Method for High Numerical Aperture Split-Source Mask Optimization

Abstract

This document describes a method for source mask optimization using a lithographic projection apparatus. The lithographic projection apparatus includes an illumination source and projection optics configured to image a mask design layout onto a substrate. The method includes determining a multi-variable source mask optimization function using a plurality of tunable design variables for the illumination source, the projection optics, and the mask design layout. The multi-variable source mask optimization function takes into account imaging variations at different positions corresponding to different stripes of the mask design layout across an exposure slit, where the different stripes are exposed by the same slit position of the exposure apparatus. The method includes iteratively adjusting the plurality of tunable design variables in the multi-variable source mask optimization function until a termination condition is satisfied.

Description

[0001] Cross - reference to related applications

[0002] This application claims priority to U.S. Application No. 62 / 743,058, filed on October 9, 2018, the entire content of which is incorporated herein by reference. Technical field

[0003] This specification generally relates to improving and optimizing lithography processes. More specifically, apparatuses, methods, and computer programs are described that take into account slit pupil variations during source mask optimization. Background art

[0004] A lithographic projection apparatus can be used, for example, to manufacture integrated circuits (ICs). In such a case, a patterning device (e.g., a mask) can contain or provide a pattern corresponding to a single layer of the IC ("design layout"), and this pattern can 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 ("resist") by, for example, irradiating the target portion through the pattern on the patterning device. Typically, a single substrate contains multiple adjacent target portions, and the pattern is transferred to the multiple adjacent target portions successively, one target portion at a time, by the lithographic projection apparatus. In one type of lithographic projection apparatus, the pattern on the entire patterning device is transferred to one target portion in one operation. Such an apparatus is commonly referred to as a stepper. In an alternative apparatus, commonly referred to as a step - scan device, the projection beam is scanned over the patterning device in a given reference direction ("scan direction") while the substrate is moved synchronously parallel or anti - parallel to this reference direction. Different portions of the pattern on the patterning device are gradually transferred to one target portion. Typically, since the lithographic projection apparatus will have a reduction ratio M (e.g., 4) and the reduction ratios in the x - and y - direction features may be different, the speed F of the substrate movement will be 1 / M times the speed at which the projection beam scans the patterning device. More information about lithographic apparatuses as described herein can be gathered, for example, from US6,046,792, which is incorporated herein by reference.

[0005] Before transferring the pattern from the pattern forming device to the substrate, the substrate may undergo various processes such as priming, resist coating, and soft baking. After exposure, the substrate may be subjected to other processes ("post-exposure processes") such as post-exposure bake (PEB), development, hard bake, and measurement / detection of the transferred pattern. This array of processes serves as the basis for fabricating a single layer of a device (e.g., an IC). Then, the substrate may undergo various processes such as etching, ion implantation (doping), metallization, oxidation, chemical-mechanical polishing, etc., all of which are intended to finish the single layer of the device. If multiple layers are required in the device, the entire process or a variant thereof is repeated for each layer. Eventually, there will be a device in each target portion on the substrate. Then, these devices are separated from each other by techniques such as dicing or sawing, whereby the individual devices can be mounted on a carrier, connected to pins, etc.

[0006] Thus, manufacturing a device such as a semiconductor device typically involves using multiple fabrication processes to process a substrate (e.g., a semiconductor wafer) to form various features and multiple layers of the device. Processes such as deposition, lithography, etching, chemical mechanical polishing, and ion implantation are commonly used to fabricate and process these layers and features. Multiple devices can be fabricated on multiple die on the substrate and then separated into individual devices. The device manufacturing process can be considered a patterning process. The patterning process involves performing a patterning step using a pattern forming device in a lithography apparatus, such as optical and / or nanoimprint lithography, to transfer the pattern on the pattern forming device to the substrate, and the patterning process typically but optionally involves one or more associated pattern processing steps such as resist development by a developing device, baking the substrate using a baking tool, etching using a pattern with an etching apparatus, etc.

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

[0008] As the semiconductor manufacturing process has continued to progress, over the decades, the size of the functional elements has been continuously decreasing, while the number of functional elements such as transistors per device has been steadily increasing, following a trend commonly referred to as "Moore's Law". In current technology, lithography projection equipment is used to fabricate the layers of a device, which uses irradiation from a deep ultraviolet radiation source to project a design layout onto the substrate, thereby producing individual functional elements with dimensions far below 100 nm, i.e., less than half the wavelength of the radiation from the radiation source (e.g., a 193 nm radiation source).

[0009] The process of printing features with dimensions smaller than the classical resolution limit of a lithographic projection apparatus is commonly referred to as low-k1 lithography according to the resolution formula CD = k1 × λ / NA, where λ is the wavelength of the radiation used (currently 248 nm or 193 nm in most cases), NA is the numerical aperture of the projection optics in the lithographic projection apparatus, CD is the "critical dimension" (usually the smallest feature size printed), and k1 is an empirical resolution factor. Generally, the smaller k1 is, the more difficult it becomes to reproduce on the substrate a pattern similar in shape and size to that planned by the designer in order to achieve a particular electrical functionality and performance. To overcome these difficulties, complex fine-tuning steps are applied to the lithographic projection apparatus, the design layout, or the patterning device. These steps include (by way of example and not limitation) optimization of the NA and optical coherence settings, customized illumination schemes, use of phase-shifting patterning devices, optical proximity correction (OPC, sometimes also referred to as "optical and process correction") in the design layout, or other methods generally defined as "resolution enhancement techniques" (RET). As used in the present invention, the term "projection optics" should be interpreted broadly to cover various types of optical systems, including, for example, refractive optics, reflective optics, apertures, and catadioptric optics. The term "projection optics" may also include components that operate according to any of these design types for collectively or individually guiding, shaping, or controlling a projection radiation beam. The term "projection optics" may include any optical component in a lithographic projection apparatus, regardless of where the optical component is located in the optical path of the lithographic projection apparatus. The projection optics may include optical components for shaping, adjusting, and / or projecting the radiation from the source before it passes through the patterning device, and / or for shaping, adjusting, and / or projecting the radiation after it passes through the patterning device. The projection optics generally excludes the source and the patterning device. SUMMARY OF THE INVENTION

[0010] According to an embodiment, there is provided a method for source mask optimization using a lithographic projection apparatus. The lithographic projection apparatus includes an illumination source and projection optics configured to image a mask design layout onto a substrate. The method includes: using a hardware computer system to determine a multivariable source mask optimization function using a plurality of tunable design variables for the illumination source, the projection optics, and the mask design layout. The multivariable source mask optimization function describes imaging variations over a plurality of portions ("stripes") corresponding to different positions of the slit of the exposure apparatus over the mask design layout. The method includes: iteratively adjusting, using the hardware computer system, the plurality of tunable design variables in the multivariable source mask optimization function until a termination condition is satisfied.

[0011] In an embodiment, the multivariable source mask optimization function describes imaging variations at different positions in one or more stripes throughout the mask design layout.

[0012] In an embodiment, the multivariable source mask optimization function includes respective multivariable source mask optimization functions corresponding to different positions in one or more stripes of the mask design layout.

[0013] In an embodiment, the multivariable source mask optimization function describes imaging variations at different positions in one or more stripes of the mask design layout corresponding to at least a center and another position along a first slit.

[0014] In an embodiment, the imaging variations are caused by variations in the slit throughout the different positions in the one or more stripes of the mask design layout.

[0015] In an embodiment, the imaging variations are caused by pupil variations across the different positions in the one or more stripes of the mask design layout.

[0016] In an embodiment, the pupil variations are caused by pupil rotation and / or blinking light spots in the pupil at the different positions in the one or more stripes of the mask design layout.

[0017] In an embodiment, the termination condition is associated with the image quality of the mask design layout on the substrate.

[0018] In an embodiment, the termination condition is associated with the pupil shape.

[0019] In an embodiment, the design layout includes one or more of the following: the entire design layout, a segment, or one or more critical features of the design layout.

[0020] In an embodiment, one or more of the tunable design variables for the illumination source, the projection optics, and / or the mask design layout are associated with extreme ultraviolet lithography.

[0021] In an embodiment, the termination condition includes one or more of the following: maximization of the multivariable source mask optimization function, minimization of the multivariable source mask optimization function, or a value that breaks through a threshold of the multivariable source mask optimization function.

[0022] In an embodiment, the termination condition includes one or more of a predetermined number of iterations or a predetermined calculation time.

[0023] In an embodiment, the termination condition is associated with values of the tunable design variables for the illumination source, the projection optics, and the mask design layout that define a process window for extreme ultraviolet lithography.

[0024] In an embodiment, the termination condition is associated with values of the tunable design variables for the illumination source, the projection optics, and the mask design layout that are available for the pupil over multiple locations of the mask design layout and that can be used for extreme ultraviolet lithography.

[0025] In an embodiment, in the absence of constraints that limit the range of possible values of the tunable design variables, an iterative adjustment of the multiple tunable design variables in the multi-variable source mask optimization function is performed until a termination condition is met.

[0026] In an embodiment, in the presence of at least one constraint that limits the range of possible values of at least one tunable design variable, an iterative adjustment of the multiple tunable design variables in the multi-variable source mask optimization function is performed until a termination condition is met.

[0027] In an embodiment, the at least one constraint is associated with one or more of the physical characteristics of the lithographic projection apparatus, the dependence of a design variable on one or more other design variables, or mask manufacturability.

[0028] In an embodiment, iteratively adjusting the at least one tunable design variable in the multi-variable source mask optimization function includes repeatedly changing the value of the at least one tunable design variable within the limits of the possible values until the termination condition is met.

[0029] In an embodiment, the multi-variable source mask optimization function is associated with high numerical aperture source mask optimization.

