Method, apparatus and medium for lithography simulation

Abstract

Embodiments of the present disclosure relate to a method, device, and medium for photolithography simulation. The method proposed herein includes: dividing the photoresist area to be simulated into multiple photoresist units; determining one or more target parameters associated with the photoresist potential energy based on the mechanical properties of the photoresist in the photoresist area, the equilibrium distance between the photoresist units, and a cutoff radius set by the user for neighbor interaction, wherein the cutoff radius is used to limit the range of action of the embedded potential energy; and determining the corresponding target positions of the multiple photoresist units by minimizing the total potential energy of the multiple photoresist units based on the one or more target parameters, the cutoff radius, and the equilibrium distance. In this way, by comprehensively considering multiple influencing factors, high-precision simulation of the photoresist morphology is achieved, and the complexity of the calculation is effectively controlled.

Description

Technical Field

[0001] Example embodiments of the present disclosure generally relate to the field of integrated circuit technology, and more particularly, to a method, apparatus, and medium for lithography simulation. Background Art

[0002] Photolithography, a core process in modern integrated circuit manufacturing, undertakes the critical task of projecting the design pattern from the mask onto the photoresist. During this process, the photoresist undergoes a series of complex chemical reactions and physical processes, the control of which is crucial for subsequent process steps. After steps such as post-baking and development, the final pattern is revealed on the photoresist. Notably, the topography of the photoresist directly defines the key feature dimensions of semiconductor devices, and therefore its accuracy has a decisive impact on device performance. Precisely controlling the photoresist topography has become one of the core challenges that need to be addressed in the photolithography process. Summary of the Invention

[0003] In a first aspect of the present disclosure, a method for photolithography simulation is provided. The method comprises: dividing a photoresist region to be simulated into a plurality of photoresist cells; determining one or more target parameters associated with the photoresist potential energy based on the mechanical properties of the photoresist in the photoresist region, the equilibrium distance between the photoresist cells, and a user-set cutoff radius for neighbor interaction, wherein the cutoff radius is used to limit the range of action of the embedded potential energy; and determining corresponding target positions of the plurality of photoresist cells by minimizing the total potential energy of the plurality of photoresist cells based on the one or more target parameters, the cutoff radius, and the equilibrium distance.

[0004] In a second aspect of the present disclosure, an electronic device is provided. The device includes at least one processing unit; and at least one memory coupled to the at least one processing unit and storing instructions for execution by the at least one processing unit. When executed by the at least one processing unit, the instructions cause the device to perform the method for lithography simulation according to the first aspect.

[0005] In a third aspect of the present disclosure, a computer-readable storage medium is provided, wherein a computer program is stored on the computer-readable storage medium, and the computer program can be executed by a processor to implement the method for lithography simulation according to the first aspect.

[0006] In a fourth aspect of the present disclosure, a computer program product is provided, which includes computer-executable instructions, which, when executed by a processor, implement the method for lithography simulation according to the first aspect of the present disclosure.

[0007] According to an embodiment of the present disclosure, the photoresist area to be simulated is first divided into a plurality of photoresist units, so that the microstructure and behavior of the photoresist can be simulated more accurately. By comprehensively considering the mechanical properties of the photoresist, the equilibrium distance between the photoresist units, and the cutoff radius set by the user for neighbor interactions, this embodiment can more comprehensively reflect the real photoresist material properties and complex mechanical behaviors. In addition, when determining the target parameters associated with the photoresist potential energy, the embodiment of the present disclosure limits the scope of action of the embedded potential energy by the cutoff radius, and determines the corresponding target position of each unit by minimizing the total potential energy of multiple photoresist units, thereby simulating a photoresist morphology close to the real one.

[0008] It should be understood that the content described in this summary section is not intended to limit the key features or important features of the embodiments of the present disclosure, nor is it intended to limit the scope of the present disclosure. Other features of the present disclosure will become easily understood through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0009] The above and other features, advantages and aspects of the embodiments of the present disclosure will become more apparent with reference to the following detailed description in conjunction with the accompanying drawings. In the accompanying drawings, the same or similar reference numerals represent the same or similar elements, wherein:

[0010] Figure 1 A schematic diagram illustrating an example environment according to an embodiment of the present disclosure is shown;

[0011] Figure 2 A flowchart illustrating an example process of a method for lithography simulation according to some embodiments of the present disclosure;

[0012] Figures 3A to 3C A schematic diagram showing the topography of a photoresist simulation area before a post-bake process according to some embodiments of the present disclosure is shown;

[0013] Figures 4A to 4C A schematic diagram showing the morphology of a photoresist simulation area after a post-bake process according to some embodiments of the present disclosure;

[0014] Figure 5 A schematic diagram showing the relationship between the elastic modulus of a photoresist and the concentration of protecting groups according to some embodiments of the present disclosure;

[0015] Figure 6 A schematic diagram schematically illustrates the relationship between the strain softening factor and strain according to some embodiments of the present disclosure;

[0016] Figure 7 A schematic diagram showing an example of simulated photoresist topography according to some embodiments of the present disclosure; and

[0017] Figure 8A block diagram of an electronic device is shown in which one or more embodiments of the present disclosure may be implemented. DETAILED DESCRIPTION

[0018] The following describes embodiments of the present disclosure in more detail with reference to the accompanying drawings. Although certain embodiments of the present disclosure are shown in the accompanying drawings, it should be understood that the present disclosure can be implemented in various forms and should not be construed as limited to the embodiments described herein. Rather, these embodiments are provided to provide a more thorough and complete understanding of the present disclosure. It should be understood that the drawings and embodiments of the present disclosure are for illustrative purposes only and are not intended to limit the scope of protection of the present disclosure.

[0019] It should be noted that the titles of any section / subsection provided herein are not limiting. Various embodiments are described throughout this document, and any type of embodiment may be included under any section / subsection. Furthermore, the embodiments described in any section / subsection may be combined in any manner with any other embodiments described in the same section / subsection and / or in different sections / subsections.

[0020] In the description of the embodiments of the present disclosure, the term "including" and similar terms should be understood as open inclusion, that is, "including but not limited to". The term "based on" should be understood as "based at least in part on". The term "one embodiment" or "the embodiment" should be understood as "at least one embodiment". The term "some embodiments" should be understood as "at least some embodiments". Other explicit and implicit definitions may be included below. The terms "first", "second", etc. may refer to different or the same objects. Other explicit and implicit definitions may be included below.

[0021] As briefly described above, the topography of the photoresist directly defines the key feature dimensions of the semiconductor device. How to accurately control the photoresist topography has become one of the core issues that need to be urgently addressed in the photolithography process.

[0022] The morphology of photoresist is influenced not only by the mechanical properties of the material itself but also by multiple factors such as light intensity, concentration, and temperature, resulting in deformations that can exceed 20%. To accurately predict photoresist morphology changes and finely control lithography process parameters, 3D photoresist morphology simulation technology is particularly important.

[0023] A 3D photoresist topography simulation method based on analytical solutions of elastic mechanics has attracted attention due to its simple model and fast computational speed. However, this method has certain practical limitations because it relies on simplified material parameters and mechanical models, making it difficult to fully reflect the true properties and complex mechanical behavior of photoresist materials.

[0024] To overcome this limitation, another 3D photoresist topography simulation method based on elastic finite element methods has emerged. While this method can more accurately simulate the actual photoresist topography, its computational efficiency is relatively low due to the need to construct a large stiffness matrix and solve a complex system of linear equations. This has become a problem that requires further optimization for practical applications.

[0025] In view of this, an embodiment of the present disclosure provides a scheme for photolithography simulation. According to the scheme, the photoresist area to be simulated is first divided into a plurality of photoresist units. Then, based on the mechanical properties of the photoresist in the photoresist area, the equilibrium distance between the photoresist units, and the cutoff radius for neighbor interaction set by the user, one or more target parameters associated with the photoresist potential energy are determined. The cutoff radius is used to limit the scope of action of the embedded potential energy. Then, based on the one or more target parameters, the cutoff radius, and the equilibrium distance, the corresponding target positions of the plurality of photoresist units are determined by minimizing the total potential energy of the plurality of photoresist units.

