A method, system, apparatus, and medium for simulating a thin film atomic layer etching process

Abstract

This invention provides a method, system, equipment, and medium for simulating the atomic layer etching process of thin films, relating to the field of thin film fabrication simulation technology. The method includes: constructing a geometric model of the thin film structure based on the simulation region of the atomic layer etching process; determining phase-field variables on the geometric model according to the physical characteristics of the atomic layer etching process, and constructing a free energy functional based on the phase-field variables; constructing governing equations reflecting the evolution of the thin film structure based on the phase-field variables and the free energy functional; determining the boundary conditions and initial conditions of the phase-field variables according to the actual process conditions of the thin film structure, and constructing an initial-boundary value problem based on the governing equations; and solving the initial-boundary value problem using numerical methods to obtain the evolution results of the thin film structure during the atomic layer etching process. This invention improves the simulation accuracy and scale of the atomic layer etching process.

Description

Technical Field

[0001] This invention relates to the field of thin film preparation simulation technology, and more specifically, to a method, system, equipment, and medium for simulating the atomic layer etching process of thin films. Background Technology

[0002] Atomic layer etching (ALE) is a leading thin film fabrication technique that allows for precise control of the size and shape of thin film structures while minimizing damage to the substrate material through highly selective material removal. Because the ALE process involves complex chemical kinetics and interface evolution, simulation is necessary. Simulation methods typically include molecular dynamics, density functional theory, and interface dynamics models.

[0003] In related technologies, both molecular dynamics simulations and density functional theory methods consume significant computational resources and have limited applicability (molecular dynamics simulations are only suitable for short timescales from picoseconds to nanoseconds, while density functional theory methods are inefficient for simulating dynamic processes over long timescales). Meanwhile, interface dynamics models are based on local theories, and abrupt changes in field variables at the interface lead to inaccurate interface descriptions and numerical instability. In summary, traditional simulation methods struggle to accurately reproduce the chemical kinetic mechanisms and interface evolution patterns during atomic layer etching. Summary of the Invention

[0004] The problem addressed by this invention is how to improve the simulation accuracy and scale of atomic layer etching processes.

[0005] To address the above problems, this invention provides a method, system, equipment, and medium for simulating thin film atomic layer etching processes.

[0006] In a first aspect, the present invention provides a method for simulating a thin-film atomic layer etching process, comprising: Based on the simulated region of the thin film atomic layer etching process, a geometric model of the thin film structure is constructed; Based on the physical characteristics of the thin film atomic layer etching process, phase field variables are determined on the geometric model, and a free energy functional is constructed based on the phase field variables. Based on the phase field variables and the free energy functional, a control equation reflecting the evolution of the thin film structure is constructed. Based on the actual process conditions of the thin film structure, the boundary conditions and initial conditions of the phase field variables are determined, and the initial boundary value problem is constructed in conjunction with the governing equations. The initial boundary value problem is solved using numerical methods to obtain the evolution of the thin film structure during the etching process of the thin film atomic layer.

[0007] Optionally, the simulation region based on the thin film atomic layer etching process is used to construct a geometric model of the thin film structure, including: Obtain the solution domain size and element mesh size of the simulation region; The solution domain size and the unit grid size are combined to perform mesh generation, resulting in discrete grid units for the thin film structure. The geometric model is determined based on the discrete mesh elements.

[0008] Optionally, the step of determining phase field variables on the geometric model based on the physical characteristics of the thin film atomic layer etching process, and constructing a free energy functional based on the phase field variables, includes: At the mesh element nodes of the geometric model, the phase field variables are determined based on the material state of the thin film structure; Based on the phase field variables, and combined with the preset free energy density term, gradient energy term, and chemical potential energy term, the free energy functional is generated.

[0009] Optionally, constructing the governing equations reflecting the evolution of the thin film structure based on the phase field variables and the free energy functional includes: Based on the phase field variables, select the dynamic evolution equation; Obtain the variation of the free energy functional with respect to the phase field variables, and substitute the variation of the free energy functional with respect to the phase field variables as the driving force into the selected dynamic evolution equation to obtain the control equation.

[0010] Optionally, selecting the dynamic evolution equation based on the phase field variables includes: When the phase field variables are non-conservative field variables, the Allen-Cahn equation is used as the dynamic evolution equation; When the phase field variables are conservative field variables, the Cahn-Hilliard equation is used as the dynamic evolution equation.

[0011] Optionally, determining the boundary and initial conditions of the phase field variables based on the actual process conditions of the thin film structure, and constructing an initial-boundary value problem in conjunction with the governing equations, includes: The left and right boundaries of the simulation region are set as periodic boundary conditions, and the upper and lower boundaries are set as fixed boundary conditions. The periodic boundary condition and the fixed boundary condition are used as the boundary conditions. Based on the actual process conditions of the thin film structure, the surface defects of the thin film structure are determined, and the initial conditions are set based on the surface defects; The boundary conditions, initial conditions, and governing equations are combined to form the initial-boundary value problem.

