System and method for predicting post-etch stochastic variations

Abstract

Described herein is a method for predicting post-etch random variations when transferring a target layout onto a substrate using a lithographic apparatus. The method includes predicting a random change in transferring a target layout onto a substrate by predicting a random etch bias; and combining the random etch bias with post-lithographic process random variations to predict the random variations in the etch process. The method includes determining performance in transferring the target layout to the substrate based on the random change.

Description

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority to U.S. Application No. 63 / 388,099 filed on July 11, 2022 and U.S. Application No. 63 / 401,391 filed on August 26, 2022, which are incorporated herein by reference in their entirety. Technical Field

[0002] The description herein relates to lithographic apparatus and processes, and more particularly, to optimizing lithographic processes for improved process yield and throughput. Background Art

[0003] A lithographic apparatus is a machine that applies a desired pattern onto a target portion of a substrate. A lithographic apparatus may be used, for example, in the manufacture of integrated circuits (ICs). For example, an IC chip in a smartphone may be as small as a human thumbnail and may include more than 2 billion transistors. Manufacturing ICs is a complex and time-consuming process, where circuit components are in different layers and include hundreds of individual steps. Even an error in one step has the potential to cause problems with the final IC and may cause device failure. The presence of defects may affect high process yields and high wafer throughput.

[0004] A metrology process is used at various steps during the patterning process to monitor and / or control the process. For example, a metrology process is used to measure one or more characteristics of the substrate, such as the relative position (e.g., registration, overlap, alignment, etc.) or size (e.g., line width, critical dimension (CD), thickness, etc.) of features formed on the substrate during the patterning process or random variations, so that, for example, the performance of the patterning process can be determined from the one or more characteristics. If one or more characteristics are unacceptable (e.g., outside a predetermined range of (multiple) characteristics), one or more variables of the patterning process can be designed or changed, such as based on the measured values ​​of the one or more characteristics, so that the substrate manufactured by the patterning process has (multiple) acceptable characteristics.

[0005] Some of the defects are caused by random variations at both the lithography and etching steps, for example, local CD uniformity (LCDU), line edge roughness (LER), or local edge placement error (LEPE). In some embodiments, randomness is an event with random variation. These variations, known as random effects, sometimes cause unwanted defects and pattern roughness in the chip. Both may affect the performance of the chip or even cause device failure. Random variations usually dominate the edge placement error (EPE) budget at advanced technology nodes. Randomly induced defects have become a large part of the yield Pareto. In order to minimize the impact of random variations and achieve high process yield, an integrated solution that measures random variations, models random variations, and predicts random induced defects at the full chip level may be preferred.

[0006] Among various randomly induced defects, inter-layer random defects have attracted the attention of the industry because they may be the final and compound effect of EPE between two subsequent layers (e.g., metal and contact layers) or between two process steps (e.g., lithography and etching). In the extreme ultraviolet (EUV) era, such defects may have become the main source of chip failure. The industry is working hard to find a way to detect, characterize and prevent such defects, and a solution is needed to predict such defects at the full chip level before cutting masks, exposing wafers or etching wafers. In order to provide such a solution, not only post-lithography random modeling solutions but also post-etching random modeling solutions are needed. Summary of the invention

[0007] In some embodiments, a non-transitory computer-readable medium having instructions is provided, which, when executed by a computer, causes the computer to perform a method for predicting post-etching random variations when a target layout is transferred to a substrate using a lithography device. The method includes: predicting random variations when the target layout is transferred to the substrate by executing a stochastic model, the stochastic model being configured to predict the random variations in the etching process, wherein the stochastic model is configured to predict the random variations based on random etching deviations and post-lithography process random variations; and determining performance when the target layout is transferred to the substrate based on the random variations.

[0008] In some embodiments, a non-transitory computer-readable medium having instructions is provided, which, when executed by a computer, causes the computer to perform a method for predicting post-etching random variations when transferring a target layout to a substrate using a lithography device. The method includes: obtaining post-lithography random variations associated with printing a target layout on a substrate using a lithography process; predicting a random etching deviation, the random etching deviation indicating a random variation in an etching process of etching a pattern corresponding to the target layout on the substrate, wherein the random etching deviation is determined as a function of at least one of a concentration etching method, a density map, or a smoothing factor; and obtaining the random variation based on the random etching deviation and the post-lithography random variation.

[0009] In some embodiments, a method for predicting post-etching random variations when transferring a target layout to a substrate using a lithography device is provided. The method includes: predicting random variations when transferring the target layout to the substrate by executing a stochastic model, the stochastic model being configured to predict the random variations during the etching process, wherein the stochastic model is configured to predict the random variations based on random etching deviations and post-lithography random variations; and determining performance when transferring the target layout to the substrate based on the random variations.

[0010] In some embodiments, a device for predicting post-etching random variations when a target layout is transferred to a substrate using a lithography device is provided. The device includes a memory and a processor, the memory storing a set of instructions, the processor being configured to execute the set of instructions to cause the device to perform a method, the method predicting random variations when the target layout is transferred to the substrate by executing a stochastic model, the stochastic model being configured to predict the random variations in the etching process, wherein the stochastic model is configured to predict the random variations based on random etching deviations and post-lithography random variations; and determining performance when the target layout is transferred to the substrate based on the random variations. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0012] Figure 1 is a block diagram of various subsystems of a lithography system according to an embodiment.

[0013] Figure 2 is according to an embodiment corresponding to Figure 1 Block diagram of the simulation model of the subsystem in .

[0014] Figure 3 is a block diagram of an exemplary system for predicting post-etch stochastic variations when transferring a target layout onto a substrate consistent with various embodiments.

[0015] Figure 4A Distributions of post-etch profiles consistent with various embodiments are shown.

[0016] Figure 4B An image of a predicted post-etch profile based on post-etch stochastic variation consistent with various embodiments is shown.

[0017] Figure 5 is a flow chart of an exemplary method for predicting post-etch stochastic variations when transferring a target layout onto a substrate consistent with various embodiments.

[0018] Fig. 6A An image showing an overlay of profiles of two layers of a portion of a target layout generated based on post-etch stochastic variations predicted by a stochastic etching model consistent with various embodiments.

[0019] Figure 6B An enlarged view of an area where the profiles of a first feature and a second feature overlap is shown, consistent with various embodiments.

[0020] Figure 6C Pairs of profiles are shown separated by specified distances consistent with various embodiments.

[0021] Figure 7 is a block diagram of an exemplary system for predicting post-etch inter-layer random defects consistent with various embodiments.

[0022] Figure 8 is a flow chart of an exemplary method for predicting post-etch inter-layer random defects consistent with various embodiments.

[0023] Fig. 9 is a block diagram of an exemplary computer system according to an embodiment.

[0024] Fig.10 is a flow chart of another method for predicting post-etch stochastic variations when transferring a target layout onto a substrate consistent with various embodiments.

[0025] Fig.11 are illustrations of resist profiles and etch profiles consistent with various embodiments.

[0026] Embodiments will now be described in detail with reference to the accompanying drawings, which are provided as illustrative examples so that those skilled in the art can practice the embodiments. It is noteworthy that the following figures and examples are not meant to limit the scope to a single embodiment, but other embodiments are possible by exchanging some or all of the elements described or illustrated. As long as it is convenient, the same reference numerals will be used throughout the drawings to represent the same or similar parts. In the case where some elements of these embodiments can be implemented partially or completely using known parts, only those parts of such known parts required for understanding the embodiment will be described, and the detailed description of other parts of such known parts will be omitted so as not to obscure the description of the embodiment. In this specification, embodiments showing a single component should not be considered restrictive; on the contrary, unless otherwise expressly stated herein, the scope is intended to encompass other embodiments including multiple identical components, and vice versa. In addition, unless expressly stated so, the applicant does not intend to attribute any term in the specification or claims to an uncommon or special meaning. In addition, the scope encompasses the current and future known equivalents of the components mentioned herein by way of illustration. DETAILED DESCRIPTION

[0027] A lithographic apparatus is a machine that applies a desired pattern to a target portion of a substrate. This process of transferring the desired pattern to a substrate is called a patterning process. The patterning process may include a patterning step to transfer a pattern from a patterning device (e.g., a mask) to a substrate. A mask is a master template for a given IC design. It is placed in a lithographic apparatus that projects light through a mask. That in turn is used to pattern an image on a wafer (e.g., on a resist layer). In addition, there may then be one or more associated pattern processing steps, such as resist development by a developing apparatus, baking the substrate using a baking tool, etching the pattern onto the substrate using an etching apparatus, and the like.

[0028] Various variations (e.g., variations in the patterning process or lithography equipment) may potentially limit lithography implementations for semiconductor high volume manufacturing (HVM). For example, variations in the number of photons or energy in the illumination source of the lithography equipment, focus or dose variations in the projection optics of the lithography equipment, molecular size or photoacid diffusion variations in the resist chemistry, plasma density distribution and pattern density variations during etching, etc. may lead to stochastic effects, such as significant line edge roughness (LER), edge placement error (EPE), or local critical dimension (CD) variations in small two-dimensional features of the pattern. In some embodiments, the EPE (e.g., the distance between a point in the resist image and the expected location of the point in the target layout or design layout) dominates the error budget. Certain stochastic models can predict stochastic variations, such as variations in CD or stochastic edge placement error (SEPE), based on predicted resist profiles (e.g., the profile of a pattern on a resist after a substrate is exposed to the pattern using a lithography process in a lithography equipment). Such predictions can be used when detecting defects and when optimizing various design variables (e.g., target CD, pupil shape associated with the illumination source, mask deviation, dose value, focus value, mask type, mask deviation, etch deviation, etc.) to achieve the desired output from the lithography process.

[0029] In some embodiments, due to random effects in the etching process, the CD or EPE of a feature of a pattern may change after the etching process, for example, compared to before the etching process. Such a change between two layers of the target layout may cause interlayer defects. That is, interlayer random defects may be the compound effect of the EPE between two subsequent layers (e.g., a metal layer and a contact layer). Such defects have become a major source of chip failure. Conventional technology does not have a way to detect, characterize, predict or prevent such post-etch interlayer or intralayer random defects at the full chip level.

[0030] Disclosed are embodiments for predicting random variations after an etching process and identifying interlayer defects based on the random variations after etching. Embodiments may predict random variations after etching when transferring a target layout to a substrate using a lithography apparatus. Embodiments may include predicting random variations after etching by predicting random etch deviations and combining the random etch deviations with random variations after a lithography process. Embodiments may include determining performance when transferring a target pattern to a substrate based on the random variations.

