A subset of components determining an optical property of a patterning device

Abstract

A method for determining components of an optical characteristic of a patterning process is described herein. The method comprises obtaining ( i ) multiple desired features, ( ii ) based on the optical properties of the plurality of simulated features and the patterning process of the plurality of desired features, and ( iii ) a performance metric associated with a desired feature among the plurality of desired features and an associated simulated feature among the plurality of simulated features (e.g., EPE ); determining a set of optical sensitivities of the patterning process by calculating a change in a value of a performance metric based on a change in the value of the optical characteristic; and identifying a set of components of the optical characteristic (e.g., principal components) that include major contributors to the change in the value of the performance metric based on the set of optical sensitivities.

Description

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims priority to U.S. Application No. 62 / 786,642, filed on December 31, 2018, which is incorporated herein by reference in its entirety. Technical Field

[0003] The description herein relates to patterning apparatus and processes, and more particularly to methods or tools for tuning of equipment for patterning processes, such as optical parameters associated with lithographic apparatus. Background Art

[0004] A lithographic apparatus is a machine that applies a desired pattern to a target portion of a substrate. For example, a lithographic apparatus can be used to manufacture devices such as integrated circuits (ICs). In this case, a patterning device (e.g., a mask or reticle) can be used to generate a pattern corresponding to a single layer of the device, and the pattern can be transferred to a target portion (e.g., including a portion, one or more dies) on a substrate (e.g., a silicon wafer) having, for example, a layer of radiation-sensitive material (resist) by methods such as irradiating the target portion via a pattern on the patterning device. Typically, a single substrate will contain multiple adjacent target portions, to which the pattern is transferred successively by the lithographic apparatus, one target portion at a time. In one type of lithographic apparatus, the pattern on the entire patterning device is transferred to one target portion at a time; such an apparatus is generally referred to as a stepper. In an alternative apparatus, generally referred to as a step-and-scan apparatus, a projection beam scans the patterning device in a given reference direction (the "scanning" direction) while synchronously moving the substrate parallel or antiparallel to the reference direction. Different portions of the pattern on the patterning device are gradually transferred to one target portion. Since typically a lithographic projection apparatus will have a demagnification factor M (typically > 1), the speed F of the substrate movement will be M times the speed at which the projection beam scans the patterning device.

[0005] Before the pattern is transferred from the pattern forming device to the substrate, various processes such as primer, resist coating and soft baking can be performed on the substrate. After exposure, other processes such as post-exposure baking (PEB), development, hard baking and measurement / inspection of the transfer pattern can be performed on the substrate. This series of processes is used as the basis for manufacturing a single 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 intended to complete a single layer of the device. If several layers are required in the device, the entire process or its variants are repeated for each layer. Ultimately, the device will appear in each target portion on the substrate. These devices are then separated from each other by techniques such as cutting or sawing, so that the individual devices can be mounted on a carrier, connected to pins, and so on.

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

[0007] The optical system can play a role in the performance of the patterning process. Therefore, a technique is provided herein to enable the design, modification, control, etc. of a patterning process based on the characteristics of the optical system of a patterning device, such as a scanner.

[0008] In one embodiment, a method for determining components of an optical characteristic of a patterning process is provided. The method includes: obtaining (i) a plurality of desired features, (ii) a plurality of simulated features based on the plurality of desired features and an optical characteristic of the patterning process, and (iii) a performance metric associated with the desired features in the plurality of desired features and the associated simulated features in the plurality of simulated features; determining a set of optical sensitivities of the patterning process by calculating a change in a value of the performance metric based on a change in the value of the optical characteristic; and identifying a set of components of the optical characteristic including a major contributor to a change in the value of the performance metric based on the set of optical sensitivities.

[0009] In one embodiment, identifying a set of components of optical properties involves: performing a principal component analysis on the set of optical sensitivities; and determining a linear combination of optical properties that accounts for substantial variation within the set of optical sensitivities.

[0010] In one embodiment, the dominant contributors include linear combinations of optical properties.

[0011] In one embodiment, the optical property characterizes an optical aberration of an optical system of the patterning device.

[0012] In one embodiment, the optical properties are defined by Zernike polynomials.

[0013] In one embodiment, the components of the set of components of the optical property are coefficients of Zernike polynomials.

[0014] In one embodiment, the components correspond to correctable Zernike coefficients, wherein the correctable Zernike coefficients are tunable via an adjustment mechanism of the patterning device.

[0015] In one embodiment, the linear combination includes correctable Zernike coefficients and uncorrectable Zernike coefficients, wherein the uncorrectable Zernike coefficients are not tunable via an adjustment mechanism of the patterning device.

[0016] In one embodiment, the correctable Zernike coefficients are low-order Zernike coefficients.

[0017] In addition, in one embodiment, a source mask optimization method based on optical sensitivity of a patterning process is provided. The method involves: obtaining (i) a set of optical sensitivities, and (ii) a set of components including optical characteristics that are main contributors to variations in the set of optical sensitivities; determining a source pattern or a mask pattern via a patterning process model based on the set of components including optical characteristics so that a performance metric of the patterning process is improved.

[0018] Furthermore, in one embodiment, a computer program product is provided, the computer program product comprising a non-transitory computer-readable medium having instructions recorded thereon, the instructions implementing the above method when executed by a computer system. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] The above aspects and other aspects and features will become clear to those skilled in the art after reading the following description of specific embodiments in conjunction with the accompanying drawings, in which:

[0020] Figure 1 schematically depicts a lithographic apparatus according to an embodiment;

[0021] Figure 2 schematically depicts an embodiment of a lithography cell or cluster according to one embodiment;

[0022] Figure 3 is a flow chart for modeling and / or simulating portions of a patterning process according to one embodiment;

[0023] Figure 4 is a flow chart for determining one or more optical characteristics of a patterning device according to one embodiment;

[0024] Figure 5A , 5B , 5C, 5D, 5E, 5F and 5G show different mask patterns or desired patterns to be printed on a wafer according to one embodiment;

[0025] Figure 6 shows a collection of optical wavefront sensitivities according to one embodiment;

[0026] Fig. 7A shows a wavefront representation including a Zernike Z8 principal component according to one embodiment;

[0027] Figure 7B According to one embodiment, a Fig. 7A The histogram representation of the principal components of Zernike Z8;

[0028] Figure 7C shows a wavefront representation including a Zernike Z7 principal component according to one embodiment;

[0029] Fig.7D A representation according to one embodiment is shown comprising Figure 7C Bar plot of the principal components of Zernike Z7;

[0030] Fig. 7E shows a wavefront representation including a Zernike Z5 principal component according to one embodiment;

[0031] Figure 7F A representation according to one embodiment is shown comprising Fig. 7E Bar plot of the principal components of Zernike Z5;

[0032] Figure 7G shows a wavefront representation including a Zernike Z9 principal component according to one embodiment;

[0033] Figure 7H A representation according to one embodiment is shown comprising Figure 7G Bar plot of the principal components of Zernike Z9;

[0034] Fig. 8A and 8B shows performance measurements based on profiles of reference and simulated features (eg, resulting from perturbed optical properties) according to one embodiment;

[0035] Fig. 9 is an example correction potential for a lithographic apparatus according to an embodiment;

[0036] Fig. 10A is a flow chart of a method for optimizing optical sensitivity based on a patterning process according to one embodiment;

[0037] Fig. 10B shows field points along a slit of a projection optics box according to one embodiment;

[0038] Fig.11 is a flow chart illustrating aspects of an example method of joint optimization according to one embodiment.

[0039] Fig.12 An embodiment of another optimization method according to an embodiment is shown.

[0040] Fig.13A , 13B 14 show example flow charts of various optimization processes according to one embodiment.

[0041] Fig.15 is a block diagram of an example computer system in which embodiments may be implemented according to one embodiment;

[0042] Fig.16 is a schematic diagram of another lithographic projection apparatus according to an embodiment;

[0043] Fig.17 According to an embodiment Fig.16 A more detailed view of the devices in the

[0044] Fig.18 According to an embodiment Fig.16 and Fig.17 A more detailed view of the source collector module of a device.

[0045] Embodiments will now be described in detail with reference to the accompanying drawings, which are provided as illustrative examples to enable those skilled in the art to practice these embodiments. It is noteworthy that the following figures and examples are not intended to limit the scope to a single embodiment, but other embodiments are possible by exchanging some or all of the described or illustrated elements. Whenever convenient, the same reference numerals will be used throughout the drawings to refer to the same or similar parts. Where certain elements of these embodiments can be partially or completely implemented using known components, only the parts necessary for understanding the embodiments of such known components will be described, and detailed descriptions of other parts of such known components will be omitted to avoid confusion in the description of the embodiments. In this specification, embodiments showing a single component should not be considered as limiting; on the contrary, the scope is intended to cover other embodiments including multiple identical components, and vice versa, unless otherwise expressly stated herein. In addition, the applicant does not intend to give uncommon or special meanings to any term in the specification or claims, unless so expressly stated. In addition, the scope includes current and future known equivalents of the components mentioned herein by description. DETAILED DESCRIPTION

[0046] Before describing the embodiments in detail, it is helpful to present an example environment in which the embodiments may be implemented.

[0047] Figure 1An embodiment of a lithographic apparatus LA is schematically depicted. The apparatus comprises:

[0048] - an illumination system (illuminator) IL configured to condition a radiation beam B (e.g. extreme ultraviolet (EUV) radiation or electromagnetic radiation such as UV radiation or DUV);

[0049] a support structure (e.g., mask table) MT constructed 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;

[0050] 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

[0051] - a projection system (e.g., a refractive, reflective or reflective-refractive projection system) PS, configured to project the pattern imparted to the radiation beam B by the pattern forming device MA onto a target portion C (e.g., comprising one or more dies and commonly referred to as a field) of the substrate W, the projection system being supported on a reference frame (RF).

[0052] As depicted here, the device is transmissive (eg, employing a transmissive mask). Alternatively, the device may be reflective (eg, employing a programmable mirror array or LCD matrix, or employing a reflective mask).

[0053] The illuminator IL receives a radiation beam from a radiation source SO, for example a mercury lamp or an excimer laser. The radiation source and the lithographic apparatus may be separate entities, for example when the radiation source is an excimer laser. In this case, the radiation source is not considered to form part of the lithographic apparatus, and the radiation beam is transferred from the radiation source SO to the illuminator IL with the aid of a beam transfer system BD comprising, for example, suitable directional mirrors and / or a beam expander. In other cases, the radiation source may be an integral part of the apparatus, for example when the radiation source is a mercury lamp. If desired, the radiation source SO and the illuminator IL together with the beam transfer system BD may be referred to as a radiation system.

[0054] The illuminator IL may vary the intensity distribution of the beam. The illuminator may be arranged to limit the radial extent of the radiation beam so that the intensity distribution is non-zero within an annular region in a pupil plane of the illuminator IL. Additionally or alternatively, the illuminator IL may be operable to limit the distribution of the beam in the pupil plane so that the intensity distribution is non-zero in a plurality of equally spaced sectors in the pupil plane. The intensity distribution of the radiation beam in the pupil plane of the illuminator IL may be referred to as an illumination pattern.

[0055] Therefore, the illuminator IL may include an adjuster AM configured to adjust the (angular / spatial) intensity distribution of the beam. Typically, at least the outer and / or inner radial extent (typically referred to as outer σ and inner σ, respectively) of the intensity distribution in the pupil plane of the illuminator can be adjusted. The illuminator IL may be operable to change the angular distribution of the beam. For example, the illuminator may be operable to change the number and angular extent of sectors in the pupil plane in which the intensity distribution is not zero. By adjusting the intensity distribution of the beam in the pupil plane of the illuminator, different illumination modes may be achieved. For example, by limiting the radial and angular extent of the intensity distribution in the pupil plane of the illuminator IL, the intensity distribution may have a multipole distribution, such as, for example, a dipole, quadrupole or hexapole distribution. The desired illumination mode may be obtained, for example, by inserting an optical device providing the illumination mode into the illuminator IL or by using a spatial light modulator to obtain the desired illumination mode.

[0056] The illuminator IL may be operable to change the polarization of the beam and may be operable to adjust the polarization using the adjuster AM. The polarization state of the radiation beam over the entire pupil plane of the illuminator IL may be referred to as a polarization mode. The use of different polarization modes may allow greater contrast to be achieved in the image formed on the substrate W. The radiation beam may be unpolarized. Alternatively, the illuminator may be arranged to linearly polarize the radiation beam. The polarization direction of the radiation beam may vary over the entire pupil plane of the illuminator IL. In different regions in the pupil plane of the illuminator IL, the polarization direction of the radiation may be different. The polarization state of the radiation may be selected according to the illumination mode. For a multipolar illumination mode, the polarization of each pole of the radiation beam may be generally perpendicular to the position vector of the pole in the pupil plane of the illuminator IL. For example, for a dipole illumination mode, the radiation may be linearly polarized in a direction substantially perpendicular to a line of two opposite sectors bisecting the dipole. The radiation beam may be polarized in one of two different orthogonal directions, which may be referred to as X polarization and Y polarization states. For a quadrupole illumination mode, the radiation in the sector of each pole may be linearly polarized in a direction substantially perpendicular to a line bisecting the sector. This polarization mode may be referred to as XY polarization. Similarly, for a hexapole illumination mode, the radiation in the sector of each pole may be linearly polarized in a direction substantially perpendicular to a line bisecting the sector. This polarization mode may be referred to as TE polarization.

[0057] Furthermore, 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.

[0058] The illuminator thus provides a conditioned radiation beam B having a desired uniformity and intensity distribution in its cross-section.

[0059] 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 can use mechanical, vacuum, electrostatic or other clamping techniques to hold the patterning device. The support structure can be, for example, a frame or a stage, which can be fixed or movable as required. The support structure can ensure that the patterning device is in a desired position, for example relative to a projection system. Any use of the term "reticle" or "mask" herein may be considered synonymous with the more general term "patterning device".

[0060] The term "patterning device" as used herein 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 one embodiment, the patterning device is any device that can be used to impart a pattern to a cross-section of a radiation beam so as to produce a pattern in the target portion of the substrate. It should be noted that the pattern imparted to the radiation beam may not exactly correspond to the desired pattern in the target portion of the substrate, for example if the pattern includes phase-shifting features or so-called assist features. Typically, the pattern imparted to the radiation beam will correspond to a specific functional layer in a device produced in the target portion, such as an integrated circuit.