[0026] It will be more clearly understood through the description below that according to the scheme of the present disclosure, the photoresist area to be simulated is first divided into multiple photoresist units, so that the microstructure and behavior of the photoresist can be simulated more accurately. By comprehensively considering the mechanical properties of the photoresist, the equilibrium distance between the photoresist units, and the cutoff radius set by the user for neighbor interactions, the scheme can more comprehensively reflect the real photoresist material properties and complex mechanical behaviors. In addition, when determining the target parameters associated with the photoresist potential energy, the scheme of the present disclosure limits the scope of action of the embedded potential energy by the cutoff radius, and determines the corresponding target position of each unit by minimizing the total potential energy of multiple photoresist units, thereby simulating a photoresist morphology close to the real one.

[0027] In this way, the solution disclosed herein achieves high-precision simulation of photoresist morphology by comprehensively considering multiple influencing factors. This process does not require constructing a huge stiffness matrix and solving a complex set of linear equations, thereby effectively controlling the complexity of the calculation.

[0028] Various example implementations of this solution will be described in detail below with reference to the accompanying drawings.

[0029] Figure 1 Schematic diagram of an example environment 100 according to an embodiment of the present disclosure is shown. Figure 1 , the example environment 100 may include a terminal device 110 and an electronic device 120 .

[0030] In this example environment 100, an application 130 for interacting with an electronic device 120 is installed in a terminal device 110. A user 140 can interact with the application 130 via the terminal device 110 and / or its attached devices. As an example, the user 140 can issue instructions to the electronic device 120 using the application 130. Alternatively, in some embodiments, the application 130 can also be installed at the electronic device 120 (not shown). The user 140 can directly issue instructions to the electronic device 120 through the application installed on the electronic device 120. After receiving the instructions from the application 130, the electronic device 120 can perform a simulation operation on the photoresist morphology. In addition, the terminal device 110 can present an interface 150 of the application 130. The morphology of the photoresist simulated by the electronic device 120 can be presented to the user 140 via the interface 150.

[0031] In some embodiments, the terminal device 110 can be any type of mobile, fixed, or portable terminal, including a mobile phone, desktop computer, laptop computer, notebook computer, netbook computer, tablet computer, media computer, multimedia tablet, personal communication system (PCS) device, personal navigation device, personal digital assistant (PDA), audio / video player, digital camera / camcorder, positioning device, television receiver, radio receiver, e-book device, gaming device, or any combination thereof, including accessories and peripherals of these devices or any combination thereof. In some embodiments, the terminal device 110 can also support any type of user interface (such as "wearable" circuitry, etc.).

[0032] The electronic device 120 may be a standalone physical server, a server cluster or distributed system consisting of multiple physical servers, or a cloud server that provides basic cloud computing services such as cloud services, cloud databases, cloud computing, cloud functions, cloud storage, network services, cloud communications, middleware services, domain name services, security services, content distribution networks, and big data and artificial intelligence platforms. The electronic device 120 may include, for example, a computing system / server, such as a mainframe, an edge computing node, a computing device in a cloud environment, and the like.

[0033] A communication connection may be established between the electronic device 120 and the terminal device 110. The communication connection may be established via a wired or wireless method. The communication connection may include, but is not limited to, a Bluetooth connection, a mobile network connection, a Universal Serial Bus connection, a Wi-Fi connection, etc., and the embodiments of the present disclosure are not limited in this respect. In the embodiments of the present disclosure, the electronic device 120 and the terminal device 110 may exchange data and / or signaling via the communication connection between them.

[0034] It should be understood that the structure and function of the various elements in the environment 100 are described for illustrative purposes only and do not imply any limitation on the scope of the present disclosure.

[0035] Figure 2 FIG. 2 is a flow chart illustrating an example process 200 of a method for lithography simulation according to some embodiments of the present disclosure. The process 200 may be implemented at the electronic device 120 .

[0036] Figures 3A to 3C A top view, a side view, and a perspective view are respectively shown of a topography 300 of a photoresist simulation region before a post-bake process according to some embodiments of the present disclosure. Figures 4A to 4C 4 and 5 show a top view, a side view and a perspective view of the morphology 400 of the photoresist simulation area after the post-bake process according to some embodiments of the present disclosure. Figures 3A to 4C After the post-bake process, the positions between the photoresist units 310 change, resulting in deformation 410 of the photoresist simulation area. The embodiment of the present disclosure is at least intended to simulate the real morphology of the photoresist at each stage of the lithography by comprehensively considering the mechanical properties of the photoresist, the equilibrium distance between the photoresist units, and the cutoff radius set by the user for the nearest neighbor interaction. Figures 3A to 4C The process 200 will be described.

[0037] Reference Figure 2 In block 210 , the electronic device 120 divides the photoresist region to be simulated into a plurality of photoresist cells 310 .

[0038] As an example, each photoresist unit 310 can be considered as an independent entity, which contains a group of photoresist molecules. These photoresist molecules are unique in each unit, which means that different photoresist units 310 contain different groups of photoresist molecules.

[0039] To simplify and abstract the model, each photoresist cell 310 can be represented in the simulation as a spherical photoresist cell 310. This representation method not only reduces the complexity of the simulation, but also preserves the key physical properties of the photoresist cell 310, making the simulation results closer to reality. In addition, each photoresist cell 310 can also be represented in the simulation using other shapes as needed.

[0040] As an example, a plurality of photoresist units 310 can constitute a three-dimensional simulation area formed by uniformly stacking a large number of identical spherical photoresist units 310. Optionally, these spherical photoresist units 310 can be uniformly stacked in any appropriate manner. For example, simple cubic stacking, that is, each photoresist unit 310 is located at the vertex of a cube, forming a regular grid structure; face-centered stacking, that is, the photoresist unit 310 is located at the center of each face of the cube; body-centered stacking, that is, the photoresist unit 310 is located at the center of the body of the cube; and hexagonal stacking, that is, the photoresist units 310 are closely arranged in a hexagonal manner. These different stacking methods can be selected according to the specific simulation requirements and the physical properties of the photoresist to achieve the best simulation effect.

[0041] As an example, the distance L between the closest photoresist cells 310 can be set to 1-30 nanometers (nm), for example, 5-20 nm. It should be noted that the distance L between the closest photoresist cells 310 can be determined based on the required simulation accuracy. The higher the simulation accuracy requirement and the smaller the simulation area, the smaller the value of distance L can be. It should be understood that the example values of distance L listed herein are merely illustrative and non-limiting.

[0042] At block 220 , the electronic device 120 determines one or more target parameters associated with the photoresist potential based on the mechanical properties of the photoresist in the photoresist region, the equilibrium distance between the photoresist cells 310 , and a user-set cutoff radius for neighbor interactions. The cutoff radius is used to limit the range of action of the embedded potential.

[0043] As an example, the mechanical properties of the photoresist may include elastic modulus, viscosity, Poisson's ratio, etc. These mechanical properties determine the response behavior of the photoresist when subjected to external forces.

[0044] As an example, each photoresist unit 310 is considered an independent entity, and the interaction between them maintains the equilibrium of the system. The equilibrium distance reflects the natural spacing between these units in the absence of external forces. It is closely related to factors such as the molecular structure and density of the photoresist and the interaction force.

[0045] As an example, the cutoff radius is used to limit the range of the embedded potential energy. For example, only when the distance between two photoresist units 310 is less than or equal to the cutoff radius, the interaction between them will be considered in the simulation calculation.

[0046] As an example, the target parameters may include at least a pair potential coefficient between the photoresist cells 310 and an embedding potential coefficient of the photoresist cells 310 .

[0047] The following describes a process of determining the potential energy coefficient and the embedding potential energy coefficient of the photoresist unit 310 according to an embodiment of the present disclosure.

[0048] In the photolithography process, the patterned mask creates an uneven distribution of protection group concentrations within the photoresist. This uneven distribution significantly impacts the photoresist's morphology and performance, and therefore must be fully accounted for during simulations. The disclosed embodiments explicitly factor the impact of the protection group concentration distribution on photoresist morphology into consideration when determining target parameters.

