CRITICAL DIMENSION ERROR ANALYSIS METHOD

Abstract

The present invention disclosures a critical dimension error analysis method, comprising: S01: performing lithography processes on a wafer, measuring the critical dimension (CD) values of the test points in each of the fields respectively; M and N are integers greater than 1; S02: removing extreme outliers from the critical dimension (CD) values; S03: rebuilding remaining CD values by a reconstruction model fitting method, and obtaining rebuilt critical dimension (CD″) values, according to relative error between CD″ and CD, dividing the rebuilt critical dimension (CD″) values into scenes and the number of the scenes is A; S04: calculating components and corresponding residuals of the test points in each of the scenes under a reference system corresponding to a correction model by parameter estimation; S05: modifying machine parameters and masks by the correction model according to above calculation results. The present invention uses an outer limit to remove extreme outliers, so as to analyze a critical dimension error during a lithography process quickly and accurately.

Claims

1. A critical dimension error analysis method, comprising: S01: performing lithography processes on a wafer, wherein the wafer comprises fields and the number of the fields is M, the lithography processes are the same in each of the fields, setting the same number of test points in each of the fields and the number of the test points is N, measuring the critical dimension (CD) values of the test points in each of the fields respectively; M and N are integers greater than 1; S02: removing extreme outliers from the critical dimension (CD) values; S03: rebuilding remaining CD values by a reconstruction model fitting method, and obtaining rebuilt critical dimension (CD″) values, according to relative error between CD″ and CD, dividing the rebuilt critical dimension (CD″) values into scenes and the number of the scenes is A, and the the same test points in the fields are in the same scene, and the relative error between CD″ and CD of any two fields in each of the scenes is non-periodic in spatial distribution; A is an integer greater than 0; S04: calculating components and corresponding residuals of the test points in each of the scenes under a reference system corresponding to a correction model by parameter estimation; S05: modifying machine parameters and masks by the correction model according to above calculation results.

2. The method of claim 1, wherein in step S02, removing the extreme outliers by the parameter estimation, which comprises: S021: setting the critical dimension value (CD.sub.i,j) of the j-th test point in the i-th field as CD.sub.i,j=inter.sub.i+intra.sub.j+Er.sub.i,j, wherein, inter.sub.i is the inter-field component of the j-th test point, intra.sub.j is the intra-field component of the j-th test point, and Er.sub.i,j is error; treating inter.sub.i and intra.sub.j as dummy variables of a inter-field component set (inter) and a intra-field component set (intra) respectively, taking inter.sub.i and intra.sub.j as parameters without considering Er.sub.i,j, and estimating parameters of CD to obtain the inter-field component (inter0.sub.i) and the intra-field component (intra0.sub.j) of the j-th test point, and after reconstruction, the rebuilt critical dimension value (CD′) of the j-th test point equals inter0.sub.i plus intra0.sub.j, which is CD′=inter0.sub.i+intra0.sub.j; S022: setting the relative error (Er_r′) between CD′ and CD as Er_r′=(CD′−CD)/CD′, and calculating the outer limit of the relative error between CD′ and CD; S023: removing extreme outliers which exceed the outer limit of the relative error between CD′ and CD; S024: repeating from step S021 to S023 until the extreme outliers is removed, or ratio of number of remaining test points to number of original test points is less than a number threshold after removing, or number of iterations is greater than a iteration threshold.

3. The method of claim 2, wherein in step S023, a calculation method for the outer limit comprises sorting the the relative error between CD′ and CD, and calculating a 25th quantile (Q1) and a 75th quantile (Q3), and setting IQR=Q3−Q1, the lower limit of the outer limit is Q1−3*IQR, and the upper limit of the outer limit is Q3+3*IQR.