[0030] In an embodiment, determining the multi-variable source mask optimization function using the multiple tunable design variables for the illumination source, the projection optics, and the mask design layout includes: identifying a subset of the multiple tunable design variables for the multi-variable source mask optimization function based on the termination condition. The subset of the multiple tunable design variables has a relatively greater impact on the termination condition when adjusted compared to other tunable design variables among the tunable design variables. Iteratively adjusting the multiple tunable design variables in the multi-variable source mask optimization function includes assigning starting values to each of the tunable design variables included in the multi-variable source mask optimization function and adjusting the starting values until the termination condition is met.

[0031] According to another embodiment, there is provided a computer program product comprising a non-transitory computer-readable medium having instructions recorded thereon, the instructions, when executed by a computer, implementing the method described above. Description of the Drawings

[0032] Figure 1 A block diagram showing various subsystems of a lithographic system.

[0033] Figure 2 A flowchart of a method for determining a pattern forming device pattern or a target pattern to be printed on a substrate according to an embodiment.

[0034] Figure 3 Illustrates the variation in the pupil across the slit according to an embodiment.

[0035] Figure 4 Illustrates an exemplary flowchart for simulating lithography in a lithographic projection apparatus according to the present method and / or using the current system.

[0036] Figure 5 Illustrates the generalized operations for performing the method described herein according to an embodiment.

[0037] Figure 6 Shows an exemplary method of source mask optimization according to an embodiment.

[0038] Figure 7 A block diagram of an exemplary computer system according to an embodiment.

[0039] Figure 8 A schematic diagram of a lithographic projection apparatus according to an embodiment.

[0040] Figure 9 A schematic diagram of another lithographic projection apparatus according to an embodiment.

[0041] Figure 10 is according to an embodiment of Figure 9 a more detailed view of the device in

[0042] Figure 11 is according to an embodiment of Figure 9 and Figure 10 a more detailed view of the source collector module SO of the device of Detailed Description

[0043] Although specific reference may be made in this invention to the manufacture of integrated circuits, it should be clearly understood that the description herein has many other possible applications. For example, the description herein may be used in the manufacture of integrated optical systems, guidance and detection patterns for magnetic domain memories, liquid crystal display panels, thin film magnetic heads, and the like. Those skilled in the art will appreciate that, in the context of such alternative applications, any use herein of the terms "reticle", "wafer", or "die" should be considered interchangeable with the more general terms "mask", "substrate", and "target portion", respectively.

[0044] In this document, the terms "radiation" and "beam" are used to encompass 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 extreme ultraviolet radiation (EUV, e.g., having a wavelength in the range of about 5 nm to 100 nm).

[0045] The patterning device may include or may form one or more design layouts. Design layouts may be generated using computer-aided design (CAD) programs. This process is often referred to as electronic design automation (EDA). Most CAD programs follow a set of predefined design rules in order to generate functional design layouts / patterning devices. These rules are set based on processing and design limitations. For example, design rules define the space allowances between devices (such as gates, capacitors, etc.) or interconnect lines to ensure that the devices or lines do not interact with each other in an undesired manner. One or more of the design rule limitations may be referred to as "critical dimension" (CD). The critical dimension of a device may be defined as the minimum width of a line or a hole, or the minimum space between two lines or two holes. Thus, the CD regulates the overall size and density of the designed device. One of the goals in device fabrication is to faithfully reproduce the original design intent (via the patterning device) on the substrate.

[0046] As used herein, the term "mask" or "patterning device" can be broadly interpreted as referring to a general patterning device that can be used to endow an incident radiation beam with a patterned cross-section corresponding to a pattern to be created in a target portion of a substrate. In this context, the term "light valve" can also be used. In addition to classical masks (transmission or reflection; binary, phase-shifting, hybrid, etc.), examples of other such patterning devices include programmable mirror arrays. An example of such a device is a matrix-addressable surface with a viscoelastic control layer and a reflective surface. The underlying principle implicit in such a device is, for example, that the addressed regions of the reflective surface reflect the incident radiation as diffracted radiation, while the non-addressed regions reflect the incident radiation as non-diffracted radiation. In the presence of an appropriate filter, this non-diffracted radiation can be filtered out of the reflected beam, leaving only the diffracted radiation; thus, the beam becomes patterned according to the addressing pattern of the matrix-addressable surface. Appropriate electronic components can be used to perform the required matrix addressing. Examples of other such patterning devices also include programmable LCD arrays. An example of such a configuration is given in U.S. Patent No. 5,229,872, which is incorporated herein by reference.

[0047] As a brief introduction, Figure 1 Exemplary lithographic projection apparatus 10A is shown. The main components are: a radiation source 12A, which can be a deep ultraviolet (DUV) excimer laser source or other type of source including an extreme ultraviolet (EUV) source (as discussed above, the lithographic projection apparatus itself need not have a radiation source); illumination optics, which, for example, define partial coherence (represented as sigma) and can include optics 14A, 16Aa, and 16Ab that shape the radiation from source 12A; a patterning device (or mask) 18A; and projection optics 16Ac, which project an image of the pattern of the patterning device onto substrate plane 22A.

[0048] Pupil 20A can be included in projection optics 16Ac. In some embodiments, one or more pupils can be present before and / or after mask 18A. As described in further detail herein, pupil 20A can provide patterning of the light that ultimately reaches substrate plane 22A. An adjustable filter or aperture at the pupil plane of the projection optics can define the range of beam angles incident on substrate plane 22A, where the maximum possible angle defines the numerical aperture NA = n sin(Θ max ) of the projection optics, where n is the refractive index of the medium between the substrate and the last element of the projection optics, and Θ max is the maximum angle of the beam emerging from the projection optics that can still be incident on substrate plane 22A.

[0049] In a lithographic projection apparatus, a source provides an illumination (i.e., radiation) to a patterning device, and projection optics direct the illumination onto a substrate via the patterning device and shape the illumination. The projection optics may include at least some of components 14A, 16Aa, 16Ab, and 16Ac. A spatial image (AI) is the radiation intensity distribution at the substrate level. A resist model can be used to calculate a resist image from the spatial image, and an example of such can be found in U.S. Patent Application Publication No. US 2009-0157630, the entire disclosure of which is incorporated herein by reference. The resist model is only related to the properties of the resist layer (e.g., the effects of chemical processes occurring during exposure, post-exposure bake (PEB), and development). The optical properties of the lithographic projection apparatus (e.g., the properties of the illumination, patterning device, and projection optics) define the spatial image and can be defined in an optical model. Since the patterning device used in the lithographic projection apparatus can be changed, it is necessary to separate the optical properties of the patterning device from the optical properties of the remainder of the lithographic projection apparatus, which at least includes the source and the projection optics. Details of those techniques and models for transforming a design layout into various lithographic images (e.g., spatial images, resist images, etc.), applying OPC using 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 entire disclosure of each of which is incorporated herein by reference.

[0050] One aspect of understanding the lithographic process is understanding the interaction of radiation with the patterning device. The electromagnetic field of the radiation after it passes through the patterning device can be determined based on the electromagnetic field of the radiation before it reaches the patterning device and a function characterizing the interaction. This function may be referred to as a mask transmission function (which can be used to describe the interaction produced by a transmissive patterning device and / or a reflective patterning device).

[0051] The mask transmission function can have a variety of different forms. One form is binary. The binary mask transmission function has either of two values (e.g., zero and a positive constant) at any given location on the patterning device. A mask transmission function in binary form can be referred to as a binary mask. Another form is continuous. That is, the modulus of the transmittance (or reflectance) of the patterning device is a continuous function of the location on the patterning device. The phase of the transmittance (or reflectance) can also be a continuous function of the location on the patterning device. A mask transmission function in continuous form can be referred to as a continuous tone mask or a continuous transmission mask (CTM). For example, a CTM can be represented as a pixelated image, where a value between 0 and 1 (e.g., 0.1, 0.2, 0.3, etc.) can be assigned to each pixel instead of a binary value of 0 or 1. In an embodiment, the CTM can be a pixelated grayscale image, where each pixel has a plurality of values (e.g., normalized values in the range [-255, 255], in the range [0, 1] or [-1, 1] or other suitable ranges).

[0052] The thin mask approximation (also known as the Kirchhoff boundary condition) is widely used to simplify the determination of the interaction of radiation with the patterning device. The thin mask approximation assumes that the thickness of the structures on the patterning device is extremely small compared to the wavelength, and the width of the structures on the mask is extremely large compared to the wavelength. Thus, the thin mask approximation assumes that the electromagnetic field after the patterning device is the product of the incident electromagnetic field and the mask transmission function. However, as the lithography process uses radiation with an increasingly short wavelength, and the structures on the patterning device become smaller and smaller, the assumptions of the thin mask approximation may be violated. For example, due to the finite thickness of the structures (e.g., the edges between the top surface and the sidewalls), the interaction of radiation with the structures ("mask 3D effect" or "M3D") may become important. Incorporating this scattering into the mask transmission function can enable the mask transmission function to better capture the interaction of radiation with the patterning device. A mask transmission function based on the thin mask approximation can be referred to as a thin mask transmission function. A mask transmission function that incorporates M3D can be referred to as an M3D mask transmission function.

[0053] Figure 2 is a flowchart of a method 200 for determining a patterning device pattern (or mask pattern hereinafter) from an image (e.g., a continuous transmission mask image, a binary mask image, a curve mask image, etc.), the image corresponding to a target pattern to be printed on a substrate via a patterning process involving a lithography process. In an embodiment, the design layout or target pattern can be a binary design layout, a continuous tone design layout, or a design layout having another suitable form.

[0054] Method 200 is an iterative process in which an initial image (e.g., an enhanced image, a mask variable initialized from a CTM image, etc.) is progressively modified to generate different types of images according to different processes of the present disclosure, so as to finally generate information including a mask pattern or an image (e.g., a mask variable corresponding to a final curved mask) further for making / fabricating a mask. The iterative modification of the initial image can be based on a cost function, where during the iteration, the initial image can be modified such that the cost function decreases and is minimized in an embodiment. In an embodiment, method 200 can also be referred to as a binary CTM program, where the initial image is an optimized CTM image, and the optimized CTM image is further processed according to the present disclosure to generate a curved mask pattern (e.g., the geometry or polygon representation shape of a curved mask or a curved pattern). In an embodiment, the initial image can be an enhanced image of a CTM image. The curved mask pattern can be in the form of a vector, a table, a mathematical equation, or other forms representing a geometric / polygon shape.