[0031] Embodiments determine a random etching bias (SEB) that may be a result of random effects induced during the etching process. In some embodiments, the random etching bias may be modeled as a function of several etching process related parameters (e.g., concentration etching method (CEM) parameters, pattern density map, or smoothing factor). In some embodiments, the random etching bias indicates a random variation (σSEPE-E ) and the random variation after the lithography process (σ SEPE-L ). The random etch bias can then be compared to the post-lithography random variation (σ SEPE-L ) combination to determine the random variation after etching (σ SEPE-E In some embodiments, the post-etch random variation is a variance value (σ) indicating the probability of a change in the predicted profile due to the random effects of the etching process. 2 ). Post-etch random variation can be characterized (e.g., in the form of random variation bands) based on the variance and position of the average profile of the feature. The random variation bands of variation probability can represent the possible position of the profile predicted after the etching process relative to the average profile or nominal profile. For example, the random variation band can indicate the possible position of the profile anywhere between ±3σ distance from the average profile. Such post-etch random variation predictions can be generated for various features of the target layout or for all features of the target layout at full chip scale. Embodiments can also generate an image with a post-etch profile predicted based on post-etch random variation. In some embodiments, embodiments can generate multiple post-etch profiles for a feature, each profile at a different distance from the average profile of the feature.

[0032] Post-etch random variations can be determined for multiple layers of a target layout, and inter-layer defects can be determined by selecting two features of the target layout at specified locations in two different layers, overlapping the profiles of the two features, and determining the failure probability of the defect based on the distance between the profiles. For example, if the distance between the two profiles is less than a threshold distance, a defect can be detected. In some embodiments, the failure probability is the cumulative probability of all combinations of two post-etch profiles where the spacing is less than the threshold distance. By predicting post-etch random variations, various defects (e.g., inter-layer or intra-layer defects) can be predicted, and the patterning process can be optimized accordingly to prevent or minimize defects and improve manufacturing yield. For example, the patterning process can be optimized by adjusting illumination source parameters, projection optical device parameters, mask parameters, resist parameters, or etching process parameters. In addition, by predicting post-etch random variations, embodiments are superior to traditional defect detection techniques that require actual inspection of printed wafers, which not only do not prevent or minimize the occurrence of defects (because the wafers have been printed), but also require obtaining a large amount of measurement data, which is time-consuming and resource-intensive.

[0033] Embodiments are disclosed for determining random variations in an etch profile (referred to as "post-lithography random variations") as a function of the sensitivity of the etch profile (e.g., etch profile) to variations in a resist profile (e.g., resist profile) (referred to as "post-lithography random variations"). In some embodiments, the sensitivity is a local sensitivity of the etch or resist profile. In some embodiments, the sensitivity may correspond to a derivative of the etch profile with respect to the resist profile. The sensitivity may be determined based on a derivative of an etch model (e.g., a machine learning model, a physical or empirical etch model, a physical or empirical etch bias model, etc.) configured to predict the etch profile. The sensitivity may be determined as a function of several parameters that are typically used to calibrate an etch bias model to determine an etch bias, or to calibrate a stochastic lithography model to determine a post-lithography random variation model. For example, the etch bias may be modeled as a function of several etch process related parameters (e.g., CEM parameters, a pattern density map or a smoothing factor (referred to as a "bias term"), a coefficient associated with the bias term, and a constant indicating variations induced by the etch process). The sensitivity can be determined as a function of one or more of the coefficients, the convolution of the resist profile with the kernel (e.g., determined based on some bias terms), and the truncation of the convolution of the resist profile (e.g., determined based on the bias terms or some of the terms used to calibrate the stochastic lithography model), and the correlation length of the resist. After determining the sensitivity, the post-etch random variation can be determined based on the product of the sensitivity and the post-lithography random variation and a constant.

[0034] As a brief introduction, Figure 1 An exemplary lithographic projection apparatus 10A is illustrated.

[0035] Although specific reference may be made herein to the manufacture of ICs, it should be clearly understood that the description herein has many other possible applications. For example, it may be employed in the manufacture of integrated optical systems, guidance and detection patterns for magnetic domain memories, liquid crystal display panels, thin film magnetic heads, etc. Those skilled in the art will appreciate that in the context of such alternative applications, any use of the terms "mask", "wafer" or "die" herein may be considered interchangeable with the more general terms "mask", "substrate" and "target portion", respectively.

[0036] In this document, the terms "radiation" and "beam" are used to encompass all types of electromagnetic radiation, including UV radiation (e.g., having a wavelength of 365 nm, 248 nm, 193 nm, 157 nm or 126 nm) and EUV (extreme ultraviolet radiation, e.g., having a wavelength in the range of 5 nm to 20 nm).

[0037] As used herein, the terms “optimizing” and “optimization” mean adjusting the lithographic projection apparatus so that the result or process of lithography has more desirable characteristics, for example, higher accuracy of projection of the design layout on the substrate, a larger process window, etc.

[0038] Furthermore, the lithographic projection apparatus may be of a type having two or more substrate tables (or two or more patterning device tables). In such a "multi-stage", additional tables may be used in parallel, or preparatory steps may be performed on one or more tables while one or more other tables are being used for exposure. For example, a dual-stage lithographic projection apparatus is described in US 5,969,441, which is incorporated herein by reference.

[0039] The patterning device mentioned above includes or can form a design layout. The design layout can be generated using a CAD (computer-aided design) program, which is generally referred to as EDA (electronic design automation). Most CAD programs follow a set of predetermined design rules to create a functional design layout / patterning device. These rules are set by processing and design constraints. For example, the design rule defines the spatial tolerance between circuit devices (e.g., gates, capacitors, etc.) or interconnects to ensure that the circuit devices or lines do not interact with each other in an undesirable manner. The design rule restrictions are generally referred to as "critical dimensions" (CD). The critical dimension of a circuit can be defined as the minimum width of a line or hole or the minimum spacing between two lines or two holes. Therefore, CD determines the overall size and density of the designed circuit. Of course, one of the goals in integrated circuit fabrication is to faithfully reproduce the original circuit design on a substrate (via a patterning device).

[0040] The term "mask" or "patterning device" as employed herein may be broadly interpreted as referring to a general patterning device that can be used to impart a patterned cross-section to an incident radiation beam that corresponds to the pattern to be produced in a target portion of the substrate; the term "light valve" may also be used in this context. In addition to classical masks (transmissive or reflective; 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 having a viscoelastic control layer and a reflective surface. The basic principle behind such a device is that (for example) addressed areas of the reflective surface reflect incident radiation as diffracted radiation, while unaddressed areas reflect incident radiation as non-diffracted radiation. Using appropriate filters, the non-diffracted radiation can be filtered out from the reflected beam, leaving only the diffracted radiation behind; in this way, the beam becomes patterned according to the addressing pattern of the matrix-addressable surface. Suitable electronic devices can be used to perform the required matrix addressing. More information about such mirror arrays can be gleaned, for example, from U.S. Patents Nos. 5,296,891 and 5,523,193, which are incorporated herein by reference. - A programmable LCD array. An example of such a configuration is given in US Pat. No. 5,229,872, which is incorporated herein by reference.

[0041] The main components are a radiation source 12A, which may be a deep ultraviolet excimer laser source or other types of sources including an extreme ultraviolet (EUV) source (as discussed above, the lithographic projection apparatus itself need not have a radiation source), illumination optics that define a partial coherence (denoted as sigma), and which may include: optics 14A, 16Aa, and 16Ab that shape the radiation from source 12A; a patterning device 18A; and transmission optics 16Ac that projects an image of the patterning device pattern onto a substrate plane 22A. An adjustable filter or aperture 20A at a pupil plane of the projection optics may limit the range of beam angles impinging on the substrate plane 22A, with the maximum possible angle defining the numerical aperture NA of the projection optics = sin(θ max ).

[0042] In the optimization process of the system, the quality factor of the system can be expressed as a cost function. The optimization process is reduced to the process of finding a set of parameters (design variables) of the system that minimizes the cost function. Depending on the goal of the optimization, the cost function can have any suitable form. For example, the cost function can be the weighted root mean square (RMS) of the deviation of certain characteristics (evaluation points) of the system from the expected values ​​(e.g., ideal values) of these characteristics; the cost function can also be the maximum value (i.e., the worst deviation) of these deviations. The term "evaluation point" in this article should be interpreted broadly to include any characteristics of the system. Due to the practicality of the implementation scheme of the system, the design variables of the system can be limited to a limited range or be interdependent. In the case of a lithographic projection device, the constraints are usually associated with the physical properties and characteristics of the hardware (e.g., the tunable range or the patterning device manufacturability design rules), and the evaluation points can include physical points on the resist image on the substrate as well as non-physical characteristics (e.g., dose and focus).

[0043] In a lithographic projection apparatus, a source provides illumination (i.e., light); the projection optics guides and shapes the illumination via a patterning device, and guides and shapes the illumination onto a substrate. The term "projection optics" is broadly defined here to include any optical component that can modify the wavefront of a radiation beam. For example, the projection optics may include at least some of components 14A, 16Aa, 16Ab, and 16Ac. An aerial image (AI) is a distribution of radiation intensity at the substrate level. A resist layer on the substrate is exposed, and the aerial image is transferred to the resist layer as a potential "resist image" (RI) therein. A resist image (RI) may be defined as a spatial distribution of the solubility of the resist in the resist layer. A resist model may be used to calculate a resist image based on an aerial image, an example of which may be found in commonly assigned U.S. Pat. No. 8,200,468, the disclosure of which is hereby incorporated by reference in its entirety. The resist model is only related to the properties of the resist layer (e.g., the effects of chemical processes occurring during exposure, PEB, and development). The optical properties of a lithographic projection apparatus (e.g., properties of the source, patterning device, and projection optics) determine the aerial image. Since the patterning device used in a lithographic projection apparatus can be varied, it may be desirable to separate the optical properties of the patterning device from the optical properties of the rest of the lithographic projection apparatus, including at least the source and projection optics.

[0044] exist Figure 2An exemplary flow chart for simulating lithography in a lithographic projection apparatus is illustrated in FIG. As will be appreciated, the models may represent different patterning processes and need not include all of the models described below. The source model 31 represents the optical properties of the source (including the radiation intensity distribution or phase distribution). The projection optics model 32 represents the optical properties of the projection optics (including the changes in the radiation intensity distribution or phase distribution caused by the projection optics). The patterning device / design layout model 35 represents the optical properties of the design layout (e.g., a device design layout corresponding to features of an integrated circuit, memory, electronic device, etc.) (including the changes in the radiation intensity distribution or phase distribution caused by a given design layout), which is a representation of the arrangement of features on or formed by the patterning device. An aerial image 36 may be simulated based on the source model 31, the projection optics model 32, and the design layout model 35. A resist image 38 may be simulated from the aerial image 36 using a resist model 37. In some embodiments, the resist image 38 may be used as an input to a post-pattern transfer process model 39. The post-pattern transfer process model 39 defines the performance of one or more post-resist development processes (e.g., etching, developing, etc.). For example, the post-pattern transfer process model 39 may be an etching model 39 that can predict an etching image using the resist image 38. The etching image may represent the profile etched on the substrate after the etching process. Simulation of lithography may, for example, predict the profile and CD in the resist image.