[0061] The patterning device may be transmissive or reflective. Examples of patterning devices include masks, programmable mirror arrays, and programmable LCD panels. Masks are well known in lithography and include mask types such as binary, alternating phase shift, and attenuated phase shift, as well as various hybrid mask types. An example of a programmable mirror array employs a matrix arrangement of small mirrors, each of which can be individually tilted to reflect an incoming radiation beam in different directions. The tilted mirrors impart a pattern in the radiation beam, which is reflected by the matrix of mirrors.

[0062] The term "projection system" as used herein should be broadly interpreted to cover any type of projection system, including refractive, reflective, catadioptric, magnetic, electromagnetic and electrostatic optical systems, or any combination thereof, depending on the exposure radiation used or other factors, such as the use of immersion liquid or the use of a vacuum. Any use of the term "projection lens" herein may be considered synonymous with the more general term "projection system".

[0063] The projection system PS has an optical transfer function that may be non-uniform, which affects the pattern imaged onto the substrate W. For non-polarized radiation, this effect can be well described by two scalar diagrams 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 diagrams (which may be referred to as transmission diagrams and relative phase diagrams) can be expressed as linear combinations of a complete set of basis functions. A particularly convenient set is the Zernike polynomials, which form a set of orthogonal polynomials defined on the unit circle. The determination of each scalar diagram may involve determining the coefficients in such an expansion. Since the Zernike polynomials are orthogonal on the unit circle, the Zernike coefficients may be determined by computing the inner product of the measured scalar diagrams of each Zernike polynomial in turn and dividing it by the square of the norm of the Zernike polynomial.

[0064] The transmission diagram and the relative phase diagram depend on the field and the system. That is, in general, each projection system PS will have a different Zernike expansion for each field point (i.e., for each spatial position in its image plane). The relative phase of the projection system PS in its pupil plane can be determined by, for example, projecting radiation from a point source in the object plane of the projection system PS (i.e., the plane of the pattern forming device MA) through the projection system PS and measuring the wavefront (i.e., the trajectory of points with the same phase) using a shearing interferometer. One type of shearing interferometer is a common path interferometer, and therefore, advantageously, no auxiliary reference beam is required to measure the wavefront. The shearing interferometer may include 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 with the pupil plane of the projection system PS. The interference pattern is related to the derivative of the phase of the radiation relative to the coordinates in the pupil plane in the shear direction. The detector may include an array of sensing elements (such as, for example, a charge coupled device (CCD)).

[0065] The projection system PS of the lithographic apparatus may not produce visible fringes, and therefore the accuracy of the wavefront determination can be enhanced using a phase stepping technique such as, for example, moving a diffraction grating. Stepping can be performed in the plane of the diffraction grating and in a direction perpendicular to the scanning direction of the measurement. The stepping range can be one grating period, and at least three (evenly distributed) phase steps can be used. Thus, for example, three scanning measurements can be performed in the y direction, each scanning measurement being performed for a different position in the x direction. Such stepping of the diffraction grating effectively converts phase changes into intensity changes, so that phase information can be determined. The grating can be stepped in a direction perpendicular to the diffraction grating (z direction) to calibrate the detector.

[0066] The diffraction grating may be scanned sequentially in two perpendicular directions, which may coincide with the axes (x and y) of the coordinate system of the projection system PS or may be at an angle, such as 45 degrees, to these axes. The scan may be performed over an integer number of grating periods (e.g., one grating period). The scan averages the phase changes in one direction to allow reconstruction of the phase changes in the other direction. This allows the wavefront to be determined as a function of the two directions.

[0067] The transmission (apodization) of the projection system PS in its pupil plane can be determined, for example, by projecting radiation through the projection system PS from a point source in the object plane of the projection system PS (i.e. the plane of the patterning device MA) 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 used for measuring the wavefront to determine aberrations can be used.

[0068] The projection system PS may include multiple optical (e.g., lens) elements and may also include an adjustment mechanism AM configured to adjust one or more optical elements to correct aberrations (phase changes in the entire pupil plane throughout the field). To achieve this, the adjustment mechanism may be operable to manipulate one or more optical (e.g., lens) elements within the projection system PS in one or more different ways. The projection system may have a coordinate system in which its optical axis extends in the z direction. The adjustment mechanism may be operable to perform any combination of the following: displacing one or more optical elements; tilting one or more optical elements; and / or deforming one or more optical elements. The displacement of the optical element may be in any direction (x, y, z, or a combination thereof). The tilting of the optical element is typically performed outside the plane perpendicular to the optical axis by rotating about an axis in the x and / or y direction, but for non-rotationally symmetric aspheric optical elements, rotation about the z axis may be possible. The deformation of the optical element may include low-frequency shapes (e.g., astigmatism) and / or high-frequency shapes (e.g., free-form aspheric surfaces). The deformation of the optical element may be performed, for example, by applying a force on one or more sides of the optical element using one or more actuators and / or by heating selected one or more regions of the optical element using one or more heating elements. Typically, it may not be possible to adjust the projection system PS to correct for apodization (variation of transmission across the pupil plane). When designing a patterning device (e.g., mask) MA for the lithographic apparatus LA, a transmission map of the projection system PS may be used. Using computational lithography techniques, the patterning device MA may be designed to at least partially correct for apodization.

[0069] The lithographic apparatus may be of a type having two (dual stage) or more worktables (e.g. two or more substrate tables WTa, WTb, two or more patterning device tables, a substrate table WTa and a worktable WTb below the projection system in the absence of a dedicated substrate for, e.g., facilitating measurement and / or cleaning etc.). In such a "multi-stage" machine, additional worktables may be used in parallel, or preparatory steps may be performed on one or more worktables while exposure is being carried out using one or more other worktables. For example, alignment measurements using an alignment sensor AS and / or level (height, tilt etc.) measurements using a level sensor LS may be performed.

[0070] 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) 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 between the patterning device and the projection system. Immersion techniques are well known in the art and are used to increase the numerical aperture of the projection system. The term "immersion" as used herein does not imply that structures such as the substrate are necessarily submerged in the liquid, but only that the liquid is located between the projection system and the substrate during exposure.

[0071] 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. After passing through 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 interferometric device, a linear encoder, a 2D 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, a first positioner PM and a further position sensor (in Figure 1The support structure MT may be used to accurately position the patterning device MA relative to the path of the radiation beam B, for example after mechanical retrieval from a mask library, or during scanning. Typically, movement of the support structure MT may be achieved with the aid 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 patterning device MA and the substrate W may be aligned using patterning device alignment marks M1, M2 and substrate alignment marks P1, P2. Although the substrate alignment marks as shown occupy dedicated target portions, they may be located in the spaces between target portions (these are referred to as scribe alignment marks). Similarly, where more than one die is provided on the patterning device MA, the patterning device alignment marks may be located between the dies.

[0072] The depicted device can be used in at least one of the following modes:

[0073] 1. In step mode, the support structure MT and the substrate table WT remain substantially stationary while the entire pattern imparted to the radiation beam is projected onto a target portion C at one time (i.e. a single static exposure). The substrate table WT is then moved 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.

[0074] 2. In scan mode, the support structure MT and substrate table WT are scanned synchronously while a pattern imparted to the radiation beam is projected onto a target portion C (i.e. a single dynamic exposure). The speed and direction of the substrate table WT relative to the support structure MT may be determined by the (de-)magnification and image reversal characteristics of the projection system PS. In scan mode, the maximum size of the exposure field limits the width of the target portion in a single dynamic exposure (in the non-scanning direction), while the length of the scanning movement determines the height of the target portion (in the scanning direction).

[0075] 3. In another mode, the support structure MT is kept substantially stationary to hold 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 employed and the programmable patterning device is updated as required after each movement of the substrate table WT or between successive radiation pulses during a scan. This mode of operation can be readily applied to maskless lithography utilizing a programmable patterning device, such as a programmable mirror array of the type described above.

[0076] Combinations and / or variations of the above-described modes of use or entirely different modes of use may also be employed.

[0077] like Figure 2 As shown, the lithography apparatus LA may form part of a lithography cell LC, sometimes also referred to as a lithography cell or cluster, which also includes equipment for performing pre-exposure and post-exposure processes on a substrate. Typically, these include one or more spin coaters SC for depositing one or more resist layers, one or more developers DE for developing the exposed resist, one or more chill plates CH and / or one or more baking plates BK. A substrate handler or robot RO picks up one or more substrates from input / output ports I / O1, I / O2, moves them between different processing devices, and transfers them to a feed station LB of the lithography apparatus. These devices (often collectively referred to as tracks) are under the control of a track control unit TCU, which itself is controlled by a supervisory control system SCS, which also controls the lithography apparatus via a lithography control unit LACU. Thus, different devices may be operated to maximize output and processing efficiency.

[0078] As device manufacturing processes used to make devices such as ICs continue to advance, the size of functional elements continues to decrease, while the number of functional elements such as transistors per device has been steadily increasing for decades, following a trend generally referred to as "Moore's Law." To achieve this, some processes are designed to create patterns at or below the classical resolution limit.

[0079] According to the resolution formula CD = k 1 ×λ / NA, the process of printing features with dimensions smaller than the classical resolution limit of lithographic projection equipment is often referred to as low-k 1 lithography, where λ is the wavelength of radiation employed (e.g., 193 nm or about 13 nm, e.g., about 13.5 nm), NA is the numerical aperture of the projection optics in the lithographic projection apparatus, CD is the “critical dimension” (usually the smallest feature size printed), and k1 is an empirical resolution factor. In general, k 1 The smaller it is, the more difficult it is to replicate on a substrate a pattern similar in shape and size to that planned by the device designer to achieve a specific electrical function and performance. To overcome these difficulties, complex fine-tuning steps are applied to the lithographic projection apparatus and / or the patterning device pattern. These include, for example, but not limited to, optimization of optical coherence settings, customized illumination schemes, use of phase-shifted patterning devices, optical proximity correction (OPC) in the patterning device pattern, optimization of NA, or other methods generally defined as "resolution enhancement techniques" (RET).

[0080] 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 one embodiment, the projection optics enable the formation of an aerial image (AI), which is the 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 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. In one embodiment, the simulation of the lithographic process can simulate the generation of an aerial image and / or a resist image.

[0081] Figure 3 An exemplary flow chart for modeling and / or simulating portions of a patterning process is shown in FIG. It will be appreciated that the models may represent different patterning processes and need not include all of the models described below.

[0082] The illumination model 31 represents the optical characteristics of the illumination mode (including the radiation intensity distribution and / or the 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 the numerical aperture setting, the illumination sigma (σ) setting, and any specific illumination mode shape (e.g., off-axis radiation shape, such as toroidal, quadrupole, dipole, etc.), where σ (or sigma) is the outer radial extent of the illuminator.

[0083] 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, distortions, refractive indices, physical dimensions, physical dimensions, absorptivity, etc. The optical properties of the lithographic projection apparatus (e.g., the nature of the illumination, the patterning device pattern, and the projection optics) determine 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 projection optics. The illumination model 31 and the projection optics model 32 may be combined into a transmission cross coefficient (TCC) model.

[0084] The patterning device pattern model 33 represents the optical properties of a patterning device pattern (e.g., a device design layout corresponding to features of an integrated circuit, memory, electronic device, etc.), including changes in radiation intensity distribution and / or phase distribution caused by a given patterning device pattern, which is 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 detailed physical properties of the patterning device and a representation of the patterning device pattern, as described, for example, in U.S. Pat. No. 7,587,704 (which is incorporated herein by reference in its entirety).

[0085] 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. Pat. No. 8,200,468 (which is incorporated herein by reference in its entirety). The resist model typically describes the effects of chemical processes occurring during resist exposure, post-exposure baking (PEB), and development to predict, for example, the profile of resist features formed on the substrate, so it is typically only related to such properties of the resist layer (e.g., the effects of chemical processes occurring during exposure, post-exposure baking, and development). In one embodiment, the optical properties of the resist layer (e.g., refractive index, film thickness, propagation, and polarization effects) can be captured as part of the projection optics model 32.

[0086] 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 the substrate level. The optical properties of the lithographic projection apparatus (e.g., the properties of the illumination, patterning device and projection optics) determine the aerial image.

[0087] The resist layer on the substrate is exposed by the 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. The resist image 38 can be simulated according to 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 in the resist layer, which is generated by the projection of radiation onto the substrate, the refraction at the resist interface, and the multiple reflections in the resist film stack. By absorbing the incident energy, the radiation intensity distribution (spatial image intensity) becomes a potential "resist image", which is further modified by diffusion processes and various load effects. An efficient simulation method that is fast enough for full-chip applications approximates the real three-dimensional intensity distribution in the resist stack through a two-dimensional spatial (and resist) image.

[0088] In one 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.

[0089] Thus, the model formula describes most, if not all, of the known physical and chemical properties of the entire process, and each model parameter ideally corresponds to a different physical or chemical effect. Thus, the model formula sets an upper limit on the extent to which the model can be used to simulate the entire manufacturing process.

[0090] The simulation of the patterning process can, for example, predict the contours in the spatial, resist and / or etched images, CD, edge position (e.g., edge position error), pattern shift, etc. Thus, the purpose of the simulation is to accurately predict, for example, edge position, and / or contour, and / or pattern shift, and / or spatial image intensity slope, and / or CD, etc. of the printed pattern. These values ​​can be compared to the expected design, for example, to correct the patterning process, identify locations where defects are expected to occur, etc. The expected 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 format.

[0091] Details of techniques and models for transforming pattern forming device patterns into various lithographic images (e.g., aerial images, resist images, etc.), applying OPC using these techniques and models, and evaluating performance (e.g., in terms of process window) are described in U.S. Patent Application Publication Nos. US 2008-0301620, 2007-0050749, 2007-0031745, 2008-0309897, 2010-0162197, 2010-0180251, and 2011-0099526 (each of which is incorporated herein by reference in its entirety).

[0092] In one embodiment, the optical properties of the pattern forming device (e.g., scanner) affect the performance of the patterning process. As previously described, the optical properties can be represented by Zernike polynomials. In one embodiment, the optical properties are optical aberrations of the lenses of the projection optics of the pattern forming device. According to one embodiment, the optical aberrations can be decomposed into multiple components. For example, the optical aberrations can be decomposed into multiple Zernike coefficients (e.g., Z1-Z37), wherein each Zernike coefficient is associated with an amplitude value. Therefore, in one embodiment, one or more Zernike coefficients and the associated amplitude value together determine the value of the optical aberration.

