Method and system for optimizing source, mask and wavefront based on diffraction pattern to reduce m3d fading

Abstract

Described is a method and system for reducing a mask three-dimensional (M3D) induced contrast loss in a lithography process. A diffraction pattern of a target pattern is determined based on a zeroth and first order diffraction of the target pattern. The diffraction pattern is discretized and partitioned into zeroth order and first order diffraction zones to create partitioned zones. A wavefront target is determined based on the partitioned zones and a desired phase shift between the zeroth order diffraction and the first order diffraction.

Description

METHOD AND SYSTEM FOR OPTIMIZING SOURCE, MASK AND WAVEFRONT BASED ONDIFFRACTION PATTERN TO REDUCE M3D FADINGCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority to U.S. Application No. 63 / 534,286, which was filed on August 23, 2023, and U.S. Application No. 63 / 567,646, which was filed on March 20, 2024, both of which are incorporated herein in their entireties by reference.TECHNICAL FIELD

[0002] The description herein relates to lithographic apparatuses and processes, and more particularly to a tool to mitigate mask 3D fading effect.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, especially if operator intervention is required for reviewing the defects.

[0004] The patterning device may refer to device that can be used to endow an incoming radiation beam with a patterned cross-section, corresponding to a pattern that is to be created in a target portion of the substrate. An example of such a patterning device is a mask. The concept of a mask is well known in lithography, and it includes mask types such as binary, alternating phase-shift, and attenuated phase-shift, as well as various hybrid mask types. Placement of such a mask in the radiation beam causes selective transmission (in the case of a transmissive mask) or reflection (in the case of a reflective mask) of the radiation impinging on the mask, according to the pattern on the mask. In the case of a mask, the support structure will generally be a mask table, which ensures that the mask can be held at a desired position in the incoming radiation beam, and that it can be moved relative to the beam if so desired.

[0005] An emerging candidate for finer resolution lithography uses Extreme Ultraviolet (EUV) light to image patterns on an area of a wafer. EUV light has a wavelength in a range of about 10 nm to 20 nm, in particular about 13.4 nm to 13.5 nm. EUV lithography (EUVL) employs reflective masksrather than transmissive masks since the EUV light at such a small wavelength is prone to be absorbed by materials used in a transmissive mask.

[0006] Mask 3D effects (also referred to as “M3D effect”) involve the mask. In some embodiments, the mask is a multi-layer structure having three dimensional (3D)-like features jutting out on top of the mask. In operation, when the radiation from an illumination source of the lithographic apparatus (e.g., EUV light) is incident on the mask at an angle (e.g., 6-degrees), the oblique incident radiation field and the 3D features, alone or in combination, may lead to phase modulation of the diffracted orders, causing various effects in the lithographic projection process such as a shift in the aerial images of the pattern from different illumination poles, which results in imaging contrast loss (e.g., M3D fading). Conventional techniques either do not reduce, or have drawbacks in minimizing, M3D fading. For example, the conventional methods use a fixed wavefront (e.g., controlled aberrations - Zernike Z6) to cure the M3D effects, which is not effective as M3D fading still remains. The conventional methods neither use multiple Zernike parameters, nor co-optimize the pupil or mask with the wavefront, thereby not maximizing an overlap between the pupil and the wavefront, causing the M3D fading to still persist.SUMMARY

[0007] In some aspects, the techniques described herein relate to a method for reducing a mask three- dimensional (M3D) induced contrast loss in a lithography process. The method includes: determining a diffraction pattern of a target pattern based on a zeroth order and first order diffraction of the target pattern; partitioning of the diffraction pattern into zeroth order and first order diffraction zones to create partitioned zones; and determining a wavefront target based on the partitioned zones and a desired phase shift between the zeroth order diffraction and the first order diffraction.

[0008] In some aspects, the techniques described herein relate to a method for reducing a mask three- dimensional (M3D) induced contrast loss in a lithography process. The method includes: determining a diffraction pattern of a target pattern based on a zeroth order and first order diffraction of the target pattern; partitioning a representation of the diffraction pattern into zeroth order and first order diffraction zones to create partitioned zones; determining a wavefront target based on the partitioned zones and a desired phase shift between the zeroth order diffraction and the first order diffraction; and adjusting at least one of the wavefront target, source parameters of a lithography apparatus or mask parameters of a mask corresponding to the target pattern based on a cost function.

[0009] In some aspects, the techniques described herein relate to a method for reducing M3D induced contrast loss in a lithography process. The method includes: determining an absorber height and a first mask bias based on a contrast of an aerial image of a target pattern and a threshold-to-size associated with the aerial image; determining a desired phase shift between a zeroth order diffraction and a first order diffraction of the target pattern based on the absorber height and the first mask bias; andperforming a dose-aware optimization to obtain the desired phase shift and reduce an amount of dose required to print the target pattern on a substrate.

[0010] In some embodiments, the techniques described herein relate to an apparatus, 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 embodiments.

[0011] In some embodiments, 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 embodiments.BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Figure 1 illustrates a block diagram of various subsystems of a lithographic projection apparatus, according to an embodiment.

[0013] Figure 2 is a schematic diagram of a lithographic projection apparatus, according to an embodiment.

[0014] Figure 3 illustrates an exemplary flow chart for simulating lithography in a lithographic projection apparatus, according to an embodiment.

[0015] Figure 4 shows determination of wavefront target based on diffraction pattern to reduce M3D effects, consistent with various embodiments.

[0016] Figure 5 is a flow diagram of a process for determining a wavefront target based on a diffraction pattern to reduce M3D effects in a lithography process, consistent with various embodiments.

[0017] Figure 6 shows an overlap of the pupil and diffraction pattern, consistent with various embodiments.

[0018] Figures 7A and 7B illustrate partitioning of a discretized diffraction pattern in various ways, consistent with various embodiments.

[0019] Figure 8 illustrates symmetric and asymmetric mask patterns, consistent with various embodiments.

[0020] Figure 9 shows a graph of pattern placement error (PPE) vs. sigma y of a lithographic apparatus, consistent with various embodiments.

[0021] Figure 10 illustrates wavefront target optimization for a contact hole pattern, consistent with various embodiments.

[0022] Figure 11 is a flow diagram for performing dose-aware source mask optimization (SMO) for mitigating M3D fading in a low-n mask, consistent with various embodiments.

[0023] Figure 12 is a flow diagram of a process for simulating contrast and threshold-to-size (T2S) of an aerial image, and a phase difference between diffracted orders of a target pattern for different absorber heights and mask bias values, consistent with various embodiments.

[0024] Figure 13 illustrates a relationship between mask bias and NILSE for various absorber thicknesses, consistent with various embodiments.

[0025] Figure 14 shows the NILS value and the dose required to print different pattern types for various absorber heights of a low-n mask prior to and post dose aware optimization, consistent with various embodiments.

[0026] Figure 15 is a block diagram that illustrates a computer system which can assist in implementing the systems and methods disclosed herein.DETAILED DESCRIPTION

[0027] According to the present disclosure, mask three-dimensional (M3D) effects in lithography, such as image contrast loss, may be reduced by adding an optimized wavefront target to a projection optics box wavefront, and optimizing a source or mask in a lithographic process. In some embodiments, M3D fading impact can be reduced by additionally introducing an optimized target wavefront during lithograph process to cause a desired phase shift between zeroth and first order diffraction, thereby making the aerial images corresponding to different poles to overlap. The wavefront target can be determined and co-optimized with pupil in SMO. In some embodiments, for a given pattern to be printed on a substrate, a diffraction pattern associated with the zeroth and the first order diffraction pattern is determined, and a desired magnitude of phase shift between the zeroth and the first order diffraction pattern to make the diffraction orders overlap (e.g., thereby make the aerial images of the different poles overlap to reduce fading) is determined based on the diffraction pattern. A wavefront target is determined (e.g., in the form of a combination of multiple Zernike parameters) based on the desired phase shift and the wavefront target is injected into the lithography process, which causes the diffraction orders to overlap, thereby resulting in a reduction of the image contrast loss. The wavefront target may be further optimized along with at least one of a source or mask of the lithography process to reduce any adverse impact the introduction of the wavefront target may have on printing other pattern features on the substrate. In some embodiments, by optimizing the wavefront target using multiple Zernike or phase parameters, an overlapping of the pupil and wavefront is maximized, thereby reducing the imaging contrast loss significantly. In some embodiments, the imaging performance may further be improved by co-optimizing the wavefront target with the source or mask.

[0028] In some embodiments, the M3D effects in low-n masks (e.g., masks with low-n, that is, low refractive index, absorber material) may be reduced by optimizing the absorber thickness of a mask. For some patterns (e.g., vertical line space patterns) a thicker mask absorber may be required to mitigate M3D fading compared to the other patterns (e.g., horizontal line space patterns), which may require a significantly increased dose (e.g., the amount of energy that a photoresist is subjected to upon exposure by a lithographic apparatus) to print the patterns, which, in turn, results in a reducedmanufacturing productivity. Furthermore, multiple blank types with different absorber thicknesses may have to be maintained for manufacturing the masks, which increases the manufacturing cost.

