Aberration budget range determination method and apparatus, storage medium, and computer device
By screening Zernike single terms and coupling terms related to exposure results in the lithography system, establishing an analytical model and fitting it, the problem of low efficiency in the aberration budget range of the lithography system is solved, and efficient determination of the aberration budget range is achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- INST OF MICROELECTRONICS CHINESE ACAD OF SCI LTD
- Filing Date
- 2023-05-29
- Publication Date
- 2026-06-30
Smart Images
Figure CN116819895B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of budget decomposition technology for high-resolution imaging systems, and in particular to a method, apparatus, storage medium, and computer device for determining the budget range of aberrations. Background Technology
[0002] Photolithography machines are crucial equipment in the manufacturing of large-scale integrated circuits. In the optical system of a photolithography machine, due to diffraction limitations and processing / manufacturing errors, the propagation direction and phase of the ideal wavefront on the image plane change. The difference between the actual wavefront and the ideal wavefront is defined as wave aberration. To determine whether a specific aberration can satisfy the exposure conditions, it is often necessary to calculate the aberration budget range of the photolithography system. Aberration values within the aberration budget range are then determined as meeting the exposure conditions of the photolithography system.
[0003] However, existing methods for determining the aberration budget range of a lithography system mostly involve conducting a large number of experiments to determine the correspondence between the parameters of each aberration and the process conditions, thereby determining the aberration budget range. However, the above methods are too inefficient for determining the aberration budget range of a lithography system. Summary of the Invention
[0004] In view of this, this application provides a method, apparatus, storage medium and computer equipment for determining the budget range of aberrations, with the main purpose of solving the technical problem of low efficiency in obtaining the budget range of aberrations in a lithography system.
[0005] According to a first aspect of the present invention, a method for determining the budget range of aberrations is provided, applied to a photolithography system, the method comprising:
[0006] Multiple target Zernike polynomials are obtained, wherein the target Zernike polynomial is the Zernike polynomial among multiple Zernike polynomials whose causal correlation with the exposure result of the lithography system based on the Zernike polynomial satisfies a first preset condition;
[0007] The Zernike polynomial is fitted with deterministic screening to identify the target second-order coupling term in the Zernike polynomial, and based on the target Zernike term, the higher-order coupling term corresponding to the target Zernike term is obtained.
[0008] An analytical model is established based on the target Zernike single term, the target second-order coupling term, and the higher-order coupling term. The analytical model is then fitted based on random experiments to obtain a fitted model.
[0009] Based on a predetermined exposure result range, the budget range of the aberration is obtained through the fitting model.
[0010] According to a second aspect of the present invention, an aberration budget range determination apparatus is provided, the apparatus comprising:
[0011] A single-item acquisition module is used to acquire multiple target Zernike items, wherein the target Zernike item is the Zernike item among multiple Zernike polynomials whose causal correlation with the exposure result of the lithography system based on the Zernike polynomial satisfies a first preset condition.
[0012] A higher-order coupling module is used to perform a fitting deterministic screening of the Zernike polynomial, determine the target second-order coupling term in the Zernike polynomial, and obtain the higher-order coupling term corresponding to the target Zernike term based on the target Zernike term.
[0013] The model fitting module is used to establish an analytical model based on the target Zernike single term, the target second-order coupling term, and the higher-order coupling term, and to fit the analytical model based on random experiments to obtain a fitted model.
[0014] The range determination module is used to obtain the budget range of the aberration based on a pre-determined exposure result range through the fitting model.
[0015] According to a third aspect of the invention, a storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the above-described method for determining the budget range of aberrations.
[0016] According to a fourth aspect of the present invention, a computer device is provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the program, implements the above-described method for determining the budget range of aberrations.
[0017] This invention provides a method, apparatus, storage medium, and computer device for determining the budget range of aberrations. First, the target Zernike polynomial with a significant impact on the exposure results of the lithography system is obtained. Then, based on a fitting deterministic screening experimental design, the second-order coupling term corresponding to the Zernike polynomial with a significant impact on the exposure results of the lithography system is determined. Further, higher-order coupling terms corresponding to the target Zernike polynomial are determined, including second-order, third-order, and fourth-order coupling terms. Based on the target Zernike polynomial, the target second-order coupling term, and the higher-order coupling terms, an analytical model is established, and the analytical model is fitted through random experiments to obtain a fitted model. Finally, based on a predetermined exposure result range, the budget range of aberrations is obtained through the fitted model. The technical solution of this application obtains Zernike polynomials that are highly sensitive to exposure results, determines the second-order coupling terms between the terms that have a significant impact on the exposure results through deterministic screening experimental design, and introduces higher-order coupling terms between Zernike polynomials that are highly sensitive to the exposure results. Based on the above Zernike polynomials, second-order coupling terms, and higher-order coupling terms, an analytical model is constructed, and a fitted model is obtained by fitting the analytical model through random experiments. Then, by using the fitted model and a preset exposure result range that meets the process requirements, the aberration budget range is obtained, which greatly improves the efficiency of obtaining the aberration budget range.
[0018] The above description is only an overview of the technical solution of this application. In order to better understand the technical means of this application and to implement it in accordance with the contents of the specification, and to make the above and other objects, features and advantages of this application more obvious and understandable, specific embodiments of this application are given below. Attached Figure Description
[0019] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this application, illustrate exemplary embodiments of the invention and, together with their description, serve to explain the invention and do not constitute an undue limitation thereof. In the drawings:
[0020] Figure 1 A flowchart illustrating a method for determining the budget range of aberrations according to an embodiment of the present invention is shown.