[0012] Optionally, solving the initial boundary value problem using numerical methods to obtain the evolution of the thin film structure during the etching process of the thin film atomic layers includes: The control equations are spatially discretized using the finite difference method to obtain the discretized control equations. The Crank-Nicholson method is used to perform time integration on the discretized control equations to obtain the phase field variable distributions at multiple time steps; The phase field variable distribution at all time steps is iteratively solved to obtain the evolution result of the thin film structure during the etching process of the thin film atomic layer.

[0013] In a second aspect, the present invention provides a thin-film atomic layer etching process simulation system, comprising: The model building unit is used to construct the geometric model of the thin film structure based on the simulation area of ​​the thin film atomic layer etching process; The free energy functional construction unit is used to determine the phase field variables on the geometric model based on the physical characteristics of the thin film atomic layer etching process, and to construct the free energy functional based on the phase field variables. The evolution equation solving unit is used to construct the governing equations reflecting the evolution of the thin film structure based on the phase field variables and the free energy functional; determine the boundary conditions and initial conditions of the phase field variables based on the actual process conditions of the thin film structure, and construct the initial boundary value problem based on the governing equations; solve the initial boundary value problem using numerical methods to obtain the evolution results of the thin film structure during the etching process of the thin film atomic layer.

[0014] Thirdly, an electronic device according to the present invention includes: a processor and a memory, the memory being used to store a computer program; When the computer program is loaded by the processor, it causes the processor to execute the thin film atomic layer etching process simulation method as described above.

[0015] Fourthly, the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, it implements the thin film atomic layer etching process simulation method as described above.

[0016] The present invention provides a method, system, device, and medium for simulating the thin film atomic layer etching process. It constructs a geometric model of the thin film structure based on the simulation region of the thin film atomic layer etching process. Based on the mesoscopic scale characteristics of the phase-field method, it forms a regularized solution domain and mesh to meet the simulation requirements, thus establishing the structural foundation. Furthermore, it determines the phase-field variables and constructs a free energy functional based on the physical characteristics of the etching process. This free energy functional comprehensively considers local thermodynamic free energy, gradient energy, and long-range interaction energy, thereby reflecting the material distribution and energy change laws during the etching process, thus conforming to the complex physicochemical mechanism of atomic layer etching. Finally, it combines the phase-field variables to construct governing equations characterizing the evolution of the thin film structure, ensuring that the evolution process conforms to the thermodynamic laws of materials and facilitating the capture of the changing trends of the field variables over time. Then, based on the actual process conditions, the boundary conditions and initial conditions were determined, and the initial boundary value problem was constructed to ensure that the simulation scenario closely matches the actual process and reduce errors caused by deviations in condition settings. Finally, the initial boundary value problem was solved numerically, avoiding the traditional method of tracking individual atoms and reducing computational resource consumption. At the same time, since the free energy functional includes a gradient energy term, the gradient energy only exists at and around the interface (where the field variables change), which can maintain the existence of the diffuse interface (i.e., the diffusion interface). This solves the problems of inaccurate interface description and unstable numerical calculation in traditional interface dynamics models, enabling simulation of larger-scale systems on a longer time scale. Furthermore, the accurate matching of the free energy functional with the governing equations ensures the accuracy of the simulation results. Attached Figure Description

[0017] Figure 1 This is a schematic flowchart illustrating the simulation method for thin film atomic layer etching in an embodiment of the present invention; Figure 2 This is a schematic diagram showing the morphological evolution of the SiGe thin film during the ALE process in an embodiment of the present invention. Figure 3 This is a schematic diagram of the structure of the thin film atomic layer etching process simulation system in an embodiment of the present invention. Detailed Implementation

[0018] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Although some embodiments of the present invention are shown in the drawings, it should be understood that the present invention can be implemented in various forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided to provide a more thorough and complete understanding of the present invention. It should be understood that the accompanying drawings and embodiments of the present invention are for illustrative purposes only and are not intended to limit the scope of protection of the present invention.

[0019] It should be understood that the various steps described in the method embodiments of the present invention may be performed in different orders and / or in parallel. Furthermore, the method embodiments may include additional steps and / or omit the steps shown. The scope of the present invention is not limited in this respect.