[0029] According to the present disclosure, the M3D fading may be reduced by selecting an absorber of a specified height or thickness for all types of patterns, and performing a “dose-aware” optimization, which includes increasing the mask bias to decrease a dose required to print the patterns to target at the required local CD uniformity, and performing an SMO or other pupil-mask-wavefront co-optimization technique to adjust at least one of wavefront target, source parameters of a source of the lithographic apparatus or mask parameters of a mask having a mask pattern corresponding to a target pattern to be printed on a substrate. The dose-aware optimization not only reduces the image contrast loss to mitigate the M3D effect, but also reduces an amount of dose required to print the patterns on the substrate at the required local CD uniformity, thereby increasing, or reducing an impact on, the manufacturing productivity.

[0030] Although embodiments describe in greater details with reference to Zernikes, the present disclosure can be applied to any other mathematical or physics form of wavefront representation, characterization or description system that is well known in the art, e.g., Tatians.

[0031] Although embodiments describe in greater details with reference to zeroth and first order of diffraction pattern, the present disclosure can be applied to any other higher order or any other combination of orders.

[0032] Although embodiments describe in greater details with reference to a low-n mask, the techniques may be applied to other mask types (e.g., Ta-based masks, or high-k masks (e.g., masks with absorber material having a high extinction coefficient)).

[0033] In the present disclosure, although specific reference may be made to the manufacture of ICs, it should be explicitly understood that the description herein has many other possible applications. For example, it may be employed in the manufacture of integrated optical systems, guidance and detection patterns for magnetic domain memories, liquid crystal display panels, thin film magnetic heads, etc. The skilled artisan will appreciate that, in the context of such alternative applications, any use of the terms “reticle”, “wafer” or “die” in this text should be considered as interchangeable with the more general terms “mask”, “substrate” and “target portion”, respectively.

[0034] In the present document, the terms “radiation” and “beam” are used to encompass all types of electromagnetic radiation, including ultraviolet radiation (e.g., with a wavelength of 365, 248, 193, 157 or 126 nm) and EUV (extreme ultra-violet radiation, e.g., having a wavelength in the range of about 5-100 nm). In the present document, the term “radiation source” or “source” is used to encompass all types of sources of radiation, including laser sources, incandescent sources, etc. which may include treatment of the radiation between the radiation source and the target or other parts of the optics, including filtering, collimating, focusing, etc.

[0035] A patterning device can comprise, or can form, one or more design layouts. The design layout can be generated utilizing CAD (computer-aided design) programs. This process is often referred toas EDA (electronic design automation). Most CAD programs follow a set of predetermined design rules in order to create functional design layouts / patterning devices. These rules are set based processing and design limitations. For example, design rules define the space tolerance between devices (such as gates, capacitors, etc.) or interconnect lines, to ensure that the devices or lines do not interact with one another in an undesirable way. One or more of the design rule limitations may be referred to as a “critical dimension” (CD). A critical dimension of a device can be defined as the smallest width of a line or hole, or the smallest space between two lines or two holes. Thus, the CD regulates the overall size and density of the designed device. One of the goals in device fabrication is to faithfully reproduce the original design intent on the substrate (via the patterning device).

[0036] The term “mask” or “patterning device” as employed in this text may be broadly interpreted as referring to a generic patterning device that can be used to endow an incoming radiation beam with a patterned cross-section, corresponding to a pattern that is to be created in a target portion of the substrate. The term “light valve” can also be used in this context. Besides the classic mask (transmissive or reflective; binary, phase-shifting, hybrid, etc.), examples of other such patterning devices include a programmable mirror array. An example of such a device is a matrix-addressable surface having a viscoelastic control layer and a reflective surface. The basic principle behind such an apparatus is that (for example) addressed areas of the reflective surface reflect incident radiation as diffracted radiation, whereas unaddressed areas reflect incident radiation as undiffracted radiation. Using an appropriate filter, the said undiffracted radiation can be filtered out of the reflected beam, leaving only the diffracted radiation behind; in this manner, the beam becomes patterned according to the addressing pattern of the matrix-addressable surface. The required matrix addressing can be performed using suitable electronic means. Examples of other such patterning devices also include a programmable LCD array. An example of such a construction is given in U.S. Patent No. 5,229,872, which is incorporated herein by reference.

[0037] The term “projection optics” as used herein should be broadly interpreted as encompassing various types of optical systems, including refractive optics, reflective optics, apertures and catadioptric optics, for example. The term “projection optics” may also include components operating according to any of these design types for directing, shaping, or controlling the projection beam of radiation, collectively or singularly. The term “projection optics” may include any optical component in the lithographic projection apparatus, no matter where the optical component is located on an optical path of the lithographic projection apparatus. Projection optics may include optical components for shaping, adjusting and / or projecting radiation from the source before the radiation passes the patterning device, and / or optical components for shaping, adjusting and / or projecting the radiation after the radiation passes the patterning device. The projection optics generally exclude the source and the patterning device.

[0038] Figure 1 illustrates a block diagram of various subsystems of a lithographic projection apparatus 10A, according to an embodiment. Major components are a radiation source 12A, whichmay be a deep-ultraviolet excimer laser source or other type of source including an extreme ultra violet (EUV) source (the lithographic projection apparatus itself need not have the radiation source), illumination optics which, e.g., define the partial coherence (denoted as sigma) and which may include optics 14A, 16Aa and 16Ab that shape radiation from the source 12A; a patterning device (or mask) 18 A; and transmission optics 16Ac that project an image of the patterning device pattern onto a substrate plane 22A.

[0039] A pupil 20A can be included with transmission optics 16Ac. In some embodiments, there can be one or more pupils before and / or after mask 18 A. As described in further detail herein, pupil 20A can provide patterning of the light that ultimately reaches substrate plane 22A. An adjustable filter or aperture at the pupil plane of the projection optics may restrict the range of beam angles that impinge on the substrate plane 22A, where the largest possible angle defines the numerical aperture of the projection optics NA= n sin(0max), wherein n is the refractive index of the media between the substrate and the last element of the projection optics, and ©max is the largest angle of the beam exiting from the projection optics that can still impinge on the substrate plane 22A.

[0040] In a lithographic projection apparatus, a source provides illumination (i.e., radiation) to a patterning device and projection optics direct and shape the illumination, via the patterning device, onto a substrate. This is not to disclaim that the source does not itself provide patterning, directing, or shaping to the radiation or that patterning, directing, or shaping does not occur between the source and the projection optics. The projection optics may include at least some of the components 14A, 16Aa, 16Ab and 16Ac. An aerial image (Al) is the radiation intensity distribution at substrate level. A 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 Application Publication No. US 2009-0157360, the disclosure of which is hereby incorporated by reference in its entirety. The resist model is related to properties of the resist layer (e.g., effects of chemical processes which occur during exposure, post-exposure bake (PEB) and development). Optical properties of the lithographic projection apparatus (e.g., properties of the illumination, the patterning device, and the projection optics) dictate the aerial image and can be defined in an optical model. 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 source and the projection optics. Details of techniques and models used to transform a design layout into various lithographic images (e.g., an aerial image, a resist image, etc.), apply OPC using those techniques and models and evaluate performance (e.g., in terms of process window) are described in U.S. Patent Application Publication Nos. US 2008-0301620, 2007-0050749, 2007-0031745, 2008-0309897, 2010-0162197, and 2010-0180251, the disclosure of each which is hereby incorporated by reference in its entirety.

[0041] One aspect of understanding a lithographic process is understanding the interaction of the radiation and the patterning device. The electromagnetic field of the radiation after the radiationpasses the patterning device may be determined from the electromagnetic field of the radiation before the radiation reaches the patterning device and a function that characterizes the interaction. This function may be referred to as the mask transmission function (which can be used to describe the interaction by a transmissive patterning device and / or a reflective patterning device).

[0042] The mask transmission function may have a variety of different forms. One form is binary. A binary mask transmission function has either of two values (e.g., zero and a positive constant) at any given location on the patterning device. A mask transmission function in the binary form may be referred to as a binary mask. Another form is continuous. Namely, the modulus of the transmittance (or reflectance) of the patterning device is a continuous function of the location on the patterning device. The phase of the transmittance (or reflectance) may also be a continuous function of the location on the patterning device. A mask transmission function in the continuous form may be referred to as a continuous tone mask or a continuous transmission mask (CTM). For example, the CTM may be represented as a pixelated image, where each pixel may be assigned a value between 0 and 1 (e.g., 0.1, 0.2, 0.3, etc.) instead of binary value of either 0 or 1. In an embodiment, CTM may be a pixelated gray scale image, where each pixel having values (e.g., within a range [-255, 255], normalized values within a range [0, 1] or [-1, 1] or other appropriate ranges).

