Method and device for simulating photoresist morphology and medium

Abstract

The embodiment of the invention relates to a method and equipment for simulating photoresist morphology and a medium. The method provided by the invention comprises the following steps: aiming at a plurality of photoresist units at a target simulation area of photoresist, determining a plurality of developing solution concentration characteristics and a plurality of photoresist concentration characteristics corresponding to the plurality of photoresist units; based on the plurality of developing solution concentration characteristics and the plurality of photoresist concentration characteristics, determining developing solution concentration distribution and photoresist concentration distribution at the target simulation area after development; and determining the photoresist morphology at the target simulation area based on the developing solution concentration distribution and the photoresist concentration distribution.

Description

Technical Field

[0001] Example embodiments of the present disclosure generally relate to the field of semiconductor technology, and more particularly, to a method, apparatus, and medium for simulating photoresist topography. Background Art

[0002] Photolithography is the core process in modern integrated circuit manufacturing. Photolithography projects the design pattern on the mask onto the photoresist to trigger various chemical reactions in the photoresist. The solubility of photoresists exposed to different degrees in the developer is significantly different, so that the final photoresist pattern can be formed through the development process. With the advancement of process nodes, how to accurately control the morphology of photoresist has become a technical problem that needs to be solved in the photolithography process. Summary of the invention

[0003] In a first aspect of the present disclosure, a method for simulating photoresist morphology is provided. The method comprises: determining a plurality of developer concentration characteristics and a plurality of photoresist concentration characteristics corresponding to a plurality of photoresist units at a target simulation area of ​​the photoresist; determining a developer concentration distribution and a photoresist concentration distribution at the target simulation area after development based on the plurality of developer concentration characteristics and the plurality of photoresist concentration characteristics; and determining the photoresist morphology at the target simulation area based on the developer concentration distribution and the photoresist concentration distribution.

[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, the at least one memory is coupled to the at least one processing unit and stores instructions for execution by the at least one processing unit. When the instructions are executed by the at least one processing unit, the device executes the method of 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 of 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 according to the first aspect of the present disclosure.

[0007] It should be understood that the contents described in this content section are not intended to limit the key features or important features of the embodiments of the present disclosure, nor are they 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

[0008] 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: Figure 1 A schematic diagram showing an example environment according to an embodiment of the present disclosure is shown; Figure 2 A flowchart showing an example process of a method for simulating photoresist topography according to some embodiments of the present disclosure; Figure 3 A schematic diagram showing a process of determining a developer concentration and a photoresist concentration at a point in time according to an embodiment of the present disclosure; and Figure 4 A block diagram of an electronic device is shown in which one or more embodiments of the present disclosure may be implemented. DETAILED DESCRIPTION

[0009] Embodiments of the present disclosure will be described in more detail below 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 being limited to the embodiments set forth herein. On the contrary, 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 only for exemplary purposes and are not intended to limit the scope of protection of the present disclosure.

[0010] It should be noted that the titles of any sections / subsections provided herein are not restrictive. Various embodiments are described throughout this article, and any type of embodiment may be included under any section / subsection. In addition, 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 different sections / subsections.

[0011] 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.

[0012] As briefly described above, how to accurately control the photoresist morphology has become a technical problem that needs to be solved in the photolithography process. At present, the morphological changes of the photoresist development process can be simulated in combination with the level set method. However, this scheme ignores the actual process of the developer gradually diffusing on the photoresist surface and simplifies it to be completed instantly. This is obviously inconsistent with the actual development situation. Therefore, the accuracy of this simulation method is subject to certain limitations.

[0013] In view of this, an embodiment of the present disclosure provides a scheme for simulating photoresist morphology. According to the scheme, firstly, for multiple photoresist units at a target simulation area of ​​the photoresist, multiple developer concentration characteristics and multiple photoresist concentration characteristics corresponding to the multiple photoresist units are determined. Then, based on the multiple developer concentration characteristics and the multiple photoresist concentration characteristics, the developer concentration distribution and the photoresist concentration distribution at the target simulation area after development are determined. Then, based on the developer concentration distribution and the photoresist concentration distribution, the photoresist morphology at the target simulation area is determined.

[0014] It will be more clearly understood through the following description that the embodiments of the present disclosure propose a more accurate scheme for simulating the photoresist morphology, which effectively solves the problems existing in the prior art. The scheme of the present disclosure first considers the developer concentration characteristics and photoresist concentration characteristics of the developer and the photoresist at each photoresist unit in the target simulation area. These concentration characteristics indicate the concentrations of the developer and the photoresist at multiple time points, thereby truly reflecting the gradual diffusion process of the developer on the photoresist surface and the corresponding changes in the photoresist concentration. By capturing and quantifying these concentration characteristics, the present scheme can accurately construct the developer concentration distribution and the photoresist concentration distribution of the target simulation area after development. Based on the developer concentration distribution and the photoresist concentration distribution, the present scheme can accurately predict and determine the photoresist morphology at the target simulation area.

