Methods, apparatus, media, and program product for structural stress analysis

Abstract

Methods, apparatuses, devices, media, and program products for structural stress analysis are provided. The method includes obtaining a temperature and stress state of a target material in a target structure; determining a viscosity parameter of the target material based on the temperature and stress state; constructing a model of the target material based on the viscosity parameter, the model being used to represent a relationship between a stress of the target material and a strain state of the target material, wherein the relationship is related to the temperature and stress state; and determining a stress distribution result of the target material in the target structure based on the model.

Description

Technical Field

[0001] The examples in this article generally relate to the field of computer science, and in particular to methods, devices, media, and program products used for structural stress analysis. Background Technology

[0002] With the development of semiconductor manufacturing technology, device structures are constantly evolving towards higher integration and higher performance. In the design and manufacturing process of semiconductor devices, it is usually necessary to analyze the mechanical response of the device structure under different process conditions in order to evaluate the structural stability and stress distribution.

[0003] In related technologies, structural stress analysis is commonly used in scenarios such as semiconductor device process simulation, material behavior simulation, and device performance evaluation. In these scenarios, it is necessary to calculate the mechanical response of materials under external conditions based on the device structure and its material properties, thereby obtaining the stress distribution results inside the device structure. Summary of the Invention

[0004] In a first aspect of this paper, a method for structural stress analysis is provided, comprising: obtaining the temperature and stress state of a target material in a target structure; determining the viscosity parameters of the target material based on the temperature and stress state; constructing a model of the target material based on the viscosity parameters, the model representing the relationship between the stress and strain state of the target material, wherein the relationship is related to the temperature and stress state; and determining the stress distribution of the target material in the target structure based on the model.

[0005] In a second aspect of this document, an electronic device is provided, comprising: at least one processing unit; and at least one memory coupled to the at least one processing unit and storing instructions for execution by the at least one processing unit, the instructions causing the electronic device to perform the method according to the first aspect when executed by the at least one processing unit.

[0006] In a third aspect of this document, a computer-readable storage medium is provided having a computer program stored thereon, the computer program being executable by a processor to implement the method according to the first aspect.

[0007] In a fourth aspect of this document, a computer program product is provided, which is tangibly stored in a computer storage medium and includes computer-executable instructions that, when executed by a device, cause the device to perform the method according to the first aspect.

[0008] In this way, by incorporating the influence of temperature and stress state on viscosity parameters into the model construction, it is possible to accurately characterize the nonlinear mechanical response of the target material over a wide temperature range and multiple time scales, and significantly improve the prediction accuracy of stress distribution results.

[0009] It should be understood that the content described in this section is not intended to limit the key or important features of the examples in this article, nor is it intended to restrict the scope of the solution. Other features will become readily apparent from the following description. Attached Figure Description

[0010] The above and other features, advantages, and aspects of the various examples herein will become more apparent when taken in conjunction with the accompanying drawings and the following detailed description. In the accompanying drawings, the same or similar reference numerals denote the same or similar elements, wherein: Figure 1 A schematic diagram of the example environment is shown; Figure 2 Flowcharts of methods for structural stress analysis in some scenarios are shown; Figure 3A Schematic diagrams of semiconductor device structures in some scenarios are shown; Figure 3B Contour maps of stress field distribution in some scenarios are shown; Figure 3C The graphs showing the effect of relaxation time on stress in viscoelastic materials under some conditions are shown. Figure 3D The graphs showing the effect of temperature on the stress of viscoelastic materials in some cases are shown. Figure 4 A block diagram of an electronic device capable of implementing multiple illustrative scenarios is shown. Detailed Implementation

[0011] The examples in the text will now be described in more detail with reference to the accompanying drawings. While some examples are shown in the drawings, it should be understood that solutions can be implemented in various forms and should not be construed as limited to the examples presented herein. Rather, these examples are provided to provide a more thorough and complete understanding of the solutions. It should be understood that the drawings and examples in this document are for illustrative purposes only and are not intended to limit the scope of protection of the solutions.

[0012] It should be noted that the headings of any section / subsection provided herein are not restrictive. Various examples are described throughout this document, and examples of any type may be included under any section / subsection. Furthermore, examples described in any section / subsection may be combined in any way with any other examples described in the same section / subsection and / or different sections / subsections.

[0013] In the description of the examples in this document, the term "including" and similar terms should be understood as open inclusion, i.e., "including but not limited to". The term "based on" should be understood as "at least partially based on". The term "an example" or "the example" should be understood as "at least one example". The term "some examples" should be understood as "at least some examples". Other explicit and implicit definitions may also be included below. The terms "first", "second", etc., may refer to different or the same objects. Other explicit and implicit definitions may also be included below.

[0014] The examples in this document may involve user data, data acquisition, and / or use. All of these aspects comply with relevant laws, regulations, and rules. In the examples, all data collection, acquisition, processing, manipulation, forwarding, and use are conducted with the user's knowledge and confirmation. Accordingly, when implementing each example, the type, scope of use, and usage scenarios of any data or information that may be involved should be communicated to the user and their authorization obtained through appropriate means, in accordance with relevant laws and regulations. The specific methods of notification and / or authorization can vary depending on the actual situation and application scenario; the scope of the solution is not limited in this regard.