[0043] The thin-mask approximation, also called the Kirchhoff boundary condition, is widely used to simplify the determination of the interaction of the radiation and the patterning device. The thin-mask approximation assumes that the thickness of the structures on the patterning device is very small compared with the wavelength and that the widths of the structures on the mask are very large compared with the wavelength. Therefore, the thin-mask approximation assumes the electromagnetic field after the patterning device is the multiplication of the incident electromagnetic field with the mask transmission function. However, as lithographic processes use radiation of shorter and shorter wavelengths, and the structures on the patterning device become smaller and smaller, the assumption of the thin-mask approximation can break down. For example, interaction of the radiation with the structures (e.g., edges between the top surface and a sidewall) because of their finite thicknesses (“mask 3D effect” or “M3D”) may become significant. Encompassing this scattering in the mask transmission function may enable the mask transmission function to better capture the interaction of the radiation with the patterning device. A mask transmission function under the thin-mask approximation may be referred to as a thin-mask transmission function. A mask transmission function encompassing M3D may be referred to as a M3D mask transmission function.

[0044] Figure 2 schematically depicts an exemplary lithographic projection apparatus whose illumination source could be optimized utilizing the methods described herein. The apparatus comprises:- an illumination system IL, to condition a beam B of radiation. In this particular case, the illumination system also comprises a radiation source SO;- a first object table (e.g., mask table, patterning device table or reticle stage) MT provided with a patterning device holder to hold a patterning device MA (e.g., a reticle), and connected to a first positioner to accurately position the patterning device with respect to item PS;- a second object table (substrate table or wafer stage) WT provided with a substrate holder to hold a substrate W (e.g., a resist-coated silicon wafer), and connected to a second positioner to accurately position the substrate with respect to item PS;- a projection system (“lens”) PS (e.g., a refractive, catoptric or catadioptric optical system) to image an irradiated portion of the patterning device MA onto a target portion C (e.g., comprising one or more dies) of the substrate W.

[0045] As depicted herein, the apparatus is of a transmissive type (i.e., has a transmissive mask). However, in general, it may also be of a reflective type, for example (with a reflective mask). Alternatively, the apparatus may employ another kind of patterning device as an alternative to the use of a classic mask; examples include a programmable mirror array or LCD matrix.

[0046] The source SO (e.g., a mercury lamp or excimer laser) produces a beam of radiation. This beam is fed into an illumination system (illuminator) IL, either directly or after having traversed conditioning means, such as a beam expander Ex, for example. The illuminator IL may comprise adjusting means AD for setting the outer or inner radial extent (commonly referred to as o-outer and o-inncr, respectively) of the intensity distribution in the beam. In addition, it will generally comprise various other components, such as an integrator IN and a condenser CO. In this way, the beam B impinging on the patterning device MA has a desired uniformity and intensity distribution in its cross-section.

[0047] It should be noted with regard to Figure 2 that the source SO may be within the housing of the lithographic projection apparatus (as is often the case when the source SO is a mercury lamp, for example), but that it may also be remote from the lithographic projection apparatus, the radiation beam that it produces being led into the apparatus (e.g., with the aid of suitable directing mirrors); this latter scenario is often the case when the source SO is an excimer laser (e.g., based on KrF, ArF or F2 lasing).

[0048] The beam B subsequently intercepts the patterning device MA, which is held on a patterning device table MT. Having traversed the patterning device MA, the beam B passes through the lens PS, which focuses the beam B onto a target portion C of the substrate W. With the aid of the second positioning means (and interferometric measuring means IF), the substrate table WT can be moved accurately, e.g., so as to position different target portions C in the path of beam B. Similarly, the first positioning means can be used to accurately position the patterning device MA with respect to the path of the beam B, e.g., after mechanical retrieval of the patterning device MA from a patterning device library, or during a scan. In general, movement of the object tables MT, WT will be realized with the aid of a long-stroke module (coarse positioning) and a short-stroke module (fine positioning),which are not explicitly depicted in Figure 11. However, in the case of a wafer stepper (as opposed to a step-and-scan tool) the patterning device table MT may just be connected to a short stroke actuator, or may be fixed.

[0049] The depicted tool can be used in two different modes:- In step mode, the patterning device table MT is kept essentially stationary, and an entire patterning device image is projected in one go (i.e., a single “flash”) onto a target portion C. The substrate table WT is then shifted in the x or y directions so that a different target portion C can be irradiated by the beam B;- In scan mode, essentially the same scenario applies, except that a given target portion C is not exposed in a single “flash”. Instead, the patterning device table MT is movable in a given direction (the so-called “scan direction”, e.g., the y direction) with a speed v, so that the projection beam B is caused to scan over a patterning device image; concurrently, the substrate table WT is simultaneously moved in the same or opposite direction at a speed V = Mv, in which M is the magnification of the lens PS (typically, M = 1 / 4 or 1 / 5). In this manner, a relatively large target portion C can be exposed, without having to compromise on resolution.

[0050] Figure 3 illustrates an exemplary flow chart for simulating lithography in a lithographic projection apparatus, according to an embodiment. As will be appreciated, the models may represent a different patterning process and need not comprise all the models described below. A source model 300 represents optical characteristics (including radiation intensity distribution, bandwidth and / or phase distribution) of the illumination of a patterning device. The source model 300 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.

[0051] A projection optics model 310 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 310 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.

[0052] The patterning device / design layout model module 320 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 320 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 patterningdevice. 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.

[0053] An aerial image 330 can be simulated from the source model 300, the projection optics model 310 and the patterning device / design layout model module 320. 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.

[0054] 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 350 can be simulated from the aerial image 330 using a resist model 340. 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 Application No. 8,200,468, the disclosure of which is hereby incorporated by reference in its entirety. The resist model 340 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 310.

[0055] 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 3-dimensional aerial (and resist) image.

[0056] In an embodiment, the resist image 350 can be used an input to a post-pattern transfer process model module 360. The post-pattern transfer process model module 360 defines performance of one or more post-resist development processes (e.g., etch, development, etc.).

[0057] Simulation of the patterning 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.

[0058] Thus, the model formulation describes most, if not all, of the known 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.

[0059] The following paragraphs describe determining a wavefront target, and optimizing the wavefront target with a source, or mask in a lithographic process to reduce M3D effects, such as an M3D induced image contrast loss. While the following process describes the process optimizing a wavefront target with reference to a line / space pattern and a dipole illumination source, the process may be used for other pattern types as well (e.g., contact holes) or other illumination sources (e.g., quadrupole) as well.

[0060] Figure 4 illustrates wavefront target determination process based on a selected diffraction pattern to reduce M3D fading effects, consistent with various embodiments. A diffraction pattern (DP) 412 for a given target pattern 402 (e.g., line / space pattern) is obtained using a pupil 410 to be used in lithography process performed by a lithographic apparatus (e.g., a lithographic projection apparatus 10A of Fig. 1 or a lithographic projection apparatus of Fig. 2). The pupil has a dipole illumination source in this example. In some embodiments, the pupil 410 represents continuous source intensity distribution on a pupil plane. The pupil 410 may be obtained from a process that determines a pupil for a given set of parameters (e.g., source parameters, mask parameters) of the lithographic process or the lithographic apparatus. For example, the pupil 410 may be obtained using a source-mask optimization (SMO) process, source optimization (SO) process, or another process. In some embodiments, an SMO process determines optimum source and / or mask variables for imaging a pattern on a substrate. Additional details of the SMO process is described in International Patent Publication No. W02010 / 059954, titled “Fast Freeform Source and Mask Co-Optimization Method”, and U.S. Patent No. 8,786,824, titled “Source-Mask Optimization in Lithographic Apparatus”, which are hereby incorporated by reference in their entirety. A discretized DP 414 may be generated from the diffraction pattern 412. In some embodiments, the discretized DP may be determined as a convolution of the diffraction orders from a pattern of interest using a unit disk pupil (e.g., NA=1). In the example of Fig. 4, the discretized DP 414 has two imaging areas - a first imaging area 452a and a second imaging area 452b (e.g., these are the areas in which the image of the pattern 402 is formed) - in the pupil 410 where diffraction orders corresponding to the two poles are present.

[0061] The discretized DP 414 is partitioned into various partition zones such that there are no overlaps between the zeroth and first order diffraction from each pole. In the example of Fig. 4, the discretized DP 414 is partitioned along x-axis 458 to generate a partitioned DP 416. As illustrated inthe partitioned DP 416, the first imaging area 452a is partitioned along the x-axis into (a) a first partition corresponding to zeroth order diffraction 454a from a first pole, and (b) a second partition corresponding to a first order diffraction 456b from a second pole. Similarly, the second imaging area 452b is partitioned into (a) a third partition corresponding to a zeroth order diffraction 456a from the second pole, and (b) a fourth partition corresponding to the first order diffraction 454b from the first pole.

