Pinhole probability analysis methods for photoresist films

Abstract

A probability-based simulation analysis method to predict pinhole formation in a photoresist is provided. The method determines a statistical distribution of cross-linking in the photoresist based on exposure stochastics and post-exposure bake randomness. The method updates the distribution of cross-linking in the photoresist as a result of film inhomogeneity. The effect of dry development on the updated distribution of cross-linking in the photoresist can be evaluated to determine a threshold value associated with a threshold amount of cross-linked states in the photoresist. A probability of pinhole formation can be determined based on the amount of cross-linked states that are below the threshold value.

Description

PINHOLE PROBABILITY ANALYSIS METHODS FOR PHOTORESIST FILMSINCORPORATION BY REFERENCE

[0000] A PCT Request Form is filed concurrently with this specification as part of the present application. Each application that the present application claims benefit of or priority to as identified in the concurrently filed PCT Request Form is incorporated by reference herein in its entirety and for all purposes.FIELD

[0001] The present disclosure relates to predictive analysis of defects in a photolithography process flow, and more particularly to probability analysis of pinhole formation in a photolithography process flow for an extreme ultraviolet (EUV) resist.BACKGROUND

[0002] The fabrication of semiconductor devices, such as integrated circuits, is a multi-step process involving photolithography. In general, the process includes the deposition of material on a wafer, and patterning the material through lithographic techniques to form structural features (e.g., transistors and circuitry) of the semiconductor device. The steps of a typical photolithography process known in the art include: preparing the substrate; applying a photoresist, such as by spin coating; exposing the photoresist to light in a desired pattern, causing the more exposed areas of the photoresist to become more or less soluble in a developer solution; developing by applying a developer solution to remove either the more exposed or the less exposed areas of the photoresist; and subsequent processing to create features on the areas of the substrate from which the photoresist has been removed, such as by etching or material deposition.

[0003] The evolution of semiconductor design has created the need, and has been driven by the ability, to create ever smaller features on semiconductor substrate materials. This progression of technology has been characterized in “Moore’s Law” as a doubling of the density of transistors in dense integrated circuits every two years. Indeed, chip design and manufacturing has progressed such that modern microprocessors may contain billions of transistors and other circuit features on a single chip. Individual features on such chips may be on the order of 22 nanometers (nm) or smaller, in some cases less than 10 nm.

[0004] One challenge in manufacturing devices having such small features is the ability to reliably and reproducibly create photolithographic masks having sufficient resolution. Current photolithography processes typically use 193 nm ultraviolet (UV) light to expose a photoresist. The fact that the light has a wavelength significantly greater than the desired size of the featuresto be produced on the semiconductor substrate creates inherent issues. Achieving feature sizes smaller than the wavelength of the light requires use of complex resolution enhancement techniques, such as multipatteming. Thus, there is significant interest and research effort in developing photolithographic techniques using shorter wavelength light, such as extreme ultraviolet radiation (EUV), having a wavelength of from 10 nm to 15 nm, e.g., 13.5 nm.

[0005] EUV photolithographic processes can present challenges, however, including low power output and loss of light during patterning. Traditional organic chemically amplified resists (CAR) similar to those used in 193 nm UV lithography have potential drawbacks when used in EUV lithography, particularly as they have low absorption coefficients in EUV region and the diffusion of photo-activated chemical species can result in blur or line edge roughness. Furthermore, in order to provide the etch resistance required to pattern underlying device layers, small features patterned in conventional CAR materials can result in high aspect ratios at risk of pattern collapse. Metal oxide resist has been proposed as an alternative to CAR materials because of its triple absorptivity under EUV. Metal oxide resist exhibit a high exposure latitude and can maintain a stable pattern down to even a half pitch of 16 nm and below. Metal oxide resist can demonstrate enhanced stability and is suitable for high volume manufacturing. In some instances, metal oxide resist offers environmental benefits, reducing waste and cost by 5-10 times compared to conventional CAR materials.

[0006] The background description provided herein is for the purpose of generally presenting the context of the present technology. Work of the presently named inventors, to the extent it is described in this background section, as well as aspects of the description that may not otherwise qualify as prior art at the time of filing, are neither expressly nor impliedly admitted as prior art against the present technology.SUMMARY

[0007] Provided herein is a method of determining a probability of pinhole formation in a photoresist. The method includes determining an amount of cross-linked states in the photoresist, where the amount of cross-linked states is based at least in part on an analysis of exposure stochastics, bake randomness, and film inhomogeneity, and determining the probability of pinhole formation in the photoresist based at least in part on the amount of cross-linked states in the photoresist that are below a threshold value associated with a threshold amount of cross-linked states in the photoresist.

[0008] In some implementations, the method further includes identifying the threshold value associated with the threshold amount of cross-linked states in the photoresist. In some implementations, the identified threshold value is dependent on dry development conditions fordry developing the photoresist. In some implementations, the amount of cross-linked states is based at least in part on an analysis of exposure stochastics, bake-induced transitions, and film inhomogeneity. In some implementations, the exposure stochastics is related to one or more EUV exposure conditions. In some implementations, the bake-induced transitions is related to one or more post-exposure bake conditions. In some implementations, the one or more post-exposure bake conditions include one or more of bake temperature, pressure, gas species, flow rates of gas species, and duration of exposure. In some implementations, the film inhomogeneity is related to deposition processes and chemistries. In some implementations, the method further includes optimizing one or more of: (1) deposition processes and chemistries, (2) dry development processes and conditions, or (3) exposure and post-exposure bake conditions, where the optimization is related to the determination of the probability of pinhole formation in the photoresist. In some implementations, the photoresist is an EUV-sensitive metal oxide-containing photoresist. In some implementations, the method further includes providing a plurality of inputs to a digital twin of a photolithography process, where the plurality of inputs include a photoresist unit cluster for the photoresist, bridging locations using the photoresist unit cluster for the photoresist, one or more inputs associated with EUV exposure, one or more inputs associated with a material of the photoresist, one or more inputs associated with bake parameters, and one or more inputs associated with development parameters, determining, in the digital twin, post-exposure states of the bridging locations after EUV exposure of the photolithography process, and determining, in the digital twin, post-bake states of the bridging locations after bake of the photolithography process, where the amount of cross-linked states in the photoresist is determined from the post-bake states of the bridging locations after bake.

[0009] Also provided herein is a model to predict pinhole formation in a photoresist including one or more non-transitory machine readable media. The one or more non-transitory machine readable media includes logic configured to implement exposure stochastics configured to determine cross-linking fraction distribution in the photoresist due to EUV exposure, bake randomness configured to adjust the cross-linking fraction distribution in the photoresist due to post-exposure bake, and film inhomogeneity further configured to update the cross-linking fraction distribution in the photoresist due to voids in the photoresist, where the model is configured to predict pinhole formation in the photoresist based at least in part on the updated cross-linking fraction distribution in the photoresist due to exposure stochastics, bake randomness, and film inhomogeneity.

[0010] In some implementations, the model is configured to predict a probability of pinhole formation in the photoresist based at least in part on an amount of cross-linked states in the updatedcross-linking fraction distribution in the photoresist that are below a threshold value associated with a threshold amount of cross-linked states in the photoresist. In some implementations, the threshold value associated with a threshold amount of cross-linked states in the photoresist is identified and dependent on dry development conditions for dry developing the photoresist. In some implementations, the exposure stochastics is related to one or more EUV exposure conditions. In some implementations, the bake randomness is related to one or more post-exposure bake conditions. In some implementations, the film inhomogeneity is related to void area and size. In some implementations, the void area and size are related to one or more exposure conditions and one or more of EUV exposure conditions and one or more post-exposure bake conditions. In some implementations, the photoresist is an EUV-sensitive metal oxide-containing photoresist. In some implementations, the one or more non- transitory machine readable media including the logic is further configured to implement: an EUV exposure model of a photolithography process, where the EUV exposure model is configured to receive pre-exposure inputs comprising a photoresist unit cluster for an EUV resist, bridging locations using the photoresist unit cluster for the EUV resist, and one or more inputs associated with EUV exposure, and configured to generate postexposure states of the bridging locations after EUV exposure, a bake model of the photolithography process, where the bake model is configured to receive the post-exposure states of the bridging locations and bake parameters, and configured to generate post-bake states of the bridging locations after bake using the post-exposure states of the bridging locations and the bake parameters, where the cross-linking fraction distribution in the photoresist is determined from the post-bake states of the bridging locations after bake.BRIEF DESCRIPTION OF DRAWINGS

[0011] Figure 1 presents a flow diagram of an example patterning process flow involving an EUV resist according to some implementations.

[0012] Figures 2A-2D present schematic illustrations of various stages of pinhole generation in a photoresist according to some implementations.

[0013] Figure 3 presents a schematic of a molecular cluster of an example EUV photoresist unit according to some implementations.

[0014] Figure 4 presents an example reaction pattern between EUV photoresist unit clusters that can define states (e.g., si, s2, s3) representing an extent of chemical conversion between EUV photoresist unit clusters according to some implementations.

[0015] Figure 5A presents a schematic illustration of an example fundamental EUV photoresist unit cluster according to some implementations of a digital twin of a photolithography workflow.

[0016] Figure 5B presents a schematic illustration of bridging locations between EUV photoresist unit clusters for tracking according to some implementations of a digital twin of a photolithography workflow.

[0017] Figure 6 presents a graph illustrating an extent of chemical conversion represented by a first state (si), second state (s2), and a third state (s3) for various doses with a certain post-exposure bake condition according to some implementations of a digital twin of a photolithography workflow.

[0018] Figure 7 presents a flow diagram of an example method of determining a probability of pinhole formation in a photoresist according to some implementations.

[0019] Figure 8 presents a block diagram of coupled models of a digital twin of a photolithography workflow according to some implementations.

[0020] Figure 9A presents a schematic illustration of an example image of a photoresist film and an amount of EUV light absorbed by the photoresist film according to some implementations.

[0021] Figure 9B presents a schematic illustration of an example photoresist film cross-section made up of a plurality of photoresist units with an indication of a photon absorption excitation event and an indication of secondary electron excitation event according to some implementations.

[0022] Figure 10A illustrates a cross-sectional view of a statistical cross-linking fraction distribution in a photoresist due to exposure stochastics and post-exposure bake randomness according to some implementations.

[0023] Figure 10B illustrates the cross-sectional view of the statistical cross-linking fraction distribution in the photoresist of Figure 10A with an identified threshold amount of cross-linking calculated from a dry development threshold according to some implementations.

[0024] Figure 11 shows a three-dimensional schematic model of a photoresist with randomized voids that affect a cross-linking ratio distribution in the photoresist according to some implementations .

[0025] Figure 12A presents a graph illustrating void area versus shrinkage in a photoresist after exposure and bake according to some implementations.