[0015] In this manual and the sample solutions, any processing of personal information will be conducted only under legal grounds (such as obtaining the consent of the data subject or being necessary for the performance of a contract) and will only be carried out within the scope stipulated or agreed upon. A user's refusal to process personal information beyond what is necessary for basic functions will not affect the user's use of basic functions.

[0016] The term “constitutive model” as used in this article refers to a mathematical model used to describe the relationship between stress and strain of a material under the action of external forces. It is also called constitutive equation or constitutive relation. Different constitutive models can be used to characterize the mechanical behavior of different materials.

[0017] The term “strain state” as used in this article refers to the deformation of the target material under the action of external force, including but not limited to the strain rate tensor and its components, which can be decomposed into a spherical tensor component (representing volume change) and a partial tensor component (representing shape change).

[0018] The term “material stiffness term” as used in this paper refers to the term derived from the constitutive equations and used to construct the stiffness matrix during the finite element solution process. It is also called the uniform tangent modulus or constitutive stiffness matrix, which reflects the contribution of the constitutive model to the overall stiffness of the structure.

[0019] The term "finite element method" used in this paper refers to an efficient numerical method for solving problems in continuum mechanics. By discretizing and assembling the structure into elements, partial differential equations are transformed into a system of linear equations for solution. It is particularly suitable for stress analysis with complex geometries and boundary conditions.

[0020] The term "process and device simulation" as used in this article refers to a computer-aided simulation technology, abbreviated as Technology Computer-Aided Design (TCAD), used to numerically simulate the manufacturing process and electrical characteristics of semiconductor devices.

[0021] The term “stress relaxation” as used in this article refers to the phenomenon that the internal stress of a viscoelastic material gradually decreases over time under constant strain conditions. It is also known as stress relaxation, and its relaxation rate is affected by factors such as temperature, time, and stress state.

[0022] As mentioned above, with the continuous miniaturization of semiconductor device feature sizes, mechanical stress has become one of the important factors affecting their electrical performance. Its impact is mainly reflected in two aspects: first, stress modulates mobility and effective mass by changing the carrier transport environment; second, stress affects the diffusion process of dopant atoms, thereby altering the doping distribution within the device and its final electrical characteristics. Therefore, accurate numerical calculation of the stress field distribution within the device structure is of great significance in the design and process optimization of semiconductor devices.

[0023] In structural stress analysis techniques, numerical simulations of device structures are typically performed based on continuum mechanics theory. Specifically, the calculation process begins by meshing the target device structure into finite element units (FEUs), discretizing the continuous structure into multiple FEUs. Then, a mechanical equilibrium relationship is established for each FEU, and a set of discrete algebraic equations for solving the displacement field is formed by jointly solving the equilibrium equations, geometric equations, and material constitutive equations. The equilibrium equations describe the force balance within the device structure; the geometric equations describe the geometric mapping between nodal displacements and strains; and the constitutive equations describe the relationship between stress and strain in the material under stress. By solving these coupled equations, the displacement distribution of the device structure can be obtained, and further, the stress distribution results can be derived.

[0024] In semiconductor device manufacturing, device structures typically undergo high-temperature processing steps, such as annealing or heat treatment. Under high-temperature environments, some dielectric materials (such as oxides or nitrides) exhibit time-varying mechanical response characteristics under sustained stress; that is, the internal stress of the material gradually releases or decays over time. This process is related to the time-dependent mechanical behavior of the material. In numerical simulations, this type of behavior is usually described using viscoelastic constitutive relations.

[0025] In related technologies, viscoelastic constitutive models are typically used to model materials to describe their time-dependent mechanical behavior. For example, Maxwell-type models are used to describe the stress decay process over time in materials under constant temperature conditions. In finite element simulations, these models usually characterize stress relaxation behavior by setting a fixed viscosity parameter and treating time as the sole influencing factor.

[0026] However, in actual semiconductor manufacturing environments, the mechanical response of materials is also influenced by both temperature field distribution and local stress states. For example, during high-temperature annealing, the presence of temperature gradients and stress concentration effects in different regions can cause changes in the local stress release rate of the material, resulting in significant nonlinear viscoelastic behavior. In such cases, if a time-dependent linear viscoelastic model is still used for calculation, it will be difficult to accurately reflect the true mechanical response of the material under complex process conditions. This leads to discrepancies between the stress distribution results obtained from finite element analysis and the actual process behavior, reducing the accuracy of simulation results in device performance analysis.

[0027] In view of this, a scheme for structural stress analysis is proposed. According to this scheme, the temperature and stress state of the target material in the target structure are obtained. Then, the viscosity parameter of the target material is determined based on the temperature and stress state; this viscosity parameter is influenced by both temperature and stress state, rather than being merely a constant. Furthermore, a model of the target material is constructed based on this viscosity parameter. This model represents the relationship between the stress and strain states of the target material, and this relationship is related to both temperature and stress state, thus enabling the model to reflect the multi-physics coupling effects of temperature, time, and stress state. Finally, the stress distribution of the target material in the target structure is determined based on this model.