[0049] Specifically, in some embodiments, the electronic device 120 obtains concentration information of the photoresist region. The concentration information indicates the distribution of the protecting group concentration of the photoresist within the photoresist region. The electronic device 120 can then determine the corresponding protecting group concentrations at the multiple photoresist units 310 based on the concentration information. Subsequently, the electronic device 120 can determine the corresponding parameter values of one or more target parameters at the multiple photoresist units 310 based on the corresponding protecting group concentrations, mechanical properties, cutoff radius, and equilibrium distance at the multiple photoresist units 310.

[0050] For example, the concentration information may describe the distribution of the concentration of the protecting groups in the photoresist within the photoresist region. This distribution may be non-uniform, reflecting the specific impact of the patterned mask on the concentration of the protecting groups in the photoresist.

[0051] After obtaining the concentration information, the electronic device 120 further determines the corresponding protecting group concentrations at the plurality of photoresist cells 310 based on the information. Since the photoresist region has been divided into a plurality of cells, the protecting group concentration in each cell may be different.

[0052] By considering the specific impact of the concentration distribution of protecting groups on the photoresist morphology, the photoresist morphology simulation can be closer to the actual situation, providing strong support for the research and development and optimization of the photolithography process.

[0053] In some embodiments, the electronic device 120 determines a target elastic modulus value for a first photoresist cell among the plurality of photoresist cells 310 based on a protective group concentration at the first photoresist cell and at least one reference elastic modulus value. The electronic device 120 may then determine at least one of the following at the first photoresist cell based on the target elastic modulus value, the Poisson's ratio of the photoresist, and the cutoff radius: a value of a pair potential energy coefficient or a value of an embedding potential energy coefficient.

[0054] For example, when exposed to light, negative-development photoresist undergoes a complex series of chemical reactions that generate a large amount of photoacids. These photoacids play a key role in the post-bake process, catalyzing the decomposition of protective groups on the organic resin molecules in the photoresist. This decomposition process produces volatile decomposition products. As the post-bake heats up, these decomposition products gradually evaporate, forming numerous voids within the photoresist region. The formation of these voids leads to unbalanced stresses, which significantly alter the morphology of the photoresist region. Furthermore, it is noteworthy that the elastic modulus of the organic resin in the photoresist changes significantly before and after the decomposition reaction. For widely used negative-development photoresists, the elastic modulus of the organic resin is typically lower than that of its decomposition products. Therefore, it can be inferred that the elastic modulus of a real photoresist is closely related to the concentration of protective groups in the photoresist.

[0055] As an example, at least one reference elastic modulus value can be determined by experiment or calculation at different protecting group concentrations. The electronic device 120 can determine the target elastic modulus value at the first photoresist unit by combining the reference elastic modulus values, such as by weighted summation.

[0056] Once the target elastic modulus is determined, electronic device 120 can perform further calculations based on the photoresist's Poisson's ratio (a physical quantity that describes the relationship between a material's lateral and longitudinal deformation when subjected to force) and cutoff radius (a parameter used to limit the range of neighbor interactions) to determine the potential energy coefficient or embedding potential energy coefficient. These coefficients are important parameters that describe the strength of interactions between photoresist cells 310 and directly impact the accuracy and reliability of the simulation model.

[0057] Specifically, the potential energy coefficient may reflect the rate of change of potential energy due to the change in relative position between the photoresist units 310 , while the embedding potential energy coefficient may describe the rate of increase of potential energy when the photoresist unit 310 is embedded or compressed.

[0058] In this way, the electronic device 120 can perform refined mechanical property analysis for each photoresist unit 310, thereby more accurately simulating the actual behavior and performance of the photoresist.

[0059] In some embodiments, the target elastic modulus value at the first photoresist unit may be determined as follows.

[0060] Specifically, the at least one reference elastic modulus value includes, but is not limited to, a first reference elastic modulus value when the protecting group concentration is a first predetermined concentration and a second reference elastic modulus value when the protecting group concentration is a second predetermined concentration. For example, the second predetermined concentration is different from the first predetermined concentration. In some embodiments, the electronic device 120 may perform a weighted sum of the first reference elastic modulus value and the second reference elastic modulus value based on the protecting group concentration at the first photoresist unit to provide the target elastic modulus value.

[0061] The weighted summation method allows the simulation model to obtain more accurate elastic modulus values through interpolation or extrapolation within a continuously varying range of protecting group concentrations. This approach not only improves simulation accuracy but also enables the model to better adapt to the complex variations in photoresist processing during actual manufacturing.

[0062] As an example, as described above, there is a linear relationship between the elastic modulus of the photoresist and the concentration of the protecting group in the photoresist. Therefore, the elastic modulus of the photoresist and the concentration of the protecting group in the photoresist can be expressed by Formula 1.

[0063] ;

[0064] Formula 1

[0065] in, Lithography Unit The target elastic modulus value at (e.g., the first photoresist unit), Lithography Unit The concentration of protecting groups, is the elastic modulus of the photoresist (e.g., a first reference elastic modulus value) when the percentage of the protecting group concentration is 0 (e.g., at the first predetermined concentration), is the elastic modulus of the photoresist (e.g., the second reference elastic modulus value) when the percentage of the protective group concentration is 1 (e.g., the second predetermined concentration). In particular, when and When they are equal, the elastic modulus of the photoresist is a constant value.

[0066] The inventors discovered that during the development process of negative-development photoresist, because the organic resin molecules in the photoresist are more soluble in the organic developer, the unexposed or lightly exposed photoresist dissolves in the developer and is ultimately removed. The elastic modulus of the removed photoresist is zero. This removed portion significantly alters the relationship between the elastic modulus of the photoresist and the concentration of the material components within the photoresist.

[0067] In the embodiments of the present disclosure, the portion of the photoresist removed after exposure and development can be reflected by the concentration of the protecting group. Figure 5Schematic diagram 500 showing the relationship between the elastic modulus of a photoresist and the concentration of protecting groups according to some embodiments of the present disclosure. Figure 5 Specifically, if the protecting group concentration is higher than the developing concentration threshold of the protecting group, that portion will be removed. In this case, the photoresist elastic modulus is close to 0, and the elastic modulus of this portion of the photoresist is nonlinearly related to the protecting group concentration within the photoresist. Conversely, if the protecting group concentration is lower than the developing concentration threshold of the protecting group, that portion of the photoresist will be retained, and the elastic modulus of this portion of the photoresist is approximately linearly related to the protecting group concentration within the photoresist.

[0068] For the portion where the elastic modulus of the photoresist is approximately linearly related to the concentration of protecting groups within the photoresist, the target elastic modulus value can be determined using the aforementioned formula 1. For the portion where the elastic modulus is nonlinearly related to the concentration of protecting groups within the photoresist, the target elastic modulus value can be determined using the following method.

[0069] As described above, at least one reference elastic modulus value includes but is not limited to: a first reference elastic modulus value when the protecting group concentration is a first predetermined concentration and a second reference elastic modulus value when the protecting group concentration is a second predetermined concentration. As an example, the second predetermined concentration is different from the first predetermined concentration. In some embodiments, the electronic device 120 can determine the target elastic modulus value at the first photoresist unit in the following manner. First, the electronic device 120 performs a weighted summation of the first reference elastic modulus value and the second reference elastic modulus value based on the protecting group concentration at the first photoresist unit. Then, the electronic device 120 determines a scaling factor for the elastic modulus based on the protecting group concentration at the first photoresist unit. Subsequently, the electronic device 120 obtains the target elastic modulus value by applying the scaling factor to the result of the weighted summation.

[0070] As an example, as previously described, electronic device 120 requires at least two reference elastic modulus values: a first reference elastic modulus value corresponding to a first predetermined protective group concentration, and a second reference elastic modulus value corresponding to a second predetermined protective group concentration. These two predetermined concentrations are different to reflect the effect of varying protective group concentrations on the elastic modulus.