[0026] Figure 12B presents a graph illustrating void size versus shrinkage in a photoresist after exposure and bake according to some implementations.

[0027] Figure 13 presents a graph illustrating a cross-linking ratio distribution based on stochastic-only model and on a stochastic plus film inhomogeneity model according to some implementations.

[0028] Figure 14 presents an example computer system that may be employed to implement certain embodiments described in the present disclosure.DETAILED DESCRIPTION

[0029] The terms “semiconductor wafer,’" “wafer,’" “substrate,’" “wafer substrate,” and “partially fabricated integrated circuit” are used interchangeably. One of ordinary skill in the art would understand that the term “partially fabricated integrated circuit” can refer to a semiconductor wafer during any of many stages of integrated circuit fabrication. A wafer or substrate used in the semiconductor device industry typically has a diameter of 200 mm, or 300 mm, or 450 mm. The following detailed description assumes the present disclosure is implemented on a wafer. However, the present disclosure is not so limited. The work piece may be of various shapes, sizes, and materials. In addition to semiconductor wafers, other work pieces that may take advantage of the present disclosure include various articles such as printed circuit boards and the like.Introduction

[0030] A computational model or simulation of a photolithography process can be used to determine a statistical distribution of cross-linking in a photoresist and / or determine a patterning performance of the photoresist after development. In some embodiments, the computational model or simulation can be a digital twin of the photolithography process. In some embodiments, the digital twin can include multiple models that are coupled together to form the digital twin. Each of the steps of the photolithography process flow can have its own model for tracking changes to a photoresist fdm during the course of the patterning process. In some cases, the models are coupled to one another to determine a statistical distribution of cross-linking in an EUV-sensitive photoresist film after exposure and bake.

[0031] Patterning of thin films in semiconductor processing is often an important step in the fabrication of semiconductors. Patterning involves lithography. In conventional photolithography, such as 193 nm photolithography, patterns are printed by emitting photons from a photon source onto a mask and printing the pattern onto a photosensitive photoresist, thereby causing a chemical reaction in the photoresist that, after development, removes certain portions of the photoresist to form the pattern.

[0032] Advanced technology nodes (as defined by the International Technology Roadmap for Semiconductors) include nodes 22 nm, 16 nm, and beyond. In the 16 nm node, for example, thewidth of a typical via or line in a Damascene structure is typically no greater than about 30 nm. Scaling of features on advanced semiconductor integrated circuits (ICs) and other devices is driving lithography to improve resolution.

[0033] EUV lithography can extend lithography technology by moving to smaller imaging source wavelengths than would be achievable with conventional photolithography methods. EUV light sources at approximately 10-20 nm, or 11-14 nm wavelength, for example 13.5 nm wavelength, can be used for leading-edge lithography tools, also referred to as scanners. The EUV radiation is strongly absorbed in a wide range of solid and fluid materials including quartz and water vapor, and so operates in a vacuum.

[0034] EUV lithography makes use of EUV resists that are patterned to form masks for use in etching underlying layers. EUV resists may be polymer-based chemically amplified resists (CARs) produced by liquid-based spin-on techniques. An alternative to CARs is directly photopatternable metal oxide-containing films, such as those available from Inpria, Corvallis, OR, and described, for example, in U.S. Patent Publication No. 2017 / 0102612, U.S. Patent Publication No. 2016 / 021660, and U.S. Patent Publication No. 2016 / 0116839, incorporated by reference herein at least for their disclosure of photopatternable metal oxide-containing films. Such films may be produced by spin-on techniques or dry vapor-deposited. The metal oxide-containing film can be patterned directly (i.e., without the use of a separate photoresist) by EUV exposure in a vacuum ambient providing sub-30 nm patterning resolution, for example as described in U.S. Patent 9,996,004, issued June 12, 2018 and titled “EUV PHOTOPATTERNING OF VAPOR- DEPOSITED METAL OXIDE-CONTAINING HARDMASKS,” and / or in International Patent Application No. PCT / US2019 / 31618, filed May 9, 2019, and titled “METHODS FOR MAKING EUV PATTERNABLE HARD MASKS,” the disclosures of which at least relating to the composition, deposition, and patterning of directly photopatternable metal oxide films to form EUV resist masks is incorporated by reference herein. Generally, the patterning involves exposure of the EUV resist with EUV radiation to form a photo pattern in the resist, followed by development to remove a portion of the resist according to the photo pattern to form the mask.

[0035] Directly photopatternable EUV resists may be composed of or contain metals and / or metal oxides mixed within organic components. The metals / metal oxides are highly promising in that they can enhance the EUV photon adsorption and generate secondary electrons and / or show increased etch selectivity to an underlying film stack and device layers.

[0036] Figure 1 presents a flow diagram of an example patterning process flow involving an EUV resist according to some implementations. The operations of a process flow 100 may be performed in different orders and / or with different, fewer, or additional operations. In someimplementations, the operations of the process flow 100 may be implemented, at least in part, according to software stored in one or more non-transitory computer readable media.

[0037] The process flow 100 for patterning an EUV resist is performed on a substrate such as a semiconductor substrate. In some embodiments, the substrate is or includes a partially fabricated semiconductor device film stack. At block 104 of the process flow 100, an underlayer may be deposited on the substrate. In some embodiments, the underlayer may be deposited over a hard mask such as an ashable hard mark (AHM). The underlayer is configured to increase adhesion between the subsequently-formed EUV resist and the substrate. The underlayer is also configured to reduce EUV dose for effective EUV exposure of the EUV resist. The underlayer may include a vapor-deposited film of hydronated carbon doped with a non-carbon heteroatom such as oxygen (O), silicon (Si), nitrogen (N), tungsten (W), boron (B), iodine (I), chlorine (Cl), or a combination thereof. For example, an underlayer comprising a hydronated carbon film doped with iodine may improve generation of secondary electrons in the EUV resist upon exposure to EUV radiation. The underlayer may have a thickness equal to or less than about 25 nm, such as a thickness between about 2 nm and about 20 nm. In some implementations, the underlayer may be deposited using a vapor deposition technique such as PECVD or ALD.

[0038] At block 106 of the process flow 100, an EUV resist is deposited. The EUV resist may be deposited on the underlayer. Deposition of the EUV resist may be a dry deposition process such as a vapor deposition process or a wet process such as a spin-on deposition process. EUV lithography makes use of EUV resists, which may be metal oxide-based resists produced by dry vapor-deposited techniques. In some cases, the EUV resist may be a metal-containing EUV resist. The EUV resist may be an EUV-sensitive film, where the EUV-sensitive film can include one or more ligands (e.g., EUV labile ligands) that can be removed, cleaved, or cross-linked by radiation (e.g., EUV radiation). Accordingly, the EUV-sensitive film itself can be altered by exposure to such radiation. In some implementations, the EUV resist includes an organometallic material or metal-oxide-containing material. The EUV resist comprises a metal that can have a high patterning radiation absorption (e.g., an EUV absorption cross-section that is equal to or greater than IxlO7cm2 / mol). In some implementations, the metal is selected from a group consisting of tin (Sn), bismuth (Bi), tellurium (Te), cesium (Cs), antimony (Sb), indium (In), molybdenum (Mo), hafnium (Hf), iodine (I), zirconium (Zr), iron (Fe), cobalt (Co), nickel, (Ni), copper (Cu), zinc (Zn), silver (Ag), platinum (Pt), germanium (Ge), and lead (Pb). For example, the metal includes tin. As such, the EUV resist may include organotin oxide in some implementations.

[0039] Though not shown in the process flow 100, an optional cleaning process is performed to clean a backside and bevel edge of the substrate. This can be performed after deposition of theEUV resist and prior to EUV exposure. The backside and bevel edge clean may remove unintended deposits of the EUV resist from the backside and bevel edge of the substrate. The backside and bevel edge clean may be accomplished using wet cleaning techniques or dry cleaning techniques, or in combination with one another.

[0040] Though not shown in the process flow 100, an optional post-application bake (PAB) may be performed after deposition of the EUV resist and prior to EUV exposure. The PAB treatment may involve a combination of thermal treatment, chemical exposure, and moisture to increase the EUV sensitivity of the EUV resist, which can reduce the EUV dose to develop a pattern.

[0041] At block 108 of the process flow 100, the EUV resist is exposed to EUV radiation. Exposure to EUV radiation forms a photo pattern in the EUV resist. In some embodiments, EUV exposure may occur at doses ranging from about 10 mJ / cm2to about 100 mJ / cm2. Generally speaking, EUV exposure causes a change in the chemical composition and cross-linking in the EUV resist, creating a contrast in latent image that can be exploited for subsequent development. The EUV resist may be photo patterned by exposing a region to EUV light, typically under relatively high vacuum. More exposed areas of the EUV resist are created through EUV photo patterning that have altered physical or chemical properties relative to less exposed areas. The difference in properties between more exposed and less exposed areas may be exploited in subsequent processing.

[0042] At block 110 of the process flow 100, the EUV resist is exposed to a post-exposure bake (PEB). The PEB treatment may further increase contrast in etch selectivity of the EUV resist after photo patterning by EUV exposure. During PEB, the EUV resist is thermally treated in the presence of various chemical species to facilitate cross-linking in the more EUV-exposed regions of the EUV resist. The PEB treatment temperature may be controlled to further increase etch contrast in the EUV resist, where the PEB treatment temperature may be between about 100°C and about 300°C, such as between about 170°C and about 290°C. The bake ambient may be controlled to further increase etch contrast in the EUV resist, where the bake ambient may control pressure as well as introduction of reactive gases such as air, H2O, H2O2, CO2, CO, O2, O3, CH4, CH3OH, N2, H2, NH3, N2O, NO, alcohol, acetyl acetone, formic acid, Ar, He, or their mixtures. The PEB treatment can be designed to drive evaporation of organic fragments that are generated during EUV exposure, oxidize the metal hydride species into metal hydroxide, and facilitate crosslinking between neighboring -OH groups and form a cross-linked metal oxide network.