[0021] Figure 2 A schematic diagram of an aberration budget range determination device provided in an embodiment of the present invention is shown.
[0022] Figure 3 A schematic diagram of another aberration budget range determination device provided by an embodiment of the present invention is shown. Detailed Implementation
[0023] The present invention will be described in detail below with reference to the accompanying drawings and embodiments. It should be noted that, unless otherwise specified, the embodiments and features described in the present application can be combined with each other.
[0024] Existing methods for determining the aberration budget range of a lithography system mostly involve conducting a large number of experiments to determine the correspondence between the parameters of each aberration and the process conditions, thereby determining the aberration budget range. However, the above methods are too inefficient in determining the aberration budget range of a lithography system.
[0025] To address the above problems, in one embodiment, such as Figure 1 As shown, a method for determining the budget range of aberrations is provided. Taking the application of this method to a computer device in a lithography system as an example, the method includes the following steps:
[0026] 101. Obtain multiple target Zernike items.
[0027] The target Zernike polynomial is the Zernike polynomial among multiple Zernike polynomials that has a causal correlation with the exposure result of the lithography system based on the Zernike polynomial that satisfies a first preset condition. Furthermore, the Zernike polynomial can represent wavefront aberrations in the lithography system, and each term of the Zernike polynomial can represent a type of geometric aberration, such as spherical aberration, coma, astigmatism, etc. Wavefront aberration effects have a significant impact on the lithographic imaging quality.
[0028] Furthermore, the target Zernike polynomial can include a first Zernike polynomial and a second Zernike polynomial. The first Zernike polynomial has a significant impact on the critical dimension of the exposure result, while the second Zernike polynomial has a significant impact on the pattern offset. Causal correlation represents the magnitude of the influence of changes in the Zernike polynomial on the exposure result; it allows the value of one Zernike polynomial in the Zernike polynomial to vary within a preset range, while the values of other Zernike polynomials remain at preset ideal values. Exposure experiments are conducted on the lithography system based on the aforementioned Zernike polynomial. The range of variation of the critical dimension and the pattern offset based on the aforementioned Zernike polynomial are obtained in the exposure results. The causal correlation between the Zernike polynomial and the critical dimension and pattern offset is then determined, thereby identifying the degree of influence of the Zernike polynomial on the critical dimension and pattern offset results. Furthermore, through multiple exposure experiments, the influence of each Zernike element on the key dimensions and offset of the graphic is obtained. A predetermined number of Zernike elements with a significant impact on the key dimensions are designated as the first Zernike element, and a predetermined number of Zernike elements with a significant impact on the offset are designated as the second Zernike element. The first and second Zernike elements are then designated as the target Zernike elements. As an example, the number of first and second Zernike elements can each be 5, and the specific values can be determined based on the actual situation.
[0029] 102. Perform a fitting deterministic screening on the Zernike polynomial, identify the target second-order coupling term in the Zernike polynomial, and obtain the higher-order coupling term corresponding to the target Zernike term based on the target Zernike term.
[0030] Among these methods, the fitting deterministic screening can be a deterministic screening experimental design method, which can help design an experimental scheme to significantly reduce the experimental scale and avoid complete confounding between any effects below the second order. Furthermore, the target second-order coupling term can include a first second-order coupling term and a second second-order coupling term. The first second-order coupling term is a second-order coupling term in the Zernike polynomial with a high causal correlation to the key dimensions of the image in the exposure result, and it has a significant impact on the range of variation of the key dimensions of the image in the exposure result. The second second-order coupling term is a second-order coupling term in the Zernike polynomial with a high causal correlation to the image offset in the exposure result, and it has a significant impact on the range of variation of the image offset in the exposure result.
[0031] Furthermore, higher-order coupling terms refer to second-order, third-order, fourth-order, and higher-order coupling terms that can be formed from multiple target Zernike terms. For example, if there are five target Zernike terms, the higher-order coupling terms formed from these target Zernike terms include second-order, third-order, and fourth-order coupling terms. Further, higher-order coupling terms can be divided into first-order coupling terms that significantly affect the range of changes in the key dimensions of the image in the exposure result, and second-order coupling terms that significantly affect the range of changes in the image offset in the exposure result. Specifically, deterministic screening experimental design methods can be used to determine the first second-order coupling terms that significantly affect the range of changes in the key dimensions of the image in the exposure result, and the second second-order coupling terms that significantly affect the range of changes in the image offset in the exposure result. Further, based on the obtained first Zernike terms, first-order coupling terms corresponding to multiple first Zernike terms can be determined, and based on the obtained second Zernike terms, second-order coupling terms corresponding to multiple second Zernike terms can be determined.
[0032] 103. Based on the target Zernike single term, the target second-order coupling term, and the higher-order coupling term, establish an analytical model, and fit the analytical model based on random experiments to obtain a fitted model.
[0033] The parameters of the randomized experiments are preset randomized experimental values for each Zernike item included in the analytical model. Through randomized experiments, exposure results under each preset randomized experimental value can be obtained, including image key size results and image offset results. Furthermore, the analytical model can include an image key size analytical model and an image offset analytical model. Fitting the image key size analytical model to the randomized experiments yields an image key size fitting model, used to determine the budget range of image key size Zernike aberrations while meeting image key size requirements. Similarly, fitting the image offset analytical model to the randomized experiments yields an image offset fitting model, used to determine the budget range of image offset Zernike aberrations while meeting image offset requirements.
