EP4684247A1 - Method and system for generating a lithography process aware pupil profile - Google Patents

Abstract

Described is a method and system for determining a pupil profile for imaging a pattern on a substrate in a photolithography process. Data indicating a relationship between lithographic performance variation and source variation across a pupil plane is obtained, and a first pupil profile is optimized based on the data to generate a second pupil profile. The second pupil profile is a discrete pupil profile corresponding to a desired freeform pupil profile that may be used for printing a pattern on a substrate using a lithographic apparatus. An illumination system (e.g., field facet mirrors) may be configured based on the second pupil profile to print the pattern on the substrate.

Description

METHOD AND SYSTEM FOR GENERATING A LITHOGRAPHY PROCESS AWARE PUPIL PROFILE

CROSS-REFERENCE TO RELATED APPLICATION

[0001] This application claims priority of US application 63/454,022 which was filed on 22 March 2023, and which is incorporated herein in its entirety by reference.

TECHNICAL FIELD

[0002] The description herein relates to a lithographic apparatus or process, and more particularly to a tool to optimize an illumination source and/or patterning device/design layout for use in the lithographic apparatus or process.

BACKGROUND

[0003] A lithographic apparatus is a machine constructed to apply a desired pattern onto a substrate. A lithographic apparatus can be used, for example, in the manufacture of integrated circuits (ICs). A lithographic apparatus may, for example, project a pattern (also often referred to as “design layout” or “design”) of a patterning device (e.g., a mask) onto a layer of radiation-sensitive material (resist) provided on a substrate (e.g., a wafer). This manufacturing process may be referred to as a patterning process or a lithographic process. For example, an IC chip in a smart phone, can be as small as a person’s thumbnail, and may include over 2 billion transistors. Making an IC is a complex and timeconsuming process, with circuit components in different layers and including hundreds of individual steps. Errors in even one step have the potential to result in problems with the final IC and can cause device failure. High process yield and high wafer throughput can be impacted by the presence of defects.

[0004] An illumination source (“source”) of a lithographic apparatus can be optimized, either jointly a patterning device optimization or separately, in an effort to improve the overall lithography fidelity. Conventional technology uses glass discs called diffractive optical elements (DOEs) to shape the light from the source. The light from the source can be characterized using a pupil profile (e.g., an image representative of spatial intensity distribution at a pupil plane). For complex pupil profiles, these DOEs may have to be custom designed and manufactured. Some types of source may use a programmable array of individually adjustable mirrors (e.g., field facet mirrors). It can create an arbitrary pupil profile in a short duration — eliminating the long cycle time associated with DOE design and fabrication.

[0005] Although the number of the adjustable mirrors may be as large as several hundred, they are still spatially discrete. In some lithographic projection systems, each mirror can be configured to one of several (e.g., 2-6) discrete states. Due to the discrete nature of the mirrors, the pupil profile actually rendered using the array of mirrors resembles but may still substantially deviate from the desired pupil profile which is typically a spatially continuous profile. The desired pupil profile may be obtained from source optimization (SO), source mask optimization (SMO), source mask lens optimization (SMLO), empirical pupil profile, a pupil profile from another lithographic projection system, etc. This deviation tends to be greater in an EUV source. This deviation may be reduced if the discrete nature of the mirrors is considered when the source is optimized. However, traditional discrete optimization (e.g., branch-and-bound algorithm) is computational costly (with run time increasing exponentially with the number of mirrors). Some discrete pupil profile generators are geometry-based and do not consider lithographic performance in generating the discrete pupil profile. More particularly, these methods do not differentiate between “more beneficial regions” (e.g., regions with less lithographic performance cost) vs “less beneficial regions.” (e.g., regions with more lithographic performance cost). Some other methods may consider lithographic performance, but are computationally expensive (e.g., they may require a simulation model that simulates an entire lithography process to be executed every time a change is made to the pupil profile to determine whether the pupil profile is optimized).

SUMMARY

[0006] In some aspects, the techniques described herein relate to a method for determining a pupil profile for imaging a pattern on a substrate in a photolithography process. The method includes: obtaining a first pupil profile for printing a pattern on a substrate using a lithographic apparatus; obtaining data indicating a relationship between lithographic performance variation and source variation across a pupil plane; and discretizing the first pupil profile based on the data to generate a second pupil profile.

[0007] In some aspects, the techniques described herein relate to a method for determining a pupil profile for imaging a pattern on a substrate in a photolithography process. The method includes: obtaining a first pupil profile for printing a pattern on a substrate using a lithographic apparatus; obtaining lithographic performance-based source optimization map that is indicative of a relationship between lithographic performance variation and source variation across a pupil plane; and generating a discrete pupil profile using the lithographic performance-based source optimization map by iteratively optimizing the first pupil profile until a cost function is minimized.

[0008] In some aspects, the techniques described herein relate to an apparatus for determining a pupil profile for imaging a pattern on a substrate in a photolithography process, the apparatus including: a memory storing a set of instructions; and a processor configured to execute the set of instructions to cause the apparatus to perform a method of any of the above aspects.

[0009] In some aspects, the techniques described herein relate to a non-transitory computer-readable medium having instructions recorded thereon, the instructions when executed by a computer implementing the method of any of the above aspects. BRIEF DESCRIPTION OF THE DRAWINGS

[0010] Figure 1 is a schematic diagram of a lithographic projection apparatus, according to an embodiment.

[0011] Figure 2 is a schematic diagram of another lithographic projection apparatus, according to an embodiment.

[0012] Figure 3 is a detailed view of the lithographic projection apparatus, according to an embodiment.

[0013] Figure 4 is a block diagram of field facet mirrors and pupil facet mirrors of a lithographic apparatus, consistent with various embodiments.

[0014] Figure 5 shows a flow for a lithographic process or patterning simulation method, consistent with various embodiments.

[0015] Figure 6 is a block diagram of a system for generating a source optimization guidance (SOG) map, consistent with various embodiments.

[0016] Figure 7 is a block diagram of a system for generating a discrete pupil profile using the SOG map, consistent with various embodiments.

[0017] Figures 8A and 8B are flow diagrams of a method for generating a discrete pupil profile using the SOG map, consistent with various embodiments.

[0018] Figure 9 is a block diagram that illustrates a computer system 100 which can assist in implementing the systems and methods disclosed herein.

DETAILED DESCRIPTION

[0019] Disclosed are embodiments for generating a discrete pupil profile using a source optimization guidance (SOG) map. The SOG map indicates a relationship between lithographic performance variation and source variation across a pupil plane. In some embodiments, each value on the SOG map indicates an impact of source intensity at a specific location on the pupil plane to a lithographic performance (e.g., performance of a photolithography/lithography process in imaging a pattern on a substrate). For example, the SOG map represents a gradient of a source variable of the lithographic apparatus. Increasing the source intensity on the pupil plane at locations corresponding to more positive values in SOG map increases lithography performance cost (e.g., decreases a lithographic performance) while increasing the source intensity at locations corresponding to more negative values in the SOG map decreases the lithography performance cost (e.g., increases the lithographic performance). Accordingly, by configuring an illumination system (e.g., field facet mirrors) to distribute source intensity to the selected locations, particularly, locations on pupil plane corresponding to more negative values on SOG map, a desired pupil may be determined.