[0093] The manner in which optical properties (e.g., optical aberrations) affect printed features (e.g., features of a target pattern / desired pattern). In one embodiment, one feature may be more sensitive to a particular optical property (e.g., Z8) while another feature may be more sensitive to a different optical property (e.g., Z9). In one embodiment, the optical sensitivities of a limited set of features may be determined, such as hot spots or representative features corresponding to a pattern to be printed on a substrate. Evaluating the optical sensitivity of a limited set of patterns may be desirable because the computational time for simulations of patterning processes (such as SO, MO, SMO, or other optimization processes) for full-chip applications is relatively high compared to clamping. In addition, based on the optical sensitivity of the selected pattern, a limited number of components of the optical property are determined to reduce the number of parameters to be tuned to improve the performance of the patterning process. Therefore, any image tuning recipe based on tuning parameters will effectively improve the patterning process, such as down to minimal tuning of the optical property.

[0094] Figure 5A-5G , example mask patterns M1-M7 and selected features therein are shown. In one embodiment, mask patterns M1-M7 may be different portions of a single mask. Each mask pattern (e.g., M1, M2, M3, M4, M5, M6, or M7) includes features corresponding to a portion of a desired circuit, such as a memory, SRAM, microprocessor, etc., that is desired to be printed on a substrate. Within each mask pattern, a set of representative features for which optical sensitivity can be determined may be selected. According to one embodiment, the selected features are contained within a unit cell that serves as a desired portion (e.g., a hot spot or representative portion) of the mask. For example, a first unit cell 510 of mask pattern M1 includes three features, a second unit cell 520 of mask pattern M2 includes seven features, a third unit cell 530 of mask pattern M3 includes four features, a fourth unit cell 540 of mask pattern M4 includes two features, a fifth unit cell 550 of mask pattern M5 includes two features, a sixth unit cell 560 of mask pattern M6 includes two features, and a seventh unit cell 570 of mask pattern M7 includes two features. It can be seen that the features in a unit cell (e.g., 510) have features with similar geometric properties, such as shape and size, and are placed equidistant from each other. In another unit cell (e.g., 530), the features have different geometric properties, such as size, and the features may be placed at different distances relative to each other.

[0095] In one embodiment, such different layouts of features within a unit cell will result in different optical sensitivities. The optical sensitivity is related to lithographic effects, such as the output of a patterning process simulation (e.g., edge position, CD, line position, etc.) with aberration (or wavefront) variations. Therefore, the optical sensitivity can be represented by a sensitivity vector (e.g., d(edge ​​position) / d(Zernike number)) or a sensitivity wavefront (e.g., d(edge ​​position) / d(wavefront pixel)).

[0096] Depending on how many unit cells and features therein are evaluated, a large number of optical sensitivity values ​​may be obtained. In addition, features within unit cells are sensitive to dose and focus values. Thus, in one embodiment, thousands of optical sensitivities may be obtained that may not be individually tuned to improve the performance of the patterning process. Thus, in accordance with the present disclosure, method 400 determines a subset of components of an optical property that may be adjusted to improve the performance of the patterning process.

[0097] Figure 4 A method 400 of determining one or more components of an optical property of a patterning device (e.g., an optical sensitivity or Zernike coefficients corresponding to the optical sensitivity) that primarily affects the performance of a patterning process. In one embodiment, the Zernike coefficients approximate an optical wavefront, and further, the full wavefront can be approximated by the inner product of the Zernike coefficients and a Zernike polynomial. In one embodiment, the optical sensitivity describes how the edge position is affected by a particular Zernike or a particular wavefront. Thus, the optical sensitivity corresponds to a sensitivity vector (or map), where the inner product of the sensitivity vector and the Zernike coefficients describes the expected edge position. Similarly, inner producting the wavefront sensitivity map with the actual wavefront can return the expected edge position.

[0098] In one embodiment, method 400 determines components including optical properties (e.g., optical sensitivities or Zernike coefficients corresponding to optical sensitivities). The optical sensitivity determines how the edges of features of the pattern are affected when, for example, optical aberrations are introduced during the patterning process. Then, according to one embodiment, the number of optical sensitivities is reduced by a decomposition technique that describes the cross-covariance between data sets (e.g., principal component analysis "principal component analysis" (PCA)). For example, PCA determines linear combinations of optical properties that explain the main variations in optical sensitivity. Therefore, the optical sensitivity can be characterized by one or more principal components (e.g., P1, P2, P3, etc., including linear combinations of optical properties, such as sensitivity coefficients such as d / d(Z5), d / d(Z8), d / d(Z7), d / d(Z9), d / d(Z11), etc.). Based on the identified components, the method can be used for optimization of source optimization, mask optimization, source mask optimization processes, or other processes. About Figure 11-Figure 14Discuss an example of the optimization process.

[0099] In process P42, method 400 involves obtaining (i) a plurality of desired features 401, (ii) a plurality of simulated features 403 based on the plurality of desired features 401 and optical parameters of a patterning device, and (iii) a performance metric 405 associated with desired features in the plurality of desired features 401 and associated simulated features in the plurality of simulated features 403. In one embodiment, performance metric 405 is a characteristic of a feature of a substrate and / or a patterning process. In one embodiment, performance metric 405 is at least one of an edge position error, a critical dimension, a displacement between edges of two features on a substrate, and / or other known lithography-related performance metrics 405.

[0100] In one embodiment, the plurality of desired features 401 are selected from, for example, Figure 5A-5G One or more portions of the mask pattern in question. In one embodiment, obtaining a plurality of desired features 401 involves simulating a patterning process model assuming ideal optical properties (e.g., no optical aberrations) and perturbed values ​​of process parameters. For example, a design layout or mask pattern can be used to simulate a pattern on a substrate to obtain desired features 401 on the substrate. Thus, the patterning process model includes an ideal optics model, in which the values ​​of optical aberrations can be zero and only the values ​​of process parameters can be varied. In one embodiment, the process parameter is at least one of dose and / or focus whose values ​​can be varied during the simulation. For example, optical sensitivity is obtained under different process conditions such as different dose and focus values.

[0101] In one embodiment, desired feature 401 may be a target pattern or design layout. Desired features in multiple desired features 401 are used as references for determining the performance of a patterning device or patterning process. For example, the desired features may be compared to printed features or predicted features on a substrate that are affected by defects (e.g., optical aberrations) of the patterning device or patterning process. In one embodiment, improving the performance of the patterning process involves comparing the actual or predicted features to the desired features or reference features.

[0102] Obtaining the plurality of simulated features 403 involves simulating the patterning process model perturbation optical parameters, and values ​​of process parameters, to obtain the plurality of simulated features 403 associated with each of the plurality of desired features 401. In one embodiment, the process parameter is at least one of dose and / or focus whose value may be changed during the simulation. Furthermore, the values ​​of dose and focus used during the simulation are similar to the values ​​used to obtain the desired features or reference features.

[0103] As previously described, a desired feature in the plurality of desired features and a related simulated feature in the plurality of simulated features can be compared to obtain a performance metric 405 (e.g., EPE) for the patterning process. For example, the EPE between the desired feature and the simulated feature can be determined. In one embodiment, the EPE can be determined in a particular direction, such as in the horizontal and vertical directions, such as Fig. 8A and 8B shown.

[0104] Reference again Figure 4 In process P44, method 400 involves: determining a set 440 of optical sensitivities of the patterning process by calculating a change in a value of performance metric 405 based on a change in a value of an optical parameter. In one embodiment, the optical sensitivity of the patterning process is a difference in performance metric 405 relative to a Zernike coefficient. Therefore, the set 440 of optical sensitivities can be obtained by obtaining a difference in performance metric 405 with each Zernike coefficient.

[0105] In one embodiment, determining the change in performance metric 405 involves overlaying the desired feature and the simulated feature; and measuring the difference between the overlay profiles of the desired feature and the simulated feature in a predetermined direction. In one embodiment, the difference is measured in the horizontal direction and / or the vertical direction. The performance metric 405 then becomes the EPE along the x-direction and the y-direction.

[0106] exist Fig. 8A and 8B , desired feature 810 (also referred to as target feature 810) and simulated feature 820 are overlapped to determine the difference between the profiles of overlapped features 810 and 820. As previously described, feature 810 may be a desired feature obtained via simulation, or a designed feature of a design layout. Feature 820 is an example of a simulated feature that is distorted compared to the associated desired feature due to, for example, a perturbation in the value of an optical aberration of a patterning device (e.g., the magnitude of a Zernike coefficient).

[0107] In one embodiment, the difference is calculated along the vertical direction and / or the horizontal direction. Fig. 8A 810. In one embodiment, the difference is positive when the edge of 820 moves outward relative to 810, and negative when the edge of 820 moves inward relative to 810. Thus, the difference along the y direction is y12 (e.g., 0.1 nm) between points 1 and 2, and y34 (e.g., 0.2 nm) between points 3 and 4. Similarly, the difference along the x direction is x12 between points 1 and 2, and x34 between points 3 and 4. In one embodiment, the difference can be the sum of the differences in a particular direction.

[0108] In one embodiment, Figure 8B As shown, the difference can be calculated along the inclined cutting line CL3. In one embodiment, the difference along the inclined cutting line can be solved in the x component (along the x-axis) and the y component (along the y-axis) using simple trigonometric relationships. Then, the x difference and the y difference can also be used, for example, during PCA. This edge difference is called EPE, which can be used as a performance metric 405.

[0109] When edge position error is used as the performance metric 405 and the optical characteristics are defined by Zernike polynomials, the optical sensitivity vector for the patterning process is calculated using the following differential equation:

[0110]

[0111] In the above formula, Z n For the nth Zernike (such as Z2, Z3, Z4, Z5, Z6, Z7, Z8, Z9, etc.), EPE k is the kth edge position error corresponding to the nth Zernike. Figure 6 An example of optical sensitivity 440 based on the above formula is shown in . For example, if the simulation involves 41 clips, 2 edges of the feature, 5 focus levels, and 3 dose levels, a total of 1230 optical sensitivity vectors are obtained. In addition, most imaging metrics that characterize the features of the substrate are linearly proportional to the optical sensitivity. For example, the lithography metric can be calculated as follows. Wherein the sensitivity is determined based on the performance metric 405, as described above. In one embodiment, the sensitivity value (e.g., the differential of the performance metric) and the corresponding Zernike coefficient (Zernike coefficient) can be calculated based on the sensitivity value (e.g., the differential of the performance metric) and the corresponding Zernike coefficient (Zernike coefficient). k ) to calculate the lithography metrics.

[0112] Lithography metrology = ∑ k Sensitivity k ·Z k

[0113] In process P46, method 400 involves identifying a set 460 of components including optical properties that are major contributors to changing the value of performance metric 405 based on the set 440 of optical sensitivities. In one embodiment, a component (interchangeably referred to as an optical component) is an optical property that can be described via a Zernike coefficient, and thus the set 460 of components including optical properties can be described via a set of Zernike coefficients. For example, the set 460 of components (e.g., P1, P2, P3, etc.) includes relatively large contributions from Z8, Z11, Z15, Z20, and Z24, which in combination explain most of the variation in optical sensitivity values ​​within the set 440 of optical sensitivities calculated above. In other words, the set 460 of components (P1, P2, P3, etc., including relatively large contributions from Z8, Z11, Z15, Z20, and Z24) is a major contributor to changing the value of performance metric 405. Thus, in one embodiment, only some of the optical properties of the set of components 460 (eg, including contributions from Z5, Z8, etc.) may be tuned to improve the performance of the patterning process.

[0114] In one embodiment, the process P46 of identifying a set 460 of components comprising optical properties involves: performing a principal component analysis on the set 440 of optical sensitivities; and determining a linear combination of optical properties that takes into account substantial variations within the set 440 of optical sensitivities. Such a linear combination is referred to as a principal component of the set 440 of optical sensitivities. For example, a principal component is a linear combination of d / d(Z8), d / d(Z11), d / d(Z15), d / d(Z20), and d / d(Z24). Therefore, modifying the value of one or more (optical) properties (e.g., Z4, Z5, Z8) within the linear combination is sufficient to improve the performance of the patterning process. For example, a feature (e.g., Z8) that is the most important contributor to a principal component (e.g., P1).

[0115] In one embodiment, a plurality of principal components (e.g., 3 or 4 components, P1-P4) are identified that together explain more than 90% of the variation in, for example, optical sensitivity 440. In one embodiment, the principal components may be identified based on other criteria such as a covariance matrix that is based on covariances determined for principal components with the same variables (e.g., Z8). Thus, the principal components reduce the number of variables to be adjusted (e.g., optical parameters related to optical aberrations) to a selected few that explain most of the variation or meet other criteria such as covariance used in PCA. For example, Figure 6 The optical sensitivity of 1230 can be reduced to four principal components that explain 90% of the performance variation. Four example principal components are Figure 7B , 7D , 7F and 7H. In addition, in the principal component, Fig. 7A, 7C The wavefront sensitivity plots for low-order Zernikes that explain most of the variation are shown in 7E and 7F.

[0116] In one embodiment, it may be desirable for low order Zernike coefficients such as Z2-Z9 (or optical properties in general) to be part of the dominant contribution, as such low order Zernikes may be adjustable via an adjustment mechanism (e.g., connected to one or more mirrors) to adjust the performance of the patterning process. Therefore, having any low order Zernike in the principal components that can account for most variations may be particularly advantageous, as modifying one component (e.g., Z8) will help to cancel out other higher order components (e.g., Z11, Z15, Z20, etc.) within the linear combination of the principal components. In one embodiment, the ability to correct for higher order Zernikes is highly desirable, as the patterning device may not have the potential to correct for higher order Zernikes. For example, only the effects of low order Zernikes may be correctable (e.g., via an adjustment mechanism of a mirror), such as Fig. 9 The example correction potential relationships in are shown. For example, constant Z2 indicates the translation of the substrate table in the x-direction, constant Z3 indicates the translation of the substrate table in the y-direction, and constant Z4 mainly indicates the translation of the substrate table in the z-direction. Therefore, all of these can be compensated without any mirror movement. Similarly, Z5, Z7 and Z8 can be used as offsets for the substrate table.

[0117] In one embodiment, performance impacts due to higher order components may not be directly correctable. In other words, no tuning knob or adjustment mechanism may be used to correct for the effects of higher order optical components (e.g., higher order optical aberrations). Therefore, identifying one or more optical components (e.g., Z8, Z7, etc.) that can account for the greatest variation and compensate for the effects of higher order uncorrectable optical components is particularly beneficial for improving performance with minimal tuning effort.