[0028] The above approach allows the viscosity parameter in the material model to be treated not only as a fixed constant, but also in relation to both temperature and stress state, thus introducing the state-dependent characteristics of the material under different process conditions at the modeling level. Furthermore, this model can be used to describe the stress response changes of the target material over time, enabling the comprehensive consideration of the influence of temperature and stress state changes on the material's mechanical behavior during structural stress analysis. This improves the ability to describe the stress distribution behavior of the target structure under complex process conditions and enhances the adaptability of the structural stress analysis results to actual process environments.

[0029] The following describes various examples of this scheme in further detail with reference to the accompanying drawings.

[0030] Figure 1 A schematic diagram of example environment 100 is shown. (e.g.) Figure 1 As shown, the example environment 100 includes a device structure 120, an electronic device 110, and a calculation result 130. The electronic device 110 can receive data corresponding to the device structure 120 (such as device geometric data, material property data, temperature distribution data, initial stress data, etc.), and process and calculate this data to generate the calculation result 130 (such as stress distribution result, strain distribution result, etc.).

[0031] Electronic 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, handheld computers, portable gaming terminals, VR / AR devices, personal communication system (PCS) devices, personal navigation devices, personal digital assistants (PDAs), audio / video players, digital cameras / camcorders, positioning devices, television receivers, radio receivers, e-book devices, gaming devices, or any combination thereof, including accessories and peripherals of these devices or any combination thereof. In some cases, electronic device 110 may also support any type of user-facing interface (such as "wearable" circuitry).

[0032] In some situations, electronic device 110 can communicate with a remote server. This remote server can be a standalone physical server, a server cluster or distributed system consisting of multiple physical servers, or a cloud server that provides basic cloud computing services such as cloud services, cloud databases, cloud computing, cloud functions, cloud storage, network services, cloud communication, middleware services, domain name services, security services, content delivery networks, and big data and artificial intelligence platforms.

[0033] It should be understood that the structure and function of the various elements in environment 100 are described for illustrative purposes only and do not imply any limitation on the scope of the scheme.

[0034] The following description of the example will continue with reference to the accompanying drawings.

[0035] Figure 2 A flowchart of an example procedure 200 for structural stress analysis is shown, based on several scenarios. Procedure 200 can be implemented at electronic device 110. (See below for reference.) Figure 2 To describe process 200.

[0036] like Figure 2 As shown in block 210, electronic device 110 can acquire the temperature and stress state of the target material in the target structure. In some cases, the target structure can be a device structure or process structure to be mechanically analyzed, such as a metal-oxide-semiconductor field-effect transistor (MOSFET) device structure, a gate structure, dielectric layer structure, or multilayer thin film stack structure in a semiconductor device structure. After finite element discretization, the target structure can be divided into multiple finite element elements for subsequent stress calculation.

[0037] The target material can be the material constituting the target structure or a local material region located within the target structure, such as oxide materials, nitride materials, or other dielectric materials. In some examples, the target material can correspond to the element material properties in a finite element mesh, used to characterize the constitutive behavior of that element in mechanical simulations.

[0038] In some cases, temperature can be the process temperature during the manufacturing process, such as the annealing process temperature, the heat treatment process temperature, or the temperature corresponding to other high-temperature process steps. Stress state can refer to the stress distribution within the target material, including but not limited to the stress tensor and its components, such as volumetric stress (the spherical part of the stress tensor) and shear stress (the deviatoric part of the stress tensor). In some embodiments, the stress state may also include the maximum shear stress within the target material to characterize the current stress state of the target material.

[0039] For example, under high-temperature processing conditions, temperature changes affect the stress release capability of the target material, while changes in stress state affect the mechanical response characteristics of the target material under current stress conditions. Therefore, the viscosity parameters of the target material are not only related to temperature but may also change with variations in the internal stress state of the material. By obtaining the corresponding temperature and stress state of the target material, input conditions can be provided for subsequently determining the viscosity parameters of the target material. This allows the subsequently constructed material model to reflect the combined effects of temperature, time, and stress state on the material's mechanical behavior and supports the calculation of subsequent stress distribution results.

[0040] In box 220, electronic device 110 can determine the viscosity parameters of the target material based on temperature and stress state. As previously mentioned, under high-temperature processing conditions, the stress release behavior of the target material is not only time-dependent but also affected by temperature and the internal stress state of the material. Therefore, during stress analysis, the viscosity parameters of the target material can be dynamically determined based on the current temperature and stress state to characterize the mechanical response characteristics of the target material under the current processing conditions and to be used for subsequent material model construction.

[0041] As used herein, the term "viscosity parameter" refers to a parameter used to characterize the viscoelastic behavior of a target material. In some embodiments, the viscosity parameter may include a bulk viscosity parameter, a shear viscosity parameter, or a combination of both. The bulk viscosity parameter can be used to characterize the mechanical response characteristics of the target material when its volume changes, while the shear viscosity parameter can be used to characterize the mechanical response characteristics of the target material when its shape changes.

