Virtual experimentation platform for photolithography process flow

Abstract

A digital twin of an EUV photolithography workflow determines a patterning performance of an EUV photolithography process. The digital twin includes an EUV exposure model, a bake model coupled to the EUV exposure model, and a development model coupled to the bake model. The digital twin receives inputs related to photons used in EUV exposure, a material of the EUV resist, and processes used in bake and development. Using a semi-empirical kinetic Monte Carlo framework, the digital twin can predict patterning outcomes of the EUV photolithography process.

Description

VIRTUAL EXPERIMENTATION PLATFORM FOR PHOTOLITHOGRAPHY PROCESS FLOWINCORPORATION BY REFERENCE

[0001] 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

[0002] The present disclosure relates to modeling of a photolithography process flow, and more particularly to a digital twin of a photolithography process flow for processing an extreme ultraviolet (EUV) resist in semiconductor fabrication.BACKGROUND

[0003] 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 exposed areas of the photoresist to become more or less soluble in a developer solution; developing by applying a developer solution or dry chemistry to remove either the exposed or the unexposed 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. To achieve smaller feature features on semiconductor substrate materials, there has been significant interest and research effort in 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.

[0004] An accurate and comprehensive model of a photolithography process is useful in the fabrication of semiconductor devices. The model may be used to evaluate a fabrication recipe, measure a performance of a patterning workflow, predict patterning outcomes of various lithography inputs, etc. However, it can be difficult to provide a model of an entire photolithography process flow because each of the steps in the photolithography process flowinvolve different physical phenomena and interactions that are very complex. Even less known and less studied are the physical phenomena and complex interactions that occur in an EUV photolithography process flow. Each of the steps in the photolithography process flow can involve different models themselves, which can be difficult to combine in a unifying model or virtual experimentation platform.

[0005] 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

[0006] Provided herein is a method of determining a patterning performance of a photolithography process. The method includes providing a plurality of inputs to a digital twin of a photolithography workflow, where the plurality of inputs comprise a photoresist unit cluster for an EUV resist, bridging locations using the photoresist unit cluster for the EUV resist, 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. The method further includes determining, in the digital twin, post-exposure states of the bridging locations after EUV exposure of the photolithography process, determining, in the digital twin, post-bake states of the bridging locations after bake of the photolithography process, determining, in the digital twin, post-development states of the bridging locations after development of the photolithography process, and determining one or more patterning metrics of the photolithography process.

[0007] In some implementations, the one or more inputs associated with EUV exposure include an EUV dose and an aerial image of the EUV resist from the EUV exposure. In some implementations, the one or more inputs associated with the material of the EUV resist include 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. In some implementations, the one or more inputs associated with the bake parameters include a bake ambient and one or more bake kinetic constants. In some implementations, the one or more inputs associated with the development parameters include whether development is wetor dry. In some implementations, the one or more patterning metrics include one or more of the following: critical dimension (CD), line edge roughness (LER), line width roughness (LWR), dose-to-size (DtS), and defects. In some implementations, the method further includes generating an image representing the EUV resist after development, where determining the one or more patterning metrics of the photolithography process includes determining the one or more patterning metrics using the image representing the EUV resist after development. In some implementations, determining the post-exposure states of the bridging locations after exposure includes receiving, in the digital twin, the bridging locations, an aerial image of the EUV resist from EUV exposure, an EUV dose, and an absorption coefficient of the EUV resist, obtaining photon absorption coordinates of the EUV resist representing photon absorption excitation events in the EUV resist, obtaining secondary electron coordinates of the EUV resist representing secondary electron excitation events in the EUV resist using the photon absorption coordinates, an external quantum efficiency of the EUV resist, and a secondary electron blur radius of the EUV resist, and determining the post-exposure states of the bridging locations after exposure using the photon absorption coordinates and the secondary electron coordinates. In some implementations, the digital twin includes an EUV exposure model of the photolithography workflow configured to determine the post-exposure states of the bridging locations after EUV exposure, a bake model of the photolithography workflow configured to determine the post-bake states of the bridging locations after bake, and a development model of the photolithography workflow configured to determine the post-development states of the bridging locations after development, where the development model uses a semi-empirical kinetic Monte Carlo method and surface particle-tracing model. In some implementations, the EUV resist includes a metal-oxide-containing EUV resist.

[0008] Also provided herein is digital twin of a photolithography workflow including one or more non-transitory machine readable media comprising logic configured to implement: an EUV exposure model of the photolithography workflow, wherein the EUV exposure model is configured to receive pre-exposure inputs including 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, a bake model of the photolithography workflow, 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, and adevelopment model of the photolithography workflow, where the development model is configured to receive the post-bake states of the bridging locations and development parameters, and configured to generate post-development states of the bridging locations after development using the post-bake states of the bridging locations and the development parameters, where the digital twin is configured to generate one or more patterning metrics using the post-development states of the bridging locations after development.

[0009] In some implementations, the pre-exposure inputs further include one or more material parameters associated with the EUV resist. In some implementations, the one or more material parameters associated with the EUV resist include 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. In some implementations, the one or more inputs associated with the EUV exposure include an EUV dose and an aerial image of the EUV resist from the EUV exposure. In some implementations, the bake parameters include a bake ambient and one or more bake kinetic constants. In some implementations, the bake ambient includes a bake temperature, pressure, gas species, flow rates of gas species, and duration of exposure. In some implementations, the development parameters include whether the development is wet or dry. In some implementations, the EUV resist includes a metal- oxide-containing EUV resist. In some implementations, the digital twin is configured to generate an image representing the EUV resist after development, where the one or more patterning metrics are generated using the image representing the EUV resist after development. In some implementations, the one or more patterning metrics include one or more of the following: critical dimension (CD), line edge roughness (LER), line width roughness (LWR), dose-to-size (DtS), and defects. In some implementations, the EUV exposure model is further configured to generate photon absorption coordinates of the EUV resist representing photon absorption excitation events in the EUV resist using the bridging locations, an aerial image of the EUV resist from the EUV exposure, an EUV dose, and an absorption coefficient of the EUV resist, where the EUV exposure model is configured to generate the post-exposure states of the bridging locations after exposure using the photon absorption coordinates, an external quantum efficiency of the EUV resist, and a secondary electron blur radius of the EUV resist.BRIEF DESCRIPTION OF DRAWINGS

[0010] Figure 1 presents a flow diagram of an example patterning process flow involving an EUV resist according to some implementations.

[0011] Figure 2 presents a schematic of a molecular cluster of an example EUV photoresist unit according to some implementations.

[0012] Figure 3 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.

[0013] Figure 4A presents a schematic illustration of an example fundamental EUV photoresist unit cluster according to some implementations of a digital twin of a photolithography workflow.

[0014] Figure 4B 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.

[0015] Figure 5 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 according to some implementations of a digital twin of a photolithography workflow.

[0016] Figure 6 presents a block diagram of coupled models of a digital twin of a photolithography workflow according to some implementations.

[0017] Figure 7A 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.

[0018] Figure 7B presents a schematic illustration of an example photoresist film crosssection 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.

[0019] Figure 8A presents a graph illustrating an extent of chemical conversion for various doses after EUV exposure only according to some implementations.

[0020] Figure 8B presents a graph illustrating an extent of chemical conversion for various doses after EUV exposure and bake according to some implementations.

[0021] Figure 9 presents a schematic illustration of a connectivity-based wet development model according to some implementations.

[0022] Figure 10A presents two graphs illustrating development ratio as a function of EUV dose at two different bake temperatures.

[0023] Figure 10B presents two graphs illustrating development ratio as a function of crosslinking ratio of third states (s3) relative to the total states (si, s2, and s3).

[0024] Figure 10C presents a graph illustrating a cross-linking ratio of an EUV resist film as a function of an x-direction of the EUV resist film for various EUV exposure and bake conditions.

[0025] Figures 11A-11B present graphs comparing simulated results using the static threshold model against experimental data.

[0026] Figure 12 presents a flow diagram of an example method of determining a patterning performance of a dry development process according to some implementations.

[0027] Figure 13 A presents a graph illustrating EUV resist thickness remaining (fraction) as a function of dry development time (seconds) for different EUV doses.

[0028] Figure 13B presents a graph illustrating EUV resist thickness removed (A) as a function of dry development time (seconds) for different EUV doses.

[0029] Figure 13C shows a cross-sectional schematic illustration of an EUV resist separated into at least three different layers representing at least three different dry development regimes according to some implementations.

[0030] Figure 14 presents a schematic illustration of a dry development model using a semi- empirical kinetic Monte Carlo approach with surface particle-tracing according to some implementations.

[0031] Figure 15A presents a flow diagram of an example method of determining a patterning performance of a dry development process according to some implementations.

[0032] Figure 15B presents a flow diagram of an example method of generating an image of an EUV resist profile with a dry development process using a transient particle tracing model according to some implementations.

[0033] Figure 16A presents an example SEM image based on experimental results after patterning EUV resist.

[0034] Figure 16B presents an example SEM-like image based on simulations from a virtual experimentation platform after patterning EUV resist.

[0035] Figure 17 presents example cross-sectional SEM-like images at different times during dry development based on simulations.

[0036] Figure 18 presents a flow diagram of an example method of determining a patterning performance of a photolithography process according to some implementations.

[0037] Figure 19 presents an example computer system that may be employed to implement certain embodiments described in the present disclosure.DETAILED DESCRIPTION

[0038] 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

[0039] A digital twin of a photolithography process flow is described herein. The digital twin can include multiple models that are coupled together to form the digital twin. For example, an EUV photolithography process flow can include various steps such as EUV exposure, bake, and development. Each of the steps of the EUV photolithography process flow can have its own model for tracking changes to an EUV resist film during the course of the patterning process. The models are coupled to one another to predict a patterning performance of a photolithography process. In some implementations, the patterning performance can be reflected in images of the EUV resist film such as SEM images. In some implementations, thepatterning performance can be reflected in critical dimension (CD), line width roughness (LWR), line edge roughness (LER), dose-to-size (DtS), defects, etc.

[0040] 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.

[0041] 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, the width 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.

[0042] 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.

[0043] 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.

[0044] 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.

[0045] 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 some implementations, 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.

[0046] 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.

[0047] 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 depositionprocess 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 metalcontaining 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.

[0048] 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 the EUV 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.

[0049] 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.

[0050] 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 crosslinking in the EUV resist, creating a contrast in etch selectivity that can be exploited for subsequent development. The EUV resist may be photo patterned by exposing a region toEUV light, typically under relatively high vacuum. Exposed areas of the EUV resist are created through EUV photo patterning that have altered physical or chemical properties relative to unexposed areas. The difference in properties between exposed and unexposed areas may be exploited in subsequent processing.