[0020] In some embodiments, a discrete pupil profile generation process includes selecting, for each field facet mirror (FFM) of a number of FFMs in the illumination system, a state of the FFM based on the SOG map. Each FFM is associated with several pupil facet mirrors (PFMs), and selecting a state of the FFM includes selecting one of the several PFMs that is located in, for example, a low negative value (representing low lithographic performance cost) on the SOG map, and setting the corresponding location on a pupil profile to a first value indicative of a presence of source intensity and other locations on the pupil profile corresponding to the other PFMs associated with the FFM to a second value indicative of an absence of source intensity. The pupil profile can be iteratively optimized by decreasing the number of field facet mirrors in every iteration until a cost function, which may be determined based on the SOG map and the source intensity values in the updated pupil profile, is minimized. The above method of generating the discrete pupil profile using the SOG map is advantageous over the conventional discrete optimization techniques. For example, generating the discrete pupil profile using the SOG map consumes significantly lesser computing resources compared to the conventional discrete optimization techniques as the need for executing a lithography simulation model that simulates an entire lithography process every time a change is made to the pupil profile is eliminated. Thus, the embodiments provide an improved discrete pupil profile generation process.

[0021] FIG. 1 schematically depicts a lithographic apparatus in accordance with one or more embodiments. The apparatus comprises: an illumination system (illuminator) IL configured to condition a radiation beam B (e.g., UV radiation or DUV radiation); a first object holder or a support structure (e.g., a mask table) MT constructed to hold a patterning device (e.g., a mask) MA and connected to a first positioner PM configured to accurately position the patterning device in accordance with certain parameters; a second object holder such as a substrate holder or substrate table (e.g., a wafer table) WT constructed to hold a substrate (e.g., a resist coated wafer) W and connected to a second positioner PW configured to accurately position the substrate in accordance with certain parameters; and a projection system (e.g., a refractive projection lens system) PS configured to project a pattern imparted to the radiation beam B by patterning device MA onto a target portion C (e.g., comprising one or more dies) of the substrate W.

[0022] The illumination system may include various types of optical components, such as refractive, reflective, magnetic, electromagnetic, electrostatic, or other types of optical components, or any combination thereof, for directing, shaping, or controlling radiation.

[0023] The support structure holds the patterning device in a manner that depends on the orientation of the patterning device, the design of the lithographic apparatus, and other conditions, such as for example whether or not the patterning device is held in a vacuum environment. The support structure can use mechanical, vacuum, electrostatic or other clamping techniques to hold the patterning device. The support structure may be a frame or a table, for example, which may be fixed or movable as required. The support structure may ensure that the patterning device is at a desired position, for example with respect to the projection system. Any use of the terms “reticle” or “mask” herein may be considered synonymous with the more general term “patterning device.”

[0024] The term “patterning device” used herein should be broadly interpreted as referring to any device that can be used to impart a radiation beam with a pattern in its cross-section such as to create a pattern in a target portion of the substrate. It should be noted that the pattern imparted to the radiation beam may not exactly correspond to the desired pattern in the target portion of the substrate, for example if the pattern includes phase-shifting features or so-called assist features. Generally, the pattern imparted to the radiation beam will correspond to a particular functional layer in a device being created in the target portion, such as an integrated circuit.

[0025] The patterning device may be transmissive or reflective. Examples of patterning devices include masks, programmable mirror arrays, and programmable LCD panels. Masks are well known in lithography, and include mask types such as binary, alternating phase-shift, and attenuated phaseshift, 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 so as to reflect an incoming radiation beam in different directions. The tilted mirrors impart a pattern in a radiation beam which is reflected by the mirror matrix.

[0026] The term “projection system” used herein should be broadly interpreted as encompassing any type of projection system, including refractive, reflective, catadioptric, magnetic, electromagnetic, and electrostatic optical systems, or any combination thereof, as appropriate for the exposure radiation being used, or for other factors such as the use of an immersion liquid or the use of a vacuum. Any use of the term “projection lens” herein may be considered as synonymous with the more general term “projection system”.

[0027] As here depicted, the apparatus is of a transmissive type (e.g., employing a transmissive mask). Alternatively, the apparatus may be of a reflective type (e.g., employing a programmable mirror array of a type as referred to above, or employing a reflective mask).

[0028] The lithographic apparatus may be of a type having two (dual stage) or more substrate tables (and/or two or more support structures). In such “multiple stage” machines the additional tables / support structure may be used in parallel, or preparatory steps may be carried out on one or more tables / support structure while one or more other tables / support structures are being used for exposure.

[0029] Referring to FIG. 1, the illuminator IL receives a radiation beam from a radiation source SO. The source and the lithographic apparatus may be separate entities, for example when the source is an excimer laser. In such cases, the source is not considered to form part of the lithographic apparatus and the radiation beam is passed from the source SO to the illuminator IL with the aid of a beam delivery system BD comprising, for example, suitable directing mirrors and/or a beam expander. In other cases, the source may be an integral part of the lithographic apparatus, for example when the source is a mercury lamp. The source SO and the illuminator IL, together with the beam delivery system BD if required, may be referred to as a radiation system.

[0030] The illuminator IL may comprise an adjuster AD configured to adjust the angular intensity distribution of the radiation beam. Generally, at least the outer and/or inner radial extent (commonly referred to as o-outcr and o-inner, respectively) of the intensity distribution in a pupil plane of the illuminator can be adjusted. In addition, the illuminator IL may comprise various other components, such as an integrator IN and a condenser CO. The illuminator may be used to condition the radiation beam, to have a desired uniformity and intensity distribution in its cross section.

[0031] The radiation beam B is incident on the patterning device (e.g., mask) MA, which is held on the support structure (e.g., mask table) MT, and is patterned by the patterning device. Having traversed the patterning 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 positioner PW and position sensor IF (e.g., an interferometric device, linear encoder, or capacitive sensor), the substrate table WT can be moved accurately, e.g., so as to position different target portions C in the path of the radiation beam B. Similarly, the first positioner PM and another position sensor (which is not explicitly depicted in FIG. 1) can be used to accurately position the patterning device MA with respect to the path of the radiation beam B, e.g., after mechanical retrieval from a mask library, or during a scan. In general, movement of the support structure MT may be realized with the aid of a long-stroke module (coarse positioning) and a short-stroke module (fine positioning), which form part of the first positioner PM. Similarly, movement of the substrate table WT may be realized using a long-stroke module and a short-stroke module, which form part of the second positioner PW. In the case of a stepper (as opposed to a scanner) the support structure MT may be connected to a short-stroke actuator only, or may be fixed. Patterning device MA and substrate W may be aligned using patterning device alignment marks Ml, M2 and substrate alignment marks Pl, P2. Although the substrate alignment marks as illustrated occupy dedicated target portions, they may be located in spaces between target portions (these are known as scribe-lane alignment marks). Similarly, in situations in which more than one die is provided on the patterning device MA, the patterning device alignment marks may be located between the dies.

[0032] The depicted apparatus could be used in at least one of the following modes:

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

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 velocity and direction of the substrate table WT relative to the support structure MT may be determined by the (de-)magnification and image reversal characteristics of the projection system PS. In scan mode, the maximum size of the exposure field limits the width (in the non-scanning direction) of the target portion in a single dynamic exposure, whereas the length of the scanning motion determines the height (in the scanning direction) of the target portion.

3. In another mode, the support structure MT is kept essentially stationary holding a 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, generally a pulsed radiation source is employed, and the programmable patterning device is updated as required after each movement of the substrate table WT or in between successive radiation pulses during a scan. This mode of operation can be readily applied to maskless lithography that utilizes programmable patterning device, such as a programmable mirror array of a type as referred to above.

[0033] Combinations and/or variations on the above-described modes of use or entirely different modes of use may also be employed.

[0034] Figure 2 is a schematic diagram of another lithographic projection apparatus (LPA), according to an embodiment. LPA can include source collector module SO, illumination system (illuminator) IL configured to condition a radiation beam B (e.g., EUV radiation), support structure MT, substrate table WT, and projection system PS.

[0035] Support structure (e.g., a patterning device table) MT can be constructed to support a patterning device (e.g., a mask or a reticle) MA and connected to a first positioner PM configured to accurately position the patterning device;

[0036] Substrate table (e.g., a wafer table) WT can be constructed to hold a substrate (e.g., a resist coated wafer) W and connected to a second positioner PW configured to accurately position the substrate.

