Method for determining aberration sensitivity of a pattern

Abstract

A method (300) for determining a process window limit pattern (PWLP) based on aberration sensitivity associated with a pattern forming device is described herein. The method includes: P (301) obtaining (i) a first kernel set (301) and a second kernel set (302) associated with an aberration wavefront of the pattern forming device, and (ii) a design layout (303) to be printed on a substrate via the pattern forming device; and determining P (303) an aberration sensitivity map associated with the aberration wavefront through a process simulation using the design layout, the first kernel set, and the second kernel set, the aberration sensitivity map indicating the sensitivity of one or more parts of the design layout to individual aberrations and interactions between different aberrations; and determining P (305) the PWLP (315) associated with the design layout having a relatively high sensitivity compared to other parts of the design layout based on the aberration sensitivity map.

Description

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims priority to U.S. application No. 62 / 895,372 filed on September 03, 2019, the entire contents of which are incorporated herein by reference. Technical Field

[0003] The present specification generally relates to aberration sensitivity of patterns and apparatus and methods for optimizing patterning processes, or aspects of patterning processes based on the aberration sensitivity. Background Art

[0004] Lithographic projection apparatus may be used, for example, in the manufacture of integrated circuits (ICs). In this case, a patterning device (e.g., a mask) may contain or provide a pattern corresponding to a single layer of the IC (a "design layout"), and this pattern may be transferred to a target portion (e.g., comprising one or more dies) on a substrate (e.g., a silicon wafer) that has been coated with a layer of radiation-sensitive material ("resist") by methods such as irradiating the target portion through the pattern on the patterning device. Typically, a single substrate comprises a plurality of adjacent target portions to which the pattern is transferred successively, one target portion at a time, by the lithographic projection apparatus. In one type of lithographic projection apparatus, the pattern on the entire patterning device is transferred to one target portion at a time; such an apparatus is typically referred to as a stepper. In an alternative apparatus, typically referred to as a stepper-scan apparatus, the projection beam is scanned over the patterning device in a given reference direction (the "scanning" direction) while the substrate is synchronously moved in a direction parallel or antiparallel to this reference direction. Different portions of the pattern on the patterning device are progressively transferred to one target portion. Since typically the lithographic projection apparatus will have a reduction ratio M (e.g. 4), the rate F at which the substrate is moved will be 1 / M times the rate at which the projection beam scans the patterning device. Further information on the lithographic apparatus described herein can be gleaned from, for example, US 6,046,792, which is incorporated herein by reference.

[0005] Before the pattern is transferred from the pattern forming device to the substrate, the substrate may undergo various processes, such as primer coating, resist coating and soft baking. After exposure, the substrate may undergo other processes ("post-exposure processes"), such as post-exposure baking (PEB), development, hard baking and measurement / inspection of the transferred pattern. This series of processes is used as the basis for manufacturing a single layer of a device (e.g., IC). The substrate may then undergo various processes, such as etching, ion implantation (doping), metallization, oxidation, chemical mechanical polishing, etc., all of which are intended to ultimately complete a single layer of the device. If several layers are required in the device, the entire process or its variation is repeated for each layer. Ultimately, the device will be present in each target portion on the substrate. These devices are then separated from each other by techniques such as slicing or cutting, whereby multiple individual devices can be mounted on a carrier, connected to pins, and so on.

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

[0007] As mentioned, photolithography is a core step in the manufacture of devices such as ICs, where patterns formed on a substrate define the functional elements of the device, such as microprocessors, memory chips, etc. Similar photolithography techniques are also used to form flat panel displays, microelectromechanical systems (MEMS), and other devices.

[0008] As semiconductor manufacturing processes continue to advance, the size of functional elements has continued to decrease over the decades while the number of functional elements (such as transistors) per device has steadily increased, following a trend generally referred to as "Moore's Law." In the current state of the art, multiple layers of a device are fabricated using a lithographic projection apparatus that projects a design layout onto a substrate using illumination from a deep ultraviolet illumination source, thereby forming multiple individual functional elements having dimensions well below 100 nm (i.e., less than half the wavelength of the radiation from the illumination source (e.g., a 193 nm illumination source)).

[0009] This process in which features with dimensions smaller than the classical resolution limit of the lithographic projection apparatus are printed is generally referred to as low-k1 lithography, and is based on the resolution formula CD=k1×λ / NA, where λ is the wavelength of the radiation employed (currently 248 nm or 193 nm in most cases), 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, the smaller k1 is, the more difficult it becomes to reproduce on the substrate a pattern that resembles the shape and dimensions planned by the designer in order to achieve specific electrical functionality and performance. In order to overcome these difficulties, complex fine-tuning steps are applied to the lithographic projection apparatus, the design layout, or the patterning device. These steps include, for example, but are not limited to: optimization of NA and optical coherence settings, customized illumination schemes, use of phase-shifting patterning devices, optical proximity correction (OPC, sometimes also called "optical and process correction") in the design layout, or other methods generally defined as "resolution enhancement techniques" (RET). The term "projection optics" as used herein should be broadly interpreted to cover various types of optical systems, including, for example, refractive optics, reflective optics, apertures, and reflective-refractive optics. The term "projection optics" may also include components that operate according to any of these design types for guiding, shaping, or controlling a projection radiation beam, either collectively or individually. The term "projection optical element" may include any optical component in the lithographic projection apparatus, regardless of where the optical component is located on the optical path of the lithographic projection apparatus. Projection optics may include optical components for shaping, adjusting, and / or projecting radiation from the source before it is passed through the pattern forming device, or optical components for shaping, adjusting, and / or projecting the radiation after the radiation passes through the pattern forming device. The projection optics typically do not include the source and the pattern forming device. Summary of the invention

[0010] According to an embodiment, a method for determining a process window limit pattern (PWLP) based on an aberration sensitivity associated with a pattern forming device is provided. The method includes: obtaining (i) a first kernel set and a second kernel set associated with an aberration wavefront of the pattern forming device, and (ii) a design layout to be printed on a substrate via the pattern forming device; and determining an aberration sensitivity map associated with the aberration wavefront through a process simulation using the design layout, the first kernel set, and the second kernel set, the aberration sensitivity map indicating the sensitivity of one or more parts of the design layout to specific aberrations and interactions between different aberrations; and determining the PWLP associated with the design layout having a relatively high sensitivity compared to other parts of the design layout based on the aberration sensitivity map. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Embodiments will now be described, by way of example only, with reference to the accompanying drawings, in which:

[0012] Figure 1 schematically depicts a lithographic apparatus according to an embodiment;

[0013] Figure 2 schematically depicts an embodiment of a lithography cell or lithography cluster according to an embodiment;

[0014] Figure 3 is a flow chart of a method 300 of determining a pattern window limit pattern (PWLP) based on aberration sensitivity associated with a pattern forming device according to an embodiment;

[0015] Figure 4A illustrates an example Zernike polynomial Z7 in image format according to an embodiment;

[0016] Figure 4B illustrates an example first-order kernel obtained for Zernike polynomial Z7 according to an embodiment;

[0017] Figure 5A illustrates an example first-order spatial image obtained using a first set of kernels for designing a pattern according to an embodiment;

[0018] Figure 5B illustrates an aberration-free aerial image for the design pattern according to an embodiment;

[0019] 6A to 6H illustrates an example first order image associated with an example first order ZCC kernel associated with Zernike polynomials Z5 to Z10 and Z35 to Z36 of a set of Zernike polynomials Z5 to Z36 according to an embodiment;

[0020] Figure 7illustrates an example matrix generated using pixel intensities of each of the Zernike images according to an embodiment;

[0021] Figure 8 is the Zernike image according to an embodiment (e.g. 6A to 6H (center) Graphical representation of an example PCA component PC1;

[0022] Fig. 9 is an example design layout according to an embodiment;

[0023] Fig. 10A According to the embodiment, Fig. 9 An example of aberration sensitivity mapping of the design layout in;

[0024] Fig. 10B According to the embodiment Fig. 9 4 selected fragments of the design layout and Fig. 10A An example of a corresponding aberration map fragment of the aberration map;

[0025] Fig.11 illustrates example aberration sensitivity segments corresponding to 2 selected segments of a design pattern after applying wavefront optimization according to an embodiment;

[0026] Fig.12 An example method of determining EPE, CD, and PPE for determining hot spots according to an embodiment is illustrated;

[0027] Fig.13 is a flow chart of a simulation of a patterning process according to an embodiment;

[0028] Fig.14 is a flow chart of determining a hotspot pattern according to an embodiment;

[0029] Fig.15 is a block diagram of an example computer system according to an embodiment;

[0030] Fig.16 is a schematic diagram of another lithographic projection apparatus according to an embodiment;

[0031] Fig.17 is a device for an extreme ultraviolet scanner according to an embodiment Figure 1 a view of the device in;

[0032] Fig.18 According to the embodiment Fig.16 and Fig.17 A more detailed view of the source collector module SO of the device. DETAILED DESCRIPTION

[0033] Before describing the embodiments in detail, it is instructive to present an example environment in which the embodiments may be implemented.

[0034] Figure 1 An embodiment of a lithographic apparatus LA is schematically depicted. The apparatus comprises:

[0035] - an illumination system (illuminator) IL configured to condition a radiation beam B (e.g. UV radiation or DUV radiation);

[0036] a support structure (e.g. mask table) MT configured to support a patterning device (e.g. mask) MA and connected to a first positioning device PM configured to accurately position the patterning device according to certain parameters;

[0037] 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 positioning device PW configured to accurately position the substrate according to certain parameters; and

[0038] - a projection system (e.g. a refractive projection lens system) PS, which is configured to project the pattern imparted to the radiation beam B by the pattern forming device MA onto a target portion C (e.g. comprising one or more dies and commonly referred to as a field) of the substrate W, the projection system being supported on a reference frame (RF).

[0039] As depicted here, the device is of the transmissive type (eg, employing a transmissive mask). Alternatively, the device may be of the reflective type (eg, employing a programmable mirror array of the type mentioned above, or employing a reflective mask).

[0040] The illuminator IL receives a radiation beam from a radiation source SO. For example, when the source is an excimer laser, the source and the lithographic apparatus may be separate entities. In this case, the source is not considered to form a part of the lithographic apparatus, and the radiation beam is transferred from the source SO to the illuminator IL with the help of a beam delivery system BD comprising, for example, suitable directional mirrors and / or a beam expander. In other cases, for example, when the source is a mercury lamp, the source may be an integral part of the apparatus. The source SO and the illuminator IL, and the beam delivery system BD if necessary, may be referred to as a radiation system.

[0041] 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 segments 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.

[0042] 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 radial extent and / or the inner radial extent (typically referred to as σ-outer and σ-inner, respectively) of the intensity distribution in a pupil plane of the illuminator may be adjusted. The illuminator IL may be operable to change the angular distribution of the beam. For example, the illuminator may be operable to change the number and angular extent of the segments in which the intensity distribution in the pupil plane is non-zero. By adjusting the intensity distribution of the beam in the pupil plane of the illuminator, different illumination modes may be achieved. For example, by limiting the radial extent and the angular extent of the intensity distribution in the pupil plane of the illuminator IL, the intensity distribution may have a multipole distribution, such as, for example, a dipole, a quadrupole or a hexapole distribution. The desired illumination mode may be obtained, for example, by inserting an optical device providing an illumination mode into the illuminator IL or by using a spatial light modulator.