[0051] 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 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 cross-linking between neighboring -OH groups and form a cross-linked metal oxide network.

[0052] At block 112 of the process flow 100, the EUV resist is developed to form a resist mask. In various embodiments, the exposed regions are removed (positive tone) or the unexposed regions are removed (negative tone). For instance, development may involve selective removal of unexposed regions of the EUV resist relative to 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 Ch, H2 and Brc, 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, COBrc, andC0I2. A thionyl halide can include but is not limited to SOF2, SOCI2, SoBrc, 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 100 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.

[0053] 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 defectivity and LWR. Plasma treatment may expose the resist mask to plasma such as a direct (in-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 the foregoing treatments are applied to the resist mask after development to improve the performance of the resist mask during pattern transfer.

[0054] 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.

[0055] The process flow 100 illustrates some of the many steps that are performed in anexample 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.

[0056] 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.

[0057] 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, a mechanistic understanding of the behaviors and interactions of metal-oxide-containing EUV resists at a molecular level is scant. To obtain a computational model that accurately and comprehensively simulates an EUV photolithography workflow for a metal-oxide-containing EUV resist, it is important to ascertain a mechanistic understanding of the behaviors and interactions of metal-oxide-containing EUV resist. Specifically, a visual of what is happening at the molecular level, e.g., what structures are formed, how the structures interact with one another, what reactions are taking place, etc., provides essential information of the EUV photolithography workflow. This mechanistic understanding facilitates construction of computational methods and models that approximate and simulate the processes taking place in the EUV photolithography workflow. Experimental data alone is insufficient to construct an accurate and comprehensive model of an EUV photolithography workflow.

[0058] To address the challenges associated with the process development of EUV resists(e.g., metal-oxide-containing EUV resists) that require complex patterning evaluation workflows, new or improved methods are needed. The present disclosure relates to a digital twin or virtual experimentation platform that simulates the EUV photolithography process flow to predict patterning performance. The digital twin includes a plurality of models that are coupled to one another. The plurality of models include models that simulate steps of the EUV photolithography workflow, which can include an EUV exposure model, a bake model, and a development model. Some or all of the models implement a semi-empirical Monte Carlo simulation framework. The framework uses a mechanistic understanding of photons, materials, and process behaviors to construct algorithms that can accurately predict patterning performance. This enables faster cycles of learning with reduced cost, systematic process mapping, mechanism understanding, and efficient optical proximity correction. This provides significant improvements over physical experimentation to evaluate processes and materials of a photolithography process.Digital Twin of EUV Photolithography Workflow

[0059] The digital twin of the present disclosure can take inputs associated with an EUV photolithography process and generate predicted resist patterning characteristics as an output. The digital twin can be used to evaluate, optimize, or validate a process recipe. However, unlike traditional parameter-based models that are typically used in software simulation platforms, the models in the digital twin examine the inputs through a mechanistic understanding to generate the predicted output. In other words, the digital twin leverages an understanding of what is happening with the EUV resist at a molecular level to determine patterning performance.

[0060] Typically, many current commercial software simulation platforms rely on a parameter-based framework. Initially, a model is constructed by finding necessary inputs, deriving a physical mechanism, and converting into a mathematical representation with one or more parameters. An optimization method is utilized to update the one or more parameters so that the mathematical representation fits results from training data sets, thereby improving the performance of the parameter-based framework.

[0061] In one example, a commercial photoresist model relies on a general mechanism and parameter-based framework referred to as a Synopsys®. Within this framework, several mechanisms are considered with various floating parameters in each: one of the mechanismsor models may describe molecular cluster organization and reactive volume, another one of the mechanisms or models may describe light exposure with Dill parameters, another one of the mechanisms or models may describe different orders of reactive formation and species diffusion during the post-exposure bake step, and one or the mechanisms or models may be derived from experimental data and may capture the behavior of wet development using various different forms of a Mack model.

[0062] To achieve predictive power, a broad range and size of patterning data sets are necessary for fitting the resist and process parameters. The optimization method typically involves construction of a function based on a model equation defined by these process parameters and a Mean Squared Error (MSE) of relevant patterning metrics, such as CD and roughness.

[0063] Algorithms typically evaluate the magnitude of changes (gradients) in the parameters and determine the direction of steepest descent for parameter updates. However, these optimization methods are often semi-automated or manually executed. Despite the mathematical rigor of the optimization process, the resulting model parameters may still significantly deviate from their initial guesses based on physical insights. Consequently, these model parameters may lose their physical meaning. Correlation analysis, which investigates how actual film parameters (such as thickness and blur) impact patterning metrics, can yield unrealistic results. This limitation prevents the model from being effectively used for parameter understanding and process or film improvements.

[0064] In contrast, the bottom-up approach developed in the present disclosure relates to intricately designed studies involving blanket-exposed films. These studies investigate and extract underlying mechanisms and parameters associated with each processing step. For instance, the construction of the bake model may be illustrated through Fourier Transform Infrared (FTIR) analysis, as discussed in more detail below. One of the advantages of this approach involves the elimination of parameter optimization steps. As a result, the final parameters retain their physical significance. By utilizing this kind of model, it is possible to evaluate the contribution of each film and process parameter to the final patterning performance. This further provides valuable physical and chemical insights and directions for process improvements.

[0065] The digital twin of the present disclosure is a predictive model that is able to receive inputs and generate predicted outputs regarding patterning outcomes. However, the digitaltwin is further constructed using a mechanistic understanding of the EUV resist through the EUV photolithography workflow. The digital twin of the present disclosure does not need any parameter optimization step. The digital twin provides a more fundamental semi-empirical framework for simulating the EUV photolithography workflow.

[0066] The EUV photolithography process is a highly complex process. An EUV resist (e.g., metal-oxide-containing EUV resist) undergoes a series of transformations and changes at each step of the EUV photolithography process. How the EUV resist changes over time depends on a variety of factors to consider in modeling the EUV photolithography process. An EUV resist material may have a certain absorption coefficient, which can affect how it responds to different EUV exposures and different bake conditions. An EUV resist material may have a certain thickness or density, which can influence its response to EUV exposure and bake. Changes in the bake conditions can result in different patterning outcomes. Changes in a development chemistry or a development method can lead to changes in patterning outcomes. Changes in EUV dose can lead to different development behaviors that result in different patterning performances. All this to say that variations in photons, materials, and processes can influence a patterning performance of an EUV photolithography process. In some implementations of the present disclosure, algorithms of the predictive model can account for the parameters in the following categories: (1) photons, (2) materials, and (3) processes. Parameters related to photons may include but are not limited to EUV dose and an aerial image of the EUV resist. Parameters related to materials may include but are not limited to absorption coefficient, external quantum efficiency, cluster size, film density, and film thickness. Parameters related to processes may include but are not limited to bake conditions and development methods.

[0067] To properly account for how parameters related to photons, materials, and processes can affect patterning performance in the EUV photolithography process, it may be necessary to develop a mechanistic understanding of what is happening with the EUV resist at the molecular level. This mechanistic understanding can build upon a three-dimensional (3-D) rendering of the EUV resist and provide a simulation of the EUV photolithography process as to what is taking place in 3-D space. Figure 2 presents a schematic of a molecular cluster of an example EUV photoresist unit according to some implementations. The molecular cluster provides an EUV cluster 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, chlorido, hydrido, 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.

[0068] 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. Figure 3 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. 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 3 show that individual EUV photoresist unit clusters may undergo cross-linking to create a network that is resistant to development. To monitor the extent to which EUV photoresist units 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.

[0069] 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 astate with cross-linking between individual EUV photoresist units. Without being limited by any theory, the 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 oxygen-containing counterreactant, 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. 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 3, 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.

[0070] To build the algorithms of the digital twin for the EUV photolithography workflow, the algorithms rely on a fundamental understanding of the underlying mechanisms that are responsible for the performance of the EUV resist. To obtain this fundamental understanding, it may be necessary to break down the chemical reactions taking place in an EUV photolithography process into components and possible states that the components are in. In other words, it may be necessary to define a fundamental photoresist unit cluster and a way to monitor a behavior of the fundamental photoresist unit cluster. Monitoring the behavior of the fundamental photoresist unit cluster can be accomplished by defining film states, each of the film states representing an extent of chemical conversion between clusters.

[0071] Figure 4 A presents a schematic illustration of an example fundamental EUV photoresist unit cluster according to some implementations of a digital twin of a photolithography workflow. In the digital twin, a fundamental EUV photoresist unit cluster is defined. Though the illustration in Figure 4A 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 digital twin. 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. There are many different possible tin precursors that can be employed in the deposition of EUV resist. In some cases, a single precursor is used to deposit EUV resist. In some cases, two or more precursorsare used to deposit EUV resist. Deposition may involve any suitable deposition technique such as ALD (e.g., thermal ALD and plasma-enhanced ALD), spin-coat deposition, PVD including PVD co-sputtering, CVD (e.g., PE-CVD or LP-CVD), sputter deposition, e-beam deposition including e-beam co-evaporation, etc., or combinations thereof.

[0072] As shown in Figure 4A, 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 402. The oxo cage 402 is surrounded by several R-groups 404a, 404b, and 404c located around a perimeter of the oxo cage 402. Each of the R-groups 404a, 404b, and 404c 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 4A, though it will be understood that a different number of R-groups can be defined in the fundamental EUV photoresist unit cluster. R-groups 404a represent R-groups oriented into the page. R-groups 404b represent R-groups oriented in plane with the page. R-groups 404c 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 digital twin. 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), mixture of 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 4A.

[0073] The fundamental EUV photoresist unit cluster can represent a simplified molecular structure. This simplified molecular structure also provides an understanding of the interactions and transformations that the EUV resist undergoes during each of the steps of the EUV photolithography workflow.

[0074] Figure 4B 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. After the digital twin identifies the fundamental EUV photoresist unit cluster, the digital twin identifies the bridging locations. The bridging locations represent points in three-dimensional space where cross-linking can take place. Though the illustration in Figure 4B 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 providesuch bridging locations. The digital twin may identify such points 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. As a layer of EUV resist is composed of several EUV photoresist unit clusters arranged in 3-D space, several bridging locations can be identified by the digital twin. These bridging locations are mapped and monitored by the digital twin throughout the EUV photolithography workflow.

