Random perceptual source mask optimization based on probability distribution of edge placement

Abstract

A method of random perceptual source mask optimization is described. A probability distribution of edge placement that takes into account randomness is determined. Based on the probability distribution, the source configuration, the mask configuration, or a combination of the source configuration and the mask configuration may be optimized for the lithographic process. The probability distribution of edge placement may take into account the distribution of random effects over edge placement, including random edge placement error contributions. The probability distribution of edge placement may be compared to the contour to determine a simulated distribution of edge placement errors. The source configuration, the mask configuration, or a combination of the source configuration and the mask configuration may be optimized using a cost function that takes into account the probability distribution of edge placement.

Description

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims priority to U.S. application No. 63 / 388,353, filed on July 12, 2022, and the entirety of which is incorporated herein by reference. Technical Field

[0003] The description herein relates to a method and system for optimizing a lithography process based on a probability distribution of edge placement. Background Art

[0004] For example, a lithographic projection apparatus may be used to manufacture integrated circuits (ICs). A patterning device (e.g., a mask) may contain or provide a pattern corresponding to a single layer (a "design layout") of an IC, and the pattern may be transferred to a target portion (e.g., including one or more dies) on a substrate (e.g., a silicon wafer) that has been coated with a layer of radiation-sensitive material (a "resist") by methods such as irradiating the target portion through the pattern on the patterning device. Generally, a single substrate includes a plurality of adjacent target portions, to which the lithographic projection apparatus sequentially transfers the pattern, one target portion at a time. In one type of lithographic projection apparatus, the pattern on the entire patterning device is transferred to one target portion in one operation. Such an apparatus is often referred to as a stepper. In an alternative apparatus, often referred to as a stepper-scan apparatus, the projection beam scans the patterning device along a given reference direction (the "scanning" direction) while the substrate is synchronously moved parallel or antiparallel to the reference direction. Different portions of the pattern on the patterning device are progressively transferred to one target portion. Since the lithographic projection apparatus typically has a reduction factor M (e.g., 4), and the reduction factor may be different for x- and y-directional features, the speed F at which the substrate moves will be 1 / M times the speed at which the projection beam scans the patterning device. For example, more information about the lithographic apparatus described herein may be gleaned from U.S. Pat. No. 6,046,792, which is incorporated herein by reference.

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

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

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

[0008] As semiconductor manufacturing processes have advanced, the size of functional elements has continued to decrease, while the number of functional elements (such as transistors) per device has been steadily increasing for decades, following a trend often referred to as "Moore's Law." At the current state of the art, the layers of a device are fabricated using a lithography projection apparatus that projects a design layout onto a substrate using illumination from a deep ultraviolet illumination source, thereby creating individual functional elements having dimensions well below 100 nm (i.e., less than half the wavelength of the radiation from the illumination source (e.g., an illumination source of 193 nm)).

[0009] This process of printing features with dimensions smaller than the traditional resolution limit of the lithographic projection apparatus is often referred to as low-k1 lithography, according to the resolution formula CD=k1×λ / NA, where λ is the wavelength of the radiation employed (currently 248 nm or 193 nm in most cases), NA is the numerical aperture of the projection optics in the lithographic projection apparatus, CD is the "critical dimension" - usually the minimum feature size printed - and k1 is an empirical resolution factor. In general, the smaller the k1, the more difficult it is to reproduce on a substrate a pattern similar in shape and size to that planned by the designer to achieve a specific electrical function and performance. To overcome these difficulties, complex fine-tuning steps need to be applied to the lithographic projection apparatus, the design layout, or the patterning device. These steps include, but are not limited to, for example, optimizing NA and optical coherence settings, customizing the illumination scheme, using a phase-shifted patterning device, optical proximity correction (OPC, sometimes also called "optical and process correction") in the design layout, or other methods generally defined as "resolution enhancement techniques" (RET). Summary of the invention

[0010] According to an embodiment, a method for determining source and mask configurations of a lithography process is provided. The method includes: obtaining a source configuration, a mask configuration, or a combination of a source configuration and a mask configuration; calculating a probability distribution of edge placement errors of the lithography process based on the source configuration, the mask configuration, or a combination of the source configuration and the mask configuration; and adjusting the source configuration, the mask configuration, or a combination of the source configuration and the mask configuration based on the probability distribution.

[0011] In an embodiment, the edge placement error comprises a simulated edge placement error.

[0012] In an embodiment, the edge placement error is obtained based on a model calibrated with the measured edge placement error.

[0013] In an embodiment, the probability distribution corresponds to a random probability distribution.

[0014] In an embodiment, the probability distribution is calibrated based on the measured probability distribution.

[0015] In an embodiment, the probability distribution comprises a cumulative probability function.

[0016] In an embodiment, the method further comprises calculating an offset function between the probability distribution and a reference probability distribution, and wherein the adjusting is based on the offset function.

[0017] In an embodiment, the shift function between the probability distribution and the reference probability distribution is the Lp norm.

[0018] In an embodiment, the adjusting comprises: adjusting a source configuration, a mask configuration, or a combination of the source configuration and the mask configuration until a difference between the probability distribution and the reference probability distribution is within a threshold range.

[0019] In an embodiment, the adjusting comprises adjusting the source configuration, the mask configuration, or a combination of the source configuration and the mask configuration based on a sum of probability distributions in at least two planes of the plurality of planes.

[0020] In an embodiment, the one or more imaging performance indicators include at least one of the following: critical dimension (CD), critical dimension uniformity (CDU), local critical dimension uniformity (LCDU), line edge roughness (LER), line width roughness (LWR), resist profile characteristics, maximum defect size, exposure latitude, pattern position error, mask error enhancement factor, focal length, depth of focus (DOF), DOF tolerance, critical dimension depth of focus, process window, process window tolerance, common process window, common process window tolerance, image contrast, image logarithmic slope (ILS), normalized image logarithmic slope (NILS), available process window above a specific NILS threshold (nDOF), mask error enhancement factor (MEEF), or a combination of the foregoing.

[0021] In an embodiment, the one or more imaging performance indicators include at least one of the following: critical dimension (CD), critical dimension uniformity (CDU), local critical dimension uniformity (LCDU), line edge roughness (LER), line width roughness (LWR), resist profile characteristics, maximum defect size, exposure latitude, pattern placement error, mask error enhancement factor, focal length, depth of focus (DOF), DOF tolerance, critical dimension depth of focus, process window, process window tolerance, common process window, common process window tolerance, image contrast, image logarithmic slope (ILS), normalized image logarithmic slope (NILS), available process window above a specific NILS threshold (nDOF), mask error enhancement factor (MEEF), or a combination of the foregoing.

[0022] In an embodiment, the adjustment includes: determining a multivariate cost function of a lithography process based on a probability distribution of edge placement errors, wherein the lithography process includes a lithography process corresponding to a source configuration, a mask configuration, or a combination of a source configuration and a mask configuration; and reconfiguring one or more characteristics of the lithography process until a termination criterion is met.

[0023] According to another embodiment, a method is provided: determining, by a computer system, a multivariate cost function of multiple design variables representing characteristics of a lithography process, wherein the multivariate cost function is related to a probability distribution of edge placement, wherein the probability distribution of edge placement takes into account randomness of edge placement; and reconfiguring, by the computer system, one or more characteristics of the lithography process by adjusting one or more of the multiple design variables until a termination criterion is met.

[0024] In an embodiment, the probability distribution of edge placements includes contributions from a random edge placement distribution and a deterministic edge placement distribution.

[0025] In an embodiment, further comprising calculating a distance between the probability distribution of edge placements and a reference distribution of edge placements, and wherein the reconfiguration is based on the distance.

[0026] In an embodiment, the determining includes: determining, by a computer system, a first multivariate cost function of a plurality of design variables representing characteristics of a lithography process, wherein the first multivariate cost function is related to edge placement; and reconfiguring, by the computer system, one or more characteristics of the lithography process by adjusting one or more of the plurality of design variables until a first termination criterion is met.

[0027] In an embodiment, wherein the random probability distribution of edge placements comprises a random probability distribution of edge placement errors. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate certain aspects of the subject matter disclosed herein and, together with the description, help explain some principles associated with the disclosed embodiments.

[0029] Figure 1 A block diagram of various subsystems of a lithographic projection apparatus according to an embodiment is shown.

[0030] Figure 2 An exemplary flow chart for simulating lithography in a lithographic projection apparatus according to an embodiment is shown.

[0031] Figure 3 An exemplary method of stochastic-aware source mask optimization based on probability distribution of edge placement according to an embodiment is shown.

[0032] Figure 4 An exemplary method of stochastic-aware source mask optimization based on a probability distribution of random edge placements according to an embodiment is shown.

[0033] Figure 5 A schematic diagram depicting stochastic-aware optimization of a lithography process in accordance with an embodiment is depicted.

[0034] Figure 6 Depicted is a graphical representation of edge placement distribution in accordance with an embodiment.

[0035] FIG. 7A to FIG. 7B An exemplary distance function for the Lp norm is depicted, according to an embodiment.

[0036] FIG. 8A to FIG. 8B Depicted is an exemplary distance function for the Lp norm, according to an embodiment.

[0037] Fig. 9 is a block diagram of an exemplary computer system according to an embodiment.

[0038] Fig.10 is a schematic diagram of a lithographic projection apparatus according to an embodiment.

[0039] Fig.11 is a schematic diagram of another lithography projection apparatus according to an embodiment.

[0040] Fig.12 is a detailed view of a lithographic projection apparatus according to an embodiment.

[0041] Fig.13 is a detailed view of a source collector module of a lithographic projection apparatus according to an embodiment. DETAILED DESCRIPTION

[0042] The present disclosure describes the use of a probability distribution of edge placements to optimize a source configuration, a mask configuration, or a combination of a source configuration and a mask configuration for a lithography process. The probability distribution of edge placements can account for random effects in edge placements, such as random effects that cause random edge placement errors (SEPEs). The randomness can be a function of the physics of the lithography process and can be difficult to remove at the lithography wavelength. A probability distribution of random edge placements can be determined and convolved with the edge placement distribution to generate a probability distribution of edge placements that accounts for the randomness.

[0043] Although the manufacture of ICs may be specifically mentioned herein, it should be clearly understood that the description herein has many other possible applications. For example, the description herein can be used to manufacture integrated optical systems, guidance and detection patterns of magnetic domain memories, liquid crystal display panels, thin film magnetic heads, etc. The skilled person will understand that in the context of such alternative applications, any use of the terms "reticle", "wafer", or "die" herein should be considered to be interchangeable with the more general terms "mask", "substrate", and "target portion".

[0044] In this document, the terms "radiation" and "beam" are used to cover all types of electromagnetic radiation, including ultraviolet radiation (e.g., having a wavelength of 365 nm, 248 nm, 193 nm, 157 nm, or 126 nm) and EUV (extreme ultraviolet radiation, e.g., having a wavelength in the range of about 5 nm to 100 nm). In this document, the terms "radiation source" or "source" are used to cover all types of radiation sources, including laser sources, incandescent sources, etc., which may include processing of the radiation between the radiation source and a target or other part of an optical device, including filtering, collimation, focusing, etc.