[0034] Specifically, the target Zernike single term, the target second-order coupling term, and the higher-order coupling term are introduced into the analytical model, and some random experiments are used to fit the model parameters. Furthermore, the first Zernike single term, the first second-order coupling term, and the first higher-order coupling term can be introduced into the analytical model to form an analytical model of the graphic key dimensions, and the graphic key dimensions fitting model is obtained by fitting the graphic key dimensions analytical model through random experiments. Conversely, the second Zernike single term, the second second-order coupling term, and the second higher-order coupling term can be introduced into the analytical model to form an analytical model of the graphic offset, and the graphic offset fitting model is obtained by fitting the graphic offset analytical model through random experiments.
[0035] 104. Based on a predetermined exposure result range, the budget range of the aberration is obtained through the fitting model.
[0036] The exposure result range can be the range of results from the lithography system that conforms to the process standards, including the critical dimension range and the pattern offset range. For example, the critical dimension range can be ±10% of the ideal critical dimension, and the pattern offset range can be ±1nm of the ideal pattern offset. The specific range can be determined based on actual conditions. Specifically, verification experiments can be conducted on the lithography system. The budget range for the Zernike aberration of the critical dimension can be obtained using the critical dimension range and the critical dimension fitting model, and the budget range for the Zernike aberration of the pattern offset can be obtained using the pattern offset range and the pattern offset fitting model. Furthermore, the budget range for the geometric aberration that meets the requirements of the critical dimension and pattern offset can be obtained through a preset conversion relationship between Zernike aberration and geometric aberration.
[0037] The method for determining the aberration budget range provided in this embodiment first obtains the target Zernike polynomial that has a significant impact on the exposure results of the lithography system, and determines the second-order coupling term corresponding to the Zernike polynomial that has a significant impact on the exposure results of the lithography system based on a fitting deterministic screening experimental design. Further, it determines the higher-order coupling terms corresponding to the target Zernike polynomial, including second-order, third-order, and fourth-order coupling terms. Based on the target Zernike polynomial, the target second-order coupling term, and the higher-order coupling terms, an analytical model is established, and the analytical model is fitted through random experiments to obtain a fitted model. Finally, based on a predetermined exposure result range, the aberration budget range is obtained through the fitted model. The technical solution of this application obtains Zernike polynomials that are highly sensitive to exposure results, determines second-order coupling terms between terms that have a significant impact on exposure results by defining a row screening experimental design, and introduces higher-order coupling terms between Zernike polynomials that are highly sensitive to exposure results. Based on the above Zernike polynomials, second-order coupling terms, and higher-order coupling terms, an analytical model is constructed, and a fitted model is obtained by fitting the analytical model through random experiments. Then, by using the fitted model and a preset exposure result range that meets the process requirements, the aberration budget range is obtained, which greatly improves the efficiency of obtaining the aberration budget range.
[0038] In one embodiment, the target second-order coupling term includes a first second-order coupling term and a second second-order coupling term; the target Zernike single term includes a first Zernike single term and a second Zernike single term; the method for determining the first Zernike single term and the second Zernike single term included in step 101 includes: firstly, determining a first causal correlation parameter between each first Zernike single term and the graphic key size contained in the exposure result, and a second causal correlation parameter between each second Zernike single term and the graphic offset contained in the exposure result. The first causal correlation parameter represents the magnitude of the influence of the Zernike single term on the graphic key size in the exposure result; the higher the first causal correlation parameter, the greater the influence of the Zernike single term on the graphic key size in the exposure result. Conversely, the second causal correlation parameter represents the magnitude of the influence of the Zernike single term on the graphic offset in the exposure result; the higher the second causal correlation parameter, the greater the influence of the Zernike single term on the graphic offset in the exposure result. Specifically, based on exposure experiments, the influence of each Zernike element on the critical dimensions of the graphic can be determined to obtain the first causal correlation parameter of each Zernike element, and the influence of each Zernike element on the graphic offset can be determined to obtain the second causal correlation parameter of each Zernike element.
[0039] Furthermore, based on the descending order of the values of each of the first and second causal correlation parameters, the first and second causal correlation parameters are arranged to obtain a first causal correlation parameter sequence and a second causal correlation parameter sequence. Specifically, the first preset number of first causal correlation parameters in the first causal correlation parameter sequence satisfies the first preset condition, and the second preset number of second causal correlation parameters in the second causal correlation parameter sequence satisfies the first preset condition. For example, the values of the first and second preset numbers can be 5, and the specific values can be determined based on actual conditions. Finally, the Zernike item corresponding to the first causal correlation parameter that satisfies the first preset condition is determined as the first Zernike item, and the Zernike item corresponding to the second causal correlation parameter that satisfies the first preset condition is determined as the second Zernike item. The embodiments of this application can determine the first and second Zernike items that have a significant impact on the graphic key size and graphic offset in the exposure results, thereby improving the efficiency of subsequent modeling.
[0040] In one embodiment, each Zernike item corresponds to a preset fixed value and a value range; wherein the fixed value can be the ideal value of the aberration represented by the corresponding Zernike item, and the value range can be the range of numerical variation of the Zernike item. Further, the method for determining the first causal correlation parameter between each first Zernike item and the key graphic dimension included in the exposure result, and the second causal correlation parameter between each second Zernike item and the graphic offset included in the exposure result, can be: executing a loop process until a preset loop condition is met, wherein the preset loop condition is: each Zernike item obtains its corresponding first causal correlation parameter and second causal correlation parameter, and the loop process includes:
[0041] First, select one Zernike term from the Zernike polynomial as the variable term, define the range of values corresponding to the variable term as the variable range, and set the values of all other Zernike terms to the fixed values. For example, Z1 in the Zernike polynomial can be selected as the variable term, the range of values corresponding to Z1 can be defined as the variable range, and the values of the other Zernike terms in a Zernike polynomial containing 37 Zernike terms can be set to the fixed values corresponding to the respective Zernike terms. Then, determine multiple sub-variable terms corresponding to the variable term. Each sub-variable term corresponds to a value within the variable range. For example, if the variable range corresponding to Z1 is [-1 to 1] and the unit value of this variable term is set to 0.1, then the number of sub-variable terms for this variable term is 20, and the value corresponding to each sub-variable term is a value within [-1 to 1], such as 0.1, 0.2, etc.