[0020] The term "comprising" and its variations as used herein are open-ended, meaning "including but not limited to"; the term "based on" means "at least partially based on"; the term "one embodiment" means "at least one embodiment"; the term "another embodiment" means "at least one additional embodiment"; the term "some embodiments" means "at least some embodiments"; and the term "optionally" means "optional embodiments". Definitions of other terms will be given in the following description. It should be noted that the concepts of "first," "second," etc., mentioned in this invention are used only to distinguish different devices, modules, or units, and are not intended to limit the order of functions performed by these devices, modules, or units or their interdependencies.

[0021] It should be noted that the terms "one" and "more" used in this invention are illustrative rather than restrictive. Those skilled in the art should understand that, unless otherwise expressly indicated in the context, they should be understood as "one or more".

[0022] The names of the messages or information exchanged between the multiple devices in the embodiments of the present invention are for illustrative purposes only and are not intended to limit the scope of these messages or information.

[0023] Combination Figure 1 As shown in the figure, an embodiment of the present invention provides a method for simulating a thin film atomic layer etching process, comprising: A geometric model of the thin film structure is constructed based on the simulated region of the thin film atomic layer etching process.

[0024] Specifically, by setting the solution domain size (e.g., 60 nm × 70 nm) and the grid cell size (e.g., 1 nm × 1 nm), the simulation region is divided into regular rectangular grids. This regularized approach fully utilizes the characteristic that the solution domain of the phase-field method is usually relatively regular at the mesoscopic scale, reducing the complexity of model construction. Furthermore, the resulting geometric model provides a structural foundation for subsequently defining phase-field variables and performing spatial discretization numerical solutions, ensuring computational feasibility and efficiency.

[0025] Based on the physical characteristics of the thin film atomic layer etching process, phase field variables are determined on the geometric model, and a free energy functional is constructed based on the phase field variables.

[0026] Specifically, the phase field variables are defined at each grid node of the geometric model, which can accurately describe the distribution state of matter in the system. The free energy functional is not a single energy term, but integrates the local thermodynamic free energy density (such as the double potential well function) that drives phase separation, the gradient energy term that maintains interface stability, and the energy term that reflects long-range interactions such as chemical potential difference. It comprehensively considers the local thermodynamic free energy, gradient energy and long-range interaction energy in the etching process, and fully reflects the energy change law of the system. Its construction directly determines the direction and driving force of thin film structure evolution, and provides a key energy theoretical basis for the establishment of subsequent governing equations, ensuring that the simulation can fit the complex physicochemical mechanism of atomic layer etching.

[0027] Based on the phase field variables and the free energy functional, a governing equation reflecting the evolution of the thin film structure is constructed.

[0028] Specifically, based on the phase field variables, governing equations for the evolution of the thin film structure are constructed. These equations, grounded in materials thermodynamics and driven by variations in the free energy functional, accurately characterize the changes in phase field variables over time, thus reflecting the evolution trend of the thin film structure during etching. By matching the properties of the phase field variables with the corresponding equation forms, the adaptability of the equations to the dynamic behaviors such as material migration and phase transitions during etching is ensured, enabling the simulation to accurately capture the kinetic characteristics of the etching process.

[0029] Based on the actual process conditions of the thin film structure, the boundary conditions and initial conditions of the phase field variables are determined, and the initial boundary value problem is constructed in conjunction with the governing equations.

[0030] Specifically, the boundary conditions simulate the constraint state of the solution domain boundary during actual etching, while the initial conditions restore the initial state of the film before etching begins (such as initial morphology and material distribution). Combining the boundary and initial conditions, which conform to the actual process conditions, with the governing equations constitutes a complete initial-boundary value problem. This allows the abstract mathematical model to be solved for specific simulation scenarios (such as films of specific sizes and defects), reducing simulation deviations caused by idealized assumptions and enhancing the practical reference value of the results.

[0031] The initial boundary value problem is solved using numerical methods to obtain the evolution of the thin film structure during the etching process of the thin film atomic layer.

[0032] Specifically, solving the initial-boundary value problem using numerical methods eliminates the need to track the position and motion of individual atoms, significantly reducing computational resource consumption and enabling simulations of etching processes over larger-scale regions and longer time scales. Furthermore, the numerical solution method efficiently handles complex governing equations and boundary conditions, accurately calculating the state of the thin film structure at different time points and ultimately outputting clear evolution results. This effectively solves the problems of inaccurate interface description and numerical instability in traditional interface dynamics models. Therefore, while maintaining accuracy, it enables efficient and stable simulations of the evolution of larger-scale systems over longer time scales, ultimately obtaining detailed results of the time-varying surface morphology of the thin film.