[0042] In this approach, the viscosity parameter can be determined based on the current temperature and stress state of the target material. Therefore, the viscosity parameter can be a function of temperature and / or stress state, allowing it to be dynamically adjusted according to changes in process conditions and stress state. In this way, the subsequently constructed material model can reflect the changes in the mechanical behavior of the target material under different temperature conditions and stress states, improving the characterization ability of the stress release process.

[0043] In some cases, the stress state may include the maximum shear stress within the target material, and the viscosity parameter may include the shear viscosity parameter. Electronic device 110 can determine the shear viscosity parameter based on temperature and the maximum shear stress.

[0044] It should be noted that for some dielectric materials within the target material, such as oxide or nitride materials, under high-temperature processing conditions, their stress release behavior mainly manifests as a shear relaxation process caused by shape changes in the internal structure of the material. Therefore, in stress analysis, the shear viscosity parameter usually has a more significant impact on the material's mechanical response. In contrast, while the bulk viscosity parameter may also be affected by temperature and stress state, its impact on stress distribution results is relatively small. Therefore, in some cases, it is possible to focus on dynamically updating the shear viscosity parameter to characterize the viscoelastic behavior of the target material under current processing conditions.

[0045] In some cases, the electronic device 110 can first determine a first viscosity parameter based on temperature, and then adjust the first viscosity parameter based on the maximum shear stress to determine the final shear viscosity parameter. The first viscosity parameter can be understood as a temperature-related fundamental viscosity parameter, used to reflect the basic flow characteristics of the target material under the current temperature conditions; the adjustment process corresponding to the maximum shear stress can be used to reflect the nonlinear response characteristics of the material under different stress states.

[0046] In some cases, the electronic device 110 can determine the thermal activation relationship of the target material based on preset material parameters corresponding to the target material. Furthermore, the electronic device 110 can determine a first viscosity parameter based on the thermal activation relationship and temperature.

[0047] The term "thermal activation relation" as used herein refers to a temperature-dependent relationship describing the correspondence between temperature changes and changes in material viscosity. In some embodiments, the thermal activation relation may be described using an Arrhenius relation. For media materials such as oxides and nitrides, increased temperature promotes the rearrangement of the internal structure of the material, making it more susceptible to stress relaxation; therefore, the primary viscosity parameter may decrease with increasing temperature. In other words, at higher temperatures, the target material experiences faster stress release, while at lower temperatures, the target material maintains a higher viscosity level.

[0048] In some cases, the electronic device 110 can also adjust the first viscosity parameter based on the maximum shear stress. Specifically, the electronic device 110 can determine an adjustment coefficient based on the ratio between the maximum shear stress and the shear stress threshold of the target material, wherein the shear viscosity parameter decreases as this ratio increases. The term "shear stress threshold" as used herein refers to the characteristic stress value used to characterize the target material at which a significant nonlinear mechanical response begins, also known as the critical shear stress. When the maximum shear stress within the target material approaches or exceeds this threshold, the stress release behavior of the material is significantly enhanced, resulting in a decrease in the corresponding shear viscosity parameter.

[0049] Furthermore, the electronic device 110 can multiply the first viscosity parameter by an adjustment coefficient to obtain the final shear viscosity parameter. In this way, the influence of temperature on the basic flow characteristics of the material and the influence of stress on the nonlinear response characteristics of the material can be uniformly characterized.

[0050] In some cases, the electronic device 110 can determine the shear viscosity parameter using the following formula:

[0051] (1), Where T represents temperature, and η(T) represents the first viscosity parameter at temperature T. This represents the adjustment factor, and k represents a preset physical constant, such as the Boltzmann constant. and This represents the preset material parameters corresponding to the target material. Indicates the shear stress threshold. This represents the maximum shear stress.

[0052] As shown in equation (1), the shear viscosity parameter is jointly determined by the temperature-dependent first viscosity parameter and the adjustment coefficient related to the maximum shear stress. The temperature-dependent part is used to characterize the change in the stress relaxation ability of the material with temperature changes, while the adjustment coefficient is used to characterize the nonlinear response behavior of the material under different stress states.

[0053] Furthermore, when the maximum shear stress is relatively small compared to the shear stress threshold, the adjustment coefficient is close to 1, and the shear viscosity parameter is mainly determined by temperature. As the maximum shear stress gradually increases and approaches or exceeds the shear stress threshold, the adjustment coefficient gradually decreases, thereby significantly reducing the shear viscosity parameter. Thus, the stress release behavior of the material in high-stress regions can be enhanced.

[0054] By employing the above methods, the viscosity parameter can simultaneously respond to changes in temperature and stress state, thereby achieving a unified description of the viscoelastic behavior of the target material under the coupled effects of multiple process conditions. During the numerical solution process, this state-dependent characteristic allows the model parameters to be dynamically updated with each calculation iteration, thus avoiding separate parameter calibration for different process conditions and improving the model's applicability and computational consistency. Furthermore, because the model can more accurately characterize the material softening and stress relaxation behavior in local high-stress regions, it can reduce the number of global iteration corrections caused by local stress prediction errors, thereby improving the convergence efficiency of the finite element numerical solution process to a certain extent.

[0055] In box 230, electronic device 110 can construct a model of the target material based on viscosity parameters. This model can be used to characterize the mechanical response relationship of the target material under different state conditions. The mechanical response relationship includes the correspondence between stress and strain states, and this correspondence is associated with information such as temperature, time, and stress state.