[0043] The illuminator IL may be operable to change the polarization of the beam and may be operable to adjust the polarization using an adjuster AM. The polarization state of the radiation beam across the entire pupil plane of the illuminator IL may be referred to as a polarization mode. The use of different polarization modes may allow a greater contrast to be obtained in the image formed on the substrate W. The radiation beam may be unpolarized. Alternatively, the illuminator may be arranged to linearly polarize the radiation beam. The polarization direction of the radiation beam may vary across the entire pupil plane of the illuminator IL. The polarization direction of radiation may be different in different regions in the pupil plane of the illuminator IL. 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 generally be perpendicular to the position vector of the pole in the pupil plane of the illuminator IL. For example, for a dipole illumination mode, the radiation may be linearly polarized in a direction substantially perpendicular to a line bisecting two opposite segments of a dipole. The radiation beam may be polarized in one of two different orthogonal directions, which may be referred to as an X polarization state and a Y polarization state. For a quadrupole illumination mode, the radiation in the segment of each pole may be linearly polarized in a direction substantially perpendicular to a line bisecting the segment. This polarization mode may be referred to as XY polarization. Similarly, for a sextupole illumination mode, the radiation in the segment of each pole may be linearly polarized in a direction substantially perpendicular to a line bisecting the segment. This polarization mode may be referred to as TE polarization.

[0044] In addition, the illuminator IL typically includes various other components, such as an integrator IN and a condenser CO. The illumination system may include various types of optical components for directing, shaping or controlling the radiation, such as refractive, reflective, magnetic, electromagnetic, electrostatic or other types of optical components, or any combination thereof.

[0045] Thus, the illuminator provides a conditioned radiation beam PB having a desired uniformity and intensity distribution in its cross-section.

[0046] The support structure MT supports the pattern forming device in a manner that depends on the orientation of the pattern forming device, the design of the lithographic apparatus, and other conditions (such as, for example, whether the pattern forming device is maintained in a vacuum environment). The support structure can use mechanical, vacuum, electrostatic or other clamping techniques to hold the pattern forming device. The support structure can be, for example, a frame or a table, which can be fixed or movable as required. The support structure can ensure that the pattern forming device is in a desired position, for example relative to the projection system. Any use of the term "reticle" or "mask" herein can be considered synonymous with the more general term "pattern forming device".

[0047] 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 the substrate. In an embodiment, a patterning device is any device that can be used to impart a pattern to a radiation beam in its cross-section so as to create a pattern in a target portion of the substrate. It should be noted that, for example, if the pattern imparted to the radiation beam includes phase-shifting features or so-called assist features, the pattern may not exactly correspond to the desired pattern in the target portion of the substrate. Typically, the pattern imparted to the radiation beam will correspond to a specific functional layer in a device (such as an integrated circuit) created in the target portion.

[0048] 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 masks, alternating phase shift masks, and attenuated phase shift masks, 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 incident radiation beam in different directions. The tilted mirrors impart a pattern in the radiation beam reflected by the mirror matrix.

[0049] The term "projection system" as used herein should be interpreted broadly to cover any type of projection system suitable for the exposure radiation used, or for other factors such as the use of an immersion liquid or the use of a vacuum, including refractive, reflective, catadioptric, magnetic, electromagnetic and electrostatic optical systems, or any combination thereof. Any use of the term "projection lens" herein should be considered synonymous with the more general term "projection system".

[0050] The projection system PS has an optical transfer function that may be non-uniform and may affect the pattern imaged onto the substrate W. For unpolarized radiation, these effects can be described fairly well by two scalar maps or scalar diagrams that describe the transmission (apodization) and relative phase (aberration) of the radiation exiting the projection system PS as a function of position in a pupil plane of the projection system PS. These scalar maps, which may be referred to as transmission maps and relative phase maps, may 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. Determination of each scalar map may involve determining coefficients in such an expansion. Since the Zernike polynomials are orthogonal on the unit circle, the Zernike coefficients may be determined by calculating the inner product of the measured scalar map with each Zernike polynomial in turn and dividing this inner product by the square of the norm of the Zernike polynomial.

[0051] The transmission map and the relative phase map are field and system dependent. That is, typically, each projection system PS will have a different Zernike expansion for each field point (i.e., for each spatial location in the image plane of the projection system PS). The relative phase of the projection system PS in its pupil plane can be determined by projecting radiation (e.g.) from a point source in the object plane of the projection system PS (i.e., the plane of the pattern forming device MA) through the projection system PS and using a shearing interferometer to measure the wavefront (i.e., the trajectory of points with the same phase). A shearing interferometer is a common path interferometer and therefore, advantageously, no secondary reference beam is required to measure the wavefront. The shearing interferometer may comprise a diffraction grating, e.g., a two-dimensional grid in the image plane of the projection system (i.e., the substrate table WT); and a detector arranged to detect an interference pattern in a plane conjugate to the pupil plane of the projection system PS. The interference pattern is related to the derivative of the phase of the radiation with respect to the coordinate in the pupil plane in the shear direction. The detector may comprise an array of sensing elements, such as, for example, a charge coupled device (CCD).

[0052] The projection system PS of the lithographic apparatus may not produce visible fringes, and therefore, a phase stepping technique (such as, for example, moving the diffraction grating) may be used to enhance the accuracy of determining the wavefront. Stepping may be performed in the plane of the diffraction grating and in a direction perpendicular to the scanning direction of the measurement. The stepping range may be one grating period, and at least three (uniformly distributed) phase steps may be used. Thus, for example, three scanning measurements may be performed in the y direction, each for a different position in the x direction. Such stepping of the diffraction grating effectively converts phase changes into intensity changes, thereby allowing phase information to be determined. The grating may be stepped in a direction perpendicular to the diffraction grating (z direction) to calibrate the detector.

[0053] 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, such as one grating period. The scan averages the phase changes in one direction, thereby allowing reconstruction of the phase changes in the other direction. This allows the wavefront to be determined as a function of the two directions.

[0054] The transmission (apodization) of the projection system PS in its pupil plane may be determined by projecting radiation, for example, from a point source in its object plane (i.e. the plane of the patterning device MA) through the projection system PS and using a detector to measure the intensity of the radiation in a plane conjugate to the pupil plane of the projection system PS. The same detector may be used as that used to measure the wavefront to determine the aberrations.

[0055] The projection system PS may include a plurality of optical (e.g., lens) elements and may further include an adjustment mechanism AM configured to adjust one or more of the optical elements so as to correct aberrations (phase variations across the entire pupil plane throughout the field). To achieve such correction, the adjustment mechanism may be operable to manipulate one or more optical (e.g., lens) elements within the projection system PS according to 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. Displacing of optical elements may be performed in any direction (x, y, z, or a combination thereof). Tilt of an optical element is typically deviated from a plane perpendicular to the optical axis by rotating around an axis in the x and / or y direction, although for non-rotationally symmetric aspherical optical elements, rotation around the z-axis may be used. Deformation of the optical element may include low frequency shapes (e.g., astigmatism) and / or high frequency shapes (e.g., free form asphericity). Deformation of the optical element may be performed, for example, by using one or more actuators to apply forces on one or more sides of the optical element, and / or by using one or more heating elements to heat one or more selected regions of the optical element. Typically, it is not possible to adjust the projection system PS to correct for apodization (i.e., transmission variations across the pupil plane). A transmission map of the projection system PS may be used when designing a patterning device (e.g., mask) MA for the lithographic apparatus LA. Using computational lithography techniques, the patterning device MA may be designed to at least partially correct for apodization.

[0056] The lithographic apparatus may be of a type having two (dual-stage) or more tables (e.g. two or more substrate tables WTa, WTb, two or more patterning device tables, substrate table WTa and table WTb below the projection system in the absence of a dedicated substrate for, e.g., facilitating measurement and / or cleaning etc.). In these "multi-stage" machines, it may be possible to use additional tables in parallel, or preparatory steps may be performed on one or more tables while one or more other tables are being used for exposure. For example, alignment measurements using an alignment sensor AS and / or level (height, inclination etc.) measurements using a level sensor LS may be performed.

[0057] The lithographic apparatus may also be of a type in which at least a portion of the substrate may be covered by a liquid having a relatively high refractive index (e.g., water) so as to fill a space between the projection system and the substrate. Immersion liquid may also be applied to other spaces in the lithographic apparatus, for example, between the patterning device and the projection system. Immersion techniques are well known in the art for increasing the numerical aperture of projection systems. The term "immersion" as used herein does not mean that structures such as substrates must be immersed in liquid, but only means that liquid is located between the projection system and the substrate during exposure.

[0058] Thus, in operation of the lithographic apparatus, a radiation beam is conditioned and provided by the illumination system IL. The radiation beam B is incident on the pattern forming device (e.g., mask) MA held on the support structure (e.g., mask table) MT and is patterned by the pattern forming device. Having traversed the pattern forming device MA, the radiation beam B passes through the projection system PS, which focuses the beam onto a target portion C of the substrate W. With the aid of the second positioning device PW and a position sensor IF (e.g., an interferometric measurement device, a linear encoder, a two-dimensional encoder or a capacitive sensor), the substrate table WT can be accurately moved, for example, so as to position different target portions C in the path of the radiation beam B. Similarly, the first positioning device PM and a further position sensor (which is located in Figure 1 The support structure MT is a first positioning device (not explicitly depicted in the figure) that can be used to accurately position the patterning device MA relative to the path of the radiation beam B, for example after mechanical acquisition from a mask library or during scanning. Typically, movement of the support structure MT can be achieved with the help of a long-stroke module (coarse positioning) and a short-stroke module (fine positioning) that form part of the first positioning device PM. Similarly, movement of the substrate table WT can be achieved using a long-stroke module and a short-stroke module that form part of the second positioning device PW. In the case of a stepper (as opposed to a scanner), the support structure MT may be connected only to a short-stroke actuator, or may be fixed. The patterning device MA and the substrate W can be aligned using patterning device alignment marks M1, M2 and substrate alignment marks P1, P2. Although the substrate alignment marks occupy dedicated target portions as shown, the substrate alignment marks may be located in the space between target portions (these marks are called scribe alignment marks). Similarly, in the case where more than one die is provided on the patterning device MA, the patterning device alignment marks may be located between the dies.

[0059] The depicted device can be used in at least one of the following modes:

[0060] 1. In step mode, the support structure MT and the substrate table WT are held substantially stationary (i.e. a single static exposure) while the entire pattern imparted to the radiation beam is projected at once onto a target portion C. Next, the substrate table WT is shifted in the X and / or Y direction so that a different target portion C can be exposed. In step mode, the maximum size of the exposure field limits the size of the target portion C that is imaged in a single static exposure.

[0061] 2. In scan mode, the support structure MT and the substrate table WT are scanned synchronously while a pattern imparted to the radiation beam is projected onto a target portion C (i.e. a single dynamic exposure). The speed and direction of the substrate table WT relative to the support structure MT may be determined by the (or less) magnification and image reversal characteristics of the projection system PS. In scan mode, the maximum size of the exposure field limits the width of the target portion (in the non-scanning direction) in a single dynamic exposure, while the length of the scanning movement determines the height of the target portion (in the scanning direction).

[0062] 3. In another mode, the support structure MT is held substantially stationary, thereby holding the programmable patterning device, and the substrate table WT is moved or scanned, while a pattern imparted to the radiation beam is projected onto a target portion C. In this mode, a pulsed radiation source is typically employed, and the programmable patterning device is updated as required after each movement of the substrate table WT or between successive radiation pulses during a scan. This mode of operation may readily be applied to maskless lithography employing a programmable patterning device, such as a programmable mirror array of the type mentioned above.

[0063] Combinations and / or variations on the above-described modes of use, or entirely different modes of use, may also be employed.

[0064] Although specific reference may be made herein to the use of lithographic apparatus in IC manufacturing, it should be understood that the lithographic apparatus described herein may have other applications, such as manufacturing integrated optical systems, guidance and detection patterns for magnetic domain memories, liquid crystal displays (LCDs), thin film magnetic heads, etc. Those skilled in the art will understand that in the context of such alternative applications, any use of the term "wafer" or "die" herein may be considered synonymous with the more general term "substrate" or "target portion", respectively. The substrate referred to herein may be processed before or after exposure in, for example, a coating and developing system or track (a tool that typically applies a resist layer to a substrate and develops the exposed resist), or a measurement tool or an inspection tool. Where applicable, the disclosure herein may be applied to such and other substrate processing tools. In addition, the substrate may be processed more than once, for example to produce a multi-layer IC, so that the term substrate used herein may also refer to a substrate that already contains multiple processed layers.