[0043] At block 112 of the process flow 100, the EUV resist is developed to form a resist mask. In various embodiments, the more exposed regions are removed (positive tone) or the less exposed regions are removed (negative tone). For instance, development may involve selective removal ofless exposed regions of the EUV resist relative to more exposed regions of the EUV resist. Development may be performed using wet or dry processes. A wet development process exposes the EUV resist to a solvent for selective removal of portions of the EUV resist. A dry development process exposes the EUV to an etch gas for selective removal of portions of the EUV resist. In some embodiments, the etch gas can include a halide such as a hydrogen halide. Accordingly, development chemistries may include but are not limited to a halide-containing gas includes a hydrogen halide (e.g., HBr, HC1, etc.), hydrogen and halogen gas (e.g., H2 and CI2, H2 and Br2, etc.), boron trichloride, an organic halide, an acyl halide, a carbonyl halide, a thionyl halide, or mixtures thereof. An organic halide can include but is not limited to CxHyFz, CxHyClz, CxHyBrz, and CxHyIz, where x, y, and z are values equal to or greater than 0. An acyl halide can include but is not limited to CH3COF, CH3COCI, CHsCOBr, and CH3COI. A carbonyl halide can include but is not limited to COF2, COCI2, COBr2, and COE. A thionyl halide can include but is not limited to SOF2, SOCI2, SOBP, and SOI2. In some embodiments, the etch gas may be flowed with or without inert / carrier gas such as He, Ne, Ar, Xe, and N2. In some embodiments, the dry development can involve a thermal process, a plasma process, or a combination of a thermal process and a plasma process. Parameters such as chamber pressure, gas flow rates, substrate temperature, and duration of exposure may be tuned. In some embodiments, a chamber pressure may be between about 20 mTorr and about 1000 mTorr. In some alternative embodiments, a chamber pressure may be between about 50 Torr and about 760 Torr. In some embodiments, a substrate temperature may be between about -60°C and about 300°C. In some embodiments where plasma is applied, the RF levels may be tuned at RF power levels equal to or less than about 1000 W. Selection of the development method along with optimization of the development parameters may influence development selectivity, roughness, descumming, and other characteristics of development.

[0044] Though not shown in the process flow 100, a post-development treatment may be performed after development and prior to pattern transfer etching. The treatment may be a thermal treatment, plasma treatment, chemical treatment, selective deposition treatment, or a combination of the aforementioned treatments. Thermal treatment may expose the resist mask to an elevated temperature reduce detectivity and LWR. Plasma treatment may expose the resist mask to plasma such as a direct (jn-situ) plasma or remote plasma in order to densify the resist mask, reduce LWR, and / or clear open area scum in a descumming process. Chemical treatment may expose the resist mask to reactive chemical species such as halide-based species to improve etch resistance, reduce outgassing, and increase line CD. Selective deposition treatment may expose the resist mask to chemical precursors for selectively depositing a protective coating on the resist mask to reduce DtS, improve etch resistance, reduce outgassing, and increase line CD. Any one or more of theforegoing treatments are applied to the resist mask after development to improve the performance of the resist mask during pattern transfer.

[0045] At block 114 of the process flow 100, pattern transfer is performed using the resist mask. During pattern transfer, one or more substrate layers are etched using the resist mask for pattern transfer. Such substrate layers are underlying the resist mask and may be removable by lithographic etching. Pattern transfer etching may etch materials to a desired depth to form a plurality of patterned features. In some embodiments, the one or more substrate layers include the hard mask and the underlayer. Any defects, roughness, or variations in CD in the resist mask are replicated in the material(s) being patterned during pattern transfer etching.

[0046] The process flow 100 illustrates some of the many steps that are performed in an example EUV photolithography workflow. After deposition of an EUV resist, the EUV photolithography workflow can typically proceed with EUV exposure, bake, and development prior to pattern transfer. Each of the many steps in the EUV photolithography workflow can be performed using different photoresist materials, different techniques (e.g., wet or dry), and different conditions (e.g., bake conditions, development chemistries, EUV dose, etc.). And variations in photoresist materials, techniques, and / or conditions can affect patterning outcomes such as CD, LWR, LER, DtS, and defects in the patterned resist mask. Pinholes are one of the possible defects that form after development in the patterned resist mask.

[0047] With all these different steps and different parameters that can be tuned in each of the steps, it can be particularly cumbersome and time-consuming to optimize an EUV photolithography process to achieve desired patterning outcomes. Extensive experimentation is required and time-intensive evaluations are needed to determine optimal parameters, materials, and processes for an EUV photolithography process. Performing such physical experiments to evaluate processes and materials can take weeks to months to achieve one cycle of learning. This lengthy process flow and evaluation flow is not only highly complex, but also time-consuming and cost-prohibitive.

[0048] Recent advances in EUV photolithography technology have necessitated resist materials with higher absorptivity and quantum efficiency as technology nodes scale to smaller feature sizes. Metal-containing EUV resists such as metal-oxide-containing EUV resists are potential candidates to replace polymer-based chemically amplified resists for EUV lithography because of their higher absorptivity and quantum efficiency. However, the driving root causes of defectivity with respect to process conditions and metal oxide film response are unclear.

[0049] It is important to ascertain a mechanistic understanding of defect generation in the resist. One such defect found in photoresist films are pinholes. Having an understanding of pinholegeneration facilitates construction of computational methods and models that can determine a source of pinholes so that process conditions and details can be optimized to minimize formation of such defects.Determining Probability of Pinhole Formation in a Photoresist

[0050] The present disclosure relates to a probability-based simulation analysis method or computational model to estimate pinhole behavior based on cross-linking behavior created during the patterning process workflow and an associated dry development threshold. The methodology computes a statistical distribution of cross-linking between photoresist unit clusters based on exposure stochastics and post-exposure bake randomness. The methodology further updates the statistical distribution of cross-linking between photoresist unit clusters based on film inhomogeneity. Film inhomogeneity can be modeled from experimental observations and analysis. The effect of processes and film characteristics on the resulting film state distribution can be evaluated with this methodology. A dry development threshold can be applied to obtain a probability of pinhole formation and gain an understanding of the root cause of pinhole formation.

[0051] Metal oxide resist is a promising material for EUV lithography because of its advantages in EUV photon absorption, film stability, and deposition flexibility. However, the aggressive requirement on small pitch and the demand for higher EUV lithography productivity require the metal oxide resists to have extremely small cluster unit volume and strong film reactivity and cross-linking induced volume change. This poses several detectivity challenges, including pinholes, that tend to form in metal oxide resists through a large range of doses.

[0052] Experimental quantification and root cause analysis of the problem associated with pinholes are challenging and time-consuming. Ordinarily, a way to study the probability of pinhole formation involves conducting experimental analysis. Conducting complex experiments and performing advanced metrology is cumbersome, time-consuming, and costly. It is difficult to detect pinholes in regions with dense 2D line / space (L / S) features because such regions are rare. Accordingly, alternative regions that are designed to have worse performance are needed as test vehicles, adding to the cost of performing experimental studies.

[0053] Pinholes act as a critical defect in a photoresist film in device fabrication. Pinholes extend through a depth of a photoresist film, forming voids and empty spaces in regions of the photoresist film that should be occupied by photoresist material. Pinholes generally represent small penetrations from a top surface of the photoresist film that extend partially or fully towards a bottom of the photoresist film. Pinholes are formed after development of the photoresist film.Pinholes have been observed experimentally in metal oxide-containing EUV-sensitive photoresist films. Pinholes have been observed through a range of EUV doses, with low EUV doses exhibiting more pinholes.

[0054] Figures 2A-2D present schematic illustrations of various stages of pinhole generation in a photoresist according to some implementations. The various stages of pinhole generation shown in Figures 2A-2D illustrate hypothesized mechanisms by which pinholes in a photoresist film may be potentially generated.

[0055] Figure 2A shows a cross-sectional 2-D schematic illustration of an example as-deposited photoresist film. The as-deposited photoresist film 200 in the cross-section may include a plurality of photoresist unit clusters 210 and some film inhomogeneities 212 randomly distributed throughout the photoresist film 200. The film inhomogeneities 212 can be film impurities such as volatile small fragment species. Without being limited by any theory, the volatile small fragment species may be smaller clusters or incomplete photoresist unit clusters. In an alternative theory, the film inhomogeneities 212 may be water molecules. Typically, photoresist unit clusters can have a metal atom surrounded by ligands or R- groups. The volatile small fragment species may have fewer ligands and may be more readily volatilized. The film inhomogeneities 212 may be formed in the as-deposited photoresist film 200 due at least in part to deposition process parameters and chemistries.

[0056] An example of a photoresist unit may be illustrated in Figure 3. A molecular depiction of an example EUV photoresist unit is illustrated in Figure 3 according to some implementations. The EUV photoresist unit is rendered in 3-D space. An EUV resist can be composed of several EUV photoresist units. The EUV photoresist unit can include an organometal-oxy cage that includes metal atoms (M) and oxygen atoms (O), which form a network of M-O-M bonds. The metal atom can include but is not limited to indium, tin, bismuth, antimony, tellurium, hafnium, or zirconium. In some embodiments, the metal atom is tin. Tin itself can have different oxidation states. In particular embodiments, the metal atom is tin(II). In other embodiments, the metal atom is tin(IV). Attached to the metal atoms are ligands (R), which are responsive to radiation exposure. The ligands (R) can be removed, cleaved, or cross-linked by radiation. The ligands (R) are formed on the perimeter of the organometal-oxy cage. By way of an example, each R can be independently, H, halo, optionally substituted alkyl, optionally substituted cycloalkyl, optionally substituted cycloalkenyl, optionally substituted alkenyl, optionally substituted alkynyl, optionally substituted alkoxy (e.g., -OR1, in which R1can be optionally substituted alkyl), optionally substituted alkanoyloxy, optionally substituted aryl, optionally substituted amino, optionally substituted bis(trialkylsilyl)amino, optionally substituted trialkylsilyl, oxo, an anionic ligand (e.g.,oxido, chloride, hydride, acetate, iminodiacetate, propanoate, butanoate, benzoate, etc.), a neutral ligand, or a multidentate ligand. The ligands (R) surround the metal-oxy (e.g., Sn-O) cage made of M-O-M bonds. The ligands (R) on the perimeter of the organometal-oxy cage can be removable to enable cross-linking between EUV photoresist unit clusters. Such cross-linking can take place during the course of EUV exposure and / or bake.

[0057] Returning to Figures 2A-2D, film inhomogeneities 212 may become voids 220 after exposure and bake as shown in Figure 2B. The film inhomogeneities 212 in Figure 2A may be species that are more volatile than the photoresist unit clusters 210. In Figure 2B, the volatile species are vaporized after exposure and bake, thereby forming the voids 220 that produce empty spaces in the photoresist film 200. Ligand cleavage and cross-linking may occur at the molecular level during exposure and / or bake steps. R-groups are cleaved and the elimination of ligands (R) leave an increased number of cross-linking points. In the presence of moisture and / or oxygencontaining counter-reactant, metal-hydroxyl (M-OH) bonds or metal-oxygen-metal (M-O-M) bonds form at the cross-linking points, where the metal-hydroxyl (M-OH) bonds may participate in further reactions to form metal-oxygen-metal (M-O-M) bonds. Cross-linking and ligand cleavage as a result of exposure and / or bake may lead to volume losses and differential initial strain in the photoresist film 200. This leads to shrinkage and local pulling forces, which further accentuates the empty space occupied by the voids 220 and increase the void area / size.

