimal dose can be determined to be about 53 mJ / cm 2 , the optimal CD is about 22.5 nm and the optimal focus position is -11 nm at the center of the window. This advantageously provides an experimental setup and the size of the process window that can be used to operate the patterning process so that the printed pattern will be within a certain failure rate.

[0174] Figure 14B FIGURE 2 shows exemplary simulated process windows PW2′ and PW3′ generated using a calibrated simulation process, wherein the process windows PW2′ and PW3′ are simulated based on DB-PW data (eg, Figure 14A In this example, DB-PW data (e.g., CD lim or PW2) guides the simulator as to how much margin is available at the bottom and top of the resist. Therefore, the parameters of the model used in the simulation process are modified to match the experimental results. In this example, the adjusted simulation parameters are absorptivity / dilLB=5μm -1 , resist thickness T resist =44nm, Z meas =T resist In an embodiment, the blurriness, flicker and other parameters of the AI can also be applied or modified so that the simulated process window (e.g., PW3′) is aligned with or closely matches the DB-PW (e.g., PW3). According to the present invention, not only can the parameters associated with the classic CD-PW (e.g., the σ of the resist) be fitted, but also the parameters of the AI can be fitted. blur , flicker, SEM shift, etc.), and parameters associated with the "CD limit" can be fitted, for example the CD limit is characterized by the CD at different heights of the resist profile of the pattern obtained according to the simulation.

[0175] According to the present invention, a calibrated simulation process offers several advantages. In one embodiment, the local CD response can also be calibrated, so that the measured CD variation can be correlated with the simulated CD variation, for example, regarding dose sensitivity. Furthermore, the calibration can be extended to include CD variations in the mask, which in turn cause CD variations in the resist. In another example, simulations can also be performed to determine how the process window changes with increasing dose, resist, or resist sensitivity. Furthermore, simulations can be performed to investigate what happens if CD deviation at the mask level is altered.

[0176] Additional dose can improve the process window but may change the target CD and optimal focus. For example, as the dose is adjusted, local CD uniformity decreases, CD target deviation decreases, and the CD window grows. However, increasing dose can also increase the depth of focus (DoF), which may be undesirable. From a productivity perspective, it may be desirable to keep the dose as low as possible, but from a performance perspective (e.g., increased PW), a higher dose may be desirable. Thus, based on changes in several parameters (dose, CD window, LCDU@BEBF, BF, DoF), dose values between solutions can be selected.

[0177] In another example, in Table 2, the mask deviation can be adjusted to increase the target CD deviation. For example, the optimal CD window can be achieved at a 20% mask deviation. Furthermore, at a 20% mask deviation, the LCDU at the optimal focus distance changes, and the DoF also changes accordingly.

[0178] In some embodiments, the exposure latitude is a dose range and the DoF is a window (e.g., Figure 14A In an embodiment, the exposure latitude can be converted into a CD window, such as the CD at a higher dose minus the CD at a lower dose.

[0179] In another example, resist parameters can be adjusted to determine the optimal resist thickness at a given absorption rate for different resist materials (eg, CAR resist versus non-CAR resist).

[0180] In embodiments, if the behavior of the resist can be modeled (e.g., how the photon absorption rate or local variation CD varies depending on the thickness of the resist), the resist thickness can be varied to determine the optimal process window. It will be appreciated that the aforementioned resist parameters are presented as examples and do not limit the scope of the present invention. In embodiments, additional relationships between resist parameters can be determined experimentally and used to calibrate the simulation process based on resist-related measurements.

[0181] In embodiments, there may be several factors that determine DoF. For example, the classic CD window is determined using the Burson-Bartz curve, local CDU degradation, and the actual resist profile and its impact on CD margin. Such behavior can also be simulated using embodiments of the present invention.

[0182] Figure 14C An exemplary simulation illustrating how changes in DoF affect CD margins resulting in non-obvious process windows is shown. Figure 14C The available margin at different DoFs is illustrated, with curve Mup indicating the upper margin associated with the top resist CD, curve Mb indicating the inner margin associated with the bottom resist CD, and curve Mtot indicating the total margin that can be expected as a function of focal length. The curves indicate that DoF affects the resist profile quite significantly, indicating that less CD margin is available at the bottom or top of the resist profile when the DoF is too far from the center (e.g., the best focal length or the nominal focal length).

[0183] In an embodiment, a calibration of a simulation process related to a patterning process may be performed, such as with respect to Figure 15 For example, method 1500 includes steps P1501 and P1503 as discussed in detail below.

[0184] The process P1501 includes: (i) obtaining a characteristic limit 1501 of a characteristic of the printed pattern based on a threshold failure rate of the printed pattern, and (ii) obtaining a reference process window 1503 based on the characteristic limit 1501 .

[0185] In an embodiment, the characteristic model is determined by fitting parameters of the characteristic model based on the characteristics of the simulated pattern and the characteristics of the printed pattern.

[0186] In an embodiment, obtaining characteristic limits 1501 for a characteristic of a printed pattern (e.g., via computer hardware system 100) includes: printing selected patterns of a target layout on a substrate via a lithographic apparatus; determining a failure rate for each selected pattern based on inspection data of the printed patterns (e.g., via computer hardware system 100); fitting a failure rate model based on the failure rate and the characteristic of each selected pattern, the failure rate model configured to determine a failure rate associated with the characteristic of the pattern; and executing the failure rate model (e.g., on a processor of computer hardware system 100) to determine characteristic limits 1501 for the characteristic of the selected pattern such that a threshold failure rate is met.

[0187] In an embodiment, when obtaining the characteristic limits 1501, not only the characteristic limits 1501 but also the behavior of the CD of the pattern and the related higher order moments (e.g., variance, skew, kurtosis, etc.) can be calibrated. In an embodiment, calibrating, for example, variance and skewness helps to better match the predictions of the characteristic model with the simulated data. Examples of calibrating CD distributions are discussed in detail in the previously mentioned PCT application PCT / EP2018 / 085159. In an embodiment, CD is calibrated via dose / focus by adjusting process variables (including, for example, scintillation, resist blur). Variance can be calibrated by dose sensitivity ("ILS") and / or MEEF simulations, for example as discussed in the present invention. In an embodiment, higher order moments can also be characterized over the entire window and the higher order moments are fitted to match the predictions.

[0188] Step P1505 includes calibrating the simulation process (e.g., via the computer hardware system 100) so that the simulated process window is within an acceptable threshold of the reference process window 1503. In an embodiment, the simulated pattern comprises an outline of a pattern within a layer of the substrate. In an embodiment, a characteristic of the simulated pattern comprises a difference between a first characteristic at the top of the layer and a second characteristic at the bottom of the layer. In an embodiment, the simulation process includes a source mask optimization process and an optical proximity correction process configured to adjust mask parameters, source parameters, or process parameters so that the printed pattern is within an acceptable threshold of a target characteristic value.

[0189] In an embodiment, obtaining the reference process window 1503 includes determining (eg, via the computer hardware system 100 ) values of dose and focus corresponding to characteristics of each selected pattern that satisfies the characteristic limits 1501 based on inspection data associated with the printed substrate.

[0190] In an embodiment, calibration of the simulated process includes: executing (e.g., on a processor of the computer hardware system 100) one or more process models to determine a simulated pattern; and adjusting parameter values associated with the one or more process models until characteristics of the simulated pattern meet characteristic limits 1501. In an embodiment, calibration includes determining (e.g., via the computer hardware system 100) whether a simulated process window and a simulated process window are within an acceptable threshold of a reference process window 1503 based on the characteristics of the simulated pattern.

[0191] In an embodiment, the one or more process models include a characteristic model that is fit based on the simulated pattern and characteristic limits associated with the printed pattern 1501. In an embodiment, the characteristic model is determined by fitting parameters of the characteristic model based on characteristics of the simulated pattern and characteristics of the printed pattern.

[0192] In an embodiment, the parameters of the one or more process models may include parameters of a characteristic model, such as mean, variance, skewness, etc., that explain the behavior of CD in a particular process (eg, ADI or AEI).

[0193] In an embodiment, the parameters of the one or more process models may include spatial image parameters associated with a spatial model associated with the patterning process.

[0194] In an embodiment, the parameters of one or more process models may include resist parameters associated with a resist model for the patterning process. In an embodiment, the resist parameters include one or more of the following: a parameter related to blurriness of an aerial image, resist thickness of a resist layer, absorption associated with the resist (material), surface tension of the resist layer, stress and strain at the resist layer, or other resist-related parameters included in the resist model or simulator. In an embodiment, the effect of these resist parameters on CD may be linear or nonlinear in nature.

[0195] In an embodiment, the parameters of the one or more process models may include etch parameters associated with an etch model associated with the patterning process.

[0196] In an embodiment, calibration of the simulation process is an iterative process. One or more iterations include: executing one or more process models (e.g., on a processor of the computer hardware system 100) using a selected pattern to be printed on a substrate to determine a simulated pattern on the substrate; adjusting values of parameters associated with the one or more process models so that characteristics of the simulated pattern meet characteristic limits associated with the selected pattern 1501; and determining (e.g., via the computer hardware system 100) based on the characteristics of the simulated pattern whether a simulated process window and a simulated process window are within an acceptable threshold of a reference process window 1503.

[0197] In an embodiment, the adjustment of the parameters of one or more process models includes adjusting the values of the parameters associated with the characteristic model so that the margin between the characteristics of the simulated pattern at the top and the characteristics of the simulated pattern at the bottom is maximized relative to the characteristic limit 1501.

[0198] In an embodiment, method 1500 also includes: obtaining a set of hot spot patterns, each hot spot pattern being a user-selected pattern from a target layout and / or a pattern associated with a relatively higher probability of failure compared to other patterns of the target layout; determining a defect-based process window for each hot spot pattern by simulating a calibrated simulation process (e.g., via computer hardware system 100) using the set of hot spot patterns and a failure rate model; and determining optimal values of one or more process variables associated with a threshold failure rate based on an overlay of each defect-based process window.

[0199] As mentioned earlier with respect to Equation 4, the total failure can be calculated as (1-FR final )=Π i (1-FR feamre-i ) Ni , where FR feature Depends on process parameters (eg dose / focus).

[0200] In an embodiment, one or more process variables are selected from: optimal focus, optimal dose, dose-focus window characterized by a threshold failure rate, aberration (e.g., aberration that is selectable / adjustable on the scanner), MSD, OVL (e.g., in the case of an “EPE” setting that is affected by the CD of the pattern on two separate layers).

[0201] In an embodiment, method 1500 further includes: determining a yield associated with each hot spot pattern based on a failure rate model (e.g., via computer hardware system 100); and determining an overall yield for the full chip layout by calculating the product of each yield associated with each hot spot pattern across the entire full chip layout.

[0202] In an embodiment, method 1500 further includes: determining, by simulating a calibrated simulation process, whether a margin is available for adjusting a characteristic of a retargeted pattern to result in a target characteristic value being printed on a substrate; and in response to the margin being unavailable, determining an adjustment to a process associated with a patterning process by simulating the calibrated simulation process using the retargeted pattern so that the target characteristic value is printed on the substrate.

[0203] In an embodiment, adjusting the process includes adjusting (e.g., via the computer hardware system 100) one or more of the etch bias values at the developed image, including an isotropic etch-back or spacer process, and the amount of process load. In an embodiment, the amount of process load can be a function of the etch rate and / or deposition rate determined by the plasma density, the redeposition rate, or by adjusting the partial pressure of the gas used. In an example, the load can be modeled by relying on the open-frame etch rate or deposition rate within a Gaussian radius.

[0204] In an embodiment, method 1500 further includes: using a simulation process after full-chip layout simulation calibration to determine a residual error between a simulation characteristic value and a target characteristic value associated with the full-chip layout; determining via a lithography manufacturing inspection whether the simulation characteristic value associated with the full-chip layout meets a desired yield; and in response to not meeting the desired yield, adjusting source parameters, mask parameters, or process parameters via the calibrated simulation process to reduce the residual error so that the desired yield is met.

[0205] Once the simulation process is calibrated according to the DB-PW experimental data, as described above for Figure 11 and Figure 15 As discussed, the calibrated simulation process can then be used to perform so-called defect-based source mask optimization, which includes, for example, retargeting. In an embodiment, retargeting refers to generating an updated pattern based on deviating a target pattern. In this embodiment, retargeting can be performed by deviating a characteristic (e.g., a target CD) based on a CD limit obtained from a failure rate model and a CD distribution model. In an embodiment, the CD distribution model can be determined as discussed herein or in PCT / EP2018 / 085159, which is incorporated herein in its entirety. The CD distribution model determined in accordance with the present invention can provide a more accurate prediction of CD for a specific dose and / or mask deviation, as will be discussed later herein.

[0206] Figure 18 An example of dynamic retargeting according to the present invention is illustrated. In an embodiment, DB-PW data is used in conjunction with a source-mask optimization process. For example, within SMO, ±dose, ±mask deviation, and ΔBF (i.e., change in best focus) are used to balance CD margins. For example, (e.g., as in step P1101) CD margins are determined relative to CD limits obtained from DB-PW experiments. Furthermore, within SMO, if CD limits are available, dynamic retargeting can be applied to features of the target pattern.

[0207] Dynamic retargeting begins with an initial target pattern TP181, also referred to as an initial target segment TP181 or a segment of a target pattern. Retargeting of target pattern TP181 is based on predicted drift in characteristics of the target pattern (e.g., CD drift). In embodiments, for a given failure rate, one skilled in the art can estimate how much dose and mask drift there is in CD. Exemplary dose- and mask-based equations for determining drift are discussed herein.

[0208] In this example, the initial target pattern TP181 includes a plurality of contact holes arranged as shown. Characteristic limit data L181 (as illustrated) is used to determine the retargeting pattern. In this example, characteristic limit L181 is CD limit L181 determined based on DB-PW experiments. In this example, feature TF181 of the initial target pattern TP181 is retargeted based on CD limit L181.

[0209] The characteristic limit data L181 includes the CD upper limit CDL1 and CD lower limit CDL2 determined by the DB-PW experiment. In addition, the nominal or target CD TCD is shown as an overlay on the CD limit data L181. The estimated CD drift EV1 and EV2 for the contact hole at a given failure rate are also shown. Figure 21 An example of evaluating CD drift is discussed below. An exemplary CD margin calculated as the difference between CD drift and CD limit is also shown. In an embodiment, CD drift EV1 and EV2 are CD values calculated at, for example, 3 standard deviations from the nominal CD or target CD at a given failure rate. Figure 11 and Figure 15 The calibrated simulation process discussed is used to simulate these extreme value drifts.

[0210] The limits in box L181 also show that relatively larger margins can be used on the upper side (e.g., CDL1-EV1) than on the lower side (e.g., CDL2-EV2). These margins indicate that the feature size of target pattern TP181 can be increased rather than decreased. Therefore, as shown in the figure, retargeting pattern RTP181 can be generated to include retargeting features RTF181 having a larger CD than the target CD shown in TF181.

[0211] In an embodiment, the above steps may be repeated to generate a final retargeting pattern or retargeting segment. In addition, in an embodiment, for the retargeting segment, the source may also be optimized.

[0212] therefore, Figure 18 The retargeting process in

[15] can predict how many features are under the CD limit and which ones are outside the limit. In addition, given the number of occurrences of a feature in the target layout, a statistical analysis can be performed to determine which features can be kept and which can be removed. For example, feature #1 has 10 -10 and Feature #2 has a failure rate of 10 -6If the failure rate of feature #2 is much greater than the number of feature #1 types, then based on the margin it can be determined whether to allow the target size of feature #2 or to retarget feature #2. In another example, if there is no margin left for retargeting the feature, a process change can be recommended. Example process changes include, for example, Figure 16 and Figure 17 Changes in resist parameters, etching parameters, etc. discussed.

[0213] Figure 19 Illustrated are exemplary CD drift and CD margin associated with characteristic limits (eg, CD limits) of a pattern according to an embodiment of the present invention. Figure 20A and Figure 20B Illustrated are examples of how the CD margin and extreme value (EV) drift of a CD behave under different process conditions (eg, dose, focus, mask deviation, etc.) according to an embodiment of the present invention.

[0214] exist Figure 19 In , an exemplary probability distribution function PDF 191 is a modeled CD distribution based on failure rate data to calculate the failure probability of a specific CD. In an embodiment, the CD distribution PDF 191 can be determined based on dose and mask variations and a tuning model discussed later herein.

[0215] The cumulative density function (CDF) can be calculated by integrating the CD distribution PDF 191 over the CD (x-axis) from left to right. In this example, the left CDF can be calculated by integrating the PDF 191 over the CD (x-axis) from left to right. Similarly, the right CDF can be calculated by integrating the PDF 191 over the CD (x-axis) from right to left.

[0216] In an embodiment, a CD limit can be determined based on failure rate data of the printed substrate (e.g., see process P1101). In an embodiment, a pattern with a CD value below the CD limit is considered a failed pattern. In an embodiment, an acceptable failure rate TFR (also referred to as a threshold failure rate) can be specified to improve the yield of the patterning process. The acceptable failure rate or threshold failure rate can be greater than the actual failure rate of the pattern. Retargeting or process adjustments can then be performed relative to this threshold failure rate TFR.

[0217] In an embodiment, EV drift refers to the value of a characteristic or process variable determined at the edge of a defect-based process window. For example, EV drift in CD can be the CD deviation relative to the nominal CD or target CD TCD, where the CD deviation is determined at the dose extremes and / or focus extremes of the DB-PW. In an embodiment, EV drift can be determined based on 3 standard deviations of the modeled CD distribution. In an embodiment, a dynamic retargeting process (e.g., Figure 18) iteratively modifies the CD value of the feature to minimize the CD EV drift or improve the CD margin (maximize the CD margin in an embodiment). In an embodiment, minimizing the EV drift results in maximizing the CD margin on both sides, such as Figure 19 In embodiments, a calibrated SMO including the dose drift and / or mask drift equations discussed herein may be used to minimize EV drift by varying the dose and / or mask bias.

[0218] In an embodiment, depending on the shape of the CD distribution or CDF, relatively more CD margin (nm) may be available on one side than on the other side. For example, a CD distribution with a relatively long tail may have a smaller CD margin at the tail.

[0219] Figure 20A An example of what happens if the CD distribution PDF 191, or the corresponding CDF, shifts to the right is shown. As shown, the CD margin CDM1′ on the left increases, but CDM2′ on the right becomes negative. Consequently, the shift in the CDF can cause the CD EV to drift beyond the CD limit, and larger features may not meet the target failure rate criteria. In other words, there is no margin available to increase the size of the retargeted CD, and the retargeted CD will likely cause failures in the pattern. In embodiments, both CD margins may become negative, which is undesirable. Figure 20B An example is shown in which the CD margin CDM3 is negative and the CD margin on the left side is zero, which is also undesirable.

