Photolithography process window analysis method, system, and readable storage medium

Abstract

The present application relates to a kind of photolithography process window analysis method, system and readable storage medium, method includes: obtaining critical dimension measurement data and according to preset filter point rule carries out filter point processing;Based on the data after filter point constructs antisymmetry fitting function, respectively establishes the first, second fitting model with focus energy as independent variable and with exposure energy as independent variable, respectively calculates the fitting root mean square error of both and selects the smaller as boundary fitting function;According to boundary fitting function, solve theoretical boundary, and according to measurement data, determine actual boundary, take intersection and generate process effective area;With the minimum target of the area of ellipse covering this area, solve ellipse parameter using differential evolution algorithm, the parameter corresponding to the center of ellipse is output as best focus energy and best exposure energy.The present application can realize high-precision, self-controllable process window analysis, effectively replace foreign commercial software, improve analysis precision and efficiency.

Description

Technical Field

[0001] This invention relates to the field of semiconductor lithography technology, and in particular to a method, system, and readable storage medium for analyzing lithography process windows. Background Technology

[0002] In semiconductor lithography, the process window refers to the permissible range of variation in focus and exposure energy while ensuring that the critical dimension (CD) meets specifications. Accurately determining the process window is crucial for optimizing lithography process parameters and improving product yield.

[0003] In early process nodes, because the critical dimensions of lithographic patterns changed relatively smoothly, the industry typically used simple mathematical models such as second-order polynomial fitting for process window analysis. These methods were computationally simple and met the basic analytical needs under the then-current process conditions. However, as semiconductor processes have progressed to advanced nodes, the dimensional fluctuations of lithographic patterns exhibit strong nonlinearity, local distortion, and high-order spatial correlations. Traditional second-order fitting methods have become insufficient in accurately reflecting the true characteristics of the process window in terms of modeling accuracy and adaptability, leading to a significant discrepancy between the analysis results and actual process capabilities.

[0004] To address the demands of advanced lithography processes, commercial EDA (Electronic Design Automation) tool vendors have launched more sophisticated solutions. For example, Synopsys' S-Litho platform incorporates an advanced Process Window Analysis (PWA) algorithm, combined with adaptive nonlinear fitting technology, significantly improving the prediction accuracy of process windows in advanced lithography processes such as extreme ultraviolet (EUV), making it a leading process window analysis tool in the industry. However, as a foreign-dominated EDA tool, S-Litho suffers from high licensing fees, limited licensing resources, and reliance on suppliers for technological iteration, making it difficult to meet the needs of large-scale deployment and continuous optimization by domestic semiconductor manufacturers. Furthermore, in the current domestic EDA ecosystem, there are no functionally equivalent alternatives, and key technological gaps remain. This dependence on foreign technology not only increases operating costs for enterprises but also, to some extent, hinders the independent development of advanced process research and manufacturing in China.

[0005] Besides relying on commercial software tools, engineers currently still primarily analyze Focus-Exposure Matrix (FEM) data manually in actual production. Specifically, engineers typically determine the process window based on Bossung charts and critical dimension thresholds through simple range selection. For example, in a wafer CD map, a rectangle is drawn to select an area within ±10% of the CD Target to determine the approximate process window range. For the selection of the Best Focus, engineers compare the critical dimension deviations in the three central columns of different patterns and set the optimal focus position based on personal experience; while the Best Exposure Energy is empirically set within the determined Best Focus Energy and approximate process window range, based on the magnitude and trend of critical dimension values. The entire analysis process lacks clear quantitative rules and a systematic algorithmic flow, and involves a significant amount of subjective judgment. The analysis results between different engineers may vary considerably, making it difficult to guarantee the accuracy and consistency of process window determination. Furthermore, manual analysis is inefficient and cannot meet the needs of rapid iteration and large-scale production at advanced process nodes.

[0006] In summary, current technologies, whether traditional simple mathematical models, foreign commercial EDA tools, or manual empirical analysis methods, cannot simultaneously meet the requirements of high precision, independent controllability, objective quantification, and efficient automation. Therefore, there is an urgent need to develop a high-precision and independently controllable method for analyzing lithography process windows. This method would enhance the ability to model complex process effects, break the dependence on foreign software, and support the sustainable development of advanced process research and manufacturing. Summary of the Invention

[0007] The purpose of this invention is to provide a method, system, and readable storage medium for analyzing photolithography process windows, in order to solve the problems existing in the prior art.