[0071] In some embodiments, for a first photoresist cell, electronic device 120 first performs a weighted summation of the first reference elastic modulus value and the second reference elastic modulus value based on the protecting group concentration at the cell. This weighted summation can take into account the difference between the actual protecting group concentration and the two predetermined concentrations, thereby obtaining a preliminary elastic modulus estimate.

[0072] Next, the electronic device 120 determines a scaling factor for the elastic modulus based on the protecting group concentration at the first photoresist unit. This scaling factor is used to further adjust the weighted summation result to more accurately reflect the effect of the actual protecting group concentration on the elastic modulus.

[0073] In some embodiments, the electronic device 120 determines a concentration influencing factor based on the concentration of the protecting group at the first photoresist unit and the development concentration characteristic of the protecting group in the photoresist, and then obtains a scaling factor based on the inverse of the concentration influencing factor.

[0074] As an example, the electronic device 120 considers the development concentration characteristics of the protecting groups within the photoresist. These characteristics indicate how the protecting groups behave during development, such as how they respond to the developer and how they affect the overall properties of the photoresist at different concentrations.

[0075] As an example, the concentration influencing factor may be determined based on a developing concentration threshold, a slope of a protecting group developing concentration threshold, and a protecting group concentration at the first lithography unit.

[0076] As an example, the concentration influencing factor can be expressed by Formula 2.

[0077] ;

[0078] Formula 2

[0079] in, is the developing concentration threshold of the protecting group, is the threshold slope of the protecting group development concentration.

[0080] Finally, the electronic device 120 calculates the inverse of the concentration influence factor to obtain a scaling factor, which is directly used to adjust the calculation of the elastic modulus.

[0081] In this way, the electronic device 120 can dynamically adjust the calculation of the elastic modulus based on the actual concentration of the protecting groups, thereby more accurately simulating the physical properties of the photoresist at different processing stages.

[0082] Finally, the electronic device 120 obtains the target elastic modulus value by applying the scaling factor to the result of the weighted summation.

[0083] As an example, the above process can be expressed by Formula 3.

[0084] ;

[0085] Formula 3

[0086] in, Indicates the scaling factor. Figure 5 If the concentration of protecting groups is higher than the developing concentration threshold of protecting groups, the elastic modulus of photoresist approaches 0, while if the concentration of protecting groups is lower than the developing concentration threshold of protecting groups, the elastic modulus of photoresist is approximately linearly related to the concentration of protecting groups in photoresist. The relationship between the elastic modulus of actual photoresist and the percentage of protecting group concentration can be obtained by fitting and To approximate.

[0087] In this way, the determination of the target elastic modulus value is not only applicable to the case where the elastic modulus and the concentration of protecting groups in the photoresist are in an approximately linear relationship, but can also handle the case where the elastic modulus and the concentration of protecting groups in the photoresist are in a non-linear relationship, thereby improving the accuracy and reliability of the photoresist morphology simulation.

[0088] As described above, after determining the target elastic modulus value, electronic device 120 may determine at least one of the following at the first photoresist cell based on the target elastic modulus value, the Poisson's ratio of the photoresist, and the cutoff radius: a value of a pair potential energy coefficient or a value of an embedded potential energy coefficient. Furthermore, electronic device 120 may determine the total potential energy of the plurality of photoresist cells 310 based on the value of the pair potential energy coefficient and / or the value of the embedded potential energy coefficient.

[0089] Specifically, the total potential energy of the plurality of photoresist units 310 can be obtained as follows.

[0090] For each photoresist unit 310 in the plurality of photoresist units 310, the electronic device 120 determines a first group of neighboring photoresist units and a second group of neighboring photoresist units based on the cutoff radius. Then, the electronic device 120 determines the pair potential energy of the photoresist unit 310 based on the corresponding pair potential energy terms between the photoresist unit 310 and the first group of neighboring photoresist units. Furthermore, the electronic device 120 determines the embedded potential energy of the photoresist unit 310 based on the corresponding embedded potential energy terms between the photoresist unit 310 and the second group of neighboring photoresist units. After determining the pair potential energy and the embedded potential energy, the electronic device 120 calculates the total potential energy based on the pair potential energy and the embedded potential energy determined for the plurality of photoresist units 310.

[0091] As an example, the first group of neighboring photoresist cells may refer to the photoresist cells 310 and the current photoresist cell 310 (the current photoresist cell is also referred to as the photoresist cell in this document). ) and the photoresist unit 310 that is closest and second closest (which can be determined by setting a distance threshold) and within the cutoff radius, and the second group of neighboring photoresist units can include the photoresist units 310 that are closest to the current photoresist unit 310 (for example, the photoresist unit ) is the closest photoresist unit 310 that is within the cutoff radius.

[0092] As an example, the potential cutoff radius can be set to , the embedding potential cutoff radius can be set as It should be noted that the potential energy cutoff radius and the embedded potential energy cutoff radius can also be set to other values, which can be determined according to actual needs, so they will not be described in detail here.

[0093] As an example, the first group of neighboring photoresist cells may include photoresist cells 6 nearest neighbor photoresist units and 12 next nearest neighbor photoresist units (a total of 18 nearest neighbor photoresist units), and the second group of nearest neighbor photoresist units may include photoresist unit 310 The 6 nearest neighbor photoresist units.

[0094] Pair potential energy can be energy generated by interactions between photoresist cells 310, reflecting energy changes caused by changes in the relative positions of the photoresist cells 310. The electronic device 120 determines the pair potential energy of each photoresist cell 310 based on the corresponding pair potential energy terms between these photoresist cells 310. Embedding potential energy reflects the energy generated when a photoresist cell 310 is "embedded" or compressed by its surrounding cells. This energy is generally related to the deformation of the photoresist cell 310 and the resulting internal stress.

[0095] As an example, the process of determining the total potential energy can be expressed by Equations 4 to 7.

[0096] ;

[0097] Formula 4

[0098] ;

[0099] Formula 5

[0100] ;

[0101] Formula 6

[0102] ;

[0103] Formula 7

[0104] in, is the total potential energy of the photoresist simulation area, is the potential energy between the photoresist units 310, is the embedding potential energy of the photoresist unit 310, Photoresist unit and the first group of neighboring photoresist cells (eg, photoresist cells ), Photoresist unit The potential energy, Photoresist unit and a second group of neighboring photoresist cells (e.g., photoresist cells ), Photoresist unit The embedded potential energy, 、 and Photoresist unit Photoresist unit The potential energy coefficient, distance and equilibrium distance between them, Indicates the photoresist unit All photoresist units within the potential energy cutoff radius , Photoresist unit The embedding potential energy coefficient, Indicates the photoresist unit All photoresist units within the potential energy cutoff radius are embedded , and Photoresist unit Photoresist unit The three-dimensional coordinates of . In the formula is the unknown coefficient, which is the target parameter described above.

[0105] As an example, the potential energy coefficient and embedding potential energy coefficient It can be determined by formula 8 and formula 9.

[0106] ;

[0107] Formula 8

[0108] ;

[0109] Formula 9

[0110] in, and Photoresist unit and photoresist unit The elastic modulus of the photoresist, is the Poisson's ratio of the photoresist material.

[0111] As an example, the equilibrium distance can be determined from the protecting group concentration and the deformation bulk modulus coefficient . It can be determined specifically by formula 10.

[0112] ;

[0113] Formula 10

[0114] in, is the deformation bulk modulus coefficient of the photoresist, is the equilibrium distance between the photoresist units 310 before the post-bake process, wherein the distance between the nearest neighboring photoresist units is for , between the next nearest neighbor photoresist units for .

[0115] After completing the calculation of the pair potential energy and the embedding potential energy of each photoresist unit 310 , the electronic device 120 sums these potential energies using Formula 4 to obtain the total potential energy of the photoresist unit 310 .

[0116] The inventors discovered through research that the organic resin in photoresist is a polymer material that exhibits strain-softening mechanical properties. Specifically, when the material is subjected to significant strain, the stress-strain relationship is no longer linear, but rather exhibits a phenomenon in which the material's elastic modulus decreases. Therefore, the elastic modulus of a photoresist is not only related to the concentration of the protecting groups but also to the strain of the photoresist. This nonlinear effect cannot be ignored when the photoresist undergoes significant deformation during the photolithographic process.