[0075] In Figure 4B, 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 412 has four R-groups 414a, 414b, 414c, and 414c. A second EUV photoresist unit cluster 414 also has four R-groups 424a, 424b, 424c, and 424d. The R-group 414d from the first EUV photoresist unit cluster 412 is close in proximity to the R-group 424d from the second EUV photoresist unit cluster 422. The digital twin can identify this region between R-group 414d and R-group 424d, and that is occupied by the R-group 414d and occupied by the R-group 424d, as a bridging location 430. This bridging location 430 is mapped in 3-D space by the digital twin and establishes a framework for tracking the progress of chemical conversion throughout the EUV photolithography workflow.

[0076] “ States” of the bridging location 430 may change through each step of EUV photolithography workflow. These states are defined by the digital twin as a way to monitor chemical conversion through the EUV photolithography workflow. These states provide a helpful marker or indicator of the progress of interactions between EUV photoresist unit clusters. These states are particularly useful markers for tracking change after EUV exposure and after bake. In some implementations, the digital twin defines at least two states. In some implementations, the digital twin defines at least three states. Here, the digital twin in this example shows three possible states. A first state (si) represents a state in which there is no cross-linking and where the R-groups are intact at the bridging location. For example, the M- R bonds at the bridging location 430 are intact, where M is a metal atom. A second state (s2) represents a state that is an intermediate state between the first state (si) and the third state (s3). For example, the R-groups may be removed or cleaved from the metal atom at the bridging location 430. A third state (s3) represents a state in which there is cross-linking and the R- groups are not present. For example, M-O-M bonds are formed at the bridging location 430. After exposure or after bake, each bridging location 430 must be in one of the three states defined by the digital twin. Prior to exposure, it is generally assumed that most or all of the bridging locations 430 are in the same state, e.g., the first state (si).

[0077] Figure 5 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 of a digital twin of a photolithography workflow. The fraction of states in Figure 5 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 si states has decreased significantly and the fraction in the s3 states has increased significantly. This shows that higher EUV doses lead to greater amounts of removal of R-groups and greater amounts of cross-linking.

[0078] Figure 6 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.

[0079] 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 istwo-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.

[0080] 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.

[0081] The digital twin can be configured to output various types of information about a photolithography process. In particular, the digital twin can be used for determining one or more patterning metrics of the photolithography process. Predicted patterning metrics can serve as the output of the digital twin. In addition or in the alternative, the digital twin can be configured to output an image of a patterned resist mask of the photolithography process.

[0082] In Figure 6, a digital twin 600 of a photolithography process is shown in accordance with some implementations of the disclosed subject matter. The digital twin 600 is a model covering multiple steps of a photolithography process, where the digital twin 600 can include models of different steps of the photolithography process. Such steps can include EUV exposure, bake, and development, among other possible steps in the photolithography process. For instance, pre-processing steps such as PAB treatment or deep ultraviolet (DUV) treatment can impact film states of the EUV resist. The digital twin 600 may be utilized to account for such changes in film states these kinds of steps, e.g., pre-processing steps. In some implementations, the digital twin 600 can include fewer, more, or different steps of the photolithography process.

[0083] In some embodiments, the digital twin 600 can receive inputs 610 and generate patterning outcomes as outputs 650. The inputs 610 may include user-defined inputs or computer-implemented inputs that are generated by the digital twin 600. 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 aregenerated 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.

[0084] The inputs 610 provide a starting point for the digital twin 600 to simulate the EUV photolithography process. The inputs 610 may at least include a material and material properties associated with the EUV resist. In some implementations, the inputs 610 further include a map of bridging locations associated with the as-deposited EUV resist, which may be rendered in 3-D space.

[0085] The inputs 610 received by the digital twin 600 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 of gas 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 610 are merely exemplary. In some embodiments, some of the inputs shown in Figure 6 may be omitted. Additionally or alternatively, in some embodiments, any other parameters not shown in Figure 6 can be included in the inputs 610. For instance, such inputs may be related to EUV resist deposition (e.g., deposition precursor(s), deposition conditions, etc.) or relatedto 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.

[0086] The digital twin 600 may further analyze the inputs 610 to determine additional parameters. For instance, using the material of the EUV resist, the digital twin 600 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 600 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.

[0087] After receiving user-defined inputs and calibrating parameters to further define computer-implemented inputs in the digital twin 600, some or all of the inputs 610 are received at an EUV exposure model 620. The EUV exposure model 620 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. Obtaining the post-exposure states of the bridging locations of the EUV resist can be accomplished in a multi-step process such as a two-step process. However, it will be understood that obtaining the post-exposure states can also be obtained in a one-step process. In some embodiments, the EUV exposure model 620 can determine a photon absorption pattern 622, and the photon absorption pattern 622 can be used to determine a secondary electron pattern 624.

[0088] In some particular embodiments, the EUV exposure model 620 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 620 can obtain the photon absorption pattern 622. The photon absorption pattern 622 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. Determining the photon absorption coordinates is described below with reference to Figures 7A and 7B.

[0089] In some embodiments, the photon absorption coordinates taken from the photon absorption pattern 622 are provided as inputs to determine a secondary electron pattern 624.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 620 can obtain the secondary electron pattern 624. 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 624 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. Determining the secondary electron coordinates is described below with reference to Figures 7 A and 7B.

[0090] Figure 7A 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 EUV-exposed areas and EUV-unexposed 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. In some cases, the intensity of the EUV light may have a Gaussian distribution. 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 7A, the amount of photon absorption is highest near the top of the photoresist film and near the center of the photoresist film. 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 image in Figure 7A shows a gradient that illustrates a distribution of light absorption in the photoresist film, where a lighter color is indicative of a higher probability of photon absorption than a darker color. The absorbed light distribution shown in Figure 7A shows the impact of light distribution primarily along the z-direction. An aerial image shows the impact of light distribution primarily along 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.

[0091] 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.

[0092] 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.

[0093] Figure 7B presents a schematic illustration of an example photoresist film crosssection 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 700 includes a plurality of photoresist units 704. EUV light introduces photons 710 that are absorbed by the photoresist film 700. In view of the probability of photon absorption shown in Figure 7A, 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 720 can be captured by stochastics. The probability of excitation due to a photon 710 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 720, secondary electrons are generated. Secondary electrons propagate to areas around the photon absorption excitation event 720 and may cause a secondary electron excitation event 730. The probability of secondary electron excitation events 730 can also be captured by stochastics, with higher probabilities closer to the photon absorption excitation event 720 than farther from the photon absorption excitation event 720. Various factors can influence the probability distribution associated with secondary electronexcitation events 730, 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 720.

[0094] Returning to the digital twin 600 of Figure 6, the EUV exposure model 620 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 inputs such as the aerial image of the EUV resist, EUV dose, bridging locations, absorption coefficient of the EUV resist, external quantum efficiency of the EUV resist, and the secondary electron blur radius of the EUV resist. Using the photon absorption coordinates and the secondary electron coordinates, the EUV exposure model 620 can determine where transitions to new states are taking place in the EUV resist. Accordingly, the EUV exposure model 620 can determine post-exposure states of the bridging locations of the EUV resist. In some implementations, post-exposure states of the bridging locations can be represented as si state, s2 state, or s3 state.

[0095] The post-exposure states of the bridging locations of the EUV resist are received at a bake model 630. The bake model 630 is coupled to the EUV exposure model 620. The bake model 630 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 630 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 630 utilizes an analytical framework described by kinetic Monte Carlo simulation approaches.

[0096] 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.Ps — > 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.

[0097] The probabilities can be further understood kinetically. Physical constants that describe bake-induced cross-linking and bake-induced removal of R-groups can be determined analytically from experimental data such as FTIR data. These physical constants, referred to as bake kinetic constants, can be derived so that simulation parameters match experimental results. Rather than using a random optimizer, the bake kinetic constants can be derived utilizing a more bottom-up approach through parameters and blanket studies. The blanket studies may be performed on a checkboard exposed coupon. Multiple exposure only starting points are provided to ensure sufficient independent ordinary differential equation (ODE). The extraction of the kinetics is done through a numerical iterative calculation process to solve for the system of ODE. No significant tailoring of the parameters through optimization is required.

[0098] 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[Si]) —> 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.

[0099] Figure 8A presents a graph illustrating an extent of chemical conversion for various doses after EUV exposure according to some implementations. Figure 8A shows the three states and the FTIR signals through dose after EUV exposure but without any bake-related effects. FTIR data can determine an amount of M-R bonds in a photoresist film. The amount of Sn-R bonds can be indicative of an amount of M-R loss in the photoresist film, which can be correlated to bridging locations that transition from a lower state to a higher state. In Figure 8A, the three states (si, s2, s3) are shown through different EUV doses and FTIR signals are plotted through different EUV doses. The predicted FTIR signal compares very closely to the experimentally measured FTIR signal. At higher doses, the fraction of si states decreases and the fractions of s2 and s3 states increase.

[0100] Figure 8B presents a graph illustrating an extent of chemical conversion for various doses after EUV exposure and bake according to some implementations. Figure 8B shows the three states and the FTIR signals through dose after EUV exposure and bake. In Figure 8B, the three states (si, s2, s3) are shown through different EUV doses and FTIR signals are plotted through different EUV doses. The predicted FTIR signal compares very closely to the experimentally measured FTIR signal. At higher doses, the fraction of si states decreases and the fractions of s2 and s3 states increase. The fraction of s3 states increases more rapidly as a function of dose in Figure 8B compared to Figure 8A.

[0101] Returning to the digital twin 600 of Figure 6, the bake model 630 can determine postbake states of the bridging locations 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, post-bake states of the bridging locations can be represented as si state, s2 state, or s3 state.

[0102] The post-bake states of the bridging locations of the EUV resist are received at a development model 640. The development model 640 is coupled to the bake model 630. The development model 640 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 640 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. Whereas the post-bake states and the post-exposure states of bridging locations generally reflect an extent of chemical conversion at the bridging locations (e.g., si, s2, s3), the post-development states of the bridging locations generally reflect whether the bridging locations (and their corresponding photoresist clusters) are removed or remain intact (e.g., dl - intact, d2 - removed).

[0103] 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 states of the bridging locations refer to whether a bridging location is left intact (dl) or removed (d2) after development. Postexposure states and post-bake states refer to the extent of chemical conversion at the bridging locations, which can include a non-cross-linked state where R-groups are intact (si), anintermediate state (s2), and a cross-linked state (s3). Depending on whether the development method is a wet development method or a dry development method, 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 (e.g., si, s2, s3) of the bridging locations. Using experimental data, a relationship can be established between the post-bake states of the bridging locations and the post-development states of the bridging locations. That way, it can be accurately predicted what portions of the EUV resist are removed depending on the postbake states of the bridging locations.