[0055] In an embodiment, process P201 can involve obtaining an initial image (e.g., a CTM image, an optimized CTM image, or a binary mask image). In an embodiment, the initial image 201 can be a CTM image generated by a CTM generation process based on a target pattern to be printed on a substrate. Then, the CTM image can be received through process P201. In an embodiment, process P201 can be configured to generate a CTM image. For example, in CTM generation technology, the inverse lithography problem is formulated as an optimization problem. The variables are related to the pixel values in the mask image, and lithography metrics such as EPE or sidelobe printing are used as the cost function. In the iterative optimization, a mask image is constructed from the variables, and then a process model (e.g., the Tachyon model) is applied to obtain an optical or resist image and calculate the cost function. Then, the cost calculation gives a gradient value, which is used in an optimization solver to update the variables (e.g., pixel intensity). After multiple iterations during the optimization, a final mask image is generated, which is further used as a guiding map for pattern extraction (e.g., implemented in Tachyon SMO software). This initial image (e.g., the CTM image) can include one or more features corresponding to the target pattern to be printed on the substrate via a patterning process (e.g., features of the target pattern, SRAF, SRIF, etc.).

[0056] In an embodiment, a CTM image (or an enhanced version of the CTM image) can be used to initialize a mask variable that can be used as the initial image 201, and the initial image is iteratively modified as discussed below.

[0057] Process P201 may involve generating an enhanced image 202 based on an initial image 201. The enhanced image 202 may be an image in which certain selected pixels within the initial image 201 are magnified. The selected pixels may be pixels within the initial image 201 having relatively low values (or weak signals). In an embodiment, the selected pixels are pixels having a signal value lower than, for example, the average intensity of the pixels throughout the initial image, or a given threshold. In other words, the pixels within the initial image 201 having weaker signals are magnified, thus enhancing one or more features within the initial image 201. For example, the second-order SRAF around a target feature may have a weak signal, which can be magnified. Thus, the enhanced image 202 may highlight or identify additional features (or structures) that may be included in a mask image (to be generated later in the method). In a conventional method for determining the mask image (such as the CTM method), the weak signals within the initial image may be ignored, and thus the mask image may not include features that may be formed by the weak signals in the initial image 201.

[0058] The generation of the enhanced image 202 involves applying an image processing operation such as a filter (e.g., an edge detection filter) to magnify the weak signals within the initial image 201. Alternatively or additionally, the image processing operation may be deblurring, averaging, and / or feature extraction or other similar operations. Examples of edge detection filters include the Prewitt operator, the Laplacian operator, the Laplacian of Gaussian (LoG) filter, etc. The generation step may further involve combining the magnified signal of the initial image 201 with the original signal of the initial image 201 with or without modifying the original strong signals of the initial image 201. For example, in an embodiment, for one or more pixel values at one or more locations throughout the initial image 201 (such as at contact holes), if the original signal is relatively strong (e.g., higher than a certain threshold such as 150 or lower than -50), then the original signals at those one or more locations (such as at contact holes) may not be modified or combined with the magnified signals at those locations.

[0059] In an embodiment, the noise in the initial image 201 (e.g., random variations in brightness or color or pixel values) may also be magnified. Thus, alternatively or additionally, a smoothing procedure may be applied to reduce the noise (e.g., random variations in brightness or color or pixel values) in the combined image. Examples of image smoothing methods include Gaussian blur, moving average, low-pass filter, etc.

[0060] In an embodiment, an edge detection filter can be used to generate an enhanced image 202. For example, an edge detection filter can be applied to an initial image 201 to generate a filtered image that highlights edges of one or more features within the initial image 201. The resulting filtered image can be further combined with the original image (i.e., the initial image 201) to generate the enhanced image 202. In an embodiment, the combination of the initial image 201 and the image obtained after edge filtering can involve modifying only those portions of the initial image 201 that have weak signals without modifying regions having strong signals, and the combination procedure can be weighted based on signal strength. In an embodiment, amplifying the weak signals can also amplify noise within the filtered image. Thus, according to an embodiment, a smoothing procedure can be performed on the combined image. Smoothing of the image can involve an approximation function that attempts to capture important patterns (e.g., target patterns, SRAF) in the image while ignoring noise or other fine-scale structures / rapid phenomena. In smoothing, the data points of the signal can be modified such that individual points (roughly due to noise) can be decreased and points that may be below neighboring points can be increased, resulting in a smoother signal or a smoother image. Thus, after the smoothing operation, according to an embodiment of the present disclosure, a further smoothed version of the enhanced image 202 with reduced noise can be obtained.

[0061] In process P203, the method can involve generating a mask variable 203 based on the enhanced image 202. In a first iteration, the enhanced image 202 can be used to initialize the mask variable 203. In later iterations, the mask variable 203 can be iteratively updated.

[0062] The contour extraction of a real-valued function f of n real variables is a combination of the following form:

[0063]

[0064] In two-dimensional space, this set defines the points on the surface where the function f equals a given value c. In two-dimensional space, the function f is capable of extracting a closed contour that will become a mask image.

[0065] In the above equation, x1, x2,... x n refers to a mask variable such as the intensity of a single pixel that determines the locations where the curve mask edge exists at a given constant value c (e.g., at a threshold plane as discussed in the following process P205).

[0066] In an embodiment, during iteration, the generation of the mask variable 203 can involve modifying one or more values (e.g., pixel values at one or more locations) of variables within the enhanced image 202 based on, for example, initialization conditions or a gradient map (which can be generated subsequently in the method). For example, one or more pixel values can be increased or decreased. In other words, the amplitude of one or more signals within the enhanced image 202 can be increased or decreased. This modified amplitude of the signal can result in different curve patterns depending on the amount of change in the amplitude of the signal. Thus, the curve pattern gradually evolves until the cost function decreases and is minimized in an embodiment. In an embodiment, further smoothing can be performed on the horizontal mask variable 203.

[0067] In addition, process P205 involves generating a curved mask pattern 205 (e.g., having a polygonal shape represented in vector form) based on the mask variable 203. The generation of the curved mask pattern 205 can involve threshold setting of the mask variable 203 to trace or generate a curve (or curved) pattern based on the mask variable 203. For example, threshold setting can be performed using a threshold plane (e.g., an x - y plane) with a fixed value that intersects the signal of the mask variable 203. The intersection of the threshold plane with the signal of the mask variable 203 produces a trace or contour (i.e., a curved polygonal shape), and the trace or contour forms a polygonal shape of the curve pattern that serves as the curved mask pattern 205. For example, the mask variable 203 can intersect a zero plane parallel to the (x, y) plane. Thus, the curved mask pattern 205 can be any curve pattern generated as described above. In an embodiment, the curve pattern traced or generated from the mask variable 203 depends on the signal of the enhanced image 202. Thus, the image enhancement process P203 facilitates the improvement of the pattern for the final curved mask pattern. The final curved mask pattern can be further used by a mask manufacturer to fabricate a mask for use in a lithography process.

[0068] Process P207 can involve rendering the curved mask pattern 205 to produce a mask image 207. Rendering is an operation performed on the curved mask pattern and is a process similar to converting a rectangular mask polygon into a discrete grayscale image representation. This process can generally be understood as sampling the box function of continuous coordinates (polygon) into values at each point of the image pixels.

[0069] The method further involves a forward simulation of the patterning process using a process model that generates or predicts a pattern 209 that can be printed on a substrate based on a mask image 207. For example, process P209 may involve performing and / or simulating the process model using the mask image 207 as an input and generating a process image 209 (e.g., a aerial image, a resist image, an etch image, etc.) on the substrate. In an embodiment, the process model may include a mask transmission model coupled to an optical device model, which is further coupled to a resist model and / or an etch model. The output of the process model may be a process image 209 that takes into account different process variations during the simulation procedure. The process image may be further used to determine parameters of the patterning process (e.g., EPE, CD, overlay, side lobes, etc.) by, for example, tracing the contours of the patterns within the process image. The parameters may be further used to define a cost function, which is further used to optimize the mask image 207 such that the cost function is reduced or, in an embodiment, minimized.

[0070] In process P211, a cost function may be evaluated based on the process model image 209 (also referred to as the simulated substrate image or the substrate image or the wafer image). Thus, the cost function may be considered process-aware in the case of patterning process variations, enabling the generation of a curved mask pattern that takes into account the variations in the patterning process. For example, the cost function may be an edge placement error (EPE), a side lobe, a mean squared error (MSE), a pattern placement error (PPE), a normalized image logarithm, or other suitable variable defined based on the pattern contours in the process image. The EPE may be the edge placement error associated with one or more patterns and / or the sum of all edge placement errors associated with all patterns in the process model image 209 and the corresponding target patterns. In an embodiment, the cost function may include more than one condition that can be reduced or minimized simultaneously. For example, in addition to the MRC violation probability, the number of defects, EPE, overlay, CD, or other parameters may be included, and all conditions may be reduced (or minimized) simultaneously.

[0071] In addition, one or more gradient maps (discussed later) may be generated based on the cost function (e.g., EPE), and the mask variables may be modified based on such gradient maps. The mask variable (MV) refers to the intensity ∅. Thus, the gradient calculation may be expressed as dEPE / d∅, and the gradient value is updated by capturing the inverse mathematical relationship from the mask image (MI) to the curved mask polygon to the mask variable. Thus, a derivative chain of the cost function can be calculated with respect to the mask image according to the mask image to the curved mask polygon and from the curved mask polygon to the mask variable, which allows modifying the value of the mask variable at the mask variable.