[0045] The pattern forming device may include or may form one or more design layouts. The design layout may be generated using a CAD (computer-aided design) program. This process is often referred to as EDA (electronic design automation). Most CAD programs follow a set of predetermined design rules to create a functional design layout / pattern forming device. These rules are set based on process and design constraints. For example, the design rules define the spatial tolerances between devices (e.g., gates, capacitors, etc.) or interconnects to ensure that the devices or lines do not interact in an undesirable manner. One or more of the design rule constraints may be referred to as a "critical dimension" (CD). The critical dimension of a device may be defined as the minimum width of a line or hole, or the minimum space between two lines or two holes. Therefore, CD regulates the overall size and density of the designed device. One of the goals of device manufacturing is to faithfully reproduce the original design intent on the substrate (through the pattern forming device).

[0046] The terms "mask" or "patterning device" as used herein may be broadly interpreted as referring to a general patterning device that can be used to impart a patterned cross-section to an incident radiation beam corresponding to a pattern to be created in a target portion of a substrate. The term "light valve" may also be used in this context. In addition to the classical masks (transmissive or reflective; binary, phase-shift, hybrid, etc.), other examples of such patterning devices include programmable mirror arrays. 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 a device is that (for example) the addressed areas of the reflective surface reflect the incident radiation as diffracted radiation, while the unaddressed areas reflect the incident radiation as non-diffracted radiation. Using appropriate filters, the non-diffracted radiation can be filtered out of the reflected beam, leaving only the diffracted radiation; in this way, the beam is patterned according to the addressing pattern of the matrix-addressable surface. The required matrix addressing can be performed using suitable electronic devices. Other examples of such patterning devices also include programmable LCD arrays. Examples of such configurations are given in US Pat. No. 5,229,872, which is incorporated herein by reference.

[0047] The term "projection optics" as used herein should be interpreted broadly to include various types of optical systems, including, for example, refractive optics, reflective optics, apertures, and reflective-refractive optics. The term "projection optics" may also include components for collectively or individually directing, shaping, or controlling a projection radiation beam that operates according to any of these design types. The term "projection optics" may include any optical component in a lithographic projection apparatus, regardless of where the optical component is located on the optical path of the lithographic projection apparatus. Projection optics may include optical components for shaping, adjusting, and / or projecting radiation from a source before the radiation passes through a patterning device, and / or optical components for shaping, adjusting, and / or projecting radiation after the radiation passes through a patterning device. Projection optics typically do not include a source and a patterning device.

[0048] Figure 1 A block diagram of various subsystems of a lithographic projection apparatus 10A according to an embodiment is shown. The main components are: a radiation source 12A, which may be a deep ultraviolet excimer laser source or other type of source, including an extreme ultraviolet (EUV) source (the lithographic projection apparatus itself need not have a radiation source); an illumination optical device, which, for example, defines a partial coherence (expressed as sigma) and may include optical devices 14A, 16Aa and 16Ab, which shape the radiation from source 12A; a patterning device (or mask) 18A; and a transmission optical device 16Ac, which projects an image of the patterning device pattern onto a substrate plane 22A.

[0049] Pupil 20A may be included with transmission optics 16Ac. In some embodiments, there may be one or more pupils before and / or after mask 18A. As described in further detail herein, pupil 20A may provide patterning of light that ultimately reaches substrate plane 22A. An adjustable filter or aperture at the pupil plane of the projection optics may limit the range of beam angles impinging on substrate plane 22A, wherein the maximum possible angle defines the numerical aperture NA=nsin(θ max ), where n is the refractive index of the medium between the substrate and the last element of the projection optics, θ max is the maximum angle of the beam from the projection optics that can still impinge on the substrate plane 22A.

[0050] In a lithographic projection apparatus, a light source provides illumination (i.e., radiation) to a pattern forming device, and the projection optical device directs and shapes the illumination onto a substrate via the pattern forming device. This does not deny that the light source itself does not provide patterning, directing, or shaping of radiation, or that patterning, directing, or shaping does not occur between the light source and the projection optical device. The projection optical device may include at least some of components 14A, 16Aa, 16Ab, and 16Ac. The aerial image (AI) is the radiation intensity distribution at the substrate level. A resist image can be calculated from an aerial image using a resist model, and an example of calculating a resist image from an aerial image using a resist model can be found in U.S. Patent Application Publication No. US 2009-0157630, the disclosure of which is incorporated herein by reference in its entirety. The resist model is related to the properties of the resist layer (e.g., the effects of chemical processes occurring during exposure, post-exposure baking (PEB), and development). The optical properties of the lithographic projection apparatus (e.g., the characteristics of the illumination, pattern forming device, and projection optical device) determine the aerial image and can be defined in the optical model. Because the patterning device used in the lithographic projection apparatus can vary, it is desirable to separate the optical properties of the patterning device from the optical properties of the rest of the lithographic projection apparatus, including at least the light source and projection optics. Details of techniques and models for converting a design layout into various lithographic images (e.g., aerial images, resist images, etc.), applying OPC using these techniques and models, and evaluating performance (e.g., in terms of process window) are described in U.S. Patent Application Publication Nos. US 2008-0301620, 2007-0050749, 2007-0031745, 2008-0309897, 2010-0162197, and 2010-0180251, the disclosures of each of which are incorporated herein by reference in their entirety.

[0051] One aspect of understanding the lithography process is understanding the interaction of radiation and patterning devices. The electromagnetic field of radiation after passing through the patterning device can be determined by the electromagnetic field of the radiation before it reaches the patterning device and a function that characterizes the interaction. This function can be called the mask transmission function (the mask transmission function can be used to describe the interaction of the transmission patterning device and / or the reflection patterning device).

[0052] The mask transfer function can have a variety of different forms. One form is binary. A binary mask transfer function has either of two values ​​(e.g., zero and a positive constant) at any given position on the pattern forming device. A mask transfer function in binary form may be referred to as a binary mask. Another form is continuous. That is, the modulus of the transmittance (or reflectance) of the pattern forming device is a continuous function of the position on the pattern forming device. The phase of the transmittance (or reflectance) may also be a continuous function of the position on the pattern forming device. A mask transfer function in continuous form may be referred to as a continuous tone mask or a continuous transmission mask (CTM). For example, a 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.), rather than a binary value of 0 or 1. In an embodiment, the CTM may be a pixelated grayscale image, where each pixel has a value (e.g., a normalized value in the range [-255, 255], in the range [0,1] or [-1,1] or other appropriate range).

[0053] The thin mask approximation, also known as the Kirchhoff boundary condition, is widely used to simplify the determination of the interaction between radiation and the patterning device. The thin mask approximation assumes that the thickness of the structures on the patterning device is very small compared to the wavelength, while the width of the structures on the mask is very large compared to the wavelength. Therefore, the thin mask approximation assumes that the electromagnetic field behind the patterning device is the product of the incident electromagnetic field and the mask transfer function. However, as the lithography process uses radiation with shorter and shorter wavelengths, the structures on the patterning device become smaller and smaller, and the assumption of the thin mask approximation may fail. For example, due to the finite thickness of the structures ("mask 3D effect" or "M3D"), the interaction of radiation with the structures (e.g., the edge between the top surface and the sidewall) may become significant. Including this scattering in the mask transfer function allows the mask transfer function to better capture the interaction of radiation with the patterning device. The mask transfer function under the thin mask approximation can be referred to as a thin mask transfer function. The mask transfer function that includes M3D can be referred to as an M3D mask transfer function.

[0054] Figure 2An exemplary flow chart for simulating lithography in a lithographic projection apparatus according to an embodiment is shown. A source model 31 represents the optical properties of a source (including radiation intensity distribution and / or phase distribution). A projection optics model 32 represents the optical properties of the projection optics (including changes in radiation intensity distribution and / or phase distribution caused by the projection optics). A design layout model 35 represents the optical properties of a design layout (including changes in radiation intensity distribution and / or phase distribution caused by the design layout 33), the optical properties of the design layout representing the arrangement of features on a pattern forming device or the arrangement of features formed by a pattern forming device. An aerial image 36 can be simulated from the design layout model 35, the projection optics model 32, and the design layout model 35. A resist image 38 can be simulated from the aerial image 36 using a resist model 37. The simulation of lithography can, for example, predict the profile and CD in the resist image.

[0055] More specifically, the source model 31 may represent the optical properties of the source, including but not limited to numerical aperture settings, illumination sigma (σ) settings, and any specific illumination shapes (e.g., off-axis radiation sources such as toroidal, quadrupole, dipole, etc.). The projection optics model 32 may represent the optical properties of the projection optics, including aberrations, distortions, one or more refractive indices, one or more physical sizes, one or more physical dimensions, etc. The design layout model 35 may represent one or more physical properties of a physical pattern forming device, such as described in U.S. Pat. No. 7,587,704, which is incorporated herein by reference in its entirety. The purpose of the simulation is to accurately predict, for example, edge placement, aerial image intensity slope, and / or CD, which can then be compared to an expected design. An expected design is typically defined as a pre-OPC design layout that can be provided in a standardized digital file format such as GDSII or OASIS or other file formats.

[0056] From the design layout, one or more portions referred to as "segments" may be identified. In an embodiment, a set of segments representing complex patterns in the design layout (typically about 50 to 1000 segments, but any number of segments may be used) are extracted. These patterns or segments represent multiple smaller portions of the design (i.e., circuits, cells, or patterns), and more specifically, segments typically represent multiple smaller portions that require special attention and / or verification. In other words, segments may be multiple portions of the design layout, or may be similar portions of the design layout or have similar behaviors of multiple portions of the design layout, wherein one or more key features are identified through experience (including customer-provided segments), trial and error, or by running full-chip simulations. A segment may contain one or more test patterns or instrumentation patterns.

[0057] The customer may pre-provide an initial larger set of clips based on one or more known key feature areas in the design layout that require specific image optimization. Alternatively, in another embodiment, the initial larger set of clips may be extracted from the entire design layout using some automatic (e.g., machine vision) or manual algorithm that identifies one or more key feature areas.

[0058] For example, in a lithography projection device, the cost function can be expressed as the following equation 1:

[0059] (1)

[0060] in, are N design variables or the values ​​of N design variables. Can be a design variable functions, such as design variables The difference between the actual and expected values ​​of a characteristic for a set of values. is with The associated weight constant. For example, a characteristic may be the position of an edge of a pattern measured at a given point on the edge of the pattern. Different May have different weights For example, if a particular edge has a narrow range of allowed positions, then you can have a value that represents the difference between the actual position of the edge and the expected position. Weight Assign a higher value. It can also be a function of the interlayer characteristics, which are in turn design variables Of course, It is not limited to the form in Equation 1. It may be in any other suitable form.

