Method for establishing opc model, electronic device, storage medium and program product
By introducing the LASSO linear regression algorithm and threshold control mechanism into the OPC model, the overfitting problem of the OPC model is solved, the physical interpretability of the model threshold and the imaging accuracy are improved, and the reliability of the lithography process is ensured.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- QUANXIN INTELLIGENT MFG TECH CO LTD
- Filing Date
- 2026-05-26
- Publication Date
- 2026-07-07
AI Technical Summary
Existing OPC models are at risk of overfitting during iterative optimization, rendering them unusable in practical applications. Furthermore, the traditional LASSO linear regression algorithm lacks effective constraints on model thresholds, leading to reduced physical interpretability.
The LASSO (Lassively Oriented Simplified and Selective) linear regression algorithm is used to iteratively determine the intermediate model threshold and physical effect coefficient values of the OPC model. Under predetermined conditions, the final model threshold is determined. By introducing correlation and loss function minimization operations, the model threshold is controlled within a reasonable range.
This effectively avoids deviations of the model threshold from physical phenomena, improves the reliability and accuracy of the OPC model, ensures that the final imaging results conform to physical laws, and enhances the precision of the photolithography process.
Smart Images
Figure CN122345950A_ABST
Abstract
Description
Technical Field
[0001] This disclosure relates primarily to integrated circuits, and more specifically to methods for establishing optical proximity correction (OPC) models, electronic devices, computer-readable storage media, and computer program products. Background Technology
[0002] Photolithography is a crucial process in integrated circuit manufacturing. It utilizes photochemical reactions and chemical and physical etching methods to transfer patterns pre-prepared on a mask onto a substrate. The photolithography process can be described using optical and chemical models and mathematical formulas. When light shines on the mask, it diffracts; this diffraction is collected by a projection lens and converges onto the photoresist surface—this imaging process is optical. The image projected onto the photoresist excites a photochemical reaction, and after baking, the photoresist becomes locally soluble in the developer—this is a chemical process.
[0003] Typically, the pattern on a mask is projected onto photoresist using an exposure system. Due to imperfections in the optical system and diffraction effects, the pattern on the photoresist and the pattern on the mask are not perfectly identical. Optical proximity correction (OPC) uses computational methods to correct the pattern on the mask, ensuring that the pattern projected onto the photoresist conforms as closely as possible to the design requirements.
[0004] Currently, in the modeling process of OPC lithography, algorithms are used to simulate a series of optical effects and photoresist physicochemical effects in the lithography machine in order to optimize the corresponding algorithm coefficients and model thresholds.
[0005] However, the above methods only aim to minimize the error between model predictions and measured data. This leads to the risk of overfitting during iterative optimization, rendering the model unusable in practical applications. Summary of the Invention
[0006] According to an example embodiment of this disclosure, an improved scheme for establishing an optical proximity correction (OPC) model is provided to at least partially overcome the above or other potential drawbacks.
[0007] In a first aspect of this disclosure, a method for establishing an optical proximity effect corrected OPC model is provided, the method comprising: iteratively determining intermediate model thresholds and corresponding physical effect coefficient values of the OPC model in each iteration based on a minimum absolute value shrinkage and selection operator LASSO linear regression algorithm; determining a final model threshold, at least based on a comparison of the final model threshold corresponding to the last iteration among the determined intermediate model thresholds with a predetermined threshold; and establishing the OPC model based on the final model threshold and the physical effect coefficient values corresponding to the final model threshold.
[0008] In some embodiments, the LASSO linear regression algorithm based on minimum absolute value shrinkage and selection operator iteratively determines the intermediate model threshold and the corresponding physical effect coefficient value of the OPC model in each iteration, including: in each iteration, performing a loss function minimization operation, which minimizes the loss function by redetermining the intermediate model threshold and the corresponding physical effect coefficient value, wherein the residual represents the difference between the signal strength at each simulation point in the OPC model and the intermediate model threshold.
[0009] In some embodiments, the residuals are determined based on the following formula:
[0010]
[0011] Among them, y yes Represents simulation point p i The residual, y i This indicates that the pure optical model is at simulation point p. i signal strength, x ij This indicates that the physical effect j at simulation point p i The physical effect parameter, β jt T represents the coefficient value of physical effect j. t Let t represent the intermediate model threshold, t represent the number of iterations, r represent the number of physical effects in the OPC model, and j is a positive integer where 1 ≤ j ≤ r.
[0012] In some embodiments, the method further includes: in each iteration, introducing new physical effects into the OPC model based on correlation, where correlation represents the degree of influence of the physical effects on the residuals; and redetermining multiple physical effect coefficient values and intermediate model thresholds for the multiple physical effects that have been introduced.
[0013] In some embodiments, the physical effect includes at least one of the following: optical effect and photoresistive effect.
[0014] In some embodiments, the optical effects include at least one of the following: light source distribution, light intensity, and light source depth of focus.
[0015] In some embodiments, the photoresist effect includes at least one of the following: simulating acid-base diffusion effect and simulating shrinkage effect after drying.
[0016] In some embodiments, determining the final model threshold based at least on a comparison of the final model threshold corresponding to the last iteration among the determined intermediate model thresholds with a predetermined threshold includes: comparing the final model threshold and the intermediate model threshold of the previous iteration with the predetermined threshold; and determining the final model threshold based on the result of the comparison.