[0072] In an embodiment, image regularization may be added to reduce the complexity of the mask pattern that may be generated. Such image regularization may be mask rule checking (MRC). MRC refers to the constraints of the mask manufacturing process or equipment. Thus, the cost function may include different components based on, for example, EPE and MRC violation penalties. The penalty may be a term of the cost function that depends on the amount of violation, such as the difference between the mask measurement value and a given MRC or mask parameter (e.g., mask pattern width and the allowed (e.g., minimum or maximum) mask pattern width). Thus, according to an embodiment of the present disclosure, the mask pattern may be designed and the corresponding mask may be fabricated not only based on the forward simulation of the patterning process but also additionally based on the manufacturing constraints of the mask manufacturing equipment / procedure. Thus, a manufacturable curved mask that yields a high yield (i.e., minimum defects) and high accuracy in terms of, for example, EPE or overlap of the printed pattern may be obtained.

[0073] The pattern corresponding to the process image should be exactly the same as the target pattern. However, such an exact target pattern may not be feasible (e.g., typically sharp corners), and some contradictions are introduced due to variations in the patterning process itself and / or approximations in the model of the patterning process. In the first iteration of the method, the mask image 207 may not produce a pattern similar to the target pattern (in the resist image). The determination of the accuracy or acceptability of the printed pattern in the resist image (or etched image) may be based on a cost function such as EPE. For example, if the EPE of the resist pattern is high, it indicates that the printed pattern using the mask image 207 is unacceptable, and the pattern in the mask variable 203 must be modified.

[0074] To determine whether the mask image 207 is acceptable, the process P213 may involve determining whether the cost function is reduced or minimized, or whether a given number of iterations is reached. For example, the EPE value of the previous iteration may be compared with the EPE value of the current iteration to determine whether the EPE is reduced, minimized, or converged (i.e., no substantial improvement in the printed pattern is observed). When the cost function is minimized, the method may stop, and the resulting curved mask pattern information is regarded as the optimized result.

[0075] However, if the cost function is not reduced or minimized, the mask-related variables or enhanced image-related variables (e.g., pixel values) may be updated. In an embodiment, the update may be based on a gradient-based method. For example, if the cost function is not reduced, the method 200 proceeds to the next iteration that generates the mask image after performing processes P215 and P217 that indicate how to further modify the mask variable 203.

[0076] Process P215 may involve generating a gradient map 215 based on a cost function. The gradient map may be a derivative and / or partial derivative of the cost function. In an embodiment, the partial derivative of the cost function may be determined with respect to the pixels of the mask image, and the derivatives may be further chained to determine the partial derivative with respect to the mask variable 203. Such gradient calculations may involve determining the inverse relationship between the mask image 207 and the mask variable 203. In addition, the inverse relationship of any smoothing operations (or functions) performed in processes P205 and P203 must be considered.

[0077] The gradient map 215 may provide suggestions on increasing or decreasing the value of the mask variable in a way that decreases (minimized in an embodiment) the value of the cost function. In an embodiment, an optimization algorithm may be applied to the gradient map 215 to determine the mask variable value. In an embodiment, an optimization solver may be used to perform gradient-based calculations (in process P217).

[0078] In an embodiment, for an iteration, the mask variable may change while the threshold plane may remain fixed or unchanged to gradually decrease or minimize the cost function. Thus, the resulting curve pattern may gradually evolve during the iteration such that the cost function decreases or is minimized in an embodiment. In another embodiment, both the mask variable and the threshold plane may change to achieve faster convergence of the optimization process. A final set of binary CTM results (i.e., a modified version of the enhanced image, mask image, or curve mask) may be produced after multiple iterations and / or minimization of the cost function.

[0079] In an embodiment of the present disclosure, the transition from CTM optimization via a grayscale image to binary CTM optimization via a curve mask may be simplified by replacing the threshold setting processes (i.e., P203 and P205) with a different process in which a sigmoid transformation is applied to the enhanced image 202 and corresponding changes to the gradient calculation are performed. The sigmoid transformation of the enhanced image 202 produces a transformed image that gradually evolves into a curve pattern during the optimization process (e.g., minimizing the cost function). During an iteration or optimization step, variables associated with the sigmoid function (e.g., steepness and / or threshold) may be modified based on the gradient calculation. Since the sigmoid transformation becomes steeper during successive iterations (e.g., the steepness of the slope of the sigmoid transformation increases), a gradual transition from the CTM image to the final binary CTM image can be achieved, thereby allowing improved results for the final binary CTM optimization via the curve mask pattern.

[0080] In embodiments of the present disclosure, additional steps / processes can be inserted into the optimized iterative loop to enhance the result to have the selected or desired properties. For example, smoothness can be ensured by adding a smoothing step, or other filters can be used to enhance the image in favor of horizontal / vertical structures.

[0081] The method has multiple features or aspects. For example, an optimized CTM mask image obtained by an image enhancement method is used to improve the signal, which can further be used as a seed in the optimization process. In another aspect, a threshold setting method (referred to as binary CTM) using CTM technology can generate a curve mask pattern. In yet another aspect, the complete formulation of gradient calculation (i.e., closed-loop formulation) also allows the use of a gradient-based solver for mask variable optimization. The binary CTM result can be used as a local solution (as a hot spot fix) or as a full-chip solution. The binary CTM result can be used as an input together with machine learning. This can allow the use of machine learning to accelerate binary CTM. In yet another aspect, the method includes an image regularization method to improve the result. In another aspect, the method involves a continuous optimization stage to achieve a smoother transition from a grayscale image CTM to a binary curve mask binary CTM. The method allows tuning of the optimization threshold to improve the result. The method includes additional transformations to the optimized iteration to enhance the good properties of the result (requiring smoothness in the binary CTM image).

[0082] As lithography nodes continue to shrink, more and more complex masks are required. The present method can be used in critical layers using DUV scanners, EUV scanners, and / or other scanners. The method according to the present invention can be included in different aspects of mask optimization processes including source mask optimization (SMO), mask optimization, and / or OPC.

[0083] For example, the prior art source mask optimization process is described in U.S. Patent No. 9,588,438, titled "Optimization Flows of Source, Mask and Projection Optics," which is incorporated herein by reference in its entirety. This prior art source mask optimization process is performed for the slit center on a typical layout segment. The resulting optimization of the source and mask variables is considered to represent all positions (and / or other positions) on the slit. However, in high-NA and other systems, there are known pupil and / or slit variations across the slit and between different slits. For example, known pupil variations include pupil rotation (e.g., about 0.025 sigma) and flashing spots in the pupil caused by pupil presentation. This means that the source mask optimization pupil optimized at the slit center on a typical segment in a prior art system may not necessarily produce optimal performance for other positions along a given slit.

[0084] As a non-limiting example, Figure 3 shows the variation of the pupil 300 optimized for the feature 312 across the slit 302. As Figure 3 shown, as the pupil 300 moves away from the center 310 of the slit 302 through the slit positions 306, 308, the shape 304 of the occluding portion and the center changes (e.g., from circular to elliptical). Each position in the slit 302 of the exposure apparatus exposes different portions of the mask 320 (in a scanning manner), which are referred to herein as mask stripes 322, 324, and 326, see Figure 3 . It should be noted that Figure 3 shows the change in the occluding portion shape and the (outer) NA shape. Additionally, the term slit can be and / or refer to a physical exposure slit (e.g., of a scanner), different slit positions generated by, for example, a grating, and / or an exposure tool having multiple physical slits.

[0085] According to an embodiment of the present disclosure, a multi-variable source mask optimization function (full slit optimization function) is defined using a plurality of tunable design variables for the illumination source, projection optics, and mask design layout or other components involved in the lithography process. This function takes into account the pupil within the slit and / or slit variations. This function optimizes the imaging through the slit taking into account the known pupil variation through the slit and the Jones pupil variation. The source mask optimization function of the present invention is the sum (or combination) of the imaging quality (NILS, edge placement, etc.) of the variations caused by the known (through-slit) pupil variations at a plurality of (up to and including all) slit positions across the slit positions. For example, maximizing this function optimizes the imaging through the slit such that the known pupil variation through the slit is taken into account. Despite the disadvantages of high NA illuminator designs (caused by design choices made to maximize high NA productivity), this function still optimizes the imaging. In an embodiment, the multi-variable source mask optimization function can be and / or include a cost function and / or other functions.

[0086] As described above, the present disclosure describes a method for source mask optimization using a lithographic projection apparatus. The lithographic projection apparatus includes an illumination source and projection optics configured to image a mask design layout onto a substrate. The method includes determining a multivariable source mask optimization function using a plurality of tunable design variables for the illumination source, the projection optics, and the mask design layout. The multivariable source mask optimization function can be more generally described as an expression that takes into account imaging variations over a plurality of locations (e.g., over slots and between different slots) throughout the mask design layout. The design layout can include the entire design layout, a fragment, or one or more critical features of the design layout and / or one or more in other layouts. For example, the design layout can be a set of fragments selected by a pattern selection method based on diffraction marker analysis or any other method. Alternatively, full-chip simulations can be performed, "hot spots" and / or "warm spots" can be identified from the full-chip simulations, and then a pattern selection step can be performed. Optimization can be performed based on the selected patterns (e.g., performing the methods described herein).