[0061] The cost function may represent any one or more suitable characteristics of the lithographic projection apparatus, the lithographic process, or the substrate, such as focal length, CD, image offset, pattern position error, image distortion, image rotation, random variation, throughput, local CD variation, process window, inter-layer characteristics, or a combination of the foregoing. In an embodiment, the design variables The cost function may include one or more selected from the group consisting of dose, global bias of the pattern forming device, and / or shape of the irradiation. Since the resist image often determines the pattern on the substrate, the cost function may include a function representing one or more characteristics of the resist image. For example, can simply be the distance between a point in the resist image and the expected position of that point (i.e., edge placement error ). Design variables may include any adjustable parameters, such as adjustable parameters of the source, patterning device, projection optics, dose, focal length, etc.

[0062] The lithographic apparatus may include components collectively referred to as "wavefront manipulators" that can be used to adjust the shape of the wavefront and the intensity distribution and / or phase shift of the radiation beam. In an embodiment, the lithographic apparatus can adjust the wavefront and intensity distribution at any position along the optical path of the lithographic projection apparatus, such as before the pattern forming device, near the pupil plane, near the image plane, and / or near the focal plane. The wavefront manipulator can be used to correct or compensate for certain distortions of the wavefront and intensity distribution and / or phase shift caused by, for example, temperature changes in the source, pattern forming device, lithographic projection apparatus, thermal expansion of components of the lithographic projection apparatus, etc. Adjusting the wavefront and intensity distribution and / or phase shift can change the value of the characteristic represented by the cost function. This change can be simulated from a model or actually measured. The design variables may include parameters of the wavefront manipulator.

[0063] Design variables may have constraints, which can be expressed as , where Z is a set of possible values ​​for the design variables. The desired throughput of the lithographic projection apparatus may impose a possible constraint on the design variables. Without such a constraint imposed by the desired throughput, the optimization may produce a set of values ​​for the design variables that are unrealistic. For example, if dose is a design variable, then in the absence of such a constraint, the optimization may produce dose values ​​that make the throughput economically impossible to achieve. However, the usefulness of constraints should not be interpreted as required. For example, throughput may be affected by pupil fill rate. For certain illumination designs, a lower pupil fill rate may discard radiation, resulting in reduced throughput. Throughput may also be affected by the chemical properties of the resist. Slower resists (e.g., resists that require a larger amount of radiation to be properly exposed) result in reduced throughput.

[0064] The term "process model" as used herein refers to a model that includes one or more simulated pattern formation processes. For example, the process model may include any combination of the following: an optical model (e.g., an optical model that models a lens system / projection system used to transmit light during a lithography process and may include a model that models the final optical image of light entering the resist), a resist model (e.g., a resist model that simulates physical effects of the resist, such as chemical effects caused by light), an optical proximity correction (OPC) model (e.g., an optical proximity correction model that may be used to make a mask or a reticle and may include sub-resolution resist features (SRAF), etc.).

[0065] As used herein, the term "simultaneously" means that two or more things occur at approximately the same time, but not necessarily at exactly the same time. For example, changing the pupil design and the mask pattern simultaneously may mean making a minor modification to the pupil design, then making a minor adjustment to the mask pattern, and then making another modification to the pupil design, etc. However, the present disclosure contemplates that in some parallel processing applications, "simultaneously" may refer to operations that occur simultaneously or have some overlap in time.

[0066] The present disclosure provides, among other things, devices, methods, and computer program products that relate to modifying or optimizing features of lithographic equipment to improve performance and manufacturing efficiency. Features that can be modified can include optical spectra of light used in the lithographic process, masks, pupils, etc. Any combination of these features (and possibly other features) can be implemented to improve, for example, depth of focus, process window, contrast, etc. of the lithographic equipment. In some embodiments, modifying one feature can affect other features. Thus, in order to achieve the desired improvement, multiple features can be modified / changed simultaneously, as described below.

[0067] Figure 3 An exemplary method 300 of random-aware source mask optimization based on a probability distribution of edge placement according to an embodiment is shown. Each of these operations is described in detail below. The operations of method 300 described below are intended to be illustrative. In some embodiments, method 300 may be accomplished by one or more additional operations not described and / or without one or more of the operations discussed. In addition, Figure 3 The order of the operations of method 300 shown in and described below is not intended to be limiting. In some embodiments, one or more portions of method 300 may be implemented in one or more processing devices (e.g., one or more processors) (e.g., by simulation, modeling, etc.). One or more processing devices may include one or more devices that perform some or all of the operations of method 300 in response to instructions stored electronically on an electronic storage medium. For example, one or more processing devices may include one or more devices that are configured to be specifically designed to perform one or more of the operations of method 300 through hardware, firmware, and / or software.

[0068] At operation 302, a source configuration is obtained. The source configuration may be a configuration of a source for a lithography process. The source configuration may be obtained based on a set of design constraints of a design layout and a lithography process, including through source optimization.

[0069] At operation 304, a mask configuration is obtained. The mask configuration may be a configuration of a mask for the lithography process of operation 302. The mask configuration may be obtained based on a design layout and a set of design constraints, including through mask optimization. The source configuration and the mask configuration may also be jointly optimized for the lithography process. The source configuration and the mask configuration may be jointly optimized using an unconstrained free-form source and CTM mask co-optimization. The optimization of the source configuration, the mask configuration, or a combination of the source configuration and the mask configuration may include optimization using sub-resolution assist features (SRAF). The source configuration and the mask configuration may be jointly optimized using a free-form source and a polygonal mask co-optimization. The optimization of the source configuration, the mask configuration, or a combination of the source configuration and the mask configuration may include optimization based on one or more models including a Hopkins model. The optimization of the source configuration, the mask configuration, or a combination of the source configuration and the mask configuration may be based on a cost function. The cost function may be based on edge placement. In some embodiments, the cost function may be based on edge placement error.

[0070] A source configuration, a mask configuration, or a combination of a source configuration and a mask configuration can be optimized using a cost function based on an edge placement error (EPE), where the EPE represents the difference between a feature edge at manufacture and an expected feature edge (e.g., a feature edge in a design layout). The EPE can be measured at multiple points on a feature and for multiple features on a layout. The cost function can determine the sum of the EPEs (or the EPE norm) for a set of evaluation points that can be selected for the feature. The cost function can also include penalty terms, such as sidelobe penalty terms, mask rule checking (MRC) penalty terms, and the like. The cost function can be evaluated for multiple process conditions, where a process window consists of a set of process conditions. An exemplary cost function is given by Equation 2:

[0071] (2)

[0072] Among them, s represents the source and mask The cost function of a function of . The cost function can be determined based on the sum of the process window (pw) of the evaluation points (eval). The cost function can use a norm p to account for or take into account the EPE, and the norm can be 1, 2, etc., where the power to which the EPE is raised can be adjusted to account for or take into account different EPE conditions. For example, p=1 can be used, where the cost function depends on the EPE 2 The increase in p can be used to explain or take into account the more steeply rising costs as EPE increases. The cost function can be explained or taken into account by the process window weights and evaluation point weights Weighted EPE. The cost function may also include penalty terms, such as sidelobe penalty terms , slope penalty , MRC penalty term , source penalty Etc. The process window conditions may include ranges of various lithography metrics, including dose, defocus, mask error, glare, aberrations, etc. The cost function may also be used to optimize process window latitudes, such as exposure latitude (EL), normalized image logarithmic slope (NILS), depth of focus (DOF), mask error enhancement factor (MEEF), resist profile, etc. The cost function may be used to optimize source configurations, mask configurations, or a combination of source configurations and mask configurations by minimizing EPE (e.g., by gradient descent or other appropriate optimization methods). Optimization of the cost function may be driven by reducing EPE so that the printed profile is as close to the design layout as possible (or within an acceptable threshold).

[0073] At operation 306, a probability distribution of edge placement is determined based on at least one of a source configuration, a mask configuration, or a combination of a source configuration and a mask configuration and at least one random component. The probability distribution of edge placement may be determined based on a resist model, a photon shot model, an optical model, an etching model, a mask model, or a combination of a resist model, a photon emission model, an optical model, an etching model, and a mask model. The determination of the probability distribution of edge placement may include a determination based on a model of edge placement error, a model of random edge placement error, or a combination of a model of edge placement error and a model of random edge placement error. The probability distribution of edge placement may include a convolution of edge placement and a random edge placement distribution.

[0074] Various lithographic processes may introduce random noise into the lithographic process. For example, various processes (photon shot noise in optical processes, resist chemistry, local non-uniformity of mask CD due to variations in mask writing, etc.) have a random (e.g., stochastic) component and may produce random effects in lithography (including in edge placement). Random effects can affect local variations in features (e.g., feature edges) and result in line edge roughness / line width roughness (LER / LWR) effects for linear features and local CD uniformity (LCDU) for two-dimensional (e.g., hole) features. The randomness of the lithographic process can be characterized by metrology, where a large number of printed features (e.g., profiles) can be measured and the statistical distribution of the randomness can be determined. From the measured statistical edge placement distribution, properties of the randomness such as mean, variance, standard deviation, symmetry, higher-order moments, etc. can be calculated.

[0075] The cost function may account for or take into account the EPE depending on the model. Models of edge placement (e.g., lithography models) may not account for stochasticity, but rather determine edge placement for the simulated profile equal to the mean of the probability distribution of edge placement. In some models, a random component may be added to the simulation stochasticity, where the stochasticity may be approximately equal to the standard deviation of the edge placement distribution. For example, the stochasticity may be approximated using Equation 3:

[0076] (3)

[0077] in, is the weight of randomness, SEPE represents the random edge placement error, and represents various penalty terms. However, adding randomness to the EPE using a weight term may complicate the optimization, as the SEPE weights may need to be adjusted to match experimental values. Furthermore, the addition of the SEPE may drive the optimization toward non-convergent source configurations or higher EPEs.

[0078] At operation 306, a cost function combining a deterministic lithography metric (such as EPE) and a stochastic lithography metric (such as SEPE) is used. The cost function can then be used to optimize the lithography process to minimize the EPE (e.g., to maximize the consistency between the manufactured pattern and the design layout). The edge placement is represented by a probability distribution function (PDF) that can be converted to (e.g., used to calculate) a cumulative distribution function (CDF). The cumulative distribution function can be further converted to a pattern probability map or a pattern probability profile (e.g., in a one-dimensional case considering a direction perpendicular to the profile). The pattern of the pattern probability map or pattern probability profile can be a resist pattern (e.g., after development), a device pattern (e.g., after etching, after deposition, etc.), or another pattern. The pattern of the pattern probability map can be a two-dimensional pattern that can be calculated for multiple different depths (e.g., a pattern at a two-dimensional plane or projected on a two-dimensional plane at a depth perpendicular to the lithography surface). The pattern of the pattern probability can alternatively or additionally be a three-dimensional pattern (e.g., a pattern of a three-dimensional volume). Since edge placement depends on a non-negligible random contribution, edge placement can be better characterized by a probability distribution function that includes such a non-negligible random contribution rather than a mean value with or without a standard deviation contribution. Edge placement can be represented by a probability distribution such as the one shown in Equation 4 below:

[0079] (4)

[0080] in, is the target pattern probability profile Probability profiles of simulated (e.g., modeled) patterns The distance between them. Pattern probability profile can be equal to 1 minus the cumulative distribution profile of the edge placement error probability distribution (i.e. ).