[0033] The present invention provides a method for simulating the thin film atomic layer etching process. This method constructs a geometric model of the thin film structure based on the simulation region of the etching process. It then uses the mesoscopic scale characteristics of the phase-field method to form a regularized solution domain and mesh to meet the simulation requirements, thus establishing the structural foundation. Furthermore, it determines the phase-field variables and constructs a free energy functional based on the physical characteristics of the etching process. This free energy functional comprehensively considers local thermodynamic free energy, gradient energy, and long-range interaction energy, thereby reflecting the material distribution and energy change patterns during the etching process, thus conforming to the complex physicochemical mechanism of atomic layer etching. Finally, it combines the phase-field variables to construct governing equations characterizing the evolution of the thin film structure, ensuring that the evolution process conforms to the thermodynamic laws of materials and facilitating the capture of the changing trends of the field variables over time. Subsequently, based on actual... The process conditions determine the boundary and initial conditions and construct the initial boundary value problem, making the simulation scenario highly consistent with the actual process and reducing errors caused by deviations in condition settings. Finally, the initial boundary value problem is solved numerically, avoiding the traditional method of tracking individual atoms and reducing computational resource consumption. At the same time, since the free energy functional includes a gradient energy term, the gradient energy only exists at and around the interface (where the field variables change), which can maintain the existence of the diffuse interface (i.e., the diffusion interface). This solves the problems of inaccurate interface description and unstable numerical calculation in traditional interface dynamics models, enabling the simulation of larger-scale systems on a longer time scale. Furthermore, the accurate matching of the free energy functional with the governing equations ensures the accuracy of the simulation results.

[0034] Optionally, the simulation region based on the thin film atomic layer etching process is used to construct a geometric model of the thin film structure, including: Obtain the solution domain size and element mesh size of the simulation region; The solution domain size and the unit grid size are combined to perform mesh generation, resulting in discrete grid units for the thin film structure. The geometric model is determined based on the discrete mesh elements.

[0035] Specifically, based on the application characteristics of the phase-field method at the mesoscopic scale and the simulation requirements of thin film atomic layer etching, the solution domain size (which needs to be adapted to the solution characteristics of the phase-field method which is much smaller than the macroscopic size) and the unit grid size (taking into account both simulation accuracy and computational efficiency) corresponding to the simulation region are first determined. Then, according to the matching relationship between the solution domain size and the unit grid size, the solution domain is divided into rectangular or cubic discrete grid units using a regularized partitioning method to ensure that the grid units are adapted to the shape of the solution domain. Finally, based on the partitioned discrete grid units, the initial structural features of the thin film (such as thickness, surface defect location, etc.) are integrated to form a geometric model that can accurately reflect the morphology of the thin film in the simulation region. In a preferred embodiment of the present invention, in the simulation of the atomic layer etching process of SiGe thin film, the solution domain size of the simulation region is first obtained as 60nm×70nm, and the unit grid size is 1nm×1nm; then, combining the solution domain size and the unit grid size, the 60nm×70nm solution domain is divided into rectangular grids to obtain 60×70 discrete rectangular grid units; finally, based on these discrete grid units, the initial structural information of the SiGe thin film with a thickness of 50nm, a surface containing rectangular pits with a depth of 16nm and a width of 10nm is incorporated to determine the geometric model corresponding to the atomic layer etching simulation of SiGe thin film.

[0036] In this embodiment of the invention, by first clarifying the parameters of the solution domain size and the unit mesh size, and then performing targeted meshing and determining the geometric model, it is possible not only to ensure that the spatial range of the geometric model is highly consistent with the simulation requirements of thin film atomic layer etching, avoiding the model from being out of touch with the actual simulation scenario due to fuzzy size parameters, but also that the regularized discrete mesh units can provide a regular and efficient computational foundation for subsequent assignment of phase field variables, calculation of free energy functionals, and numerical solution, reducing the numerical computation complexity in the subsequent simulation process. At the same time, the accurate geometric model can realistically restore the initial structural features of the thin film.

[0037] Optionally, the step of determining phase field variables on the geometric model based on the physical characteristics of the thin film atomic layer etching process, and constructing a free energy functional based on the phase field variables, includes: At the mesh element nodes of the geometric model, the phase field variables are determined based on the material state of the thin film structure; Based on the phase field variables, and combined with the preset free energy density term, gradient energy term, and chemical potential energy term, the free energy functional is generated.

[0038] Specifically, based on the discrete mesh unit nodes of the geometric model, and according to the material states of the thin film structure during atomic layer etching, such as the distribution of the solid domain and air domain, the types, properties, and specific physical meanings of the phase field variables are clarified to ensure that the phase field variables can accurately describe the distribution of matter in the system. Then, using the determined phase field variables as the core, and combining the preset free energy density term (reflecting local thermodynamic properties), gradient energy term (existing only at and around the interface, maintaining the diffusion interface), and chemical potential energy term (reflecting the chemical potential difference between phases, providing the driving force for evolution), the three types of energy terms are fused through integration to generate a complete system free energy functional, comprehensively covering both short-range and long-range chemical interactions during the etching process. The free energy functional consists of local thermodynamic free energy and chemical energy, and is a single-valued function of the field variable c, with the specific expression as follows: ; in, V The solution domain volume or simulation region volume of the system. Here is the expression for the intrinsic free energy. Here is the expression for the volume free energy.