[0056] In some cases, the model may include a first correlation term and a second correlation term. The first correlation term represents the relationship between the volume change of the target material and the volumetric component of the stress; the second correlation term represents the relationship between the shape change of the target material and the shear component of the stress. Accordingly, the viscosity parameters may include a volumetric viscosity parameter related to the volume change and a shear viscosity parameter related to the shape change.

[0057] It should be noted that the deformation of a target material under stress can generally be decomposed into two independent deformation forms: volume change and shape change. Volume change corresponds to the overall expansion or compression of the material, in which case the material's shape remains essentially unchanged; shape change corresponds to the change in shape of the material while its total volume remains essentially constant. Therefore, mechanical response relationships corresponding to different deformation types can be established separately to describe the response behavior of the target material under different deformation modes.

[0058] In some cases, the electronic device 110 can construct a first correlation term based on the bulk modulus of the target material, and a second correlation term based on the shear modulus and shear viscosity parameters of the target material. The second correlation term describes the time-dependent response characteristics of the target material during shape changes.

[0059] In some examples, for semiconductor dielectric materials such as oxides and nitrides, the stress relaxation process under high-temperature processing conditions mainly manifests as shear relaxation behavior caused by shape adjustment of the material's internal structure. Therefore, the shear viscosity parameter determined based on temperature and stress state can be introduced into the second correlation term to describe the nonlinear viscoelastic behavior of the material under different temperature and stress states. For example, the mechanical response corresponding to volume change can be characterized using elasticity, while the mechanical response corresponding to shape change can be characterized using viscoelasticity, thus enabling the model to more specifically reflect the main stress release behavior of the target material during actual processing.

[0060] In some cases, the strain state can include a strain rate tensor. Volumetric changes are represented by the spherical tensor part of the strain rate tensor, while shape changes are represented by the partial tensor part. It should be noted that during numerical simulation, the strain rate tensor can be calculated from the displacement changes between two adjacent calculation steps, for example, by differentiating the displacement difference between the current and previous time steps. Therefore, the strain rate can represent the rate of change of strain over time, enabling the material model to reflect the response differences of the target material under different deformation rates.

[0061] In some cases, electronic device 110 can be modeled using the following formula:

[0062] (2), Where K represents the bulk modulus and G represents the shear modulus; The volumetric portion representing stress, The shear portion of the stress. The spherical tensor portion representing the strain rate tensor. This represents the partial tensor portion of the strain rate tensor. This represents the volumetric viscosity parameter. This represents the shear viscosity parameter.

[0063] As can be seen from equation (2), this model decomposes the mechanical response of the material into two parts: volume change and shape change, and describes them separately. Among them, the volume part is mainly used to characterize the response characteristics of the material under uniform compression or expansion, and the shear part is mainly used to characterize the response characteristics of the material during shape change.

[0064] Furthermore, the model describes material behavior in the form of "stress change rate + stress decay term = strain rate driving term", where "stress change rate" corresponds to the change of internal stress in the material over time, "stress decay term" describes the stress release process caused by viscous flow in the material under high temperature conditions, and "strain rate driving term" reflects the influence of external deformation loading on the material.

[0065] The model constructed in this way makes the stress response of the material depend not only on the current deformation state, but also explicitly on the deformation process over time, i.e., the rate at which deformation occurs. Therefore, in the finite element numerical solution process, the internal stress state of the material can be updated step by step over time, thus more realistically reflecting the dynamic evolution process of the gradual accumulation and release of material stress over time under high-temperature processing conditions.

[0066] In some cases, the model can degenerate into a linear elastic constitutive model when the temperature is below a certain temperature threshold or the stress release time of the target material is less than a certain time threshold. For example, when the temperature is below a certain temperature threshold, the thermal motion of atoms inside the material is weak, and the stress mainly exhibits a reversible elastic deformation response. In this case, the model degenerates into a linear elastic behavior described only by the elastic modulus. When the stress release time of the material is much smaller than the time scale of the process, the internal stress of the material can be released in a very short time, and the viscous effect is no longer significant. In this case, the model is equivalent to a purely elastic isotropic model.

[0067] This mechanism allows the proposed solution to automatically switch between different material mechanics description methods under varying process conditions. Under low-temperature or short-duration loading conditions, the model does not incorporate viscoelastic-related time evolution calculations, thus reducing unnecessary iterative calculations. Under high-temperature or long-duration loading conditions, viscoelastic response is used to describe stress changes over time. This enables the model to cover nonlinear mechanical behavior under complex process conditions while maintaining computational efficiency and stability consistent with traditional linear elastic simulation methods under simple conditions, thereby achieving adaptive modeling and solving for different process scenarios.

[0068] In box 240, electronic device 110 can determine the stress distribution of the target material in the target structure based on the model. Specifically, this process is used to convert the mechanical response of the target structure under given process temperature and load conditions into stress distribution results at various locations within the structure through numerical calculation, thereby characterizing the changes in the stress state of the target structure during the process.