[0062] An initial wavefront 418 is determined based on the partitioned DP 416. In some embodiments, the initial wavefront 418 may have a shape that features constant phase difference between the diffraction orders. For example, the initial wavefront 418 may have four quadrants, which is suitable for a line / space pattern 402, as depicted in Fig. 4. A required / desired phase shift between the diffraction orders for given a pole is determined based on a pitch of the target pattern 402 and a sigma value of the lithographic apparatus. For example, the required phase shift between the zeroth order diffraction 454a and the first order diffraction 454b is determined such that the diffraction orders for the first pole overlap, thereby reduce M3D induced image contrast loss.

[0063] The initial wavefront 418 is then optimized to generate a wavefront target 420 that can provide the desired phase shift. In some embodiments, the wavefront target optimization process includes determining a combination of Zernike parameters which generates the wavefront target that can produce the desired phase shift. The Zernike parameters may be determined using a number of ways. For example, the Zernike parameters may be determined using Zernike fitting, which may be based on a least square fitting method, or using pixel-based wavefront map.

[0064] In some embodiments, the wavefront target 420 may be further optimized along with source or mask parameters of the lithographic process. For example, the co-optimization process may include a cost function that is representative of various source and mask parameters (e.g., edge placement error (EPE) cost function) and a group root mean square error (gRMS) associated with set of Zernike parameters. A source, mask, or wavefront target (e.g., Zernike parameters) parameters may be adjusted to reduce (e.g., minimize) the cost function, thereby co-optimizing the source, mask, or wavefront target. In some embodiments, the wavefront associated with a projection optics box (POB) of the lithographic apparatus may also be added to the above co-optimization process. During a lithography process, the determined Zernike parameters may be input to the POB to control a driver lens model (DLM) of the lithographic apparatus. The co-optimization process may ensure balancing of the M3D fading effect mitigation as described above with other SMO variables optimization. The co-optimization can effectively control any adverse or counteracting effects on wafer imaging caused by the addition of the wavefront target. Additional details of the wavefront target generation or optimization is described at least with reference to Figures 5-10 below.

[0065] Figure 5 is a flow diagram of a process for determining a wavefront target based on a diffraction pattern to reduce M3D effects in a lithography process, consistent with various embodiments. At process P510, a diffraction pattern of a target pattern is determined based on a pupiland a zeroth and first order diffraction of the target pattern. For example, the diffraction pattern 412 for the target pattern 402 may be determined based on the pupil 410 and the zeroth and first order diffraction of the target pattern 402. In some embodiments, the pupil 410 is determined using an SMO process that determines optimum source and / or mask variables for imaging a pattern on a substrate. The diffraction orders may be determined as a Fourier transform of a mask, which includes a pattern corresponding to the target pattern 402, and the diffraction pattern 412 may be determined as a convolution of the diffraction orders with the pupil 410.

[0066] In some embodiments, a pupil to diffraction (PDP) ratio is indicative of an extent of overlap between the pupil 410 and the diffraction pattern 412. Figure 6 shows an overlap of the pupil and diffraction pattern, consistent with various embodiments. The image 605 is representative of the pupil 410 overlapped with the diffraction pattern 412. In some embodiments, the PDP ratio may be used to determine whether the desired phase shift may be introduced by optimizing the wavefront target to reduce the M3D effects (e.g., reduce image contrast loss). The PDP ratio may be determined as follows:

[0067] In some embodiments, the greater the PDP ratio, the more complex is the wavefront optimization (e.g., wavefront target generation or optimization) and the lesser is the degree of image contrast improvement. In some embodiments, if the PDP ratio is outside of a specified range, the wavefront optimization may not be performed, or even if performed, may not be beneficial in improving the image contrast. If the PDP ratio is within the specified range (e.g., 50%<PDP<100%), the wavefront optimization may be performed to reduce the M3D effects (e.g., reduce M3D induced image contrast loss). Accordingly, the PDP ratio may be used as a metric to determine whether injecting a wavefront target would be beneficial in reducing M3D induced image contrast loss.

[0068] At process P520, the diffraction pattern is partitioned into the zeroth order and first order diffraction zones to create partitioned zones. In some embodiments, partitioning the diffraction pattern includes determining a discretized DP (e.g., discretized DP 414) and partitioning the discretized DP such that there is no overlap between the partitions corresponding to the zeroth order and first order diffraction. In some embodiments, a discretized DP 414 may be determined as a convolution of the diffraction orders from a pattern of interest using a unit disk pupil (e.g., NA=1). In the discretized DP 414, the two imaging areas - the first imaging area 452a and a second imaging area452b - are the areas where diffraction orders corresponding to the two poles are present (e.g., these are the areas in which the image of the target pattern 402 is formed).

[0069] The discretized DP 414 may be partitioned in various ways such that the partitioned zones have non-overlapping region between the zeroth and first order diffraction from the poles. Figures 7 A and 7B illustrate partitioning of a discretized diffraction pattern in various ways, consistent with various embodiments. For example, for a pupil such as pupil 712, the discretized DP 414 may be partitioned vertically, e.g., along y-axis 714, to create four different zones in which the first imaging area 452a is partitioned along the y-axis into two zones - a first zone representative of a zeroth order diffraction 754a from a first pole and a second zone representative of a first order diffraction 756b from a second pole, as illustrated in the partitioned DP 716. Similarly, the second imaging area 452b is partitioned into a third zone representative of a zeroth order diffraction 756a from the second pole and a fourth zone representative of the first order diffraction 754b from the first pole. Note that the four partitioned zones have non-overlapping region between the zeroth and first order diffraction from the poles. In another example, as illustrated in Fig. 4, the two imaging areas 452a and 452b may be partitioned horizontally, e.g., along the x-axis 458, to create four different zones in which the first imaging area 452a is partitioned along the x-axis into two zones - a first zone representative of a zeroth order diffraction 454a from a first pole and a second zone representative of a first order diffraction 456b from a second pole. Similarly, the second imaging area 452b is partitioned into two zones - a third zone representative of a zeroth order diffraction 456a from the second pole and a fourth zone representative of the first order diffraction 454b from the first pole.

[0070] In another example, for the pupil 722 illustrated in Fig. 7B, the diffraction pattern may be represented as diffraction pattern 724, and its discretized diffraction pattern may be partitioned across a tilted axis 778 to generate a partitioned DP 726. The partitioned DP 726 includes four different zones in which the first imaging area 452a is partitioned along the axis 778 into two zones - a first zone representative of a zeroth order diffraction 764a from a first pole and a second zone representative of a first order diffraction 766b from a second pole. Similarly, the second imaging area 452b is partitioned into a third zone representative of a zeroth order diffraction 766a from the second pole and a fourth zone representative of the first order diffraction 764b from the first pole. Accordingly, the discretized diffraction pattern may be partitioned in various ways.

[0071] The partitions may be symmetric or asymmetric. For example, the partitions in the partitioned DP 716 of Figure 7A are symmetric along the y-axis 736. In another example, the partitions in the partitioned DP 416 of Fig. 4 and the partitioned DP 726 of Fig. 7B are asymmetric. In some embodiments, symmetric partitioning may be preferred over asymmetric partitioning (e.g., as asymmetric partitioning may result in more complex mask patterns, which makes the mask manufacturing process more challenging). Figure 8 illustrates symmetric and asymmetric mask patterns, consistent with various embodiments. The symmetric partitioning may advantageously aid in generating (e.g., during an optimal proximity correction (OPC) process) more symmetric maskpatterns, such as symmetric mask pattern 804, and asymmetric partitioning may result in asymmetric mask patterns, such as an asymmetric mask pattern 802.

[0072] Referring back to Fig. 5, at process P530, a wavefront target is determined based on the partitioned zones and a desired phase shift between the zeroth order diffraction and the first order diffraction. In some embodiments, the partitioned DP may be used in guiding a wavefront target optimization process. For example, an initial wavefront or a wavefront target region of interest (ROI) 418 is determined such that there is constant phase difference between the zones, which may be determined based on the partitioned DP. For example, for a diffraction pattern with horizontal partitioning, such as the partitioned DP 416 of Fig. 4, a quadrant-based wavefront may be determined as the initial wavefront 418. Different diffraction orders may be assigned to different regions of interest (e.g., quadrants) of the initial wavefront based on the partitioned DP.