[0220] From the perspective of source mask optimization, EV drift can be correlated with the dose setting within the target failure rate. In other words, the dose setting for the target failure rate can cause a shift in the tail of the PDF or CDF. Therefore, according to the present invention, the source mask optimizer can be configured to track CD margin by looking at specific dose values within the target failure rate (TFR). Thus, CD margin or EV drift can be tracked by tracking dose.

[0221] In an embodiment, only the source may be optimized and the following dose drift equation may be used to track the dose at a specific target rate:

[0222]

[0223] In the above equation (5), dose EV Indicates the target failure rate or expected failure rate FR target (ie, TFR) and at extreme excursions associated with characteristic values at 3 standard deviations from the mean characteristic value, NDS is the dose sensitivity of the characteristic of the pattern, LCDU dose3σ represents the variation associated with a characteristic value at 3 standard deviations from the mean characteristic value and at a particular dose, and CDF represents the cumulative distribution function of the characteristic's PDF. In one embodiment, a dose range can be determined that tracks the CD margin, regardless of whether the CD margin is positive or negative at a target failure rate. In one embodiment, focus or focus control can be minimized by tracking the dose range.

[0224] In an embodiment, both the source and the mask can be optimized, and the drift of CD can be caused by both the dose and the mask parameters (e.g., mask bias). In such a case, a combination of mask CD variation and dose CD variation can be considered. For example, the dose drift equation (6) given below can be used to track the dose at a specific target rate TFR. In addition, the mask bias drift equation (7) described below can be used to track the mask parameters (e.g., mask bias) at a specific target rate TFR.

[0225] In an embodiment, the dose drift equation is given by:

[0226]

[0227] In the above equation (6), dose EV Indicates the target failure rate or threshold failure rate FR target (ie, TFR) and at extreme excursions associated with characteristic values at 3 standard deviations from the mean characteristic value, NDS is the dose sensitivity of the characteristic of the pattern, LCDU dose Indicates the change in properties at a specific dose, LCDU total Indicates the total change in the characteristics of the pattern, LCDU dose 3σ represents the variation associated with the value of a property at 3 standard deviations from the mean property value and the value of the property at a specific dose, and CDF represents the cumulative distribution function of the PDF of the property.

[0228] In an embodiment, the mask bias drift equation is given by:

[0229]

[0230] In the above equation (7), mask EV Indicates the failure rate at the threshold FR target The mask deviation under extreme drift associated with the characteristic value at 3 standard deviations from the mean characteristic value, LCDU mask@W It is the change in characteristics associated with the resist pattern due to mask deviation, LCDU total represents the total variation of a characteristic of a pattern, and CDF represents the cumulative distribution function of the PDF of the characteristic.

[0231] In an embodiment, Equations 5, 6, and / or 7 are inserted or used in conjunction with the SMO process to maximize CD margin or minimize drift.

[0232] Figure 21 is a flow chart of a method 2100 for generating a retargeting pattern associated with a patterning process. For example, the method 2100 includes steps P2101 and P2103 as discussed in detail below.

[0233] Step P2101 includes obtaining (i) a target value for a characteristic associated with a target pattern to be printed on a substrate, (ii) characteristic limits 2101 associated with the target pattern, wherein the characteristic limits 2101 are values of the characteristic beyond which a printed pattern corresponding to the target pattern will be considered defective, and (iii) a source mask optimization (SMO) process configured to calculate dose and / or mask parameters based on a threshold failure rate associated with the characteristic of the target pattern.

[0234] In an embodiment, as discussed herein, characteristic limits are obtained 2101 based on a failure rate model that is calibrated using failure rate data and threshold failure rates associated with a printed pattern on a substrate, the printing being performed using initial SMO data.

[0235] Step P2103 includes simulating a source mask optimization process using the target pattern to generate a retargeted pattern such that the characteristics of the retargeted pattern further fall within the characteristic limits associated with the target pattern. In an embodiment, whether the characteristics of the retargeted pattern are further within the limits is determined based on a margin associated with the characteristic limits 2101 at a threshold failure rate. In an embodiment, such a margin is increased or maximized in an embodiment. Generating the retargeted pattern includes: simulating a source mask optimization process using initial SMO data to determine a drift of a characteristic associated with the target pattern at a threshold failure rate; determining (e.g., via computer hardware system 100) a margin between the characteristic limits 2101 and the drift at the threshold failure rate; and adjusting a characteristic value of the target pattern such that the margin is increased without exceeding the characteristic limits 2101 associated with the target pattern, the adjusted characteristic value being used to generate the retargeted pattern.

[0236] In an embodiment, obtaining a source mask optimization (SMO) process comprises including a dose drift equation to calculate a dose based on a probability density function (PDF) of a characteristic, local critical dimension uniformity, a dose sensitivity of the characteristic of the pattern, and a threshold failure rate; and / or including a mask equation to calculate a mask characteristic based on a probability density function (PDF) of the characteristic, local CD uniformity caused by mask deviation, and a threshold failure rate.

[0237] In an embodiment, the dose drift equation is given by equation (5) or (6) discussed herein, and the mask equation is given by equation (7) discussed herein. In an embodiment, the extreme value drifts may be global drifts. These drifts may be implemented using a cost function or merit function used in the SMO process.

[0238] In an embodiment, determining the retarget pattern (e.g., via computer hardware system 100) is an iterative process, the iterations comprising: simulating a source mask optimization process using initial SMO data comprising optimized source and optimized mask parameters and an initial target pattern or a retarget pattern as input to determine a drift of a characteristic associated with the target pattern at a threshold failure rate; determining a margin between a characteristic limit 2101 and the drift of the characteristic at the threshold failure rate; and adjusting a characteristic value of the target pattern such that the margin is increased without exceeding the characteristic limit 2101 associated with the target pattern, the adjusted characteristic value being used to generate the retarget pattern.

[0239] In an embodiment, a margin between a characteristic limit of a characteristic and an extreme value of the characteristic is maximized, where the extreme value of the characteristic is a value caused by a contributing factor from one or more process variables, an expected failure rate, such as a process variable that varies statistically globally (e.g., data related to the entire target layout compared to a fragment of the target layout).

[0240] In embodiments, extreme values of a characteristic are caused by focus, dose or global dose, moving standard deviation (MSD) of the error between measured and target values, resist thickness, and / or resist components including acids or quenchers.

[0241] In an embodiment, method 2100 further includes: simulating a source mask optimization (SMO) process using a retargeted pattern to determine analog characteristic values associated with a full chip layout; determining via a lithography manufacturing inspection whether the analog characteristic values associated with the full chip layout meet a desired yield; and in response to not meeting the desired yield, adjusting source parameters, mask parameters, or process parameters so that the desired yield is met, the adjusted source parameters, mask parameters, or process parameters are used to produce an optimized source, an optimized illumination pupil, and / or an optimized mask.

[0242] The approach discussed above has several advantages. One advantage is that process adjustments can be made based on available CD margins. Exemplary applications of using SMO or calibrated SMO simulation processes and dynamic retargeting based on CD margins or EV drift to determine process adjustments are discussed in further detail below. Process adjustments are made by considering the characteristics of the etching process, deposition process, or other post-development process used to create the final pattern (or structure) on the substrate.

[0243] Conventional SMO considers a specific set of rules for lithography design targets (e.g., ADI targets) and considers lithography-etch-bias. Bias rules may be desired for the following reasons. First, the etching process introduces a proximity effect. This can be mitigated in the final OPC step, but considering this situation earlier in SMO will lead to different results. Second, the conversion of CD and pattern placement error (PPE) or edge placement error (EPE) from ADI to AEI is very different. Typically, the CD error is reduced by a factor of two (e.g., 2) after etching, but the PPE or EPE is not reduced. As a result, a suboptimal pupil can be obtained by a conventional SMO process. Third, the etching process can cause significant focal length changes between features due to differences in the resist profile. This focal length change cannot be repaired by the final OPC step.

[0244] According to the present invention, a pattern transfer, or etch-aware SMO, is described that accounts for the characteristics of the etching process. Specifically, these include: (i) etch proximity effects (e.g., between features, 2D shape, CD versus pitch). These etch proximity effects are typically CD-dependent only; (ii) the conversion of CD and pattern placement errors from ADI to AEI by assigning different weights to each. In practice, SMO optimizes edge position ADI, which is a combination of CD and placement error. Therefore, edge position AEI is now predicted and used for optimization; and (iii) etch-induced focus changes. To enable SMO to include this scenario in the optimization, a resist profile is calculated and a simple etch model is used. For example, to obtain the resist profile, the edge position is calculated at multiple resist thresholds. The etch model can then calculate how this resist profile converts to CD AEI; and (iv) the expected LCDU reduction is included, which varies depending on the lithography-etch bias. This relationship can be feature-dependent. This can result in a suboptimal LCDU at ADI but an optimal LCDU at AEI.

[0245] Figure 16 Explain the typical options available after development, such that the substrate includes an exemplary target pattern 1601 (interchangeably referred to herein as target AEI). Target pattern 1601 includes a dense array of contact holes (3×3) and isolated contact holes, each of which is desirably 25 nm in size. In an exemplary process, target AEI 1601 can be achieved by performing one or more post-development processes, including deposition, etching, atomic layer etching (ALE), and atomic layer deposition (ALD).

[0246] In this example, referring to the process in 1602, the deposition process results in less deposition on the dense array than on the isolated contact holes. Therefore, the dense array CD increases to 30nm, while the isolated contact holes increase to 50nm, because the loading effect for the dense array and the isolated contact holes can be different. Another option can be to perform an etching process after the deposition process. After the etching process, the dense array CD is reduced to 20nm, while the isolated contact hole CD is reduced to 10nm. Again, the difference in CD can be caused by the etching loading effect on the dense array and the isolated holes. In another option, ALD or ALE can be performed to linearly grow or linearly etch the dense array and the isolated holes. In other words, the amount of material deposited (or the amount of etched material) for the isolated holes and the dense array is the same, so that each CD in the pattern can be 30nm (or 20nm for ALE).

[0247] Typically, adjustments can be made to balance the load by performing etching and deposition simultaneously or performing each process in cycles. For example, first performing a regular deposition, a regular etch cycle, and then performing ALE and / or ALD.

[0248] In this article, the SMO or the calibrated SMO can be modified to include a patterned model such as an etching model, a deposition model, or other related models to determine the characteristic values (e.g., CD, PPE, EPE) of the etching pattern, the deposition pattern, and the corresponding pattern by adjusting the etching parameters or the deposition parameters. In an embodiment, the etching and / or deposition process model can be fitted based on the geometric parameters of the etching pattern and the deposition pattern. For example, the fitting can be based on pattern data after etching, deposition pattern data obtained from the substrate after etching, and experimental data after deposition.

[0249] As discussed earlier, according to embodiments, SMO simulations are configured to be defect-aware. For example, a check is performed to determine whether the simulated characteristics meet the CD margin at a target failure rate. In embodiments, by including an etch model and / or a deposition model in the SMO process, the etch CD and / or deposition CD can be checked against the available CD margin.

[0250] like Figure 16As discussed in

[15] , existing etch processes, deposition processes, ALE, ALD can produce etch CD or post-deposition CD for patterns (e.g., dense patterns or isolated patterns) that are not within acceptable limits (e.g., CD limits), which can result in exceeding target failure rates. Therefore, by using etch models and / or deposition models and comparing the results to characteristic limits associated with threshold failure rates at ADI, defect-based process windows can also be improved. For example, by adjusting etch or deployment parameters based on available CD margin or by biasing isolated features differently than features in dense arrays.

[0251] refer to Figure 17 , pattern transfer aware SMO is further detailed below. An exemplary target AEI pattern 1701 includes a dense array of contact holes and isolated holes. In an embodiment, the retargeting method using SMO supplemented with an etch model is discussed above, and a deposition model is applied to produce an optimized retargeted pattern 1703, wherein the dense array of contact holes DF1 has a different deviation than the isolated holes IF1 and IF2. The retargeted pattern 1703 may also be accompanied by, for example, a deposition amount and an ALE amount. In an embodiment, the CD margin guides the deviation of the target AEI pattern 1701 and how much etching and deposition can be performed, thereby accounting for the LCDU associated with the dense holes and isolated holes in a manner that meets the target failure rate specification. In an embodiment, in conjunction with the SMO simulation, the etching parameters and deposition parameters are adjusted to determine the amount of etching and deposition that affects the final etch profile and the CD associated therewith. Therefore, the amount of etching and deposition is also performed relative to the characteristic limits and CD margin associated with the target failure rate.

[0252] In an embodiment, a characteristic limit can be expressed in terms of PPE (or EPE) associated with patterns on the same layer or on two separate layers. For example, after a deposition and etching cycle, the resulting etch profile of a line on a first layer may not align with a contact hole on a second layer, resulting in PPE or EPE between etched patterns on the substrate. Such defects can affect the functionality of the chip due to a lack of electrical connection between features. The PPE (or EPE) between patterns can be minimized based on etching parameters and deposition parameters. In an embodiment, the characteristic limit can be a PPE margin (or EPE margin) associated with a target failure rate. The PPE margin (or EPE margin) can also be determined similarly to the CD limit discussed in the present invention. For example, the characteristic PDF can be determined based on PPE or EPE measurements of a printed substrate and a failure rate associated with the PPE or EPE. In an embodiment, the CD margin and / or EPE margin, for example, guides a simulation process to determine how much local CD (e.g., dense hole CD and isolated hole CD) can be changed to obtain better edge placement based on defect-based limits.

[0253] In an embodiment, if a simulation determines that there is slightly too much or too little margin for CD adjustment after etch, but sufficient margin for CD adjustment at ADI, this indicates that there is more freedom to make process changes at the development stage or photolithography patterning step so that the post-etch CD is within the desired range while meeting the target failure rate specification. In another example, the margin on the upper and lower sides (i.e., top or bottom) of the etch profile depends on the aspect ratio at which the pattern failures are located. Based on the top CD or bottom CD of the etch profile, no margin is available for any particular process after etch, but at the ADI stage, the retargeted pattern meets the defect-based limits. Therefore, the defect-based window serves as a guide that indicates that a particular feature may be slightly too shrunken at the ADI stage, so a process update can be recommended or a different mask pattern must be determined that provides more margin after etch.

[0254] In another example, after etching, the CD distribution (or CD behavior) of a feature can be quite different from the CD behavior at ADI. In embodiments, post-etch CD can cause focus changes associated with the lithographic equipment. This is because the CD after the development step (e.g., resist CD) can be more representative of a CD limit that is different from the CD limit associated with pattern transfer. For example, the resist CD at the bottom of the resist can determine which pattern is transferred to the substrate, but the CD can be more sensitive to the behavior of features at the top of the resist.

[0255] According to the present invention, a defect-based window after etching and after development can not only guide the simulator as to what etch bias is appropriate, but also simulate the resist profile from the stacked layers of the substrate. In one example, features that touch or are in contact with each other can be more sensitive to the CD behavior at the top of the resist. In another example, merged or closed features can be more sensitive to the CD behavior at the bottom of the resist. Based on the stacked resist profile, the simulator can determine the top CD and bottom CD. For example, as discussed earlier, when using a simulated resist profile, the difference between the top CD and the bottom CD can be used to fit the model to the CD limits. Therefore, the etching model and the CD limit-based model can also be used to evaluate the post-etch CD behavior at the top and bottom. Therefore, adjustments to the etching process can be determined so that the margins related to the top CD and bottom CD are within the acceptable failure rate limits.

[0256] In an embodiment, the etching process model and / or the deposition process model can be configured to determine that etching parameters or deposition parameters, such as etching rate or deposition rate, are sensitive to the angle of incidence of the etching or deposition. Because these rates are sensitive to the angle of incidence, the simulator can determine that, for example, at an angle of incidence of 45 degrees, the rate may be very sensitive, indicating that the process deposits or etches very strongly compared to other angles of incidence.

[0257] Therefore, as discussed above, if limits associated with the post-etch process are available, such limits may also be included in the SMO simulation process to determine optimized sources, optimized masks, and / or process adjustments.

[0258] The method of the present invention has several advantages. The method proposes to manufacture only a single mask and perform a DB-PW experiment, and then calibrate the simulation process associated with the patterning process or semiconductor manufacturing process. The calibrated simulation process allows to predict whether a sufficient yield of the selected semiconductor manufacturing process can be achieved. In addition, feedback can be received about which designs are feasible (or not feasible) and the associated target CD. This allows very fast process cycling and calibration associated with the simulator. The DB-PW based experiment can be finally fitted in about 8 hours, which is usually what the user desires. On the other hand, as Figure 10 As shown in , the conventional simulation process for such a determination requires several cycles, each cycle requiring mask fabrication and defect detection before retargeting can occur.

[0259] Dynamic retargeting ensures that the illumination pupil is optimized with the optimal target CD while taking into account product yield. Thus, improved SMO solutions are expected, such as improved CD control and better exposure latitude. In addition, dynamic retargeting includes appropriate drift (at a threshold failure rate) and is therefore implicitly located in the source mask optimization, and a person skilled in the art can change the dose and / or focus to find your optimal dose and focus. In an embodiment, the results of DB-PW on the observed actual measured dose / mask variance can be used to set practical range limits for dose, focus and / or mask deviations by monitoring the relative extreme drift of CD at a given target failure rate. Tracking EV drift can lead to significantly different SMO solutions. For example, EUV typically needs to be optimized for a dose drift of ±30% to minimize or at least account for the tail of the skew. The method described in the present invention allows the determination of the relevant drift per feature type.

[0260] In embodiments, situations may arise where a trade-off must be analyzed between hard limits (e.g., affecting defect and product yield) and soft limits (e.g., affecting efficient chip operation, also known as parametric yield). For example, a hard limit could be a CD limit based on DB-PW, and a soft limit could be a user-defined CD that will impact the parametric yield of the device. For example, such a soft limit could be a CD value that causes thermal or electrical issues during operation of the device (e.g., a printed substrate within the device). In other words, a soft limit need not necessarily correlate to device failure, but could be problematic if exceeded. In such cases, dynamic retargeting allows for the selection of a maximum or minimum nominal CD that still provides the desired yield while optimizing the device's performance or parametric yield. Thus, for example, if a certain CD margin is available or the retargeted pattern is within that margin, this could also allow for increasing the size of features (e.g., contact holes) as this would result in better device performance. In embodiments, a soft limit could be a feature area (e.g., a contact hole area) that could contact an area between two layers, or even within a layer of a substrate used in the device. An exemplary simulation process for parameter optimization based on lithography variations is discussed in detail in U.S. application Ser. No. 16 / 541,420, which is incorporated herein by reference in its entirety.