[0042] Furthermore, the lithography system is subjected to test exposure based on the Zernike polynomials containing different sub-variable terms, respectively, to obtain test exposure results. Specifically, multiple Zernike polynomials are constructed by combining one of the multiple sub-variable terms with the other Zernike terms, and test exposure is performed on each of these Zernike polynomials to obtain test exposure results for each sub-variable term. These test exposure results include the key dimension of the pattern and the pattern offset. Then, the variation range of the dimension parameter of the key dimension and the variation range of the offset parameter of the pattern in the test exposure results are determined. Specifically, the value of the key dimension in each test exposure result is obtained, and all key dimension values constitute the variation range of the dimension parameter; similarly, the value of the pattern offset in each test exposure result is obtained, and all offset values constitute the variation range of the offset parameter.
[0043] Furthermore, the ratio of the variation range of the dimensional parameter to the range of the variable is used as the first causal correlation parameter for the variable, and the ratio of the variation range of the offset parameter to the range of the variable is used as the second causal correlation parameter for the variable. Specifically, the first causal correlation parameter can be obtained by subtracting the lowest value from the highest value of the variation range of the dimensional parameter, and then dividing the difference by the difference between the highest and lowest values of the variable range.
[0044] Correspondingly, the highest value of the offset parameter range can be subtracted from the lowest value, and the difference can be divided by the difference between the highest and lowest values of the variable range to obtain the second causal correlation parameter. Finally, the variable item is determined as the Zernike item to facilitate subsequent iterations. The embodiments provided in this application can quickly determine the first and second causal correlation parameters for each Zernike item, improving the efficiency of determining the budget range of aberrations.
[0045] In one embodiment, the implementation of step 102, which involves performing a fitting deterministic screening of the Zernike polynomial to determine the target second-order coupling term in the Zernike polynomial, can be as follows: based on the fitting deterministic screening experimental design method, determine the first second-order coupling term in the Zernike polynomial whose causal correlation with the key dimensions of the graphic satisfies the second preset condition, and determine the second second-order coupling term in the Zernike polynomial whose causal correlation with the offset of the graphic satisfies the third preset condition.
[0046] Among these, deterministic screening experimental design can help design experimental schemes for exposure experiments, which can significantly reduce the experimental scale and avoid complete confounding between any effects below the second order. At the same time, under the condition of sparsity of significant factors, the coefficients of the main effect terms, the quadratic terms of the main effect terms, and the second-order interaction terms of all significant factors can be estimated, so as to obtain the main effects and second-order coupling terms between experimental parameters and experimental exposure results with only a small number of experiments.
[0047] Furthermore, the second preset condition is used to calibrate the conditions that the causal correlation between the second-order coupling term and the key dimension of the image must satisfy, and to determine the degree of influence of the second-order coupling term on the key dimension of the image in the exposure result; correspondingly, the third preset condition is used to calibrate the conditions that the causal correlation between the second-order coupling term and the image offset must satisfy, and to determine the degree of influence of the second-order coupling term on the image offset in the exposure result. When the degree of influence of the second-order coupling term on the key dimension of the image in the exposure result meets the second preset condition, the second-order coupling term can be determined as the first second-order coupling term; when the degree of influence of the second-order coupling term on the image offset in the exposure result meets the third preset condition, the second-order coupling term can be determined as the second second-order coupling term. The embodiments provided in this application can obtain factors for modeling by fitting a deterministic screening experimental design. The factors contain certain Zernike items, second-order coupling terms between some Zernike items, and secondary effects, providing a foundation for subsequent modeling work.
[0048] In one embodiment, step 103 can be implemented as follows: First, construct the graphic key dimension analytical model contained in the analytical model using the first Zernike single term, the first second-order coupling term, and the higher-order coupling term, respectively; and construct the graphic offset analytical model contained in the analytical model using the second Zernike single term, the second second-order coupling term, and the higher-order coupling term, respectively. Specifically, the graphic key dimension analytical model can be constructed based on the first higher-order coupling term, the first Zernike single term, and the first second-order coupling term in the higher-order coupling term, so as to introduce the higher-order coupling term, the Zernike single term, the second-order coupling term, and the quadratic effect into the graphic key dimension analytical model; conversely, the graphic offset analytical model can be constructed based on the second higher-order coupling term, the second Zernike single term, and the second second-order coupling term in the higher-order coupling term, so as to introduce the higher-order coupling term, the Zernike single term, the second-order coupling term, and the quadratic effect into the graphic offset analytical model.
[0049] Furthermore, experimental exposure operations are performed on the lithography system based on preset experimental parameters to obtain experimental exposure results. These results include key dimension results and pattern offset results. Specifically, random experiments are conducted on the analytical model. The parameters of these random experiments are preset random experimental values for each Zernike item included in the analytical model. Through these random experiments, exposure results are obtained for each preset random experimental value, and these exposure results include key dimension results and pattern offset results.