[0015] In this way, the solution disclosed in the present invention significantly improves the accuracy of photoresist morphology simulation and provides more reliable technical support for photoresist morphology control in the photolithography process.

[0016] Various example implementations of the solution will be described in detail below in conjunction with the accompanying drawings.

[0017] Figure 1 A 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 .

[0018] In the 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 device. As an example, the user 140 can issue instructions to the electronic device 120 with the aid of the application 130. In addition, 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.

[0019] After receiving the instruction from the application 130, the electronic device 120 may perform the simulation of the photoresist morphology. In addition, the terminal device 110 may present the interface 150 of the application 130. The morphology of the photoresist simulated by the electronic device 120 may be presented to the user 140 through the interface 150.

[0020] In some embodiments, the terminal device 110 may be any type of mobile terminal, fixed terminal or portable terminal, including a mobile phone, a desktop computer, a laptop computer, a notebook computer, a netbook computer, a tablet computer, a media computer, a multimedia tablet, a personal communication system (PCS) device, a personal navigation device, a personal digital assistant (PDA), an audio / video player, a digital camera / camcorder, a positioning device, a television receiver, a radio broadcast receiver, an electronic book device, a gaming device or any combination thereof, including accessories and peripherals of these devices or any combination thereof. In some embodiments, the terminal device 110 may also support any type of interface for the user (such as a "wearable" circuit, etc.).

[0021] The electronic device 120 may be an independent physical server, or a server cluster or distributed system composed 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.

[0022] A communication connection may be established between the electronic device 120 and the terminal device 110. The communication connection may be established in a wired manner or a wireless manner. The communication connection may include, but is not limited to, a Bluetooth connection, a mobile network connection, a universal serial bus connection, a wireless fidelity 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 implement data / or signaling interaction through the communication connection between the two.

[0023] It should be understood that the structure and function of the various elements in the environment 100 are described for exemplary purposes only and do not imply any limitation on the scope of the present disclosure.

[0024] Figure 2 A flowchart of an example process 200 of a method for simulating photoresist topography according to some embodiments of the present disclosure is shown. The process 200 may be implemented at the electronic device 120.

[0025] Reference Figure 2 In block 210, the electronic device 120 determines a plurality of developer concentration characteristics and a plurality of photoresist concentration characteristics corresponding to a plurality of photoresist cells at a target simulation region of the photoresist. The developer concentration characteristics indicate the concentration of the developer at the corresponding photoresist cell at different time points during the development process. The photoresist concentration characteristics indicate the concentration of the photoresist at the corresponding photoresist cell at different times during the development process.

[0026] As an example, the electronic device 120 divides the target simulation area into a plurality of polyhedral grids based on a grid division method. Each polyhedral grid can be understood as a photoresist unit. For example, the electronic device 120 divides the target simulation area into a plurality of hexahedral grids based on a grid division method.

[0027] As an example, the size of a single polyhedral mesh can be expressed by equations (1) to (3): ; (1) ; (2) ; (3) in, , and For a single polyhedral mesh , and The mesh size in the direction, , and The target simulation area is , and The size in the direction, , and The target simulation area is , and The number of polyhedral meshes divided in the direction, where L and N can be any appropriate real numbers.

[0028] As an example, for at least one photoresist unit, the developer concentration characteristic corresponding to the photoresist unit indicates the concentration of the developer in the photoresist unit (or the developer concentration value). The concentration indicated by the developer concentration characteristic changes accordingly with the advancement of the development process to indicate the developer concentration value of the developer at different time points. As an example, the photoresist concentration characteristic corresponding to the photoresist unit indicates the concentration of the photoresist at the photoresist unit (or the photoresist concentration value). The concentration indicated by the photoresist concentration characteristic changes accordingly with the advancement of the development process to indicate the photoresist concentration value of the photoresist at different time points.

[0029] Such developer concentration characteristics and photoresist concentration characteristics can reflect the concentration distribution of the developer and the photoresist at different time points, thereby indicating how the developer gradually diffuses on the photoresist surface.