[0261] In an embodiment, similar DB-PW experiments can be performed using both ADI and AEI data. The methods herein enable the user to analyze whether there is flexibility in adjusting the mask CD to result in a desired resist CD (e.g., when the resist has a sufficient CD window or yield). The methods herein also enable the user to analyze whether to adjust the process (e.g., litho-etch bias, use of another isotropic etch or spacer process, etc.) to achieve the final AEI CD. Thus, the methods of the present invention can provide recommendations related to process adjustments or what final target CD will work for a selected process.

[0262] In the case of a new reticle design (e.g., a mask for use in high volume manufacturing (HVM)), there may be substrate-dependent CD errors. In an embodiment, the CD errors are caused by simulation results obtained after a fixed number of iterations compared to reference simulation results obtained from a reference simulation process performed for a relatively long period of time (such as a week). In an embodiment, there may be residual CD errors due to the mask across the substrate because the mask pattern may not be determined by optimization for a considerable period of time or until the CD errors are zero. In an embodiment, the CD errors are also referred to as convergence residuals from full-chip OPC. In an embodiment, the convergence residuals may be used during final reticle verification (e.g., lithography manufacturing check (LMC)) to determine whether the OPC full-chip results in a reticle that is expected to provide the desired yield. In an embodiment, the CD errors may be determined and checked to see if the errors are within acceptable limits for a particular hot spot on the reticle. In an embodiment, a hot spot may be a user-defined location on the reticle that is defined as a portion of the reticle that includes a critical pattern or a location with a relatively high probability of defect occurrence.

[0263] As mentioned earlier, PCT application PCT / EP2018 / 085159 proposes defining a defect-based process window based on the expected CD distribution at the edge of the process window and the measured failure rate. The previously proposed method includes a step of predicting the shape of the CD distribution at a very low probability level under optimal exposure and best-before-focus (BEBF) conditions. To determine the CD distribution, the dose-response curve is expected to be nonlinear, which results in a skewed final CD distribution. However, for the effects of the mask, the MEEF is assumed to be linear. This implies that a Gaussian distribution on the mask translates into a Gaussian distribution of the average CD per mask contact hole on the substrate.

[0264] In an embodiment, the present invention provides an improved method for determining a defect-based process window by taking into account the asymmetry of the CD distribution due to a nonlinear mask error enhancement factor (MEEF) and the dependence of the resist LCDU on the mask feature size. Figure 24 middle).

[0265] The method ( Figure 24 ) The shape of the CD distribution on the substrate can be preferably predicted by taking into account the nonlinearities in the MEEF and the dependence of the resist LCDU on feature size using limited additional measurements and / or simulations.

[0266] The following description shows measurement results indicating that nonlinearity in the MEEF affects the skewness of the distribution of the average CD per mask feature size (e.g., contact hole size) on a substrate. The following description also shows that the resist LCDU depends on the mask feature size (e.g., contact hole size). In addition, it explains how these two effects can be taken into account in the prediction of the CD distribution on the substrate.

[0267] Figure 22 The plot shows the measured data (dots) of the average substrate CD minus the average CD for each contact hole in the mask. As can be seen, the distribution of the measured data (dots) is skewed. In this example, a Gaussian function was fitted to the measured data. However, the Gaussian fit does not accurately explain the measured data. On the other hand, the nonlinear fit determined according to this method provides a relatively better fit than the Gaussian fit.

[0268] Figure 23 Plotting the measured resist LCDU deviation (δCD) relative to the mask CD associated with each mask contact hole plotted. mask ). Despite the presence of substantial inherent measurement noise, the moving average of the measured data clearly shows that the resist LCDU increases strongly with decreasing mask contact hole size. The measured sensitivity is stronger than predicted from simulations associated with the patterning process (e.g., using Hyperlith software). In this example, the moving average curve represents the relationship between mask contact hole size and the local CDU of the substrate (i.e., the standard deviation of the CD).

[0269] Figure 24 is a flow chart of a method for determining a probability density function associated with characteristics of features to be printed on a substrate.Exemplary method 2400 includes steps P2401 and P2403 of using a dose PDF and a mask PDF to determine a CD PDF.

[0270] Step P2401 includes obtaining (e.g., via computer hardware system 100): (i) a dose probability density function (dose PDF) for determining the probability of a dose, and (ii) a mask probability density function (mask PDF) for determining the probability of a deviation from a mask characteristic. In an embodiment, the dose PDF is a function of (a) a characteristic of the feature (e.g., CD) and (b) the deviation from the mask characteristic (δCD mask ). In an embodiment, a mask characteristic (eg, mask CD) is associated with a mask used to print features on a substrate.

[0271] Step P2403 includes determining (e.g., via computer hardware system 100) a probability density function associated with the characteristic by convolving (i) the dose PDF with (ii) the mask PDF over a given range of mask characteristic values. In an example, the probability density function associated with the characteristic is represented as a CD PDF or a PDF CD (CD, d).

[0272] In an embodiment, step P2404 includes adjusting a process window associated with a patterning process based on the determined PDF of the characteristic. In an embodiment, such a process window can be used to determine a CD limit, such as used in methods 1100, 1500, and 2100 discussed herein. In an embodiment, the process window can be used by a lithographic apparatus during a patterning process. Those skilled in the art will appreciate that the application of determining a PDF is not limited to adjusting a process window. The PDF can be used to improve other patterning-related processes, simulations, or manufacturing operations.

[0273] In an embodiment, the dose PDF and the mask PDF are then combined to determine the CD PDF using exemplary equation (8):

[0274] PDF CD (CD, d) = ∫δCD mask PDF dose (CD, d, δCD mask )×PDF mask (δCD mask )…(8)

[0275] The terms in equation (8) are discussed further below.

[0276] In an embodiment, the mask PDF includes a nonlinear mask error enhancement factor (MEEF) dependency that causes skewness of the mask PDF. The nonlinear MEEF is calculated using an inverse function of the relationship between the mask characteristics and the characteristics printed on the substrate.

[0277] In an embodiment, the mask PDF may be calculated using the following equation (9). In an embodiment, PDF mask (δCD mask ) indicates that δCD is found on the substrate mask The probability density function, δCD mask is the average CD deviation of all contact holes on the substrate associated with the same mask contact hole.

[0278]

[0279] In the above equation 10, G mask It is used to determine whether a given size is found on the mask maskThe probability of a contact hole is a Gaussian distribution of the mask characteristics, which is calculated based on the inverse function of the relationship between the mask characteristics and the characteristics printed on the substrate. mask The average value μ mask , the inverse function is given by g mask (δCD mask ) indicates that G mask The standard deviation of mask ,σ mask is based on the inverse function and the standard deviation of the measured value δCD mask The standard deviation is determined, and Determine the nonlinear MEEF. In an embodiment, G mask Can be size mask Gaussian distribution or Gaussian distribution.

[0280] In the examples, reference Figure 25 , size mask =g mask (δCD mask ), which provides size mask With δCD mask If the size of the hole in the mask is size mask , then the average deviation of the contact hole size is This also determines μ mask , σ mask In an example, the relationship may be a second order polynomial, a third order polynomial, a spline fit, or other fitting function determined using simulation or measurement data.

[0281] In an embodiment, the dose PDF includes a dependency on the local critical dimension uniformity (LCDU) of the resist pattern on the substrate. The LCDU is caused by mask characteristics. Figure 23 An exemplary relationship between the deviation of resist LCDU and mask CD is illustrated.

[0282] In an embodiment, a dose PDF is determined using a normal distribution, Poisson distribution, or compound Poisson distribution having a mean dose and a dose standard deviation. The mean dose is determined by the inverse function of the relationship between dose and CD for a given deviation from mask characteristics, and the dose standard deviation is determined by the LCDU associated with the resist pattern on the substrate, which is caused by the mask characteristics. It will be appreciated that the dose PDF is not limited to a normal distribution or a Poisson distribution. Those skilled in the art may select other known distribution functions to determine the dose PDF, as discussed herein.

[0283] In an embodiment, the dose PDF can be calculated by the following equation (10):

[0284] PDFdose (g d (CD, δCD mask ); μ d (δCD mask ), σ d (δCD mask )) …(10)

[0285] In the above equation 10, a given deviation δCD of the characteristic for the mask characteristic is used mask The dose g is determined by the inverse function of the relationship between the dose and the characteristic CD d (CD, δCD mask ), and the dose standard deviation σ d Based on the inverse function g d (CD, δCD mask ) and the standard deviation of the measured in, represents the LCDU(1σ) due to dose variation and resist variation for a given mask deviation.

[0286] In the examples, reference Figure 26 , the figure shows different δCD mask Two exemplary relationships between the dose (D) and CD on the substrate. In the embodiment, g d (CD, δCD mask ) represents the dose D, CD and δCD mask In the example, D is Gaussian or ∈D is Poisson, where ∈ is the fitting parameter. In the embodiment, g d (CD, δCD mask ) can be a second-order bivariate polynomial, a higher-order bivariate polynomial, a spline fit, or other fitting functions based on fitting of simulated or measured data.

[0287] In an embodiment, method 2400 further includes a step P2405 of executing the determined probability density function using failure rate data 2410 associated with the target layout (e.g., on a processor of computer hardware system 100) to determine a characteristic limit associated with a threshold failure rate. In an embodiment, the failure rate data may be obtained in a manner similar to that discussed above with respect to defect-based process windows and is discussed in further detail in PCT / EP2018 / 085159, which is incorporated herein by reference in its entirety.

[0288] In an embodiment, another method for determining the CD distribution based on weighting of dose contributions to the CD distribution is provided.

[0289] Random noise is a common area of concern in EUV lithography. Random noise not only affects local CD uniformity (LCDU), local pattern placement error, and line edge roughness (LER), but also causes defects through rare events known as random defects. The CD variability and failure rate of random defects have become important for EUV lithography process control. Conventional process window analysis based on average CD measured over hundreds of data points is no longer sufficient to determine a robust process without considering the entire distribution of CDs for the target layout.

[0290] As previously mentioned and described in detail in PCT / EP2018 / 085159, a software product (e.g., PFScan) can be configured to determine a stochastic perception process window characterization. The software product can take CD and failure rate data (or defect data) as input. Using the input data, statistical analysis of the CD distribution and failure rate modeling can be performed to generate a stochastic perception process window. Determining the failure rate model includes CD / LCDU Bosan fitting, CD distribution modeling, and failure rate process window generation. At the CD distribution modeling step, a CD probability density function (PDF) is modeled by convolving a linear (normal) CD distribution with a nonlinear distribution that is reported to be induced by effective dose variations for post-development processes.

[0291] However, in practical terms, several factors contribute to the total LCDU, such as dose variation, mask errors and metrology noise, etch noise from post-etch processes, background noise, etc. As a result, the modeled dose contribution used to determine the CD PDF may be insufficient. Figure 27 , a possible overestimation of the dose contribution would result in a wider tail in the modeled CD distribution.In this example, the CD PDF is modeled or fitted in terms of a nonlinear dose contribution to the measured CD data (raw CD).

[0292] In this paper, additional LCDU contribution factors are applied to the CD PDF model. The adjustment factor is applied to the measured LCDU to adjust for the effect of dose variation, and another part of the measured LCDU is fitted to the model contributions from mask error, SEM noise, etching error, etc. The following equation (11) expresses the different contributions to the total LCDU

[0293]

[0294] In the above equation, adj_factor is a value or set of values that applies to the dose variation across a given dose-focus matrix or setting. In an embodiment, adj_factor is optimized across different dose and focus settings, as discussed later herein.

[0295] In embodiments, applying a constant but optimized adj_factor value across the entire focus / dose matrix allows for efficient modeling of CD distributions across different dose-focus settings for simple patterns in many cases (e.g., SRAM and regular via arrays). However, in other use cases, it becomes important to adjust the adj_factor value across the entire focus-exposure setting so that the modeled PDF represents the measured PDF. The measured PDF is the PDF represented by plotting the actual measured CD data of the printed substrate.

[0296] Figure 28 An example of a PDF fitted across different focus-exposure conditions using a constant adj_factor value to model nonlinear dose contributions is shown. The fitted PDF for the highlighted dose-focus setting deviates considerably from the measured PDF. The further away from the nominal (center) condition, the greater the difference seen between the modeled PDF and the measured PDF. This indicates that the PDF for the highlighted condition should be further optimized.

[0297] In an embodiment, the PDF of the nonlinear dose contribution (e.g., PDF NL , d) can be based on adj_factor*σ dose 2 In an embodiment, based on The PDFs contributing to other factors (e.g., PDF linear ) are modeled separately. A convolution between the two PDFs is performed to determine the final CD distribution (also referred to as the modeled PDF or modeled CD PDF), as shown below, where Represents the convolution operation:

[0298]

[0299] In this paper, the modeling parameters of each PDF are determined based on the difference or error between the modeled PDF and the measured PDF so that the error is minimized. According to the present invention, the introduction of the adjustment model and the additional Gaussian distribution from other contributing factors can help to effectively model the measured CD distribution.

[0300] In an embodiment, adj_factor is a model whose parameters are optimized such that adj_factor is dynamic across different dose-focus settings, effectively changing the modeled PDF (e.g., PDF CDThe ratio of the nonlinear dose sensitivity contribution of (CD, d)) is calculated. Both the nonlinear and linear distributions are optimized simultaneously at each dose-focus setting, and the optimized adj_factor is then modeled as a function of focus and dose for failure rate modeling.

[0301] Various optimization algorithms can be applied to optimize the adj_factor model based on metrics such as the root mean square error (RMS) between the modeled PDF and the measured PDF. One example is to apply the Adaptive Moment Estimation (Adam) algorithm in the entire FEM (ie, dose-focus setting).

[0302] Figure 29 is a probability density function (e.g., PDF) associated with a characteristic of a pattern to be printed on a substrate according to an embodiment of the present invention. CD (CD, d)) Flowchart of an exemplary method.

[0303] In an embodiment, method 2900 can start with a constant adj_factor across the FEM for the dose contribution. In an embodiment, the user can manually adjust the adj_factor by adjusting the value of the adj_factor but keeping it the same across the FEM, or by varying the adj_factor with dose and focus. Manual adjustment helps the user find a roughly acceptable spot for near-nominal focus / dose conditions. Manual adjustment may not be satisfactory when the RMS fit error is greater than a user-specified threshold (e.g., 0.1). In an embodiment, the optimal result (with the smallest error) from the manual adjustment can be used as the initial input for automatic optimization to save runtime.

[0304] Once the initial setup is complete, an automated optimization can be run using a set of focus and dose settings. In one embodiment, the user can specify a sample of focus and dose settings to be optimized, rather than the complete FEM setup, to save runtime. Method 2900 is further discussed below in steps P2901 and P2903.

[0305] Step P2901 includes obtaining (i) a plurality of dose-focus settings 2901, and (ii) a reference distribution 2903 based on measured values of a characteristic of the printed pattern associated with each of the plurality of dose-focus settings. In an embodiment, the reference distribution 2903 is also referred to as a measured PDF.

[0306] Step P2903 includes determining (eg, via computer hardware system 100) a characteristic (eg, PDF) based on the adjustment model and the plurality of dose-focus settings. CD) such that the error between the PDF and a reference distribution is reduced, the PDF being a function of the adjustment model and a variance associated with the dose. The adjustment model is configured to change the proportion of the nonlinear dose sensitivity contribution to the PDF. In an embodiment, the adjustment model is a polynomial function of the dose and the focal length.

[0307] In an embodiment, step P2904 includes adjusting a process window associated with a patterning process based on the determined PDF of the characteristic. In an embodiment, such a process window can be used to determine a CD limit, such as used in methods 1100, 1500, and 2100 discussed herein. In an embodiment, the process window can be used by a lithographic apparatus during a patterning process. Those skilled in the art will appreciate that the application of determining a PDF is not limited to adjusting a process window. The PDF can be used to improve other patterning-related processes, simulations, or manufacturing operations.

[0308] In an embodiment, a PDF (e.g., PDF CD ) is an iterative process, the iteration comprising: determining an adjustment value for a given dose-focus setting in a plurality of dose-focus settings based on the adjustment model; determining the characteristic of the pattern (e.g., PDF) based on the adjustment value; CD ) of the PDF; determining an error between the PDF and the reference distribution; and adjusting the parameters of the adjustment model for a given dose and focus setting in a plurality of dose-focus settings such that the error is minimized.

[0309] In an embodiment, a PDF (e.g., PDF CD ) is the convolution of a first PDF and a second PDF, wherein the first PDF is a function of a first variation that is the product of a variation of the adjustment model and dose, and the second PDF is a function of a second variation associated with a factor other than dose that contributes to the variation of the characteristic of the pattern.

[0310] In an embodiment, the determination of the PDF is an iterative process comprising: convolving a first PDF with a second PDF to determine a PDF of a characteristic of the pattern; determining an error between the PDF and a reference distribution; and adjusting parameters of the first and second variations for a given dose and focus setting in a plurality of dose-focus settings such that the error is minimized.

[0311] In an embodiment, the adjustment of the parameters of the adjustment model for the plurality of dose-focus settings is performed by an optimization algorithm selected from adaptive moment estimation or a gradient descent method.

[0312] In an embodiment, method 2900 further includes: determining, for each dose and each focus setting in a plurality of dose-focus settings, a plurality of adjustment values associated with a PDF having a minimum error relative to a reference distribution; and fitting a polynomial function of dose and focus based on the plurality of adjustment values to determine an adjustment model, such that a difference between the fitted polynomial function and the plurality of adjustment model values is minimized.

[0313] Figure 30A and Figure 30B The dependence of the adjustment value (adj_factor) according to an embodiment of the present invention on the dose and the focal length are respectively illustrated. Figure 30A and Figure 30B Optimized tuning values used to create the tuning model are shown. Figure 30A The value of the adjustment factor, adj_factor, which defines the nonlinear CD distribution, is shown to be primarily or mostly linear with respect to dose and significantly affected by dose. The value of adj_factor decreases as dose decreases. This illustrates the impact of random effects on the nonlinear CD distribution: at lower doses, the random effect is larger, and therefore the adjustment value is larger, meaning that a greater proportion of the CD variation comes from dose variation.

[0314] The adjustment value also changes with the focal length ( Figure 30B ), the adjustment value is a high-order relationship. Figure 30 also shows that at higher doses there is more variation through the focal length. The adjustment value increases with increasing defocus.

[0315] The dynamically optimized adjustment value has better performance in modeling CD distribution under all dose / focus conditions. In an embodiment, dynamic optimization refers to a different optimized adjustment value for each dose-focus setting. For example, Figure 31 As shown in , the modeled PDF uses the optimized adj_factor model to fit more accurately to model the nonlinear dose contribution in all different dose-focus settings. Figure 28 , does not fit the CD distribution throughout the dose-focus setup far from the nominal conditions, as explained before.