[0073] After selecting the initial wavefront 418, the phase difference required to cause the diffraction orders to overlap (e.g., thereby causing the aerial images to overlap, which results in a reduction of the M3D effects caused due to diffraction orders from different poles) is determined. In some embodiments, the desired phased shift is determined based on a pitch of the target pattern 402 and the sigma value of the lithographic apparatus. Figure 9 shows a graph of pattern placement error (PPE) vs. sigma y of a lithographic apparatus, consistent with various embodiments. The graph 905 indicates the distance by which an aerial image is shifted for different phase values. The x-axis 902 of the graph 905 is representative of sigma y value (e.g., phase shift) and the y-axis 904 is representative of the PPE, which is indicative of the distance by which a pattern is shifted. In some embodiments, the graph 905 is determined for a lithographic apparatus with a specified numeric aperture, NA, and a wavelength of light source, A. The magnitude of the required phase shift may be determined as follows: phaseeffective= (piimit / p) * (RM 3D / 2 * 5ensZ2(3))... Eq. (2) where phaseeffectiveis the desired phase shift, p, is the pitch of the target pattern, RMSD isM3D fading range, which is a pupil geometry dependent parameter, determined by the PPE shift range from the most outer sigma point of a given pupil, SensZ2^ is a constant = “-3.03”, and Piimitis pitch limit, which may be represented for a two beam imaging system as:... Eq. (3)

[0074] For example, for a 0.33NA EUV lithography apparatus, the Pumn may be determined as “20.5nm.” Accordingly, for a target pattern 402 having a pitch “32nm,” the desired phase shift for moving the aerial image by “-3nm” may be determined as “20.5 / 32”= “0.64.” That is, for a given pole (e.g., the first pole) the phase shift required for the quadrant in the initial wavefront 418 having the zeroth order diffraction 454a of the first pole is determined as “-0.64,” and the phase shift required for the quadrant in the initial wavefront 418 having the first order diffraction 454b of the first pole is determined as “+0.64.”

[0075] After determining the desired phase shift, a wavefront target 420 that is required to generate the desired phase shift is determined. In some embodiments, determining the wavefront target includes determining a combination of multiple Zernike parameters that generates the wavefront target 420 to obtain the desired phase shift. The Zernike parameters may be determined in a number of ways. For example, the set of Zernike parameters may be obtained using Zernike fitting, which may be based on least square fit as follows:... Eq. (4) where s({Zj}) is a set of Zernike parameters, Zi, wps a weight associated with each Zernike parameter and the WFtargetis the wavefront target 420. The Zernike parameters could be a combination of any of a number of Zernike parameters (e.g.,to Z36).

[0076] In another example, the set of Zernike parameters may be determined using a pixel-based wavefront map. In some embodiments, in a pixel-based wavefront representation, each pixel from an initial wavefront map may be optimized or modified to obtain the pixel-based wavefront map representative of the wavefront target.

[0077] After determining the set of Zernike parameters that can be used to generate the desired phase shift, the set of Zernike parameters may be validated to determine whether the wavefront target 420 reduces the M3D effects successfully. For example, a pupil correlation factor, CRFPor the DP correlation factor, CRFDP, may be determined for the wavefront target 420. The CRFPand the CRFDP, may be determined as follows:... Eq. (5)... Eq. (6)

[0078] In some embodiments, the higher the correlation factor, the more optimized the wavefront target 420. If the correlation factor does not satisfy a validation criterion, then the process of determining the initial wavefront, desired phase shift, and set of Zernike parameters is repeated until the validation criterion is satisfied at which point the wavefront target 420 (e.g., therefore, the Zernike parameters) are considered optimized. The validation criterion may be that the correlation factor be greater than a specified threshold, greater than baseline correlation factors (e.g., correlation factors without the wavefront target injection), etc. Thus, the optimized wavefront target 420 (e.g., a set of Zernike parameters) may be determined as described above. The optimized wavefront target 420 may be injected into the lithography process by configuring a projection optics box of the lithography apparatus with values of the set of Zernike parameters associated with the optimized wavefront target 420 to reduce the M3D effects (e.g., minimize the M3D induced imaging contrast loss).

[0079] While the foregoing process P530 describes generating a wavefront target 420 from a quadrant-based initial wavefront 418, other types of initial wavefront shapes may also be used to generate a wavefront target. For example, for a diffraction pattern that is partitioned vertically such as the partitioned DP 716, as illustrated in Figure 7A, an initial wavefront 718 having vertical partitions, which is determined based on the partitioned DP 716, may be used. The initial wavefront 718 may be optimized (e.g., as described above) to generate a wavefront target 720 or wavefront target 732. In some embodiments, the wavefront target may be optimized for an entire pupil (e.g., wavefront target 732), or may be optimized for the diffraction pattern region only (e.g., imaging areas 452), such as wavefront target 720, to minimize any adverse impact of the optimization process on patterns other than the target pattern 402.

[0080] In another example, for a pupil that is tilted, such as pupil 722 in Fig. 7B, an initial wavefront 768 having tilted quadrants may be determined based on the partitioned DP 726. The initial wavefront 768 may be optimized (e.g., as described above) to generate a wavefront target 770.

[0081] In some embodiments, the injection of the wavefront target 420 may have an adverse impact on patterns other than the target pattern 402. Accordingly, to minimize the impact of the optimization on other patterns, the wavefront target 420 may be co-optimized with at least one of a source of the lithographic apparatus or a mask.

[0082] At process P540, the wavefront target 420 may be adjusted (e.g., co-optimized) along with at least one of a source of the lithographic apparatus or a mask. In some embodiments, the cooptimization process, which includes adjusting one or more of wavefront target 420 (e.g., one or more Zernike parameters), source parameters or mask parameters, is performed until a cost function is reduced (e.g., minimized). The cost function may be any function, such as an EPE cost function, thatmay be used to optimize source or mask variables. In some embodiments, to optimize the wavefront target 420 along with the source or mask variables, the cost function may be modified to include a penalty associated with wavefront target 420, such as gRMS. An EPE-based cost function may be represented as follows:... Eq. (7) wherein the cost function s is in this case specified in terms of variables of the illumination mode (vsrc), variables of creating the mask pattern (vmask), variables of the wavefront (e.g., the projection system) (vwavefront). Further, pw corresponds to the process window conditions simulated (e.g., focus and dose metric), eval corresponds to the evaluation features placed within the design pattern, w is a weighting factor for the particular pw and / or evaluation feature eval, EPE is edge placement error being evaluated for the particular combination of pw, and evaluation feature eval, index p is a natural number for the approximation of the cost function, psideiobeis apenalty corresponding to undesired side edge printing of the pattern, the slope of the edge of the simulated contour based on the applied evaluation features, psiopeis apenalty corresponding to the image slope (e.g., image log slope) of the pattern image, PMRC is apenalty corresponding to one or more patterning device manufacturing rule checks, and psrcpenalty corresponding to the design of the illumination mode, and pzrmsis a penalty (e.g., gRMS error) associated with a set of Zernike parameters of the wavefront target 420. As will be appreciated, less (including none), more or different penalties can be applied. In some embodiments, the pzrmsmay be represented as follows:... Eq. (8) where rmax is defined as the max limit for a given Zernike RMS group, rmargin is defined as the + / - area around the rmax value where the penalty starts to be applied, and r is the gRMS, which may be represented as:... Eq. (9)2(n+1which is RMS weight for a Zernike coefficient Zi having a radial order of n, and k=2 for spherical terms or 1 otherwise.

[0083] In some embodiments, the wavefront target 420, and at least one of the source variables or mask variables are co-optimized (e.g., adjusted) until the cost function is reduced (e.g., the gRMS is reduced). Such a co-optimization may result in a significant reduction of M3D effects, thereby improving the image contrast at the substrate, with minimum to no adverse effects on the other patterns. In some embodiments, a wavefront of a projection optics box of the lithography apparatus may also be included in the co-optimization process for optimizing the wavefront of the projection optics box along with the wavefront target and source or mask variables.

[0084] While the foregoing wavefront optimization process is described with reference to line / space pattern, the optimization process may be implemented for other pattern types. Figure 10 illustrates wavefront optimization for a contact hole pattern, consistent with various embodiments. In the example of Fig. 10, a pupil 1006 is obtained for a hexagonal contact hole target pattern 1004 (e.g., using an SMO process), and a diffraction pattern 1008 is calculated based on the pupil 1006 and zeroth and first order diffraction. A discretized DP 1010 is generated and partitioned to separate the diffraction orders, as illustrated in partitioned DP 1012. The partitioned DP 1012 includes a partition corresponding to zeroth order diffraction 1022a, and a pair of partitions corresponding to a pair of first order diffraction from a first pole - first order diffraction 1022b and 1022c, respectively. Similarly, the partitioned DP 1012 includes a partition corresponding to the zeroth diffraction order 1024a, and a pair of partitions corresponding to the first order diffraction 1024b and 1024c from a second pole, respectively. An initial wavefront 1014 is determined based on the partitioned DP 1012. In some embodiments, the initial wavefront 1014 has four regions of interest instead of six partitions depicted in the partitioned DP 1012. The four regions of interest includes two regions of interest corresponding to the zeroth order diffraction from each pole, respectively, and two regions of interest corresponding to the first order diffraction from both the poles. For example, the partitions corresponding to the first order diffraction 1022b and 1024b may be combined into one region of interest in the initial wavefront 1014, and the partitions corresponding to the first order diffraction 1022c and 1024c may be combined into another region of interest. The initial wavefront 1014 may be optimized to determine a wavefront target 1016 (e.g., a set of Zernike parameters) by Zernike fitting, a pixel-based wavefront map or other methods, as described above.