[0045] More specifically, it is noted that the source model 31 can represent the optical properties of the source, including but not limited to numerical aperture settings, NA-sigma (σ) settings, and any specific illumination source shape (e.g., off-axis radiation sources, such as annular, quadrupole, and dipole, etc.). The projection optics model 32 can represent the optical properties of the projection optics, including aberrations, distortions, refractive index, physical size, physical dimensions, etc. The design layout model 35 can also represent the physical properties of the physical patterning device, as described, for example, in U.S. Pat. No. 7,587,704, which is incorporated by reference in its entirety. The purpose of the simulation is to accurately predict, for example, edge placement, aerial image intensity slope, and CD, which can then be compared to the expected design. The expected design is typically defined as a pre-optical proximity correction (OPC) design layout that can be provided in a standardized digital file format (e.g., GDSII or OASIS or other file format).

[0046] Thus, the model formula describes most, if not all, of the known physical and chemical properties of the overall process, and each of the model parameters corresponds to a different physical or chemical effect in an expected manner. Thus, the model formula sets an upper limit on how well the model can be used to simulate the overall manufacturing process.

[0047] In an example, computational analysis of a lithography or etching process employs a predictive model (e.g., as described above with respect to Figure 2 As discussed above), the predictive model, when correctly calibrated, can produce accurate predictions of dimensions based on the lithography or etching process. The model of the lithography or etching process is usually calibrated based on empirical measurements. The calibration may include: running a test wafer with different process parameters to measure the resulting critical dimensions after the lithography process; and calibrating the model to fit the measured results. In practice, fast and accurate models are used to improve device performance or yield, enhance process windows, or increase design options. It will be appreciated by those skilled in the art that the methods described herein are not limited to specific models of lithography. In order to calibrate the desired model, images can be obtained after any semiconductor fabrication step. For example, aerial images, resist images, etching images, images after chemical mechanical polishing, or other images related to the process of the patterning process.

[0048] In computational lithography models, the CD meter measured by CD-SEM (scanning electron microscope) is usually used as input data to calibrate the model. The goal of lithography modeling is to predict an accurate resist profile for each site on the substrate. Similarly, the goal of etching modeling is to predict an accurate etching profile for each site on the substrate. In some embodiments, computational analysis of the etching process employs a calibrated prediction model that can predict the size of the etched structure caused by the etching process. For example, an etching model associated with the etching process can be calibrated based on empirical measurements. The calibration process can include: patterning a test wafer with different process parameters, thereby measuring the CD of the pattern on the test wafer after the etching process; and calibrating the etching model based on the measured CD. In practice, a fast and accurate model can be used to improve the performance of the patterning equipment, the patterning yield, the process window of the patterning process, or to increase design options related to, for example, determining the mask pattern.

[0049] The following paragraphs describe the predictions for the use of lithography equipment (e.g. Figure 1 Systems and methods for post-etch random variations when transferring a target layout to a substrate using a device (e.g., a 3D image processing device). Figure 3 is a block diagram of an exemplary system 300 for predicting post-etch stochastic variations when transferring a target layout onto a substrate, consistent with various embodiments. Figure 5 is a flow chart of an exemplary method 500 for predicting post-etch stochastic variations when transferring a target layout onto a substrate, consistent with various embodiments.

[0050] At process P505, the random lithography model 325 obtains the post-lithography random variation 326 (eg, σ SEPE-L). Post-lithography random variation 326 indicates the variance of the profile of the features of the target layout in the resist layer of the substrate after the lithography process of printing the target layout is completed (e.g., the variance from the average profile predicted by the resist model). In some embodiments, the variation may be due to random effects when printing the target layout. In some embodiments, post-lithography random variation 326 (σ SEPE-L ) can be calculated from σ-sigma (e.g., standard deviation) or from which the variance of σ can be obtained (σ 2 ). The stochastic lithography model 325 can determine a post-lithography random variation band based on the variance, which represents the probability of the location of the resist profile (e.g., the profile of a feature of a target layout in the resist of the substrate) relative to the average profile or nominal profile after the lithography process. For example, the post-lithography random variation band can indicate the probability of the profile changing at a distance between ±3σ from the average profile. The location or position of the average profile on the resist can be determined based on the EPE of the average profile (e.g., the distance between the average profile and the corresponding profile in the target layout), which can be obtained from a simulation of the lithography process (e.g., Figure 2 obtained through the simulation process).

[0051] The post-lithography random variation 326 may be the result of random effects. In some embodiments, these random effects may be modeled or simulated using various parameters 305 associated with the lithography process or lithography equipment. For example, some of the parameters may include optical sensitivity parameters 305, such as image log slope (ILS), optical image slope, or contrast (e.g., optical lmax and lmin). In another example, the parameters 305 may include photon and photoacid kinetic parameters, such as PK and PKI representing the 2D and 3D distribution of photons on the substrate, respectively. In another example, the parameters 305 may include resist chemistry parameters.

[0052] In some embodiments, the stochastic lithography model 325 can be implemented as a predictive model to predict post-lithography random variation 326. The stochastic lithography model 325 can be configured (e.g., calibrated with empirical data) to predict post-lithography random variation 326. For example, the calibration process can include: patterning a test substrate with different process parameters; measuring the random variation of CD or EPE of the pattern on the test substrate after the lithography process; and calibrating the stochastic lithography model to fit the measured CD or EPE and the values ​​of the parameters 305. Once calibrated, the stochastic lithography model 325 can be used to predict the post-lithography random variation 326 (σ ) of any part or feature in a given target layout for a given set of parameters 305. SEPE-L ). An exemplary embodiment of calibrating and deploying the calibrated model to predict post-lithography random variations 326 is described below.

[0053] As described above, the post-lithography random variation 326 may be determined as a function of the various parameters 305. That is, the stochastic lithography model 325 may be expressed as: σ sepe-l =f(ILS, Slope, CTMX, CTMN, PK, PKI, Ap, Bp, Am, Bn)…Equation (1) Among them, σ sepe-l is the post-lithography random variation 326, such as the parameter PK (photon dynamics) 305 is the photon 2D distribution on the substrate; PKI is the photon 3D distribution on the substrate; ILS is the optical image logarithmic slope; Slope is the optical image slope; CTMX and CTMN are derived from the optical lmax or lmin of the image envelope; Ap / Bp / Am / Bn are various resist cutoffs for base / acid reactions; and a1-a n , b, x, and y are coefficients.

[0054] The stochastic lithography model 325 may be calibrated using empirical data obtained from inspecting a test substrate on which a pattern is printed. For example, σ may be obtained from metrology data associated with the test substrate (eg, obtained by inspecting an SEM image of the test substrate). sepe-l and CD, and an optical proximity correction (OPC) model can be used to determine the value of the image parameter 305, which is used to optimize the design layout or patterning device. Such empirical data can be obtained for a variety of such substrates. Both the empirical data and the OPC model can be input to the stochastic lithography model 325, which determines the coefficients a1-a n The values ​​of a, b, x, and y are determined (eg, using a linear solver). After the coefficients are determined, the stochastic lithography model 325 can be considered calibrated.

[0055] The calibrated stochastic lithography model 325 can be used to determine (e.g., predict) post-lithography random variations 326 when printing any target layout / design layout on any substrate. For example, a simulation engine configured to predict the value of the image parameter 305 (e.g., based on the CD value) can be used to determine the value of the parameter 305 for a sample location on a given design layout / target layout. The parameter value is then input to the stochastic lithography model 325, which can determine the post-lithography random variations 326 (σ ) based on the parameter value and the coefficient. sepe-l ).

[0056] refer to Figure 5 At process P510, the random etching deviation model 330 obtains (eg, predicts) a random etching deviation 331 (eg, SEB). In some embodiments, the random etching deviation 331 indicates a random variation (σ SEPE-E) and the random variation after the lithography process (σ SEPE-L The random etch deviation can be a value that can be combined with the post-lithography random variation of the profile of the feature (e.g., the profile of the feature on the substrate after the lithography process) to obtain the post-etch random variation and the post-etch profile of the feature (e.g., the profile of the feature on the substrate after the etch process).

[0057] The random etch bias model 330 may be implemented as a predictive model configured to predict the random etch bias based on parameters that may be used to model the random effects during the etching process. In some embodiments, the random etch bias may be defined as a plasma etching process related parameter (e.g., a CEM term C of a plasma concentration based approach that describes the effect of material plasma interaction on the profile / CD evolution during the etching process). R (resist area) and C T The CEM parameters may be a function of the etch rate, etch profile, reaction time, CEM describing the material plasma interaction, etc. T and C R etc. The pattern density map is defined as a function of the two-dimensional distribution of the design pattern features on the mask. In some embodiments, a smoothing factor (Sm) is defined as describing optical sensitivity or design geometry or resist chemistry related parameters, such as ILS, Slope, contrast, PK terms, and resist cutoff terms Ap / Bp / Am / Bn.

[0058] The random etch bias model 330 can be expressed as: SEB = f (CEM, pattern density map, smoothing factor) …Equation (2)

[0059] The present disclosure is not limited to any particular mathematical form of SEB. The factors may be mathematically combined in any suitable manner, for example, based on theory or empirically. In some embodiments, the function of Equation 2 may be expressed using a linear equation, a polynomial form, or a logarithmic form or an exponential form. For example, each factor of the equation may be associated with a calibration parameter.

[0060] The random etch bias model 330 may be calibrated. In some embodiments, the random etch bias model 330 may be calibrated using empirical data obtained from examining a test substrate on which a pattern is transferred or simulated process parameters from the design geometry and OPC model, or a combination thereof. For example, σ may be obtained from metrology data associated with the test substrate after the lithography and etching processes, respectively (e.g., obtained by examining SEM images of the test substrate). sepe-l and σsepe-e , and the random etching deviation can be determined as σ sepe-e and σ sepe-l The difference between. In addition, the value of parameter 307 (e.g., Ct, Cr, PM, or Sm) can be simulated using an OPC model or other model. Such empirical data can be obtained for various substrates. The empirical data and simulated parameters can be input to the random etch bias model 330, which determines the value of the coefficient. After determining the coefficient, the random etch bias model 330 can be considered to be calibrated.