[0316] In an embodiment, the method 2900 further includes a step P2905, which includes executing the determined probability density function (e.g., PDF) using the failure rate data 2910 associated with the pattern (e.g., on a processor of the computer hardware system 100). CD ) to determine the characteristic limits associated with the threshold failure rate.

[0317] In an embodiment, the adjustment model can be saved and reused for other failure rate model runs. The optimized adjustment values can be applied to other features from the same layer even if the other features from the same layer include different patterns or groups of patterns. Before running a failure rate model on a different pattern from the same layer, a check is performed to see if there is an existing adjustment model available for use.

[0318] Combinations and subcombinations of the disclosed elements constitute separate embodiments according to the present invention. For example, a first combination includes determining a retargeted pattern based on a defect-based process window using a target pattern or a separately generated optimized OPC pattern. A second combination determines a calibrated simulation process. In another combination, process adjustments can be determined to simulate or manufacture a pattern that meets a threshold failure rate. In another combination, a lithographic apparatus includes a mask manufactured using a mask pattern determined as discussed herein.

[0319] In an embodiment, the methods discussed herein (e.g., 1100, 1500, 2100, 2400, and 2900) may be provided as a computer program product or non-transitory computer-readable medium having instructions recorded thereon that, when executed by a computer, implement the operations of the methods discussed above. For example, Figure 36 The example computer system 100 in includes a non-transitory computer-readable medium (e.g., memory) that includes instructions that, when executed by one or more processors (e.g., 104), cause the operations (e.g., processes) of the methods discussed above.

[0320] The following description provides an optical proximity correction (OPC) process. OPC addresses the fact that, except for any reduction achieved by the lithographic projection apparatus, the final size and placement of the image of the patterning device pattern projected onto the substrate will be different from, or only depend on, the size and placement of the corresponding patterning device pattern features on the patterning device. It should be noted that the terms "mask," "reticle," and "patterning device" are used interchangeably herein. Furthermore, those skilled in the art will recognize that the terms "mask pattern," "reticle pattern," and "patterning device pattern" can be used interchangeably, particularly in the context of lithographic simulation / optimization, where, for example, a physical patterning device need not be used, but a patterning device pattern can be used to represent the physical patterning device. For the smaller feature sizes and higher feature densities present on some patterning device patterns, the position of a particular edge of a given feature will be affected to some extent by the presence or absence of other adjacent features. These proximity effects arise from minute amounts of radiation coupled from one feature to another and / or non-geometric optical effects such as diffraction and interference. Similarly, proximity effects can arise from diffusion and other chemical effects during the post-exposure bake (PEB), resist development, and etching that typically follows photolithography.

[0321] In order to ensure that the projected image of the pattern forming device pattern is in accordance with the requirements of a given target design, complex numerical models, corrections or pre-distortions of the pattern forming device pattern should be used to predict and compensate for proximity effects. The paper "Full-Chip Lithography Simulation and Design Analysis - how OPC Is Changing IC Design" (C. Spence, Proc. SPIE, Vol. 5751, pp. 1-14 (2005)) provides an overview of current "model-based" optical proximity effect correction processes. In a typical high-end design, almost every feature of the pattern forming device pattern has some modification in order to achieve higher fidelity of the projected image to the target design. These OPC modifications can include offsets or deviations in edge position or line width and / or the application of "auxiliary" features that are intended to assist in the projection of other features.

[0322] With millions of features typically present in a device design, applying model-based OPC to a target design involves good process models and considerable computational resources. However, applying OPC is generally not an exact science, but rather an empirical, iterative process that does not always compensate for all possible proximity effects. Therefore, the effects of OPC, such as the patterning device pattern after applying OPC and any other RET, should be verified by design checks, such as intensive full-chip simulations using a calibrated numerical process model, in order to reduce or minimize the likelihood of design flaws being built into the patterning device pattern. This is driven by the significant cost of manufacturing high-end patterning devices, which is in the millions of dollars range, and the impact on the turnaround time caused by reworking or repairing the actual patterning device once it has been manufactured. Both OPC and full-chip RET verification can be based on numerical modeling systems and methods, as described, for example, in U.S. Pat. No. 7,003,758, which is incorporated herein by reference in its entirety, and in the paper by Y. Cao et al., entitled “Optimized Hardware and Software For Fast, Full Chip Simulation,” Proc. SPIE, Vol. 5754, 405 (2005).

[0323] One of the simplest forms of OPC is selective bias. Given a CD vs. pitch data relationship, by varying the CD at the patterning device level, all different pitches can be forced to produce the same CD, at least at optimal focus and exposure. Thus, if a feature is printed too small at substrate level, the patterning device-level feature will be biased to be slightly larger than the nominal feature, and vice versa. Because the pattern transfer process from patterning device level to substrate level is nonlinear, the bias is not simply the CD error measured at optimal focus and exposure multiplied by the reduction ratio; instead, an appropriate bias can be determined using modeling and experimentation. Selective bias, especially when applied only under nominal process conditions, is an incomplete solution to the problem of proximity effects. While such a bias can, in principle, be applied to produce a uniform CD vs. pitch curve at optimal focus and exposure, once the exposure process is altered from nominal, each biased pitch curve will respond differently, resulting in different process windows for different features. The process window is the range of values of two or more process parameters (e.g., focus and radiation dose in a lithographic apparatus) within which features are sufficiently adequately produced (e.g., the CD of the feature is within a certain range, such as ±10% or ±5%). Thus, deviations from the "optimum" for giving the same CD versus pitch relationship can even have a negative impact on the overall process window, thereby narrowing rather than widening the focus and exposure range within which all target features can be printed on a substrate within the desired process tolerances.

[0324] Other, more complex OPC techniques have been developed for applications beyond the one-dimensional deviation example above. A two-dimensional proximity effect is line-end shortening. Line ends have a tendency to "pull back" from their intended endpoints depending on exposure and focus. In many cases, the degree of shortening of the ends of long line ends can be several times greater than the corresponding line narrowing. This type of line-end pullback can cause catastrophic failure in the fabricated device if the line end does not completely cross over the underlying layer it is intended to overlay, such as the polysilicon gate layer above the source-drain region. Because this type of pattern is extremely sensitive to focus and exposure, simply deviating the line end longer than the designed length is not sufficient because the line at optimal focus and exposure or underexposure will be too long, leading to shorts when the extended line end touches adjacent structures or unnecessarily large circuit sizes if more space is added between individual features in the circuit. Since one of the goals of device design and manufacturing is often to minimize the area required per chip while maximizing the number of functional elements, adding excessive spacing is an undesirable solution.

[0325] Two-dimensional OPC methods can help solve the problem of line end pullback. Additional structures such as "hammerheads" or "serifs" (also known as "auxiliary features") can be added to the line ends to effectively anchor the line ends in place and provide reduced pullback throughout the entire process window. These additional structures are not resolved even at optimal focus and exposure, but they change the appearance of the main features without being fully resolved themselves. "Main feature" as used herein means a feature that is expected to be printed on the substrate under some or all conditions in the process window. The auxiliary features can take a much more radical form than a simple hammerhead added to the line end, to the extent that the pattern on the patterning device is no longer just the desired substrate pattern increased in size according to the reduction ratio. Compared to simply reducing line end pullback, auxiliary features such as serifs can be applied to more situations. Inner or outer serifs can be applied to any edge, especially two-dimensional edges, to reduce corner rounding or edge squeezing. With sufficient selective bias and assist features of all sizes and polarities, the features on the patterning device bear increasingly less resemblance to the desired final pattern at substrate level. Typically, the patterning device pattern becomes a pre-distorted version of the substrate-level pattern, where the distortion is intended to offset or reverse pattern deformations that will occur during the manufacturing process to produce a pattern on the substrate that is as close as possible to that intended by the designer.

[0326] Another OPC technique involves using completely independent and indistinguishable assist features instead of or in addition to those assist features (e.g., serifs) that are connected to the main features. The term "independent" here means that the edges of these assist features are not connected to the edges of the main features. These independent assist features are not intended or required to be printed on the substrate as features, but are intended to modify the aerial image of nearby main features to enhance the printability and process tolerances of the main features. These assist features (often referred to as "scattering bars" or "SBARs") can include: sub-resolution assist features (SRAFs), which are features outside the edge of the main feature; and sub-resolution inverse features (SRIFs), which are features dug out from inside the edge of the main feature. The presence of SBARs adds another layer of complexity to the pattern forming device pattern. A simple example of the use of scattering bars is where a regular array of indistinguishable scattering bars is drawn on either side of an isolated line feature. From an aerial image perspective, this has the effect of making the isolated line appear more representative of a single line within an array of dense lines, resulting in a process window with focus and exposure tolerances closer to those of the dense pattern. The shared process window between such a decorated isolated feature and the dense pattern will have a greater shared tolerance to focus and exposure variations than would be the case if the feature were drawn as isolated at patterning device level.

[0327] Assist features can be considered the difference between features on the patterning device and features in the patterning device pattern.The terms "main feature" and "assist feature" do not imply that a particular feature on the patterning device must be labeled as a main feature or an assist feature.

[0328] In addition to or in lieu of optimization of the patterning device pattern (e.g., OPC), the illumination mode can also be optimized in conjunction with or separately from the patterning device optimization in an effort to improve overall lithographic fidelity. Many off-axis illumination modes, such as annular, quadrupole, and dipole, can be used and provide more degrees of freedom for OPC design, thereby improving imaging results. As is known, off-axis illumination is a proven way to resolve fine structures (i.e., target features) contained in patterning devices. However, compared to traditional illumination modes, off-axis illumination modes generally provide less radiation intensity for aerial images. Thus, it is desirable to attempt to optimize the illumination mode to achieve an optimal balance between finer resolution and reduced radiation intensity. For example, several illumination optimization methods can be found in the paper by Rosenbluth et al., entitled "Optimum Mask and Source Patterns to Print a Given Shape," Journal of Microlithography, Microfabrication, Microsystems 1(1), pp. 13-20 (2002), which is incorporated herein by reference in its entirety.

[0329] The pressure of ever-decreasing design rules is driving semiconductor chipmakers deeper into low-k1 lithography. The move toward lower-k1 lithography places significant demands on RET, exposure tools, and the need for lithography-friendly design. Consequently, to help ensure that device designs can be produced onto substrates using a viable process window, illumination mode-patterning device pattern optimization (sometimes referred to as source-mask optimization or SMO) is becoming an important RET to achieve, for example, smaller features.

[0330] Therefore, for low-k1 lithography, optimization of both the illumination pattern and the patterning device pattern can be used to ensure a feasible process window for projecting critical device patterns. Some algorithms (e.g., as described in Socha et al., “Simultaneous Source Mask Optimization (SMO)” (Proc. SPIE, Vol. 5853, pp. 180-193 (2005), which is incorporated herein by reference in its entirety) discretize the illumination into independent illumination distribution points and the patterning device pattern into diffraction orders in the spatial frequency domain, and separately formulate objective functions (which are defined as functions of selected design variables) based on process window metrics such as exposure latitude that can be predicted by an optical imaging model based on the illumination distribution point intensities and the patterning device pattern diffraction orders.

[0331] Another illumination mode and patterning device pattern optimization method and system that uses an objective function to enable simultaneous optimization of the illumination mode and patterning device pattern without constraints and within a feasible amount of time is described in PCT Patent Application Publication No. WO 2010 / 059954, entitled “Fast Freeform Source and Mask Co-Optimization Method,” which is hereby incorporated by reference in its entirety. Another illumination and patterning device optimization method and system involving optimizing illumination by adjusting pixels of an illumination distribution is described in U.S. Patent Application Publication No. 2010 / 0315614, entitled “Source-Mask Optimization in Lithographic Apparatus,” which is hereby incorporated by reference in its entirety.

[0332] Now, the patterning device mentioned above may include one or more patterning device patterns. Patterning device patterns can be generated using a CAD (computer-aided design) program, a process often referred to as EDA (electronic design automation). Most CAD programs follow a set of predetermined design rules in order to create functional patterning device patterns for the patterning device. These rules are set by process and design constraints. For example, design rules define the spatial tolerances between device features (such as gates, capacitors, etc.) or interconnects to ensure that the devices or lines do not interact with each other in an undesirable manner. Design rule constraints can be referred to as "critical dimensions" (CD). The critical dimension of a device can be defined as the minimum width of a line or hole or the minimum space between two lines or two holes. Thus, the CD determines the overall size and density of the designed device. One of the goals in device fabrication is to faithfully reproduce the original device design on the substrate (via the patterning device).

[0333] Furthermore, during the optimization of a system, the quality factor of the system can be expressed as an objective function (e.g., a cost function or merit function). The optimization process generally boils down to finding a set of system parameters (design variables) that minimizes or maximizes the objective function. Depending on the goal of the optimization, the objective function can have any suitable form. For example, the objective function can be the weighted root mean square (RMS) of the deviations of certain system characteristics (evaluation points) from the expected values (e.g., ideal values) of these characteristics; the objective function can also be the maximum value of these deviations. As used herein, the term "design variables" includes a set of parameters of a patterning process (e.g., a lithographic process, a lithographic projection apparatus, etc.), for example, parameters that can be adjusted by a user of the lithographic projection apparatus. It should be understood that any characteristic of the patterning process (including the illumination mode, the patterning device pattern (or patterning device configuration), the characteristics of the projection optics, and / or the resist characteristics) can be among the design variables being optimized. The objective function is often a nonlinear function of the design variables. Standard optimization techniques are then used, for example, to minimize or maximize the objective function. The term "evaluation point" herein should be broadly interpreted to include any characteristic of a system or process. Due to the practicality of how a system or process is implemented, the design variables of a system may be constrained to a limited range and / or be interdependent. In the case of a lithographic projection apparatus, the constraints are often associated with the physical properties and characteristics of the hardware (such as the adjustable range and / or patterning device manufacturability design rules (MRCs)), and the evaluation points may include physical points on the resist image on the substrate, as well as non-physical characteristics such as dose and focus.

[0334] Thus, in a lithographic projection apparatus, an illumination system provides illumination (i.e., radiation) to a patterning device, and projection optics direct the illumination from the patterning device onto a substrate. In an embodiment, the projection optics enable the formation of an aerial image (AI), which is a distribution of radiation intensity on the substrate. A resist layer on the substrate is exposed, and the aerial image is transferred to the resist layer as a latent image "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 an embodiment, the simulation of the lithographic process can simulate the generation of the aerial image and / or the resist image.

[0335] Figure 32 An exemplary flow chart for modeling and / or simulating portions of a patterning process is illustrated in As will be appreciated, the models may represent different patterning processes and need not include all of the models described below.

[0336] The illumination model 31 represents the optical characteristics of the illumination pattern (including the radiation intensity distribution and / or phase distribution) used to generate the patterned radiation beam. The illumination model 31 can represent the optical characteristics of the illumination, including but not limited to: a numerical aperture setting, an illumination sigma (σ) setting, and any specific illumination pattern shape (e.g., an off-axis radiation shape such as a toroidal, quadrupole, dipole, etc.), where sigma (or σ) is the outer radial extent of the illuminator.

[0337] The projection optics model 32 represents the optical properties of the projection optics (including changes in 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 heating of components of the projection optics, stress caused by mechanical connections of components of the projection optics, etc. The projection optics model 32 may represent the optical properties of the projection optics, including one or more selected from the following: aberrations, distortion, refractive index, physical size, physical dimensions, absorptivity, etc. The optical properties of the lithographic projection apparatus (e.g., the illumination, the patterning device pattern, and the properties of the projection optics) define the aerial image. Since the patterning device pattern used in the lithographic projection apparatus can be changed, it is desirable to separate the optical properties of the patterning device pattern from the optical properties of the rest of the lithographic projection apparatus, including at least the illumination and the projection optics. The illumination model 31 and the projection optics model 32 may be combined into a transfer cross coefficient (TCC) model.

[0338] The patterning device pattern model 33 represents the optical properties (including changes in radiation intensity distribution and / or phase distribution caused by a given patterning device pattern) of a patterning device pattern (e.g., a device design layout corresponding to features of an integrated circuit, memory, electronic device, etc.), the patterning device pattern being a representation of the arrangement of features on or formed by the patterning device. The patterning device model 33 captures how the design features are arranged in the pattern of the patterning device and may include a representation of detailed physical properties of the patterning device and patterning device pattern, as described, for example, in U.S. Patent No. 7,587,704, which is incorporated by reference in its entirety.

[0339] The resist model 37 can be used to calculate the resist image from the aerial image. An example of such a resist model can be found in U.S. Patent No. 8,200,468, which is hereby incorporated by reference in its entirety. The resist model typically describes the effects of the chemical processes that occur during resist exposure, post-exposure baking (PEB), and development in order to predict, for example, the profile of the resist features formed on the substrate, and therefore is typically only related to these properties of the resist layer (e.g., the effects of the chemical processes that occur during exposure, post-exposure baking, and development). In an embodiment, the 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.

[0340] With these models, an aerial image 36 can be simulated from the illumination model 31, the projection optics model 32, and the patterning device pattern model 33. The aerial image (AI) is the radiation intensity distribution at substrate level. The optical properties of the lithographic projection apparatus (e.g., the properties of the illumination, patterning device, and projection optics) dictate the aerial image.

[0341] 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 image "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. The resist image 38 can be simulated from the aerial image 36 using a resist model 37. Therefore, in general, the connection between the optical model and the resist model is the simulated aerial image intensity within the resist layer, which is derived from the projection of radiation onto the substrate, the refraction at the resist interface, and multiple reflections in the resist film stack. The radiation intensity distribution (spatial image intensity) is transformed into a latent image "resist image" by absorbing the incident energy, and the latent image resist image is further modified by diffusion processes and various loading effects. An efficient simulation method that is fast enough for full-chip applications approximates the realistic three-dimensional intensity distribution in the resist stack by a two-dimensional aerial image (and a resist image).

[0342] In an embodiment, the resist image may be used as input to a post-pattern transfer process model 39. The post-pattern transfer process model 39 defines the performance of one or more post-resist development processes (eg, etch, CMP, etc.) and may generate a post-etch image.

[0343] Thus, the model formula describes most (if not all) known physical and chemical properties of the entire process, and each of the model parameters desirably corresponds to a different physical or chemical effect. Thus, the model formula sets an upper limit on how well the model can be used to simulate the entire manufacturing process.