4. The method of claim 2, wherein the approach to the parameter estimation is maximum likelihood estimation.

5. The method of claim 1, wherein step S03 comprises: S031: inputting the global coordinates of the wafer as independent variables into the reconstruction model, and inputting the remaining critical dimension values as dependent variables into the reconstruction model, and reconstructing the critical dimension values by adjusting reconstruction model parameters to obtain the rebuilt critical dimension (CD″) values after reconstruction; S032: calculating the relative error (Er″) between CD″ and CD and Er″=(CD″−CD)/CD″, and dividing the remaining critical dimension values into the scenes according to the relative error between CD″ and CD, and the number of the scenes is A; S033: recording the reconstruction model parameters corresponding to each of the scenes.

6. The method of claim 5, wherein the reconstruction model is a GBDT model or an XGBoost model.

7. The method of claim 1, wherein in S03, determining whether the relative error between CD″ and CD of any two fields in each of the scenes is periodic in the spatial distribution by a Pearson coefficient; while the Pearson coefficient of any two fields in one scene is less than the set threshold, then the relative error between CD″ and CD of the two fields in the scene is non-periodic in the spatial distribution.

8. The method of claim 1, wherein in S04, the components and the corresponding residuals of the test points under the reference system corresponding to the correction model comprise a overall residual, intra-field X components, intra-field Y components, intra-field residuals, inter-field X components, inter-field Y components, and inter-field residuals of the test points.

9. The method of claim 8, wherein in S04 comprises: S041: setting the critical dimension value (CD.sub.i,j″) of the j-th test point in the i-th field as CD.sub.i,j″=inter.sub.i″+intra.sub.j″+res.sub.i,j, wherein, inter.sub.i″ is the inter-field component of the j-th test point, intra.sub.j″ is the intra-field component of the j-th test point, and res.sub.i,j is the overall residual; treating inter.sub.i″ and intra.sub.j″ as dummy variables of a inter-field component set (inter) and a intra-field component set (intra) respectively, taking inter.sub.j″ and intra.sub.j″ as parameters without considering res.sub.i,j, and estimating parameters of CD″ to obtain the inter-field component (inter0.sub.i″) and the intra-field component (intra0.sub.j″) of the j-th test point, the overall residual (res.sub.i,j) equals CD.sub.i,j″ minus inter0.sub.i″ minus intra0.sub.j″, which is res.sub.i,j=CD.sub.i,j″−inter0.sub.i″−intra0.sub.j″; S042: setting the inter-field component (inter.sub.k,1″) of the k-th row and the 1-th column on the wafer as inter.sub.k,1″=inter_x.sub.k″+inter_y.sub.1″+inter_res.sub.k,1″, wherein, inter_x.sub.k″ is the inter-field X component between fields, inter_y.sub.1 is the inter-field Y component between fields, and inter_res.sub.k,1″ is the inter-field residual between fields; treating inter_x.sub.k″ and inter_y.sub.1″ as dummy variables of a inter-field X component set (inter_x) and a inter-field Y component set (inter_y) respectively, taking inter_x.sub.k″ and inter_y.sub.1″ as parameters without considering inter_res.sub.k,1″, and estimating parameters of inter″ to obtain the inter-field X component (inter_x0.sub.k″) and the inter-field Y component (inter_y0.sub.1″) between fields, and the inter-field residual (inter_res.sub.k,1″) between fields equals inter.sub.k,1″ minus inter_x0.sub.k″ minus inter_y0.sub.1″, which is inter_res.sub.k,1″=inter.sub.k,1″−inter_x0.sub.k″−inter_y0.sub.1″; S043: setting the intra-field component (intra.sub.m,n″) of the m-th row and the n-th column in the i-th field as intra.sub.m,n″=intra_x.sub.m″+intra_y.sub.n″+intra_res.sub.m,n″, wherein, intra_x.sub.m″ is the intra-field X component of the j-th test point, intra_y.sub.n″ is the intra-field Y component of the field, and intra_res.sub.m,n″ is the intra-field residual of the field; treating intra_x.sub.m″ and intra_y.sub.n″ as dummy variables of a intra-field X component set (intra_x) and a intra-field Y component set (intra_y) respectively, taking intra_x.sub.m″ and intra_y.sub.n″ as parameters without considering intra_res.sub.m,n″, and estimating parameters of intra″ to obtain the intra-field X component (intra_x0.sub.m″) and the intra-field Y component (intra_y0.sub.n″) of the field, and the inter-field residual (inter_res.sub.k,1″) of the field equals intra.sub.m.n″ minus intra_x0.sub.m″ minus intra_y0.sub.n″, which is inter_res.sub.k,1″=intra.sub.m.n″−intra_x0.sub.m″−intra_y0.sub.n″; S044: repeating from step S041 to S043 until calculating the overall residual, the intra-field X components, the intra-field Y components, the intra-field residuals, the inter-field X components, the inter-field Y components, and the inter-field residuals of all the test points of all the fields in all the senses.

