OPC Modeling Method

Abstract

The present invention provides an OPC modeling method, comprising: determining optical model parameters and resist model parameters; randomly selecting values for each parameter to generate multiple parameter combinations; performing photolithography simulation and etching on a wafer, calculating the root mean square value and Poisson curve error value of the difference between the photolithography simulation critical dimension and the wafer etching critical dimension; evaluating according to the Pareto law, calculating a Pareto optimal set to a Pareto Nth suboptimal set, and arranging multiple parameter combinations in descending order; performing crossover and / or mutation processing on the multiple parameter combinations using a genetic algorithm to form a new parameter combination; iterating the new parameter combination according to steps S3 to S5 until the number of times reaches a first set value, and using the parameter combination with the highest ranking obtained at this time for OPC modeling. The present invention simultaneously adjusts the optical model parameters and the resist model parameters during modeling, and can simultaneously find the optimal values of the optical model parameters and the resist model parameters.

Description

Technical Field

[0001] The present invention relates to the field of semiconductor technology, and in particular to an OPC modeling method. Background Art

[0002] Photolithography is a process that uses a mask to transfer the desired pattern onto the wafer, thereby creating corresponding patterns in different areas. In order to ensure that the pattern transferred to the wafer is consistent with the ideal pattern and to reduce the impact of the optical proximity effect on the transferred pattern during the photolithography process, optical proximity correction (OPC) of the mask pattern needs to be continuously performed.

[0003] OPC correction requires OPC modeling first. The parameters of OPC modeling, or lithography model parameters, are generally determined by optical model parameters and resist model parameters. Therefore, it is necessary to ensure that the optical model parameters and resist model parameters are optimized at the same time in order to optimize the lithography model parameters.

[0004] The existing OPC modeling method is to simulate the optical model parameters and the resist model parameters separately using a segmented model optimization process, for example, to first find the optimal optical model parameters, and then continue to find the optimal resist model parameters based on the optimal optical model parameters.

[0005] However, in the existing OPC modeling methods described above, the second step of segmented optimization is based on the optimal solution found in the first step. In other words, not all possible solutions are explored in the second step. Therefore, when one model parameter reaches its optimal value, the optimal solution found for another model parameter may not be the true optimal value. In other words, using segmented optimization methods, it is difficult to simultaneously find the optimal values for both the optical and resist model parameters. This results in an inability to achieve an optimal balance between the optical and resist model parameters, and consequently, an inability to optimize the lithography model parameters. Summary of the Invention

[0006] The object of the present invention is to provide an OPC modeling method that can adjust optical model parameters and resist model parameters simultaneously to find the optimal values of the optical model parameters and the resist model parameters at the same time, so that the optical model parameters and the resist model parameters are balanced, thereby optimizing the lithography model parameters.

[0007] In order to achieve the above object, the present invention provides an OPC modeling method, comprising:

[0008] S1: Determine optical model parameters, resist model parameters and the value range of each parameter;

[0009] S2: generating a plurality of parameter combinations by randomly selecting values for each parameter within the value range, wherein each parameter combination includes both an optical model parameter value and a resist model parameter value, and different parameter combinations include different optical model parameter values and resist model parameter values;

[0010] S3: performing photolithography simulation and etching the wafer using multiple parameter combinations, and calculating root mean square values and Poisson curve error values of differences between photolithography simulation critical dimensions and wafer etching critical dimensions, to obtain root mean square values of multiple differences and multiple Poisson curve error values;

[0011] S4: Evaluate the root mean square values of the multiple differences and the multiple Poisson curve error values according to the Pareto theorem, and calculate a Pareto optimal set, a Pareto suboptimal set, a Pareto second-optimal set, and a Pareto Nth-suboptimal set, so as to arrange the multiple parameter combinations in order from best to worst, where N is an integer greater than 1;

[0012] S5: using a genetic algorithm to perform a co-location crossover and / or mutation process on the multiple parameter combinations arranged in step S4 to form multiple new parameter combinations;

[0013] S6: Iterate the new multiple parameter combinations according to steps S3 to S5 until the number of iterations reaches a first set value, and use the parameter combination with the highest order obtained at this time for OPC modeling.