[0037] Projection system (e.g., a reflective projection system) PS can be configured to project a pattern imparted to the radiation beam B by patterning device MA onto a target portion C (e.g., comprising one or more dies) of the substrate W.

[0038] As here depicted, LPA can be of a reflective type (e.g., employing a reflective patterning device). It is to be noted that because most materials are absorptive within the EUV wavelength range, the patterning device may have multilayer reflectors comprising, for example, a multi-stack of molybdenum and silicon. In one example, the multi-stack reflector has a 40-layer pairs of molybdenum and silicon where the thickness of each layer is a quarter wavelength. Even smaller wavelengths may be produced with X-ray lithography. Since most material is absorptive at EUV and x-ray wavelengths, a thin piece of patterned absorbing material on the patterning device topography (e.g., a TaN absorber on top of the multi-layer reflector) defines where features would print (positive resist) or not print (negative resist).

[0039] Illuminator IL can receive an extreme ultraviolet radiation beam from source collector module SO. Methods to produce EUV radiation include, but are not necessarily limited to, converting a material into a plasma state that has at least one element, e.g., xenon, lithium, or tin, with one or more emission lines in the EUV range. In one such method, often termed laser produced plasma ("LPP") the plasma can be produced by irradiating a fuel, such as a droplet, stream or cluster of material having the line-emitting element, with a laser beam. Source collector module SO may be part of an EUV radiation system including a laser, not shown in Figure 2, for providing the laser beam exciting the fuel. The resulting plasma emits output radiation, e.g., EUV radiation, which is collected using a radiation collector, disposed in the source collector module. The laser and the source collector module may be separate entities, for example when a CO2 laser is used to provide the laser beam for fuel excitation.

[0040] In such cases, the laser may not be considered to form part of the lithographic apparatus and the radiation beam can be passed from the laser to the source collector module with the aid 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, often termed as a DPP source.

[0041] Illuminator IL may comprise an adjuster for adjusting the angular intensity distribution of the radiation beam. Generally, at least the outer and/or inner radial extent (commonly referred to as o- outer and o-inner, respectively) of the intensity distribution in a pupil plane of the illuminator can be adjusted. In addition, the illuminator IL may comprise various other components, such as facetted field and pupil mirror devices. The illuminator may be used to condition the radiation beam, to have a desired uniformity and intensity distribution in its cross section.

[0042] The radiation beam B can be incident on the patterning device (e.g., mask) MA, which is held on the support structure (e.g., patterning device table) MT, and is patterned by the patterning device. After being reflected from the patterning device (e.g., mask) 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 positioner PW and position sensor PS2 (e.g., an interferometric device, linear encoder, or capacitive sensor), the substrate table WT can be moved accurately, e.g., so as to position different target portions C in the path of radiation beam B. Similarly, the first positioner PM and another position sensor PSI can be used to accurately position the patterning device (e.g., mask) MA with respect to the path of the radiation beam B. Patterning device (e.g., mask) MA and substrate W may be aligned using patterning device alignment marks Ml, M2 and substrate alignment marks Pl, P2.

[0043] The depicted apparatus LPA could be used in at least one of the following modes, step mode, scan mode, and stationary mode.

[0044] In step mode, the support structure (e.g., patterning device table) MT and the substrate table WT are kept essentially stationary, while an entire pattern imparted to the radiation beam is projected onto a target portion C at one time (i.e., a single static exposure). The substrate table WT is then shifted in the X and/or Y direction so that a different target portion C can be exposed.

[0045] 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 target portion C (i.e., a single dynamic exposure). The velocity and direction of 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.

[0046] In stationary mode, the support structure (e.g., patterning device table) MT is kept essentially stationary holding a programmable patterning device, and 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, generally a pulsed radiation source is employed, and the programmable patterning device is updated as required after each movement of the substrate table WT or in between successive radiation pulses during a scan. This mode of operation can be readily applied to maskless lithography that utilizes programmable patterning device, such as a programmable mirror array of a type as referred to above. [0047] Figure 3 is a detailed view of the lithographic projection apparatus, according to an embodiment. As shown, LPA can include the source collector module SO, the illumination system IL, and the projection system PS. The source collector module SO is constructed and arranged such that a vacuum environment can be maintained in an enclosing structure 220 of the source collector module SO. An EUV radiation emitting plasma 210 may be formed by a discharge produced plasma source. EUV radiation may be produced by a gas or vapor, for example Xe gas, Li vapor or Sn vapor in which the very hot plasma 210 is created to emit radiation in the EUV range of the electromagnetic spectrum. The very hot plasma 210 is created by, for example, an electrical discharge causing at least partially ionized plasma. Partial pressures of, for example, 10 Pa of Xe, Li, Sn vapor or any other suitable gas or vapor may be required for efficient generation of the radiation. In an embodiment, a plasma of excited tin (Sn) is provided to produce EUV radiation.

[0048] The radiation emitted by the hot plasma 210 is passed from a source chamber 211 into a collector chamber 212 via an optional gas barrier or contaminant trap 230 (in some cases also referred to as contaminant barrier or foil trap) which is positioned in or behind an opening in source chamber 211. The contaminant trap 230 may include a channel structure. Contamination trap 230 may also include a gas barrier or a combination of a gas barrier and a channel structure. The contaminant trap or contaminant barrier 230 further indicated herein at least includes a channel structure, as known in the art.

[0049] The collector chamber 212 may include a radiation collector CO which may be a so-called grazing incidence collector. Radiation collector CO has an upstream radiation collector side 251 and a downstream radiation collector side 252. Radiation that traverses collector CO can be reflected off a grating spectral filter 240 to be focused on a virtual source point IF along the optical axis indicated by the dot-dashed line ‘O’ . The virtual source point IF is commonly referred to as the intermediate focus, and the source collector module is arranged such that the intermediate focus IF is located at or near an opening 221 in the enclosing structure 220. The virtual source point IF is an image of the radiation emitting plasma 210. [0050] Subsequently the radiation traverses the illumination system IL, which may include a facetted field mirror device 22 and a facetted pupil mirror device 24 arranged to provide a desired angular distribution of the radiation beam 21, at the patterning device MA, as well as a desired uniformity of radiation intensity at the patterning device MA. Upon reflection of the beam of radiation 21 at the patterning device MA, held by the support structure MT, a patterned beam 26 is formed and the patterned beam 26 is imaged by the projection system PS via reflective elements 28, 30 onto a substrate W held by the substrate table WT.

[0051] More elements than shown may generally be present in illumination optics unit IL and projection system PS. The grating spectral filter 240 may optionally be present, depending upon the type of lithographic apparatus. Further, there may be more mirrors present than those shown in the figures, for example there may be 1- 6 additional reflective elements present in the projection system PS than shown in Figure 3.

[0052] Collector optic CO, as illustrated in Figure 3, is depicted as a nested collector with grazing incidence reflectors 253, 254 and 255, just as an example of a collector (or collector mirror). The grazing incidence reflectors 253, 254 and 255 are disposed axially symmetric around the optical axis O and a collector optic CO of this type may be used in combination with a discharge produced plasma source, often called a DPP source.