[0081] At operation 308, it is determined whether a termination criterion is reached based on the probability distribution of edge placement. The termination criterion may be a value of a cost function, a number of iterations, or another stopping criterion. The termination criterion may be a value of a distribution of edge placements such that the distribution of edge placements is within a threshold of a target distribution. The termination criterion may be a value of a derivative of a cost function such that it may be determined that further optimization may not improve the optimization of a source configuration, a mask configuration, or a combination of a source configuration and a mask configuration, or may not improve the optimization by an amount exceeding a threshold. If it is determined that the termination criterion is not reached, the process may continue to operation 310, where the source configuration, the mask configuration, or a combination of a source configuration and a mask configuration may be adjusted based on the probability distribution of edge placement. Otherwise, the process may continue to operation 312, where a lithography matching scheme may be output. At operation 308, it may also be determined that a termination criterion is reached that a source configuration, a mask configuration, or a combination of a source configuration and a mask configuration does not converge. Determining that the source configuration, the mask configuration, or a combination of the source configuration and the mask configuration is not converged may result in outputting a lithography profile at operation 312 where the non-convergent lithography profile may be indicated as non-convergent.

[0082] At operation 310, at least one of a source configuration, a mask configuration, or a combination of a source configuration and a mask configuration is adjusted based on a probability distribution of edge placement. The source configuration, the mask configuration, or a combination of a source configuration and a mask configuration may be adjusted along a direction indicated by an offset between a simulated pattern probability profile and a target pattern probability profile. The offset may be an offset between a simulated pattern probability profile and a target pattern probability profile in one or more planes perpendicular to the lithographic surface, such as in a resist volume or in other planes parallel to the lithographic surface, at one or more depths. The offset may also be an offset in a direction that is not parallel to the lithographic surface (e.g., perpendicular to the lithography, inclined to the lithographic surface, etc.). The offset may include an offset determined for a three-dimensional volume, such as a resist volume or other three-dimensional volume describing a lithographic process. The adjustment may be determined based on a cost function, including based on a derivative of the cost function relative to one or more variables of the cost function.

[0083] At operation 312, a lithography matching scheme is output. The lithography matching scheme may include a source configuration, a mask configuration, or a combination of a source configuration and a mask configuration. The lithography matching scheme may include multiple lithography variables, including dose, process window, etc. The lithography matching scheme may be output to a memory. The lithography matching scheme may be output to one or more components of the lithography process (e.g., a mask writer, a source configurator, etc.). The lithography matching scheme may be output as a mask configuration, a source configuration, or a combination of a source configuration and a mask configuration. The lithography matching scheme may include a predicted result of the lithography process so that the lithography process may be controlled using process control techniques. The lithography matching scheme may include a resist matching scheme, a mask production matching scheme, an etching matching scheme, a resist development matching scheme, or other component matching schemes.

[0084] As described above, method 300 (and / or other methods and systems described herein) is configured to optimize a lithography process based on knowledge of a probability distribution of random edge placements.

[0085] Figure 4 An exemplary method of random-aware source mask optimization based on a probability distribution of random edge placement according to an embodiment is shown. Each of these operations is described in detail below. The operations of method 400 described below are intended to be illustrative. In some embodiments, method 400 may be accomplished by one or more additional operations not described and / or without one or more of the operations discussed. In addition, Figure 4 The order of the operations of method 400 shown in and described below is not intended to be limiting. In some embodiments, one or more portions of method 400 may be implemented in one or more processing devices (e.g., one or more processors) (e.g., by simulation, modeling, etc.). One or more processing devices may include one or more devices that perform some or all of the operations of method 400 in response to instructions stored electronically on an electronic storage medium. For example, one or more processing devices may include one or more devices that are configured to be specifically designed to perform one or more of the operations of method 400 through hardware, firmware, and / or software.

[0086] At operation 402, a source configuration is obtained. This can be done by any suitable method (such as reference Figure 3 The method described in operation 302) obtains the source configuration.

[0087] At operation 404, a mask configuration is obtained. This can be done by any suitable method (such as reference Figure 3 The method described in operation 304) obtains the mask configuration.

[0088] At operation 406, a probability distribution of edge placement is determined based on at least one of the source configuration, the mask configuration, or a combination of the source configuration and the mask configuration. The probability distribution of edge placement may or may not include a random component. The probability distribution of edge placement may be determined by any suitable method (such as reference Figure 3 The method described in operation 306 of the present invention) determines a probability distribution of edge placement.

[0089] At operation 408, it is determined whether a first termination criterion is met based on the probability distribution of edge placement. The first termination criterion may be an intermediate termination criterion. The first termination criterion may be based on any appropriate method (e.g., reference Figure 3 The method described in operation 308 of the present invention) determines whether the first termination criterion is met.

[0090] If it is determined that the first termination criterion is not met, the process may proceed to operation 410, where the source configuration, the mask configuration, or the combination of the source configuration and the mask configuration may be adjusted based on the probability distribution of the edge placement. Otherwise, the process may proceed to operation 412, where the probability distribution of the edge placement considering randomness is determined based on at least one of the source configuration, the mask configuration, or the combination of the source configuration and the mask configuration.

[0091] At operation 410, at least one of the source configuration, the mask configuration, or a combination of the source configuration and the mask configuration is adjusted based on the probability distribution of edge placement. Any suitable method (such as previously described with reference to Figure 3 The method described in operation 310 of the present invention) adjusts at least one of the source configuration, the mask configuration, or a combination of the source configuration and the mask configuration.

[0092] At operation 412, a probability distribution of edge placement is determined based on at least one of a source configuration, a mask configuration, or a combination of a source configuration and a mask configuration that takes into account randomness. Any suitable method (including reference Figure 3 The method described in operation 306 of ) is used to determine a probability distribution that takes into account randomness.

[0093] At operation 414, it is determined whether a second termination criterion is met based on a probability distribution of edge placement taking into account randomness. The second termination criterion may be a final termination criterion. The second termination criterion may be based on any appropriate method (e.g., reference Figure 3 The method described in operation 308 of ) determines whether the second termination criterion is met. The first termination criterion and the second termination criterion may be related, wherein the second termination criterion may be a more stringent criterion than the first termination criterion.

[0094] If it is determined that the second termination criterion is not met, the process may proceed to operation 416, where the source configuration, the mask configuration, or a combination of the source configuration and the mask configuration may be adjusted based on the probability distribution of edge placement. Otherwise, the process may proceed to operation 418, where a lithography profile may be output.

[0095] At operation 416, at least one of a source configuration, a mask configuration, or a combination of a source configuration and a mask configuration is adjusted based on the probability distribution of edge placement accounting for randomness. The source configuration, the mask configuration, or the combination of the source configuration and the mask configuration may be adjusted in a direction indicated by an offset between the probability distribution of edge placement accounting for randomness and a target probability distribution of edge placement. The adjustment may be determined based on a cost function, including based on a derivative of the cost function with respect to one or more variables of the cost function.

[0096] The adjustment of the source configuration, the mask configuration, or the combination of the source configuration and the mask configuration in operation 416 may be of a different type than the adjustment of the source configuration, the mask configuration, or the combination of the source configuration and the mask configuration in operation 410. For example, the adjustment in operation 410 may correspond to a joint optimization of a free-form source and a polygonal mask, while the adjustment in operation 416 may correspond to a mask-only optimization based on a Hopkins model.

[0097] At operation 418, the lithography configuration is output. Any suitable method (including reference Figure 3 The method described in operation 312) outputs a lithography matching scheme.

[0098] Figure 5 A schematic diagram of stochastic-aware optimization of a lithography process 500 is depicted. The lithography process 500 can be any type of lithography process, including UV, EUV, etc. The lithography process can be characterized by a design layout 502 and a set of requirements 504. The design layout 502 can include information about multiple layers. The design layout 502 can include information about the three-dimensional shape of the features contained in the design layout 502. The set of requirements 504 can be instrument requirements (e.g., corresponding to limitations, ranges, etc. of process equipment), material requirements (e.g., limitations, ranges, etc. imposed on the lithography process by the materials of the devices to be manufactured, which may or may not be exposed or patterned by the current lithography process), customer requirements (e.g., limitations, ranges, etc. required by the supplier of the design layout 502), etc. The set of requirements 504 can include a set of design rules that the lithography process options 530 can prioritize to comply with.

[0099] The process optimizer 506 can be operated to optimize the lithography process 500. The design layout 502 and the set of requirements 504 can be input to the process optimizer 506 or obtained by the process optimizer 506. The process optimizer 506 can optimize the configuration 530 of the lithography process 500 to meet the design layout 502 and the set of requirements 504. The process optimizer 506 can also optimize process window conditions (including exposure latitude, common process window, etc.) or other lithography indicators (including EPE, LCDU, etc.) that may not be related to the design layout 502 or the set of requirements 504. The process optimizer 506 can operate based on the cost function 508.

[0100] The cost function 508 may include weighted contributions from lithography metrics such as EPE. The cost function 508 may include contributions from multiple pattern probability profiles including pattern probability profiles calculated for various directions perpendicular to the lithography surface, such as various heights along the z direction in the resist volume or other three-dimensional volume. The cost function 508 may include contributions from the sum of multiple pattern probability profiles such as pattern probability profiles calculated for various directions perpendicular to the lithography surface, such as various heights along the z direction in the resist volume or other three-dimensional volume. The cost function 508 may include contributions from three-dimensional pattern probability profiles such as pattern probability profiles calculated for three-dimensional resist volumes, three-dimensional process volumes (e.g., including etching volumes, developing volumes, deposition volumes, etc.). The cost function 508 may also include penalty terms for various parameters that may be used to drive the process optimizer 506 toward a selection scheme 530 that satisfies the design layout 502 and a set of requirements 504. The cost function 508 may be a multivariate cost function. The cost function 508 may be a differentiable function. The process optimizer 506 may use the cost function 508 to optimize the recipe 530, such as by gradient descent or other methods. The cost function 508 may be determined based on an iteration of the lithography recipe, where the recipe 530 is an optimized iteration of the lithography recipe. Optimization includes determining a recipe, source configuration, mask configuration, etc. that satisfies the design layout 502 and the set of requirements 504. Optimization is not limited to determining the best recipe or configuration among all possible recipes or configurations, but also includes determining a recipe or configuration that is within an allowable threshold range of an ideal recipe or configuration or otherwise satisfies the design layout 502 and the set of requirements 504. Optimization may include selecting between multiple recipes or configurations that satisfy the design layout 502 and the set of requirements 504, including selecting based on process window considerations, lithography metric considerations, etc.