[0017] In some embodiments, determining the final model threshold based on the comparison results includes: discarding the data from the last iteration in response to determining that neither the final model threshold nor the intermediate model threshold of the previous iteration is within a predetermined threshold range; and re-executing the iteration process by using the intermediate model threshold of the previous iteration as the new final model threshold.
[0018] In some embodiments, determining the final model threshold based on the comparison results includes: in response to determining that both the final model threshold and the intermediate model threshold of the previous iteration are within a predetermined threshold range, using the final model threshold and the corresponding multiple physical effect coefficient values to establish an OPC model.
[0019] In some embodiments, determining the final model threshold based on the comparison results includes: in response to determining that the final model threshold is not within a predetermined threshold range and that the intermediate model threshold of the previous iteration is within the predetermined threshold range, adjusting the corresponding plurality of physical effect coefficient values and the final model threshold to generate adjusted plurality of physical effect coefficient values and adjusted final model threshold; and establishing an OPC model based on the adjusted plurality of physical effect coefficient values and adjusted final model threshold.
[0020] In some embodiments, adjusting the corresponding plurality of physical effect coefficient values and the final model threshold includes multiplying each physical effect coefficient value and the final model threshold among the corresponding plurality of physical effect coefficients by the same scaling factor, such that the adjusted final model threshold is within a predetermined threshold range.
[0021] In some embodiments, the range of the predetermined threshold is: [Tth-Δ, Tth+Δ], where Tth is the basic optical model threshold and Δ is the allowable deviation value.
[0022] In some embodiments, the predetermined conditions include at least one of the following: all physical effects have been introduced and the residual is less than a predetermined residual.
[0023] In a second aspect of this disclosure, an electronic device is provided, comprising: one or more processors; and a storage device for storing one or more programs, which, when executed by the one or more processors, cause the electronic device to perform the method according to the first aspect of this disclosure.
[0024] In a third aspect of this disclosure, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the method according to a first aspect of this disclosure.
[0025] It should be understood that the description in the Summary of the Invention is not intended to limit the key or essential features of the embodiments of this disclosure, nor is it intended to restrict the scope of this disclosure. Other features of this disclosure will become readily apparent from the following description. Attached Figure Description
[0026] The above and other features, advantages, and aspects of the embodiments of this disclosure will become more apparent from the accompanying drawings and the following detailed description. In the drawings, the same or similar reference numerals denote the same or similar elements, wherein:
[0027] Figure 1 A schematic diagram of an example environment in which embodiments of the present disclosure can be implemented is shown;
[0028] Figure 2 A flowchart of a method for establishing an OPC model according to an embodiment of the present disclosure is shown;
[0029] Figure 3 A flowchart is shown for iteratively determining intermediate model thresholds and corresponding physical effect coefficient values of an OPC model in each iteration, according to embodiments of the present disclosure.
[0030] Figure 4 A flowchart for determining a final model threshold according to an embodiment of the present disclosure is shown;
[0031] Figure 5 An example comparison of the results of running a LASSO-based linear regression algorithm with threshold control and a LASSO-based linear regression algorithm without threshold control under the same conditions, according to an embodiment of the present disclosure, is shown.
[0032] Figure 6 A block diagram of an electronic device capable of implementing embodiments of the present disclosure is shown. Detailed Implementation
[0033] Embodiments of this disclosure will now be described in more detail with reference to the accompanying drawings. While some embodiments of this disclosure are shown in the drawings, it should be understood that this disclosure can be implemented in various forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided to provide a more thorough and complete understanding of this disclosure. It should be understood that the accompanying drawings and embodiments of this disclosure are for illustrative purposes only and are not intended to limit the scope of protection of this disclosure.
[0034] In the description of embodiments of this disclosure, the term "comprising" and similar terms should be understood as open-ended inclusion, i.e., "including but not limited to". The term "based on" should be understood as "at least partially based on". The term "one embodiment" or "the embodiment" should be understood as "at least one embodiment". The terms "first", "second", etc., may refer to different or the same objects. Other explicit and implicit definitions may also be included below.
[0035] As briefly mentioned earlier, OPC uses computational methods to correct the pattern on the mask, ensuring that the pattern projected onto the photoresist conforms as closely as possible to the design requirements. Model-based optical proximity correction (hereinafter referred to as "OPC model") has been widely used. Establishing the OPC model is a crucial step in the optical proximity correction process. When establishing the OPC model, fitting calculations are performed to minimize the difference between the simulation results and the actual measurement results; for example, minimizing the difference between the pattern simulated by the OPC model and the photoresist pattern.
[0036] In the process of modeling OPC (Optical Processing) models, algorithms are typically used to simulate a series of optical and photoresist effects in lithography machines. The optimal solution is obtained by optimizing the corresponding algorithm parameters, thus establishing the OPC model. In traditional approaches, genetic algorithms are commonly used. Genetic algorithms are search algorithms used to solve optimization problems. However, applying genetic algorithms to OPC modeling leads to slow iterative convergence, and the optimal solution is strongly correlated with the generated algorithm parameters. Therefore, the ability of genetic algorithms to find the optimal solution is limited. Known traditional methods only focus on minimizing the error between model predictions and measured data, without imposing any constraints on the crucial parameter of the model threshold. This results in the model threshold potentially deviating too much from its physically reasonable initial value (usually determined based on a purely optical model) during iterative optimization, thus posing a risk of overfitting and rendering the model unusable in practical applications.