[0030] In some embodiments, multiple developer concentration characteristics and multiple photoresist concentration characteristics are determined in the following manner. First, the electronic device 120 determines the developer concentration change characteristics and the photoresist concentration change characteristics. The developer concentration change characteristics indicate the change of the developer concentration over time during the development process, and the photoresist concentration change characteristics indicate the change of the photoresist concentration over time during the development process. Then, the electronic device 120 discretizes the developer concentration change characteristics based on the difference of the developer concentration change characteristics in at least one dimension to determine multiple developer concentration characteristics. The electronic device 120 discretizes the photoresist concentration change characteristics based on the difference of the photoresist concentration change characteristics in at least one dimension to determine multiple photoresist concentration characteristics.

[0031] As an example, the developer concentration variation characteristic indicates the variation of the developer concentration over time during the development process. The developer concentration variation characteristic describes how the developer concentration changes over time from the beginning to the end of the development. For example, the developer concentration variation characteristic can be represented by partial differential or any other appropriate form, thereby indicating the variation trend of the developer concentration over time, such as the increase, stability or decrease of the concentration.

[0032] As an example, the photoresist concentration variation characteristic indicates the change of the concentration of the photoresist over time during the development process. The photoresist concentration variation characteristic describes how the photoresist concentration changes over time from the beginning to the end of the development. For example, the photoresist concentration variation characteristic can also be represented by partial differential or any other appropriate form to indicate the change trend of the photoresist concentration over time, such as the increase, stability or decrease of the concentration.

[0033] In order to convert the continuous concentration change characteristics into discrete data points that can be used for simulation, the electronic device 120 can discretize the two characteristics using a differential method. In this way, the electronic device 120 can convert the continuous concentration change characteristics of the developer and the photoresist during the development process into a series of discrete concentration characteristic values. These characteristic values ​​not only reflect the concentration changes of the developer and the photoresist during the development process, but also provide an accurate data basis for subsequent simulation and analysis.

[0034] For the sake of clarity, the process of determining the developer concentration variation characteristics and the photoresist concentration variation characteristics will be first described below.

[0035] In some embodiments, the developer concentration variation characteristics and the photoresist concentration variation characteristics are determined based on at least a configurable reaction rate coefficient. The reaction rate coefficient indicates the development reaction rate of the photoresist at multiple positions in a predetermined direction, and the predetermined direction at least includes a direction from the lower surface of the photoresist to the upper surface of the photoresist.

[0036] As described above, the developer concentration variation characteristic describes how the developer concentration at various locations of the photoresist changes over time during the development process. This characteristic is not only affected by the properties of the developer itself, but also by the reaction rate of the photoresist. In order to accurately capture this change, the embodiment of the present disclosure introduces a configurable reaction rate coefficient. The reaction rate coefficient can be configured separately at multiple positions in a predetermined direction (for example, in a direction from the lower surface of the photoresist to the upper surface), and such a reaction rate coefficient reflects the difference in reaction rate at different locations due to surface inhibition and substrate adhesion.

[0037] Specifically, the reaction rate coefficient is subdivided into multiple intervals in a predetermined direction, and each interval corresponds to a specific reaction rate. These rates take into account the slower reaction rates on the photoresist surface and near the substrate area, and simulate this rate change by adjusting the coefficient value. Therefore, when the developer contacts the photoresist and starts to react, the electronic device 120 can calculate the concentration change of the developer at different times and different positions based on these configured reaction rate coefficients, thereby forming an accurate developer concentration change feature.

[0038] As described above, the photoresist concentration variation characteristics reflect how the concentration of the photoresist itself changes over time during the development process. This feature is also affected by the reaction rate coefficient. Due to the presence of the surface inhibition effect and the substrate viscosity effect, the reaction rate of the photoresist at different positions will be different, resulting in differences in its concentration variation. By configuring the reaction rate coefficient, the electronic device 120 can accurately simulate the concentration variation of the photoresist during the development process. These coefficients not only take into account the overall reaction rate of the photoresist, but also pay special attention to the reaction rate changes on the surface and near the substrate area. Therefore, during the simulation process, the electronic device 120 can obtain accurate photoresist concentration variation characteristics based on these coefficients.

[0039] The discrete processes of the developer concentration variation characteristics and the photoresist concentration variation characteristics are described below.

[0040] In some embodiments, in the discretization process of the developer concentration change characteristics and the photoresist concentration change characteristics, at least one dimension on which the discretization is based includes at least one of the following: a time dimension of the development process, and / or a spatial dimension based on at least one photoresist unit among a plurality of photoresist units.

[0041] As an example, the electronic device 120 can divide the entire development process into a series of continuous or discrete time points, each of which represents a specific reaction stage. For the concentration change characteristics of the developer and the photoresist, the electronic device 120 can calculate the concentration value at each selected time point. The concentration values ​​at these discrete time points together constitute a discrete representation of the concentration change characteristics in the time dimension.

