Method, apparatus, and medium for simulating photoresist topography

Abstract

Embodiments of the present disclosure relate to methods, apparatuses, and media for simulating photoresist topography. The method proposed herein includes: determining, for a plurality of photoresist units at a target simulation region of a photoresist, a plurality of developer concentration characteristics and a plurality of photoresist concentration characteristics corresponding to the plurality of photoresist units; determining, based on the plurality of developer concentration characteristics and the plurality of photoresist concentration characteristics, a developer concentration distribution and a photoresist concentration distribution at the target simulation region after development; and determining, based on the developer concentration distribution and the photoresist concentration distribution, the photoresist topography at the target simulation region.

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, and when the instructions are executed by a processor, the method according to the first aspect of the present disclosure is implemented.

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

[0009] Figure 1 A schematic diagram of an example environment according to an embodiment of the present disclosure is shown;

[0010] Figure 2 A flowchart of an example process of a method for simulating a photoresist topography according to some embodiments of the present disclosure is shown;

[0011] Figure 3 A schematic diagram of a process for determining a developer concentration and a photoresist concentration at a point in time according to an embodiment of the present disclosure is shown; and

[0012] Figure 4 A block diagram of an electronic device in which one or more embodiments of the present disclosure may be implemented is shown. Detailed Description of Specific Embodiments

[0013] Embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. Although some embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be construed as limited to the embodiments set forth herein. On the contrary, these embodiments are provided to more thoroughly and completely understand 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.

[0014] It should be noted that the titles of any sections / subsections provided herein are not restrictive. Various embodiments are described throughout this document, and any type of embodiment may be included under any section / subsection. In addition, the embodiments described in any section / subsection may be combined with any other embodiments described in the same section / subsection and / or different sections / subsections in any manner.

[0015] In the description of the embodiments of the present disclosure, the term "comprising" and its like shall be understood as an open inclusion, that is, "including but not limited to". The term "based on" shall be understood as "at least partially based on". The term "one embodiment" or "the embodiment" shall be understood as "at least one embodiment". The term "some embodiments" shall be understood as "at least some embodiments". There may also be other explicit and implicit definitions hereinafter. The terms "first", "second", etc. may refer to different or the same objects. There may also be other explicit and implicit definitions hereinafter.

[0016] As briefly described above, how to accurately control the photoresist morphology has become a technical problem to be urgently solved in the photolithography process. Currently, the level set method can be combined to simulate the morphological changes during the photoresist development process. However, this solution ignores the actual process of the developer gradually diffusing on the photoresist surface and simplifies it to be completed instantaneously. This is significantly inconsistent with the actual development situation. Therefore, the accuracy of this simulation method is limited to a certain extent.

[0017] In view of this, embodiments of the present disclosure provide a solution for simulating the photoresist morphology. According to this solution, first, for a plurality of photoresist units at the target simulation area of the photoresist, a plurality of developer concentration characteristics and a plurality of photoresist concentration characteristics corresponding to the plurality of photoresist units are determined. Then, based on the plurality of developer concentration characteristics and the plurality of photoresist concentration characteristics, the developer concentration distribution and the photoresist concentration distribution at the target simulation area after development are determined. Subsequently, based on the developer concentration distribution and the photoresist concentration distribution, the photoresist morphology at the target simulation area is determined.

[0018] As will be more clearly understood from the following description, embodiments of the present disclosure propose a more accurate solution for simulating the photoresist morphology, effectively solving the problems existing in the prior art. The solution of the present disclosure first considers the developer concentration characteristics and the photoresist concentration characteristics of the developer and the photoresist at each photoresist unit within the target simulation area. These concentration characteristics indicate the concentrations of the developer and the photoresist at multiple time points, thus 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, this solution 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, this solution can accurately predict and determine the photoresist morphology at the target simulation area.

[0019] In this way, the solution of the present disclosure significantly improves the accuracy of photoresist morphology simulation, providing more reliable technical support for photoresist morphology control in the photolithography process.