[0117] Based on this, the embodiments of the present disclosure determine the corresponding pair potential energy terms between the photoresist unit 310 and the first group of neighboring photoresist units in the following manner to address the above problem.

[0118] Specifically, corresponding pair potential energy terms between a second photoresist unit in the plurality of photoresist units 310 and a first group of neighboring photoresist units of the second photoresist unit may be determined as follows.

[0119] First, for each adjacent photoresist unit in the first group of adjacent photoresist units, the electronic device 120 determines the strain between the adjacent photoresist unit and the second photoresist unit based on the distance between the adjacent photoresist unit and the second photoresist unit. Then, the electronic device 120 determines a potential energy coefficient related to strain softening based on the strain and a threshold strain for strain softening. Subsequently, the electronic device 120 determines a potential energy term between the adjacent photoresist unit and the second photoresist unit based on the potential energy coefficient related to strain softening.

[0120] As an example, based on the distance between the adjacent photoresist unit and the second photoresist unit, the electronic device 120 can determine the strain between the two units. The strain reflects the degree of deformation caused by the change in the relative position between the two units.

[0121] As an example, electronic device 120 can consider the effects of strain softening. Strain softening is a phenomenon in which a material's ability to resist further deformation decreases when subjected to significant strain. To simulate this effect, electronic device 120 can set a threshold strain for strain softening. When the calculated strain exceeds this threshold, strain softening is considered to have occurred.

[0122] Based on the calculated strain and the set threshold strain, the electronic device 120 determines a potential energy coefficient related to strain softening, which reflects the effect of strain softening on the interaction energy between the two photoresist units 310 .

[0123] Next, the electronic device 120 calculates a potential energy term between the adjacent photoresist unit and the second photoresist unit using the determined potential energy coefficient related to strain softening.

[0124] In some embodiments, the electronic device 120 determines a strain softening factor corresponding to the strain based on the strain, the threshold strain, and the minimum strain softening factor. The electronic device 120 then determines a potential energy coefficient associated with strain softening based on the strain softening factor and the potential energy coefficient without strain softening.

[0125] As an example, strain may be calculated by comparing relative position changes between the photoresist units 310. It reflects the degree of deformation of the photoresist under external force or internal stress.

[0126] As an example, the threshold strain can be a critical value, and when the actual strain exceeds this value, the photoresist material begins to exhibit strain softening characteristics. In other words, the effect of strain softening on the potential energy will only be considered when the strain reaches or exceeds this threshold.

[0127] As an example, the minimum strain softening factor can be the lowest limit of the strain softening effect, and even if the strain is very large, the strain softening factor will not fall below this minimum value. This is done to ensure the stability and physical plausibility of the simulation model.

[0128] After obtaining these key parameters, the electronic device 120 may calculate a strain softening factor corresponding to the current strain according to the current strain, the threshold strain, and the minimum strain softening factor.

[0129] Finally, electronic device 120 can use this calculated strain softening factor to adjust the potential energy coefficient that originally did not account for strain softening. Specifically, electronic device 120 can multiply the strain softening factor with the original potential energy coefficient to obtain a new potential energy coefficient that accounts for the strain softening effect. This new potential energy coefficient will be used in subsequent potential energy calculations and photoresist topography simulations to ensure that the simulation results can more accurately reflect the behavior of the photoresist in the actual process.

[0130] As an example, the electronic device 120 calculates the distance between each photoresist unit 310 and its nearest neighbor and next nearest neighbor photoresist units according to the position of the photoresist unit 310 in the photoresist simulation area. .

[0131] Next, the electronic device 120 calculates the strain softening factor of the connection line between each photoresist unit 310 and its nearest neighbor and next nearest neighbor photoresist units and the potential energy coefficient including the strain softening effect. .

[0132] As an example, the potential energy coefficient including the strain softening effect It can be determined by Formulas 11 to 13.

[0133] ;

[0134] Formula 11

[0135] ;

[0136] Formula 12

[0137] ;

[0138] Formula 13

[0139] in, is the strain softening factor, Photoresist unit Photoresist unit The strain between is the potential energy coefficient including the strain softening effect, is the minimum strain softening factor, is the strain softening threshold strain, is the threshold slope of the strain softening factor.

[0140] Figure 6 FIG. 6 schematically illustrates a relationship 600 between a strain softening factor and strain according to some embodiments of the present disclosure. Figure 6, with the increase of strain, the hard-softening factor gradually decreases and reaches regional saturation. For the relationship between the strain softening factor and strain of actual photoresist, the parameters can be fitted by experimental data. 、 and To approximate.

[0141] In this manner, the electronic device 120 determines the total potential energy of the plurality of photoresist cells 310 .

[0142] Continue to refer Figure 2 At block 230 , the electronic device 120 determines corresponding target positions of the plurality of photoresist cells 310 by minimizing a total potential energy of the plurality of photoresist cells 310 based on the one or more target parameters, the cutoff radius, and the equilibrium distance.

[0143] As an example, the electronic device 120 calculates the distance between each photoresist unit 310 and its nearest neighbor and next nearest neighbor photoresist units according to the position of the photoresist unit 310 in the photoresist simulation area. , and together with the previously calculated (Or the potential energy coefficient ), embedded potential energy coefficient and equilibrium distance Substitute into Formula 4 to Formula 7 to calculate the total potential energy of the photoresist simulation area.

[0144] As an example, the electronic device 120 first determines a gradient vector of the total potential energy of the plurality of photoresist cells 310 with respect to the coordinates of each photoresist cell 310 .

[0145] As an example, the electronic device 120 will (Or the potential energy coefficient ), embedded potential energy coefficient and equilibrium distance And the calculated distance Substituted into the gradient vector calculation formula, the gradient vector of the total potential energy with respect to the coordinates of each photoresist unit 310 is calculated.

[0146] As an example, the gradient vector of the total potential energy of the plurality of photoresist cells 310 with respect to the coordinates of each photoresist cell 310 can be expressed by Equations 14 to 16.

[0147] ;

[0148] Formula 14

[0149] ;

[0150] Formula 15

[0151] ;

[0152] Formula 16

[0153] As an example, the electronic device 120 uses the total potential energy of the photoresist unit 310 and the gradient vector of the total potential energy with respect to the coordinates of each photoresist unit 310 as parameters of the optimizer, and uses the optimizer to minimize the total potential energy of the simulation area to obtain the position coordinates of each photoresist unit 310 when the total potential energy is minimized.

[0154] As an example, the optimizer includes but is not limited to an optimizer based on gradient descent, an optimizer based on Newton iteration method, and an optimizer based on quasi-Newton iteration method (eg, BFGS optimizer, L-BFGS optimizer, etc.).

[0155] As an example, the electronic device 120 may obtain the position coordinates of each photoresist unit 310 when the total potential energy is minimum in the following manner.

[0156] First, the electronic device 120 multiplies the gradient vector of the total potential energy with respect to the coordinates of each photoresist unit 310 by the iteration step size to obtain the iterative displacement of each photoresist unit 310. Then, the electronic device 120 adds the iterative displacement of each photoresist unit 310 to the three-dimensional coordinates of each photoresist unit 310 to obtain the new three-dimensional coordinates of each photoresist unit 310.

[0157] As an example, this process can be expressed by Equations 17 to 19.

[0158] ;

[0159] Formula 17

[0160] ;

[0161] Formula 18

[0162] ;

[0163] Formula 19

[0164] in, 、 and Photoresist unit In the The three-dimensional coordinates of the iteration step, 、 and Photoresist unit In the The three-dimensional coordinates of the iteration step, 、 and are the iteration steps in the three-dimensional directions respectively. Furthermore, the iteration step can be a fixed value or determined by methods such as Adagrad.

[0165] As another example, the electronic device 120 may also obtain the position coordinates of each photoresist unit 310 when the total potential energy is minimum in the following manner.