[0008] To achieve the above objectives, the present invention provides a method for analyzing photolithography process windows, comprising:

[0009] Acquire key dimension measurement data under different focusing energies and exposure energies during the photolithography process, and perform filter processing on the measurement data according to preset filter rules;

[0010] Based on the key dimension measurement data after filter point processing, an antisymmetric fitting function is constructed. A first fitting model with the focusing energy as the independent variable and a second fitting model with the exposure energy as the independent variable are established respectively. The root mean square error of the first fitting model and the second fitting model is calculated respectively. The fitting model with the smaller error is selected as the boundary fitting function of the target process window.

[0011] The theoretical boundary is determined based on the boundary fitting function of the target process window, and the actual boundary is determined based on the data points in the key dimension measurement data that meet the key dimension specifications. The intersection of the theoretical boundary and the actual boundary is used to generate the effective process area.

[0012] With the goal of minimizing the area of ​​the ellipse covering the effective region of the process, the parameters of the ellipse are solved in a two-dimensional parameter space composed of the focusing energy and the exposure energy using the differential evolution algorithm. The focusing energy and exposure energy corresponding to the center of the ellipse obtained by the solution are taken as the optimal focusing energy and the optimal exposure energy, respectively, and the process window analysis results are output.

[0013] Optionally, the preset filter point rule is a statistical rule of the average value plus three times the standard deviation, and supports engineers to manually correct key dimension data based on process experience.

[0014] Optionally, the antisymmetric fitting function is a fourth-order antisymmetric fitting function.

[0015] Optionally, the first fitting model is a fractional function with focusing energy F and exposure energy E as variables, expressed as:

[0016]

[0017] The expression for the second fitting model is:

[0018]

[0019] in, to The coefficients are to be fitted.

[0020] Optionally, the theoretical boundary is the solution set of focusing energy and exposure energy obtained by substituting the upper and lower limits of the key dimensions into the boundary fitting function of the target process window.

[0021] Optionally, the actual boundary is the area boundary defined by the focusing energy and exposure energy corresponding to the data points in the critical dimension measurement data that meet the critical dimension specification requirements.

[0022] Optionally, the step of solving for the parameters of the ellipse in a two-dimensional parameter space composed of the focusing energy and the exposure energy using the differential evolution algorithm includes:

[0023] A set of elliptic parameters is randomly initialized in the two-dimensional parameter space as an initial population. The elliptic parameters are iteratively updated through mutation, crossover and selection operations. The ellipse area is used as the fitness function. When the preset convergence condition is met, the optimal elliptic parameters are output.

[0024] Optionally, the method further includes:

[0025] The output of the optimal focusing energy and the optimal exposure energy are applied to the adjustment and optimization of the focusing and exposure parameters of the photolithography process.

[0026] Based on the same inventive concept, the present invention also provides a photolithography process window analysis system, comprising:

[0027] The data acquisition and processing module is configured to acquire key dimension measurement data under different focusing energies and exposure energies during the photolithography process, and to perform filter processing on the measurement data according to preset filter rules.

[0028] The fitting optimization module is configured to construct an antisymmetric fitting function based on the key dimension measurement data after filter point processing, establish a first fitting model with the focusing energy as the independent variable and a second fitting model with the exposure energy as the independent variable, calculate the root mean square error of the first fitting model and the second fitting model respectively, and select the fitting model with the smaller error as the boundary fitting function of the target process window.

[0029] The boundary intersection module is configured to determine the theoretical boundary based on the boundary fitting function of the target process window, and to determine the actual boundary based on the data points in the key dimension measurement data that meet the key dimension specifications. The intersection of the theoretical boundary and the actual boundary is then used to generate the effective process area.

[0030] The solution module is configured to minimize the area of ​​the ellipse covering the effective region of the process, and use the differential evolution algorithm to solve for the parameters of the ellipse in a two-dimensional parameter space composed of the focusing energy and the exposure energy. The focusing energy and exposure energy corresponding to the center of the ellipse obtained by the solution are respectively taken as the optimal focusing energy and the optimal exposure energy, and the process window analysis results are output.

[0031] Based on the same inventive concept, the present invention also provides a readable storage medium having a computer program stored thereon, which, when executed by a processor, can implement the photolithography process window analysis method as described above.