[0037] The physical effect coefficient is one of the core parameters of the OPC model. The physical effect coefficient value indicates the strength of the influence of the physical effect corresponding to that value on the imaging process. The larger the absolute value of the physical effect coefficient, the more significant the influence of the physical effect (e.g., specific aberrations, high-frequency diffraction) on the imaging process. The sign of the physical effect coefficient value indicates the direction of the physical effect's action in the imaging process: a positive physical effect coefficient value indicates that the corresponding physical effect will produce a light intensity enhancement effect, which may cause the simulated pattern to expand relative to the design pattern; a negative physical effect coefficient value indicates that the corresponding physical effect will produce a light intensity reduction effect, which may cause the simulated pattern to shrink. The OPC model threshold characterizes the reference signal intensity associated with the reference lithographic pattern in the lithographic pattern set and corresponds to the measurement linewidth of that reference lithographic pattern.
[0038] The physical effect coefficients and the OPC model threshold are tightly coupled and work synergistically. Specifically, if the physical effect coefficients are inaccurate, the simulated light intensity distribution will be distorted regardless of how the OPC model threshold is adjusted; conversely, if the OPC model threshold is set incorrectly, the predicted graphic contour will exhibit an overall size deviation (e.g., too large or too small) even if the physical effect coefficients are accurate. Therefore, the physical effect coefficients and the OPC model threshold must be jointly optimized as a whole to obtain an OPC model with high accuracy and good generalization ability.
[0039] Traditional linear regression algorithms based on the Least Absolute Shrinkage and Selection Operator (LASSO) lack effective constraints on the model threshold when building OPC models. Their optimization objective typically focuses solely on minimizing the fitting error, without limiting the model threshold to a reasonable range based on prior physical knowledge. This can lead to the final calculated model threshold deviating from its physically expected range. While such models may exhibit smaller fitting errors on training data, their physical interpretability is reduced, and in practical applications, threshold deviations can trigger correction errors.
[0040] In view of this, this disclosure provides an improved scheme for building OPC models.
[0041] According to embodiments of this disclosure, a method for establishing an OPC model is provided, the method comprising: iteratively determining intermediate model thresholds and corresponding physical effect coefficients of the OPC model in each iteration based on the LASSO linear regression algorithm; determining a final model threshold based at least on a comparison of the final model threshold corresponding to the last iteration among the determined intermediate model thresholds with a predetermined threshold; and establishing an OPC model based on the final model threshold and the physical effect coefficients corresponding to the final model threshold.
[0042] The embodiments of this disclosure will now be described in detail with reference to the accompanying drawings.
[0043] Figure 1 An example environment 100 in which embodiments of this disclosure can be implemented is shown. For example... Figure 1 As shown, electronic device 110 can receive a first mask pattern 102 and a target pattern 104. The target pattern 104 is a complete or partial wafer pattern desired to be obtained on a silicon wafer. The first mask pattern 102 can be a mask pattern of a complete circuit layout or a portion thereof.
[0044] A first mask pattern 102 is associated with a target pattern 104. The first mask pattern 102 may be a mask pattern determined based on the target pattern 104. In some embodiments, the first mask pattern 102 may be the same as the target pattern 104. In some embodiments, the first mask pattern 102 may be a modified target pattern 104.
[0045] In some embodiments, an OPC model 112 is deployed in the electronic device 110. The OPC model 112 can use computational methods to modify a mask pattern (e.g., a first mask pattern 102) and obtain a modified mask pattern (e.g., a second mask pattern 106), so that the pattern projected onto the photoresist conforms as closely as possible to the design requirements, for example, it is closer to the target pattern 104.
[0046] In some embodiments, the OPC model 112 in the electronic device 110 can determine the pattern edges in the target pattern 104 based on the received target pattern 104, and can obtain the pattern edges of the simulated pattern of the first mask pattern 102 after photolithography through simulation operations. The OPC model 112 in the electronic device 110 can compare the pattern edges in the target pattern 104 with the pattern edges of the simulated pattern to determine the edge placement error. The OPC model 112 corrects the first mask pattern 102 by minimizing or making the edge placement error an acceptable value, and outputs a second mask pattern 106. Accordingly, the second mask pattern 106 is a corrected version of the first mask pattern 102 obtained based on the OPC model 112. Compared with the wafer pattern obtained based on the first mask pattern 102, the wafer pattern obtained based on the second mask pattern 106 is closer to the target pattern 104.
[0047] In the process of building an OPC model, an important indicator for evaluating the model's fit is the linewidth (critical dimension; CD). For example, the measured linewidth of the lithographic pattern obtained after exposing the mask pattern of the test pattern to photoresist can be measured. The fit of the OPC model is evaluated by comparing this measured linewidth with the simulated linewidth in the simulated pattern obtained by simulating the test pattern using the OPC model. The smaller the difference between the measured and simulated linewidths, the better the fit of the OPC model.
[0048] According to some embodiments of this disclosure, during the modeling process of the OPC model, the difference between the simulated linewidth of the pattern in the simulated pattern obtained from the OPC model simulation and the measured linewidth of the corresponding pattern in the photolithographic pattern is converted into the signal intensity difference between the signal intensity of the simulated point corresponding to the simulated linewidth and the signal intensity of the measured point corresponding to the measured linewidth. The smaller the signal intensity difference, the higher the accuracy of the model.