[0061] The calibrated random etch deviation model 330 can be used to predict the random etch deviation of any sampling location in the design layout. For example, the value of parameter 307 (e.g., Ct, Cr, PM, or Sm) can be obtained using a simulation engine configured to predict the parameter value of any sampling location on the design layout / target layout. The value of parameter 307 can be input to the random etch deviation model 330, which determines the random etch deviation 331 based on the parameter value and the coefficient.

[0062] Referring to method 500, at process P515, the random etching model 350 may predict the post-etching random variation 351 based on the post-lithography random variation 326 and the random etching deviation 331 (e.g., which are obtained in processes P505 and P510, respectively). For example, the random etching model 350 may determine the post-etching random variation 351 as a combination of the post-lithography random variation 326 and the random etching deviation 331. For example, the post-etching random variation 351 may be expressed as: σ sepe-e =σ sepe-l +SEB …Equation (3)

[0063] As described above, the post-etch random variation 351 is calculated as a variance indicating the variation of the predicted post-etch profile due to the random effects of the etching process. The post-etch random variation 351 (e.g., represented in the form of a random variation band) can be characterized based on the variance of the post-etch profile simulated by the etching model 39 and the position of the average post-etch profile of the feature. The random variation band can represent the possible position of the predicted post-etch profile relative to the average profile. In some embodiments, the random variation band can be simulated as a Gaussian distribution of the predicted post-etch profile around the position of the average profile. Figure 4A 405 (or location) of the average profile μ on the substrate can be determined based on the EPE of the average profile (e.g., the distance between the average profile and the corresponding profile in the target layout), which can be obtained from a simulation of the patterning process. After determining the location 405 of the average profile, the σ value obtained from Equation 5 (e.g., σsepe-e ) The post-etch random variation band is determined as a Gaussian distribution. For example, the post-etch random variation band may indicate the probability of a post-etch profile variation within a ±3σ distance from the position 405 of the average profile.

[0064] In some embodiments, the random etching model 350 can then generate an image of the post-etch profile (eg, an after-etch image (AEI)) based on the predicted post-etch random variation band. For example, the random etching model 350 can generate Figure 4B A first image 425 of the post-etch profiles 410a and 410b of the features shown in FIG. Figure 4B A first image 425 of a post-etch profile predicted based on post-etch random variation consistent with various embodiments is shown. The random etch model 350 predicts a random variation band 415, which is a range of random variation that may occur in the etch profile of the feature after the etching process. For example, the random etch model 350 can generate a first etch profile 410a (e.g., an outer profile) of the feature from the average profile 336 at a first sigma value, and generate a second etch profile 410b (e.g., an inner profile) of the feature from the average profile 336 at a second sigma value.

[0065] In some embodiments, an average profile 336 may be generated using an etch model 335. As described above, etch modeling may be used to predict an etch profile across a substrate. In some embodiments, an etch model 335 may be used in obtaining or predicting a post-etch profile of a feature in a design layout. For example, a parameter 309 (e.g., a resist image having a resist profile for a given target layout) may be generated using a resist model (e.g., as at least a reference Figure 2 The etching model 335 simulates, predicts or generates a post-etching profile based on the resist image. For example, the etching model 335 generates an image (eg, AEI) having a nominal profile 336 of the feature.

[0066] Thus, the random etching model 350 can predict or generate a second image 355 (eg, AEI) having a post-etch profile determined based on the post-etch random variation 351. In some embodiments, the second image 355 or at least a portion of the second image 355 can be similar to Figure 4B The first image 425 .

[0067] Although the preceding paragraphs describe a random etch model 350 that predicts post-etch random variation 351 based on post-lithography random variation 326 and random etch bias 331, the random etch model 350 may consider other processes when predicting post-etch random variation 351. For example, the random etch model 350 may also be incorporated into a lithography manufacturability check (LMC), which is a procedure that follows an OPC or source mask optimization (SMO) process to verify whether a mask generated based on a determined mask pattern meets manufacturability requirements (e.g., it may involve simulating at least a reference to the mask pattern). Figure 2 351). If the LMC procedure fails, then one or more design variables in the SMO or OPC process can be adjusted, and method 500 can be performed again to determine post-etch random variation 351. In some embodiments, the design variables can include one or more of the following: a target CD for a target layout, a mask bias, a mask type (e.g., a binary mask, an optical mask, an EUV mask, etc.), a pupil of an illumination source of the lithographic apparatus, a dose of the illumination source, or a focus associated with radiation from the illumination source, or any other suitable variable that can be optimized in an OPC or SMO process, an etch bias, etc.

[0068] Randomly induced defects may occur intra-layer (within a layer such as a metal or gate layer) or inter-layer (between two adjacent layers). Intra-layer defects can be predicted by using a single-layer stochastic model at post-lithography or post-etch, but prediction of inter-layer defects can be done using a stochastic model from two layers (e.g., a stochastic etch model 350 for two layers).

[0069] The following paragraphs describe an exemplary method for predicting post-etch inter-layer random defects at a full chip level according to an embodiment of the present disclosure. FIG. 6A to FIG. 6C Post-etch profiles of one or more layers of a design layout predicted based on post-etch stochastic variations consistent with various embodiments are illustrated. Figure 7 is a block diagram of an exemplary system 700 for predicting post-etch inter-layer random defects consistent with various embodiments. Figure 8 is a flow chart of an exemplary method 800 for predicting post-etch inter-layer random defects consistent with various embodiments.

[0070] In some embodiments, the method 500 of determining post-etch random variation 351 is performed at a full chip level to determine post-etch random variation 351 for all features of a target layout (eg, for all features in multiple layers of a target layout). Fig. 6AAn image 600 of overlapping outlines of two layers of a portion of a target layout generated based on post-etch random variations 351 predicted by a random etch model consistent with various embodiments is shown. Image 600 shows one or more outlines of a set of features in a first layer (A) of the target layout overlapping with one or more outlines of a set of features in a second layer (B) of the target layout, where the first and second layers are consecutive layers of the target layout. For example, multiple outlines of first features 604 in the first layer overlap with multiple outlines of second features 609 in the second layer. Figure 6B An enlarged view of an area 625 where the profiles of the first feature 604 and the second feature 609 overlap is shown consistent with various embodiments. The three profiles 605a-605c of the first feature 604 overlap with the three profiles 610a-610c of the second feature 609. In some embodiments, the first profile 605a (e.g., the outer profile) of the first feature 604 is generated at a distance of +1σ from the average profile 605b, and the second profile 605c (e.g., the inner profile) of the first feature 604 is generated at a distance of -1σ from the average profile 605b. Similarly, the first profile 610a (e.g., the outer profile) of the second feature 609 is generated at a distance of +1σ from the average profile 610b, and the second profile 610c (e.g., the inner profile) of the second feature 609 is generated at a distance of -1σ from the average profile 610b. Although the preceding paragraphs describe determining post-etch inter-layer random defects between two layers, post-etch inter-layer random defects may be determined for more than two layers of a target layout.

[0071] At process P805, a post-etching profile of a first feature in a first layer of a target layout is obtained. For example, the defect prediction model 725 may use a random etching model as described above to obtain a profile 605a-605c of a first feature 604 in a first layer of the target layout. The random etching model may determine a random variation band for the profile of the first feature 604, and generate one or more profiles 605a-605c based on the random variation band of the first feature 604, for example, as at least referenced. FIG. 4A to FIG. 4B and Figure 5 as described.

[0072] At process P810, a post-etching profile of a second feature in a second layer of the target layout is obtained. For example, the defect prediction model 725 may use a random etching model to obtain profiles 610a-610c of a second feature 609 in the second layer of the target layout. The random etching model may determine a random variation band for the profile of the second feature 609, and generate one or more profiles 610a and 610c based on the random variation band of the second feature 609, for example, as at least referenced. FIG. 4A to FIG. 4B and Figure 5 as described.

[0073] In some embodiments, different random etching models can be used to simulate the post-etch profile for different layers of the target layout. For example, a first random etching model can be calibrated to obtain post-etch random variations for features in a first layer of the target layout (and simulate the post-etch profile), and a second random etching model can be calibrated to obtain post-etch random variations for features in a second layer of the target layout (and simulate the post-etch profile).

[0074] At process P815, an image in which the outlines of the first feature and the second feature are overlapped can be generated. For example, the outline 605 (e.g., 605a-605c) of the first feature 604 and the outline 610 (e.g., 610a-610c) of the second feature 609 can be provided as input to the defect prediction model 725, and the defect prediction model 725 generates Fig. 6A Image 600 overlaps the outlines of features from different layers.

[0075] At process P820, a threshold distance 705 for determining a defect is received. In some embodiments, the threshold distance 705 may be a minimum distance that needs to exist between the profiles of two features, below which they may be considered failure profiles. The defect prediction model 725 may obtain the threshold distance 705 in a variety of ways. For example, a user may input the threshold distance into the defect prediction model 725.

[0076] At process P825, a failure probability 805 is determined, which is the cumulative probability of all combinations of two post-etch profiles of two features where the separation is less than the threshold distance 705. For example, the defect prediction model 725 may determine the profile distance 630,d, which is the distance between the profile pair 605m and 610m (e.g., Figure 6C )) is less than the threshold distance 705. In some embodiments, the profile pair includes a first post-etch profile of the first feature and a second post-etch profile of the second feature. Profile 605m can be any one of profiles 605a-605c or any profile in a Gaussian distribution associated with first feature 604, and profile 610m can be any one of profiles 610a-610c or any profile in a Gaussian distribution associated with second feature 609. Defect prediction model 725 can determine such failure probabilities for any and all combinations of profile pairs of features 604 and 609 in a cumulative manner (e.g., using a cumulative distribution function).

[0077] At process P830, defects may be detected based on the probability of failure satisfying the threshold probability 710. For example, if the probability of failure 805 is equal to or exceeds the threshold probability 710, the defect prediction model 725 may determine the presence of an interlayer defect. The defect prediction model 725 may obtain the threshold probability 710 in various ways (e.g., via user input). In some embodiments, the defect prediction model 725 may perform the above process on some or all features in two layers or various other layers in a full-chip-scale design layout, and determine the interlayer defects and their locations and output a performance report 730. The performance report 730 may include information about the various defects detected and their locations in the substrate or design layout. In some embodiments, the performance report 730 indicates the performance of (a) the lithography process used to print the target layout on the substrate or (b) the etching process used to transfer the target layout to the substrate. The performance report 730 may be used as a guide for various optimization processes to optimize one or more design variables of the patterning process to transfer the target layout to the substrate. In some embodiments, the design variables may include one or more of the following: a target CD of a target layout, a mask deviation, a mask type (e.g., a binary mask, an optical mask, an EUV mask, etc.), a pupil of an illumination source of a lithographic apparatus, a dose of the illumination source, or a focus associated with radiation from the illumination source, an etching deviation, or any other suitable variable that can be optimized in an OPC or SMO process, etc.