[0050] Furthermore, based on the experimental parameters and the results of the key dimensions of the graphics, the analytical model of the key dimensions of the graphics is fitted to obtain a fitting model of the key dimensions of the graphics included in the fitting model. Specifically, the first Zernike single term, the first second-order coupling term, and the first higher-order coupling term are introduced into the analytical model of the key dimensions of the graphics, and some random experiments are introduced to fit the model parameters. The coefficients of each term of the fitted model are calculated to obtain a fitting model of the key dimensions of the graphics. Furthermore, based on the experimental parameters and the results of the graphics offset, the analytical model of the graphics offset is fitted to obtain a fitting model of the graphics offset included in the fitting model. Specifically, the second Zernike single term, the second second-order coupling term, and the second higher-order coupling term are introduced into the analytical model of the graphics offset. Some random experiments are introduced to fit the model parameters. The coefficients of each term of the fitted model are calculated to obtain a fitting model of the graphics offset. In the embodiments of this application, Zernike single term parameters, quadratic effects up to fourth-order coupling terms can be introduced into the analytical model, and some random experiments can be introduced to fit the model parameters. Thus, the final fitting model of the key dimensions of the graphics and the fitting model of the graphics offset are obtained.
[0051] In one embodiment, the exposure result range includes a graphic critical size range and a graphic offset range; further, step 104 can be implemented as follows: first, based on the graphic critical size range and the graphic critical size fitting model, obtain the budget range of the graphic critical size Zernike aberration that satisfies the graphic critical size range.
[0052] Here, the Zernikal aberration of the graphic critical dimension can be a parameter of the Zernikal aberration related to the graphic critical dimension, and the graphic critical dimension range can be a range of graphic critical dimensions that conform to the process standards. As an example, the graphic critical dimension range can be a range of ±10% of the ideal graphic critical dimension, and the specific range can be determined according to the actual situation. Specifically, the graphic critical dimension fitting model can be experimentally verified based on the graphic critical dimension range to obtain the budget range of the Zernikal aberration related to the graphic critical dimension.
[0053] Furthermore, based on the pattern offset interval and the pattern offset fitting model, the budget range of the pattern offset Zernike aberration that satisfies the pattern offset interval is obtained. Here, the pattern offset Zernike aberration can be a parameter of the Zernike aberration related to the pattern offset, and the pattern offset interval can be a range of pattern offsets conforming to process standards. As an example, the pattern offset interval can be a range of ±1nm for the ideal pattern offset; the specific interval range can be determined according to actual conditions. Specifically, the pattern offset fitting model can be experimentally verified based on the pattern offset interval to obtain the budget range of the Zernike aberration related to the pattern offset.
[0054] Furthermore, based on the budget range of the Zernikal aberration of the key graphic dimension, the budget range of the Zernikal aberration of the graphic offset, and a preset conversion formula, the budget range of the aberration is obtained. The conversion formula can be a conversion formula between Zernikal aberration and geometric aberration, and specific conversion formulas are shown in Table 1.
[0055]
[0056] Table 1
[0057] In this context, each term in the transformation relationship represents a Zernike aberration obtained from the fitted model. The budget range for each geometric aberration can be obtained through the Zernike aberration and the transformation relationship. Specifically, based on the fitting models for key dimensions and offsets, the budget ranges for key dimension Zernike aberrations and offset Zernike aberrations are obtained. Further, based on the budget ranges for key dimension Zernike aberrations and the transformation relationship, the budget ranges for aberrations related to key dimensions are obtained; conversely, based on the budget ranges for offset Zernike aberrations and the transformation relationship, the budget ranges for aberrations related to offsets are obtained. Furthermore, the intersection of the budget ranges for key dimension aberrations and offset aberrations is determined as the budget range for geometric aberrations. Additionally, each geometric aberration can be displayed in the form of a box plot. The embodiments provided in this application can obtain feasible aberration distribution ranges using the fitted model, and can quickly obtain aberration budgets with a small number of experiments, reducing the cost of experiments and testing.
[0058] In one embodiment, after step 104, the method further includes: first, acquiring the aberration parameters of the projection lens to be tested. The projection lens to be tested can be a projection lens that will be applied to a lithography system. Before its formal use, it can be tested to determine whether its geometric aberration parameters meet the process standards. Specifically, the aberration parameters of geometric aberrations such as spherical aberration and coma of the projection lens to be tested are acquired. Further, it is determined whether all the aberration parameters are within the aberration budget range. Specifically, it can be determined whether each aberration parameter of the projection lens is within the geometric aberration budget range. If all the aberration parameters are within the aberration budget range, the projection lens is determined to meet the aberration requirements of the lithography system. Correspondingly, if there are aberration parameters outside the aberration budget range, the projection lens is determined to not meet the aberration requirements of the lithography system, and an alarm message is issued for relevant personnel to confirm. The embodiments of this application can verify the projection lens to be applied to a lithography system and confirm whether it meets the aberration requirements of the lithography system.
[0059] The aberration budget range determination method provided in this embodiment can determine the overall variables of the fitted model based on a defined row screening experimental design, including individual Zernike items and the coupling relationships between Zernike items. Subsequently, by introducing higher-order couplings between some highly sensitive Zernike items and fitting them using random aberrations, the final model of aberrations and exposure results is obtained, the budget range of geometric aberrations is calculated, and the aberration parameters of the projection lens can be confirmed to determine whether the projection lens meets the geometric aberration requirements of the process.