[0069] In some cases, the electronic device 110 can gradually obtain the stress distribution results through model and numerical solution processes. For example, firstly, the model is used to determine the material stiffness characteristics of the target material under the current state; then, based on the material stiffness characteristics, the deformation results of the target structure under the current conditions are solved; then, based on the deformation results, the strain state of the target material is calculated; finally, the stress distribution results corresponding to the target material are obtained by combining model updates.

[0070] In some examples, the above solution process can be implemented using the finite element method. Before computation, the target structure can be divided into multiple finite computational elements. Each computational element represents a local material region within the target structure and is assigned corresponding material parameters to describe the response characteristics of that local region in the mechanical calculation. In this way, a continuous structure can be transformed into a discrete computational problem for numerical solution.

[0071] After discretization and unit assembly, the mechanical problem of the overall structure can be transformed into a problem with nodal displacements as unknowns. The overall response of the structure is determined by both the "structural resistance to deformation" and the "external loads". The structural resistance to deformation is characterized by the stiffness matrix, while the external loads and internal stresses introduced during the manufacturing process are characterized by the load terms.

[0072] Furthermore, the formation of the stiffness matrix can include contributions from two parts: one part describes the relationship between structural geometric deformation and displacement, and the other part describes the material's resistance to deformation. The latter corresponds to the material stiffness term, which can be determined by the model constructed above. For example, during the finite element solution process, the electronic device 110 can iteratively solve for the nodal displacement increments at each time step and calculate the strain increments at each integration point based on the displacement increments. Subsequently, in each iteration, the model is invoked to calculate the stress update value based on the strain increment, temperature, and historical stress state at the current integration point, while simultaneously determining the consistent tangent modulus corresponding to the current state to update the material stiffness matrix.

[0073] In some cases, solving for the displacement of the target structure may include: obtaining the initial internal forces and boundary constraints acting on the target structure, and calculating the displacement distribution of the structure based on the material stiffness term, the initial internal forces, and the boundary constraints. Boundary constraints are used to restrict the overall translation or rotation of the structure, thereby ensuring the uniqueness of the displacement solution and enabling the numerical calculation to converge stably.

[0074] Within the current solution framework, simply replacing the calculation process of the material stiffness term with the model calculation process of this scheme allows for the introduction of the nonlinear mechanical behavior of the target material without altering the overall solution flow, thus ensuring compatibility with existing finite element calculation systems. Subsequently, the structural displacement distribution is obtained by solving this system of equations, and the structural strain distribution is calculated based on the displacement results. Finally, the strain results are input into the constitutive model to obtain the corresponding stress distribution results.

[0075] Considering the changes in the process over time, the entire calculation process can be divided into multiple consecutive time steps for iterative solution. In each time step, the electronic device 110 first calculates the deformation change at the current time based on the structural deformation results of the previous time step, and obtains the strain change rate accordingly; then, it updates the material parameters based on the current temperature conditions and the current stress state, and calculates the material stiffness term corresponding to the current time step; then, it solves for the structural displacement and strain of the current time step based on the updated material stiffness term; finally, it calculates the stress distribution result at the current time step through the constitutive model, and uses this result as the initial state for the calculation of the next time step.

[0076] By using the above method, the stress calculation process can be gradually advanced over time, so that the stress release, accumulation and redistribution process of the material under high temperature process conditions can be continuously reflected in the numerical solution, thereby obtaining the stress distribution result of the target structure evolving with process time.

[0077] The following is for reference. Figures 3A to 3D A verification example of this scheme is provided. To verify the applicability of the constitutive model described in this scheme in semiconductor process stress simulation, a multi-material device structure is constructed and comparative simulation analysis is performed under different temperature and stress release time conditions to observe the evolution law of stress with changes in process conditions.

[0078] Figure 3A A schematic diagram of the semiconductor device structure 310 is shown. (As shown) Figure 3A As shown, the device structure 310 corresponds to the cross-sectional structure of a PMOS device in actual manufacturing processes. It contains various material regions, such as monocrystalline silicon, polycrystalline silicon, high-dielectric-constant materials, and dielectric layers (e.g., oxides, nitrides). During simulation, the structure can be meshed using finite element methods, and corresponding mechanical constitutive models can be assigned to different material regions for subsequent stress calculations.

[0079] Figure 3B A contour plot of the stress field distribution 320 under certain conditions is shown. For example... Figure 3B As shown, the stress field distribution 320 of the XX component (e.g., the normal stress component in the X direction) corresponds to the calculation results under high-temperature conditions and a relaxation time of 0 s. At this time, the material basically does not undergo time-dependent stress relaxation behavior, and the overall response exhibits an instantaneous elastic state; therefore, it can be used as the initial stress reference distribution. Figure 3B In the diagram, different colored areas correspond to different material types (such as Silicon, Oxide, Nitride, etc.), and the stress at the material interface exhibits a zonal variation characteristic.