[0087] Figure 4 An exemplary flowchart is shown for simulating lithography in a lithographic projection apparatus according to the present method and / or using the current system. The source model 431 represents the optical characteristics of the source (including the light intensity distribution and / or phase distribution). In contrast to prior art systems, the source model 431 includes information related to slit dependence. The source model 431 includes information indicative of known pupil through-slit variations associated with the optical characteristics of the source. This is caused by specific selections in the illuminator design, for example, to enhance productivity, and can be practically similar to the rotation of the pupil through-slit. Additionally, certain pupil points can be bright in one slit position and dim or nearly absent in other slit positions (and vice versa), i.e., so-called "flickering" pupil points through-slits. The projection optics model 432 represents the optical characteristics of the projection optics (including the changes in the light intensity distribution and / or phase distribution caused by the projection optics). The projection optics model 432 also includes information related to slit dependence. The source model 431 includes information indicative of known pupil through-slit variations (e.g., Figure 3the information (shown in). One can consider deliberately varying the Zernike coefficients of the POB slit in a manner that compensates for imaging effects such as changes in the pupil slit. In some embodiments, the source model 431 and the projection optics model 432 can be combined into a transmission cross coefficient (TCC) model. The design layout model 435 represents the optical characteristics of the design layout (including changes in the light intensity distribution and / or phase distribution caused by a given design layout), which is a representation of the configuration of features on a mask. The aerial image 436 can be simulated based on the transmission cross coefficient and the design layout model 435. The resist image 437 can be simulated based on the aerial image 436 using the resist model 438. In contrast to prior art systems, the resist model 438 now takes into account known (described above) slit pupil variations (e.g., the calibrated resist model varies the slit while the photoresist material does not vary the slit). The simulation of lithography can, for example, predict the profiles and CDs in the resist image.

[0088] In an embodiment, the source model 431 can represent the optical characteristics of the source, which include but are not limited to NA-sigma (σ) settings and any particular illumination source shape (e.g., off-axis sources such as annular, quadrupole, and dipole, etc.). The projection optics model 432 can represent the optical characteristics of the projection optics, which include aberration, distortion, refractive index, physical size, physical dimension, etc. The design layout model 435 can also represent the physical attributes of a physical mask, as described, for example, in U.S. Patent No. 7,587,704, which is hereby incorporated by reference in its entirety. The goal of the simulation should be to accurately predict, for example, the edge placement and CD, and then the edge placement and CD can be compared with the expected design. The expected design is typically defined as the pre-OPC design layout, which can be provided in a standardized digital file format such as GDSII or OASIS or other file formats.

[0089] As described in the present invention, the method includes iteratively adjusting a plurality of tunable design variables in a multivariable source mask optimization function until a termination condition is met. In an embodiment, the multivariable source mask optimization function describes the imaging variations at different positions in the slits throughout the mask design layout. The multivariable source mask optimization function includes respective multivariable source mask optimization functions (e.g., the sum of) corresponding to different positions in one or more stripes of the mask design layout. In an embodiment, the multivariable source mask optimization function describes the imaging variations at different positions in one or more stripes of the mask design layout, the one or more stripes including at least a mask stripe that corresponds to the center of a first exposure slit and another position along the first slit. For example, the exemplary function can be expressed as:

[0090]

[0091] where (z1, z2, ..., z n ) are n design variables or their values; f p (z1, z2, ..., z n ) is the difference between the actual value and the expected value of a characteristic at the p-th evaluation point for a set of values of the design variables (z1, z2, ..., z n ), and w p is the weight constant assigned to the p-th evaluation point. A higher w p value can be assigned, for example, to an evaluation point or pattern that is more critical than other evaluation points or patterns. A higher w p value can also be assigned to a pattern and / or evaluation point with a larger number of occurrences. Examples of evaluation points can be any physical point or pattern on a wafer, or any point on a virtual design layout, or a resist image, or a spatial image (e.g., one or more points along a slit in any of these components). The function can represent any suitable characteristic of a lithographic projection apparatus or a substrate (e.g., by tuning the design variables), such as focus, CD, image shift, image distortion, image rotation, etc. The function takes into account known stitch image variations, as the function is evaluated for multiple points along the slit. The design variables can be any adjustable parameters, such as adjustable parameters of a source, a mask, projection optics, dose, focus, etc. Preferably, at least some of the design variables are adjustable characteristics of the projection optics. The projection optics can adjust the wavefront and intensity distribution at any location along the optical path of the lithographic projection apparatus, such as in front of the mask, near the pupil plane, near the image plane, near the focal plane. The projection optics can be used to correct or compensate for certain distortions of the wavefront and intensity distribution caused, for example, by temperature variations in the source, mask, components of the lithographic projection apparatus, or thermal expansion of the components of the lithographic projection apparatus. Adjusting the wavefront and intensity distribution can change the values of the evaluation points and the function. These changes can be simulated from a model or actually measured.

[0092] In an embodiment, the imaging variation is caused by a variation in the exposure slit at different positions in one or more corresponding stripes throughout the mask design layout. In an embodiment, the imaging variation is caused by a variation in the slit pupil across different positions in one or more stripes throughout the mask design layout (as described above). The slit pupil variation can be caused by pupil rotation and / or a scintillating spot in the pupil at different positions in one or more stripes of the mask design layout and / or other factors, such as the characteristics of the illuminator design. In some embodiments, the light intensity distribution (or uncorrected dose slit uniformity) can also vary (systematically) across the slit. In some embodiments, the mask can include a thin film diaphragm (pellicle) that protects the front side of the mask from falling particles. Some embodiments can also include a thin film diaphragm that protects the projection optics from contamination by photoresist outgassing products. Both diaphragm types can exhibit systematic variations across the slit, resulting in additional pupil variations and / or light intensity distribution variations across the slit. As described above, the function of the present method takes into account any such variations by facilitating the evaluation of the function at each position along a given slit. Possible variables include: pupil parameters, such as inner σ and outer σ within the pupil, the pupil point distribution in the pupil plane, the pupil intensity distribution in the pupil plane; the light intensity distribution across the slit; and mask variables, such as the bias or shape of the critical feature slit. The variables of the equation (and / or other similar equations) described above can be adjusted iteratively until a termination condition is met.

[0093] In an embodiment, the termination condition is associated with the image quality of the mask design layout on the substrate. For example, the tunable design variables in the multi-variable source mask optimization function can be adjusted iteratively until a set of values of the variables that results in sufficient (e.g., user-defined, based on subsequent process requirements, etc.) image quality across the mask design is determined. In prior art systems, the set of values is determined based only on the evaluation of the multi-variable source mask optimization function, where the pupil is aligned to the center of a single slit, rather than across the slit as in the present method.

[0094] In an embodiment, the termination condition is associated with the pupil shape. For example, the termination condition can specify that the values of the tunable variables should define a pupil shape that results in sufficient image quality across multiple portions of the slit. This pupil shape may not be the optimal shape for any single portion along the slit, but will result in an optimal overall result across the slit. In an embodiment, the termination condition includes one or more of: maximization of the multi-variable source mask optimization function (e.g., optimal image quality), minimization of the multi-variable source mask optimization function (e.g., the worst pupil that still results in sufficient results), a value of the multi-variable source mask optimization function that breaks a threshold, and / or other termination conditions. In an embodiment, the termination condition includes one or more of a predetermined number of iterations or a predetermined computation time.

[0095] Figure 5 A general method of performing the methods described herein according to an embodiment is shown. The method includes a step 502 of defining a multivariable source mask optimization function for a plurality of design variables. At least some of the design variables may be characteristics of a projection optical device associated with a pupil and / or a slit at a plurality of positions along the slit, as shown in step 500B. Other design variables may be associated with an illumination source (step 500A) and a design layout (step 500C), which also have variables associated with portions along the slit and / or known pupil variations along the slit. In step 504, the design variables are adjusted simultaneously such that the cost function moves towards convergence. In step 506, it is determined whether a predefined termination condition is satisfied. The predefined termination condition may include various possibilities, i.e., for example, depending on the numerical technique used, the function may be minimized or maximized; the value of the function is equal to or has breached a threshold; the value of the function has reached a value within a default error limit; or a preset number of iterations has been reached. If the termination condition 505 is satisfied in step 506, the method ends. If the termination condition 507 is not satisfied in step 506, steps 504 and 506 are iteratively repeated until a desired result is obtained.

[0096] In an embodiment, the iterative adjustment of the plurality of tunable design variables in the multivariable source mask optimization function is performed until a termination condition is satisfied without a constraint condition defining a range of possible values for the tunable design variables. In an embodiment, the iterative adjustment of the plurality of tunable design variables in the multivariable source mask optimization function is performed until a termination condition is satisfied with at least one constraint condition defining a range of possible values for at least one tunable design variable. In an embodiment, at least one of the constraint conditions is associated with one or more of the physical characteristics of a lithographic projection apparatus, the dependence of a design variable on one or more other design variables, or mask manufacturability. In an embodiment, the iterative adjustment of at least one tunable design variable in the multivariable source mask optimization function includes repeatedly changing the value of at least one tunable design variable within a defined range of possible values until a termination condition is satisfied. The possible ranges of the variables include ranges of pupil parameters, such as inner σ (>0) and outer σ (<1) within the pupil, the pupil point distribution in the pupil plane (e.g., density between 0 and 1 within a certain σ range), the pupil intensity distribution in the pupil plane (e.g., normalized pupil spot intensity distribution between 0 and 1), and mask variables for critical feature through-slits, such as bias (between 0 nm and X nm) or shape (e.g., angle with respect to between X and Y and Y degrees).

[0097] In an embodiment, one or more of the tunable design variables for an illumination source, a projection optical device, and / or a mask design layout are associated with extreme ultraviolet lithography (EUV). In an embodiment, a termination condition is associated with a value that defines a process window for EUV lithography for the tunable design variables for the illumination source, the projection optical device, and the mask design layout. In an embodiment, the termination condition is associated with a value of a tunable design variable of a pupil that can be used over a plurality of positions of the mask design layout for EUV lithography for the illumination source, the projection optical device, and the mask design layout. For DUV, an illuminator can incorporate a latest number of optical elements to ensure an accurate shape of the pupil as a constant slit by means of a low (<< 1%) intensity loss when passing through an optical surface (from vacuum or air to optically dense material), in combination with the availability of a laser having sufficient power to compensate for any intensity loss. For EUV, due to a large intensity loss (about ~30%) per optical surface reflection, pupil shaping and slit behavior need to be achieved by using as few optical elements as possible. This means that a balance must be struck between an acceptable pupil shape (including slit behavior) and a transmittance of the illuminator that is high enough to ensure an acceptable throughput of the optical path and thus ensure economy, which is also because EUV light sources having sufficient power to compensate for the increased losses are not readily available.