10. The method of claim 9, the approach to the parameter estimation is maximum likelihood estimation.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0017] FIG. 1 is a frame diagram of critical dimension error analysis method of the present invention.

DETAILED DESCRIPTION

[0018] In order to make the objectives, technical solutions and advantages of the present invention clearer, the specific embodiments of the present invention will be further described in detail below in conjunction with the accompanying drawings.

[0019] It should be noted that in the following specific embodiments, in detailing the embodiments of the present invention, in order to clearly show the structure of the present invention for ease of explanation, the structure in the drawings is not drawn in accordance with the general scale, and carried out In order to partially enlarge, deform and simplify the process, it should be avoided as a limitation of the present invention.

[0020] A critical dimension error analysis method, comprising following steps:

[0021] S01: performing lithography processes on a quantity of wafers, wherein each of the wafers comprises fields and the number of the fields is M, the lithography processes are the same in each of the fields, setting the same number of test points in each of the fields and the number of the test points is N, measuring the critical dimension (CD) values of the test points in each of the fields respectively. A CD-SEM or a scatterometry equipment can be used to measure the CD values. In S01, the lithography process can be used to etch a specific pattern or only expose photo-resist. M and N are integers greater than 1.

[0022] S02: removing extreme outliers from the critical dimension (CD) values; specific steps can be as following:

[0023] S021: setting the critical dimension value (CD.sub.i,j) of the j-th test point in the i-th field as CD.sub.i,j=inter.sub.i+intra+Er.sub.i,j, wherein, inter.sub.i is the inter-field component of the j-th test point, intra.sub.j is the intra-field component of the j-th test point, and Er.sub.i,j is error; treating inter.sub.i and intra.sub.j as dummy variables of a inter-field component set (inter) and a intra-field component set (intra) respectively, taking inter.sub.i and intra.sub.j as parameters without considering Er.sub.i,j, and estimating parameters of CD to obtain the inter-field component (inter0.sub.i) and the intra-field component (intra0.sub.j) of the j-th test point, and after reconstruction, the rebuilt critical dimension value (CD′) of the j-th test point equals inter0.sub.i plus intra0.sub.j, which is CD′=inter0.sub.i+intra0.sub.j. The specific parameter estimation can be maximum likelihood estimation, which is assumed that the error (Er.sub.i,j) follows Gaussian distributed with expected values and variances of parameters (inter.sub.i, intra.sub.j). Assuming inter.sub.i and intra.sub.j are irrelevant, considered the variances are equal, the maximum likelihood estimation can be reduced to ordinary least squares.

[0024] S022: setting the relative error (Er_r′) between CD′ and CD as Er_r′=(CD′−CD)/CD′, and calculating the outer limit of the relative error between CD′ and CD; wherein, a calculation method for the outer limit comprises sorting the the relative error between CD′ and CD, and calculating a 25th quantile (Q1) and a 75th quantile (Q3), and setting IQR=Q3−Q1, the lower limit of the outer limit is Q1−3*IQR, and the upper limit of the outer limit is Q3+3*IQR. That is, in S022, the outer limit comprises the upper limit and the lower limit, and the critical dimension values located at the upper limit and the lower limit of the outer limit need to be removed.