[0085] The following paragraphs describe mitigating the M3D fading based on selection of a specified absorber height and mask bias. In some embodiments, the M3D fading may be reduced by selecting an absorber of a specified height (or thickness) for all types of patterns, increasing the mask bias, and performing a dose-aware optimization, which not only mitigates the M3D effect due to phase shift but also reduces an amount of dose required to print the patterns on the substrate, thereby increasing, or reducing an impact on, the manufacturing productivity.

[0086] The dose-aware optimization is described at least with reference to Figures 11-12.

[0087] Figure 11 is a flow diagram for performing dose-aware optimization for mitigating M3D fading in a low-n mask, consistent with various embodiments. At step Pl 110, an absorber height (or thickness) and a first mask bias for a mask having a mask pattern corresponding to a target pattern to be printed on a substrate is determined. The absorber height and the first mask bias may be determined based on a contrast of an aerial image of a target pattern and a threshold-to-size (“T2S”) associated with the aerial image. In some embodiments, T2S is a threshold intensity of the aerial image at which a critical dimension (CD) of a pattern printed on the substrate matches a defined CD of the corresponding target pattern. For example, an absorber height and a first mask bias for which the contrast of the aerial image is the highest at the largest T2S may be selected. In some embodiments, the contrast and the T2S of the aerial image may be determined for various absorber heights and mask bias values using known simulation methods, such as the method described at least with reference to Figure 12 below.

[0088] Figure 12 is a flow diagram of a process for simulating contrast and T2S of an aerial image, and a phase difference between diffracted orders of a target pattern for different absorber heights and mask bias values, consistent with various embodiments. At process P1210, an amplitude of the aerial image of a target pattern and a phase of each of the diffracted orders (e.g., zeroth order and the first order diffraction of the target pattern) may be determined (e.g., via simulation using known methods) for a range of mask bias values for a particular absorber height. The process P1210 may be repeated for a range of absorber heights to obtain the amplitudes and phase of each of the diffracted orders for each absorber height-mask bias combination. In some embodiments, the absorber height may range up to the manufacturable aspect ratio, and the mask bias may range up to mask rule check (MRC) limit.

[0089] At process Pl 220, a contrast of the aerial image and the phase difference between diffracted orders (e.g., the zeroth order and the first order diffraction) are determined for each absorber heightmask bias value combination. For example, the contrast may be determined based on the amplitude of the aerial image corresponding to the diffraction orders. For example, contrast may be computed using the following equation:Contrast... Eq. (10) where Aoand AT arc amplitudes of the aerial images resulting from the zeroth and first order diffractions. A contrast dataset having contrast value for each absorber height-mask bias value combination may be generated. In some embodiments, a metric such as normalized image log slope (NILS) of the aerial image may also be computed based on the contrast, and a NILS dataset having NILS value for each absorber height-mask bias value combination may be generated.

[0090] The image shift of the aerial image with respect to its intended position may be determined based on the phase difference between the zeroth order and the first diffraction orders, and a phase difference dataset having a phase difference between the diffracted orders for each absorber heightmask bias value combination may be generated. In some embodiments, the desired image shift of the aerial images from different illumination poles (so that the aerial image positions overlap with each other) to mitigate the M3D fading may be determined based on the phase difference between the diffracted orders The image shift may be determined, for example, as follows:Image Shift = - — P ■ r [Atp0,i i ]... Eq. (11) where p is pitch and [Acp0 1] is phase difference between the zeroth and first diffraction orders.

[0091] In some embodiments, the optical properties of different mask stacks (e.g., multilayer, capping layer and absorber) may be considered in determining the image shift as they may influence the simulated phase difference that needs to be corrected.

[0092] At process P1230, the T2S, which is the threshold intensity of the aerial image at which a CD of a pattern printed on the substrate matches a defined CD of the corresponding target pattern, may be determined (e.g., via simulation) for each absorber height and mask bias value combination. A T2S dataset having the T2S value for each absorber height-mask bias value combination may be generated.

[0093] At process Pl 240, the absorber height and the first mask bias value for generating the mask may be selected based on the contrast and T2S values. For example, the contrast dataset and the T2S dataset may be processed to determine the absorber height and the first mask bias value for which the contrast of the aerial image is highest at the largest T2S. In some embodiments, the phase difference between the diffracted orders may not be considered for the determining the absorber height and the first mask bias value.

[0094] After determining the absorber height and the first mask bias value, referring back to Figure 11, at process Pl 120, a phase shift between the diffracted orders (e.g., a zeroth order diffraction and afirst order diffraction) of the target pattern may be determined for the selected absorber height and the first mask bias value.

[0095] At process Pl 130, a dose-aware optimization is performed to obtain the desired phase shift and reduce the amount of dose required to print the target pattern on a substrate. In some embodiments, the dose-aware optimization process includes optimizing, or adjusting (e.g., increasing), the first mask bias value to increase (e.g., maximize) a metric such as NILSE to decrease the required dose to print the pattern to target at the required local CD uniformity, and then performing a pupil-mask-wavefront co-optimization (e.g., SMO, as described at least with reference to Figure 5 above) to obtain the desired image shift to mitigate any residual M3D fading. In some embodiments, NILSE may be determined based on NILS and T2S. For example, NILSE may be represented as:NILSE = NILS * / T2S... Eq. (12)

[0096] The first mask bias value may be increased until the metric satisfies a specified condition (e.g., until the metric is maximized) at which point the dose required to print the pattern to target at the required local CD uniformity is decreased. In some embodiments, the higher the metric the lower is the dose required to print the target pattern on the substrate. Accordingly, by increasing the metric, the amount of dose required to print the target pattern on the substrate at the required local CD uniformity is reduced.

[0097] Since the first mask bias value is adjusted (e.g., increased to a second mask bias value), the phase difference between the diffracted orders may also change. Note that from process P1220 of Figure 12, for a given absorber thickness, the phase difference may change with the mask bias value. Accordingly, the updated phase difference at the second mask bias value is obtained (e.g., from the phase difference dataset for a given value of the absorber thickness and the second mask bias value). The updated phase difference is the desired phase shift to be obtained to mitigate the M3D effect. The desired phase shift may be achieved by performing an SMO process, which adjusts, or co-optimizes, the wavefront target along with at least one of a source of the lithographic apparatus or a mask. In some embodiments, the co-optimization process includes adjusting one or more of wavefront target (e.g., one or more Zernike parameters), source parameters or mask parameters (e.g., as described at least with reference to Figure 5 above) to minimize the phase shift and therefore, mitigate the M3D effect. Accordingly, by performing the dose-aware optimization process, not only the M3D fading due to phase shift is reduced, but also the amount of dose required to print the pattern on the substrate is also reduced, which increases, or reduces the impact on, the manufacturing productivity.

[0098] Figure 13 illustrates a relationship between mask bias and NIESE for various absorber thicknesses, consistent with various embodiments. In the graph 1300, the y-axis is a metric such as NILSE and the x-axis is mask bias value. A first curve 1302 shows the NILSE values across variousmask bias values for a first absorber thickness (e.g., 46nm low-n mask) and a second curve 1312 shows the NILSE values across various mask bias values for a second absorber thickness, which is lesser than the first absorber thickness (e.g., 39nm low-n mask). A first point 1325 indicates the NILSE at a specified mask bias value for a reference condition. Note that by increasing the mask bias value and performing dose-aware optimization to reduce the resulting phase shift, the NILSE metric is increased. For example, the NILSE metric is increased from a first value 1325 to a second value 1306 for the first absorber thickness, and to a third value 1316 for the second absorber thickness. Accordingly, by increasing the mask bias value, the NILSE is increased, which reduces the amount of dose required to print the pattern on the substrate.

[0099] Figure 14 shows the NILS value and the dose required to print different pattern types for various absorber heights of a low-n mask prior to and post dose aware optimization, consistent with various embodiments. In the graph 1425, the y-axis indicates NILS. The graph 1425 shows a first peak NILS 1402 of a first type of pattern (e.g., horizontal line / space pattern) and a second peak NILS 1408 of a second type of pattern (e.g., vertical line / space pattern) for a low-n mask with a first absorber thickness (e.g., 46nm) and without any wavefront target adjustment (e.g., dose-aware optimization). The graph 1425 shows a third peak NILS 1406 of the vertical line / space pattern for a low-n mask with the first absorber thickness after wavefront target adjustment. The graph 1425 shows a fourth peak NILS 1404 of the vertical line / space pattern for a low-n mask with a second absorber thickness greater than the first absorber thickness (e.g., 56nm) and without any wavefront target adjustment.