[0049] Electronic device 110 can be any device with computing capabilities. As a non-limiting example, electronic device 110 can be any type of fixed electronic device, mobile electronic device, or portable electronic device, including but not limited to desktop computers, laptop computers, notebook computers, netbook computers, tablet computers, multimedia computers, mobile phones, smart home devices, wearable electronic devices, etc. In some embodiments, all or some components of electronic device 110 can be distributed in the cloud. This disclosure does not limit the specific type of electronic device 110.
[0050] Figure 2 A flowchart of a method 200 for establishing an OPC model according to an embodiment of the present disclosure is shown. For ease of discussion, it will be combined with... Figure 1 Let's describe method 200. Figure 2 Method 200 can be found in Figure 1 The steps are executed at electronic device 110 and any suitable electronic device. Furthermore, the numbers in the flowchart do not indicate the order in which these steps are executed; some or all of these steps may be executed in parallel, or their execution order may be interchanged, and this disclosure does not limit this.
[0051] In box 202, the intermediate model threshold and corresponding physical effect coefficient values of the OPC model in each iteration can be determined iteratively based on the LASSO linear regression algorithm.
[0052] In some embodiments, for each simulation point p i It is possible to obtain a purely optical model at each simulation point p. i signal strength y i (Where i is a positive integer, 1≤i≤n, and n is the number of simulation points in OPC model 112). The signal strength of the pure optical model at each simulation point can be determined using algorithms known in the art.
[0053] In some embodiments, it can be based on multiple physical effect parameters x ij (where j is a positive integer, 1≤j≤r, and r is the number of physical effects in the OPC model) and the multiple physical effect coefficients β corresponding to these physical effects to be determined. j (where j is a positive integer, 1≤j≤r, and r is the number of physical effects in the OPC model), to determine each simulation point p. i Physical effect signal strength b i In some embodiments, multiple physical effect coefficient values β jThese are the physical effect coefficient values to be determined. For example, electronic device 110 can determine these multiple physical effect coefficient values β using a LASSO linear regression algorithm. j .
[0054] In some embodiments, the physical effect may include at least one of the following: optical effect and photoresistive effect. Furthermore, it is understood that the physical effect may also include other physical effects besides those listed above, and this disclosure does not limit this. In some embodiments, the optical effect may include at least one of the following: light source distribution, light intensity, and light source depth of focus. Furthermore, it is understood that the optical effect may also include other optical effects besides those listed above, and this disclosure does not limit this. In some embodiments, the photoresistive effect may include at least one of the following: simulated acid-base diffusion effect and simulated shrinkage effect after drying. Furthermore, it is understood that the photoresistive effect may also include other photoresistive effects besides those listed above, and this disclosure does not limit this.
[0055] In some embodiments, each simulation point p i Physical effect signal strength b i It can be determined by the following formula (1):
[0056] (1)
[0057] It is understandable that, due to the multiple physical effect coefficient values β j The corresponding physical effect signal strength b is to be determined. i It is still to be determined.
[0058] In some embodiments, the signal strength y of the purely optical model at each simulation point can be calculated. i With physical effect signal strength b i Signal strength difference Δs i In some embodiments, the strength difference can be determined by the following formula (2):
[0059] (2)
[0060] The calculated signal strength difference Δs i Determine each simulation point p i The signal strength.
[0061] Multiple physical effect coefficients β can be determined using the LASSO linear regression algorithm. jIn some embodiments, the OPC model threshold is a threshold to be determined and used in the OPC model 112. In the LASSO-based linear regression algorithm, the OPC model threshold can be equivalent to the intercept term in the algorithm, which is also the fitted value to be obtained when modeling the OPC model 112. The specific process of constructing the loss function L based on the LASSO linear regression algorithm can be implemented in a conventional manner, and will not be described in detail in this invention.
[0062] The specific process for iteratively determining the intermediate model threshold and corresponding physical effect coefficient values of the OPC model in each iteration will be described below. Figure 3 It was described in further detail.
[0063] In box 204, in response to the iteration satisfying predetermined conditions, the final model threshold is determined at least based on a comparison between the final model threshold corresponding to the last iteration among the determined intermediate model thresholds and the predetermined threshold. The predetermined conditions can be user-specified conditions, such as the iteration count reaching a predetermined number, all physical effects being introduced, the residual in LASSO being less than a predetermined residual, or the loss function of the OPC model being lower than a predetermined threshold, etc. The specific process for determining the final model threshold will be described below. Figure 4 It was described in further detail.
[0064] In box 206, the OPC model is established based on the final model threshold and the physical effect coefficient values corresponding to the final model threshold.
[0065] In some embodiments, the OPC model threshold characterizes the reference signal intensity associated with a reference lithographic pattern in the lithographic pattern set and corresponds to the measurement linewidth of the reference lithographic pattern. The multiple lithographic patterns in the lithographic pattern set are obtained by exposing mask patterns of multiple test patterns onto photoresist, respectively.
[0066] Advantageously, the improved method for building an OPC model according to embodiments of the present disclosure constrains the model threshold within a reasonable range determined based on the threshold of the basic optical model during the modeling process of the OPC model, effectively avoiding threshold deviation caused by algorithm optimization, making the final model threshold physically interpretable, and improving the reliability of the model.