[0025] S023: removing extreme outliers which exceed the outer limit of the relative error between CD′ and CD;

[0026] S024: repeating from step S021 to S023 until the extreme outliers is removed, or ratio of number of remaining test points to number of original test points after removing is less than a number threshold, or number of iterations is greater than a iteration threshold. In S024, three iteration stop conditions are set, one is that the critical dimension values outside the outer limit is removed, and the other two are whether the critical dimension values outside the outer limit is removed or not, the ratio of the number of the remaining test points to the number of the original test points is required to less than the number threshold, or the number of the iterations (the number of times to repeat from step S021 to S023) is greater than the iteration threshold, that is, a removing process is automatically stopped. Wherein, the number threshold and the iteration threshold can be set based on empirical values, the two iteration stop conditions are set in S024 to prevent the removing process from entering an endless loop and to ensure the entire analysis process is carried out sequentially.

[0027] S03: rebuilding remaining CD values by a reconstruction model fitting method, and obtaining rebuilt critical dimension (CD″) values, according to relative error between CD″ and CD, dividing the rebuilt critical dimension (CD″) values into scenes and the number of the scenes is A, and the the same test points in the fields are in the same scene, and the relative error between CD″ and CD of any two fields in each of the scenes is non-periodic in spatial distribution; A is an integer greater than 0.

[0028] In S03, determining whether the relative error between CD″ and CD of any two fields in each of the scenes is periodic in the spatial distribution by a Pearson coefficient; the Pearson coefficient can be calculated by the two fields, the closer the absolute value of the Pearson coefficient is to 1, the more similar the two fields are, and the closer to 0, the less similar the two fields are, the two fields are hoped to be not related to each other. While the Pearson coefficient of any two fields in one scene is less than the set threshold, then the relative error between CD″ and CD of the two fields in the scene is non-periodic in the spatial distribution. In the present invention, the distribution of critical dimension error at the same position of each of exposure fields is 0 as expected distribution, it is regarded as no periodicity; otherwise, it is regarded as periodic, which indicates that the critical dimension error has not been decomposed completely, and some problems will be missed. In the present invention, under a set of reconstruction model parameters, when all the test points is satisfied that the relative error between CD″ and CD of any two fields is non-periodic in the spatial distribution, that is, A=1, and the reconstruction model parameters is just needed to be recorded; when all the test points is not satisfied that the relative error between CD″ and CD of any two fields is non-periodic in the spatial distribution, the test points are needed to be divided into the scenes and the number of the scenes is A, each of the scenes can correspond to different reconstruction model parameters, and the reconstruction model parameters corresponding to each of the scenes are recorded separately for obtaining the rebuilt critical dimension values (CD″) after reconstruction. The reconstruction model in the present invention can specifically be a GBDT Model or an XGBoost model. It is worth noting that each of the critical dimension values in the present invention corresponds to a global coordinate, a inter-field coordinate and a intra-field coordinate of a critical dimension value, that is, the critical dimension value, the global coordinate, the inter-field coordinate and the intra-field coordinate of the critical dimension value form the data set of the test point, wherein, the combination of the intra-field coordinate and the inter-field coordinate is approximately equal to the global coordinate. The four items in the data set exist at the same time, when removing the extreme outliers, a critical dimension value exceed the outer limit is deleted, that is, the data set corresponding to the abnormal critical dimension value is deleted.

[0029] A specific parameter reconstruction process in S03 comprises following steps:

[0030] S031: inputting the global coordinates of the wafer as independent variables into the reconstruction model, and inputting the remaining critical dimension values as dependent variables into the reconstruction model, and reconstructing the critical dimension values by adjusting reconstruction model parameters to obtain the rebuilt critical dimension (CD″) values after reconstruction;

[0031] S032: calculating the relative error (Er″) between CD″ and CD and Er″=(CD″−CD)/CD″, and dividing the remaining critical dimension values into the scenes according to the relative error between CD″ and CD, and the number of the scenes is A. The meaning of the scene in S032 is: when rebuilding a model by only one set of reconstruction model parameters, and the relative error between CD″ and CD of any two fields in each of the scenes is non-periodic in the spatial distribution, dividing the data set into the scenes and the number of the scenes is A, fitting by groups of reconstructed model parameters and the number of the groups is A, thus each of fitting errors is non-periodic, that is, the groups of the reconstructed model parameters are regarded as reconstructed models and the number of the reconstructed models is A, which is corresponding to the scenes.