[0118] In one embodiment, Figure 7B The first principal component PC1 including the effect of the low-order Zernike coefficient Z8 is shown in FIG. 1 , which is the largest contributor and can therefore be used as a correction knob. The first principal component PC1 includes a linear combination of several Zernike coefficients with different amplitudes. For example, the first principal component PC1 includes the linear combination: 0.8*Z8-0.4*Z11-0.1*Z15+0.2*Z20. In one embodiment, the first principal component PC1 corresponds to the linear combination of the Zernike coefficients along the y direction (e.g., Fig. 8A In the specific case of FIG7 , all holes of FIG5 are used. So PC1 is related to the EPEy position of all holes in FIG5 .

[0119] Therefore, by tuning the Zernike Z8, the behavior of the feature or the movement along the y-direction can be adjusted. Fig. 7A The wavefront sensitivity diagram for the first principal component P1 or related performance metric (e.g., EPE) is shown, which can account for, for example, a change of about 34% in optical sensitivity. After modifying parameters (e.g., the orientation of the mirror), it can be minimized Fig. 7A The part of the wavefront described (the first principal component) can be considered due to Z11, Z15 and Z20 (the correctable potential is very low or uncorrectable, according to Fig. 9 ) caused by the performance changes, thereby improving the performance of the patterning process.

[0120] In one embodiment, Fig.7D The second principal component PC2 is shown in FIG. 1 , which includes the influence of the low-order Zernike coefficient Z7. The second principal component PC2 is the largest contributor and can therefore be used as a correction knob. The second principal component PC2 also includes a linear combination of several Zernike coefficients with different amplitudes. For example, the second principal component PC2 includes the linear combination: 0.9*Z7+0.4*Z10+0.1*Z14+0.2*Z23+... In one embodiment, the second principal component PC2 corresponds to the linear combination along the x direction (e.g., Fig. 8A In the specific case of FIG7 , all holes of FIG5 are used. So PC1 is related to the EPEx positions of all holes in FIG5 .

[0121] Therefore, by tuning the Zernike Z7, the behavior of the feature or the movement along the x-direction can be adjusted. Figure 7C A wavefront sensitivity graph of the second principal component or related performance metric (e.g., EPE) is shown, which can account for, for example, a change of approximately 26% in optical sensitivity. After modifying parameters (e.g., the orientation of the mirror), it can be minimized Figure 7B The part of the wavefront described (the second principal component) can be considered due to Z10, Z14, Z23, etc. (the correctable potential is very low or uncorrectable, according to Fig. 9 ) caused by the performance changes, thereby improving the performance of the patterning process.

[0122] Similar to the first principal component PC1 and the second principal component PC2, the third principal component PC3 can be obtained ( Figure 7F ) and the fourth principal component PC4( Figure 7H). For example, the third principal component PC3 includes a correctable Zernike coefficient Z5, which can be used to correct for effects due to other Zernike coefficients (such as Z9 and Z12) within the linear combination of PC3 (with low or no correction potential). Similarly, the fourth principal component PC4 includes a correctable Zernike coefficient Z9, which can be used to correct for effects due to other uncorrectable Zernikes (such as Z12, Z16, or other Zernikes within the linear combination of PC4).

[0123] In summary, with all lenses adjusted (e.g., finding the best mirror position and tilt), wavefront aberrations can be minimized in the absence of any process knowledge. In one embodiment, wavefront aberrations are minimized by minimizing the sum of squares of the Zernike coefficients. Due to the orthogonality and the complete expansion of the Zernike polynomials, this is equivalent to minimizing the sum of squares of the wavefront. Therefore, going from wavefront to Zernike coefficients is a large data reduction without losing relevant content.

[0124] According to the method of the present disclosure, the Zernike coefficients are mapped to a new (orthogonal) basis, i.e., principal components. In one embodiment, these principal components are used for an orthogonal and complete set in EPE space (all possible edge positions at different orientations and under different conditions (focus and dose)). So from the sensitivity of all features to only a few principal components, the data is greatly reduced without losing much information. Combining these two can optimize the lens by minimizing the sum of the squares of the principal components.

[0125] In one embodiment, process P46 provides values ​​of the identified components of the optical characteristic corresponding to correctable Zernike coefficients, wherein the correctable Zernike coefficients are tunable via an adjustment mechanism of the pattern forming device. In one embodiment, the linear combination includes correctable Zernike coefficients and uncorrectable Zernike coefficients, wherein the uncorrectable Zernike coefficients are not tunable via an adjustment mechanism of the pattern forming device.

[0126] Once the optical component can account for a majority of the variation (e.g., greater than 90% of the variation) in the performance value of the patterning process (e.g., related to feature shape or size), in process P48, method 400 also includes: adjusting one or more mirrors of the pattern forming device via an adjustment mechanism based on the identified set of optical components to improve the performance metric of the patterning process.

[0127] In one embodiment, adjusting one or more mirrors includes: obtaining an optical correction potential of the patterning device, wherein the correction potential is a relationship between Zernike coefficients and orders that are correctable or uncorrectable via an adjustment mechanism of the patterning device. In addition, based on the correction potential, one or more mirrors of the optical system of the patterning device are identified as being associated with correctable Zernike coefficients within a set of optical components. Once the mirrors are identified, the adjustment process involves manipulating the identified mirrors to compensate for the effects of the uncorrectable Zernike coefficients such that a performance metric of the patterning process is improved.

[0128] The above method has a variety of applications, including source optimization, mask optimization, source-mask optimization, or other process parameter optimization. For example, based on the set of optical sensitivities and subsets of correctable optical components (e.g., within PC1, PC2, PC3, PC4, etc.), the illumination mode, mask pattern, etc. can be modified. In one embodiment, the optimization process involves determining values ​​of design variables (e.g., mask correlation, dose values, focus values, etc.) based on a reduction in a cost function. An example of an optimization process is shown below. Fig. 10A and Figure 11-14 discussed in.

[0129] refer to Fig. 10A , a method for optimizing optical sensitivity based on a patterning process is provided. In process P101, the method involves obtaining (i) a set 1001 of optical sensitivities, and (ii) a set 1003 of optical components that are major contributors to variations in the set of optical sensitivities (e.g., Figure 4 Components 460, such as elements of principal components).

[0130] In process P103, the method involves: determining a source pattern 1030 or a mask pattern 1031 via a patterning process model based on the set 1003 of optical components so that the performance metric is improved. In one embodiment, determining the source pattern or the mask pattern is an iterative process. Iteration includes: simulating the patterning process model using a set of values ​​of optical parameters and perturbing parameters related to the source pattern and / or the mask pattern, determining the performance metric based on the simulation results, and determining the values ​​of the parameters related to the source pattern and / or the mask pattern so that the performance metric is improved. In one embodiment, the parameter of the source model is at least one of the illumination mode and the intensity. In one embodiment, the parameter of the mask model is at least one of the following: the placement position of the auxiliary feature, the size of the feature, the shape of the auxiliary feature and / or the distance between two auxiliary features.

[0131] In one embodiment, the performance metric is an edge location error, and improving the performance metric includes minimizing the edge location error.

[0132] In one embodiment, the patterning process model is a source model, a mask model, an optical device model, a resist model, and / or an etch model. Figure 3 Examples of simulations of patterning processes including one or more of the above-described process models are discussed in .

[0133] In one embodiment, the method can also be extended to perform lens optimization based on a lens optimization evaluation function. In one embodiment, the lens optimization evaluation function is based on, for example, the principal components of the optical parameters identified in process P46 (e.g., Figures 7A-7H ). For example, the lens optimization merit function (S) is given in the following equation:

[0134] S=∑ i ∑ k (w k .ΔZ k，i ) 2 +∑ i ∑ m w m ·(∑ k pC m，k ΔZ k，i ) 2

[0135] In the above equation, the first part of the equation is the Zernike term based on the weights, and the second part is the additional term including the principal components (e.g., as in Figure 4 and Figure 7B , 7D , 7F, 7H). In addition, i is at each field point 1010 of the slit (see Fig. 10B ), k is run on different Zernike coefficients (2 to 25, 36, 49, 64, or 100), ΔZ corresponds to the difference between the measured Zernike coefficients and the lens model-induced Zernike coefficients (for example, introduced for simulation purposes), PC m，n is the transformation of the mth principal component to Zernike n, and w m are the associated principal component weights.

[0136] In one embodiment, the method may further include printing a pattern on a substrate using tunable properties (e.g., low-order Zernike coefficients within the principal components). In addition, measurement data of the printed pattern may be obtained, and the performance of the patterning device (e.g., a scanner) may be verified based on the measurement data against a reference performance.

[0137] The method according to the present disclosure has several advantages. For example, natural variations in non-adjustable parameters can result in large performance variations relative to the desired specifications. According to the present disclosure, such variations can be reduced by adjusting only selected optical parameters. When the cause of the performance mismatch is non-tunable optical characteristics, it may be necessary to replace the hardware associated with the cause of the non-tunable characteristics. However, according to the present disclosure, if non-tunable characteristics are present, it may be proposed to tune a single or multiple scanner knobs to compensate for the non-tunable characteristics. Therefore, in one embodiment, non-tunable characteristics (e.g., high-order Zernike coefficients) can be corrected by tuning the tunable characteristics of the scanner (e.g., low-order Zernike coefficients within the principal components).

[0138] As discussed in method 400, the identified optical properties can be used to optimize the patterning process or adjust parameters of the patterning process. For example, OPC addresses the fact that the final size and position of the image of the design layout projected on the substrate will not be the same as, or will only depend on, the size and position of the design layout on the patterning device. Note that the terms "mask", "reticle", and "patterning device" are used interchangeably herein. In addition, those skilled in the art will recognize that the terms "mask" / "patterning device" and "design layout" can be used interchangeably, especially in the context of lithography simulation / optimization, such as in lithography simulation / optimization, it is not necessary to use a physical patterning device, but a design layout can be used to represent the physical patterning device. For small feature sizes and high feature densities present on certain design layouts, the location of a particular edge of a given feature is affected to some extent by the presence or absence of other adjacent features. These proximity effects arise from trace 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 processes that typically follow lithography.

[0139] In order to ensure that the projected image of the design layout meets the requirements of a given target circuit design, complex numerical models, corrections or pre-distortions of the design layout are required to predict and compensate for proximity effects. The article "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 the current "model-based" optical proximity correction process. In a typical high-end design, almost every feature of the design layout has been modified in some way to achieve high fidelity of the projected image with the target design. These modifications can include the movement or offset of edge position or line width, and the application of "auxiliary" features intended to assist the projection of other features.

[0140] With millions of features typically present in a chip 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 (e.g., design layout after applying OPC and any other RET) need to be verified through design checking, i.e., intensive full-chip simulations using calibrated digital process models to minimize the likelihood that design defects are built into the patterning device pattern. This is driven by the huge cost of manufacturing high-end patterning devices (these devices run in the multi-million dollar range) and the impact on turnaround time of rework or repair after the actual patterning device is manufactured.

[0141] Both OPC and full-chip RET verification can be based on digital modeling systems and methods, such as those described in U.S. Patent Application No. 10 / 815,573 and Y. Cao et al., “Optimized Hardware and Software For Fast, Full Chip Simulation” (Proc. SPIE, Vol. 5754, 405 (2005)).

[0142] One RET is related to the adjustment of the global deviation of the design layout. The global deviation is the difference between the pattern in the design layout and the pattern intended to be printed on the substrate. For example, a circular pattern with a diameter of 25 nm can be printed on the substrate with a pattern with a diameter of 50 nm in the design layout or with a pattern with a diameter of 20 nm in the design layout but at a high dose.

[0143] In addition to the optimization of the design layout or pattern forming device (e.g., OPC), the illumination source can also be optimized in conjunction with or separately from the pattern forming device optimization in an effort to improve the overall lithography fidelity. The terms "irradiation source" and "source" are used interchangeably in this document. Since the 1990s, a variety of off-axis illumination sources such as annular, quadrupole, dipole, etc. have been introduced, and the off-axis illumination source provides greater freedom for OPC design, thereby improving the imaging effect. It is known that off-axis illumination is a proven method for addressing fine structures (i.e., target features) contained in pattern forming devices. However, compared with traditional illumination sources, off-axis illumination sources generally provide less radiation intensity for aerial images (AI). Therefore, it is necessary to try to optimize the illumination source to achieve the best balance between finer resolution and reduced radiation intensity.

[0144] Many illumination source optimization methods can be found, for example, in the article entitled "Optimum Mask and Source Patterns to Print A given Shape" by Rosenbluth et al. (Journal of Microlithography, Microfabrication, Microsystems 1 (1), pp. 13-20, (2002)). The source is divided into several regions, each corresponding to a certain region of the pupil spectrum. Then, it is assumed that the source distribution in each source region is uniform, and the brightness of each region is optimized for the process window. However, this assumption of uniform source distribution in each source region is not always valid, so the effectiveness of this method is affected. In another example presented in the article entitled "Source Optimization for Image Fidelity and Throughput" by Granik (Journal of Microlithography, Microfabrication, Microsystems 3 (4), pp. 509-522, (2004)), several existing source optimization methods are summarized and an illuminator pixel-based method is proposed, which converts the source optimization problem into a series of non-negative least squares optimizations. Although these methods have demonstrated some success, they often require multiple complex iterations to converge. In addition, it can be difficult to determine the appropriate / optimal values ​​of some additional parameters (such as γ in Granik's method), which determine the trade-off between the source that optimizes substrate image fidelity and the smoothness requirement of the source.

[0145] For low-k 1Optimization of both the lithography, source and pattern forming device is useful for ensuring a feasible process window for projection of critical circuit patterns. Some algorithms (e.g., Socha et al., see Proc. SPIE vol. 5853, 2005, p. 180) discretize the illumination into independent source points and the mask into diffraction orders in the spatial frequency domain, and separately formulate a cost function (defined as a function of the selected design variables) based on a process window metric (such as exposure latitude), which can be predicted from the source point intensity and the pattern forming device diffraction order by an optical imaging model. The term "design variables" used herein includes a set of parameters of a lithography projection device or a lithography process, for example, parameters that can be adjusted by a user of the lithography projection device, or image characteristics that can be adjusted by the user by adjusting these parameters. It should be understood that any characteristics of the lithography projection process (including the characteristics of the source, pattern forming device, projection optical device, and / or resist characteristics) can be design variables in the optimization. The cost function is typically a nonlinear function of the design variables. Standard optimization techniques are then used to minimize the cost function.

[0146] Relatedly, the pressure to continually reduce design rules has driven semiconductor chip manufacturers to move deeper into low-k via existing 193nm ArF lithography. l The era of photolithography. Towards lower k 1 The lithography of 2×nm has placed high demands on RET, exposure tools, and lithography-friendly design. 1.35ArF ultra-numerical aperture (NA) exposure tools may be used in the future. To help ensure that circuit designs can be made on substrates with feasible process windows, source patterning device optimization (referred to as source mask optimization or SMO in this article) is becoming an important RET for the 2×nm node.