[0101] The cost function 508 can be determined based on a mask configuration, which in turn can be determined based on a mask optimization 510. The mask optimization 510 can iteratively operate on the mask configuration, including making changes to the mask configuration based on the cost function 508. The mask optimization 510 can include continuous transmission mask (CTM) optimization, polygon optimization, Manhattan optimization, etc. The mask optimization 510 can include generating one or more assist features. The mask optimization 510 can interact with a lithography model (e.g., a resist model, a photon model, an etch model, etc.) that can be used to generate a predicted output of the lithography process 500 for iterations of the mask optimization 510.

[0102] The cost function 508 can be determined based on a source configuration, which in turn can be determined based on a source optimization 512. The source optimization can iteratively operate on the source configuration, including making changes to the mask configuration based on the cost function 508. The source optimization 512 can include an unconstrained free-form optimization, a free-form optimization, etc. The source optimization 512 can include an optimization of one or more parameters of a spectrum of radiation. The source optimization 512 can interact with a lithography model (e.g., a resist model, a photon model, an etch model, etc.) that can be used to generate a predicted output of the lithography process 500 for iterations of the source optimization 512.

[0103] The process optimizer 506 may also interact with other optimization processes, including dose optimization, focus optimization, spectrum optimization, etc. The mask optimization 510 and source optimization 512 may occur simultaneously, alternately, on different time scales, etc. The process optimizer 506 operates to jointly optimize the mask optimization 510 and source optimization 512.

[0104] The process optimizer 506 may determine a cost function 508 based on a current iteration of a recipe for the lithography process 500. The process optimizer 506 may determine the cost function 508 based on a modeled output of the current iteration of the lithography process 500. The process optimizer 506 may determine the cost function 508 based on an output of an edge placement estimator 520. The edge placement estimator 520 may be a product of a model generated based on the current iteration of the lithography process 500. The edge placement estimator 520 may estimate a mean, a median, or a mode of edge placements. The edge placement estimator 520 may estimate one or more measures of dispersion of edge placements, such as a standard deviation. The edge placement estimator 520 may be informed by measured edge placements, including measured edge placements from devices produced by lithography recipes similar to the lithography recipe of the current iteration.

[0105] The edge placement estimator 520 may communicate with or include a random edge placement estimator 522. The random edge placement estimator 522 may be a product of a model generated based on the current iteration of the lithography process 500. The random edge placement estimator 522 may be a product of multiple models that estimate randomness, including a chemical resist model, a photon shot model, a mask CD non-uniformity model, etc. The random edge placement estimator 522 may determine edge placement randomness based on multiple physical models of randomness including photon randomness, chemical randomness, etc. The random edge placement estimator 522 may determine randomness based on a convolution of one or more estimates of constituent process randomness. The random edge placement estimator 522 may determine a distribution of randomness, including a mean, a standard deviation, higher-order moments, etc. The random edge placement estimator 522 may estimate a random edge placement error. The random edge placement estimator 522 may determine an asymmetric distribution of randomness. The random edge placement estimator 522 may be informed by measured random edge placements, including measured random edge placements from devices produced by lithography profiles similar to the current iteration's lithography profile.

[0106] A cost function 508 may be determined based at least in part on an evaluation of edge placement for a current iteration of the lithography process 500, any of which may include an evaluation of random edge placement for the current iteration. The cost function 508 may include random effects in some iterations but not in other iterations, such as when refining the cost function or performing certain types of optimizations. The edge placement can be compared to the edge placement of the design layout 502. The difference between the edge placement of the current iteration of the lithography process 500 and the design layout 502 may be encompassed by an edge placement error. The difference between the edge placement of the current iteration of the lithography process 500 and the design layout 502 may take into account randomness and may be encompassed by a random edge placement error (SEPE). The edge placement error may measure the distance, direction, or a combination of distance and direction of the difference between the edge placement of the current iteration of the lithography process 500 and the design layout 502. The edge placement errors may be measured for a plurality of evaluation points based on the modeled output of the current iteration of the lithography process 500. The evaluation points may be selected based on the CD of the design layout 502. SEPE can be a distribution including an EPE distribution taking into account randomness. SEPE can be a CDF. SEPE can be represented alternatively by the inverse of a CDF or 1-CDF. SEPE can be calculated as a Gaussian distribution convolved with an EPE distribution or other measurement or EPE. In some other embodiments, SEPE can be calculated as a Poisson distribution. SEPE can be an asymmetric distribution so that randomness does not evenly distribute EPE in all directions.

[0107] Figure 6 A graphical representation of the edge placement distribution is depicted. Figure 6 A graph 600 depicting the randomness of edge placement in one dimension along an x-axis 602 for a set of manufactured features is depicted. The x-axis 602 may represent a direction perpendicular to the profile of the manufactured feature. The dashed line 608 depicts the distribution of random edge placement corresponding to the number of manufactured features in the set of manufactured features having a given edge placement value. The number of manufactured features corresponding to the edge placement value is depicted as an intensity along the y-axis 604. The distribution of random edge placements that may be SEPE compared to the target edge placement is depicted as a Gaussian shape. However, the distribution may include other shapes, including Lorentzian, Poisson, etc. The distribution of random edge placements may include multiple contributions, such as multiple Gaussian shapes, convolution of Gaussian and Poisson distributions, etc. The distribution of random edge placements may be centered around an average edge placement 606 with a standard deviation 610. The average edge placement may alternatively be a median edge placement, a mode of edge placements, etc. The distribution of random edge placements is depicted as symmetric, but may also be asymmetric. The distribution of random edge placements may have different dispersions in different regions of the distribution. The distribution of random edge placements can be determined based on one or more models. The distribution of random edge placements can be based on measured randomness. The distribution of random edge placements can be informed by the measured randomness, for example, the distribution of random edge placements can include modeled parameters and measured parameters.

[0108] Figure 6 Also depicted is a graph 650 of a pattern probability profile along an x-axis 652 for a set of manufactured features of graph 600. The x-axis 652 can represent the same direction perpendicular to the profile of the manufactured features represented by the x-axis 602. The dashed line 658 depicts the pattern probability profile based on the distribution of edge placement taking into account randomness. The pattern probability profile mean 660 corresponds to the average edge placement position of a set of manufactured features. The mean can alternatively be another measure of central tendency, including the median, weighted mean, mode, etc. The number of manufactured features corresponding to the pattern probability profile value is depicted as the intensity along the y-axis 654. The median pattern probability profile corresponds to the average edge placement 606, as shown in the graph 600. A target pattern probability profile 656 is also depicted. The difference between the target pattern probability profile 656 and the simulated pattern probability profile (e.g., the pattern probability profile represented by the dashed line 658) gives the distribution of EPE.

[0109] The probability distribution of edge placement error can be described by a relationship that depends on EPE and SEPE, where EPE can correspond to an average EPE and SEPE can correspond to discrete values ​​of EPE. The probability distribution of edge placement error can be described by the following equation 5:

[0110] (5)

[0111] This equation is for a Gaussian distribution. Other equations may be used instead.

[0112] The target profile (or distribution) can be described as a step function, such as the step function described by Equation 6 below:

[0113] (6)

[0114] Wherein, the target probability distribution is a step function, which is zero when the x value is greater than the target value, and is 1 when the x value is less than the target value. Alternatively, the target profile can be a step function, a linear function, etc. The target distribution can be a function of the design layout, such as an ideal profile.

[0115] The simulated profile (or distribution) can be determined based on the probability distribution of EPE and SEPE. The simulated profile can be 1 minus the cumulative distribution function. The simulated profile can be described by the following equation 7:

[0116] (7)

[0117] in, is the simulated profile. The simulated profile can be summarized as the inverse of the CDF of the probability distribution of the EPE (e.g., for the general 1-CDF of θ).

[0118] The photolithography process can be optimized by minimizing the EPE. Minimizing the EPE can be achieved by minimizing the target profile (or ) and the simulated contour (or ). The distance between contours (or probability distributions) can be determined in a variety of different ways, where different distance formulas may be more suitable for different cost functions, different lithography models, different relationships between CD and EPE, etc. Common distance calculations involve the use of Lp norms, such as L1 norms, L2 norms, etc. for various p values. However, other distance calculations may be used in addition or alternatively.

[0119] FIG. 7A to FIG. 7B An exemplary distance function for the Lp norm is depicted. Fig. 7A A graph 710 depicts an exemplary distance function of the L1 norm. The exemplary distance function may have a general form given by Equation 8 as follows:

[0120] (8)

[0121] Wherein, the L1 norm is based on the sum of the absolute values ​​of the distance vectors. For the specific simulated distribution function of Equation 5, Equation 8 can be calculated more directly as the following Equation 9:

[0122] (9)

[0123] Here, EPE represents the determined EPE, and SEPE represents the determined SEPE.

[0124] Graph 710 depicts the value of distance as a function of the EPE value on axis 702, the SEPE value on axis 704. The contribution of the value of distance to the cost function is shown on axis 706.

[0125] Figure 7B Graphs 750 and 760 depict exemplary distance functions of the L1 norm raised to a power of p. The exemplary distance function may have the general form given by Equation 10 below:

[0126] (10)

[0127] Wherein, for distances less than 1, p can be selected to mitigate the effect of distance on the cost function and for distances greater than 1, p can be selected to increase the effect of distance on the cost function. A weighting factor can also be used to adjust the value of the cost function between mitigating the effect of distance and increasing the effect of distance. For the specific simulated distribution of Equation 5, Equation 8 can be calculated more directly as the following Equation 11:

[0128] (11)

[0129] Here, p can be chosen to change the effect of distance on the cost function.

[0130] Graph 750 depicts the value of distance for p=1 as a function of the EPE value on axis 752, the SEPE value on axis 754. The contribution of the value of distance to the cost function is shown on axis 756.

[0131] Graph 760 depicts the value of distance for p=2 as a function of the EPE value on axis 762, the SEPE value on axis 764. The contribution of the value of distance to the cost function is shown on axis 766.

[0132] FIG. 8A to FIG. 8B An exemplary distance function for the Lp norm is depicted. Fig. 8A A graph 810 depicts an exemplary distance function of the L2 norm. The exemplary distance function may have the general form given by Equation 12 below:

[0133] (12)

[0134] Wherein, the L2 norm is based on the Euclidean distance. For the specific simulated distribution function of Equation 5, Equation 12 can be calculated more directly as the following Equation 12:

[0135] (13)

[0136] Here, EPE represents the determined EPE, and SEPE represents the determined SEPE.

[0137] Graph 810 depicts the value of distance as a function of the EPE value on axis 802, the SEPE value on axis 804. The contribution of the value of distance to the cost function is shown on axis 806.

[0138] Figure 8B Graphs 850 and 860 depict exemplary distance functions of the L2 norm raised to a power of p. The exemplary distance function may have the general form given by Equation 14 below:

[0139] (14)

[0140] Wherein, for distances less than 1, p can be selected to mitigate the effect of distance on the cost function and for distances greater than 1, p can be selected to increase the effect of distance on the cost function. A weighting factor can also be used to adjust the value of the cost function between mitigating the effect of distance and increasing the effect of distance. For the specific simulated distribution of Equation 5, Equation 14 can be calculated more directly as the following Equation 15:

[0141] (15)

[0142] Here, p can be chosen to change the effect of distance on the cost function.