[0032] S033: recording the reconstruction model parameters corresponding to each of the scenes.

[0033] In S033, the critical dimensions are reconstructed, and the critical dimension values after reconstruction of the reconstruction model only retain low-frequency components. As shown in FIG. 1, high-frequency components are automatically filtered out. In S04, the low-frequency components are further decomposed into the intra-field components, the inter-field components and the overall residual. The overall residual is others shown in FIG. 1.

[0034] S04: calculating components and corresponding residuals of the test points in each of the scenes under a reference system corresponding to a correction model by the parameter estimation; wherein, the components and the corresponding residuals of the test points under the reference system corresponding to the correction model by the parameter estimation comprise the overall residual, intra-field X components, intra-field Y components, intra-field residuals, inter-field X components, inter-field Y components, and inter-field residuals of the test points. The calibration model refers to a model used for calibration in step S05. Any calibration model in the prior art can be used for calibration. Since the selected calibration model is different, components and corresponding residuals for a reference system corresponding to the selected calibration model is required in S04, wherein, the reference system comprise a inter-field coordinate system, a intra-field coordinate system and a Cartesian (rectangular) coordinate system, and the reference system can also comprise a polar coordinate system, etc. Specifically, the Cartesian coordinates in the reference system can be replaced with a polar coordinate system, etc., or the inter-field coordinate system, the intra-field coordinate system, the Cartesian coordinate system and the polar coordinate system can be comprised in the reference system simultaneously. Since the test points are divided into the scenes and the number of the scenes is A in S03, analyzing the test points in each of the scenes in turn in S04, taking one of the scenes as an example to explain, calculation methods of other scenes are the same; a specific calculation method comprises:

[0035] S041: setting the critical dimension value (CD.sub.i,j″) of the j-th test point in the i-th field as CD.sub.i,j″=inter.sub.i″+intra.sub.j″+res.sub.i,j, wherein, inter.sub.i″ is the inter-field component of the j-th test point, intra.sub.j″ is the intra-field component of the j-th test point, and res.sub.i,j is the overall residual; treating inter.sub.i″ and intra.sub.j″ as dummy variables of a inter-field component set (inter) and a intra-field component set (intra) respectively, taking inter.sub.i″ and intra.sub.j″ as parameters without considering res.sub.i,j, and estimating parameters of CD″ to obtain the inter-field component (inter0.sub.i″) and the intra-field component (intra0.sub.j″) of the j-th test point, the overall residual (res.sub.i,j) equals CD.sub.i,j″ minus inter0.sub.j″ minus intra0.sub.j″, which is res.sub.i,j=CD.sub.i,j″-inter0.sub.i″−intra0.sub.j″. the approach to the parameter estimation is the maximum likelihood estimation, which is assumed that the overall residual (res.sub.i,j) follows the Gaussian distributed with the expected values and the variances of parameters (inter.sub.i″ and intra.sub.j″). Assuming inter.sub.i″ and intra.sub.j″ are irrelevant, considered the variances are equal, the maximum likelihood estimation can be reduced to the ordinary least squares.

[0036] S042: setting the inter-field component (inter.sub.k,1″) of the k-th row and the 1-th column on the wafer as inter.sub.k,1″=inter_x.sub.k″+inter_y.sub.1″+inter_res.sub.k,1″, wherein, inter_x.sub.k″ is the inter-field X component between fields, inter_y.sub.1 is the inter-field Y component between fields, and inter_res.sub.k,1″ is the inter-field residual between fields; treating inter_x.sub.k″ and inter_y.sub.1″ as dummy variables of a inter-field X component set (inter_x) and a inter-field Y component set (inter_y) respectively, taking inter_x.sub.k″ and inter_y.sub.1″ as parameters without considering inter_res.sub.k,1″, and estimating parameters of inter″ to obtain the inter-field X component (inter_x0.sub.k″) and the inter-field Y component (inter_y0.sub.1″) between fields, and the inter-field residual (inter_res.sub.k,1″) between fields equals inter_res.sub.k,1″ minus inter_x0.sub.k″ minus inter_y0.sub.1″, which is inter_res.sub.k,1″=inter.sub.k,1″-inter_x0.sub.k″−inter_y0.sub.1″. The approach to the parameter estimation is the maximum likelihood estimation, which is assumed that the overall residual (inter_res.sub.k,1″) follows the Gaussian distributed with the expected values and the variances of parameters (inter_x.sub.k″ and inter_y.sub.1). Assuming inter_x.sub.k″ and inter_y.sub.1″ are irrelevant, considered the variances are equal, the maximum likelihood estimation can be reduced to the ordinary least squares.