[0014] Optionally, in the OPC modeling method, a method for calculating the root mean square value of the difference between the photolithography simulation critical dimension and the wafer etching critical dimension includes:

[0015] Measure wafer etching critical dimensions and lithography model simulation critical dimensions;

[0016] Calculate the difference between wafer etching critical dimensions and lithography model simulation critical dimensions;

[0017] A root mean square of the difference is calculated to serve as the root mean square value of the difference.

[0018] Optionally, in the OPC modeling method, the method for calculating the Poisson curve error of the photolithography simulation critical dimension and the wafer etching critical dimension includes:

[0019] forming a first Poisson curve according to values of a plurality of wafer etching critical dimensions;

[0020] forming a second Poisson curve according to a plurality of values of photolithography simulation critical dimensions;

[0021] An error score between the first Poisson curve and the second Poisson curve is calculated as a Poisson curve error value.

[0022] Optionally, in the OPC modeling method, the maximum information coefficient MIC is used to evaluate the Poisson curve error value, and the higher the maximum information coefficient MIC is, the smaller the Poisson curve error value is.

[0023] Optionally, in the OPC modeling method, the method for calculating the maximum information coefficient MIC includes:

[0024]

[0025] Among them, n x and n y is the number of buckets on the x-axis and y-axis, and G represents n in (X, Y) x ×n y Grid number, I G (X, Y) represents the mutual information under the grid G, B(n, a) is a function of the data size n, equal to n^α, where 0<a<1, log2min(n x , n y ) is a normalization term used to ensure that the MIC is in the range of 0 to 1.

[0026] Optionally, in the OPC modeling method, the method of evaluating the root mean square values of the multiple differences and the multiple Poisson curve error values according to the Pareto law includes:

[0027] A combination of a root mean square value of the difference and a Poisson curve error value is defined as Y(RMS, BCE) to form a plurality of Y(RMS, BCE);

[0028] By Find the combination of the root mean square value of the difference and the error value of the Poisson curve that meets the requirements of the plurality of Y (RMS, BCE); wherein: y" is the Pareto optimal solution.

[0029] Optionally, in the OPC modeling method, in step S5, a genetic algorithm is applied to the multiple parameter combinations after arrangement with different weights according to the arrangement order, wherein the probability of performing co-location crossover on the parameter combinations decreases according to the arrangement order.

[0030] Optionally, in the OPC modeling method, the method of performing co-location crossover on the parameter combination includes:

[0031] The parameter values at a certain position in at least two parameter combinations are cross-calculated to generate the parameter value at the same position in the current parameter combination.

[0032] Optionally, in the OPC modeling method, the method of performing mutation processing on the parameter combination includes:

[0033] Determine whether the number of iterations in which the Pareto optimal set is not updated exceeds a second set value;

[0034] If not, performing conventional mutation on the optical model parameter values and the resist model parameter values in accordance with the original setting conditions;

[0035] If so, some optical model parameter values and resist model parameter values are randomly selected to perform enhanced mutation based on the original setting conditions.

[0036] Optionally, in the OPC modeling method, the optical model parameters include one or more of the numerical aperture, resolution, aberration, polarization or optical constants of the projection objective; the resist model parameters include one or more of the refractive index, film thickness, optical propagation and polarization effects of the photoresist.

[0037] Optionally, in the OPC modeling method, step S1 also includes determining the precision of each parameter, and the parameter combination with the highest ranking obtained in step S6 includes the parameter combination with the highest ranking in each sub-range after the value range is divided according to precision, and the set of parameter combinations with the highest ranking corresponding to each sub-range forms the optimal parameter combination set for OPC modeling.

[0038] In the OPC modeling method provided by the present invention, the optical model parameters and the resist model parameters are adjusted simultaneously, and the optimal values of the optical model parameters and the resist model parameters are found at the same time, so that the optical model parameters and the resist model parameters reach the best balance, thereby making the parameters of the lithography model reach the optimal level and establishing the optimal OPC model. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 4 is a flow chart of an OPC modeling method according to an embodiment of the present invention. DETAILED DESCRIPTION

[0040] The following is a more detailed description of the specific embodiments of the present invention with reference to schematic diagrams. The advantages and features of the present invention will become more apparent from the following description. It should be noted that the drawings are greatly simplified and not to exact scale, and are only used for the purpose of conveniently and clearly illustrating the embodiments of the present invention.