[0058] The extent of cross-linking between photoresist unit clusters can be represented by film states. Figure 4 presents an example reaction pattern between EUV photoresist unit clusters that can define film states (e.g., s 1 , s2, s3) representing an extent of chemical conversion between EUV photoresist unit clusters according to some implementations. As individual EUV photoresist unit clusters interact at a molecular level during EUV and bake operations, the EUV photoresist unit clusters may undergo chemical reactions. The reaction mechanisms in Figure 4 show that individual EUV photoresist unit clusters may undergo cross-linking and ligand cleavage to create a network that is resistant to development. To monitor the extent to which EUV photoresist unit clusters undergo chemical conversion, two or more states may be defined. In some embodiments, a first state and a second state are defined: (si) no cross-linking, and (s2) cross-linked. In some embodiments, a first, state, a second state, and a third state are defined: (si) no cross-linking, (s2) intermediate, and (s3) cross-linked. In some embodiments, a first, state, a second state, a third state, and a fourth state are defined: (si) no cross-linking, (s2) first intermediate, (s3) second intermediate, and (s4) cross-linked. Any number of states may be defined to reflect the extent of chemical conversion for EUV photoresist unit clusters.

[0059] In one example, the first state (si) represents a state with no cross-linking between individual EUV photoresist units. The EUV photoresist units are intact, and the R-groups of the EUV photoresist units remain bonded to the metal atoms. The third state (s3) represents a state with cross-linking between individual EUV photoresist units. The second state (s2) represents an intermediate state in between the first state (si) and the third state (s3). For instance, the intermediate state can represent a state in which the individual EUV photoresist units and R-groups are not necessarily intact, but the individual EUV photoresist units are not necessarily cross-linked either. In one example shown in Figure 4, the second state (s2) no longer has attached R-groups. In place of R-groups can be dangling bonds, hydroxyl groups, or other suitable species that are intermediate between M-O-M bonds and M-R bonds, which can be denoted by M-X bonds. To obtain a statistical distribution of cross-linking in a photoresist film, it may be necessary to break down the chemical reactions taking place in an EUV photolithography process into components and possible film states that the components are in. Put another way, it may be necessary to define a fundamental photoresist unit cluster and define film states, each of the film states representing an extent of chemical conversion or cross-linking between photoresist unit clusters.

[0060] Figure 5 A presents a schematic illustration of an example fundamental EUV photoresist unit cluster according to some implementations. Though the illustration in Figure 5A is shown in two-dimensional (2-D) space, it will be understood that the fundamental EUV photoresist unit cluster is a cluster that is rendered in 3-D space in the methodology or simulation. The fundamental EUV photoresist cluster is defined based on precursor and deposition behavior. Depending on the choice of precursor and the selected deposition conditions, different fundamental EUV photoresist unit clusters may be defined. In some implementations, the precursor is a metal-containing compound. An example fundamental EUV photoresist unit cluster may be a metal oxide cluster. A center of the fundamental EUV photoresist unit cluster is an oxo cage 502. The oxo cage 502 is surrounded by several R-groups 504a, 504b, and 504c located around a perimeter of the oxo cage 502. Each of the R-groups 504a, 504b, and 504c represents a ligand (R) attached to a metal atom. Example metal atoms include but are not limited to indium, tin, bismuth, antimony, tellurium, hafnium, or zirconium. There are 12 R-groups in Figure 5A, though it will be understood that a different number of R-groups can be defined in the fundamental EUV photoresist unit cluster. R-groups 504a represent R-groups oriented into the page. R-groups 504b represent R-groups oriented in plane with the page. R-groups 504c represent R-groups oriented out of the page. It will be understood that the fundamental EUV photoresist cluster is illustrative only and other possible fundamental EUV photoresist clusters may be defined in the present disclosure. There can be different- sized clusters, clusters with different metal centers, different number of and arrangements of R-groups, R-groups with absorbers, etc. Depending on the precursor(s), mixtureof precursors, and the deposition conditions / methods, the fundamental EUV photoresist unit cluster may be different in size, chemistry, and arrangement than what is shown in Figure 5A.

[0061] Figure 5B presents a schematic illustration of bridging locations between EUV photoresist unit clusters for tracking according to some implementations. The bridging locations represent points in three-dimensional space where cross-linking can take place. Though the illustration in Figure 5B is shown only in 2-D space, it will be understood that the bridging locations monitored by the digital twin are potential cross-linking points monitored in 3-D space. R-groups from individual EUV photoresist unit clusters in proximity to one another can provide such bridging locations. Such points may be identified in proximity to one another by accounting for various factors, e.g., if a distance between two discrete R-groups is within a certain threshold. These bridging locations can be mapped and monitored by the methodology or simulation throughout the photolithography workflow.

[0062] In Figure 5B, two EUV photoresist unit clusters are adjacent to one another. For simplicity, only R-groups that are oriented in plane with the page are shown. A first EUV photoresist unit cluster 512 has four R-groups 514a, 514b, 514c, and 514c. A second EUV photoresist unit cluster 514 also has four R-groups 524a, 524b, 524c, and 524d. The R-group 514d from the first EUV photoresist unit cluster 512 is close in proximity to the R-group 524d from the second EUV photoresist unit cluster 522. This region can be identified between R-group 514d and R-group 524d as a bridging location 530. This bridging location 530 is mapped in 3-D space and establishes a framework for tracking the progress of chemical conversion or cross-linking throughout the photolithography workflow. After exposure or after bake, each bridging location 530 may be in one of the three states defined by the methodology or simulation. Prior to exposure, it is generally assumed that most or all of the bridging locations 530 are in the same state, e.g., the first state (si).

[0063] Figure 6 presents a graph illustrating an extent of chemical conversion represented by a first state (si), a second state (s2), and a third state (s3) for various doses according to some implementations. The fraction of film states in Figure 6 are obtained after a PEB step. Without EUV exposure, a substantial fraction (i.e., greater than 80%) of the bridging locations are in the si state, while a negligible fraction (i.e., less than 10%) of the bridging locations are in the s3 state. The amount of bridging locations in the s2 state is similar to the amount in the s3 state. This shows that hardly any cross-linking has taken place without EUV exposure. At a small EUV dose of 5 mJ / cm2, the amount of cross-linking increases. This is reflected by an increase in s3 states and a slight increase in s2 states, and a decrease in si states. At a high EUV dose such as 25 mJ / cm2, the fraction in the s 1 states has decreased significantly and the fraction in the s3 states has increasedsignificantly. This shows that higher EUV doses lead to greater amounts of removal of R-groups and greater amounts of cross-linking.

[0064] Returning to Figures 2A-2D, the photoresist film 200 undergoes thermal dry development. Some of the voids 220 may increase in void area after thermal dry development as shown in Figure 2C. However, the voids 220 do not enlarge or expand sufficiently to form pinholes after thermal dry development. A thermal dry development selectively removes photoresist material to form a patterned mask without exposure to plasma. In negative tone development, the less exposed regions are selectively removed. In positive tone development, the more exposed regions are selectively removed. Thermal dry development may be isotropic or substantially isotropic. This means that the incoming developer species does not have a preferred angle or direction, but interacts with the photoresist film 200 coming from all angles and directions so as to provide a uniform distribution of angles / directions. The thermal dry development is highly selective between more exposed and less exposed regions. Thus, pinholes are generally not observed from the thermal dry development process.

[0065] In Figure 2D, the photoresist film 200 is exposed to plasma dry development. The plasma dry development process leads to pinholes 230 that extend from a top of the photoresist film 200 towards a center or bottom of the photoresist film 200. Plasma dry development generally occurs at low pressures with high energy developer species (e.g., high energy radicals and ions). The high energy developer species are highly directional in plasma dry development. The high energy developer species will repeatedly bombard the photoresist film 200 with directional vertical species that will increase the probability of removal of photoresist unit clusters 210 that have less cross-linking. The plasma dry development with high energy developer species will continue to “dig” and extend through the voids 220 to form the pinholes 230 in the photoresist film 200.

[0066] Figure 7 presents a flow diagram of an example method of determining a probability of pinhole formation in a photoresist according to some implementations. The operations of a process 700 may be performed in different orders and / or with different, fewer, or additional operations. One or more operations of the process 700 may be implemented in accordance with any of the techniques, simulations, or models described in the present disclosure. In some implementations, the operations of the process 700 may be implemented, at least in part, according to software stored in one or more non-transitory computer readable media. An example of a system implementing software stored in one or more non-transitory computer readable media is described in Figure 14.

[0067] At block 710 of the process 700, a distribution of cross-linking in a photoresist is determined, where the distribution of cross-linking in the photoresist is based at least in part on an analysis of exposure stochastics, bake randomness, and film inhomogeneity. A computationalmodel or simulation can generate the distribution of cross-linking in the photoresist. The photoresist may be dry or wet deposited on a substrate. In some embodiments, the photoresist is a metal oxide-containing photoresist such as an organotin oxide photoresist. The metal oxidecontaining photoresist may be an EUV-sensitive metal oxide-containing photoresist. In some embodiments, the photoresist is a negative-tone-development photoresist, or metal oxide- containing negative-tone-development photoresist.

[0068] Stochastics refers to a modeling approach that provides a random probability distribution. A distribution of cross-linking in the photoresist can be represented by stochastics. The impact of exposure on cross-linking behavior in the photoresist can be calculated using the computational model or simulation. The computational model or simulation can generate the exposure stochastics to capture the effect of exposure on cross-linking in the photoresist. In some implementations, the computational model or simulation can generate exposure stochastics and bake randomness to capture the effect of exposure and bake on cross-linking in the photoresist. Film inhomogeneity refers to a model that incorporates voids in the photoresist to affect the distribution of cross-linking in the photoresist. Thus, the distribution of cross-linking in the photoresist is not solely the result of exposure stochastics and bake randomness. Random voids also impact the distribution of cross-linking. The computational model or simulation can update the distribution of cross-linking in the photoresist by accounting for random voids. The presence of voids in the photoresist can be dependent on the deposition process and / or chemistries used to deposit the photoresist. In some embodiments, void area and void size can be estimated from exposure conditions and / or bake conditions.

[0069] In some implementations, the distribution of cross-linking in the photoresist based at least in part on exposure stochastics can be determined using a digital twin of a photolithography workflow. The digital twin can take inputs associated with an EUV photolithography workflow and generate predicted resist patterning characteristics as an output. The digital twin may leverage an understanding of what is happening with the photoresist at a molecular level to determine patterning performance. A detailed description of an example of a digital twin for an EUV photolithography workflow is described in U.S. Provisional Patent Application No. 63 / 572,723 filed April 1, 2024, entitled “Virtual Experimentation Platform for Photolithography Process Flow,” and U.S. Provisional Patent Application No. 63 / 572,731 filed April 1, 2024, entitled “Dry Development Simulation Methods for Photoresist Films,” each of which is incorporated herein by reference in its entirety and for all purposes. The application of the digital twin as described in the present disclosure for determining the distribution of cross-linking in the photoresist is illustrative only. Though the distribution of cross-linking in the photoresist based on exposure stochastics andpost-exposure bake randomness may be estimated using the digital twin as described in the present disclosure, it will be understood that the distribution of cross-linking based on exposure stochastics and post-exposure bake randomness can be obtained using any other algorithm, program, simulation, model, or methodology.