[0143] Graph 850 depicts the value of distance for p=1 as a function of the EPE value on axis 852, the SEPE value on axis 854. The contribution of the value of distance to the cost function is shown on axis 856.

[0144] Graph 860 depicts the value of distance for p=2 as a function of the EPE value on axis 862, the SEPE value on axis 864. The contribution of the value of distance to the cost function is shown on axis 866.

[0145] The dependence of the cost function on the distance between the target and the simulated probability distribution can be selected based on knowledge of the lithography process. Alternatively, the dependence of the cost function on the distance (e.g., norm, p-value, etc.) can be selected during the optimization process, and can even be optimized during the optimization process. The equations shown here are provided only as examples, and other distance formulas, including formulas for other norms, can be used instead or in addition.

[0146] Tolerances can also be used to compare edge placement to a target edge placement. The cost function can be modified so that when an edge placement is determined to be the same as or within a tolerance of a target edge placement, the portion of the cost function associated with that edge placement can be substantially zero. For a probabilistic edge placement distribution, this can mean that for values ​​of edge placement in the probability distribution that are within a tolerance (or offset) of a target edge placement, the portion of the cost function associated with those edge placement values ​​can be zero. For values ​​of edge placement in the probability distribution that are outside of tolerance, the edge placement error can be determined as the distance from the edge placement to the tolerance value of the edge placement, or the EPE offset value. The cost function can then be calculated based on the distance corresponding to the difference between the edge placement and the tolerance offset.

[0147] Fig. 9 is a block diagram of an exemplary computer system CS according to an embodiment. The computer system CS can assist in implementing the methods, processes, or devices disclosed herein. The computer system CS includes a bus BS or other communication mechanism for communicating information, and a processor PRO (or multiple processors) connected to the bus BS to process information. The computer system CS also includes a main memory MM, such as a random access memory (RAM) or other dynamic storage device, connected to the bus BS to store information and instructions to be executed by the processor PRO. For example, the main memory MM can also be used to store temporary variables or other intermediate information during the execution of instructions to be executed by the processor PRO. The computer system CS includes a read-only memory (ROM) ROM or other static storage device connected to the bus BS to store static information and instructions for the processor PRO. A storage device SD such as a magnetic disk or optical disk is provided and connected to the bus BS to store information and instructions.

[0148] The computer system CS can be connected to a display DS for displaying information to a computer user via a bus BS, such as a cathode ray tube (CRT) or a flat panel or touch panel display. An input device ID including alphanumeric and other keys is connected to the bus BS for communicating information and command selections to the processor PRO. Another type of user input device is a cursor control CC, such as a mouse, trackball, or cursor direction keys, for communicating direction information and command selections to the processor PRO and for controlling cursor movement on the display DS. The input device typically has two degrees of freedom on two axes (a first axis (e.g., x) and a second axis (e.g., y)) that allow the device to specify a position in a plane. A touch panel (screen) display can also be used as an input device.

[0149] In some embodiments, the computer system CS can be executed in response to the processor PRO executing one or more sequences of one or more instructions contained in the main memory MM to perform multiple parts of one or more methods described herein. Such instructions can be read into the main memory MM from another computer-readable medium (e.g., a storage device SD). The execution of the instruction sequence contained in the main memory MM causes the processor PRO to perform the processing steps described herein. One or more processors in a multi-processing arrangement can also be used to execute the sequence of instructions contained in the main memory MM. In some embodiments, hard-wired circuits can replace software instructions or be used in combination with software instructions. Therefore, the description herein is not limited to any specific combination of hardware circuits and software.

[0150] The term "computer-readable medium" used herein refers to any medium that participates in providing instructions to the processor PRO for execution. This medium can take a variety of forms, including but not limited to non-volatile media, volatile media, and transmission media. Non-volatile media include, for example, optical disks or disks, such as storage devices SD. Volatile media include dynamic memory, such as main memory MM. Transmission media include coaxial cables, copper wires, and optical fibers, including wires with bus BS. Transmission media can also take the form of sound waves or light waves, such as sound waves or light waves generated during radio frequency (RF) and infrared (IR) data communication. Computer-readable media can be non-transient, such as floppy disks, flexible disks, hard disks, tapes, any other magnetic media, CD-ROMs, DVDs, any other optical media, punch cards, paper tapes, any other physical media with patterns of holes, RAMs, PROMs, and EPROMs, FLASH-EPROMs, any other storage tube chips, or cassettes. Non-temporary computer-readable media can have instructions recorded thereon. Instructions can implement any of the features described herein when executed by a computer. Transitory computer readable media may include carrier waves or other propagated electromagnetic signals.

[0151] Various forms of computer-readable media can be used to transmit one or more sequences of one or more instructions to the processor PRO for execution. For example, the instruction may initially be carried on a disk of a remote computer. The remote computer may load the instruction into its dynamic memory and send the instruction via a telephone line using a modem. The local modem of the computer system CS may receive data on the telephone line and convert the data into an infrared signal using an infrared transmitter. An infrared detector connected to the bus BS may receive the data carried in the infrared signal and place the data on the bus BS. The bus BS transmits the data to the main memory MM, from which the processor PRO retrieves and executes the instruction. The instruction received by the main memory MM may optionally be stored on a storage device SD before or after the processor PRO executes.

[0152] The computer system CS may also include a communication interface CI connected to the bus BS. The communication interface CI provides a bidirectional data communication connected to a network link NDL connected to a local network LAN. For example, the communication interface CI may be an integrated services digital network (ISDN) card or a modem to provide a data communication connection to a telephone line of a corresponding type. As another example, the communication interface CI may be a local area network (LAN) card to provide a data communication connection to a compatible LAN. A wireless link may also be implemented. In any such implementation, the communication interface CI sends and receives electrical, electromagnetic, or optical signals carrying digital data streams representing various types of information.

[0153] The network link NDL typically provides data communication to other data devices through one or more networks. For example, the network link NDL can provide a connection to the host HC through a local network LAN. This can include data communication services provided through the global packet data communication network now commonly referred to as the "Internet" INT. The local network LAN (Internet) all use electrical signals, electromagnetic signals, or optical signals that carry digital data streams. The signals through various networks that carry digital data to and from the computer system CS, as well as the signals on the network data link NDL and through the communication interface CI are exemplary forms of carrier waves that transmit information.

[0154] The computer system CS can send messages and receive data including program code through (multiple) networks, network data links NDL, and communication interfaces CI. In the Internet example, the host HC can transmit a request code for an application through the Internet INT, the network data link NDL, the local network LAN, and the communication interface CI. For example, such a downloaded application can provide all or part of the method described herein. The received code can be executed by the processor PRO when the received code is received, and / or stored in a storage device SD or other non-volatile memory for later execution. In this way, the computer system CS can obtain the application code in the form of a carrier wave.

[0155] Fig.10 is a schematic diagram of a lithographic projection apparatus according to one or more embodiments. The lithographic projection apparatus may include an illumination system IL, a first stage MT, a second stage WT, and a projection system PS.

[0156] The illumination system IL may condition the radiation beam B. In this particular case, the illumination system also comprises a radiation source SO.

[0157] A first stage (eg, patterning device table) MT may be provided with a patterning device holder to hold a patterning device MA (eg, a reticle) and connected to a first positioner PM to accurately position the patterning device relative to the article PS.

[0158] A second worktable (substrate table) WT may be provided with a substrate holder to hold a substrate W (eg a silicon wafer coated with resist) and connected to a second positioner PW to accurately position the substrate relative to the item PS.

[0159] A projection system ("lens") PS (eg, a refractive, reflective, or catadioptric optical system) may image the illuminated portion of the patterning device MA onto a target portion C of the substrate W (eg, comprising one or more dies).

[0160] As shown, the device can be transmissive (i.e., have a transmissive patterning device). However, in general, the device can also be reflective, for example (having a reflective patterning device). The device can employ different kinds of patterning devices than conventional masks; examples include programmable mirror arrays, or LCD matrices.

[0161] A light source SO (e.g., a mercury lamp or an excimer laser, an LPP (laser produced plasma) EUV source) generates a radiation beam. This beam is fed into an illumination system (illuminator) IL, for example, directly or after having passed a conditioning device (e.g., a beam expander). The illuminator IL may include an adjustment device AD ​​for setting the outer and / or inner radial extent (commonly referred to as σ-outer and σ-inner, respectively) of the intensity distribution in the beam. Furthermore, the illuminator IL will typically include various other components, such as an integrator IN and a condenser CO. In this way, the beam B impinging on the pattern forming device MA has a desired uniformity and intensity distribution in the cross section of the beam B.

[0162] In some embodiments, the source SO can be located inside the housing of the lithographic projection device (for example, this is often the case when the source SO is a mercury lamp), but the source SO can also be remote from the lithographic projection device, and the radiation beam generated by the source SO is guided into the device (for example, with the aid of suitable guiding mirrors); this can be the latter case when the source SO is an excimer laser (for example, emitting laser light based on KrF, ArF, or F2).

[0163] The beam B may then intercept the patterning device MA which is held on the patterning device table MT. After having passed the patterning device MA, the beam B may pass through a lens which focuses the beam B onto a target portion C of the substrate W. With the aid of the second positioning device (and the interferometry device IF), the substrate table WT may be precisely moved, for example, in order to position a different target portion C in the path of the beam B. Similarly, the first positioning device may be used to precisely position the patterning device MA relative to the path of the beam B, for example, after mechanically acquiring the patterning device MA from a patterning device library, or during a scan. Typically, movement of the stage MT, WT may be realized with the aid of a long-stroke module (coarse positioning) and a short-stroke module (fine positioning). However, in the case of a stepper (as opposed to a step-and-scan tool), the patterning device table MT may be connected to the short-stroke actuator only, or may be fixed.

[0164] The depicted tool can be used in two different modes: a step mode and a scan mode. In the step mode, the patterning device table MT is held substantially stationary and the entire patterning device image is projected at once (i.e. in a single "flash") onto a target portion C. The substrate table WT may be moved in the x and / or y direction so that the beam B can illuminate a different target portion C.

[0165] 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 can be moved in a given direction (the so-called "scanning direction", e.g. the y-direction) at a speed v, so that the projection beam B scans the image of the patterning device; at the same time, the substrate table WT is synchronously moved in the same or opposite direction at a speed V=Mv, where M is the magnification of the lens (typically M=¼ or 1 / 5). In this way, a relatively large target portion C can be exposed without sacrificing resolution.

[0166] Fig.11 is a schematic diagram of another lithographic projection apparatus (LPA) according to one or more embodiments. The LPA may include a source collector module SO, an illumination system (illuminator) IL configured to condition a radiation beam B (e.g., EUV radiation), a support structure MT, a substrate table WT, and a projection system PS.