[0053] Figure 4 is a block diagram of field facet mirrors and pupil facet mirrors of a lithographic apparatus, consistent with various embodiments. In some embodiments, the field facet mirrors (FFMs), such as FFMs 401, 402, 403 and 404 and pupil facet mirrors (PFMs) 410 are similar to the FFMs and PFMs, respectively, described at least with reference to Figure 2, or to the facetted field mirror device 22 and facetted pupil mirror device 24, respectively, described in Figure 3. As described above at least with reference to Figure 2, the illuminator IL may adjust the angular intensity distribution of the radiation beam. In some embodiments, the illuminator may adjust the angular intensity distribution through the use of FFMs and PFMs. Further, each FFM may be associated with several PFMs and may be configured (e.g., flipped) to direct the radiation to one of those PFMs. For example, a FFM 401 may be associated with PFMs 421, 422, 423 and 424 and may be configured to direct the radiation to one of the PFMs 421-424. Similarly, a FFM 403 may be associated with PFMs 431, 432, 433 and 434 and may be configured to direct the radiation to one of the PFMs 431-434. In other words, the PFMs associated with an FFM are mutually exclusive in nature.

[0054] Each FFM may be flipped to (or configured to) one of a number of states and each state may cause the FFM to direct the radiation to one of the PFMs associated with the FFM. For example, when the FFM 401 is flipped to a first state, the FFM 401 may direct the radiation to the PFM 424, when the FFM 401 is flipped to a second state, the FFM 401 may direct the radiation to the PFM 422 and so on.

[0055] An exemplary flow chart for modelling and/or simulating parts of a patterning process (or a lithographic process) is illustrated in Figure 5. As will be appreciated, the models may represent a different patterning process and need not comprise all the models described below. A source model 500 represents optical characteristics (including radiation intensity distribution, bandwidth and/or phase distribution) of the illumination of a patterning device. The source model 500 can represent the optical characteristics of the illumination that include, but not limited to, numerical aperture settings, illumination sigma (o) settings as well as any particular illumination shape (e.g., off-axis radiation shape such as annular, quadrupole, dipole, etc.), where o (or sigma) is outer radial extent of the illuminator.

[0056] A projection optics model 510 represents optical characteristics (including changes to the radiation intensity distribution and/or the phase distribution caused by the projection optics) of the projection optics. The projection optics model 510 can represent the optical characteristics of the projection optics, including aberration, distortion, one or more refractive indexes, one or more physical sizes, one or more physical dimensions, etc.

[0057] The patterning device / design layout model module 520 captures how the design features are laid out in the pattern of the patterning device and may include a representation of detailed physical properties of the patterning device, as described, for example, in U.S. Patent No. 7,587,704, which is incorporated by reference in its entirety. In an embodiment, the patterning device / design layout model module 520 represents optical characteristics (including changes to the radiation intensity distribution and/or the phase distribution caused by a given design layout) of a design layout (e.g., a device design layout corresponding to a feature of an integrated circuit, a memory, an electronic device, etc.), which is the representation of an arrangement of features on or formed by the patterning device. Since the patterning device used in the lithographic projection apparatus can be changed, it is desirable to separate the optical properties of the patterning device from the optical properties of the rest of the lithographic projection apparatus including at least the illumination and the projection optics. The objective of the simulation is often to accurately predict, for example, edge placements and CDs, which can then be compared against the device design. The device design is generally defined as the pre-OPC patterning device layout, and will be provided in a standardized digital file format such as GDSII or OASIS.

[0058] An aerial image 530 can be simulated from the source model 500, the projection optics model 510 and the patterning device / design layout model module 520. An aerial image (Al) is the radiation intensity distribution at substrate level. Optical properties of the lithographic projection apparatus (e.g., properties of the illumination, the patterning device, and the projection optics) dictate the aerial image.

[0059] A resist layer on a substrate is exposed by the aerial image and the aerial image is transferred to the resist layer as a latent “resist image” (RI) therein. The resist image (RI) can be defined as a spatial distribution of solubility of the resist in the resist layer. A resist image 550 can be simulated from the aerial image 530 using a resist model 540. The resist model can be used to calculate the resist image from the aerial image, an example of which can be found in U.S. Patent No. US 8,200,468, the disclosure of which is hereby incorporated by reference in its entirety. The resist model typically describes the effects of chemical processes which occur during resist exposure, post exposure bake (PEB) and development, in order to predict, for example, contours of resist features formed on the substrate and so it typically related only to such properties of the resist layer (e.g., effects of chemical processes which occur during exposure, post-exposure bake and development). In an embodiment, the optical properties of the resist layer, e.g., refractive index, film thickness, propagation and polarization effects — may be captured as part of the projection optics model 510. [0060] So, in general, the connection between the optical and the resist model is a simulated aerial image intensity within the resist layer, which arises from the projection of radiation onto the substrate, refraction at the resist interface and multiple reflections in the resist film stack. The radiation intensity distribution (aerial image intensity) is turned into a latent “resist image” by absorption of incident energy, which is further modified by diffusion processes and various loading effects. Efficient simulation methods that are fast enough for full-chip applications approximate the realistic 3- dimensional intensity distribution in the resist stack by a 2-dimensional aerial (and resist) image. [0061] In an embodiment, the resist image can be used an input to a post-pattern transfer process model module 560. The post-pattern transfer process model module 560 defines performance of one or more post-resist development processes (e.g., etch, development, etc.).

[0062] Simulation of the patterning process or the lithographic process can, for example, predict contours, CDs, edge placement (e.g., edge placement error), etc. in the resist and/or etched image. Thus, the objective of the simulation is to accurately predict, for example, edge placement, and/or aerial image intensity slope, and/or CD, etc. of the printed pattern. These values can be compared against an intended design to, e.g., correct the patterning process, identify where a defect is predicted to occur, etc. The intended design is generally defined as a pre-OPC design layout which can be provided in a standardized digital file format such as GDSII or OASIS or other file format.

[0063] Thus, the model formulation describes most, if not all, of physics and chemistry of the overall process, and each of the model parameters desirably corresponds to a distinct physical or chemical effect. The model formulation thus sets an upper bound on how well the model can be used to simulate the overall manufacturing process.

[0064] The following paragraphs describe generation of a discrete pupil profile using a source optimization guidance (SOG) map according to embodiments of the present disclosure. The discrete pupil profile may be used in configuring a source of the lithographic apparatus to generate a desired pupil. A pupil profile (or a pupil) describes spatial intensity distribution at a pupil plane, which is an imaginary plane in the illumination system formed by, at, or proximate the PFMs. In some embodiments, the pupil profile may be represented using an image. A discrete pupil profile may be indicative of a presence or absence of source intensity at a specific location on the pupil plane.

[0065] Figure 6 is a block diagram of a system 600 for generating an exemplary SOG map, consistent with various embodiments. The SOG map (or lithographic performance-based source optimization map) indicates a relationship between lithographic performance variation and source variation across the pupil plane. In some embodiments, each value on a SOG map 604 indicates an impact of source intensity variation at a specific location on the pupil plane to the lithographic performance (e.g., performance of a lithographic process in imaging a pattern on a substrate). For example, the SOG map 604 is a map of a gradient of a source variable of the lithographic apparatus. A legend 623 shows example values associated with various locations in the SOG map 604. In some embodiments, increasing the source intensity on the pupil plane at locations corresponding to more positive values in the SOG map 604 increases a lithography performance cost (e.g., decreases a lithographic performance) while increasing the source intensity at locations corresponding to more negative values in the SOG map 604 decreases the lithography performance cost (e.g., increases the lithographic performance). For example, increasing the source intensity in a first region 621 of the SOG map 604 may have a better lithographic performance (e.g., more beneficial region) than increasing the source intensity in a second region 622 of the SOG map 604 (e.g., less beneficial region). Accordingly, by configuring the FFMs to distribute source intensity to the PFMs corresponding to the selected locations (e.g., locations on pupil plane corresponding to more negative values on the SOG map 604), a desired pupil profile (e.g., pupil profile 602) may be determined.