[0070] Figure 8 presents a block diagram of coupled models of a digital twin of a photolithography workflow according to some implementations. A digital twin of a photolithography workflow refers to a model of a process flow for a photolithography process. The term “digital twin” can be used synonymously with a virtual experimentation platform. The photolithography steps can include some or all of the steps described in a process flow 100 of Figure 1. In some implementations, the process flow of the photolithography process includes at least EUV exposure and development. In some implementations, the process flow of the photolithography process includes at least EUV exposure, bake, and development. The digital twin provides a 3-D simulation model of the various patterning steps performed in the photolithography process.

[0071] The digital twin can be made up of multiple models of different steps of the photolithography workflow. For example, one model can include a bake model, another model can include an exposure model, and another model can include a development model. The models can be coupled to one another. By “coupled” or “coupling,” this refers to using an output of one model as an input to another model, or vice versa. For instance, the exposure model can be coupled with the bake model in the digital twin, and the bake model can be coupled with the development model in the digital twin. In some embodiments, the models may be sequentially coupled. Two models can be “sequentially coupled” if there is one-way communication from a first model to a second model. For example, an output of the first model can be used as an input to the second model. Two models can be “fully coupled” if there is two-way communication between a first model and a second model. For example, an output of the first model can be used as an input to the second model, and an output of the second model can be used as an input to the first model.

[0072] In some implementations, at least one of the models in the digital twin is a semi-empirical Monte Carlo model. Semi-empirical models involve approximations to simplify calculations and take empirical data to adjust parameters and make improvements to the model. Monte Carlo models are probabilistic models that rely on repeated random sampling to obtain numerical results that capture a stochastic rather than deterministic outcome. In some implementations, two or more models in the digital twin are semi-empirical Monte Carlo models.

[0073] In Figure 8, the digital twin 800 is a model covering multiple steps of a photolithography process, where the digital twin 800 can include models of different steps of the photolithographyprocess. Such steps can include EUV exposure, bake, and development, among other possible steps in the photolithography process. The digital twin 800 may monitor changes in film states that occur as a result of these steps in the photolithography process.

[0074] In some embodiments , the digital twin 800 can receive inputs 810 and generate patterning outcomes and / or defectivity as outputs 850. The inputs 810 may include user-defined inputs or computer- implemented inputs that are generated by the digital twin 800. Examples of user-defined inputs include but are not limited to aerial image, EUV dose, bake parameters, and development parameters. Other examples of user-defined inputs may include deposition precursor and deposition conditions. The user-defined inputs may be used to calculate and generate additional inputs. In some implementations, the computer-implemented inputs are generated by calibrating parameters based on user-defined inputs. For example, computer-implemented inputs may include but are not limited to EUV resist external quantum efficiency, bake kinetic constants, EUV resist density, EUV resist cluster size, EUV resist absorption coefficient, and EUV resist molecular weight. Some or all of these parameters may be calibrated based on a selected material of the EUV resist. In some cases, the material of the EUV resist may be obtained by the deposition precursor(s) and deposition conditions.

[0075] The inputs 810 provide a starting point for the digital twin 800 to simulate the EUV photolithography process. The inputs 810 may at least include a material and material properties associated with the EUV resist. In some implementations, the inputs 810 further include a map of bridging locations associated with the as-deposited EUV resist, which may be rendered in 3-D space.

[0076] The inputs 810 received by the digital twin 800 may include one or more inputs associated with EUV exposure, one or more inputs associated with a material of the EUV resist, one or more inputs associated with bake parameters, and one or more inputs associated with development parameters. Inputs associated with EUV exposure may include but are not limited to EUV dose and aerial image of the EUV resist from EUV exposure. An aerial image may include a planar intensity distribution of incoming light that the substrate observes. It may be calculated by a rigorous lithography simulator such as HyperLith™ or PROLITH™, considering the light source, mask pattern, mask stack material, and focus, among other possible effects. Inputs associated with the material of the EUV resist may include but are not limited to an absorption coefficient of the EUV resist, an external quantum efficiency of the EUV resist, a cluster size of the EUV resist, a density of the EUV resist, and a thickness of the EUV resist. Inputs associated with bake parameters may include a bake ambient and one or more bake kinetic constants. The bake ambient may include factors such as a bake temperature, pressure, gas species, flow rates ofgas species, duration of exposure, and other bake-related conditions. Inputs associated with development parameters may include but are not limited to whether the development is wet or dry development. Other development parameters may include factors such as development chemistry, development temperature, development pressure, duration of exposure, and other development- related conditions. Note that the inputs 810 are merely exemplary. In some embodiments, some of the inputs shown in Figure 8 may be omitted. Additionally or alternatively, in some embodiments, any other parameters not shown in Figure 8 can be included in the inputs 810. For instance, such inputs may be related to EUV resist deposition (e.g., deposition precursor(s), deposition conditions, etc.) or related to underlayer deposition (e.g., composition of the underlayer, underlayer deposition conditions, thickness, etc.), or related to a system state, or related to a configuration of hardware or software, etc.

[0077] The digital twin 800 may further analyze the inputs 810 to determine additional parameters. For instance, using the material of the EUV resist, the digital twin 800 may identify an EUV photoresist unit cluster (including its cluster size) and identify bridging locations. The bridging locations represent potential cross-linking points between adjacent EUV photoresist unit clusters in an EUV resist. The identified bridging locations are mapped and modeled in 3-D space. The digital twin 800 builds upon the 3-D rendering of the photoresist unit cluster (including its cluster size) and maps and monitors the bridging locations in 3-D space.

[0078] After receiving user-defined inputs and calibrating parameters, some or all of the inputs 810 are received at an EUV exposure model 820. The EUV exposure model 820 receives at least pre-exposure states of the bridging locations of the EUV resist and determines the post-exposure states of the bridging locations of the EUV resist. In some embodiments, the EUV exposure model 820 can determine a photon absorption pattern 822, and the photon absorption pattern 822 can be used to determine a secondary electron pattern 824. The photon absorption pattern 822 and the secondary electron pattern 824 can be used to determine the exposure stochastics in the EUV resist.

[0079] In some particular embodiments, the EUV exposure model 820 receives inputs including an aerial image of the EUV resist, an EUV dose, bridging locations, pre-exposure states of the bridging locations, and an absorption coefficient of the EUV resist. In some embodiments, the pre-exposure states of the bridging locations may be the same (e.g., si state). Using these inputs associated with EUV exposure and associated with the material of the EUV resist, the EUV exposure model 820 can obtain the photon absorption pattern 822. The photon absorption pattern 822 provides photon absorption coordinates of the EUV resist indicative of photon absorption events in the EUV resist. In some implementations, the photon absorption coordinates are represented as stochastics.

[0080] In some embodiments, the photon absorption coordinates taken from the photon absorption pattern 822 are provided as inputs to determine a secondary electron pattern 824. Using the photon absorption coordinates, an external quantum efficiency (EQE) of the EUV resist, and a secondary electron blur radius of the EUV resist, the EUV exposure model 820 can obtain the secondary electron pattern 824. The external quantum efficiency is related to a number of free electrons produced by incident photons. This can be calculated based on a material of the EUV resist. The secondary electron blur radius is related to the distances that the secondary electrons travel from their origin. The secondary electron pattern 824 provides secondary electron coordinates of the EUV resist representing secondary electron events in the EUV resist. In some implementations, the secondary electron coordinates are represented as stochastics.

[0081] Figure 9A presents a schematic illustration of an example image of a photoresist film and an amount of EUV light absorbed by the photoresist film according to some implementations. At an EUV module or scanner, the photoresist film is exposed to EUV light to cause photo patterning of the photoresist film, thereby forming more EUV-exposed areas and less EUV-exposed areas. Photons of the EUV light are absorbed by the photoresist film, but photon absorption by the photoresist film is not necessarily evenly distributed across the photoresist film. Photon absorption can depend on a variety of factors, such as the absorption coefficient of the EUV resist, the density of the EUV resist, and the EUV dose. The intensity of the EUV light entering the photoresist film may be strongest at the center and gradually weaken outwards from the center. An amount of photon absorption in the photoresist film may vary along the thickness (z-direction) of the film and along the plane (xy-plane) of the film. As shown in Figure 9A, the amount of photon absorption gradually decreases along the thickness (i.e., depth) of the photoresist film and gradually decreases closer to the boundaries between the line and the trench of the photoresist film. The absorbed light distribution shown in Figure 9A shows the impact of light distribution primarily along the z-direction. Generally speaking, an aerial image shows the impact of light distribution primarily along both the x-direction and y-direction. By accounting for the distribution of light absorption in the x, y, and z-directions, a 3-D model of the EUV exposure can be accounted for in the EUV exposure model.

[0082] Photon absorption by the photoresist film represents a discrete event that can be captured by stochastics. Assuming that the photoresist film can be made of a plurality of discrete photoresist units, each photoresist unit can have a corresponding probability of a photon absorption excitation event. The photon absorption excitation event represents a transition from one state to another state (e.g., si to s2) due to photon absorption at the photoresist unit. Factors such as aerial image,absorption coefficient, film density, film thickness, and EUV dose can influence a number of possible photon absorption sites where photon absorption excitation events can take place.

[0083] Excitation may occur not only by photon absorption, but also by secondary electrons. EUV light absorbed by the photoresist film may produce highly energetic photoelectrons that in turn cascade to generate low-energy secondary electrons that diffuse laterally by a few or several nanometers. These secondary electrons increase the extent of chemical reactions in the photoresist film. Secondary electrons may cause transitions from one state to another state (e.g., si to s2) in the photoresist unit. Because secondary electrons may cause secondary electron excitation events in various directions from a photon absorption site, secondary electron excitation events may cause observable LER variation, LWR variation, and defects in an exposure pattern.