[0039] In this embodiment of the invention, for the simulation of atomic layer etching of SiGe thin film, firstly, on the geometric model grid cell node with a grid size of 1nm×1nm and a grid size of 60nm×70nm, the phase field variable is determined to be a non-conservative variable, namely the atomic concentration c (c=1 represents the solid domain, c=0 represents the air domain), based on the material state of the SiGe thin film (solid domain SiGe and air domain), and each grid node corresponds to an atomic concentration value. Subsequently, based on the phase field variable c, the free energy density term is presupposed to be a function containing a double potential well. , where A is the two-phase energy barrier.

[0040] The gradient energy term is ,in, The gradient energy coefficient, The gradient of the field variable. This ensures that the energy is only available at the interface location (0). <c<1, ≠0) Has a value, used to maintain the existence of the diffusion interface.

[0041] The local thermodynamic free energy density can be expressed as: .

[0042] The chemical potential energy term is ( c ),in, The chemical potential energy of SiGe ( c This is a normalized density field that takes into account the mass distribution.

[0043] The volume free energy density is: .

[0044] In summary, the specific expression for the free energy functional of the SiGe thin film system in the ALE process is: ; in, V The solution domain volume or simulation region volume of the system. Here is the expression for the intrinsic free energy. Here is the expression for the volume free energy.

[0045] In this embodiment of the invention, by combining the material state at the grid cell nodes to determine the phase field variables, the high degree of fit between the variables and the actual physical state of the thin film is ensured, avoiding the problem of the variable definition being out of touch with the actual scenario. At the same time, by integrating the free energy density term, gradient energy term, and chemical potential energy term to construct the free energy functional, the local thermodynamic characteristics and interface energy characteristics during the etching process are comprehensively considered, and the chemical potential energy factors driving the evolution are also included, so that the free energy functional can accurately characterize the energy distribution and evolution trend of the system.

[0046] Optionally, constructing the governing equations reflecting the evolution of the thin film structure based on the phase field variables and the free energy functional includes: Based on the phase field variables, select the dynamic evolution equation; Obtain the variation of the free energy functional with respect to the phase field variables, and substitute the variation of the free energy functional with respect to the phase field variables as the driving force into the selected dynamic evolution equation to obtain the control equation.

[0047] Specifically, firstly, based on the core properties (conservative or non-conservative) of the determined phase field variables, the corresponding type of dynamic evolution equation is matched to ensure that the equation form is compatible with the migration and evolution characteristics of the field variables; then, based on the thermodynamics of materials, the gradient of the total free energy of the system as a function of the phase field variables is obtained by taking the variation of the phase field variables through the free energy functional of the constructed system. This variational result is the core thermodynamic driving force that drives the evolution of the thin film structure; finally, the variational driving force is directly substituted into the selected dynamic evolution equation, replacing the general driving force term in the equation, to form the control equation that can accurately reflect the structural evolution law during the etching of the thin film atomic layer.

[0048] In this embodiment of the invention, by matching the properties of phase field variables with the dynamic evolution equations, the adaptability of the equation form to the material evolution characteristics during the etching process is ensured, avoiding the blind selection of equations. At the same time, using the variation of the free energy functional as the driving force, the driving force of the control equations is directly derived from the energy change law of the system, which essentially fits the thermodynamic evolution mechanism of thin film atomic layer etching, ensuring the physical rationality of the equations. By substituting the variational driving force into the equations to form the control equations, the organic unity of energy theory and dynamic model is achieved, which can accurately capture the time evolution trend of phase field variables, and thus accurately restore the etching characteristics such as interface movement and morphological changes of the thin film structure.

[0049] Optionally, selecting the dynamic evolution equation based on the phase field variables includes: When the phase field variables are non-conservative field variables, the Allen-Cahn equation is used as the dynamic evolution equation; When the phase field variables are conservative field variables, the Cahn-Hilliard equation is used as the dynamic evolution equation.

[0050] Specifically, firstly, the core properties of phase field variables are clarified: conservative field variables must satisfy the total conservation of physical quantities such as mass and composition during evolution (e.g., atomic concentration field), while non-conservative field variables do not have this conservation constraint (e.g., order parameters characterizing phase state) (c=1 represents the solid domain, c=0 represents the air domain). This serves as the core criterion for equation selection. Then, based on the classical theory and dynamic characteristics of the phase field method, suitable equations are matched for the two types of variables. For non-conservative field variables, the Allen-Cahn equation is selected. The Allen-Cahn equation is obtained through L… 2 Gradient descent drives non-conservative interface motion, which does not require total conservation and adapts to the evolution of variables such as phase identifiers; the conservative field variables correspond to the Cahn-Hilliard equation, which is obtained through H -1 Gradient flow achieves phase separation under mass conservation, matching the migration characteristics of conserved quantities such as composition and concentration.