[0167] The support structure (eg, patterning device table) MT may be constructed to support a patterning device (eg, mask or reticle) MA and be connected to a first positioner PM configured to accurately position the patterning device.

[0168] The substrate table (eg, wafer stage) WT may be configured to hold a substrate (eg, a resist-coated wafer) W and connected to a second positioner PW configured to accurately position the substrate.

[0169] The projection system (eg, a reflective projection system) PS may be configured to project the pattern imparted to the radiation beam B by the patterning device MA onto a target portion C of the substrate W (eg, comprising one or more dies).

[0170] As depicted here, the LPA can be reflective (e.g., using a reflective patterning device). Note that since most materials are absorptive in the EUV wavelength range, the patterning device can have a multilayer reflector including, for example, a multilayer stack of molybdenum and silicon. In one example, the multilayer stack reflector has 40 layers of molybdenum and silicon pairs, where each layer is a quarter wavelength thick. Even smaller wavelengths can be produced using x-ray lithography. Since most materials are absorptive at EUV and x-ray wavelengths, a thin sheet of patterned absorbing material on the patterning device topography (e.g., a TaN absorber on top of a multilayer reflector) defines where features will be printed (positive resist) or not (negative resist).

[0171] The illuminator IL may receive an extreme ultraviolet radiation beam from a source collector module SO. Methods of generating EUV radiation include, but are not necessarily limited to, converting a material into a plasma state having at least one element (e.g., xenon, lithium, or tin) having one or more emission lines in the EUV range. In one such method, a plasma often referred to as laser produced plasma ("LPP") may be generated by irradiating a fuel (e.g., a droplet, stream, or cluster of a material having a line-emitting element) with a laser beam. The source collector module SO may be part of an EUV radiation system that includes a laser for providing a laser beam that excites the fuel. The generated plasma emits output radiation, such as EUV radiation, that is collected using a radiation collector disposed in the source collector module. For example, when a CO2 laser is used to provide a laser beam for fuel excitation, the laser and the source collector module may be separate entities.

[0172] In this case, the laser may not be considered as part of the lithographic apparatus, and the radiation beam may be delivered from the laser to the source collector module by means of a beam delivery system including, for example, suitable guiding mirrors and / or a beam expander. In other cases, such as when the source is a discharge produced plasma EUV generator, often referred to as a DPP source, the source may be an integral part of the source collector module.

[0173] The illuminator IL may include an adjuster for adjusting the angular intensity distribution of the radiation beam. Typically, at least the outer and / or inner radial extent of the intensity distribution in a pupil plane of the illuminator (commonly referred to as σ-outer and σ-inner, respectively) may be adjusted. Furthermore, the illuminator IL may include various other components, such as a faceted field mirror arrangement and a faceted pupil mirror arrangement. The illuminator may be used to adjust the radiation beam so as to have a desired uniformity and intensity distribution in a cross-section of the radiation beam.

[0174] The radiation beam B may be incident on and patterned by a patterning device (e.g., mask) MA held on a support structure (e.g., patterning device table) MT. After reflection from the patterning device (e.g., mask) MA, the radiation beam B passes through a projection system PS, which focuses the beam onto a target portion C of a substrate W. With the aid of a second positioner PW and a position sensor PS2 (e.g., an interferometer, a linear encoder, or a capacitive sensor), the substrate table WT may be precisely moved, for example, in order to position a different target portion C in the path of the radiation beam B. Similarly, a first positioner PM and a further position sensor PS1 may be used to precisely position the patterning device (e.g., mask) MA relative to the path of the radiation beam B. The patterning device (e.g., mask) MA and the substrate W may be aligned using patterning device alignment marks M1, M2 and substrate alignment marks P1, P2.

[0175] The depicted device LPA can be used in at least one of the following modes: a stepping mode, a scanning mode, and a stationary mode.

[0176] In step mode, the support structure (e.g. patterning device table) MT and the substrate table WT remain essentially stationary, and an entire pattern imparted by the radiation beam is projected at once onto a target portion C (i.e. a single static exposure). The substrate table WT is then moved in the X and / or Y direction so that a different target portion C can be exposed.

[0177] In scan mode, the support structure (e.g. patterning device table) MT and the substrate table WT are scanned synchronously while a pattern imparted to the radiation beam is projected onto a target portion C (i.e. a single dynamic exposure). The speed and direction of the substrate table WT relative to the support structure (e.g. patterning device table) MT may be determined by the (de-)magnification and image reversal characteristics of the projection system PS.

[0178] In stationary mode, the support structure (e.g., patterning device table) MT remains substantially stationary so as to hold the programmable patterning device and the substrate table WT is moved or scanned while a pattern imparted to the radiation beam is projected onto a target portion C. In this mode, a pulsed radiation source is typically employed and the programmable patterning device is updated as required after each movement of the substrate table WT or between successive radiation pulses during a scan. This mode of operation can be readily applied to maskless lithography using a programmable patterning device (e.g., a programmable mirror array).

[0179] Fig.12 Detailed view of a lithographic projection apparatus according to one or more embodiments. As shown, the LPA may include a source collector module SO, an illumination system IL, and a projection system PS. The source collector module SO is configured so that a vacuum environment can be maintained in an enclosure structure ES of the source collector module SO. EUV radiation emitting a thermal plasma HP may be formed by a plasma source generated by a discharge. EUV radiation may be generated by a gas or vapor (e.g., Xe gas, Li vapor, or Sn vapor), wherein the thermal plasma HP is generated to emit radiation in the EUV range of the electromagnetic spectrum. The thermal plasma HP is generated by, for example, an electrical discharge that causes at least partially ionized plasma. A partial pressure (e.g., 10 Pa) of Xe, Li, Sn vapor, or any other suitable gas or vapor may be required to effectively generate radiation. In an embodiment, a plasma that excites tin (Sn) is provided to generate EUV radiation.

[0180] The radiation emitted by the hot plasma HP is transferred from the source chamber SC to the collection chamber CC through an optional gas barrier or contamination trap CT (also referred to as a contamination barrier or foil trap in some cases), which is located in or behind an opening in the source chamber SC. The contamination trap CT may include a channel structure. The contamination trap CT may also include a gas barrier or a combination of a gas barrier and a channel structure. The contamination trap or contamination barrier CT further indicated herein includes at least a channel structure, as known in the art.

[0181] The collector cavity CC may include a radiation collector CO which may be a so-called grazing incidence collector. The radiation collector CO has an upstream radiation collector side US and a downstream radiation collector side DS. Radiation passing through the radiation collector CO may be reflected from the grating spectral filter SF to be focused in a virtual source point IF along the optical axis indicated by the dashed line "O". The virtual source point IF may be referred to as an intermediate focus, and the source collector module may be arranged such that the intermediate focus IF is located at or near an opening OP in the enclosing structure ES. The virtual source point IF is an image of the radiation emitting plasma HP.

[0182] The radiation then passes through an illumination system IL which may include a faceted field mirror arrangement FM and a faceted pupil mirror arrangement PM which are arranged to provide a desired angular distribution of the radiation beam B at the patterning device MA, and a desired uniformity of radiation amplitude at the patterning device MA. When the radiation beam B is reflected at the patterning device MA held by the support structure MT, a patterned beam PB is formed, and the projection system PS images the patterned beam PB via a reflective element RE onto a substrate W held by a substrate table WT.

[0183] Typically, more elements than shown may be present in the illumination optics unit IL and the projection system PS. A grating spectral filter SF may optionally be present, depending on the type of lithographic apparatus. Furthermore, more mirrors may be present than shown in the figures, for example, from 1 to 6 additional reflective elements may be present in the projection system PS.

[0184] The collector optics CO may be a nested collector with a grazing incidence reflector GR, which is just an example of a collector (or collector mirror) that is arranged axisymmetrically around the optical axis O. This type of collector optics CO may be used in conjunction with a discharge produced plasma source, often referred to as a DPP source.

[0185] Fig.13Detailed view of a source collector module SO of a lithographic projection apparatus LPA according to one or more embodiments. The source collector module SO may be part of a radiation system of the LPA. A laser LA may be arranged to deposit laser energy into a fuel, such as xenon (Xe), tin (Sn), or lithium (Li), thereby producing a highly ionized plasma HP having an electron temperature of tens of eV. Energy radiation produced during deexcitation and recombination of these ions is emitted from the plasma, collected by a near normal incidence collector optics CO, and focused onto an opening OP in an enclosure structure ES.

[0186] The concepts disclosed herein can simulate or mathematically model any general imaging system for imaging sub-wavelength features, and are particularly useful for emerging imaging technologies that can produce shorter and shorter wavelengths. Emerging technologies already in use include EUV (extreme ultraviolet), DUV lithography that can produce wavelengths of 193 nm using ArF lasers and even 157 nm using fluorine lasers. In addition, EUV lithography can produce wavelengths in the range of 20 nm to 50 nm by using synchrotrons or by bombarding materials (solid or plasma) with high-energy electrons to produce photons in this range.

[0187] The embodiments of the present disclosure may be further described by the following aspects.

[0188] 1. A method for determining a source and mask configuration for a lithography process, the method comprising:

[0189] obtaining a source configuration, a mask configuration, or a combination of a source configuration and a mask configuration;

[0190] calculating a probability distribution of edge placement errors for a lithography process based on the source configuration, the mask configuration, or a combination of the source configuration and the mask configuration; and

[0191] The source configuration, the mask configuration, or a combination of the source configuration and the mask configuration is adjusted based on the probability distribution.

[0192] 2. The method of clause 1, wherein the edge placement error comprises a simulated edge placement error.

[0193] 3. The method of clause 1, wherein the edge placement error is obtained from a model calibrated based on the measured edge placement error.

[0194] 4. The method of aspect 1, wherein the probability distribution corresponds to a random probability distribution.

[0195] 5. The method of aspect 1, wherein the probability distribution is a simulated probability distribution.

[0196] 6. The method of clause 1, wherein the probability distribution is calibrated based on a measured probability distribution.

[0197] 7. The method as described in aspect 1 also includes determining the convolution of the probability distribution of the edge placement error and at least one additional probability distribution, and wherein adjusting the source configuration, the mask configuration, or the combination of the source configuration and the mask configuration based on the probability distribution includes adjusting the source configuration, the mask configuration, or the combination of the source configuration and the mask configuration based on the convolution.

[0198] 8. The method of clause 7, wherein the convolution is an asymmetric distribution.

[0199] 9. The method of clause 1, wherein the probability distribution of the edge placement error is a Gaussian distribution or a Poisson distribution.

[0200] 10. The method of clause 1, wherein the probability distribution comprises a cumulative probability function.

[0201] 11. The method of clause 1, further comprising: calculating an offset function between the probability distribution and a reference probability distribution, and wherein the adjustment is based on the offset function.

[0202] 12. The method of clause 11, wherein the reference probability distribution is a cumulative probability function.