[0084] Figure 9B presents a schematic illustration of an example photoresist film cross-section made up of a plurality of photoresist units with an indication of a photon absorption excitation event and an indication of secondary electron excitation event according to some implementations. The photoresist film 900 includes a plurality of photoresist units 904. EUV light introduces photons 910 that are absorbed by the photoresist film 900. In view of the probability of photon absorption shown in Figure 9A, with the highest probability closer to the top of the photoresist film than at the bottom and closer to the center of the photoresist film than at the periphery, photon absorption excitation events 920 can be captured by stochastics. The probability of excitation due to a photon 910 can be based on the number of available excitation events and the number of available bridging locations. At the location of the photon absorption excitation event 920, secondary electrons are generated. Secondary electrons propagate to areas around the photon absorption excitation event 920 and may cause a secondary electron excitation event 930. The probability of secondary electron excitation events 930 can also be captured by stochastics, with higher probabilities closer to the photon absorption excitation event 920 than farther from the photon absorption excitation event 920. Various factors can influence the probability distribution associated with secondary electron excitation events 930, including but not limited to an external quantum efficiency (EQE) of the photoresist film and a secondary electron blur radius. In other words, the EQE and the secondary electron blur radius can dictate the number of excitation events caused by secondary electrons per photon absorption excitation event 920.

[0085] Referencing the digital twin 800 of Figure 8, the EUV exposure model 820 can determine photon absorption coordinates (e.g., x, y, z coordinates) from photon absorption excitation events and secondary electron coordinates from secondary electron excitation events. Using the photon absorption coordinates and the secondary electron coordinates, the EUV exposure model 820 can determine where transitions to new states are taking place in the EUV resist. Accordingly, theEUV exposure model 820 can determine post-exposure states (e.g., si state, s2 state, or s3 state) of the bridging locations of the EUV resist. The post-exposure states in the EUV resist can represent exposure stochastics for a distribution of cross-linking in the EUV resist.

[0086] Returning to the process 700 of Figure 7, the distribution of cross-linking in the photoresist can be further determined using bake-induced transitions or bake randomness. Bake- induced transitions from a post-exposure bake step can further impact the distribution of crosslinking in the photoresist. Post-exposure bake conditions can affect the amount of cross-linking in the photoresist and the distribution of cross-linking in the photoresist. Post-exposure bake conditions can include but are not limited to bake temperature, pressure, gas species, flow rates of gas species, and duration of exposure. Accounting for bake-induced transitions in addition to exposure stochastics and film inhomogeneity can provide a more accurate statistical distribution of cross-linking in the photoresist. An example of an analysis of post-exposure bake randomness and its impact on the distribution of cross-linking in the photoresist is described in a bake model 830 of Figure 8.

[0087] In the digital twin 800 of Figure 8, the post-exposure states of the bridging locations of the EUV resist are received at a bake model 830. The bake model 830 is coupled to the EUV exposure model 820. The bake model 830 receives the post-exposure states of the bridging locations and determines post-bake states of the bridging locations. Using bake parameters such as a bake ambient and one or more bake kinetic constants, the bake model 830 can predict updated states of the bridging locations. The bake ambient can describe conditions such as bake temperature, pressure, gas species, flow rates of gas species, and duration of exposure, among other bake-related conditions. The values of the one or more bake kinetic constants can be determined from experimental data and the bake ambient. In some embodiments, the bake model 830 utilizes an analytical framework described by kinetic Monte Carlo simulation approaches.

[0088] In some embodiments, the probabilities of thermally-induced bridging location transformations during the bake process can be described in the following manner:Pi — > i (t): probability of a bridging location remaining in si state.Pi — > 2 (t): probability of a bridging location transitioning from si to s2 state.P2 — > 2 (t): probability of a bridging location remaining in s2 state.P2 — > 3 (t): probability of a bridging location transitioning from s2 to s3 state.P3 — > 3 (t): probability of a bridging location remaining in s3 state.Pi — > 3 (t): probability of a bridging location transitioning from si to s3 state.

[0089] The probabilities can be further understood kinetically. Physical constants, referred to as bake kinetic constants, that describe bake-induced cross-linking and bake-induced removal of R-groups can be determined analytically from experimental data. The bake kinetic constants are implemented in analytical relationships that can describe transitions from one state to another, where the bake kinetic constants reflect rates of reactions for such transitions. For example, a first bake kinetic constant ki can be implemented to describe a number of bake-induced transitions from an si to s2 state: Si (ki [S i]) — > S2. A second bake kinetic constant k2 combined with the first bake kinetic constant ki can be implemented to describe a number of bake-induced transitions from an s2 to s3 state: S2 ((ki+k2)[S2]) — > S3. The analytical relationships are implemented stochastically using a temporal probability based Monte Carlo model. The temporal probability based Monte Carlo model is employed to ascertain the probabilities of thermally-induced transitions from one state to another state at bridging locations in the EUV resist.

[0090] In the digital twin 800 of Figure 8, the bake model 830 can determine post-bake states of the bridging loc2ations in the EUV resist using temporal probability based Monte Carlo model. The temporal probability based Monte Carlo model provides a kinetic understanding of bake- induced transitions and the probability of bake-induced transitions using the one or more bake kinetic constants. In some implementations, the post-bake states in the EUV resist can represent bake-induced stochastics or randomness for a distribution of cross-linking in the EUV resist.

[0091] In some implementations, an amount of cross-linking in a photoresist can be represented by a cross-linking ratio. The cross-linking ratio can represent an average value of a number of cross-linked states divided by a total number of states or bridging locations in a portion of the photoresist. By way of an example, the cross-linking ratio in a portion of the photoresist can be: (s3 states) / (sl+s2+s3 states). Each area, region, or portion of the photoresist can have photoresist unit clusters that are capable of forming cross-linked states. The cross-linking ratio shows the extent of cross-linking in a particular area, region, or portion of the photoresist.

[0092] Figure 10A illustrates a 2-D cross-section example of a statistical cross-linking fraction distribution in a photoresist due to at least exposure stochastics and post-exposure bake randomness according to some implementations. The statistical distribution of cross-linking in the photoresist is shown along the height of the photoresist in the y-direction and along a horizontal dimension in the x-direction. The statistical distribution of cross-linking can also be referred to as a cross-linking ratio spatial distribution. The statistical distribution of cross-linking in the photoresist is exhibited as an averaged histogram or grid with values in each of the cells of the grid. Each cell corresponds to a particular area, region, or portion of the photoresist. The values represent a cross-linking ratio in that particular area, region, or portion of the photoresist. Thevalues can be understood as the fraction of cross-linking in that particular area, region, or portion of the photoresist. Thus, 0.3 refers to 30% cross-linking in a portion of a photoresist, and 0.2 refers to 20% cross-linking in another portion of the photoresist. The cross-linking ratio spatial distribution may be generated using a digital twin as described in Figure 8 or other computational model, simulation, program, algorithm, or methodology. The cross-linking ratio spatial distribution may be generated using exposure stochastics and bake-induced stochastics or randomness, where the exposure stochastics and bake-induced stochastics or randomness depend on the exposure conditions and post-exposure bake conditions, respectively.

[0093] Figure 10B illustrates the 2-D cross-section statistical cross-linking fraction distribution in the photoresist of Figure 10A with an identified threshold amount of cross-linking calculated from a dry development threshold according to some implementations. Along the height of the cross-section of the photoresist, an average cross-linking ratio can be calculated through height. Hence, each column in the grid can have an associated average cross-linking value. Since pinholes are generated along the depth or height of the photoresist, the average cross-linking ratio through the height of the photoresist is a relevant value. As shown in Figure 10B, the average cross-linking ratio through the height of the photoresist includes: 0.21, 0.24, 0.24, 0.11, 0.24, 0.21, and 0.27. These values can be compared against a threshold value such as a dry development threshold value. As discussed in more detail below, the dry development threshold value can be determined experimentally under a dry development threshold test. Areas with cross-linking ratios or average cross-linking ratios below the threshold value determine a probability of pinhole generation. In some examples, average cross-linking values through height that are below the threshold value may be identified candidates for pinhole generation. The likelihood of generating a pinhole in the photoresist at one of the columns is determined by comparison against the threshold value. In Figure 10B, the threshold value is identified as 0.15. The column having an average cross-linking ratio of 0.1 1 (highlighted in Figure 10B) is less than the threshold value of 0.15, for which a probability of pinhole generation can be calculated.

[0094] The statistical distribution of cross-linking in the photoresist can be determined from exposure stochastics and bake-induced transitions. In some implementations, the exposure stochastics and bake-induced transitions (e.g., post-exposure bake randomness) can be calculated from exposure and post-exposure bake conditions. In some cases, the exposure stochastics and bake-induced transitions can be estimated using a digital twin of a photolithography process as disclosed herein. However, the exposure stochastics and bake-induced transitions in the photoresist are insufficient to accurately predict pinhole probability in a photoresist. In other words, stochastics alone do not sufficiently explain experimentally-observed pinholes in aphotoresist. The statistical distribution of cross-linking in the photoresist needs to be updated to account for film inhomogeneities and voids to accurately predict pinhole probability in the photoresist.

[0095] The presence of film inhomogeneities may lead to voids in the photoresist, and the presence of voids impact the average cross-linking through a depth of the photoresist because no cross-linking takes place in areas with voids. Such voids are distributed throughout the photoresist and impact the statistical distribution of cross-linking in the photoresist. Exposure and postexposure bake steps induce cross-linking and ligand cleavage, which results in shrinkage, deformation, and volume loss in the photoresist. Void area increases with shrinkage, and void size increases with shrinkage.

[0096] Figure 11 shows a 3-D schematic model of a photoresist with randomized voids that affect a cross-linking ratio distribution in the photoresist according to some implementations. The model can be constructed by performing a three-dimensional film state simulation on a blanket film with actual exposure and post-exposure bake kinetics. Without being limited by any theory, film inhomogeneities such as volatile small fragment species can be formed in an as-deposited photoresist as a result of deposition process parameters and chemistries. These film inhomogeneities can become voids after exposure and post-exposure bake steps. These voids may be randomly distributed throughout the photoresist. Void area and void size may increase with shrinkage and local pulling that results from cross-linking and ligand cleavage during the exposure and bake steps. Randomized voids in the photoresist impact the cross-linking ratio distribution and will ultimately impact the probability of pinhole generation in the photoresist. Though voids are illustrated as uniform spheres in Figure 11 for simplicity, it will be understood that void size and shape can be of different sizes and shapes that can be originated from a particular distribution.

[0097] Referencing the digital twin 800 of Figure 8, the post-bake states of the bridging locations of the EUV resist are received at a film inhomogeneity model 835. The film inhomogeneity model 835 may be coupled to the bake model 830. Alternatively, the film inhomogeneity model 835 may be coupled to the EUV exposure model 820. The film inhomogeneity model 835 receives the film states from one or both of the EUV exposure model 820 and bake model 830 to update the film states. Film inhomogeneities and voids impact the distribution of cross-linking in the EUV resist. Using experimental observation and analysis based on various deposition process conditions and chemistries, the film inhomogeneity model 835 can estimate the distribution of voids in the EUV resist. Void area and size can be further estimated based on exposure and bake conditions. The post-bake states of bridging locations in the EUV resist can be updated by the film inhomogeneitymodel 835 that determines the impact of voids on the distribution of cross-linking in the EUV resist.