[0042] In addition to the time dimension, since each photoresist unit may have different reaction conditions, the photoresist can be regarded as a series of spatial units, each of which represents the space where one or more photoresist units are located. For the concentration variation characteristics of the developer and the photoresist, the electronic device 120 can calculate the concentration value at each selected spatial unit point. The concentration values ​​on these discrete spatial units together constitute a discrete representation of the concentration variation characteristics in the spatial dimension.

[0043] In some embodiments, the developer concentration variation characteristics and the photoresist concentration variation characteristics are discretized in the time dimension in the following manner. The electronic device 120 discretizes the developer concentration variation characteristics based on the difference associated with a set of first time points. Furthermore, the electronic device 120 discretizes the photoresist concentration variation characteristics based on the difference associated with a set of second time points. The first time point and the second time point are different time points in the development process.

[0044] As an example, the electronic device 120 selects the difference of the developer concentration change feature in the time dimension, that is, calculates the difference of the concentration values ​​of adjacent first time points in a set of first time points. Through these differences, the electronic device 120 can divide the continuous developer concentration change feature into a series of discrete concentration values, thereby forming a developer concentration feature. The developer concentration feature indicates the developer concentration at multiple specific time points during the development process.

[0045] Similarly, the electronic device 120 selects the difference of the photoresist concentration variation characteristics in the time dimension, that is, calculates the difference of the photoresist concentrations at adjacent second time points in a group of second time points. Through differential processing, the concentration variation characteristics of the photoresist are also discretized into a series of specific concentration values ​​to form a photoresist concentration characteristic. The photoresist concentration characteristic indicates the photoresist concentration at multiple specific time points during the development process.

[0046] In the actual development process, the concentration changes of the developer and the photoresist may be asynchronous. By means of the staggered first time point and the second time point, this asynchrony can be more truly reflected, and the interaction relationship between the developer and the photoresist can be analyzed.

[0047] In some embodiments, the difference includes at least a second-order central difference. In addition, according to actual needs, the electronic device 120 can also use more methods to discretize the developer concentration change characteristics and the photoresist concentration change characteristics. Using a second-order central difference to discretize the concentration change characteristics of the developer and the photoresist can significantly improve the accuracy and reliability of the simulation. This high-order difference method helps to smooth the concentration change curve and reduce the impact of noise.

[0048] In some embodiments, the developer concentration characteristic and the photoresist concentration characteristic are determined based on predetermined boundary conditions. The predetermined boundary conditions indicate at least one of the following: the penetration degree of the developer at the upper surface of the photoresist, the penetration degree of the developer at the lower surface of the photoresist, and / or the penetration degree of the developer at the side of the photoresist.

[0049] As an example, when discretizing the developer concentration variation characteristics and the photoresist concentration variation characteristics, predetermined boundary conditions are required to constrain the discrete process. The predetermined boundary conditions focus on the interaction between the developer and the photoresist, especially at their contact interface. The degree of developer penetration at the upper surface of the photoresist describes how the developer starts to penetrate from the upper surface of the photoresist, as well as the depth and speed of penetration. The degree of developer penetration at the lower surface of the photoresist is similar to that of the upper surface. This boundary condition focuses on how the developer penetrates from the lower surface of the photoresist. This is usually closely related to the adhesion between the photoresist and the substrate (such as a silicon wafer) and the penetration ability of the developer. In addition to the upper and lower surfaces, the developer may also penetrate from the side of the photoresist. This boundary condition takes into account the sidewall morphology of the photoresist, the fluidity of the developer, and possible sidewall erosion effects.

[0050] In certain embodiments, the penetration degree of developer at the upper surface of photoresist is determined based on the concentration of developer at the upper surface of photoresist. The concentration of developer at the upper surface of photoresist reflects the intensity and scope of interaction between developer and the upper surface of photoresist. When developer begins to contact the upper surface of photoresist, due to the existence of concentration difference, the chemical composition in the developer can begin to diffuse inside the photoresist. The speed and depth of this diffusion process depend on the concentration of developer at the photoresist surface and the difference of its concentration infiltrating into the photoresist during the development process. Introducing such boundary conditions enables electronic device 120 to consider the interaction between developer and photoresist more meticulously, particularly the dynamic change at the upper surface.