[0051] In summary, in a preferred embodiment of the present invention, when the material point is in the air domain, When the material point is in the solid domain, . Its derivative is: ; ; Among them, when c =0 and c When =1, for A first derivative of c that approaches zero as a positive decimal indicates that the driving force for the phase transition in the stable phase region is zero. When c When =0.5, The maximum value indicates that atomic etching is most likely to occur at the interface.

[0052] In the simulation of atomic layer etching of SiGe thin films, the phase field variable has been determined to be a scalar nonconservative variable (atomic concentration c). Subsequently, the variational equation of the phase field variable c is obtained by applying the constructed free energy functional F, and the governing equation is as follows: ; in, ,and K(x) is the gradient energy coefficient at spatial location x, where, Let c be the rate of change of atomic concentration with time t. The first variational derivative of the free energy. and These are the driving force components corresponding to intrinsic free energy and volume free energy, respectively.

[0053] In this embodiment of the invention, by clarifying the conservation characteristics of the phase field variables and the fit relationship between the two types of classical equations, the blindness in equation selection is avoided, ensuring that the dynamic evolution equations are highly consistent with the physical nature and evolution laws of the variables.

[0054] Optionally, determining the boundary and initial conditions of the phase field variables based on the actual process conditions of the thin film structure, and constructing an initial-boundary value problem in conjunction with the governing equations, includes: The left and right boundaries of the simulation region are set as periodic boundary conditions, and the upper and lower boundaries are set as fixed boundary conditions. The periodic boundary condition and the fixed boundary condition are used as the boundary conditions. Based on the actual process conditions of the thin film structure, the surface defects of the thin film structure are determined, and the initial conditions are set based on the surface defects; The boundary conditions, initial conditions, and governing equations are combined to form the initial-boundary value problem.

[0055] Specifically, firstly, considering the actual process scenario of thin film atomic layer etching, targeted settings are adopted for different boundaries of the simulation region. The left and right boundaries are set as periodic boundary conditions, so that the numerical values ​​and distribution characteristics of the phase field variables at the boundaries are continuously matched to simulate the infinitely extended lateral structure of the thin film, avoiding simulation distortion caused by boundary effects. The upper and lower boundaries are set as fixed boundary conditions, specifying the fixed values ​​of the phase field variables at the boundaries. For example, the phase field variable in the air domain is 0, restoring the actual contact constraints between the upper and lower surfaces of the thin film and the environment. Then, based on the surface defects such as pits and protrusions that may exist in the thin film in the actual process, the position, size, shape and other parameters of the defects are transformed into the initial spatial distribution of the phase field variables, so that the initial state is consistent with the real thin film structure. Finally, the boundary conditions, initial conditions and the previously constructed control equations are organically integrated to form a complete initial-boundary value problem that includes dynamic laws, boundary constraints and initial states, providing a comprehensive and realistic mathematical model for numerical solution.

[0056] In this embodiment of the invention, by combining left and right periodic boundaries with upper and lower fixed boundaries, the interference of boundary effects on simulation results is effectively avoided, and the actual spatial constraint state of the thin film is accurately restored. The initial conditions are set based on the surface defects of the actual process, so that the simulation starting point is highly consistent with the real thin film structure, avoiding the deviation of evolution results caused by the distortion of the initial state. The organic integration of boundary conditions, initial conditions and governing equations forms a physically meaningful initial boundary value problem, which provides a comprehensive and realistic computational basis for subsequent numerical solutions.

[0057] Optionally, solving the initial boundary value problem using numerical methods to obtain the evolution of the thin film structure during the etching process of the thin film atomic layers includes: The control equations are spatially discretized using the finite difference method to obtain the discretized control equations. The Crank-Nicholson method is used to perform time integration on the discretized control equations to obtain the phase field variable distributions at multiple time steps; The phase field variable distribution at all time steps is iteratively solved to obtain the evolution result of the thin film structure during the etching process of the thin film atomic layer.