[0098] In an embodiment, determining a multi-variable source mask optimization function using a plurality of tunable design variables for an illumination source, a projection optical device, and a mask design layout includes identifying a subset of the plurality of tunable design variables for the multi-variable source mask optimization function based on a termination condition. The subset of the plurality of tunable design variables can have a relatively greater impact on the termination condition compared to other tunable design variables among the tunable design variables when adjusted. In an embodiment, an initial set of tunable design variables is identified and then iteratively expanded to include more and more variables. In an embodiment, iteratively adjusting the plurality of tunable design variables in the multi-variable source mask optimization function includes assigning an initial value to each of the tunable design variables included in the multi-variable source mask optimization function and adjusting the initial value until the termination condition is met.

[0099] For example, Figure 6An exemplary method of source mask optimization according to an embodiment of the present method is shown. In step 602, an initial value of a design variable is obtained, including a tuning range of the design variable if any. In step 604, a multi-variable source mask optimization function is determined. In step 606, the function is expanded within a sufficiently small neighborhood around a starting value of the design variable for the first iteration step (i = 0). In step 608, standard multi-variable optimization techniques are applied to maximize, minimize the function and / or otherwise move the function towards convergence. It should be noted that constraint conditions, such as a tuning range, can be imposed during the optimization process in 608 or at a later stage in the optimization process. Step 620 indicates that each iteration is performed for a given test pattern for identified evaluation points (e.g., multiple positions along a slit) selected for optimizing the lithography process. In step 610, the lithography response is predicted. In step 612, the result of step 610 is compared with a desired or ideal lithography response value obtained in step 622. If the termination condition is satisfied in step 614, i.e., the optimization yields a lithography response value that is sufficiently close to the desired value, then in step 618, the final value of the design variable is output. The output step may also include using the final value of the design variable to output other functions, such as outputting a wavefront aberration adjustment map at the pupil plane (or other planes), an optimized source mask, and an optimized design layout, etc. If the termination condition is not satisfied, then in step 616, the value of the design variable is updated using the result of the i-th iteration, and the process returns to step 606.

[0100] Figure 7 FIG. is a block diagram illustrating a computer system 100 that may assist in implementing the methods, processes, or apparatuses disclosed herein. The computer system 100 includes a bus 102 or other communication mechanism for communicating information, and a processor 104 (or processors 104 and 105) coupled to the bus 102 for processing information. The computer system 100 also includes a main memory 106 coupled to the bus 102 for storing information and instructions to be executed by the processor 104, such as random access memory (RAM) or other dynamic storage devices. The main memory 106 may also be used to store transient variables or other intermediate information during the execution of instructions to be executed by the processor 104. The computer system 100 further includes a read-only memory (ROM) 108 or other static storage device coupled to the bus 102 for storing static information and instructions for the processor 104. A memory 110, such as a magnetic disk or optical disk, is provided and the memory 110 is coupled to the bus 102 for storing information and instructions.

[0101] The computer system 100 can be coupled via a bus 102 to a display 112 for displaying information to a computer user, such as a cathode ray tube (CRT), a flat panel display, or a touch panel display. An input device 114 including alphanumeric keys and other keys is coupled to the bus 102 for communicating information and command selections to the processor 104. Another type of user input device is a cursor control 116 for communicating direction information and command selections to the processor 104 and for controlling the movement of a cursor on the display 112, such as a mouse, a trackball, or cursor direction keys. This input device typically has two degrees of freedom in two axes (a first axis (e.g., x) and a second axis (e.g., y)), which allows the device to specify a position in a plane. A touch panel (screen) display can also be used as an input device.

[0102] According to one embodiment, a portion of one or more of the methods described in the present invention can be performed by the computer system 100 in response to one or more sequences of one or more instructions contained in the main memory 106 being executed by the processor 104. Such instructions can be read from another computer-readable medium, such as the memory 110, into the main memory 106. Execution of the instruction sequences contained in the main memory 106 causes the processor 104 to perform the process steps described herein. One or more processors in a multiprocessing configuration can also be used to execute the instruction sequences contained in the main memory 106. In alternative embodiments, hardwired circuitry can be used in place of or in combination with software instructions. Thus, the description herein is not limited to any specific combination of hardware circuitry and software.

[0103] The term "computer-readable medium" as used herein refers to any medium that participates in providing instructions to the processor 104 for execution. The medium can take many forms, including but not limited to non-volatile media, volatile media, and transmission media. Non-volatile media includes, for example, optical or magnetic disks, such as the memory 110. Volatile media includes volatile memory, such as the main memory 106. Transmission media includes coaxial cables, copper wire, and fiber optics, including the wires that make up the bus 102. Transmission media can also take the form of acoustic or light waves, such as acoustic or light waves generated during radio frequency (RF) and infrared (IR) data communications. Common forms of computer-readable media include, for example, floppy disks, flexible disks, hard disks, magnetic tape, any other magnetic medium, CD-ROM, DVD, any other optical medium, punch cards, paper tape, any other physical medium with hole patterns, RAM, PROM, and EPROM, FLASH-EPROM, any other memory chip or cartridge, a carrier wave as described below, or any other medium readable by a computer.

[0104] In carrying one or more sequences of one or more instructions to the processor 104 for execution, various forms of computer-readable media may be involved. For example, the instructions may initially be carried on a disk, a solid-state storage device, and / or other parts of a remote computer (such as a server and / or other computing devices). The remote computer may load the instructions into its dynamic memory and send the instructions via a modem over a telephone line in a wireless communication network (such as the Internet, a cellular communication network, etc.) and / or by other means. A modem and / or other data receiving components local to the computer system 100 may receive data over the telephone line via the wireless communication network and use an infrared transmitter to convert the data into an infrared signal. An infrared detector coupled to the bus 102 may receive the data carried in the infrared signal and place the data on the bus 102. The bus 102 carries the data to the main memory 106, from which the processor 104 retrieves and executes the instructions. The instructions received by the main memory 106 may optionally be stored on the storage device 110 before or after being executed by the processor 104.

[0105] The computer system 100 may also include a communication interface 118 coupled to the bus 102. The communication interface 118 provides a two-way data communication coupling to a network link 120 that is connected to a local area network 122. For example, the communication interface 118 may be an integrated services digital network (ISDN) card or a modem to provide a data communication connection to a corresponding type of telephone line. As another example, the communication interface 118 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 118 sends and receives electrical, electromagnetic, or optical signals that carry digital data streams representing various types of information.

[0106] The network link 120 typically provides data communication to other data devices via one or more networks. For example, the network link 120 may provide a connection via the local area network 122 to a main computer 124 or to a data device operated by an Internet service provider (ISP) 126. The ISP 126 in turn provides data communication services via the global packet data communication network (now commonly referred to as the “Internet”) 128. Both the local area network 122 and the Internet 128 use electrical, electromagnetic, or optical signals that carry digital data streams. Signals via the various networks and signals on the network link 120 and via the communication interface 118 that carry digital data to and from the computer system 100 are exemplary forms of carrier waves for conveying information.

[0107] The computer system 100 can send information and receive data, including code, via a network, network link 120, and communication interface 118. In an Internet example, server 130 may transfer requested code for an application via Internet 128, ISP 126, local area network 122, and communication interface 118. For example, one such downloaded application may provide all or part of the methods described herein. The received code may be executed by processor 104 when it is received and / or stored in storage device 110 or other non-volatile memory for later execution. Thus, the computer system 100 can obtain application code in the form of a carrier wave.

[0108] Figure 8 Schematically depicts an exemplary lithographic projection apparatus that can be utilized in conjunction with the techniques described herein. The apparatus includes:

[0109] - an illumination system IL for conditioning a radiation beam B. In this particular case, the illumination system also includes a radiation source SO;

[0110] - a first stage (e.g., a patterning device stage) MT having a patterning device holder for holding a patterning device MA (e.g., a mask) and connected to a first positioner for accurately positioning the patterning device relative to the device PS;

[0111] - a second stage (substrate stage) WT having a substrate holder for holding a substrate W (e.g., a silicon wafer coated with resist) and connected to a second positioner for accurately positioning the substrate relative to the device PS; and

[0112] - a projection system (“lens”) PS (e.g., a refractive, reflective, or catadioptric optical system) for imaging an irradiated portion of the patterning device MA onto a target portion C (e.g., including one or more dies) of the substrate W.

[0113] As depicted in the present invention, the apparatus is of the transmissive type (i.e., having a transmissive patterning device). However, in general, it may also be of the reflective type, for example (having a reflective patterning device). The apparatus may use different kinds of patterning devices relative to a classical mask; examples include programmable mirror arrays or LCD matrices.

[0114] A source SO (e.g., a mercury lamp or an excimer laser, a laser-produced plasma (LPP) free electron laser or other EUV source) generates a radiation beam. For example, the beam is fed directly or after having traversed an adjusting member such as a beam expander Ex into an illumination system (illuminator) IL. The illuminator IL may include an adjusting member AD for setting an outer radial extent and / or an inner radial extent of the intensity distribution in the beam (commonly referred to as σ outer and σ inner respectively). Additionally, the illuminator IL will typically include various other components such as an integrator IN and a condenser CO. Thus, the beam B incident on the patterning device MA has a desired uniformity and intensity distribution in its cross-section.

[0115] Regarding Figure 8 It should be noted that the source SO may be within the housing of the lithographic projection apparatus (which is typically the case when the source SO is, for example, a mercury lamp), but it may also be remote from the lithographic projection apparatus and the radiation beam generated by it is directed into the apparatus (e.g., by means of suitable directing mirrors); the latter case is often the case when the source SO is an excimer laser (e.g., based on KrF, ArF or F2 laser action).