[0100] In the example of Figure 14, for a first absorber thickness (e.g., 46nm), the second peak NILS 1408 for the vertical line / space pattern is lesser than the first peak NILS 1402 for the horizontal line / space pattern due to residual M3D fading. In some embodiments, in order to mitigate the M3D fading for the vertical line / space pattern, the absorber height may have to be increased from the first absorber thickness to a second absorber thickness. If the absorber thickness is increased to the second absorber thickness greater than the first absorber thickness (e.g., 56nm), the peak NILS increases, as indicated by fourth peak NILS 1404, which is closer to, but still lesser than, the first peak NILS 1402 of the horizontal line / space pattern for the first absorber thickness. However, having different absorber heights for different pattern types may increase the complexity and cost of manufacturing as it requires maintaining different mask blanks (e.g., mask blanks with different absorber heights) for different pattern types. In some embodiments, by employing dose-aware optimization (e.g., wavefront target adjustment using Zernike parameters) at the first absorber thickness (e.g., 46nm), the peak NILS of the vertical line / space pattern can be increased, as indicated by third peak NILS 1406, compared to the second peak NILS 1408 of the vertical line / space pattern with no wavefront target adjustment at the first absorber thickness (e.g., indicated by bar graph 1408). In some embodiments, by performing the wavefront target adjustment at the first absorber thickness, the third peak NILS 1406 of the vertical line / space pattern is not only greater than the second peak NILS 1408 without thewavefront target adjustment, but also greater than the fourth peak NILS 1404 at the second absorber thickness (e.g., 56nm). Accordingly, by performing the dose-aware optimization, the need for having different mask blanks for different pattern types to mitigate the M3D fading is eliminated. In some embodiments, the dose-aware optimization allows for using “non-optimal” absorber heights (e.g., absorber heights other than those typically used in low-n masks to mitigate M3D fading). Correcting the residual M3D fading using the dose-aware optimization allows for using a single mask blank for multiple applications, which decreases the manufacturing cost and complexity.

[0101] Further, as indicated in the graph 1450, by performing dose-aware optimization, the dose required to print the pattern on the substrate may also be reduced, which improves, or reduces an impact on, the manufacturing productivity of the semiconductor chips. In the graph 1450, the y-axis indicates dose. As illustrated in Figure 14, the graph 1450 shows a first dose 1412 required for printing a first type of pattern (e.g., horizontal line / space pattern) at a specified percentage of line width roughness (LWR) for a low-n mask with the first absorber thickness (e.g., 46nm) and without any wavefront target adjustment (e.g., dose-aware optimization). The graph shows a second dose 1418 required for printing a second type of pattern (e.g., vertical line / space pattern) for the mask with the first absorber thickness and without any wavefront target adjustment. Note that the second dose 1418 required to print the vertical line / space pattern is greater than the first dose 1412 required to print the horizontal line / space pattern. The graph 1450 shows a third dose 1414 required for printing the vertical line / space pattern with the mask having a second absorber thickness greater than the first absorber thickness (e.g., 56nm) and without any wavefront target adjustment. Note that even with the increase in the absorber thickness, the third dose 1414 required to print the vertical line / space pattern is still greater than the second dose 1418 required to print the vertical line / space pattern, and the first dose 1412 required to print the horizontal line / space pattern, at the first absorber thickness without any wavefront target adjustment. The graph 1450 shows a fourth dose 1416 required for printing the vertical line / space pattern for the mask with the first absorber thickness after wavefront target adjustment (e.g., dose-aware optimization). Note that the fourth dose 1416 is the least among the doses required in other cases. That is, by performing dose-aware optimization (e.g., having an increased mask bias) at the first absorber thickness, the dose required to print the vertical line / space pattern decreases from the second dose 1418 (e.g., without wavefront target adjustment) to the fourth dose 1416 to print the vertical line / space pattern. Thus, by performing dose-aware optimization, the dose required to print a pattern decreases significantly, thereby improving, or reducing an impact on, the manufacturing productivity.

[0102] Figure 15 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 storagedevice, 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.

[0103] 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.

[0104] 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.

[0105] 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.

[0106] 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.

[0107] 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.

[0108] 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.

[0109] 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.

[0110] 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.

[0111] 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.

[0112] 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.