[0104] The development model 640 can include a plurality of models 642, 644, and 646 that predict development behavior using the post-bake states of the bridging locations from the bake model 630. Examples of development models include but are not limited to: (1) wet development model 642, (2) static dry development model 644, and (3) transient particle tracing model 646. The wet development model 642 is used when the development method is a wet development method. The static dry development model 644 or the transient particle tracing model 646 is used when the development method is a dry development method.

[0105] In some implementations, a wet development model can employ a connectivity -based dissolution approach to determine whether certain post-bake states of bridging locations in an EUV resist are removed by wet development. In this wet development model, all the bridging locations that are in a cross-linked state (e.g., s3 state) are identified. Resist clusters having bridging locations that are in a cross-linked state and that are in direct contact with the substrate / underlayer are considered insoluble. Resist clusters having bridging locations that are in a cross-linked state and that are connected to those insoluble resist clusters will also be considered insoluble. Thus, all resist clusters that are not within a network directly or indirectly connected by M-O-M cross-linking with the substrate / underlayer are developed by wet development.

[0106] Figure 9 presents a schematic illustration of a connectivity-based wet development model according to some implementations. An EUV resist 900 can be comprised of several photoresist clusters 910. The photoresist clusters 910 in the EUV resist 900 can be indicated by either single outlined squares or double outlined squares. Prior to development, the EUV resist 900 comprises photoresist clusters 910 arranged in a grid or array to form a uniform distribution of clusters that span vertically and horizontally. In the connectivity-based wet development model of Figure 9, bridging locations are provided between photoresist clusters910. The bridging locations are indicated by small circles at the corners of each of the photoresist clusters 910. After bake and prior to development, the bridging locations are determined to be in one of the following states: si state, s2 state, or s3 state. Cross-linked bridging locations 920 are bridging locations in the s3 state. These are indicated by small circles with hatchings that are dense. Non-cross-linked bridging locations 930 are bridging locations in either the si or s2 state. These are indicated by small circles with hatchings that are sparse. In the connectivity -based wet development model, photoresist clusters 910 having cross-linked bridging locations 920 are identified. First, photoresist clusters 910 having one or more cross-linked bridging locations 920 that are in contact with a substrate or underlying stack 940 are identified. Such photoresist clusters 910 are labeled as insoluble clusters 950, which are indicated by a large circle with hatchings that are sparse. These insoluble clusters 950 are not removed during wet development. Second, photoresist clusters 910 having one or more cross-linked bridging locations 920 that are connected to the aforementioned insoluble clusters 950 in contact with the substrate or underlying stack 940 are identified. These are also labeled as insoluble clusters 950. This criteria is applied through a remainder of the photoresist clusters 910 to determine which clusters are soluble or insoluble. Any photoresist clusters 910 not within a network connected by cross-linked bridging locations 920 with the substrate or underlying stack 940 are considered soluble clusters 960, which are indicated as doubleoutlined squares. After development, insoluble clusters 950 remain while soluble clusters 960 are removed.

[0107] As discussed earlier, EUV resists may be composed of or contain metals and / or metal oxides mixed with organic components. Generally, these EUV resists are often developed using a wet (solvent) approach , which requires the wafer to move to the track, where it is exposed to developer solution, dried, and baked. Wet development not only limits productivity but also leads to line collapse due to surface tension effects and / or delamination. Developer solutions used in wet development may also add to environmental costs and waste.

[0108] Dry development techniques have been proposed to overcome these issues by eliminating substrate delamination and interface issues and providing an environmentally friendly solution that reduces waste and cost associated with solvent usage. Dry development can improve performance at narrower linewidths (e.g., prevent line collapse due to surface tension and delamination seen in wet development) and potentially enhance throughput (e.g., by avoiding need for wet development tracks). Other advantages may include eliminating the use of organic solvent developers, reduced sensitivity to underlayer adhesion, and a lack ofsolubility-based limitations. Dry development can also provide more tunability and give further critical dimension control and scum removal.

[0109] Dry development has its own challenges, including development selectivity between unexposed and EUV exposed resist material. This can lead to a higher dose to size requirement for effective resist exposure when compared to wet development. Suboptimal selectivity can also cause photoresist corner rounding due to lower contrast at feature edges which may increase line CD variation in a subsequent transfer etch step.

[0110] Dry development currently lacks a comprehensive understanding of the interaction between the developer and the EUV resist film. Though dry development may exhibit poor development selectivity between unexposed and exposed resist material even at high exposure doses, the photoresist mask profile may be relatively linear and the roughness may be minimal. The connectivity-based wet development model and other prevailing algorithms, such as dissolution, are not suitable for predicting patterning outcomes associated with dry development. In other words, the wet development algorithm is not directly applicable because the dry development process involves a fundamentally different reaction and different transport mechanism. Without algorithms that provide a comprehensive and accurate understanding of dry development and its underlying mechanisms, intricate experimental designs and workflows are necessary. Process engineers come up with recipe development, test vehicle preparations, and experimental procedures. This can take up to weeks and months for each cycle of learning.[OHl] Disclosed herein are dry development models, including the algorithms and experiments that provide an understanding of the mechanisms associated with dry development. The algorithms for the dry development models integrate semi-empirical parameters, which can be derived from various EUV experiments. The EUV experiments are analyzed to establish a relationship between the predicted pre-development states of the EUV resist film and experimentally-determined patterning outcomes. In some cases, the EUV experiments are analyzed to understand the dry development mechanism(s) over time and account for gas-phase incoming impact. The algorithms for the dry development models receive pre-development states of the EUV resist film and dry development process conditions, and predict patterning outcomes such as CD, profile, and / or roughness of the EUV resist mask. One example of a dry development model in the present disclosure is a static threshold model. Another example of a dry development model in the present disclosure is a transient surface particle-tracing model.

[0112] In some implementations, a dry development model can employ a static threshold approach to determine whether certain post-bake states of bridging locations in an EUV resist are removed by dry development. To generate the static threshold model, experimental data is collected and a relationship between the predicted post-bake states and the experimental data is established and validated. As used herein, “post-bake states” may be used interchangeably with “pre-development states” of bridging locations in the EUV resist. The relationship identifies a completion point at a location in the EUV resist where a quantitative amount of post-bake states exist at a threshold value in the EUV resist.

[0113] Blanket experiments may be performed to confirm the relationship between the predicted film states and dry development performance. In particular, blanket experiments reveal that dry development has the same performance wherever the predicted film states are the same. Dry development performance is the same depending on the intrinsic state of the EUV resist. Figure 10A presents two graphs illustrating development ratio as a function of EUV dose at two different bake temperatures. The bake temperatures may range from about 120°C to about 300°C. The EUV doses may range from about 0 mJ / cm2to about 30 mJ / cm2. By baking at a first temperature (tempi) and at a second temperature (temp2), the development ratios proved to be different at the same doses. This shows that films at different states, even if exposed to the same EUV dose, result in different amounts of development. Figure 10B presents two graphs illustrating development ratio as a function of cross-linking ratio of third states (s3) relative to the total states (si, s2, and s3). As the cross-linking ratio increases, the development ratio decreases. Regardless of whether the EUV was exposed to the first bake temperature (tempi) or the second bake temperature (temp2), the development amount was relatively the same depending on the cross-linking ratio. Accordingly, dry development performance can be correlated with predicted film states, irrespective of what combination of EUV dose conditions and bake conditions are used to reach that film state. The predicted film states, such as a cross-linking ratio at various locations in the EUV resist, can be obtained using our EUV exposure model and bake model as described earlier herein.

[0114] A quantitative amount of pre-development states can be expressed at various locations of the EUV resist. In some implementations, the quantitative amount can be expressed as a cross-linking ratio of third states (s3) relative to the total states (si, s2, and s3). It will be understood that other expressions may be used that reflect an amount of cross-linking in the EUV resist or the intrinsic film states of the EUV resist.

[0115] Experiments are performed under different EUV processes / conditions and under different bake processes / conditions. These experiments are associated with a certain dry development process / condition that achieves a target CD. A first set of experiments may be performed under a first EUV exposure process / condition and under a first bake process / condition that achieve a certain line CD for a dry development process / condition. A second set of experiments may be performed under a second EUV exposure process / condition and under a second bake process / condition that achieve the same line CD for the same dry development process / condition. And so forth. In an EUV resist mask, the edge of the line basically corresponds to a location where dry development stops. In some implementations of the static threshold model, a plurality of data sets are collected for various EUV processes / conditions and various bake processes / conditions, where each data set comprises: (1) an EUV exposure process / condition and bake process / condition, and (2) a corresponding CD, e.g., a corresponding line CD, for a dry development process / condition.

[0116] EUV parameters and bake parameters may be simulated in the digital twin to determine the pre-development states of bridging locations in the EUV resist. Thus, an amount of cross-linked states (s3) or predicted film states of a simulated EUV resist can be determined from the EUV parameters and bake parameters. In some implementations, a quantitative amount of cross-linked states (s3) out of the pre-development states may be determined along one or more directions (e.g., x-direction) of the EUV resist. By way of an example, the quantitative amount of cross-linked states (s3) out of the pre-development states may be determined in the x-direction. An average of the cross-linked states (s3) out of the predevelopment states may be calculated in the z-direction and y-direction for various points along the x-axis. Therefore, the quantitative amount of cross-linked states (s3) out of the predevelopment states may represent an average number of cross-linked states (s3) in the yz-plane at a particular location in the x-direction.

[0117] The static threshold model is a semi-empirical model. To identify a threshold value at which dry development stops, data sets including EUV exposure processes / conditions, bake processes / conditions, and a corresponding CD define pattern edge locations in a simulated EUV resist. The pattern edge locations map to locations in the simulated EUV resist where dry development stops for a particular dry development process / condition. Furthermore, the data sets including EUV exposure processes / conditions and bake processes / conditions also define intrinsic states or pre-development states of the simulated EUV resist. Using the EUV exposure processes / conditions and bake processes / conditions, the exposure model and bakemodel of the digital twin can predict the intrinsic states or pre-development states of the simulated EUV resist, from which values of cross-linked states (s3) can be calculated. Quantitative amounts of cross-linked states (s3) can be determined at various locations of the simulated EUV resist, such as along an x-direction of the simulated EUV resist. Because the pattern edge location map to a location in the simulated EUV resist where dry development stops for the particular dry development process / condition, this location corresponds to a certain quantitative amount of cross-linked states in the simulated EUV resist. This identifies the threshold value cross-linked states (s3), and this location represents the completion point for dry development at the 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.