[0032] The photolithography process window analysis method, system, and readable storage medium provided by this invention have at least one of the following beneficial effects:

[0033] (1) By using an antisymmetric fitting function to perform bidirectional fitting and optimization of key dimension measurement data under different focusing and exposure energies during the photolithography process, a high-precision boundary fitting function is obtained. Then, the intersection of the theoretical boundary and the actual boundary is combined to obtain a reliable effective process region. Finally, the differential evolution algorithm is used to solve for the minimum ellipse covering this region, and the center of the ellipse is taken as the optimal process condition. This scheme can effectively replace foreign commercial software, achieve independent control, and improve analysis accuracy and efficiency.

[0034] (2) The antisymmetric fitting function preferably adopts the fourth order form, which helps to capture the asymmetric characteristics and high-order nonlinear effects of key size changes in the photolithography process, while avoiding the risk of overfitting caused by excessively high order, and achieving a better balance between fitting accuracy and model complexity.

[0035] (3) By adopting a more conservative filter point method of average value plus three times the standard deviation, and giving engineers the ability to manually modify key dimension data, it helps to retain effective process information while automatically removing abnormal data, and allows engineers to flexibly adjust the filter point results according to the actual situation, taking into account both the efficiency and reliability of data processing.

[0036] (4) By minimizing the area of ​​the ellipse covering the region, the differential evolution algorithm is used for global optimization, which helps to reduce the possibility of getting trapped in local optima and accurately solve for the optimal focusing energy and the optimal exposure energy. Attached Figure Description

[0037] Those skilled in the art will understand that the accompanying drawings are provided to better understand the invention and do not constitute any limitation on the scope of the invention. Wherein:

[0038] Figure 1 A flowchart of a photolithography process window analysis method provided in an embodiment of the present invention;

[0039] Figure 2 The visualization results of process window analysis provided in an embodiment of the present invention. Detailed Implementation

[0040] To make the objectives, technical solutions, and advantages of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0041] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0042] In the description of this invention, it should be understood that the terms "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship commonly used when the product is in use, or the orientation or positional relationship commonly understood by those skilled in the art. They are only used to facilitate the description of this invention and to simplify the description, and are not intended to indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0043] Furthermore, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such an article or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the article or apparatus that includes that element. Those skilled in the art will understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0044] Please refer to Figure 1 This invention provides a method for analyzing photolithography process windows, comprising the following steps:

[0045] S100: Acquire key dimension measurement data under different focusing energy and exposure energy conditions during the photolithography process, and perform filter processing on the measurement data according to the preset filter rules;

[0046] S200. Based on the key dimension measurement data after filter point processing, an antisymmetric fitting function is constructed. A first fitting model with focusing energy as the independent variable and a second fitting model with exposure energy as the independent variable are established respectively. The root mean square error of the first fitting model and the second fitting model are calculated respectively. The fitting model with the smaller error is selected as the boundary fitting function of the target process window.

[0047] S300. Determine the theoretical boundary based on the boundary fitting function of the target process window, and determine the actual boundary based on the data points in the key dimension measurement data that meet the key dimension specifications. Take the intersection of the theoretical boundary and the actual boundary to generate the effective process area.

[0048] S400: With the goal of minimizing the elliptical area covering the effective region of the process, the differential evolution algorithm is used to solve the parameters of the ellipse in a two-dimensional parameter space composed of focusing energy and exposure energy. The focusing energy and exposure energy corresponding to the center of the ellipse obtained by the solution are taken as the optimal focusing energy and optimal exposure energy, respectively, and the process window analysis results are output.

[0049] This invention employs an antisymmetric fitting function to perform bidirectional fitting and optimization of key dimension measurement data under different focusing and exposure energies during photolithography, obtaining a high-precision boundary fitting function. Then, by combining the intersection of the theoretical and actual boundaries, a reliable effective process region is obtained. Finally, a differential evolution algorithm is used to solve for the minimum ellipse covering this region, with the center of the ellipse as the optimal process condition. This approach can effectively replace foreign commercial software, achieving independent control while improving analysis accuracy and efficiency.

[0050] First, execute S100 to acquire key dimension measurement data under different focusing and exposure energy conditions during the photolithography process, and then perform filter processing on the measurement data according to the preset filter rules.

[0051] In photolithography, test patterns are typically formed under different combinations of focusing and exposure energies, and critical dimension measurement data is acquired using metrology equipment. This data forms the basis of the Bossung image. After acquiring the measurement data, due to potential noise or outliers during the measurement process, the measurement data needs to be filtered according to preset filtering rules.