[0060] Furthermore, as Figure 1The specific implementation of the method shown in this embodiment provides an aberration budget range determination device, such as... Figure 2 As shown, the device includes: a single-item acquisition module 21, a high-order coupling module 22, a model fitting module 23, and a range determination module 24.
[0061] The single-item acquisition module 21 can be used to acquire multiple target Zernike items, wherein the target Zernike item is the Zernike item among multiple Zernike items of the Zernike polynomial whose causal correlation with the exposure result of the lithography system based on the Zernike polynomial satisfies a first preset condition.
[0062] The higher-order coupling module 22 can be used to perform a fitting deterministic screening of the Zernike polynomial, determine the target second-order coupling term in the Zernike polynomial, and obtain the higher-order coupling term corresponding to the target Zernike term based on the target Zernike term.
[0063] The model fitting module 23 can be used to establish an analytical model based on the target Zernike single term, the target second-order coupling term, and the higher-order coupling term, and to fit the analytical model based on random experiments to obtain a fitted model;
[0064] The range determination module 24 can be used to obtain the budget range of the aberration based on a pre-determined exposure result range through the fitting model.
[0065] In a specific application scenario, the target second-order coupling term includes a first second-order coupling term and a second second-order coupling term; the target Zernike single term includes a first Zernike single term and a second Zernike single term; the single term acquisition module 21 can be used to determine the first causal correlation parameter between each first Zernike single term and the graphic key size contained in the exposure result, and the second causal correlation parameter between each second Zernike single term and the graphic offset contained in the exposure result; according to the order of the values of each first causal correlation parameter and the second causal correlation parameter from largest to smallest, the first causal correlation parameter and the second causal correlation parameter are arranged to obtain a first causal correlation parameter sequence and a second causal correlation parameter sequence, wherein the first preset number of first causal correlation parameters arranged in the first causal correlation parameter sequence satisfies the first preset condition, and the second preset number of second causal correlation parameters arranged in the second causal correlation parameter sequence satisfies the first preset condition; the Zernike single term corresponding to the first causal correlation parameter that satisfies the first preset condition is determined as the first Zernike single term, and the Zernike single term corresponding to the second causal correlation parameter that satisfies the first preset condition is determined as the second Zernike single term.
[0066] In specific application scenarios, each Zernike polynomial corresponds to a preset fixed value and a value range. The polynomial acquisition module 21 can be used to execute a loop process until a preset loop condition is met. The loop process includes: selecting one Zernike polynomial as a variable polynomial; determining the value range corresponding to the variable polynomial as a variable range; setting the values of all Zernike polynomials other than the variable polynomial to the fixed value; determining multiple sub-variable polynomials corresponding to the variable polynomial, where each sub-variable polynomial corresponds to a value within the variable range; and determining the values of each sub-variable polynomial based on the value of the sub-variable polynomial. The Zernike polynomial of the term is used to test the exposure of the lithography system to obtain test exposure results; the range of variation of the size parameter of the key dimension of the pattern and the range of variation of the offset parameter of the pattern offset in the test exposure results are determined; the ratio of the range of variation of the size parameter to the range of the variable is used as the first causal correlation parameter of the variable term, and the ratio of the range of variation of the offset parameter to the range of the variable is used as the second causal correlation parameter of the variable term; the variable term is determined as the Zernike term; wherein, the preset loop condition is: each Zernike term obtains the corresponding first causal correlation parameter and the second causal correlation parameter.
[0067] In specific application scenarios, the higher-order coupling module 22 can be used to determine the first second-order coupling term in the Zernike polynomial that satisfies the second preset condition of the causal correlation between the Zernike polynomial and the key dimensions of the graphic, and to determine the second second-order coupling term in the Zernike polynomial that satisfies the third preset condition of the causal correlation between the Zernike polynomial and the offset of the graphic.
[0068] In specific application scenarios, the model fitting module 23 can be used to construct the graphic key dimension analytical model contained in the analytical model through the first Zernike single term, the first second-order coupling term, and the higher-order coupling term, respectively, and to construct the graphic offset analytical model contained in the analytical model through the second Zernike single term, the second second-order coupling term, and the higher-order coupling term, respectively; to perform experimental exposure operations on the lithography system based on preset experimental parameters to obtain experimental exposure results, wherein the experimental exposure results include graphic key dimension results and graphic offset results; to fit the graphic key dimension analytical model based on the experimental parameters and the graphic key dimension results to obtain the graphic key dimension fitting model contained in the fitting model; and to fit the graphic offset analytical model based on the experimental parameters and the graphic offset results to obtain the graphic offset fitting model contained in the fitting model.
[0069] In specific application scenarios, the exposure result range includes a key dimension range and a key offset range. The range determination module 24 can be used to obtain a budget range of Zernike aberrations of the key dimension that satisfy the key dimension range based on the key dimension range and the key dimension fitting model, and to obtain a budget range of Zernike aberrations of the offset that satisfy the offset range based on the key dimension range and the offset fitting model. The budget range of the aberration is obtained according to the budget range of the key dimension Zernike aberration, the budget range of the offset Zernike aberration, and a preset conversion formula.
[0070] In specific application scenarios, such as Figure 3 As shown, the device also includes an objective lens inspection module 35, which is specifically used to acquire the aberration parameters of the projection objective lens to be tested; determine whether the aberration parameters are all within the aberration budget range; if the aberration parameters are all within the aberration budget range, then the projection objective lens is determined to meet the aberration requirements of the lithography system.
[0071] It should be noted that other corresponding descriptions of the functional units involved in the aberration budget range determination device provided in this embodiment can be found in [reference]. Figure 1 The corresponding descriptions in [the document] will not be repeated here.