[0098] Figure 12A presents a graph illustrating void area versus shrinkage in a photoresist after exposure and bake according to some implementations. As shown in Figure 12A, the void area increases with shrinkage in the photoresist that is induced as a result of exposure and post-exposure bake. Figure 12B presents a graph illustrating void size versus shrinkage in a photoresist after exposure and bake according to some implementations. As shown in Figure 12B, void size increases with shrinkage in the photoresist that is induced as a result of exposure and post-exposure bake. Size and area of the voids in the photoresist can be controlled by adjusting exposure and post-exposure bake conditions. Void size and void area are dependent on particular definitions and metrology methods that are employed.

[0099] The impact of voids can be studied and evaluated with minimal experimental observation. The methodology of the present disclosure can test the impact of various levels of film inhomogeneities and its impact on the statistical distribution of cross-linking. The varying levels of film inhomogeneities can be controlled by adjusting deposition, exposure, and postexposure bake conditions. Modeling and simulations can be performed to calculate a cross-linking ratio distribution inside the photoresist under two scenarios: (1) exposure / PEB stochastics only and (2) exposure / PEB stochastics plus voids. A simulation can be performed on a blanket film under certain exposure and post-exposure bake conditions. An average cross-linking ratio through height can be recorded at each (x, y) coordinate position. This can be presented as a histogram of values representing the average cross-linking ratio. The values at each bin / cell with respect to film size can be normalized to get a probability of each cross-linking ratio.

[0100] Returning to the process 700 of Figure 7, at block 720 of the process 700, a threshold value is optionally identified that is associated with a threshold amount of cross-linked states in the photoresist. The threshold value may correspond to a dry development threshold value. The dry development threshold value is determined experimentally using a dry development threshold test. The dry development threshold value is determined based on specific thermal dry development and plasma dry development conditions. The threshold value determines the likelihood of generating a pinhole in the photoresist. By way of an example, a threshold value (e.g., 0.15) can be determined for a specific thermal dry development and plasma dry development condition. The probability of pinhole generation can be calculated using the threshold value, where the probability of pinhole generation can be calculated based on areas, regions, or portions of the photoresist that have cross-linking ratios below the threshold value.

[0101] As an example, the threshold value associated with an amount of cross-linked states can be determined using a static threshold model. To generate the static threshold model, experimental data is collected and a relationship between the predicted film states and the experimental data is established and validated. Blanket experiments may reveal that dry development has the same performance whenever the predicted film states are the same. Accordingly, in the static threshold model, dry development performance is correlated with predicted film states, regardless of what combination of dose conditions and bake conditions are used to reach a particular film state. In some examples, the predicted film state, such as a cross-linking ratio at various locations in the photoresist, can be obtained using the EUV exposure model and bake model (and optionally a film inhomogeneity model) of a digital twin as described in the present disclosure.

[0102] Experiments are performed under different exposure processes / conditions and under different bake processes / conditions. In a resist mask, an edge of the line corresponds to a location where dry development stops. To identify the threshold value where dry development stops, pattern edge locations are mapped to locations in a simulated photoresist where dry development stops for a particular dry development process / condition. These locations correspond to a quantitative amount of cross-linked states (e.g., cross-linking ratio) in the simulated photoresist. This identifies the dry development threshold value, which marks the pattern edge location or completion points for dry development given a particular dry development process / condition. In some cases, the dry development process / condition can include a dry development time, dry development pressure, dry development temperature, and dry development chemistry, among other parameters. In some cases, the dry development process / condition may account for a thermal dry development process / condition as well as a plasma dry development process / condition. Threshold values can be experimentally determined for various dry development recipes.

[0103] Referencing the digital twin 800 of Figure 8, the post-bake states of the bridging locations of the EUV resist are received at a development model 840. The development model 840 may be coupled to the bake model 830. In some implementations, the development model 840 may be coupled to the film inhomogeneity model 835 that updates the post-bake states to account for film inhomogeneities and voids. The dry development model 840 receives the post-bake states of the bridging locations of the EUV resist and determines post-development states of the bridging locations of the EUV resist. Using development parameters such as whether the development is wet or dry, the development model 840 can determine what bridging locations are removed and what bridging locations are intact after development. This can map to what portions of the EUV resist are removed and what portions of the EUV resist are intact in 3-D space. In some implementations of the present disclosure, the dry development model 840 can further determinewhere pinholes are generated in the EU V resist or calculate a probability of pinhole generation in the EUV resist. Whereas post-bake states and post-exposure states of bridging locations generally reflect an extent of chemical conversion at the bridging locations (e.g., si, s2, s3 or cross-linking ratio), the post-development states of the bridging locations generally reflect whether the bridging locations (and their corresponding photoresist unit clusters) are removed or remain intact (e.g., dl - intact, d2 - removed).

[0104] Here, the post-development states of the bridging locations are not characterized in the same manner as the post-exposure states of the bridging locations or the post-bake states of the bridging locations. Rather, the post-development sates of the bridging locations refer to whether a bridging location is left intact (dl) or removed (d2) after development. Particular models can be selected that establish a relationship between the post-development states (e.g., dl, d2) of the bridging locations and the post-bake states of the bridging locations. The development model 840 can include a plurality of models 842, 844, and 846 that predict development behavior using the post-bake states of the bridging locations from the bake model 830 or film inhomogeneity model 835. Examples of development models include but are not limited to: (1) wet development model 842, (2) static dry development model 844, and (3) transient particle tracing model 846. The wet development model 842 is used when the development method is a wet development method. The static dry development model 844 or the transient particle tracing model 846 is used when the development method is a dry development method. Detailed descriptions of these models can be found in U.S. Provisional Patent Application No. 63 / 572,731 filed April 1, 2024, entitled “Dry Development Simulation Methods for Photoresist Films,” which is incorporated herein by reference in its entirety and for all purposes.

[0105] Outputs 850 of the digital twin 800 can include one or more of image generation 852, patterning metrics 854, and pinhole generation or pinhole probability 856.

[0106] In some embodiments, pinhole generation or pinhole probability 856 can be determined directly from the development model 840. Pinhole generation or pinhole probability 856 outputted by the digital twin 800 may closely compare to actual experimental results.

[0107] Returning to Figure 7, at block 730 of the process 700, a probability of pinhole formation in the photoresist is determined based at least in part on an amount of cross-linked states that are below the threshold value. The statistical distribution of cross-linking in the photoresist can be determined from an analysis of exposure stochastics and film inhomogeneity. This can be represented in a histogram or other visual representation of quantitative data. Film states or crosslinked states can be mapped to various locations throughout the photoresist. In some implementations, an average cross-linking value through height can be calculated in thephotoresist. Average cross-linking values through height that fall below the threshold value may be determined to form a pinhole in the photoresist. The computational model or simulation can determine the probability of pinhole formation or determine locations where pinholes are formed after development of the photoresist.

[0108] Pinhole formation or a probability of pinhole formation may be determined using the computational model or simulation. The computational model or simulation receives the statistical distribution of cross-linking in the photoresist. The statistical distribution of cross-linking in the photoresist may account for changes in film states due to exposure, bake, and film inhomogeneity. For example, the statistical distribution of cross-linking in the photoresist may be determined using the digital twin 800 comprising the EUV exposure model 820, bake model 830, and film inhomogeneity model 835. The computational model or simulation may identify a dry development threshold value associated with a threshold cross-linking state for removal. By way of an example, the dry development threshold value may be calculated using a static threshold model. The dry development threshold value is related to the dry development processes and conditions. Cross-linked states that are below the dry development threshold value may be deemed to be removed as a result of dry development or calculated with a probability of removal.

[0109] In some embodiments, the statistical distribution of cross-linking in the photoresist can be represented graphically as a percentage of each average cross-linking ratio as a function of cross-linking ratio. In other words, percentages of average cross-linking ratios in the photoresist can be visually represented. An example is shown in Figure 13. Figure 13 presents a graph illustrating a cross-linking ratio distribution based on a stochastic-only model and a stochastic plus film inhomogeneity model according to some implementations. As shown in Figure 13, the stochastic-only model result behaves like a Gaussian distribution. The stochastic and film inhomogeneity model has a distribution with a longer tail on the low cross-linking side. This shows that with incorporation of the film inhomogeneity model into the statistical distribution of cross-linking in a photoresist, the resulting distribution will show greater amounts of low crosslinking ratios than a stochastics-only model, manifested by a long tail on the left side. Quite simply, there are fewer cross-linked states in the photoresist by accounting for voids in the photoresist. This is consistent with experimental observations.

[0110] The threshold value such as a dry development threshold value can be shown as a vertical dashed line in Figure 13. In some implementations, the threshold value is identified using a static threshold model or test. Cross-linking ratios below the threshold value are removed after dry development. As shown in Figure 13, there is a higher percentage of cross-linking ratios below the threshold value in the stochastics plus film inhomogeneity model compared to the stochastics-only model. The probability of pinhole formation in the photoresist can be calculated using integration to calculate an area formed by each curve and bounded by the threshold value.

[0111] Using knowledge from the aforementioned process 700, it can be understood by the computational model and simulation that pinholes generated in the photoresist can be strongly correlated to film inhomogeneities and all process conditions. Film inhomogeneities contribute to a greater percentage of low cross-linking ratios that cause a higher probability of pinhole formation. Dry development processes and conditions can be tailored to shift the threshold value (e.g., dry development threshold value) that can lead to a greater or reduced probability of pinhole formation. The methodology that can predict the probability of pinhole formation can be leveraged to gain a mechanistic understanding of pinhole formation. Such simulation results are corroborated with experimental results through exposure doses, FEB conditions, and thermal dry development conditions. With a mechanistic understanding of pinhole formation, process conditions during the photolithography workflow can be calibrated and optimized to identify the driving root cause and to minimize pinhole formation.

[0112] Mitigation of pinholes can be achieved by: (1) improving the quality of the as-deposited photoresist, thereby reducing volatile fragments that are formed in the as-deposited photoresist that can result in voids. Improving the quality of the as-deposited photoresist can be accomplished by optimizing deposition conditions and chemistries so that fewer volatile fragment species are formed. Mitigation of pinholes can also be achieved by: (2) increasing the dry development threshold value by optimizing the thermal dry development and plasma dry development recipe. The dry development threshold value can be shifted to reduce the probability of pinhole generation. For instance, the plasma dry development conditions can be adjusted to be less harsh and having fewer energized ions and / or radicals. In some cases, mitigation of pinholes can also be achieved by: (3) adjusting the exposure and bake parameters. An amount of cross-linking in the photoresist can be obtained by providing a higher dose and more carefully designed post-exposure bake conditions (e.g., higher temperatures, longer duration). With greater amounts of cross-linking from the extra dosage or more carefully designed post-exposure bake conditions, the photoresist may be more resistant to pinhole generation from thermal and plasma dry development processes.