[0078] Although Figure 8 The foregoing description describes the detection of inter-layer defects, but the method 800 may also be implemented for determining intra-layer defects. For example, just as a defect is determined by comparing two features 604 and 609 in two different layers and determining a probability of failure 805 as described above, an intra-layer defect may be determined by comparing two features within the same layer of the design layout and determining a probability of failure. If the probability of failure is equal to or greater than a threshold probability, an intra-layer defect may be detected.

[0079] Fig. 91 is a block diagram illustrating a computer system 100 that can assist in implementing the various methods and systems disclosed herein. The computer system 100 includes a bus 102 or other communication mechanism for communicating information; and a processor 104 (or multiple processors 104 and 105) coupled to the bus 102 for processing information. The computer system 100 also includes a main memory 106 (e.g., a random access memory (RAM) or other dynamic storage device) coupled to the bus 102, the main memory for storing information and instructions to be executed by the processor 104. The main memory 106 can also be used to store temporary variables or other intermediate information during the execution of instructions to be executed by the processor 104. The computer system 100 further includes a read-only memory (ROM) 108 or other static storage device coupled to the bus 102 for storing instructions for the processor 104 and static information. A storage device 110 (e.g., a magnetic disk or optical disk) is provided and coupled to the bus 102 for storing information and instructions.

[0080] The computer system 100 can be connected to a display 112, such as a cathode ray tube (CRT) or a flat panel or touch panel display, via the bus 102 for displaying information to a computer user. An input device 114 including alphanumeric keys and other keys is connected to the bus 102 for communicating information and command selections to the processor 104. Another type of user input device is a cursor control 116, such as a mouse, trackball, or cursor direction keys, for communicating direction information and command selections to the processor 104 and for controlling cursor movement on the display 112. The input device typically has two degrees of freedom on two axes, a first axis (e.g., x) and a second axis (e.g., y), which allows the device to specify a position in a plane. A touch panel (screen) display can also be used as an input device.

[0081] According to one embodiment, the computer system 100 may be responsive to the processor 104 executing one or more sequences of one or more instructions contained in the main memory 106 to perform a portion of one or more methods described herein. Such instructions may be read from another computer-readable medium (e.g., storage device 110) into the main memory 106. The execution of the sequence of instructions contained in the main memory 106 causes the processor 104 to perform the processing steps described herein. One or more processors in a multi-processing arrangement may also be employed to execute the sequence of instructions contained in the main memory 106. In alternative embodiments, hard-wired circuits may be used to replace or combine software instructions. Therefore, the description herein is not limited to any specific combination of hardware circuitry and software.

[0082] As used herein, the term "computer-readable medium" refers to any medium that participates in providing instructions to the processor 104 for execution. Such media can take many forms, including but not limited to non-volatile media, volatile media, and transmission media. Non-volatile media include, for example, optical or magnetic disks, such as storage device 110. Volatile media include dynamic memory, such as main memory 106. Transmission media include coaxial cables, copper wires, and optical fibers, including wires with bus 102. Transmission media can also take the form of sound waves or light waves, such as those generated during radio frequency (RF) and infrared (IR) data communications. Common forms of computer-readable media include, for example, floppy disks, flexible disks, hard disks, magnetic tapes, any other magnetic media, CD-ROMs, DVDs, any other optical media, punch cards, paper tapes, any other physical media with hole patterns, RAM, PROMs and EPROMs, FLASH-EPROMs, any other memory chips or cassettes, carriers as described below, or any other media from which a computer can read.

[0083] Various forms of computer readable media may be involved in carrying one or more sequences of one or more instructions to the processor 104 for execution. For example, the instructions may initially be carried on a disk of a remote computer. The remote computer may load the instructions into its dynamic memory and send the instructions over a telephone line using a modem. A modem local to the computer system 100 may receive the data on the telephone line and convert the data into an infrared signal using an infrared transmitter. An infrared detector connected to the bus 102 may receive the data carried in the infrared signal and place the data on the bus 102. The bus 102 carries the data to the main memory 106, from which the processor 104 retrieves and executes the instructions. The instructions received by the main memory 106 may optionally be stored on the storage device 110 before or after execution by the processor 104.

[0084] The computer system 100 also preferably includes a communication interface 118 coupled to the bus 102. The communication interface 118 provides a two-way data communication coupled to a network link 120 connected to a local network 122. For example, the communication interface 118 can be an integrated services digital network (ISDN) card or a modem to provide a data communication connection to a telephone line of a corresponding type. As another example, the communication interface 118 can be a local area network (LAN) card to provide a data communication connection to a compatible LAN. A wireless link can also be implemented. In any such embodiment, the communication interface 118 sends and receives electrical signals, electromagnetic signals, or optical signals that carry digital data streams representing various types of information.

[0085] The network link 120 typically provides data communication to other data devices through one or more networks. For example, the network link 120 can provide a connection to a host computer 124 or to data equipment operated by an Internet Service Provider (ISP) 126 through a local network 122. The ISP 126, in turn, provides data communication services through a global packet data communication network, now commonly referred to as the "Internet" 128. Both the local network 122 and the Internet 128 use electrical, electromagnetic or optical signals that carry digital data streams. The signals through the various networks and the signals on the network link 120 and through the communication interface 118, which carry the digital data to and from the computer system 100, are exemplary forms of carrier waves that transport the information.

[0086] The computer system 100 can send messages and receive data, including program code, through the network(s), network link 120, and communication interface 118. In the Internet example, the server 130 can transmit the requested code of the application program through the Internet 128, ISP 126, local network 122, and communication interface 118. For example, one such downloaded application program can provide lighting optimization of an embodiment. The received code can be executed by the processor 104 as it is received, or stored in the storage device 110 or other non-volatile memory for later execution. In this way, the computer system 100 can obtain application code in the form of a carrier wave.

[0087] Although the concepts disclosed herein may be used for imaging on substrates (e.g., silicon wafers), it should be understood that the disclosed concepts may be used with any type of lithography imaging system (e.g., those used for imaging on substrates other than silicon wafers).

[0088] As used herein, the terms "optimizing" and "optimization" refer to or mean adjusting a patterning device (e.g., a lithographic device), a patterning process, etc., so that the result and / or process has more desirable characteristics, for example, a higher accuracy of the projection of the design pattern on the substrate, a larger process window, etc. Therefore, as used herein, the terms "optimizing" and "optimization" refer to or mean the process of identifying one or more values ​​of one or more parameters that provide an improvement, e.g., a local optimum, in at least one related metric compared to an initial set of one or more values ​​of those one or more parameters. "Optimal" and other related terms should be interpreted accordingly. In an embodiment, the optimization steps may be applied iteratively to provide further improvements in one or more metrics.

[0089] Aspects of the present invention may be implemented in any convenient form. For example, an embodiment may be implemented by one or more appropriate computer programs, which may be carried on an appropriate carrier medium, which may be a tangible carrier medium (e.g., a disk) or an intangible carrier medium (e.g., a communication signal). Embodiments of the present invention may be implemented using a suitable device, which may specifically take the form of a programmable computer running a computer program, which is arranged to implement the method as described herein. Therefore, embodiments of the present disclosure may be implemented in hardware, firmware, software, or any combination thereof. Embodiments of the present disclosure may also be implemented as instructions stored on a machine-readable medium, which may be read and executed by one or more processors. A machine-readable medium may include any mechanism for storing or transmitting information in a form readable by a machine (e.g., a computing device). For example, a machine-readable medium may include: a read-only memory (ROM); a random access memory (RAM); a disk storage medium; an optical storage medium; a flash memory device; an electrical, optical, acoustic or other form of propagation signal (e.g., a carrier wave, an infrared signal, a digital signal, etc.), and others. In addition, firmware, software, routines, instructions may be described herein as performing certain actions. However, it should be understood that such descriptions are merely for convenience and that such actions are actually caused by a computing device, processor, controller, or other device executing firmware, software, routines, instructions, etc.

[0090] In the block diagrams, the illustrated components are depicted as discrete functional blocks, but the embodiments are not limited to systems in which the functionality described herein is organized as illustrated. The functionality provided by each of the components may be provided by software or hardware modules organized differently than currently depicted, for example, such software or hardware may be mixed, combined, replicated, decomposed, distributed (e.g., within a data center or geographically), or otherwise organized differently. The functionality described herein may be provided by one or more processors of one or more computers executing code stored on a tangible, non-transitory machine-readable medium. In some cases, a third-party content delivery network may host some or all of the information transmitted over the network, in which case, to the extent that information (e.g., content) is allegedly supplied or otherwise provided, the information may be provided by sending instructions to retrieve the information from the content delivery network.

[0091] Unless otherwise specifically stated, as is apparent from the discussion, it should be understood that throughout this specification, discussions utilizing terms such as "processing," "computing," "calculating," "determining," or the like refer to the actions or processes of a specific apparatus such as a special purpose computer or similar special purpose electronic processing / computing device.

[0092] The reader should be aware that several inventions are described in this application. Rather than dividing those inventions into multiple independent patent applications, these inventions have been grouped into a single file because their related subject matter contributes to economy in the application process. However, the different advantages and aspects of such inventions should not be combined. In some cases, embodiments solve all the defects described herein, but it should be understood that the present invention is independently useful, and some embodiments only solve a subset of such problems or provide other unmentioned benefits, which will be obvious to those skilled in the art who read this disclosure. Due to cost constraints, some of the inventions disclosed herein may not be claimed for protection at present, and may be claimed in a later submission (e.g., a continuation application) or by amending the present claims. Similarly, due to space constraints, the abstract and content of the invention sections of this document should not be regarded as a comprehensive list containing all such inventions or all aspects of such inventions.

[0093] It should be understood that the description and drawings are not intended to limit the disclosure to the particular forms disclosed, but on the contrary, the disclosure is to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the present invention as defined by the appended claims.

[0094] In view of this specification, modifications and alternative embodiments of various aspects of the present invention will be apparent to those skilled in the art. Therefore, this specification and the accompanying drawings are interpreted as illustrative only, and are for the purpose of teaching those skilled in the art to implement the general mode of the present invention. It should be understood that the forms of the present invention shown and described herein will be regarded as examples of embodiments. Elements and materials can replace those illustrated and described herein, parts and processes can be reversed or omitted, certain features can be utilized independently, and the features of embodiments or embodiments can be combined, all of which will be apparent to those skilled in the art after benefiting from this specification. Changes can be made to the elements described herein without departing from the spirit and scope of the present invention as described in the appended claims. The titles used herein are only for organizational purposes and are not meant to be used to limit the scope of the specification.