[0080] Figure 3C Graph 330 shows the effect of relaxation time on stress in viscoelastic materials under various conditions. For example... Figure 3C As shown in Figure 330, the stress distribution results under different relaxation times at a constant temperature of 1000°C are obtained. The horizontal axis represents the spatial location within the device structure, and the vertical axis represents the stress component values. It can be observed that as the relaxation time gradually increases from 0s to 100s, the overall stress level gradually decreases, the tensile stress region converges towards zero, and the compressive stress amplitude decreases simultaneously, indicating that the internal stress of the material is gradually released over time. At the material interface, the curve shows a significant abrupt change. This location corresponds to the interface between different material regions, and the stress difference arises from the discontinuity of the constitutive parameters of different materials. This phenomenon is consistent with the element attribute switching in the finite element discrete model.

[0081] Figure 3D Graph 340 shows the effect of temperature on the stress of viscoelastic materials under various conditions. For example... Figure 3D As shown in Figure 340, the stress distribution results under different process temperatures under a fixed relaxation time of 1s are obtained. The horizontal axis represents spatial location, and the vertical axis represents stress component values. It can be observed that as the temperature increases from 800°C to 1100°C, the overall stress level gradually decreases and converges towards zero, indicating that increasing the temperature can accelerate the stress relaxation process inside the material, allowing for more complete stress release.

[0082] The comparative simulation results from the two sets above demonstrate that the model constructed in this scheme can stably characterize the stress evolution process of materials at different temperatures and time scales, maintaining a consistent stress release trend across a wide process window. Therefore, it is suitable for process stress analysis and TCAD simulation calculations of multi-material structures in semiconductor devices. Compared to traditional linear constitutive models, this model can more accurately reflect the stress variation law under the combined effects of temperature and time, thereby improving the stability of stress prediction in multi-material interface regions and the engineering applicability of the simulation results.

[0083] Figure 4 A block diagram of an electronic device 400 in which one or more examples may be implemented is shown. It should be understood that... Figure 4 The electronic device 400 shown is merely exemplary and should not be construed as limiting the functionality and scope of the examples described herein. Figure 4 The illustrated electronic device 400 can be used to implement the electronic device 110 discussed above.

[0084] like Figure 4 As shown, electronic device 400 is in the form of a general-purpose electronic device. Components of electronic device 400 may include, but are not limited to, one or more processors 410 or processing units, memory 420, 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 may be a physical or virtual processor and is capable of performing various processes according to programs stored in memory 420. In a multiprocessor system, multiple processing units execute computer-executable instructions in parallel to improve the parallel processing capability of electronic device 400.

[0085] Electronic device 400 typically includes multiple computer storage media. Such media can be any available media accessible to electronic device 400, including but not limited to volatile and non-volatile media, removable and non-removable media. Memory 420 can be volatile memory (e.g., registers, cache, random access memory (RAM)), non-volatile memory (e.g., read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory), or some combination thereof. Storage device 430 can be a removable or non-removable medium and can include machine-readable media, such as flash drives, disks, or any other media that can be used to store information and / or data (e.g., training data for training) and can be accessed within electronic device 400.

[0086] Electronic device 400 may further include additional removable / non-removable, volatile / non-volatile storage media. Although not explicitly stated... Figure 4 As shown, disk drives for reading from or writing to removable, non-volatile disks (e.g., "floppy disks") and optical disk drives for reading from or writing to removable, non-volatile optical disks can be provided. In these cases, each drive can be connected to a bus (not shown) via one or more data media interfaces. Memory 420 may include computer program product 425 having one or more program modules configured to perform various methods or actions of various embodiments of this disclosure.

[0087] The communication unit 440 enables communication with other electronic devices via a communication medium. Additionally, the functionality of the components of the electronic device 400 can be implemented using a single computing cluster or multiple computing machines capable of communicating via communication connections. Therefore, the electronic device 400 can operate in a networked environment using logical connections to one or more other servers, networked personal computers (PCs), or another network node.

[0088] Input device 450 can be one or more input devices, such as a mouse, keyboard, trackball, etc. Output device 460 can be one or more output devices, such as a monitor, speaker, printer, etc. Electronic device 400 can also communicate with one or more external devices (not shown) via communication unit 440 as needed. These external devices include storage devices, display devices, etc., and can communicate with one or more devices that enable user interaction with electronic device 400, or with any device that enables electronic device 400 to communicate with one or more other electronic devices (e.g., network card, modem, etc.). Such communication can be performed via input / output (I / O) interface (not shown).

[0089] According to an exemplary implementation of this disclosure, a computer-readable storage medium is provided that stores one or more computer instructions, wherein one or more computer instructions are executed by a processor to implement the methods described above.

[0090] Various aspects of this disclosure are described herein with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products implemented according to this disclosure. It should be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer-readable program instructions.

[0091] These computer-readable program instructions can be provided to a processing unit of a general-purpose computer, a special-purpose computer, or other programmable data processing apparatus to produce a machine such that, when executed by the processing unit of the computer or other programmable data processing apparatus, they create means for implementing the functions / actions specified in one or more blocks of the flowchart and / or block diagram. These computer-readable program instructions can also be stored in a computer-readable storage medium that causes a computer, programmable data processing apparatus, and / or other device to operate in a particular manner. Thus, the computer-readable medium storing the instructions comprises an article of manufacture that includes instructions for implementing aspects of the functions / actions specified in one or more blocks of the flowchart and / or block diagram.