[0067] Figure 3 A flowchart is shown for iteratively determining intermediate model thresholds and corresponding physical effect coefficient values of an OPC model in each iteration, according to an embodiment of the present disclosure. Figure 3 Method 300 can be found in Figure 1The steps are executed at electronic device 110 and any suitable electronic device. Furthermore, the numbers in the flowchart do not indicate the order in which these steps are executed; some or all of these steps may be executed in parallel, or their execution order may be interchanged, and this disclosure does not limit this.
[0068] In box 302, the optical model can be initialized. In some embodiments, the optical model is initialized considering only the pure optical model, without considering any optical or photoresistive effects, in which case the value of each physical effect coefficient β is... jt All are set to 0 (where t represents the current iteration number, t is a non-negative integer, 0≤t≤m, and m is the total number of iterations, i.e., t=0 at this point). In some embodiments, the initial model threshold T0 is the optical model at simulation point p. i The average signal strength at that location.
[0069] In box 304, new physical effects can be introduced into the OPC model based on correlation in each iteration. In some embodiments, in each iteration, a loss function minimization operation is performed, which minimizes the loss function by redetermining the intermediate model threshold and the corresponding physical effect coefficient values. The loss function is determined by the residuals and the L1 regularized loss function, where the residuals represent the difference between the signal strength at each simulation point in the OPC model and the intermediate model threshold. In some embodiments, the residuals can be determined based on the following formula:
[0070] (3)
[0071] Among them, y yes Represents simulation point p i The residual, t represents the number of iterations, Δs it The simulation point p in the t-th iteration is represented by i signal strength, T t This represents the intermediate model threshold in the t-th iteration. In some embodiments, known algorithms such as coordinate descent or minimum angle regression, or various algorithms developed in the future, can be used to solve the loss function to obtain the model threshold and the corresponding physical effect coefficient values.
[0072] In some embodiments, the LASSO-based linear regression algorithm automatically introduces new physical effects in each iteration. In some embodiments, correlation represents the degree of influence of a physical effect on the residuals. In some embodiments, the physical effect with the highest correlation is introduced in the first iteration; and in each subsequent iteration, a new physical effect is introduced, with the correlation of the new physical effect being consistent with that of the physical effect introduced in the previous iteration. In some embodiments, the correlation changes dynamically during the solution process of each iteration. The LASSO algorithm continuously monitors the correlation of physical effects, and when the correlation of one of the physical effects to be introduced is consistent with that of the previously introduced physical effect, it records the model threshold and the corresponding physical effect coefficient value, and then introduces the physical effect.
[0073] In box 306, the multiple physical effect coefficient values and intermediate model thresholds for the multiple physical effects that have been introduced can be redefined. In some embodiments, in each iteration, after introducing a new physical effect, the physical effect coefficient value β corresponding to the introduced physical effect is resolved. 1t ,…,β rt and intermediate model threshold T t To minimize the loss function.
[0074] The above process can be implemented in electronic device 110 or performed on any other suitable device with computing power.
[0075] The following describes, in conjunction with Table 1, an example process for iteratively determining the intermediate model threshold and corresponding physical effect coefficient values of the OPC model in each iteration according to an embodiment of the present disclosure. Table 1
[0076] Here, Term represents an optical or photoresistive effect. When the iteration number is 0, no optical or photoresistive effect is introduced into the OPC model. In the first iteration, i.e., t=1, the correlation of each physical effect is compared, i.e., the correlation of Term1, Term2, Term3, and Term4. Assuming that Term1 has the highest correlation at this time, Term1 is introduced. After introducing Term1, in the first iteration, the simulation point p... i The residuals are:
[0077] (4)
[0078] Among them, y i This indicates that the pure optical model is at simulation point p. i signal strength, x i1 This indicates that Term1 is at simulation point p. iThe physical effect parameter, β 11 This represents the coefficient value of Term1 in the first iteration, and T1 represents the intermediate model threshold in the first iteration. i With x i1 The coefficient β for Term1 is known. 11 The intermediate model threshold T1 is then calculated to minimize the loss function. In the first iteration, the coefficients of Term2, Term3, and Term4 remain at 0 and are not involved in the solution process. During the solution process, the algorithm continuously monitors the correlation degree of each physical effect. Assuming that at a certain moment the correlation degree of Term2 is consistent with the correlation degree of Term1, the β obtained at this time can be recorded. 11 Then proceed to T1 and move on to the next iteration.
[0079] In the second iteration, Term2 was introduced based on the correlation degree. After introducing Term2, the simulation point p i The residuals are:
[0080] (5)
[0081] Where, x i2 This indicates that Term2 is at simulation point p. i The physical effect parameter, β 12 β represents the coefficient value of Term1 in the second iteration. 22 y represents the coefficient value of Term2 in the second iteration, and T2 represents the intermediate model threshold in the second iteration. i x i1 With x i2 It is known that y i x i1 The coefficient β remains unchanged, consistent with the first iteration. 12 The coefficient β of Term2 22 The intermediate model threshold T2 is recalculated to minimize the loss function. In the second iteration, the coefficients of Term3 and Term4 remain 0 and are not involved in the solution process. During the solution process, the algorithm continuously monitors the correlation degree of each physical effect. Assuming that at a certain moment the correlation degree of Term3 is consistent with the correlation degree of Term2, the β obtained at this time can be recorded. 12 β 22 Then proceed to T2 and move on to the next iteration.