[0095] As used herein, except where it is not feasible, the term "or" encompasses all possible combinations unless specifically stated otherwise. For example, if the description component includes A or B, then unless otherwise specifically stated or not feasible, the component may include A, or B, or A and B. As a second example, if the description component includes A, B, or C, then unless otherwise specifically stated or not feasible, the component may include A, or B, or C, or A and B, or A and C, or B and C, or A and B and C. For example, the expression "at least one of..." does not necessarily modify the entirety of the following list, and does not necessarily modify each member of the list, so that "at least one of A, B, and C" should be understood to include only one of A, only one of B, only one of C, or any combination of A, B, and C. The phrase "one of A and B" or "any one of A and B" should be interpreted in the broadest sense to include one of A or one of B.

[0096] The description herein is intended to be illustrative rather than limiting. Therefore, it will be apparent to those skilled in the art that modifications may be made as described without departing from the scope of the appended claims.

[0097] The following paragraphs describe determining random variations in an etch profile (e.g., an etch profile) (referred to as "post-etch random variations") as a function of the sensitivity of the etch profile (e.g., an etch profile) to variations in a resist profile (e.g., a resist profile) (referred to as "post-lithography random variations"). In some embodiments, the sensitivity indicates a local sensitivity of the etch or resist profile. In some embodiments, the sensitivity may correspond to a derivative of the etch profile with respect to the resist profile, where the resist profile may be predicted based on one or more lithography models as described above, or may be obtained by measurement or inspection of a wafer. In some embodiments, the sensitivity may be determined based on a derivative of an etch model (e.g., a machine learning model, a physical or empirical etch model, a physical or empirical etch bias model, etc.) configured to predict an etch profile.

[0098] In some embodiments, the sensitivity may be obtained based on an etch bias model (e.g., a conventional etch bias model) and post-lithography random variation (e.g., which is determined using stochastic lithography model 325). In some embodiments, the post-lithography random variation indicates a change in a feature profile (e.g., “resist profile”) in a resist on a substrate after a lithography process, and the post-etch random variation indicates a probability of a change in a feature profile (e.g., “etch profile”) after an etching process. In this example, the sensitivity of the etch bias model indicates the sensitivity of the etch profile to random variations in the resist profile. For example, the post-etch random variation may be expressed as: …Equation (4) in It is along the contour. is the measured or predicted random variation after lithography, b is a constant representing the etch-induced roughness, and the function is the sensitivity of the etch bias model and is the etch reduction factor.

[0099] For example, if If it is less than "1", the random variation after etching decreases after the etching process. When greater than "1", the post-etch random variation is amplified after the etching process. It can be derived from a calibrated etch bias model for shifting the average profile through the etching process. For example, the etch bias model can determine the etch bias as a function of several etching process related parameters (e.g., CEM parameters, pattern density map or smoothing factor (referred to as "bias term"), coefficients associated with the bias term, and constants indicating variations induced by the etching process). The etch bias can be expressed as: …Equation (5) in, is the i-th deviation term, c i is the coefficient of the ith deviation term, is a constant indicating the etch-induced deviation from the average resist profile.

[0100] In some embodiments, the sensitivity of the etch bias model corresponds to the sensitivity of the etch profile to changes in the resist profile. For example, the sensitivity can be determined as a function of several parameters that are typically used to calibrate the etch bias model or the stochastic lithography model. Thus, based on equations (4) and (5), the post-etch stochastic variation can be expressed as: …Equation (6)

[0101] Therefore, the sensitivity can be expressed as: …Equation (7) where Γ is the Euler gamma function, ξ is the correlation length of the resist, α is an exponent in the form of a stretched exponential, and K i is the convolution of the resist profile with a kernel (eg, which is determined based on some of the deviation terms such as CEM parameters, pattern density map, or smoothing factors), and θ i is the cutoff of the convolution of the resist profile (eg, which is determined based on some of the resist cutoff bias terms such as Ap / Bp / Am / Bn).

[0102] That is, the sensitivity can be determined as a function of one or more of the coefficient, the convolution of the resist profile with the kernel and the truncation of the convolution of the resist profile, and the correlation length of the resist. After determining the sensitivity, the post-etch random variation used to transfer any target layout to the substrate is based on a constant and the product of the sensitivity and the measured or predicted post-lithography random variation, for example, as illustrated in equation (4).

[0103] Fig.10 is a flow chart of another method 1000 for predicting post-etch stochastic variations when transferring a target layout onto a substrate, consistent with various embodiments.

[0104] At process P1005, a resist profile 1005 of a feature in a target layout is obtained. The resist profile 1005 may be obtained in a variety of ways. For example, the resist profile 1005 may be obtained by executing a resist model (e.g., Figure 2 The resist model 37) is configured to predict the resist profile 1005 of the feature from the aerial image, as at least referring to Figure 2 As described. The resist profile may also be obtained by wafer measurement. In some embodiments, the resist profile 1005 is an average resist profile. The target layout may include multiple features, and the resist profile may be obtained for one or more features. Fig.11 An exemplary resist profile 1005 is illustrated.

[0105] At process P1010, an etch profile 1010 is obtained from the resist profile 1005. The etch profile 1010 can be obtained in a variety of ways. For example, the etch profile can be generated from the resist profile by executing an etch model (e.g., Figure 2 Etching Model 39 or Figure 3 335) to obtain an etch profile 1010. As described above, etch modeling can be used to predict an etch profile across a substrate. For example, parameters (e.g., a resist image having a resist profile for a given target layout) can be obtained using a resist model (e.g., as described at least with reference to process P1005) and input to an etch model, which simulates, predicts, or generates an etch profile based on the resist image. For example, the etch model generates Fig.11 . In some embodiments, etch profile 1010 is an average etch profile.

[0106] At process P1015, the sensitivity 1015 of the etch profile 1010 to the change in the resist profile 1005 is determined. In some embodiments, the sensitivity of the etch profile 1010 can be determined based on a calibrated etch bias model. For example, the change 1102 can be added to the resist profile 1005 to generate a modified resist profile 1105. In addition, an updated etch profile 1110 can be obtained from the modified resist profile 1105 using the etch model. Then, the sensitivity 1015 can be calculated based on the updated etch profile 1110, the modified resist profile 1105 using the calibrated etch bias model. In some embodiments, the sensitivity can be determined as a function of one or more of the coefficients of the etch bias model, the convolution of the resist profile with the kernel and the truncation of the convolution of the resist profile, and the correlation length of the resist. For example, the sensitivity 1015 can be determined using equation (7) above.

[0107] At process P1020, post-etch random variation 1020 may be determined for any target layout based on sensitivity 1015. For example, a user may input a target layout and measured or predicted post-lithography random variation 1018, and the random etch model 350 may determine the post-etch random variation 1020 based on sensitivity 1015 (e.g., using equation (4)).

[0108] Although the foregoing description relates to determining the sensitivity of the etch profile to changes in the resist profile based on an etch bias model, other models may be used to determine the sensitivity. For example, a machine learning (ML) model trained to generate an etch profile from a resist profile may be used to determine the sensitivity. In some embodiments, the resist model (e.g., resist model 37) may be an ML model trained to generate a resist image from an aerial image. The contour of a feature (e.g., a resist profile or a resist image) may be extracted from the resist image. Similarly, an etching model (e.g., etching model 39) may be an ML model trained to generate an etching image using a resist image. The contour of a feature (e.g., an etching profile or an etching image) may be extracted from the etching image.

[0109] The following paragraphs describe the use of a model M (e.g., an etching model or an etching bias model) to determine sensitivity. For example, a resist profile (e.g., resist profile 1005) is input to an etching model (e.g., ML model) to generate an etching profile (e.g., etching profile 1010). In some embodiments, the resist profile is an average resist profile. The etching profile can be expressed as a function of the model M used to generate the etching profile 1010 as follows: …Equation (8) Where EC is the etch profile and RC is the resist profile.

[0110] The sensitivity of the model M can be determined as the derivative of the etch profile with respect to the resist profile. In some embodiments, to determine the derivative, the model M can be determined by The model is evaluated by adding a perturbation 1102 to the average resist profile at 1105 and generating a modified etch profile 1110 for the modified average resist profile 1105. The size of the perturbation 1102 can be denoted as ε, and the perturbation shape can be the point of interest The modified etch profile can then be considered as the average etch profile plus the delta peaks at some points along the profile. The etch profile can be expressed as: …Equation (9)

[0111] Then, you can point The sensitivity S of the perturbation at is defined as a function of the modified resist profile, the average resist profile, and the size of the deformation added to the resist profile. The sensitivity can be expressed as follows: …Equation (10)

[0112] Note that for fixed values , is a function for all profile points along the etched profile For the resist profile All values ​​of is dependent on the position along the resist profile and position along the etched profile In some embodiments, the resist profile The profile deformation at the same point in the etched profile The profile deformation occurs at can be considered to have a strong diagonal component. Therefore, the sensitivity change δS can be expressed as: …Equation (11) in is the identity matrix, and Usually small in magnitude (e.g. or ).