[0051] In some embodiments, the developer concentration characteristic and the photoresist concentration characteristic are determined based on at least the rate at which the concentration of the photoresist decreases during the development reaction. When the developer contacts the photoresist, it gradually erodes the exposed portion of the photoresist, causing the concentration of the photoresist to begin to decrease. This rate of decrease is the concentration decrease rate. The electronic device 120 can measure or calculate the concentration decrease rate of the photoresist under specific development conditions (such as developer type, temperature, time, etc.) through experiments or simulations. This rate can be a constant value or a function that varies with factors such as time or temperature. Next, the electronic device 120 incorporates this concentration decrease rate as a key parameter into the description of the developer concentration characteristic and the photoresist concentration characteristic.

[0052] In this way, the determination of developer concentration characteristics and photoresist concentration characteristics deeply considers the dynamic changes of photoresist during development reaction, especially the rate at which its concentration decreases. This method can more accurately describe and simulate the concentration changes in the photolithography process.

[0053] In some embodiments, the concentration reduction rate is determined in the following manner. The electronic device 120 determines the concentration reduction rate based on at least the concentration order characteristic of the developer and the concentration order characteristic of the photoresist. The concentration order characteristic of the developer indicates the degree of influence of the material of the developer on the concentration reduction rate. The concentration order characteristic of the photoresist at least indicates the degree of influence of the material of the photoresist on the concentration reduction rate.

[0054] As an example, for a developer, its concentration order characteristics reflect how the concentration of each component (such as solvent, solute, catalyst, etc.) in the developer affects the rate of the development reaction, and thus affects the rate of concentration reduction of the photoresist. Similarly, the concentration order characteristics of the photoresist at least reveal the effect of the photoresist material itself on the rate of the development reaction. This includes how factors such as the chemical composition, molecular structure, and degree of cross-linking of the photoresist work together on the rate of concentration reduction. By deeply analyzing these characteristics, the electronic device 120 can more accurately grasp the changes in the behavior of the photoresist during the development process.

[0055] The following will describe in more detail how to determine the developer concentration characteristics and the photoresist concentration characteristics in the embodiment of the present disclosure in combination with formula (4) to formula (20).

[0056] As an example, the developer concentration variation characteristics and photoresist concentration variation characteristics It can be expressed by formula (4) to formula (6): ; (4) ; (5) ; (6) in, and are the concentrations of the developer and photoresist, respectively. is the concentration reduction rate of the photoresist during the development reaction, is the diffusion coefficient of the developer in the photoresist, and are configurable reaction rate coefficients, is the concentration order characteristic of the photoresist, is the concentration order characteristic of the developer, is the concentration of protecting groups in the photoresist, and t is the time during the development process.

[0057] The above parameters that need to be provided by the user include the developer diffusion coefficient , development reaction rate coefficient and , the concentration order characteristics of photoresist and the concentration order characteristics of the developer , and the concentration of protecting groups in the photoresist Optionally, the developer diffusion coefficient It can be a constant or a function of the photoresist concentration R. Optionally, the development reaction rate coefficient and It can be a constant or a function of variables such as temperature or a predetermined direction.

[0058] In some embodiments, the developer concentration variation characteristic and photoresist concentration variation characteristics It can also be expressed by formula (7) and formula (8): ; (7) ; (8) in, and The reaction rate coefficient is about The specific functional relationship of the coordinates can be determined according to actual needs, and the embodiments of the present disclosure do not limit this.

[0059] In some embodiments, the initial conditions in the discrete process can be expressed by formula (9) and formula (10): ; (9) ; (10) in, Indicates the concentration of the photoresist at the initial moment of the development process, Indicates the concentration of the developer at the initial moment of the development process. Set the value for the user.

[0060] In some embodiments, before development begins, the boundary condition regarding the degree of intrusion on the photoresist surface can be expressed by formula (11): ; (11) in, is the surface of the photoresist coordinate, is the concentration of the developer when no development reaction occurs, Set the value for the user.

[0061] In some embodiments, during the development process, the boundary condition regarding the degree of intrusion on the photoresist surface can be expressed by formula (12): ; (12) in, is the normal vector of the upper surface, is the developer diffusion constant, Set the value for the user.

[0062] In some embodiments, during the development process, the boundary condition regarding the degree of intrusion of the lower surface of the photoresist can be expressed by formula (13): ; (13) in, The area below the photoresist is calculated coordinate.

[0063] Optionally, the boundary conditions of the other lateral surfaces except the upper and lower surfaces may be symmetric boundary conditions or periodic boundary conditions.