[0082] In the third iteration, Term3 is introduced based on the correlation. The new residuals can be obtained in a similar manner to the previous one, with respect to the coefficient β of Term1. 13 The coefficient β of Term2 23 The coefficient β of Term3 33The intermediate model threshold T3 is recalculated to minimize the loss function. In the third iteration, the coefficient of Term4 remains 0 and is not involved in the solution process. During the solution process, the algorithm continuously monitors the correlation of each physical effect. Assuming that at a certain moment the correlation of Term4 is consistent with the correlation of Term3, the β obtained at this time can be recorded. 13 β 23 β 33 And T3, and proceed to the next iteration.
[0083] In the fourth iteration, Term4 is introduced based on the correlation degree. The new residuals can be obtained in a similar manner to the above, with respect to the coefficient β of Term1. 14 The coefficient β of Term2 24 The coefficient β of Term3 34 The coefficient β of Term4 44 The intermediate model threshold T4 is then recalculated to minimize the loss function. The iteration stops when a predetermined condition is met (e.g., the residual is less than a predetermined residual), and the obtained β is recorded. 14 β 24 β 34 β 44 And T4. It is understood that Table 1 is merely exemplary and not intended to limit this disclosure in any way.
[0084] Figure 4 A flowchart for determining a final model threshold according to an embodiment of the present disclosure is shown. For ease of discussion, it will be combined with... Figure 1 To describe method 400. Figure 4 Method 400 can be found in Figure 1 The steps are executed at electronic device 110 and any suitable electronic device. Furthermore, the numbers in the flowchart do not indicate the order in which these steps are executed; some or all of these steps may be executed in parallel, or their execution order may be interchanged, and this disclosure does not limit this.
[0085] In box 402, the final model threshold and the intermediate model threshold of the previous iteration can be obtained. In some embodiments, for example, in conjunction with Table 1, the final model threshold T4 and the intermediate model threshold T3 of the previous iteration can be obtained.
[0086] In decision box 404, it can be determined whether both the final model threshold and the intermediate model threshold of the previous iteration are outside the range of a predetermined threshold. In some embodiments, the range of the predetermined threshold is: [Tth-Δ, Tth+Δ], where Tth is the basic optical model threshold and Δ is the allowable deviation value. In some embodiments, the range of the predetermined threshold can be determined by the user or the system.
[0087] If neither the final model threshold nor the intermediate model threshold from the previous iteration is within the predetermined threshold range, the process proceeds to box 406. In box 406, the final model threshold and the corresponding multiple physical effect coefficient values can be discarded, and the process proceeds to box 408. In box 408, the intermediate model threshold from the previous iteration can be used as the new final model threshold, and the process returns to box 402 and restarts.
[0088] In some embodiments, for example, referring to Table 1, if neither T4 nor T3 is within [Tth-Δ, Tth+Δ], then T4 and the corresponding multiple physical effect coefficient values (i.e., β) are... 14 β 24 β 34 and β 44 If T3 is discarded and T2 becomes the new final model threshold, then T2 becomes the new intermediate model threshold of the previous iteration. Then, we return to decision box 404 to determine whether neither T3 nor T2 is within the range of the predetermined threshold.
[0089] If at least one of the final model threshold and the intermediate model threshold of the previous iteration is within the range of a predetermined threshold, that is, if the final model threshold is within the range of a predetermined threshold or the intermediate model threshold of the previous iteration is within the range of a predetermined threshold, the process proceeds to decision box 410. In decision box 410, it can be determined whether the final model threshold is within the range of the predetermined threshold.
[0090] If the final model threshold is within a predetermined threshold range, the process proceeds to box 412. In box 412, the final model threshold and the corresponding multiple physical effect coefficient values can be used to build an OPC model. In some embodiments, for example, referring to Table 1, if T4 is within [Tth-Δ, Tth+Δ], then T4 and the corresponding multiple physical effect coefficient values (i.e., β) can be used. 14 β 24 β 34 and β 44 To establish the OPC model.
[0091] If the final model threshold is not within the predetermined threshold range, the process proceeds to box 414. In box 414, the corresponding multiple physical effect coefficient values and the final model threshold can be adjusted to generate adjusted multiple physical effect coefficient values and an adjusted final model threshold. Then, the process proceeds to box 412, where an OPC model can be built based on the adjusted multiple physical effect coefficient values and the adjusted final model threshold.
[0092] In some embodiments, adjusting the corresponding plurality of physical effect coefficient values and the final model threshold includes multiplying each of the corresponding plurality of physical effect coefficient values and the final model threshold by the same scaling factor, such that the adjusted final model threshold is within a predetermined threshold range.
[0093] In some embodiments, for example, referring to Table 1, if T4 is not within [Tth-Δ, Tth+Δ] while T3 is within [Tth-Δ, Tth+Δ], then T4 and the corresponding multiple physical effect coefficient values (i.e., β) are... 14 β 24 β 34 and β 44 Multiplying by the same scaling factor γ yields the adjusted final model threshold T'4 and the adjusted values of multiple physical effect coefficients β'. 14 ,β' 24 ,β' 34 and β' 44 This ensures that T'4 lies within [Tth-Δ, Tth+Δ]. Then, based on T'4 and β'... 14 ,β' 24 ,β' 34 and β' 44 To establish the OPC model.