[0147] A source and pattern forming device (design layout) optimization method and system are described in the commonly assigned International Patent Application No. PCT / US2009 / 065359, filed on November 20, 2009, with publication number WO2010 / 059954 and entitled “Fast Freeform Source and Mask Co-Optimization Method” (which is incorporated herein by reference in its entirety), which allows the source and pattern forming device to be optimized simultaneously using a cost function without constraints and within a feasible time.

[0148] Another source and mask optimization method and system involving optimizing a source by adjusting pixels of the source is described in commonly assigned U.S. Patent Application No. 12 / 813,456, filed on June 10, 2010, publication number 2010 / 0315614 and entitled “Source-Mask Optimization in Lithographic Apparatus,” which is incorporated herein by reference in its entirety.

[0149] In a lithographic projection apparatus, as an example, the cost function is expressed as

[0150]

[0151] Among them (z 1 , z 2 , ..., z N ) are N design variables or their values. p (z 1 , z 2 , ..., z N ) can be a design variable (z 1 , z 2 , ..., z N ), such as for the design variable (z 1 , z 2 , ..., z N ) is the difference between the actual value and the expected value of the characteristic at the evaluation point. p is with f p (z 1 , z 2 , ..., z N ) is the weight constant associated with . More critical evaluation points or patterns can be assigned higher w p Patterns and / or evaluation points that occur more often can also be assigned higher w p Examples of evaluation points may be any physical point or pattern on the substrate, any point on the virtual design layout, or a resist image, or an aerial image, or a combination thereof. p (z 1 , z 2 , ..., z N ) may also be a function of one or more optical properties identified, such as LWR, that are design variables (z 1 , z 2 , ..., z N). The cost function may represent any suitable characteristic of the lithographic projection apparatus or substrate, such as a failure rate of a feature, an identified optical property, focus, CD, image shift, image distortion, image rotation, random effects, yield, CDU, or a combination thereof. CDU is the local CD variation (e.g., three times the standard deviation of the local CD distribution). CDU may be interchangeably referred to as LCDU. In one embodiment, the cost function represents (i.e., is a function of) CDU, yield, and random effects. In one embodiment, the cost function represents (i.e., is a function of) EPE, yield, and random effects. In one embodiment, the design variables (z 1 , z 2 , ..., z N ) includes dose, global bias of the patterning device, shape of the illumination from the source, or a combination thereof. Since the resist image usually determines the circuit pattern on the substrate, the cost function usually includes a function representing some characteristic of the resist image. For example, such an evaluation point f p (z 1 , z 2 , ..., z N ) can simply be the distance between a point in the resist image and the expected position of that point (i.e., the edge position error EPE p (z 1 , z 2 , ..., z N )). The design variables can be any adjustable parameters, such as adjustable parameters of the source, pattern forming device, projection optics, dose, focus, etc. The projection optics may include components collectively referred to as "wavefront manipulators", which can be used to adjust the shape of the wavefront and the intensity distribution and / or phase shift of the irradiation beam. The projection optics can preferably adjust the wavefront and intensity distribution at any position along the optical path of the lithographic projection apparatus, such as before the pattern forming device, near the pupil plane, near the image plane, near the focal plane. The projection optics can be used to correct or compensate for certain distortions of the wavefront and intensity distribution caused by, for example, temperature changes in the source, pattern forming device, lithographic projection apparatus, 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 cost function. This change can be simulated from a model or actually measured. Of course, CF(z 1 , z 2 , ..., z N ) is not limited to the form in equation 1. CF(z 1 , z 2 , ..., z N ) may be in any other suitable form.

[0152] It should be noted that f p (z 1 , z2 , ..., z N ) is defined as Therefore, minimizing f p (z 1 , z 2 , ..., z N ) is equivalent to minimizing the cost function defined in Equation 1 Therefore, for simplicity of notation, f may be used interchangeably here. p (z 1 , z 2 , ..., z N ) and the weighted RMS of Eq. 1.

[0153] In addition, if maximizing PW (process window) is considered, the same physical location from different PW conditions can be regarded as different evaluation points in the cost function in (Equation 1). For example, if N PW conditions are considered, the evaluation points can be classified according to their PW conditions, and the cost function can be written as:

[0154]

[0155] in is the uth PW condition u=1,...,U under f p (z 1 , z 2 , ..., z N ) value. When f p (z 1 , z 2 , ..., z N ) is the EPE, minimizing the above cost function is equivalent to minimizing the edge offset under various PW conditions, resulting in maximizing PW. In particular, if PW also consists of different mask biases, minimizing the above cost function also includes minimizing MEEF (mask error enhancement factor) (which is defined as the ratio between the substrate EPE and the induced mask edge bias).

[0156] Design variables can have constraints, which can be expressed as (z 1 , z 2 , ..., z N)∈Z, where Z is a set of possible values ​​of the design variables. One possible constraint on the design variables may be imposed by the desired output of the lithographic projection apparatus. The desired output may limit the dose and therefore have an impact on the random effects (e.g., impose a lower limit on the random effects). Higher outputs typically result in lower doses, shorter exposure times, and larger random effects. Since the random effects are functions of the design variables, considering the substrate output and minimizing the random effects can limit the possible values ​​of the design variables. Without such constraints imposed by the desired output, the optimization may produce a set of unrealistic values ​​of the design variables. For example, if the dose is in the design variables, without such constraints, the optimization may produce dose values ​​that make the output economically impossible. However, the usefulness of the constraints should not be interpreted as necessity. The output may be affected by the failure rate-based adjustment of the parameters of the patterning process. It is desirable to keep the failure rate of the features low while maintaining a high output. The output may also be affected by the chemical properties of the resist. Slower resists (e.g., resists that require more light to be properly exposed) result in lower output. Therefore, appropriate parameters for the patterning process can be determined based on an optimization process involving feature failure rates due to resist chemistry or fluctuations, and dose requirements for higher throughput.

[0157] Therefore, the optimization process is performed under the constraint (z 1 , z 2 , ..., z N )∈Z to find the set of values ​​of the design variables that minimize the cost function, that is, find

[0158]

[0159] A general method for optimizing a lithographic projection apparatus according to an embodiment Fig.11. The method includes a step 302 of defining a multivariate cost function for a plurality of design variables. The design variables may include any suitable combination selected from the following: characteristics of the illumination source (300A) (e.g., pupil fill rate, i.e., the percentage of radiation of the source that passes through the pupil or aperture), characteristics of the projection optics (300B), and characteristics of the design layout (300C). For example, the design variables may include characteristics of the illumination source (300A) and characteristics of the design layout (300C) (e.g., global deviation), but not characteristics of the projection optics (300B), which results in SMO. Alternatively, the design variables may include characteristics of the illumination source (300A), characteristics of the projection optics (300B), and characteristics of the design layout (300C), which results in source mask lens optimization (SMLO). In step 304, the design variables are adjusted simultaneously so that the cost function moves toward convergence. In step 306, it is determined whether a predefined termination condition is satisfied. The predetermined termination condition may include various possibilities, namely, the cost function may be minimized or maximized, the value of the cost function has equaled a threshold or has crossed a threshold, the value of the cost function has reached a preset error range, or a preset number of iterations has been reached, depending on the requirements of the numerical technique used. If any of the conditions in step 306 is met, the method ends. If none of the conditions in step 306 is met, steps 304 and 306 are iteratively repeated until the desired result is obtained. Optimization does not necessarily result in a set of values ​​for the design variables, as there may be physical limitations caused by factors such as failure rate, pupil fill factor, resist chemistry, output, etc. Optimization may provide multiple sets of values ​​for design variables and related performance characteristics (e.g., output) and allow a user of the lithographic apparatus to select one or more sets.

[0160] In a lithographic projection apparatus, the source, the patterning device, and the projection optics may be optimized alternately (referred to as alternating optimization) or simultaneously (referred to as simultaneous optimization). As used herein, the terms "simultaneously," "simultaneously," "jointly," and "jointly" refer to design variables that allow the characteristics of the source, the patterning device, the projection optics, and / or any other design variables to be changed simultaneously. As used herein, the terms "alternating" and "alternatingly" mean that not all design variables are allowed to be changed simultaneously.

[0161] exist Fig.11 In the optimization of all design variables, the optimization is performed simultaneously. This process can be called a simultaneous process or a collaborative optimization process. Alternatively, the optimization of all design variables is performed alternately, such as Fig.12As shown in Figure 1. In this process, in each step, some design variables are fixed while other design variables are optimized to minimize the cost function; then in the next step, a different set of variables is fixed while other variables are optimized to minimize the cost function. These steps are performed alternately until convergence or some termination condition is met.

[0162] like Fig.12 As shown in the non-limiting example flow chart of , first a design layout is obtained (step 402), and then a source optimization step is performed in step 404, in which all design variables of the illumination source are optimized (SO) to minimize the cost function, while all other design variables are fixed. Then in the next step 406, a mask optimization (MO) is performed, in which all design variables of the pattern forming device are optimized to minimize the cost function, while all other design variables are fixed. These two steps are performed alternately until some termination conditions are met in step 408. Various termination conditions can be used, such as the value of the cost function becomes equal to a threshold, the value of the cost function crosses a threshold, the value of the cost function reaches a preset error limit, or a preset number of iterations is reached, etc. Note that SO-MO-alternating optimization is used as an example of an alternative flow. The alternative flow can take many different forms, such as SO-LO-MO alternating optimization, in which SO, LO (lens optimization) and MO are performed alternately and iteratively; or SMO can be performed once, and then LO and MO are performed alternately and iteratively; etc. Finally, the output of the optimization results is obtained in step 410, and the process stops.

[0163] As previously mentioned, the pattern selection algorithm can be combined with simultaneous or alternating optimization. For example, when alternating optimization is used, full chip SO can be performed first, "hot spots" and / or "warm spots" can be identified, and then MO can be performed. In view of the present disclosure, multiple permutations and combinations of sub-optimizations are possible in order to achieve the desired optimization results.

[0164] Fig.13AAn exemplary optimization method is shown in which a cost function is minimized. In step S502, initial values ​​of the design variables are obtained, including their tuning ranges (if any). In step S504, a multivariate cost function is established. In step S506, the cost function is expanded within a sufficiently small neighborhood around the starting point values ​​of the design variables of the first iteration step (i=0). In step S508, standard multivariate optimization techniques are applied to minimize the cost function. Note that the optimization problem can apply constraints, such as tuning ranges, during the optimization process in S508 or later in the optimization process. Step S520 indicates that each iteration is performed for a given test pattern (also called a "gauge") for the identified evaluation points that have been selected to optimize the lithography process. In step S510, the lithography response is predicted. In step S512, the results of step S510 are compared with the expected or ideal lithography response values ​​obtained in step S522. If the termination condition is met in step S514, that is, the optimization generates a lithography response value that is close enough to the expected value, then the final value of the design variable is output in step S518. The output step may also include outputting other functions using the final value of the design variable, such as outputting a wavefront aberration adjustment map of the pupil plane (or other planes), an optimized source map, and an optimized design layout. If the termination condition is not met, then in step S516, the value of the design variable is updated with the result of the i-th iteration, and the process returns to step S506. The following is a detailed description of the output step. Fig.13A process.

[0165] In the exemplary optimization process, no design variables (z 1 , z 2 , ..., z N ) and f p (z 1 , z 2 , ..., z N ) except for f p (z 1 , z 2 , ..., z N ) is sufficiently smooth (e.g., there is a first-order derivative ), which is usually effective in lithography projection equipment. Algorithms such as Gauss-Newton algorithm, Levenberg-Marquardt algorithm, gradient descent algorithm, simulated annealing, genetic algorithm, etc. can be applied to find

[0166] Here, we take the Gauss-Newton algorithm as an example. The Gauss-Newton algorithm is an iterative method applicable to general nonlinear multivariable optimization problems. In the i-th iteration, the design variable (z 1 , z 2 , ..., z N) takes the value of (z 1i , z 2i , ..., z Ni ), Gauss-Newton algorithm in (z 1i , z 2i , ..., z Ni ) nearby f p (z 1 , z 2 , ..., z N ) is linearized, and then (z 1i , z 2i , ..., z Ni ) is calculated near CF(z 1 , z 2 , ..., z N ) is the minimum value (z 1 (i+1), z 2 (i+1),...,z N In the (i+1)th iteration, the design variable (z 1 , z 2 , ..., z N ) takes the value of (z 1(i+1) , z 2(i+1) , ..., z N(i+1) ). This iteration continues until convergence (i.e., CF(z 1 , z 2 , ..., z N ) no longer decreases), or the preset number of iterations is reached.

[0167] Specifically, in the i-th iteration, in (z 1i , z 2i , ..., z Ni )nearby,

[0168]

[0169] Under the approximation of Equation 3, the cost function becomes:

[0170]

[0171] This is the design variable (z 1 , z 2 , ..., z N ). In addition to the design variables (z 1 , z 2 , ..., z N ), each term is a constant.

[0172] If the design variable (z 1 , z2 , ..., z N ) is not subject to any constraints, then we can solve the following N linear equations to obtain (z 1(i+1) , z 2(i+1) , ..., z N(i+1) ): Where n=1, 2, ...N.

[0173] If the design variable (z 1 , z 2 , ..., z N ) is subject to constraints of the form: J inequalities (e.g., (z 1 , z 2 , ..., z N ) tuning range for j = 1, 2, ... J; and K equations (e.g., interdependencies between design variables) For k = 1, 2, ... K, the optimization process becomes a classic quadratic programming problem, where A nj , B j , C nk , D k is a constant. Additional constraints can be imposed on each iteration. For example, a “damping factor” Δ D To limit (z 1(i+1) , z 2(i+1) , ..., z N(i+1) ) and (z 1i , z 2i , ..., z Ni ), so that the approximation of Equation 3 holds. This constraint can be expressed as z ni -Δ D ≤z n ≤z ni +Δ D . (z 1(i+1) , z 2(i+1) , ..., z N(i+1) ) can be used, for example, in Numerical Optimization (2 nd ed.)

[0174] Instead of minimizing f p (z 1 , z 2 , ..., z N), the optimization process can minimize the amount of maximum deviation (worst defect) between the evaluation points to their expected values. In this approach, the cost function can also be expressed as

[0175]

[0176] Among them, CL p Yes p (z 1 , z 2 , ..., z N ). This cost function represents the worst defect among the evaluation points. Optimization using this cost function can minimize the amount of the worst defect. An iterative greedy algorithm can be used for this optimization.