[0118] In the static threshold model, a dry development process / condition is provided. The dry development process / condition has a specific threshold value of cross-linked states in the EUV resist where development stops. Threshold values are experimentally determined for various dry development recipes. Upon determining the pre-development states of the bridging locations of the EUV resist, the static threshold model can predict where dry development stops for various dry development recipes.

[0119] Figure 10C presents a graph illustrating a cross-linking ratio of an EUV resist film as a function of an x-direction of the EUV resist film for various EUV exposure and bake conditions. Different EUV exposure and bake conditions are performed to generate various experimental data sets: (1) a first temperature at a first dose, (2) a second temperature at a second dose, (3) a third temperature at a third dose, (4) a fourth temperature at a fourth dose, and (5) a two-step bake process at the second dose. The bake temperatures may range from about 120°C to about 300°C, and the dose may range from about 20 mJ to about 60 mJ. It was found that these different EUV exposure and bake conditions resulted in a line CD of about 14 nm after dry development for a specific dry development recipe. According to the static threshold model, experimental data sets (different EUV exposure and bake conditions) are selected that reaches a target CD. The target CD can be leveraged to determine the edge locations of the patterned EUV resist film. It will be understood that the values of the crosslinking ratio in Figure 10C are illustrative only of a particular example and subject to change depending on material properties and other model details.

[0120] Using the digital twin of the present disclosure, the intrinsic states or pre-development states of the EUV resist film can be determined at various locations along the x-direction of the EUV resist film. The intrinsic states or pre-development states along the x-direction of the EUV resist film can be an average number of cross-linked states (s3) in the yz-plane of the EUV resist film. As shown in Figure 10C, these average numbers are plotted along the x- direction of the EUV resist film. The average number of cross-linked states (s3) at a location in the EUV resist film that corresponds to the edge location represents the threshold value or completion point where dry development stops for the specific dry development recipe.

[0121] With the static threshold model, the quantitative amount of cross-linked states at the threshold value is the same at the pattern edge location of the EUV resist film. This threshold value determines where dry development stops for a particular dry development recipe. As a result, the static threshold model can predict patterning metrics such as CD and DtS.

[0122] Figures 11A-11B present graphs comparing simulated results using the static threshold model against experimental data. Figure 11A shows the predicted DtS that was simulated by the static threshold model along the y-axis and shows the actual DtS that was experimentally determined along the x-axis. As shown in Figure 11 A, the predicted DtS was largely within three standard deviations of the actual DtS. Figure 1 IB shows the predicted CD that was simulated by the static threshold model along the y-axis and shows the actual CD that was experimentally determined along the x-axis. As shown in Figure 1 IB, the predicted CD was largely within three standard deviations of the actual CD. This shows that the static threshold model can accurately predict CD and DtS for dry development of EUV resist that closely match with experimental results.

[0123] Figure 12 presents a flow diagram of an example method of determining a patterning performance of a dry development process according to some implementations. The operations of a process 1200 may be performed in different orders and / or with different, fewer, or additional operations. One or more operations of the process 1200 may be implemented in accordance with any of the techniques or models described in the present disclosure. This includes the static threshold model. In some implementations, the operations of the process 1200 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 19.

[0124] At block 1210 of the process 1200, pre-development states of bridging locations of an EUV resist are received as inputs into a dry development model. The dry development model identifies a threshold value associated with a threshold amount of cross-linked states in the EUV resist, where the threshold value represents a completion point of the dry development process The dry development model may be a static threshold model. The pre-development states of the bridging locations can be determined using parameters such as EUV resist material properties, EUV exposure conditions, and bake conditions, as described earlier herein. EUV exposure conditions may include at least an EUV dose and EUV exposure pattern. Bake conditions may include at least a bake temperature and bake ambient. In some implementations, the EUV resist includes a metal-oxide-containing EUV resist. In some implementations, the dry development process is a thermal dry development process or plasma dry development process.

[0125] Identification of the threshold value is achieved by analyzing experimental data associated with different EUV exposure conditions, bake conditions, and dry development processes. The experimental data also includes a corresponding CD that results from each EUV exposure condition, bake condition, and dry development process. The corresponding CD may be used to determine pattern edge locations at which dry development is completed. Each dry development process or recipe has an associated threshold value at which dry development is completed. Depending on the EUV exposure conditions and bake conditions, the amount of cross-linked states vary throughout the EUV resist. Given the EUV exposure condition, bake condition, dry development process, and pattern edge location derived from the corresponding CD, the pattern edge location maps to a location in the EUV resist has that has a certain amount of cross-linked states. This amount is the threshold value for the dry development process.

[0126] At block 1220 of the process 1200, the dry development model determines a location in the EUV resist that corresponds to the threshold value. The pre-development states of the bridging locations of the EUV resist received as inputs into the dry development model can be converted to an amount of cross-linked states throughout the EUV resist. Once the dry development model identifies the threshold values for a plurality of dry development processes, the dry development model identifies the threshold value for the dry development process being considered in the process 1200. The location in the EUV resist that meets that threshold value of cross-linked states reflects a completion point of the dry development process.

[0127] At block 1230 of the process 1200, the dry development model determines one or more patterning metrics of the dry development process. The location in the EUV resist that corresponds to the threshold value represents where dry development stops in the dry development process. This provides a simple estimation of a profile of an EUV resist mask that is formed by the dry development process. In some implementations, the one or more patterning metrics includes CD. In some implementations, the one or more patterning metrics includes DtS. In some implementations, the one or more patterning metrics includes both CD and DtS. The static threshold model can be used to predict a target CD and / or DtS using inputs such as EUV resist material properties, EUV exposure conditions, bake conditions, and dry development processes / conditions.

[0128] In some implementations, a dry development model can employ a transient particle tracing model to determine whether certain film locations in an EUV resist are removed by dry development through dry development time. The transient particle tracing model utilizes a semi-empirical kinetic Monte Carlo approach with mechanistic insights. The transient particle tracing model traces individual particle trajectory of developer gases on the surfaces of the EUV resist and photoresist units they interact with. The probability of the photoresist unit interacted with being removed is determined based on a dry development mechanism and dry development rate, related to the post-bake state that the photoresist unit is in.

[0129] Whereas the static threshold model may not be able to accurately obtain certain patterning metrics such as roughness, the transient particle tracing model can provide additional insights including time-evolution profile and roughness predictions. Like the static threshold model, the transient particle tracing model is a semi-empirical model. However, instead of blanket dry development studies such as dose-to-gel experiments that are unable to provide a quantitative dry development rate, the transient particle tracing model uses blanket dry development studies in time splits (e.g., fine increment time splits) designed to accurately extract dry development regimes and dry development rates within the dry development regimes.

[0130] In the transient particle tracing model, dry development rates vary according to the regime in which dry development is taking place in the EUV resist. In some implementations, the dry development rates can be calculated experimentally from checkerboard experiments, with EUV resists exposed at different doses. How much EUV resist material is removed is observed for different time increments, e.g., 10 seconds, 15 seconds, 20 seconds, 30 seconds,100 seconds, etc., of a dry development process. Dry development rates are calculated at different regimes or portions of the EUV resist.

[0131] Figure 13 A presents a graph illustrating EUV resist thickness remaining (fraction) as a function of dry development time (seconds) for different EUV doses. EUV doses of a first dose, a second dose, and a third dose were tested. Such EUV doses may range from about 2 mJ / cm2to about 60 mJ / cm2. As dry development progressed over time, the EUV thickness remaining decreased. EUV resist removal largely over time did not follow one linear trend. In particular, EUV resist removal over time was observed to remain minimal during a beginning regime of dry development, linear during a middle regime of dry development, and slowing down during an ending regime of dry development. Similarly, Figure 13B presents a graph illustrating EUV resist thickness removed (A) as a function of dry development time (seconds) for different EUV doses. An initial delay was observed during dry development, where EUV resist was almost not removed. After the initial delay, EUV resist removal proceeded at a faster rate and trended in a relatively linear manner. Once most of the EUV resist was removed, the rate of EUV removal slowed down with a non-linear transition.

[0132] The results from Figures 13 A-13B show that dry development in the EUV resist may have different dry development rates depending on the regime that the dry development is taking place in. For example, the EUV resist may be separated in two or more layers or at least three layers. Based on the observations of Figures 13A-13B, the EUV resist may be separated according to the following regimes or layers: (i) surface layer, (ii) bulk layer, and (iii) interface “slow-down” layer. Figure 13C shows a cross-sectional schematic illustration of an EUV resist separated into at least three different layers representing at least three different dry development regimes according to some implementations. An EUV resist 1300 includes a surface layer 1310, an interface “slow-down” layer 1330, and a bulk layer 1320 between the surface layer 1310 and the interface “slow-down” layer 1330. The surface layer 1310 is over the bulk layer 1320, and the bulk layer 1320 is over the interface “slow-down” layer 1330. In the surface layer 1310, the dry development rate remains close to zero. In the bulk layer 1320, the dry development rate follows an approximately linear slope. In the interface “slow-down” layer 1330, the dry development rate decreases significantly.

[0133] During dry development of the surface layer 1310, there is an initial delay in which little to no development occurs for an initial period of time. This initial delay is found to be increasing with EUV dose and exhibits an exponential relationship. The dry development ratethrough the surface layer 1310 is delayed, due at least in part to the initial time required to penetrate the surface layer 1310. This penetration / incubation period can be rendered as in a short time of zero removal probability.

[0134] During dry development of the bulk layer 1320, a rate of removal of EUV resist material is linear or substantially linear. Using linear regression for data points plotting EUV resist material removal over time, a slope can be obtained that reflects the dry development rate in the bulk layer 1320. In other words, the dry development rate does not change as the EUV resist material is removed in the bulk layer 1320. It is also observed that the dry development rate decreases with increasing EUV doses. The removal probability of the EUV resist material in the bulk layer 1320 can depend on the dry development rate that is calculated in the bulk layer 1320.

[0135] For instance, the removal probability may be calculated according to a linear combination of each pre-development state fraction (fl, f2, and f3) multiplied by its corresponding dry development probability: Ptotal = (Pl * fl) + (P2 *f2) + (P3 *f3), where fl reflects a fraction of si states in the EUV resist, f2 reflects a fraction of s2 states in the EUV resist, and f3 reflects a fraction of s3 states, and where Pl, P2, and P3 are parameters calculated with optimization, which reflects the removal probability of each state. Accounting for the EUV dose conditions and bake conditions, the fraction of si, s2, and s3 states in the EUV resist can be determined for different blanket EUV dose cases. The dry development rate for each dry development recipe can be normalized and tied to the film states and calculated for the individual removal probabilities Pl, P2, and P3. In some implementations, Pl and P2 may be assumed to be the same. The dry development rate for the bulk layer 1320 is different than the dry development rate for the surface layer 1310 and the interface “slow-down” layer 1330.