[0064] In some embodiments, the developer concentration variation characteristics are respectively discreted by formula (14) to formula (18): and photoresist concentration variation characteristics , to obtain the developer concentration characteristics and resist concentration characteristics Optionally, the finite difference method is used to analyze the concentration variation characteristics of the developer solution. and photoresist concentration variation characteristics For example, the concentration variation characteristics of the developer are The photoresist concentration variation characteristics are discretely measured at half-integer moments in the development process. Integer moments in the development process are discretized, and the spatial discretization adopts the second-order central difference discretization format: ; (14) ; (15) ; (16) ; (17) ; (18) The superscripts of the variables represent the discrete time numbers, the subscripts of the variables represent the discrete photoresist unit numbers, and the superscripts Used to indicate and By solving formula (14) and formula (15), the developer concentration and photoresist concentration at each photoresist unit at at least one time point in the development process can be obtained.

[0065] Optionally, Formula (14) and Formula (15) can be rewritten as three sets of algebraic equations in the form of tridiagonal matrices by an alternating direction implicit method to improve computational efficiency.

[0066] Optionally, the solvers of formula (14) and formula (15) include but are not limited to direct method solvers for solving sparse linear equations and iterative method solvers for solving sparse linear equations.

[0067] In some embodiments, the concentration step characteristics of the photoresist are introduced and the concentration order characteristics of the developer After that, formula (14) and formula (15) can be adjusted to formula (19) to formula (22): ; (19) ; (20) ;(twenty one) ;(twenty two) In this embodiment, the Newton method solver can be used to solve Formula (19) to Formula (22) until the convergence condition is met. Different from the solution process of Formula (14) and Formula (15), the solution process of Formula (19) to Formula (22) requires linearization of the nonlinear reaction terms therein.

[0068] Figure 3 FIG. 3 is a schematic diagram of a process 300 for determining a developer concentration and a photoresist concentration at a time point according to an embodiment of the present disclosure. The process 300 may be considered as Figure 2 An example of process 200 in FIG.

[0069] In block 301, the electronic device 120 measures the developer concentration characteristic. and resist concentration characteristics Linearize the nonlinear terms in to obtain linear terms. For example, Linearization is performed, and the linearization process can be expressed by formula (23): ; (twenty three) in, is a linear term. It should be noted that when performing the first iteration , when it is not the first iteration Calculated for the previous iteration Then, the linearization result is solved using the solver.

[0070] In block 302, the linear terms are respectively introduced into the developer concentration characteristic and resist concentration characteristics .

[0071] In block 303 , a solver is used to solve developer concentration characteristics and photoresist concentration characteristics (eg, solve equations (19) to (22)) to obtain developer concentration and photoresist concentration at at least one time point.

[0072] The above describes how to determine the developer concentration characteristics and the photoresist concentration characteristics. Figure 2 At block 220 , the electronic device 120 determines a developer concentration distribution and a photoresist concentration distribution at the target simulation region after development based on the plurality of developer concentration characteristics and the plurality of photoresist concentration characteristics.

[0073] Return to reference Figure 3 In the example described, after obtaining the developer concentration feature and the photoresist concentration feature, the electronic device 120 determines in block 304 whether the currently obtained developer concentration satisfies the convergence condition. As an example, in the example of determining the developer concentration and the photoresist concentration based on solving formula (19) to formula (22), the convergence condition is whether the residual of the developer concentration at two time points before and after is less than the critical value set by the user. As an example, the critical value can be expressed by formula (24): ;(twenty four) in, is the developer concentration value at the previous time point, is the developer concentration value at the next time point, The residual critical value set by the user. If the residual meets the convergence condition, in box 305, the electronic device 120 determines the currently obtained developer concentration and photoresist concentration as candidate concentrations; if the residual does not meet the convergence condition, in box 306, the electronic device 120 returns to continue the solution process of the developer concentration and the photoresist concentration.

[0074] In addition, the electronic device 120 also determines whether the development process reaches the set time. If both of the above two conditions are met, the electronic device 120 uses the currently obtained candidate concentration as the target concentration, and determines the developer concentration distribution and the photoresist concentration distribution based on the target concentration.

[0075] As an example, the user can set the total time of the development process and time step length The electronic device 120 determines whether If the condition is met, it is determined that the set time has been reached; if the condition is not met, the process of solving the developer concentration and the photoresist concentration is continued to solve the developer concentration and the photoresist concentration at the next time point.

[0076] The above describes how to determine the developer concentration distribution and the photoresist concentration distribution. Figure 2At block 230 , the electronic device 120 determines the photoresist profile at the target simulation region based on the developer concentration distribution and the photoresist concentration distribution.

[0077] In some embodiments, the photoresist profile is determined by a user-specified critical value of the photoresist material concentration. As an example, the final morphology of the photoresist is Contour lines at .