[0072] Based on the above, Figure 1 Accordingly, this embodiment also provides a storage medium storing a computer program that, when executed by a processor, implements the above-described method. Figure 1 The method for determining the budget range of aberrations is shown.
[0073] Based on this understanding, the technical solution of this application can be embodied in the form of a software product. The software product to be identified can be stored in a non-volatile storage medium (such as a CD-ROM, USB flash drive, or portable hard drive), including several instructions to cause a computer device (such as a personal computer, server, or network device) to execute the methods described in the various implementation scenarios of this application.
[0074] Based on the above, Figure 1 The method shown, and Figure 2 and Figure 3 The illustrated embodiment of the aberration budget range determination device, in order to achieve the above objective, also provides a physical device for determining the aberration budget range. Specifically, this device can be a personal computer, server, smartphone, tablet computer, smartwatch, or other network device, etc. The physical device includes a storage medium and a processor; the storage medium is used to store a computer program; the processor is used to execute the computer program to achieve the above-described... Figure 1 The method shown.
[0075] Optionally, the physical device may also include a user interface, a network interface, a camera, radio frequency (RF) circuitry, sensors, audio circuitry, a Wi-Fi module, etc. The user interface may include a display screen, input units such as a keyboard, etc., and optional user interfaces may also include USB interfaces, card reader interfaces, etc. The network interface may optionally include standard wired interfaces, wireless interfaces (such as Wi-Fi interfaces), etc.
[0076] Those skilled in the art will understand that the physical device structure for determining the budget range of aberrations provided in this embodiment does not constitute a limitation on the physical device, and may include more or fewer components, or combine certain components, or have different component arrangements.
[0077] The storage medium may also include an operating system and a network communication module. The operating system is a program that manages the hardware and software resources of the aforementioned physical device, supporting the operation of information processing programs and other software and / or programs to be identified. The network communication module is used to enable communication between the various components within the storage medium, as well as communication with other hardware and software in the information processing physical device.
[0078] Through the above description of the embodiments, those skilled in the art can clearly understand that this application can be implemented by means of software plus necessary general-purpose hardware platforms, or it can be implemented by hardware. By applying the technical solution of this application, firstly, multiple target Zernike terms are obtained, wherein the target Zernike term is the Zernike term among multiple Zernike polynomials whose causal correlation with the exposure result of the lithography system based on the Zernike polynomial satisfies a first preset condition; then, the Zernike polynomial is subjected to a fitting deterministic screening to determine the target second-order coupling term in the Zernike polynomial, and based on the target Zernike term, the corresponding higher-order coupling term is obtained; then, based on the target Zernike term, the target second-order coupling term, and the higher-order coupling term, an analytical model is established, and the analytical model is fitted based on random experiments to obtain a fitted model; finally, based on a predetermined exposure result range, the aberration budget range is obtained through the fitted model. Compared with the prior art, the efficiency of obtaining the aberration budget range can be improved.
[0079] Those skilled in the art will understand that the accompanying drawings are merely schematic diagrams of a preferred embodiment, and the modules or processes shown in the drawings are not necessarily essential for implementing this application. Those skilled in the art will understand that the modules in the apparatus of the embodiment can be distributed within the apparatus of the embodiment as described, or they can be located in one or more apparatuses different from this embodiment, with corresponding changes. The modules of the above-described embodiment can be combined into one module, or further divided into multiple sub-modules.
[0080] The serial numbers in this application are for descriptive purposes only and do not represent the superiority or inferiority of any particular implementation scenario. The above disclosures are merely a few specific implementation scenarios of this application; however, this application is not limited thereto, and any variations conceived by those skilled in the art should fall within the protection scope of this application.
Claims
1. A method for determining the budget range of aberrations, applied to a photolithography system, characterized in that, The method includes: Multiple target Zernike items are obtained, wherein the target Zernike item is the Zernike item among the multiple Zernike items of the Zernike polynomial that satisfies a first preset condition in terms of causal correlation with the exposure result of the lithography system based on the Zernike polynomial, and the causal correlation indicates the magnitude of the influence of the change of the Zernike item on the exposure result. The Zernike polynomial is fitted with deterministic screening to identify the target second-order coupling term in the Zernike polynomial. Based on the target Zernike term, the higher-order coupling term corresponding to the target Zernike term is obtained. The target second-order coupling term includes a first second-order coupling term and a second second-order coupling term. The target Zernike term includes a first Zernike term and a second Zernike term. An analytical model is established based on the target Zernike single term, the target second-order coupling term, and the higher-order coupling term. The analytical model is then fitted using random experiments to obtain a fitted model. This process includes: constructing an analytical model of the graphic key dimensions contained in the analytical model using the first Zernike single term, the first second-order coupling term, and the higher-order coupling term; constructing an analytical model of the graphic offset contained in the analytical model using the second Zernike single term, the second second-order coupling term, and the higher-order coupling term; performing experimental exposure operations on the lithography system based on preset experimental parameters to obtain experimental exposure results, wherein the experimental exposure results include graphic key dimension results and graphic offset results; fitting the graphic key dimension analytical model based on the experimental parameters and the graphic key dimension results to obtain a graphic key dimension fitting model contained in the fitted model; and fitting the graphic offset analytical model based on the experimental parameters and the graphic offset results to obtain a graphic offset fitting model contained in the fitted model. Based on a predetermined exposure result range, the budget range of the aberration is obtained through the fitting model, wherein the exposure result range includes the image critical size range and the image offset range.