[0166] First, the electronic device 120 obtains the inverse matrix of the approximate Hessian matrix according to the L-BFGS algorithm. Then, the electronic device 120 combines the gradient vectors of all photoresist units 310 into a column vector, multiplies the inverse matrix of the approximate Hessian matrix by the column vector, and the resulting column vector is the column vector composed of the iterative displacements of all photoresist units 310. Then, the electronic device 120 splits the column vector composed of the iterative displacements of all photoresist units 310 into the displacement of each photoresist unit 310. Finally, the electronic device 120 adds the iterative displacement of each photoresist unit 310 to the three-dimensional coordinates of each photoresist unit 310 to obtain the new three-dimensional coordinates of each photoresist unit 310.

[0167] As an example, this process can be expressed by Equations 20 to 23.

[0168] ;

[0169] Formula 20

[0170] ;

[0171] Formula 21

[0172] ;

[0173] Formula 22

[0174] ;

[0175] Formula 23

[0176] in, is the first The inverse matrix of the approximate Hessian matrix of the iteration step, For the The gradient vectors of all photoresist cells 310 in the iteration steps are combined into a column vector, For the The column vector consisting of the iterative displacements of all photoresist cells 310 in the iterative steps, 、 and Corresponding to Photoresist cells in column vector In the The displacement of the iteration step.

[0177] In some embodiments, the electronic device 120 determines the topography of the photoresist region based on the corresponding target positions of the plurality of photoresist cells 310 .

[0178] For example, these target positions represent the equilibrium positions that the photoresist cells 310 will reach after being subjected to various forces (such as internal stress and external forces). The electronic device 120 can use this target position information to construct the overall topography of a photoresist region. This process can be viewed as integrating discrete photoresist cell 310 position data into a continuous or nearly continuous topography model. This model can reflect the overall shape and structural characteristics of the photoresist under specific conditions.

[0179] In some embodiments, after determining the target position of the photoresist unit 310, the electronic device 120 performs a convergence check to ensure that the position of the photoresist unit 310 is stable and does not change significantly, thereby ensuring the accuracy and reliability of the simulation.

[0180] Specifically, the electronic device 120 checks the distance between the updated three-dimensional coordinates of each photoresist unit 310 and its pre-update three-dimensional coordinates. If this distance is less than a pre-set threshold, the position of the photoresist unit 310 is considered to have converged, meaning that its position no longer changes significantly. This threshold is typically set based on the simulation's accuracy requirements and computing resource limitations, representing an acceptable range of position variation.

[0181] If the distance between all photoresist cells 310 before and after the updated coordinates is less than or equal to this threshold, the entire optimization process has reached convergence. This means that the positions of all photoresist cells 310 have stabilized and no further adjustments are required. At this point, the electronic device 120 can stop the iterative update process and assume that the current set of photoresist cells 310 has formed a stable topography.

[0182] However, if the distance between the updated coordinates of any photoresist cell 310 and the updated coordinates is greater than this threshold, the optimization has not reached convergence. This means that the position of another photoresist cell 310 has significantly changed and requires further adjustment. In this case, the electronic device 120 repeats the previous steps (e.g., blocks 210 to 230) until the three-dimensional coordinates of all photoresist cells 310 have converged.

[0183] Figure 7 FIG. 7 is a schematic diagram illustrating an example 700 of simulated photoresist topography according to some embodiments of the present disclosure, wherein: Figure 7The middle left figure shows a schematic diagram of the photoresist morphology 710 before the post-bake process. Figure 7 The middle right figure shows a schematic diagram of the photoresist morphology 720 after the post-bake process.

[0184] Reference Figure 7 It can be clearly seen that the photoresist morphology simulated using the simulation method in the disclosed embodiment has significantly changed compared to its initial state, and is closer to the photoresist morphology in actual processes. Specifically, the photoresist morphology 720 after post-baking has obvious shrinkage deformation, and the thickness of the photoresist morphology 720 has also been significantly reduced. This is consistent with the changes that occur in photoresist during the post-baking process in actual processes, further verifying the accuracy and effectiveness of the simulation method.

[0185] Once the topography model is constructed, the electronic device 120 can perform further analysis and processing on it. For example, geometric parameters such as the surface area, volume, and curvature of the photoresist region can be calculated, or physical properties such as mechanical and optical properties can be evaluated. These analysis and processing results can provide valuable insights for photoresist process optimization, defect detection, and performance prediction.

[0186] It can be clearly understood from the various embodiments described above that the embodiments of the present disclosure provide a photolithography simulation method, which coarse-grains the photoresist material molecules into photoresist units 310, and there is a potential energy interaction between adjacent photoresist units 310. By minimizing the total potential energy of the photoresist simulation area, the photoresist morphology in the final equilibrium state can be obtained. This method is suitable for simulating the real material mechanical parameters of the photoresist, and can handle the linear / nonlinear relationship between the mechanical parameters of the photoresist and the concentration of the material components in the photoresist, as well as the linear / nonlinear stress-strain mechanical model. At the same time, the model does not need to construct a stiffness matrix, nor does it need to solve a large-scale linear equation system. The model is simple and has high computational efficiency. In addition, the model is universal for both small deformation and large deformation simulations without the need to introduce geometric nonlinear processing.

[0187] Figure 8 1 is a block diagram of an electronic device 800 in which one or more embodiments of the present disclosure may be implemented. The electronic device 800 may be used to implement, for example, Figure 1 The terminal device 110 and / or electronic device 120 shown. It should be understood that Figure 8 The illustrated electronic device 800 is merely exemplary and should not be construed as limiting the functionality and scope of the embodiments described herein.

[0188] Reference Figure 8, electronic device 800 is in the form of a general electronic device. Components of electronic device 800 may include, but are not limited to, one or more processors or processing units 810, memory 820, storage device 830, one or more communication units 840, one or more input devices 850, and one or more output devices 860. Processing unit 810 may be a real or virtual processor and is capable of performing various processes according to programs stored in memory 820. In a multi-processor system, multiple processing units execute computer-executable instructions in parallel to increase the parallel processing capabilities of electronic device 800.

[0189] The electronic device 800 typically includes a plurality of computer storage media. Such media can be any available media accessible to the electronic device 800, including but not limited to volatile and non-volatile media, removable and non-removable media. The memory 820 can be a volatile memory (e.g., registers, cache, random access memory (RAM)), a non-volatile memory (e.g., read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory), or some combination thereof. The storage device 830 can be a removable or non-removable medium and can include a machine-readable medium, such as a flash drive, a disk, or any other medium that can be used to store information and / or data and can be accessed within the electronic device 800.

[0190] The electronic device 800 may further include additional removable / non-removable, volatile / non-volatile storage media. Figure 8 As shown in FIG, a magnetic disk drive for reading from or writing to a removable, non-volatile magnetic disk (e.g., a "floppy disk") and an optical disk drive for reading from or writing to a removable, non-volatile optical disk may be provided. In these cases, each drive may be connected to a bus (not shown) by one or more data media interfaces. The memory 820 may include a computer program product 825 having one or more program modules configured to perform the various methods or actions of various embodiments of the present disclosure.

[0191] The communication unit 840 enables communication with other electronic devices via a communication medium. Additionally, the functions of the components of the electronic device 800 can be implemented in a single computing cluster or multiple computing machines that can communicate via a communication connection. Thus, the electronic device 800 can operate in a networked environment using a logical connection with one or more other servers, a network personal computer (PC), or another network node.

[0192] The input device 850 may be one or more input devices, such as a mouse, keyboard, or trackball. The output device 860 may be one or more output devices, such as a display, a speaker, or a printer. The electronic device 800 may also communicate with one or more external devices (not shown) via the communication unit 840 as needed, such as a storage device, a display device, or the like, with one or more devices that allow a user to interact with the electronic device 800, or with any device that allows the electronic device 800 to communicate with one or more other electronic devices (e.g., a network card, a modem, etc.). Such communication may be performed via an input / output (I / O) interface (not shown).

[0193] According to an exemplary implementation of the present disclosure, a computer-readable storage medium is provided, on which computer-executable instructions are stored, wherein the computer-executable instructions are executed by a processor to implement the method described above. According to an exemplary implementation of the present disclosure, a computer program product is also provided, which is tangibly stored on a non-transitory computer-readable medium and includes computer-executable instructions, and the computer-executable instructions are executed by a processor to implement the method described above.