[0020] The following will further describe various example implementations of this solution in detail with reference to the accompanying drawings.

[0021] Figure 1 A schematic diagram of an example environment 100 according to an embodiment of the present disclosure is shown. Referring to Figure 1 , the example environment 100 may include a terminal device 110 and an electronic device 120.

[0022] In the exemplary environment 100, an application 130 for interacting with the electronic device 120 is installed in the terminal device 110. The 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 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.

[0023] After receiving an instruction from the application 130, the electronic device 120 can perform a simulation of the photoresist topography. In addition, the terminal device 110 can present the interface 150 of the application 130. The topography of the photoresist simulated by the electronic device 120 can be presented to the user 140 through the interface 150.

[0024] In some embodiments, the terminal device 110 can be any type of mobile terminal, fixed terminal or portable terminal, including mobile phones, desktop computers, laptop computers, notebook computers, netbook computers, tablet computers, media computers, multimedia tablets, personal communication system (PCS) devices, personal navigation devices, personal digital assistants (PDAs), audio / video players, digital cameras / camcorders, positioning devices, television receivers, radio broadcast receivers, e-book devices, gaming devices, or any combination of the foregoing, 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 a "wearable" circuit, etc.).

[0025] The electronic device 120 can 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 delivery networks, and big data and artificial intelligence platforms. The electronic device 120 can, for example, include a computing system / server, such as a mainframe, an edge computing node, a computing device in a cloud environment, and so on.

[0026] A communication connection can be established between the electronic device 120 and the terminal device 110. The communication connection can be established in a wired or wireless manner. The communication connection can 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 regard. In the embodiments of the present disclosure, the electronic device 120 and the terminal device 110 can implement data / or signaling interaction through the communication connection therebetween.

[0027] It should be understood that the structures and functions of the various elements in the environment 100 are described only for exemplary purposes, without implying any limitation on the scope of the present disclosure.

[0028] 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 can be implemented at the electronic device 120.

[0029] Referring Figure 2 , at block 210, the electronic device 120 determines, for a plurality of photoresist units at a target simulation region of the photoresist, a plurality of developer concentration characteristics and a plurality of photoresist concentration characteristics corresponding to the plurality of photoresist units. The developer concentration characteristics indicate the concentration of the developer at the corresponding photoresist unit at different time points during the development process. The photoresist concentration characteristics indicate the concentration of the photoresist at the corresponding photoresist unit at different times during the development process.

[0030] As an example, the electronic device 120 divides the target simulation region into a plurality of polyhedral meshes based on a mesh division method. Each polyhedral mesh can be understood as a photoresist unit. For example, the electronic device 120 evenly divides the target simulation region into a plurality of hexahedral meshes.

[0031] As an example, the size of a single polyhedral mesh can be represented by equations (1) to (3):

[0032] ; (1)

[0033] ; (2)

[0034] ; (3)

[0035] Where , and are the mesh sizes of a single polyhedral mesh in the , and directions, , and are the sizes of the target simulation region in the , and directions, , and are the numbers of polyhedral meshes divided in the target simulation region in the , and directions, where L and N can be any suitable real numbers.

[0036] As an example, for at least one photoresist unit, the developer concentration characteristic corresponding to the photoresist unit indicates the concentration of the developer at the location of the photoresist unit (or the developer concentration value). The concentration indicated by the developer concentration characteristic changes correspondingly as the development process progresses, so as to indicate the developer concentration values at different time points. As an example, the photoresist concentration characteristic corresponding to the photoresist unit indicates the concentration of the photoresist at the location of the photoresist unit (or the photoresist concentration value). The concentration indicated by the photoresist concentration characteristic changes correspondingly as the development process progresses, so as to indicate the photoresist concentration values at different time points.

[0037] 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 surface of the photoresist.