[0041] Hereinafter, the terms "first," "second," and the like are used merely to distinguish between similar elements and are not necessarily intended to describe a particular order or chronological sequence. It should be understood that these terms, when used in this manner, are interchangeable where appropriate. Similarly, if a method described herein includes a series of steps, the order in which the steps are presented herein is not necessarily the only order in which the steps may be performed, and some of the steps described may be omitted and / or other steps not described herein may be added to the method.

[0042] Please refer to Figure 1 The present invention provides an OPC modeling method, comprising:

[0043] S1: Determine optical model parameters, resist model parameters and the value range of each parameter;

[0044] S2: generating a plurality of parameter combinations by randomly selecting values for each parameter within the value range, wherein each parameter combination includes both an optical model parameter value and a resist model parameter value, and different parameter combinations include different optical model parameter values and resist model parameter values;

[0045] S3: performing photolithography simulation and etching the wafer using multiple parameter combinations, and calculating root mean square values and Poisson curve error values of differences between photolithography simulation critical dimensions and wafer etching critical dimensions, to obtain root mean square values of multiple differences and multiple Poisson curve error values;

[0046] S4: Evaluate the root mean square values of the multiple differences and the multiple Poisson curve error values according to the Pareto theorem, and calculate a Pareto optimal set, a Pareto suboptimal set, a Pareto second-optimal set, and a Pareto Nth-suboptimal set, so as to arrange the multiple parameter combinations in order from best to worst, where N is an integer greater than 1;

[0047] S5: using a genetic algorithm to perform a co-location crossover and / or mutation process on the multiple parameter combinations arranged in step S4 to form multiple new parameter combinations;

[0048] S6: Iterate the new multiple parameter combinations according to steps S3 to S5 until the number of iterations reaches a first set value, and use the parameter combination with the highest order obtained at this time for OPC modeling.

[0049] In step S1, the optical model parameters may include the optical properties of the projection objective lens in the lithography apparatus, such as one or more of the numerical aperture (NA), resolution σ, aberration, polarization, or optical constant. In an embodiment of the present invention, the numerical aperture (NA), aberration, polarization, and optical constant may be selected as the optical model parameters. Next, the value ranges of the numerical aperture (NA), aberration, polarization, and optical constant are determined. For example, the ranges may be 0 to 1, 2 to 5, 6 to 10, and 6 to 10, respectively. The above parameter values are explained as examples and are not limitations on the values. In other embodiments of the present invention, other values may be selected. The resist model parameters may include the properties of the photoresist layer coated on the substrate, such as one or more of the photoresist refractive index, film thickness, optical propagation, and polarization effect. In an embodiment of the present invention, the photoresist refractive index, film thickness, optical propagation, and polarization effect are selected as the resist model parameters. Next, determine the range of the photoresist refractive index, film thickness, optical propagation and polarization effect. For example, the parameter ranges can be set to 16-20, 21-25, 26-30 and 31-35 respectively. The above parameter values are explained as examples and are not limitations on the values. In other embodiments of the present invention, other values can be used. Preferably, all the above parameters are collected for subsequent steps. In step S1, it can also include determining the accuracy of each parameter. The parameter combination with the highest ranking obtained in step S6 includes the parameter combination with the highest ranking in each sub-range after the value range is divided according to the accuracy. The set of the parameter combinations with the highest ranking corresponding to each sub-range forms the optimal parameter combination set for OPC modeling.