[0078] It can be clearly understood from the various embodiments described above that the embodiments of the present disclosure first consider the developer concentration characteristics and photoresist concentration characteristics of the developer and photoresist at each photoresist unit in the target simulation area. These concentration characteristics indicate the concentrations of the developer and photoresist at multiple time points, thereby truly reflecting the gradual diffusion process of the developer on the photoresist surface and the corresponding changes in the photoresist concentration. By capturing and quantifying these concentration characteristics, the embodiments of the present disclosure can accurately construct the developer concentration distribution and photoresist concentration distribution of the target simulation area after development. Based on the developer concentration distribution and the photoresist concentration distribution, the embodiments of the present disclosure can accurately predict and determine the photoresist morphology at the target simulation area.

[0079] In this way, the embodiments of the present disclosure construct real physical equations according to the diffusion process of the developer and the development reaction kinetics of the photoresist. The embodiments of the present disclosure can comprehensively consider the diffuse interface between the photoresist and the developer, the non-equilibrium transient diffusion and development reaction, and the non-constant diffusion coefficient. The embodiments of the present disclosure can be numerically solved using the finite difference method, with high calculation accuracy.

[0080] Figure 4 1 is a block diagram of an electronic device 400 in which one or more embodiments of the present disclosure may be implemented. The electronic device 400 may be used to implement, for example, Figure 1 The electronic device 120 shown. It should be understood that Figure 4 The electronic device 400 shown is merely exemplary and should not constitute any limitation on the functionality and scope of the embodiments described herein.

[0081] Reference Figure 4 , the electronic device 400 is in the form of a general electronic device. The components of the electronic device 400 may include, but are not limited to, one or more processors or processing units 410, a memory 420, a storage device 430, one or more communication units 440, one or more input devices 450, and one or more output devices 460. The processing unit 410 may be an actual or virtual processor and is capable of performing various processes according to a program stored in the memory 420. In a multi-processor system, multiple processing units execute computer executable instructions in parallel to improve the parallel processing capability of the electronic device 400.

[0082] The electronic device 400 typically includes a plurality of computer storage media. Such media can be any available media accessible to the electronic device 400, including but not limited to volatile and non-volatile media, removable and non-removable media. The memory 420 can be a volatile memory (e.g., registers, caches, random access memory (RAM)), a non-volatile memory (e.g., a read-only memory (ROM), an electrically erasable programmable read-only memory (EEPROM), flash memory), or some combination thereof. The storage device 430 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, which can be used to store information and / or data and can be accessed within the electronic device 400.

[0083] The electronic device 400 may further include additional removable / non-removable, volatile / non-volatile storage media. Figure 4 As shown in , a disk drive for reading or writing from a removable, non-volatile disk (e.g., a "floppy disk") and an optical drive for reading or writing from a removable, non-volatile optical disk may be provided. In these cases, each drive may be connected to the bus (not shown) by one or more data media interfaces. The memory 420 may include a computer program product 425 having one or more program modules that are configured to perform various methods or actions of various embodiments of the present disclosure.

[0084] The communication unit 440 implements communication with other electronic devices through a communication medium. Additionally, the functions of the components of the electronic device 400 can be implemented with a single computing cluster or multiple computing machines that can communicate through a communication connection. Therefore, the electronic device 400 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.

[0085] The input device 450 may be one or more input devices, such as a mouse, a keyboard, a tracking ball, etc. The output device 460 may be one or more output devices, such as a display, a speaker, a printer, etc. The electronic device 400 may also communicate with one or more external devices (not shown) through the communication unit 440 as needed, such as a storage device, a display device, etc., communicate with one or more devices that allow a user to interact with the electronic device 400, or communicate with any device that allows the electronic device 400 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).

[0086] 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.

[0087] Various aspects of the present disclosure are described herein with reference to the flowcharts and / or block diagrams of the methods, devices, equipment, and computer program products implemented according to the present disclosure. It should be understood that each box in the flowchart and / or block diagram and the combination of each box in the flowchart and / or block diagram can be implemented by computer-readable program instructions.

[0088] 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, so that when these instructions are executed by the processing unit of the computer or other programmable data processing device, a device that implements the functions / actions specified in one or more boxes in the flowchart and / or block diagram is generated. These computer-readable program instructions can also be stored in a computer-readable storage medium, and these instructions cause the computer, programmable data processing device, and / or other equipment to work in a specific manner, so that the computer-readable medium storing the instructions includes a manufactured product, which includes instructions for implementing various aspects of the functions / actions specified in one or more boxes in the flowchart and / or block diagram.

[0089] 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, so that the instructions executed on the computer, other programmable data processing apparatus, or other device implement the functions / actions specified in one or more boxes in the flowchart and / or block diagram.