[0344] The simulation of the patterning process can, for example, predict the profile, CD, edge placement (e.g., edge placement error), pattern shift, etc. in the aerial image, resist image, and / or etch image. Thus, the goal of the simulation is to accurately predict, for example, the edge placement, and / or profile, and / or pattern shift, and / or aerial image intensity slope, and / or CD, etc., of the printed pattern. These values can be compared to the intended design to, for example, correct the patterning process, identify locations where defects are predicted to occur, etc. The intended design is typically defined as a pre-OPC design layout that can be provided in a standardized digital file format such as GDSII or OASIS or other file formats.

[0345] Details of techniques and models for transforming pattern forming device patterns into various lithographic images (e.g., aerial images, resist images, etc.), and using those techniques and models to apply OPC and evaluate performance (e.g., in terms of process windows) are described in U.S. patent application publications Nos. US 2008-0301620, 2007-0050749, 2007-0031745, 2008-0309897, 2010-0162197, 2010-0180251, and 2011-0099526, the disclosures of each of which are hereby incorporated by reference in their entirety.

[0346] To facilitate evaluating the speed of the model, one or more portions, referred to as "clips," can be identified from the pattern forming device pattern. In a specific embodiment, a collection of clips is extracted, the collection representing a complex pattern in the pattern forming device pattern (typically about 50 to 1000 clips, but any number of clips can be used). As will be appreciated by those skilled in the art, these patterns or clips represent smaller portions of the design (i.e., circuits, cells, or patterns), and the clips, in particular, represent smaller portions that require special attention and / or verification. In other words, a clip can be a portion of a pattern forming device pattern, or can be similar to or have similar behavior to a portion of a pattern forming device pattern where critical features are identified empirically (including clips provided by the customer), by trial and error, or by running full chip simulations. Clips typically contain one or more test patterns or gauge patterns. An initial larger set of clips can be provided a priori by the customer based on known critical feature areas in the pattern forming device pattern that require special image optimization. Alternatively, in another embodiment, an initial large set of segments may be extracted from the entire patterning device pattern by using some automatic (such as machine vision) or manual algorithm that identifies critical feature regions.

[0347] In addition, the various patterns on the pattern forming device or the various patterns provided by the pattern forming device can have different process windows, that is, the space of process variables within which patterns within the specifications will be produced. Examples of pattern specifications related to potential systematic defects include checking for necking, line pullback, line thinning, CD, edge placement, overlap, resist top loss, resist undercut and / or bridging. The process windows of all patterns on the pattern forming device or on a region thereof can be obtained by merging the process windows of each individual pattern (e.g., overlapping the process windows). The boundaries of the process windows of all patterns contain the boundaries of the process windows of some of the individual patterns. In other words, these individual patterns limit the process windows of all patterns. These patterns can be referred to as "hot spots" or "process window limiting patterns (PWLP)", and "hot spots" or "process window limiting patterns (PWLP)" can be used interchangeably in this article. When using modeling such as that described herein to design, modify, etc., as part of a patterning process, it is possible and economical to focus on hot spots. When the hot spots are defect-free, it is most likely that all patterns are defect-free.

[0348] Returning to the modeling of the patterning process, optimization can be performed using, for example, an objective function such as

[0349]

[0350] Among them, (z1, z2, ..., z N) are N design variables or the values of the N design variables; f p (z1,z2,…,z N ) can be a set of values for the design variables (z1, z2, ..., z N ) is a function of the defect index at the pth evaluation point. p is the weight constant assigned to the pth evaluation point. A higher w may be assigned to an evaluation point or pattern that is more critical than other evaluation points or patterns. p It is also possible to assign higher w values to patterns and / or evaluation points with a greater number of occurrences. p Examples of evaluation points may be any physical point or pattern on the substrate, or any point on the patterning device pattern, or the resist image, or the aerial image.

[0351] The objective function may represent any suitable characteristic of the patterning process, such as a characteristic of the lithographic projection apparatus or substrate, e.g., focus, CD, image offset, image distortion, image rotation, etc. For example, the objective function may be a function of one or more of the following lithographic metrics: edge placement error, critical dimension, resist profile distance, worst defect size, pattern offset, random effects, three-dimensional effects of the patterning device, three-dimensional effects of the resist, optimal focus offset, pupil fill factor, exposure time, and / or throughput. Since the resist image often dictates the pattern on the substrate, the objective function often includes a function representing some characteristic of the resist image. For example, f at such an evaluation point may be a function of one or more of the following lithographic metrics: edge placement error, critical dimension, resist profile distance, worst defect size, pattern offset, random effects, three-dimensional effects of the patterning device, three-dimensional effects of the resist, optimal focus offset, pupil fill factor, exposure time, and / or throughput. p (z1,z2,…,z N ) may simply be the total number of defects in the resist image. The design variable may be any adjustable parameter such as illumination mode, patterning device pattern, projection optics, dose, focus, etc.

[0352] The lithographic apparatus may include one or more components, collectively referred to as "wavefront manipulators," that can be used to adjust the shape of the wavefront and the intensity distribution and / or phase shift of the radiation beam. The wavefront and intensity distribution can be adjusted at any location along the optical path of the lithographic projection apparatus, such as before the patterning device, near the pupil plane, near the image plane, or near the focal plane. Projection optics can be used to correct or compensate for certain distortions of the wavefront and intensity distribution caused by, for example, illumination in the lithographic projection apparatus, patterning devices, temperature changes, and / or thermal expansion of components of the lithographic projection apparatus. Adjusting the wavefront and intensity distribution can change the value of the evaluation point and the objective function. These changes can be simulated according to a model, or actually measured.

[0353] It should be noted that f p (z1,z2,…,z N ) is defined as So for example, minimizing f p (z1,z2,…,z N ) is equivalent to minimizing the objective function defined in Equation 15 Therefore, for simplicity of notation in this paper, f p (z1,z2,…,z N ) and Equation 15.

[0354] Furthermore, if the process window (PW) is maximized, the same physical part from different PW conditions may be considered as different evaluation points in the objective function in Equation 15. For example, if N PW conditions are considered, the evaluation points may be classified according to their PW conditions, and the objective function may be written as:

[0355]

[0356] in, is the set of values of the design variables (z1, z2, ..., z N ) i The objective function is a function of a defect metric at each evaluation point. When such a defect metric is the failure rate, then minimizing the above objective function is equivalent to minimizing the defects under various PW conditions, which may result in maximizing the PW. Specifically, if the PW also includes different patterning device deviations, then minimizing the above objective function also includes minimizing the mask error enhancement factor (MEEF), which is defined as the ratio between the substrate EPE and the induced patterning device pattern feature edge deviation.

[0357] The design variables may have constraints which may be expressed as (z1, z2, ..., z N )∈Z, where Z is the set of possible values for the design variables. The constraints may represent, for example, physical limitations in a hardware implementation of a lithographic projection apparatus. The constraints may include one or more selected from the following: an adjustment range, rules governing patterning device manufacturability (MRC), and / or interdependencies between two or more design variables.

[0358] Therefore, the optimization process will be under the constraints (z1, z2, ..., z N )∈Z, for example, to find a set of values of the design variables that minimizes the objective function, that is, to find the following conditions.

[0359]

[0360] Figure 33A general method for optimizing the lithographic projection apparatus according to an embodiment is illustrated in FIG. The method includes a step 302 of defining a multivariate objective function of a plurality of design variables. The design variables may include any suitable combination selected from one or more characteristics (300A) of the illumination pattern (e.g., pupil fill ratio, i.e., the percentage of the irradiated radiation that passes through the pupil or aperture), one or more characteristics (300B) of the projection optics, and / or one or more characteristics (300C) of the pattern forming device pattern. For example, the design variables may include characteristics (300A) of the illumination pattern and characteristics (300C) of the pattern forming device pattern (e.g., global deviation), but not characteristics (300B) of the projection optics, which results in SMO. Alternatively, the design variables may include characteristics (300A) of the illumination pattern, characteristics (300B) of the projection optics, and characteristics (300C) of the pattern forming device pattern, which results in optimization of the illumination, pattern forming device pattern, and projection optics (sometimes referred to as source-mask-lens optimization (SMLO)). In step 304, the design variables are adjusted simultaneously so that the objective function moves towards convergence. In step 306, it is determined whether a predefined termination condition is met. The predetermined termination condition may include various possibilities, for example, the objective function is minimized or maximized as required by the numerical technique used; the value of the objective function is equal to or exceeds a threshold, the value of the objective function is within a preset error limit, and / or a preset number of iterations of the objective function evaluation is reached. If the termination condition is met in step 306, the method ends. If the termination condition is not met in step 306, steps 304 and 306 are iteratively repeated until the desired result is obtained. Optimization does not necessarily result in a single set of values for the design variables, as there may be physical constraints caused by factors such as pupil fill factor, resist chemistry, throughput, etc. Optimization can provide multiple sets of values for the design variables and associated performance characteristics (e.g., throughput), and allow a user of the lithographic apparatus to obtain one or more sets.

[0361] In embodiments, instead of calculating and / or determining the effects on the optical properties of the illumination system and / or projection optics, or in addition to calculating and / or determining the effects on the optical properties of the illumination system and / or projection optics, it is contemplated that adjustable optical properties of the illumination system and / or projection optics may also be included in the design variables. Exemplary adjustable optical properties may include one or more lens manipulators, temperature data or signals associated with temperature data of one or more devices or components (e.g., heaters) for controlling the temperature of optical elements of the illumination system and / or projection system, one or more Zernike coefficients, etc. The SMO or SMLO process may then be performed, and the design variables including the adjustable optical properties may be adjusted simultaneously such that the objective function moves toward convergence.

[0362] exist Figure 33 In the embodiment of the present invention, the optimization of all design variables is performed simultaneously. This process can be referred to as simultaneous optimization, joint optimization, or co-optimization. As used herein, the terms "simultaneously," "simultaneously," "jointly," and "jointly" mean that the design variables of the illumination mode, the patterning device, the characteristics of the projection optics, and / or any other design variables are allowed to be changed simultaneously.

[0363] Alternatively, the optimization of all design variables is performed alternately, as Figure 34 In this process, in each step, some design variables are fixed, while other design variables are optimized as part of the evaluation of the objective function; then in the next step, a different set of variables is fixed, while other variables are optimized as part of the evaluation of the objective function. These steps are performed alternately until convergence or some termination condition is met. Figure 34 As shown in the non-limiting example flow chart of FIG, first, a patterning device pattern is obtained (step 402), followed by an illumination pattern optimization step in step 404, wherein all design variables of the illumination pattern are optimized (SO) as part of the evaluation of a suitable objective function, while all other design variables are fixed. Then, in the next step 406, mask optimization (MO) is performed, wherein all design variables of the patterning device are optimized as part of the evaluation of a suitable objective function, while all other design variables are fixed. These two steps are performed alternately until some termination condition is met in step 408. Various termination conditions can be used, such as the value of the objective function becoming equal to a threshold, the value of the objective function exceeding a threshold, the value of the objective function falling within a preset error limit, or a preset number of iterations of the evaluation of the objective function. It should be noted that the SO-MO alternating optimization is used as an example of an alternative process. The alternative process can take many different forms, such as a SO-LO-MO alternating optimization, wherein SO, lens optimization (LO), and MO are performed alternately and iteratively; or SMO can be performed once, followed by LO and MO alternately and iteratively; and so on. Finally, the output of the optimization results is obtained in step 410 and the process stops.

[0364] As previously discussed, the pattern selection algorithm can be integrated with simultaneous or alternating optimization. For example, when employing alternating optimization, full-chip SO can be performed first, "hot spots" and / or "warm spots" identified, and then MO can be performed. In light of the present disclosure, numerous permutations and combinations of sub-optimizations are possible to achieve the desired optimization results.

[0365] Figure 35An exemplary optimization method is shown in which an objective function is defined and evaluated. In step 502, initial values of the design variables are obtained, including the adjustment ranges of the design variables (if any). In step 504, a multivariate objective function is set. In step 506, the objective function is expanded in a sufficiently small neighborhood around the starting values of the design variables for the first iteration step (i=0). In step 508, standard multivariate optimization techniques are applied to minimize or maximize the objective function. It should be noted that the optimization can have constraints, such as adjustment ranges, during the optimization process in 508 or at a later stage in the optimization process. For the identified evaluation points that have been selected for optimizing the lithography process, each iteration is evaluated using a given test pattern (also referred to as a "gauge"). In step 510, the lithography response (e.g., one or more certain characteristics of the aerial image, one or more certain characteristics of the resist image, or one or more certain characteristics of the lithography process, such as the process window) is predicted. In step 512, the results of step 510 are compared with the expected or ideal lithography response value. If the termination condition is met in step 514, that is, the optimization produces a lithographic response value that is sufficiently close to the desired value, the final value of the design variable is output in step 518. The output step may also include using the final value of the design variable to output other functions, such as outputting a wavefront aberration adjustment map at the pupil plane (or other plane), an optimized illumination mode map, an optimized patterning device pattern (e.g., including optical proximity effect correction), etc. If the termination condition is not met, then in step 516, the value of the design variable is updated using the result of the i-th iteration, and the process returns to step 506. Algorithms such as Gauss-Newton algorithm, Levenberg-Marquardt algorithm, gradient descent algorithm, simulated annealing algorithm, genetic algorithm, etc. can be applied to evaluate and solve the objective function.

[0366] Optimizing the patterning process can expand the process window. A larger process window provides more flexibility in process design and device design. The process window can be defined as a set of focal lengths and dose values that keep the resist image within a certain limit of the design target of the resist image. It should be noted that all methods discussed here can also be extended to a generalized process window definition that can be established by different or additional base parameters other than or removing exposure dose and defocus. These base parameters can include, but are not limited to, optical settings such as NA, optical sigma, optical aberrations, polarization, or optical constants of the resist layer. For example, as described earlier, if PW also involves different mask deviations, optimization can include minimizing MEEF. The process window defined on focal length and dose values is only used as an example in this disclosure.

[0367] The following describes a method for maximizing the process window according to an embodiment. In a first step, starting from the known conditions (f0, ε0) in the process window, where f0 is the nominal focal length and ε0 is the nominal dose, the following performs minimization of one of the exemplary objective functions in the neighborhood (f0±Δf, ε0±ε):

[0368] or

[0369]

[0370] If the nominal focal length f0 and nominal dose ε0 are allowed to shift, then the design variables (z1, z2, ..., z N ) jointly optimizes the nominal focal length and nominal dose. In the next step, if a set of values (z1, z2, ..., z N , f, ε) makes the objective function within the preset limits, then accept (f0±Δf, ε0±ε) as part of the process window.

[0371] Alternatively, if focus and dose drift are not allowed, the design variables (z1, z2, ..., z N In an alternative embodiment, if a set of values (z1, z2, ..., z N ), so that the objective function is within the preset limits, then (f0±Δf, ε0±ε) is accepted as part of the process window.

[0372] The methods described earlier in this disclosure can be used to minimize the corresponding objective functions of equations (18) or (19). If the design variables are characteristics of the projection optics, such as Zernike coefficients, then minimizing the objective functions of equations (18) or (19) results in maximizing the process window based on projection optics optimization (i.e., LO). If the design variables are characteristics of the illumination mode and the patterning device pattern in addition to the characteristics of the projection optics, then minimizing the objective functions of equations (18) or (19) results in maximizing the process window based on SMLO. If the design variables are characteristics of the illumination mode and the patterning device pattern, then minimizing the objective functions of equations (18) or (19) results in maximizing the process window based on SMO.

[0373] The optimization described above can be used to find a set of values (z1, z2, ..., z N ). Multiple optimizations can be performed successively for different physical effects, for different components of the lithographic apparatus, and under different conditions.

[0374] Methods related to the source / mask / source-mask optimization discussed above include the use of a linearization function selected to optimize the printed wafer profile across the entire process window. The merit function is typically based on a purely optical model, as the optics in the lithography system tend to determine most of the process constraints. In one example, the merit function can be selected to reduce the worst edge placement error of the design layout across the entire process window.

[0375] Figure 36 1 is a block diagram illustrating a computer system 100 that can assist in implementing the methods and processes disclosed herein. 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 bus 102 for processing information. Computer system 100 also includes a main memory 106, such as a random access memory (RAM) or other dynamic storage device, coupled to bus 102 for storing information and instructions to be executed by processor 104. Main memory 106 can also be used to store temporary variables or other intermediate information during the execution of instructions to be executed by processor 104. Computer system 100 also includes a read-only memory (ROM) 108 or other static storage device coupled to bus 102 for storing static information and instructions for processor 104. Storage device 110, such as a magnetic disk or optical disk, is provided and coupled to bus 102 for storing information and instructions.

[0376] The computer system 100 can be coupled to a display 112, such as a cathode ray tube (CRT) or a flat panel display or a touch panel display, via the bus 102 for displaying information to a computer user. An input device 114 including alphanumeric keys and other keys is coupled to the bus 102 for communicating information and command selections to the processor 104. Another type of user input device is a cursor control 116, such as a mouse, trackball, or cursor direction keys, for communicating directional information and command selections to the processor 104 and for controlling cursor movement on the display 112. Such an input device typically has two degrees of freedom on two axes, a first axis (e.g., x) and a second axis (e.g., y), which allow the device to specify a position in a plane. A touch panel (screen) display can also be used as an input device.

[0377] According to one embodiment, portions of a process may be performed by computer system 100 in response to processor 104 executing one or more sequences of one or more instructions contained in main memory 106. These instructions may be read into main memory 106 from another computer-readable medium, such as storage device 110. Execution of the sequences of instructions contained in main memory 106 causes processor 104 to perform the process steps described herein. One or more processors in a multi-processing arrangement may also be used to execute the sequences of instructions contained in main memory 106. In alternative embodiments, hardwired circuitry may be used in place of or in combination with software instructions. Thus, the description herein is not limited to any specific combination of hardware circuitry and software.

[0378] As used herein, the term "computer-readable medium" refers to any medium that participates in providing instructions to processor 104 for execution. Such media can take many forms, including but not limited to non-volatile media, volatile media, and transmission media. Non-volatile media include, for example, optical or magnetic disks, such as storage device 110. Volatile media include volatile memory, such as main memory 106. Transmission media include coaxial cables, copper wire, and optical fibers, including the wires comprising bus 102. Transmission media can also take the form of sound waves 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 tape, any other magnetic media, CD-ROMs, DVDs, any other optical media, punch cards, paper tape, any other physical media with a pattern of holes, RAM, PROMs and EPROMs, FLASH-EPROMs, any other memory chips or cartridges, carrier waves as described below, or any other medium that can be read by a computer.

[0379] Various forms of computer-readable media are 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 of a remote computer. The remote computer may load the instructions into its dynamic memory and send the instructions over a telephone line using a modem. A modem local to computer system 100 may receive the data on the telephone line and convert the data into an infrared signal using an infrared transmitter. An infrared detector coupled to bus 102 may receive the data carried in the infrared signal and place the data on bus 102. Bus 102 carries the data to main memory 106, from which processor 104 retrieves and executes the instructions. The instructions received by main memory 106 may optionally be stored on storage device 110 before or after execution by processor 104.