[0038] 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 characteristic and the photoresist concentration change characteristic. The developer concentration change characteristic indicates the change in the concentration of the developer over time during the development process, and the photoresist concentration change characteristic indicates the change in the concentration of the photoresist over time during the development process. Then, the electronic device 120 discretizes the developer concentration change characteristic based on the difference in at least one dimension of the developer concentration change characteristic to determine multiple developer concentration characteristics. The electronic device 120 discretizes the photoresist concentration change characteristic based on the difference in at least one dimension of the photoresist concentration change characteristic to determine multiple photoresist concentration characteristics.

[0039] As an example, the developer concentration change characteristic indicates the change in the concentration of the developer over time during the development process. The developer concentration change characteristic describes how the developer concentration changes over time from the start to the end of the development. For example, the developer concentration change characteristic can be represented by partial derivatives or any other appropriate form, so as to indicate the change trend of the developer concentration over time, such as the increase, stability, or decrease of the concentration, etc.

[0040] As an example, the photoresist concentration change characteristic indicates the change in the concentration of the photoresist over time during the development process. The photoresist concentration change characteristic describes how the photoresist concentration changes over time from the start to the end of the development. For example, the photoresist concentration change characteristic can also be represented by partial derivatives or any other appropriate form, so as to indicate the change trend of the photoresist concentration over time, such as the increase, stability, or decrease of the concentration, etc.

[0041] To convert the continuous concentration change characteristics into discrete data points that can be used for simulation, the electronic device 120 can discretize these two characteristics using the difference 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 change of the developer and the photoresist during the development process, but also provide an accurate data basis for subsequent simulation and analysis.

[0042] For clarity, the determination process of the developer concentration change characteristics and the photoresist concentration change characteristics will be described first below.

[0043] In some embodiments, the developer concentration change characteristics and the photoresist concentration change characteristics are determined based at least on configurable reaction rate coefficients. The reaction rate coefficient indicates the development reaction rate at multiple positions in a predetermined direction, and the predetermined direction includes at least the direction from the lower surface of the photoresist to the upper surface of the photoresist.

[0044] As described above, the developer concentration change characteristics describe how the concentration of the developer at each part 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. To accurately capture this change, embodiments of the present disclosure introduce configurable reaction rate coefficients. The reaction rate coefficients can be configured separately at multiple positions in a predetermined direction (for example, the direction from the lower surface of the photoresist to the upper surface), and such reaction rate coefficients are used to reflect the differences in reaction rates at different positions due to surface inhibition and adhesion effects.

[0045] Specifically, the reaction rate coefficient is divided into multiple intervals in the predetermined direction, and each interval corresponds to a specific reaction rate. These rates take into account the slower reaction rates in the photoresist surface and the region close to the substrate, 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 according to these configured reaction rate coefficients, so as to form accurate developer concentration change characteristics.

[0046] As described above, the photoresist concentration change characteristic reflects how the concentration of the photoresist itself changes over time during the development process. This characteristic is also affected by the reaction rate coefficient. Due to the existence 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 change. By configuring the reaction rate coefficient, the electronic device 120 can accurately simulate the concentration change of the photoresist during the development process. These coefficients not only consider the overall reaction rate of the photoresist, but also pay special attention to the reaction rate changes in the surface and near-substrate regions. Therefore, during the simulation process, the electronic device 120 can obtain the accurate photoresist concentration change characteristic according to these coefficients.

[0047] Next, the discretization process of the developer concentration change characteristic and the photoresist concentration change characteristic will be described.

[0048] In some embodiments, during the discretization process of the developer concentration change characteristic and the photoresist concentration change characteristic, at least one dimension based on which the discretization is performed includes at least one of the following: the time dimension of the development process, and / or the spatial dimension in units of at least one photoresist unit among a plurality of photoresist units.

[0049] As an example, the electronic device 120 can divide the entire development process into a series of continuous or discrete time points, and each time point represents a specific reaction stage. For the concentration change characteristics of the developer and the photoresist, the electronic device 120 can calculate their concentration values at each selected time point. The concentration values at these discrete time points together constitute the discrete representation of the concentration change characteristic in the time dimension.