[0136] During dry development of the interface “slow-down” layer 1330, the rate of removal of EUV resist material slows down near the completion of dry development. Without being limited by any theory, the presence of scum that accumulates near the bottom of the EUV resist 1300 may slow development of remaining EUV resist material. It is observed that the dry development rate through the interface “slow-down” layer 1330 is less affected by the exposure dose in some implementations. The removal probability of the EUV resist material in the interface “slow-down” layer 1330 can depend on the dry development rate that is calculated in the interface “slow-down” layer 1330.

[0137] The dry development rates in each of the surface layer 1310, the bulk layer 1320, and the interface “slow-down” layer 1330 can be plotted against EUV dose. This is indicative of the development selectivity through the different dry development regimes of the EUV resist. As discussed above, a linear trend is generally observed between dry development rate and EUV dose, particularly in the bulk layer 1320. The dry development rate as a function of EUV dose in each of the dry development regimes can be used in the transient particle tracing model to determine a removal probability of EUV resist material in each of the dry development regimes. The dry development rates, derived from experimental data, in the surface layer 1310, the bulk layer 1320, and the interface “slow-down” layer 1330 may be used to determine removal probabilities Pl, P2, and P3 for each pre-development state fraction (fl, f2, and f3). Therefore, simulation parameters in connection with removal probabilities in the transient particle tracing model can be extracted from experimental results.

[0138] The transient particle tracing model simulates dry development by describing surface interactions between developer particles and photoresist units over time. The transient particle tracing model accounts for the gas phase impact of developer particles with the EUV resist, where each of the developer particles has a particular trajectory (angle and direction). The developer particle having a given particle trajectory strikes a photoresist unit, and a removal probability of the photoresist unit depends on various factors such as a dry development rate in the dry development regime, a pre-development state of the photoresist unit, etc. A profile / shape of the EUV resist changes over time during the course of dry development in the transient particle tracing model. The incremental site removal due to aforementioned mechanisms is important to reproduce the correct dry development evolution, and enables prediction of a transient dry development profile and roughness changes over time until dry development is complete.

[0139] Figure 14 presents a schematic illustration of a transient particle tracing model using a semi-empirical kinetic Monte Carlo approach according to some implementations. An EUV resist 1400 can be comprised of several photoresist units or photoresist units 1410. The photoresist units 1410 in the EUV resist 1400 can be indicated by circles with various types of hatchings. Etch gas used for thermal dry development is represented by developer particles 1420 that are shaded black. Developer particles 1420 in the gas phase are flowed towards the EUV resist 1400 based on a distribution of directions, and with trajectories following the chosen direction. The developer particles 1420 interact with the photoresist units 1410 located at exposed surfaces of the EUV resist 1400. A removal probability of the photoresist unit 1410depends in part on how exposed or cross-linked the photoresist unit 1410 is. Additionally, the removal probability of the photoresist unit 1410 depends in part on a dry development rate associated with the dry development regime that the photoresist unit 1410 is located in. In some implementations, the removal probability of the photoresist unit 1410 is determined based on film state and dry development rate.

[0140] Photoresist units 1410 that are least EUV-exposed are represented by least exposed photoresist units 1430. These least photoresist units 1430 can generally reflect photoresist units that have minimal amount of cross-linking. Photoresist units 1410 that are partially exposed are represented by partially-exposed photoresist units 1440. These partially-exposed photoresist units 1440 can generally reflect photoresist units that are in an intermediate state between cross-linked and non-cross-linked. Photoresist units 1410 that are more partially exposed are represented by more partially-exposed photoresist units 1450. These more partially-exposed photoresist units 1450 have received more EUV exposure than the partially- exposed photoresist units 1440. These more partially-exposed photoresist units 1450 can generally reflect photoresist units with more intermediate states between cross-linked and noncross-linked. Photoresist units 1410 that are fully exposed by EUV light are represented by exposed photoresist units 1460. These exposed photoresist units 1460 can generally reflect photoresist units that are cross-linked.

[0141] In the transient particle tracing model, each developer particle 1420 near the surface of the EUV resist 1400 has an incoming angle and direction. In some implementations of the transient particle tracing model, the directions of the developer particles 1420 may be isotropic or substantially isotropic. Depending on the incoming angle and direction of the developer particle 1420, and depending on the profile / shape of the EUV resist 1400, the developer particle 1420 will interact with one of many photoresist units 1410 in the EUV resist 1400. When one of the developer particles 1420 interacts with a photoresist unit 1410, there is a removal probability that a reaction will take place. This removal probability can depend on the dry development rate associated with the dry development regime that the photoresist unit 1410 is located in, and how cross-linked or exposed the photoresist unit 1410 is.

[0142] The transient particle tracing model uses a semi-empirical kinetic Monte Carlo approach with mechanistic insights. The model is semi-empirical because the model extracts simulation parameters from experimental results, where the simulation parameters are connected to dry development rates. Dry development rates can be determined experimentallyfor specific local film state and for specific dry development recipes, where the dry development rates depend on the dry development regime (e.g., surface layer, bulk layer, or interface “slow-down” layer) that the dry development is taking place in. The model is kinetic because the model monitors a progress of the dry development over time. As dry development proceeds, the profile of the EUV resist 1400 changes. As the profile of the EUV resist 1400 changes, this will affect what photoresist units 1410 are more likely to be struck by a developer particle 1420 having a certain incoming angle and direction. The model uses a Monte Carlo approach because the model treats each interaction with a photoresist unit 1410 using a Monte Carlo simulation. An algorithm for the removal probability of each interaction with a photoresist unit 1410 can be characterized by randomization. The model employs mechanistic insights because the model accounts for the gas phase impact of developer particles 1420 having certain incoming angles and directions as chosen from a specific distribution.

[0143] Though the schematic illustration in Figure 14 is a 2-D illustration, it will be understood that the transient particle tracing model can be a 3-D model. The developer particles 1420 may have trajectories that can be characterized by a vector in 3-D space. The EUV resist 1400 may have photoresist units 1410 arranged in 3-D space. Though the schematic illustration in Figure 14 only shows the EUV resist 1400 partially developed at a certain time, it will be understood that the transient particle tracing model is not static and produces an EUV resist profile that continuously changes over time.

[0144] Figure 15A presents a flow diagram of an example method of determining a patterning performance of a dry development process according to some implementations. The operations of a process 1500 may be performed in different orders and / or with different, fewer, or additional operations. One or more operations of the process 1500 may be implemented in accordance with any of techniques or models described in the present disclosure. This includes the transient particle tracing model. In some implementations, the operations of the process 1500 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 19.

[0145] At block 1510 of the process 1500, pre-development states of bridging locations of an EUV resist are received as inputs into a dry development model. The dry development model may be a transient particle tracing model. The pre-development states of the bridging locations can be determined using parameters such as EUV resist material properties, EUVexposure conditions, and bake conditions, as described earlier herein. In some implementations, the EUV resist includes a metal-oxide-containing EUV resist. In some implementations, the dry development process is a thermal dry development process.

[0146] The dry development model identifies dry development rates of the EUV resist in one or more layers of the EUV resist. Examples of the one or more layers of the EUV resist may include a surface layer, a bulk layer, and an interface “slow-down” layer. The dry development rates may be calculated from an analysis of EUV resist thickness removal over dry development time. The dry development rates may be determined for various EUV dose and PEB conditions for a particular dry development process / condition. As such, identification of dry development rates in different dry development regimes can be done by analysis of experimental data. The experimental data can be taken from dry development studies such as time split checkerboard exposure experiments. A dry development rate in a dry development regime, derived analytically from time split checkerboard exposure experiments, is connected with a removal probability of a photoresist as discussed below.

[0147] At block 1520 of the process 1500, one or more dry development parameters associated with a dry development process are received as additional inputs into the dry development model. The one or more dry development parameters include at least dry development time. In some implementations, the one or more dry development parameters further include a chemistry of the developer, a concentration of the developer, a temperature, and a pressure. The dry development parameters provide the dry development operating conditions for simulating the dry development process.

[0148] The dry development model simulates the dry development process over the dry development time using a semi-empirical kinetic Monte Carlo approach. The pre-development states of bridging locations in the EUV resist can be represented as film states of photoresist units in the EUV resist. In some implementations, the photoresist units are arranged in a network, lattice, grid, or array in 2-D or 3-D space. Over the course of the dry development time, the dry development model simulates interactions of developer particles in the gas phase with photoresist units at the surface of the EUV resist. For each interaction, a probability that the photoresist unit is removed by the developer particle can be captured by randomization.

[0149] In some implementations, the process 1500 further includes (i) identifying a developer particle from among a plurality of developer particles in the dry development model, where the developer particle has a trajectory, (ii) determining a photoresist unit from a pluralityof photoresist units in the EUV resist that the developer particle interacts with in the dry development model, where the photoresist unit has a corresponding pre-development state, and (iii) determining whether the developer particle removes the photoresist unit in the EUV resist in the dry development model. The process 1500 may further include (iv) repeating operations (i)-(iii) until all of the developer particles are used up. These steps are described in more detail in the process 1550 of Figure 15B.

[0150] Figure 15B presents a flow diagram of an example method of generating an image of an EUV resist mask to determine patterning metrics of a dry development process using a transient particle tracing model according to some implementations. The operations of the process 1550 in Figure 15B may be performed between blocks 1520 and blocks 1530 of the process 1500 in Figure 15A. Specifically, operations at blocks 1552, 1554, 1556, 1558, and 1560 may be performed after receiving inputs and additional inputs at blocks 1510 and 1510 of the process 1500 and before determining one or more patterning metrics of the dry development process at block 1530 of the process 1500.

[0151] At block 1552 of the process 1550, a developer particle is identified from among a plurality of developer particles in the dry development model, where the developer particle has a trajectory. Each developer particle in the dry development model has a trajectory that provides an incoming angle and direction. The developer particle identified at block 1552 is chosen from a distribution of developer particles having various trajectories. In some implementations, the directions of the developer particles may be isotropic or substantially isotropic. A total number of developer particles in the plurality of developer particles may correspond to the concentration of the developer and the dry development time. In some instances, the one or more dry development parameters, such as the dry development time, chemistry of the developer, a concentration of the developer, a temperature, and a pressure may determine the total number developer particles in the plurality of developer particles and overall reactivity.