[0194] Various aspects of the present disclosure are described herein with reference to flowcharts and / or block diagrams of methods, apparatuses, devices, and computer program products implemented according to the present disclosure. It should be understood that each block of the flowcharts and / or block diagrams, and combinations of blocks in the flowcharts and / or block diagrams, can be implemented by computer-readable program instructions.

[0195] These computer-readable program instructions can be provided to a processing unit of a general-purpose computer, a special-purpose computer, or other programmable data processing device, thereby producing a machine, such that when these instructions are executed by the processing unit of the computer or other programmable data processing device, a device is generated that implements the functions / actions specified in one or more blocks in the flowchart and / or block diagram. These computer-readable program instructions can also be stored in a computer-readable storage medium, where these instructions cause the computer, programmable data processing device, and / or other device to operate in a specific manner. Thus, the computer-readable medium storing the instructions comprises an article of manufacture that includes instructions for implementing various aspects of the functions / actions specified in one or more blocks in the flowchart and / or block diagram.

[0196] Computer-readable program instructions can be loaded onto a computer, other programmable data processing apparatus, or other device so that a series of operational steps are performed on the computer, other programmable data processing apparatus, or other device to produce a computer-implemented process, thereby causing the instructions executed on the computer, other programmable data processing apparatus, or other device to implement the functions / actions specified in one or more boxes in the flowchart and / or block diagram.

[0197] The flow charts and block diagrams in the accompanying drawings show the possible architecture, functions and operations of the systems, methods and computer program products according to multiple implementations of the present disclosure. In this regard, each box in the flow chart or block diagram can represent a part for a module, program segment or instruction, and a part for a module, program segment or instruction comprises one or more executable instructions for realizing the logical function of the specification. In some alternative implementations, the functions marked in the box can also occur in a sequence different from that marked in the accompanying drawings. For example, two continuous boxes can actually be executed substantially in parallel, and they can sometimes be executed in the opposite order, depending on the functions involved. It should also be noted that each box in the block diagram and / or flow chart, and the combination of the boxes in the block diagram and / or flow chart can be realized by a special hardware-based system that performs the function or action of the specification, or can be realized by a combination of special hardware and computer instructions.

[0198] While various implementations of the present disclosure have been described above, the foregoing description is intended to be illustrative, non-exhaustive, and not limited to the disclosed implementations. Many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the described implementations. The terminology used herein is intended to best explain the principles of the implementations, their practical applications, or improvements to existing technologies, or to enable others skilled in the art to understand the various implementations disclosed herein.

Claims

1. A method for lithography simulation, characterized in that: include: Dividing the photoresist area to be simulated into a plurality of photoresist units; Determining a pair potential energy coefficient and / or an embedding potential energy coefficient associated with the photoresist potential energy based on the mechanical properties of the photoresist in the photoresist region, the equilibrium distance between the photoresist units, and a cutoff radius for neighbor interaction set by a user, wherein the cutoff radius is used to limit the range of action of the embedding potential energy; as well as Based on the pair potential energy coefficient and / or the embedding potential energy coefficient, the cutoff radius, and the equilibrium distance, corresponding target positions of the plurality of photoresist cells are determined by minimizing a total potential energy of the plurality of photoresist cells.

2. The method for lithography simulation according to claim 1, wherein: Determining the pair potential energy coefficient and / or the embedding potential energy coefficient associated with the photoresist potential energy includes: determining corresponding protecting group concentrations at the plurality of photoresist units based on concentration information of the photoresist region, the concentration information indicating a distribution of protecting group concentrations of the photoresist within the photoresist region; For a first photoresist unit among the plurality of photoresist units, performing a weighted summation on at least one reference elastic modulus value based on a concentration of protecting groups at the first photoresist unit to determine a target elastic modulus value at the first photoresist unit; and The pair potential coefficient and / or embedding potential coefficient is determined by: Wherein, i is the first photoresist unit among the plurality of photoresist units, j is the neighboring photoresist unit within the cutoff radius of the first photoresist unit among the plurality of photoresist units, and k is the number of photoresist units. ij is the potential energy coefficient between the first photoresist unit and the adjacent photoresist unit, B i is the embedding potential energy coefficient of the first photoresist unit, E i is the target elastic modulus at the first photoresist unit, E j is the target elastic modulus of the neighboring photoresist unit of the first photoresist unit, ν is the Poisson's ratio of the photoresist material, and L is the distance between the nearest photoresist units.

3. The method for lithography simulation according to claim 2, wherein: The at least one reference elastic modulus value comprises: a first reference elastic modulus value when the protecting group concentration is a first predetermined concentration; a second reference elastic modulus value when the protecting group concentration is a second predetermined concentration, the second predetermined concentration being different from the first predetermined concentration, and Determining the target elastic modulus value at the first photoresist unit includes: Based on the concentration of the protecting group at the first photoresist unit, a weighted sum of the first reference elastic modulus value and the second reference elastic modulus value is performed as the target elastic modulus value.

4. The method for lithography simulation according to claim 2, wherein: The at least one reference elastic modulus value comprises: a first reference elastic modulus value when the protecting group concentration is a first predetermined concentration; a second reference elastic modulus value when the protecting group concentration is a second predetermined concentration, the second predetermined concentration being different from the first predetermined concentration, and Determining the target elastic modulus value at the first photoresist unit includes: performing a weighted summation of the first reference elastic modulus value and the second reference elastic modulus value based on a concentration of protecting groups at the first photoresist unit; and The target elastic modulus value is obtained by applying a scaling factor to the result of the weighted summation, and The scaling factor is determined as follows: Among them, C i is the concentration of protective groups at the first photoresist unit, C t is the developing concentration threshold of the protecting group, and S is the slope of the developing concentration threshold of the protecting group.

5. The method for lithography simulation according to claim 1, wherein: The total potential energy of the plurality of photoresist units is obtained by: For a first photoresist unit among the plurality of photoresist units, The potential energy of the first photoresist unit is determined by: The embedding potential energy of the first photoresist unit is determined by: as well as calculating the total potential energy based on the pair potential energy and the embedding potential energy determined for the plurality of photoresist cells, and Wherein, i is the first photoresist unit among the plurality of photoresist units, j is the neighboring photoresist unit within the cutoff radius of the first photoresist unit among the plurality of photoresist units, and k is the number of photoresist units. ij is the potential energy coefficient between the first photoresist unit and the adjacent photoresist unit, B i is the embedding potential energy coefficient of the first photoresist unit, l ij is the distance between the first photoresist unit and the adjacent photoresist unit, is the equilibrium distance between the first photoresist unit and its adjacent photoresist unit, represents the neighboring photoresist cells within the potential energy cutoff radius of the first photoresist cell, represents the neighboring photoresist cells within the embedding potential cutoff radius of the first photoresist cell.

6. The method for lithography simulation according to claim 5, characterized in that: The potential energy of the first photoresist unit is also determined by: in, is the potential energy coefficient related to strain softening, which indicates the influence of the interaction energy between two photoresist units.

7. The method for lithography simulation according to claim 6, characterized in that: The potential energy coefficient associated with strain softening is determined by: Among them, F ij is the strain softening factor, F0 is the minimum value of the strain softening factor, ε t is the threshold strain, ε ij is the strain between the first photoresist unit and the adjacent photoresist unit, S s is the threshold slope of the strain softening factor, the minimum value of the strain softening factor F0 and the threshold slope of the strain softening factor S s Fitted by experimental data.

8. The method for lithography simulation according to claim 1, wherein: The method further comprises: The topography of the photoresist region is determined based on corresponding target positions of the plurality of photoresist units.