[0116] The beam B then intercepts the patterning device MA held on the patterning device table MT. In the case of having traversed the patterning device MA, the beam B passes through a lens PS which focuses the beam B onto a target portion C of the substrate W. By means of a second positioning member (and an interferometric member IF), the substrate table WT can be accurately moved, for example, so as to bring different target portions C into the path of the beam B. Similarly, a first positioning member can be used to accurately position the patterning device MA relative to the path of the beam B, for example, after having mechanically retrieved the patterning device MA from a patterning device library or during a scan. Typically, the movement of the tables MT, WT will be achieved by means of long-stroke modules (coarse positioning) and short-stroke modules (fine positioning) not explicitly depicted in Figure 8 However, in the case of a stepper (relative to a step-and-scan tool), the patterning device table MT may be connected only to a short-stroke actuator or may be fixed.

[0117] The tool depicted can be used in two different modes:

[0118] - In the step mode, the patterning device table MT is held substantially stationary and the entire patterning device image is projected once (i.e., a single "flash") onto the target portion C. Then the substrate table WT is displaced in the x-direction and / or the y-direction such that different target portions C can be irradiated by the beam PB;

[0119] - In the scanning mode, substantially the same situation applies, but the given target portion C is not exposed in a single "flash". Instead, the patterning device table MT is movable at a speed v in a given direction (the so-called "scanning direction", e.g., the y-direction) such that the projection beam B scans across the patterning device image; simultaneously, the substrate table WT is moved simultaneously at a speed V = Mv in the same or opposite direction, where M is the magnification of the lens PL (usually M = 1 / 4 or = 1 / 5). In this way, a relatively large target portion C can be exposed without sacrificing resolution.

[0120] Figure 9 Schematically depicts another exemplary lithographic projection apparatus 1000 that can be utilized in conjunction with the techniques described herein.

[0121] The lithographic projection apparatus 1000 includes:

[0122] - A source collector module SO;

[0123] - An illumination system (illuminator) IL configured to condition a radiation beam B (e.g., EUV radiation);

[0124] - A support structure (e.g., a patterning device table) MT configured to support a patterning device (e.g., a mask or reticle) MA and connected to a first positioner PM configured to accurately position the patterning device;

[0125] - A substrate table (e.g., a wafer table) WT configured to hold a substrate (e.g., a wafer coated with resist) W and connected to a second positioner PW configured to accurately position the substrate; and

[0126] - A projection system (e.g., a reflective projection system) PS configured to project the pattern imparted to the radiation beam B by the patterning device MA onto a target portion C (e.g., including one or more dies) of the substrate W.

[0127] As Figure 9 depicted, the apparatus 1000 is of the reflective type (e.g., using a reflective patterning device). It should be noted that since most materials are absorptive in the EUV wavelength range, the patterning device can have a multilayer reflector including, for example, multiple stacks of molybdenum and silicon. In one example, the multi-stack reflector has 40 layer pairs of molybdenum and silicon, where the thickness of each layer is a quarter wavelength. X-ray lithography can be utilized to generate smaller wavelengths. Since most materials are absorptive at EUV and X-ray wavelengths, patterned absorptive material thin segments (e.g., TaN absorbers on top of the multilayer reflector) in the patterning device configuration define where features will be printed (positive resist) or not printed (negative resist).

[0128] The illuminator IL receives an extreme ultraviolet radiation beam from the source collector module SO. Methods for generating EUV radiation include, but are not necessarily limited to, converting a material into a plasma state having at least one element (such as xenon, lithium, or tin) using one or more emission spectral lines in the EUV range. In one such method, often referred to as laser-produced plasma "LPP", a plasma can be generated by irradiating a fuel (such as a droplet, stream, or cluster of material having the spectral line-emitting element) with a laser beam. The source collector module SO can be a component of an EUV radiation system that includes a laser ( Figure 9 not shown in the figure) for providing the laser beam that excites the fuel. The resulting plasma emits output radiation, such as EUV radiation, which is collected using a radiation collector placed in the source collector module. For example, when a CO2 laser is used to provide the laser beam for fuel excitation, the laser and the source collector module can be separate entities.

[0129] In this case, the laser is not considered to form a component of the lithographic apparatus, and the radiation beam is transferred from the laser to the source collector module by means of a beam delivery system that includes, for example, appropriate guiding mirrors and / or beam expanders. In other cases, for example, when the source is a discharge-produced plasma EUV generator (often referred to as a DPP source), the source can be an integral part of the source collector module. In an embodiment, a DUV laser source can be used.

[0130] The illuminator IL can include an adjuster for adjusting the angular intensity distribution of the radiation beam. Generally, at least the outer radial range and / or the inner radial range (commonly referred to as σ outer and σ inner, respectively) of the intensity distribution in the pupil plane of the adjustable illuminator can be adjusted. Additionally, the illuminator IL can include various other components, such as faceted field mirror devices and faceted pupil mirror devices. The illuminator can be used to adjust the radiation beam to have a desired uniformity and intensity distribution in its cross-section.

[0131] A radiation beam B is incident on a patterning device (e.g., a mask) MA which is held on a support structure (e.g., a patterning device table) MT, and is patterned by the patterning device. After being reflected by the patterning device (e.g., a 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. By means of a second positioner PW and a position sensor PS2 (e.g., an interferometric device, a linear encoder or a capacitive sensor), the substrate table WT can be accurately moved, e.g., so as to position different target portions C in the path of the radiation beam B. Similarly, a first positioner PM and another position sensor PS1 can be used to accurately position the patterning device (e.g., a mask) MA relative to the path of the radiation beam B. Patterning device alignment marks M1, M2 and substrate alignment marks P1, P2 can be used to align the patterning device (e.g., a mask) MA and the substrate W.

[0132] The depicted apparatus 1000 can be used in at least one of the following modes:

[0133] In the step mode, while projecting the entire pattern to be imparted to the radiation beam onto the target portion C at once, the support structure (e.g., the patterning device table) MT and the substrate table WT are kept substantially stationary (i.e., single static exposure). Subsequently, the substrate table WT is shifted in the X and / or Y direction so that different target portions C can be exposed.

[0134] In the scan mode, while projecting the pattern to be imparted to the radiation beam onto the target portion C, the support structure (e.g., the patterning device table) MT and the substrate table WT are scanned synchronously (i.e., single dynamic exposure). The speed and direction of the substrate table WT relative to the support structure (e.g., the patterning device table) MT can be determined by the magnification (reduction ratio) and image inversion characteristics of the projection system PS.

[0135] In another mode, while projecting the pattern to be imparted to the radiation beam onto the target portion C, the support structure (e.g., the patterning device table) MT is kept substantially stationary so as to hold a programmable patterning device, and the substrate table WT is moved or scanned. In this mode, a pulsed radiation source is typically used, and the programmable patterning device is updated as needed after each movement of the substrate table WT or between successive radiation pulses during the scan. This operating mode can be readily applied to maskless lithography using a programmable patterning device such as a programmable mirror array of the type mentioned above.

[0136] Figure 10Device 1000 is shown in more detail and includes a source collector module SO, an illumination system IL, and a projection system PS. The source collector module SO is constructed and configured such that a vacuum environment can be maintained within the enclosure structure 220 of the source collector module SO. An EUV radiation-emitting plasma 210 can be formed by a discharge-produced plasma source (and / or other sources described above). EUV radiation can be generated by a gas or vapor (e.g., Xe gas, Li vapor, or Sn vapor), where an extremely hot plasma 210 is generated to emit radiation in the EUV range of the electromagnetic spectrum. For example, the extremely hot plasma 210 is generated by causing a discharge that at least partially ionizes the plasma. For efficient generation of the radiation, a partial pressure of Xe, Li, Sn vapor, or any other suitable gas or vapor may be required, which is, for example, 10 Pa. In an embodiment, an excited tin (Sn) plasma is provided to generate EUV radiation.

[0137] The radiation emitted by the hot plasma 210 is transferred from the source chamber 211 to the collector chamber 212 via an optional gas barrier or contaminant trap 230 located in or behind an opening in the source chamber 211 (which is also referred to as a contaminant barrier or foil trap in some cases). The contaminant trap 230 may include a channel structure. The contamination trap 230 may also include a gas barrier, or a combination of a gas barrier and a channel structure. As is known in the art, the contaminant trap or contaminant barrier 230 further indicated herein includes at least a channel structure.

[0138] The collector chamber 211 may include a radiation collector CO that may be a so-called grazing incidence collector. The radiation collector CO has an upstream radiation collector side 251 and a downstream radiation collector side 252. The radiation traversing the collector CO can be reflected from the grating spectral filter 240 and focused onto a virtual source point IF along the optical axis indicated by the dotted line "O". The virtual source point IF is generally referred to as an intermediate focus, and the source collector module is configured such that the intermediate focus IF is located at or near the opening 221 in the enclosure structure 220. The virtual source point IF is an image of the radiation-emitting plasma 210.

[0139] Subsequently, the radiation traverses the illumination system IL, which may include a faceted field mirror device 22 and a faceted pupil mirror device 24, which are configured to provide a desired angular distribution of the radiation beam 21 at the patterning device MA, and a desired uniformity of the radiation intensity at the patterning device MA. After reflection of the radiation beam 21 at the patterning device MA held by the support structure MT, a patterned beam 26 is formed, and the patterned beam 26 is imaged onto a substrate W held by a substrate table WT by the projection system PS via reflection elements 28, 30.

[0140] More elements than those shown may generally be present in the illumination optics unit IL and the projection system PS. Depending on the type of lithographic apparatus, a grating spectral filter 240 may optionally be present. Additionally, there may be more mirrors than those shown in the figures. For example, in the projection system PS, there may be 1 to 10 or more additional reflective elements than the Figure 10 reflective elements shown.

[0141] As Figure 10 further illustrated, the collector optics CO is depicted as a nested collector having grazing-incidence reflectors 253, 254, and 255, merely as an example of a collector (or collector mirror). The grazing-incidence reflectors 253, 254, and 255 are placed axially symmetrically about the optical axis O, and a collector optics CO of this type may be used in combination with a discharge-produced plasma source, often referred to as a DPP source.