[0152] At block 1554 of the process 1550, a photoresist unit from among a plurality of photoresist units in the EUV resist is determined that interacts with the developer particle in the dry development model, where the photoresist unit has a corresponding pre-development state. Using the trajectory of the developer particle and the profile of the EUV resist at a given time, the developer particle identified at block 1552 strikes the photoresist unit determined at block 1554. The location of the photoresist unit determined at block 1554 is significant. Thedry development rate may depend on the region that the photoresist unit is located in. In some implementations, the region is selected from a group consisting of: a surface layer, a bulk layer, and an interface “slow-down” layer. The dry development rate is tied to a removal probability of the photoresist unit. The film state of the photoresist unit determined at block 1554 is also significant. The film state may be indicative of EUV exposure, PEB treatment, and / or the degree of cross-linking at the photoresist unit. In some implementations, the film state be a first state (si), second state (s2), or third state (s3).

[0153] At block 1556 of the process 1550, whether the developer particle removes the photoresist unit in the EUV resist is determined in the dry development model. Whether the photoresist unit determined at block 1554 is removed depends on a removal probability. As used herein, a removal probability may be used interchangeably with a reaction probability. An algorithm associated with the removal probability uses a Monte Carlo approach, where each interaction can be characterized by randomization. The algorithm associated with the removal probability uses semi-empirical parameters derived from EUV experimental data such as time split checkerboard exposure experiments. The semi-empirical parameters may be tied to dry development rates calculated from the EUV experimental data, so that the removal probability closely corresponds to the dry development rate. The dry development rate may depend on the film state of the photoresist cluster, the dry development process / condition, and the region that the photoresist unit is located in. In some implementations, the removal probability is calculated using the film state of the photoresist unit and the dry development rate of the region that the photoresist unit is located in for the dry development process / condition.

[0154] At block 1558 of the process 1550, a profile of the EUV resist is updated in the dry development model. As photoresist units are removed by developer particles, the transient particle tracing model monitors changes to the EUV resist profile and changes to roughness. As time progresses, EUV resist material is removed and a profile of the EUV patterned mask is revealed. The EUV resist is generally more recessed in a space between lines of the EUV patterned mask. Irregularities and deformities in the EUV resist profile may be revealed through the time evolution of dry development process, where such irregularities and deformities may result in roughness and defects in the EUV patterned mask.

[0155] If the transient particle tracing model determines that the developer particles are not used up after block 1558, then the process 1550 returns to block 1552. Another developer particle is identified at block 1552, and the process 1550 repeats the operations at blocks 1552to blocks 1558 to identify a developer particle, determine a photoresist unit that the developer particle interacts with, determine whether the developer particle removes the photoresist unit, and update the profile of the EUV resist. Once the transient particle tracing model determines that the developer particles are used up after block 1558, then the process 1550 proceeds to block 1560.

[0156] At block 1560 of the process 1550, an image of the EUV resist is generated in the dry development model. The image of the EUV resist is processed to determine one or more patterning metrics of the dry development process. The image of the EUV resist shows the EUV patterned mask at the completion of the dry development time. The image of the EUV patterned mask may be processed and analyzed to ascertain the CD, DtS, roughness, profile, and defects associated with the EUV patterned mask. In some implementations, the image of the EUV resist may include a top-down SEM image of the EUV resist. In some implementations, the image of the EUV resist may include a cross-sectional SEM image of the EUV resist.

[0157] Returning to Figure 15 A, at block 1530 of the process 1500, one or more patterning metrics of the dry development process are determined in the dry development model. Using the transient particle tracing model, a transient dry development profile is accurately modeled and roughness changes are simulated. At the completion of the dry development time of the dry development process, the EUV resist profile can be used to generate an image of the EUV resist mask. This can include a top-down image of the EUV resist mask or a cross-sectional image of the EUV resist mask. The image of the EUV resist mask can be analyzed and processed to determine patterning metrics such as CD, LER, LWR, DtS, and defects. These one or more patterning metrics can predict the patterning performance of the dry development process. This can lead to an improved understanding of the dry development mechanism, faster learning cycles, and reduced experimental costs.

[0158] The transient particle tracing model is grounded in a physical understanding of the transport mechanisms associated with developer particles and reaction mechanisms associated with interactions between developer particles and photoresist units. The transient particle tracing model utilizes algorithms with semi-empirical parameters that provide an analytical and 3D mode based characterization of dry development on EUV resist. The algorithms describe dry development and predict evolution of EUV resist profile, roughness, and CD that closely match with experimental results.

[0159] Figure 16A presents an example SEM image based on experimental results after patterning EUV resist. An analysis of the top-down SEM image of a patterned EUV resist mask based on experimental results can ascertain at least the CD and LWR / LER of the patterned EUV resist mask after development. Figure 16B presents an example SEM-like image based on simulations from a virtual experimentation platform after patterning EUV resist. The SEM-like image based on simulations from the virtual experimentation platform are substantially similar to the SEM image based on experimental results. An analysis of the top-down SEM-like image of a patterned EUV resist mask based on simulations from the virtual experimentation platform can ascertain similar values of at least the CD and LWR / LER of the patterned EUV resist mask after development.

[0160] Figure 17 presents example cross-sectional SEM images at different times during dry development based on simulations. The simulation uses the transient particle tracing model for modeling dry development. The cross-sectional SEM images similarly show an EUV resist profile after a first time (tl), after a second time (t2) greater than the first time, after a third time (t3) greater than the second time, after a fourth time (t4) greater than the third time, after a fifth time (t5) greater than the fourth time, and after a sixth time (t6) greater than the fifth time of dry development. The dry development time may be between about 10 seconds and about 5000 seconds, or between about 20 seconds and about 3000 seconds. The EUV resist profiles in Figure 17 using the transient particle tracing model in a virtual experimentation platform closely matches with experimental results.

[0161] Returning to the digital twin 600 of Figure 6, the development model 640 can determine post-development states of the bridging locations in the EUV resist. These postdevelopment states ultimately describe what photoresist unit clusters are removed and what photoresist unit clusters remain after development. Using a wet development model such as the wet development model 642 or a dry development model such as the static dry development model 644 or the transient particle tracing model 646, the development model 640 predicts the EUV photoresist unit clusters that are removed using the post-bake states of the bridging locations. As a result, a list of positions or coordinates (e.g., x, y, z coordinates) of what remains in the EUV resist is determined by the development model 640. In some implementations, the development model 640 obtains a profile of an EUV resist mask after development. This can be used to generate an image of the EUV resist mask or patterning metrics of the EUV resist mask. Though the image or profile may be shown in a 2-D representation, the digital twin 600 can extract an image or profile in 3-D space. This canprovide an understanding of pattern edges throughout depth of the EUV resist mask after development, which can be important for defect-related studies.

[0162] The post-development states of the bridging locations of the EUV resist can be correlated with the list of positions or coordinates of EUV photoresist unit clusters in 3-D space that survived development. The list of positions or coordinates of the EUV photoresist unit clusters in 3-D space that survived development is provided to outputs 650 of the digital twin 600. Outputs 650 of the digital twin 600 can include one or both of image generation 652 and patterning metrics 654. In some implementations, the digital twin 600 can process the list of positions or coordinates of the EUV photoresist unit clusters in 3-D space that survived development and output a top-down image of an EUV resist mask (e.g., top-down SEM image). In some implementations, the digital twin 600 can process the list of positions or coordinates of the EUV photoresist unit clusters that survived development and output a cross-sectional image of an EUV resist mask (e.g., cross-sectional SEM image). Other images of the EUV resist mask are possible in image generation 652.

[0163] In some embodiments, image generation 652 can be coupled to patterning metrics 654, where the image of the EUV resist mask obtained at the image generation 652 is used to determine one or more patterning metrics in the patterning metrics 654. The one or more patterning metrics can include one or more of the following: CD, LER, LWR, DtS, and defects. Thus, the digital twin 600 serves as a model for an EUV photolithography process to determine one or more patterning metrics such as CD, LER, LWR, DtS, and defects as outputs 650 using the inputs 610. Defects may include but are not limited to line necking and line break defects. In some implementations, other defects that may be captured by the digital twin 600 may include pinhole defects and bridge defects, with an appropriate parameter adjustments and tailored analysis algorithm. The one or more patterning metrics reflect the patterning performance of the EUV photolithography process. In some embodiments, the patterning metrics 654 can be obtained directly from the development model 640 independent of the image generation 652. The patterning metrics 654 outputted by the digital twin 600 may closely compare to actual experimental results of the photolithography process.

[0164] Figure 18 presents a flow diagram of an example method of determining a patterning performance of a photolithography process according to some implementations. The operations of a process 1800 may be performed in different orders and / or with different, fewer, or additional operations. One or more operations of the process 1800 may be implemented inaccordance with any of the techniques or models described in Figures 2, 3, 4A, 4B, 5, 6, 7A, 7B, 8A, 8B, 9, 10A-10C, 11 A, 11B, 12, 13A-13C, 14, 15A, and 15B. The photolithography process being modeled and evaluated may comprise some or all of the steps described in Figure 1. In some implementations, the operations of the process 1800 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 19.

[0165] At block 1810 of the process 1800, a plurality of inputs are provided to a digital twin of a photolithography workflow. The plurality of inputs comprise a photoresist unit cluster for an EUV resist, bridging locations using the photoresist unit cluster for the EUV resist, 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. The bridging locations may be mapped in 3-D space using the photoresist unit cluster that may be rendered in 3-D.

[0166] In some implementations, the one or more inputs associated with EUV exposure include an EUV dose and an aerial image of the EUV resist from the EUV exposure. In some implementations, the one or more inputs associated with the material of the EUV resist include 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. In some implementations, the EUV resist is a metal-oxide-containing EUV resist. In some implementations, the one or more inputs associated with the bake parameters include a bake ambient and one or more bake kinetic constants. The bake ambient can include factors such as a bake temperature, pressure, gas species, flow rates of gas species, and duration of exposure, among other bake-related conditions. The one or more bake kinetic constants may correspond to reaction rates of chemical reactions that describe transitions from one chemical state to another chemical state (e.g., si to s2 state, s2 to s3 state, or si to s3 state). The values of the one or more bake kinetic constants can be determined from experimental data and the bake ambient. In some implementations, the one or more inputs associated with the development parameters include whether a development method is wet or dry. Other development parameters may include a development chemistry, duration of exposure, development temperature, and pressure, among other development-related conditions.