[0066] The present disclosure is not limited to any specific method of generating an SOG map. In some embodiments, the SOG map 604 may be obtained from a source mask optimization (SMO) process. In some embodiments, an SMO process determines optimum source and/or mask variables for imaging a pattern on a substrate. A source and patterning device (design layout) optimization method and system that allows for simultaneous optimization of the source and patterning device using a cost function without constraints is described in a commonly assigned International Patent Application No. PCT/US2009/065359, filed on November 20, 2009, and published as WO2010/059954, titled “Fast Freeform Source and Mask Co-Optimization Method”, which is hereby incorporated by reference in its entirety. Another source and mask optimization method and system that involves optimizing the source by adjusting pixels of the source is described in a commonly assigned U.S. Patent Application No. 12/813456, filed on June 10, 2010, and published as U.S. Patent No. 8,786,824, titled “Source-Mask Optimization in Lithographic Apparatus”, which is hereby incorporated by reference in its entirety.

[0067] The SMO process may optimize the source and/or mask variables based on various parameters (e.g., edge placement error (EPE), wavefront aberration, critical dimension (CD)). In the example of Figure 6, an SMO component 605 optimizes source and mask variables 606 based on a cost function 610, which is determined based on one or more parameters, such as EPE 608. The source and mask variables 606 are input to a lithographic process component 625, which when executed, simulates a lithographic process (e.g., process described at least with reference to Figure 5) to compute various parameters, including the EPE 608 at every iteration. Subsequently the cost function 610 and its gradient with respect to the EPE 608 (ds/dEPE) are calculated and propagated back to the lithographic process component 625. The lithographic process component 625 converts the gradient with respect to the EPE 608 (ds/dEPE) into gradient with respect to source and/or mask variables (e.g., source gradient (ds/dv)) 609, which along with the cost function 610 is sent back to the SMO component 605 to complete the iteration loop. The SMO component 605 may continue the iterations of optimizing the source and/or mask variables 606 until a condition is satisfied (e.g., the cost function 610 is minimized) at which point the source and/or mask variables 606 are considered to be optimized and the SMO process is considered to be in a well-converged stage. For example, a pupil profile 602 shows an optimized continuous source intensity distribution on the pupil plane, which may be discretized to generate a discrete pupil profile, as described at least with reference to the following paragraphs. The SOG map 604 may be generated based on the source gradient (ds/dv) 609 values obtained from the well-converged state of the SMO process. According to embodiments of the present disclosure, the SOG map 604 is utilized to guide a pupil generation, e.g., a pupil discretization process.

[0068] Figure 7 is a block diagram of an exemplary system 700 for generating a discrete pupil profile using a SOG map, consistent with various embodiments. Figures 8A and 8B are flow diagrams of an exemplary method 800 and 850, respectively, for generating a discrete pupil profile using the SOG map, consistent with various embodiments.

[0069] At process P810, a SOG map component 725 may obtain a first pupil profile. For example, the SOG map component 725 may obtain a first pupil profile 705, which may be a discrete pupil profile. In some embodiments, the first pupil profile is a random discrete pupil profile or generated from the continuous pupil resulting from SMO in any other suitable method.

[0070] At process P820, the SOG map component 725 may obtain data indicating a relationship between lithographic performance variation and source variation across a pupil plane. For example, the SOG map component 725 may obtain the SOG map 604 (e.g., as described at least with reference to Figure 6) in which each value on the SOG map 604 indicates an impact of source intensity variation at a specific location on the pupil plane to the lithographic performance.

[0071] At process P830, a pupil profile generation component 750 discretizes the first pupil profile based on the SOG map 604 to generate a second pupil profile 760. The second pupil profile 760 may be a discrete pupil profile that corresponds to a desired pupil profile (e.g., such as the freeform pupil profile 602, which is a representation of continuous source intensity distribution on the pupil pattern) used to image a pattern on a substrate. The second pupil profile 760 may be indicative of a presence or absence of source intensity at a specific location on the pupil plane. In some embodiments, the presence of the source intensity may be indicated using a first value and the absence of source intensity may be indicated using a second value. In some embodiments, the pupil profile generation component 750 may generate the second pupil profile 760 by iteratively optimizing the first pupil profile 705 based on the SOG map 604 until a specified condition is satisfied. In some embodiments, a cost function determined based on the SOG map value and the source intensity in the first pupil profile 705 is minimized. In some embodiments, generating the second pupil profile 760 may include determining a state of the FFMs based on the SOG map 604, as described at least with reference to the process in Figure 8B below.

[0072] In some embodiments, the method 850 of Figure 8B may be performed as part of the process P830 of Figure 8A. The SOG map component 725 generates a resampled SOG map 710, which is generated by interpolating an image representation of a grid of PFMs on the SOG map 604.

[0073] At process P850, the pupil profile generation component 750 may determine, for each FFM of a number of FFMs, a state 712 of the FFM based on the SOG map 604. For example, the pupil profile generation component 750 may determine the state 712 of a specified FFM based on one of the PFMs associated with the FFM that is located in the lowest value or the most negative value on the SOG map 604. For example, in the example of Figure 7, a first FFM 401 is associated with four PFMs 421-424, and the pupil profile generation component 750 may select the PFM 422 as it is located in the most negative value on the SOG map 604. Accordingly, the pupil profile generation component 750 may determine the state 712 of the first FFM 401 based on the selected PFM. For example, if the first FFM 401 has four states (e.g., state “1” to state “4”), and if state “2” corresponds to the position of the first FFM 401 that directs the radiation to the PFM 422, then the pupil profile generation component 750 may determine the value of state 712 as “2.”

[0074] At process P860, the pupil profile generation component 750 updates the first pupil profile 705 based on the determined state of each FFM of the number of FFMs. In some embodiments, updating the first pupil profile 705 based on a state 712 of the first FFM 401 includes setting a location on the first pupil profile 705 corresponding to the location of a PFM associated with the determined state 712 of the first FFM 401 to a first value indicative of a presence of source intensity, and setting locations on the first pupil profile 705 corresponding to locations of PFMs associated with other states of the first FFM 401 to a second value indicative of an absence of source intensity.

[0075] At determination process P870, the pupil profile generation component 750 determines whether a specified condition is satisfied for optimizing the first pupil profile 705. In some embodiments, a cost function 752 may be computed based on SOG map values and the source intensity values in the first pupil profile 705. In some embodiments, the cost function 752 may be a product of an intensity value at each selected location in the first pupil profile and a value of the SOG map 604 at the selected location. For example, the cost function may be represented as:

(Eq. 1) where S_L is the source intensity at the /-th location in the first pupil profile 705, and G₍ is the SOG map value at the same location in the SOG map 604. In some embodiments, the specified condition for optimizing the first pupil profile 705 is satisfied when the cost function is minimized.

[0076] Based on a determination that the cost function 752 is not minimized, at process P880, the pupil profile generation component 750 decreases the number of FFMs (e.g., the number used in process P850), and the method 850 continues to process P850 for further determination of the states of the FFMs. The method 850 continues until the cost function 752 is reduced (e.g., minimized), whereby in every iteration the number of FFMs is decreased and the first pupil profile 705 is further optimized (e.g., updated based on the states of the FFMs).

[0077] Based on a determination that the cost function 752 is minimized, at process P870, the method 850 returns to the process P830 of the method 800 where the pupil profile generation component 750 outputs the updated first pupil profile 705 as the second pupil profile 760.

[0078] In some embodiments, the pupil profile generation component 750 may also generate state information of the FFMs based on the second pupil profile. For example, the state information may include the determined state of each FFM in the illumination system. The state information may be used in configuring the lithographic apparatus in printing a pattern on the substrate. For example, the state information may be input to the lithographic apparatus to cause the lithographic apparatus to flip the field facet mirrors to their respective states based on the state information. A patterning process may be performed via the lithographic apparatus to print patterns corresponding to a target layout on the substrate.