[0050] In addition to the time dimension, since there may be different reaction situations at each photoresist unit, the photoresist can be regarded as a series of spatial units, and each spatial unit represents the space where one or more photoresist units are located. For the concentration change characteristics of the developer and the photoresist, the electronic device 120 can calculate their concentration values at each selected spatial unit point. The concentration values at these discrete spatial units together constitute the discrete representation of the concentration change characteristic in the spatial dimension.

[0051] In some embodiments, the developer concentration change characteristic and the photoresist concentration change characteristic are discretized in the time dimension in the following manner. The electronic device 120 discretizes the developer concentration change characteristic based on the difference related to a set of first time points. And, the electronic device 120 discretizes the photoresist concentration change characteristic based on the difference related to a set of second time points. The first time points and the second time points are different time points during the development process.

[0052] As an example, the electronic device 120 selects the difference in the development solution concentration change characteristics in the time dimension, that is, calculates the difference in 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 development solution concentration change characteristics into a series of discrete concentration values, thereby forming the development solution concentration characteristics. The development solution concentration characteristics indicate the development solution concentration at multiple specific time points during the development process.

[0053] Similarly, the electronic device 120 selects the difference in the photoresist concentration change characteristics in the time dimension, that is, calculates the difference in the photoresist concentration of adjacent second time points in a set of second time points. Through the difference processing, the concentration change characteristics of the photoresist are also discretized into a series of specific concentration values, forming the photoresist concentration characteristics. The photoresist concentration characteristics indicate the photoresist concentration at multiple specific time points during the development process.

[0054] In the actual development process, the concentration changes of the development solution and the photoresist may not be synchronized. By means of the staggered setting of the first time points and the second time points, this non-synchronization can be more realistically reflected, and the interaction relationship between the development solution and the photoresist can be analyzed.

[0055] In some embodiments, the difference at least includes the second-order central difference. In addition, according to actual needs, the electronic device 120 can also use more methods to discretize the development solution concentration change characteristics and the photoresist concentration change characteristics. Using the second-order central difference to discretize the concentration change characteristics of the development solution 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 influence of noise.

[0056] In some embodiments, the development solution concentration characteristics and the photoresist concentration characteristics are determined based on predetermined boundary conditions. The predetermined boundary conditions indicate at least one of the following: the penetration degree of the development solution at the upper surface of the photoresist, the penetration degree of the development solution at the lower surface of the photoresist, and / or the penetration degree of the development solution at the side surface of the photoresist.

[0057] As an example, when discretizing the characteristics of the developer solution concentration and the photoresist concentration, predefined boundary conditions are required to constrain the discretization process. The predefined boundary conditions focus on the interaction between the developer solution and the photoresist, especially at their contact interface. The penetration degree of the developer solution at the upper surface of the photoresist describes how the developer solution starts to penetrate from the upper surface of the photoresist, as well as the depth and speed of penetration. The penetration degree of the developer solution at the lower surface of the photoresist is similar to that at the upper surface. This boundary condition focuses on how the developer solution 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 solution. In addition to the upper and lower surfaces, the developer solution may also penetrate from the sidewalls of the photoresist. This boundary condition takes into account the sidewall topography of the photoresist, the fluidity of the developer solution, and the possible sidewall erosion effect.

[0058] In some embodiments, the penetration degree of the developer solution at the upper surface of the photoresist is determined based on the concentration of the developer solution at the upper surface of the photoresist. The concentration of the developer solution at the upper surface of the photoresist reflects the intensity and range of the interaction between the developer solution and the upper surface of the photoresist. When the developer solution starts to contact the upper surface of the photoresist, due to the existence of the concentration difference, the chemical components in the developer solution will start to diffuse into the photoresist. The speed and depth of this diffusion process depend on the concentration difference between the developer solution at the surface of the photoresist and the concentration that has penetrated into the photoresist during the development process. Introducing such boundary conditions enables the electronic device 120 to more carefully consider the interaction between the developer solution and the photoresist, especially the dynamic changes at the upper surface.