[0052] Preferably, the preset filtering rule is a statistical rule based on the mean plus three standard deviations, and it supports engineers manually correcting critical dimension data based on their process experience. In practice, the mean and standard deviation of all critical dimension measurements are calculated, and data points exceeding the range of the mean plus three standard deviations are identified as outliers and removed. This rule is based on the normal distribution assumption and can effectively remove the vast majority of random noise and outliers. Simultaneously, this invention also supports engineers manually correcting critical dimension data based on their process experience. For example, through a graphical user interface, engineers can observe the Bossung plot, manually delete points that significantly deviate from the trend, or restore points that were automatically filtered out but are actually valid. Manual correction allows engineers to fine-tune the automatic filtering results using domain knowledge.

[0053] In practical application verification, the method of this invention performs similarly to the PWA (Process Window Analysis) in Synopsys' S-Litho platform. Analysis revealed that the main difference lies in the filtering process for critical dimension data. S-Litho's filtering rules are opaque and overly strict, easily leading to the accidental deletion of valid data points. In contrast, this invention employs a more conservative filtering method using the average value plus three times the standard deviation, and provides engineers with the ability to manually modify critical dimension data, effectively suppressing outliers while preserving valid process information to the greatest extent possible. Experimental data shows that, without considering filtering errors, the analysis results of this invention deviate from those of S-Litho by less than 5%. This level of accuracy is sufficient to meet the stringent requirements of advanced lithography process window calculations, ensuring the accuracy of lithography process window calculations.

[0054] Then, S200 is executed. Based on the key dimension measurement data after filter point processing, an antisymmetric fitting function is constructed. A first fitting model with focusing energy as the independent variable and a second fitting model with exposure energy as the independent variable are established respectively. The root mean square error of the first fitting model and the second fitting model are calculated respectively. The fitting model with the smaller error is selected as the boundary fitting function of the target process window.

[0055] In this embodiment, the antisymmetric fitting function refers to a function form that can describe the asymmetric features in the Bossung plot. Specifically, a first fitting model is established with focusing energy as the independent variable, and a second fitting model is established with exposure energy as the independent variable. These two models fit the data from two different directions, reflecting the idea of ​​bidirectional fitting. Then, the root mean square error of the two fitting models is calculated separately; the smaller the error, the higher the fitting accuracy. The fitting model with the smaller error is selected as the boundary fitting function of the target process window. This bidirectional fitting optimization mechanism can adaptively select the fitting direction that is more suitable for the current data distribution, overcoming the limitations of traditional unidirectional symmetric fitting.

[0056] The preferred antisymmetric fitting function is a fourth-order antisymmetric fitting function. In photolithography, the relationship between critical dimensions and focusing and exposure energies typically exhibits complex nonlinearity and is often asymmetric. Fourth-order functions can capture this asymmetry, achieving a better balance between fitting accuracy and computational complexity. Compared to lower-order functions, fourth-order functions better describe the steep edges and plateau regions of the Bossung diagram, reducing fitting errors. Compared to higher-order functions, fourth-order functions are less prone to overfitting, have stronger generalization ability, and require moderate computation.

[0057] In this embodiment, the first fitting model is a fractional function with focusing energy F and exposure energy E as variables, and its expression is:

[0058]

[0059] This expression uses focusing energy as the independent variable and exposure energy in the denominator, reflecting the nonlinear coupling relationship between focusing and exposure.

[0060] The expression for the second fitting model is:

[0061]

[0062] This expression uses exposure energy as the independent variable, with focus energy appearing in the denominator. This fractional structure can more accurately describe the nonlinear response of key dimensions in the Bossung plot as a function of focus and exposure. to The coefficients to be fitted can be solved using methods such as least squares, regularized least squares, or robust regression.

[0063] The aforementioned fractional function form is specifically designed for the characteristics of Bossung maps in photolithography, capable of simultaneously capturing the high-order nonlinear effects of focusing and exposure, as well as the coupling effect between them. Through bidirectional fitting, the same physical process can be described from two different perspectives. Then, by optimizing the root mean square error, the final selected boundary fitting function is ensured to have higher accuracy.

[0064] Next, S300 is executed to determine the theoretical boundary based on the boundary fitting function of the target process window, and to determine the actual boundary based on the data points in the critical dimension measurement data that meet the critical dimension specifications. The intersection of the theoretical boundary and the actual boundary is then used to generate the effective process area.