[0065] The terms "radiation" and "beam" as used herein encompass all types of electromagnetic radiation, including ultraviolet (UV) radiation (e.g., having a wavelength of 365 nm, 248 nm, 193 nm, 157 nm or 126 nm) and extreme ultraviolet (EUV) radiation (e.g., having a wavelength in the range of 5 nm to 20 nm), as well as particle beams such as ion beams or electron beams.

[0066] Various patterns on or provided by a pattern forming device may have different process windows (i.e., the space of process variables under which patterns within specifications will be produced). Examples of pattern specifications related to potential systematic defects include checks for necking, line pullback, line thinning, CD, edge placement, overlap, resist top loss, resist undercut and / or bridging. The process windows of all patterns on a pattern forming device or on an area of ​​a pattern forming device may be obtained by merging (e.g., overlapping) the process windows of each individual pattern. The boundaries of the process windows of all patterns contain the boundaries of the process windows of some of the multiple individual patterns. In other words, these individual patterns limit the process windows of all patterns. These patterns may be referred to as "hot spots" or "process window limiting patterns (PWLP)", which are used interchangeably herein. When controlling a portion of a patterning process, it is possible and economical to focus on the hot spots. When the hot spots are defect-free, it is most likely that all patterns are defect-free.

[0067] like Figure 2As shown, the lithographic apparatus LA may form part of a lithographic cell LC (sometimes also referred to as a lithographic cell or lithographic cluster), which also includes equipment for performing pre-exposure processes and post-exposure processes on a substrate. Typically, these devices include one or more spin coaters SC for depositing one or more resist layers, one or more developers DE for developing the exposed resist, one or more chill plates CH and / or one or more baking plates BK. A substrate conveyor, or robot RO, picks up one or more substrates from an input port I / O1, an output port I / O2, moves these substrates between different process devices, and transfers them to a feed station LB of the lithographic apparatus. These devices, often collectively referred to as a coating and developing system or track, are under the control of a coating and developing system control unit or track control unit TCU, which itself is controlled by a management control system SCS, which also controls the lithographic apparatus via a lithographic control unit LACU. Thus, different devices may be operated to maximize throughput and processing efficiency.

[0068] In order to correctly and consistently expose a substrate exposed by the lithographic apparatus, and / or in order to monitor a portion of the patterning process (e.g. a device manufacturing process) comprising at least one pattern transfer step (e.g. an optical lithography step), it is desirable to inspect the substrate or other object to measure or determine one or more properties, such as alignment, overlay (which may be, for example, between structures in superimposed layers, or between structures in the same layer that have been separately provided to the layer by, for example, a double patterning process), line thickness, critical dimension (CD), focus offset, material properties, etc. Therefore, the manufacturing facility in which the lithographic cell LC is located also typically comprises a metrology system MET, which measures some or all substrates W that have been processed in the lithographic cell or other objects in the lithographic cell. The metrology system MET may be part of the lithographic cell LC, for example, it may be part of the lithographic apparatus LA (such as an alignment sensor AS).

[0069] One or more measured parameters may include, for example, overlap between successive layers formed in or on a patterned substrate, critical dimensions (CD) of features formed in or on a patterned substrate (e.g., critical line width), focus or focus error of an optical lithography step, dose or dose error of an optical lithography step, optical aberrations of an optical lithography step, etc. Such measurements may be performed on a target on the product substrate itself and / or on a dedicated metrology target disposed on the substrate. The measurements may be performed after resist development but before etching, or may be performed after etching.

[0070] There are a variety of techniques for measuring the structure formed in the patterning process, including the use of scanning electron microscopes, image-based measurement tools and / or various special tools. As described above, in a fast and non-invasive form of a special measurement tool, a radiation beam is directed to a target on the surface of the substrate, and the properties of the scattered (diffraction / reflection) beam are measured. By evaluating one or more properties of the radiation scattered by the substrate, one or more properties of the substrate can be determined. This can be called diffraction-based measurement. One such application of this diffraction-based measurement is in the measurement of characteristic asymmetry within a target. For example, this can be used as an overlapping measurement, but other applications are also known. For example, asymmetry can be measured by comparing opposite parts of the diffraction spectrum (for example, comparing the -1 and +1 orders in the diffraction spectrum of a periodic grating). This can be achieved as described above, and can be achieved as described, for example, in U.S. Patent Application Publication US2006-066855, which is incorporated herein by reference in its entirety. Another application of diffraction-based metrology is in the measurement of feature width (CD) within a target. Such techniques may use the apparatus and methods described below.

[0071] Thus, during a device fabrication process (e.g., a patterning process or a lithography process), a substrate or other object may be subjected to various types of measurements during or after the process. The measurements may determine whether a particular substrate is defective, may adjust the process and the equipment used in the process (e.g., aligning two layers on the substrate, or aligning the patterning device with the substrate), may measure the performance of the process and the equipment, or may be used for other purposes. Examples of measurements include optical imaging (e.g., optical microscopy), non-imaging optical measurements (e.g., diffraction-based measurements, such as ASML YieldStar metrology tools, ASML SMASH metrology systems), mechanical measurements (e.g., profiling using a stylus, atomic force microscopy (AFM)), and / or non-optical imaging (e.g., scanning electron microscopy (SEM)). U.S. Patent No. 6,961,116 (the entire contents of which are incorporated herein by reference) describes a SMASH (Smart Alignment Sensor Hybrid) system that employs a self-referencing interferometer that produces two overlapping and relatively rotated images of an alignment mark, detects intensities in a pupil plane where the Fourier transforms of the images interfere, and extracts position information based on the phase difference between the diffraction orders of the two images, which manifests itself as intensity variations of the interference orders.

[0072] The measurement results may be provided directly or indirectly to the supervisory control system SCS. If an error is detected, the exposure of subsequent substrates (especially if the inspection can be completed quickly and quickly enough that one or more other substrates of the batch remain to be exposed) and / or the subsequent exposure of the exposed substrate may be adjusted. In addition, the exposed substrate may be stripped and reworked to improve the yield, or discarded, thereby avoiding further processing of the substrate known to be defective. In the case that only some target portions of the substrate are defective, additional exposures may be performed only on those target portions that are good.

[0073] In the metrology system MET, metrology equipment is used to determine one or more properties of the substrate, and in particular to determine how one or more properties of different substrates vary, or how different layers of the same substrate vary from layer to layer. As described above, the metrology equipment may be integrated in the lithography apparatus LA or the lithography cell LC, or may be a separate device.

[0074] In order to achieve the measurement, one or more targets may be disposed on the substrate. In an embodiment, the target is specially designed and may include a periodic structure. In an embodiment, the target is a part of a device pattern, for example, a periodic structure of the device pattern. In an embodiment, the device pattern is a periodic structure of a memory device (for example, a bipolar transistor (BPT), a bit line contact (BLC), etc.).

[0075] In an embodiment, the target on the substrate may include one or more one-dimensional periodic structures (e.g., gratings) that are printed such that after development, the periodic structural features are formed by solid resist lines. In an embodiment, the target may include one or more two-dimensional periodic structures (e.g., gratings) that are printed such that after development, the one or more periodic structures are formed by solid resist columns or vias in the resist. The bars, columns or vias may alternatively be etched into the substrate (e.g., etched into one or more layers on the substrate).

[0076] The production process (eg Figure 2 ) includes more than one scanner (i.e., lithographic apparatus) that exhibits different performance (e.g., according to a pattern printed on a substrate). In order to provide consistent performance (e.g., consistent profile or CD) between different scanners or relative to a reference performance, wavefront optimization can be performed according to the methods of the present disclosure.

[0077] In an embodiment, the optimization may be performed using, for example, an objective function such as

[0078]

[0079] where (z1,z2,…,z N ) are N design variables or their values; f p (z1,z2,…,z N ) can be (z1,z2,…,z N ) is a function of the difference between the actual value and the expected value of the characteristic at the pth evaluation point of the set of values ​​of the design variables. p is the weight constant assigned to the pth evaluation point. A higher w may be assigned to an evaluation point or pattern that is more critical than other evaluation points or patterns. p It is also possible to assign higher w values ​​to patterns and / or evaluation points with larger numbers of occurrences. p Examples of evaluation points may be any physical point or pattern on the substrate, or any point on a patterning device pattern, or a resist image, or an aerial image.

[0080] The objective function may represent any suitable characteristic of a patterning process such as that performed on the lithographic projection apparatus or the substrate, such as focus, CD, image shift, image deformation, image rotation, etc. For example, the objective function may be a function of one or more of the following lithography metrics: edge placement error, critical dimension, resist profile distance, worst defect size, pattern shift, random effects, three-dimensional effects of the patterning device, three-dimensional effects of the resist, optimal focus shift, pupil fill factor, exposure time, and / or throughput. Because the resist image often dictates the pattern on the substrate, the objective function often includes a function representing some characteristic of the resist image. For example, such an evaluation point f p (z1,z2,…,z N ) may simply be the distance between a point in the resist image and the expected position of the point (i.e., the edge placement error EPE p (z1,z2,…,z N )). The design variable may be any adjustable parameter, such as an adjustable parameter of the wavefront.

[0081] The lithographic apparatus may include one or more components, collectively referred to as "wavefront manipulators", that can be used to adjust the wavefront shape, intensity distribution, and / or phase shift of the radiation beam. The wavefront can be adjusted at any location along the optical path of the lithographic projection apparatus, such as before the pattern forming device, near the pupil plane, near the image plane, or near the focus plane. The projection optical device can be used to correct or compensate for certain deformations of the wavefront caused by, for example, temperature changes in the irradiating element, the pattern forming device, the lithographic projection apparatus, and / or thermal expansion of components of the lithographic projection apparatus. Adjusting the wavefront can change the value of the evaluation point and the objective function. These changes can be simulated according to a model or actually measured.

[0082] It should be noted that f p (z1,z2,…,z N ) is defined as So, for example, minimizing f p (z1,z2,…,z N ) is equivalent to minimizing the objective function defined in Equation 1 Therefore, for simplicity of notation in this article, f p (z1,z2,…,z N ) and Equation 1.

[0083] The optimization process is performed under the constraints (z1, z2, ..., z N )∈Z, for example, to find a set of values ​​of the design variables that minimizes the objective function, that is, to find

[0084]

[0085] The optimization need not produce a single set of values ​​for the design variables (e.g. wavefront parameters). Additionally, there may be physical constraints due to factors such as pupil fill factor, resist chemistry, throughput, etc. The optimization may provide multiple sets of values ​​for design variables and associated performance characteristics (e.g. throughput), and allow a user of the lithographic apparatus to select one or more sets.

[0086] In an embodiment, algorithms such as Gauss-Newton algorithm, Levenberg-Marquardt algorithm, gradient descent algorithm, simulated annealing, genetic algorithm, etc. may be applied to evaluate and solve the objective function.

[0087] Existing methods for determining the aberration sensitivity of a pattern (e.g., of a design layout) are based on Zernike sensitivity analysis, e.g., for CD, or pattern placement error (PPE) of the pattern. Such CD- or PPE-based analysis involves evaluating the aberration sensitivity of a pattern at an evaluation point (e.g., on a tangent line across the pattern, see Fig.12 ) to determine CD and / or PPE. Such CD and / or PPE determination requires a priori knowledge about aberration hotspots. For example, hotspot determination based on lithography manufacturability check (LMC) includes classifying, sorting, and ranking all hotspots. Subsequently, the hotspots caused by aberrations must be identified.

[0088] In an example prior art method, hotspot detection is based on tracking image contours within an error budget of, for example, 0.05 nm. For example, a simulated image or a measured image (e.g., a SEM image) of a pattern on a substrate is obtained. Based on the image, an image processing algorithm such as edge detection or other edge tracking algorithms is used to track the pattern contour. Subsequently, the tracked contour is used to calculate the difference relative to the expected contour. In addition, a check is performed whether the difference exceeds the error budget (e.g., 0.05 nm).