[0059] In some embodiments, the developer solution concentration characteristics and the photoresist concentration characteristics are determined based at least on the rate of decrease in the concentration of the photoresist during the development reaction. When the developer solution contacts the photoresist, it gradually erodes the exposed part of the photoresist, causing the concentration of the photoresist to start to decrease. This rate of decrease is the rate of concentration decrease. The electronic device 120 can measure or calculate the rate of decrease in the concentration of the photoresist under specific development conditions (such as the type of developer solution, temperature, time, etc.) through experiments or simulation means. 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 rate of concentration decrease as a key parameter into the description of the developer solution concentration characteristics and the photoresist concentration characteristics.

[0060] In this way, the determination of the developer solution concentration characteristics and the photoresist concentration characteristics takes into deep consideration the dynamic changes of the photoresist during the development reaction, especially the rate of decrease in its concentration. This method can more accurately describe and simulate the concentration changes during the lithography process.

[0061] In some embodiments, the concentration reduction rate is determined as follows. The electronic device 120 determines the concentration reduction rate based at least on the concentration order characteristics of the developer and the concentration order characteristics of the photoresist. The concentration order characteristics of the developer indicate the degree of influence of the material of the developer on the concentration reduction rate. The concentration order characteristics of the photoresist indicate at least the degree of influence of the material of the photoresist on the concentration reduction rate.

[0062] As an example, for the developer, its concentration order characteristics reflect how the concentrations of various components (such as solvents, solutes, catalysts, etc.) in the developer affect the rate of the developing reaction, and thus affect the concentration reduction rate of the photoresist. Similarly, the concentration order characteristics of the photoresist at least reveal the influence of the photoresist material itself on the rate of the developing reaction. This includes how factors such as the chemical composition, molecular structure, and degree of crosslinking of the photoresist act together on the concentration reduction rate. By analyzing these characteristics in depth, the electronic device 120 can more accurately grasp the behavioral changes of the photoresist during the developing process.

[0063] More details on determining the developer concentration characteristics and the photoresist concentration characteristics in the embodiments of the present disclosure will be described below in conjunction with formulas (4) to (20).

[0064] As an example, the developer concentration change characteristics and the photoresist concentration change characteristics can be represented by formulas (4) to (6):

[0065] ; (4)

[0066] ; (5)

[0067] ; (6)

[0068] Wherein, and are the concentration of the developer and the concentration of the photoresist respectively, is the concentration reduction rate when the photoresist undergoes the developing reaction, is the diffusion coefficient of the developer in the photoresist, and are configurable reaction rate coefficients respectively, is the concentration order characteristic of the photoresist, is the concentration order characteristic of the developer, is the concentration of the protecting group in the photoresist, and t is the time during the developing process.

[0069] Among the above parameters, those that need to be given by the user include the developer diffusion coefficient , the developing reaction rate coefficient and , the concentration order characteristics of the photoresist and the concentration order characteristics of the developer , and the concentration of the protecting group in the photoresist . Optionally, the developer diffusion coefficient can be a constant or a function of the photoresist concentration R. Optionally, the development reaction rate coefficient and can be a constant or a function of variables such as temperature or a predetermined direction.

[0070] In some embodiments, the developer concentration change characteristics and the photoresist concentration change characteristics can also be represented by formulas (7) and (8):

[0071] ; (7)

[0072] ; (8)

[0073] wherein, and represent that the reaction rate coefficient is a function of coordinates, and the specific functional relationship can be determined according to actual needs, and the embodiments of the present disclosure do not limit this.

[0074] In some embodiments, the initial conditions during the discretization process can be represented by formulas (9) and (10):

[0075] ; (9)

[0076] ; (10)

[0077] wherein, represents the concentration of the photoresist at the initial moment during the development process, represents the concentration of the developer at the initial moment during the development process, is a user-set value.