[0380] The computer system 100 also desirably includes a communication interface 118 coupled to the bus 102. The communication interface 118 provides a two-way data communication coupling to a network link 120 connected to a local area network 122. For example, the communication interface 118 can be an integrated services digital network (ISDN) card or a modem to provide a data communication connection to a corresponding type of telephone line. As another example, the communication interface 118 can be a local area network (LAN) card to provide a data communication connection to a compatible LAN. A wireless link can also be implemented. 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.

[0381] The network link 120 typically provides data communication to other data devices through one or more networks. For example, the network link 120 can provide a connection through a local area network 122 to a host computer 124 or to data equipment operated by an Internet service provider (ISP) 126. The ISP 126, in turn, provides data communication services through the global packet data communication network, now commonly referred to as the "Internet" 128. Both the local area network 122 and the Internet 128 use electrical, electromagnetic, or optical signals that carry digital data streams. The signals through the various networks and the signals on the network link 120 and through the communication interface 118, which carry the digital data to and from the computer system 100, are exemplary forms of carrier waves transporting the information.

[0382] Computer system 100 can send messages and receive data, including process code, via one or more networks, network link 120, and communication interface 118. In the example of the Internet, server 130 can transmit the requested code for an application via Internet 128, ISP 126, local area network 122, and communication interface 118. For example, one such downloaded application can provide illumination optimization of an embodiment. The received code can be executed by processor 104 as it is received and / or stored in storage device 110 or other non-volatile storage for later execution. In this manner, computer system 100 can obtain application code in the form of a carrier wave.

[0383] Figure 37 Another exemplary lithographic projection apparatus LA is schematically depicted comprising:

[0384] - A source collector module SO for providing radiation.

[0385] - an illumination system (illuminator) IL configured to condition the radiation beam B (eg EUV radiation) coming from the source collector module SO.

[0386] a support structure (e.g., mask table) MT configured to support a patterning device (e.g., mask or reticle) MA and connected to a first positioner PM configured to accurately position the patterning device;

[0387] a substrate table (e.g. wafer stage) WT configured to hold a substrate (e.g. a resist-coated wafer) W and connected to a second positioner PW configured to accurately position the substrate; and

[0388] - a projection system (eg, a reflective projection system) PS configured to project the pattern imparted to the radiation beam B by the patterning device MA onto a target portion C of the substrate W (eg, comprising one or more dies).

[0389] As depicted here, device LA is of the reflective type (e.g., using a reflective mask). Note that because most materials absorb in the EUV wavelength range, the patterning device can have a multilayer reflector comprising, for example, a multilayer stack of molybdenum and silicon. In one example, the multilayer reflector has 40 layer pairs of molybdenum and silicon, where each layer is a quarter wavelength thick. X-ray lithography can be used to produce smaller wavelengths. Because most materials absorb in EUV and x-ray wavelengths, a thin sheet of patterned absorbing material on the patterning device topography (e.g., a TaN absorber on top of the multilayer reflector) defines where features will be printed (positive resist) or where they will not be printed (negative resist).

[0390] refer to Figure 26 , the illuminator IL receives a beam of extreme ultraviolet radiation from a source collector module SO. Methods for generating EUV radiation include, but are not necessarily limited to, converting a material into a plasma state having at least one element, such as xenon, lithium, or tin, using one or more emission lines in the EUV range. In one such method, often referred to as laser produced plasma ("LPP"), a plasma may be generated by irradiating a fuel (such as a droplet, stream, or cluster of material having a line emitting element) with a laser beam. The source collector module SO may be a laser ( Figure 26 The laser is used as part of an EUV radiation system (not shown) for providing a laser beam that excites the fuel. The resulting plasma emits output radiation, such as 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 the laser beam for fuel excitation, the laser and source collector module may be separate entities.

[0391] In these cases, the laser is not considered to form part of the lithographic apparatus, and the radiation beam is delivered from the laser to the source collector module by means of a beam delivery system comprising, for example, suitable directing mirrors and / or a beam expander. In other cases, such as when the radiation source is a discharge produced plasma EUV generator, often referred to as a DPP radiation source, the radiation source may be an integral part of the source collector module.

[0392] The illuminator IL may include an adjuster for adjusting the angular intensity distribution of the radiation beam. Typically, at least the outer radial extent and / or the inner radial extent (commonly referred to as σ-outer and σ-inner, respectively) of the intensity distribution in a pupil plane of the illuminator can be adjusted. In addition, the illuminator IL may include various other components, such as a faceted field mirror arrangement and a faceted pupil mirror arrangement. The illuminator can be used to condition the radiation beam to have a desired uniformity and intensity distribution in the cross-section of the radiation beam.

[0393] A radiation beam B is incident on a patterning device (e.g., mask) MA, which is held on a support structure (e.g., mask table) MT, and is patterned by the patterning device. After reflection from the patterning device (e.g., mask) MA, the radiation beam B passes through a projection system PS, which focuses the beam onto a target portion C of the substrate W. With the aid of a second positioner PW and a position sensor PS2 (e.g., an interferometry device, a linear encoder, or a capacitive sensor), the substrate table WT can be accurately moved, for example, to position a different target portion C in the path of the radiation beam B. Similarly, a first positioner PM and a further position sensor PS1 can be used to accurately position the patterning device (e.g., mask) MA relative to the path of the radiation beam B. The patterning device (e.g., mask) MA and the substrate W can be aligned using patterning device alignment marks M1, M2 and substrate alignment marks P1, P2.

[0394] The depicted device LA can be used in at least one of the following modes:

[0395] 1. In step mode, the entire pattern imparted to the radiation beam is projected at once onto a target portion C while the support structure (e.g. mask table) MT and substrate table WT are held essentially stationary (i.e. a single static exposure). Subsequently, the substrate table WT is shifted in the X and / or Y direction so that a different target portion C can be exposed.

[0396] 2. In scan mode, the support structure (e.g. mask table) MT and substrate table WT are scanned synchronously while projecting a pattern imparted to the radiation beam onto a target portion C (i.e. a single dynamic exposure). The speed and direction of the substrate table WT relative to the support structure (e.g. mask table) MT may be determined by the (de-)magnification and image reversal characteristics of the projection system PS.

[0397] 3. In another mode, the support structure (e.g., mask table) MT is held essentially stationary, thereby holding the programmable patterning device, and the substrate table WT is moved or scanned while a pattern imparted to the radiation beam is projected onto a target portion C. In this mode, a pulsed radiation source is typically used, and the programmable patterning device is updated as required after each movement of the substrate table WT or between successive radiation pulses during a scan. This mode of operation can be readily applied to maskless lithography using a programmable patterning device, such as a programmable mirror array of the type mentioned above.

[0398] Figure 38 The apparatus LA is shown in more detail and comprises a source collector module SO, an illumination system IL and a projection system PS. The source collector module SO is constructed and arranged so that a vacuum environment can be maintained in an enclosure 220 of the source collector module SO. An EUV radiation emitting plasma 210 can be formed by generating a plasma radiation source by discharge. EUV radiation can be generated by a gas or vapor (e.g., Xe gas, Li vapor or Sn vapor), wherein a very hot plasma 210 is generated to emit radiation in the EUV range of the electromagnetic spectrum. The very hot plasma 210 is generated, for example, by a discharge causing an at least partially ionized plasma. For efficient generation of radiation, a partial pressure of, for example, 10 Pa of Xe, Li, Sn vapor or any other suitable gas or vapor may be required. In an embodiment, an excited tin (Sn) plasma is provided to generate EUV radiation.

[0399] The radiation emitted by the hot plasma 210 is transferred from the source chamber 211 to the collector chamber 212 through an optional gas barrier or contaminant trap 230 (also referred to as a contaminant barrier or foil trap in some cases) positioned in or behind an opening in the source chamber 211. The contaminant trap 230 may include a channel structure. The contaminant trap 230 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 barrier 230, further referred to herein, includes at least a channel structure.

[0400] The collector chamber 211 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 251 and a downstream radiation collector side 252. Radiation traversing the collector CO may be reflected from the grating spectral filter 240 to be focused along the optical axis indicated by the dotted line "O" into a virtual source point IF. The virtual source point IF is often referred to as the intermediate focal length, and the source collector module is arranged so that the intermediate focal length IF is located at or near an opening 221 in the enclosure structure 220. The virtual source point IF is an image of the radiation emitting plasma 210.

[0401] The radiation then traverses an illumination system IL, which may include a faceted field mirror arrangement 22 and a faceted pupil mirror arrangement 24 arranged to provide a desired angular distribution of the radiation beam 21 at the patterning device MA, and a desired uniformity of radiation intensity at the patterning device MA. After reflection of the radiation beam 21 at the patterning device MA, which is held by the support structure MT, a patterned beam 26 is formed and is imaged by the projection system PS via reflective elements 28, 30 onto a substrate W held by a substrate table WT.

[0402] Typically, more elements than shown may be present in the illumination optics unit IL and the projection system PS. Depending on the type of lithographic apparatus, a grating spectral filter 240 may optionally be present. Additionally, more mirrors than shown may be present, for example, more than 100 mirrors may be present in the projection system PS. Figure 38 The reflective elements shown have 1 to 6 additional reflective elements.

[0403] like Figure 38 The collector optics CO illustrated in FIG2 is depicted as a nested collector with grazing incidence reflectors 253, 254, and 255, merely as an example of a collector (or collector mirror). The grazing incidence reflectors 253, 254, and 255 are arranged axially symmetrically about the optical axis O, and this type of collector optics CO is desirably used in combination with a discharge produced plasma radiation source.

[0404] Alternatively, the source collector module SO may be as follows Figure 39 . The laser LAS is arranged to deposit laser energy into a fuel such as xenon (Xe), tin (Sn) or lithium (Li), thereby generating a highly ionized plasma 210 with an electron temperature of tens of eV. The high-energy radiation generated during the deexcitation and recombination of these ions is emitted from the plasma, collected by the near normal incidence collector optics CO, and focused onto an opening 221 in the enclosure 220.

[0405] The concepts disclosed herein can simulate or mathematically model any general imaging system for imaging sub-wavelength features and may be particularly useful in emerging imaging technologies that are capable of producing wavelengths with increasingly smaller dimensions. Emerging technologies already in use include EUV (extreme ultraviolet) lithography, which can produce wavelengths of 193 nm using ArF lasers and even 157 nm using fluorine lasers. In addition, EUV lithography can produce wavelengths in the range of 20 nm to 5 nm using synchrotrons or by using high-energy electrons to impinge on materials (solids or plasmas) to produce photons in this range.

[0406] While the concepts disclosed herein may be used for imaging on substrates such as silicon wafers, it should be understood that the disclosed concepts may be used with any type of lithographic imaging system, for example, a lithographic imaging system for imaging on substrates other than silicon wafers.

[0407] Although specific reference may be made herein to the use of embodiments in IC manufacturing, it should be understood that the embodiments herein may have many other possible applications. For example, the embodiments herein may be used to manufacture integrated optical systems, guidance and detection patterns for magnetic domain memories, liquid crystal displays (LCDs), thin film heads, micromechanical systems (MEMs), and the like. Those skilled in the art will appreciate that, in the context of such alternative applications, any use of the terms "reticle," "wafer," or "die" herein may be considered synonymous with or interchangeable with the more general terms "patterning device," "substrate," or "target portion," respectively. The substrates mentioned herein may be processed before or after exposure in, for example, a coating and developing system (a tool that typically applies a resist layer to a substrate and develops the exposed resist) or a measurement or inspection tool. Where applicable, the disclosure herein may be applied to these and other substrate processing tools. In addition, a substrate may be processed more than once, for example, to produce a multi-layer IC, such that the term substrate used herein may also refer to a substrate comprising multiple processed layers.

[0408] In this disclosure, the terms "radiation" and "beam" as used herein encompass all types of electromagnetic radiation, including ultraviolet radiation (e.g., having a wavelength of about 365 nm, about 248 nm, about 193 nm, about 157 nm, or about 126 nm) and extreme ultraviolet (EUV) radiation (e.g., having a wavelength in the range of 5 nm to 20 nm), as well as particle beams, such as ion beams or electron beams.

[0409] As used herein, the term "optimizing" or "optimization" refers to or means adjusting a pattern forming device (e.g., a lithographic device), a patterning process, or the like so that the result and / or process has more desired characteristics, such as a higher accuracy of projection of the design pattern on the substrate, a larger process window, or the like. Thus, as used herein, the terms "optimization" and "optimized" refer to or mean a process of identifying one or more values of one or more parameters that provide an improvement in at least one relevant indicator, such as a local optimum, compared to an initial set of one or more values of those one or more parameters. "Optimal" and other related terms should be interpreted accordingly. In an embodiment, the optimization step can be applied iteratively to provide further improvement in one or more indicators.

[0410] Aspects of the present invention may be implemented in any convenient form. For example, an embodiment may be implemented by one or more appropriate computer programs, which may be carried on an appropriate carrier medium that may be a tangible carrier medium (e.g., a disk) or an intangible carrier medium (e.g., a communication signal). An embodiment of the present invention may be implemented using a suitable device that can specifically take the form of a programmable computer, which runs a computer program arranged to implement the method as described herein. Therefore, the embodiments of the present disclosure may be implemented in hardware, firmware, software, or any combination thereof. The embodiments of the present disclosure may also be implemented as instructions stored on a machine-readable medium, which 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 that can be read by a machine (e.g., a computing device). For example, a machine-readable medium may include: read-only memory (ROM); random access memory (RAM); magnetic disk storage media; optical storage media; flash memory devices; electrical, optical, acoustic, or other forms of propagation signals (e.g., carrier waves, infrared signals, digital signals, etc.); and the like. In addition, firmware, software, routines, instructions may be described herein as performing certain actions. However, it should be understood that these descriptions are for convenience only and that these actions actually result from a computing device, processor, controller, or other device executing firmware, software, routines, instructions, etc.

[0411] The embodiments of the present invention can be further described through the following aspects.

[0412] 1. A method for calibrating a simulation process, the method comprising:

[0413] obtaining (i) a characteristic limit of a characteristic of the printed pattern based on a threshold failure rate of the printed pattern, and obtaining (ii) a reference process window based on the characteristic limit; and

[0414] Calibrating the simulation process so that the simulated process window is within an acceptable threshold of the reference process window, calibrating the simulation process includes:

[0415] executing one or more process models to determine a simulated pattern; and

[0416] Parameter values associated with the one or more process models are adjusted based on the characteristics of the simulated pattern and the characteristic limits.

[0417] 2. A method according to aspect 1, wherein the simulation process includes: a source mask optimization process and an optical proximity effect correction process, wherein the source mask optimization process and the optical proximity effect correction process are configured to adjust mask parameters, source parameters or process parameters so that the printed pattern is within an acceptable threshold of a target characteristic value.

[0418] 3. The method of clause 1, wherein the one or more process models include a characteristic model that is fitted based on the simulated pattern and the characteristic limits associated with the printed pattern.

[0419] 4. The method according to clause 3, wherein the characteristic model is determined by fitting parameters of the characteristic model based on the characteristics of the simulated pattern and the characteristics of the printed pattern.

[0420] 5. A method according to aspect 4, wherein the characteristics of the simulated pattern and the printed pattern are critical dimensions, edge placement errors between two patterns on different layers of a substrate, or pattern placement errors between two patterns on the same layer or different layers of the substrate.

[0421] 6. The method of clause 5, wherein the simulated pattern comprises an outline of the pattern within a layer of the substrate.

[0422] 7. The method of clause 6, wherein the characteristic of the simulated pattern comprises a difference between a first characteristic at a top portion of the layer and a second characteristic at a bottom portion of the layer.

[0423] 8. The method of clause 1, wherein the parameters of the one or more process models include one or more of:

[0424] Parameters of the characteristic model;

[0425] spatial image parameters associated with a spatial model associated with the patterning process;

[0426] Resist parameters associated with a resist model associated with the patterning process; and

[0427] Etch parameters associated with an etch model associated with the patterning process.

[0428] 9. The method of clause 8, wherein the parameters of the one or more process models include one or more parameters selected from blurriness of an aerial image, resist thickness, or resist-related absorption.

[0429] 10. The method of clause 1, wherein obtaining the characteristic limit of the characteristic of the printed pattern comprises:

[0430] Printing a selected pattern of a target layout onto a substrate via a photolithography apparatus;

[0431] determining a failure rate for each selected pattern based on inspection data of the printed pattern;

[0432] fitting a failure rate model based on the failure rate and the characteristic of each selected pattern, the failure rate model being configured to determine a failure rate associated with the characteristic of the pattern; and

[0433] The failure rate model is executed to determine the characteristic limits of the characteristic of the selected pattern such that the threshold failure rate is met.

[0434] 11. The method according to clause 1, wherein obtaining the reference process window comprises:

[0435] Based on inspection data associated with the printed substrate, values of dose and focus corresponding to the characteristic that satisfy the characteristic limits are determined for each selected pattern.

[0436] 12. The method according to aspect 1, wherein the calibrating the simulation process is an iterative process, the iteration comprising:

[0437] (a) executing the one or more process models using a selected pattern to be printed on a substrate to determine the simulated pattern on the substrate;

[0438] (b) adjusting the values of the parameters associated with the one or more process models so that the characteristics of the simulated pattern meet the characteristic limits associated with the selected pattern;

[0439] (c) determining the simulated process window based on the characteristics of the simulated pattern and whether the simulated process window is within an acceptable threshold of the reference process window; and

[0440] (d) In response to the acceptability threshold not being met, performing steps (a) to (c).

[0441] 13. The method of clause 1, wherein adjusting the parameters of the one or more process models comprises:

[0442] Values of parameters associated with the characteristic model are adjusted so as to maximize a margin between the characteristic of the simulated pattern at a top and the characteristic of the simulated pattern at a bottom with respect to the characteristic limit.

[0443] 14. The method according to aspect 1, further comprising:

[0444] obtaining a set of hot spot patterns, each hot spot pattern being a user-selected pattern from a target layout and / or a pattern associated with a relatively higher probability of failure compared to other patterns of the target layout;

[0445] determining a defect-based process window for each hot spot pattern by simulating the calibrated simulation process using the set of hot spot patterns and the failure rate model; and

[0446] Based on the superposition of each defect-based process window, optimal values of one or more process variables associated with the threshold failure rate are determined.

[0447] 15. The method of clause 14, wherein the one or more process variables are selected from the group consisting of: optimal focus, optimal dose, a dose-focus window characterized by the threshold failure rate, aberrations of a lens system, a level setting, an overlay setting.