[0089] In addition, determining hot spots requires obtaining an accurate outline of the pattern. Therefore, the calculation of the outline tracing of the pattern (or the simulation of the pattern) should be as accurate as possible. Therefore, existing models may require 48 transfer cross coefficient (TCC) kernels, which are computationally expensive. For example, an aerial image can be determined using Hopkin's formula with 48 transfer cross coefficients (TCC) for representing image intensity. TCC is the autocorrelation of the illumination pupil multiplied by the projection pupil (e.g., lens pupil).

[0090] Therefore, existing methods require extensive pre-processing to identify hot spots and subsequently determine the aberration sensitivity of such hot spots.

[0091] In addition to computational limitations, existing methods have several other limitations. For example, LMC-based hot spots are detected per Zernike term, and do not consider the constructive / destructive effects of combined Zernike terms that overestimate the hot spots. For example, when Zernike polynomials interact, some interactions amplify the aberration effects on the pattern, while some interactions cancel the aberration effects. Such interactions may not be considered in existing methods. Moreover, current calculations performed by finite differences between aberrated and unaberrated spatial images may require 48th order or higher TCC cores, which are computationally intensive for full-chip applications.

[0092] The method disclosed herein can use, for example, Zernike cross coefficient (ZCC) kernels to identify aberration-induced hot spot detection. The number of ZCC kernels is significantly less (e.g., 4 ZCC kernels) than the number of TCC kernels used for wafer profile tracking and CD calculation. Thus, the present method greatly reduces the computational burden compared to existing methods. In addition, the present method does not require profile tracking, CD and / or PPE determination. Thus, the present method is computationally faster and / or less resource-intensive than existing methods.

[0093] Figure 3Flowchart of method 300 for determining pattern window limiting pattern (PWLP) based on aberration sensitivity associated with pattern forming device. Various patterns on or provided by a pattern forming device may have different process windows, i.e., the space of process variables within which patterns within specifications will be produced. Examples of pattern specifications related to potential systematic defects include checking for necking, line pullback, line thinning, CD, edge placement, overlap, resist top loss, resist undercut and / or bridging. This is a non-exhaustive list of defects, and additional defect types and corresponding defect detectors may be defined. The process windows of all patterns on a pattern forming device or a region thereof may be obtained by merging the process windows of each individual pattern (e.g., overlapping the process windows). The boundaries of the process windows of all patterns contain the boundaries of the process windows of some of the multiple individual patterns. In other words, these individual patterns limit the process windows of all patterns. These patterns may be referred to as "hot spots" or "process window limiting patterns (PWLP)", which are used interchangeably in the present invention. It is possible and economical to focus on hot spots when controlling a portion of a patterning process. When the hot spot is defect-free, it is most likely that all patterns are defect-free.

[0094] Such hot spots may be caused by one or more of process parameters (e.g., dose, focus, etc.), characteristics of the apparatus (e.g., aberrations of a lens pupil of a lithographic apparatus), or other variables related to hot spots. According to the present disclosure, methods for determining aberration-induced hot spots are described.

[0095] The present method 300 has several advantages. As previously mentioned, the present method requires a significantly smaller number of cores to compute the aberration sensitivity map than those used for tracing image contours and contour-based hotspot detection. In an embodiment, the Zernike image is computed by the convolution between the electric field (e.g., mask image) and the ZCC kernel. The calculation can be performed on a coarse grid size (e.g., for EUV model pixel sizes of >4 nm) without intensive computational burden. The fast image-based aberration sensitivity calculation method enables full-chip calculations.

[0096] In addition, the method 300 is applicable to any polynomial expansion of the wavefront, including Zernike polynomials, Bessel functions, and Legendre polynomials, etc. The method 300 is not limited by a specific process model and is applicable to any (for example) optical model and resist model used to model the patterning process. The method 300 is applicable to any NA and wavelength. The method 300 is applicable to any chip design (memory, logic device, and microprocessor) including a full chip design. The steps or processes of the method 300 are described in detail as follows.

[0097] Step P301 includes obtaining (i) a first set of kernels 301 and a second set of kernels 302 associated with an aberration wavefront of the patterning device, and (ii) a design layout 303 to be printed on a substrate via the patterning device.

[0098] In an embodiment, the aberration wavefront is represented by any normal and complete set of functions, such as Zernike, Bessel functions, or orthonormal user-defined functions. As a non-limiting example, the aberration wavefront is represented by a set of Zernike polynomials or a bitmap image. The present method proposes the following example formula to obtain the aberration sensitivity of the pattern. For example, the aberration wavefront W(ρ) can be expanded by Zernike polynomials:

[0099]

[0100] In an embodiment, the aberration wavefront may be perturbed to determine the aberration sensitivity. For example, for the wavefront perturbation of W(ρ), a Taylor expansion may be performed as follows:

[0101]

[0102] In the above formula, W is the aberration wavefront, k0 is the wave vector (nm -1 ), ρ is the normalized wave vector (unitless), Z m represents the Zernike polynomial, c m The Zernike polynomials Z are associated with m Zernike coefficients for the amount of aberration explained (nm). The above example Taylor series expansion is up to 2nd order terms. However, the present disclosure is not limited to this expansion and may also include other higher order terms.

[0103] In an embodiment, the first set of kernels 301 is obtained by eigendecomposition of a first vector associated with a first order aerial image comprising linear aberration terms of the aberrated wavefront. In an embodiment, the first aerial image is calculated by convolution of a source function, a pupil function and first order aberrations, the first order aberrations characterizing the influence of linear aberration terms. In an embodiment, the source function is a mathematical representation characterizing an illumination source of the patterning device, and the pupil function is another mathematical representation characterizing a lens pupil of the patterning device. Such mathematical representations of the pupil and illumination source are known and do not limit the scope of the present disclosure.

[0104] In an embodiment, the first order spatial image may be determined using:

[0105]

[0106] In the above equation, I1 is the Zernike m (nm 1 ), x represents any part of the aerial image (e.g., an evaluation point on a pattern), S is a mathematical representation of the illumination source, H is the aerial image at each source point ρ0, M(ρ) is the mask diffraction pattern, and P is the pupil function. In an embodiment, the source function is represented as a pixelated image of the illumination source used by the pattern forming device. The first vector in the above formula can be calculated as follows:

[0107]

[0108] In determining the specific Zernike (e.g. Figure 4A and 4B The Z7 shown in the figure Afterwards, execute The eigendecomposition of m is performed to obtain a first Zernike kernel (also called a first Zernike cross coefficient (ZCC) kernel). In an embodiment, the first ZCC kernel can be regarded as a first-order aberration sensitivity filter for a specific Zernike term m.

[0109] Figure 4A An example Zernike polynomial Z7 in image format is illustrated and Figure 4B An example first-order kernel obtained for the Zernike polynomial Z7 (an example of the first set of kernels) is shown. Applying the equation Equation, where m=7 and given a source function (eg, a source image) and a given pupil function (eg, a lens pupil image), the first vector can be calculated In addition, you can Perform eigendecomposition to produce the elements of the first-order kernel. Figure 4B , the first three elements of the first kernel are ZCC1, ZCC2 and ZCC3. In this example, ZCC1, ZCC2 and ZCC3 are represented as images. However, in embodiments, the kernel may be represented in vector or matrix format for computational purposes.

[0110] Further using the first-order kernel, a first-order spatial image 500A (e.g., Figure 5A middle).

[0111]

[0112] Figure 5A The diagram shows the use of the above equation Example first order aerial image 500A obtained, where the mask or design layout (M) includes vertical lines.

[0113] In an embodiment, the second set of kernels 302 is obtained by eigendecomposition of a second order vector associated with a second aerial image including second order aberration terms of the aberrated wavefront. In an embodiment, the second order aerial image is calculated by convolving the source function, the pupil function and the second order aberrations, the second order aberrations characterizing the effect of the interaction between the individual aberrations. The source function is a mathematical representation characterizing the illumination source of the patterning device, and the pupil function is another mathematical representation characterizing the lens pupil of the patterning device.

[0114] In an embodiment, the second order spatial image may be determined using:

[0115]

[0116] In the above equation, is Zernike m,n(nm -2 ), S is the mathematical representation of the illumination source, H is the aerial image at each source point ρ0, M(ρ) is the mask diffraction pattern, and P is the pupil function. In an embodiment, the source function is represented as a pixelated image of the illumination source used by the pattern forming device. The second vector in the above formula can be calculated as follows:

[0117] In determining the specific Zernike interaction (e.g. Z5 and Z7), Afterwards, execute The eigendecomposition of is obtained to obtain a second Zernike kernel (also called second Zernike cross coefficient (ZCC) kernel). In an embodiment, the first ZCC kernel can be regarded as a second-order aberration sensitivity filter for a specific Zernike term m,n.

[0118] In an embodiment, the first kernel set 301 and the second kernel set 302 depend on parameters associated with an illumination source of the pattern forming device, a lens pupil of the pattern forming device, and a Zernike term describing the aberration wavefront associated with the pattern forming device, but the first kernel set and the second kernel set are independent of the shape of the design layout 303.

[0119] In an embodiment, the design layout 303 is at least one of the following: a pre-OPC mask layout (e.g., a design layout before optical proximity correction (OPC) is applied); a post-OPC mask layout (e.g., a design layout after optical proximity correction (OPC) is applied); or a mask image generated according to the post-OPC mask layout, wherein the mask image represents a mask diffraction pattern obtained by illuminating the post-OPC mask layout with the illumination source. Typically, the design layout 303 will include one or more patterns, wherein a pattern may also include multiple features (e.g., lines, contact holes, etc.).

[0120] In the present method, any shape of pattern can be used in the design layout. For example, in an embodiment, a pattern in one or more patterns includes multiple features and a portion of the pattern is a feature in the multiple features. In an embodiment, the one or more patterns include straight line mask patterns; lines and spaces; contact holes; and / or curved line mask patterns.

[0121] Step P303 includes: Fig.13 ) and determining an aberration sensitivity map 310 associated with the aberrated wavefront using the design layout 303, the first set of kernels 301, and the second set of kernels 302. In an embodiment, the aberration sensitivity map 310 indicates how sensitive one or more portions of the design layout 303 are to individual aberrations (e.g., specific Zernike polynomials) and to interactions between different aberrations (e.g., between two Zernike polynomials, such as Z5 and Z7).

[0122] In an embodiment, the aberration sensitivity map 310 is a function of a set of Zernike polynomials and a set of Zernike coefficients associated therewith, each Zernike coefficient indicating the amount of aberration explained by the associated Zernike polynomial. In an embodiment, the aberration sensitivity map 310 is a pixelated image, wherein pixel values ​​indicate the aberration sensitivity.

[0123] In an embodiment, determining the aberration sensitivity map 310 includes: determining a first-order aberration sensitivity map (e.g., Figure 4B ); determining a second-order aberration sensitivity map (not shown) by applying the second kernel set 302 to the design layout 303; and determining the aberration sensitivity map 310 as the sum of the first-order aberration sensitivity map and the second-order aberration sensitivity map. In addition, the aberration sensitivity map includes an aberration-free spatial image. Therefore, the aberration sensitivity map can be called a difference image or an incremental image (delta image), wherein the difference image represents the difference between the aberration-free spatial image and the aberration spatial image.