[0037] S043: setting the intra-field component (intra.sub.m,n″) of the m-th row and the n-th column in the i-th field as intra.sub.m,n″=intra_x.sub.m″+intra_y.sub.n″+intra_res.sub.m,n″, wherein, intra_x.sub.m″ is the intra-field X component of the field, intra_y.sub.n″ is the intra-field Y component of the field, and intra_res.sub.m,n″ is the intra-field residual of the field; treating intra_x.sub.m and intra_y.sub.n″ as dummy variables of a intra-field X component set (intra_x) and a intra-field Y component set (intra_y) respectively, taking intra_x.sub.m″ and intra_y.sub.n″ as parameters without considering intra_res.sub.m,n″, and estimating parameters of intra″ to obtain the intra-field X component (intra_x0.sub.m″) and the intra-field Y component (intra_y0.sub.n″) of the field, and the inter-field residual (inter_res.sub.k,1″) of the field equals intra.sub.m.n″ minus intra_x0.sub.m″ minus intra_y0.sub.n″, which is inter_res.sub.k,1″=intra.sub.m.n″−intra_x0.sub.m″−intra_y0.sub.n″. the approach to the parameter estimation is the maximum likelihood estimation, which is assumed that the overall residual (intra.sub.m.n″) follows the Gaussian distributed with the expected values and the variances of the parameters (intra_x.sub.m″ and intra_y.sub.n″). Assuming intra_x.sub.m″ and intra_y.sub.n″ are irrelevant, considered the variances are equal, the maximum likelihood estimation can be reduced to the ordinary least squares.

[0038] S044: repeating from step S041 to S043 until calculating the overall residual, the intra-field X components, the intra-field Y components, the intra-field residuals, the inter-field X components, the inter-field Y components, and the inter-field residuals of all the test points of all the fields in all the senses.

[0039] In the present invention, the critical dimensions are reconstructed in S03, and the critical dimension values after reconstruction of the reconstruction model only retain low-frequency components. the low-frequency components are decomposed into the intra-field components, the inter-field components the overall residual by least squares, and then the intra-field components are decomposed into the intra-field X components, the intra-field Y components and the intra-field residuals; the inter-field components are decomposed into the inter-field X components, the inter-field Y components and the inter-field residuals.

[0040] S05: according to the overall residual, the intra-field X components, the intra-field Y components, the intra-field residuals, the inter-field X components, the inter-field Y components, and the inter-field residuals of all the test points calculated above, modifying machine parameters and masks by the correction model, so as to reduce the instability of the critical dimensions. Overall residuals of multiple wafers are compared and observed in the present invention, which can be used to estimate whether there are wafer abnormalities on the wafers that are not presented in units of fields globally, inter-field residuals of a wafer exposed by FEM (Focus Depth Energy Matrix) can be used to estimate the trend change of the local area of the wafer, an abrupt point appearing on the intra-field residuals can be used to estimate anomalies existing in a field unit such as masks and lens; the inter-field components can be used as a basis for adjusting machine parameters.

[0041] The above descriptions are only the preferred embodiments of the present invention, and the described embodiments are not used to limit the scope of patent protection of the present invention. Therefore, any equivalent structural changes made using the contents of the description and drawings of the present invention should be included in the same reasoning. Within the protection scope of the appended claims of the present invention.