[0050] In step S2, a parameter combination is formed by randomly selecting values. For example, taking three parameter combinations as an example, the values of the first combination parameters are 0.5, 3, 7, 12, 19, 22, 27, and 34, where 0.5, 3, 7, 12, and 19 are the values of the numerical aperture (NA), aberration, polarization, and optical constant of the optical model parameters, and 19, 22, 27, and 34 are the values of the resist model parameters of the photoresist refractive index, film thickness, optical propagation, and polarization effect. The values of the second combination parameters are 0.7, 2.5, 8, 14, 18, 23, 28, and 33, where 0.7, 2.5, 8, and 14 are the values of the numerical aperture (NA), aberration, polarization, and optical constant of the optical model parameters, and 18, 23, 28, and 33 are the values of the resist model parameters of the photoresist refractive index, film thickness, optical propagation, and polarization effect. The third combination parameters are 0.1, 4, 9, 13, 17, 24, 29 and 32, where 0.1, 4, 9 and 13 are the values of the numerical aperture (NA), aberration, polarization and optical constants of the optical model parameters, and 17, 24, 29 and 32 are the values of the resist model parameters of the photoresist refractive index, film thickness, optical propagation and polarization effect.

[0051] In step S3, the method for calculating the root mean square value of the difference between the lithography simulation critical dimension and the wafer etching critical dimension includes: measuring the wafer etching critical dimension and the lithography model simulation critical dimension; calculating the difference between the wafer etching critical dimension and the lithography model simulation critical dimension; calculating the root mean square of the difference as the root mean square value (RMS value) of the difference. The method for calculating the Poisson curve error of the lithography simulation critical dimension and the wafer etching critical dimension includes: forming a first Poisson curve based on the values of multiple wafer etching critical dimensions; forming a second Poisson curve based on the values of multiple lithography simulation critical dimensions; calculating the error fraction of the first Poisson curve and the second Poisson curve as the Poisson curve error value. Taking the first parameter combination as an example, lithography simulation and wafer etching are performed under the conditions of the first parameter combination, and lithography simulation critical dimensions and wafer etching critical dimensions at multiple points will be obtained. The lithography simulation critical dimension and wafer etching critical dimension of each point are used to calculate the difference, and then the root mean square value of the difference is calculated based on all the differences. Since each simulation yields multiple points of lithography simulation critical dimensions, and each wafer etching operation yields multiple points of wafer etching critical dimensions, a first Poisson curve and a second Poisson curve can be generated to obtain the error scores for the first and second Poisson curves. Three parameter combinations yield three root mean square (RMS) differences and three Poisson curve error values.

[0052] Using the Maximum Information Coefficient (MIC) to evaluate the Poisson curve error is equivalent to using the Maximum Information Coefficient (MIC) to evaluate the strength of the linear or nonlinear relationship between the first and second Poisson curves. The stronger the relationship, the greater the MIC value and the smaller the BCE value. Therefore, to obtain the minimum BCE value, the maximum MIC value must be obtained. The formula for calculating the MIC value is as follows:

[0053]

[0054] Among them, n x and n y is the number of buckets on the x-axis and y-axis. G represents n in (X, Y) x ×n y Grid number, I G (X, Y) represents the mutual information under the grid G. B(n, a) is a function of the data size n, which is equal to n^α (0<a<1), which limits the maximum number of buckets. log2min(n x , n y ) is a normalization term used to ensure that the MIC is within the range of 0 to 1. The MIC value increases as the correlation between x and y increases. The closer the MIC value is to 1, the stronger the correlation, and vice versa, the closer it is to 0, the weaker the correlation.

[0055] Next, in step S4, the Pareto optimal set, the Pareto suboptimal set, the Pareto second optimal set, and the Pareto Nth suboptimal set are calculated based on the RMS value and the BCE value; the population is sorted in the order of the Pareto optimal set, the Pareto second optimal set, the Pareto second optimal set, and the Pareto Nth suboptimal set. The Pareto frontier is calculated by defining the combination of the RMS value (root mean square value of the difference) and the BCE value (Poisson curve error value) as Y(RMS, BCE) to form multiple Y(RMS, BCE); by Find the combination of the root mean square value of the difference and the error value of the Poisson curve that meets the requirements of the multiple Y (RMS, BCE); where y" is the Pareto optimal solution and y' is another solution in the same interval. Specifically, in all sets Y, there exists y" that strictly dominates y' (i.e., overall advantage, BCE and RMS values are both small), that is, y">y', then the Pareto frontier is: The Pareto optimal set, also known as the Pareto frontier, is the set where both the RMS value and the BCE value can reach the minimum at the same time.