[0124] Figure 4B The first kernel set 301 is shown as an example, and the first-order spatial image is also obtained based on the kernel 301 (see Figure 5A ). Similarly, the second kernel set 302 may be used to determine the second-order spatial image. In an embodiment, the Hopkins formula may be used to obtain Figure 5B The aberration-free aerial image 500B (e.g., an ideal aerial image) shown in . Subsequently, the aberration sensitivity map can be determined as the sum of the aberration-free aerial image, the first-order image, and the second-order image. In an embodiment, the aberration sensitivity map 310 is determined using the following formula:

[0125]

[0126] In the above equations, several terms were previously solved / processed. For example, Z m refers to the Zernike polynomials, c m are the Zernike coefficients, I0(x) is the aberration-free spatial image, is the first-order spatial image, is the second order aerial image, and I(x) is the total aerial image or aberration sensitivity map according to the present disclosure. In an embodiment, the aberration sensitivity map I(x) is used as a map 310 to identify hot spots. In addition, a wavefront optimization may be performed to determine wavefront parameters (e.g., tilt, orientation, etc. of the mirror of the pupil) such that the aberration sensitivity of the hot spot is reduced.

[0127] In an embodiment, the first set of kernels 301 may be considered as a first-order aberration sensitivity filter for a given Zernike polynomial in the set of Zernike polynomials. In an embodiment, the second set of kernels 302 may be considered as a second-order aberration sensitivity filter for a given Zernike polynomial in the set of Zernike polynomials. In other words, the first set of kernels 301 and the second set of kernels 302 may be used to filter out first-order and second-order components / components of the aberration sensitivity map, respectively.

[0128] Process P305 includes determining a PWLP 315 associated with a design layout 303 having a relatively high sensitivity compared to other portions of the design layout 303 based on the aberration sensitivity map 310. In an embodiment, determining the PWLP 315 includes determining whether an intensity of a pixel of the aberration sensitivity map 310 exceeds a hotspot threshold. The hotspot threshold refers to an intensity value that may be relatively high or relatively low compared to a nominal intensity value range associated with the aberration sensitivity map (e.g., within 3 standard deviations of a mean intensity value of the image).

[0129] Then, in response to the intensity breaking through the threshold, one or more patterns associated with the pixels breaking through the threshold are identified within the design layout 303. Based on the identified patterns, the method classifies the identified patterns or a portion around the identified patterns as the PWLP 315.

[0130] In an embodiment, the PWLP 315 is determined based on the aberration sensitivity map 310 without tracking the contour of the printed pattern or simulated pattern, or calculating critical dimension or edge placement error or defect data associated with the printed substrate. Therefore, several calculation steps associated with existing methods are not performed by the present method. In this way, the computational efficiency of hotspot determination is greatly improved. In the prior art, the contour accuracy required to correctly calculate and identify the hotspot requires a large number of cores, such as more than 48 TCC cores. On the other hand, the aberration sensitivity map can achieve such hotspot detection in a significantly smaller number of cores (e.g., 4 ZCC cores) that can be used as a performance indicator, i.e., an index.

[0131] In addition, the method includes a second-order aberration sensitivity analysis that improves aberration correction. In other words, if certain Zernike effects are combined (e.g., canceled), appropriate corrections can be applied based on other Zernike effects. As a result, a more accurate correction of the aberration wavefront can be performed. When used to image a hot spot pattern, this improved aberration wavefront produces a printed pattern that meets the design specifications, thereby reducing the chance of defects occurring.

[0132] In an embodiment, the method further comprises a step P307 for determining source parameters, mask parameters and / or wavefront parameters 317 based on the aberration sensitivity map. For example, the step P307 comprises: determining a Zernike image based on an aberration-free spatial image and an aberration spatial image, wherein the aberration spatial image is determined based on first-order, second-order and higher-order (order>2) sensitivity maps; determining one or more principal components of the Zernike image via principal component analysis of the Zernike image, wherein a principal component is a linear combination of a Zernike polynomial and an associated Zernike coefficient, wherein the value of the Zernike coefficient indicates the amount of variation in the Zernike image explained by the associated Zernike polynomial; selecting a pattern associated with a relatively high sensitivity value for a particular Zernike polynomial based on at least one of the principal components; and determining source parameters, mask parameters and / or wavefront parameters via performing a source mask optimization or a wavefront optimization process using the selected pattern, so as to improve performance indicators.

[0133] In an embodiment, source mask optimization modifies source parameters (e.g., illumination intensity, focus, shape, etc.), mask parameters (e.g., OPC), or both source parameters and mask parameters for a selected pattern (e.g., hotspot 315) of the design layout. Such modification results in improved imaging performance (e.g., fewer defects) of the aberration lens of the patterning device. In an embodiment, the performance metric used may be a function of the edge placement error or CD associated with the selected pattern.

[0134] In an embodiment, the wavefront parameters may be modified via an actuator associated with the projection system of the pattern forming device. For example, the wavefront parameters are related to the coefficients of the Zernike polynomials. In an embodiment, the wavefront parameters may be the tilt, offset and / or orientation of a reflector for a lens in the pattern forming device. When these wavefront parameters are adjusted, a new wavefront is generated. In an embodiment, the wavefront parameters are determined to minimize the aberration sensitivity of the selected pattern. Once the optimized wavefront for tuning the pattern forming device is determined, the method may also involve converting the wavefront parameters into actuator movements via the lens model, and actuating the optical system of the tuning device based on the actuator movements.

[0135] 6A to 6H , Figure 7 and 8 An example of obtaining principal components of a first-order Zernike image based on a first-order kernel is illustrated. Figures 6A to 6H An example first-order image associated with an example first-order ZCC kernel associated with Zernike polynomials Z5 to Z10 and Z35 to Z36 in a set of Zernike polynomials Z5 to Z36 is illustrated. In this example, a first-order kernel of Z5 may be used to obtain a first-order image 605 of Z5. Similarly, first-order aerial images 606, 607, 608, 609, 610, ..., 635, and 636 may be obtained for each of the Zernike polynomials Z6 to Z36, respectively. In this example, the aerial images (also referred to as first-order Zernike images) 605 to 636 are for a portion of the design layout containing two vertical lines.

[0136] Figure 7 An example image matrix 700 generated using the pixel intensity of each Zernike image in the Zernike image is illustrated. For example, as illustrated, the image has N×N pixels, then the first-order Zernike image obtained for each Zernike polynomial can be represented as N 2 ×1 matrix. Further using the Zernike image matrix, principal component analysis can be performed. For example, the first principal component can be calculated as follows:

[0137] PC1=∑ i αi Z i , so that∑ i |α i | 2 =1

[0138] In the above equation, PC1 is the first principal component, α i is related to the specific Zernike polynomial i The PCA coefficients associated with the Zernike image matrix are indicative of the extent to which the variations in the Zernike image matrix are explained by a particular Zernike polynomial.

[0139] Figure 8 is a graphical representation of an example PCA component PC1 indicating that Zernike polynomials Z7 and Z23 explain the Zernike image (e.g. 6A to 6H This PCA is a linear combination of the Zernike polynomials and the associated coefficients. Therefore, the Zernike combination effect is considered in the aberration sensitivity analysis. In addition, this PCA can be used to determine hot spot patterns, such as relative to the example Figures 9 to 11 Discussed.

[0140] Figures 9 to 11 An example of obtaining a selected pattern according to a design layout based on a ZCC kernel for wavefront optimization (eg, phase controlled optimization) is illustrated. For example, as discussed in the method 300, the ZCC kernel may be applied to the design layout 900 ( Fig. 9 ) to obtain the aberration sensitivity map 950 (see Fig. 10A ).

[0141] exist Fig. 10A , the aberration sensitivity map 950 shows various parts (or locations) where the intensity of the pixel is substantially higher than other locations. For example, 6 locations 1, 2, 3, 4, 5, and 6 are marked in the map 950. In an embodiment, these locations can be selected by a threshold value of pixel intensity. For example, the pixel intensity value in the image 950 can vary from -10 to 10. The threshold value can be selected as 8 and -8. Therefore, if the pixel intensity value breaks through the threshold value of the pixel, the pixel is classified as a location to be analyzed for a hot spot. In addition, based on the identified 6 locations, the corresponding location in the design layout 900 can be selected. In an embodiment, a fragment or a portion of the design layout 900 can be selected around the selected 6 locations.

[0142] Fig. 10Bis a table showing 4 selected segments (e.g., cDL1, cDL2, cDL3, and cDL4) of the design layout 900 and corresponding aberration map segments (e.g., cASM1, cASM2, cASM3, and cASM4) of the aberration map 950. In the aberration segment cASM1, the parts P1, P2, P3, and P4 have substantially high sensitivity values. The parts P3 and P4 may have the highest sensitivity values, and these parts may be used to identify patterns in the design layout. For example, the design patterns CL5 and CL9 of the segment cDL1 are identified based on the parts P3 and P4. Similarly, based on the aberration map segments cASM2, cASM3, and cASM4, the parts P5 to P9 may be identified as having substantially higher sensitivity than other parts. Subsequently, based on the parts P5 to P9, the corresponding design patterns may be identified from the design layout segments cDL2, cDL3, and cDL4, respectively. In an embodiment, the identified design patterns corresponding to P1 to P9 or a subset thereof may be classified as hot spots.

[0143] In addition, for the identified hot spots (e.g. Fig. 10B In the example of the embodiment of the present invention, the wavefront optimization can be performed for the identified design pattern, such that the aberration sensitivity of the identified design pattern is reduced or minimized, and the source and / or mask optimization can be performed for the identified design pattern, such that the aberration sensitivity is reduced or minimized.

[0144] For example, Fig.11 Example aberration sensitivity segments cASM1' and cASM4' corresponding to the design pattern in segments cDL1 and cDL4 after applying wavefront optimization are illustrated. Fig.13 The wavefront optimization is performed by determining the simulated substrate patterns of the segments cDL1 and cDL2. During the simulation, one or more wavefront parameters (e.g., Zernike coefficients) associated with the wavefront may be determined such that the design patterns, e.g., in cDL1 and cDL4, do not become defective after being printed on a substrate (e.g., after a resist or after an etching process). For example, the simulated substrate patterns may be used for the design patterns cDL1 and cDL4 to minimize the performance indicators CD / PPE or EPE.

[0145] Furthermore, in an embodiment, LMC inspection and / or CD analysis may be performed on the simulated substrate patterns of cDL1 and cDL4 to determine whether the patterns are defective (eg, do not meet design specifications).

[0146] In this example, the Zernike image is used to select 6 hot spots for wavefront optimization. After wavefront optimization, a significant reduction in LMC defects is observed. In addition, 2 hot spots and 1 weak spot (e.g., based on the aberration sensitivity values) are identified for differential CD analysis. For two hot spots, applying the phase control optimization process (an example of a wavefront optimization process) results in significant differential CD improvements for the negative slit site. In addition, an offset movement of the Z8 component in the negative slit site is also observed. For the weak spot, there is very little CD asymmetry before and after wavefront optimization aligned with the weak Zernike image. Therefore, the experimental results indicate significant improvements in the patterning process, such as reduction of LMC defects. Therefore, the use of the aberration sensitivity map determined using the method of the present disclosure improves the existing state of the art.

[0147] Thus, in embodiments, based on the aberration sensitivity map and without performing CD / PPE or EPE calculations, hot spot patterns can be identified. Thus, in examples, the present disclosure improves the computation time for determining hot spots. Faster computations allow determination of hot spots for a full chip that includes millions or even billions of patterns. Existing methods involving CD / PPE and EPE (e.g. Fig.12 ) calculations, which require a lot of computational effort and time (which hinders such full-chip simulations to determine hotspots). Fig.14 Another example method of obtaining hotspot patterns is discussed in .

[0148] Fig.12 An example of an existing method for determining an EPE that is further used to determine a hotspot is illustrated. Fig.12 In the method, contours are extracted from the simulated pattern in which the simulation is performed for 7 different process window conditions. In addition, for each contour, the EPE is calculated as the difference (or distance) between the evaluation point on a given contour and the target contour at different locations on the contour (marked as points, also called evaluation points).

[0149] In an embodiment, the method 300 may be used in various applications. For example, the method 300 may further include determining parameters of the patterning process based on the aberration sensitivity map 310 so as to reduce the sensitivity of the PWLP 315. For example, the values ​​of dose, focus, lens tuning, and other process parameters may be adjusted.