[0094] Table 2 shows, in some examples, the final model thresholds and corresponding physical effect coefficients obtained under the same conditions using the LASSO-based linear regression algorithm with threshold control according to embodiments of the present disclosure and using the baseline algorithm (i.e., the LASSO-based linear regression algorithm without threshold control). Table 2
[0095] As can be seen from the data in Table 2, under the same conditions, when the OPC model is established using the LASSO linear regression algorithm with threshold control according to the embodiments of this disclosure, the difference between the final model threshold and the initial model threshold is no more than 0.1. Compared with the baseline algorithm, it is more consistent with physical phenomena, and the final image is also normal.
[0096] Figure 5 An example comparison of the results of running a LASSO-based linear regression algorithm with threshold control and a LASSO-based linear regression algorithm without threshold control under the same conditions, according to embodiments of the present disclosure, is shown. Figure 5In the diagram, graph 502 shows an example of the results of the LASSO-based linear regression algorithm with threshold control, while graph 504 shows an example of the results without threshold control. Graphs 502 and 504 represent the signal cross-sections of the optical model at the example sampling points. The horizontal axis represents the measurement location (in nanometers), and the vertical axis represents the signal intensity. The vertical coordinates corresponding to the intersections of the horizontal lines 510 and 520 (representing linewidth) with the vertical axis represent the final model thresholds obtained by the algorithm. It can be seen that the final threshold obtained by the LASSO-based linear regression algorithm without threshold control is negative, which does not conform to physical phenomena, and the final image is also abnormal; while the final threshold obtained by the LASSO-based linear regression algorithm with threshold control is positive, avoiding unreasonable situations that violate physical laws.
[0097] The solution of this disclosure can control the threshold of the lithography model within a reasonable range of the initial basic optical model threshold, and supports user-defined final threshold range. It can avoid unreasonable situations such as excessive deviation of the threshold that violate physical laws, so that the solved threshold parameters conform to physical reality, and at the same time ensure that the final imaging result is normal, thereby improving the rationality and accuracy of the lithography model.
[0098] Figure 6 A schematic block diagram of an example device 600 that can be used to implement embodiments of the present disclosure is shown. Device 600 can be used to implement... Figure 1 The electronic device 110. As shown, the device 600 includes a processing unit 601, such as a central processing unit (CPU), which can perform various appropriate actions and processes according to computer program instructions stored in read-only memory (ROM) 602 or loaded from storage unit 608 into random access memory (RAM) 603. The RAM 603 may also store various programs and data required for the operation of the device 600. The processing unit 601, ROM 602, and RAM 603 are interconnected via a bus 604. An input / output (I / O) interface 605 is also connected to the bus 604.
[0099] Multiple components in device 600 are connected to I / O interface 605, including: input unit 606, such as keyboard, mouse, etc.; output unit 607, such as various types of monitors, speakers, etc.; storage unit 608, such as disk, optical disk, etc.; and communication unit 609, such as network card, modem, wireless transceiver, etc. Communication unit 609 allows device 600 to exchange information / data with other devices through computer networks such as the Internet and / or various telecommunications networks.
[0100] Processing unit 601 executes the various methods and processes described above, such as methods 200, 300, and 400. For example, in some embodiments, methods 200, 300, and 400 may be implemented as computer software programs tangibly contained in a machine-readable medium, such as storage unit 608. In some embodiments, part or all of the computer program may be loaded and / or installed on device 600 via ROM 602 and / or communication unit 609. When the computer program is loaded into RAM 603 and executed by processing unit 601, one or more steps of methods 200, 300, and 400 described above may be performed. Alternatively, in other embodiments, processing unit 601 may be configured to execute methods 200, 300, and 400 by any other suitable means (e.g., by means of firmware).
[0101] The functions described above in this document can be performed at least in part by one or more hardware logic components. For example, exemplary types of hardware logic components that can be used, without limitation, include: field programmable gate arrays (FPGAs), application-specific integrated circuits (ASICs), application-specific standard products (ASSPs), systems-on-a-chip (SoCs), payload programmable logic devices (CPLDs), and so on.
[0102] The program code used to implement the methods of this disclosure may be written in any combination of one or more programming languages. This program code may be provided to a processor or controller of a general-purpose computer, special-purpose computer, or other programmable data processing apparatus, such that when executed by the processor or controller, the program code causes the functions / operations specified in the flowcharts and / or block diagrams to be implemented. The program code may be executed entirely on a machine, partially on a machine, as a standalone software package partially on a machine and partially on a remote machine, or entirely on a remote machine or server.
[0103] In the context of this disclosure, a machine-readable medium can be a tangible medium that may contain or store a program for use by or in conjunction with an instruction execution system, apparatus, or device. A machine-readable medium can be a machine-readable signal medium or a machine-readable storage medium. A machine-readable medium can be, but is not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatus, or devices, or any suitable combination of the foregoing. More specific examples of machine-readable storage media include electrical connections based on one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination of the foregoing.