[0058] Specifically, firstly, the finite difference method is used to replace the continuous spatial derivatives in the control equations with difference approximations on the grid nodes. Using the discrete grid cells of the geometric model, the continuous control equations are transformed into a system of algebraic equations involving only the phase field variables of the grid nodes, thus completing the discretization of the spatial dimension. Next, time integration is performed using the Crank-Nicholson method. This method, as a semi-implicit algorithm with second-order precision, constructs a time discretization scheme by fusing the weighted average of the driving forces of the current time step and the next time step (each accounting for 1 / 2 weight). This ensures high accuracy of time evolution and improves numerical stability, and can adapt to larger time step lengths. Finally, based on the discretized control equations and combined with the determined boundary and initial conditions, starting from the phase field variable distribution of the initial time step, the algebraic equation system of each time step is solved iteratively to obtain the spatial distribution of phase field variables at different times. Finally, the results of all time steps are integrated to form a complete thin film etching evolution process.

[0059] In a preferred embodiment of the present invention, since the solution domain is regular and simple, the time discretization scheme adopts the Crank-Nicholson method, and the time discretization weighted parameters are... The value of is between 0 and 1, and it is used to control the balance of the weighted average of the time derivative term between the current step and the next step; it is set to 0.5. Therefore, the spatiotemporal discrete form is: ; Atom concentration of the i-th grid node at the (n+1)-th time step The expression is: ; ; Where n is the index of the time step, Δt is the step size of the time step, and i is the index of the spatial grid node. Let i be the atom concentration at the (n+1)th time step and the i-th grid node. Let θ be the atomic mobility parameter of spatial grid node i, and θ be the time-discrete weighted parameter; in, The first variational derivative of the free energy. and These are the driving force components corresponding to intrinsic free energy and volume free energy, respectively.

[0060] In summary, combining Figure 2 As shown, the surface morphology evolution results of the SiGe thin film during the ALE process are presented, and the dynamic evolution of the surface morphology of the film during atomic layer etching is shown at time points of 0.9 seconds, 1.3 seconds and 1.7 seconds. Figure 2In the diagram, for the distribution of atomic concentration *c*, red corresponds to *c≈1*, representing the solid phase; blue corresponds to *c≈0*, representing the air phase. It can be observed that the pit structure initially present on the solid surface (red area) gradually expands and deepens over time, indicating that the etching reaction continues and the interface continuously advances into the solid interior. This verifies that the phase-field method-based simulation can capture key physical characteristics such as interface migration, morphological smoothing, and self-limiting reactions in atomic layer etching, confirming the predictive ability of the mathematical model for the process at the mesoscale.

[0061] In this embodiment of the invention, the spatial discretization of the governing equations is achieved through the finite difference method, adapting to the discrete grid structure of the geometric model, and quickly transforming continuous partial differential equations into a solvable system of algebraic equations. The application of the Crank-Nicholson method not only ensures the second-order accuracy of the time evolution but also possesses numerical stability superior to explicit methods, allowing for the use of larger time steps to improve computational efficiency while avoiding numerical oscillation problems. Through iterative solutions at multiple time steps, the distribution of phase field variables at different times can be continuously captured, reconstructing the dynamic evolution process of thin film etching. Furthermore, the entire numerical solution process is highly compatible with the governing equations and initial boundary conditions constructed above, reducing computational resource consumption while ensuring the accuracy of the evolution results.

[0062] Combination Figure 3 As shown, another embodiment of the present invention provides a simulation system for thin film atomic layer etching process, comprising: The model building unit is used to construct the geometric model of the thin film structure based on the simulation area of ​​the thin film atomic layer etching process; The free energy functional construction unit is used to determine the phase field variables on the geometric model based on the physical characteristics of the thin film atomic layer etching process, and to construct the free energy functional based on the phase field variables. The evolution equation solving unit is used to construct the governing equations reflecting the evolution of the thin film structure based on the phase field variables and the free energy functional; determine the boundary conditions and initial conditions of the phase field variables based on the actual process conditions of the thin film structure, and construct the initial boundary value problem based on the governing equations; solve the initial boundary value problem using numerical methods to obtain the evolution results of the thin film structure during the etching process of the thin film atomic layer.

[0063] The thin film atomic layer etching process simulation system of the present invention has the same advantages over the prior art as the aforementioned thin film atomic layer etching process simulation method, and will not be repeated here.

[0064] Another embodiment of the present invention provides an electronic device comprising: a processor and a memory, wherein the memory is used to store a computer program; When the computer program is loaded by the processor, it causes the processor to execute the thin film atomic layer etching process simulation method as described above.

[0065] The electronic device of the present invention has the same advantages over the prior art as the above-mentioned thin film atomic layer etching process simulation method, and will not be repeated here.

[0066] Another embodiment of the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, it implements the thin film atomic layer etching process simulation method as described above.

[0067] The advantages of the computer-readable storage medium of the present invention compared to the prior art are the same as the advantages of the above-described thin film atomic layer etching process simulation method compared to the prior art, and will not be repeated here.

[0068] While the present invention has been disclosed above, its scope of protection is not limited thereto. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the present invention, and all such changes and modifications will fall within the scope of protection of the present invention.