[0203] 13. The method according to clause 11, wherein the reference probability distribution is a step function or a ladder function.

[0204] 14. The method of clause 11, wherein the offset function between the probability distribution and the reference probability distribution is the Lp norm.

[0205] 15. The method of aspect 1, wherein the adjusting comprises adjusting the source configuration, the mask configuration, or a combination of the source configuration and the mask configuration until a difference between the probability distribution and a reference probability distribution is within a threshold range.

[0206] 16. A method as described in aspect 1, wherein the calculation includes: calculating the probability distribution of the edge placement error at multiple positions in the plane, and wherein the adjustment includes: adjusting the source configuration, the mask configuration, or a combination of the source configuration and the mask configuration based on the probability distribution at multiple positions in the plane.

[0207] 17. A method as described in aspect 1, wherein the calculation includes: calculating the probability distribution of the edge placement error in multiple planes, and wherein the adjustment includes: adjusting the source configuration, the mask configuration, or a combination of the source configuration and the mask configuration based on the probability distribution in multiple planes.

[0208] 18. The method of clause 17, wherein the adjusting comprises adjusting the source configuration, the mask configuration, or a combination of the source configuration and the mask configuration based on a sum of probability distributions in at least two planes of the plurality of planes.

[0209] 19. A method as described in aspect 1, wherein the calculation also includes: calculating one or more imaging performance indicators, and wherein the adjustment includes: adjusting the source configuration, the mask configuration, or a combination of the source configuration and the mask configuration based on the probability distribution of edge placement error and the one or more imaging performance indicators.

[0210] 20. The method of clause 19, wherein the one or more imaging performance indicators include: critical dimension (CD), critical dimension uniformity (CDU), local critical dimension uniformity (LCDU), line edge roughness (LER), line width roughness (LWR), resist profile characteristics, maximum defect size, exposure latitude, pattern position error, mask error enhancement factor, focal length, depth of focus (DOF), DOF tolerance, critical dimension depth of focus, process window, process window tolerance, common process window, common process window tolerance, image contrast, image logarithmic slope (ILS), normalized image logarithmic slope (NILS), available process window above a specific NILS threshold (nDOF), mask error enhancement factor (MEEF), or at least one of a combination of the foregoing.

[0211] 21. The method of aspect 1, wherein the adjusting comprises:

[0212] determining a multivariate cost function for the lithography process based on the probability distribution of edge placement errors,

[0213] wherein the lithography process comprises a lithography process corresponding to the source configuration, the mask configuration, or a combination of the source configuration and the mask configuration; and

[0214] One or more characteristics of the lithography process are reconfigured until a termination criterion is met.

[0215] 22. A method as described in aspect 21, wherein the multivariate cost function includes a multivariate cost function of multiple design variables representing characteristics of the lithography process, and wherein the reconfiguration includes: reconfiguring one or more characteristics of the lithography process by adjusting one or more of the multiple design variables until the termination criterion is met.

[0216] 23. The method of aspect 1, wherein the obtaining comprises: obtaining the source configuration, the mask configuration, or a combination of the source configuration and the mask configuration from a source model, a mask model, or a combination of the source model and the mask model.

[0217] 24. A method comprising:

[0218] determining, by a computer system, a multivariate cost function of a plurality of design variables representing characteristics of a lithography process, wherein the multivariate cost function is associated with a probability distribution of edge placements,

[0219] wherein the probability distribution of edge placement takes into account the randomness of edge placement; and

[0220] One or more characteristics of the lithography process are reconfigured by the computer system by adjusting one or more of the plurality of design variables until a termination criterion is met.

[0221] 25. The method of clause 24, wherein the probability distribution of edge placements comprises a probability distribution of edge placement errors.

[0222] 26. The method of clause 24, wherein the probability distribution of edge placements is a simulated probability distribution of edge placements.

[0223] 27. The method of clause 24, wherein the probability distribution of edge placements is informed by a measured probability distribution of edge placements.

[0224] 28. The method of clause 24, wherein the probability distribution of edge placements includes contributions from a random edge placement distribution and a deterministic edge placement distribution.

[0225] 29. The method of clause 28, wherein the random edge placement distribution comprises a convolution of two or more randomly distributed distributions.

[0226] 30. The method of clause 29, wherein at least one of the random distributions comprises at least one random edge placement error distribution, a photon shot noise distribution, a random dose error distribution, a random mask error distribution, a measurement noise distribution, or a combination thereof.

[0227] 31. The method of clause 24, further comprising: calculating a distance between the probability distribution of edge placements and a reference distribution of edge placements, and wherein the reconfiguring is based on the distance.

[0228] 32. The method of clause 24, wherein the multivariate cost function is a function of the probability distribution of edge placements.

[0229] 33. The method of clause 24, wherein the multivariate cost function is a function of variables that are functions of the probability distribution of edge placements.

[0230] 34. The method of clause 24, wherein the probability distribution of edge placement is a function of a variable that affects the probability distribution of edge placement.

[0231] 35. The method of clause 24, wherein the determining comprises:

[0232] determining, by a computer system, a first multivariate cost function of a plurality of design variables characteristic of the lithography process, wherein the first multivariate cost function is related to edge placement; and

[0233] One or more characteristics of the lithography process are reconfigured by the computer system by adjusting one or more of the plurality of design variables until a first termination criterion is met.

[0234] 36. The method of clause 35, wherein the edge placement includes an edge placement error.

[0235] 37. The method of clause 35, wherein the determining further comprises:

[0236] determining, by the computer system, a second multivariate cost function of a plurality of design variables characteristic of the lithography process, wherein the second multivariate cost function is associated with a random probability distribution of edge placements; and

[0237] One or more characteristics of the lithography process are reconfigured by the computer system by adjusting one or more of the plurality of design variables until a second termination criterion is met.

[0238] 38. The method of clause 37, wherein the random probability distribution of edge placements comprises a random probability distribution of edge placement errors.

[0239] 39. One or more non-transitory machine-readable media having instructions thereon, the instructions being configured to, when executed by a processor, perform the method of any one of clauses 1 to 38.

[0240] 40. A system comprising:

[0241] Processor; and

[0242] One or more non-transitory machine-readable media having instructions thereon, the instructions being configured to, when executed by a processor, perform the method of any of clauses 1 to 38.

[0243] While the concepts disclosed herein may be used for imaging on substrates such as silicon wafers, it should be understood that the disclosed concepts can be used with any type of lithographic imaging system, such as those used for imaging on substrates other than silicon wafers. In addition, combinations and sub-combinations of the disclosed elements may include separate embodiments. For example, the addition of a single or multiple assist features described herein may include their own separate embodiments, or the addition of a single or multiple assist features described herein may be included in one or more other embodiments described herein.

[0244] The above description is intended to be illustrative rather than limiting. Accordingly, those skilled in the art will appreciate that modifications may be made as described without departing from the scope of the claims set forth below.

Claims

1. One or more non-transitory machine-readable media having instructions thereon, the instructions, when executed by a processor, being configured to perform a method for determining a source and mask configuration for a lithography process, the method comprising: obtaining a source configuration, a mask configuration, or a combination of a source configuration and a mask configuration; calculating a probability distribution of edge placement errors for a lithography process based on the source configuration, the mask configuration, or a combination of the source configuration and the mask configuration; as well as The source configuration, the mask configuration, or a combination of the source configuration and the mask configuration is adjusted based on the probability distribution.

2. The medium of claim 1, wherein: The edge placement error comprises a simulated edge placement error, and wherein the probability distribution is a simulated probability distribution.

3. The medium according to claim 1, wherein The probability distribution comprises a random probability distribution.

4. The medium according to claim 1, wherein The method also includes: determining a convolution of the probability distribution of the edge placement error and at least one additional probability distribution, and wherein adjusting the source configuration, the mask configuration, or a combination of the source configuration and the mask configuration based on the probability distribution includes: adjusting the source configuration, the mask configuration, or a combination of the source configuration and the mask configuration based on the convolution.

5. The medium of claim 4, wherein: The convolution includes an asymmetric distribution.

6. The medium of claim 1, wherein: The probability distribution comprises a cumulative probability function, wherein the method further comprises calculating an offset function between the probability distribution and a reference probability distribution, wherein the adjusting is based on the offset function, and wherein the reference probability distribution is a cumulative probability function.

7. The medium of claim 6, wherein: The reference probability distribution is a step function or a staircase function, wherein the offset function between the probability distribution and the reference probability distribution is an Lp norm, wherein the probability distribution of the edge placement error is a Gaussian distribution or a Poisson distribution.

8. The medium of claim 1, wherein: The calculating comprises calculating a probability distribution of the edge placement error at a plurality of locations in a plane, and wherein the adjusting comprises adjusting the source configuration, the mask configuration, or a combination of the source configuration and the mask configuration based on the probability distribution at a plurality of locations in the plane.

9. The medium of claim 1, wherein: The calculating includes calculating a probability distribution of the edge placement error in a plurality of planes, and wherein the adjusting includes adjusting the source configuration, the mask configuration, or a combination of the source configuration and the mask configuration based on the probability distribution in the plurality of planes.

10. The medium of claim 1, wherein: The calculating further comprises calculating one or more imaging performance indicators, and wherein the adjusting comprises adjusting the source configuration, the mask configuration, or a combination of the source configuration and the mask configuration based on the probability distribution of edge placement errors and the one or more imaging performance indicators.

11. The medium of claim 1, wherein: The adjustments include: determining, by a computer system, a multivariate cost function of a plurality of design variables characteristic of the lithography process, wherein the multivariate cost function is associated with a probability distribution of edge placements, wherein said probability distribution of edge placement takes into account the randomness of edge placement; and One or more characteristics of the lithography process are reconfigured by the computer system by adjusting one or more of the plurality of design variables based on the multivariate cost function.

12. The medium of claim 1, wherein: The probability distribution of edge placements includes contributions from a random edge placement distribution and a deterministic edge placement distribution.

13. The medium of claim 11, wherein: At least one of the random distributions includes at least one random edge placement error distribution, a photon shot noise distribution, a random dose error distribution, a random mask error distribution, a measurement noise distribution, or a combination thereof.

14. The medium of claim 11, wherein: The multivariate cost function is at least one of: a function of the probability distribution of edge placement; a function of variables that are a function of the probability distribution of edge placement; and a function of variables that affect the probability distribution of edge placement.

15. The medium according to claim 11, in, The determination includes: determining, by a computer system, a first multivariate cost function of a plurality of design variables characteristic of the lithography process, wherein the first multivariate cost function is related to edge placement; and reconfiguring, by the computer system, one or more characteristics of the lithography process by adjusting one or more of the plurality of design variables until a first termination criterion is met, The determination further includes: determining, by the computer system, a second multivariate cost function of a plurality of design variables characteristic of the lithography process, wherein the second multivariate cost function is associated with a random probability distribution of edge placements; and One or more characteristics of the lithography process are reconfigured by the computer system by adjusting one or more of the plurality of design variables until a second termination criterion is met.

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