[0113] Embodiments of the present disclosure can be described further by the following clauses. 1. A method for reducing a mask three-dimensional (M3D) induced contrast loss in a lithography process, the method comprising: determining a diffraction pattern of a target pattern based on a zeroth order and first order diffraction of the target pattern;partitioning of the diffraction pattern into zeroth order and first order diffraction zones to create partitioned zones; and determining a wavefront target based on the partitioned zones and a desired phase shift between the zeroth order diffraction and the first order diffraction.2. The method of clause 1, wherein determining the wavefront target includes: determining a magnitude of the desired phase shift based on a pitch of the target pattern and a sigma value, which is determined based on a numerical aperture of an illuminator and numerical aperture of an objective lens of a lithographic apparatus.3. The method of clause 1, wherein determining the wavefront target includes: determining a set of Zernike parameters that generate the wavefront target to obtain the desired phase shift.4. The method of clause 3, wherein the set of Zernike parameters are determined based on Zernike fitting or a pixel-based wavefront map.5. The method of clause 1 further comprising: adjusting the wavefront target, and at least one of source parameters of a lithography apparatus and mask parameters of a mask corresponding to the target pattern based on a cost function.6. The method of clause 5, wherein adjusting of the wavefront target includes: adjusting a set of Zernike parameters of the wavefront target during the Zernike fitting.7. The method of clause 5, wherein the cost function includes a grouped root mean square (RMS) error associated with a set of Zernike parameters of the wavefront target as a penalty.8. The method of clause 5, wherein the cost function is an edge placement error (EPE) based cost function.9. The method of clause 1 further comprising: configuring a projection optics box of a lithographic apparatus with values of a set of Zernike parameters associated with the wavefront target.10. The method of clause 1, wherein determining the wavefront target includes: generating an initial wavefront target based on the diffraction pattern, wherein the initial wavefront target features a constant phase difference; and adjusting the initial wavefront target based on the desired phase shift.11. The method of clause 1, wherein partitioning the diffraction pattern includes: generating a discretized representation of the diffraction pattern based on an overlapping of the zeroth and first order of the diffraction; and partitioning the discretized representation of the diffraction pattern into the partitioned zones, wherein the partitioned zones have non-overlapping region between the zeroth and the first orders of diffraction from each pole of a source of a lithographic apparatus.12. The method of clause 11, wherein the partitioning includes partitioning the discretized representation of the diffraction pattern into symmetric partition zones.13. The method of clause 11, wherein the partitioning includes partitioning the discretized representation of the diffraction pattern into asymmetric partition zones.14. The method of clause 1, wherein determining the diffraction pattern includes: determining the diffraction pattern based on a pupil and zeroth order and the first order diffraction.15. The method of clause 14, wherein the pupil is formed by at least one of a dipole, quadrupole, hexapole, or annular illumination source.16. The method of clause 14, wherein the diffraction pattern pupil is formed by at least one of a dipole, quadrupole, hexapole, or annular illumination source.17. The method of clause 14, wherein determining the diffraction pattern includes: obtaining the pupil using a source mask optimization (SMO) process that is configured to determine the pupil representing continuous source intensity distribution on a pupil plane.18. The method of clause 14 further comprising: determining the diffraction pattern by overlapping the pupil and the first order diffraction.19. The method of clause 1, determining the diffraction pattern includes: determining the zeroth and first order of diffraction, and convolving the zeroth and first order of diffraction with the pupil to obtain the diffraction pattern.20. The method of clause 1, wherein determining the diffraction pattern further includes: determining a ratio of overlapping of pupil area to diffraction pattern area; and determining that the ratio is within a specified range.21. A method for reducing a mask three-dimensional (M3D) induced contrast loss in a lithography process, the method comprising: determining a diffraction pattern of a target pattern based on a zeroth order and first order diffraction of the target pattern; partitioning a representation of the diffraction pattern into zeroth order and first order diffraction zones to create partitioned zones; determining a wavefront target based on the partitioned zones and a desired phase shift between the zeroth order diffraction and the first order diffraction; and adjusting at least one of the wavefront target, source parameters of a lithography apparatus or mask parameters of a mask corresponding to the target pattern based on a cost function.22. The method of clause 21, wherein determining the wavefront target includes: determining the desired phase shift based on a pitch of the target pattern and a sigma of a lithographic apparatus.23. The method of clause 21, wherein determining the wavefront target includes: performing Zernike fitting to determine a set of Zernike parameters that generate the wavefront target to obtain the desired phase shift.24. The method of clause 21, wherein the cost function includes a grouped root mean square (RMS) error associated with a set of Zernike parameters of the wavefront target as a penalty.25. The method of clause 21, wherein the cost function is an edge placement error (EPE) based cost function.26. The method of clause 21, wherein the adjusting includes: adjusting a wavefront of a projection optics box of the lithography apparatus based on the cost function.27. The method of clause 1, wherein determining the wavefront target includes: determining an absorber height and a first mask bias based on a contrast of an aerial image of the target pattern and a threshold-to-size associated with the aerial image; determining the desired phase shift based on the absorber height and the first mask bias; and performing a dose-aware optimization based on a cost function to obtain the desired phase shift and reduce an amount of dose required to print the target pattern on a substrate.28. The method of clause 27, wherein the absorber height is a height of an absorber of a mask having a mask pattern corresponding to the target pattern, and wherein the threshold-to-size is a threshold intensity of the aerial image at which a critical dimension (CD) of the target pattern printed on the substrate matches a defined CD of the target pattern.29. The method of clause 27, wherein the cost function includes a metric that is computed based on normalized image log slope and a threshold intensity of the aerial image.30. The method of clause 29, wherein the metric is indicative of the amount of dose required to print the target pattern on the substrate, and wherein the higher the metric the lower is the amount of dose required to print the target pattern.31. The method of clause 29, wherein performing the dose-aware optimization includes: adjusting the wavefront target, and at least one of source parameters of a lithography apparatus and mask parameters of a mask corresponding to the target pattern to increase the metric and obtain the desired phase shift.32. The method of clause 31, wherein the adjusting includes: adjusting the first mask bias to a second mask bias to increase the metric.33. The method of clause 32, wherein adjusting the first mask bias includes: increasing the first mask bias to the second mask bias.34. The method of clause 27, wherein determining the absorber height and the first mask bias includes: determining, via simulation, the contrast of aerial image and phase difference between the zeroth order and the first order diffraction for each absorber height-mask bias combination of a range of absorber height-mask bias combinations; and determining, via simulation, the threshold-to-size associated with the aerial image for each absorber height-mask bias combination of the range of absorber height-mask bias combinations.35. The method of clause 34 further comprising: determining the absorber height and the first mask bias for which the contrast of the aerial image is the highest at the largest threshold-to-size.36. The method of clause 34, wherein determining the contrast of the aerial image and the phase difference includes: determining, via simulation, an amplitude and a phase of each of the zeroth order and the first order diffraction of the target pattern for each absorber height-mask bias combination of the range of absorber height-mask bias combinations; and determining the contrast of aerial image and the phase difference between the zeroth order and the first order diffraction based on the amplitude and the phase for each absorber height-mask bias combination of the range of absorber height-mask bias combinations.37. A method for reducing a mask three-dimensional (M3D) induced contrast loss in a lithography process, the method comprising: determining an absorber height and a first mask bias based on a contrast of an aerial image of a target pattern and a threshold-to-size associated with the aerial image; determining a desired phase shift between a zeroth order diffraction and a first order diffraction of the target pattern based on the absorber height and the first mask bias; and performing a dose-aware optimization to obtain the desired phase shift and reduce an amount of dose required to print the target pattern on a substrate.38. The method of clause 37, wherein performing the dose-aware optimization includes: adjusting the first mask bias to a second mask bias that is optimized to reduce the amount of dose required to print the target pattern.39. The method of clause 38, wherein adjusting the first mask bias to reduce the amount of dose includes: performing the dose-aware optimization based on a cost function, wherein the cost function includes a metric that is computed based on normalized image log slope and a threshold intensity of the aerial image.40. The method of clause 39, wherein the metric is indicative of the amount of dose required to print the target pattern on the substrate, and wherein the higher the metric the lower is the amount of dose required to print the target pattern.41. The method of clause 39, wherein adjusting the first mask bias includes: increasing the first mask bias to the second mask bias to increase the metric.42. The method of clause 37, wherein determining the absorber height and the first mask bias includes: determining, via simulation, the contrast of aerial image and phase difference between the zeroth order and the first order diffraction for each absorber height-mask bias combination of a range of absorber height-mask bias combinations; anddetermining, via simulation, the threshold-to-size associated with the aerial image for each absorber height-mask bias combination of the range of absorber height-mask bias combinations.43. The method of clause 42 further comprising: determining the absorber height and the first mask bias for which the contrast of the aerial image is the highest at the largest threshold-to-size.44. The method of clause 42, wherein determining the contrast of the aerial image and the phase difference includes: determining, via simulation, an amplitude and a phase of each of the zeroth order and the first order diffraction of the target pattern for each absorber height-mask bias combination of the range of absorber height-mask bias combinations; and determining the contrast of aerial image and the phase difference between the zeroth order and the first order diffraction based on the amplitude and the phase for each absorber height-mask bias combination of the range of absorber height-mask bias combinations.45. The method of clause 37, wherein performing the dose-aware optimization includes: determining a wavefront target based on the desired phase shift between the zeroth order diffraction and the first order diffraction.46. The method of clause 45, wherein determining the wavefront target includes: determining a set of Zernike parameters that generate the wavefront target to obtain the desired phase shift.47. The method of clause 46, wherein the set of Zernike parameters are determined based on Zernike fitting or a pixel-based wavefront map.48. The method of clause 37, wherein performing the dose-aware optimization includes: adjusting a wavefront target, and at least one of source parameters of a lithography apparatus and mask parameters of a mask corresponding to the target pattern based on a cost function to obtain the desired phase shift.49. The method of clause 48, wherein the cost function is an edge placement error (EPE) based cost function.50. The method of clause 48 further comprising: configuring a projection optics box of a lithographic apparatus with values of a set of Zernike parameters associated with the wavefront target.51. The method of clause 37, wherein the absorber height is a height of an absorber of a mask having a mask pattern corresponding to the target pattern, and wherein the threshold-to-size is a threshold intensity of the aerial image at which a critical dimension (CD) of the target pattern printed on the substrate matches a defined CD of the target pattern.52. An apparatus, the apparatus comprising: a memory storing a set of instructions; anda processor configured to execute the set of instructions to cause the apparatus to perform a method of any of the above clauses.53. 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.

[0114] 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.

[0115] 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.

[0116] 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.

[0117] 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.

[0118] 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 thedrawings 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.

[0119] 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.

[0120] 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. Unlessotherwise 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.

[0121] 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.

[0122] 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.

[0123] 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

CLAIMS1. A method for reducing a mask three-dimensional (M3D) effect in a lithography process, the method comprising: determining a diffraction pattern of a target pattern based on a zeroth order and first order diffraction of the target pattern; partitioning of the diffraction pattern into zeroth order and first order diffraction zones to create partitioned zones; and determining a wavefront target based on the partitioned zones and a desired phase shift between the zeroth order diffraction and the first order diffraction.

2. The method of claim 1, wherein determining the wavefront target includes: determining a magnitude of the desired phase shift based on a pitch of the target pattern and a sigma value, which is determined based on a numerical aperture of an illuminator and numerical aperture of an objective lens of a lithographic apparatus.

3. The method of claim 1, wherein determining the wavefront target includes: determining a set of Zernike parameters that generate the wavefront target to obtain the desired phase shift.

4. The method of claim 3, wherein the set of Zernike parameters are determined based on Zernike fitting or a pixel-based wavefront map.

5. The method of claim 1 further comprising: adjusting the wavefront target, and at least one of source parameters of a lithography apparatus and mask parameters of a mask corresponding to the target pattern based on a cost function.

6. The method of claim 5, wherein adjusting of the wavefront target includes: adjusting a set of Zernike parameters of the wavefront target during the Zernike fitting.

7. The method of claim 5, wherein the cost function includes at least one of: a grouped root mean square (RMS) error associated with a set of Zernike parameters of the wavefront target as a penalty; and an edge placement error (EPE).

8. The method of claim 1 further comprising: configuring a projection optics box of a lithographic apparatus with values of a set of Zernike parameters associated with the wavefront target, and wherein the pupil is formed by at least one of adipole, quadrupole, hexapole, or annular illumination source.

9. The method of claim 1, wherein determining the wavefront target includes: generating an initial wavefront target based on the diffraction pattern, wherein the initial wavefront target features a constant phase difference; and adjusting the initial wavefront target based on the desired phase shift.

10. The method of claim 1, wherein partitioning the diffraction pattern includes: generating a discretized representation of the diffraction pattern based on an overlapping of the zeroth and first order of the diffraction; and partitioning the discretized representation of the diffraction pattern into the partitioned zones, wherein the partitioned zones have non-overlapping region between the zeroth and the first orders of diffraction from each pole of a source of a lithographic apparatus.

11. The method of claim 10, wherein the partitioning includes partitioning the discretized representation of the diffraction pattern into symmetric or asymmetric partition zones.

12. The method of claim 1, wherein determining the diffraction pattern includes: determining the diffraction pattern based on a pupil and zeroth order and the first order diffraction, and wherein the diffraction pattern pupil is formed by at least one of a dipole, quadrupole, hexapole, or annular illumination source.

13. The method of claim 1, wherein determining the diffraction pattern includes: obtaining the pupil using a source mask optimization (SMO) process that is configured to determine the pupil representing continuous source intensity distribution on a pupil plane; and overlapping the pupil and the first order diffraction.

14. The method of claim 1, determining the diffraction pattern includes: determining the zeroth and first order of diffraction, and convolving the zeroth and first order of diffraction with the pupil to obtain the diffraction pattern.

15. The method of claim 1, wherein determining the diffraction pattern further includes: determining a ratio of overlapping of pupil area to diffraction pattern area; and determining that the ratio is within a specified range.

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