[0113] Certain embodiments disclosed herein relate to computational systems for generating and / or using various computational models. Certain embodiments disclosed herein relate to methods for generating and / or using a computational model implemented on such systems. A system for generating a computational model may also be configured to receive data and instructions such as program code representing physical processes occurring during thesemiconductor device fabrication operation. In this manner, a computational model is generated or programmed on such system.

[0114] Many types of computing systems having any of various computer architectures may be employed as the disclosed systems for implementing computational models and algorithms for generating and / or optimizing such models. For example, the systems may include software components executing on one or more general purpose processors or specially designed processors such as Application Specific Integrated Circuits (ASICs) or programmable logic devices (e.g., Field Programmable Gate Arrays (FPGAs)). Further, the systems may be implemented on a single device or distributed across multiple devices. The functions of the computational elements may be merged into one another or further split into multiple sub-modules.

[0115] In some embodiments, code executed during generation or execution of a computational model on an appropriately programmed system can be embodied in the form of software elements which can be stored in a nonvolatile storage medium (such as optical disk, flash storage device, mobile hard disk, etc.), including a number of instructions for making a computer device (such as personal computers, servers, network equipment, etc.).

[0116] At one level a software element is implemented as a set of commands prepared by the programmer / developer. However, the module software that can be executed by the computer hardware is executable code committed to memory using “machine codes” selected from the specific machine language instruction set, or “native instructions,” designed into the hardware processor. The machine language instruction set, or native instruction set, is known to, and essentially built into, the hardware processor(s). This is the “language” by which the system and application software communicates with the hardware processors. Each native instruction is a discrete code that is recognized by the processing architecture and that can specify particular registers for arithmetic, addressing, or control functions; particular memory locations or offsets; and particular addressing modes used to interpret operands. More complex operations are built up by combining these simple native instructions, which are executed sequentially, or as otherwise directed by control flow instructions.

[0117] The inter-relationship between the executable software instructions and the hardware processor is structural. In other words, the instructions per se are a series of symbols or numeric values. They do not intrinsically convey any information. It is the processor, which by design was preconfigured to interpret the symbols / numeric values, which imparts meaning to the instructions.

[0118] The models used herein may be configured to execute on a single machine at a single location, on multiple machines at a single location, or on multiple machines at multiple locations. When multiple machines are employed, the individual machines may be tailored for their particulartasks. For example, operations requiring large blocks of code and / or significant processing capacity may be implemented on large and / or stationary machines.

[0119] In addition, certain embodiments relate to tangible and / or non-transitory computer readable media or computer program products that include program instructions and / or data (including data structures) for performing various computer-implemented operations. Examples of computer-readable media include, but are not limited to, semiconductor memory devices, phasechange devices, magnetic media such as disk drives, magnetic tape, optical media such as CDs, magneto-optical media, and hardware devices that are specially configured to store and perform program instructions, such as read-only memory devices (ROM) and random access memory (RAM). The computer readable media may be directly controlled by an end user or the media may be indirectly controlled by the end user. Examples of directly controlled media include the media located at a user facility and / or media that are not shared with other entities. Examples of indirectly controlled media include media that is indirectly accessible to the user via an external network and / or via a service providing shared resources such as the “cloud.” Examples of program instructions include both machine code, such as produced by a compiler, and files containing higher level code that may be executed by the computer using an interpreter.

[0120] In various embodiments, the data or information employed in the disclosed methods and apparatus is provided in an electronic format. Such data or information may include design layouts, simulation values, sensor values, and the like. As used herein, data or other information provided in electronic format is available for storage on a machine and transmission between machines. Conventionally, data in electronic format is provided digitally and may be stored as bits and / or bytes in various data structures, lists, databases, etc. The data may be embodied electronically, optically, etc.

[0121] In some embodiments, a computational model can be viewed as a form of application software that interfaces with a user and with system software. System software typically interfaces with computer hardware and associated memory. In some embodiments, the system software includes operating system software and / or firmware, as well as any middleware and drivers installed in the system. The system software provides basic non-task- specific functions of the computer. In contrast, the modules and other application software are used to accomplish specific tasks. Each native instruction for a module is stored in a memory device and is represented by a numeric value.

[0122] An example computer system 1400 is depicted in Figure 14. As shown, computer system 1400 includes an input / output subsystem 1402, which may implement an interface for interacting with human users and / or other computer systems depending upon the application. Embodimentsof the disclosure may be implemented in program code on system 1400 with I / O subsystem 1402 used to receive input program statements and / or data from a human user (e.g., via a GUI or keyboard) and to display them back to the user. The I / O subsystem 1402 may include, e.g., a keyboard, mouse, graphical user interface, touchscreen, or other interfaces for input, and, e.g., an LED or other flat screen display, or other interfaces for output.

[0123] Communication interfaces 1407 can include any suitable components or circuitry used for communication using any suitable communication network (e.g., the Internet, an intranet, a wide-area network (WAN), a local-area network (LAN), a wireless network, a virtual private network (VPN), and / or any other suitable type of communication network). For example, communication interfaces 1407 can include network interface card circuitry, wireless communication circuitry, etc.

[0124] Program code may be stored in non-transitory media such as secondary memory 1410 or memory 1408 or both. In some embodiments, secondary memory 1410 can be persistent storage. One or more processors 1404 reads program code from one or more non-transitory media and executes the code to enable the computer system to accomplish the methods performed by the embodiments herein, such as those involved with generating or using a model as described herein. Those skilled in the art will understand that the processor may accept source code, such as statements for executing training and / or modelling operations, and interpret or compile the source code into machine code that is understandable at the hardware gate level of the processor. A bus 1405 couples the I / O subsystem 1402, the processor 1404, peripheral devices 1406, communication interfaces 1407, memory 1408, and secondary memory 1410.Conclusion

[0125] It is understood that the examples and implementations described herein are for illustrative purposes only and that various modifications or changes in light thereof will be suggested to persons skilled in the art. Although various details have been omitted for clarity’s sake, various design alternatives may be implemented. Therefore, the present examples are to be considered as illustrative and not restrictive, and the disclosure is not to be limited to the details given herein, but may be modified within the scope of the disclosure.

Claims

CLAIMS1. A method of determining a probability of pinhole formation in a photoresist, the method comprising: determining an amount of cross-linked states in the photoresist, wherein the amount of cross-linked states is based at least in part on an analysis of exposure stochastics, bake randomness, and film inhomogeneity; and determining the probability of pinhole formation in the photoresist based at least in part on the amount of cross-linked states in the photoresist that are below a threshold value associated with a threshold amount of cross-linked states in the photoresist.

2. The method of claim 1, further comprising: identifying the threshold value associated with the threshold amount of cross-linked states in the photoresist.

3. The method of claim 2, wherein the identified threshold value is dependent on dry development conditions for dry developing the photoresist.

4. The method of claim 1 , wherein the amount of cross-linked states is based at least in part on an analysis of exposure stochastics, bake-induced transitions, and film inhomogeneity.

5. The method of claim 4, wherein the exposure stochastics is related to one or more EUV exposure conditions.

6. The method of claim 4, wherein the bake-induced transitions is related to one or more post-exposure bake conditions.

7. The method of claim 6, wherein the one or more post-exposure bake conditions comprise one or more of bake temperature, pressure, gas species, flow rates of gas species, and duration of exposure.

8. The method of claim 4, wherein the film inhomogeneity is related to deposition processes and chemistries.

9. The method of claim 1, further comprising: optimizing one or more of: (1) deposition processes and chemistries, (2) dry development processes and conditions, or (3) exposure and post-exposure bake conditions, wherein the optimization is related to the determination of the probability of pinhole formation in the photoresist.

10. The method of claim 1, wherein the photoresist is an EUV-sensitive metal oxidecontaining photoresist.

11. The method of claim 1 , further comprising: providing a plurality of inputs to a digital twin of a photolithography process, wherein the plurality of inputs comprise a photoresist unit cluster for the photoresist, bridging locations using the photoresist unit cluster for the photoresist, one or more inputs associated with EUV exposure, one or more inputs associated with a material of the photoresist, one or more inputs associated with bake parameters, and one or more inputs associated with development parameters; determining, in the digital twin, post-exposure states of the bridging locations after EUV exposure of the photolithography process; and determining, in the digital twin, post-bake states of the bridging locations after bake of the photolithography process, wherein the amount of cross-linked states in the photoresist is determined from the post-bake states of the bridging locations after bake.

12. A model to predict pinhole formation in a photoresist comprising one or more non- transitory machine readable media comprising logic configured to implement: exposure stochastics configured to determine cross-linking fraction distribution in the photoresist due to EUV exposure; bake randomness configured to adjust the cross-linking fraction distribution in the photoresist due to post-exposure bake; and film inhomogeneity further configured to update the cross-linking fraction distribution in the photoresist due to voids in the photoresist, wherein the model is configured to predict pinhole formation in the photoresist based at least in part on the updated cross-linking fraction distribution in the photoresist due to exposure stochastics, bake randomness, and film inhomogeneity.

13. The model of claim 12, wherein the model is configured to predict a probability of pinhole formation in the photoresist based at least in part on an amount of cross-linked states in the updated cross-linking fraction distribution in the photoresist that are below a threshold value associated with a threshold amount of cross-linked states in the photoresist.

14. The model of claim 13, wherein the threshold value associated with a threshold amount of cross-linked states in the photoresist is identified and dependent on dry development conditions for dry developing the photoresist.

15. The model of claim 12, wherein the exposure stochastics is related to one or more EUV exposure conditions.

16. The model of claim 12, wherein the bake randomness is related to one or more postexposure bake conditions.

17. The model of claim 12, wherein the film inhomogeneity is related to void area and size.

18. The model of claim 17, wherein the void area and size are related to one or more exposure conditions and one or more of EUV exposure conditions and one or more postexposure bake conditions.

19. The model of claim 12, wherein the photoresist is an EUV-sensitive metal oxide- containing photoresist.

20. The model of claim 12, wherein the one or more non- transitory machine readable media comprising the logic is further configured to implement: an EUV exposure model of a photolithography process, wherein the EUV exposure model is configured to receive pre-exposure inputs comprising a photoresist unit cluster for an EUV resist, bridging locations using the photoresist unit cluster for the EUV resist, and one or more inputs associated with EUV exposure, and configured to generate post-exposure states of the bridging locations after EUV exposure; and a bake model of the photolithography process, wherein the bake model is configured to receive the post-exposure states of the bridging locations and bake parameters, and configured to generate post-bake states of the bridging locations after bake using the post-exposure states of the bridging locations and the bake parameters, wherein the cross-linking fraction distribution in the photoresist is determined from the post-bake states of the bridging locations after bake.

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