[0177] The cost function of Equation 5 can be approximated as:

[0178]

[0179] Where q is an even positive integer, such as at least 4, preferably at least 10. Equation 6 mimics the behavior of Equation 5 while allowing the optimization to be analytically performed and accelerated using methods such as the deepest descent method, the conjugate gradient method, and the like.

[0180] Minimizing the worst defect size can also be done with f p (z 1 , z 2 , ..., z N ). Specifically, f p (z 1 , z 2 , ..., z N ) is approximated as in Equation 3. The constraint on the worst defect size is then written as the inequality E Lp ≤f p (z 1 , z 2 , ..., z N )≤E Up Where E Lp and E Up are two constants that specify f p (z 1 , z 2 , ..., z N ). Inserting into Equation 3, these constraints are transformed into, for p=1, ...P,

[0181]

[0182] and

[0183]

[0184] Since Equation 3 is usually only valid for (z 1i , z 2i , ..., z Ni ), so if the desired constraint E cannot be achieved in this area Lp ≤f p (z 1 , z 2 , ..., z N )≤E Up (this can be determined by any conflicts between inequalities and constants), the constraint E Lp and E Up can be relaxed until the constraints can be achieved. This optimization process minimizes (z 1i , z 2i , ..., z Ni ). Each step then gradually reduces the worst defect size, and each step is performed iteratively until a certain termination condition is met. This will lead to an optimal reduction in the worst defect size.

[0185] Another way to minimize the worst-case defect is to adjust the weight w at each iteration p For example, after the i-th iteration, if the r-th evaluation point is the worst defect, then W can be increased in the (i+1)-th iteration. r , so that reducing the defect size at this evaluation point has higher priority.

[0186] Furthermore, the cost functions in Equations 4 and 5 can be modified by introducing Lagrange multipliers to achieve a trade-off between RMS optimization of defect size and optimization of the worst defect size, i.e.,

[0187]

[0188] Where λ is a preset constant that specifies the tradeoff between optimization of the RMS of defect size and optimization of the worst defect size. In particular, if λ=0, this becomes Equation 4 and the RMS of defect size is only minimized; while if λ=1, this becomes Equation 5 and the worst defect size is only minimized; if 0<λ<1, both are considered in the optimization. This optimization can be solved using a variety of methods. For example, the weights in each iteration can be adjusted, similar to the weights described previously. Alternatively, similar to minimizing the worst defect size from inequalities, the inequalities of Equations 6′ and 6″ can be viewed as constraints on the design variables in the process of solving the quadratic programming problem. Then, the bound on the worst defect size can be gradually relaxed, or the weight can be gradually increased for the bound on the worst defect size, the cost function value for each achievable worst defect size is calculated, and the design variable value that minimizes the total cost function is selected as the starting point for the next step. By doing this iteratively, minimization of this new cost function can be achieved.

[0189] Optimizing the lithography projection equipment can expand the process window. A larger process window provides greater flexibility for process design and chip design. The process window can be defined as a set of focus and dose values ​​that keep the resist image within specific limits of the design target of the resist image. Note that all methods discussed here can also be extended to a generalized process window definition that can be established by different or additional basis parameters other than exposure dose and defocus. These may include, but are not limited to, optical settings such as NA, mean square deviation, aberration, polarization, or optical constants of the photoresist layer. For example, as previously described, if the PW also contains different mask biases, the optimization includes minimization of the mask error enhancement factor (MEEF), which is defined as the ratio between the substrate EPE and the induced mask edge bias. The process window defined on the focus and dose values ​​is used only as an example in the present disclosure. A method for maximizing the process window according to one embodiment is described below.

[0190] In the first step, from the known conditions (f 0 , ε 0 ) starts, where f 0 is the nominal focus and ε 0 is the nominal dose, minimized near (f 0 ±Δf, ε 0 ±Δε) below:

[0191]

[0192] or

[0193]

[0194] or

[0195]

[0196] If the nominal focus f is allowed 0 and the nominal dose ε 0 offset, they can be compared with the design variables (z 1 , z 2 , ..., z N ) joint optimization. In the next step, if a value (z 1 , z 2 , ..., z N , f, ε) makes the cost function within the preset limit, then (f 0 ±Δf, ε 0 ±Δε) is accepted as part of the process window.

[0197] Alternatively, if focus and dose drift are not allowed, the focus and dose are fixed at the nominal focus f 0 and the nominal dose ε 0 Optimize the design variables (z 1 , z 2 , ..., z N In an alternative embodiment, if a set of values ​​(z 1 , z 2 , ..., z N ), so that the cost function is within the preset limit, then (f 0 ±Δf, ε 0 ±Δε) is accepted as part of the process window.

[0198] The methods described earlier in this disclosure can be used to minimize the corresponding cost functions of Eq. 7, 7′, or 7″. If the design variables are characteristics of the projection optics, such as Zernike coefficients, then minimizing the cost function of Eq. 7, 7′, or 7″ results in maximizing the process window based on projection optics optimization (i.e., LO). If the design variables are characteristics of the light source and pattern forming device as well as characteristics of the projection optics, then minimizing the cost function of Eq. 7, 7′, or 7″ results in maximizing the process window based on SMLO, such as Fig.11 If the design variables are characteristics of the source and the pattern forming device, minimizing the cost function of Equation 7, 7′, or 7″ results in maximizing the SMO-based process window. The cost function of Equation 7, 7′, or 7″ may also include at least one f such as in Equation 7 or Equation 8 p (z 1 , z 2 , ..., z N ), which is a function of one or more of the random effects such as LWR or local CD variations of the two-dimensional features and the output.

[0199] Fig.14 A specific example of how a simultaneous SMLO process can be optimized using the Gauss-Newton algorithm is shown. In step S702, starting values ​​for the design variables are identified. The tuning range for each variable can also be identified. In step S704, a cost function is defined using the design variables. In step S706, the cost function is expanded around the starting values ​​of all evaluation points in the design layout. In optional step S710, a full-chip simulation is performed to cover all key patterns in the full-chip design layout. In step S714, the expected lithography response metric (such as CD or EPE) is obtained, and in step S712, it is compared to the predicted values ​​of these quantities. In step S716, the process window is determined. Steps S718, S720, and S722 are similar to those described above. Fig.13A The corresponding steps S514, S516 and S518 described above. As mentioned above, the final output can be a wavefront aberration map in the pupil plane, which is optimized to produce the desired imaging performance. The final output can also be an optimized source map and / or an optimized design layout.

[0200] Fig. 13B An exemplary method for optimizing a cost function is shown, where the design variables (z 1 , z 2 , ..., z N ) includes design variables that can take only discrete values.

[0201] The method begins by defining pixel groups of an illumination source and patterning device tiles of a patterning device (step 802). In general, pixel groups or patterning device tiles may also be referred to as partitions of a lithography process component. In one exemplary method, the illumination source is partitioned into 117 pixel groups and 94 patterning device tiles are defined for the patterning device, substantially as described above, resulting in a total of 211 partitions.

[0202] In step 804, a lithography model is selected as the basis for the lithography simulation. The results generated by the lithography simulation are used to calculate the lithography metric or response. A specific lithography metric is defined as the performance metric to be optimized (step 806). In step 808, the initial (pre-optimization) conditions of the illumination source and the patterning device are set. The initial conditions include the initial state of the pixel group of the illumination source and the patterning device block of the patterning device, so that the initial illumination shape and the initial patterning device pattern can be referenced. The initial conditions may also include mask bias, NA, and focus slope range. Although steps 802, 804, 806, and 808 are depicted as sequential steps, it should be understood that in other embodiments of the present invention, these steps may be performed in other orders.

[0203] In step 810, the pixel groups and patterning device tiles are sorted. The pixel groups and patterning device tiles may be interleaved in the sorting. Various sorting methods may be used, including: sequentially (e.g., from pixel group 1 to pixel group 117 and from patterning device tile 1 to patterning device tile 94), randomly, based on the physical location of the pixel groups and patterning device tiles (e.g., sorting pixel groups closer to the center of the illumination source higher), and based on how changes to the pixel groups or patterning device tiles affect the performance metric.

[0204] Once the pixel groups and patterning device tiles are sorted, the illumination source and patterning device are adjusted to improve the performance metric (step 812). In step 812, each pixel group and patterning device tile is analyzed in the sorted order to determine whether a change in the pixel group or patterning device tile will result in an improved performance metric. If it is determined that the performance metric will be improved, the pixel group or patterning device tile is changed accordingly, and the resulting improved performance metric and the modified illumination shape or modified patterning device pattern form a baseline for comparison for subsequent analysis of the lower ranked pixel groups and patterning device tiles. In other words, the changes to improve the performance metric are retained. As changes to the states of the pixel groups and patterning device tiles are made and retained, the initial illumination shape and the initial patterning device pattern are changed accordingly so that the modified illumination shape and the modified patterning device pattern are produced by the optimization process in step 812.

[0205] In other approaches, patterning device polygon shape adjustments and pairwise polling of pixel groups and / or patterning device tiles are also performed during the optimization process at 812 .

[0206] In an alternative embodiment, the staggered simultaneous optimization process may include changing the pixel groups of the illumination source, and if an improvement in the performance metric is found, then stepping up and down the dose to look for further improvement. In yet another alternative embodiment, the stepping up and down of the dose or intensity may be replaced with a bias change of the patterning device pattern to look for further improvement in the simultaneous optimization process.

[0207] In step 814, it is determined whether the performance metric has converged. For example, the performance metric may be considered to have converged if little or no improvement in the performance metric was seen in the last few iterations of steps 810 and 812. If the performance metric has not converged, steps 810 and 812 are repeated in the next iteration, where the modified illumination shape and modified patterning device from the current iteration are used as the initial illumination shape and initial patterning device for the next iteration (step 816).

[0208] The above optimization method can be used to increase the output of a lithographic projection apparatus. For example, the cost function may include f as a function of exposure time. p (z 1 , z 2 , ..., z N ). The optimization of such a cost function is preferably constrained or influenced by a measure of the random effects or other measures. Specifically, a computer-implemented method for increasing the output of a lithography process may include optimizing a cost function as a function of one or more random effects of the lithography process and an exposure time of the substrate to minimize the exposure time.

[0209] In one embodiment, the cost function includes at least one f as a function of one or more random effects p (z 1 , z 2 , ..., z N ). Random effects may include feature failures, LWR, or local CD variations of 2D features. In one embodiment, the random effects include random variations in properties of the resist image. For example, such random variations may include failure rate, line edge roughness (LER), line width roughness (LWR), and critical dimension uniformity (CDU) of a feature. Including random variations in the cost function allows finding values ​​of the design variables that minimize the random variations, thereby reducing the risk of defects due to random effects.

[0210] In one embodiment, a method for determining components of an optical characteristic of a patterning process is provided. The method includes: obtaining (i) a plurality of desired features, (ii) a plurality of simulated features based on the plurality of desired features and an optical characteristic of the patterning process, and (iii) a performance metric associated with the desired features in the plurality of desired features and the associated simulated features in the plurality of simulated features; determining a set of optical sensitivities of the patterning process by calculating a change in a value of the performance metric based on a change in the value of the optical characteristic; and identifying a set of components of the optical characteristic including a major contributor to a change in the value of the performance metric based on the set of optical sensitivities.

[0211] In one embodiment, identifying a set of components of optical properties involves: performing a principal component analysis on the set of optical sensitivities; and determining a linear combination of optical properties that accounts for substantial variation within the set of optical sensitivities.

[0212] In one embodiment, the dominant contributors include linear combinations of optical properties.

[0213] In one embodiment, the optical property characterizes an optical aberration of an optical system of the patterning device.

[0214] In one embodiment, the optical properties are defined by Zernike polynomials.

[0215] In one embodiment, the components of the set of components of the optical property are coefficients of Zernike polynomials.

[0216] In one embodiment, the components correspond to correctable Zernike coefficients, wherein the correctable Zernike coefficients are tunable via an adjustment mechanism of the patterning device.

[0217] In one embodiment, the linear combination includes correctable Zernike coefficients and uncorrectable Zernike coefficients, wherein the uncorrectable Zernike coefficients are not tunable via an adjustment mechanism of the patterning device.

[0218] In one embodiment, the correctable Zernike coefficients are low order Zern ik e coefficient.

[0219] In one embodiment, calculating a change in the performance metric involves: overlaying the desired feature and the simulated feature; and measuring a difference in a particular direction between the overlay profiles of the desired feature and the simulated feature.

[0220] In one embodiment, the difference is measured in the horizontal direction and / or the vertical direction.

[0221] In one embodiment, obtaining the plurality of desired features involves simulating a patterning process model using ideal optical properties and perturbed values ​​of process parameters, wherein the ideal optical properties do not include optical aberrations.

[0222] In one embodiment, obtaining the plurality of simulated features involves: utilizing the plurality of desired features and simulating a patterning process model by perturbation values ​​associated with the optical property to obtain a plurality of simulated features associated with the plurality of desired features.

[0223] In one embodiment, the procedure parameter is at least one of dose and / or focus.

[0224] In one embodiment, the method further involves adjusting, via an adjustment mechanism, one or more mirrors of the patterning device based on the set of components of the optical characteristic to improve a performance metric of the patterning process.

[0225] In one embodiment, adjusting one or more mirrors involves: obtaining an optical correction potential for the pattern forming device, wherein the correction potential is a relationship between Zernike coefficients and orders that are correctable or uncorrectable via an adjustment mechanism of the pattern forming device; identifying a mirror of the optical system of the pattern forming device that corresponds to a correctable Zernike coefficient within a set of components of the optical characteristic; and manipulating the identified mirror to compensate for the effects of the uncorrectable Zernike coefficients such that a performance metric of the patterning process is improved.

[0226] In one embodiment, the performance metric is at least one of an edge location error, a critical dimension, and / or a displacement between edges of two features on the substrate.

[0227] In addition, in one embodiment, a source mask optimization method based on optical sensitivity of a patterning process is provided. The method involves: obtaining (i) a set of optical sensitivities, and (ii) a set of components including optical characteristics that are main contributors to variations in the set of optical sensitivities; determining a source pattern or a mask pattern via a patterning process model based on the set of components including optical characteristics, so that a performance metric of the patterning process is improved.

[0228] In one embodiment, determining the source pattern or the mask pattern is an iterative process. Iteration involves: simulating a patterning process model using a set of components including optical characteristics and perturbing parameters related to the source pattern and / or the mask pattern; determining a performance metric based on the simulation results; and determining values ​​of the parameters related to the source pattern and / or the mask pattern such that the performance metric is improved.