[0142] Alternatively, the source collector module SO may be a component of an LPP radiation system as shown in Figure 11 . A laser LA is arranged to deposit laser energy into a fuel such as xenon (Xe), tin (Sn), or lithium (Li), thereby generating a highly ionized plasma 210 having an electron temperature of several tens of electron volts. The energy radiation generated during the de-excitation and recombination of these ions is emitted from the plasma, collected by a near-normal-incidence collector optics CO, and focused onto an opening 221 in an enclosure structure 220.

[0143] The embodiments may be further described in connection with the following aspects:

[0144] 1. A method for source mask optimization using a lithographic projection apparatus, the lithographic projection apparatus including an illumination source and projection optics configured to image a mask design layout onto a substrate, the method comprising:

[0145] Using a hardware computer system, determining a multivariable source mask optimization function using a plurality of tunable design variables for the illumination source, the projection optics, and the mask design layout, the multivariable source mask optimization function describing imaging variations over a plurality of positions across the mask design layout; and

[0146] Using the hardware computer system to iteratively adjust the plurality of tunable design variables in the multivariable source mask optimization function until a termination condition is met.

[0147] 2. The method according to aspect 1, wherein the multivariable source mask optimization function describes imaging variations over different positions in an exposure slit, the different positions in the exposure slit corresponding to different positions in the mask design layout.

[0148] 3. The method according to aspect 2, wherein the multi-variable source mask optimization function includes respective multi-variable source mask optimization functions corresponding to different positions in the exposure slit, the different positions in the exposure slit corresponding to different positions of the mask design layout, and wherein the different positions of the mask design layout are stripes.

[0149] 4. The method according to aspect 2, wherein the multi-variable source mask optimization function describes imaging variations across different positions corresponding to stripes of the mask design layout in the exposure slit, the stripes including at least the center of the slit and another position along the slit.

[0150] 5. The method according to any one of aspects 2 to 4, wherein the imaging variations are caused by variations in the exposure slit across different positions in one or more corresponding stripes of the mask design layout with or without assist features.

[0151] 6. The method according to any one of aspects 2 to 4, wherein the imaging variations are caused by through-slit pupil variations across different positions in the one or more stripes of the mask design layout.

[0152] 7. The method according to aspect 6, wherein the through-slit pupil variations are caused by pupil rotation and / or blinking light spots in the pupil at different positions in the slit of the mask design layout.

[0153] 8. The method according to any one of aspects 1 to 7, wherein the termination condition is associated with the image quality of the mask design layout on the substrate.

[0154] 9. The method according to any one of aspects 1 to 7, wherein the termination condition is associated with the pupil shape.

[0155] 10. The method according to any one of aspects 1 to 9, wherein the design layout includes one or more of the following: the entire design layout, a fragment, or one or more critical features of the design layout.

[0156] 11. The method according to any one of aspects 1 to 10, wherein one or more of the tunable design variables for the illumination source, the projection optics, and / or the mask design layout are associated with extreme ultraviolet lithography.

[0157] 12. The method according to any one of aspects 1 to 11, wherein the termination condition includes one or more of the following: maximization of the multi-variable source mask optimization function, minimization of the multi-variable source mask optimization function, or a value that breaks through a threshold of the multi-variable source mask optimization function.

[0158] 13. The method according to any one of aspects 1 to 11, wherein the termination condition includes one or more of a predetermined number of iterations or a predetermined calculation time.

[0159] 14. The method according to any one of aspects 1 to 13, wherein the termination condition is associated with values for defining a process window for extreme ultraviolet lithography for the tunable design variables for the illumination source, the projection optics, and the mask design layout.

[0160] 15. The method according to any one of aspects 1 to 14, wherein the termination condition is associated with values for the pupil that can be used for extreme ultraviolet lithography for the tunable design variables for the illumination source, the projection optics, and the mask design layout over a plurality of positions of the mask design layout.

[0161] 16. The method according to any one of aspects 1 to 15, wherein, in the absence of constraint conditions that limit the range of possible values of the tunable design variables, iterative adjustment of the plurality of tunable design variables in the multivariable source mask optimization function is performed until the termination condition is satisfied.

[0162] 17. The method according to any one of aspects 1 to 15, wherein, in the presence of at least one constraint condition that limits the range of possible values of at least one tunable design variable, iterative adjustment of the plurality of tunable design variables in the multivariable source mask optimization function is performed until the termination condition is satisfied.

[0163] 18. The method according to aspect 17, wherein the at least one constraint condition is associated with one or more of physical characteristics of the lithographic projection apparatus, the dependence of one design variable on one or more other design variables, or mask manufacturability.

[0164] 19. The method according to aspect 17, wherein iteratively adjusting the at least one tunable design variable in the multivariable source mask optimization function includes repeatedly changing the value of the at least one tunable design variable within the limits of the possible values until the termination condition is satisfied.

[0165] 20. The method according to any one of aspects 1 to 19, wherein the multivariable source mask optimization function is associated with high numerical aperture source mask optimization.

[0166] 21. The method according to any one of aspects 1 to 20, wherein determining the multivariable source mask optimization function using the plurality of tunable design variables for the illumination source, the projection optics, and the mask design layout includes: identifying a subset of the plurality of tunable design variables for the multivariable source mask optimization function based on the termination condition, the subset of the plurality of tunable design variables having a relatively greater impact on the termination condition when adjusted compared to other tunable design variables among the tunable design variables; and wherein,

[0167] Iteratively adjusting the plurality of tunable design variables in the multivariable source mask optimization function includes: assigning starting values to each of the tunable design variables included in the multivariable source mask optimization function and adjusting the starting values until the termination condition is satisfied.

[0168] 22. A computer program product comprising a computer non-transitory readable medium having instructions recorded thereon, the instructions, when executed by a computer, implementing the method according to any one of aspects 1 to 21.

[0169] The concepts disclosed herein can simulate or be mathematically modeled for any general imaging system for imaging sub-wavelength features and can be used in particular by emerging imaging technologies capable of generating increasingly shorter wavelengths. Emerging technologies already in use include extreme ultraviolet (EUV), DUV lithography capable of generating a wavelength of 193 nm by using an ArF laser and even capable of generating a wavelength of 157 nm by using a fluorine laser. In addition, EUV lithography can generate wavelengths in the range of 5 to 20 nm by using a synchrotron or by using high-energy electrons to impinge on a material (solid or plasma) in order to generate photons in this range.

[0170] Although the concepts disclosed herein can be used for imaging on a substrate such as a silicon wafer, it should be understood that the disclosed concepts can be used with any type of lithographic imaging system, for example, a lithographic imaging system for imaging on a substrate different from a silicon wafer.

[0171] The above description is intended to be illustrative and not restrictive. Thus, it will be apparent to those skilled in the art that modifications can be made as described without departing from the scope of the claims set forth below.

Claims

1. A method for source mask optimization using a lithographic projection apparatus, the lithographic projection apparatus including an illumination source and a projection optical device configured to image a mask design layout onto a substrate, the method comprising: Using a hardware computer system, a multivariable source mask optimization function is determined using a plurality of tunable design variables for the illumination source, the projection optics, and the mask design layout, the multivariable source mask optimization function describing imaging variations across the slots and multiple positions of different slots of the mask design layout; And using the hardware computer system to iteratively adjust the plurality of tunable design variables in the multivariable source mask optimization function until a termination condition is met.

2. The method according to claim 1, wherein, The multivariable source mask optimization function describes imaging variations across different positions in an exposure slot, the different positions in the exposure slot corresponding to different positions of the mask design layout.

3. The method according to claim 2, wherein, The multivariable source mask optimization function includes respective multivariable source mask optimization functions corresponding to different positions in the exposure slot, the different positions in the exposure slot corresponding to different positions of the mask design layout, and wherein the different positions of the mask design layout are stripes.

4. The method according to claim 2, wherein, The multivariable source mask optimization function describes imaging variations across different positions in the exposure slot corresponding to the stripes of the mask design layout, the stripes including mask stripes corresponding to the center of the slot and another position along the slot.

5. The method according to claim 2, wherein, The imaging variations are caused by variations in the exposure slot across different positions in one or more corresponding stripes of the mask design layout with or without assist features.

6. The method according to claim 2, wherein, The imaging variations are caused by slit pupil variations across different positions in one or more stripes of the mask design layout, and / or wherein the slit pupil variations are caused by pupil rotation and / or blinking light spots in the pupil at different positions in the slit of the mask design layout.

7. The method according to claim 1, wherein, The termination condition is associated with the image quality of the mask design layout on the substrate.

8. The method according to claim 1, wherein, The termination condition is associated with the pupil shape.

9. The method according to claim 1, wherein, The mask design layout includes one or more of the following: the entire design layout, a fragment, or one or more critical features of the mask design layout.

10. The method according to claim 1, wherein, One or more of the tunable design variables for the illumination source, the projection optics, and / or the mask design layout are associated with extreme ultraviolet lithography.

11. The method according to claim 1, wherein, The termination condition includes one or more of the following: maximization of the multivariable source mask optimization function, minimization of the multivariable source mask optimization function, or a value that breaks through a threshold of the multivariable source mask optimization function.

12. The method according to claim 1, wherein, The termination condition includes one or more of a predetermined number of iterations or a predetermined calculation time.

13. The method according to claim 1, wherein, The termination condition is associated with a value that defines a process window for extreme ultraviolet lithography for the tunable design variables for the illumination source, the projection optics, and the mask design layout.

14. The method according to claim 1, wherein, The termination condition is associated with a value that defines a pupil that can be used for extreme ultraviolet lithography across multiple positions of the mask design layout for the tunable design variables for the illumination source, the projection optics, and the mask design layout.

15. The method according to claim 1, wherein, In the absence of constraints that limit the range of possible values of the tunable design variables, perform iterative adjustment of the multiple tunable design variables in the multivariable source mask optimization function until a termination condition is satisfied.

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