[0065] After obtaining the boundary fitting function, the boundary of the process window needs to be determined. This invention adopts the method of taking the intersection of the theoretical boundary and the actual boundary. The theoretical boundary is calculated based on the boundary fitting function and the specifications of the critical dimensions, representing the range of process conditions that meet the specifications under the ideal model. The actual boundary is directly determined based on the data points in the measured data that meet the critical dimension specifications, reflecting the actual process capability. Taking the intersection of the theoretical boundary and the actual boundary generates the effective process region. This region satisfies both the prediction of the theoretical model and the constraints of the actual measurement data, thus being more reliable and practical.

[0066] In this embodiment, the theoretical boundary is determined as follows: The upper and lower limits of the critical dimension are substituted into the boundary fitting function of the target process window, respectively, to obtain the solution sets of focusing energy and exposure energy. Specifically, for the upper limit, it is substituted into the boundary fitting function to obtain an equation concerning focusing energy and exposure energy. The solution set of this equation corresponds to a set of points, which constitute part of the theoretical boundary. Similarly, for the lower limit, another solution set is obtained after substitution. Combining these two solution sets forms the complete theoretical boundary. By substituting the upper and lower limits of the specifications into the fitting function, the theoretical boundary accurately reflects the theoretically permissible range of focusing energy and exposure energy under the condition of meeting the critical dimension specifications, providing a reliable theoretical basis for process design.

[0067] The actual boundary is defined by the focusing energy and exposure energy corresponding to the data points in the critical dimension measurement data that meet the critical dimension specifications. In practice, critical dimension specifications typically refer to critical dimension values ​​falling between the upper and lower limits of the specification. Therefore, by traversing all measurement data points and retaining those that meet the critical dimension requirements, the coordinates of these points constitute the effective data point set. The actual boundary can be extracted by performing convex hull calculation or the Alpha Shapes algorithm on these effective data point sets. Alternatively, interpolation can be used to fit surfaces to the effective data points, and then contour lines can be extracted as boundaries; or kernel density estimation can be used to determine the boundaries of high-density regions. The actual boundary is directly based on measured data, reflecting the true process capability and avoiding overly optimistic estimations caused by theoretical model errors. By selecting points that meet the specifications from the measured data and defining the boundaries, the actual boundary objectively reflects the actual achievable process window under current process conditions.

[0068] Finally, S400 is executed, aiming to minimize the elliptical area covering the effective process region. The differential evolution algorithm is used to solve the parameters of the ellipse in a two-dimensional parameter space composed of focusing energy and exposure energy. The focusing energy and exposure energy corresponding to the center of the ellipse obtained by solving are taken as the optimal focusing energy and optimal exposure energy, respectively, and the process window analysis results are output.

[0069] Differential evolutionary algorithm is a population-based global optimization algorithm that continuously evolves the population through mutation, crossover, and selection operations to ultimately find the parameter combination that minimizes the area of ​​the ellipse. The focusing energy and exposure energy corresponding to the center of the ellipse are the optimal focusing energy and optimal exposure energy. The output process window analysis results include optimal process conditions and the effective range of the process.

[0070] In this embodiment, the differential evolution algorithm is used to solve for the parameters of an ellipse in a two-dimensional parameter space composed of focusing energy and exposure energy. Specifically, this includes: randomly initializing a set of ellipse parameters as an initial population in the two-dimensional parameter space. Ellipse parameters may include the ellipse center coordinates, major semi-axis, minor semi-axis, rotation angle, etc. The population size can be set according to the problem complexity, such as 50 to 200 individuals. Then, the ellipse parameters are iteratively updated through mutation, crossover, and selection operations. The mutation operation can adopt a differential strategy, such as DE / rand / 1, that is, for the current individual, three different individuals in the population are selected and differentially weighted to generate a mutation vector. The crossover operation adopts binomial crossover or exponential crossover, mixing the mutation vector with the current individual to generate a trial vector. The selection operation adopts a greedy strategy, comparing the fitness of the trial vector and the current individual, and retaining the individual with better fitness to enter the next generation. The fitness function is defined as the area of ​​the ellipse, and the goal is to minimize this area. The convergence condition can be set to reach the maximum number of iterations or the fitness value changing less than a preset threshold over several consecutive generations. When the convergence condition is met, the optimal ellipse parameters are output. Furthermore, the specific parameters of the Differential Evolutionary Algorithm (DEA) can be adjusted empirically or adaptively. DEA possesses powerful global optimization capabilities, is less prone to getting trapped in local optima, and is particularly suitable for solving nonlinear, multi-peak optimization problems such as minimizing the area of ​​the bounding ellipse. Through parallel search of the population, the algorithm can efficiently explore the entire parameter space and quickly converge to the global optimum. By minimizing the ellipse area, the algorithm ensures that the found process window is both compact and reliable, with the ellipse center representing the optimal process condition and the most robust operating point within the allowable fluctuation range.