2. The method according to claim 1, characterized in that, The methods for determining the first Zenik term and the second Zenik term include: A first causal correlation parameter is determined between each of the first Zernike items and the graphic key dimensions contained in the exposure result, and a second causal correlation parameter is determined between each of the second Zernike items and the graphic offset contained in the exposure result; Based on the descending order of the values of each of the first and second causal correlation parameters, the first and second causal correlation parameters are arranged to obtain a first causal correlation parameter sequence and a second causal correlation parameter sequence. Wherein, the first causal correlation parameters arranged in the first causal correlation parameter sequence first preset number satisfy the first preset condition, and the second causal correlation parameters arranged in the second causal correlation parameter sequence second preset number satisfy the first preset condition; The Zernike item corresponding to the first causal correlation parameter that satisfies the first preset condition is determined as the first Zernike item, and the Zernike item corresponding to the second causal correlation parameter that satisfies the first preset condition is determined as the second Zernike item.
3. The method according to claim 2, characterized in that, The Zernike item corresponds to a preset fixed value and a value range; the step of determining the first causal correlation parameter between each first Zernike item and the graphic key size included in the exposure result, and the second causal correlation parameter between each second Zernike item and the graphic offset included in the exposure result, includes: The loop process is executed until a preset loop condition is met, wherein the loop process includes: Select one Zernike polynomial as a variable term, define the range of values corresponding to the variable term as the variable range, and set the values of all Zernike terms other than the variable term to the fixed values. Determine multiple sub-variable items corresponding to the single variable item, wherein each sub-variable item corresponds to a value within the range of the variable; The lithography system is tested and exposed based on the Zernik polynomial containing different terms of the sub-variables, and the test exposure results are obtained. Determine the range of variation of the dimensional parameters of the key dimensions of the graphic and the range of variation of the offset parameters of the graphic offset in the test exposure results; The ratio of the variation range of the size parameter to the range of the variable is used as the first causal correlation parameter of the variable item, and the ratio of the variation range of the offset parameter to the range of the variable is used as the second causal correlation parameter of the variable item. The variable item is identified as the Zernike item; The preset loop condition is that each Zernike item obtains the corresponding first causal correlation parameter and the second causal correlation parameter.
4. The method according to any one of claims 1 to 3, characterized in that, The step of performing a deterministic fitting and screening of the Zernike polynomial to determine the target second-order coupling term in the Zernike polynomial includes: Based on the fitting deterministic screening experimental design method, the first second-order coupling term in the Zernike polynomial that satisfies the second preset condition of causal correlation with the key dimensions of the graphic is determined, and the second second-order coupling term in the Zernike polynomial that satisfies the third preset condition of causal correlation with the offset of the graphic is determined.
5. The method according to claim 1, characterized in that, The process of obtaining the budget range of the aberration based on the predetermined exposure result range through the fitting model includes: Based on the key dimension range of the graphic and the key dimension fitting model of the graphic, the budget range of the key dimension Zernikal aberration of the graphic that satisfies the key dimension range of the graphic is obtained, and based on the offset range of the graphic and the offset fitting model of the graphic, the budget range of the offset Zernikal aberration of the graphic is obtained. The budget range of the aberration is obtained based on the budget range of the Zernike aberration of the key dimension of the image, the budget range of the Zernike aberration of the image offset, and a preset conversion formula.
6. The method according to claim 1, characterized in that, The method further includes: Obtain the aberration parameters of the projection lens to be tested; Determine whether all aberration parameters are within the budget range of the aberration; If all the aberration parameters are within the aberration budget range, then the projection lens is determined to meet the aberration requirements of the lithography system.
7. An aberration budget range determination device, characterized in that, The device includes: A single-item acquisition module is used to acquire multiple target Zernike items, wherein the target Zernike item is the Zernike item among multiple Zernike items of the Zernike polynomial that satisfies a first preset condition in terms of causal correlation with the exposure result of the lithography system based on the Zernike polynomial, and the causal correlation indicates the magnitude of the influence of the change of the Zernike item on the exposure result. A higher-order coupling module is used to perform a fitting deterministic screening of the Zernike polynomial, determine the target second-order coupling term in the Zernike polynomial, and obtain the higher-order coupling term corresponding to the target Zernike single term based on the target Zernike single term. The target second-order coupling term includes a first second-order coupling term and a second second-order coupling term, and the target Zernike single term includes a first Zernike single term and a second Zernike single term. The model fitting module is used to establish an analytical model based on the target Zernike single term, the target second-order coupling term, and the higher-order coupling term, and to fit the analytical model based on random experiments to obtain a fitted model. This includes: constructing an analytical model of the graphic key dimensions included in the analytical model using the first Zernike single term, the first second-order coupling term, and the higher-order coupling term; constructing an analytical model of the graphic offset included in the analytical model using the second Zernike single term, the second second-order coupling term, and the higher-order coupling term; performing experimental exposure operations on the lithography system based on preset experimental parameters to obtain experimental exposure results, wherein the experimental exposure results include graphic key dimension results and graphic offset results; fitting the graphic key dimension analytical model based on the experimental parameters and the graphic key dimension results to obtain a graphic key dimension fitting model included in the fitted model; and fitting the graphic offset analytical model based on the experimental parameters and the graphic offset results to obtain a graphic offset fitting model included in the fitted model. The range determination module is used to obtain the budget range of the aberration based on a pre-determined exposure result range through the fitting model, wherein the exposure result range includes the image critical size range and the image offset range.
8. A storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 6.
9. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 6.