[0150] In an embodiment, the method 300 may further include: ranking one or more patterns of the design layout 303 based on the sensitivity values ​​of the aberration sensitivity map 310 or a performance indicator or index of the aberration sensitivity map 310, wherein patterns of the one or more patterns associated with relatively high sensitivity values ​​are ranked higher than other patterns; selecting one or more patterns with relatively high rankings based on the rankings; and modifying the selected pattern of the design layout 303 using the aberration sensitivity map 310 and a mask optimization process so as to reduce the sensitivity of the selected pattern. In an embodiment, the performance indicator or index may be such as by, for example Fig.11 The CD / PPE asymmetry is indicated by the positive and negative values ​​of the Zernike images of the two grating patterns shown in FIG.

[0151] In an embodiment, a computer program product (eg, Fig.15 ) includes a non-transitory computer-readable medium having instructions recorded thereon, which, when executed by a computer, implement any process in the process of the method described in this document.

[0152] Combinations and sub-combinations of the disclosed elements constitute separate embodiments according to the present disclosure. For example, a first combination may be determining a process window limit pattern (PWLP) based on the aberration sensitivity. Another example combination may be determining the aberration sensitivity map itself.

[0153] Fig.13 An exemplary flow chart for modeling and / or simulating portions of a patterning process (e.g., lithography in a lithographic apparatus) is illustrated in . As will be appreciated, the models may represent different patterning processes and need not include all of the models described below. Source model 1300 represents the optical characteristics of the illumination of the patterning device (including the radiation intensity distribution, bandwidth, and / or phase distribution). The source model 1300 may represent the optical characteristics of the illumination, including, but not limited to, numerical aperture settings, illumination standard deviation (σ) settings, and any specific illumination shape (e.g., off-axis radiation shapes such as toroidal, quadrupole, dipole, etc.), where σ (or standard deviation) is the outer radial extent of the illuminator.

[0154] The projection optics model 1310 represents the optical properties of the projection optics (including changes to the radiation intensity distribution and / or the phase distribution caused by the projection optics). The projection optics model 1310 may represent the optical properties of the projection optics, including aberrations, deformations, one or more refractive indices, one or more physical sizes, one or more physical dimensions, etc.

[0155] The patterning device model module 120 captures how design features are arranged in the pattern of the patterning device and may include a representation of the detailed physical properties of the patterning device, as described, for example, in U.S. Pat. No. 7,587,704. The goal of the simulation is to accurately predict, for example, edge placement and CD, which can then be compared to the device design. The device design is typically defined as a pre-OPC patterning device layout and will be provided in a standardized digital file format such as GDSII or OASIS.

[0156] The design layout model 1320 represents the optical properties of a design layout (e.g., a device design layout corresponding to features of an integrated circuit, memory, electronic device, etc.) (including changes to the radiation intensity distribution and / or phase distribution caused by a given design layout), which is a representation of the arrangement of features on or formed by the patterning device. The design layout model 1320 can represent one or more physical properties of a physical patterning device, such as described, for example, in U.S. Patent No. 7,587,704, which is incorporated herein by reference in its entirety. Because the patterning device used in the lithographic projection apparatus can be varied, it is desirable to separate the optical properties of the patterning device from the optical properties of the remainder of the lithographic projection apparatus, including at least the illumination element and the projection optics.

[0157] An aerial image 1330 may be simulated based on the source model 1300, the projection optics model 1310, and the design layout model 1320. 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, the patterning device, and the projection optics) dictate the aerial image.

[0158] 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. A resist model 1340 can be used to simulate a resist image 1350 based on the aerial image 1330. The resist model can be used to calculate the resist image based on the aerial image, and an example thereof can be found in U.S. Patent Application Publication No. US 2009-0157360, the disclosure of which is hereby 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, in order to predict, for example, the profile of the resist features formed on the substrate, and therefore it is typically only related to these properties of the resist layer (e.g., the effects of chemical processes occurring during exposure, post-exposure baking and development). In an embodiment, the optical properties of the resist layer (eg, refractive index, film thickness, propagation and polarization effects) may be captured as part of the projection optics modeling 1310 .

[0159] Therefore, in general, the connection between the optical model and the resist model is the simulated spatial image intensity in the resist layer, which is caused by the projection of radiation onto the substrate, the refraction at the resist interface, and multiple reflections in the resist film stack. The radiation intensity distribution (spatial image intensity) becomes a potential "resist image" by absorbing the incident energy, which is further modified by diffusion processes and various loading effects. For full-chip applications, efficient simulation methods that are fast enough approximate the actual 3D intensity distribution in the resist stack by a 2D spatial image (and a resist image).

[0160] In an embodiment, the resist image may be used as an input to a post-pattern transfer process model module 150. The post-pattern transfer process model 150 defines the performance of one or more post-resist development processes (eg, etching, developing, etc.).

[0161] The simulation of the patterning process can, for example, predict the profile, CD, edge placement (e.g., edge placement error), etc. in the resist and / or etched image. Thus, the goal of the simulation is to accurately predict, for example, edge placement of the printed pattern, and / or aerial image intensity slope, and / or CD, etc. These values ​​can be compared to the expected design to, for example, correct the patterning process, identify where defects are predicted 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.

[0162] Thus, the model formula describes most, if not all, of the known physical and chemical processes in the overall process, and each of the model parameters desirably corresponds to a different physical or chemical effect. The model formula thus sets an upper limit on how well the model can be used to simulate the overall manufacturing process.

[0163] Sub-resolution tools based on optical devices (bright field inspection) are often used to perform inspections of, for example, semiconductor wafers. However, in some cases, certain features to be measured are too small to be effectively measured using bright field inspection. For example, bright field inspection of defects in features of semiconductor devices can be challenging. In addition, over time, features produced using patterning processes (e.g., semiconductor features made using photolithography) become smaller, and in many cases, the density of features also gradually increases. Therefore, higher resolution inspection techniques are used and desired. An example inspection technique is electron beam inspection. Electron beam inspection involves focusing an electron beam on a smaller spot, i.e., a smaller light spot, on the substrate to be inspected. An image is formed by providing a relative movement between the beam and the substrate (hereinafter referred to as scanning the electron beam) over the area of ​​the substrate being inspected and collecting secondary electrons and / or backscattered electrons using an electron detector. The image data is then processed to, for example, identify defects.

[0164] Thus, in an embodiment, the inspection device may be an electron beam inspection device (e.g., the same as or similar to a scanning electron microscope (SEM)) that produces an image of structures exposed or transferred on the substrate (e.g., some or all of the structures of a device such as an integrated circuit).

[0165] Fig.14A flow chart of a method for determining the presence of a defect in a lithography process according to an embodiment is shown. In process P411, a hot spot or a portion thereof is identified from a pattern (e.g., a pattern on a pattern forming device) using any suitable method. For example, a hot spot can be identified by analyzing a pattern on a pattern using an empirical model or a computational model. In an empirical model, an image of the pattern (e.g., a resist image, an optical image, an etching image) is not simulated; instead, the empirical model predicts a defect or a probability of a defect based on a correlation between a processing parameter, a parameter of the pattern, and the defect. For example, the empirical model can be a classification model or a database of defect-prone patterns. In a computational model, a portion or characteristic of the image is calculated or simulated, and a defect is identified based on the portion or the characteristic. For example, a line pullback defect can be identified by finding a line end that is too far away from its desired location; a bridging defect can be identified by finding a location where two lines are unexpectedly joined; an overlay defect can be identified by finding two features that are unexpectedly overlapped or unexpectedly not overlapped on a separate layer. An empirical model is generally less computationally expensive than a computational model. It is possible to determine the process window of the hot spot based on the hot spot location and process window of multiple individual hot spots and / or compile the process window of the hot spot into a mapping - that is, determine the process window according to the location. Such a process window mapping can characterize the layout-specific sensitivity and processing margin of the pattern. In another example, hot spots, their locations, and / or their process windows can be determined experimentally, such as by FEM wafer inspection or suitable measurement tools. Defects can include those defects that cannot be detected in post-development inspection (ADI) (usually optical inspection), such as resist top loss, resist undercut, etc. Conventional inspections only reveal these defects after irreversibly processing (e.g., etching) the substrate, when the wafer cannot be reworked. Therefore, current optical technology cannot be used to detect such resist top loss defects when drafting this document. However, simulations can be used to determine where resist top loss may occur and to what extent the severity will be. Based on this information, a decision can be made to inspect a particular possible defect using a more accurate inspection method (and typically more time consuming) to determine whether the defect requires rework, or a decision can be made to rework the imaging of a particular resist layer (remove the resist layer with the resist top loss defect and re-coat the wafer to re-image the particular layer) before performing an irreversible process (e.g., etching).

[0166] In process P412, the processing parameters at which the hotspot is processed (e.g., imaged or etched onto a substrate) are determined. The processing parameters may be local—depending on the location of the hotspot, the die, or both the hotspot and the die. The processing parameters may be global—independent of the location of the hotspot and the die, i.e., independent of the location of the hotspot and the die. One exemplary way to determine the processing parameters is to determine the state of the lithographic apparatus. For example, laser bandwidth, focus, dose, source parameters, projection optics parameters, and spatial or temporal variations of these parameters may be measured from the lithographic apparatus. Another exemplary way is to infer the processing parameters from data obtained from measurements performed on the substrate or from an operator of the processing apparatus. For example, measurements may include inspecting the substrate using a diffraction tool (e.g., ASML YieldStar), an electron microscope, or other suitable inspection tool. Processing parameters may be obtained for any location on the processed substrate, including the identified hotspot. The processing parameters may be compiled into a mapping—lithographic parameters or process conditions—as a function of location. Of course, other processing parameters may be represented as a function of location, i.e., a mapping. In an embodiment, the processing parameters may be determined prior to, and preferably immediately prior to, processing each hotspot.

[0167] In process P413, the presence, probability of presence, characteristics, or a combination thereof of a defect at the hotspot are determined using the processing parameters for processing the hotspot. This determination may be to simply compare the processing parameters with the process window of the hotspot—if the processing parameters fall within the process window, there are no defects; if the processing parameters fall outside the process window, at least one defect is expected to exist. This determination may also be made using a suitable empirical model (including a statistical model). For example, a classification model may be used to provide the probability of the presence of a defect. Another way to make this determination is to use a computational model to simulate an image of the hotspot or an expected patterned profile of the hotspot based on the processing parameters, and to measure the image or profile parameters. In an embodiment, the processing parameters may be determined immediately after processing a pattern or substrate (i.e., before processing the pattern or the next substrate). The determined presence and / or characteristics of a defect may be used as a basis for a decision to make a disposition (rework or acceptance). In an embodiment, the processing parameters may be used to calculate a moving average of the lithography parameters. Moving averages are useful for capturing long-term drifts of the lithography parameters without being disturbed by short-term fluctuations.

[0168] In an embodiment, hot spots are detected based on simulated images of patterns on substrates. Once the simulation of the patterning process (e.g., a process model including such OPC and manufacturability checks) is completed, potential weaknesses in the design according to process conditions, i.e., hot spots, can be calculated according to one or more definitions (e.g., certain rules, thresholds, or indicators). Hot spots can be determined based on the following: absolute CD value, rate of change of CD with one or more parameters in the parameters that change in the simulation ("CD sensitivity"), slope of spatial image intensity, or NILS (i.e., "edge slope" or "normalized image logarithmic slope", often abbreviated as "NILS.", indicating a lack of sharpness or image blur), wherein the edge of the resist feature is expected (calculated according to a simple threshold / bias model or a more complete resist model). Alternatively, hot spots may be determined based on a set of predetermined rules, such as those used in design rule checking systems, including, but not limited to, line end pull-back, corner rounding, proximity to adjacent features, pattern necking or pinching, and other indicators of pattern deformation relative to the desired pattern. CD sensitivity to small changes in mask CD is a particularly important lithography parameter, referred to as the mask error factor (MEF) or mask error enhancement factor (MEEF). Calculation of the variation of MEF with focus and exposure provides a critical metric / indicator of the probability that mask process variations convolved with wafer process variations will result in unacceptable pattern degradation for a particular pattern element. Hot spots may also be identified based on variations in overlay error relative to underlying or subsequent process layers and CD variations, or by sensitivity to variations in overlay and / or CD between exposures in a multi-exposure process.