[0090] The flow chart and block diagram in the accompanying drawings show the possible architecture, function and operation of the system, method and computer program product according to multiple implementations of the present disclosure. In this regard, each square box in the flow chart or block diagram can represent a part of a module, program segment or instruction, and a part of a module, program segment or instruction includes one or more executable instructions for realizing the logical function of the specification. In some implementations as replacements, the function marked in the square box can also occur in a sequence different from that marked in the accompanying drawings. For example, two continuous square boxes can actually be executed substantially in parallel, and they can sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each square box in the block diagram and / or flow chart, and the combination of the square 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.

[0091] The above descriptions of various implementations of the present disclosure are exemplary, non-exhaustive, and not limited to the disclosed implementations. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described implementations. The determination of the terms used herein is intended to best explain the principles of the implementations, practical applications, or improvements to the technology in the market, or to enable other persons of ordinary skill in the art to understand the various implementations disclosed herein.

Claims

1. A method for simulating photoresist morphology, characterized in that: include: For a plurality of photoresist units at a target simulation area of ​​the photoresist, determining a plurality of developer concentration characteristics and a plurality of photoresist concentration characteristics corresponding to the plurality of photoresist units; Determining a developer concentration distribution and a photoresist concentration distribution at the target simulation area after development based on the multiple developer concentration characteristics and the multiple photoresist concentration characteristics; as well as Based on the developer concentration distribution and the photoresist concentration distribution, the photoresist morphology at the target simulation area is determined.

2. The method according to claim 1, characterized in that The plurality of developer concentration characteristics and the plurality of photoresist concentration characteristics are determined in the following manner: Determine the developer concentration variation characteristics and the photoresist concentration variation characteristics; discretize the developer concentration variation feature based on the difference of the developer concentration variation feature in at least one dimension to determine the plurality of developer concentration features; as well as Based on the difference of the photoresist concentration variation characteristic in the at least one dimension, the photoresist concentration variation characteristic is discretized to determine the plurality of photoresist concentration characteristics.

3. The method according to claim 2, characterized in that The at least one dimension includes at least one of the following: the temporal dimension of the development process, and / or A spatial dimension in units of at least one photoresist cell among the plurality of photoresist cells.

4. The method according to claim 3, characterized in that The developer concentration variation characteristics and the photoresist concentration variation characteristics are discretized in the time dimension in the following manner: discretizing the developer concentration variation characteristics based on differences associated with a set of first time points; and The photoresist concentration variation characteristics are discretized based on differences associated with a set of second time points, wherein the first time point and the second time point are different time points in the development process.

5. The method according to claim 2, characterized in that: The difference comprises at least a second order central difference.

6. The method according to claim 2, characterized in that The developer concentration variation characteristics and the photoresist concentration variation characteristics are determined based on at least a configurable reaction rate coefficient, wherein the reaction rate coefficient indicates the development reaction rate of the photoresist at multiple positions in a predetermined direction, and wherein the predetermined direction at least includes a direction from the lower surface of the photoresist to the upper surface of the photoresist.

7. The method according to claim 1, characterized in that The developer concentration characteristic and the photoresist concentration characteristic are determined based on a predetermined boundary condition, and the predetermined boundary condition indicates at least one of the following: the degree of penetration of the developer at the upper surface of the photoresist, the degree of penetration of the developer into the lower surface of the photoresist, and / or The degree of penetration of the developer at the sides of the photoresist.

8. The method according to claim 7, characterized in that The penetration degree of the developer at the upper surface of the photoresist is determined based on the concentration of the developer at the upper surface of the photoresist.

9. The method according to claim 1, characterized in that: The developer concentration characteristic and the photoresist concentration characteristic are determined based on at least a concentration reduction rate of the photoresist when a development reaction occurs.

10. The method according to claim 9, characterized in that The concentration reduction rate is determined as follows: The concentration reduction rate is determined based at least on the concentration order characteristics of the developer and the concentration order characteristics of the photoresist, wherein the concentration order characteristics of the developer indicate the degree of influence of the material of the developer on the concentration reduction rate, and the concentration order characteristics of the photoresist at least indicate the degree of influence of the material of the photoresist on the concentration reduction rate.

11. An electronic device, characterized in that: include: at least one processing unit; as well as At least one memory, the at least one memory is coupled to the at least one processing unit and stores 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 the method according to any one of claims 1 to 10.

12. A computer-readable storage medium having a computer program stored thereon, characterized in that: The computer program can be executed by a processor to implement the method according to any one of claims 1 to 10.

13. A computer program product comprising computer executable instructions, characterized in that: The computer executable instructions implement the method according to any one of claims 1 to 10 when executed by a processor.

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