[0448] 16. The method according to aspect 1, further comprising:

[0449] determining a yield rate associated with each hot spot pattern based on the failure rate model;

[0450] The overall yield of the full chip layout is determined by calculating the product of each yield associated with each hot spot pattern across the entire full chip layout.

[0451] 17. The method according to aspect 1, further comprising:

[0452] determining, by simulating the calibrated simulation process, whether the margin can be used to adjust a characteristic of the retargeted pattern to result in a target characteristic value being printed on the substrate; and

[0453] In response to the margin being unavailable, adjustments to processes associated with the patterning process are determined via simulating the calibrated simulation process using the retargeted pattern so that the target characteristic value will be printed on the substrate.

[0454] 18. The method of clause 17, wherein adjusting the process comprises at least one of adjusting an etch bias at the developed image, including an isotropic etch back or spacer process, an amount of process loading, an etch rate, a deposition rate, and an angle of incidence for etching or deposition.

[0455] 19. The method according to aspect 1, further comprising:

[0456] simulating the calibrated simulation process using a full chip layout to determine a residual error between a simulated characteristic value associated with the full chip layout and a target characteristic value;

[0457] determining, via lithographic manufacturing inspection, whether the analog characteristic values associated with the full chip layout meet a desired yield; and

[0458] In response to the desired yield not being met, source parameters, mask parameters, or process parameters are adjusted via the calibrated simulation process to reduce the residual error so that the desired yield is met.

[0459] 20. A method for generating a retargeting pattern associated with a patterning process, the method comprising:

[0460] obtaining (i) characteristic limits associated with a target pattern, the characteristic limits being values of a characteristic beyond which a printed pattern corresponding to the target pattern is considered defective, and (ii) a source mask optimization (SMO) process configured to calculate dose and / or mask parameters based on a threshold failure rate associated with the characteristic of the target pattern; and

[0461] The retargeted pattern is generated by simulating the source mask optimization process using the target pattern, the characteristics associated with the retargeted pattern falling further within the characteristic limits associated with the target pattern.

[0462] 21. The method of clause 20, wherein the characteristic limits are obtained based on a failure rate model, the failure rate model being calibrated using failure rate data associated with the printed pattern on a substrate and the threshold failure rate, the printing being performed using initial SMO data.

[0463] 22. The method of clause 20, wherein obtaining the source mask optimization (SMO) process comprises:

[0464] A dose drift equation is included to calculate the dose based on the probability density function (PDF) of the characteristic, the local critical dimension uniformity, the dose sensitivity of the characteristic of the pattern, and the threshold failure rate.

[0465] 23. The method of aspect 22, wherein the dose drift equation is given by:

[0466]

[0467] Among them, dose EV Indicates the failure rate at the threshold FR target The dose value under the extreme drift associated with the characteristic value at 3 standard deviations from the mean characteristic value, NDS is the dose sensitivity of the characteristic of the pattern, LCDU dose 3σ represents the variation associated with the value of a property at 3 standard deviations from the mean property value and at a particular dose, and CDF represents the cumulative distribution function of the PDF of the property.

[0468] 24. The method according to aspect 22, wherein the dose drift equation is given by:

[0469]

[0470] Among them, dose EV Indicates the failure rate at the threshold FR target The dose value under the extreme drift associated with the characteristic value at 3 standard deviations from the mean characteristic value, NDS is the dose sensitivity of the characteristic of the pattern, LCDU dose Indicates the change in the property at a specific dose, LCDU total represents the total variation of the characteristic of the pattern, LCDU dose 3σ represents the variation associated with the value of a property at 3 standard deviations from the mean property value and at a particular dose, and CDF represents the cumulative distribution function of the PDF of the property.

[0471] 25. The method of clause 20, wherein obtaining the source mask optimization (SMO) process comprises:

[0472] A mask deviation drift equation is included to calculate the mask characteristic based on the probability density function (PDF) of the characteristic, the local CD uniformity caused by the mask deviation, and the threshold failure rate.

[0473] 26. The method of clause 25, wherein the mask bias drift equation is given by:

[0474]

[0475] Among them, mask EV Indicates the failure rate at the threshold FR targetThe mask deviation under extreme drift associated with the characteristic value at 3 standard deviations from the mean characteristic value, LCDU mask@W is the change in characteristics associated with the resist pattern due to the mask deviation, LCDU total represents the total variation of the characteristic of the pattern, and CDF represents the cumulative distribution function of the PDF of the characteristic.

[0476] 27. The method of clause 20, wherein generating the retargeting pattern such that a margin associated with the characteristic limit at the threshold failure rate is increased, generating the retargeting pattern comprises:

[0477] simulating the source mask optimization process using initial SMO data to determine a drift in characteristics associated with the target pattern at the threshold failure rate;

[0478] determining a margin between the characteristic limit and the drift at the threshold failure rate; and

[0479] A characteristic value of the target pattern is adjusted so that the margin increases without exceeding the characteristic limit associated with the target pattern, and the adjusted characteristic value is used to generate the retargeting pattern.

[0480] 28. The method of clause 20, wherein generating the retargeting pattern is an iterative process, the iterations comprising:

[0481] (a) simulating the source mask optimization process using initial SMO data including optimized source and optimized mask parameters and an initial target pattern or a retargeted pattern as input to determine a drift of a characteristic associated with the target pattern at the threshold failure rate;

[0482] (b) determining a margin between the characteristic limit and the drift of the characteristic at the threshold failure rate;

[0483] (c) adjusting a characteristic value of the target pattern so that the margin increases without exceeding the characteristic limit associated with the target pattern, the adjusted characteristic value being used to generate the retargeting pattern; and

[0484] (d) In response to the margin exceeding the characteristic limit or not being maximized, performing steps (a) to (c).

[0485] 29. The method of aspect 28, wherein a margin between the characteristic limit of the characteristic and an extreme value of the characteristic, the extreme value of the characteristic being a value caused by a contributing factor from one or more process variables at the threshold failure rate, is maximized.

[0486] 30. The method of clause 20, wherein the extreme values of the characteristic are caused by focus, dose, moving standard deviation (MSD) of the error between a measured value and a target value, resist thickness, and / or resist components including an acid or a quencher.

[0487] 31. The method of aspect 20, further comprising:

[0488] simulating the source mask optimization (SMO) process using the retargeted pattern to determine simulated characteristic values associated with a full chip layout;

[0489] determining, via lithographic manufacturing inspection, whether the analog characteristic values associated with the full chip layout meet a desired yield; and

[0490] In response to the desired yield not being met, source parameters, mask parameters or process parameters are adjusted so that the desired yield is met, and the adjusted source parameters, mask parameters or process parameters are used to generate an optimized source, an optimized illumination pupil and / or an optimized mask.

[0491] 32. A method for adjusting a process window, comprising:

[0492] obtaining (i) a dose probability density function (dose PDF) for determining a probability of a dose and (ii) a mask probability density function (mask PDF), the dose PDF being a function of (a) a characteristic of a feature and (b) a deviation of a mask characteristic associated with a mask used to print the feature on a substrate, the mask probability density function for determining the probability of the deviation of the mask characteristic;

[0493] determining the probability density function associated with the characteristic by convolving (i) the dose PDF with (ii) the mask PDF over a given range of mask characteristic values; and

[0494] A process window associated with the patterning process is adjusted based on the determined probability density function associated with the characteristic.

[0495] 33. A method according to clause 32, wherein the mask PDF includes a nonlinear mask error enhancement factor (MEEF) dependency that causes skewness of the mask PDF, wherein the nonlinear MEEF is calculated using an inverse function of the relationship between the mask characteristics and the characteristics printed on the substrate.

[0496] 34. The method of clause 33, wherein the mask PDF can be calculated by:

[0497]

[0498] Among them, G mask is the Gaussian distribution of the mask characteristics, and G is calculated based on the inverse function of the relationship between the mask characteristics and the characteristics printed on the substrate. mask The average value μ mask , the inverse function is given by g mask (δCD mask ) indicates that G mask The standard deviation of mask ,σ mask is based on the inverse function and the standard deviation of the measured value δCD mask The standard deviation is determined, and The nonlinear MEEF is determined.

[0499] 35. The method of clause 32, wherein the dose PDF includes a dependency on a local critical dimension uniformity (LCDU) associated with a resist pattern on the substrate, the LCDU being caused by the mask characteristics.

[0500] 36. A method according to clause 35, wherein the dose PDF is determined using a normal distribution or a Poisson distribution having a mean dose and a dose standard deviation, the mean dose is determined by an inverse function of the relationship between the dose and CD for a given deviation of the mask characteristic, and the dose standard deviation is determined by an LCDU caused by the mask characteristic based on the resist pattern on the substrate.

[0501] 37. The method of aspect 36, wherein the dose PDF can be calculated by the following formula:

[0502] PDF dose (g d (CD, δCD mask ); μ d (δCD mask ), σ d (δCD mask ))

[0503] wherein a given deviation δCD of the feature for the mask characteristic is used mask The dose g is determined by the inverse function of the relationship between the dose and the characteristic CD d (CD, δCD mask ), and the dose standard deviation σ d Based on the inverse function g d (CD, δCD mask ) and the standard deviation of the measured in, represents the LCDU(1σ) due to dose and resist variation for a given mask deviation.

[0504] 38. The method of clause 32, further comprising:

[0505] The determined probability density function is executed using failure rate data associated with a target layout to determine a characteristic limit associated with a threshold failure rate.

[0506] 39. A method for adjusting a process window, comprising:

[0507] obtaining (i) a plurality of dose-focus settings and (ii) a reference distribution based on measurements of a characteristic of a printed pattern associated with each of the plurality of dose-focus settings;

[0508] determining a probability density function (PDF) of the characteristic based on an adjustment model and the plurality of dose-focus settings such that an error between the PDF and the reference distribution is reduced, the PDF being a function of the adjustment model and a variance associated with dose, the adjustment model being configured to change a proportion of a nonlinear dose sensitivity contribution to the PDF; and

[0509] A process window associated with a patterning process is adjusted based on the determined PDF of the characteristic.

[0510] 40. The method of clause 39, wherein determining the PDF is an iterative process, the iterations comprising:

[0511] determining an adjustment value for a given dose-focus setting of the plurality of dose-focus settings based on the adjustment model;

[0512] determining a PDF of the characteristic of the pattern based on the adjustment value;

[0513] determining an error between the PDF and the reference distribution; and

[0514] Parameters of the adjustment model are adjusted for the given dose and focus setting of the plurality of dose-focus settings such that the error is minimized.

[0515] 41. A method according to aspect 39, wherein the PDF is a convolution of a first PDF and a second PDF, wherein the first PDF is a function of a first variation that is a product of the adjustment model and a variation in dose, and the second PDF is a function of a second variation associated with a factor other than dose that contributes to the variation in the characteristic of the pattern.

[0516] 42. The method of clause 41, wherein determining the PDF is an iterative process, the iterations comprising:

[0517] convolving the first PDF with the second PDF to determine a PDF of a characteristic of the pattern;

[0518] determining an error between the PDF and the reference distribution; and

[0519] Parameters of the first variation and the second variation are adjusted for a given dose and focus setting of the plurality of dose-focus settings such that the error is minimized.

[0520] 43. The method according to any one of aspects 40 to 42, wherein the adjusting of the parameters of the adjustment model for the plurality of dose-focus settings is performed by an optimization algorithm selected from adaptive moment estimation or a gradient descent method.

[0521] 44. The method of clause 39, wherein the adjustment model is a polynomial function of dose and focus.

[0522] 45. The method of clause 42, further comprising:

[0523] determining, for each dose and each focus setting in the plurality of dose-focus settings, a plurality of adjustment values associated with a PDF having a minimum error relative to the reference distribution; and

[0524] A polynomial function of dose and focus is fitted based on the plurality of adjustment values to determine the adjustment model such that a difference between the fitted polynomial function and the plurality of adjustment model values is minimized.

[0525] 46. The method of clause 39, further comprising:

[0526] The determined probability density function is executed using failure rate data associated with the pattern to determine a characteristic limit associated with a threshold failure rate.

[0527] 47. A non-transitory computer-readable medium comprising instructions that, when executed by one or more processors, result in operations comprising:

[0528] obtaining (i) a characteristic limit of a characteristic of the printed pattern based on a threshold failure rate of the printed pattern and (ii) a reference process window based on the characteristic limit; and

[0529] Calibrating the simulation process so that the simulated process window is within an acceptable threshold of the reference process window, calibrating the simulation process includes:

[0530] executing one or more process models to determine a simulated pattern; and

[0531] Parameter values associated with the one or more process models are adjusted until characteristics of the simulated pattern meet the characteristic limits.

[0532] 48. A non-transitory computer-readable medium according to aspect 47, wherein the simulation process includes: a source mask optimization process and an optical proximity effect correction process, wherein the source mask optimization process and the optical proximity effect correction process are configured to adjust mask parameters, source parameters or process parameters so that the printed pattern is within an acceptable threshold of a target characteristic value.

[0533] 49. The non-transitory computer-readable medium of aspect 47, wherein the one or more process models include a characteristic model that is fit based on the simulated pattern and the characteristic limits associated with the printed pattern.

[0534] 50. The non-transitory computer-readable medium of clause 49, wherein the characteristic model is determined by fitting parameters of the characteristic model based on the characteristics of the simulated pattern and the characteristics of the printed pattern.

[0535] 51. The non-transitory computer-readable medium of aspect 50, wherein the characteristics of the simulated pattern and the printed pattern are a critical dimension, an edge placement error between two patterns on different layers of a substrate, or a pattern placement error between two patterns on the same or different layers of the substrate.

[0536] 52. The non-transitory computer-readable medium of clause 51, wherein the simulated pattern comprises an outline of a pattern within a layer of a substrate.

[0537] 53. The non-transitory computer-readable medium of clause 52, wherein the characteristic of the simulated pattern comprises a difference between a first characteristic at a top of the layer and a second characteristic at a bottom of the layer.

[0538] 54. The non-transitory computer-readable medium of clause 47, wherein the parameters of the one or more process models include one or more of:

[0539] Parameters of the characteristic model;

[0540] spatial image parameters associated with a spatial model associated with the patterning process;

[0541] Resist parameters associated with a resist model associated with the patterning process; and

[0542] Etch parameters associated with an etch model associated with the patterning process.

[0543] 55. The non-transitory computer-readable medium of clause 54, wherein the parameters of the one or more process models include one or more parameters selected from blurriness of an aerial image, resist thickness, or an amount of absorption associated with the resist.

[0544] 56. The non-transitory computer-readable medium of clause 47, wherein obtaining the characteristic limit of the characteristic of the printed pattern comprises:

[0545] Printing a selected pattern of a target layout onto a substrate via a photolithography apparatus;

[0546] determining a failure rate for each selected pattern based on inspection data of the printed pattern;

[0547] fitting a failure rate model based on the failure rate and the characteristic of each selected pattern, the failure rate model being configured to determine a failure rate associated with the characteristic of the pattern; and

[0548] The failure rate model is executed to determine the characteristic limits of the characteristic of the selected pattern such that the threshold failure rate is met.

[0549] 57. The non-transitory computer-readable medium of clause 47, wherein obtaining the reference process window comprises:

[0550] Based on inspection data associated with the printed substrate, values of dose and focus corresponding to the characteristic that satisfy the characteristic limits are determined for each selected pattern.

[0551] 58. The non-transitory computer-readable medium of clause 47, wherein the calibrating the simulation process is an iterative process, the iterations comprising:

[0552] (a) executing the one or more process models using a selected pattern to be printed on a substrate to determine the simulated pattern on the substrate;

[0553] (b) adjusting the values of the parameters associated with the one or more process models so that the characteristics of the simulated pattern meet the characteristic limits associated with the selected pattern;

[0554] (c) determining the simulated process window based on the characteristics of the simulated pattern and whether the simulated process window is within an acceptable threshold of the reference process window; and

[0555] (d) In response to the acceptability threshold not being met, performing steps (a) to (c).

[0556] 59. The non-transitory computer-readable medium of clause 47, wherein adjusting the parameters of the one or more process models comprises:

[0557] Values of parameters associated with the characteristic model are adjusted so as to maximize a margin between the characteristic of the simulated pattern at a top and the characteristic of the simulated pattern at a bottom with respect to the characteristic limit.

[0558] 60. The non-transitory computer-readable medium of clause 47, further comprising:

[0559] obtaining a set of hot spot patterns, each hot spot pattern being a user-selected pattern from a target layout and / or a pattern associated with a relatively higher probability of failure compared to other patterns of the target layout;

[0560] determining a defect-based process window for each hot spot pattern by simulating the calibrated simulation process using the set of hot spot patterns and the failure rate model; and

[0561] Based on the superposition of each defect-based process window, optimal values of one or more process variables associated with the threshold failure rate are determined.

[0562] 61. The non-transitory computer-readable medium of aspect 60, wherein the one or more process variables are selected from the group consisting of: optimal focus, optimal dose, a dose-focus window characterized by the threshold failure rate, aberrations of a lens system, a level setting, and an overlap setting.

[0563] 62. The non-transitory computer-readable medium of clause 47, further comprising:

[0564] determining a yield rate associated with each hot spot pattern based on the failure rate model;

[0565] The overall yield of the full chip layout is determined by calculating the product of each yield associated with each hot spot pattern across the entire full chip layout.

[0566] 63. The non-transitory computer-readable medium of clause 47, further comprising:

[0567] determining, by simulating the calibrated simulation process, whether the margin can be used to adjust a characteristic of the retargeted pattern to result in a target characteristic value being printed on the substrate; and

[0568] In response to the margin being unavailable, adjustments to processes associated with the patterning process are determined via simulating the calibrated simulation process using the retargeted pattern so that the target characteristic value will be printed on the substrate.

[0569] 64. The non-transitory computer-readable medium of aspect 63, wherein the adjustment to the process comprises at least one of adjusting an etch bias at the developed image, including an isotropic etch back or spacer process, an amount of process loading, an etch rate, a deposition rate, and an angle of incidence for etching or deposition.

[0570] 65. The non-transitory computer-readable medium of clause 47, further comprising:

[0571] simulating the calibrated simulation process using a full chip layout to determine a residual error between a simulated characteristic value associated with the full chip layout and a target characteristic value;

[0572] determining, via lithographic manufacturing inspection, whether the analog characteristic values associated with the full chip layout meet a desired yield; and

[0573] In response to the desired yield not being met, source parameters, mask parameters, or process parameters are adjusted via the calibrated simulation process to reduce the residual error so that the desired yield is met.