[0113] Therefore, based on equations (6) and (11), the random variation after etching can be expressed as: …Equation (12)

[0114] Therefore, the sensitivity can be expressed as: …Equation (13)

[0115] The embodiments of the present disclosure may be further described through the following aspects. 1. A non-transitory computer readable medium having instructions which, when executed by a computer, cause the computer to perform a method for predicting post-etch stochastic variations when transferring a target layout onto a substrate using a lithographic apparatus, the method comprising: predicting random variations in transferring a target layout onto a substrate by executing a stochastic model, the stochastic model being configured to predict the random variations in an etching process, wherein the stochastic model is configured to predict the random variations based on random etching biases and post-lithography process random variations; and A performance when transferring the target layout to the substrate is determined based on the random variation. 2. The computer readable medium of clause 1, wherein the random variation indicates a probability of variation of the post-etching profile. 3. The computer readable medium of clause 1, wherein the post-lithography random variation indicates a variation in a profile associated with the target layout in the resist on the substrate after a lithography process. 4. The computer-readable medium of aspect 1, wherein predicting the random variation comprises: The random etch deviation is determined using at least one of a concentration etch method, a density map, or a smoothing factor. 5. The computer-readable medium according to aspect 1, further comprising: obtaining a substrate-level random etch deviation based on metrology data associated with a specified substrate; and A first stochastic model is calibrated based on the substrate-level random etch deviation to determine parameters associated with the first stochastic model. 6. The computer readable medium of aspect 5, wherein the parameter comprises a term C related to a method based on plasma concentration. T and C R , a coefficient associated with at least one of a pattern density map or a smoothing factor of a sub-layer. 7. The computer readable medium of clause 5, wherein obtaining the substrate-level random etch deviation comprises: obtaining a first random variation after a photolithography process of printing a pattern on the specified substrate based on the metrology data; obtaining a second random variation after an etching process of etching the pattern on the specified substrate based on the metrology data; and The substrate-level random etch deviation is determined as a difference between the first random variation and the second random variation. 8. The computer-readable medium according to aspect 5, further comprising: The plasma concentration-based method T and C R , a pattern density map of a sub-layer, or a smoothing factor of a feature of the target layout is input into the first stochastic model; and The random etch bias for the feature is obtained from the first stochastic model. 9. The computer readable medium of clause 1, wherein the post-lithography stochastic variation is determined by executing a second stochastic model configured to predict the post-lithography stochastic variation of a profile associated with the target layout in the resist on the substrate. 10. The computer readable medium of clause 9, wherein the second stochastic model is configured to predict the post-lithography process stochastic variation based on at least one of an optical sensitivity associated with the lithographic apparatus, a two-dimensional distribution of photons on the substrate, a three-dimensional distribution of photons on the substrate, or a resist chemistry associated with a resist used in printing the target layout on the substrate. 11. The computer readable medium of clause 1, wherein the stochastic model is configured to predict the stochastic variation as a combination of the stochastic etch bias and the post-lithography process stochastic variation. 12. The computer-readable medium according to aspect 1, further comprising: obtaining an average profile of features in the target layout by executing an etching model, the etching model being configured to predict the average profile of the features after completing the etching process; and A post-etch profile is predicted based on the average profile and the random variation. 13. The computer readable medium of clause 12, wherein predicting the post-etch profile comprises: determining a first post-etch profile at a first distance from the average profile based on the random variation; and A second post-etch profile at a second distance from the average profile is determined based on the random variation. 14. The computer readable medium of clause 1, wherein determining the performance of printing the target layout on the substrate comprises: A performance of at least one of a lithography process or an etching process in transferring the target layout to the substrate is determined based on the random variation. 15. The computer-readable medium of clause 1, wherein determining the performance of transferring the target layout comprises: At least one of an intra-layer defect or an inter-layer defect on the substrate is determined based on the random variation. 16. The computer readable medium of clause 15, wherein determining the intra-layer defect comprises: For feature pairs in the same layer of the target layout, wherein each feature in the feature pairs includes a plurality of predicted post-etch profiles, determining a probability of failure when a distance between any of the plurality of profile pairs is less than a threshold distance, wherein the profile pairs in the plurality of profile pairs include a first post-etch profile of a first feature and a second post-etch profile of a second feature; and A defect is predicted based on the failure probability satisfying a threshold probability. 17. The computer readable medium of clause 15, wherein determining the interlayer defects comprises: For feature pairs in consecutive layers of the target layout, wherein a first feature in the feature pair is located in a first layer of the target layout and a second feature in the feature pair is located in a second layer of the target layout, wherein each feature in the feature pair includes a plurality of predicted post-etch profiles, thereby determining a probability of failure where a distance between any of the plurality of profile pairs is less than a threshold distance, wherein a profile pair in the plurality of profile pairs includes a first post-etch profile for the first feature and a second post-etch profile for the second feature; and A defect is predicted based on the failure probability satisfying a threshold probability. 18. The computer readable medium according to aspect 1, further comprising: One or more of a mask or an illumination source of the lithographic apparatus is configured based on the performance of the lithographic process. 19. The computer readable medium of aspect 18, further comprising: The lithography process is performed in the lithography apparatus using the mask to print a target layout on the substrate. 20. The computer readable medium of clause 1, wherein predicting the random changes in transferring the target layout comprises: obtaining a resist profile of a feature, the feature corresponding to one of a plurality of features in the target layout; obtaining an etch profile from the resist profile by executing an etch model, the etch profile representing the profile of the feature after the etching process; determining sensitivity of the etch profile to random variations in the resist profile; and The random variation in the etch profile is determined based on the random variation in the resist profile and the sensitivity. 21. The computer readable medium of clause 20, wherein determining the random variation in the etch profile comprises determining a product of the random variation in the resist profile and the sensitivity. 22. The computer readable medium of aspect 21, further comprising: The random variation in the etch profile is determined as a function of a constant that is indicative of the variation induced by the etching process. 23. The computer readable medium of clause 20, wherein the sensitivity is a function of a correlation length of the resist. 24. The computer readable medium of clause 20, wherein determining the sensitivity comprises executing an etch bias model to determine the etch bias based on a plurality of parameters. 25. The computer readable medium of aspect 24, wherein the parameter comprises a term C of a method based on plasma concentration. T and C R , a pattern density map or a smoothing factor of the sub-layer and at least one of the coefficients associated with the parameters. 26. The computer readable medium of clause 25, wherein the sensitivity is determined as a function of the coefficient. 27. The computer readable medium of clause 20, wherein the sensitivity is determined as a function of one or more convolutions of the resist profile with a kernel. 28. The computer readable medium of clause 20, wherein the sensitivity is determined as a function of a cutoff of a convolution of the resist profile. 29. The computer readable medium of clause 20, wherein obtaining the resist profile comprises executing a resist model configured to predict the resist profile of the feature from an aerial image. 30. The computer readable medium of aspect 20, wherein obtaining the resist profile further comprises: The random variation in the resist profile is determined by executing a post-lithography process random variation model configured to predict the random variation in the resist profile. 31. The computer readable medium of clause 20, wherein the post-lithography process stochastic variation model is configured to predict the stochastic variation in the resist profile based on at least one of an optical sensitivity associated with the lithographic apparatus, a two-dimensional distribution of photons on the substrate, a three-dimensional distribution of photons on the substrate, or a resist chemistry associated with a resist used in printing the target layout on the substrate. 32. The computer readable medium of clause 20, wherein the random variations in the resist profile are indicative of variations in profile associated with features in the resist on the substrate after a photolithography process. 33. The computer readable medium of clause 20, wherein the random variation in the etch profile indicates a probability of a change in the profile of the feature after an etching process. 34. The computer readable medium of clause 20, wherein determining the sensitivity comprises: The sensitivity is determined based on a derivative of the etch model configured to predict the etch profile from the resist profile. 35. The computer readable medium of clause 20, wherein determining the sensitivity comprises: A derivative of the etch profile with respect to the resist profile is determined. 36. The computer readable medium of clause 35, wherein determining the derivative comprises: adding a perturbation to the resist profile to generate a modified resist profile; and The etch model is executed to generate the modified etch profile using the modified resist profile. 37. The computer readable medium of clause 36, further comprising: The derivative is determined based on the modified etch profile, the etch profile, and a magnitude of the perturbation. 38. The computer readable medium of clause 35, wherein determining the sensitivity comprises: The sensitivity is determined based on the derivative and a correlation length of the resist. 39. A non-transitory computer readable medium having instructions which, when executed by a computer, cause the computer to perform a method for predicting post-etch stochastic variations when transferring a target layout to a substrate using a lithographic apparatus, the method comprising: obtaining post-lithography random variations associated with printing a target layout on a substrate using the lithography process; predicting a random etch deviation indicative of random variations in an etching process for etching a pattern corresponding to the target layout on the substrate, wherein the random etch deviation is determined as a function of at least one of a concentration etching method, a density map, or a smoothing factor; and The random variation is obtained based on the random etching bias and the post-lithography random variation. 40. The computer readable medium of clause 39, wherein the random variation indicates a probability of variation in the post-etch profile. 41. The computer readable medium of clause 39, wherein the post-lithography process random variation indicates a variation in a profile associated with the target layout in a resist on the substrate after the lithography process. 42. The computer readable medium of clause 39, wherein determining the random etch bias comprises: obtaining a substrate-level random etch deviation based on metrology data associated with a specified substrate; and A first stochastic model is calibrated based on the substrate-level random etch deviation to determine parameters associated with the first stochastic model. 43. The computer readable medium of aspect 42, wherein the parameter comprises a term C related to a method based on plasma concentration. T and C R , a coefficient associated with at least one of a pattern density map or a smoothing factor of a sub-layer. 44. The computer readable medium of clause 42, wherein obtaining the substrate level random etch bias comprises: obtaining a first random variation after a photolithography process of printing a pattern on the specified substrate based on the metrology data; obtaining a second random variation after an etching process of etching the pattern on the specified substrate based on the metrology data; and The substrate-level random etch deviation is determined as a difference between the first random variation and the second random variation. 45. The computer readable medium of clause 42, further comprising: The plasma concentration-based method T and C R , a pattern density map of a sub-layer, or a smoothing factor of a feature of the target layout is input into the first stochastic model; and The random etch bias for the feature is obtained from the first stochastic model. 46. ​​The computer readable medium of clause 42, wherein the post-lithography stochastic variation is determined by executing a second stochastic model configured to predict the post-lithography stochastic variation of a profile associated with the target layout in the resist on the substrate. 47. The computer readable medium of clause 46, wherein the second stochastic model is configured to predict the post-lithography process stochastic variation based on at least one of an optical sensitivity associated with the lithographic apparatus, a two-dimensional distribution of photons on the substrate, a three-dimensional distribution of photons on the substrate, or a resist chemistry associated with a resist used in printing the target layout on the substrate. 48. The computer readable medium of clause 39, further comprising: obtaining an average profile of features in the target layout by executing an etching model, the etching model being configured to predict the average profile of the features after completing the etching process; and A post-etch profile is predicted based on the average profile and the random variation. 49. The computer readable medium of clause 48, wherein predicting the post-etch profile comprises: determining a first post-etch profile at a first distance from the average profile based on the random variation; and A second post-etch profile at a second distance from the average profile is determined based on the random variation. 50. The computer readable medium of clause 39, further comprising: A performance of at least one of the lithography process or the etching process in transferring the target layout to the substrate is determined based on the random variation. 51. The computer readable medium of clause 50, wherein determining the performance when transferring the target layout comprises: At least one of an intra-layer defect or an inter-layer defect on the substrate is determined based on the random variation. 52. The computer readable medium of clause 51, wherein determining the intra-layer defect comprises: For feature pairs in the same layer of the target layout, wherein each feature in the feature pairs includes a plurality of predicted post-etch profiles, determining a probability of failure when a distance between any of the plurality of profile pairs is less than a threshold distance, wherein the profile pairs in the plurality of profile pairs include a first post-etch profile of a first feature and a second post-etch profile of a second feature; and A defect is predicted based on the failure probability satisfying a threshold probability. 53. The computer readable medium of clause 51, wherein determining the interlayer defects comprises: For feature pairs in consecutive layers of the target layout, wherein a first feature in the feature pair is located in a first layer of the target layout and a second feature in the feature pair is located in a second layer of the target layout, wherein each feature of the feature pair includes a plurality of predicted post-etch profiles, thereby determining a probability of failure where a distance between any of the plurality of profile pairs is less than a threshold distance, wherein a profile pair in the plurality of profile pairs includes a first post-etch profile of the first feature and a second post-etch profile of the second feature; and A defect is predicted based on the failure probability satisfying a threshold probability. 54. A method for predicting post-etch random variations when transferring a target layout onto a substrate using a lithographic apparatus, the method comprising: predicting random variations in transferring a target layout onto a substrate by executing a stochastic model, the stochastic model being configured to predict the random variations in an etching process, wherein the stochastic model is configured to predict the random variations based on random etching biases and post-lithography process random variations; and A performance when transferring the target layout to the substrate is determined based on the random variation. 55. An apparatus for predicting post-etch random variations when transferring a target layout onto a substrate using a lithographic apparatus, the apparatus comprising: a memory storing a set of instructions; and A processor configured to execute the set of instructions to cause the device to perform the following method: predicting random variations in transferring a target layout onto a substrate by executing a stochastic model, the stochastic model being configured to predict the random variations in an etching process, wherein the stochastic model is configured to predict the random variations based on random etching biases and post-lithography process random variations; and A performance when transferring the target layout to the substrate is determined based on the random variation. 56. A non-transitory computer readable medium having instructions which, when executed by a computer, cause the computer to perform a method for predicting post-etch stochastic variations when transferring a target layout onto a substrate using a lithographic apparatus, the method comprising: obtaining a resist profile of a feature corresponding to one of a plurality of features in a target layout to be transferred onto a substrate; Obtaining an etch profile from the resist profile by executing an etch model, the etch profile representing the profile of the feature after an etching process; determining a sensitivity of the etch profile to random variations in the resist profile; and Random variations in the etch profile are determined based on the random variations in the resist profile and the sensitivity. 57. The computer readable medium of clause 56, wherein determining the random variation in the etch profile comprises determining a product of the random variation in the resist profile and the sensitivity. 58. The computer readable medium of clause 57, further comprising: The random variations in the etch profile are determined as a function of a constant that is indicative of variations induced by the etching process. 59. The computer readable medium of clause 56, wherein the sensitivity is a function of a correlation length of the resist. 60. The computer readable medium of clause 56, wherein determining the sensitivity comprises executing an etch bias model to determine the etch bias based on a plurality of parameters. 61. The computer readable medium of aspect 60, wherein the parameter comprises a term C of a method based on plasma concentration. T and C R , a pattern density map or a smoothing factor of the sub-layer and at least one of the coefficients associated with the parameters. 62. The computer readable medium of clause 61, wherein the sensitivity is determined as a function of the coefficient. 63. The computer readable medium of clause 56, wherein the sensitivity is determined as a function of one or more convolutions of the resist profile with a kernel. 64. The computer readable medium of clause 56, wherein the sensitivity is determined as a function of a cutoff of a convolution of the resist profile. 65. The computer readable medium of clause 56, wherein obtaining the resist profile comprises executing a resist model configured to predict the resist profile of the feature from an aerial image. 66. The computer readable medium of clause 56, wherein obtaining the resist profile further comprises: The random variation in the resist profile is determined by executing a post-lithography process random variation model configured to predict the random variation in the resist profile. 67. The computer readable medium of clause 66, wherein the post-lithography process stochastic variation model is configured to predict the stochastic variation in the resist profile based on at least one of an optical sensitivity associated with the lithographic apparatus, a two-dimensional distribution of photons on the substrate, a three-dimensional distribution of photons on the substrate, or a resist chemistry associated with a resist used in printing the target layout on the substrate. 68. The computer readable medium of clause 56, wherein the random variations in the resist profile are indicative of variations in profile associated with features in the resist on the substrate after a photolithography process. 69. The computer readable medium of clause 56, wherein the random variation in the etch profile indicates a probability of a change in the profile of the feature after an etching process. 70. The computer readable medium of clause 56, further comprising: One or more of a mask or an illumination source of a lithographic apparatus is configured based on the random variation in the etch profile. 71. The computer readable medium of aspect 56, further comprising: A lithography process is performed in the lithography apparatus using the mask to print a target layout on the substrate. 72. The computer readable medium of clause 56, wherein determining the sensitivity comprises: The sensitivity is determined based on a derivative of the etch model configured to predict the etch profile from the resist profile. 73. The computer readable medium of clause 56, wherein determining the sensitivity comprises: A derivative of the etch profile with respect to the resist profile is determined. 74. The computer readable medium of clause 73, wherein determining the derivative comprises: adding a perturbation to the resist profile to generate a modified resist profile; and The etch model is executed to generate the modified etch profile using the modified resist profile. 75. The computer readable medium of clause 74, further comprising: The derivative is determined based on the modified etch profile, the etch profile, and a magnitude of the perturbation. 76. The computer readable medium of clause 73, wherein determining the sensitivity comprises: The sensitivity is determined based on the derivative and a correlation length of the resist. 77. A method for predicting post-etch random variations when transferring a target layout onto a substrate using a lithographic apparatus, the method comprising: obtaining a resist profile of a feature corresponding to one of a plurality of features in a target layout to be transferred onto a substrate; Obtaining an etch profile from the resist profile by executing an etch model, the etch profile representing the profile of the feature after an etching process; determining a sensitivity of the etch profile to random variations in the resist profile; and Random variations in the etch profile are determined based on the random variations in the resist profile and the sensitivity. 78. An apparatus for predicting post-etch random variations when transferring a target layout onto a substrate using a lithographic apparatus, the apparatus comprising: a memory storing a set of instructions; and A processor configured to execute the set of instructions to cause the device to perform the following method: obtaining a resist profile of a feature corresponding to one of a plurality of features in a target layout to be transferred onto a substrate; Obtaining an etch profile from the resist profile by executing an etch model, the etch profile representing the profile of the feature after an etching process; determining a sensitivity of the etch profile to random variations in the resist profile; and Random variations in the etch profile are determined based on the random variations in the resist profile and the sensitivity.