[0169] Fig.15 1 is a block diagram illustrating a computer system 100 that may assist in implementing the methods, processes, or apparatus disclosed herein. The computer system 100 includes a bus 102 or other communication mechanism for communicating information, and a processor 104 (or multiple processors 104 and 105) coupled to the bus 102 for processing information. The computer system 100 also includes a main memory 106, such as a random access memory (RAM) or other dynamic storage device, coupled to the bus 102 for storing information and instructions to be executed by the processor 104. The main memory 106 may also be used to store temporary variables or other intermediate information during the execution of instructions to be executed by the processor 104. The computer system 100 also includes a read-only memory (ROM) 108 or other static storage device coupled to the bus 102 for storing static information and instructions for the processor 104. A storage device 110, such as a magnetic disk or optical disk, is provided and coupled to the bus 102 for storing information and instructions.

[0170] The computer system 100 can be connected to a display 112, such as a cathode ray tube (CRT) or a flat panel display or a touch panel display, via the bus 102 for displaying information to a computer user. An input device 114 including alphanumeric keys and other keys is connected to the bus 102 for communicating information and command selections to the processor 104. Another type of user input device is a cursor controller 116 (such as a mouse, a trackball, or cursor direction keys) for communicating direction information and command selections to the processor 104 and for controlling cursor movement on the display 112. Such an input device typically has two degrees of freedom on two axes (a first axis (e.g., x) and a second axis (e.g., y)), which allows the device to specify a position in a plane. A touch panel (screen) display can also be used as an input device.

[0171] According to one embodiment, portions of one or more methods 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 sequence of instructions contained in main memory 106 causes processor 104 to perform the process steps described herein. One or more processors in a multi-processing arrangement may also be used to execute the sequence of instructions contained in main memory 106. In alternative embodiments, hard-wired circuits may be used in place of or in combination with software instructions. Thus, the description herein is not limited to any particular combination of hardware circuitry and software.

[0172] The term "computer-readable medium" as used herein refers to any medium that participates in providing instructions to the processor 104 for execution. Such media can take many forms, including but not limited to non-volatile media, volatile media, and transmission media. Non-volatile media include, for example, optical or magnetic disks, such as storage device 110. Volatile media include dynamic memory, such as main memory 106. Transmission media include coaxial cables, copper wires, and optical fibers, including wires (which include bus 102). Transmission media can also take the form of sound waves or light waves, such as those generated during radio frequency (RF) and infrared (IR) data communications. Common forms of computer-readable media include, for example, floppy disks, flexible disks, hard disks, magnetic tapes, any other magnetic media, CD-ROMs, DVDs, any other optical media, punch cards, paper tapes, any other physical media with hole patterns, RAM, PROMs and EPROMs, FLASH-EPROMs, any other memory chips or boxes, carrier waves as described below, or any other media from which a computer can read.

[0173] Various forms of computer readable media may be involved in carrying one or more sequences of one or more instructions to the processor 104 for execution. For example, the instructions may initially be carried on a disk of a remote computer. The remote computer may load the instructions into its dynamic memory and send the instructions over a telephone line using a modem. A modem local to the computer system 100 may receive the data over the telephone line and convert the data into an infrared signal using an infrared transmitter. An infrared detector connected to the bus 102 may receive the data carried in the infrared signal and place the data on the bus 102. The bus 102 carries the data to the main memory 106, from which the processor 104 retrieves and executes the instructions. The instructions received by the main memory 106 may optionally be stored on the storage device 110 before or after being executed by the processor 104.

[0174] The computer system 100 may also include a communication interface 118 coupled to the bus 102. The communication interface 118 provides bidirectional data communications coupled to a network link 120, which is connected to a local 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. A wireless link may also be implemented. In any such implementation, the communication interface 118 sends and receives electrical signals, electromagnetic signals, or optical signals that carry digital data streams representing various types of information.

[0175] The network link 120 typically provides data communications with other data devices through one or more networks. For example, the network link 120 may provide a connection to a host computer 124 through a local network 122, or provide a connection 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.

[0176] The computer system 100 can send messages and receive data, including program code, through the network, network link 120, and communication interface 118 (from database 152). In the Internet example, server 130 can transmit the requested code for an application program through Internet 128, ISP 126, local network 122, and communication interface 118. For example, one such downloaded application can provide all or part of the methods described herein. The received code can be executed by processor 104 when it is received, and / or stored in storage device 110 or other non-volatile storage for later execution. In this way, computer system 100 can obtain application code in the form of a carrier wave.

[0177] Reference Fig.16 , the illuminator IL receives the extreme ultraviolet radiation beam emitted from the source collector module SO. Methods for generating EUV radiation include, but are not necessarily limited to, converting a material into a plasma state having at least one element (e.g., xenon, lithium, or tin) having one or more emission lines in the EUV range. In one such method, commonly referred to as laser produced plasma ("LPP"), the plasma can be generated by irradiating a fuel (such as a droplet, a beam, or a cluster of a material having a line emitting element) with a laser beam. The source collector module SO can be a laser ( Fig.16 The resulting plasma emits output radiation, such as EUV radiation, which is collected using a radiation collector disposed within the source collector module. The laser and the source collector module may be separate entities, such as when a CO2 laser is used to provide the laser beam for fuel excitation.

[0178] In these cases, the laser is not considered to form part of the lithographic apparatus, and the radiation beam is delivered from the laser to the source collector module by means of a beam delivery system comprising, for example, suitable directing mirrors and / or a beam expander. In other cases, the source may be an integral part of the source collector module, for example when the source is a discharge produced plasma EUV generator (commonly referred to as a DPP source).

[0179] The illuminator IL may comprise an adjuster for adjusting the angular intensity distribution of the radiation beam. Typically, at least the outer radial extent and / or the inner radial extent (commonly referred to as σ-outer and σ-inner, respectively) of the intensity distribution in a pupil plane of the illuminator may be adjusted. Furthermore, the illuminator IL may comprise various other components, such as a faceted field mirror arrangement and a faceted pupil mirror arrangement. The illuminator may be used to adjust the radiation beam to have a desired uniformity and intensity distribution in its cross section.

[0180] The radiation beam B is incident on the patterning device (e.g., mask) MA held on the support structure (e.g., patterning device table) MT and is patterned by the patterning device. After having been reflected from the patterning device (e.g., mask) MA, the radiation beam B passes through the projection system PS, which focuses the radiation beam onto a target portion C of the substrate W. With the aid of the second positioning device PW and a position sensor PS2 (e.g., an interferometer device, a linear encoder, or a capacitive sensor), the substrate table WT can be accurately moved, for example, so as to position different target portions C in the path of the radiation beam B. Similarly, the first positioning device PM and a further position sensor PS1 can be used to accurately position the patterning device (e.g., mask) MA relative to the path of the radiation beam B. The patterning device (e.g., mask) MA and the substrate W can be aligned using patterning device alignment marks M1, M2 and substrate alignment marks P1, P2.

[0181] The depicted device 1000 may be used in at least one of the following modes:

[0182] 1. In step mode, the support structure (e.g. patterning device table) MT and the substrate table WT are held substantially stationary while an entire pattern imparted to the radiation beam is projected 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.

[0183] 2. In scan mode, the support structure (e.g. patterning device 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. patterning device table) MT may be determined by the (de)magnification and image reversal characteristics of the projection system PS.

[0184] 3. In another mode, the support structure (e.g. patterning device table) MT holding a programmable patterning device is held substantially stationary and the substrate table WT is moved or scanned while a pattern imparted to the radiation beam is projected onto a target portion C. In this mode, a pulsed radiation source is typically employed and the programmable patterning device is updated as required after each movement of the substrate table WT or between successive radiation pulses during a scan. This mode of operation may be readily applicable to maskless lithography using a programmable patterning device such as a programmable mirror array of the type mentioned above.

[0185] Fig.17 The device 1000 is shown in more detail, including the source collector module SO, the illumination system IL and the projection system PS. The source collector module SO is constructed and arranged to maintain a vacuum environment in the enclosure structure 220 of the source collector module SO. The plasma 210 emitting EUV radiation can be formed by a discharge-generated plasma source. EUV radiation can be generated by a gas or vapor, such as xenon, lithium vapor or tin vapor, in which a very hot plasma 210 is generated to emit radiation in the EUV range of the electromagnetic spectrum. For example, the very hot plasma 210 is generated by a discharge that causes a plasma that is at least partially ionized. In order to effectively generate the radiation, it may be necessary to have a xenon, lithium, tin vapor or any other suitable gas or vapor, for example, at a partial pressure of 10Pa. In an embodiment, an excited tin (Sn) plasma is provided to generate EUV radiation.

[0186] The radiation emitted by the hot plasma 210 is transferred from the source chamber 211 to the collector chamber 212 via an optional gas barrier or contaminant trap 230 (also referred to as a contaminant barrier or foil trap in some cases) positioned in or behind an opening in the source chamber 211. The contaminant trap 230 may include a channel structure. The contaminant trap 230 may also include a gas barrier, or a combination of a gas barrier and a channel structure. As known in the art, the contaminant trap or contaminant barrier 230 further indicated herein includes at least a channel structure.

[0187] 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 off of the grating spectral filter 240 to be focused at a virtual source point IF along the optical axis indicated by the dash-dotted 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.

[0188] The radiation then traverses the illumination system IL which may include a faceted field mirror arrangement 22 and a faceted pupil mirror arrangement 24 arranged to provide a desired angular distribution of the radiation beam 21 at the patterning device MA and a desired uniformity of radiation intensity at the patterning device MA. After reflection of the radiation beam 21 at the patterning device MA held by the support structure MT, a patterned beam 26 is formed and is imaged by the projection system PS via reflective elements 28, 30 onto a substrate W held by the substrate table WT.

[0189] 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, the grating spectral filter 240 may optionally be present. Furthermore, there may be more mirrors than shown in the figures, for example there may be as many as in the embodiment of the projection system PS. Fig.17 The elements shown have 1 to 6 additional reflective elements compared to the elements shown.

[0190] like Fig.17 The collector optics CO shown 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 to be axisymmetric around the optical axis O, and this type of collector optics CO can be used in combination with a discharge produced plasma source, often referred to as a DPP source.

[0191] Alternatively, the source collector module SO may be as follows Fig.18 A portion of the LPP radiation system shown. The laser LA is arranged to deposit laser energy into a fuel such as xenon (Xe), tin (Sn) or lithium (Li), thereby producing a highly ionized plasma 210 with an electron temperature of several tens of electron volts. The high-energy radiation produced during the deexcitation and recombination, i.e., recombination, of these ions is emitted from the plasma, collected by a near normal incidence collector optic CO, and focused onto an opening 221 in the enclosure 220.

[0192] The embodiments may be further described using the following aspects:

[0193] 1. A method of determining a process window limit pattern (PWLP) based on an aberration sensitivity associated with a pattern forming device, the method comprising:

[0194] obtaining (i) a first set of kernels and a second set of kernels associated with an aberrated wavefront of the patterning device, and (ii) a design layout to be printed on a substrate via the patterning device;

[0195] determining, via a process simulation using the design layout, the first set of kernels, and the second set of kernels, an aberration sensitivity map associated with the aberration wavefront, the aberration sensitivity map indicating how sensitive one or more portions of the design layout are to specific aberrations and interactions between different aberrations; and

[0196] Based on the aberration sensitivity map, the PWLP associated with the design layout having a relatively high sensitivity compared to other portions of the design layout is determined.