[0071] The optimization objective of the differential evolution algorithm can be formally expressed as a constrained optimization mathematical model, whose objective function is the area of ​​an ellipse:

[0072]

[0073] The objective is to minimize this area, specifically by defining the process window using the smallest ellipse that covers all acceptable process points, thereby obtaining the most compact and robust range of process conditions. Decision variables include the optimal exposure energy. Optimal Focused Energy The algorithm must satisfy the following constraints: (The equations are missing from the original text.)

[0074]

[0075] That is, all qualified process points It must fall under the The center point is located inside or on the boundary of an ellipse with axis lengths a and b; simultaneously, the axis length constraints a > 0 and b > 0 must be satisfied; and the center point feasibility constraint must also be satisfied. ∈Area, meaning that the center of the ellipse obtained by solving must be located within the aforementioned effective process area.

[0076] The effective process area is defined by data points that meet critical dimensional specifications, as follows:

[0077]

[0078] in, and These represent the upper and lower boundary fitting functions of the process window, respectively. Both are piecewise functions. Different fourth-order antisymmetric fitting functions are used to describe the relationship between exposure energy and focusing energy according to different focusing energy ranges. and These represent the left and right boundaries or the start / end points of the focused energy, respectively; This indicates the breakpoints or nodes used for piecewise fitting within different focusing energy ranges. This indicates the specifications for critical dimensions.

[0079] To verify the effectiveness of the above algorithm, this embodiment of the invention provides a visualization of the process window analysis results. For example... Figure 2 The graph shows the energy variation with focus position, with the horizontal axis representing focus energy and the vertical axis representing exposure energy. Multiple colored lines represent energy-focus response curves (i.e., Bossung family of graphs) under different process parameters or patterns, with red curves indicating key response boundaries. Based on this, the optimal process window obtained through a differential evolution algorithm is marked with a red ellipse, the center of which is at (0.005, 37.03). This means the algorithm outputs an optimal focus energy of 0.005 and an optimal exposure energy of 37.03. The graph also indicates that the process window area is 7.5%, reflecting the allowable fluctuation range and robustness of process parameters under the current process conditions. The experimental results demonstrate that the method proposed in this invention can automatically and accurately lock a compact and stable process window from complex multi-curve response data and determine the optimal process conditions.

[0080] After outputting the optimal focusing energy and optimal exposure energy, these parameters can be applied to adjust and optimize the focusing and exposure parameters of the lithography process. Specifically, the focal length of the lithography machine can be set to the focal length value corresponding to the optimal focusing energy, and the exposure dose can be set to the dose value corresponding to the optimal exposure energy. Furthermore, these optimal parameters can be used as a benchmark to establish a feedback control system that monitors critical dimensions in real time and dynamically adjusts the focusing and exposure parameters to maintain the stability of the process window. For example, when a critical dimension drift is detected, the required focus and exposure dose can be calculated in reverse based on the offset, achieving closed-loop control. By directly applying the optimal process conditions obtained from the analysis to actual production, automatic optimization of lithography process parameters can be achieved, reducing manual debugging time and trial-and-error costs, and improving product yield and process stability. Simultaneously, data-driven optimization methods can continuously accumulate process knowledge, forming a virtuous cycle and continuously improving the process level.

[0081] Based on the same inventive concept, this invention also proposes a photolithography process window analysis system, including:

[0082] The data acquisition and processing module is configured to acquire key dimension measurement data under different focusing energies and exposure energies during the photolithography process, and to perform filter processing on the measurement data according to preset filter rules.

[0083] The fitting optimization module is configured to construct an antisymmetric fitting function based on the key dimension measurement data after filter point processing. It establishes a first fitting model with focusing energy as the independent variable and a second fitting model with exposure energy as the independent variable, respectively, and calculates the root mean square error of the first fitting model and the second fitting model. The fitting model with the smaller error is selected as the boundary fitting function of the target process window.

[0084] The boundary intersection module is configured to determine the theoretical boundary based on the boundary fitting function of the target process window, and to determine the actual boundary based on the data points in the key dimension measurement data that meet the key dimension specifications. The intersection of the theoretical boundary and the actual boundary is then used to generate the effective process area.