[0079] The above method of generating the discrete pupil profile using the SOG map is advantageous over the conventional discrete optimization techniques. For example, generating the discrete pupil profile (e.g., second pupil profile 760) using the SOG map 604 consumes significantly lesser computing resources compared to the conventional discrete optimization techniques as the need for executing a lithography simulation model (e.g., the process described at least with reference to Figure 5) that simulates an entire lithography process every time a change is made to the pupil profile is eliminated.

[0080] Figure 9 is a block diagram that illustrates a computer system 100 which can assist in implementing the systems and methods disclosed herein. Computer system 100 includes a bus 102 or other communication mechanism for communicating information, and a processor 104 (or multiple processors 104 and 105) coupled with bus 102 for processing information. Computer system 100 also includes a main memory 106, such as a random-access memory (RAM) or other dynamic storage device, coupled to bus 102 for storing information and instructions to be executed by processor 104. Main memory 106 also may be used for storing temporary variables or other intermediate information during execution of instructions to be executed by processor 104. Computer system 100 further includes a read only memory (ROM) 108 or other static storage device coupled to bus 102 for storing static information and instructions for processor 104. A storage device 110, such as a magnetic disk or optical disk, is provided and coupled to bus 102 for storing information and instructions.

[0081] Computer system 100 may be coupled via bus 102 to a display 112, such as a cathode ray tube (CRT) or flat panel or touch panel display for displaying information to a computer user. An input device 114, including alphanumeric and other keys, is coupled to bus 102 for communicating information and command selections to processor 104. Another type of user input device is cursor control 116, such as a mouse, a trackball, or cursor direction keys for communicating direction information and command selections to processor 104 and for controlling cursor movement on display 112. This input device typically has two degrees of freedom in two axes, a first axis (e.g., x) and a second axis (e.g., y), that allows the device to specify positions in a plane. A touch panel (screen) display may also be used as an input device.

[0082] According to one embodiment, portions of the optimization process may be performed by computer system 100 in response to processor 104 executing one or more sequences of one or more instructions contained in main memory 106. Such instructions may be read into main memory 106 from another computer-readable medium, such as storage device 110. Execution of the sequences of instructions contained in main memory 106 causes processor 104 to perform the process steps described herein. One or more processors in a multi-processing arrangement may also be employed to execute the sequences of instructions contained in main memory 106. In an alternative embodiment, hard-wired circuitry may be used in place of or in combination with software instructions. Thus, the description herein is not limited to any specific combination of hardware circuitry and software. [0083] The term “computer-readable medium” as used herein refers to any medium that participates in providing instructions to processor 104 for execution. Such a medium may 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 wire and fiber optics, including the wires that comprise bus 102. Transmission media can also take the form of acoustic 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, a floppy disk, a flexible disk, hard disk, magnetic tape, any other magnetic medium, a CD-ROM, DVD, any other optical medium, punch cards, paper tape, any other physical medium with patterns of holes, a RAM, a PROM, and EPROM, a FLASH-EPROM, any other memory chip or cartridge, a carrier wave as described hereinafter, or any other medium from which a computer can read. [0084] Various forms of computer readable media may be involved in carrying one or more sequences of one or more instructions to processor 104 for execution. For example, the instructions may initially be borne on a magnetic disk of a remote computer. The remote computer can load the instructions into its dynamic memory and send the instructions over a telephone line using a modem. A modem local to computer system 100 can receive the data on the telephone line and use an infrared transmitter to convert the data to an infrared signal. An infrared detector coupled to bus 102 can receive the data carried in the infrared signal and place the data on bus 102. Bus 102 carries the data to main memory 106, from which processor 104 retrieves and executes the instructions. The instructions received by main memory 106 may optionally be stored on storage device 110 either before or after execution by processor 104.

[0085] Computer system 100 also preferably includes a communication interface 118 coupled to bus 102. Communication interface 118 provides a two-way data communication coupling to a network link 120 that is connected to a local network 122. For example, communication interface 118 may be an integrated services digital network (ISDN) card or a modem to provide a data communication connection to a corresponding type of telephone line. As another example, communication interface 118 may be a local area network (LAN) card to provide a data communication connection to a compatible LAN. Wireless links may also be implemented. In any such implementation, communication interface 118 sends and receives electrical, electromagnetic or optical signals that carry digital data streams representing various types of information.

[0086] Network link 120 typically provides data communication through one or more networks to other data devices. For example, network link 120 may provide a connection through local network 122 to a host computer 124 or to data equipment operated by an Internet Service Provider (ISP) 126. ISP 126 in turn provides data communication services through the worldwide packet data communication network, now commonly referred to as the “Internet” 128. Local network 122 and Internet 128 both use electrical, electromagnetic, or optical signals that carry digital data streams. The signals through the various networks and the signals on network link 120 and through communication interface 118, which carry the digital data to and from computer system 100, are exemplary forms of carrier waves transporting the information.

[0087] Computer system 100 can send messages and receive data, including program code, through the network(s), network link 120, and communication interface 118. In the Internet example, a server 130 might transmit a requested code for an application program through Internet 128, ISP 126, local network 122 and communication interface 118. One such downloaded application may provide for the illumination optimization of the embodiment, for example. The received code may be executed by processor 104 as it is received, and/or stored in storage device 110, or other non-volatile storage for later execution. In this manner, computer system 100 may obtain application code in the form of a carrier wave.

[0088] While the concepts disclosed herein may be used for imaging on a substrate such as a silicon wafer, it shall be understood that the disclosed concepts may be used with any type of lithographic imaging systems, e.g., those used for imaging on substrates other than silicon wafers.

[0089] The terms “optimizing” and “optimization” as used herein refers to or means adjusting a patterning apparatus (e.g., a lithography apparatus), a patterning process, etc. such that results and/or processes have more desirable characteristics, such as higher accuracy of projection of a design pattern on a substrate, a larger process window, etc. Thus, the term “optimizing” and “optimization” as used herein refers to or means a process that identifies one or more values for one or more parameters that provide an improvement, e.g., a local optimum, in at least one relevant metric, compared to an initial set of one or more values for those one or more parameters. "Optimum" and other related terms should be construed accordingly. In an embodiment, optimization steps can be applied iteratively to provide further improvements in one or more metrics.

[0090] Aspects of the invention can be implemented in any convenient form. For example, an embodiment may be implemented by one or more appropriate computer programs which may be carried on an appropriate carrier medium which may be a tangible carrier medium (e.g., a disk) or an intangible carrier medium (e.g., a communications signal). Embodiments of the invention may be implemented using suitable apparatus which may specifically take the form of a programmable computer running a computer program arranged to implement a method as described herein. Thus, embodiments of the disclosure may be implemented in hardware, firmware, software, or any combination thereof. Embodiments of the disclosure may also be implemented as instructions stored on a machine-readable medium, which may be read and executed by one or more processors. A machine-readable medium may include any mechanism for storing or transmitting information in a form readable by a machine (e.g., a computing device). For example, a machine-readable medium may include read only memory (ROM); random access memory (RAM); magnetic disk storage media; optical storage media; flash memory devices; electrical, optical, acoustical, or other forms of propagated signals (e.g., carrier waves, infrared signals, digital signals, etc.), and others. Further, firmware, software, routines, instructions may be described herein as performing certain actions. However, it should be appreciated that such descriptions are merely for convenience and that such actions in fact result from computing devices, processors, controllers, or other devices executing the firmware, software, routines, instructions, etc.

[0091] Embodiments of the present disclosure can be further described by the following clauses.

1. A method for determining a pupil profile for imaging a pattern on a substrate in a photolithography process, the method comprising: obtaining a first pupil profile for printing a pattern on a substrate using a lithographic apparatus; obtaining data indicating a relationship between lithographic performance variation and source variation across a pupil plane; and optimizing the first pupil profile based on the data to generate a second pupil profile.