9. An electronic device, characterized in that: include: at least one processing unit; as well as at least one memory coupled to the at least one processing unit and storing instructions for execution by the at least one processing unit, the instructions, when executed by the at least one processing unit, causing the electronic device to perform a method for lithography simulation, the method comprising: Dividing the photoresist area to be simulated into a plurality of photoresist units; Determining a pair potential energy coefficient and / or an embedding potential energy coefficient associated with the photoresist potential energy based on the mechanical properties of the photoresist in the photoresist region, the equilibrium distance between photoresist units, and a cutoff radius for neighbor interaction set by a user, wherein the cutoff radius is used to limit the range of action of the embedding potential energy; and Based on the pair potential energy coefficient and / or the embedding potential energy coefficient, the cutoff radius, and the equilibrium distance, corresponding target positions of the plurality of photoresist cells are determined by minimizing a total potential energy of the plurality of photoresist cells.

10. The electronic device according to claim 9, characterized in that Determining the pair potential energy coefficient and / or the embedding potential energy coefficient associated with the photoresist potential energy includes: determining corresponding protecting group concentrations at the plurality of photoresist units based on concentration information of the photoresist region, the concentration information indicating a distribution of protecting group concentrations of the photoresist within the photoresist region; For a first photoresist unit among the plurality of photoresist units, performing a weighted summation on at least one reference elastic modulus value based on a concentration of protecting groups at the first photoresist unit to determine a target elastic modulus value at the first photoresist unit; and The pair potential coefficient and / or embedding potential coefficient is determined by: Wherein, i is the first photoresist unit among the plurality of photoresist units, j is the neighboring photoresist unit within the cutoff radius of the first photoresist unit among the plurality of photoresist units, and k is the number of photoresist units. ij is the potential energy coefficient between the first photoresist unit and the adjacent photoresist unit, B i is the embedding potential energy coefficient of the first photoresist unit, E i is the target elastic modulus at the first photoresist unit, E j is the target elastic modulus of the neighboring photoresist unit of the first photoresist unit, ν is the Poisson's ratio of the photoresist material, and L is the distance between the nearest photoresist units.

11. The electronic device according to claim 10, characterized in that The at least one reference elastic modulus value comprises: a first reference elastic modulus value when the protecting group concentration is a first predetermined concentration; a second reference elastic modulus value when the protecting group concentration is a second predetermined concentration, the second predetermined concentration being different from the first predetermined concentration, and Determining the target elastic modulus value at the first photoresist unit includes: Based on the concentration of the protecting group at the first photoresist unit, a weighted sum of the first reference elastic modulus value and the second reference elastic modulus value is performed as the target elastic modulus value.

12. The electronic device according to claim 10, wherein: The at least one reference elastic modulus value comprises: a first reference elastic modulus value when the protecting group concentration is a first predetermined concentration; a second reference elastic modulus value when the protecting group concentration is a second predetermined concentration, the second predetermined concentration being different from the first predetermined concentration, and Determining the target elastic modulus value at the first photoresist unit includes: performing a weighted summation of the first reference elastic modulus value and the second reference elastic modulus value based on a concentration of protecting groups at the first photoresist unit; and The target elastic modulus value is obtained by applying a scaling factor to the result of the weighted summation, and The scaling factor is determined as follows: Among them, C i is the concentration of protective groups at the first photoresist unit, C t is the developing concentration threshold of the protecting group, and S is the slope of the developing concentration threshold of the protecting group.

13. The electronic device according to claim 9, wherein: The total potential energy of the plurality of photoresist units is obtained by: For a first photoresist unit among the plurality of photoresist units, The potential energy of the first photoresist unit is determined by: The embedding potential energy of the first photoresist unit is determined by: as well as calculating the total potential energy based on the pair potential energy and the embedding potential energy determined for the plurality of photoresist cells, and Wherein, i is the first photoresist unit among the plurality of photoresist units, j is the neighboring photoresist unit within the cutoff radius of the first photoresist unit among the plurality of photoresist units, and k is the number of photoresist units. ij is the potential energy coefficient between the first photoresist unit and the adjacent photoresist unit, B i is the embedding potential energy coefficient of the first photoresist unit, l ij is the distance between the first photoresist unit and the adjacent photoresist unit, is the equilibrium distance between the first photoresist unit and its adjacent photoresist unit, represents the neighboring photoresist cells within the potential energy cutoff radius of the first photoresist cell, represents the neighboring photoresist cells within the embedding potential cutoff radius of the first photoresist cell.

14. The electronic device according to claim 13, wherein: The potential energy of the first photoresist unit is also determined by: in, is the potential energy coefficient related to strain softening, which indicates the influence of the interaction energy between two photoresist units.

15. The electronic device according to claim 14, characterized in that The potential energy coefficient associated with strain softening is determined by: Among them, F ij is the strain softening factor, F0 is the minimum value of the strain softening factor, ε t is the threshold strain, ε ij is the strain between the first photoresist unit and the adjacent photoresist unit, S s is the threshold slope of the strain softening factor, the minimum value of the strain softening factor F0 and the threshold slope of the strain softening factor S s Fitted by experimental data.

16. The electronic device according to claim 9, characterized in that The method further comprises: The topography of the photoresist region is determined based on corresponding target positions of the plurality of photoresist units.

17. A computer-readable storage medium, characterized in that A computer program is stored thereon, the computer program being executable by a processor to implement a method for lithography simulation, the method comprising: Dividing the photoresist area to be simulated into a plurality of photoresist units; Determining a pair potential energy coefficient and / or an embedding potential energy coefficient associated with the photoresist potential energy based on the mechanical properties of the photoresist in the photoresist region, the equilibrium distance between photoresist units, and a cutoff radius for neighbor interaction set by a user, wherein the cutoff radius is used to limit the range of action of the embedding potential energy; and Based on the pair potential energy coefficient and / or the embedding potential energy coefficient, the cutoff radius, and the equilibrium distance, corresponding target positions of the plurality of photoresist cells are determined by minimizing a total potential energy of the plurality of photoresist cells.

18. The storage medium according to claim 17, wherein: Determining the pair potential energy coefficient and / or the embedding potential energy coefficient associated with the photoresist potential energy includes: determining corresponding protecting group concentrations at the plurality of photoresist units based on concentration information of the photoresist region, the concentration information indicating a distribution of protecting group concentrations of the photoresist within the photoresist region; For a first photoresist unit among the plurality of photoresist units, performing a weighted summation on at least one reference elastic modulus value based on a concentration of protecting groups at the first photoresist unit to determine a target elastic modulus value at the first photoresist unit; and The pair potential coefficient and / or embedding potential coefficient is determined by: Wherein, i is the first photoresist unit among the plurality of photoresist units, j is the neighboring photoresist unit within the cutoff radius of the first photoresist unit among the plurality of photoresist units, and k is the number of photoresist units. ij is the potential energy coefficient between the first photoresist unit and the adjacent photoresist unit, B i is the embedding potential energy coefficient of the first photoresist unit, E i is the target elastic modulus at the first photoresist unit, E j is the target elastic modulus of the neighboring photoresist unit of the first photoresist unit, ν is the Poisson's ratio of the photoresist material, and L is the distance between the nearest photoresist units.

19. The storage medium according to claim 17, wherein: The total potential energy of the plurality of photoresist units is obtained by: For a first photoresist unit among the plurality of photoresist units, The potential energy of the first photoresist unit is determined by: The embedding potential energy of the first photoresist unit is determined by: as well as calculating the total potential energy based on the pair potential energy and the embedding potential energy determined for the plurality of photoresist cells, and Wherein, i is the first photoresist unit among the plurality of photoresist units, j is the neighboring photoresist unit within the cutoff radius of the first photoresist unit among the plurality of photoresist units, and k is the number of photoresist units. ij is the potential energy coefficient between the first photoresist unit and the adjacent photoresist unit, B i is the embedding potential energy coefficient of the first photoresist unit, l ij is the distance between the first photoresist unit and the adjacent photoresist unit, is the equilibrium distance between the first photoresist unit and its adjacent photoresist unit, represents the neighboring photoresist cells within the potential energy cutoff radius of the first photoresist cell, represents the neighboring photoresist cells within the embedding potential cutoff radius of the first photoresist cell.

20. A computer program product, characterized in that The method comprises computer executable instructions, wherein the computer executable instructions implement the method for lithography simulation according to any one of claims 1 to 8 when executed by a processor.

Images