[0574] 66. A non-transitory computer-readable medium comprising instructions that, when executed by one or more processors, result in operations comprising:

[0575] obtaining (i) characteristic limits associated with a target pattern, the characteristic limits being values of a characteristic beyond which a printed pattern corresponding to the target pattern is considered defective, and (ii) a source mask optimization (SMO) process configured to calculate dose and / or mask parameters based on a threshold failure rate associated with the characteristic of the target pattern; and

[0576] By simulating the source mask optimization process using the target pattern, a retargeted pattern is generated, the characteristics associated with the retargeted pattern falling further within the characteristic limits associated with the target pattern.

[0577] 67. The non-transitory computer-readable medium of clause 66, wherein the characteristic limits are obtained based on a failure rate model, the failure rate model being calibrated using failure rate data associated with the printed pattern on a substrate and the threshold failure rate, the printing being performed using initial SMO data.

[0578] 68. The non-transitory computer-readable medium of clause 66, wherein obtaining the source mask optimization (SMO) process comprises:

[0579] A dose drift equation is included to calculate the dose based on the probability density function (PDF) of the characteristic, the local critical dimension uniformity, the dose sensitivity of the characteristic of the pattern, and the threshold failure rate.

[0580] 69. The non-transitory computer-readable medium of aspect 68, wherein the dose drift equation is given by:

[0581]

[0582] Among them, dose EV Indicates the failure rate at the threshold FR target The dose value under the extreme drift associated with the characteristic value at 3 standard deviations from the mean characteristic value, NDS is the dose sensitivity of the characteristic of the pattern, LCDU dose 3σ represents the variation associated with the value of a property at 3 standard deviations from the mean property value and at a particular dose, and CDF represents the cumulative distribution function of the PDF of the property.

[0583] 70. The non-transitory computer-readable medium of aspect 68, wherein the dose drift equation is given by:

[0584]

[0585] Among them, dose EV Indicates the failure rate at the threshold FR target The dose value under the extreme drift associated with the characteristic value at 3 standard deviations from the mean characteristic value, NDS is the dose sensitivity of the characteristic of the pattern, LCDU dose Indicates the change in the property at a specific dose, LCDU total represents the total change of the characteristic of the pattern, LCDU dose 3σ represents the variation associated with the value of a property at 3 standard deviations from the mean property value and at a particular dose, and CDF represents the cumulative distribution function of the PDF of the property.

[0586] 71. The non-transitory computer-readable medium of clause 66, wherein obtaining the source mask optimization (SMO) process comprises:

[0587] A mask deviation drift equation is included to calculate the mask characteristic based on the probability density function (PDF) of the characteristic, the local CD uniformity caused by the mask deviation, and the threshold failure rate.

[0588] 72. The non-transitory computer-readable medium of clause 71, wherein the mask bias drift equation is given by:

[0589]

[0590] Among them, mask EV Indicates the failure rate at the threshold FR target The mask deviation under extreme drift associated with the characteristic value at 3 standard deviations from the mean characteristic value, LCDU mask@W is the change in characteristics associated with the resist pattern due to the mask deviation, LCDU total represents the total variation of the characteristic of the pattern, and CDF represents the cumulative distribution function of the PDF of the characteristic.

[0591] 73. The non-transitory computer-readable medium of clause 66, wherein generating the retargeting pattern such that a margin associated with the characteristic limit at the threshold failure rate is increased, generating the retargeting pattern comprises:

[0592] simulating the source mask optimization process using initial SMO data to determine a drift in characteristics associated with the target pattern at the threshold failure rate;

[0593] determining a margin between the characteristic limit and the drift at the threshold failure rate; and

[0594] A characteristic value of the target pattern is adjusted so that the margin increases without exceeding the characteristic limit associated with the target pattern, and the adjusted characteristic value is used to generate the retargeting pattern.

[0595] 74. The non-transitory computer-readable medium of clause 66, wherein generating the retargeting pattern is an iterative process, the iterations comprising:

[0596] (a) simulating the source mask optimization process using initial SMO data including optimized source and optimized mask parameters and an initial target pattern or a retargeted pattern as input to determine a drift of a characteristic associated with the target pattern at the threshold failure rate;

[0597] (b) determining a margin between the characteristic limit and the drift of the characteristic at the threshold failure rate;

[0598] (c) adjusting a characteristic value of the target pattern so that the margin increases without exceeding the characteristic limit associated with the target pattern, the adjusted characteristic value being used to generate the retargeting pattern; and

[0599] (d) In response to the margin exceeding the characteristic limit or not being maximized, performing steps (a) to (c).

[0600] 75. The non-transitory computer-readable medium of aspect 74, wherein a margin between the characteristic limit of the characteristic and an extreme value of the characteristic is maximized, the extreme value of the characteristic being a value caused by a contributing factor from one or more process variables at the threshold failure rate.

[0601] 76. The non-transitory computer-readable medium of aspect 66, wherein the extreme value of the characteristic is caused by focus, dose, moving standard deviation (MSD) of the error between the measured value and the target value, resist thickness, and / or a resist component including an acid or a quencher.

[0602] 77. The non-transitory computer-readable medium of clause 66, further comprising:

[0603] simulating the source mask optimization (SMO) process using the retargeted pattern to determine simulated characteristic values associated with a full chip layout;

[0604] determining, via lithographic manufacturing inspection, whether the analog characteristic values associated with the full chip layout meet a desired yield; and

[0605] In response to the desired yield not being met, source parameters, mask parameters or process parameters are adjusted so that the desired yield is met, the adjusted source parameters, mask parameters or process parameters being used to generate an optimized source, an optimized illumination pupil and / or an optimized mask.

[0606] 78. A non-transitory computer-readable medium comprising instructions that, when executed by one or more processors, result in operations comprising:

[0607] obtaining (i) a dose probability density function (dose PDF) for determining a probability of a dose and (ii) a mask probability density function (mask PDF), the dose probability density function (dose PDF) being a function of (a) a characteristic of a feature and (b) a deviation of a mask characteristic associated with a mask used to print the feature on a substrate, the mask probability density function (mask PDF) being used to determine the probability of the deviation of the mask characteristic;

[0608] determining the probability density function associated with the characteristic by convolving (i) the dose PDF with (ii) the mask PDF over a given range of mask characteristic values; and

[0609] A process window associated with the patterning process is adjusted based on the determined probability density function associated with the characteristic.

[0610] 79. A non-transitory computer-readable medium according to aspect 78, wherein the mask PDF includes a nonlinear mask error enhancement factor (MEEF) dependency that causes skewness of the mask PDF, wherein the nonlinear MEEF is calculated using an inverse function of the relationship between the mask characteristics and the characteristics printed on the substrate.

[0611] 80. The non-transitory computer-readable medium of clause 79, wherein the mask PDF can be calculated by:

[0612]

[0613] Among them, G mask is the Gaussian distribution of the mask characteristics, and G is calculated based on the inverse function of the relationship between the mask characteristics and the characteristics printed on the substrate. mask The average value μ mask , the inverse function is given by g mask (δCD mask ) indicates that G mask The standard deviation of mask ,σ mask is based on the inverse function and the standard deviation of the measured value δCD mask The standard deviation is determined, and The nonlinear MEEF is determined.

[0614] 81. The non-transitory computer-readable medium of clause 78, wherein the dose PDF includes a dependency on a local critical dimension uniformity (LCDU) associated with a resist pattern on the substrate, the LCDU being caused by the mask characteristics.

[0615] 82. A non-transitory computer-readable medium according to aspect 81, wherein the dose PDF is determined using a normal distribution or a Poisson distribution with a mean dose and a dose standard deviation, the mean dose is determined by an inverse function of the relationship between the dose and CD for a given deviation of the mask characteristic, and the dose standard deviation is determined by an LCDU caused by the mask characteristic related to the resist pattern on the substrate.

[0616] 83. The non-transitory computer-readable medium of aspect 82, wherein the dose PDF can be calculated by the following formula:

[0617] PDF dose (g d (CD, δCDmask ); μ d (δCD mask ), σ d (δCD mask ))

[0618] Wherein, the characteristic δCD of the mask is used mask The dose g is determined by the inverse function of the relationship between the dose and the characteristic CD for a given deviation d (CD, δCD mask ), and the dose standard deviation σ d Based on the inverse function g d (CD, δCD mask ) and the standard deviation of the measured in, represents the LCDU(1σ) due to dose and resist variation for a given mask deviation.

[0619] 84. The non-transitory computer-readable medium of clause 78, further comprising:

[0620] The determined probability density function is executed using failure rate data associated with a target layout to determine a characteristic limit associated with a threshold failure rate.

[0621] 85. A non-transitory computer-readable medium comprising instructions that, when executed by one or more processors, result in operations comprising:

[0622] obtaining (i) a plurality of dose-focus settings and (ii) a reference distribution based on measurements of a characteristic of a printed pattern associated with each of the plurality of dose-focus settings;

[0623] determining a probability density function (PDF) of the characteristic based on an adjustment model and the plurality of dose-focus settings such that an error between the PDF and the reference distribution is reduced, the PDF being a function of the adjustment model and a variance associated with dose, the adjustment model being configured to change a proportion of a nonlinear dose sensitivity contribution to the PDF; and

[0624] A process window associated with a patterning process is adjusted based on the determined PDF of the characteristic.

[0625] 86. The non-transitory computer-readable medium of clause 85, wherein determining the PDF is an iterative process, the iterations comprising:

[0626] determining an adjustment value for a given dose-focus setting of the plurality of dose-focus settings based on the adjustment model;

[0627] determining a PDF of the characteristic of the pattern based on the adjustment value;

[0628] determining an error between the PDF and the reference distribution; and

[0629] Parameters of the adjustment model are adjusted for the given dose and focus setting of the plurality of dose-focus settings such that the error is minimized.

[0630] 87. The non-transitory computer-readable medium of aspect 85, wherein the PDF is a convolution of a first PDF and a second PDF, wherein the first PDF is a function of a first variation that is a product of the adjustment model and a variation in dose, and the second PDF is a function of a second variation associated with a factor other than dose that contributes to the variation in the characteristic of the pattern.

[0631] 88. The non-transitory computer-readable medium of clause 87, wherein determining the PDF is an iterative process, the iterations comprising:

[0632] convolving the first PDF with the second PDF to determine a PDF of a characteristic of the pattern;

[0633] determining an error between the PDF and the reference distribution; and

[0634] Parameters of the first variation and the second variation are adjusted for a given dose and focus setting of the plurality of dose-focus settings such that the error is minimized.

[0635] 89. The non-transitory computer-readable medium of any one of aspects 86 to 88, wherein the adjusting of the parameters of the adjustment model for the plurality of dose-focus settings is performed by an optimization algorithm selected from an adaptive moment estimation or a gradient descent method.

[0636] 90. The non-transitory computer-readable medium of clause 85, wherein the adjustment model is a polynomial function of dose and focus.

[0637] 91. The non-transitory computer-readable medium of clause 88, further comprising:

[0638] determining, for each dose and each focus setting in the plurality of dose-focus settings, a plurality of adjustment values associated with a PDF having a minimum error relative to the reference distribution; and

[0639] A polynomial function of dose and focus is fitted based on the plurality of adjustment values to determine the adjustment model such that a difference between the fitted polynomial function and the plurality of adjustment model values is minimized.

[0640] 92. The non-transitory computer-readable medium of clause 85, further comprising:

[0641] The determined probability density function is executed using failure rate data associated with the pattern to determine a characteristic limit associated with a threshold failure rate.

[0642] In the block diagrams, the illustrated components are depicted as discrete functional blocks, but embodiments are not limited to systems in which the functionality described herein is organized as illustrated. The functionality provided by each of the components may be provided by software or hardware modules that are organized differently than currently depicted, for example, such modules may be intermixed, combined, replicated, disbanded, distributed (e.g., within a data center or by region), or such software or hardware may be organized in other different ways. The functionality described herein may be provided by one or more processors of one or more computers executing process 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 via the network, in which case, where information (e.g., content) is allegedly supplied or otherwise provided, the information may be provided by sending instructions to obtain the information from the content delivery network.

[0643] Unless otherwise specifically stated, as is clear from the discussion, it should be understood that throughout this specification, discussions utilizing terms such as "processing," "computing / calculating," "determining," etc., refer to actions or processes of a specific apparatus such as a special-purpose computer or similar special-purpose electronic processing / computing device.

[0644] The reader should understand that this application describes several inventions. These inventions have been combined into a single file, rather than separating those inventions into multiple separate patent applications, because the related themes of the inventions make them helpful to economic development in the application process. However, the different advantages and projects of these inventions should not be combined. In some cases, the embodiments solve all the shortcomings mentioned herein, but it should be understood that the inventions are independently useful, and some embodiments only solve a subset of these problems or provide other unmentioned benefits, and those skilled in the art who review this disclosure will understand the other unmentioned benefits. Due to cost constraints, some of the inventions disclosed herein may not be claimed at present, and some of the inventions may be claimed in a later application (such as, a continued application or by amending the claims of the present invention). Similarly, due to space limitations, the chapters and sections of the abstract and summary of the invention of this document should not be regarded as a comprehensive list containing all these inventions or all the projects of these inventions.

[0645] It should be understood that the description and drawings are not intended to limit the disclosure to the particular forms disclosed, but on the contrary, the disclosure is to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the present invention as defined by the appended claims.

[0646] In view of this specification, modifications and alternative embodiments of the various items of the present invention will be apparent to those skilled in the art. Therefore, this specification and the accompanying drawings should be understood to be illustrative only and for the purpose of teaching those skilled in the art the general manner of carrying out the present invention. It should be understood that the forms of the invention shown and described herein should be regarded as examples of embodiments. Elements and materials can replace the parts and materials illustrated and described herein, parts and processes can be reversed or omitted, certain features can be utilized independently, and embodiments or features of embodiments can be combined, as will be understood by those skilled in the art after obtaining the benefit of this specification. Changes may be made to the elements described herein without departing from the spirit and ...

Claims

1. A method for adjusting a process window of a photolithography process, comprising: obtaining (i) a plurality of dose-focus settings and (ii) a reference distribution based on measurements of a characteristic of a printed pattern associated with each of the plurality of dose-focus settings; determining a probability density function (PDF) of the characteristic based on an adjustment model and the plurality of dose-focus settings such that an error between the PDF and the reference distribution is reduced, the PDF being a function of the adjustment model and a variance associated with dose, the adjustment model being configured to change a proportion of a nonlinear dose sensitivity contribution to the PDF; as well as A process window associated with a patterning process is adjusted based on the determined PDF of the characteristic.

2. The method according to claim 1, wherein Determining the PDF is an iterative process, with the iterations comprising: determining an adjustment value for a given dose-focus setting of the plurality of dose-focus settings based on the adjustment model; determining a PDF of the characteristic of the pattern based on the adjustment value; determining an error between the PDF and the reference distribution; and Parameters of the adjustment model are adjusted for the given dose-focus setting of the plurality of dose-focus settings such that the error is minimized.

3. The method according to claim 1, wherein The PDF is determined by convolving a first PDF that is a function of a first variation that is a product of the adjustment model and a variation in dose, and a second PDF that is a function of a second variation associated with a factor other than dose that contributes to the variation in the characteristic of the pattern.

4. The method according to claim 3, wherein: Determining the PDF is an iterative process, with the iterations comprising: convolving the first PDF with the second PDF to determine a PDF of the characteristic of the pattern; determining an error between the PDF and the reference distribution; and Parameters of the first variation and the second variation are adjusted for a given dose-focus setting of the plurality of dose-focus settings such that the error is minimized.

5. The method according to claim 2, wherein: The adjusting of the parameters of the adjustment model for the plurality of dose-focus settings is performed by an optimization algorithm selected from adaptive moment estimation or a gradient descent method.

6. The method according to claim 1, wherein The adjustment model is a polynomial function of dose and focus.

7. The method according to claim 4, further comprising: determining, for each dose and each focus setting in the plurality of dose-focus settings, a plurality of adjustment values associated with a PDF having a minimum error relative to the reference distribution; as well as A polynomial function of dose and focus is fitted based on the plurality of adjustment values to determine the adjustment model such that a difference between the fitted polynomial function and the plurality of adjustment values is minimized.

8. The method according to claim 1, further comprising: The determined probability density function is executed using failure rate data associated with the pattern to determine a characteristic limit associated with a threshold failure rate.

9. A method comprising: obtaining (i) a dose probability density function (dose PDF) for determining a probability of a dose and (ii) a mask probability density function (mask PDF), the dose PDF being a function of (a) a characteristic of a feature and (b) a deviation of a mask characteristic associated with a mask used to print the feature on a substrate, the mask probability density function being used to determine the probability of the deviation of the mask characteristic; determining the probability density function associated with the characteristic by convolving (i) the dose PDF with (ii) the mask PDF over a given range of mask characteristic values; as well as A process window associated with a patterning process is adjusted based on the determined probability density function associated with the characteristic.

10. The method according to claim 9, wherein: The mask PDF includes a nonlinear mask error enhancement factor (MEEF) dependency that causes skewness of the mask PDF, wherein the nonlinear MEEF is calculated using an inverse function of a relationship between the mask characteristics and the properties of the features printed on the substrate.

11. The method according to claim 10, wherein: The mask PDF can be calculated by the following formula: in, is a Gaussian distribution of the mask characteristics, calculated based on the inverse function of the relationship between the mask characteristics and the characteristics of the features printed on the substrate Average value , the inverse function is given by express, The standard deviation of , is based on the inverse function and the standard deviation of the measured value The standard deviation is determined, and The nonlinear MEEF is determined.

12. The method according to claim 10, wherein: The dose PDF includes a dependency on the local critical dimension uniformity (LCDU) of the resist pattern on the substrate, the LCDU being caused by the mask characteristics.

13. The method according to claim 12, wherein: The dose PDF is determined using a normal distribution or a Poisson distribution having a mean dose and a dose standard deviation, the mean dose is determined by an inverse function of the relationship between the dose and CD for a given deviation of the mask characteristics, and the dose standard deviation is determined by an LCDU caused by the mask characteristics based on the resist pattern on the substrate.

14. The method according to claim 12, wherein: The dose PDF can be calculated by the following formula: wherein a given deviation of the feature for the mask characteristic is used The dose PDF is determined by the inverse function of the relationship between the dose and the CD, and the dose standard deviation (δCD mask ) is based on the inverse function and the standard deviation of the measured Of which, represents the LCDU(1σ) due to dose and resist variation for a given mask deviation, where 1σ represents one standard deviation.

15. The method according to claim 9, further comprising: The determined probability density function is executed using failure rate data associated with a target layout to determine a characteristic limit associated with a threshold failure rate.

16. A non-transitory computer-readable medium comprising instructions that, when executed by one or more processors, cause the one or more processors to perform a method comprising any one of claims 1 to 15.

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