[0092] Computer-readable program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other device to cause a series of operational steps to be performed on the computer, other programmable data processing apparatus, or other device to produce a computer-implemented process, thereby causing the instructions that execute on the computer, other programmable data processing apparatus, or other device to perform the functions / actions specified in one or more boxes of a flowchart and / or block diagram.

[0093] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of this disclosure. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of an instruction, which contains one or more executable instructions for implementing the specified logical function. In some alternative implementations, the functions indicated in the blocks may occur in a different order than those indicated in the drawings. For example, two consecutive blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, may be implemented using a dedicated hardware-based system that performs the specified function or action, or using a combination of dedicated hardware and computer instructions.

[0094] Various implementations of this disclosure have been described above. The foregoing description is exemplary and not exhaustive, nor is it limited to the disclosed implementations. Many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the described implementations. The terminology used herein is chosen to best explain the principles, practical applications, or improvements to technology in the market, or to enable others skilled in the art to understand the implementations disclosed herein.

Claims

1. A method for structural stress analysis, characterized in that, include: Obtain the temperature and stress state of the target material in the target structure; Determine the viscosity parameters of the target material based on temperature and stress state; A model of the target material is constructed based on viscosity parameters. The model is used to represent the relationship between the stress and strain state of the target material, where the relationship is related to temperature and stress state. as well as Based on the model, the stress distribution of the target material in the target structure is determined.

2. The method according to claim 1, characterized in that, The stress state includes the maximum shear stress within the target material, the viscosity parameter includes the shear viscosity parameter, and determining the viscosity parameter includes: The shear viscosity parameter is determined based on the temperature and the maximum shear stress.

3. The method according to claim 2, characterized in that, Determining the shear viscosity parameter based on the temperature and the maximum shear stress includes: The first viscosity parameter is determined based on the temperature; and The first viscosity parameter is adjusted based on the maximum shear stress to determine the shear viscosity parameter.

4. The method according to claim 3, characterized in that, Adjusting the first viscosity parameter based on the maximum shear stress includes: An adjustment coefficient is determined based on the ratio between the maximum shear stress and the shear stress threshold of the target material, wherein the shear viscosity parameter decreases as the ratio increases; and The first viscosity parameter is multiplied by the adjustment coefficient to obtain the shear viscosity parameter.

5. The method according to claim 3, characterized in that, Determining the first viscosity parameter includes: The thermal activation relationship of the target material is determined based on the preset material parameters corresponding to the target material. Based on the thermal activation relationship and the temperature, the first viscosity parameter is determined, wherein the first viscosity parameter decreases as the temperature increases.

6. The method according to claim 4, characterized in that, The shear viscosity parameter is determined according to the following formula: Where T represents the temperature, and η(T) represents the first viscosity parameter at temperature T. This represents the adjustment coefficient, where k represents a preset physical constant. and This represents the preset material parameters corresponding to the target material. This represents the shear stress threshold. This represents the maximum shear stress.

7. The method according to claim 1, characterized in that, The model includes: A first correlation term, which represents the relationship between the volume change of the target material and the volume fraction of the stress; and The second correlation term represents the relationship between the shape change of the target material and the shear portion of the stress. The viscosity parameter includes a volumetric viscosity parameter related to the volume change and a shear viscosity parameter related to the shape change.

8. The method according to claim 7, characterized in that, The construction of the model includes: Based on the bulk modulus of the target material, the first correlation term is constructed; and Based on the shear modulus and shear viscosity parameters of the target material, the second correlation term is constructed.

9. The method according to claim 8, characterized in that, The strain state includes a strain rate tensor, the volume change is represented by the spherical tensor portion of the strain rate tensor, and the shape change is represented by the partial tensor portion of the strain rate tensor.

10. The method according to claim 9, characterized in that, The model is constructed based on the following formula: Wherein, K represents the bulk modulus, and G represents the shear modulus; This represents the volumetric portion of the stress. This represents the shear portion of the stress. The spherical tensor portion of the strain rate tensor represents this. This represents the partial tensor portion of the strain rate tensor. This represents the volumetric viscosity parameter. This represents the shear viscosity parameter.

11. The method according to claim 1, characterized in that, The determination of the stress distribution results includes: The model is used to determine the material stiffness term corresponding to the target material; The displacement of the target structure is determined based on the material stiffness term. Based on the displacement, determine the strain state of the target material; and Based on the strain state, the stress distribution result is determined using the model.

12. The method according to claim 1, characterized in that, The target material includes a dielectric material in a semiconductor device, the dielectric material including at least one of oxides and nitrides, and the target structure includes a semiconductor device structure.

13. An electronic device, characterized in that, include: At least one processing unit; as well as At least one memory, coupled to the at least one processing unit and storing instructions for execution by the at least one processing unit, the instructions causing the electronic device to perform the method according to any one of claims 1 to 12 when executed by the at least one processing unit.

14. A computer-readable storage medium, characterized in that, It stores a computer program that can be executed by a processor to implement the method according to any one of claims 1 to 12.

15. A computer program product, characterized in that, The computer program product is tangibly stored in a computer storage medium and includes computer-executable instructions that, when executed by a device, cause the device to perform the method according to any one of claims 1 to 12.

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