[0085] The solution module is configured to minimize the area of ​​the ellipse covering the effective process region. It uses a differential evolution algorithm to solve for the parameters of the ellipse in a two-dimensional parameter space consisting of the focusing energy and the exposure energy. The focusing energy and exposure energy corresponding to the center of the ellipse obtained by the solution are taken as the optimal focusing energy and the optimal exposure energy, respectively, and the process window analysis results are output.

[0086] Since the lithography process window analysis system provided by this invention belongs to the same inventive concept as the lithography process window analysis method described above, the lithography process window analysis system provided by this invention has all the advantages of the lithography process window analysis method described above. Therefore, the beneficial effects of the lithography process window analysis system provided by this invention will not be described in detail here.

[0087] Based on the same inventive concept, this invention also proposes a readable storage medium storing a computer program, which, when executed by a processor, can realize the above-mentioned photolithography process window analysis method.

[0088] A readable storage medium can be a tangible device capable of holding and storing instructions for use by an instruction execution device, such as, but not limited to, electrical storage devices, magnetic storage devices, optical storage devices, electromagnetic storage devices, semiconductor storage devices, or any suitable combination thereof. More specific examples of readable storage media (a non-exhaustive list) include: portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), static random access memory (SRAM), portable compact disc read-only memory (CD-ROM), digital multifunction disc (DVD), memory sticks, floppy disks, mechanical encoding devices, such as punch cards or recessed protrusions storing instructions thereon, and any suitable combination thereof. The computer programs described herein can be downloaded from the readable storage medium to various computing / processing devices, or downloaded via a network, such as the Internet, local area network, wide area network, and / or wireless network, to an external computer or external storage device. Networks can include copper transmission cables, fiber optic transmissions, wireless transmissions, routers, firewalls, switches, gateway computers, and / or edge servers. Each computing / processing device's network adapter card or network interface receives and forwards a computer program from the network for storage on a readable storage medium within the respective computing / processing device. The computer program used to perform the operations of this invention can be execution instructions, instruction set architecture (ISA) instructions, machine instructions, machine-dependent instructions, microcode, firmware instructions, status setting data, or source code or object code written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Smalltalk, C++, etc., and conventional procedural programming languages ​​such as "C" or similar languages. The computer program can execute entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving remote computers, the remote computer can be connected to the user's computer via any type of network, including a local area network (LAN) or a wide area network (WAN), or it can be connected to an external computer (e.g., via the Internet using an Internet service provider). In some embodiments, electronic circuits, such as programmable logic circuits, field-programmable gate arrays (FPGAs), or programmable logic arrays (PLAs), are personalized by utilizing state information from a computer program. These electronic circuits can execute computer-readable program instructions, thereby realizing various aspects of the present invention.

[0089] Various aspects of the present invention are described herein with reference to flowchart illustrations and / or block diagrams of methods, systems, and computer program products according to embodiments of the invention. 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 a computer program. These computer programs can be provided to a processor 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 processor 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 illustrations and / or block diagrams. These computer programs can also be stored in a readable storage medium that causes a computer, programmable data processing apparatus, and / or other device to operate in a particular manner; thus, the readable storage medium storing the computer program comprises an article of manufacture including instructions for implementing aspects of the functions / actions specified in one or more blocks of the flowchart illustrations and / or block diagrams.

[0090] A computer program 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 computer program executing 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.

[0091] Since the readable storage medium provided by this invention belongs to the same inventive concept as the photolithography process window analysis method described above, the readable storage medium provided by this invention has all the advantages of the photolithography process window analysis method described above. Therefore, the beneficial effects of the readable storage medium provided by this invention will not be described in detail here.

[0092] In summary, this invention provides a method, system, and readable storage medium for analyzing photolithography process windows. It uses an antisymmetric fitting function to perform bidirectional fitting and optimization of key dimension measurement data under different focusing and exposure energies during photolithography, obtaining a high-precision boundary fitting function. Then, by combining the intersection of the theoretical and actual boundaries, a reliable effective process region is obtained. Finally, a differential evolution algorithm is used to solve for the minimum ellipse covering this region, with the center of the ellipse as the optimal process condition. This invention not only improves the accuracy and efficiency of process window analysis but also provides reliable data support for adjusting and optimizing photolithography process parameters.