2. The method of clause 1, wherein the first pupil profile is a discrete pupil profile.

3. The method of clause 1, wherein the data indicates a map of a gradient of a source variable of the lithographic apparatus, wherein each value on the map indicates an impact of source intensity variation at a specific location on the pupil plane to a lithographic performance.

4. The method of clause 3, wherein the map is obtained from a source mask optimization (SMO) process.

5. The method of clause 3, wherein the map is obtained by: executing an SMO process that is configured to determine a pupil profile representing continuous source intensity distribution on the pupil plane; and generating the map based on source intensity gradient values determined in the SMO process.

6. The method of clause 5, wherein the SMO process is configured to optimize the pupil profile based on an edge placement error.

7. The method of clause 3, wherein the discretizing includes iteratively optimizing the first pupil profile based on the map to generate the second pupil profile.

8. The method of clause 7, wherein the iteratively optimizing is based on a cost function of a combination of the map and the first pupil profile.

9. The method of clause 8, wherein the cost function a product of an intensity value at each selected location in the first pupil profile and a value of a map at the selected location.

10. The method of clause 7, wherein each iteration includes: for each of a specified number of multiple field facet mirrors of the lithographic apparatus, determining a state of a first field facet mirror based on a value on the map; updating the first pupil profile based on the state of the first field facet mirror; and determining whether a cost function is reduced based on the state.

11. The method of clause 10 further comprising: responsive to a determination that the cost function is not minimized, decreasing the specified number of the field facet mirrors.

12. The method of clause 10, wherein updating the first pupil profile based on the state of the first field facet mirror includes: obtaining, from a resampled map, a location of a first pupil facet mirror that corresponds to the lowest value on the resampled map, wherein the first pupil facet mirror is one of a set of pupil facet mirrors associated with the first field facet mirror; and setting a first location corresponding to the first pupil facet mirror on the first pupil profile to a first value and locations of remaining pupil facet mirrors associated with the first field facet mirror to a second value to update the first pupil profile.

13. The method of clause 12, wherein the first value is indicative of a presence of source intensity and the second value is indicative of an absence of the source intensity.

14. The method of clause 12, wherein the resampled map is generated by interpolating the map on an image representation of a grid of pupil facet mirrors in the pupil plane.

15. The method of clause 1 further comprising: generating state information using the second pupil profile, wherein the state information indicates for each of multiple field facet mirrors a state of the corresponding field facet mirror for printing the pattern on the substrate.

16. The method of clause 15 further comprising: inputting the state information to the lithographic apparatus; and adjusting the state of the field facet mirrors based on the state information.

17. The method of clause 16 further comprising: performing a patterning process via the lithographic apparatus to print patterns corresponding to a target layout on the substrate.

18. A method for determining a pupil profile for imaging a pattern on a substrate in a photolithography process, the method comprising: obtaining a first pupil profile for printing a pattern on a substrate using a lithographic apparatus; obtaining lithographic performance-based source optimization map that is indicative of a relationship between lithographic performance variation and source variation across a pupil plane; and generating a second pupil profile using the lithographic performance-based source optimization map by iteratively optimizing the first pupil profile until a cost function is minimized.

19. The method of clause 18, wherein the lithographic performance -based source optimization map is a map of a gradient of a source variable of the lithographic apparatus, wherein each value on the map indicates an impact of source intensity variation at a specific location on the pupil plane to a lithographic performance.

20. The method of clause 18, wherein the first pupil profile is a discrete pupil profile.

21. The method of clause 18, wherein generating the second pupil profile includes iteratively optimizing the first pupil profile based on the lithographic performance-based source optimization map.

22. The method of clause 21, wherein the iteratively optimizing is based on a cost function of a combination of the lithographic performance-based source optimization map and the first pupil profile.

23. The method of clause 22, wherein the cost function a product of an intensity value at each selected location in the first pupil profile and a value of the lithographic performance -based source optimization map at the selected location.

24. The method of clause 21, wherein each iteration includes: for each of a specified number of multiple field facet mirrors of the lithographic apparatus, determining a state of a first field facet mirror based on a value on the lithographic performance -based source optimization map; updating the first pupil profile based on the state of the first field facet mirror; and determining whether a cost function is reduced based on the state.

25. The method of clause 24 further comprising: responsive to a determination that the cost function is not minimized, decreasing the specified number of the field facet mirrors.

26. The method of clause 24, wherein updating the first pupil profile based on the state of the first field facet mirror includes: obtaining, from a resampled map, a location of a first pupil facet mirror that corresponds to the lowest value on the resampled map, wherein the first pupil facet mirror is one of a set of pupil facet mirrors associated with the first field facet mirror; and setting a first location corresponding to the first pupil facet mirror on the first pupil profile to a first value and locations of remaining pupil facet mirrors associated with the first field facet mirror to a second value to update the first pupil profile.

27. The method of clause 26, wherein the first value is indicative of a presence of source intensity and the second value is indicative of an absence of the source intensity.

28. The method of clause 26, wherein the resampled map is generated by interpolating the lithographic performance-based source optimization map on an image representation of a grid of pupil facet mirrors in the pupil plane.

29. The method of clause 18, wherein the map is obtained by: executing an SMO process that is configured to determine a pupil profile representing continuous source intensity distribution on the pupil plane; and generating the lithographic performance -based source optimization map based on source intensity gradient values determined in the SMO process.

30. The method of clause 18 further comprising: generating state information using the second pupil profile, wherein the state information indicates for each of multiple field facet mirrors a state of the corresponding field facet mirror for printing the pattern on the substrate.

31. The method of clause 29 further comprising: inputting the state information to the lithographic apparatus; and adjusting the state of the field facet mirrors based on the state information.

32. The method of clause 30 further comprising: performing a patterning process via the lithographic apparatus to print patterns corresponding to a target layout on the substrate.

33. An apparatus for determining a pupil profile for imaging a pattern on a substrate in a photolithography process, the apparatus comprising: a memory storing a set of instructions; and a processor configured to execute the set of instructions to cause the apparatus to perform a method of any of the above clauses.

34. A non-transitory computer-readable medium having instructions recorded thereon, the instructions when executed by a computer implementing the method of any of the above clauses.

[0092] In block diagrams, illustrated components are depicted as discrete functional blocks, but embodiments are not limited to systems in which the functionality described herein is organized as illustrated. The functionality provided by each of the components may be provided by software or hardware modules that are differently organized than is presently depicted, for example such software or hardware may be intermingled, conjoined, replicated, broken up, distributed (e.g., within a data center or geographically), or otherwise differently organized. The functionality described herein may be provided by one or more processors of one or more computers executing code stored on a tangible, non-transitory, machine-readable medium. In some cases, third party content delivery networks may host some or all of the information conveyed over networks, in which case, to the extent information (e.g., content) is said to be supplied or otherwise provided, the information may be provided by sending instructions to retrieve that information from a content delivery network.

[0093] Unless specifically stated otherwise, as apparent from the discussion, it is appreciated that throughout this specification discussions utilizing terms such as “processing,” “computing,” “calculating,” “determining” or the like refer to actions or processes of a specific apparatus, such as a special purpose computer or a similar special purpose electronic processing/computing device.

[0094] The reader should appreciate that the present application describes several inventions. Rather than separating those inventions into multiple isolated patent applications, these inventions have been grouped into a single document because their related subject matter lends itself to economies in the application process. But the distinct advantages and aspects of such inventions should not be conflated. In some cases, embodiments address all of the deficiencies noted herein, but it should be understood that the inventions are independently useful, and some embodiments address only a subset of such problems or offer other, unmentioned benefits that will be apparent to those of skill in the art reviewing the present disclosure. Due to costs constraints, some inventions disclosed herein may not be presently claimed and may be claimed in later filings, such as continuation applications or by amending the present claims. Similarly, due to space constraints, neither the Abstract nor the Summary sections of the present document should be taken as containing a comprehensive listing of all such inventions or all aspects of such inventions.