Claims

1. A non-transitory computer readable medium having instructions which, when executed by a computer, cause the computer to perform a method for predicting post-etch stochastic variations when transferring a target layout onto a substrate using a lithographic apparatus, the method comprising: predicting random variations in transferring a target layout onto a substrate by executing a stochastic model, the stochastic model being configured to predict the random variations in an etching process, wherein the stochastic model is configured to predict the random variations based on random etching biases and post-lithography process random variations; and A performance when transferring the target layout to the substrate is determined based on the random variation.

2. The computer-readable medium of claim 1, wherein: The random variation indicates the probability of variation of the profile after etching.

3. The computer-readable medium of claim 1, wherein: The post-lithography random variation indicates a variation in a profile associated with the target layout in the resist on the substrate after a lithography process.

4. The computer-readable medium of claim 1, wherein: Predicting the random variation includes: The random etch deviation is determined using at least one of a concentration etch method, a density map, or a smoothing factor.

5. The computer-readable medium of claim 1 , further comprising: obtaining a substrate-level random etch deviation based on metrology data associated with a specified substrate; A first stochastic model is calibrated based on the substrate-level random etch deviation to determine parameters associated with the first stochastic model.

6. The computer-readable medium of claim 5, wherein: The parameters include coefficients associated with at least one of a term of a plasma concentration based method, a pattern density map of a sub-layer, or a smoothing factor.

7. The computer-readable medium of claim 5, wherein: Obtaining the substrate-level random etching deviation comprises: obtaining a first random variation after a photolithography process of printing a pattern on the specified substrate based on the metrology data; obtaining a second random variation after an etching process of etching the pattern on the specified substrate based on the metrology data; and The substrate-level random etch deviation is determined as a difference between the first random variation and the second random variation.

8. The computer-readable medium of claim 1, wherein: The post-lithography stochastic variation is determined by executing a second stochastic model configured to predict the post-lithography stochastic variation of a profile associated with the target layout in resist on the substrate.

9. The computer-readable medium of claim 8, wherein: The second stochastic model is configured to predict the post-lithography process stochastic variation based on at least one of an optical sensitivity associated with the lithographic equipment, a two-dimensional distribution of photons on the substrate, a three-dimensional distribution of photons on the substrate, or a resist chemistry associated with a resist used when printing the target layout on the substrate.

10. The computer-readable medium of claim 1, wherein: The stochastic model is configured to predict the stochastic variation as a combination of the stochastic etch bias and the post-lithography process stochastic variation.

11. The computer-readable medium of claim 1 , further comprising: obtaining an average profile of features in the target layout by executing an etching model, the etching model being configured to predict the average profile of the features after completing the etching process; and Predicting a post-etching profile based on the average profile and the random variation, wherein predicting the post-etching profile comprises: determining a first post-etch profile at a first distance from the average profile based on the random variation; and A second post-etch profile at a second distance from the average profile is determined based on the random variation.

12. The computer-readable medium of claim 1, wherein: Determining the performance when transferring the target layout includes: At least one of an intra-layer defect or an inter-layer defect on the substrate is determined based on the random variation.

13. The computer-readable medium of claim 12, wherein: Determining the intra-layer defects includes: For feature pairs in the same layer of the target layout, wherein each feature in the feature pairs includes a plurality of predicted post-etch profiles, determining a probability of failure when a distance between any of the plurality of profile pairs is less than a threshold distance, wherein the profile pairs in the plurality of profile pairs include a first post-etch profile for a first feature and a second post-etch profile for a second feature; and A defect is predicted based on the failure probability satisfying a threshold probability.

14. The computer-readable medium of claim 12, wherein: Determining the interlayer defects includes: For feature pairs in consecutive layers of the target layout, wherein a first feature in the feature pair is in a first layer of the target layout and a second feature in the feature pair is in a second layer of the target layout, wherein each feature of the feature pair includes a plurality of predicted post-etch profiles, determining a probability of failure where a distance between any of the plurality of profile pairs is less than a threshold distance, wherein a profile pair in the plurality of profile pairs includes a first post-etch profile for the first feature and a second post-etch profile for the second feature; and A defect is predicted based on the failure probability satisfying a threshold probability.

15. The computer-readable medium of claim 1, further comprising: configuring one or more of a mask or an illumination source of the lithographic apparatus based on performance of a lithographic process; or The lithography process is performed in the lithography apparatus using the mask to print a target layout on the substrate.

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