[0056] In step S5, a plurality of parameter combinations after arrangement are implemented genetic algorithm with different weights according to the order of arrangement, wherein, the probability of carrying out parity crossover according to the parameter combination of the order of arrangement decreases successively, and the probability of carrying out parity crossover by the parameter combination closer to the front is larger. If the order of arrangement is just the first parameter combination, the second parameter combination, the third parameter combination and the fourth parameter combination, then the probability of selecting the first parameter combination and the second parameter combination parity crossover is larger, the probability of the first parameter combination and the third parameter combination parity crossover is smaller, and the probability of the first parameter combination and the fourth parameter combination parity crossover is minimum. For example, the numerical aperture (NA) of the first parameter combination and the numerical aperture (NA) of the second parameter combination intersect, i.e., 0.5 and 0.7 intersect, and the value of obtaining offspring may be 0.6, and the above-mentioned crossover mode is explained as an example, and in other embodiments of the present invention, can be other crossover modes. The aberration of the first parameter combination and the aberration of the second parameter combination intersect, i.e., 3 and 2.5 intersect, and the value of obtaining offspring is 2.75, and 0.6 and 2.75 are the partial parameter values in the combined parameters after crossover process. Similarly, other parameters are also crossed in this way, and no further examples are given.

[0057] In step S5, the method for performing mutation processing on the parameter combination after cross processing includes: determining whether the number of iterations of the Pareto optimal set that has not been updated exceeds a second set value, which can be, for example, 10 times. In other embodiments of the present invention, it can also be other values, such as selected within the range of 10 to 20 times; if not, performing conventional mutations on the optical model parameter values and the resist model parameter values that meet the original set conditions, with the mutation rate decreasing as the number of iterations increases; if so, randomly selecting some optical model parameter values and the resist model parameter values to perform enhanced mutations of the original set conditions, in addition to the conventional mutations of the original set conditions, additional enhanced mutations are required, and the mutation rate in the enhanced mutations is random. The upper and lower limits of the random mutation rate are set, and the mutation rate is selected between the upper and lower limits.

[0058] In step S6, the first set value is 100 times. In other embodiments of the present invention, it can be set to other values, such as 200, or selected within the range of 100 to 200. Each iteration generates a combination of parameters sorted in order from best to worst, and each time it is necessary to save the top several parameter combinations. When it is detected that the number of iterations reaches the first set value, the top several parameter combinations at this time are output. Each parameter combination output includes an optical model parameter and a resist model parameter. At this time, a parameter combination, i.e., an optical model parameter and a resist model parameter combination, can be selected as required to form a lithography model for use in establishing an OPC model.

[0059] In summary, in the OPC modeling method provided in the embodiment of the present invention, the optical model parameters and the resist model parameters are adjusted at the same time, and the optimal values of the optical model parameters and the resist model parameters are found at the same time, so that the optical model parameters and the resist model parameters reach the best balance, thereby making the parameters of the lithography model reach the optimal level and establishing the optimal OPC model.

[0060] The above description is merely a preferred embodiment of the present invention and does not limit the present invention in any way. Any person skilled in the art who, without departing from the scope of the present invention, makes any equivalent substitution, modification, or other changes to the technical solution and technical content disclosed in the present invention shall be deemed to be within the scope of the present invention and still fall within the scope of protection of the present invention.

Claims

1. An OPC modeling method, characterized in that: include: S1: Determine optical model parameters, resist model parameters and the value range of each parameter; S2: generating a plurality of parameter combinations by randomly selecting values for each parameter within the value range, wherein each parameter combination includes both an optical model parameter value and a resist model parameter value, and different parameter combinations include different optical model parameter values and resist model parameter values; S3: performing photolithography simulation and etching the wafer using multiple parameter combinations, and calculating root mean square values and Poisson curve error values of differences between photolithography simulation critical dimensions and wafer etching critical dimensions, to obtain root mean square values of multiple differences and multiple Poisson curve error values; S4: Evaluate the root mean square values of the multiple differences and the multiple Poisson curve error values according to the Pareto theorem, and calculate a Pareto optimal set, a Pareto suboptimal set, a Pareto second-optimal set, and a Pareto Nth-suboptimal set, so as to arrange the multiple parameter combinations in order from best to worst, where N is an integer greater than 1; S5: using a genetic algorithm to perform a co-location crossover and / or mutation process on the multiple parameter combinations arranged in step S4 to form multiple new parameter combinations; S6: Iterate the new multiple parameter combinations according to steps S3 to S5 until the number of iterations reaches a first set value, and use the parameter combination with the highest order obtained at this time for OPC modeling.