[0095] It should be understood that the description and the drawings are not intended to limit the present disclosure to the particular form disclosed, but to the contrary, the intention is to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the inventions as defined by the appended claims.

[0096] Modifications and alternative embodiments of various aspects of the inventions will be apparent to those skilled in the art in view of this description. Accordingly, this description and the drawings are to be construed as illustrative only and are for the purpose of teaching those skilled in the art the general manner of carrying out the inventions. It is to be understood that the forms of the inventions shown and described herein are to be taken as examples of embodiments. Elements and materials may be substituted for those illustrated and described herein, parts and processes may be reversed or omitted, certain features may be utilized independently, and embodiments or features of embodiments may be combined, all as would be apparent to one skilled in the art after having the benefit of this description. Changes may be made in the elements described herein without departing from the spirit and scope of the invention as described in the following claims. Headings used herein are for organizational purposes only and are not meant to be used to limit the scope of the description. [0097] As used throughout this application, the word “may” is used in a permissive sense (i.e., meaning having the potential to), rather than the mandatory sense (i.e., meaning must). The words “include”, “including”, and “includes” and the like mean including, but not limited to. As used throughout this application, the singular forms “a,” “an,” and “the” include plural referents unless the content explicitly indicates otherwise. Thus, for example, reference to “an” element or "a” element includes a combination of two or more elements, notwithstanding use of other terms and phrases for one or more elements, such as “one or more.” As used herein, unless specifically stated otherwise, the term “or” encompasses all possible combinations, except where infeasible. For example, if it is stated that a component may include A or B, then, unless specifically stated otherwise or infeasible, the component may include A, or B, or A and B. As a second example, if it is stated that a component may include A, B, or C, then, unless specifically stated otherwise or infeasible, the component may include A, or B, or C, or A and B, or A and C, or B and C, or A and B and C.

[0098] Terms describing conditional relationships, e.g., "in response to X, Y," "upon X, Y,", “if X, Y,” "when X, Y," and the like, encompass causal relationships in which the antecedent is a necessary causal condition, the antecedent is a sufficient causal condition, or the antecedent is a contributory causal condition of the consequent, e.g., "state X occurs upon condition Y obtaining" is generic to "X occurs solely upon Y" and "X occurs upon Y and Z." Such conditional relationships are not limited to consequences that instantly follow the antecedent obtaining, as some consequences may be delayed, and in conditional statements, antecedents are connected to their consequents, e.g., the antecedent is relevant to the likelihood of the consequent occurring. Statements in which a plurality of attributes or functions are mapped to a plurality of objects (e.g., one or more processors performing steps A, B, C, and D) encompasses both all such attributes or functions being mapped to all such objects and subsets of the attributes or functions being mapped to subsets of the attributes or functions (e.g., both all processors each performing steps A-D, and a case in which processor 1 performs step A, processor 2 performs step B and part of step C, and processor 3 performs part of step C and step D), unless otherwise indicated. Further, unless otherwise indicated, statements that one value or action is “based on” another condition or value encompass both instances in which the condition or value is the sole factor and instances in which the condition or value is one factor among a plurality of factors. Unless otherwise indicated, statements that “each” instance of some collection have some property should not be read to exclude cases where some otherwise identical or similar members of a larger collection do not have the property, i.e., each does not necessarily mean each and every. References to selection from a range includes the end points of the range.

[0099] In the above description, any processes, descriptions or blocks in flowcharts should be understood as representing modules, segments or portions of code which include one or more executable instructions for implementing specific logical functions or steps in the process, and alternate implementations are included within the scope of the exemplary embodiments of the present advancements in which functions can be executed out of order from that shown or discussed, including substantially concurrently or in reverse order, depending upon the functionality involved, as would be understood by those skilled in the art. [00100] To the extent certain U.S. patents, U.S. patent applications, or other materials (e.g., articles) have been incorporated by reference, the text of such U.S. patents, U.S. patent applications, and other materials is only incorporated by reference to the extent that no conflict exists between such material and the statements and drawings set forth herein. In the event of such conflict, any such conflicting text in such incorporated by reference U.S. patents, U.S. patent applications, and other materials is specifically not incorporated by reference herein.

[00101] While certain embodiments have been described, these embodiments have been presented by way of example only, and are not intended to limit the scope of the present disclosures. Indeed, the novel methods, apparatuses and systems described herein can be embodied in a variety of other forms; furthermore, various omissions, substitutions, and changes in the form of the methods, apparatuses and systems described herein can be made without departing from the spirit of the present disclosures. The accompanying claims and their equivalents are intended to cover such forms or modifications as would fall within the scope and spirit of the present disclosures.

Claims

1. A non-transitory computer-readable medium having instructions recorded thereon, the instructions when executed by a computer implementing the method for determining a pupil profile for imaging a pattern on a substrate in a photolithography process, the method comprising: obtaining a first pupil profile for printing a pattern on a substrate using a lithographic apparatus; obtaining data indicating a relationship between lithographic performance variation and source variation across a pupil plane; and optimizing the first pupil profile based on the data to generate a second pupil profile.

2. The medium of claim 1, wherein the first pupil profile is a discrete pupil profile.

3. The medium of claim 1, wherein the data indicates a map of a gradient of a source variable of the lithographic apparatus, wherein each value on the map indicates an impact of source intensity variation at a specific location on the pupil plane to a lithographic performance.

4. The medium of claim 3, wherein the map is obtained by: executing an SMO process that is configured to determine a pupil profile representing continuous source intensity distribution on the pupil plane; and generating the map based on source intensity gradient values determined in the SMO process.

5. The medium of claim 4, wherein the SMO process is configured to optimize the pupil profile based on an edge placement error.

6. The medium of claim 3, wherein the method further comprises discretizing the first pupil profile, and wherein the optimizing includes iteratively optimizing the first pupil profile based on the map to generate the second pupil profile.

7. The medium of claim 6, wherein the iteratively optimizing is based on a cost function of a combination of the map and the first pupil profile.

8. The medium of claim 7, wherein the cost function a product of an intensity value at each selected location in the first pupil profile and a value of a map at the selected location.

9. The medium of claim 6, wherein each iteration includes: for each of a specified number of multiple field facet mirrors of the lithographic apparatus, determining a state of a first field facet mirror based on a value on the map; updating the first pupil profile based on the state of the first field facet mirror; and determining whether a cost function is reduced based on the state.

10. The medium of claim 9, wherein updating the first pupil profile based on the state of the first field facet mirror includes: obtaining, from a resampled map, a location of a first pupil facet mirror that corresponds to the lowest value on the resampled map, wherein the first pupil facet mirror is one of a set of pupil facet mirrors associated with the first field facet mirror; and setting a first location corresponding to the first pupil facet mirror on the first pupil profile to a first value and locations of remaining pupil facet mirrors associated with the first field facet mirror to a second value to update the first pupil profile.

11. The medium of claim 10, wherein the first value is indicative of a presence of source intensity and the second value is indicative of an absence of the source intensity.

12. The medium of claim 10, wherein the resampled map is generated by interpolating the map on an image representation of a grid of pupil facet mirrors in the pupil plane.

13. The medium of claim 1, wherein the method further comprises: generating state information using the second pupil profile, wherein the state information indicates for each of multiple field facet mirrors a state of the corresponding field facet mirror for printing the pattern on the substrate.

14. The medium of claim 13, wherein the method further comprises: inputting the state information to the lithographic apparatus; and adjusting the state of the field facet mirrors based on the state information.

15. The medium of claim 14, wherein the method further comprises: performing a patterning process via the lithographic apparatus to print patterns corresponding to a target layout on the substrate.