[0229] In one embodiment, the performance metric is at least one of an edge location error, a critical dimension, and / or a displacement between edges of two features on the substrate.

[0230] In one embodiment, the improvement of the performance metric includes minimizing edge location error.

[0231] In one embodiment, the patterning process model is a source model, a mask model, an optics model, a resist model, and / or an etch model.

[0232] In one embodiment, the parameter of the source model is at least one of illumination mode and intensity.

[0233] In one embodiment, the parameter of the mask model is at least one of: a placement position of an assist feature, a size of a feature, a shape of an assist feature, and / or a distance between two assist features.

[0234] Furthermore, in one embodiment, a computer program product is provided, the computer program product comprising a non-transitory computer-readable medium having instructions recorded thereon, the instructions implementing the above method when executed by a computer system.

[0235] Fig.15 1 is a block diagram illustrating a computer system 100 that can help implement the optimization methods and processes disclosed herein. The computer system 100 includes a bus 102 or other communication mechanism for transmitting information, and a processor 104 (or multiple processors 104 and 105) coupled to the bus 102 for processing information. The computer system 100 also includes a main memory 106, such as a random access memory (RAM) or other dynamic storage device, coupled to the bus 102 to store information and instructions to be executed by the processor 104. The main memory 106 can also be used to store temporary variables or other intermediate information during the execution of instructions to be executed by the processor 104. The computer system 100 also includes a read-only memory (ROM) 108 or other static storage device coupled to the bus 102 to store static information and instructions for the processor 104. A storage device 110, such as a magnetic disk or optical disk, is provided and coupled to the bus 102 to store information and instructions.

[0236] The computer system 100 may be coupled via the bus 102 to a display 112, such as a cathode ray tube (CRT) or a flat panel or touch panel display, for displaying information to a computer user. An input device 114, including alphanumeric and other keys, is coupled to the bus 102 to communicate 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. The input device typically has two degrees of freedom in two axes, a first axis (e.g., x) and a second axis (e.g., y), to allow the device to specify a position in a plane. A touch panel (screen) display may also be used as an input device.

[0237] According to one embodiment, portions of the processes described herein 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. Such 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 processing steps described herein. One or more processors of a multi-processing arrangement may also be employed to execute the sequences of instructions contained in main memory 106. In alternative embodiments, hard-wired circuitry may be used in place of or in combination with software instructions. Thus, embodiments are not limited to any specific combination of hardware circuitry and software.

[0238] As used herein, the term "computer-readable medium" refers to any medium that participates in providing instructions to the processor 104 for execution. Such media can take many forms, including but not limited to non-volatile media, volatile media, and transmission media. Non-volatile media include, for example, optical or magnetic disks, such as storage device 110. Volatile media include dynamic memory, such as main memory 106. Transmission media include coaxial cables, copper wires, and optical fibers, including wires that constitute bus 102. Transmission media can also take the form of sound waves or light waves, such as sound waves or light waves generated during radio frequency (RF) and infrared (IR) data communications. Common forms of computer-readable media include, for example, floppy disks, flexible disks, hard disks, magnetic tapes, any other magnetic media, CD-ROMs, DVDs, any other optical media, punch cards, paper tapes, any other physical media with hole patterns, RAM, PROMs and EPROMs, FLASH-EPROMs, any other storage chips or boxes, carrier waves described below, or any other media from which a computer can read.

[0239] Various forms of computer readable media may be involved in carrying one or more sequences of one or more instructions to processor 104 for execution. For example, the instructions may initially be carried on a disk of a remote computer. The remote computer may load the instructions into its dynamic memory and then 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 use an infrared transmitter to convert the data to an infrared signal. 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.

[0240] The computer system 100 may also include a communication interface 118 coupled to the bus 102. The communication interface 118 provides bidirectional data communications to couple to a network link 120 connected to a local area network 122. For example, the communication interface 118 may be an integrated services digital network (ISDN) card or a modem for providing a data communication connection with a corresponding type of telephone line. As another example, the communication interface 118 may be a local area network (LAN) card for providing a data communication connection with a compatible LAN. Wireless links may also be implemented. In any such implementation, the communication interface 118 sends and receives electrical, electromagnetic or optical signals carrying digital data streams representing various types of information.

[0241] The network link 120 generally provides data communication through one or more networks to other data devices. For example, the network link 120 can provide a connection through the local 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 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 that transport the information.

[0242] The computer system 100 can send messages and receive data, including program code, through the network, network link 120, and communication interface 118. In the Internet example, server 130 can send the requested code for an application through Internet 128, ISP 126, local network 122, and communication interface 118. According to one or more embodiments, for example, one such downloaded application provides 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.

[0243] Fig.16 Another exemplary lithographic projection apparatus LA is schematically depicted, the lithographic projection apparatus LA comprising:

[0244] - a source collector module SO providing radiation;

[0245] - an illumination system (illuminator) IL configured to condition a radiation beam B (e.g. EUV radiation) coming from the source collector module SO;

[0246] 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;

[0247] a substrate table (eg, wafer stage) WT configured to hold a substrate (eg, a resist-coated wafer) W and connected to a second positioner PW configured to accurately position the substrate; and

[0248] - 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).

[0249] As depicted here, the device LA is reflective (e.g., employing a reflective mask). It should be noted that because most materials are absorptive 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 pairs of molybdenum and silicon layers, each of which is a quarter wavelength thick. X-ray lithography can produce even smaller wavelengths. Since most materials are absorptive at both EUV and X-ray wavelengths, a thin piece of patterned absorbing material (e.g., a TaN absorber on a multilayer reflector) on the topography of the patterning device defines where features are printed (positive resist) or where features are not printed (negative resist).

[0250] refer to Fig.16 , the illuminator IL receives a beam of extreme ultraviolet radiation from the source collector module SO. Methods for generating EUV radiation include, but are not limited to, converting a material into a plasma state of at least one element having one or more emission lines in the EUV range (e.g., xenon, lithium, or tin). In one such method, 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, commonly referred to as laser produced plasma ("LPP"). The source collector module SO may be part of an EUV radiation system that includes Fig.16 A laser not shown in the figure is used to provide a laser beam for exciting 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. The laser and the source collector module may be separate entities, for example, when a CO2 laser is used to provide a laser beam for fuel excitation.

[0251] In this case, 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 including, for example, suitable guide mirrors and / or a beam expander. In other cases, the radiation source may be an integral part of the source collector module, for example when the radiation source is a discharge produced plasma EUV generator (commonly referred to as a DPP source).

[0252] The illuminator IL may include an adjuster for adjusting the angular intensity distribution of the radiation beam. Typically, at least the outer and / or inner radial extent of the intensity distribution in a pupil plane of the illuminator (commonly referred to as outer σ and inner σ, respectively) may be adjusted. In addition, the illuminator IL may include various other components, such as faceted field and pupil mirror devices. The illuminator may be used to adjust the radiation beam to have a desired uniformity and intensity distribution in its cross-section.

[0253] The radiation beam B is incident on a patterning device (e.g. a mask) MA, which is held on a support structure (e.g. a mask table) MT, and is patterned by the patterning device. After reflection from the patterning device (e.g. a mask) MA, the radiation beam B passes through a projection system PL, which focuses the beam onto a target portion C of a substrate W. With the aid of a second positioner PW and a position sensor PS2 (e.g. an interferometric device, a linear encoder or a capacitive sensor), the substrate table WT can be precisely moved, for example, in order 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 precisely position the patterning device (e.g. a mask) MA relative to the path of the radiation beam B. The patterning device (e.g. a mask) MA and the substrate W can be aligned using patterning device alignment marks M1, M2 and substrate alignment marks P1, P2.

[0254] The depicted device LA can be used in at least one of the following modes:

[0255] 1. In step mode, the support structure (e.g. mask table) MT and the substrate table WT remain substantially stationary while an entire pattern imparted to the radiation beam is projected at once onto a target portion C (i.e. a single static exposure). The substrate table WT is then shifted in the X and / or Y direction so that a different target portion C can be exposed.

[0256] 2. In scan mode, the support structure (e.g. mask table) MT and the substrate table WT are scanned synchronously while a pattern imparted to the radiation beam is projected onto a target portion C (i.e. a single dynamic exposure). The 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.

[0257] 3. In another mode, the support structure (e.g., mask table) MT remains substantially stationary so as to hold 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, typically a pulsed radiation source is employed, and the programmable patterning device is updated as required after each movement of the substrate table WT or between consecutive 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 described above.

[0258] Fig.17The apparatus LA including the source collector module SO, the irradiation system IL and the projection system PS is shown in more detail. The source collector module SO is constructed and arranged so that a vacuum environment can be maintained in the closed structure 220 of the source collector module SO. The 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 (such as xenon, lithium vapor or tin 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 that causes a plasma that is at least partially ionized. In order to effectively generate radiation, a partial pressure of Xe, Li, Sn vapor or any other suitable gas or vapor of, for example, 10Pa may be required. In one embodiment, a plasma that excites tin (Sn) is provided to generate EUV radiation.

[0259] The radiation emitted by the hot plasma 210 enters the collector chamber 212 from the source chamber 211 via an optional gas barrier or contaminant collector 230 (also referred to as a contaminant barrier or foil collector in some cases) located in or below an opening in the source chamber 211. The contaminant collector 230 may include a channel structure. The contaminant collector 230 may also include a gas barrier or a combination of a gas barrier and a channel structure. As known in the art, the contaminant collector or contaminant barrier 230 further indicated herein includes at least a channel structure.

[0260] 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 passing through the collector CO may be reflected from the grating spectral filter 240 to be focused in a virtual source point IF along the optical axis indicated by the dash-dot line "O". The virtual source point IF is often referred to as an intermediate focus, and the source collector module is arranged so that the intermediate focus IF is located at or near an opening 221 in the enclosure 220. The virtual source point IF is an image of the radiation emitting plasma 210.

[0261] The radiation then passes through an illumination system IL which may include a polygonal field mirror arrangement 22 and a polygonal pupil mirror arrangement 24 which are arranged to provide a desired angular distribution of the radiation beam 21 at the patterning device MA and to provide a desired uniformity of radiation intensity at the patterning device MA. When the radiation beam 21 held by the support structure MT is reflected at the patterning device MA, a patterned beam 26 is formed and the patterned beam 26 is imaged by the projection system PS via reflective elements 28, 30 onto a substrate W held by a substrate table WT.

[0262] There may typically be more elements than shown 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. Furthermore, there may be more mirrors than shown in the figures, for example with Fig.17 Compared to the ones shown, there may be 1-6 more reflective elements in the projection system PS.

[0263] like Fig.17 As shown, the collector optics CO 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 around the optical axis O, and this type of collector optics CO is expected to be used in conjunction with a discharge produced plasma radiation source.

[0264] Alternatively, the source collector module SO may be as follows Fig.18 Part of the LPP radiation system shown. The laser LAS is arranged to deposit laser energy into a fuel such as xenon (Xe), tin (Sn) or lithium (Li) to produce a highly ionized plasma 210 with an electron temperature of tens of eV. The high-energy radiation generated during the de-excitation and recombination of these ions is emitted from the plasma, collected by the collector optics CO at near normal incidence and focused onto an opening 221 in the closed structure 220.

[0265] The embodiments may be further described using the following terms:

[0266] 1. A method for determining a component of an optical characteristic of a patterning process, the method comprising:

[0267] obtaining (i) a plurality of desired features, (ii) a plurality of simulated features based on the plurality of desired features and an optical characteristic of the patterning process, and (iii) a performance metric associated with desired features in the plurality of desired features and associated simulated features in the plurality of simulated features;

[0268] determining a set of optical sensitivities of the patterning process by calculating a change in the value of the performance metric based on a change in the value of the optical characteristic; and

[0269] A set of components of the optical characteristic that include major contributors to changing the value of the performance metric are identified based on the set of optical sensitivities.

[0270] 2. The method of clause 1, wherein said identifying the set of components of the optical property comprises:

[0271] performing a principal component analysis on the set of optical sensitivities; and

[0272] A linear combination of the optical properties is determined that accounts for substantial variation within the set of optical sensitivities.

[0273] 3. A method according to any one of clauses 1 to 2, wherein the main contributor comprises the linear combination of the optical properties.

[0274] 4. A method according to any one of clauses 1 to 3, wherein the optical property characterizes an optical aberration of the optical system of the pattern forming device.

[0275] 5. The method of clause 4, wherein the optical properties are defined by Zernike polynomials.

[0276] 6. A method according to clause 5, wherein components of the set of components of the optical property are coefficients of the Zernike polynomials.

[0277] 7. The method of clause 6, wherein the components correspond to correctable Zernike coefficients, wherein the correctable Zernike coefficients are tunable via an adjustment mechanism of the patterning device.

[0278] 8. A method according to any one of clauses 6 to 7, wherein the linear combination comprises correctable Zernike coefficients and uncorrectable Zernike coefficients, wherein the uncorrectable Zernike coefficients are not tunable via an adjustment mechanism of the pattern forming device.

[0279] 9. The method of clause 8, wherein the correctable Zernike coefficients are low-order Zernike coefficients.

[0280] 10. A method according to any one of clauses 1 to 9, wherein said calculating said change in said performance metric comprises:

[0281] Overlaying the desired feature and the simulated feature; and

[0282] The difference between the overlaid profiles of the desired feature and the simulated feature in a particular direction is measured.

[0283] 11. The method according to any one of clauses 1 to 10, wherein the difference is measured in the horizontal direction and / or the vertical direction.

[0284] 12. The method according to any one of clauses 1 to 11, wherein said obtaining said plurality of desired features comprises:

[0285] A patterning process model is simulated using ideal optical properties and perturbed values ​​of process parameters, wherein the ideal optical properties do not include optical aberrations.

[0286] 13. The method according to any one of clauses 1 to 12, wherein obtaining the plurality of simulation features comprises:

[0287] The patterning process model is simulated using the plurality of desired features and by perturbation values ​​associated with the optical characteristic to obtain the plurality of simulated features associated with the plurality of desired features.

[0288] 14. The method according to any of clauses 12 to 13, wherein the process parameter is at least one of dose and / or focus.

[0289] 15. The method according to any one of clauses 1 to 14, further comprising:

[0290] One or more mirrors of a patterning device are adjusted via an adjustment mechanism based on the set of components of the optical characteristic to improve a performance metric of the patterning process.