[0078] In some embodiments, before the development starts, the boundary condition regarding the intrusion degree of the upper surface of the photoresist can be represented by formula (11):

[0079] ; (11)

[0080] wherein, is the coordinate at the upper surface of the photoresist, is the concentration of the developer when no development reaction occurs, is a user-set value.

[0081] In some embodiments, during the development process, the boundary condition regarding the intrusion degree of the upper surface of the photoresist can be expressed by Equation (12):

[0082] ; (12)

[0083] Wherein, is the normal vector of the upper surface, is the diffusion constant of the developer, is the user-defined value.

[0084] In some embodiments, during the development process, the boundary condition regarding the intrusion degree of the lower surface of the photoresist can be expressed by Equation (13):

[0085] ; (13)

[0086] Wherein, is the coordinate at the lower surface of the calculation region of the photoresist.

[0087] Optionally, the boundary conditions for the other lateral surfaces except the upper and lower surfaces can be symmetric boundary conditions or periodic boundary conditions.

[0088] In some embodiments, the characteristics of the developer concentration change and the characteristics of the photoresist concentration change are discretized by Equations (14) to (18) respectively to obtain the developer concentration characteristics . Optionally, the finite difference method is used here to discretize the characteristics of the developer concentration change and the characteristics of the photoresist concentration change , and the time dimension adopts alternating time. For example, the characteristics of the developer concentration change are discretized at the half-integer moments during the development process, and the characteristics of the photoresist concentration change are discretized at the integer moments during the development process. The spatial discretization adopts the second-order central difference discretization format:

[0089] ; (14)

[0090] ; (15)

[0091] ; (16)

[0092] ; (17)

[0093] ; (18)

[0094] Among them, the superscript of each variable represents the discrete time number, and the subscript of the variable represents the discrete photoresist unit number. The superscript is used to represent and . By solving equations (14) and (15), the developer concentration and photoresist concentration at each photoresist unit can be obtained at at least one time point during the development process.

[0095] Optionally, equations (14) and (15) can be rewritten into a set of three algebraic equations in the form of a tridiagonal matrix by the alternating direction implicit method to improve the calculation efficiency.

[0096] Optionally, the solvers for equations (14) to (15) include, but are not limited to, the direct method for solving sparse linear equation systems and the iterative method for solving sparse linear equation systems.

[0097] In some embodiments, by introducing the concentration order characteristics of the photoresist and the concentration order characteristics of the developer , equations (14) and (15) can be adjusted to equations (19) to (22):

[0098] ; (19)

[0099] ; (20)

[0100] ; (21)

[0101] ; (22)

[0102] In this embodiment, the Newton method solver can be used to solve equations (19) to (22) until the convergence condition is satisfied. Different from the solution process of equations (14) and (15), the solution process of equations (19) to (22) requires linearization of the nonlinear reaction terms therein.

[0103] Figure 3 FIG. shows a schematic diagram of a process 300 for determining the developer concentration and photoresist concentration at a time point according to an embodiment of the present disclosure. Process 300 can be regarded as an example of process 200 in Figure 2 .

[0104] At block 301, the electronic device 120 linearizes the nonlinear terms in the developer concentration characteristic and the photoresist concentration characteristic to obtain the linear terms. For example, it is necessary to linearize Linearization is performed, and the linearization process can be represented by Equation (23):

[0105] ; (23)

[0106] wherein, is the linear term. It should be noted that when performing the first iteration , and when performing non-first iterations is the calculated in the previous iteration step. Subsequently, a solver is used to solve the linearized result.

[0107] In block 302, the linear terms are respectively substituted into the developer concentration feature and the photoresist concentration feature .

[0108] In block 303, a solver is used to solve the developer concentration feature and the photoresist concentration feature respectively (for example, solving Equations (19) to (22)) to obtain the developer concentration and the photoresist concentration at at least one time point.

[0109] The above describes how to determine the developer concentration feature and the photoresist concentration feature. Continuing to refer to Figure 2 . In block 220, the electronic device 120 determines the developer concentration distribution and the photoresist concentration distribution at the target simulation area after development based on multiple developer concentration features and multiple photoresist concentration features.