[0104] Furthermore, although the operations are described in a specific order, this should be understood as requiring that such operations be performed in the specific order shown or in sequential order, or requiring that all illustrated operations be performed to achieve the desired result. In certain environments, multitasking and parallel processing may be advantageous. Similarly, although several specific implementation details are included in the above discussion, these should not be construed as limiting the scope of this disclosure. Certain features described in the context of individual embodiments may also be implemented in combination in a single implementation. Conversely, various features described in the context of a single implementation may also be implemented individually or in any suitable sub-combination in multiple implementations.
[0105] Although the subject matter has been described using language specific to structural features and / or methodological logic, it should be understood that the subject matter defined in the appended claims is not necessarily limited to the specific features or actions described above. Rather, the specific features and actions described above are merely illustrative examples of implementing the claims.
Claims
1. A method for establishing an optical proximity effect correction OPC model, comprising: Based on the LASSO linear regression algorithm with minimum absolute value contraction and selection operator, the intermediate model threshold and corresponding physical effect coefficient values of the OPC model are determined iteratively in each iteration. In response to the iteration satisfying a predetermined condition, the final model threshold is determined at least based on a comparison between the final model threshold corresponding to the last iteration among the determined intermediate model thresholds and the predetermined threshold. as well as The OPC model is established based on the final model threshold and the physical effect coefficients corresponding to the final model threshold.
2. The method according to claim 1, wherein iteratively determining the intermediate model threshold and corresponding physical effect coefficient values of the OPC model in each iteration based on the LASSO linear regression algorithm with minimum absolute value shrinkage and selection operator includes: In each iteration, a loss function minimization operation is performed, which minimizes the loss function by redetermining the intermediate model threshold and the corresponding physical effect coefficient value, wherein the loss function is determined by the residual and the L1 regularized loss function, and the residual represents the difference between the signal strength at each simulation point in the OPC model and the intermediate model threshold.
3. The method according to claim 2, wherein the residual is determined based on the following formula: in, y yes Represents simulation point p i The residual, y i This indicates that the purely optical model is at simulation point p. i signal strength, x ij This indicates that the physical effect j is at the simulation point p. i The physical effect parameter, β jt T represents the coefficient value of the physical effect j. t The intermediate model threshold is represented by t, the number of iterations is represented by r, the number of physical effects in the OPC model is represented by j, and j is a positive integer and 1≤j≤r.
4. The method according to claim 1, further comprising: In each iteration, a new physical effect is introduced into the OPC model based on the correlation degree, which represents the degree of influence of the physical effect on the residual. as well as The coefficient values of the multiple physical effects that have been introduced, as well as the threshold values of the intermediate model, are redefined.
5. The method according to claim 4, wherein the physical effect includes at least one of the following: optical effect and photoresistive effect.
6. The method according to claim 5, wherein the optical effect includes at least one of the following: light source distribution, light intensity, and light source depth of focus.
7. The method according to claim 5, wherein the photoresist effect includes at least one of the following: simulating acid-base diffusion effect and simulating shrinkage effect after drying.
8. The method of claim 1, wherein determining the final model threshold based at least on a comparison of the final model threshold corresponding to the last iteration among the determined intermediate model thresholds with a predetermined threshold comprises: The final model threshold and the intermediate model threshold of the previous iteration are compared with the predetermined threshold; as well as The final model threshold is determined based on the results of the comparison.
9. The method of claim 8, wherein determining the final model threshold based on the result of the comparison comprises: In response to the determination that neither the final model threshold nor the intermediate model threshold of the previous iteration is within the predetermined threshold range, the data of the last iteration is discarded; as well as The intermediate model threshold from the previous iteration is used as the new final model threshold to re-execute the iteration process.
10. The method of claim 8, wherein determining the final model threshold based on the result of the comparison comprises: In response to determining that both the final model threshold and the intermediate model threshold of the previous iteration are within a predetermined threshold range, the OPC model is established using the final model threshold and the corresponding multiple physical effect coefficient values.
11. The method of claim 8, wherein determining the final model threshold based on the result of the comparison comprises: In response to determining that the final model threshold is not within the predetermined threshold range and that the intermediate model threshold of the previous iteration is within the predetermined threshold range, the corresponding plurality of physical effect coefficient values and the final model threshold are adjusted to generate adjusted plurality of physical effect coefficient values and adjusted final model threshold. as well as The OPC model is established based on the adjusted values of multiple physical effect coefficients and the adjusted final model threshold.
12. The method of claim 11, wherein adjusting the corresponding plurality of physical effect coefficient values and the final model threshold comprises: Each physical effect coefficient value in the corresponding plurality of physical effect coefficients and the final model threshold are multiplied by the same scaling factor, such that the adjusted final model threshold is within the predetermined threshold range.
13. The method according to any one of claims 1 to 12, wherein the range of the predetermined threshold is: [Tth-Δ, Tth+Δ], where Tth is the basic optical model threshold and Δ is the allowable deviation value.
14. The method according to any one of claims 2 to 4, wherein the predetermined condition includes at least one of the following: all physical effects have been introduced and the residual is less than a predetermined residual.
15. An electronic device comprising: One or more processors; as well as A storage device for storing one or more programs, which, when executed by one or more processors, cause the electronic device to perform the method according to any one of claims 1-14.
16. A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method according to any one of claims 1-14.
17. A computer program product comprising program code that, when executed by a processor, implements the method according to any one of claims 1-14.