[0167] The digital twin can include multiple models coupled to one another. In some implementations, the digital twin may include an EUV exposure model, a bake model, and a development model. The EUV exposure model is configured to receive pre-exposure inputs such as a material of the EUV resist, an EUV dose, and an aerial image of the EUV resist. In some embodiments, the pre-exposure inputs may include one or more material parameters associated with the material of the EUV resist. The one or more material parameters associated with the EUV resist can include 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. Bridging locations of the EUV resist may be further provided to the EUV exposure model. The bridging locations represent potential cross-linking points between adjacent EUV photoresist unit clusters in the EUV resist. The EUV exposure model is configured to determine post-exposure states of the bridging locations after EUV exposure. Post-exposure states can identify an extent of chemical conversion at the bridging locations after EUV exposure. A post-exposure state can be one of the following states: a noncross-linked state with intact R-groups, a cross-linked state, and optionally one or more intermediate states between the non-cross-linked state and the cross-linked state. The bake model is coupled to the EUV exposure model. The bake model is configured to receive the post-exposure states of the bridging locations and determine post-bake states of the bridging locations. The post-bake states can identify an extent of chemical conversion at the bridging locations after bake. A post-bake state can be one of the following states: a non-cross-linked state with intact R-groups, a cross-linked state, and optionally one or more intermediate states between the non-cross-linked state and the cross-linked state. The development model is coupled to the bake model. The development model is configured to receive the post-bake states of the bridging locations and determine post-development states of the bridging locations. The post-development states identify whether EUV photoresist unit clusters at the bridging locations are removed or remain intact after development. A post-development state can be one of the following states: a removed state and an intact state.

[0168] At block 1820 of the process 1800, post-exposure states of the bridging locations are determined in the digital twin after EUV exposure of the photolithography process. In some implementations, inputs provided to the digital twin are used to determine the post-exposure states of the bridging locations. At least some of the inputs provided to the digital twin are leveraged to calibrate parameters that serve as pre-exposure inputs. The pre-exposure inputs may be provided to the EUV exposure model of the digital twin. In some implementations, theEUV exposure model of the digital twin determines photon absorption excitation events and secondary electron excitation events using stochastics to determine the post-exposure states of the bridging locations.

[0169] At block 1830 of the process 1800, post-bake states of the bridging locations are determined in the digital twin after bake of the photolithography process. In some implementations, the post-exposure states of the bridging locations serve as inputs in a bake model to determine the post-bake states of the bridging locations. One or more bake kinetic constants in analytical relationships that describe the probabilities of bake-induced transitions are leveraged to determine transitions between states at the various bridging locations. The one or more bake kinetic constants may be calculated from experimental data. Factoring the bake ambient (e.g., a bake temperature, pressure, gas species, etc.) and accounting for the one or more bake kinetic constants, the post-bake states of the bridging locations are determined.

[0170] At block 1840 of the process 1800, post-development states of the bridging locations are determined in the digital twin after development of the photolithography process. In some implementations, the post-bake states of the bridging locations serve as inputs in a development model to determine the post-development states of the bridging locations. The development model may depend on whether the development method is wet or dry. Using the appropriate model and the development parameters, a relationship is established that correlates the postbake states of the bridging locations to the post-development states of the bridging locations. The post-development states of the bridging locations are indicative of whether EUV resist clusters corresponding to the bridging locations are removed or remain intact.

[0171] At block 1850 of the process 1800, one or more patterning metrics of the photolithography process are determined. Using the development model, the postdevelopment states of the bridging locations correspond to locations in the EUV resist that are removed and locations in the EUV resist that are intact after development. What portions of the EUV resist are intact after development can map to a profile an EUV resist mask after development. This can be used to generate an image of the EUV resist mask after development, such as a top-down image of the EUV resist mask or a cross-sectional image of the EUV resist mask. The profile of the EUV resist mask or the image of the EUV resist mask can be analyzed and processed to determine the one or more patterning metrics of the EUV resist mask. The one or more patterning metrics can include one or more of the following: CD, LER, LWR, DtS, and defects. The one or more patterning metrics can determine the patterning performance ofthe photolithography process. Rather than relying on physical experiments to evaluate a photolithography process, which can be time-intensive and cost-prohibitive, the process 1800 using the digital twin provides the patterning performance of the photolithography process in an accurate, low-cost, and speedy manner. The digital twin enables faster cycles of learning with reduced cost, systematic process mapping, mechanism understanding, and efficient optical proximity correction.

[0172] 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 the semiconductor device fabrication operation. In this manner, a computational model is generated or programmed on such system.

[0173] 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 submodules.

[0174] 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.).

[0175] 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, andessentially 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.

[0176] 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.

[0177] 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 particular tasks. For example, operations requiring large blocks of code and / or significant processing capacity may be implemented on large and / or stationary machines.

[0178] 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, phase-change 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.

[0179] 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.

[0180] 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.

[0181] An example computer system 1900 is depicted in Figure 19. As shown, computer system 1900 includes an input / output subsystem 1902, which may implement an interface for interacting with human users and / or other computer systems depending upon the application. Embodiments of the disclosure may be implemented in program code on system 1900 with VO subsystem 1902 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 1902 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.

[0182] Communication interfaces 1907 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 1907 can include network interface card circuitry, wireless communication circuitry, etc.

[0183] Program code may be stored in non-transitory media such as secondary memory 1910 or memory 1908 or both. In some embodiments, secondary memory 1910 can be persistent storage. One or more processors 1904 reads program code from one or more non-transitorymedia 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 1905 couples the I / O subsystem 1902, the processor 1904, peripheral devices 1906, communication interfaces 1907, memory 1908, and secondary memory 1910. Conclusion

[0184] 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 patterning performance of a photolithography process, the method comprising: providing a plurality of inputs to a digital twin of a photolithography workflow, wherein the plurality of inputs comprise a photoresist unit cluster for an EUV resist, bridging locations using the photoresist unit cluster for the EUV resist, 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; determining, in the digital twin, post-exposure states of the bridging locations after EUV exposure of the photolithography process; determining, in the digital twin, post-bake states of the bridging locations after bake of the photolithography process; determining, in the digital twin, post-development states of the bridging locations after development of the photolithography process; and determining one or more patterning metrics of the photolithography process.

2. The method of claim 1, wherein the one or more inputs associated with EUV exposure comprise an EUV dose and an aerial image of the EUV resist from the EUV exposure.

3. The method of claim 1, wherein the one or more inputs associated with the material of the EUV resist comprise 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.

4. The method of claim 1, wherein the one or more inputs associated with the bake parameters comprise a bake ambient and one or more bake kinetic constants.

5. The method of claim 1, wherein the one or more inputs associated with the development parameters comprise whether development is wet or dry.

6. The method of claim 1, wherein the one or more patterning metrics comprise one or more of the following: critical dimension (CD), line edge roughness (LER), line width roughness (LWR), dose-to-size (DtS), and defects.

7. The method of claim 1, further comprising: generating an image representing the EUV resist after development, wherein determining the one or more patterning metrics of the photolithography process comprises determining the one or more patterning metrics using the image representing the EUV resist after development.

8. The method of claim 1, wherein determining the post-exposure states of the bridging locations after exposure comprises: receiving, in the digital twin, the bridging locations, an aerial image of the EUV resist from EUV exposure, an EUV dose, and an absorption coefficient of the EUV resist; obtaining photon absorption coordinates of the EUV resist representing photon absorption excitation events in the EUV resist; obtaining secondary electron coordinates of the EUV resist representing secondary electron excitation events in the EUV resist using the photon absorption coordinates, an external quantum efficiency of the EUV resist, and a secondary electron blur radius of the EUV resist; and determining the post-exposure states of the bridging locations after exposure using the photon absorption coordinates and the secondary electron coordinates.

9. The method of claim 1, wherein the digital twin comprises an EUV exposure model of the photolithography workflow configured to determine the post-exposure states of the bridging locations after EUV exposure, a bake model of the photolithography workflow configured to determine the post-bake states of the bridging locations after bake, and a development model of the photolithography workflow configured to determine the postdevelopment states of the bridging locations after development, wherein the development model uses a semi-empirical kinetic Monte Carlo method and surface particle-tracing model.

10. The method of claim 1, wherein the EUV resist comprises a metal-oxide-containing EUV resist.

11. A digital twin of a photolithography workflow comprising one or more non- transitory machine readable media comprising logic configured to implement: an EUV exposure model of the photolithography workflow, wherein the EUV exposure model is configured to receive pre-exposure inputs comprising a photoresist unitcluster 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; a bake model of the photolithography workflow, 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; and a development model of the photolithography workflow, wherein the development model is configured to receive the post-bake states of the bridging locations and development parameters, and configured to generate post-development states of the bridging locations after development using the post-bake states of the bridging locations and the development parameters; wherein the digital twin is configured to generate one or more patterning metrics using the post-development states of the bridging locations after development.

12. The digital twin of claim 11, wherein the pre-exposure inputs further comprise one or more material parameters associated with the EUV resist.

13. The digital twin of claim 12, wherein the one or more material parameters associated with the EUV resist comprise 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.

14. The digital twin of claim 11, wherein the one or more inputs associated with the EUV exposure comprise an EUV dose and an aerial image of the EUV resist from the EUV exposure.

15. The digital twin of claim 11, wherein the bake parameters comprise a bake ambient and one or more bake kinetic constants.

16. The digital twin of claim 15, wherein the bake ambient comprises a bake temperature, pressure, gas species, flow rates of gas species, and duration of exposure.

17. The digital twin of claim 11, wherein the development parameters comprise whether the development is wet or dry.

18. The digital twin of claim 11, wherein the EUV resist comprises a metal-oxide- containing EUV resist.

19. The digital twin of claim 11, wherein the digital twin is configured to generate an image representing the EUV resist after development, wherein the one or more patterning metrics are generated using the image representing the EUV resist after development.

20. The digital twin of claim 11, wherein the one or more patterning metrics comprise one or more of the following: critical dimension (CD), line edge roughness (LER), line width roughness (LWR), dose-to-size (DtS), and defects.

21. The digital twin of claim 11, wherein the EUV exposure model is further configured to generate photon absorption coordinates of the EUV resist representing photon absorption excitation events in the EUV resist using the bridging locations, an aerial image of the EUV resist from the EUV exposure, an EUV dose, and an absorption coefficient of the EUV resist, wherein the EUV exposure model is configured to generate the post-exposure states of the bridging locations after exposure using the photon absorption coordinates, an external quantum efficiency of the EUV resist, and a secondary electron blur radius of the EUV resist.

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