[0110] Returning to the example referred to Figure 3 , after the electronic device 120 obtains the developer concentration feature and the photoresist concentration feature, in block 304, it determines whether the currently obtained developer concentration meets the convergence condition. As an example, in the example of determining the developer concentration and the photoresist concentration by solving Equations (19) to (22), the convergence condition is whether the residual of the developer concentration at two consecutive time points is less than the critical value set by the user. As an example, the critical value can be represented by Equation (24):

[0111] ; (24)

[0112] wherein, is the developer concentration value at the previous time point, is the developer concentration value at the subsequent time point, is the residual critical value set by the user. If the residual meets this convergence condition, in block 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 block 306, the electronic device 120 returns to continue the solving process of the developer concentration and the photoresist concentration.

[0113] In addition, the electronic device 120 also determines whether the development process has reached the set time. Under the condition that both of the above two conditions are satisfied, the electronic device 120 takes the currently obtained candidate concentration as the target concentration, and based on this target concentration, determines the developer concentration distribution and the photoresist concentration distribution.

[0114] As an example, the user can set the total time of the development process and the time advancement step . The electronic device 120 determines whether the condition is satisfied. If this condition is satisfied, it is determined that the set time has been reached; if this condition is not satisfied, the process of solving the developer concentration and the photoresist concentration continues to solve the developer concentration and the photoresist concentration at the next time point.

[0115] The above describes how to determine the developer concentration distribution and the photoresist concentration distribution. Continuing to refer to Figure 2 . At block 230, the electronic device 120 determines the photoresist topography at the target simulation region based on the developer concentration distribution and the photoresist concentration distribution.

[0116] In some embodiments, the photoresist topography is determined by a critical value of the photoresist material concentration given by the user . As an example, the final topography of the photoresist is the contour line at

[0117] 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 the photoresist concentration characteristics of the developer and the photoresist at each photoresist unit within the target simulation region. These concentration characteristics indicate the concentrations of the developer and the photoresist at multiple time points, thus 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 the photoresist concentration distribution of the target simulation region 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 topography at the target simulation region.

[0118] In this way, the embodiments of the present disclosure construct a real physical equation 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 diffusion interface between the photoresist and the developer, non-equilibrium transient diffusion and development reaction, and non-constant diffusion coefficients. The embodiments of the present disclosure can use the finite difference method for numerical solution with high calculation accuracy.

[0119] Figure 4 The block diagram of an electronic device 400 in which one or more embodiments of the present disclosure can be implemented is shown. The electronic device 400 can be used, for example, to implement asFigure 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 to the functions and scopes of the embodiments described herein.

[0120] Referring to 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 be capable of performing various processes according to the programs stored in the memory 420. In a multi-processor system, multiple processing units execute computer-executable instructions in parallel to improve the parallel processing ability of the electronic device 400.

[0121] The electronic device 400 generally includes multiple computer storage media. Such media may be any accessible media available to the electronic device 400, including but not limited to volatile and non-volatile media, removable and non-removable media. The memory 420 may be a volatile memory (such as registers, caches, random access memory (RAM)), a non-volatile memory (such as read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory), or some combination thereof. The storage device 430 may be a removable or non-removable medium and may include machine-readable media, such as a flash drive, a magnetic disk, or any other medium that can be used to store information and / or data and can be accessed within the electronic device 400.

[0122] The electronic device 400 may further include additional removable / non-removable, volatile / non-volatile storage media. Although not shown in Figure 4 , a disk drive for reading from or writing to a removable, non-volatile magnetic disk (such as 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 420 may include a computer program product 425 having one or more program modules that are configured to perform various methods or actions of the various embodiments of the present disclosure.

[0123] The communication unit 440 enables communication with other electronic devices via a communication medium. Additionally, the functions of the components of the electronic device 400 may be implemented in a single computing cluster or multiple computing machines that are capable of communicating via a communication connection. Thus, the electronic device 400 may operate in a networked environment using a logical connection to one or more other servers, network personal computers (PCs), or another network node.