[0093] The above description is merely a description of preferred embodiments of the present invention and is not intended to limit the scope of the invention in any way. Any changes or modifications made by those skilled in the art based on the above disclosure are within the protection scope of the present invention. Obviously, those skilled in the art can make various modifications and variations to the present invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the present invention and its equivalents, the present invention also intends to include these modifications and variations.

Claims

1. A method for analyzing photolithography process windows, characterized in that, include: Acquire key dimension measurement data under different focusing energies and exposure energies during the photolithography process, and perform filter processing on the measurement data according to preset filter rules; Based on the key dimension measurement data after filter point processing, an antisymmetric fitting function is constructed. A first fitting model with the focusing energy as the independent variable and a second fitting model with the exposure energy as the independent variable are established respectively. The root mean square error of the first fitting model and the second fitting model is calculated respectively. The fitting model with the smaller error is selected as the boundary fitting function of the target process window. The theoretical boundary is determined based on the boundary fitting function of the target process window, and the actual boundary is determined based on the data points in the key dimension measurement data that meet the key dimension specifications. The intersection of the theoretical boundary and the actual boundary is used to generate the effective process area. With the goal of minimizing the area of ​​the ellipse covering the effective region of the process, the parameters of the ellipse are solved in a two-dimensional parameter space composed of the focusing energy and the exposure energy using the differential evolution algorithm. The focusing energy and exposure energy corresponding to the center of the ellipse obtained by the solution are taken as the optimal focusing energy and the optimal exposure energy, respectively, and the process window analysis results are output.

2. The photolithography process window analysis method according to claim 1, characterized in that, The preset filter point rule is a statistical rule of the average value plus three times the standard deviation, and it supports engineers to manually correct key dimension data based on process experience.

3. The photolithography process window analysis method according to claim 1, characterized in that, The antisymmetric fitting function is a fourth-order antisymmetric fitting function.

4. The photolithography process window analysis method according to claim 3, characterized in that, The first fitting model is a fractional function with focusing energy F and exposure energy E as variables, and its expression is: The expression for the second fitting model is: in, to The coefficients are to be fitted.

5. The photolithography process window analysis method according to claim 1, characterized in that, The theoretical boundary is the solution set of focusing energy and exposure energy obtained by substituting the upper and lower limits of the key dimensions into the boundary fitting function of the target process window.

6. The photolithography process window analysis method according to claim 1, characterized in that, The actual boundary is the area boundary defined by the focusing energy and exposure energy corresponding to the data points in the critical dimension measurement data that meet the critical dimension specification requirements.

7. The photolithography process window analysis method according to claim 1, characterized in that, The method of solving for the parameters of the ellipse in a two-dimensional parameter space composed of the focusing energy and the exposure energy using the differential evolution algorithm includes: A set of elliptic parameters is randomly initialized in the two-dimensional parameter space as an initial population. The elliptic parameters are iteratively updated through mutation, crossover and selection operations. The ellipse area is used as the fitness function. When the preset convergence condition is met, the optimal elliptic parameters are output.

8. The photolithography process window analysis method according to claim 1, characterized in that, The method further includes: The output of the optimal focusing energy and the optimal exposure energy are applied to the adjustment and optimization of the focusing and exposure parameters of the photolithography process.

9. A photolithography process window analysis system, characterized in that, include: The data acquisition and processing module is configured to acquire key dimension measurement data under different focusing energies and exposure energies during the photolithography process, and to perform filter processing on the measurement data according to preset filter rules. The fitting optimization module is configured to construct an antisymmetric fitting function based on the key dimension measurement data after filter point processing, establish a first fitting model with the focusing energy as the independent variable and a second fitting model with the exposure energy as the independent variable, calculate the root mean square error of the first fitting model and the second fitting model respectively, and select the fitting model with the smaller error as the boundary fitting function of the target process window. The boundary intersection module is configured to determine the theoretical boundary based on the boundary fitting function of the target process window, and to determine the actual boundary based on the data points in the key dimension measurement data that meet the key dimension specifications. The intersection of the theoretical boundary and the actual boundary is then used to generate the effective process area. The solution module is configured to minimize the area of ​​the ellipse covering the effective region of the process, and use the differential evolution algorithm to solve for the parameters of the ellipse in a two-dimensional parameter space composed of the focusing energy and the exposure energy. The focusing energy and exposure energy corresponding to the center of the ellipse obtained by the solution are respectively taken as the optimal focusing energy and the optimal exposure energy, and the process window analysis results are output.

10. A readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it can implement the photolithography process window analysis method according to any one of claims 1-8.

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