Claims

1. A method for simulating the etching process of a thin film atomic layer, characterized in that, include: Based on the simulated region of the thin film atomic layer etching process, a geometric model of the thin film structure is constructed; Based on the physical characteristics of the thin film atomic layer etching process, phase field variables are determined on the geometric model, and a free energy functional is constructed based on the phase field variables. Based on the phase field variables and the free energy functional, a control equation reflecting the evolution of the thin film structure is constructed. Based on the actual process conditions of the thin film structure, the boundary conditions and initial conditions of the phase field variables are determined, and the initial boundary value problem is constructed in conjunction with the governing equations. The initial boundary value problem is solved using numerical methods to obtain the evolution of the thin film structure during the etching process of the thin film atomic layer.

2. The method for simulating thin film atomic layer etching process according to claim 1, characterized in that, The simulated region based on the thin film atomic layer etching process is used to construct a geometric model of the thin film structure, including: Obtain the solution domain size and element mesh size of the simulation region; The solution domain size and the unit grid size are combined to perform mesh generation, resulting in discrete grid units for the thin film structure. The geometric model is determined based on the discrete mesh elements.

3. The method for simulating thin film atomic layer etching process according to claim 1, characterized in that, The step of determining phase-field variables on the geometric model based on the physical characteristics of the thin film atomic layer etching process, and constructing a free energy functional based on the phase-field variables, includes: At the mesh element nodes of the geometric model, the phase field variables are determined based on the material state of the thin film structure; Based on the phase field variables, and combined with the preset free energy density term, gradient energy term, and chemical potential energy term, the free energy functional is generated.

4. The method for simulating thin film atomic layer etching process according to claim 1, characterized in that, The construction of the governing equations reflecting the evolution of the thin film structure based on the phase field variables and the free energy functional includes: Based on the phase field variables, select the dynamic evolution equation; Obtain the variation of the free energy functional with respect to the phase field variables, and substitute the variation of the free energy functional with respect to the phase field variables as the driving force into the selected dynamic evolution equation to obtain the control equation.

5. The method for simulating thin film atomic layer etching process according to claim 4, characterized in that, The step of selecting the dynamic evolution equation based on the phase field variables includes: When the phase field variables are non-conservative field variables, the Allen-Cahn equation is used as the dynamic evolution equation; When the phase field variables are conservative field variables, the Cahn-Hilliard equation is used as the dynamic evolution equation.

6. The method for simulating thin film atomic layer etching process according to claim 1, characterized in that, The process of determining the boundary and initial conditions of the phase field variables based on the actual process conditions of the thin film structure, and constructing an initial-boundary value problem in conjunction with the governing equations, includes: The left and right boundaries of the simulation region are set as periodic boundary conditions, and the upper and lower boundaries are set as fixed boundary conditions. The periodic boundary condition and the fixed boundary condition are used as the boundary conditions. Based on the actual process conditions of the thin film structure, the surface defects of the thin film structure are determined, and the initial conditions are set based on the surface defects; The boundary conditions, initial conditions, and governing equations are combined to form the initial-boundary value problem.

7. The method for simulating thin film atomic layer etching process according to claim 1, characterized in that, The step of solving the initial boundary value problem using numerical methods to obtain the evolution of the thin film structure during the etching process of the thin film atomic layers includes: The control equations are spatially discretized using the finite difference method to obtain the discretized control equations. The Crank-Nicholson method is used to perform time integration on the discretized control equations to obtain the phase field variable distribution at multiple time steps; The phase field variable distribution at all time steps is iteratively solved to obtain the evolution result of the thin film structure during the etching process of the thin film atomic layer.

8. A simulation system for thin film atomic layer etching process, characterized in that, include: The model building unit is used to construct the geometric model of the thin film structure based on the simulation area of ​​the thin film atomic layer etching process; The free energy functional construction unit is used to determine the phase field variables on the geometric model based on the physical characteristics of the thin film atomic layer etching process, and to construct the free energy functional based on the phase field variables. The evolution equation solving unit is used to construct the control equations that reflect the evolution of the thin film structure based on the phase field variables and the free energy functional. Based on the actual process conditions of the thin film structure, the boundary conditions and initial conditions of the phase field variables are determined, and the initial boundary value problem is constructed in conjunction with the governing equations. The initial boundary value problem is solved using numerical methods to obtain the evolution of the thin film structure during the etching process of the thin film atomic layer.

9. An electronic device, characterized in that, include: Processor and memory, the memory being used to store computer programs; When the computer program is loaded by the processor, it causes the processor to execute the thin film atomic layer etching process simulation method as described in any one of claims 1-7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the thin film atomic layer etching process simulation method as described in any one of claims 1-7.

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