[0197] 2. The method of clause 1, wherein the aberration wavefront is represented by a set of Zernike polynomials, Bessel functions, a complete set of normal functions, or a bitmap image.

[0198] 3. A method according to any one of clauses 1 to 2, wherein the aberration sensitivity map is a pixelated image, wherein pixel values ​​are indicative of the aberration sensitivity.

[0199] 4. A method according to any one of clauses 1 to 3, wherein the first set of kernels is obtained by eigendecomposition of a first vector associated with a first order aerial image, the first order aerial image comprising linear aberration terms of the aberrated wavefront, wherein:

[0200] The first aerial image is calculated by convolution of a source function, a pupil function, and a first-order aberration, the first-order aberration characterizing the effect of linear aberration terms,

[0201] The source function is a mathematical representation that characterizes the illumination source of the patterning device, and

[0202] The pupil function is another mathematical representation that characterizes the pupil of the lens of the patterning device.

[0203] 5. A method according to any one of clauses 1 to 3, wherein the second set of kernels is obtained by eigendecomposition of a second order vector associated with a second aerial image, the second aerial image comprising second order aberration terms of the aberrated wavefront, wherein:

[0204] computing the second order spatial image by convolution of the source function, the pupil function, and second order aberrations, the second order aberrations characterizing the effects of the interaction between different aberrations,

[0205] The source function is the mathematical representation that characterizes the illumination source of the patterning device, and

[0206] The pupil function is the further mathematical representation characterizing the lens pupil of the patterning device.

[0207] 6. A method according to any one of clauses 2 to 5, wherein the aberration sensitivity map is a function of the set of Zernike polynomials and a set of Zernike coefficients associated therewith, each Zernike coefficient indicating an amount of aberration explained by the associated Zernike polynomial.

[0208] 7. A method according to any one of clauses 1 to 6, wherein the determination of the aberration sensitivity map comprises:

[0209] determining a first-order aberration sensitivity map by applying the first set of kernels to the design layout;

[0210] determining a second-order aberration sensitivity map by applying the second set of kernels to the design layout; and

[0211] The aberration sensitivity map is determined as a sum of the first-order aberration sensitivity map and the second-order aberration sensitivity map.

[0212] 8. A method according to any one of aspects 1 to 7, wherein the first kernel set and the second kernel set depend on parameters associated with an illumination source of the pattern forming device, a lens pupil of the pattern forming device, and a Zernike term describing the aberration wavefront associated with the pattern forming device, but the first kernel set and the second kernel set are independent of the shape of the design layout.

[0213] 9. The method according to any one of aspects 1 to 8, wherein the determination of the PWLP comprises:

[0214] determining whether an intensity of a pixel of the aberration sensitivity map exceeds a hotspot threshold;

[0215] In response to the intensity breaching the threshold, identifying one or more patterns within the design layout associated with pixels that breached the threshold; and

[0216] The recognized pattern or a portion around the recognized pattern is classified as the PWLP.

[0217] 10. The method of clause 9, wherein a pattern of the one or more patterns comprises a plurality of features, and a portion of the pattern is a feature of the plurality of features.

[0218] 11. The method according to any one of aspects 9 to 10, wherein the one or more patterns comprise:

[0219] Straight line mask pattern;

[0220] lines and spaces;

[0221] contact holes; and / or

[0222] Curved mask pattern.

[0223] 12. A method according to any one of aspects 1 to 11, wherein the PWLP is determined based on the aberration sensitivity map without tracing the contour of the printed pattern or simulated pattern, or without calculating critical dimension or edge placement error or defect data associated with the printed substrate.

[0224] 13. The method according to any one of aspects 1 to 12, further comprising:

[0225] Determining a Zernike image based on an aberration-free spatial image and an aberration spatial image, wherein the aberration spatial image is determined based on a first-order sensitivity map, a second-order sensitivity map, or a higher-order (order greater than 2) sensitivity map;

[0226] determining, via a principal component analysis of the Zernike image, one or more principal components of the Zernike image, a principal component being a linear combination of a Zernike polynomial and an associated Zernike coefficient, wherein a value of the Zernike coefficient indicates an amount of variation in the Zernike image explained by the associated Zernike polynomial;

[0227] selecting, based on at least one of the principal components, a pattern associated with a relatively high sensitivity value for a particular Zernike polynomial; and

[0228] By performing a source mask optimization or wavefront optimization process using the selected pattern, source parameters, mask parameters and / or wavefront parameters are determined such that the performance metrics are improved.

[0229] 14. The method of clause 13, wherein the performance metric is a function of CD or edge placement error associated with the selected pattern.

[0230] 15. A method according to any one of clauses 1 to 14, wherein the first set of kernels is a first-order aberration sensitivity filter for a given Zernike in the set of Zernike polynomials.

[0231] 16. A method according to any one of clauses 1 to 14, wherein the second set of kernels is a second-order aberration sensitivity filter for a given Zernike in the set of Zernike polynomials.

[0232] 17. A method according to any one of aspects 1 to 16, wherein the source function is represented as a pixelated image of an illumination source used by the pattern forming device.

[0233] 18. The method of any one of clauses 1 to 17, wherein the design layout is at least one of:

[0234] Pre-OPC mask layout;

[0235] Post-OPC mask layout; or

[0236] A mask image is generated based on the post-OPC mask layout, wherein the mask image represents a mask diffraction pattern obtained by illuminating the post-OPC mask layout with the illumination source.

[0237] 19. The method according to any one of aspects 1 to 18, further comprising:

[0238] Parameters of the patterning process are determined based on the aberration sensitivity map such that the sensitivity of the PWLP is reduced.

[0239] 20. The method according to any one of aspects 1 to 18, further comprising:

[0240] ranking one or more patterns of the design layout based on the sensitivity values ​​of the aberration sensitivity map or a performance indicator of the aberration sensitivity map, wherein patterns of the one or more patterns associated with relatively high sensitivity values ​​are ranked higher than other patterns;

[0241] selecting one or more patterns having relatively high rankings based on the rankings; and

[0242] A selected pattern of the design layout is modified using the aberration sensitivity map and a mask optimization process such that the sensitivity of the selected pattern is reduced.

[0243] 21. A computer program product, comprising a non-transitory computer-readable medium having instructions recorded thereon, the instructions implementing the method of any one of the above aspects when executed by a computer.

[0244] The concepts disclosed herein can simulate or mathematically model any general imaging system for imaging sub-wavelength features, and can be used in particular with emerging imaging technologies that can produce shorter and shorter wavelengths. Emerging technologies already in use include extreme ultraviolet (EUV) lithography, deep ultraviolet (DUV) lithography that can produce 193nm wavelengths by using ArF lasers, and even 157nm wavelengths by using fluorine lasers. In addition, EUV lithography can produce wavelengths in the range of 5nm to 20nm by using a synchrotron or by using high energy electrons to bombard materials (solid or plasma) in order to produce photons in this range.

[0245] 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, for example, a lithography imaging system for imaging on substrates other than silicon wafers.

[0246] The above description is intended to be illustrative rather than limiting. Accordingly, those skilled in the art will appreciate that modifications may be made as described without departing from the scope of the claims set forth below.

Claims

1. A method of determining a process window limit pattern (PWLP) based on an aberration sensitivity associated with a patterning device, the method comprising: obtaining (i) a first set of kernels and a second set of kernels, each associated with an aberration wavefront of the patterning device, wherein the first set of kernels is a first-order aberration sensitivity filter for a given Zernike in a set of Zernike polynomials and the second set of kernels is a second-order aberration sensitivity filter for a given Zernike in the set of Zernike polynomials, and (ii) a design layout to be printed on a substrate via the patterning device; determining, via a process simulation using the design layout, the first set of kernels, and the second set of kernels, an aberration sensitivity map associated with the aberration wavefront, the aberration sensitivity map indicating how sensitive one or more portions of the design layout are to specific aberrations and interactions between different aberrations; as well as Based on the aberration sensitivity map, the PWLP associated with the design layout having a relatively high sensitivity compared to other portions of the design layout is determined.

2. The method of claim 1, wherein the aberration wavefront is represented by a set of Zernike polynomials, Bessel functions, a complete set of normal functions, or a bitmap image. The method of claim 1 , wherein the aberration sensitivity map is a pixelated image, wherein pixel values ​​indicate the aberration sensitivity.

4. The method of claim 1 , wherein the first set of kernels is obtained by eigendecomposition of a first vector associated with a first order aerial image, the first order aerial image comprising linear aberration terms of the aberrated wavefront, wherein: The first-order spatial image is calculated by convolution of a source function, a pupil function, and a first-order aberration, the first-order aberration characterizing the effect of linear aberration terms, The source function is a mathematical representation that characterizes the illumination source of the patterning device, and The pupil function is another mathematical representation that characterizes the pupil of the lens of the patterning device.

5. The method of claim 4, wherein the second set of kernels is obtained by eigendecomposition of a second order vector associated with a second order aerial image, the second order aerial image comprising second order aberration terms of the aberrated wavefront, wherein: computing the second order spatial image by convolution of the source function, the pupil function, and second order aberrations, the second order aberrations characterizing the effects of the interaction between different aberrations, The source function is the mathematical representation that characterizes the illumination source of the patterning device, and The pupil function is the further mathematical representation characterizing the lens pupil of the patterning device.

6. The method of claim 2, wherein the aberration sensitivity map is a function of the set of Zernike polynomials and a set of Zernike coefficients associated therewith, each Zernike coefficient indicating an amount of aberration explained by the associated Zernike polynomial.

7. The method of claim 1 , wherein the determining of the aberration sensitivity map comprises: determining a first-order aberration sensitivity map by applying the first set of kernels to the design layout; determining a second-order aberration sensitivity map by applying the second set of kernels to the design layout; as well as The aberration sensitivity map is determined as a sum of the first-order aberration sensitivity map and the second-order aberration sensitivity map.

8. The method of claim 1 , wherein the first kernel set and the second kernel set depend on parameters associated with an illumination source of the pattern forming device, a lens pupil of the pattern forming device, and a Zernike term describing the aberration wavefront associated with the pattern forming device, but the first kernel set and the second kernel set are independent of a shape of the design layout.

9. The method of claim 1 , wherein the determining of the PWLP comprises: determining whether an intensity of a pixel of the aberration sensitivity map exceeds a hotspot threshold; In response to the intensity breaching the threshold, identifying one or more patterns within the design layout associated with pixels that breached the threshold; as well as The recognized pattern or a portion around the recognized pattern is classified as the PWLP.

10. The method of claim 9, wherein a pattern of the one or more patterns comprises a plurality of features, and a portion of the pattern is a feature of the plurality of features; as well as The one or more patterns include: Straight line mask pattern; lines and spaces; contact holes; and / or Curved mask pattern.

11. The method of claim 1 , wherein the PWLP is determined based on the aberration sensitivity map without tracing the contour of a printed or simulated pattern, or calculating critical dimension or edge placement errors or defect data associated with the printed substrate.

12. The method according to claim 1, further comprising: Determining a Zernike image based on an aberration-free spatial image and an aberration-based spatial image, wherein the aberration-based spatial image is determined based on a first-order sensitivity map, a second-order sensitivity map, or a higher-order (order greater than 2) sensitivity map; determining, via a principal component analysis of the Zernike image, one or more principal components of the Zernike image, a principal component being a linear combination of a Zernike polynomial and an associated Zernike coefficient, wherein a value of the Zernike coefficient indicates an amount of variation in the Zernike image explained by the associated Zernike polynomial; selecting, based on at least one of the principal components, a pattern associated with a relatively high sensitivity value for a particular Zernike polynomial; as well as By performing a source mask optimization or wavefront optimization process using the selected pattern, source parameters, mask parameters and / or wavefront parameters are determined such that the performance metrics are improved.

13. The method of claim 12, wherein the performance metric is a function of CD or edge placement error associated with the selected pattern.

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

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