[0124] The input device 450 may be one or more input devices, such as a mouse, keyboard, trackball, etc. The output device 460 may be one or more output devices, such as a display, speakers, printer, etc. The electronic device 400 may also communicate, as needed, with one or more external devices (not shown) via the communication unit 440, such as a storage device, a display device, etc., communicate with one or more devices that enable a user to interact with the electronic device 400, or communicate with any device that enables 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).

[0125] According to an exemplary implementation of the present disclosure, a computer-readable storage medium is provided, on which computer-executable instructions are stored, where 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, the computer program product being tangibly stored on a non-transitory computer-readable medium and including computer-executable instructions, and the computer-executable instructions being executed by a processor to implement the method described above.

[0126] Aspects of the present disclosure are described herein with reference to the flowcharts and / or block diagrams of methods, apparatuses, devices, and computer program products 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.

[0127] These computer-readable program instructions may be provided to a processing unit of a general-purpose computer, a special-purpose computer, or other programmable data processing apparatus, thereby producing a machine such that the instructions, when executed by the processing unit of the computer or other programmable data processing apparatus, create a means for implementing the functions / acts specified in one or more blocks of the flowchart and / or block diagram. These computer-readable program instructions may also be stored in a computer-readable storage medium, which instructions cause a computer, a programmable data processing apparatus, and / or other devices to operate in a particular manner, so that the computer-readable medium storing the instructions includes a manufacture, which includes instructions for implementing various aspects of the functions / acts specified in one or more blocks of the flowchart and / or block diagram.

[0128] Computer-readable program instructions may be loaded onto a computer, other programmable data processing apparatus, or other devices, causing a series of operational steps to be performed on the computer, other programmable data processing apparatus, or other devices to generate a computer-implemented process, such that the instructions executed on the computer, other programmable data processing apparatus, or other devices implement the functions / acts specified in one or more blocks of the flowchart and / or block diagram.

[0129] The flowcharts and block diagrams in the figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various implementations of the present disclosure. In this regard, each block in the flowchart or block diagram may represent a module, a segment of a program, or a portion of an instruction, which contains one or more executable instructions for implementing the specified logical function. In some alternative implementations, the functions noted in the blocks may occur out of the order noted in the figures. For example, two consecutive blocks may in fact be executed substantially in parallel, or they may sometimes be executed in the reverse order, depending on the functions involved. It should also be noted that each block of the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, can be implemented by a dedicated hardware-based system that performs the specified functions or acts, or by a combination of dedicated hardware and computer instructions.

[0130] The various implementations of the present disclosure have been described above. The above description is exemplary, not exhaustive, and is not limited to the disclosed implementations. Many modifications and variations will be apparent to those of ordinary skill in the art in the field 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, the practical application, or the improvement of the technology in the market, or to enable other ordinary skilled artisans in the field 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 the developer concentration and the photoresist concentration at multiple time points during the development process based on the multiple developer concentration characteristics and the multiple photoresist concentration characteristics; For a current time point among the multiple time points, in response to the developer concentration at the current time point satisfying a convergence condition and the development process reaching a set time, determining a developer concentration distribution and a photoresist concentration distribution at the target simulation area after development based on the developer concentration and the photoresist concentration at the current time point; as well as The photoresist morphology at the target simulation area is determined by comparing the photoresist concentration distribution with a critical value of the photoresist material concentration.

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 characteristic based on the difference of the developer concentration variation characteristic in at least one dimension to determine the plurality of developer concentration characteristics; 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 2, characterized in that The developer concentration variation characteristics and the photoresist concentration variation characteristics are expressed by the following formulas: ； ； ； in, is the characteristic of developer concentration change, is the characteristic of photoresist concentration variation, 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.

8. 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.

9. The method according to claim 8, 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.

10. 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.

11. The method according to claim 10, 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.

12. 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 11.

13. 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 11.

14. 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 11 when executed by a processor.

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