2. The OPC modeling method according to claim 1, wherein: Methods for calculating the root mean square value of the difference between the lithography simulation critical dimension and the wafer etching critical dimension include: Measure wafer etching critical dimensions and lithography model simulation critical dimensions; Calculate the difference between wafer etching critical dimensions and lithography model simulation critical dimensions; A root mean square of the difference is calculated to serve as the root mean square value of the difference.

3. The OPC modeling method according to claim 1, wherein: Methods for calculating Poisson curve errors for lithography simulation critical dimensions and wafer etch critical dimensions include: forming a first Poisson curve according to values of a plurality of wafer etching critical dimensions; forming a second Poisson curve according to a plurality of values of photolithography simulation critical dimensions; An error score between the first Poisson curve and the second Poisson curve is calculated as a Poisson curve error value.

4. The OPC modeling method according to claim 3, wherein: The maximum information coefficient MIC is used to evaluate the Poisson curve error value. The higher the maximum information coefficient MIC is, the smaller the Poisson curve error value is.

5. The OPC modeling method according to claim 4, wherein: The method for calculating the maximum information coefficient MIC includes: Among them, n x and n y is the number of buckets on the x-axis and y-axis, and G represents n in (X, Y) x ×n y Grid number, I G (X, Y) represents the mutual information under the grid G, B(n, α) is a function of the data size n, equal to n^α, where 0<α<1, log2min(n x , n y ) is a normalization term used to ensure that the MIC is in the range of 0 to 1.

6. The OPC modeling method according to claim 1, wherein: The method for evaluating the root mean square values of the plurality of difference values and the plurality of Poisson curve error values according to the Pareto principle includes: A combination of a root mean square value of the difference and a Poisson curve error value is defined as Y(RMS, BCE) to form a plurality of Y(RMS, BCE); By Find the combination of the root mean square value of the difference and the error value of the Poisson curve that meets the requirements of the plurality of Y (RMS, BCE); wherein: y" is the Pareto optimal solution, and y' is another solution in the same interval.

7. The OPC modeling method according to claim 1, wherein: In step S5 , a genetic algorithm is applied to the arranged parameter combinations with different weights according to the arrangement order, wherein the probability of performing co-location crossover on the parameter combinations decreases according to the arrangement order.

8. The OPC modeling method according to claim 7, wherein: Methods for performing parity crossover on parameter combinations include: The parameter values at a certain position in at least two parameter combinations are cross-calculated to generate the parameter value at the same position in the current parameter combination.

9. The OPC modeling method according to claim 7, wherein: Methods for mutating parameter combinations include: Determine whether the number of iterations in which the Pareto optimal set is not updated exceeds a second set value; If not, performing conventional mutation on the optical model parameter values and the resist model parameter values in accordance with the original setting conditions; If so, some optical model parameter values and resist model parameter values are randomly selected to perform enhanced mutation based on the original setting conditions.

10. The OPC modeling method according to claim 1, wherein: The optical model parameters include one or more of the numerical aperture, resolution, aberration or polarization of the projection objective lens; the resist model parameters include one or more of the refractive index, film thickness and polarization effect of the photoresist.

11. The OPC modeling method according to claim 1, wherein: Step S1 also includes determining the accuracy of each parameter. The parameter combination with the highest ranking obtained in step S6 includes the parameter combination with the highest ranking in each sub-range after the value range is divided according to the accuracy. The set of parameter combinations with the highest ranking corresponding to each sub-range forms the optimal parameter combination set for OPC modeling.

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