[0291] 16. The method of clause 15, wherein said adjusting said one or more reflectors comprises:

[0292] obtaining an optical correction potential of the patterning device, wherein the correction potential is a relationship between a Zernike coefficient and an order that is correctable or uncorrectable via the adjustment mechanism of the patterning device;

[0293] identifying a mirror of the optical system of the patterning device corresponding to the correctable Zernike coefficient within the set of components of the optical characteristic; and

[0294] Manipulating the identified mirrors to compensate for the effects of the uncorrectable Zernike coefficients results in improvements in the performance metric of the patterning process.

[0295] 17. A method according to any of clauses 15 to 16, wherein the performance metric is at least one of an edge position error, a critical dimension and / or a displacement between edges of two features on a substrate.

[0296] 18. A method for optimizing a source mask based on optical sensitivity of a patterning process, the method comprising:

[0297] obtaining (i) a set of optical sensitivities, and (ii) a set of components including optical properties that are major contributors to variations in the set of optical sensitivities;

[0298] A source pattern or a mask pattern is determined via a patterning process model based on the set of components comprising the optical property such that the performance metric of the patterning process is improved.

[0299] 19. The method of clause 18, wherein the determining the source pattern or the mask pattern is an iterative process, the iteration comprising:

[0300] simulating the patterning process model using the set of components including the optical characteristics and perturbing parameters associated with the source pattern and / or the mask pattern;

[0301] determining the performance metric based on the simulation results;

[0302] Determining values ​​of the parameters related to the source pattern and / or the mask pattern results in an improvement of the performance metric.

[0303] 20. A method according to any of clauses 18 to 16, wherein the performance metric is at least one of an edge position error, a critical dimension and / or a displacement between edges of two features on a substrate.

[0304] 21. A method according to any of clauses 18 to 20, wherein the improvement of the performance metric comprises minimizing the edge position error.

[0305] 22. The method according to any of clauses 18 to 21, wherein the patterning process model is a source model, a mask model, an optics model, a resist model and / or an etch model.

[0306] 23. A method according to any of clauses 18 to 22, wherein the parameter of the source model is at least one of illumination mode and intensity.

[0307] 24. The method according to any one of clauses 18 to 22, wherein the parameter of the mask model is at least one of: a placement position of an assist feature, a size of the feature, a shape of the assist feature and / or a distance between two assist features.

[0308] 25. A computer program product comprising a non-transitory computer readable medium having recorded thereon instructions which, when executed by a computer system, implement the method according to any one of clauses 1 to 24.

[0309] The concepts disclosed herein can simulate or mathematically model any general imaging system for imaging sub-wavelength features and are particularly useful for emerging imaging technologies that are capable of producing wavelengths of increasingly smaller sizes. Emerging technologies already in use include EUV (extreme ultraviolet) lithography, which is capable of producing 193nm wavelengths using ArF lasers and even 157nm wavelengths using fluorine lasers. In addition, EUV lithography is capable of producing wavelengths in the 20-5nm range by using a synchrotron or by bombarding materials (solid or plasma) with high-energy electrons to produce photons in this range.

[0310] Although 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 lithography imaging system (e.g., those used for imaging on substrates other than silicon wafers).

[0311] 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, it may be used to manufacture integrated optical systems, guidance and detection patterns for magnetic domain memories, liquid crystal displays (LCDs), thin film magnetic heads, micromechanical systems (MEMs), etc. The skilled person will understand that in the context of such alternative applications, any use of the terms "reticle", "wafer" or "die" herein may be considered synonymous or interchangeable with the more general terms "patterning device", "substrate" or "target portion", respectively. Before or after exposure, the substrate referred to herein may be processed in, for example, a 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 herein may be applied to such and other substrate processing tools. In addition, the substrate may be processed more than once, for example to create, for example, a multi-layer IC, so the term substrate used herein may also refer to a substrate that already contains multiple processed layers.

[0312] In this document, 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, about 248, about 193, about 157, or about 126 nm) and extreme ultraviolet (EUV) radiation (e.g., having a wavelength in the range of 5-20 nm), as well as particle beams, such as ion beams or electron beams.

[0313] As used herein, the terms "optimizing" and "optimization" refer to or mean adjusting a pattern forming device (e.g., a lithographic apparatus), a patterning process, etc., so that the result and / or process has more desirable characteristics, such as higher projection accuracy of the design pattern on the substrate, a larger process window, etc. Thus, as used herein, the terms "optimizing" and "optimization" refer to or mean the process of identifying one or more values ​​of one or more parameters that provide an improvement, such as a local optimum in at least one relevant metric 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 one embodiment, the optimization steps may be iteratively applied to provide further improvements in one or more metrics.

[0314] 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, which may be a tangible carrier medium (e.g., a disk) or an intangible carrier medium (e.g., a communication signal). Embodiments of the present invention may be implemented using a suitable device, which may specifically take the form of a programmable computer running a computer program, which is arranged to implement the method as described herein. Therefore, embodiments of the present disclosure may be implemented in hardware, firmware, software, or any combination thereof. Embodiments of the present disclosure may also be implemented as instructions stored on a machine-readable medium, which may be read and executed by one or more processors. A machine-readable medium may include any mechanism for storing or transmitting information in a form readable by a machine (e.g., a computing device). For example, a machine-readable medium may include a read-only memory (ROM); a random access memory (RAM); a disk storage medium; an optical storage medium; a flash memory device; an electrical, optical, acoustic, or other form of propagation signal (e.g., a carrier wave, an infrared signal, a digital signal, etc.), etc. In addition, firmware, software, routines, instructions may be described herein as performing certain actions. However, it should be understood that such descriptions are merely for convenience and that such actions are actually caused by the computing device, processor, controller or other device executing firmware, software, routines, instructions, etc.

[0315] In the block diagrams, the components shown are depicted as discrete functional blocks, but the embodiments are not limited to systems in which the functionality described herein is organized as shown. The functionality provided by each component may be provided by software or hardware modules organized differently than currently described, for example such software or hardware may be mixed, combined, replicated, decomposed, distributed (e.g., in a data center or geographically), or otherwise organized. The functionality described herein may be provided by one or more processors of one or more computers that execute code stored on a tangible, non-transitory machine-readable medium. In some cases, a third-party content delivery network may host some or all of the information transmitted over the network, in which case, to the extent that information (e.g., content) is referred to as provided or otherwise provided, the information may be provided by sending instructions for retrieving the information from the content delivery network.

[0316] Unless otherwise specifically stated, as will be clear from the discussion, it should be understood that throughout the discussion of this specification, terms such as "processing," "computing," "calculating," "determining," etc. are used to refer to the actions or processes of a specific apparatus such as a special purpose computer or similar special purpose electronic processing / computing device.

[0317] The reader should understand that this application describes several inventions. Rather than dividing these inventions into multiple independent patent applications, it is better to combine these inventions into one file because their related subject matter helps save the application process. However, the unique advantages and aspects of such inventions should not be lumped together. In some cases, the embodiments solve all the defects pointed out in this article, but it should be understood that the present invention is independently useful, and some embodiments only solve a subset of such problems or provide other unmentioned benefits, which are clear to those skilled in the art who review this disclosure. Due to cost constraints, some inventions disclosed in this article may not be claimed for protection at present, and may be claimed in later applications, such as continued applications or by amending current claims. Similarly, due to space limitations, the abstract and summary sections of this document should not be regarded as a comprehensive list containing all such inventions or all aspects of such inventions.

[0318] It should be understood that the specification and drawings are not intended to limit the disclosure to the particular forms disclosed, but on the contrary, the intention is to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the present invention as defined by the appended claims.

[0319] In view of this description, modifications and alternative embodiments of various aspects of the present invention will be clear to those skilled in the art. Therefore, this specification and the drawings are to be interpreted as illustrative only, and are intended to teach those skilled in the art the general manner of implementing the present invention. It should be understood that the forms of the present invention shown and described herein will be considered as examples of embodiments. Elements and materials may replace those shown and described herein, parts and processes may be reversed or omitted, certain features may be used independently, and embodiments or features of embodiments may be combined, all of which are clear to those skilled in the art who benefit from this specification. Changes may be made to the elements described herein without departing from the spirit and scope of the present invention as described in the following claims. The headings used herein are for organizational purposes only and are not intended to limit the scope of the specification.

[0320] As used throughout this application, the word "may" is used in a permissive sense (i.e., indicating potential) rather than a mandatory sense (i.e., indicating must). The words "include", "including", and "includes" and the like mean, but are not limited to. The singular forms "a", "an", and "the" used throughout this application include plural referents unless the content clearly indicates otherwise. Thus, for example, reference to "an" element or "a" element includes a combination of two or more elements, although other terms and phrases, such as "one or more", are used for one or more elements. Unless otherwise indicated, the term "or" is non-exclusive, i.e., includes both "and" and "or". Terms describing conditional relationships such as "in response to X, Y", "at X, Y", "if X, Y", "when X, Y", etc. include causal relationships in which the antecedent is a necessary causal condition, the antecedent is a sufficient causal condition, or the antecedent is a contributing causal condition of the consequent, for example, "the statement X occurs when condition Y holds" is a general form of "X only occurs when Y" and "X occurs when Y and Z". Such conditional relationships are not limited to consequences that occur immediately after the antecedent is obtained, as some consequences may be delayed, and in conditional statements, the antecedent is related to its consequences, for example, the antecedent is related to the likelihood of the consequence occurring. A statement in which multiple attributes or functions are mapped to multiple objects (e.g., one or more processors perform steps A, B, C, and D) includes all of these attributes or functions mapped to all of these objects, as well as subsets of attributes or functions mapped to subsets of these attributes or functions (e.g., all processors perform steps AD, and the case in which processor 1 performs step A, processor 2 performs step B and part of step C, and processor 3 performs part of step C and step D), unless otherwise specified. Furthermore, unless otherwise stated, a statement that a value or action is "based on" another condition or value includes both the case where the condition or value is the only factor and the case where the condition or value is one of multiple factors. Unless otherwise stated, a statement that "each" instance of some set has some property should not be understood to exclude the case where some other identical or similar member of the larger set does not have that property, i.e., each does not necessarily mean every. References to selections from a range include the endpoints of the range.

[0321] In the above description, any process, description or block in the flowchart should be understood to represent a module, segment or code portion, which includes one or more executable instructions for implementing specific logical functions or steps in the process, and alternative implementations are included in the scope of the exemplary embodiments of this advancement, in which the functions may be performed in a different order than shown or discussed, including substantially simultaneously or in reverse order, depending on the functions involved, as will be understood by those skilled in the art.

[0322] To the extent that certain U.S. patents, U.S. patent applications, or other materials (e.g., articles) are incorporated by reference, the text of such U.S. patents, U.S. patent applications, and other materials is incorporated by reference only to the extent that there is no conflict between such materials and the statements and drawings set forth herein. In the event of such a conflict, any such conflicting text in such incorporated by reference U.S. patents, U.S. patent applications, and other materials is not expressly incorporated by reference herein.

[0323] Although certain embodiments have been described, these embodiments are presented by way of example only and are not intended to limit the scope of the present disclosure. In fact, the new methods, devices, and systems described herein may be embodied in a variety of other forms; moreover, various omissions, substitutions, and changes in the form of the methods, devices, and systems described herein may be made without departing from the spirit of the present disclosure. The accompanying claims and their equivalents are intended to cover such forms or modifications that fall within the scope and spirit of the present disclosure.

Claims

1. A method for determining a component of an optical characteristic of a patterning process, the method comprising: obtaining (i) a plurality of desired features, (ii) a plurality of simulated features based on the plurality of desired features and an optical characteristic of the patterning process, and (iii) a performance metric associated with desired features in the plurality of desired features and associated simulated features in the plurality of simulated features; determining a set of optical sensitivities of the patterning process by calculating a change in the value of the performance metric based on the change in the value of the optical characteristic; as well as A set of components of the optical characteristic that include one or more major contributors to variations in the value of the performance metric are identified based on the set of optical sensitivities.

2. The method of claim 1 , wherein said identifying the set of components of the optical property comprises: performing a principal component analysis on the set of optical sensitivities; as well as A combination of the optical characteristics is determined that accounts for substantial variation within the set of optical sensitivities.

3. The method of claim 1, wherein the one or more primary contributors comprise linear combinations of the optical properties. The method of claim 3 , wherein the optical property characterizes an optical aberration of an optical system of the patterning device. The method according to claim 4 , wherein the optical characteristic is represented by a Zernike polynomial.

6. The method of claim 5, wherein components of the set of components of the optical property are coefficients of the Zernike polynomials.

7. The method of claim 6, wherein the components correspond to correctable Zernike coefficients, wherein the correctable Zernike coefficients are tunable via an adjustment mechanism of the patterning device.

8. The method of claim 6, wherein the linear combination comprises correctable Zernike coefficients and uncorrectable Zernike coefficients, wherein the uncorrectable Zernike coefficients are not tunable via an adjustment mechanism of the patterning device.

9. The method of claim 8, wherein the correctable Zernike coefficients are low-order Zernike coefficients.

10. The method of claim 1, wherein said calculating said change in said performance metric comprises: Overlaying the desired feature and the associated simulated feature; as well as A difference between the overlay profiles of the desired feature and the associated simulated feature in a particular direction is determined.

11. The method of claim 1 , wherein obtaining the plurality of desired features comprises: Simulating a patterning process model using ideal optical properties and perturbed values ​​of process parameters, wherein the ideal optical properties do not include optical aberrations, and / or Wherein obtaining the plurality of simulation features comprises: The patterning process model is simulated using the plurality of desired features and using a perturbation value associated with the optical characteristic and the value of the process parameter to obtain the plurality of simulated features associated with the plurality of desired features.

12. The method of claim 11, wherein the process parameter is at least one of dose and focus.

13. The method according to claim 1, further comprising: adjusting, via an adjustment mechanism, one or more mirrors of a patterning device based on the set of components of the optical property and based on a performance metric of the patterning process, and Wherein said adjusting said one or more reflectors comprises: obtaining an optical correction potential for the patterning device, wherein the correction potential represents a relationship between Zernike coefficients and orders that are correctable or uncorrectable via the adjustment mechanism of the patterning device; identifying a mirror of an optical system of the patterning device corresponding to a correctable Zernike coefficient within the set of components of the optical characteristic; and The identified mirrors are manipulated based on the performance metric of the patterning process to compensate for the effects of uncorrectable Zernike coefficients.

14. The method of claim 1, wherein the performance metric is at least one of an edge location error, a critical dimension, and / or a displacement between edges of two features on a substrate.

15. A computer program product comprising a non-transitory computer readable medium having recorded thereon instructions, the instructions implementing the method according to claim 1 when executed by a computer system.

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